Prolongation of Seventh Chords in Tonal Music

PROLONGATION OF SEVENTH CHORDS IN TONAL MUSIC

Volume I Text

Y osef Goldenberg

With a Foreword by L. Poundie Burstein

The Edwin Mellen Press Lewiston•Queenston • Lampeter Library of Congress Cataloging-in-Publication Data

Goldenberg, Y osef.. Prolongation of seventh chords in tonal music : volume I : text I Y osef Goldenberg ; with a foreword by L.. Poundie Burstein .. p.cm .. Includes bibliographical references and index .. ISBN-13: 978-0-7734-4846-9 ISBN-10: 0-7734-4846-2 L Title. hors serie.

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To my parents, Gideon and Esther

TABLE OF CONTENTS

LIST OF ABBREVIATIONS ...... i

FOREWORD by Prof. L. Poundie Burstein ...... iii

PREFACE...... v

1. BASIC CONCEPTS AND DEFINITIONS ...... 1 1.1 The Concept of Prolongation...... 1 1.1.1 Selected Problems Concerning Prolongation...... 3 1.1.2 Terms Related to Prolongation: Proposed Distinctions ...... 5 1.1.3 Minimal Conditions for True Prolongation: Subordination...... 14 1.2 Seventh Chords ...... 15 1.3 The Concept of Dissonance ...... 17 1.3.1 Absolute versus Contextual Dissonances ...... 18 1.3.2 Dissonances as Carriers of Motion and Tension...... 22

2. PROBLEMS CONCERNING PROLONGATION OF SEVENTH CHORDS...... 23 2.1 Prolongation of Dissonance ...... 23 2.1.1 Schenker’s Normative View ...... 23 2.1.2 Theoretical Gaps that Raise the Possibility of Prolonging Dissonances . 26 2.2 Lack of Distinction between Steps and Leaps...... 35

2.3 Related Situations which Do Not Constitute Genuine Prolongation of Seventh Chords ...... 37 2.3.1 Stretching of Seventh Chords ...... 37 2.3.2 Space-Filling Motion (SFM) in Seventh Chords ...... 39 2.3.3 Highlighted Unprolonged Dissonances and Seventh Chords ...... 41 2.3.4 Delayed Resolution...... 43 2.4 Aesthetic and Theoretical Background to Schenker’s Position...... 44

3. LITERATURE SURVEY...... 47 3.1 Precedents to Schenker and Non-Schenkerian Literature ...... 47 3.2 The Approach to the Seventh in Schenker’s Published Writings...... 49 3.2.1 Harmonielehre (1906) [Harmony]...... 50 3.2.2 Counterpoint I (1910) ...... 52 3.2.3 The Analytical Monographs (1910–1920)...... 54 3.2.4 Counterpoint II (1922)...... 58 3.2.5 Der Tonwille (1921–1924), including the Elucidations...... 59 3.2.6 The Masterwork in Music (1925, 1926, 1930)...... 61 3.2.7 Free Composition (1935, posth.) ...... 66 3.3 Approaches of Schenker’s Followers...... 68 3.3.1 The Spectrum of Opinions ...... 68 3.3.2 Specific Studies on PD in Tonal Music ...... 74 3.4 Studies of PD in Twentieth Century Music ...... 79

4. SEVENTH CHORDS AT THE DEEPEST STRUCTURAL LEVELS.... 85 4.1 Dissonances and Sevenths in Particular at the Background (with Unfilled Bass Arpeggiation) ...... 85 4.2 Sevenths at the Middleground with Unprolonged Urlinie (and Prolonged Bass) ...... 88 4.2.1 The Combination of an Unprolonged Urlinie with Two Bass Arpeggiations...... 89 4.2.2 Other Dissonances at the Middleground with Unprolonged Urlinie ...... 90 4.3 Prolongation of Dissonances at the Deep Middleground (with Prolonged Urlinie)...... 91 4.3.1 The Complete Upper Neighbor to 3...... 91

4.3.2 The Connection between 4 and 2 and the Incomplete Upper Neighbor .. 94 4.3.3 Reaching-over...... 97 4.3.4 Unfolding ...... 98 4.4 Structural Dissonances and Chromaticism ...... 100 4.4.1 Structural Dissonances as the Product of Mixture...... 100 4.4.2 Conflicts between the Priorities of Consonance and of the Diatonic System...... 101 4.4.3 Structural Dissonances in the Later Middleground: Secondary Dominant Seventh Chords ...... 102

5. GENERAL OVERVIEW OF PROLONGATION OF SEVENTH CHORDS...... 105 5.1 The Contrapuntal Function of the Seventh ...... 105 5.2 Comparative Investigation of Various Types of Seventh Chords ...... 106 5.3 Comparative Investigation of Prolongations of Seventh Chords...... 108 5.4 Criteria for Recognizing True Seventh Progressions ...... 109 5.4.1 Further Investigation of Oster’s Criterion...... 112 5.4.2 Intermediate Situations between True and Illusory Seventh Progressions ...... 115 5.4.3 Rhythmic Normalization of Seventh Progressions ...... 116

6. PROCEDURES FOR PROVIDING V7 WITH STRUCTURAL MEANING WITHOUT FULL CIRCULAR PROLONGATION ...... 119 6.1 Analogies between the Structural V7 and Strict Counterpoint...... 120 6.1.1 V8–7 with Priority of the Seventh ...... 121 6.2 Processes toward V7 ...... 124 6.2.2 Space-Filling Motion (SFM) toward the Seventh of V7 ...... 126 6.3 Subordinations to V7 ...... 128 6.3.1 Specific Types of Subordination to V7 ...... 129 6.3.2 Apparent Subordinations to V7 ...... 132 6.3.3 Filling in of Spaces Created by the Subordination Process ...... 132

7. FULL CIRCULAR PROLONGATION OF V7 ...... 137 7.1 Harmonies that Emerge within Prolongations of V7 ...... 137 7.2 Linear Progressions within V7 ...... 139 7.2.1 Third Progressions within V7...... 140 7.2.2 Inverted Thirds: Sixth Progressions within V7 ...... 151 7.2.3 Fifth Progressions within V7 ...... 152 7.2.4 Inverted Fifths: Fourth Progressions within V7 ...... 158 7.2.5 Seventh Progressions within V7...... 159 7.2.6 Inverted Sevenths: Filling the Second-Space 8–7...... 160 7.2.7 ‘Octave progressions’: Complete Register Transfers within V7 ...... 161 7.2.8 Counterpointing Linear Progressions of Different Sizes within V7...... 164 7.3 Neighbors to V7 ...... 166 7.3.1 Neighbor Motion below (or above) a Stationary Seventh ...... 167 7.3.2 Neighbors to the Tone of the Seventh Itself ...... 170 7.3.3 Double Neighbors to V7...... 177 7.3.4 Combinations of Neighbors with Linear Progressions ...... 178 7.4 Mixture within V7 Prolongation...... 180 7.5 Reaching-Over within V7 Prolongation ...... 181 7.6 Arpeggiation of V7...... 182 7.7 Prolongations of Inverted V7 ...... 188 7.7.1 Prolongation of V7 in Changing Inversion...... 190 7.8 Enharmonic Parentheses (EP) in General and within V7...... 192 7.8.1 Enharmonic Parentheses within V7...... 193 7.9 Prolongation of Major-Minor Seventh Chords in Functions other than V7 194 7.10 Large-Scale Prolongation of V7 and Form...... 196 7.10.1 Prolongation of V7 in Dependent Sections ...... 197 7.10.2 Prolongation of V7 throughout Complete Independent Sections...... 207 7.11 An integrative analysis of a complete movement: Beethoven, String Quartet Op. 18,2/IV (Ex. 7.115) ...... 211

8. PROLONGATION OF DIMINISHED SEVENTH CHORDS (VIIº7) ... 215 8.0 General Features of Diminished Seventh Chords and their Consequences 215 8.1 Harmonies that Prolong VIIº7...... 216 8.2 Subordination to VIIº7 ...... 217 8.3 Linear Progressions within VIIº7 ...... 219 8.3.1 Third Progressions within VIIº7 ...... 219 8.3.2 Inverted thirds: Sixth progressions within a VIIº7 ...... 225 8.3.3 Fifth Progressions within VIIº7 ...... 226 8.3.4 Inverted Fifths: Fourth Progressions within VIIº7 ...... 229 8.3.5 Diminished Seventh Progressions...... 230 8.3.6 ‘Octave Progressions’: Register Transfers within VIIº7 ...... 235 8.3.7 Counterpointing Linear Progressions of Different Sizes within VIIº7... 239 8.4 Neighbors to VIIº7 ...... 240 8.4.1 Neighbors under a Stationary Diminished Seventh ...... 240 8.4.2 Neighbors to the Tone of the Diminished Seventh...... 241 8.5 Enharmonic Parentheses within Diminished Seventh Chords...... 242 8.6 Prolongation of Diminished Seventh Chords in Special Contexts...... 245 8.7 Large-scale Prolongations of Diminished Seventh Chords...... 247

9. PROLONGATION OF THE REMAINING SEVENTH CHORDS...... 251 9.0 General Considerations...... 251 9.1 Prolongations of II7...... 252 9.1.1 Prolongation of Half-Diminished Seventh Chords as II7 in Minor...... 253 9.1.2 Minor-Minor as II7 in Major ...... 258 9.2 Prolongation of Half-Diminished Seventh Chords in Other Functions...... 261 9.2.1 Half-Diminished VII7 in Major...... 261 9.2.2 Half-Diminished Seventh Chords as Altered IV7 ...... 262 9.3 Prolongation of Minor-Minor Seventh Chords in Other Functions ...... 262 9.3.1 Minor-Minor Seventh Chords as IV7 in Minor...... 262 9.3.2 Minor-minor Seventh Chord as VI7 in Major ...... 263 9.4 Prolongation of Seventh Chords with a Major Seventh...... 264 9.4.1 Non-tonic Seventh Chords with a Major Seventh ...... 264 9.4.2 Prolongations of I7 ...... 265

10. PROLONGATION OF AUGMENTED-SIXTH SEVENTH CHORDS ...... 267 10.1 Problems in the Ordinary View of Augmented Sixth Chords...... 268 10.2 Structural Priority of the German Augmented Sixth chord ...... 269 10.2.1 Priority of the German chord (Gr) over a preceding (ß)VI...... 269 10.2.2 Motion from the Tone of the Augmented Sixth...... 272 10.3 Full Circular Prolongations of German-Type Chords ...... 274 10.3.1 Prolongations of German-Type Chords without Enharmonic Association...... 274 10.3.2 Enharmonic Parentheses within German-Type Augmented-Sixth Seventh Chords...... 279 10.4 Prolongations of Other Augmented-Sixth Seventh Chords...... 285 10.4.1 Prolongation of the French-Structured $ ...... 285 10.4.2 Prolongation of Rare Types of Augmented-Sixth Seventh Chords ...... 287

11. CONCLUSIONS ...... 289 11.1 Theoretical-Analytical Conclusions...... 289 11.1.2 Locations in the Form ...... 292 11.2 Historical Conclusions...... 293 11.3 Aesthetic Observations...... 295 11.4 Areas of Future Research ...... 297

APPENDIX : Prolongation of Dissonance in Free Composition...... 299

BIBLIOGRAPHY...... 305

INDEX...... 329

VOL.2

LIST OF EXAMPLES

LIST OF ABBREVIATIONS USED IN THE EXAMPLES...... i

FOREWORD by Prof. L. Poundie Burstein ...... iii

PREFACE...... v

EXAMPLES ...... 1

INDEX OF MUSICAL EXAMPLES...... 247

LIST OF ABBREVIATIONS

CP Counterpoint = Schenker [1910. 1922] 1987 (see bibliography) EP enharmonic parentheses FC Free Composition = Schenker [1935/1956] 1979 (see bibliography) FGA Five Graphic Analyses = Schenker [1933] 1969 (see bibliography) Gr German augmented-sixth chord HD half-diminished seventh chord MW Das Meisterwerk in der Musik = Schenker [1925. 1926. 1930] = 1994. 1996. 1997. (see bibliography) PD prolongation of dissonance SFM space-filling motion TW Der Tonwille = Schenker [1921–24] 2004. 2005. (see bibliography) WTC The Well-tempered Clavier

FOREWORD

The contrast between consonance and dissonance is fundamental to most tonal music. Typically, intervals and chords are regarded either as consonant or as dissonant, with a sharp line demarcating these two categories. But attempts at an absolute separation of the functions and capabilities of consonances and dissonances fall apart under certain circumstances. Most notably, seventh chords often are treated differently than other dissonant configurations. Indeed, sometimes seventh chords are treated as ersatz consonances, even within music of the eighteenth and nineteenth centuries. To be sure, it is not easy for music theorists to account for the special status of seventh chords, but it is also not easy for them to ignore it. Heinrich Schenker was among those who grappled with the treatment of sevenths and seventh chords. For Schenker, the tension created by dissonance and the sense of stability and resolution afforded by consonance form a primal source of tonal expression, drama, and structure. This principle, as codified in the concepts of species counterpoint, lies at the core of his theories. Although Schenker identifies many instances in which an apparent consonance can function as a dissonance on a deeper level and vice versa, for the most part he insists that on deeper levels dissonances will be subordinate to consonances. One consequence of this attitude is Schenker’s famous prohibition against the prolongation of sevenths. It should be noted, however, Schenker’s opinions concerning the prolongation of sevenths did waver over the course of his career. Indeed, even in Der freie Satz he shows a more flexible attitude regarding this issue than is commonly

iv acknowledged. As with Schenker himself, his followers likewise have shown ambivalence in their attitudes regarding the prolongation of sevenths. While a few have adhered in their analyses to the Schenker’s admonition against prolonging sevenths, others either have ignored this prohibition or have argued against it. But to allow the prolongation of sevenths in Schenkerian analysis welcomes inevitable risks: how can one allow certain dissonances freer reign without upsetting the distinctive roles of consonance and dissonance that lie at very heart of Schenker’s theoretic system? It is this issue that Yosef Goldenberg addresses in the present study. Although many other theorists have written intelligently regarding the prolongation of dissonance, arguably none have examined this problem with the care and thoroughness as seen here. In this book, Goldenberg examines at length the writings of Schenker and others regarding the prolongation of dissonance, provides a logical and musical justification for such prolongations based on principles of strict counterpoint and related concepts, and offers a variety of compelling analyses to support these views. The ideas presented here are not a mere revision of Schenker’s ideas, but rather stand as a reengagement and elucidation of principles that are central to Schenker’s method. As such, this study should have a profound impact on approaches to Schenkerian theory as well as to tonal music in general.

Prof. L. Poundie Burstein, Music Department, Hunter College and the Graduate Center, CUNY

PREFACE

Prolongation of seventh chords is a subject that has both a clear focus that enables the meticulous detailed presentation of the entire spectrum of its specific manifestations, and by the same time also rather wide theoretical and analytical implications, including the essence of prolongation and of dissonance. Based on the theories of Heinrich Schenker, this study explores one of the most problematic issues in the theory, an issue that has caused recurring confusion. Theoretically, prolongation of seventh chords ought not to exist, mainly because sevenths are dissonances, whereas normative prolongations apply to consonances only. In fact, the original subject planned for this work was Prolongation of Dissonances in Tonal Music, based in turn on a general idea to work on Prolongation of Dissonances (mainly in post-tonal music). As I realized the sheer amount and variety of material, I have decided to concentrate on prolongation of seventh chords alone. However, the general theoretical problem concerning prolongation of dissonance is crucial to the final narrower topic, and thus remained within the study. My focus in this work is more technical than philosophical. I have attempted to draw the entire range of procedures that prolong seventh chords in tonal music, based on a typology of seventh chord types and of voice leading techniques, mainly passing motion in each of the emerging chordal spaces, and neighbor motion to each tone of the seventh chord (not necessarily the tone of the seventh itself). Although in principle I studied prolongations of all seventh chords, my interest was in those prolongations that are actually used in the tonal literature. Accordingly, the chapters on prolongations of dominant and of diminished seventh chords are detailed, while those on other seventh chords are modest. The

vi repertoire discussed in this study is wide, ranging from Bach to Mahler and Skryabin. Most examples are drawn from the work of the composers Schenker himself admired. While a systematic philosophical exploration of the same topic must remain the task of other scholars, who might find this work as raw material for their purposes, various aesthetic and semiotic remarks do crop up in the present work in passim. The musical examples are separated from the text, but they are of course an essential part of the work. Most of the examples are Schenkerian voice-leading graphs. Others include recompositions, quotations of musical excerpts and compositional experiments. In both text and examples, raised and lowered tones are indicated in relation to the key, and not necessarily in their actual appearance, e.g., c in A major is ß3, not 3. Accidentals to the left of a chord relate to the root, and to the right of the chord relate to the third, e.g., in C major ßVI is Aß major, VIƒ is A major, and ßVIß is Aß minor. Bibliographic references in the body of the work usually indicate author and year. References to Schenker’s main writings are made in abbreviations, which are explained in the list of abbreviations. With some works, especially by Schenker, I have tried to indicate the exact date of the original editions /source language, but with later works I used a later edition. I wish to thank Eytan Agmon, Dalia Cohen, Roger Kamien, Timothy Jackson and Naphtali Wagner for their perceptive comments on various stages of this work.

1. BASIC CONCEPTS AND DEFINITIONS

The methodological framework of this study is essentially based on the theories of Heinrich Schenker: the problems with which I am concerned only arise within an approach that involves a hierarchy of structural levels, and my main analytical tool is Schenkerian graphs. My solutions, however, occasionally diverge from normative Schenkerian ideas, and the topic as a whole is intended to refute a central claim of Schenker’s theory. Before I discuss the individual terms, let me comment on the combination of terms. Prolongation of seventh chords is a specific case of prolongation of dissonance (henceforth: PD). Throughout this work, I use the term prolongation of dissonance, rather than dissonant prolongation, adopted by Robert Morgan (1976). Morgan refers to cases where ‘both the sonority prolonged and the manner of its prolongation are dissonant’ (87, fn. 1). Consonant and dissonant qualities, however, normally apply to sonorities and not to manners of prolongation. My interest, at least, is in prolongation of the dissonant sonority of the seventh chord, and thus I find prolongation of dissonance more accurate.1

1.1 The Concept of Prolongation

Prolongation refers to the elaboration of a tonal event (chord, interval or tone), during which the event remains in effect without being literally present at every moment. This elaboration appears at a lower structural level than the event it

1 The term dissonance prolongation used by D. C. Berry (2004, 238) is also correct.

2 Basic Concepts and Definitions

2 prolongs, by means of contrapuntal procedures. The prolongation techniques in Schenker’s Free Composition (henceforth: FC) include linear progressions, unfolding, arpeggiation, coupling, reaching-over, motion from an inner voice, motion into an inner voice, neighbor motion and, arguably, mixture. Some techniques may overlap. The use of identifiable voice-leading techniques is essential to prolongation: a mere departure from and return to the same sonority is insufficient to establish prolongation (Straus 1987, 6–7). It is through voice- leading techniques that the prolonged event ‘remains in effect.’3 Not being ‘literally present’ distinguishes a prolongation from a mere lengthening of a single sonority, which I call stretching.4 The distinction between stretching and true prolongation is less strict than it might seem at first. In principle, even surface tones that are foreign to the harmony, such as unsupported passing or neighbor figuration, introduce rudimentary prolongation (Larson 1997, 126). However, in the present study, non-harmonic figuration within a single harmony is not considered prolongation. It may be called quasi-stretching. A harmony is considered prolonged only when at least one other independent chord is structurally subordinate to it. The definition of an independent chord is unclear in principle, but two criteria can be outlined: (a) At least one prolonging sonority should conform to the vocabulary of tertian chords, consonant or dissonant;5 (b)

2 This definition incorporates elements of the definitions by Drabkin (1980), Jonas (1963) and Forte and Gilbert (1982, 142). To my knowledge, Schenker himself left no clear-cut definition of prolongation. Salzer (1952/1962, 143) explains it as the ‘shaping and individual treatment through elaboration, expansion and detour’ of ‘the music’s basic direction,’ which is the structure. Occasionally, especially in Schenker’s early writings (e.g., CP II, §§1, 2 and 5; MW II, 10), prolongation is applied to the laws of counterpoint (Dubiel 1990, 293). Snarrenberg (1996, 324) even claims that ‘Schenker rarely, if ever, uses ‘prolongation’ to refer to the elaboration or extension of a musical entity,’ but in fact Schenker does use Prolongation in that meaning in a rather systematic manner, as a general name for voice-leading techniques (MW III, 8; FC, §§127 [Prolongierung], 133, 138, 143, 155, 184,185,189 and headings of II/2/B and section II/2/B/1). For non-Schenkerian usage of the term see Rosen 1995, 615. 3 Notice, however, that a tone that ‘remains in effect’ need not be an implied tone—a conceptual member of the harmony—at every given moment within the prolongation. At least in neighbor harmonies, the prolonged tone is not implied in this sense. 4 The phenomenon described by Green (1965/1979, 43) as ‘prolongation of a note or chord’ is actually stretching. Satyendra (1997, 184–5) describes what I call stretching as ‘temporal expansion.’ I have chosen to avoid this terminology, since the term ‘expansion’ has a different meaning, which also has temporal aspects. 5 I reject the requirement that the prolonging harmonies themselves should be necessarily consonant. Laufer (1996, 212, quoted below [fn. 20]) invokes this requirement with respect to composing out, but he seems to apply it to prolongation too.

Basic Concepts and Definitions 3

The prolonging activity occupies a sufficient duration, normally at least one complete unit of a steady harmonic rhythm (cf. discussion of expansion below, §1.1.2.3). I shall say more about stretching in the specific context of seventh chords (§2.3.1). The rudimentary level of prolongation is known as diminution. Diminution may be based on the same techniques of large-scale prolongation, but FC allows for additional devices in diminution.6

1.1.1 Selected Problems Concerning Prolongation This section illustrates ideas proposed about prolongation mostly in consonant context, free of the complications caused by dissonance in general and the seventh in particular. My intention was to provide a firm basis that permits applications to seventh chords in the next chapters. 1.1.1.1 What kind of tonal event is prolonged? On this question Schenker’s practice differs from that of today’s Schenkerians. In FC, Schenker usually applies prolongation techniques (which he himself identifies as prolongations) to a single tone in one voice (e.g., a tone of the fundamental line [FC, §113] or the primary tone [§142]), or, in a shorter formulation, to a single voice, such as the fundamental line or the bass (pp. 4–5; §127).7 Schenkerian analysts today, however, tend to use these terms in reference to intervals or chords. The current usage seems justifiable: some prolongation techniques—especially unfolding, arpeggiation, and linear progressions—involve by definition more than one voice (usually incorporating inner voices). Thus, to apply them to a single voice is inaccurate. If prolongation is applied to individual voices, prolonged and unprolonged tones can occur simultaneously. Schenker uses the term in this sense in FC, section II/2/1(a) (p. 29): ‘An unprolonged fundamental line combined with an ascending bass arpeggiation I–V that is prolonged by contrapuntal-melodic means.’ (cf. below, §4.2).

6 Schachter ([1981] 1999a, 201–2, on seventh chords; and personal communication [1999]) emphasizes the difference between diminution and prolongation at deeper levels. I am unconvinced by such a clear differentiation 7 See an exceptional usage in FC, §12, where the term prolongation is applied to an interval.

4 Basic Concepts and Definitions

According to the same principle, when a prolonged chord involves tones that remain stationary (as in plagal neighbor elaboration), chord prolongation applies to the chord as a whole, including the tones that are retained throughout the prolongation (Ex. 1.1,a1), whereas tone prolongation applies only to those tones that actively move (Ex. 1.1,a2). Conversely, a genuine (albeit rudimentary) prolongation (‘quasi stretching’) of a tone may take place within a single stretched chord. This happens in simple arpeggiation: the activity requirement is fulfilled with respect to the single tone, even though the chord has not been left (Ex. 1.1b). 1.1.1.2 How is prolongation related to duration? In principle, a prolongation need not involve durational lengthening. For example, a double for a baroque dance introduces prolongations in the same time span as the unelaborated original. This concept is reflected in the term Inhaltsmehrung (as in FC, §30), which is translated as ‘content-expansion’ or sometimes simply ‘expansion.’ Usually, however, ‘expansion’ is used for Dehnung, which refers precisely to interpolations that do involve a longer span of time than their original prototype. Duration influences our perception of prolongation even in the absence of expansion (Dehnung). First, when listening to music in a slow harmonic rhythm, we tend to perceive as independent chords simultaneities that would be regarded as mere figuration in a quicker harmonic rhythm. Modest contrapuntal motion may sound like a remarkable prolongation if it occupies a long time in absolute terms.8 More importantly, there is some correlation between time span and structural status. For example, a very short embellishment of a background tone is perceived as a diminution, rather than as belonging to the first middleground. This issue is central to the system of Lerdahl and Jackendoff (1983), who introduce time-span trees as a stage on the way to prolongational trees. They formulated the idea as the Preference Rule of Time-Span Importance (p. 220). However, this preference rule is often violated, especially in cadences. 1.1.1.3 What is the aesthetic effect of prolongation? High structural weight is often equated with stability (Larson 1994, 40; id. 1997, 107 and 112; Proctor

8 As an illustration, in Chopin’s Nocturne Op. 15,2, the entire middle section prolongs V7 in an extremely slow harmonic rhythm, employing a single neighbor chord. This prolongation sounds remarkable only because of its long duration (cf. Ex. 7.71a). Compare also Exx. 2.13c and 7.7.

Basic Concepts and Definitions 5

1978, 11 and 35–41; Lerdahl and Jackendoff 1983, 295).9 According to this view, a stable event is prolonged through less stable events. This idea is appropriate for most prolongations, especially when tonicization is involved, but it is not applicable to every prolongation. Almost to the contrary, a major strength of Schenkerian theory is its capacity to explain the dynamic and unstable aspects of tonality (Schachter 1991a, 232, fn. 5). The very topic of the present study is evidence, I believe, against the equation of deeper tonal hierarchy with stability.

1.1.2 Terms Related to Prolongation: Proposed Distinctions The precise meaning of prolongation in Schenkerian theory is sometimes obscured by a terminological confusion. I find it useful to compare ‘prolongation’ with related terms in order to clarify their meanings. 1.1.2.1 Progression. In FC, progression always means a linear progression (a translation of Zug).10 In current Schenkerian literature, the term ‘harmonic progression’ is often used for large-scale transitive harmonic motion that does not return to the initial chord. When prolongation is opposed to progression, it is restricted to circular motion, which can be reduced to a single chord and usually begins and ends on the same chord. My work concentrates on circular 11 prolongations. Schenker himself did not distinguish between prolongations and progressions. In his thinking, a harmony always remains in effect until the next structural event on the same level. For example, in a major-mode sonata-form movement, an initial tonic controls the background until the structural dominant throughout the modulation.

9 Lerdahl (2001, e.g., 48–52) equates pitch space with stability. A more basic pitch space in his system is equivalent to a higher structural level for Schenker. Lerdahl and Jackendoff (1983, 109) even hypothesize about the universality of tensing and releasing (178–9), but conclude that pitch stability is insufficient for determining structural levels (and thus stability is not equivalent to higher structural status) (187). 10 Occasionally Oster’s translation uses ‘progression’ in other senses: in connection with melody (§256, for fortschreiten); harmony and melody (§313, Fortgang); rhythm (§323, Fortgang); and tonal progression approximately in the modern sense (§287, Klangfolge; §260, Schritten). 11 For the standard usage, see for example W. Berry 1980, 29. The essential distinction sometimes appears without the terminological differentiation: Katz (1945, 31) refers to the transitive type as ‘prolonging the motion;’ Beach (1995, 28) distinguishes between circular, opening and closing progressions. According to my terminology, only his circular progressions are prolongations in the narrow sense.

6 Basic Concepts and Definitions

Circularity may have different degrees. I use the term ‘circular’ to refer to any prolongation that returns to the initial harmony; but the return may include changes in chord inversion, soprano position, distribution of inner voices and register. It even may—without disrupting the sense of circular prolongation— include chromatic inflection of tones of the prolonged chord, as in chromaticized voice exchanges between an initial tonic and an augmented sixth chord.12 Fred Lerdahl and Ray Jackendoff (1983, 182) call circular prolongation with modifications weak prolongation, and notate it as a black circle in their trees, whereas they regard exact circular prolongation as a strong prolongation, notated as a white circle.13 Harmonic motion may be combined with circular melodic motion, when the initial chord does not return but some of its member tones do (Ex. 1.2a). When two tones are preserved, the progression between chords includes circular prolongation of intervals as well (Ex. 1.2b).14 Prolongation and progression are almost blurred when three of four tones are retained, as in the progression VII– V7.15 Some theorists claim that progressions are realizations on lower levels of deeper-level prolongations (Katz 1945, 10–14; Cadwallader 1990, 18, fn. 14). The opposite situation may obtain as well, namely that passing events within progressions may be prolonged circularly. Although the same passages may be viewed as both prolongations and progressions (on different levels), at any given level the distinction is essential.

12 Consult Ex. 10.2b–c. For a prolongation with extreme chromatization, see Chopin, Mazurka Op. 59,2, 82–84. The chromatization applies to all the tones (transforming Dß major into D major) and one tone may be doubly sharpened (dß into dƒ). 13 Lerdahl and Jackendoff introduce innovations in the form of representation, but their concept of prolongation remains essentially Schenkerian. Other forms of representing prolongation include networks (Pearsal 1996) and prolongational trees (Keiler 1977). The latter are less appropriate for music. They are closer to linguistic models and reduce music into functional categories, using ‘representational’ rather than ‘inclusional’ hierarchies (to use Cohn’s and Dempster’s term; see Lerdahl 1997, 147). 14 For a voice exchange within a transitive context, see Haydn, Symphony No. 104/II, 9–14. 15 The VII–V7 progression is discussed in §6.3.1. Some prolongation techniques do not clearly fall into either category (circular or transitive): a back-relating dominant is essentially circular, although it does not return to the initial harmony (see the generalization of this situation in §1.1.3 as subordination); auxiliary cadences are essentially circular prolongations of their goals, although they occur during the time span of a previous structural event (unless they appear at the beginning of a piece).

Basic Concepts and Definitions 7

1.1.2.2 Composing Out. There is a major terminological confusion between ‘prolongation’ and ‘composing out.’ Any attempt to make a single, simple distinction between these terms is doomed to failure for several reasons: (a) These terms are often used interchangeably, especially by later theorists, who are not always sensitive to the semantic differences; (b) The term ‘prolongation’ in Oster’s translation of FC is occasionally used to translate expressions other than Prolongation in the original, including Auskomponierung (e.g., §177); (c) Schenker’s original choice of terminology apparently changed over time. The later portions of Der freie Satz use Prolongation very sparingly, often replacing it with Auskomponierung. The shift from the Latin-based term Prolongation seems to reflect a nationalistic bias: in FC, §45, Schenker almost apologizes for using non- German terms like Prolongation ‘for the sake of continuity’ with his earlier writings;16 (d) Some occurrences of the term composing out (e.g., ‘composing out process’ in FC §4, translated from Auskomponierung) only mean a more general ‘working out.’ In spite of all these problems, an essential difference can be traced between the precise meanings of ‘prolongation’ and ‘composing out.’ The term ‘composing out’ suggests that the music exists potentially in a condensed form: ‘The chord, the harmonic concept, is made to unfold and extend in time’ (Jonas, introduction to Schenker’s Harmony, ix). The chord is associated with nature (the harmonic series), while composing out is the task of art (FC, §1). Composing out is based on horizontalization and is similar to unfolding in a general sense. While ‘unfolding’ in its narrow sense (Ausfaltung; FC, §§140–4) is a specific technique that only refers to intervals, composing out has a non-technical flavor and may also refer to chords (albeit not to single tones, unless we think of the basic harmonic series latent in them).17 Like horizontalization and unfolding, the term

16 The German form Prolongierung appears in FC only once (§127). The term ‘composing out’ (Auskomponierung) already appears in Schenker’s 1910 monograph of Bach’s Chromatic Fantasy and Fugue (e.g., p. 26), albeit not in the mature sense. The choice of terminology leads me to assume that the later portions of FC are also chronologically later. See, however, fn. 165. 17 Definitions of ‘composing out’ call it ‘compositional unfolding’ (Drabkin 1987) and Entfaltung (Jonas 1958), a word sometimes translated as ‘unfolding’ in FC (§177, not in a technical sense; §257 on diminution). The term ‘unfolding’ is also used to translate Aufrollung (FC, text of Fig. 1), Abrollung (MW III, 48) and Auswick(e)lung (FC, §315; MW II, 11). All these seem interchangeable with respect to their metaphorical use in music.

8 Basic Concepts and Definitions

‘composing out’ reflects Schenker’s thinking from background to foreground.18 Horizontalization occasionally occurs in a direct, unfilled manner, especially on the level of diminution; such cases are congruent with my concept of stretching or quasi-stretching (see above). However, in any significant composing out, the horizontalized interval or chord is filled in by lower-level motion. Thus, I define composing out as filled-in horizontalization. This definition allows us to recognize situations that constitute prolongation but not composing out. Strictly speaking, ‘composing out’ is an appropriate term only for those prolongation techniques that horizontalize tones that are simultaneous at a deeper level, and which outline a tonal (or chordal) space: arpeggiation, unfolding, and especially the stepwise filling of them through linear progressions. Register transfer, coupling and motion from or into an inner voice also outline tonal spaces that are conceptually vertical. The common feature of the cited prolongation techniques has been recognized by several theorists, although none of them has identified it with composing out.19 The principal prolongation techniques that are not based on horizontalization are neighbor motion and mixture (Ex. 1.3). Therefore, they do not qualify as composing out by my 20 definition.

18 Schenker presents his analyses consistently in the direction of background to foreground. Interestingly, one extremely exceptional passage in FC (§49) vehemently advocates reduction from foreground to background, claiming that the fundamental structure can be found through reduction alone. This opposite direction is also endorsed by Lerdahl and Jackendoff (1983, 112) and, at least for didactic purposes, by Biringer (1995, 150), in a review of Neumeyer and Tepping (1992), who call the analytical direction from background to foreground generative, as opposed to reductive (e.g., p. 68). Actual analysis requires a dialectic play in both directions, as Schachter ([1981] 1999a, 198) beautifully explains. On the analytic process, see also Slottow 2005. 19 Westergaard unifies all the aforementioned techniques under the ‘arpeggiation operation’ (see Peles 1997, 78), and Slatin (1967, 296) under ‘the general concept of the filler or spanning voice.’ (She discusses the term Auskomponierung also at pp. 75, and 256–8, based on her supervisor Mitchell). Rothstein is sensitive to the similarity when he substitutes ‘two-note arpeggiation’ (1990, 98) for ‘unfolding’ (the term he used in Rothstein 1981, 90). Katz (1945, 34) makes a similar observation, distinguishing between motion around a chord and motion within a chord. This distinction underlies Salzer’s harmonic versus contrapuntal prolongations (Salzer 1952/1962), adapted also by Katz, but it is difficult to apply it consistently. 20 The exclusion of neighbor motion from the definition of ‘composing out’ contrasts with Laufer’s definition (1996, 212): ‘composed out, that is, extended by means of consonant harmonies functioning as passing or neighboring chords.’ Schachter ([1987a] 1999a, 151) describes neighbor notion as composing out, but in a different way: ‘‘Keys’ . . . that compose out a structural neighbor note [in large-scale motivic parallelism].’ Other modified uses of ‘composing out’ include the composing out of suspensions (FC, §180, on Figs. 64, Nos. 1 and 3, which do not

Basic Concepts and Definitions 9

1.1.2.2.1 Intermediate situations 1.1.2.2.1.1 Horizontalization of a vertical chord which never appears in the foreground. Occasionally, a vertical chord at a deeper level is horizontalized at a more foreground level, but it never literally appears as a foreground chord. For example, FC, Fig. 134,9 (quoted with annotations in Ex. 1.4) presents the progression A–C–Eß in the bass of Schubert’s Piano Sonata D. 958/IV, 145–69 as a horizontalized diminished triad (IV [VII/V] in the key of III), which creates tension that is later resolved. However, all the tones of this conceptual diminished triad serve as roots of minor triads in the actual music. This curious situation is difficult to describe conceptually. It seems to constitute both composing out and true prolongation, but in a rather weak sense. In the present work I shall only discuss prolongations where the prolonged chord actually appears at least at one boundary of the prolongation.21 1.1.2.2.1.2 Space-filling motion. Much potential confusion concerning composing out derives from situations where a tonal space is filled in, but that tonal space is not generated by horizontalization. I shall refer to such situations as space-filling motion (SFM).22 Mere SFM does not express circular prolongation, although it is located between true structural boundaries. I recognize three categories of SFM: (a). The boundary tones of the outlined tonal space form the interval of a second. The underlying second does not compose out a simultaneous entity, but the second might be said to be itself composed out; this terminological usage is looser than the one proposed here, but it reflects Schenker’s practice.

involve hierarchical levels at all) or of suspensions and resolutions (Schenker [1912] 1992, 96); of ritenuto (ibid.); and of a fourth progression (Jonas [1934] 1982, 73); see also §7.10.1.2.4 below on FC, §314. In problematic passages where both terms (composing out and prolongation) are used, the reader may wonder whether the differentiation is significant, for example: ‘composes out tonic harmony . . . by means of dominant prolongation’ (Schachter [1995] 1999a, 178). 21 Darcy (1994, 12) presents a similar case in the immolation scene from Wagner’s Götterdämmerung (the initial tone in his example should be gß). This kind of prolongation may apply to consonant triads in cases of deep mixture (I–ßIII–V relations in major as horizontalization of Iß). It can relate to seventh chords, as in Haydn, String Quartet Op. 76,6/II, 16–31, where a series of tonicizations of cƒ–e–g–bß seems to horizontalize a conceptual diminished seventh chord (cf. Salzer 1976, 168). See also fn. 610. 22 It goes without saying that genuine composing out, too, includes SFM. My term should be understood as an abbreviation for SFM only within those tonal spaces that have no simultaneous origin at a deeper level. Although the term ‘composing out’ might be applied loosely to such situations, too (see below), it more accurately denotes the filling in of horizontalized sonorities.

10 Basic Concepts and Definitions

Schenker describes illusory linear progressions (seventh progressions or ninth progressions that represent a second, inverted or expanded, respectively; Ex. 1.5a–b) as ‘the composing-out of a second’ (FC, §206) and, with a slight terminological modification, as ‘the composing-out of a seventh [in seventh progressions] which stands for a second’ (§215). Schenker does not describe illusory linear progressions as illusory composing out.23 The outlining of an inverted or expanded second need not be filled in by a full linear progression; it may alternatively consist of illusory arpeggiation based on skips (normally of thirds), or on combination of skips and steps.24 A second can constitute the boundaries of a tonal space even without register transfer. This happens when a major second is filled by a chromatic passing tone (Ex. 1.5c),25 or it may take the form of freer realizations, by 26 means of reaching-over or ‘boundary-play’ (FC, §260). (b). Connective arpeggiations and linear progressions. Normally, arpeggiations and unfoldings represent horizontalizations of originally vertical chords and intervals, respectively (Rothstein 1981, 87–90, ‘rule of arpeggiation’ and its corollary ‘rule of unfolding,’ based on Schenker’s Elucidations), and linear progressions fill them in (MW I, ‘Further consideration of the Urlinie I,’ 107; see Rothstein 1981, 91). However, exceptions do occur to these rules. Rothstein (1981, 129–32) recognizes connective bass arpeggiations, i.e., arpeggiations in the bass that connect two different harmonies. For example,

23 Illusory linear progressions express indirect register transfers (in the sense of FC, §206; §149 speaks of indirect register transfer in another sense), and in this sense they constitute true prolongation, although they are not true linear progressions. 24 For discussion of true versus illusory seventh progressions, see §5.4. Concerning illusory unfilled seventh arpeggiation, regard FC, Fig. 123, 5: ‘cƒ2 progresses to b2 through skips of thirds, without, however, implying a seventh chord.’ The specific context, however, is different there. FC, Fig. 107, includes an illusory seventh arpeggiation within an illusory filled ninth progression. 25 The concept of chromatic passing motion to a neighbor tone creates systematic difficulties. See Proctor 1978, 79–82. For applications within V7, see below Exx. 7.62 and 7.64. 26 See in particular FC, Fig. 124, 2a and b, and the text to Fig. 124, 4: ‘the second . . . is realized by means of a detour.’ The filling in of the space of a seventh or a ninth is usually based on a series of three or four thirds, respectively. The principle of division into diatonically equal intervals may be extended to series of five or sixth thirds, as well as series of fourths or fifths. When the outlined interval is consonant, the boundary tones are conceptually simultaneous, but the inner voices of the prolonged harmony do not correspond to the points of division of the composing out. Cf. Ex. 1.8a– b.

Basic Concepts and Definitions 11

the bass of the progression I–VI–IV arpeggiates the tones of IV but is not reducible to a vertical IV (Ex. 1.6a).27 I believe that connective bass arpeggiation is only a specific case of a broader phenomenon. Connective bass may also be realized through linear progressions. First, the I–VI–IV progression may be simply filled with passing tones. Another opportunity involves a fourth progression, which establishes plagal elaboration in root position (Ex. 1.6b [Mendelssohn]). The I–IV motion outlines the space of a fourth that is part of IV, but the motion prolongs I. Connective linear progressions sometimes occur in upper voices, too. Schenker himself raises this possibility in MW II (‘Further consideration of the Urlinie II,’ 3): ‘Linear progressions in the treble that descend signify motion to an inner voice of the original chord or the ensuing one’ (my emphasis), although in FC, §115, he claims that ‘The linear progressions present a horizontalization of the originally vertical chords of the fundamental structure.’28 One illuminating case occurs in a descending linear fifth progression from 6 over a subdominant harmony (IV, II or possibly VI) towards 2 over V: when the goal tone arrives, the initial tone changes into an implied 5 (Ex. 1.6c). The outlined fifth is dissonant in minor, and as such will have implications for the present study (cf. Exx. 2.14 and 8.18), but its problematic nature is not related to the dissonant quality, since in major it appears consonant. (c). Filling in of a third-space above the fifth (or occasionally below the root) of a triad, in cases in which no vertical seventh chord is implied. This problem is central to my work, and will be explored in depth later (§§2.3.2; 6.2.2); in this chapter I would like to discuss only one situation, whose relationship with seventh chords is rather indirect.

27 Even the symmetrical motion I–VI–IV–VI–I prolongs not IV but I. See Haydn, String Quartet Op. 76,6/II, 64–86 in the reading of Salzer 1976, 182. (However, the I on m. 86 sounds to me like an illusory tonic within the motion towards the V in m. 88). 28 FC, §115 addresses middleground of the first level only, but the idea that linear progressions are horizontalizations applies to later levels too: ‘At the later levels, too, genuine relationship must exist between the first and last tones of a linear progression, a relationship determined by the earlier levels’ (FC, §205). Connective (transitive) linear progressions in upper voices are also endorsed by Cadwallader and Gagné (1998, 79–80) and Klonosky (1997, 7).

12 Basic Concepts and Definitions

Incomplete neighbors create a tonal span, normally of a third, which may be filled by a passing motion on a more immediate level. In most cases, incomplete neighbors constitute unfoldings, usually anticipations, which would be verticalized in rhythmic normalizations (Ex. 1.7a). However, in the common case of 34– 2– above I–V, the4 should not be verticalized with the2 , because the dissonant potential of the 4 over V is not usually realized.29 Thus, the passing motion within the span of 42– from an incomplete neighbor is a transitive SFM (Ex. 1.7b).30 Between genuine composing out and mere SFM is the filling in of a horizontalized interval not in accordance with the other tones of the prolonged chord: occasionally the tonal space that is filled in indeed reflects deeper-level simultaneity, but the inner voices of the prolonged harmony are not horizontalized in the prolongation. The subdivision of the tonal space in such cases is incongruent with the underlying harmony. When the tonal space is subdivided into skips, the incongruent subdivision resembles, but does not constitute, arpeggiation. The source of the segmentation is most often equal division. This is common within the space of the octave (Ex. 1.8a), but can also occur in spaces that involve two distinct pitch classes, as happens in Ex. 1.8b (Brahms): the equal division is here modified according to the diatonic system.31 Another type of incongruent subdivision includes steps, as in a fifth-line that is not divided into thirds (Ex. 1.8c).32 Such constellations form hybrids of horizontalization (and thus composing out) of the boundary interval alone and non-horizontalization of the whole chord. In such cases, it is the vertical

29 See the discussion in N. Wagner 1986, 45–52, especially on the incomplete neighbor before interruption. N. Wagner (1995, 166–7) compares analytical interpretations of an incomplete neighbor in Mozart, Piano Sonata K. 311/II, 3–4. The filling in of an incomplete neighbor might invoke an alternative reading as a complete neighbor. See the conflict in FC, Fig. 138, 5, from Chopin, Etude Op. 10,3, mm. 3–4. The incomplete neighbor is expressed by a slur a-fƒ, which contradicts the indicated complete neighbor. 30 The two first illustrations in FC, Fig. 76,1 present a similar stimulus as a complete neighbor, but the designation 8–7 contradicts this notion. 31 The seventh at m. 327 fades away at the end of this motion (m. 329). For its more daring prolongation in the following passage, see Ex. 7.21. For equal division of the octave into three, see Beethoven’s Piano Sonata Op. 57/I, 65–87 (cf. FC, Fig. 114,8). 32 I explore such fifth-lines in connection with the deep levels (§4.1) and with fifth progressions within V7 (§7.2.3).

Basic Concepts and Definitions 13 boundary chord that is prolonged, and not the sonority which is outlined horizontally. 1.1.2.3 Expansion and extension. ‘Expansion’ (Dehnung) is the metrical stretching over a larger span of time of a prototype, either explicit or implicit (FC, §297, and Oster’s footnote; Rothstein 1981, 151–2). In FC, the same term is also used to translate Inhaltsmehrung (‘content expansion’), which has no metric implications and ironically fits best when the overall duration is preserved (cf. §1.1.1.2). The term ‘extension’ is, to my knowledge, not used in FC. Rothstein (1981, 152) gives it the specific sense of ‘an expansion that affects the end of a phrase,’ i.e., a suffix (cf. Rothstein 1989, 70–73). In the context of the present work, ‘expanded seventh chords’ are seventh chords that govern a metrically expanded passage. Metrical expansion is necessarily based on prolongation (or transitive motion), unless it expresses literal augmentation in time. The reverse, however, is not true: prolongation need not involve metrical expansion (I take ‘prolongation’ to be synonymous with ‘content expansion’). 1.1.2.4 Rare terms. In FC, §45, Schenker asserts that the ‘assignment of names’ is significant. Unfortunately, he does not strive for a limited and consistent terminological vocabulary, but rather for a variety of expressive overlapping terms. In a systematic search of references to prolongation, it is important to understand that ‘continuing presence’ (FC, §115) or ‘mental retention’ (§§93, 115 [Oster] and 204) are identical to prolongation; that when a tone ‘remains in effect’ (§219) or is ‘conceptually retained’ (Schachter [1981] 1999a, 202) or ‘mentally retained’ (Rothstein 1981, 92) it is prolonged; that a ‘territory’ (FC, §244) and a ‘self-contained area’ (§226) are governed by a prolonged event; that, to Schenker, ‘essential content’ (§252) and ‘bold’ (§251) and ‘main’ (§313, Bausteine) events are structural events (not a salient expressive suspension, for example); and that when one tone or harmony aims at another tone or harmony (§229), strives for it (§139), serves it (§§132, 151, 153), points to it (§244), belongs conceptually to it (§244), applies to it (§142) or [slightly differently] represents it (§§164, 260), it prolongs that other tone or harmony.33 A rare but very precise term for deeper

33 The term ‘relates to’ also belongs to this group, but it appears in FC in the anomalous context of auxiliary cadences. In FC, §313, Es steht im Dienste von [serves] is translated as ‘prolongs.’

14 Basic Concepts and Definitions structural status is Vorrang, which appears in Der freie Satz twice, translated in FC once as ‘priority’ (§121) and the other time as ‘preeminence’ (§186). Most of the rare terms appear only once. Other terms are used whose identification as prolongation is less clear. The original German is even richer than Oster’s translation, since some terms have been already translated as ‘prolongation’ (Verwandlungen, §§47, 49; im Sinne von, §314). Applying any of these rare terms to seventh chords points to the prolongation of seventh chords, at least with high probability. I shall consistently employ the term ‘prolongation,’ at the expense of textual variety, for the sake of theoretical consistency.

1.1.3 Minimal Conditions for True Prolongation: Subordination Circular prolongation is any prolongation that relates to a single event at deeper levels. Full circular prolongation (or, in short form, full prolongation) involves departure from and return to the prolonged sonority. Prolongation is circular but not full where it appears only before or only after the prolonged event (cf. Salzer 1952/1962, 44; Forte and Gilbert 1982, 144). I shall call such cases subordination. Subordination is true circular prolongation; it differs from full prolongation only in that it does not have the prolonged event at both of its boundaries. The prolonged event sometimes appears before the subordinate one (back- relating subordination), as in the case of the back-relating dominant (Ex. 1.9a). More often, and with greater consequences for the prolongation of seventh chords, the subordinate event precedes the prolonged one (forward-relating subordination), as in the case of a dominant upbeat before opening structural tonic (Ex. 1.9b). Most forward-relating subordinations resemble appoggiaturas, in that the subordinate event appears within the temporal span of the more structural event and delays it. The progression II–V under (Ex.2 1.9c) is emblematic of this. As Rothstein (1981, 115) observes, the placement of the 2 in a rhythmic normalization of the progression II–V remains at the beginning of the II, whereas 34 the bass of V should be normalized backward to the initiation point of 2.

34 Rothstein (1981, 115) refrains from applying this rule to IV–V7 under 4 precisely because of the involvement of PD. For a similar approach, see Forte and Gilbert (1982, explanation on p. 146 and analytic application elsewhere). For subordination to seventh chords, see below, §§6.3; 8.2.

Basic Concepts and Definitions 15

The backward- and forward-relating subordinations are equivalent to right- and left-branching, respectively, in the trees of Lerdahl and Jackendoff (1983). The tree system lacks a way to represent full prolongation and thus loses the 35 distinction between full prolongation and subordination. The subordination process itself is a transitive progression at a lower level. This progression may itself include linear filling in (see Ex. 1.9d).

1.2 Seventh Chords

Seventh chords consist of a triad and a dissonant seventh. The relationship of the seventh to the rest of the chord is a source of theoretical controversy that is directly relevant to the problem of its prolongation (see further discussion in Chapter 5). In Schenker’s later works, and in the writings of his followers, the seventh is viewed basically as a tone that does not inherently belong to the chord, but rather functions as a passing tone from a (possibly elided) octave (Ex. 1.10a).36 This is a slight simplification, since the contrapuntal function of the seventh is not always the same, but the point is that the seventh does not count as a harmonic tone. This idea is an essential tenet of Schenker’s theory, but its strict presentation is not always preserved.37 Today it is often violated in graphs that designate a harmonic degree with the seventh included. I shall discuss this view in detail in subsequent chapters (esp. §§2.1.1; 3.2; 5.1). Schenker’s view rejects the traditional approach, which regards the seventh as an additional third above the two thirds of the triad, and accepts the tone of the

35 Subordination is necessarily involved in every microtonicization (‘microtonicalization’ in Harmony, §144, discussed in Proctor 1978, 68–70), but not every subordination involves microtonicization, nor is subordination restricted to the surface level. 36 See MW II, 9 ff.; Jonas [1934] 1982, 120–2. Separation of the seventh from the triad is possible also without ideas of voice leading. This approach leads to acceptance of seventh chords that include diminished or augmented thirds, and that usually do not count as seventh chords (e.g., c– eß–gß–b). See Cooper 1974, 138. 37 Within Schenkerian norms, one can trace nuances in opinion between the strictest view, which denies any vertical meaning of the seventh (MW II, 9 ff.), and the more moderate explanation of ‘the melodic origin of seventh chords’ (Aldwell and Schachter 1978/2003, 56; my emphasis). The latter approach is rather close to that in Piston’s non-Schenkerian harmony textbook (1941/1948, 138): ‘Although seventh chords may be built by superposing an interval of a third upon a triad it must not be concluded that these chords originated by that process.’

16 Basic Concepts and Definitions seventh as a legitimate component of the chord (Ex. 1.10b). This conception can be traced at least as far back as Jean Philipp Rameau ([1722] 1971, 213): ‘In order to form the seventh chord, we need only add another sound to the perfect chord in the same proportion; thus, 1, 3, 5, 7.’38 This approach led to the recognition of seventh chords as essential dissonances, although seventh chords do not always enjoy this status (see below fn. 49). Compatible with the recognition of the seventh as a chordal tone is the understanding of seventh chords as four-note chords (Vierklänge). The term Vierklang is misleadingly neutral, as if to mean ‘chords of cardinality 4’ in set theory. In fact, the name is always used for seventh chords. In Harmonielehre (§99), Schenker explains the Vierklang as the result of two interlocking triads, 39 although he later abandons this explanation (Ex. 1.10c). The dispute between the theoretical approaches to the seventh seems almost irrelevant in the pragmatic essay by C. P. E. Bach ([1753–62] 1949, 274). Bach shows alternative realizations of figured bass (Ex. 1.10d) that may approach the seventh either from the octave or from the fifth. In the latter case, ‘the octave should be held while the fifth moves to the seventh.’ Thus, it is clear that in this case the octave does not form the voice-leading source of the seventh, even though the consonant chord is established before the tone of the seventh is reached. This practical approach teaches us that the precise voice leading depends on the actual music. The duality of the seventh chord results from the simple equation 7 = 8-1 (one step below the octave) = 1+2+2+2 (three thirds above the root). The tonal space between the fifth and the seventh, which Schenker tries to reject totally, nevertheless exists. Occasionally, recognition of the 5–7 tertian

38 A modern attack by a Schenkerian aimed precisely at this idea is made by Breslauer (1984, 143), who warns against the ‘impression that a seventh chord is simply a triad on top of which an extra third has been placed.’ In fact, Rameau’s own position is inconsistent, influenced as it is by his view of the triad (‘perfect chord’) as a divided fifth rather than as piled-up thirds. See discussion in Lester 1992, 106–7. Rameau also justifies seventh chords on the basis of proportions between the harmonics, as 10:12:15:18 or 8:10:12:15 ([1722] 1971, 36, ignored by Lester). The attached argument (ibid.) invokes, however, the idea of adding extra thirds. 39 On the principle of piled-up thirds, see also §§2.4; 3.2.6. The idea that seventh chords consist of overlapping triads may be more relevant to non-functional music. See Straus (1982, 265) on Stravinsky.

Basic Concepts and Definitions 17 relationship does occur in Schenker’s writings, albeit usually without commentary (as in FC, Fig. 99,3). An illuminating deviation appears in CP I, Ex. 254 (retranscribed with added annotations in Ex. 1.11) Schenker designates harmonic versus passing tones in a passage from Schubert’s German Dance D.783 (Op. 33), 11. The last of the passing tones connects the harmonic tones of the fifth and the seventh. The seventh already appears in the accompaniment at the outset and thus undergoes true prolongation. It goes without saying that seventh chords are calculated from the root upward, so that the tone of the seventh is the dissonance. Exceptions occur in apparent seventh chords (Aldwell and Schachter 1978/2003, 415–8), such as ∞− chords that form a triad with an added sixth (Rameau [1722] 1971, 112). I will have more to say on this issue in connection with the prolongation of II7 (§9.1), since it is mainly there that the alternative approach is pertinent; the more common types of seventh chords, i.e., dominant and diminished, are not likely to sound like triads with an added sixth, since their three upper tones (lower tones in ∞− inversion) do not constitute a consonant triad.

1.3 The Concept of Dissonance

The concept of dissonance in general is relevant to the present study because the main problem in prolonging seventh chords stems from their dissonant quality. Dissonance—‘lack of agreement’40—and its positive counterpart, consonance, are general aesthetic (and arguably cognitive) concepts that go beyond the domain of music.41 In music, where the terms ‘consonance’ and ‘dissonance’ originate, they have a specific meaning concerning pitch,42 which has physical and psychoacoustic aspects. Dissonance is a sonority that sounds harsh and/or tense. Its physical basis is the lack of simple mathematical proportion between the

40 Oxford Advanced Learner’s Dictionary of Current English (Hornby 1948/1995). 41 Kreitler and Kreitler (1972/1980, 121–6) survey some approaches to consonance and dissonance in other arts and give an extensive list of sources. 42 Only in the more general sense is ‘dissonance’ applied to meter (e.g., in the work of Krebs [1987; 1994; 2003]) and to hypermeter (Cohn 1992b). According to Krebs (1987, 99; 1994, 27), the term ‘rhythmic dissonance’ comes from Schillinger. For pitch dissonance that involves metric deviations from the norm, see FC, §288 and Schachter [1987b] 1999a, 93–94.

18 Basic Concepts and Definitions frequencies of the sound waves (simple proportions exist among the frequencies of the first overtones above a natural sound).43 Definitions of consonance and dissonance have changed in the course of history; even the identification of the character of certain sonorities has changed (especially before the tonal era), in part perhaps due to different tunings. Throughout this book, I refer to equal temperament only. This seems sufficient historically for the repertoire discussed here.44 Historical surveys of consonance and dissonance recognize numerous distinct concepts (seven in Dahlhaus 1958 [esp. p. 1513]; five in Tenney 1988 [summary on pp. 95–101]; four in Voigt 1985 [pp. 13–33]; see also Palisca and Moore 2000). Many of these are irrelevant to our modern sense of dissonance or use the term in a broad, multiparametric sense that is not my concern here.45 I shall focus on a narrower range of ideas in order to clarify Schenker’s position and to distinguish it from other approaches to dissonant pitch simultaneities.

1.3.1 Absolute versus Contextual Dissonances The concept of dissonance adopted by Schenker (most succinctly in the Elucidations and MW II, 9 ff.) relies on strict counterpoint (concept no. 2 in Voigt; no. 3 in Tenney). According to this approach, the character of any given sonority is absolute and fixed, regardless of context. The sonority fits into one of a small number of categories (dissonance, perfect consonance and imperfect consonance) that differ in kind rather than in degree. The behavior of dissonances is restricted, and the restrictions apply equally to all dissonances. The basis for evaluating the quality of sonorities is dyadic (two-part counterpoint). Seconds (and ninths) fourths, sevenths and all augmented or diminished intervals are always dissonant, while all other intervals are always consonant. In three or more

43 Rasch and Plomp (1982, 19–22) survey these aspects of dissonance. They claim that ‘musical consonance [and dissonance] . . . [are] dependent on the rules of music theory, which, to a certain extent, can operate independently from perception’ (19). 44 For PD in Renaissance music, see fn. 313 (Josquin des Pres) and Travis (1959, 260, fn. 1) [Neusiedler, Der Juden Tanz]. 45 Voigt starts from the Pythagorean calculations of antiquity; Tenney starts with pre-polyphonic medieval theory, referring to the melodic dimension only. Helmholz (the source of Tenney’s concept no. 5) and Voigt (especially 1–10) take into account timbre, register and intensity, in order to deal with indefinite pitch too.

Basic Concepts and Definitions 19 parts, every sonority that includes a dissonance is wholly dissonant.46 The only exceptions are major and minor £− chords, where a perfect fourth occurs between upper voices, and in free composition certain ¢− chords as well.47 By contrast, the tonal concept of dissonance (Tenney’s concept no. 4) examines the quality of a single tone in relation to a full chord. This new principle introduces a contextual element to the definition of dissonance, as it may negate strict counterpoint when absolute dissonances are chordal or when absolute consonances are non-chordal. Recognition of dissonant chords goes back at least to Rameau, who simply identified seventh chords as the only dissonant chords legitimate according to the musical practice of his time.48 Johann Philipp Kirnberger follows the same lines when he describes certain seventh chords as ‘essential dissonances,’49 a concept that penetrated Schenker’s early writings (see §3.2). For Carl Dahlhaus (1963; 1983, 86), the difference between dissonances in the context of a full chord and interval-dissonances based on strict counterpoint is essential and is at the core of his criticism of Schenker’s belief in the validity of strict counterpoint in tonal music in all epochs and textures.50 Rameau and Kirnberger are not truly sensitive to context, since they categorize any dissonant sonority in a fixed manner. However, the very notion of

46 For another view, see Dahlhaus’s implicit objection to Kurth (Dalhaus 1983, 86). 47 Concerning the problematic status of the diminished 6/3 chord, see §2.1.2.2.3.2. 48 See Rameau [1722] 1971, 114: ‘Just as the seventh is the origin of all dissonances, similarly the seventh chord is the origin of all dissonant chords.’ This claim expresses the unity of 6/5, 4/3 and 4/2 chords as inversions of the seventh chord. Of course, it is not sensitive to dissonant triads. 49 Not all seventh chords are essential dissonances. Wason (1985, 13) claims that Kirnberger reserves this term for the V7 alone. According to the summary of Kirnberger’s ideas by his students Schulz and Sulzer (Kirnberger [1779] 1979, 169–70), ‘the dissonant essential seventh chord . . . can be formed in four ways;’ the four ways are the four possible structures of diatonic seventh chords. 50 See CP I, p. 5, quoted in §3.2.2. See also similar ideas in Jeppesen [1934] 1982, 12. Dahlhaus ([1968] 1987) also reviews Kirnberger’s and Gottfried Weber’s objections to absolute dissonance. He claims that ‘it seems as though the theory and practice of counterpoint were based on a firm and unambiguous relationship between the treatment of intervals and their degree of comprehensibility . . . but the correlation is not all-embracing’ (p. 122). He relates to tonal counterpoint, rather than that of the sixteenth century. Among Schenkerian scholars, Schachter ([1976] 1999a, 43) recognizes that ‘the great Baroque composers had developed a style of voice leading that could assimilate a prolonged treatment of dissonance’—perhaps not referring to PD; Federhofer (1993) thinks that interval-oriented and chord-oriented dissonances are compatible, but he does not consider dissonant triads. For a different kind of ‘changing concept of dissonance in baroque theory,’ see Cohen 1971.

20 Basic Concepts and Definitions chordal dissonance allows for the contextual evaluation of dyads, because any interval may be embedded within a legitimate chord. A typical problematic instance occurs in Bach’s Sinfonia in F minor, m. 1 (Ex. 1.12), which has already attracted much analytical attention (Dahlhaus 1962; 1983, 86, in debate with Federhofer 1981, 157–9; Rothgeb 1975, 263).51 In this measure, a non-chordal perfect fifth is subordinate to a chordal augmented fourth. The absolute consonance becomes a contextual dissonance (Rothgeb calls the perfect fifth ‘functionally dissonant’); The absolute dissonance becomes a contextual consonance at the given level, although it still requires resolution at a deeper level. Other writers, too, distinguish between absolute and contextual dissonance, using various terms: for Leonard B. Meyer (1992, 480), absolute dissonances are synonymous with ‘discords,’ as opposed to ‘dissonances,’ which are contextual; absolute dissonances have ‘inherent stability’ as opposed to ‘contextual stability’ (Larson 1994, 40; 1997, 107),52 and they may be described as ‘intrinsically dissonant,’ as a modification of the ‘(relatively) intrinsically consonant’ ones described by Lerdahl and Jackendoff (1983, 161).53 Contextual dissonances that are absolute consonances also appear in £−–! suspensions, which Rudolf Louis and Ludwig Thuille (1907/1920?, 45–6) describe, along with ¢−–!, as Auffasungsdissonanz (Wason [1985, 125] translates this as ‘interpretation- dissonance;’ in Snarrenberg 1997, 12, it is referred to as ‘conceptual dissonance’).54

51 Rothgeb also refers to a different interpretation by Hindemith ([1937] 1942/1945, 207). 52 The application of stability to a deeper hierarchy is problematic. See above §1.1.1.3. 53 Lerdahl and Jackendoff include in this definition an additional aspect of stability: chord inversion (cf. §3.3.1.4). Thus, in their system a major or minor 6/3 chord (an absolute consonance) may constitute a ‘relatively intrinsic’ dissonance. Toch (1948, repr. 1977, 12) refutes the idea that some sonorities are ‘by nature’ dissonant [i.e., absolute dissonances], claiming (p. 15) that ‘no sound, considered by itself and detached from any context can under any circumstances be other than neutral and meaningless.’ Toch proves his point with an example of a C major triad which functions as passing. This example is discussed by Bobbit (1959, 177) as ‘functional’ versus ‘non- functional’ musical situation: ‘Observe how the dissonant major triad . . . finds no repose in itself, but demands resolution into the following 7th chord.’ See also Green (1965/1979, 7 and Ex. 2-1), who finds ‘relative repose’ in the ‘less dissonant’ V7 that follows Wagner’s Tristan chord. 54 See also Distler 1940, 23 on ‘reale Dissonanzen’ versus ‘Auffassungsdissonanz.’ The approach of Louis and Thuille is influenced by Riemann’s Scheinkonsonanten (apparent consonances), but for him every chord except I, IV and V is only seemingly consonant (Voigt 1985, 31). Further contextual consonances are described by Bailey (1985, 125, on the V7 that follows the Tristan

Basic Concepts and Definitions 21

It is important to keep in mind that Schenker adheres strictly to the absolute definition of dissonance, and not to attribute to him recognition of contextual dissonances.55 For example, he rebels against the idea that a £− chord might be regarded as dissonant, calling it a ‘monstrous theoretical conclusion’ (CP I, 281). In fact, Schenkerian theory reveals that ‘contextual dissonances’ that are transformed into consonances are the norm, not a deviation worth dwelling on. It is in this sense that Charles Rosen (1980, discussed in Cook 1987, 15) speaks of the large-scale V as a ‘structural dissonance.’ It goes without saying that the harmonic tension of the dominant may be prolonged without creating PD in the sense that annoyed Schenker, and which attracts my attention. My work on the prolongation of seventh chords must address Schenker’s rejection of the prolongation of dissonances (presented in Chapters 2 and 3). To state that this rejection is irrelevant because seventh chords are essential dissonances would be to confuse absolute (interval) dissonances with contextual and chordal dissonances. The concept of chordal dissonance is relevant to my work due to the very fact that I recognize seventh chords as chords. The sterile absolutist approach must undergo one severe reservation, however. The chordal context is necessary for determining the sonoric character of dyads that have enharmonic equivalents. This problem is avoided in the diatonic laboratory of strict counterpoint, but it does arise in free composition. How can a dissonant augmented fifth be distinguished from a consonant minor sixth? One must relate to the context (of the whole chord, and of preceding and ensuing events).56

chord) and by Sadai (1980, xxviii–xxix), who regards (in certain examples) combinations that do not ‘appear in the catalog of tertian chords’ as consisting of chord tones alone. See fn. 100. 55 Such an attribution is made by Snarrenberg (1997, 12) in the context of the dissonant 6/3. By contrast, Dahlhaus (1983) is well aware of the position of his rival Schenker in this regard. 56 This problem is discussed in an illuminating manner by Larson (1997, 111), who is apparently unaware that this idea is inconsistent with Schenker’s own view. An earlier version (Larson 1994, 40–41) confusingly introduces contextual dissonances specifically in the context of strict counterpoint, where they are strictly banned. Full chords with enharmonic equivalents are normally dissonant in either interpretation. Enharmonic readings of consonant triads are possible, however. For example, VII ƒ7/ß3 in major is enharmonically equivalent to a minor 6/3 chord. See Wagner’s Das Rheingold, 62 measures from the end (Kurth 1920/1922, 164, Ex. 75).

22 Basic Concepts and Definitions

1.3.2 Dissonances as Carriers of Motion and Tension The rules of strict counterpoint originate in Renaissance aesthetics, which regard dissonances as inevitable sonorities that either should be avoided as much as possible because they are unpleasant sounds, or, as Zarlino ([1558] 1968, 198) claims, should appear in order to “add a sweetness to the following consonance” by way of contrast. Modern scholars emphasize the aspects of expressive tension of dissonances, which requires resolution (as in Bailey 1985, 125), reflecting the expressive exploitation of dissonance in tonal music. Schenker seems to be more interested in the contrapuntal justification of dissonances and less in their expressive character. He concentrates on the passing tone, the least expressive type of dissonance in strict counterpoint, and attempts to derive from it the suspension, which is the most expressive (cf. Slatin 1967, 243–4). In post-tonal music, Arnold Schoenberg’s emancipation of dissonance denies both the harshness of dissonance and the need to resolve it. His compositional practice seeks to deny any a priori distinction in the behavior of different sonorities. Schoenberg does implicitly acknowledge a fixed character in any sonority (like Schenker) when he describes music history as an evolution towards more remote (and more dissonant) overtones. Unlike Schenker, he assumes that the shift between consonance and dissonance is gradual, without clear distinctions like those dictated by strict counterpoint. (See further discussion in §3.2.6).

2. PROBLEMS CONCERNING PROLONGATION OF SEVENTH CHORDS

Prolongation of seventh chords raises some of the thorniest problems in Schenker’s system as a whole. The main difficulty concerns the prolongation of dissonances (PD). A related but arguably distinct problem is that the space between the seventh and the octave functions as both a chordal space and a step, contrary to normal tonal practice.

2.1 Prolongation of Dissonance

57 2.1.1 Schenker’s Normative View In most of his later writings, Schenker rejects the idea that a dissonance can be prolonged. To his way of thinking, tonal masterpieces are heard in terms of a hierarchical set of structural levels, from the background tonic chord to the surface of the individual work. Every level introduces contrapuntal motion that prolongs events (normally chords) of a more structural level, and creates new events which may themselves be the subject of prolongation in subsequent levels. Dissonances are explained solely as resulting from the prolonging counterpoint. In order for dissonances themselves to be prolonged or composed out, they must first be transformed into consonances (through consonant support) (FC, §169). Such a transformation does not cancel out their dissonant character at the deeper level (MW II, 9–10; FC, §251, p. 96). The foreground is not more dissonant than the deep levels: while the foreground dissonances are eliminated in the reduction, the

57 For a more extended survey of Schenker’s ideas, see §3.2.

24 Problems Concerning Prolongation of Seventh Chords dissonances of a deeper level might appear as consonances in the foreground. The prohibition on PD applies only to untransformed dissonances. Ex. 2.1 demonstrates a normative transformation: the passing dissonance in a) receives consonant support in b) which enables it to receive prolongation in c). This is the ordinary process, and cannot be described as PD. Schenker’s rejection of PD assumes a pivotal role in his writings, and derives from two fundamental assumptions underlying his theory: (a). The source of harmony lies in the harmonic series. For Schenker, the ultimate reduction of the background is the tonic triad, which in turn unfolds (in major) the first five overtones of the harmonic series (FC, Fig. 2). The harmonic series is the anchor in musical reality for Schenker’s philosophical statements on the subject of nature versus art.58 (b). Harmony derives from strict counterpoint. The relations between different structural levels in Schenker’s mature theory are normally based on the rules of strict counterpoint.59 Schenker’s interest in strict counterpoint does not relate to specific stylistic features of sixteenth-century music (see below, §3.2.2): he believed that contrapuntal rules govern tonal music from all epochs and in any texture. He had little regard for Palestrina’s style, considering it a mere forerunner to the true tonal masterpieces. What he found attractive about strict counterpoint was the control over the treatment of intervals, especially dissonances. The application of this control to tonal music deprives dissonances of genuine harmonic meaning, and Schenker is sometimes very single-minded on this point (especially MW II, 9 ff., quoted 60 here in §3.2.6).

58 See discussion in Schachter [1981] 1999a, 187–8. The triad in the harmonic series is of course major. To my knowledge, Schenker attempted to explain the minor mode on only one occasion, in his early work, Harmony (implicit in §22, stated as conclusion 2 at the outset of §26). The minor mode is justified there by virtue of the common feature that it shares with the major in that the triads on I, IV and V are of the same type, thus enabling better motivic imitation. Schenker’s mature theory rejects the equal status of IV and V, but does not suggest an alternative explanation for the origin of the minor triad and mode. 59 In CP, Schenker’s position is apparently different. In this book, Schenker emphasizes the differences between free composition and strict counterpoint (cf. Dubiel 1990, 292). 60 Slatin (1967, 222–3) counts the distinction between dissonance and consonance as one of five non-stylistic laws of strict counterpoint, along with a preference for stepwise motion, smooth voice leading, directed melodic motion (these last three factors are actually related) and the interrelationship between voices (which is more a definition of counterpoint).

Problems Concerning Prolongation of Seventh Chords 25

In accordance with the teachings of strict counterpoint, Schenker is only interested in the melodic justification of dissonances and is indifferent to their specific intervallic identity (MW II, 9): no dissonance may be prolonged, while any dissonance may appear in an unprolonged form.61 The three basic types of dissonance in strict counterpoint are presented in free composition: two of these— passing and neighbor motion—are posited as the most basic prolongation techniques; the third—suspension—is presented as the main procedure for rhythmic displacement, which is eliminated in rhythmic normalizations. Schenker sometimes has a tendency, especially before FC, to reduce the three contrapuntal dissonances to the single prototype of the passing tone: he derives suspensions from passing tones (discussions of fourth species in CP I and II; see §3.2.4 and fn. 140) and mentions neighbor tones only briefly in his systematic discussion in MW II, 9 ff. This approach corresponds to the status of the passing tone in strict counterpoint as the most basic type of dissonance. The relative disregard for neighbor tones until FC reflects contrapuntal preferences that are grounded precisely in the style of the Renaissance that Schenker attempts to ignore.62 It is interesting to note that among neighbor tones, strict counterpoint has a preference for lower neighbors, yet in Schenkerian voice-leading reductions 63 upper neighbors are far more frequent. The rules for the treatment of dissonance are maintained in free composition. Although Schenker allows some degree of license, none of the exceptions permits 64 PD. The freedom of free composition is based not on the behavior of actual

61 Two exceptional remarks in FC reject dissonances in specific contexts despite the fact that they do not appear to be prolonged: in the notes for FC, Fig. 104,2a, which explain substitutions avoiding dissonance; and in the commentary to Fig. 116 (Hassler), mm. 9–10, which praises the ‘avoiding of the ill-sounding total interval of the seventh,’ although this interval only occurs in contour boundaries and would not have been structural. 62 Interestingly, French theorists of the Baroque period also ignore the neighbor tone. According to Cohen (1971, 69), ‘Two specific types of dissonance are distinguished by French theorists of the Baroque: the suspension (or Syncope) and the passing dissonance.’ In CP II, xix, Schenker claims that ‘the neighboring note leads to the concept of substitution,’ but the reference (ibid., p. 76) does not show substitution in the usual sense. 63 This point was observed by Naphtaly Wagner (personal communication). 64 See exceptions that allow for the inclusion of non-diatonic intervals (CP I, 68–75), cambiatas (which Schenker rules out from strict counterpoint) (CP I, 236–9), and the problematic phenomenon of a single passing tone within a fourth (CP I, 184–5; 194, Ex. 276 [after Albrechtsberger]; 239–40); also for direct chromatic motion (FC, §249–50), incomplete neighbors (hinted in FC, §196; and not fully developed by Schenker himself), double neighbors (never

26 Problems Concerning Prolongation of Seventh Chords dissonances like the consonances of strict counterpoint (a recognition that might lead to PD), but rather the reverse, i.e., the behavior of foreground consonances like the dissonances of strict counterpoint, or as Rothgeb (1975, 279) has put it, ‘the extensibility of the principles associated with the dissonant passing tone to apparently consonant phenomena.’65 The only hint of a dissonance in free composition that behaves like a consonance in strict counterpoint concerns the ¢− as a dissonant preparation for the more dissonant suspension ¢¦ (CP II, 258–68). This procedure is sometimes referred to as ‘the consonant ¢−,’ but Schenker insists that ‘the dissonant nature of the ¢− nevertheless remains unchanged’ (CP II, 262). Although this example reveals some degree of latitude in the treatment of dissonance, the prolonged event remains consonant, namely the embracing !.

2.1.2 Theoretical Gaps that Raise the Possibility of Prolonging Dissonances 2.1.2.1 Dissonant harmonic support. Whereas the normative theory requires consonant support in order to transform dissonances into harmonic entities (cf. §2.1.1), not every support is in fact consonant. For example, in FC, Fig. 115,3b, from Bach (cf. my Ex. 2.2a),66 the bass leaps in order to support the passing tone Eß; yet the support (a diminished seventh) is no more consonant than the perfect fourth that would have resulted had the bass remained stationary. The rationale of the support is harmonic: it outlines VII7/VI. It might therefore be called a dissonant harmonic support. Ex. 2.2b shows that the chord that emerges by means of dissonant support can even be prolonged. 2.1.2.2 The seeds of PD in strict counterpoint. Strict counterpoint is often conceived as a kind of laboratory where total equilibrium prevents problems such as PD. Indeed, an investigation of strict counterpoint may not appear to be a

introduced by Schenker systematically. Salzer and Schachter (1969, 56) incorporate it within strict counterpoint itself) and unprepared appoggiaturas (not introduced systematically. Cf. for example the introduction to Chopin’s Etude Op. 10,12 in FGA). Further transformations from strict counterpoint to free composition are (as summarized in Slatin 1967, 224–7): elision (CP II, 269), rhythmic displacement, contraction of two voices into one, and substitution. 65 The passing character of foreground consonances is an especially early insight from Schenker’s Harmonielehre, perhaps as a generalization from Riemann’s Scheinkonsonanten (cf. Dubiel 1990, 317–8). 66 The chorale in Ex. 2.2a appears as Riemenschneider No. 59 (Herzliebster Jesu, was hast du).

Problems Concerning Prolongation of Seventh Chords 27 particularly fertile basis for the exploration of PD.67 Nevertheless, certain situations that arise in strict counterpoint do raise crucial problems with potentially far-reaching consequences. The issue of PD could undermine axioms not only of Schenkerian theory, but also of strict counterpoint itself. 2.1.2.2.1 Decorated suspensions in fifth species (Ex. 2.3). Tones inserted between a suspension and its resolution prolong the suspension (except where there is a mere literal anticipation of the resolution). PD in a simple leap into an ornamentation (Ex. 2.3a) is basic. In three-part counterpoint, leaps may also occur in a voice other than that of the suspension (Ex. 2.3b), in what Knud Jeppesen ([1931, trans.1939] 1992, 185–6) describes as ‘parasitic’ or ‘covered’ dissonance (i.e., a dissonance which coincides with a more correctly treated voice);68 a related procedure occurs in Bach’s Alla breve for organ, BWV 589 (Ex. 2.3c; also quoted in Clark 1982, 244). The more interesting case is that of a pair of two eighth notes (Ex. 2.3d–e). I suggest alternative interpretations of this ornamental figure. Idiomatically, the accented eighth note must be consonant,69 suggesting that this note is an anticipation which is further decorated by a complete neighbor. Nevertheless, I cannot help hearing the ornamentation as an incomplete neighbor filled with accented passing motion. The latter interpretation involves elements of PD within strict counterpoint. The decorated 2–3 in the lower voice (also 4–3 in the upper voice) is especially revealing, since it cannot appear in strict counterpoint without the accented passing tone (2–4–3). Despite this, the 4–3–2–3 configuration does not sound to me like an anticipation. The ornamented suspension is a logical model for PD only under very special circumstances: when the dissonance is indeed a suspension or at least appears on a strong beat and the prolongation has the dissonance only as a point of departure and never restates the dissonance. In the analytical literature, the explanation of prolonged dissonances as ornamented suspensions is rare. Schenker invokes this justification only once (MW II, 97–8), in his discussion of the representation of

67 Normally, the investigation of strict counterpoint is a fruitful basis for Schenkerian studies of problems with broad theoretical applications. See for example Rothstein 1981 on rhythm. 68 See also Albrechtsberger’s exception allowing for a decoration above the suspension, cited in CP I, Exx. 406–7. 69 Jeppesen ([1931, trans. 1939] 1992) states (p. 148) that ‘In such extended formulas, it is immaterial whether the first or second or both eighths dissonate,’ but in his example the first eighth is always consonant.

28 Problems Concerning Prolongation of Seventh Chords the chaos in Haydn’s Die Schöpfung, mm. 3–4 (Ex. 2.4). The Haydn passage clearly exceeds the limits of strict counterpoint. The bare texture and the avoidance of any active preservation of the dissonance are certainly reminiscent of decorated suspensions, but the sonority that precedes the decoration is not a suspension: although it is dissonant (V#), it falls on a weak beat, itself a resolution of a suspension. At the hypermeter level, this V# occupies a strong measure, yet it 70 does not constitute a suspension. 2.1.2.2.2 The cambiata. Schenker explains the cambiata as the result of two interlocking third progressions (CP I, Ex. 347).71 The second member of the cambiata is a passing tone (possibly dissonant), which does not proceed immediately towards its resolution (Ex. 2.5). In this respect, it resembles the decorated suspension. 2.1.2.2.3 Special treatment of the tritone 2.1.2.2.3.1 Occasional exceptions for diminished !. In two-part counterpoint, the established tradition rejects the notion of any special treatment of diminished fifths. Schenker permits one exception (CP I, Ex. 331, see Ex. 2.6a) where he claims that ‘the diminished fifth actually takes on the role of a consonance’ (p. 227). The situation he is referring to is, in fact, a fourth progression within consonant boundaries. The suggestion that the diminished fifth is a consonance is untenable; yet it is interesting that Schenker chose to apply the consonant character to the diminished fifth despite its metrically weak location. This remark is highly exceptional, and perhaps reveals harmonic implications, contrary to the rationale of strict counterpoint. In three-part counterpoint, there is an exception that creates dissonance priority (subordination to dissonance). Jeppesen ([1931, trans. 1939] 1992, 178), relying on his empirical studies of Renaissance music ([1925, trans. 1927] 1970, 158–9), allows the following procedure: ‘if the syncope is in the lower voice it may be resolved into a diminished triad, but always in close position’ (reproduced

70 Schenker’s text says ‘ornamentation of the resolution,’ an expression appropriate for anticipations, but no anticipation is involved in the passage. The ‘elaboration of suspensions’ serves to justify PD also in Clark (1982, 248); Kielian-Gilbert (2003, 57) also raises the issue. For a reading of a 4–2–3 decorated suspension (under a stationary seventh) in the same manner I suggest here, see Schubert’s Ihr Bild [Schwanengesang No. 9], m. 17, in Wintle 2000, 24. 71 Schenker accepts the cambiata also in a reverse contour. On interlocking progressions, see N. Wagner 1995.

Problems Concerning Prolongation of Seventh Chords 29 as Ex. 2.6b). Felix Salzer and Carl Schachter (1969, 345–6, Ex. 9-39) also suggest two instances of ‘exceptional use of the diminished triad’ (the latter reproduced as Ex. 2.6c), but the diminished fifths that they present may be better understood as the result of a contraction of the resolution of the suspension together with passing motion (Ex. 2.6d). 2.1.2.2.3.2 The diminished £− in strict counterpoint. While the exceptions discussed up to this point might well be considered esoteric, the diminished £− in strict counterpoint poses a crucial dilemma. This sonority behaves in all species of three-part counterpoint as a consonance: it is acceptable in first species, and requires no contrapuntal justification in the other species. By contrast, in the domain of harmony, £− diminished chords are regarded as dissonant; this is evidenced by the exceptional doubling of the third, which is intended to soften the dissonant effect. None of the explanations of this anomaly is completely convincing. Schenker raises two arguments in favor of diminished £− sonorities in three- part counterpoint. In CP II, 3, he states: ‘It is no contradiction of this prohibition [of the diminished ! in three-part counterpoint] . . . if, in the case of £− the diminished fifth or augmented fourth is permitted in the inner voices . . . [f]or through these positions, those intervals become thirds and sixths, which, as such, now adequately satisfy the law of consonance.’ This argument suggests that only the intervals formed with the bass voice will determine whether the chord is consonant or dissonant. This position may have been inspired by the inclusion of perfect fourths in £− consonant triads; as a general rule, this condition is insufficient, since in unambiguously dissonant #s, all the intervals are also consonant with the bass. Indeed, Schenker himself raises another argument (CP I, 114): ‘The deficiency of the fourth as a boundary-interval in comparison with the fifth in this situation [e.g., a fourth in the upper voices, as in a £−], incidentally, is so unobtrusive that even the augmented fourth must be allowed here’ (my emphasis). This can explain the distinction drawn between the # and the diminished £−: a diminished £− can be treated as a consonance due to its resemblance to consonant £− chords, and since the dissonance in the upper voices is perceptually mild; by contrast, the # is too different and tense to be similarly treated. Salzer and Schachter (1969, 27) combine both of Schenker’s points in a more explicit manner: ‘Often the diminished £− is listed among the consonant chords.

30 Problems Concerning Prolongation of Seventh Chords

Strictly speaking, this is not true since it contains an unequivocally dissonant interval. However, the fact that the dissonance does not involve the lowest part and the similarity in the degree of tension between this chord and the other £− chords allows us to employ the diminished £− as if it were a consonance.’ (Schenker is himself hesitant to label diminished £−s as consonances, describing them [CP II, 3] as ‘triads that are consonant or to be treated as consonant’ [my emphasis]). The idea of ‘similarity in the degree of tension’ (approximately related to Schenker’s idea of the ‘unobtrusive’ deficiency of the upper fourth as a boundary- interval) sounds reasonable, but the notion of ‘degree of tension’ is foreign both to strict counterpoint and to Schenker’s theories. Salzer’s and Schachter’s statement might create the impression of a system of a priori logical decisions, but in fact, it strives to reconcile the different practices of strict counterpoint and tonal musical literature. In CP II, 3, Schenker observes that the source of the difference lies in the absence of scale degrees in strict counterpoint. According to his later theory, however, scale degrees are not capable of violating the rules of strict counterpoint (see §§3.2.5–3.2.7).72 If we bear in mind that, strictly speaking, the diminished £− is essentially dissonant, then its free contrapuntal use reveals many basic prolonged dissonances. As a resolution for a dissonant suspension, the suspension is subordinate to it (Ex. 2.7a); as a point of departure for passing motion (dissonant or consonant) in second species, it remains in effect until the next strong beat, hence the passing tone may be said to prolong it (Ex. 2.7b); the diminutions of third species enable even circular motion within diminished £− chords (Ex. 2.7c). Eytan Agmon (1997) speaks of the ‘bridges that never were’ between counterpoint and harmony; perhaps these bridges have already collapsed on their way from two-part to three-part counterpoint. The most common location of the diminished £− in three-part counterpoint is at a cadence, as the penultimate sonority; in harmonic terms, it forms VII6. In this

72 I take issue with the view that strict counterpoint lacks scale degrees. In three-part counterpoint, at least when the counterpointing parts make complete chords, they might function as scale degrees, in particular, VII6–I at the conclusion. I also hear horizontalized tonal spaces with possible filling in within strict counterpoint itself.

Problems Concerning Prolongation of Seventh Chords 31 situation, the 4^ fills out the sonority of the two leading tones (Ex. 2.8a). When the lowest voice (whether cantus or counterpoint) reaches the final tone from above in whole note values, the diminished £− is the only possible penultimate harmony (CP II, 45–47). Such settings are rare, perhaps because of this necessity. When the descent [to 1]^ occurs in one of the upper voices, the completion of the two leading tones into a full harmony is the 5,^ creating the (consonant) V (Ex. 2.8b). This explanation of the V appears occasionally in Schenker (CP II, ibid.; FC, §§17 and 23). As Geoffrey Chew has pointed out (1983, 42), this idea reverses the normative order of the Schenkerian argument: normally, the bass of the structural V is derived directly from the arpeggiation of the consonant tonic, while the component of the chord that is regarded as the completion of the harmony is the (ascending) leading tone (Ex. 2.8c). Consistent consequences of the subsidiary line of thought, that derives the structural V from the harmonic completion of the two leading tones, should endow VII6 with similar structural weight to that of V. 2.1.2.2.3.3 The apparent passing tone. The bare tritone in two-part counterpoint does not enjoy the same freedom as the diminished £−. The leading tritone can appear only in second or third species, where it has a contrapuntal justification as a passing tone. Nevertheless, I would argue that the true hierarchical interpretation of such configurations does not necessarily correspond to the simple contrapuntal explanation.73 I hear the tritone as truly passing only when it is created by means of a descending motion (54– –3; Ex. 2.9a), while in ascent6 ( 7– 8– motion, always in major; Ex. 2.9b) it forms what could be called an apparent passing tone: the weak-beat tritone is more structural than the preceding consonance. Thus the consonance on the strong beat is not a normative point of departure for a normative passing tone. This consonance may be subordinate to the ensuing tritone, as a rudimentary PD. This subordination has direct applications in free

73 I believe that contrapuntal exercises, and even cantus melodies, have a tonal hierarchical structure. Schenker’s opposite view (CP II, 19 etc., summarized by Rothstein [1981, 36]) is motivated by the desire to separate counterpoint from free composition, but this view is not grounded perceptually. See exceptions in Schenker’s position in CP I, 54, discussed in Dubiel 1990, 299–300.

32 Problems Concerning Prolongation of Seventh Chords composition, especially in works by Bach, e.g., in the prelude from Cello Suite No. 5, 27–30 (Ex. 2.9c).74 However, even when a metrically weak ‘passing’ tritone serves as the harmonic element at the beat level, the situation need not involve subordination to dissonance, but can be based in certain contexts on displacement of a passing tone in the bass (Ex. 2.9d).75 The 6-7 pattern-8 may be accompanied by parallel thirds. FC shows this configuration with parallel upper thirds, in Fig. 111,d1 (the version in major is quoted in Ex. 2.10a). The accompanying commentary adheres to the normative contrapuntal explanation of the passing tone, but is very strange in other respects: ‘It is occasionally possible for IV–I to replace V–I, if IV! is omitted and the passing tones are placed over the root of the IV. An illusory VII is thus created.’ This statement flies in the face of all Schenkerian norms, which deny equivalent status for IV and V since the root of IV cannot participate in the tonic arpeggiation (cf. FC, §15, concerning Fig. 6,4). Taking this remark at face value may have hinted at the idea of a plagal structure (cf. Stein 1985, 19–57). Schenker’s reduction suggests, however, that it is the VII—which is not illusory at

74 Further examples in Bach include Violin Partita No. 3, Minuet No. 1, m. 7 (Cube [1947–55] 1988, 304, compare levels j and k); Prelude BWV 924 (12 Short Preludes No. 1), 3–5 (hinted by the placement of the numbers in Jonas [1934] 1982, Ex. 116, but not in the reduction, which shows the outer voices only); the opening of the soprano aria Öffne dich, mein ganzes Herze, No. 5 in Cantata No. 61 (also includes a consonant apparent passing tone (mm. 2–3); and the chorale excerpt in my Ex. 3.21. See also: Handel, The Messiah. No. 13 (Pastoral Symphony), m. 7 (complicated by a further suspension), and Haydn, String Quartet Op. 77,1/III. In the latter, the 6– 78– played by the second violin in mm. 14–15 isclearly an embellishment of the more basic 78– in the prototype in mm. 2–3. The configuration 8ß7– 6– 7– 8– is more problematic in respect to the apparent passing tone. I tend to hear it as an elaboration of 87– 8– , thus implying the tritone as a harmonic element, rather than as two third progressions. FC, Fig. 124,1b analyzes a case in point (Beethoven, Symphony No. 3/I, 23–27): Schenker’s reduction shows the leading tone as the more structural element, although the slurs under the score indicate two third progressions. In a detailed discussion of another relevant passage—Bach’s Cello Suite No. 4, Prelude, 1–10—Schachter (1994, 59) offers three interpretations, none of which shows the apparent passing tone. An apparent passing tone may also be chromatic, as is often the case with the augmented sixth chord. See §10.1. 75 This example investigates the scheme given in Aldwell and Schachter 1978/2003, 31, Fig. 2-15, first instance. Subordination to dissonance is only apparent in Bach, Chorales No. 4, m. 1 and No. 81, m. 9, as a result of displacement (as explained in Jonas [1934] 1982, Exx. 129–131). I read an apparent passing tone without subordination to the tritone in Mozart, Piano Sonata K. 332/I, 41– 48. The appearance of the apparent passing tone is here rather indirect. The sequence of II–VII6 may sometimes be absorbed into a consonant frame of a fourth progression, as in the theme of WTC II, Fugue in B major (see MW I, 52).

Problems Concerning Prolongation of Seventh Chords 33 all—that replaces the V. Yet this interpretation is also far from normative, and is based on subordination to an apparent passing tone. Schenker’s insistence on the IV–I preference results from his reliance on strict counterpoint; but it is VII–I, not IV–I, that can occasionally replace V–I. This approach conforms to the norms of the theory of functions, whereby VII is 76 classified together with V as a dominant harmony. Only when the 6 is literally retained simultaneously with the passing motion, will the leading tone lose its 77 local priority (Ex. 2.10b). When the thirds that accompany the 6–78– motion (in major) are lower thirds, a succession of two major thirds arises. The use of this succession in strict counterpoint is problematic since it produces a diagonal (melodic) tritone effect, albeit with no simultaneous tritones. Schenker notes that this succession ‘forces on the ear as a resultant an augmented fourth’ (CP I, 146–7; also FC, §167). From the perspective of the apparent passing tone (Ex. 2.10c), the successive major thirds merge conceptually into a vertical augmented fourth, which is relatively 78 structural and has a tone (6) subordinate to it. 2.1.2.2.3.4 General consequences of the driving force of the leading tritone. A generalization of the above observations shows that the diminished fifth above the leading tone creates a powerful effect of tonal gravitation. This feature is associated with the univalence of the diminished fifth in the tonal system, but is also applicable in harmonic minor (where this interval appears twice). The gravitation of the leading tritone has been acknowledged by great theorists of the past—François-Joseph Fétis even considered it as the most important element of the tonal system (Christensen 1996)—and also by modern scholars (Meyer [1992, 478] surveys Ratner 1962, Browne 1981 and Butler and Brown 1984); Robert O. Gjerdingen (1988) even devotes a whole monograph to the 87– 4– –3 (surface)

76 Funktionstheorie is, of course, not Schenkerian. Schenker acknowledges the kinship of VII and V at the end of Harmony, §111. 77 The configuration in Ex. 2.10b appears in Bach’s Chorale Freu’ dich sehr, o meine Seele (Riemenschneider No. 64), m. 2. 78 Jeppesen ([1931, trans. 1939] 1992, 100) advises the use of successive major thirds ‘with a certain cautiousness,’ although ‘it would be too strict to forbid the succession of two major thirds entirely.’ This procedure is opposed to the normative situation, where successive actual dissonances express a displacement of a conceptual consonance (cf. §2.3.3.2).

34 Problems Concerning Prolongation of Seventh Chords scheme, which is based on the leading tritone.79 From this perspective, it is striking to note that Schenker’s theory ignores the linear tension of the leading tritone almost completely: the leading tritone is considered a mere substitution for ^32– 1– (Ex. 2.11a, adopted from Schachter 1999b, 311, Ex. 10). The exclusion of this factor derives from its contravention of the consonance priority that controls strict counterpoint, the background models and their transference to lower structural levels.80 On exceptional occasions, Schenkerian literature recognizes the phenomenon of the gravitational tritone. Schenker himself assumes it sometimes, especially in the unfolding of neighbor harmony (FC, Fig. 43,d–e).81 Schenker’s great followers, Ernst Oster (in a footnote to FC, §316) and Oswald Jonas (fn. 11 in Schenker’s Harmony, 110), admit this ‘inherent tendency’ [Jonas’s wording] only indirectly in their discussions of the progression II–III in minor. Later Schenker- oriented scholars tend to be more sensitive to the driving force of the leading tritone, in particular Schachter, despite the former example ([1987a] 1999a, 137; 1991a, 232, fn. 5). The resolution of the gravitational tritone to the tonic is even described as a key-defining progression in the textbook by Aldwell and Schachter 82 (1978/2003, 31). Throughout all of this literature, the discrepancy of this tritone with the law of priority of consonance seems to pass unnoticed. The recognition of PD might open up the possibility of reconciling the emphasis on the leading tritone with a Schenkerian approach. The linear tension of the 47– tritone appears to me to constitute an independent force that functions alongside the laws of strict counterpoint. The

79 Gjerdingen compares his approach with Schenkerian analysis (pp. 18, 23–27, 95) as do his reviewers, Proctor (1989, 190–9) Lester (1990, 371–2), Agawu (1991b, 115–7) and Schmalfeldt (1991, 246–7), but none of them comments on the inherent contradiction between the specific scheme and Schenker’s rejection of PD. (Schmalfeldt reduces the scheme into I–V7–I). Gjerdingen looks for the scheme only as a surface event, not necessarily in direct succession, but never in a prolonged form in a Schenkerian sense. Cf. also fn. 214. 80 Cf. FC, §283: ‘The fifth between IV and VII is diminished, and so not a true fifth.’ 81 See also Harmonielehre, §140 (omitted in Harmony), where V7 is acknowledged as a better means for tonicization than the V triad; Harmony, §174, where the ‘univalent chords excellent for the purposes of modulation’ include the leading tritone (for chromatic context see ibid. §111). 82 Cadwallader and Gagné describe the leading-tone tritone as a key-defining interval in the experimental edition of their textbook (p. 3), but omit this explanation in the published edition (1998). See also Stein 1983, 166; Rothstein 1991, 305, Ex. 15 where V replaces an implied tritone; Samarotto 1999, on the beginning of Beethoven’s Bagatelle Op. 126,1.

Problems Concerning Prolongation of Seventh Chords 35 situation is perhaps analogous to the existence of competing forces in physics (for example, gravitational and magnetic). A more general theory should investigate the interdependence of such forces. Such a view of tonality could lead to a radical departure from long-accepted Schenkerian norms (as implied in Chew 1983; see Ex. 2.11b and a related problem in Exx. 4.12–4.13). An extreme application would mean imposing an implied seventh on every chord except the background tonic, even where the actual progression itself includes no vertical dissonances. This idea might sound odd to Schenkerians; it stems from Rameau’s analysis of the basic harmonic progression of descending fifths. Rameau ([1722] 1971, 117) regards the progression I–VI–II–V–I as a conceptual I–VI7–II7–V7–I. Schenker presents this idea in TW 3, 22 (2004, p. 118); cf. below, §9.3.2), and a clearer and more general voice-leading representation appears by William Renwick (1995a, 82, Ex. 3-3c, 83 quoted transposed in Ex. 2.11c; see also Benjamin 1981, 16 and 30). In this work, however, I am proposing a less radical path. The vast majority of prolonged dissonances can be represented within accepted background models, and sometimes only within such models. Preserving as much as possible of the theoretical framework could help to highlight the exceptional feature (PD) that is discussed in this study. The more revolutionary approach ought, perhaps, to be taken more seriously in future research; but for the present discussion, a preliminary glimpse at this possibility will suffice.

2.2 Lack of Distinction between Steps and Leaps

The prolongation of seventh chords is complicated by an additional problem unrelated to their dissonant character. The appearance of two adjacent (or at least diatonically adjacent) pitch classes (the seventh and the octave) in the same harmony violates the contrast between, on the one hand, steps as agents of voice leading and, on the other, leaps as horizontalized harmonies. Joseph N. Straus (1987, 5) presents this contrast as the harmony/voice leading condition (for

83 Like Schenkerism, Hugo Riemann’s functions theory also includes modifications to absorb the driving force of the leading tritone. Agmon’s adaptation of Riemann’s ideas apparently ignores the issue of the leading tritone, but it is implied in the act of selecting the tonic (Agmon 1993; 1995, 201, fn. 10).

36 Problems Concerning Prolongation of Seventh Chords prolongation), and argues that its contravention in post-tonal sonorities prevents genuine post-tonal prolongation. He claims that in a cluster (e.g., set class 3-1 [012], which might be called a ‘stack of steps’) one and the same stepwise motion presents not only a normal non-harmonic passing or neighbor tone, but also a horizontalization (‘arpeggiation’) of a simultaneous harmony (Ex. 2.12,a1, after Straus’s Ex. 3b–c). In fact, the same problem also arises in tonal music, in seventh chords (only with neighbor motion, Ex. 2.12,a2).84 The complementary problem to stepwise motion which is nevertheless harmonic would be motion in leaps which is nevertheless non-harmonic. Is this possible? Steve Larson (1997, 105) claims that it is not. He asserts that ‘Leaps leave traces; steps displace them’ and that any ‘stack of leaps’ in succession remains ‘sounding in the memory’ as a harmony, even when it is dissonant and non-triadic, as is the case with piled-up fourths (Ex. 2.12,b1, taken from Larson’s Ex. 2,c-d).85 However, at least with appropriate rhythmic emphasis, one may hear even in a ‘stack of leaps’ a stepwise line that connects adjacent tones even though they do not occur in direct succession. Stacked fourths create stepwise motion between every second tone (Ex. 2.12,b2); stacked thirds, which produce seventh chords, create stepwise motion between every third tone in the sequence (Ex. 2.12,b3).86 The seventh (sum of two fourths or three thirds) sounds as a substitution for its complementary second. This is the source of Schenker’s notion that seventh progressions are usually illusory linear progressions (FC, §§205 and 220). Of course, the seventh may represent a second even when it is not filled (or filled only in part) (see §5.4.1). I have shown that the clear distinction between

84 Straus’s position has already been presented by Benjamin (1977, 58): ‘[H]ow could we distinguish neighbor motion from arpeggiation in [Stravinsky]?’ Morgan (1978, 4) quotes Benjamin and answers: ‘exactly as we would do in traditional tonal music. How do we, for example, distinguish neighbor motion from arpeggiation in a seventh chord? . . . The chord itself cannot supply the answer . . . the context makes the matter clear.’ 85 Larson’s article attempts a response to Straus’s skeptical view of post-tonal prolongation by showing that the problems involved also occur in tonal music. The idea about the harmonic nature of any stack of leaps, however, fits Straus’s line of thought. 86 Similar ideas received mathematical formulation in Clough (1994, esp. 232–3). The only combinations of two leaps that do not imply stepwise relations coincide with triads or their inversions. The stacked leaps need not share the same size.

Problems Concerning Prolongation of Seventh Chords 37 harmonious leaps and voice-leading steps can also be violated in tonal music in 87 both directions. Schenker never addresses the step-leap problem in any systematic manner. His objections to the prolongation of the seventh only confront the PD problem and not that of the step-leap, but in discussing it he appears at least to have been influenced by the latter. This is evidenced by Schenker’s almost total disregard for those types of dissonance that do not involve steps in any form (dissonant triads, the ¢−, and altered intervals such as tritones).

2.3 Related Situations which Do Not Constitute Genuine Prolongation of Seventh Chords

In Chapter 1, I discussed several situations which resemble prolongation but which, nevertheless, should be excluded from the definition of genuine prolongation. The following remarks are aimed at applying these general situations specifically to the prolongation of seventh chords. They are intended to clarify certain configurations which I do not regard as prolongation of seventh chords, but which might otherwise lead to confusion, since they involve some special treatment of the seventh, such as stretching of a seventh chord or SFM within a seventh chord. I will also examine highlighted unprolonged seventh chords and the issue of delayed resolution. Subordination to seventh chords is excluded from this list, since it forms a kind of true—albeit not full— prolongation. I shall refer to it, therefore, in subsequent chapters.

2.3.1 Stretching of Seventh Chords Stretching refers to the retention of a chord without involving other chords (§1.1). As with stretching in general, the stretching of a seventh chord does not prolong it properly. Even mere stretchings of seventh chords, however, may be musically crucial. They often have a dramatic impact. For example, Verdi’s Otello strangles Desdemona over lengthy loud stretchings of diminished seventh chords.88 A

87 The equivalence of large spans to their complementary small intervals is not unique to the seventh: a sixth progression also stands for a third, but since both sixths and thirds are leaps, in that case, the violation of the harmony/voice leading condition is avoided. 88 For stretching of seventh chords in instrumental music, see Beethoven’s Piano Sonata Op. 90/II, 221–9; Scarlatti, Sonata K. 483, mm. 29–36.

38 Problems Concerning Prolongation of Seventh Chords stretched dissonance might also have motivic significance. For example (using a ninth), in Schubert’s Impromptu D. 899 (Op. 90),2 (Ex. 2.13a) the main section includes a lengthy stretching of V ß9/7 (mm. 44–50, finally resolving to the dissonant V¶°); the emphasis on the soprano ß6 anticipates the middle section on 89 ßVI (enharmonically notated). A particularly radical stretching of a seventh chord occurs in Schubert’s song Die Stadt [Schwanengesang No. 11], which Robert P. Morgan (1976, 58–9) uses to demonstrate PD in a stable section (Ex. 2.13b). The diminished seventh common-tone chord that governs the verses of this song is in fact merely stretched—in Morgan’s wording (ibid.) it is ‘accomplished solely by repetition of the underlying harmony;’ The melody also includes non-harmonic tones, while the accompaniment presents the stretching in a pure manner—but in such an outstanding way that it acquires the sense of a true prolongation. The unusual feature here is that the melodic descent to 1 creates the feeling of repose within the area of the dissonant chord. The tension is dissipated in the tone of the tonic, despite the retention of the dissonant harmony. For practical purposes, a quasi-stretching of a seventh chord (i.e., non- harmonic figuration within a single seventh chord) does not prolong that chord. The boundary between the quasi-stretching of a seventh chord and its true prolongation is difficult to discern, as is the boundary between quasi-stretching and true prolongation in general. Identical voice-leading stimuli might be interpreted in one context as true prolongation, and in another only as quasi- stretching. For example, the brief motion in the bass in Ex. 2.13c sounds as a mere quasi-stretching, despite the fact that the prolonging sonorities conform to the vocabulary of tertian chords. The same voice leading sounds like a true V7 prolongation in Schubert’s Ecossaise D. 781,8, mm. 9–12 (cf. Ex. 7.7 below), since there each passing chord occupies a full unit of the given harmonic rhythm, and is reinforced by sforzandi (cf. the general criteria outlined in §1.1.1.2).

89 A mere stretching of a dissonance can also form a metrical expansion. In FC, Fig. 148,1 (Mozart, Symphony No. 35/II), the dissonant 6/4 at m. 27 is correctly designated as an expansion over a whole measure of its shorter prototype in m. 21. Yet, this dissonance is not prolonged but merely stretched.

Problems Concerning Prolongation of Seventh Chords 39

2.3.2 Space-Filling Motion (SFM) in Seventh Chords Space-filling motion (SFM), as defined in §1.1.2.2.1.2, relates to a tonal span that does not originate in a vertical harmony. Seventh chords offer special opportunities for this procedure. I shall follow the three categories of SFM discussed in §1.1.2.2.1.2. (a). The boundary tones of the outlined tonal space form the interval of a second. This type is modeled after illusory seventh progressions and arpeggiations. I shall explore them when I investigate the conditions for true seventh progressions and arpeggiations (§5.4). (b). Connective linear progressions or arpeggiations. William Rothstein’s basic model refers to bass arpeggiations. Seventh arpeggiations in the bass are always connective, e.g., I–VI–IV–II is not a prolongation of II7 (Ex. 2.14a). When the goal is more structural than the initial harmony of the connective arpeggiation, as in IV–II–VII–V(7), the arpeggiation may nevertheless express subordination to the goal seventh chord (cf. §6.3.3).90 The same is also true in the upper voices. The one situation that deserves special attention is the descent from 6, which has implications for diminished seventh chords (§8.3.3.1). In minor, the descent from 6 over a subdominant harmony towards2 over V is dissonant (a diminished fifth), and as in its consonant counterpart in major (cf. Ex. 1.6c), the primary tone is not retained over the goal tone. FC shows this in Fig. 103,2a, analysis of Bach’s chorale Gott, wie gross ist deine Güte, m. 5 (quoted in Ex. 2.14b).91 The relevance to seventh chords is even clearer where the connective linear progression spans a diminished seventh from 6 over subdominant harmony to ƒ7 over V (Ex. 2.14c). This seventh progression is neither an ordinary illusory linear progression (the seventh does not stand for a second) nor a normal genuine linear progression (it does not express a

90 A dissonant connective bass that does not create a seventh occurs in motion from a structural tonic to ƒIV, without presenting the tritone in a harmonic relation. This can be done as either an arpeggiation I–VI–ƒIV or an ascending augmented fourth progression. For these procedures, see the bass in FC, Fig. 109,e1 (Haydn, Piano Trio Hob. XV: 28/II, 5) and Fig. 73,2 (Handel, Suite No. 1 in collection 2, Prelude) respectively. 91 A famous large-scale case is the development of Beethoven’s Symphony No. 5/I (mm. 130–251) according to TW 1. For further study of this configuration, see Ex. 8.18.

40 Problems Concerning Prolongation of Seventh Chords

vertical seventh): it is connective. This feature, however, is not peculiar to the interval of the seventh. The leading-tone tritone (47– ) never takes the same connective form as that of 62– in minor. Even when it moves from IV (or II)4 to 7V , the boundary harmonies are likely to merge into a conceptually prolonged V7 (cf. 92 Exx. 2.11b, 6.23 and 6.24). (c). Filling in of a third-space above the fifth (or occasionally below the root) of a triad, without implying a vertical seventh chord. The basic procedure is demonstrated in Ex. 2.15a: a seventh chord appears in the middle of the excerpt; even though its uppermost third is filled in both directions, the prolonged chord is the triad which appears at both boundaries. An example occurs in Bach’s English Suite No. 2, Bourrée No. 2 (Ex. 2.15b). Although I have indicated an alternative (plagal) reading, I hear the SFM pattern as the more plausible interpretation.93 The opposite, less common direction of SFM in this category fills in the third below the root of a triad, e.g., reaching the apparent seventh chords VI7 below I or III7 below V (Ex. 2.16a). In such cases, the seventh results from a following voice that moves in parallel lower thirds to the main voice leading. An emblematic instance is the opening of Schumann’s piece for the young Trällerliedchen (Ex. 2.16b).94 This reverse direction of SFM sheds light on the ordinary direction:

92 See discussion in §7.2.3.1. Hassler’s chorale presented in FC, Fig. 115,1c is important in this respect. See my analysis at Ex. 4.13. 93 The potential alternative interpretations of this pattern serve as a source of compositional play in Dvořak’s Silhouette Op. 8,5. The varied repeat in the first section (mm. 9–16) includes a segment (11–13) that reaches the seventh as a clear SFM. In the equivalent location in the recapitulation (mm. 59–61), the plagal interpretation wins, due to changes in the bass and with the help of changes in mode. More remote applications of SFM are also possible, for example, when the tone of the seventh is given another harmony, and when the filling in appears only in one direction. However, when the filling in takes place in descent only, the tone of the seventh might sound as if it arrives from an implied octave; see for example the theme of Tchaikovsky’s The Doll’s Burial (Album for the Young 7). This point is related to the general rule for identifying the seventh as a true primary tone. See §5.4.1. 94 See Schachter [1981] 1999a, 203–4, and a detailed but less convincing analysis in Koozin 1999. Another famous case which functions in a similar manner is the ‘VI7’ in the variation theme of Mozart’s Piano Sonata K. 331/I, m. 3. Motion from IV to II7 perhaps leads to a true seventh chord (§9.1), but can still produce SFM. A potential passage occurs in Haydn’s Piano Sonata Hob. XVI:26/I, 6–8, but perhaps there the II6/5 is indeed prolonged.

Problems Concerning Prolongation of Seventh Chords 41 perhaps it too can be regarded as the product of a following voice in parallel upper thirds to a leading voice which remains within the boundaries of the basic triad.

2.3.3 Highlighted Unprolonged Dissonances and Seventh Chords

2.3.3.1 Structural Unprolonged Dissonances and Seventh Chords

In principle, any particular structural event in a specific work might appear in an unprolonged form. Some background events (such as the final tonic) often appear unprolonged, while others (such as the primary tone) are almost always prolonged. Among background dissonances, there is one familiar situation that usually appears as a foreground dissonance (not transformed into consonance) and without prolongation. This is the ¢− under scale degree ^3 of theUrlinie , most commonly in an Urlinie from 5FC ( , Fig. 16,5, last example).95 The structural status of this dissonance results from the melodic fluency provided by the ^3. This phenomenon has received particular attention (Beach 1990a, Cadwallader 1992), and is generally accepted in the practice of analysis, although it creates theoretical problems (see §4.1).96 Analogously, seventh chords may also acquire structural weight even when they are not prolonged, provided that they form the single support for a structural tone in the upper voice. For the most part, this occurs when V7 alone supports 4. Chapter 4 is devoted to configurations in which seventh chords are involved at the deepest levels. At the later middleground, another frequently recurring situation provides unprolonged dissonances with structural weight. This is the case of augmented sixth chords at the end of chromaticizations (most often chromatic voice exchanges). Their structural value results from their location immediately prior to events which are even more structural (cf. §10.1).

95 The 6/4 under 3 is represented inFC as a middleground figure with prolongation in the bass (only) at the first level, but it could be introduced in the background itself, supported by the basic bass arpeggiation alone. 96 Forte and Gilbert (1982, sup.) adopt a ‘middle way’ approach towards the 6/4 under 3: while they admit the possibility that a 6/4 supports scale degree three (41), they prefer consonant support where possible (48). For historical comments and personal views on the 6/4 under 3 (as a surface phenomenon), see Meyer 1992, 484–5.

42 Problems Concerning Prolongation of Seventh Chords

2.3.3.2 Highlighted non-structural dissonances and seventh chords

The presence of dissonances at the highpoints of musical works contributes to their expressive character, but such dissonant events need not be structural in a Schenkerian sense. A Schenkerian approach usually underemphasizes such non- structural highpoints. This might be considered a theoretical pitfall, as has been claimed by Agawu (1984, 159–60), or at least suggest the need for complementary analytical methods that would investigate aspects that are not affected by reduction.97 The most common type of non-structural dissonant highpoints results from displacement.98 Indeed, in suspensions, which form the contrapuntal prototype of displacement, the rhetorical emphasis is given to the non-harmonic sonority, which is more often than not an inherent dissonance. A salient example of a dissonance that arises through displacement occurs when the primary tone appears above a dissonance, but relates conceptually to a former bass tone (cf. Kamien 1998). Well-known instances of this procedure open Beethoven’s Piano Sonata Op. 10,3/II (using initial ascent to m. 7) and Piano Sonata Op. 26/III (using arpeggiation to m. 17, albeit via a non-harmonic tone); Ex. 2.17a–b summarizes Schenker’s readings in FC, Figs. 39,2 and 40,6 respectively. The primary tones in both cases form part of the deeper-level consonant tonic, even though they actually arrive above dissonant VIIº7/V. Highlighted non-structural dissonances can also be heard in the horizontal dimension. A fine example can be found in Brahms’s Rhapsody Op. 79,1. The opening stresses the tones fƒ–d–aƒ rhythmically and melodically, but these tones do not unfold a vertical augmented triad, since the aƒ clearly comes from the 99 preceding b (not shown).

97 Eitan (1997, 12) proposes that such highpoints form ‘rhetorical’ emphasis, as opposed to ‘grammatical,’ structural, emphasis. See also Wintle (1985, 159) and Lester (1981). 98 See extreme dissonant textures as the product of surface displacements in Schumann, Auf einer Burg, Op. 39,7 (Salzer and Schachter 1969, 187–8) and Brahms, Intermezzo Op. 116,6 (Ch. Smith 1981, 140–1). 99 These tones also correspond to tonal areas of the piece as a whole. They might have a structural meaning in the background, but not in the foreground. Hence, this case differs from genuine motivic parallelism between structural levels: this is an associative relationship. I believe that dissonances (and harmonies in general) have the power to create associative relations (cf. Rothstein 1991, 314 and his sources), but that these must not be confused with prolongation. Even if the rhapsody is based on a large-scale equal division of the octave into three, this does not

Problems Concerning Prolongation of Seventh Chords 43

2.3.3.3 Unprolonged non-structural dissonances which are retained in reduction

Occasionally, especially at the diminution level, actual dissonances which are in no way structural may nevertheless be present in the reduction, and possibly even occupy a longer duration in the reduction than in the actual piece. This does not, however, imply that they are prolonged dissonances. For example, FC, Fig. 146,2 (Beethoven, Piano Sonata Op. 22/IV, 1–8) includes in mm. 1 and 3 dissonances that occupy a longer duration in the graph than in the actual piece, but the frame remains consonant.100

2.3.4 Delayed Resolution The melodic resolution of the seventh may be delayed through the unfolding of the chord of resolution. The tone of resolution is, in such cases, already implied (and possibly present in another voice) at the initiation point of the chord of resolution, so that at that moment, the seventh has already been replaced. Aldwell and Schachter (1978/2003, 414) make an important distinction between such a delayed resolution of the seventh and a true extension101 of the seventh: ‘With the former the chord of resolution is extended, while in the latter the seventh chord itself is extended’ (Ex. 2.18 follows their example 24-17).102 Sometimes, the expected tone of resolution is not only delayed, but avoided altogether. Even then,

function as prolongation of the augmented triad. Cf. the analogous case in Ex. 1.8a. Salient melodic dissonances are common in compound melodies. For example, the ‘unresolved major sevenths’ indicated by Burkhart (1973, 88) in Chopin’s Prelude Op. 28,6, mm. 5–8 and 9–14, do not represent tones that belong together in any structural sense. 100 Sadai (1980, xxviii–xxix) suggests a more radical realization of the same idea. He attempts to show that a non-triadic combination might serve as a true chord, while a triad in the same time- span might be non-chordal, e.g., in Schumann’s piece for the young Nordisches Lied, m. 13 (Sadai’s Exx. x–xii). This is yet not PD. A Schenkerian approach would probably show the underlying consonances and point to their displacement as a foreground procedure. 101 Aldwell and Schachter avoid the term prolongation, as they do throughout their book, apparently for methodological reasons. 102 For discussions of actual instances of delayed resolution, see Gagné 1990, 30 on Mozart’s Piano Sonata K. 332/I, 132–45 (the resolution of the retransition into the first group of the recapitulation); and Wen 1990b, 140–1 and 143, fn. 12 on Mozart Piano Concerto K. 595/I, 38–40, 56–59 (his reading of the latter passage is quite daring). As a special type of delayed resolution, I would include cases where the expected pitch class of the resolution does appear at the outset in the relevant voice (normally the soprano), but in the wrong register. See Gagné 1990, 26 on Mozart’s Piano Sonata K. 330/I, 112–7 (the parallel passage in the exposition, 25–30, shows the same configuration).

44 Problems Concerning Prolongation of Seventh Chords the tone of resolution is implied within the resolution chord, and the seventh is not 103 prolonged.

2.4 Aesthetic and Theoretical Background to Schenker’s Position

Schenker’s emphasis on the contrapuntal source of dissonances, to the extent of depriving them of any harmonic significance, plays an important role in his attack on modern music, e.g., in his article ‘Rameau or Beethoven?’ from MW III (see §3.2.6). On a more theoretical level, Schenker takes issue in that discussion with two distinct ideas: the tertian principle and the concept that dissonances are remote overtones. Schenker does not seek to distinguish clearly between them. (a). According to the tertian principle, the seventh is an additional third above a triad. This idea can be traced at least as far back as Rameau (cf. §1.2). Schenker points to the dangers of further induction of this principle: ‘Once on this slippery slope [of accepting piled-up thirds] nothing could stop recognition being given also to eleventh and thirteenth chords’ (p. 5). This argument is very logical; theoretically, accumulation of thirds could be continued ad absurdum, as Georg Sorge claims: ‘Do not laugh! C–e–g–b–d– f–a must be a chord! Why not call the entire piano or organ one chord?’ (Jonas [1937, 71–72] quotes Sorge and attacks his position. My translation). Nevertheless, it seems perceptually obvious that the height of the stack affects its validity as a chord. At least in seventh chords, the tertian connection of the 104 seventh to the triad must not be automatically denied (cf. §1.2). (b). The idea that dissonances are the remote overtones is advocated by Schoenberg ([1911] 1978, 321): ‘There are, then, no non-harmonic tones . . .

103 Rothstein (1991, 289–90) presents an interesting example at the conclusion of the aria Esurientes, from Bach’s Magnificat. The implied resolution is given in the continuo alone. Rothstein claims that the dissonance is resolved syntactically but not phenomenologically. According to this idea, a delayed resolution might be said to prolong the phenomenological tension of the seventh, even though it does not prolong the seventh itself. 104 The idea that chords are based on thirds explains other dissonant chords as well, employing different principles than the accumulation of more than two thirds: dissonant triads combine two consonant thirds into a dissonant interval; altered chords, such as augmented sixth chords, use thirds (or their inversions, sixths) which are themselves dissonant; 6/4 chords are inversions of triads, that locate in the bass the fourth that completes the triad into an octave. This last category is the most difficult to reconcile with a Schenkerian approach, since 6/4 chords are normatively conceived as true inversions only when they count as consonances.

Problems Concerning Prolongation of Seventh Chords 45

Passing tones, changing tones, suspensions, etc., are, like sevenths and ninths . . . of course, by definition, harmonies—something that sounds similar to the more remote overtones.’ Remote overtones, of course, have a weaker harmonic relationship with the fundamental than do the closer overtones. In acoustic theories this is a simple fact, but the relevance to musical hearing is 105 problematic. The polemics between Schenker and Schoenberg (cf. §§2.4; 3.2.6) were strongly influenced by their respective aesthetic approaches: Schoenberg, the advocator of new music, wanted to prove that the ‘emancipation of dissonance’ is a natural continuation of an evolutionary process inherent in tradition. Schenker’s attack on this view (and even on Rameau, in MW III) was motivated by his antagonism towards modern music that was not based on the tonal system underlying the masterpieces he most admired. For Schenker, the rules of strict counterpoint are the dam that regulates the treatment of dissonance and holds back the modernist flood. The rejection of the notion of PD scarcely points to an objective investigation of the tonal system or of its greatest works. Schenker’s value judgments inevitably infiltrate technical aspects of his theory. Revealingly, among his followers, the prohibition on PD is adhered to principally by those who share Schenker’s musical taste (Oster and Jonas, in contrast to Salzer). This over-reliance on evaluation might have prevented adequate attention being paid to those dissonances that are ordinary in the tonal literature, especially seventh chords. Schenker’s aesthetic predilections, I would argue, led him to make theoretical errors with regard to seventh chords. A greater awareness of those aspects of Schenker’s theory that are influenced by his polemical approach is perhaps symptomatic of post-modernist trends. My aim is not, however, to relativize these theories; I believe that the very awareness of such a bias will enable a refining of Schenker’s theory and thus make it more faithful to the music itself.

105 In Harmony (p. 27, Ex. 17 [21] ), Schenker shows a rare exception, where a seventh is indeed composed as reminiscence of a remote overtone. This happens at the end of Chopin’s Prelude Op. 28,23.

3. LITERATURE SURVEY

3.1 Precedents to Schenker and Non-Schenkerian Literature

Occasionally, the prolongation of seventh chords is described without using the Schenkerian concepts and terminology, either in pre-Schenkerian or twentieth- century non-Schenkerian literature. As early as 1728, Johann David Heinichen recognized the pattern 7–8–7 (on IV and VII) as an embellishment of the seventh before its resolution (Buelow 1962, 223. See Ex. 3.1). It is more surprising to 106 discover precedents in Rameau (1737 and 1760, see Ex. 3.2). Both configurations show parallel third progressions below a stationary seventh that leave the root and arrive at the triad based on the seventh chord’s upper member tones: in the former case V7–‘VI6’–VII the goal is dissonant, in the latter case. II7– ‘I6’–IV it is consonant.107 Rameau provides similar explanations: in the former case, Rameau explains that ‘chord X is passing since it does not resolve the preceding seventh chord’ (Lester 2006, 64), in the latter he claims that ‘the same dissonance is seen to continue throughout a, b, c and resolve only at d . . . as a consequence, the same fundamental bass remains.’ Other early examples appear in the work of Kirnberger. For example, he recognizes ‘the free treatment of the seventh’ where ‘the seventh is formed over a passing note in the bass that falls

106 Rameau, Génération harmonique (1737), Example 28, quoted and discussed in Lester 2006, 64, and Code de musique pratique (1760), third example N, quoted and discussed in Wignall 1992, 75–76. The Heinichen example is from Der Generalbass in der Composition (1728), p. 596. 107 On the problematic relations of II7 and IV, see §9.1. In the example, Rameau does not provide Roman numerals, but rather only figured bass. He designates the IV as a ‘6/5,’ although it literally appears as a 5/3.

48 Literature Survey between the dominant seventh chord and its first inversion’ (Kirnberger [1771] 1982, 106–7, see Ex. 3.3). However, unlike the Rameau example above, in Kirnberger’s example the root literally retains during the passing motion, and in result the passing sonorities are not themselves triads.108 In the early twentieth century, there were several precedents that may have had a direct influence on Schenker. In 1901, Anton Bruckner’s student Cyrill Hynais demonstrated a prolongation of a seventh chord by means of a voice exchange via a passing ¢− in a chromatic context (quoted in Wason 1985, 101; retranscribed as Ex. 3.4). In Harmonielehre by Louis and Thuille (1907/1920?), the concept of prolongation at the surface level becomes more common.109 They show several examples of interpolated chords (eingeschobene Accorde) within various seventh chords, and shun the more obvious possibilities by even recognizing an interpolated ! within a seventh chord as well as a leap to an interpolated chord (1907/1920?, 76, Ex. 69b–c, reproduced as Ex. 3.5a–b).110 Descriptions of miniature prolongations of seventh chords also appear in Lenormand [1913] 1915, 15 (on Chausson’s Serres Chaude) and Kurth 1920/1922 111 (e.g., 198, on Wolf’s Seufzer, cf. Ex. 10.7d). Descriptions of wide prolongations of seventh chords in non-Schenkerian literature are rare, and these might well have been influenced by Schenkerian

108 In the nineteenth century (1853–4), Simon Sechter presented schemes which, according to Slatin (1967, 94–98), form ‘composing-out ‘in embryo.’’ Slatin’s Ex. 21, from Sechter, shows motion within V9. On the other hand, Sechter’s demonstration of fractal harmonization on two levels (quoted and discussed in Eybl 1995, 44) excludes and must exclude dissonances as the deeper harmonies, since it tonicizes every prolonged chord. Rudimentary passing motion within V7 is also demonstrated by Distler (1940, 34 and 49) in a workbook for Riemannian Funktionstheorie. 109 Louis and Thuille recognize ‘interpretation-dissonances’ which appear as consonant chords but are, in fact, passing (cf. Wason 1985, 126). This idea is analogous to Schenker’s concept of prolonging chords. Their recognition of prolongation of seventh chords, however, goes beyond even this idea. Despite some aspects that anticipate Schenker, Louis and Thuille depend heavily on Riemann (ibid., 131). 110 See also p. 79, Ex. 74b (I within V7) and c (I6/4 within V7); p. 128–9, Ex. 132,a(2) and c(2) (I within II7); and pp. 81 and 292 (Exx. 77(4) and 296a) (IV within V7). Louis and Thuille also describe the prolongation of another dissonance: the cadential 6/4 (p. 67, on Ex. 55,4). I am not sure whether all these examples appear in the original edition. 111 Lenormand recognizes a neighbor chord to a half-diminished seventh chord as ‘ornamentation of the 3rd, 5th and 7th.’ His chapter 2 is entirely devoted to ‘exceptional resolutions of the seventh,’ some of them by ‘retention of the seventh’ (p. 13), but the example mentioned is the only one that actually prolongs the seventh. Kurth describes passing motion within an augmented sixth chord in terms of tension. See translation in Willamson 1996, 216–8 and discussion in §10.3.1.1.

Literature Survey 49 concepts. Rosen (1970/1972, 134) analyzes Haydn’s String Quartet Op. 64,1/I, 133–47 as ‘an expansion of [the dominant seventh chord] . . . and an example of the physical excitement this kind of expansion can generate;’ and (ibid., 442–3) directly states that (in Beethoven’s Piano Sonata Op. 111/I, 5–10) ‘The . . . diminished seventh is prolonged’ (cf. Ex. 8.33a); Dahlhaus ([1987] 1991, 106) observes that in Beethoven’s Cello Sonata Op. 5,1/I, 24–34 ‘the dominant seventh 112 chord spreads itself over an area of no less than eleven bars.’ This survey of non-Schenkerian sources excludes theoretical experiments that might be explained as prolongations of seventh chords, but which were not conceived as such by their creators. Wason (1985, 16–19 and 24) cites such experiments by Abbé Georg Joseph Vogler (1778) and Emanuel Aloys Förster (1805), which are related to what Victor Fell Yellin (1998) describes as the omnibus idea (see §7.2.1.2.1).

3.2 The Approach to the Seventh in Schenker’s Published Writings

The strongest opponent of the concept of PD in general and prolongation of the seventh (and of ‘seventh chords’) in particular, appears to be Schenker himself. Schenker’s resistance to accepting the seventh as a true harmony can be traced back as early as Counterpoint (CP) I, but does not assume a dominate role until Der Tonwille (TW). Some of his older ideas about the seventh crop up even in Free Composition (FC). In this section, I have adhered to the chronology of Schenker’s published writings. Unpublished material in the Oster Collection (in the New York Public Library of the Performing Arts Music Division) does not provide significant additions to the published ideas on PD. The dates of publication may be 113 misleading in certain cases. My survey skips over the very early writings before

112 Rosen does not address the specific means of the ‘expansion’ (i.e., in this context, prolongation) in the Haydn example. I am not sure whether this analysis is correct. See fn. 607. Dahlhaus’s observation is correct, but addresses a rather simple prolongation. Another non-Schenkerian recognition of a prolonged seventh-chord appears in Piston 1941/1948, 135, Ex. 259, which shows a prolonged ‘VI7’ (actually an altered VI7, a diminished seventh chord) in Brahms, Intermezzo Op. 116,6 (cf. my Ex. 8.9d and discussion in §3.3.2). 113 For example, the earliest version of FC had already been embarked upon in 1915 (Jonas, preface to the second German edition. See FC, xv).

50 Literature Survey

Harmonielehre and over A Contribution to the Study of Ornamentation ([1908] 1976). References to the textless Five Graphic Analyses ([1933] 1969) are limited to the body of this work.

114 3.2.1 Harmonielehre (1906) [Harmony] Seventh chords are explained in Harmonielehre (§99) as a combination of two triads in a structure ‘rising in thirds,’ which is, of course, a Rameauian principle (cf. Ex. 1.10b). Schenker does not accept stacks of thirds higher than seventh chords as true harmonies, with the sole exception of V9 (§§107–13).115 This early book already contains an insight into the hierarchical structure of tonal music, in the refusal to accept as true harmonies simultaneous combinations of tones that are created by voice leading (even if they converge into vertical harmonious structures), but its prerequisite from true harmonies is not to be consonant. Rather, two other requirements are called upon: expressing scale steps (Stufen)116 in relation to chords, and ‘harmonizability’ in relation to intervals. The presence of scale steps is said to distinguish free composition from strict counterpoint (§§84–88). The priority of consonances in strict counterpoint is regarded in Harmony as merely analogous to structural priority in free composition: ‘. . . an analogy: where in strict composition, we have notes consonant to those of the cantus firmus, we have, in free composition, the scale- step. Where, in strict composition, we have the dissonant passing note, we have,

114 References to material that is included in the abridged translation of Harmonielehre appear under the book’s English name, Harmony. I have only referred to the original Harmonielehre for material that is omitted from Harmony. 115 This stance might be the legacy of an older theoretical tradition. Sheldon (1982, 86) argues that the acceptance of the V9 in the nineteenth century [in Germany] is a compromise between the principles of Kirnberger and Marpurg. Kirnberger accepted only some seventh chords (and not the ninth chord) as ‘essential dissonances’ (see §1.3.1). 116 Stufen (scale steps or scale degrees) refer literally to tones of the scale (or their chromatic inflections) in their position relative to that scale, irrespective of whether they form roots, other chord-members or non-harmonic tones. The German usage of this term also refers to chords built on these tones. This usage predates Schenker, and according to Riemann 1882/1929, it stems from Georg Sorge. Schenker’s notion of Stufen apparently refers to chords rather than tones. His concept of Stufen is innovative, and can be regarded a predecessor of his later method: he regards the Stufe as ‘a higher and more abstract unit [that] may even comprise several harmonies, each of which could be considered individually as a triad or a seventh-chord’ (§78, p. 139). In terms of the more mature theory, Stufen (as tones) are, as Jonas ([1934] 1982, 57) describes, ‘fundamentals of composed-out chords.’

Literature Survey 51 in free composition, free voice-leading, a series of intermediate chords, unfolding in free motion’ (§88, p. 159). In the original Harmonielehre (p. 204), this analogy is also described in a drawing (retranscribed and translated as Ex. 3.6).117 According to this view, dissonances can constitute true harmonies, provided that they form scale steps. The most obvious cases of dissonant scale steps are the diminished triads VII and in minor II too, which are even diatonic (albeit that 118 scale steps need not be diatonic [Brown 1986]). In Harmony, Schenker also allows seventh chords to express genuine scale steps: he even takes an entire paragraph to emphasize this point (§86: ‘Freedom in Voice-Leading Increased in Free Composition, Owing to the Scale-Step’). He refers to his analysis of a passage from Wagner’s Tristan und Isolde, Act 3, Scene 1 (Ex. 127 [161], reproduced as Ex. 3.7), where he indicates I(ß7) as a true scale step.119 Schenker states: ‘It might be objected that . . . there is an essential difference between [Ex. 128 [162] from Fux and the Wagner example]: Fux employs only consonant triads, whereas in Wagner’s example the parts form dissonant seventh-chords as well . . . The difference, however, is only apparent. The application . . . of the principles of voice-leading, which liberates each individual harmony from the burden of having and proving the significance of a scale-step, assimilates the two quoted examples much more decisively . . . Wagner’s method represents a development, an extension120 of Fux’s method, not its abandonment or opposite.’ This approach to structural dissonances and to Wagner’s music reflects Schenker’s early period, and undergoes radical modification in his mature writings. For intervals to express true harmonic relations, they must fulfill the criterion of what is referred to as harmonizability [Harmoniefähigkeit], or ‘the possibility

117 Jonas ([1934] 1982, 57) discusses this drawing, and adds a related drawing in three-voice counterpoint. 118 Harmony, §18, Ex. 35 (40), shows diatonic triads on every diatonic tone of the major scale, including VII. The systematic representation of triads (§§95–97) shows diminished as well as augmented triads. Ex. 113 (147) presents a diminished triad that is not a true scale step ‘despite [rather than because of!] the fact that three parts have clearly converged here into a (diminished) triad’ (§79, p. 142). This idea implies that a diminished triad might, in another context, have been a true harmony. 119 This seventh chord is not prolonged. At best, it forms the structural departure point for a transitive progression. 120 Erweiterung. In §88, Schenker repeats the same point, using the term Verlängerung.

52 Literature Survey of being used in a triad or seventh chord’ (§55).121 Schenker remains silent on the necessary conditions for this possibility, but it seems that harmonizability is indebted to Rameau’s notion of piled-up thirds. The idea of harmonizability is foreign both to Schenker’s later view, which excludes all seventh chords from the true harmonic domain, and to the concept of reliance on the diatonic scale and scale steps.122 The discussion of harmonizability is anticipated by a demonstration from Beethoven, 32 variations in C minor, WoO 80, No. 9, m. 3 (Ex. 94 [107], retranscribed as Ex. 3.8). The arrows (in the original) show that some notes should be heard only horizontally, while others create vertical, harmonic relations. The true harmony in this example is a diminished seventh chord.

3.2.2 Counterpoint I (1910) CP I is devoted to Fuxian two-part counterpoint. Schenker regards strict counterpoint purely as the study of the control of intervals: ‘even a waltz or a march, to say nothing of a sonata or intermezzo, had to incorporate counterpoint precisely as a relationship of at least two voices’ (p. 5). Applying the principles of species counterpoint (particularly of dissonance treatment) to all tonal music means that even in free composition dissonances may only appear as a product of contrapuntal operations, without true harmonic origin. This principle is encapsulated in the statement ‘In the beginning was consonance’ (pp. 110; 184), which is elaborated upon in the preface (p. xxv): ‘The consonance was recognized as the first and only true prerequisite of all polyphony . . . the dissonance was discovered to be only a derivative phenomenon.’ The specific ramifications of this general principle are determined according to the traditional species, particularly as far as passing tones are concerned: ‘as a result of [the] dissonant nature [of passing dissonances], they can establish no new harmony (consonance) at all’ (213).

121 This is the view held by Dahlhaus in his criticism of Schenker’s later position. See §1.3.1. 122 The lack of reliance on the diatonic system may have applications to analyses of pre-tonal and post-Romantic music. On the problematic nature of this reliance, see Brown 1986. In the explanatory footnote that Jonas attaches to §55, he deviates clearly from the original meaning, and brings it closer to the later view, as he substitutes a requirement for consonance for that of harmonizability. Elsewhere ([1934] 1982, 56), Jonas quotes from §88 a passage that refers directly to scale steps. See also Exx. 90–91 (103–4) for resolutions into dissonances that create a hierarchical priority of dissonances. Schenker discusses these examples only briefly.

Literature Survey 53

It might be inferred from the passages cited above that by 1910 Schenker had already conceived the principles of strict counterpoint as identical, rather than analogous, to the working forces in free composition. Indeed, the very reliance on two-part counterpoint involves a shift in approach: the quality of chords (consonant or dissonant) is examined here according to their component intervals, in contrast with the harmonizability concept, which examines the intervals according to the chords of which they form a part.123 Yet CP I, just a few lines before uttering the above maxim (p. xxv), also acknowledges the rules of harmony (‘the progression of scale degrees’) as a separate power, one of ‘two basic ingredients’ that govern ‘all musical technique,’ a power that is not itself derived from contrapuntal procedures of voice leading.124 The acknowledgment of non- contrapuntal forces weakens the control of strict counterpoint over free composition. For example, on p. 117, in the commentary on Ex. 158 (from Bach’s English Suite No. 6, Gigue, mm. 9–10; quoted here as Ex. 3.9), Schenker claims that fourths (actually augmented fourths, which form part of inverted seventh chords) ‘are also supported by scale degrees, which our consciousness posits as a 125 foundation for changes of harmony.’ The explanation of seventh chords in particular that is proposed in CP I is inconsistent. A single passage (p. 283, in the section on fourth species) invokes Schenker’s later position, i.e., that the seventh is passing from a (possibly) elided octave: ‘it may be that the ultimate origin of seventh-chords is best explained with reference to the elision of a preparation or of the consonant beginning of a passing-tone motion.’126 Other passages preserve the older ideas that the seventh does have a harmonic origin. For example, the preparatory discussion of specific

123 On p. 124, Schenker is still indebted to the ‘triadic jurisdiction,’ i.e., to the earlier idea of harmonizability. Schenker here moves from chord dissonance to interval dissonance (cf. Dahlhaus 1963), or in terms of the five CDCs (Consonance-Dissonance Concepts) proposed by Tenney (1988; see discussion §1.3), from CDC 4 to CDC 3. 124 This paragraph apparently equates voice leading with the procedures of strict counterpoint, which are explained directly afterward. Only the recognition of a separate power of scale steps distinguishes this view from the more mature approach. 125 The preceding example (157, from Schumann, Piano Quintet) shows a 6/4 formation as the upper voices of a true ‘abstract scale degree,’ which happens to be V7. See Ex. 7.37b, and reference in Rothstein 1991, fn. 19. 126 Schenker uses two alternative models for approaching the seventh. See §5.1. This innovative idea is sparked off by Schenker’s observations on Ex. 473 (Brahms’s Symphony No. 4/I, 81–85), which is based on unprepared seventh chords. Jonas ([1934] 1982, 97) quotes this remark in full.

54 Literature Survey intervals says: ‘Concerning the seventh in free composition, the necessary liberty in its use there is in the first place inseparable from the necessary emergence of the seventh-chord [Vierklang] itself, in a manner of which the theory of counterpoint remains altogether ignorant’ (61). The discussion of third species, meanwhile, speaks of ‘seventh-chords, to which only free composition, but not strict counterpoint, has a right claim’ (245).127

3.2.3 The Analytical Monographs (1910–1920) Prior to the second volume of Counterpoint, Schenker published the analytical monographs J. S. Bach’s Chromatic Fantasy and Fugue ([1910/1969] 1984), Beethoven’s Ninth Symphony ([1912] 1992] and four of Die letzten fünf Sonaten von Beethoven (1913–20), on Beethoven’s Piano Sonatas Opp. 101, 109, 110, and 111. The analyses follow the chronological course of each work; opportunities to discuss prolongations of seventh chords emerge in all of the analyzed works. The view of seventh chords in the analytical monographs is more traditional than that suggested in CP I. This regression may be a consequence of the nature of these writings, which confront particular dissonances in the analyzed works, or 128 result from Schenker’s reliance on earlier drafts. The essay on Bach’s Chromatic Fantasy and Fugue ([1910/1969] 1984) tackles a highly unique work saturated with dissonances. Schenker focuses on the specific figuration of several chords in order to distinguish harmonic and non- harmonic tones in what he—by this stage—refers to as ‘composing out.’ In m. 17 of the fantasy, for example, he says, ‘The chord built on the chromatically raised IV, Gƒ–B–D–F, which is composed out, takes on the character of VII in A minor’ (p. 28). In the English edition, Hedi Siegel even quotes annotations from Schenker’s personal copy of Bach’s Prelude BWV 894, which indicate passing

127 See also the inclusion of the augmented fourth as ‘a part of the harmony of V[7],’ due to the ‘indispensability’ of the V (p. 59); the comment that in free composition, ‘all manner of triads and seventh-chords may be arpeggiated’ (250); the warning not to use several leaps that ‘establish triads or seventh-chords’ (93); and the ‘genuine seventh’ in Ex. 67, p. 280. Fn. 1.2.21 (p. 350) draws on both opposing views. The seventh ‘occurs only as the third of another triad’ (not as a passing tone), but as a consequence, it is described as dissonant, not as creating ‘harmonizability.’ With regard to the exceptional approach in Ex. 151a, see fn. 297. 128 According to Jonas (FC, p. xv, preface to the second German edition), many important ideas in the monograph on Beethoven’s ninth Symphony had already appeared in a 1901 article in Wiener Abendpost.

Literature Survey 55 motion within seventh chords (Ex. 13 on p. 32, reproduced as Ex. 3.10).129 An emblematic expression of Schenker’s great distance at this stage from his mature theories is revealed in his discussion of m. 9 of the Fugue. The entrance of the answer creates a seventh with the countersubject. Later, Schenker would have shown how this seventh arrives from a conceptual octave in the preceding measure, but here he ridicules Hans von Bülow (who modified the entrance in his edition): ‘He took fright at this seventh which—horribile dictu—enters stark and unprepared; this alone struck terror into all his limbs!’ (p. 46). Beethoven’s Ninth Symphony contains more relevant material. On several occasions, Schenker identifies seventh chords as true Stufen, e.g., I ß7 in movement 2, mm. 117–26 (p. 145, Fig. 182, reproduced as Ex. 3.11).130 One discussion is addressed specifically to the distinction between a real seventh and a seventh representing a transferred second. Even at this early stage, Schenker was disturbed by this issue, but curiously enough, his position here is opposed to the stance that he was later to adopt. In discussing movement 1, m. 143, flute part (see Ex. 3.12a), Schenker speaks in favor of a real seventh: ‘the seventh, since it is a thematic replication of the fifth . . . has thematic significance and therefore represents a real seventh, and is not, as is unfortunately assumed, to be understood as perhaps only the inversion of an originally conceived second!’ (p. 77).131 The stimulating idea of thematic significance is unfortunately abandoned in Schenker’s later theory. The goal of Schenker’s attack is revealed only a few pages later (p. 86). He rejects Wagner’s suggestion of replacing the ascending seventh with a descending

129 In the first and third quoted measures, Schenker indicates tones of diminished seventh chords as harmonic tones (‘h’); at the end of the excerpt, tones of both V7 and VIIº7 are connected by lines. The added frames are mine. The original 1910 edition quotes the prelude without additional graphic annotations. It also uses the term auskomponierten Harmonie (p. 21) and auskomponierten Durchgang (p. 22). See also m. 18 of the Fantasy, where ‘The root as well as the seventh of the dominant chord are sustained’ (p. 29), and m. 31 (my Ex. 8.6e). Composing out of other dissonant chords is acknowledged in m. 25, Ex. 11 (a diminished triad) and on p. 33 (‘the need to express the 6/4 chord’). 130 This passage begins literally in a 4/2 inversion. The retention of the seventh throughout the excerpt is questionable. Additional instances are explained only in the text: ‘rolling-out of V7’ (p. 48), and composing out of a motif within V7 (p. 91). 131 The fifth, which prepares the seventh motivically (not contrapuntally), is diminished. The discussion refers to the melodic seventh in m. 143, but the tone of the seventh is achieved before, without preparation, after a leap of a diminished fifth within V7.

56 Literature Survey second (Ex. 3.12b), as in the oboe part and Liszt’s piano reduction.132 Although the subject of the debate is the particular seventh in m. 143 and not sevenths in general, Schenker’s highly polemic tone creates the impression that he feels uncomfortable with an understanding of sevenths as transferred seconds. This stance is, of course, in direct contrast to Schenker’s later ideas. In his later works, Schenker blames the recognition of true sevenths and seventh chords (among other dissonances) for the decline of tonality, but here he points the finger at Wagner’s contrary objection against a real seventh as the disruptive modern trend. Schenker is apparently defending Beethoven from Wagner’s poisonous allegation, i.e., that Beethoven was too deaf to hear the poor effect of the flute part (quoted on p. 87). Schenker’s analyses of Beethoven’s late piano sonatas still look upon seventh chords as true harmonies, and even show them composed out, with the aid of the more sophisticated analytical concepts (and sometimes technique) that were beginning to develop. For example, in the monograph on Op. 109 (1913/1971, 46), Fig. 54 (reproduced as Ex. 3.13) shows and explains the composing out of a diminished seventh chord in Bach, WTC I, Prelude in Cƒ minor, 30–31,133 and the monograph on Op. 110 (1914/1972, 54, in Fig. 64, reproduced as Ex. 3.14) shows a seventh progression (quite on the surface, admittedly) in movement 2, mm. 45– 47, as a composing out of a seventh chord (‘im Sinne eines Dominant-Septim- Akkords auskomponiert wird’).134 The most interesting comments concern the diminished seventh chord in Op. 111/I, 5–10. Schenker concentrates on the specific complications in the sonata, and claims that in the normative situation for various seventh chords (gearteten Vierklängen), the only tonal spaces (Räume) appropriate for passing motion (Durchgänge) are third spans (Terzabshnitte), including the third between the fifth

132 Schenker (pp. 84–5) justifies Liszt’s choice on the ground that it is appropriate for its medium, and he blames Wagner for failing to understand Liszt. As Schenker points out on p. 88, Riemann also reads m. 43 as an opened-up second. 133 The Bach example is brought by way of analogy to Op. 109/III, m. 102 (m. 6 in variation 4), which composes out a V7, but in a more trivial manner. The shared feature is that the root is not present in the bass at the initiation of a new harmony. 134 This terminology is exceptional for Schenker. Pastille (1990, 74–75) cites this figure as an important stage on the road to Schenker’s discovery of the Ursatz. See also in the monograph on Op. 111 (1916/1971), 8, Fig. 8, which shows a diminished seventh chord as I7/ß3

Literature Survey 57 and the seventh. This idea assumes that seventh chords are genuine harmonies, and that the seventh is a chordal tone, a boundary tone of a tonal third-space, rather than a passing tone by itself (1916/1971, 7).135 The original edition ends with a fiercely argued attack on previous literature (omitted in the revised edition). The very last pages (93–94) ridicule Paul Bekker for not recognizing the diminished seventh chord when it appears in a composed out manner, rather than ‘third above third, three floors high’ [Terz über Terz, drei Stock hoch].136 The attached footnote attacks Schoenberg (without invoking his name; see Simms 1977, 113), and there too, diminished seventh chords are depicted as conservative phenomena that should be defended from modern trends. Schenker’s advocacy in favor of composed out seventh chords could only take place at this specific stage of his development: before this, the precise concept of composing out was not sufficiently developed; afterward, the seventh chord was no longer accepted as being among the true chords. An important lesson is found in the fact that the historical context of the debate is insufficient to explain the technical aspects of Schenker’s argument, since the technical details were later to change while the context remained essentially the same.137 The analysis of Op. 101 is somewhat exceptional, perhaps because it was published later (1920). On several occasions, where prolongation of seventh chords seems to me relevant, at least as an analytic option, Schenker avoids any discussion of the seventh.138 This avoidance perhaps reflects a new unease with the idea of seventh chords as true chords, although I am unable to verify this shift in outlook with any degree of certainty.

135 I analyze this passage in Ex. 8.33a. Schenker focuses on the exceptional segmentation of this passage, and compares it with the more normative passage in Chopin’s Nocturne Op. 27,2, mm. 7– 8 and 40–45. See Ex. 8.24c. 136 The attack on Bekker is not fully justified. Bekker (1911/1912, 189) claims that the passage creates [bildet] a leading[-tone] chord [Einleitungsakkord], an expression omitted by Schenker. Bekker’s words can even be read as a description of composing out, but they lack exactitude. The attack on Bekker is uncharacteristic of Schenker: he blames Bekker not for ignoring voice leading, but for ignoring the harmonic framework. 137 I develop this argument in Goldenberg 2004b. The monograph on Op. 111 (1916/1971, 92) also includes a detailed description of the passing motion within V7 in movement 2, mm. 111–7. 138 See Op. 101/I, m.12; /II, mm. 4–6 and 58–9; /IV, mm. 17–24 and 236–7 (the last reference is found in some editions at /III, mm. 49–56 and 268–9). All these passages are discussed, but the seventh is hardly referred to.

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3.2.4 Counterpoint II (1922) In the second volume of Counterpoint, the interpretation of seventh chords as contrapuntal non-harmonic constructs dominates for the first time. This approach is not the subject of systematic analysis, but rather, takes shape during the course of the discussion. Schenker’s new theoretical stance assumes a tighter control of the dissonance treatment that is familiar from strict counterpoint in free composition, as for example: ‘in spite of maximized possibilities of composing out, the consonant harmony . . . remains the sole measure of all that pertains to passing dissonances’ (59). More precisely, CP II introduces an additional idea in relation to free composition which, as Schenker promises, comprises ‘a technique whose great fecundity will be shown only later, in Free Composition:’ ‘dissonant concepts by means of illusory consonances’ (186). This enigmatic expression apparently refers to the transformation of dissonances into actual foreground consonances. In the final theory, such a transformation becomes a prerequisite for the prolongation of dissonances at a deeper level (see below, §3.2.5 on the Elucidations). Several passages deal with the origins of the seventh, which is explained here as a passing tone from an elided octave.139 The context of the discussion is the fourth species rather than the second. This derives from Schenker’s problematic claim that suspensions derive from passing tones.140 He says: ‘[in free composition] the seventh is sometimes a product only of a horizontal line, a true passing tone (as, for example, in the seventh-chord)’ (102).141 Schenker blames Fux’s ‘inadequate insight into the nature of the seventh-chord’ which is revealed in his attempt ‘to invoke already in strict counterpoint the concept of seventh- chords’ (158). Only combined species, as a bridge to free composition, give birth to ‘the budding seventh-chord,’ which ‘is nothing but a triad in which, by means of abbreviation, the passing tone of the seventh appears to be incorporated as a 142 chord member’ (215).

139 See above (§3.2.2) precedent of this view in CP I, 283. 140 This idea was righteously rejected by the editor Rothgeb, p. 356, fn. 2.4.3; Schachter 1988a, 526; Drabkin 1989, 199; Rothstein 1991, 299; and Agmon (1997, par. 4). The principal shortcoming of Clark 1982 is the adherence to this dubious argument. 141 This passage does acknowledge the possibility of suspensions as a separate phenomenon. 142 Clark 1982 is devoted to explaining this argument, claiming relative independence for seventh chords. On the technical aspects of this argument and its problems, see §3.3.2. Agmon (1997,

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The power of diatonic scale degrees is rarely called upon, but is still understood as a separate force, potentially competing with, and even negating, strict counterpoint. For example, Schenker presents Ex. 301 (reproduced as Ex. 3.15) as ‘composing out of a seventh-chord,’ commenting that the [unfolded] fourth f–b is ‘an augmented fourth, to be sure, but nonetheless diatonic’ (195). A more explicit discussion of the gap between the requirements of strict counterpoint and those of the diatonic system occurs at the beginning of the book (pp. 3–4). Schenker justifies VII in major or II in minor as true chords on the grounds of their emergence in the diatonic system: ‘it is merely the absence of scale degrees that prevents the diminished triad in three-part counterpoint from being included in the category of triads that are consonant or to be treated as consonant.’143 These remarks no longer represent Schenker’s view, and are perhaps remnants of previous ideas.

3.2.5 Der Tonwille (1921–1924), including the Elucidations The ten volumes of Der Tonwille (TW) consist mostly of analyses, but also feature some more general remarks, including explicit statements of the strictest opposition to the notion of prolongation of the seventh in vols. 2 and 8–9. In the same year that CP II was published (1922), a short paragraph appeared in TW 2, p. 3 (2004, 51), called ‘Laws of the art of music’ [Gesetze der Tonkunst], which was intended to be included in FC.144 This paragraph begins with a series of short statements on consonance and dissonance: ‘The life of the tone thrives in consonance and dissonance: Consonance is the sole law of everything harmonic, vertical and belongs to Nature. Dissonance belongs to voice-leading, the horizontal, and consequently is Art. Consonance lives in the triad, dissonance in

§4.19) reveals inconsistencies in this passage, resulting apparently from Schenker’s ‘tormented mind,’ which is struggling against the independence of the seventh chord. 143 See discussion §2.1.2.2.3.2. See also p. 186, directly before an innovative passage quoted above: ‘the setting of passing tones . . . takes refuge in the law of consonance, since thereby it can attain comprehensibility in an unrestricted sense which, because of the lack of scale degrees, it would not be able to attain even with freer voice-leading.’ Only in the absence of scale degrees is the law of consonance the single force. 144 The reference to FC appears as ‘Aus II3,’ i.e., from the intended third book of volume two (=CP) of New Musical Theories and Fantasies. Parts of the paragraph are incorporated into the final version of FC, §1. TW 2 includes an additional paragraph ‘Aus II3,’ which is incorporated into FC, §4.

60 Literature Survey passing. From triad and passing stem all the phenomena of tonal life: the triad can become a harmonic degree; the passing tone can be modified to become a neighbor note, accented passing tone, anticipation, as dissonant syncopation, and the seventh of a seventh chord [Vierklang, i.e., four-tone chord]. There are no laws other than consonance and dissonance, nor are there any other fundamental 145 derivations.’ This paragraph combines mainly earlier ideas that appeared previously in a scattered form. Its real innovation is considering the power of consonance as the one and only working force in music. This is stated not only as a generalization, but also through the specific derivation of scale steps and seventh chords from the 146 basic contrapuntal distinction between consonance and dissonance. Whereas Harmony considers the consonance-dissonance distinction of strict counterpoint only as analogous to the power of scale degrees in free composition, and CP I and II speak of strict counterpoint and scale degrees as two separate forces that work in tonal music, here the scale degrees themselves derive from contrapuntal procedures. Since the control of strict counterpoint over free composition is now complete, no other power can endow dissonances in free composition with the harmonic independence they lack in strict counterpoint. What remains absent from this passage is a more precise technical explanation, and, in particular, a reference to prolongation. These are provided in the Elucidations (Erläuterungen), an unusually succinct article, which formalizes the developed theoretical basis of prolongation, published for the first time in TW 8–9 (1924).147 The article presents the earliest explicit argument that dissonances cannot be prolonged: ‘dissonance is transformed into consonance because only consonance, with its tonal spaces . . . unlike dissonance, can promote new

145 The term Durchgang (passing tone) serves here in the more general sense of a ‘passing event.’ The term Wechselnote (‘changing note’) apparently means here an accented passing tone; it has also the more specific meaning of a nota cambiata (Drabkin 2000). 146 The term seventh chord (Vierklang) still implies a vertical concept, but the beginning of the passage negates this. CP I, xxv (quoted above) had already claimed that consonance is the single source of hierarchy, but the assertion there is inconsistent even with the rest of the same passage. 147 This article was published four times: in TW 8–9, 49–51 (2005, 117–8, trans. Ian Bent), TW 10, 40–42, MW I, 112–4, and MW II, 118–20.

Literature Survey 61 passing-note progressions and freshly burgeoning melodies’ (p. 49; trans. from 148 MW I, 112). The discovery that harmonic degrees themselves are a product of counterpoint seems to have had an enormous impact on Schenker. He apparently believed that he had found an exclusive key that would unlock the secrets of tonality. Yet this notion of exclusivity is misleading. The existence of dissonant scale degrees, even as triads, or the dissonances that conform to the requirement of ‘harmonizability’ cannot be adequately explained without reference to additional factors. The analyses in TW occasionally include prolongations of seventh chords, some of which are even commented upon in the text.149 While the prevalent view in TW is rather strict, such analyses are more tolerant toward PDs, perhaps because Schenker has to confront challenging situations in some pieces. The appearance of the uncompromising view, however, means that all instances of PD (including prolongation of the seventh) can no longer be regarded as normative.

3.2.6 The Masterwork in Music (1925, 1926, 1930) The Masterwork in Music (MW) deepens the rejection of PD. The reprinting of Elucidations in vols. 1 and 2 is representative of this trend, as is the passionate formulation in MW II (1926): ‘A point of musical ethics: dissonance is sterile because it does not lend itself to composing out. It exists purely to serve consonance, which alone is fertile’ (Miscellanea, p. 125). MW II also includes the most extensive and uncompromising discussion of dissonance, in the penultimate section (pp. 9–18) of the opening article.150 Seventh progressions (and ninth progressions) are explained here for the first time as ‘representing a step of the second’ (p. 10). Besides, the section restates the requirement of transformation into consonance as a prerequisite to prolongation:

148 The derivation of scale steps from strict counterpoint is incorporated into the new, more sophisticated argument: ‘As the outcome of all these transformations and unfoldings, there emerge the harmonic scale steps’ (ibid.). 149 See for example: ‘Die Kunst zu hören,’ (TW 3, 22–3 [2004, 118–9]) on Bach, WTC I, Prelude in Fƒ major, 1–4 (see below, §9.3.2, discussion of Ex. 9.20a); Bach, Prelude BWV 926 (12 Short Preludes No. 3) (TW 5, 3 [2004, 145] discussed here, fn. 369); Beethoven, Symphony No. 5/II, 123–46 (TW 5, 37 [2004, 205]; cf. fn. 422); Beethoven, Piano Sonata Op. 57/I, bridge (mm. 23– 33) (TW 7, 7 [2005, 43], analyzed below, Ex. 7.62d, and discussed §§7.3.2.1 and 7.10.1.2.2). 150 ‘Further Consideration of the Urlinie: II,’ pp. 1–22.

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‘The consonance that comes in this way to substitute for a dissonance is then further employed by free composition to sprout additional linear progressions.’151 This section focuses not on prolongation, but on the older and more general rejection of the ability of dissonances to constitute true harmonies, as suggested by the title of the section, ‘The dissonant interval is always a passing event, never a composite sound’ (p. 9). The discussion is, however, replete with innovative technical concepts, and could not have taken place in the earlier writings: ‘The meaning of the passing152 dissonance consists solely in its function of forming a melodic bridge from one consonance to the next, and of creating the tension of the third-progression, of whose duration (through the dissonance and beyond) the primary note is retained’ (ibid.); ‘The only notes that join together to count as a composite sound are, in the vertical dimension, the two consonances at the beginning and end of the third-progression’ (p. 10).153 Particularly relevant are the final pages of the section, which includes attacks against Schoenberg (as a theorist) and Stravinsky. The polemics against Schoenberg concentrate on his highlighting of the harsh sonorities that occur through embellishing motion (Schoenberg [1911] 1978, 322–4, Exx. 231–3). It is clear that Schoenberg’s motivation is ideological: he seeks precedents for his innovative ‘emancipation of dissonance’ in order to connect himself with the classical tradition (see, however, Baker 1993b, 253). The dissonances that attracted Schoenberg’s attention can barely be perceived, and Schenker demonstrates their passing character as proof that dissonances are never true harmonies. However, in the two examples from the literature, the governing chords, which these harsh dissonances serve to prolong, are seventh chords, dissonant by themselves. For example, in the first excerpt in Fig. 22

151 P. 10. The organic metaphor ‘sprouts’ stems from the translation. The original reads Spaltung. 152 The word ‘passing’ was added in the translation in order to avoid the obvious error that other types of dissonance do not exist. As explained below, the original wording is not accidental. 153 The section focuses on passing tones, with special emphasis on the simplest case, within third progressions. Little attention is paid to neighbors and appoggiaturas (but they are nonetheless noted, p. 12) and none to syncopations. It is unlikely that Schenker wanted to confine his restriction to a single type of contrapuntal procedure. Rather, the focus on passing tones reflects Schenker’s desire to derive all foreign notes from a single contrapuntal technique (compare discussion of TW 2 above), an ambition befitting the monistic trend of his theory. The text also speaks of composing out, a term which relates more precisely to outlined tonal spans, and these are strictly speaking, expressed only in linear progressions (and arpeggiations) (cf. above, §1.1.2.2).

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(Schoenberg’s Ex. 232, reproduced as Ex. 3.16, from Bach’s motet Komm, Jesu, komm) the dissonances are passing within a dominant seventh chord.154 This undermines Schenker’s argument. The contradiction cannot be reconciled by special licenses for the seventh chord, since Schenker in this article insists on precisely the opposite: ‘. . . it contradicts the nature of the dissonant passing note [which every dissonance is claimed to be] to discriminate in any substantial way among the intervals of a fourth, a seventh and a ninth, to say nothing of positing an increasing scale of dissonance for these intervals’ (p. 9); nor does the local level of the prolongation eliminate the contradiction, since Schenker also says that [in dissonances] ‘the vertical dimension is altogether excluded’ (p. 9). Schenker’s assertions here are unequivocal, and should be taken at face value as the true representation of his ideas; they aim at what might be called a 155 ‘disemancipation of dissonance,’ antithetical to the position of Schoenberg. If, in spite of Schenker’s view to the contrary, we distinguish between degrees of dissonance, it becomes apparent that the examples being debated show motion within relatively mild chords as the context for very sharp dissonances. This seems to me to be a likely context for the emergence of such sharp dissonances,156 and can explain the presence of PDs precisely in those examples that are used to prove that dissonances are always passing.

154 Katz (1945, 62) makes a similar attack on the same Bach example by Schoenberg, but admits the governing chord is by itself ‘a chord of motion.’ Fig. 21 (Schoenberg’s Ex. 231) is abstract and Fig. 23 (Schoenberg’s Ex. 233)—from Mozart’s Symphony No. 40/I, 150–2—is a four-voice appoggiatura to a dominant seventh chord (cf. Ex. 7.74b). For a survey of the historical context of this analysis by Schoenberg, see Bernstein 1993, esp. 106–10. In Fig. 29 Schenker presents an additional example of passing harsh dissonances, from Bach, WTC I, Fugue in Bß major, 55–63, and there too, a seventh chord (here a diminished one) is locally prolonged through passing motion, as is indicated in Schenker’s reduction of m. 57. 155 For an illuminating comparison between Schoenberg and Schenker, see Dahlhaus 1973–4. The passage from MW II is the climax of a lengthier debate between Schenker and Schoenberg. Schoenberg’s view is, by itself, a reaction to Schenker’s claim in Harmony that only the first five overtones should be taken into account (Schoenberg [1911] 1978, 318. See survey in Montgomery 1994, 60). Schenker took a strong stand against Schoenberg in his monograph on Beethoven’s Op. 111 (see above), and continued to refute Schoenberg in FC (§9, regarding the conception of dissonances as remote overtones). For Schenkerian ingredients in Schoenberg’s own theory, see Boss 1994. 156 Extreme dissonant texture can also occur within a consonant structure, as a product of displacement. See §2.3.3.2.

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But this is only the tip of the iceberg: paradoxically, prolonged seventh chords and vertical dissonances are ubiquitous in this article, in Schenker’s own readings. The vertical dimension is even applied to a dissonance graphically in Fig. 17 (reproduced as Ex. 3.17), from Beethoven, Piano Sonata Op. 10,2/I, through the bracket that links an augmented fourth at m. 111.157 Also of particular interest are the V7 prolongations in the two final examples of the article. Fig. 31, a negative analysis of a Stravinsky passage, tries to force the music into a consonant frame, in order to show the dullness of the possible prolongations. The prolonged V7 appears not as a deplorable Stravinskian dissonance, but as a component of the harmonic progression, whose lost traces Schenker searches for. The inclusion of the seventh in the symbol of the harmonic degree provides it with the vertical dimension that Schenker wanted to disallow (Ex. 3.18).158 Even more astonishing is to find a wide PD in Chopin’s Nocturne Op. 15,2, which is chosen to demonstrate the marvels of tonality, based on the organic composing out of the tonic triad (concluding section of the article, pp. 18–22). The whole B section consists of a neighboring embellishment of V7. The motion is minimal, but the prolongation is bold, due to the extremely slow harmonic 159 rhythm. In addition, the earlier sections of the article include an exceptionally high number of PDs. This is not a coincidence: I believe it is a by-product of another trend, which is not of itself related to problems of dissonance. Figs. 2, 11, 12 and 13 share a hidden affinity. They all present very static passages, based on an alternation of I and V degrees. Schenker apparently chooses these excerpts in order to prove that multi-layered tonal hierarchy exists even where it seems to be absent. His readings for all these passages are intentionally dynamic. The most

157 Schenker shifts the b back (to m. 107); this odd procedure apparently means that he regards mm. 107–11 as an unfolding within a diminished seventh chord. 158 The passage is taken from Stravinsky’s Concerto for Piano and Winds/I, rehearsal number 11. This analysis was appreciated by Babbitt (1964, 36) as problematic but highly insightful, and provoked the major study of Morgan 1976. Benjamin 1977 and Morgan 1978 discuss passages in this movement in its own dissonant terms. 159 Look ahead to Ex. 7.71a. Schenker’s middleground, in Fig. 32, shows mm. 17–24 as a composing out of the space V5–7, through passing motion. If 4 is a structural neighbor, as is indicated in the graph, it might be normalized to m. 17, according to ‘the rule of the primary tone’ (Rothstein 1981, 96). Reading the passage as an interruption is less appealing here, because the 4 is so strong (cf. Ex. 4.15). Concerning the slow harmonic rhythm, see fn. 8.

Literature Survey 65 extreme case concerns the Berceuse by Chopin, whose opening measures are analyzed in Fig. 2 (reproduced as Ex. 3.19). The Berceuse is perhaps the most harmonically static work in the entire tonal literature. Sounding like a cradle song, the work features a monotonous motion to and fro, between downbeat I£¦ and upbeat V7. This is the sole content of the whole piece until the coda. A straightforward reading might hear all the downbeats as true tonics, but Schenker reads a third progression in mm. 5–6 (gß2–f2–eß2). The primary tone of this progression is the dissonant 4 (top voice of V7), which is retained throughout the progression, and in this case, even preserved in an inner voice.160 The text is silent as to the dissonant aspect, although it is the same tone (4) that serves as the 161 structural neighbor tone, the subject that this figure serves to illustrate. Two opposite trends, then, contribute to this ubiquity of PDs in the very article that prohibits them altogether: one concentrates on tense passages, where the extreme dissonances that Schoenberg pointed out occur in passing; the other focuses on passages with very little tension, reading them intentionally in a dynamic manner that also gives rise to PD. In MW III (1930), Schenker’s rejection of PDs is complete; although he notices a huge true seventh progression throughout the development of Beethoven’s Eroica, he regards it as a rare deviation from the normative rules that conform to strict counterpoint (pp. 23–24).162 The opening article of MW III, ‘Rameau or Beethoven? Creeping Paralysis or Spiritual Potency in Music?,’ is largely devoted to a strongly argued case against PD. Paradoxically, Schenker blames Rameau for the faults of modern music, since

160 The foreground (levels d and e) also includes a dotted slur, which contradicts this third progression, but the text and the more structural levels point toward the dissonant interpretation. The dissonance is not shown at level (a) because the bass under the neighbor tone is omitted. 161 The reading of the Berceuse in Korsyn (1991, 24) endorses Schenker’s upper voice, but argues for a true tonic on every strong beat. This is contradictory. The other dynamic readings of passages with static potential involve I6/4s, which are interpreted either as a prolonged suspension to V (Fig. 11 [Schubert, Waltz, D. 365 (Op. 9),4]) or as prolongation of V7 with the seventh nevertheless passing (Fig. 12 [Schubert, Waltz, D. 365 (Op. 9),1, end] and Fig. 13 [Chopin, Waltz, Op. 34,1, second section]). McKee (1996, 69) creates a paraphrase in his Fig. 12, in which he more clearly reads a V7 prolongation (as he states, p. 68). I suspect that the ‘I6/4s’ here are true weakened tonics, analogous to I6. V7 is also prolonged in Fig. 8 (Chopin, Nocturne, Op. 9,2), mm. 3–4 (cf. below, Ex. 7.68e). 162 Cf Ex. 7.105. A similar remark in Schenker’s drafts on Beethoven’s Piano Sonata Op. 81a/I might be slightly earlier than the published note on the symphony (§5.4).

66 Literature Survey in his theory ‘the seed of death had already been sown’ (p. 2).163 The technical meaning of this strange claim is that ‘the seventh . . . and the ninth . . . were made out to be chord components, from which it was only a short step to bona fide seventh and ninth chords. Once on this slippery slope, nothing could stop the recognition being also given to eleventh and thirteenth chords; and so, today . . . on pretext of the higher partials of the overtone system, any and every piling-up of notes is indiscriminately taken for a chord’ (p. 5). The reference to ‘[t]he higher partials of the overtone system’ is incompatible with the complaint about ever- growing structures of piled-up thirds. Rather, it is a response to Schoenberg (cf. §2.4). It is perhaps ironic that through this attack, Schenker accepts Schoenberg’s argument that the recognition of the seventh as a chord component may apply by inference to all dissonances.

3.2.7 Free Composition (1935, posth.) Free Composition (FC), Schenker’s magnus opus, usually adheres to the restrictions that prohibit PD. The entire organization of the book from background to foreground conforms to the concept encountered in the Elucidations, as restated in Chapter 1 (the background), when it begins with the overtone series of the single tone. In FC, a true harmony is always a triad—‘The sacred triangle’ (§19)—and never a seventh chord: ‘it is the fifth that forms the boundary of any given chord in the foreground, and never the seventh’ (§176). A direct prohibition of PD appears in §169, ‘Impossibility of composing-out a dissonant passing tone’: ‘The dissonant passing tone, including the passing seventh, is itself a means of composing-out. Therefore, as long as [the dissonant passing tone] retains its dissonant quality it cannot at the same time give rise to a further composing- out.’164 Then appears the familiar idea that ‘[t]he transformation of a dissonant passing tone into a consonance’ (§170) does not alter the essence of the deeper level: ‘Those passing tones which the earlier level shows as dissonances remain

163 Schenker was previously more tolerant toward Rameau (Krebs 1988, summarized by Schenker’s translator, Bent, in fn. 1 for ‘Rameau or Beethoven’). The changing attitude, however, is unconnected to the theoretical issues themselves. Schenker does not refer to Rameau as a composer at all. 164 Of course, consonant passing tones are also ‘means for composing-out,’ but they do not require transformation in order to be composed out.

Literature Survey 67 passing tones, even though the foreground shows them as consonances’ (§251, p. 96). ‘Transformations of the seventh in free composition’ (§177) should be normatively considered to be a special case of this procedure: ‘Since it is a dissonant passing tone, the seventh cannot itself be composed out,’ but the examples that follow (Fig. 62) show ‘other means of transforming the seventh,’ i.e., deviations from the rule, some of which even occupy whole development sections. Linear seventh progressions, however, are usually only illusory linear progressions, which represent a second, and thus ‘only an indirect ascending or descending register transfer’ (§206; see Fig. 82,1–4). §215 admits the existence of exceptional true seventh progressions (see detailed discussion below, §5.4). Two sections in the later parts of FC present a far more liberal attitude toward PD. Arpeggiations in the foreground result ‘in a triad or a four-note chord’ (§230; also in commentaries on Figs. 100,2 and 100,4), and in development sections of sonata form ‘V7 may be composed out’ (§314, cf. below, §7.10.1.2.4). The actual examples for these texts do not always show form-generating PDs, and sometimes they are merely foreground lead-ins (Figs. 100,5; 154,7).165 It is puzzling to come across such passages in Schenker’s writings that have the effect of deepening the role of dissonance, sometimes beyond the demands of the music itself. Much more understandable is the converse situation, which is also very common: clear PDs in the musical figures about which the text remains silent as to their violation of the normative rule. This happens chiefly in analyses (for example Figs. 106,3a; 143,2), but sometimes even in connection to schematic models (as in Fig. 43,d,e,f). A consideration of these examples lies at the heart of

165 The section on form accepts form-generating composing out of the seventh even when the seventh only appears at the end of the prolongation, when it is ‘transferred upward’ in a development section (ibid.), or when ‘The process of “securing” a seventh whose purpose is to cancel the leading tone to the dominant can give rise to three-part form’ (§310,(b)3). See discussion at §6.2. The more liberal approach can also be traced in FC, §276, introduction to the section ‘the scale degree’: ‘there is . . . no third kind of counterpoint,’ thus implicitly accepting two kinds rather than one (i.e., the old recognition in the separate force of scale degrees). These ideas look like remnants of Schenker’s older approach. Their preservation in FC might result from the book’s publishing history: according to the editor’s preface to the first edition, Schenker has proofread the book before his death until p. 135 (§234) and Fig. 104 and has seen the examples until Fig. 122,1. The more liberal passages speak of composing out rather than prolongation (cf. §1.1.2.2), but the difference, in this case, is not terminological.

68 Literature Survey the present study. They are examined separately, according to the specific types of dissonances and contrapuntal situations they involve. FC also accepts PDs in relation to dissonances other than the seventh: ‘composing out a diminished fifth’ (§250, on Fig. 115,c) and ‘The Composing-out of Suspensions’ (§181. Among the related figures, see Fig. 64,3). FC includes deviations from the normative attitude, which point to an even greater rejection of dissonances. Some of the more extreme statements try to avoid dissonances even when they are passing and not prolonged (text for Fig. 104,2) or ‘the ill-sounding total interval of the seventh’ as a melodic interval at the boundaries of motion in one direction, implicitly denying the seventh even as a representation of a second (text for Fig. 116, mm. 9–10). Despite the many inconsistencies, it is important to remember that there is a dominant attitude toward PD in FC, namely the strict denial of PD already familiar from the Elucidations. Any prolongation of seventh chords thus lies outside Schenker’s mature normative restrictions. See further references in the appendix.

3.3 Approaches of Schenker’s Followers

3.3.1 The Spectrum of Opinions I have found a wide variety of approaches to PD among Schenker’s followers. Three ‘active’ positions can be discerned: (a) Adherence to Schenker’s strict prohibition on PD; (b) Deliberate abandonment of this prohibition; (c) Denial of the conflict between PD and Schenker’s normative theory. A fourth, ‘passive,’ approach ignores or underemphasizes the normative prohibition in full-length representations of Schenker’s theory. 3.3.1.1 Group A: Adhering to the strict prohibition. Schenker’s normative approach to PD is shared by his early followers Ernst Oster and Oswald Jonas, but is relatively rare today. Oster’s view is expressed in his attack on Roy Travis (1960, 96; see below §3.4) and in an important footnote in FC (p. 64; cf. below, §5.4). Jonas says rather more on the subject in the context of his detailed theoretical introduction to Schenker (Jonas [1934] 1982). This book is close to Schenker both conceptually and chronologically. It paraphrases Schenker’s restrictions (pp. 60; 78–79 on seventh progressions; 120–2), and even supplies unequivocal comments that emphasize precisely those aspects of the restrictions

Literature Survey 69 that are most difficult to accept: ‘we do, for convenience [i.e., inaccurately], speak of ‘seventh-chord’ . . . no dissonance (including the seventh) is ever a ‘chordal’ tone—that is, a tone generated by some ‘chordal’ (and therefore vertical) principle’ (p. 20, fn. 19). Jonas’s insistence on this idea proves it was no accidental statement on the part of Schenker. Jonas is usually highly consistent, and also very conscious of those occasions when he cites deviations (The Eroica, after Schenker [p. 143]; Brahms’s Intermezzo Op. 76,4 [p. 102]).166 Among contemporary scholars, notable adherents to the prohibition on PD are John Rothgeb167 and Edward Laufer. Laufer states categorically ‘ . . . nor could a dissonance be prolonged’ (1981, 164) and ‘a dissonance cannot itself be composed out’ (1996, 212). Laufer does not share Schenker’s anti-modernist taste, and his papers on post-tonal music (1986; 1991a) appear to permit PD. He apparently assumes that tonal and post-tonal practices are highly distinct. This separation of tonal from post-tonal music is explicitly endorsed by Straus (1987). For Straus, a true application of the concept of prolongation to post-tonal music is impossible because such music does not fulfill four conditions, one of which is ‘The consonance-dissonance condition: a consistent, pitch-defined basis for determining relative structural weight,’ while ‘Other criteria . . . are necessarily secondary’ (p. 2).168 This is another way of expressing the idea that dissonance is never prolonged in any sense (because it cannot gain structural priority over another event). Straus believed this condition to work perfectly in tonal music, although later he was persuaded of the existence of exceptions (Straus 1997; P. Smith [2000, 5] adopts Straus’s later position). This purist approach is tempting but misleading, and could not accommodate even the simplest appoggiatura to a dissonance.

166 For exceptions in Jonas’s book, that have no parallel in Schenker, see pp. 93–94 and 97 and 100, Exx. 151 and 155 (discussed in §4.2.1). On p. 90, Jonas admits the possibility of a dissonant neighbor harmony, but apparently not of its prolongation. Another relevant statement appears on p. 57, concerning Schenker’s drawing shown here as Ex. 3.6. 167 Rothgeb (1999a) quotes Schenker’s motto ‘The dissonance is always a transient element, never a chord member’ [from MW II, 9] and comments ‘That, of course, is the most basic one of all;’ See however his comment, which can be interpreted to the contrary, quoted below fn. 170. 168 Straus’s other conditions relate to scale degrees, a precise definition of the type of embellishment and a clear distinction between harmony and voice leading. Although he recognizes ‘contextual consonances’ (p. 3), he does not provide a definition as to how to distinguish them.

70 Literature Survey

3.3.1.2 Group B: Abandoning the strict prohibition. An early proponent of the prolonged seventh is William J. Mitchell (1939/1965, 183–5), who explains: ‘When tones of figuration are interpolated between a chord of the seventh and its succeeding chord, the seventh does not resolve immediately but awaits the appearance of its real successor’ (p. 183). A later scholar conspicuous for his consistent acceptance of prolongation of seventh chords is William Rothstein. In his dissertation (1981), he concludes from his rules of normalization that ‘a seventh chord may be composed out’ (104), and calls Schenker’s resistance to this possibility ‘prejudice’ (115). Rothstein also insists on this idea in later works.169 Conscious examples of PDs appear in some textbooks, even in Counterpoint in Composition (Salzer and Schachter 1969), despite its orientation toward strict counterpoint.170 Further examples can be found in harmony textbooks by Forte (1962/1979, Ex. 518), and especially by Aldwell and Schachter (1978/2003). Both books explain the melodic origin of seventh chords, but nevertheless refer to them as chords. The latter work shows various foreground prolongations of seventh chords: ‘VIIo7 extended through voice exchange’ (1989 edition, 374), ‘extended 7ths’ (413–4), ‘The Neapolitan ¢− as an embellishment of the German #’ (535) and ‘Embellishing V and V7’ (556).171 A recent Schenkerian representation of a prolongation (or at least quasi- stretching) of a seventh chord appeared in a textbook by Cadwallader and Gagné (1998), which initiates the beginner in the notion of the ‘unfolding of a dissonant span’ (p. 86). The accompanying example illustrates a prototypical true seventh progression, as the explanation in the diminution level of Beethoven’s Bagatelle Op. 119,1, mm. 25–29. My Ex. 3.20 brings the authors’ interpretation and

169 See Rothstein 1981, 131 and 132 fn.; 1989, 284 (After Morgan 1976); 1990, 98–99 and fn. 18; 1991, 296. 170 See in Salzer and Schachter 1969, Exx. 7-24, 7-37 (and text), 8-69 and text on p. 185 about dissonances prolonged by consonances. See also my discussion of the diminished 6/3 chord, §2.1.2.2.3.2. Like this book, Rothgeb’s 1975 article is also broadly concerned with the manifestations of strict counterpoint in free composition, but nevertheless admits ‘contextual features typical of free composition which are capable of overriding and even negating the normal harmonic significance of any given vertical interval’ (p. 263). 171 Other PDs in Aldwell and Schachter include ‘elaborated 6/4 chords’ (p. 314) and ‘interpolations between the 6/4 and its resolution’ (318). Cf. also their examples Nos. 8-15, 10-8, 12-11, 12-13(b–c), 19-10, 19-22, 27-6(b), 27-19, 29-16, 31-6, 31-25, and in particular, 31-30 and 31-31. Forte and Gilbert (1982, 244) outline the problem of a true seventh progression.

Literature Survey 71 suggests an alternative reading of this small diminution, which I believe to be more convincing, although perhaps less appropriate for the authors’ didactic purpose. 3.3.1.3 Group C: Denying the conflict. The contradiction between the most dogmatic phase of Schenker’s rejection of PD and some obvious cases of PD in the literature is so striking that some scholars try to interpret Schenker’s position in such a way as to eliminate the conflict altogether. Carl Schachter ([1981] 1999a, 201–2) leans in this direction when he calls Schenker’s position ‘tenable,’ but argues that Schenker ‘was not trying to say that seventh chords cannot persist for a long time or that prolonging techniques . . . cannot occur within, say, V7.’ Schachter clearly considers such configurations possible and assumes that Schenker intended his rejection of PD to be interpreted in a narrower sense. Schachter limits the problem to the specific type of true seventh progressions, with the tone of the seventh ‘conceptually retained . . . since the notion of the retained tone presupposes a vertical relationship contrary to the passing function of the seventh.’ The same contradiction also occurs, however, in other types of prolongation of the seventh (shorter linear progressions, neighbors). I see no reason to believe that Schenker accepted those other prolonging techniques.172 Schachter’s comments demonstrate an acute sensitivity to musical problems, despite the fact that we may diverge in our interpretation of Schenker’s intentions. He concludes with a challenge, which this book attempts to answer, at least in part: ‘I am not sure that the last chapter has been written about the prolonged seventh.’ William Clark (1982; discussed below at §3.3.2) puts forward a more problematic argument. He suggests that the apparent contradictions in FC are simply misunderstandings that result from a lack of acquaintance with CP I and II (p. 224). For example, in WTC I, Prelude in C major, 24–31 (a famous case of prolongation of V7, which appears in FGA and in FC, Fig. 62,5, see below Ex. 7.64) ‘everything about the treatment of dissonance . . . is easily understandable,

172 Schachter also distinguishes between ‘simple foreground figurations of seventh chords’ and ‘genuine prolongations that open up new structural levels’ (ibid.), a view which he attributes to Schenker. A surface linear progression may, however, open a new level even at the very foreground, so that such a strict distinction is problematic. Larson (1997, 126–7) makes a similar point.

72 Literature Survey provided that one understands the nature of the seventh-chord suspensions; certainly there is no need here to wonder at the seventh chord serving as a “polar harmony,” nor is there any question of a consonance “resolving” to a dissonance’ (248). Matthew G. Brown (1989) is even more extreme, e.g.: ‘any dissonance may be transformed [into new harmonies], provided that the transformation does not lead to new structural levels’ (218–9). This idea is confusing, since every transformation creates new levels.173 The trend toward reconciling statements in Schenker’s writings, which are either inconsistent with one another or which do not correspond to our own perceptions, sometimes creates the impression that a battle is being fought to defend the ‘holy scriptures’ of music theory. However, An awareness of the inconsistencies in Schenker’s work seems crucial for progress in the theory; Rothstein (1990b, 296) even regards some inconsistencies as ‘fortunate.’ 3.3.1.4 Group D: Ignoring the normative view. Schenker’s rejection of PD is so central to his theory, that it is strange when representations of his theory make only marginal references to that rejection. The early books by Adele Katz (1945) and Felix Salzer (1952/1962) include numerous seventh chords as middleground harmonies without special comment, as if they presented no problem (see also §3.4). The normative restrictions are apparently abandoned in these books, yet they are implicit in the reliance on strict counterpoint, which Salzer reviews at the outset of his book. Both Katz and Salzer regard the harmonic concept as a separate power (not as a derivative of strict counterpoint), in accordance with Schenker’s CP I, although not with his late writings. This may also have served to weaken their resistance to PD. Katz’s discussion of prolongation in common-practice tonality does not exclude dissonances at all: ‘Any chord, irrespective of its origin or function, can be prolonged by horizontalization’ (p. 16). Exx. 51 and 57–57a are bold examples of PD, and are described as such in the text. Only when Katz arrives at Wagner in

173 Brown cites FC Figs. 43,d–e and 62,5 as cases that ‘do not, strictly speaking, generate new, independent, harmonic states.’ They do generate a new level, despite the lack of full harmonies in 43,d–e and the stationary bass in 62,5. See also p. 216 and a confusing misprint (p. 218): V7–8 for V8–7. Brown’s comments on the Eroica are nevertheless illuminating, see §7.10.1.2.4.

Literature Survey 73 her historical survey does she emphasize the distinction between consonance and dissonance in tonal music (318, 390, 393–7). She describes a case of PD in Wagner as innovative: ‘dissonances define the space-outlining motion, with a consonance as a passing tone, a reversal of the usual procedure’ (242) while common-practice tonality (as opposed to Stravinsky’s tonality) is said to be ‘a concept of tonality that acknowledges distinctions between consonance and dissonance and between structure and prolongation’ (334).174 Salzer explicitly permits structural dissonances (25) and prefers V7 to the consonant V because it provides ‘better voice leading’ (88). As a pioneer in the application of Schenker’s theory to modern music, he permits in Exx. 415–7 ‘the contrapuntal prolongation of dissonant chords’ (193) or a case where ‘the triad, as an architectonic factor of structure as well as of prolongation, is replaced by seventh chords and altered chords’ (194 on Ex. 415; cf. p. 228 on polychords). The PDs in modern music are, however, ‘revolutionary achievements of contemporary music’ (193), implicitly absent in earlier tonal music. Salzer never comments on the discrepancy between the contrapuntal force and the structural dissonances that he observes. Fred Lerdahl and Ray Jackendoff (1983) assign a very minor role to the consonance-dissonance distinction. They deprive the distinction of its function as a primary determinant of structural value, in favor of multiple preference rules for structural choices. Although they take ‘as given’ ‘the traditional classifications of consonance and dissonance’ (117), they combine them with other stability factors: inversions and harmonic function. The preference for consonances over dissonances as structural events is not even formulated as a separate rule, but rather included in Time-Span Reduction Preference Rule 2: ‘Of the possible choices for head of time-span T, prefer a choice that is: (a) relatively intrinsically consonant; (b) relatively closely related to the local tonic.’ This compromise is based on Ex. 7.17 (my Ex. 3.21), from Bach’s chorale O Haupt voll Blut und Wunden, where a local V# is hierarchically superior to the IV6 that precedes it.

174 The Wagner excerpt is Tristan und Isolde, Prelude to Act 3, mm. 30–31 (Katz’s Ex. 76); in fact, no actual consonance passes there. Katz also presents PD as deviation from common practice on p. 306, and finds PDs in twentieth century compositions in her Exx. 92, 93, 104 (implied), 118 and 120. See also §3.4.

74 Literature Survey

This surface example is indeed convincing (although not a full prolongation),175 but constitutes too narrow a basis to weaken the power of consonance priority to such an extent, and to introduce the concept of ‘relative dissonance,’ which is so foreign to Schenker. One specific type of dissonance is referred to in Metrical Preference Rule No. 8 (indicated as an idiom-specific rule): ‘strongly prefer a metrical structure in which a suspension is on a stronger beat than its resolution.’176 Lerdahl (1989 and 1999) developed the multi-parametric approach to meet the requirements of post-tonal music in a way that directly opposes Straus (1987, 2), who argued for the preservation of consonance priority, not as a mere preference rule, but as an obligatory norm.177 Some degree of acceptance of PD is, in one way or another, common to groups B, C and D. My approach to prolongation of seventh chords sits uneasily with Schenker’s explicit statements, but is consistent with many of his followers, as well as with many analyses and some texts by Schenker himself. My purpose is not merely to prove that the prolongation of seventh chords is possible despite their dissonant character, but rather to investigate the entire spectrum of techniques that enable the realization of such prolongations.

3.3.2 Specific Studies on PD in Tonal Music Although the issue of PD has been raised in various studies, it has received little direct investigation. PD is normally discussed in the context of twentieth century music (see §3.4), but only rarely in relation to traditional tonal music.

175 The analyzed version is actually No. 44 in St. Matthew Passion, whose text is Befiehl du deine Wege. Lerdahl and Jackendoff also show the same reduction in their Ex. 5.4. Pearsall (1996, 46– 49) shares the same reading. Hill (1996, 530, Ex. 2) reads the V6/5 as merely passing; this is untenable in the tonic context, but the V6/5 may be deprived of structural priority if the following I is considered illusory, as in Peel and Slawson 1984, 278 (although Lerdahl and Jackendoff [1985, 152–3] refute this reading in detail). An experiment by N. Wagner (1990, 158–60) shows listeners’ preference for a non-tonic interpretation in this passage. The principal situation in this case is based on an apparent passing tone (cf. §2.1.2.2.3.3). Lerdahl and Jackendoff (1983) also invoke the priority of consonance over dissonance in this passage on pp. 93 and 109. 176 The accompanying illustration, Ex. 4.38, shows fragments of a fourth species, upper 7–6 and lower 2–3 suspension series, but this is outside the context of strict counterpoint as a whole. 177 In Plum (1988), who similarly attempts to identify various parameters to determine structural priority, the consonance-dissonance distinction is absent altogether. Also among the passive group is Federhofer 1981. However, that book concludes with conventional remarks, and the final impression is one of adherence to the normative approach.

Literature Survey 75

The milestone study on PD is Morgan 1976, which has remained influential for years (see Russ 1993, 267–8; Satyendra 1997, 184). Morgan looks for precedents for twentieth century practice, and argues (pp. 57–58) for a historical development of ‘dissonant prolongations’ (cf. introduction to §1). As the nineteenth century progresses, dissonant prolongations penetrate into ever deeper levels and govern longer spans of time, until they become the norm in Stravinsky’s work. Morgan reacts directly to Schenker’s criticisms of Stravinsky in MW II, 17 (see above §3.2.6). He cites PDs in tonal works by Bach, Schubert, Schumann, Wagner, Liszt and Skryabin. He is only interested in PDs that occupy ‘thematic statements, i.e., passages traditionally associated with formal, tonal stability’ (p. 56), especially when they ‘control complete formal sections’ (p. 58, concerning the Schubert example). His most remarkable examples consist entirely of prolonged dissonances: Liszt’s Bagatelle ohne Tonart and Skryabin’s Enigme, Op. 52,2 (for the latter, cf. my comments on Ex. 10.23).178 Morgan takes for granted the occurrence of PD in transitional sections, even in classical music,179 and presumes that Schenker would ‘respond that [the excerpts cited from FC, Fig. 62,4–5], regardless of the nature of their individual prolongations, represent only ‘passing moments’ in the total piece’ (54). Morgan thus interprets Schenker’s prohibition on PD in a too narrow sense (group C above). Morgan focuses on works of the late nineteenth century, which reveal daring PDs, and ‘depart from . . . tonally functional prolongation’ (p. 58). These examples, however, also depart from normal tonal practice in ways unrelated to the PD. From Morgan’s perspective, my focus on common-practice music might seem strange and disappointing, but it results from the discovery that prolongations of seventh chords are abundant in that music, and that reconciling them with Schenker’s strict view is not as trivial a matter as Morgan would have us believe. My perspective is necessary for a systematic examination of the entire

178 Morgan also discusses the analysis in FC, Fig. 62,5 of Bach’s Prelude in C major from WTC I (cf. my Ex. 7.64) and analyzes Wagner, Parsifal, Prelude to act 3 (cf. Ex. 8.50); Liszt, introduction to Faust symphony and Die Trauer-Gondol No. 1. His fns. 29–30 cite several additional late piano works by Liszt: Die Trauer-Gondol No. 2, Unstern and Richard Wagner. Venezia. 179 Morgan cites the Mozart passage from Symphony No. 40 that was discussed in the Schenker- Schoenberg debate (see fn. 154 and Ex. 7.74b) and the bridge of Beethoven, String Quartet Op. 132/I (my Ex. 7.103).

76 Literature Survey spectrum of manifestations of prolongations of the most common dissonance (the seventh chord), rather than merely showing diverse PDs based on various unrelated patterns within various dissonances, as Morgan did. Some studies have indeed been devoted to specific types of dissonance. Significant contributions have been made on the 6/4 (Beach 1967; 1990a; 1990b; and concerning cadenzas: Drabkin 1996a) and on the augmented triad (Cinnamon 1984; 1986, following Proctor 1978, 149–219; Todd 1996). In the field of seventh chords, one study—Clark 1982—specifically attempts to investigate Schenker’s own notions. As pointed out above (§3.3.1.3), Clark tries unsuccessfully to deny the problematic nature of the seventh. He claims, attributing his view to Schenker, that the procedures of strict counterpoint themselves endow the seventh chord with a relative independence, which is unique among dissonances. This idea is at odds with Schenker’s explicit rejection of ‘discrimination’ among dissonances (MW II, 9). Clark relies on Schenker’s dubious derivation of seventh chords from suspensions (that originate in turn from passing tones according to CP I and II. See fn. 140 for rejections). This weakens considerably the application of his findings to actual passing or neighbor sevenths. The resolution of such sevenths by a descending step is certainly similar to that of suspensions, but the complete motion from seventh chords in free composition behaves differently from the motion found in strict counterpoint (this is especially true of resolving V7 with the harmonic V–I motion). More specifically, Clark bases his argument on Schenker’s distinction between true suspensions, which may resolve through motion in a single tone (upper 9–8 or 4–3), and false suspensions (upper ∞‡, lower™− , ¢− and #) whose resolution requires motion in two voices, allowing them some independence (both types are compared in Ex. 3.22,1a–b). ‘The budding Seventh chord’ (CP II, 6/3/§8, p. 215. Clark translates ‘embryonic seventh chord’) is said to coincide with the more independent suspensions. I find that the claim for such a correlation is at best inaccurate, since several configurations clearly violate it (see Ex. 3.22,2): (a). A ∞‡ formation can appear in lower counterpoint §°∞‡. The– created octave is similar to an upper 9–8, and forms a true suspension. (b). The characteristic sonority of a seventh chord in three-voice texture, £‡, can appear as a true suspension £‡–£−, as Schenker himself demonstrates in TW 3, 23

Literature Survey 77

(2004, 118; his Ex. 4b).180 A well-known case is the theme from Chopin’s Mazurka 17,4 (cf. FC, Fig. 65,2). (c). There is an additional false suspension, which does not coincide with a seventh chord, and does not share a similar independence in free composition: the ¢‡ sonority cannot resolve without motion in an additional voice. ‘Resolving’ one suspending voice alone would produce a dissonant ¢− or £‡. A ¢‡–∞° suspension in the lowest voice is implausible, since it would require the simultaneous initiation of the upper fourth; this violates contrapuntal practice, at least in the style of Palestrina.181 Another problematic detail concerns the $. The $ inversion is said to have less chordal independence than root-position seventh chords or # or % inversions, because in $ chords the root of the seventh chord is dissonant in relation to the bass, and thus must itself be the suspending tone (CP II, 216; in Clark 1982, 240). However, in free composition $ chords may also be prolonged in the same manner as other inversions (see §7.7). (As a suspension, the $ sonority might emerge with the bass and third as suspending tones, but the bass must resolve in ascent). A more general problem with Clark’s position is that he refers to all types of seventh chords without making distinctions (cf. §5.2). The purely contrapuntal approach is insufficient to explain the significance of V7, and completely incapable of demonstrating prolongations of diminished seventh chords, since these do not feature in strict counterpoint at all. The arguments made by Clark do appear in CP II, but in combination with direct statements of Schenker’s normative view. These ideas were later abandoned by Schenker (cf. §3.2), and thus cannot serve as a clue to Schenker’s normative position. The discussion that Clark cites from CP II does not appear to result from any special insight achieved through theoretical investigations of strict counterpoint. Rather, it struggles to understand seventh chords as a phenomenon

180 The point in Schenker’s Ex. 4a (ibid.) is problematic, and apparently related to the idea of ‘preparation’ to V7, to which I object in §4.3.1). 181 For a unique, independent 7/4 in fifth species with imitation, and within a modified cambiata, see Jeppesen ([1931, trans. 1939] 1992, 198, first quarter in the second system of staves).

78 Literature Survey that Schenker had observed from external evidence, but which he may have felt did not fully concur with his theories.182 In later years, the research on PD did not progress significantly. Many studies of PD rediscover insights that have already been revealed. For example, Larson (1997, 107) shows how a root position triad may prolong a dissonance in Beethoven, Piano Sonata Op. 2,1/III, m. 3 (look ahead to Ex.7.95,a2), but a very similar point was made at least as far back as 1945.183 Lester (1981, 24) similarly comments that ‘the sense of linearity is so strong that even a root position triad can become a passing chord prolonging a diminished seventh chord’ in Brahms, Intermezzo Op. 116,6, mm. 13–14 (see Ex. 8.9d), and Forte and Gilbert (1982, 118) find in it ‘a curious reversal of relations [between consonance and dissonance].’ Admittedly, Larson’s example is stronger: in the Beethoven excerpt, the prolonging triad is an apparent tonic, while in the Brahms passage, the passing sonority is ‘equivalent’ to a ! (as Forte and Gilbert explicitly point out), but only enharmonically (Brahms has correctly spelled it b©–e–g). Yet, the principle is the same. The recurring fascination with each instance where a specific context is ‘overriding and even negating’ (Rothgeb 1975, 263) the priority of consonances is understandable,184 but time has come to progress from mere discovery of PD to a systematic exploration of its manifestations. Some studies on PD apply this concept in an overly general manner. Two studies about Wolf are symptomatic of this problem: Stein (1985, 85–86) discusses under the title Prolongation of dissonance ‘the extensive use of dissonance’ and remote harmonic relations between consonances, such as ‘the dissonance of D minor within F major;’ Williamson (1996) devotes a complete study to ‘Wolf’s Dissonant Prolongation,’ but includes in addition to true PDs (pp.

182 At the end of his article, Clark also shows Oster’s ideas from his footnote in FC, p. 64. See also fn. 285 on Clark’s discussion of the pattern [V]5–6–7. 183 Katz 1945, 242, quoted above (§3.3.1.4). The Beethoven example is also described as a prolongation of V7 in Burkhart 1978, 149, and identified as prolongation of V6/5 by Aldwell and Schachter (1978/2003, 121, Ex. 8-15). Burkhart also notes the motivic parallelism with the upper voice of mm. 1–4. 184 See also the quest for ‘relative consonance’ in Morgan 1976,54, cited in Clark 1982, 221–2. Larson 1997 devotes a whole section to the problem of PD (pp. 106–12; see also pp. 128–9 in response to Straus [1987]). See also responses by Lerdahl (1997, esp. pp. 151–4) and Straus (1997). Also Larson’s comments on prolongation and stability (1994, 40; 1997, 104–6 and 112) repeat older arguments (cf. Proctor 1978; 11 and 35–41). I take issue with this view in §1.1.1.3.

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224 and 230) a transitive progression between dissonances (225, Ex. 5), a general dissonant texture (233, Ex. 15) and even an incomplete fundamental structure (236, fn. 19). The diametric opposite of over-generalization can also be found. Satyendra (1997, 190–4) discusses ‘differences between dominant and dissonant prolongation’ in the music of Liszt, as if a dominant harmony cannot be dissonant. Satyendra’s observations seem valid—he distinguishes transitional pieces, which still require resolution, from self-contained pieces which are more removed from tonal connotations—but their presentation is unreasonable in light of common- practice music. Harmonic function and sonoric quality are simply not commensurable.185 The divergent usage of the basic concepts is problematic, and may create new misunderstandings in the future. I find that the most recent studies of PD represent a regression from the achievements of the past, particularly those by Morgan (1976). Among the older contributions that remain invaluable are Oster’s footnote in FC, p. 64 and Schachter [1981] 1999a, 201–2. All these sources, however, are far from constituting a comprehensive investigation of PD and of prolongation of the seventh in particular.

3.4 Studies of PD in Twentieth Century Music

Most of the existing literature on PD is concerned with post-tonal music. This is understandable, since recognition of PD seems necessary in order to apply prolongation to this music at all. As Laufer (1981, 161) states, ‘[t]here is no triad to be prolonged; thus, some contextually derived associative sonority must take its place.’ Indeed, most writers on post-tonal prolongation assume that PD is possible. Despite the existence of numerous meta-discussions of post-tonal prolongations (Baker 1983, 1990b, 1993a; Dale 1993, 35–44 and the review in

185 Satyendra thus thinks of tonicized dissonances only. Also Morgan (1976, 53) speaks of ‘dissonant tonics’ at one point in his study of ‘dissonant prolongation.’ Another problematic idea regarding PD appears in Snarrenberg 1997, 9–23. He states (p. 20) that ‘When the imagined background of the Zug is, say, a second-species setting, there is the possibility of connecting a consonant tone of the cantus to a dissonant passing tone in another voice.’ In the attached footnote (No. 18), Snarrenberg rejects the normative view of linear progressions as presented by Forte and Gilbert (1982, 237), but they are right.

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Nolan 1994. 252–3; Dunsby and Whittall 1988, 59–61; Lester 1970; Neumeyer and Tepping 1992, 117–24; Pearsal 1991; Straus 1997; Wilson 1991, 42–52), there appears to be no standard methodological framework. On one occasion only (MW II, 17), Schenker analyzed a modern excerpt (by Stravinsky; see §3.2.6) as a negative example. His search for triads as the subjects of prolongation in this music has been often criticized, but has also inspired important research, including Morgan 1976. Perhaps it is to be expected that applications of Schenker’s theory to modern music would concentrate on expanded tonality. This is only true, however, in relation to early discussions, mainly by Salzer and Katz. Salzer claims that PD is an innovation of the twentieth century: ‘the concept of consonance and dissonance has undergone radical changes in the course of this century. The distinction between consonance and dissonance appears replaced by a distinction between dissonances of greater and lesser degree’ (1952/1962, 192); ‘one of the outstanding revolutionary achievements of contemporary music: the contrapuntal prolongation of dissonant chords’ (p. 193). His examples (Exx. 415–7) are taken from Ravel, Copland and Stravinsky. Katz (1945), who presents Schenkerian concepts of tonality through a historical survey, devotes chapters to Debussy, Stravinsky and early Schoenberg as tonal composers. At one point (pp. 304–5), she presents PD as a technical clue to the evolution of tonality: traditional composers horizontalized triads, Debussy horizontalized seventh chords and Stravinsky did the same for ninth chords. Katz also notes that the contrast between consonance and dissonance has been abandoned in some of Stravinsky’s music (334), and that it is one of several basic features of tonality denied in atonality (390). She therefore makes no attempt to apply tonal concepts to all twentieth century music. Taking the remarks by Katz and Salzer at face value, one might think that they adhere to Schenker’s strict prohibition on PD, but only in so far as it concerns traditional tonal music. Their examples from this music, however, actually include numerous prolongations of seventh chords (cf. above §3.3.1.4).186

186 For example, see Katz’s examples from Bach (p. 62), Beethoven (148) and Wagner (242).

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The earliest study devoted specifically to twentieth century PD was made by Travis (1959).187 Like Morgan 1976, Travis looks in common-practice tonality for precedents to the PDs of twentieth century music. Unlike Morgan, however, Travis does not claim to find PDs in earlier music; rather, he argues that the relationship of prolongations in traditional tonality to the modern PDs in Stravinsky and Bartók is that of isomorphism, as in his comparison between Stravinsky (introduction to Le Sacre du Printemps) and Chopin (Nocturne Op. 62,2) (his Ex. 12, retranscribed as Ex. 3.23). The kind of isomorphism that Travis proposes is direct, i.e., identical procedures of prolongation occur in both contexts, irrespective of the prolonged sonorities. Travis’s article was the target of a biting attack by Oster (1960), on ethical, theoretical and analytical grounds. Indeed, Travis’s analyses of Mozart and Chopin often involve misunderstanding of passing chords as final boundaries of tonal motion. Since the tonal models Travis shows are false, the isomorphic argument fails too. However, Travis’s analysis of Stravinsky is valid in part at least (it is apparently based on Katz 1945, Ex. 105).188 Oster also comments on two cases where common-practice tonality involves dissonances in the structure, but not as prolonged harmonies (pp. 93–94): (illusory) sevenths or ninths subdivided into thirds, and equal division of the octave. Throughout the last generation, the focus of scholarly effort has shifted from extended tonality to atonal works, mainly by Schoenberg and his school, perhaps because this repertoire offers particular challenges to any application of prolongational procedures.189 This new focus has resulted in two notable shifts in analytical approach:

187 Travis’s title, ‘Toward a new concept of tonality?,’ is borrowed from the subtitle of Katz 1945, but while Katz refers as ‘a new concept’ to Schenker’s theory, Travis points to a concept of expanded tonality that includes twentieth-century music. 188 The analyses of the Stravinsky passage by Travis and Katz are discussed by Whittall (1982, 42– 44). Whittall prefers to describe the procedure not as prolongation, but rather ‘more neutrally as the extension and reinforcement of dissonant harmonic elements.’ The prolongation in the Stravinsky passage is based on register transfer of a dissonant non-tertian sonority. This procedure can definitely prolong any sonority when it is stated directly. See the passage from Richard Strauss’s Elektra (mm. 1–2 after No. 27) shown by Morgan (1991, 32–33). 189 Some representative works are: on Schoenberg: Ballan (on the early works), Travis 1966, Cinnamon 1984 and 1993, DeLio 1994, Jackson 1989/1990, Larson 1987a, Lester 1970, D. Lewin [1981] 2006, esp. 332, Stein 1976, Milstein 1992; on Berg: Ayrey 1982, Forte 1985, Lewis 1981,

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(a). Concentration on single voices. Since in atonal repertoire, any tonal remnant becomes significant, many Schenkerian applications in this area limit themselves to ‘directed motion’ (Travis 1966) or ‘linear continuity’ (Morrison 1985, on Ligeti), and seldom concern themselves with prolongation of the dissonances that emerge between the voices. Typical in this respect are remarks made by James M. Baker (1990b, 188): ‘Continuity is ensured [in Schoenberg’s Op. 19,1] not through the expansion of basic components, but rather by means of a web of relations among individual pitches.’190 (b). The straightforward claim for isomorphism between modern and traditional prolongational procedures is usually replaced by a more complex analogy, which argues for horizontalization of the specific chords determined by any particular work (possibly derived from the higher members of the overtone series. See Väisälä 2002, esp. 208). This approach preserves the unity of horizontal (successive) and vertical (simultaneous) dimensions in post-tonal music (see Busch 1985–6). As several scholars have pointed out (e.g., Katz 1945, 390; Straus 1987, 5), the unity of dimensions in such music may be even greater than in common-practice tonality, since in the absence of pre- determined harmonic vocabulary, any sonority can appear in both dimensions. As Straus remarks, however, it is precisely this feature that leads to problems in distinguishing between the horizontalized sonority and its prolonging chords. The analytical literature is replete with procedures that appear to be horizontalizations of dissonant non-tertian sets, but do not, in fact, constitute prolongations. Rather, they show how vertical sets are projected at salient moments in the piece.191 For example, what Straus (1990/2000, 89) presents as ‘large-scale composing-out’ is not composing out in the Schenkerian sense (see

Porter 1989/90; and on Webern: Travis 1966, Boge 1992, Forte 1974 and Travis 1974, Hanson 1983, Olson 1979, Wintle 1982. 190 Emphasis on individual pitches also appears in Larson 1987a, 424, concerning Schoenberg’s song Hain in diesen Paradiesen, Op. 15,2. Perhaps Bartók’s music still prolongs chords which also exist as vertical sonorities. See analyses of two pieces from the Mikrokosmos: Parks (1981, 270) on ‘Fourths’ (No. 131) and H. Lewin (1981, 41) on the background of Bartók’s ‘Major Seconds Broken and Together’ (No. 132). Both cases are based on contrary neighbor motion. 191 For ‘projected sets’ in Bartók, see Wilson 1991, 47–52. Antokoletz (1984, 30–31) presents the same phenomenon the other way around, as a vertically projected melody.

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Nolan 1991, 294). Straus also demonstrates what appears to be motivic parallelism between different structural levels (Ex. A1-11 [my Ex. 3.24] from Schoenberg’s Pierrot Lunaire), but this structural hierarchy is not based on voice- leading procedures.192 Many studies adopt a set-theoretical approach to horizontalization. According to this view, the horizontalized chord may be transposed or even inverted (in the sense of set theory). In terms of tonal music, this would lead to an absurd situation, since any major triad would be horizontalized by any transposition into any other major triad, and even by any inversion of set class 037 into any minor triad. Forte (1988, 334) adopts this problematic approach to the Tristan chord in Wagner’s prelude to Tristan und Isolde (Forte’s Ex. 6e, quoted as Ex. 3.25): he finds that the chord is horizontalized not only through enharmonic transformation and (in related graphs) through transposition, but also through inversion of the set class (0258) into a dominant-type seventh chord. More recently, Straus (1997) established important distinctions between prolongational, associational and transformational types of voice leading. Only the prolongational type aims to extend Schenker’s method. Straus finds that prolongation in the strict sense ‘can be useful in discussions of atonal music,’ but ‘may not be a reliable basis for sustained analytical inquiry, or for structural levels beyond the immediate musical surface’ (p. 241). This formulation consolidates skeptical ideas that were proposed by Straus years earlier (1987, 2–3). I hope that Straus’s discussion of various methods of atonal voice leading will help to standardize future discussion as well as encourage a more rigorous use of the term and concept of prolongation in post-tonal repertoire.193 While most analysts who believe in post-tonal prolongation take PD for granted, one key scholar, James M. Baker, has another approach: ‘the analyses . . .

192 For problematic uses of the concept of PD, see also Ayrey 1982 (on Berg) and Pearsal 1991, 351 (on Webern). One basic problem is the modification of the concepts of consonance and dissonance to membership/non-membership in a prominent pitch-class set. Perle (1977/1996) uses all the terms ‘large-scale progression’ (132–7), consonance and dissonance (229–34) and ‘tonic’ (120–7) in a manner which is only analogous to their traditional meanings. (See also Pople 1988, 217, commenting on a similar problem in Baker 1986). 193 This hope will perhaps not be fulfilled. For example, Milstein (1992, 52) identifies her use ‘prolongation’ as ‘stripped of its strict technical characteristics,’ similar to Straus’s ‘association.’ See also discussion by her reviewer Jackson (1994, 15).

84 Literature Survey especially of those who accept the possibility of dissonant prolongations, are invariably somewhat arbitrarily based’ (1983, 168).194 In order to eschew this arbitrariness, Baker proposes the idea of ‘implicit tonality,’ at least in his studies of Skryabin (1980; 1983, 169–86; 1986, especially chapter 3).195 The prolonged chords are tonic consonant triads, which Baker assumes at the boundaries of the work. These sometimes follow the familiar procedure of an elided boundary,196 as in Skryabin’s Poem Op. 32,2 (Baker 1980, 9; slightly modified in 1986, 52), but at other times, remove dissonant tones from the boundary chords with less justification, as in Skryabin’s Poem Op. 32,1 (Ex. 3.26, reproduced from Baker 1986, 59, Ex. 29). Baker’s analyses are nevertheless replete with PDs. Baker only appears to resist dissonant ‘tonics.’ Tonicizations of dissonances are almost entirely absent in common-practice tonality (for exceptions, see §9.4.2, Ex. 9.22), but prolonged dissonances need not function as tonics. The confusion of prolongation with stability and tonicization seems widespread (cf. §1.1.1.3; end of §3.3.2), but the problem of PD is a true one rather than a mere misunderstanding.

194 Among Baker’s three extensive surveys of post-tonal voice leading (1983, 1990b, 1993a), only the 1990 article discusses atonal music rather than extended tonality, imposing a dominant-tonic axis on Schoenberg’s Op. 19,1, although he himself regards this as ‘speculative’ (1990b, 197). 195 Two reviews of Baker’s 1986 book on Skryabin (Pople 1988; Samson 1988) criticize this approach as being too conservative. 196 Cf. the seventh in the opening chord of Beethoven, Symphony No. 1/I, which is said to pass from an elided octave; also Laufer 1996, on Bruckner, Symphony No. 9/II (cf. commentary on Ex. 10.24c). For elision of the goal of the fundamental structure, see Schachter (1999, 306), reading of Chopin’s Mazurka Op. 41,3.

4. SEVENTH CHORDS AT THE DEEPEST STRUCTURAL LEVELS

The participation of dissonances in the deepest levels should not by itself raise a theoretical problem, since these dissonances may be transformed into consonances at later levels through consonant support (cf. §2.1.1). Such dissonances may also appear without any prolongation whatsoever. For example, the ¢− under ^3 often participates in the background without prolongation. Nevertheless, a high structural rank of a dissonance may potentially point towards a location of PD at later levels. The background or deep middleground scheme would show of course only the dissonance, not the prolongation. In addition, some less conservative interpretations introduce PD into the background models themselves. The point of departure of this chapter is not chords, but—in accordance with the true nature of the Ursatz—contrapuntal constellations that arise between the outer voices.

4.1 Dissonances and Sevenths in Particular at the Background (with Unfilled Bass Arpeggiation)

The only dissonance Schenker presents at the background is the ‘unsupported stretch’ under 4 in a line from 5 (under4 and7 in a line from 8) (, FC§§35, 39).197

197 In an Urlinie from 3, the2 is dissonant against the stable tonic tone, but Schenker presents it only counterpointed by the tonic arpeggiation in the bass. This section discusses only those background configurations where neither of the outer voices is prolonged whatsoever. Strictly speaking, all further possibilities belong to the next levels (cf. §4.2).

86 Seventh Chords at the Deepest Structural Levels

In fact, this stretch hardly ever remains without support at the later levels. Where the 4 (or 7) does not receive any support, the preceding5 (or 8) is not perceived as a primary tone, but rather as a cover tone, a point of departure for an ‘initial descent’ toward the primary tone (Forte and Gilbert 1982, 181–2. See Ex. 4.1; cf. also Beach 1988, 272–3). Consequently, the ‘unsupported stretch’ under 4 (or 7) cannot serve as a background element. In this light, any speculations on prolongation of a background unsupported stretch that is not transformed into consonance at later levels are highly hypothetical.198 Even the ordinary forms of the Ursatz can accommodate dissonances in accompanying inner voices.199 The simultaneity V2 can become 7V with the dissonant 4 in an inner voice (Ex. 4.2), as Renwick (1995a, 82, his Ex. 3-3a) proposes in the voice-leading complex for fugue themes; indeed, it seems to facilitate devices of invertible counterpoint.200 PD within the background schemes themselves becomes possible when the segmentation of the Urlinie from 5 (or from 8) distorts the normative function of the Urlinie ‘to fill the spaces in the arpeggiation of the upper voice of the fundamental structure with passing tones’ (FC, §4)—normatively, the Urlinie from ^5 should divide it into two spaces of thirds (FC, §36; Figs. 10,1–2).201 If V in the bass already appears under 4 (Ex. 4.3a), this4 is a dissonant seventh, that should have theoretically remained in effect until the 2, and then resolved in an inner voice under 1 (Ex. 4.3b). Normally the melodic drive nevertheless wins and forces us to hear the 1 as the true goal of the fifth progression, even though in pure terms of voice leading, the fifth-line might be

198 Schachter ([1981] 1999a, 192) discusses the problem of the unsupported stretch, and criticizes the idea by Westergaard (1975, 426), according to which fifth progressions are ‘so rare in the underlying structures of tonal music,’ apparently since they include the unsupported stretch. Fifth progressions should only be understood as an ‘initial descent’ where the unsupported stretch is left unsupported at the lower levels. 199 Properly speaking, only the outer voices constitute the Ursatz. For an alternative approach, see Neumeyer 1987a. See also response in Larson 1987b. 200 Salzer (1952/1962, Ex. 100) shows the seventh of the same configuration as the result of contraction. An actual instance occurs in Brahms, Symphony No. 4/II, 96–97, according to the reading of Nivans (1992, Ex. 113—the dissonance is evident from the label V7). 201 In FC, §36, Schenker calls the subdivision 53– 1– ‘illusory,’ since he wants to assert the unity of the fifth-line. I argue that large linear progressions can nevertheless be subdivided. I say more on this point at §7.2.3. See also problematic segmentations at §4.2.

Seventh Chords at the Deepest Structural Levels 87 said to be replaced by a ^54– –3 line the end of which is covered by a cover tone,202 The Urlinie thus replaces the 4 melodically without resolving it harmonically. This paradox might account for Schenker’s avoidance of this setting.203 Only if ^3 is achieved in the upper voice after the descent has been completed, the context might potentially cause retroactive reinterpretation of the preceding descent, delegating the 1 into an inner voice and destroying the unity of the fifth- line (Ex. 4.3c). In such cases, the emerging V7 is truly prolonged. A connection between 4 and2 can also arise in a line from8 (Ex. 4.4a). This possibility is realized at the foreground in the opening theme of Mozart’s Symphony No. 35/I (Ex. 4.4b It is ambiguous whether the V appears here first as consonance (an empty octave on 5); The seventh4 ( ) becomes the initial boundary of the local prolongation, since it appears on a strong measure, occupies long duration and returns literally in an inner voice. In pure terms of voice leading, the line could be more accurately explained as a sixth-line ^8–3^ whose end is covered, but the closure on 1 is sufficiently salient in order to force us to hear an octave descent.204 Diatonic lines from 8 can accommodate an additional dissonant connection, namely between 7 and4 . This can be understood as an unfolding of the leading tritone (in either of the two contexts shown in Ex. 4.5a–b). Reduction of this unfolding reveals a neighbor motion underlying beyond the octave descent. The dissonant connection in this case is challenged by the fact that the dissonant

202 Rothstein 2006, 250–1, Exx. 1d, 3a and especially 3b. My examples differ from Rothstein’s in that they do not provide preparation for the seventh. On the problem of preparation, see §4.3.1. 203 For a foreground case that resembles this type of Ursatz, see Chopin, Etude Op. 10,8, mm. 73– 75. The presence of 1 in the upper voice also creates a feeling of a closure when the preceding V7 is unfolded (rather than descends linearly), in the melodic pattern 54– 7– 1– . See the final measures of Brahms, String Quartet Op. 51,2/II. Cadwallader and Gagné (1998, 321, Ex. 11.8) show a similar resolution into an inner voice in Beethoven’s Piano Sonata Op. 49,2/I, 51–52. Arrival at 1 as the uppermost final tone of a cadence creates closure even within polyphonic melodies, where the 1 clearly belongs to an inner voice. Consider Mozart, Piano Sonata K. 457/I, m. 8. 204 My reading is based on FC, which shows the theme as based on an octave line (Fig. 119,5a), and its end as connecting 4 and2 under 7V (Fig. 134,3). One passage in the last movement of the same symphony (71–79) is based on the same appoggiaturas as in mm. 5–6. Cf. also Brahms, Wie bist du, meine Königin, Op. 32,9, according to FC, Fig. 152,5. In the Urlinie, from 8, V already starts under 5, but the metrical situation in m. 19 connects4 with 2. The42– connection can also occur within octave lines with lowered seventh. According to FC, §44, such lines are unable to constitute the Urlinie, and happen mainly in codas. This procedure occurs in the coda of Schubert, Piano Sonata D. 575 (Op. Posth. 147)/II (mm. 77–79).

88 Seventh Chords at the Deepest Structural Levels element (4, seventh of 7V) appears only after the rest of the V harmony (Ex. 4.5c; cf. Oster’s criterion in §5.4).

4.2 Sevenths at the Middleground with Unprolonged Urlinie (and Prolonged Bass)

FC (II/2/1, §§53–86) presents an important notion, which is not sufficiently utilized nowadays, of the middleground with prolongation of the bass of the Ursatz but without prolongation of the Urlinie. Many of the settings of an unprolonged Urlinie from ^5 with prolongations in the bass (FC, Fig. 16) suggest segmentation that highlights the 4. In two cases it is actually the 3 that functions as an ‘unsupported stretch’ (Fig. 16,5, second example;205 Fig. 16,6, first example. See Ex. 4.6a–b). Those schemes serve as the structural frame to additional cases (16,3c, second example and 16,2d, first example, respectively).206 A consistent approach should include in this group of schemes also the last example under Fig, 16,5, which includes a cadential 6/4 under the 3 of the Urlinie (Ex. 4.6c). This subdivision can also be expressed through insertion of chromatic elements (see above Ex. 1.8c). It appears schematically also in ‘sketches for the theory of performance’ in the Oster collection.207 In all these cases, the V appears consonant, but might under certain circumstances merge with the preceding 4 into 7V through a special kind of subordination (for this term, see §1.1.3).208 This V7 acquires structural priority over other events, even though it is not circularly prolonged.

205 An instance of this model at the foreground appears in FC, Fig. 109,e5 (theme from Bach, WTC I, Fugue in Eß minor [Dƒ minor]). 206 In the latter case the 3 appears as a foreground consonance, yet a passing tone. 207 Oster Collection, reel 13, Sketches for a theory of performance, ‘Schichten,’ p. 4. The same text appears in a different organization in the added text after the Sketches for a theory of performance, as ‘Ergänzungen und Beispiele,’ p. 35 (under ‘Dynamik’). Esser, the editor of The Art of Performance, identifies this source as his own (ibid, p. xviii), but these remarks are unfortunately absent in the edited publication. In addition, the finding list of the Oster collection skips over the entry ‘Schichten.’ The drawing is identical with FC, Fig. 16,5, second example. For exceptional subdivision of fifth-lines, see also FC, §37 and Fig. 10,3. 208 The justification for this non-trivial kind of subordination to V7 is discussed in §§6.3.1; 6.3.3.

Seventh Chords at the Deepest Structural Levels 89

4.2.1 The Combination of an Unprolonged Urlinie with Two Bass Arpeggiations This procedure offers new possibilities for V7. In those cases where the first bass arpeggiation ends under 3, its divider coincides with 4, thus introducing7. VThis is especially clear with fifth-lines, where the first arpeggiation matches the segment ^5–43– (Ex. 4.7a). The configurations in FC, Fig. 19 introduce the4 always with consonant support before it transforms into V7, in what normally counts as a preparation for the V7 (Ex. 4.7b shows Fig. 19a).209 As I shall argue below (§4.3.1), the idea of preparation is here problematic, and the V belongs together 4 already since its initiation. While Schenker avoids the unprepared meeting of the bass divider with the passing 4, Jonas ([1934] 1982, 100) endorses this idea positively: ‘the divider coincides with the passing tone in a dissonant interval, the seventh. The divider model shows us the birthplace of the so-called dominant-seventh chord.’ This text accompanies Jonas’s Ex. 155, which shows ^5– 43– harmonized by an unfilled bass arpeggiation (Jonas’s Ex. 151 too is essentially identical). This concept has no counterpart in Schenker (!). Although Jonas immediately regresses to the normative idea of ‘the necessity to precede the seventh with a consonant interval’ (ibid.), what is decisive is the acceptance of the V7 as the deeper harmony.210 In actual pieces, V is quite common as the harmonization of 4 immediately from its initiation point. Admittedly, this configuration is easier to locate in transferences of the forms of the Ursatz to the foreground,211 but occasionally it occurs at the background itself.212

209 Fig. 19b shows lines from 8, one analogous to the cases I have shown in Ex. 4.6, the other similar to that in Fig. 19a. 210 See also Aldwell and Schachter (1978/2003, 90): ‘One very important function of V7 is to support 4.’ Salzer (1952/1962, Exx. 229b and 322b [abstraction from Exx.318–9]) harmonizes the 4 as ‘contrapuntal structural’ V6/5 (Ex. 322a is similar, with 4 as an upper neighbor). Neither Salzer nor Aldwell and Schachter refer specifically to the background, but I see no reason to rule out the background from the range where their comment can apply. Salzer’s Ex. 322 is discussed by Dunsby and Whittall (1988, 57) in comparison to Schenker’s background models. 211 See several examples by Mozart: (1) String Quintet K. 515/IV, opening theme. The graph in FC, Fig. 123,4 does not confront the dissonance, since it analyzes the upper voice only; (2) String Quartet K. 465/IV, theme. The theme of the third movement of the same quartet is a more elaborated version of the same structure; (3) String Quintet K. 593/IV, 104–12. The developed version 116–31 involves what I call gradual transformation into a seventh chord (see §6.2.1). The model of FC, Fig. 19a (with IV before V7) is applied in Fig. 101,4 (Beethoven, Piano Sonata Op.

90 Seventh Chords at the Deepest Structural Levels

7 That the V that emerges through ^5–43– can be prolonged at all is not trivial. At least when the prolongation takes place in the upper voice, it might be said to relate to the consonant ^5 rather than to the dissonant 4 (Ex. 4.8a). At the present stage, I offer only one very clear device how to evade this obstacle. It is possible to force on the 4 the unequivocal sense of an independently prolonged tone (in my example, a primary tone of a descent into an inner voice), by means a motivically parallel lower-level descent from ^5 before the 4 (Ex. 4.8b).213 4.2.1.1 The partial descent ^5–43– . Since the upper third of a fifth-line can be combined with a complete bass arpeggiation, it might be thought to form a possible model for an entire Urlinie. In such a configuration, the V7 as the harmonization of 4 would have acquired an even deeper status than it has in the normative Ursatz models. The deficiency of the 54– 3– line is of course the lack of definite melodic closure. Even when this model is found appropriate, the piece it governs is ‘melodically incomplete’ (Marston 1989, 308). Schachter (1999b, 306) expresses the feeling of a truncated descent that strives to continue in Chopin’s Mazurka Op. 41,3 (in some editions Op. 41,4) by supplying the hypothetical normative descent to 1 in parentheses, since ‘it would be wrong to summarize that structure as simply 54– 3– . [Better:]5 4– 3– – but where are2 and1 ?’ (p. 304).214

4.2.2 Other Dissonances at the Middleground with Unprolonged Urlinie V7 is not the only seventh chord included in the settings of the unprolonged Urlinie in FC. IV7 appears as a suspension under 3 in three settings of an Urlinie

10,2/I, dominant region, mm. 31–41), without determining the hierarchy. The reading of the same work in MW II, 26 highlights the V7, but there it appears in a line from 8. 212 See Brahms’s Tragic Overture, according to Nivans 1992, 202. He locates the V4 at mm. 278– 99. Actually, the seventh arrives only at m. 290. Jackson (1996, 92) postpones it to 299. Webster (1983, 126) graphs the bass only. 213 FC, Fig. 88,3 is similar to Ex. 4.8b, but is considerably more complicated. The passing 4 is a primary tone of a diminished fifth progression. The support of the 4 appears first as consonant II. The indicated third progression in the bass negates the structural priority of V over II (a similar hierarchy is hinted in FC, Fig. 15,6). See discussion below, §§6.3.1 and 6.3.3. 214 Schachter’s argument is fairly convincing, but it is based on the specific features of the mazurka. I am not sure one should rule out the possibility of the ‘new Ursatz form’ (ibid., 304) where 54– 3– is the sole content of theUrlinie . Marston (1989, 306–7, Ex. 1) endorses the incomplete line 54––3 in the variations theme of Beethoven’s String Quartet Op. 74/IV. Perhaps it is better to read there an ascending line. 54– 3– is considered to be the normative linear model by Gjerdingen (1988, Ex. 8-20) and his reviewer Agawu (1991b, 116). It is this scheme that they compare with the less linear paradigm 17– 4– 3– . Cf. fn. 79.

Seventh Chords at the Deepest Structural Levels 91 from 3 (Ex. 4.9a shows Fig. 15,2c, first example; see also 15,3c, second example; 15,5a) and two settings from 5 (Ex. 4.9b shows Fig. 16,2c, first example; also Fig. 16,3c, first example). The settings from 5 are self-contradictory: while the note heads in the soprano indicate that the IV7 is a suspension from a consonant harmonization of 3, the note heads and the slur in the bass show the consonant ‘origin’ of the suspension as passing tones on a more foreground level. Hence, these examples confuse structural levels. Along with seventh chords, one more dissonance is possible in the first level of prolongation of the bass: the diminished triad on II in minor. All the settings in FC, Fig. 14–18 are said to apply also in minor, although they are shown in major only. At least the schemes where II appears in first inversion (Fig. 14,2c; 14,3c and d; 14,5; 15,3, last example; 16,5 last example) should be possible in minor form too; this is admittedly more problematic with those configurations which involve II root position (Fig. 14,6; 15,2c, second example; 15,2d; 15,3, first example; 15,5b; 15,6; 16,2c, second example; 16,2d; 16,3c, last example; 16,5, third example; 16,6).215

4.3 Prolongation of Dissonances at the Deep Middleground (with Prolonged Urlinie)

The first level of middleground introduces several new opportunities for V7 to emerge. The most notable is the complete upper neighbor to 3. It also has consequences for situations that would normally count as an incomplete neighbor. Other techniques that Schenker presents as belonging to the first level of middleground and that may relate to seventh chords are reaching-over and unfolding.

4.3.1 The Complete Upper Neighbor to 3 The first level of the middleground introduces the structural neighbor tone (FC, Fig. 32). The most common type is an upper neighbor to 3. Its combination with

215 A unique II in minor in the deep middleground occurs at the end of Chopin, Mazurka Op. 30,4 (FC, Fig. 53,3), after the structural V. The 21– is harmonized by means of parallel octaves II–I. Such parallel octaves appear in the schematic Fig. 15,6 as the ordinary explanation of the progression II–V–I, but this hierarchy ignores the priority of the V from the tonic arpeggiation.

92 Seventh Chords at the Deepest Structural Levels the basic bass divider results in V7. FC, Fig. 32,5 (reproduced as Ex. 4.10)216 shows this situation, first with the 4 harmonized with IV before it proceeds to 7V, and then with a further reduction that discovers the deeper structural rank of V7. Schenker is reluctant to accept this further reduction, and attaches to it the designation ‘not.’ I am convinced that this stance is engendered by resistance to PD. Schenker regards the IV as a consonant preparation for the V7. An explicit reference to this idea is lacking in the attached commentary, but is present elsewhere in FC (text to Fig. 62,9), in reference to an analogous situation: ‘Thus, as in strict counterpoint, a preparation of the seventh is attained.’ (see discussion in §§5.1, 6.3, 6.3.1). The further reduction reveals, however, that the neighbor 4 is not at all in accord with the rules of strict counterpoint. In strict counterpoint, the concept of consonant preparation belongs to the fourth species, where consonances are the more structural events, while dissonances result from metrical displacement and are removed in reduction (Ex. 4.11a). By contrast, in the progression IV–V7, it is the dissonant V7 that is more structural (Ex. 4.11b), in accordance to Schenker’s teaching elsewhere in FC: ‘in the so-called cadence I– IV–V–I in free composition, the V has preeminence because of its prior development as arpeggiation tone of the harmony’ (§186, text for Fig. 66,2). The true hierarchy, with V7 priority, is even indicated in the schematic presentation of the structural neighbor (Fig. 32,5) itself, by means of the note heads in the bass.217 There is no escape from concluding that the consonant preparation here is only apparent, and that the application of the idea of consonant preparation to the chords that precede V7 confuses structural levels.

216 Figs. 32, 4 and 32,6 resemble other cases discussed above (see my Exx. 4.6a and 4.7b). Upper neighbor to the third is demonstrated also in the Elucidations, Fig. 7, but combination with bass divider is avoided there. The same figure also includes the Riemannian idea of Unterquint Schenker was later to abandon. 217 For an analytical application, where Schenker selects the V7 as hierarchically prior over a preceding IV (albeit in the context of circular prolongation of V), see TW 8–9, analysis of Brahms, Variations on a theme by Handel, theme and variations Nos. 1 and 5. For further observations that are based on the situation shown in FC, Fig. 32,5, see McKee 1996, 57, Ex. 6. Dahlhaus ([1966] 1990, 64) shares the notion that V7 cannot be reconciled with strict counterpoint: ‘the seventh chord on degree V is the [chronologically?] first to evade the rules of strict counterpoint. In general, it cannot be explained as a suspension . . . because it falls on the weak beat, and not as a passing tone because degree IV or ii precedes it [so that there is no consonant tone to pass from. Translator’s insertion].’

Seventh Chords at the Deepest Structural Levels 93

The negative label Schenker attaches to the reduction in Fig. 32,5 suggests that his resistance to PD embraces also cases like this, which only constitute subordination to dissonance, and is not limited to full prolongation, as some important theorists (notably Schachter [<1981> 1999a, 202]) think. Yet, Schenker is not consistent with this strict approach, not even during the specific discussion in FC (§110) of neighbor in the first middleground. The same paragraph expresses both this strict view, saying that ‘[t]he neighboring note [in some cases, 4] cannot be supported by the V in the same manner as can the2 ,’ and the contradicting idea that ‘Where it has its own cadential bass (Figs. 32,5 and 6), the neighboring note is more organically established.’ ‘Its own cadential bass’ must refer to V, since the text contrasts this situation with that of support by IV or VI (Figs. 32,3 and 4). I am not sure whether these contrasting remarks can be reconciled in a single stance. At best, it might be inferred that Schenker finds the best structural support for the neighbor 4 to be a consonant support followed by V7, at least at the background.218 For example, some of the instances that are cited as cases where ‘a neighboring note can also give rise to three-part form’ (FC, §310(d)) show V7 as the deepest harmonization of this neighbor, but all of them harmonize the neighbor by consonant chords before the actual V7 arrives.219 Actual occurrences of the neighbor V7 without consonant ‘preparation’ are ubiquitous, but perhaps limited to lower structural levels. Their absence (or at least paucity) at the deep middleground reflects the difficulty to prolong V7 over large spans of time, but must not be explained by inherent problems in its relations with the deep structure itself.220 In light of Schenker’s explicit remark concerning Fig. 32,5, it is now clear that also in the aforementioned Fig. 19 (see Ex. 4.7 above) the avoidance of the direct combination of V4 (as in Ex. 4.7a) is intentional. The IV in Fig. 19a must

218 In FC, §106, Schenker observes that ‘the neighboring note of 3 is dissonant to the I, whereas the neighboring note of 5 is consonant.’ In this perspective, one only expects Schenker to resist supporting the neighboring note of 3 with V, which fails to alter its dissonant character. 219 See FC, Figs. 7b (Chopin, Etude Op. 10,8), 42,2 (Chorale St. Anthony) and 85 (Beethoven, Piano Sonata Op. 26/I, theme). All of them are problematic readings, and I shall discuss each of them separately (fn. 236, fn. 257 and §6.1.1, respectively). 220 In MW I Schenker even devotes a detailed study for a foreground case (in response to Engelsmann) from Beethoven’s Piano Sonata Op. 110/III. Schenker says (p. 100) that the seventh, aß1, ‘belongs’ to the V at m. 169, although he emphasizes the passing character of that chord.

94 Seventh Chords at the Deepest Structural Levels have been conceived of by Schenker as a consonant preparation (a false preparation, as I have shown). He would have designated Ex. 4.7b with the same ‘not’ that he has put on the latter part of Fig. 32,5. In both cases, Schenker’s ‘not’ is a theoretical error. Yet, the error is not accidental, but grounded in the very reliance on strict counterpoint: V7 as support to 4 is problematic even when it does not receive any prolongation, because the leap to V in the bass corresponds rhythmically to the first species of strict counterpoint, where dissonances are prohibited. By contrast, the ‘unsupported stretch’ is possible as a dissonant element in the background, since it resembles the passing tone in second species.221 Rather recently, Ch. Smith (1996) has presented an exhaustive list of background configurations. His schemes (Exx. 38–39) incorporate many cases of V7, both as a structural neighbor tone and as harmonization to the 4 of the Urlinie. However, as Smith’s notation indicates, he is ready to give the V a low structural status (also in consonant forms).

4.3.2 The Connection between 4 and and2 the Incomplete Upper Neighbor The incomplete neighbor 4 in the configuration the3 4– 2– is not normally harmonized by V, nor is it considered to belong together with the ensuing V(Ex.2 4.12a). Nevertheless, it can occasionally sound as merging with this V into V7, only resolving into the 3 of the tonic, normally in an inner voice (Ex. 4.12b).222 This modifies the essence of the incomplete neighbor into a complete neighbor, especially when the 3 is actually regained in the upper voice (Ex. 4.12c). Hassler’s chorale, Lustgarten No. 24, analyzed in FC, Fig. 116, is a case in point: although Schenker indicates it as an immediate complete neighbor (Ex. 4.13a), it is better to

221 Jonas ([1934] 1982, 94) states (without counterpart in Schenker) that a neighbor tone ‘may operate over the course of a whole piece.’ This idea probably accepts the meeting between the first-level upper neighbor 4 with the bass divider (see aboveJonas's acceptance of the similar meeting between bass arpeggiation and the 4 of theUrlinie ). Gauldin (1988, 155, Ex. 11-6) presents ten patterns of ‘note-against-note with chordal dissonance.’ Of these, two (E and J) show an upper neighbor to 3, and in all other eight the seventh does not in fact receive its own harmonization. Configurations that incorporate structural V7, harmonizing 4 either as a structural neighbor tone or as a member of the Urlinie, also appear in the exhaustive list of background configurations by Ch. Smith (1996, Exx. 38–9). Ch. Smith, however, is ready to deprive the V from its structural status (even in consonant forms). See also his tables 1 and 3b. 222 This situation resembles the 42– connection in the background. See above Ex. 4.3.

Seventh Chords at the Deepest Structural Levels 95 read an incomplete neighbor, on harmonic and rhythmic grounds (Ex. 4.13b).223 However, the actual chorale ends with 3 in the soprano. While usually such final 3s are explained as cover tones, this case sounds more like the resolution of a complete neighbor after motion into an inner voice (Ex. 4.13c). The harmonic priority of V and the melodic priority of 4 combine in 7V, to which the preceding IV is subordinate, and which is fully prolonged by the descent into an inner voice.224

4.3.2.1 The problem of 4 before interruption The idea that the paradigm 34– 2– does not express an incomplete neighbor if it is embedded in the larger pattern 34– 2– 3– has an important exception where interruption occurs before the return to 3 (Ex. 4.14a). Endorsing a complete neighbor in such a situation would result in the abandonment of the interruption scheme itself (Ex. 4.14b). N. Wagner (1986, 47–49) discusses this dilemma, and concludes convincingly that only when the is4 strongly felt as the seventh of V does the complete neighbor possess sufficient power to replace the interruption. The analytical decision between the two readings cannot be determined on pure voice-leading grounds, and depends on design, for example the degree of textural break. A corollary and even more acute dilemma arises when the appears4 as a lead- in after the V2 that ends the antecedent (Ex. 4.15a–b). If one adheres to the interruption, the dissonant vanishes4 without resolution; if, on the other hand, one seeks to resolve this dissonance, the interruption is cancelled in favor of a structural neighbor. Two figures in FC graph this situation; unfortunately, both combine the two contradictory interpretations: Fig. 23 (quoted as Ex. 4.15c) indicates an interruption by the structural note heads and (in the first scheme) by the interruption symbol, but at the same time labels this 4 as a neighbor. It actually shows the 4 to be passing from an inner-voice5 under the2 of the antecedent; Fig.

223 The whole concept of the incomplete neighbor is hardly developed in FC. Schenker’s own harmonic analysis below the graph suggests a reading as an incomplete neighbor. See also discussion of incomplete neighbors in §1.1.2.2.1.2 (category C). 224 Schachter (1987c, 12, Ex. 1a) shows a similar instance in the theme of Bach’s Gavotte en Rondeau from Violin Partita No. 3, claiming (p. 11) that the seventh ‘persists’ [=is prolonged]. For essentially the same dilemma in a larger passage (Chopin, coda of Ballade No. 3), see §7.3.4, discussion of Ex. 7.77a. For a similar dilemma in a fifth progression, cf. Ex. 7.23a versus b.

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32,7 (Quoted as Ex. 4.15d) indicates interruption by its symbol, and the neighbor motion both verbally and by a flag (and a dashed slur between the boundaries of the prolongation). Most confusingly, it shows the seventh of V as unfolded from the fifth (rather than passing from the octave), and this unfolding connects both sides of the interruption.225

4.3.2.2 A further ramification of the incomplete neighbor problem: the sequence 35– 4– 2– 1– . Schenker’s interpretation of this configuration regards the3 2– 1– line as skeletal, with motion to and from a conceptually inner voice (Ex. 4.16a, after FC, Fig. 45;226 cf. also Salzer 1952/1962, Ex. 230 a versus b).227 Ex. 4.16b–c suggests alternatives that make the dissonant structural.4 As in the Hassler chorale, regaining 3 in the upper voice determines in retrospect that the belongs4 to the structure. Beethoven artfully exploits the potential of the different interpretations for this melodic formula in his Violin Sonata Op. 47/III, second theme (Ex. 4.17): the 4–succession2 functions three times (and an additional earlier time) as a true unfolding that prolongs a complete neighbor within V7 since it proceeds to I3, but in the last statement, when the upper voice proceeds to1 , the neighbor becomes incomplete and the meaning of the 42– is altered.228

225 Concerning Fig. 23b, see Schachter [1981] 1999a, 198 (further discussed in §6.1.1). Slatin (1967, Ex. 208) brings a comparison between Figs. 23b and 32,7, made by Mitchell. He separates the situation into two readings, similar to my Ex. 4.15a–b, but does not mention the inner contradictions. The text for Fig. 32,7 invokes the possibility that ‘a more significant working-out [Ausbau] of the seventh [!] could bring about a three-part form.’ Cf. also §§6.3; 7.10.1.1; 7.10.1.2.4. 226 Beethoven Piano Sonata Op. 22/III, 1–8. The reading in FC, Fig. 45 includes substitutions, in order to avoid an ascending line, which is especially evident here (see Neumeyer 1987b, esp. 293). The text for Fig. 45 contends it is not a case of genuine unfoldings, but rather an instance of ‘boundary-play.’ Schenker perhaps points to the lower rank of the uppermost tone. 227 In an analogous manner, the skeleton of 13– 2– 4– 3– is 123–– . See Salzer 1952/1962, Ex. 232, where the text (132) recognizes the latter incomplete neighbor as an ‘embellishing seventh.’ 228 For II–V progressions that merge into V7, see Ex. 6.18c. For manifestation of the same problem on a smaller scale, consider FC, Fig. 95, a8, concerning the Gavotte from Bach’s French Suite No. 6, 6–8. Schenker’s interpretation of the tetrachord 85– (=41– in the key of V) connects the4 and the 2, and merges the4 with the leading tone in the bass hus(t creating a vertical dissonance), but does not preserve the dissonant tension. In fact, the 4 perhaps resolves to3 (7 in the main key, m. 7 or 9), perhaps as the beginning of an Urlinie descent from the octave.

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4.3.3 Reaching-over The dissonant 4 as the seventh of V must resolve downwards. This is evident in the ordinary schemes – 543– and3 4– 3– . Nevertheless, the seventh,4 , can occasionally proceed in ascent, in the melodic patterns 34– 5– or, still more rarely, 54– 5– . What makes the ascent possible is the technique of reaching-over: the seventh receives its resolution in an inner voice, but the upper line nevertheless ascends. Some of the schemes for reaching-over in FC include the ascending pattern 34– 5– (Fig. 41, Nos. a3–4, b3 and c. See Ex. 4.18a). Schenker avoids the harmonization of this 4 as 7V, in favor of VII (Fig. 41,a4)—which is nevertheless dissonant229—or consonant support. Fig. 41,a3 gives under the 4 the harmonic labels II–V (consonant preparation?), but the notes of V do not appear. Harmonizing the ascending with4 V7 should nevertheless be possible (Ex. 4.18b). Its omission seems to reveal the same bias against recognition of the seventh that motivated the problematic annotation ‘not’ attached to Fig. 32,5 (cf. §4.3.1).230 The power of the 34– 5– pattern derives from the feeling of inertial motion provided in a single direction. The 54––5 (Ex. 4.19a) is more problematic precisely due to the lack of such inertia. This situation might be perhaps understood as a technique analogous to interruption 54– //53–42––1– (Schenker forbids this form of interruption in FC, §106), but a simpler explanation would interpret it as a descent into an inner voice followed by reestablishment of 5 (Ex. 4.19b). The 54– –paradigm5 makes sense only when it is supported by design, by means of textural and formal articulation, and when the melodic structural tones are unambiguous. This happens in the retransition of Mozart’s Rondo K. 485 (Ex. 4.19c, based on Rothgeb and Galand).231 The problem of the unresolved seventh

229 For discussion of the legitimate status of VII in such cases, see §4.3.4, on unfolding. 230 I have found no analysis in FC that corresponds Ex. 4.18b. Schenker reads a unique deep middleground 34– 5– reaching-over pattern inthe development of Beethoven’s Piano Sonata Op. 10,1/I (Figs. 154,3; 154,7), in parallel octaves with the bass, and as counterpoint with the descent towards the interruption. The dissonant seventh is preserved under the 5, weakening the interruption (see above, §4.3.2.1). Salzer (1952/1962, Ex. 463) offers a different reading, based on an incomplete neighbor. Federhofer (1981, 104) compares both readings and decides in favor of Salzer. I prefer Schenker’s version, where the V7 in the high register at mm. 154–5 is given sufficient weight. 231 My reading is closer to that by Rothgeb, which appears in Jonas [1934] 1982, Ex. 231. The reading by Galand (1990, 99, reproduced 1995, 35, Ex. 5) shows more clearly the 54––5 configuration, but locates the 4 as a mere lead-in at m. 91. Cf.5 –45– also in theme of Mozart, Piano Sonata K. 280/III in Beach 1983a, 10.

98 Seventh Chords at the Deepest Structural Levels before interruption (see above, §4.3.2.1) is all the more complicated in the case of interruption from 5. Assuming reaching-over acrossinterruption stands at odds with the essence of interruption (Ex. 4.19c–d; in the latter, 4 at the end of the antecedent arrives from an inner voice).232

4.3.4 Unfolding Several models of unfolding (FC, Fig. 43) relate to the interval of the diminished fifth between 4 and 7 below it as a means to prolong 4the as a prefix (possibly an appoggiatura) (Fig. 43d,1–2, shown in Ex. 4.20a) or a complete upper neighbor (Fig. 43e, my Ex. 4.20b).233 FC considers unfolding of a neighbor tone as belonging to the first level of the middleground (§142), although it should probably belong to the second. The same pattern could in fact be considered without a dissonant unfolding: the 4 might be said to be passing from an implied5 above the 7. The unfolding of the diminished fifth introduces a neighbor harmony (n.n.hrm.), which a harmonic concept would identify as VII. These schemes should also be possible in invertible counterpoint (Ex. 4.20c), where the unfolded dissonant interval is an augmented fourth.234 The same harmony also appears in FC as the product of reaching-over (Fig. 41,a1, shown in Ex. 4.20d; cf. also Fig. 41,a4, discussed above, at §4.3.3).

232 Interruption whose antecedent only descends to 4 is one possible view of the structure of Chopin, Prelude Op. 28,4. The antecedent in this case does reach 2, but without resolution of the4 . Schachter ([1995] 1999a, 166) reads the fore-phrase as a descent into 3 in an inner voice, but the clear division of the prelude is thus obscured. London and Rodman (1998, 118) propose that the prelude is based on interruption with a ‘gapped line’ (without a 3). Consider also interruption form from 5 with4 as a lead-in before the point of interruption. It is again Galand (1995, 40) who is ready to use this scheme, in Mozart, Serenade K. 525 [Eine kleine Nachtmusik]/IV, retransition (mm. 91–99). Reaching-over 45– seems to be a hallmark of thismovement, as it recurs also in the bridge (mm. 14–32) and before the coda (127–31), and reflects the appearance of lead-ins before themes which clearly begin with the fifth. For an impressive use of reaching-over in the foreground, see Ex. 7.46 (Mozart). 233 Related are also Fig. 43,d3–4. They are based on alternate unfoldings, a situation which contradicts well-formed hierarchy. See Lerdahl and Jackendoff 1983, 215, and principal discussion in N. Wagner 1995. 234 For a foreground application of the inverted form, see FC, Fig. 124,1b, analysis of Beethoven, Symphony No. 3/I, 23–27, last reduction. See further discussion of this analysis in fn. 74.

Seventh Chords at the Deepest Structural Levels 99

The schemes of unfoldings in FC show no bass. Actually, they are seldom realized without an added bass.235 Adding a normative bass arpeggiation below the diminished fifth unfolding introduces a V7 (Ex. 4.20e) which Schenker might not have accepted. In fact, his readiness to agree to the dissonant harmonization of the upper neighbor stands in contrast to his disapproval of its harmonization as V7 (as in Fig. 32,5). This difference in approach is not arbitrary: when the bass under 34– 3– moves in steps, it gains its own contrapuntal justification as a neighbor tone 87– 8– . By contrast, harmonization by 7V involves a leap in the bass, which cannot be justified on purely contrapuntal grounds.236 Very occasionally, the unfolding may connect two melodic levels of the bass itself. Such an extraordinary instance occurs in Mendelssohn’s Song without Words Op. 62,1; see Ex. 4.21 (after Cadwallader 1990, 8, Schachter [1995] 1999a, 167 and Cadwallader and Gagné 1998, 272).237 The middleground of the bass corresponds to the model from FC, Fig. 43,e2. The dissonant unfolding begins on a consonant IV, but reaches its most structural harmony, V#, which even preserves the dissonant tone 4 (all published graphs show only 6V). In this piece, the unfolding in the bass substitutes for a normal bass arpeggiation. This helps to create a single flow across formal units.

235 See realization without an added bass of the prefix model from FC, Fig. 43,d2 in Schenker’s reading of the introduction for Chopin, Etude Op. 10,12. (FGA and FC, Fig. 12a). The neighbor harmony here includes the tone of 5, which Schenker leaves out inthe deeper reduction. It should be identified in terms of conventional harmony as V6/5 (rather than VII). See also foreground unfoldings of a complete neighbor in Beethoven, Leonore Overture No. 3, 9–12, according to FC, Fig. 109,a2 (notice the ‘n.n.’ in both voices), and Schubert, theme of Impromptu D. 935 (Op. 142),3. In this case, the seventh cannot be said to be passing from a consonant implied tone, since it appears literally in an inner voice before the upper voice unfolds to the higher-register seventh. Samarotto (2001, 266) shows the unfolding most clearly, but omits the inner-voice seventh. 236 In his reading of Chopin’s Etude Op. 10,8, mm. 40–55, Schenker shows the leading-tone diminished fifth in a vertical form at the first level of middleground, below a complete neighbor (the model of FC, Fig. 43,e1). The second level unfolds this dissonance (see also FC, Fig. 7b), and labels the unfolded harmony as V7. The initiation point of the unfolding is harmonized, however, as a consonant IIIƒ, and the final V7 is understood as unfolding from a passing 4/3. I would rather hear I–(IIIƒ)–V–I arpeggiation (cf. Neumeyer and Tepping 1992, 10, Ex. 1.8). For surface tritone unfoldings, see also Ex. 7.33c (Brahms, after FC, Fig. 87,1a). 237 In Cadwallader and Gagné 1998, 267 the unfolding includes a misprint (diagonal line from G rather than C on m. 18). Cf. ibid., 272.

100 Seventh Chords at the Deepest Structural Levels

4.4 Structural Dissonances and Chromaticism

Normally, chromatic elements are insertions that do not affect the structural meaning. For example, the priority of V7 over its so-called consonant preparation in the segment 54––3FC ( , Fig. 19a) obtains also when chromatic chords are inserted into the same structure (FC, Fig. 132,8, not shown here). Nevertheless, chromaticism may introduce new forms of dissonance at the deepest levels themselves, and inserted chromatic chords may be embedded still rather deep in the structure.

4.4.1 Structural Dissonances as the Product of Mixture The deep middleground often includes ß2. Normatively, anyß2 is either preceded by 2 (as in the end of Chopin’s Nocturne Op. 9,1) or, more often, rectified by it (most usually by the progression ßII–V. See FC, §194). However, if the second melodic degree appears in a lowered variant only, as V7/ß5 (also without the seventh), possibly in the progression ßII–V7/ß5 (Ex. 4.22a), the resulting structural V is here diminished! This form can be diatonic in the Phrygian mode, or a raised leading tone in an inner voice can force it to sound in (harmonic) minor (Ex. 4.22b). The possibility of a Phrygian Ursatz can be attacked on the ground that even in the era of the ecclesiastical modes, the use of the Phrygian included anomalies in order to avoid the diminished fifth over its V. Accordingly, Burns (1995, 39–60) proposes alternative Ursatz models for Bach’s modal chorales, where the Phrygian model substitutes a subdominant model for the normal dominant model.238 As a possible theoretical construct, however, I would not rule out the Phrygian Ursatz. I have found realization of the structural ß2 at the foreground only. In Chopin’s Nocturne Op. 27,1, m. 17 (Ex. 4.22c), the cadential progression I–ßII6– V7/ß5–I creates a tritone above the local bass divider; in this case, the seventh is

238 Puffett (1992, 191), too, attacks the Phrygian Ursatz: ‘[I]n the Phrygian mode . . . any triad on the dominant would have to be a diminished one, which in the context of Schenkerian analysis amounts to a contradiction in terms.’ Applying an analogous Ursatz to the Locrian mode would create an even more acute contradiction: when the tonic itself is diminished, its genuine bass divider should arpeggiate a tritone, and the vertical chord does not express the first overtones. A possible diminished fifth bass divider occurs in Chopin’s Etude Op. 25,3, which is however in major; Salzer (1973) reads a perfect-fifth bass divider, and relegates the ƒIV to a lower level.

Seventh Chords at the Deepest Structural Levels 101 present too. The ß2 plays a predominant role throughout the outer sections of the nocturne. Even the final Urlinie (mm. 89–93) includes the 2 only in its lowered form, but there it is complicated by the lack of any support.239 It seems that immediate descents may occasionally occur with a tritone above V, and even occupy the Urlinie itself (even if diatonic 2 is stated elsewhere in the piece). Prolongations of such structural tritonal dominants seem unusual—but in principle possible.240 The relevance to seventh chords is mostly indirect through the challenge to the prohibition of structural dissonances.241

4.4.2 Conflicts between the Priorities of Consonance and of the Diatonic System Schenkerian analysis is indebted both to strict counterpoint, which determines hierarchical priority of consonance over dissonance, and to the system of scale degrees (Stufen), which is based on the diatonic system.242 Although chromatic elements do penetrate the deepest structural levels (Brown 1986; Brown, Dempster and Headlam 1997), the diatonic variants are nevertheless more likely to gain deeper status than their chromatic counterparts. As is common knowledge, the requirements of diatonicism and consonant quality do not always match: II in minor and VII in both major and minor are diatonic scale degrees, but nevertheless dissonant; chromatic chords may be consonant, and even provide consonant support for passing chromatic tones. The most important case is that of

239 Laufer (1996, 254, Exx. 9.107–8) asserts that ‘[b]ackground would show V2 however,’ i.e., supported and diatonic. He seems to assume that the background remains unaffected by the anomalies of the actual piece. I do not share this assumption. In m. 13, ß2 appears directly over V7/ß5. The V is first heard without a fifth, so it is impossible to prove that the implied fifth (2) at that moment should not be diatonic. 240 A descending non-rectified ß2 may also be counterpointed bya neighbor motion in the bass. The emerging harmony is VII ß3, possibly in the progression ßII–VII ß3. See Schubert, Piano Sonata D.959/I, coda, 350–3 (ßII5/3–VII6/3/ß1 in minor), according to Aldwell and Schachter 1978/1989, 496, Ex. 29–35 (removed in 2003 edition). This is a foreground case, occurring after the structural 1 had already arrived. 241 Other background dissonant mixtures appear only in radical modifications of the Ursatz. For example, Jackson (1995, 12. Ex. 2c) suggests a hypothetical voice exchange of the augmented second ƒ43– (in minor) within theUrsatz . 242 FC only gives the notion of scale degrees a limited place (§276–83), especially in comparison to Harmony. As surveyed in §3.2, the power of consonance gradually achieved the status of a single source of hierarchy in Schenker’s thought. However, in the conflicts discussed in the present paragraph, dissonant diatonic chords are more structural than consonant chromatic chords.

102 Seventh Chords at the Deepest Structural Levels

ßII. This chord has particular significance in minor, since in this mode it eliminates the dissonant quality of the diatonic II (Harmony, §50), and thus enables tonicization (ibid., §145); hierarchical reduction, however, would normally diatonicize the 2 (§4.4.1). More directly related to seventh chords (especially V7) is the hierarchy between variants of VII. In the progression VII ƒ5/ƒ3–5/3 (Ex. 4.23a), the diatonic dissonant variant gains priority over the chromatic consonant one. This situation is shown without hierarchy in FC, Example 2 for Fig. 111a (from Chopin, Bolero, mm. 155–72 [20–37 of the Risoluto]; cf. Ex. 4.23b). FC, Fig. 113,1b shows the goal of the same passage as the more structural event, but there it appears as V7 (with added root below the diatonic VII, in accordance to the scheme in Fig. 111a [cf. §6.3.1]). In fact the V7 is inverted (#), a feature that intensifies its affinity to VII. The harmonic power of the V reinforces the goal chord, but the priority of the dissonant variant also obtains without such an added root, due to its diatonicism.

4.4.3 Structural Dissonances in the Later Middleground: Secondary Dominant Seventh Chords The act of tonicization in the middleground normally involves secondary dominants, which often appear as seventh chords. The sevenths of those chords may serve as either suspensions, upper neighbors or descending passing tones from either 35, or8 of the original chord (Ex. 4.24). Each size of a harmonic progression in a given direction creates a different melodic context for the secondary seventh. The seventh of the potential secondary V7 is always 4 in relation to the goal, but its location in the original key is different in every case. My example demonstrates all the progressions starting from the tonic, a situation which is likely to appear in the deep middleground. In principle, the progressions may be shifted to any scale degree. For example, the progression V–V7/VI–VI behaves similarly to I–V7/II–II. Some exceptions occur, however: (a). When the goal is the tonic, the V7 is not a secondary dominant (my example excludes these configurations). The primary V7 gains priority over the initial chord of the progression, and thus modifies the hierarchy that obtains in the

Seventh Chords at the Deepest Structural Levels 103

other transpositions. For example, the hierarchy in the progression IV–V7–I differs from that in I–V7/V–V.243 (b). Since dissonances cannot normally be tonicized, VII, and in minor also II, may serve as goals in altered forms only. Progressions that start with these cannot function as local modulations. (c). The seventh as a descending passing tone from the octave is the only situation where the seventh lacks independence (especially in major) because no change of harmony is involved. (d). The chromatic details change with each relocation in the scale. Chromatic inflections may ruin the sense of suspension, and replace it by a chromatic passing tone (compare moving up a whole tone or only a semitone). Some secondary V7s are exploited fairly frequently, even at deep levels, while others seem quite rare. This can be explained by differences in the potential to integrate in the structure. The following cases deserve special attention: (a). In tonicizations of III, which are especially common in minor, the employment of the seventh in the secondary dominant (V7/III) offers the advantage of smooth voice leading, which is lacking if V/III appears as a triad (cf. §6.1.1). (b). The seventh of V7/V as suspension from the octave may account for the emergence of octave lines. It seems an important device in the limited repertoire of pieces with the Urlinie from 8244. The actual situation in any particular piece can alter the voice-leading contexts of secondary seventh chords.245 The foreground is capable of including all the proposed schemes, even those which the deeper levels cannot

243 This difference in hierarchy may create artful changes of meaning when the design is apparently symmetrical. Such situations are illuminated by Laskowsky 1980 (in response to another view in Gauldin 1979). Morgan (1998) seems less sensitive for such changes in his study of symmetrical form, especially concerning ‘the transpositional period’ (pp. 28–45). 244 See for example Bach, French Suite No. 6, Allemande, esp. mm. 5–7 (FC, background in Fig. 76,4; foreground of the relevant portion in Fig. 123,5). In Renwick 1995a, 55, Paradigm 6 for fugue subjects, where V/V appears as harmonization of 8. For this model in bridges of sonata form, see §7.10.1.2.2 (a). 245 See Haydn, Piano Sonata Hob. XVI:49/I, development. The progression V–V7/VI–VI is not based upon suspension of the fifth of V. Rather, according to Schenker (FGA; FC, Fig. 62,1 and Fig. 114,5b), the structural melodic line is the ascent in the inner register. At the foreground, the seventh (m. 74) is a boundary tone of SFM without vertical origin (cf. §1.1.2.2.1.2, category c). The graph in FC, Fig. 103,5a, by contrast, reads a change into consonance in m. 74.

104 Seventh Chords at the Deepest Structural Levels accommodate conveniently. The melodic contexts shown for sevenths at the deepest levels in general remain significant also at lower levels, however, especially in transferences of the forms of the Ursatz.246

246FC (Fig. 38c) shows schematically V7/III and V7/V (in major) with the seventh in an inner voice below an initial ascent. The indication of intervals beneath the graph omits the sevenths, and shows only the consonances between the outer voices (as elimination of parallel octaves).

5. GENERAL OVERVIEW OF PROLONGATION OF SEVENTH CHORDS

5.1 The Contrapuntal Function of the Seventh

Normative Schenkerian theory regards the seventh of seventh chords as being approached from the octave (8–7). In fact, this claim combines two distinct concepts (Ex. 5.1): (a) The seventh is a descending passing tone from the (possibly elided) octave on the same root, as in V8–7; (b) The tone of the seventh is prepared as an octave on another root, as in IV8–V7. I have already commented on the fallacy of this preparation (§4.3.1).247 In the latter model, the octave may be replaced by any other consonance, e.g., II10–V7 (Ex. 5.1c).248 To my knowledge, the gap between the two concepts of 8–7 has not so far been recognized in a systematic manner. As a rule, the dissonant tone in the interval of the seventh is the upper one, except in the rare case of apparent seventh chords, where the lower tone (the root of the seventh chord) is the dissonant element.249 The norm also assumes ‘the seventh-constraint’ (FC, §73), i.e., the contrapuntal necessity of the seventh to resolve downward, because it ‘originates in the octave’ (§178). This necessity is

247 The latter idea is de-emphasized in the later generation of Schenkerian literature, but is common in Schenker’s own writings, as well as in those by Jonas and Oster. 248 II10–V7 appears in FC, Fig. 62,9 (my Ex. 6.12b). The commentary on FC, Fig. 115,1a (Bach, WTC I, Prelude in C major) observes that in m. 23 only f (4) can prepare the seventh of the next measure. That seventh is not a suspension but rather belongs to the structural V7; the preparation is harmonized as II4/3/ß1 according to Schenker’s reading of the diminution. 249 See discussion of apparent seventh chords at the end of §1.2; and prolongations thereof, Exx. 9.6,b–c, 9.9b and 10.24b.

106 General Overview of Prolongation of Seventh Chords not eliminated when the seventh is prolonged, but rather delayed until after the prolongation.250 These norms are based solely on the seventh that is created in upper-voice counterpoint. Tonal practice totally ignores the forms that emerge in lower counterpoint (Ex. 5.2), where the seventh either descends from the sixth (cf. Peles 1997, 77, Ex. 1), or ascends from the octave. The avoidance of these forms reflects the penetration of harmonic thinking into the notion of the seventh. The tone of the seventh is perceived as the dissonant component of a seventh chord (cf. §1.2).251 Occasionally, the seventh does resolve upwards, especially as a result of reaching-over, combined with a change of harmony (refer back to Exx. 4.18–19). If it ascends to the octave without a change of harmony (Ex. 5.3), either the seventh is heard as passing, normally within the fourth-span 5–8, or the ensuing octave functions as an incomplete neighbor between the seventh and its normative resolution.

5.2 Comparative Investigation of Various Types of Seventh Chords

The classification of seventh chords involves two distinct aspects: the structure of the chord and its harmonic function, which is related to the scale degree it occupies. In the two most common types of seventh chords, a specific chord structure (major-minor and diminished seventh chord) is associated with one harmonic function (V7 and VII7 respectively) and vice versa, in both major and harmonic minor. With other types, however, these factors are more independent and defy simple organization. The various types of seventh chords differ in the frequency of their general use and of their prolongation, and in the potential width and variety of possible procedures for prolongation. The most common and developed prolongations of

250 Schachter (1996, 332) even states that ‘prolongations that incorporate sevenths can add the intensifying effect of immediate causality to the Urlinie’s downward drive.’ However, the example he is referring to—from the duet O Terra Addio from Verdi’s Aida—does not prolong the seventh, but is rather based on delayed resolution (cf. §2.3.4). 251 For realization of Ex. 5.2b, see Beethoven, String Quartet Op. 59,2/IV, 5–7 (Ex. 9.19b).

General Overview of Prolongation of Seventh Chords 107 seventh chords apply to dominant seventh chords. Diminished seventh chords also offer many opportunities, and most of the remaining prolongations relate to half- diminished or minor-minor seventh chords. The differences result, I would suggest, from three factors, none of which seems sufficient alone. (Among these factors, Schenker would apparently have objected at least to (b) and (c)): (a). Penetration into deep levels. As chapter 4 has demonstrated, V7 can take part in the deep structure in several formations. This criterion may explain the uniqueness of the V7, but not the differences between other seventh chords. For example, IV7 appears in some deep middleground schemes (FC, Fig. 16,2c and 16,3c) but is, nevertheless, rarely prolonged. By contrast, the often prolonged diminished seventh chords never penetrate into such deep levels. (b). Harmonic function. The most common, and most frequently prolonged seventh chord structures have a dominant function with its associated tension: major-minor (V7), and to a lesser extent the diminished seventh chord (VII7 in minor). Subdominant seventh chords are less often prolonged, while seventh chords on the tonic are rare (§9.4.2), and virtually never prolonged (with the possible exception of jazz music). This also means that seventh chords can hardly be tonicized. This is the true kernel in the argument that seventh chords cannot be prolonged. This criterion is also insufficient since the same scale degrees are usually occupied with different chord structures in major and [harmonic] minor (V7 is an exception), and some types of seventh chords have multiple harmonic potentials. This is true even in diatonic music, but is especially blatant where mixture is involved. (c). The type of seventh. Chords with a major seventh (i.e., augmented, major- major or minor-major seventh chords) are rarely prolonged. The major seventh poses two distinct problems that may account for the paucity of its prolongation: (a) The complementary minor second between the seventh and octave does not leave space for motion, and aggravates the problem of the step, which is both chordal and foreign to the chord (§2.2); (b) The sound of the major seventh is so noticeably harsh, that delaying its resolution highlights the dissonant character to a degree that is normally undesirable. However, the correlation between harshness and rarity does not always

108 General Overview of Prolongation of Seventh Chords

obtain: the diminished seventh chord is much more frequently prolonged than the far less harsh minor-minor seventh chord. Although presented here as separate factors, the intervallic structure of seventh chords and their harmonic function are interrelated, since the function is determined by the scale degree and the location relative to the tonic, but the choice of the tonic is dependent on the organization of the unequal intervals. The following table maps the relations between diatonic scale degrees and those seventh chord structures that are based on major and minor thirds.

Correlation between the Structure of Seventh Chords and their Scale Degree Location

Major Harmonic minor Natural minor Major-minor V V VII diminished VII half-diminished VII II II minor-minor II, III, VI IV (I, V,) IV Major-major I, IV VI III, VI minor-Major I Augmented (III)

5.3 Comparative Investigation of Prolongations of Seventh Chords

I usually refer to the subject of prolongations in terms of (seventh) chords, rather than tones or intervals (cf. §1.1.1.1): in tonal music, a complete harmony is normally implied even in thin textures, where a seventh is not accompanied by a full chord. Even passages that are apparently monophonic are embedded within fuller harmonies.252

252 For a prolongation of a dissonant dyad, see Ex. 2.9c; for a monophonic example, see Weber, Der Freischütz, 2nd Finale, Melodram. See also intentional decrease of texture in Chopin’s Waltz Op. 34,3 (Ex. 7.28c). Occasionally, graphs of the bass alone show dissonant lines, but these are not necessarily true unfoldings of tones of the same harmony. See for example the diminished fifth in FC, Fig. 158 (Bach, Italian Concerto /I), mm. 60–73.

General Overview of Prolongation of Seventh Chords 109

Only some procedures prolong the tone of the seventh itself, and as an interval within the prolongation, the seventh is active even less often. This classification is demonstrated in Ex. 5.4 with regard to voice exchanges between adjacent voices within dominant seventh chords.253 In a), the interval of the seventh is composed out as a melodic phenomenon. When the interval of the seventh is inverted (as in b), the active span is still dissonant, but now it is a second rather than a seventh. Even when the unfolded interval is consonant, the dissonant tone of the seventh may be prolonged, as in c): the active spans are smaller than the seventh, but the dissonant tone itself is active in the prolongation, as 3–7 (dissonant in some seventh chords) or 5–7. In d), neither the tone nor the interval of the seventh are properly prolonged, but the chord is prolonged (cf. Ex. 1.1), as is the interval of the seventh as a harmonic (but not melodic) entity. A similar distinction applies to neighbor motion (Ex. 5.5): some neighbors refer to the tone of the seventh itself, while others prolong other tones in the seventh chord simultaneously with a stationary seventh, which resembles a pedal point. Schenker is ill-disposed toward this latter type too: ‘a pedal point can appear on a fundamental, fifth or third of a sound, but never on its seventh’ (CP I, xxxi: an unusually early source). These observations usually obtain even if the seventh lies in an inner voice. Only at marginal cases, the sense of prolonging the seventh will be removed if the seventh lies in an inner voice (especially when the interval of the seventh is inferred from a surface that never includes it vertically; see Ex. 6.18c).

5.4 Criteria for Recognizing True Seventh Progressions

Normatively, seventh progressions are illusory progressions, which represent their complementary seconds by means of an indirect register transfer (FC, §206; see Ex. 1.5). Nevertheless, true seventh progressions do exist, and express prolongations of the seventh in all its senses, as a tone, an interval and a chord. The criteria for distinguishing true from illusory seventh progressions lie at the heart of the PD problem and of Schenker’s efforts in regard to this topic.

253 The same classification also applies to cases where the unfolded (or arpeggiated) motion lacks stepwise filling as a linear progression. Where only one voice moves (and no voice exchange takes place), it matters whether the seventh is located at the beginning or the end (see below §5.4).

110 General Overview of Prolongation of Seventh Chords

Schenker’s interest in the difference between ‘real seventh’ and ‘opened-up second’ is already evident in the 1912 monograph on Beethoven’s ninth symphony (cf. §3.2.3). In FC, the main discussion of true seventh progressions is contained in a special section on the seventh (§177, quoted above, §3.2.7), but it does not indicate how they can be recognized. Neither does the organization of the corollary examples (Fig. 62) supply any clue: it differentiates examples of ‘composing-out the seventh chord’ (nos. 1–4) from ‘arpeggiations as means of prolonging [Verwandlungen] the seventh chord’ (nos. 5–11). (Nos. 12–13 do not prolong or compose out the seventh in any structural sense). The best way to understand this distinction is that nos. 1–4 include full linear progressions rather than unfilled arpeggiations.254 Schenker’s only criterion in FC for recognizing true seventh progressions appears in §215, a very short paragraph on seventh progressions within a systematic discussion of individual linear progressions. True seventh progressions are unique in that they ‘emphasize their harmonic intervals [third and fifth of the chord], at least the third.’255 The suggested criterion is thus the inner segmentation of the seventh progressions. This idea is, I believe, erroneous, as the contrary cases prove: a composed out, inverted second may be divided into three thirds (recall Ex. 1.5a), and true harmonic intervals may be divided by tones that do not belong to the prolonged harmony, even when no dissonance is involved (Ex. 1.8b–c).256 What determines whether a linear progression is genuine are the deeper structural levels, not the manner in which it is prolonged. The segmentation into thirds seems to determine something else: it distinguishes a seventh (either true or

254 The graphs themselves generally correspond to this distinction, although in Fig. 62,10 the arpeggiation is partly filled. Arpeggiations are mentioned in §177 itself. §215, on seventh progressions, refers to Figs. 62,1–4 alone. The seventh chord in all the examples in Fig. 62 is V7, but the arguments should apply in principle to all seventh chords. 255 Schenker regards in this paragraph Figs. 62,1–4 as true seventh progressions. However, according to Oster, the seventh progressions in Figs. 62,1–2 are illusory (see below). The remark ‘at least the third’ implies that the fifth need not be emphasized. This stance is perhaps influenced by the actual example of Beethoven’s Eroica (Fig. 62,3), where this is the case (cf. §7.10.1.2.4). In FC §206, Schenker seems to reject this very same idea, when he says that ‘a succession of passing tones, even if it is subdivided, does not constitute a linear progression if its ultimate result is only the interval of a second above or below’ (my emphasis). 256 Cf. the proposed distinctions between several types of linear progressions, applied mainly to fifth progressions within V7 (§7.2.3).

General Overview of Prolongation of Seventh Chords 111 illusory) from a sixth that continues in the same direction. Ex. 5.6a–b compares these procedures in two opening themes by Mozart: Tamino’s aria Dies Bildniss from Die Zauberflöte opens with an unfolding of a sixth (after Forte and Gilbert 1982, Ex. 203; Everett 1991, Ex. 2), while in Symphony No. 40/I, emphasis on the thirds forces the listener to hear a boundary seventh (after Forte and Gilbert 1982, Ex. 198; Schenker, in MW II, 66, reads a less reasonable ninth).257 For the purpose of recognizing true seventh progressions, a much better criterion is offered by Oster, in a footnote to FC, §177: the direction of the motion.258 Oster observes that in ascending seventh progressions, as in Figs. 62,1 and 2, the tone of the seventh only appears at the end, and thus the progression expresses the motion 8–7 (Ex. 5.7a).259 By contrast, descending seventh progressions are genuine since the seventh appears in them as the initial tone (Ex. 5.7b), as in Figs. 62,3 and 4 (the development sections of Beethoven’s Symphony No. 3/I and Piano Sonata Op. 81a/I respectively; my Exx. 7.105a, 7.106a). Oster bases his observation on an unpublished note by Schenker, dating from the late 1920s, which contrasts the developments that were later illustrated as Fig. 62,1

257 The theme of the symphony is further complicated by the delay of V. The dilemma between a sixth plus continuation and an illusory seventh is part of a larger problem, namely how to determine the boundaries of linear progressions without changes in melodic direction before or after them. See also: (1) FC, Fig. 42,2 (Chorale St. Anthony, mm. 11–15)—Schenker includes contradictory indications showing both an ascending (illusory) seventh progression and a sixth followed by a second in the same direction. See Schenker 1937, 138–9 and FC, Fig. 42,2, as well as discussions of the contradiction: N. Wagner 1995, 154–9 (who reproduces Schenker’s original graphs) and Jackson 1999a, 241–9 (who reproduces additional archival material). Other graphs (discussed by Wagner) appear in Laufer 1981, 166, Ex. 5 and Forte and Gilbert 1982, 160, Ex. 148.; (2) Jonas ([1934] 1982), Ex. 162 (Mozart, Piano Sonata K. 310/I, 70–73, inner voice)—the seventh is rejected in favor of a sixth because of a voice exchange; Schubert, Ländler No. 2 in D. 145 (Op. 18), mm. 1–3—Salzer (1952/1962, Ex. 223) reads a seventh, but a sixth plus continuation is more correct. 258 Schachter ([1981] 1999a, 202) and Clark (1982, 251) concur. Oster’s footnote also raises the idea of consonant preparation of the seventh, which I have rejected above: ‘the seventh would first have to appear as a consonance.’ The word ‘first’ can imply both conceptual and chronological priority. 259 Fig. 62,1 shows the development of Haydn’s Piano Sonata Hob. XVI:49/I. The slur in the soprano from m. 117, which seems to indicate true prolongation of the seventh (notice the inner- voice Aß), is misleading. FGA has a more accurate version; Fig. 62,2 shows Beethoven, Leonore Overture No. 2, 4–31. Closer to the surface, see also illusory seventh progressions in Mozart’s Minuet K. 94, 9–12 (hinted at by Forte and Gilbert 1982 sup., 111).

112 General Overview of Prolongation of Seventh Chords and 62,4, calling the latter ‘a harmonic sin,’ although in FC Schenker dropped this comment.260

5.4.1 Further Investigation of Oster’s Criterion Oster’s principle that the seventh is only prolonged when it initiates the prolonging motion can also be applied to other prolongations of seventh chords (Ex. 5.8): unfilled arpeggiations and unfoldings, as well as linear progressions of shorter spans within seventh chords.261 Motion from the tone of the seventh includes the seventh in the prolonged harmony, while motion to the seventh should only count as space-filling motion, and does not properly prolong the seventh. Closer exploration of Oster’s rule reveals that the idea that melodic direction distinguishes between true and illusory seventh progressions is only valid in restricted circumstances. It is violated by both descending illusory seventh progressions and ascending true seventh progressions, both of which are possible. Descending seventh progressions that are nevertheless illusory are of two types: (a). Major seventh progressions. In seventh progressions that descend from a major seventh, the upper voice above the root that serves as the goal of the progression resolves the seventh into an implied octave (Ex. 5.9). In this procedure the horizontal interval of the seventh expresses a second that ascends from the tone of the seventh to the octave above it. The initial seventh fades out without proper resolution, as is also the case when unprolonged I7–8 in harmonic minor appears unprolonged. (b). Transitive descending seventh progressions where the harmony changes with the arrival at the lowest tone. Such seventh progressions are illusory even if their initial tone is the seventh of its chord (Ex. 5.10a, latter progression). Usually, the initial tone of such progressions does not even form the tone of the seventh of any vertical harmony. For example, in the theme of Beethoven’s Symphony No. 7/III (Ex. 5.10b), descending seventh

260 For similar notes on Beethoven’s Eroica in MW III, see above, §3.2.6. 261 In unfilled arpeggiations, Schenker’s criterion of segmentation into thirds is important, since in its absence the very sense of arpeggiation is lost.

General Overview of Prolongation of Seventh Chords 113

progressions (which are even motivically divided into thirds) clearly represent ascending seconds within an initial ascent.262 Less clear is the status of some other descending seventh progressions (and corollary cases), shown in Ex. 5.11. What happens if a descent from the seventh is embedded within a complete octave line? Normally, such a seventh would count as a mere passing tone from the octave,263 but such seventh progressions can nevertheless acquire independent status, most importantly, if the harmony changes on the seventh. The most usual realization of this is when I5 is followed by a seventh-descent from V4 (Ex. 5.11c). This configuration does not express an octave line, just as I3 followed by a fifth-descent from 2V does not express a sixth-line (Ex. 5.11d, after Forte and Gilbert 1982 sup., 75; Cf. also Ex. 4.8). Occasionally, a seventh within an octave descent can function as a local primary tone even without a change of harmony. Such a seventh requires a special justification for it to be perceived as more than a mere passing tone (cf. §6.1.1). Two particular factors contribute to the reinforcement of the seventh, although neither is sufficient to make the seventh function as a local primary tone (Ex. 5.12): (a) The occurrence of the seventh in a higher register than the preceding octave. The high octave is still implied before the seventh, but its presence is weaker; (b) The actual presence of the seventh at the final boundary of the harmony. Even when this condition is fulfilled, it might be argued that the octave is structurally replaced by the seventh no earlier than at this final boundary. Both devices are combined in the exposition bridge of Beethoven’s Piano Sonata Op. 106/I (Ex. 5.13). Does this passage express a fourth-descent from the octave or a third-descent from the seventh? The prolonged harmony, V/VI, starts as a consonance (m. 37); the seventh is added in an inner voice (m. 41), and

262 Cf. also the theme of Mozart, Symphony No. 40/I in Ex. 5.6b. Outside monotonal environment, transitive seventh progressions can even appear as Urlinie-substitutions. Krebs (1981, 4–5) shows such a line from 5 of C major to 1 of A minor in Schubert’s Der Alpenjäger, D. 588. Oster was, in fact, aware of the problem of merely connective arpeggiations that apparently horizontalize a seventh chord, for it was he who blamed Travis for attributing harmonic significance to such transitive sevenths (Oster 1960 against Travis 1959. Cf. §§3.3.1.1; 3.4). Transitive seventh progressions in ascent are, of course, illusory progressions too. This category of seventh progressions may encompass a major seventh, e.g., from the root of I to the third of V in Mendelssohn, Song without Words Op. 30,6, mm. 21–29 (after TW 10). See also below Ex. 5.15c. 263 This problem is unlikely to emerge with diminished seventh chords, since there the second above the tone of the seventh is augmented. Cf. §8.0.

114 General Overview of Prolongation of Seventh Chords arrives at the soprano through reaching-over, at a higher register than the original octave tone. This seventh is heard as a primary tone for a richly enlarged third progression. When the first third progression is accomplished (m. 55), the left hand reaches over the right hand and plays the seventh as the uppermost tone. Thereafter the prolongation continues with another 7–5 descent (complicated by texture), but this time it is better interpreted as the continuation of the descent from the octave. Thus, the seventh serves in this context as a passing tone within a descending tetrachord; the former descent to the fifth prolongs this seventh as motion into an inner voice, while the latter does not prolong the seventh.264 Even without the aid of the suggested factors, the seventh can acquire priority if the specific design gives it sufficient emphasis, e.g., by stretching the seventh before the more essential prolongation takes place.265 In most instances of a problematic seventh that is embedded within an octave line, the step precedes the seventh (8–7–1). Occasionally, analyses show octave lines in the bass that consist of a seventh followed by a step (8–2–1, or 8–6–4–2– 1) in the harmonic progression I–VI–IV–II–(V)–I. The seventh in this paradigm is connective and does not represent a vertical seventh chord; normally, the weight of V will override the apparent linear octave.266 Another violation of Oster’s rule is caused by true ascending seventh progressions. Ascending seventh progressions are genuine when the tone of the seventh is already established in another voice at the beginning of the seventh progression (Ex. 5.14a), or before the progression commences in the same or in a preceding harmony (Ex. 5.14b–c). Here, differences emerge between various seventh chords. For example, II7 is especially likely to appear after its seventh (1) has already been established within either I, VI or IV.

264 In the middleground graph by Kamien (1976, Ex. 1), the seventh governs from m. 45. The Roman numerals analysis by Caplin (1987, Ex. 6) ignores the seventh altogether. 265 Cf. my discussion of Ex. 7.104b (Haydn, Symphony No. 104/II), fn. 384 (concerning Haydn’s String Quartet Op. 64,3/IV); and fn. 274 (concerning FC, Fig. 100,5). 266 See FC, Fig. 90 (Beethoven, Piano Sonata Op. 109/I, 1–4) and Travis 1959, Exx. 10-14, the latter criticized by Oster (1960, 97). Jonas ([1934] 1982) shows such expanded sevenths in Mozart, String Quartet K. 421/II, 31–50 (p. 93, Ex. 143) as a representation of neighbor motion, and in Bach, Violin Partita No. 3, Prelude (p. 79, x. 119, after MW I, 42–3), as embedded within an octave-Urlinie.

General Overview of Prolongation of Seventh Chords 115

5.4.2 Intermediate Situations between True and Illusory Seventh Progressions 5.4.2.1 Paradigmatic ascending seventh progressions as semi-genuine seventh progressions. The ascending seventh progressions that Oster assumes to be paradigmatic illusory seventh progressions are in fact less illusory than some other seventh progressions; they might be called semi-genuine seventh progressions. Passages such as those shown in FC, Figs. 62,1–2 involve two distinct senses of the seventh: (a) A melodic seventh represents a step toward a passing tone. This feature accounts for the illusory nature of the progressions; (b) At the goal, a seventh is achieved above the root. The latter sense would be avoided if the descending step that is opened into a seventh aims at a passing tone other than the seventh, i.e., 5–4 or 10–9 (Ex. 5.15a–b). Those other formations are much less likely than the 8–7. The very ability of 8–7 seventh progressions (notably on V) to have the same harmony on their initial and their goal tones gives the progressions a harmonic meaning that is lacking in other seventh progressions. Yet another possibility arises if the seventh represents not the step from the initial consonance to the passing tone, but rather the step from the passing tone to its goal. Such a rare case takes place in Beethoven’s Symphony No. 4/I (Ex. 5.15c).267 This seventh is subdivided into thirds, but—in contrast to division into thirds of an 8–7 illusory seventh progression—these thirds do not correspond to tones of the underlying harmony. This lead-in sounds so much less harmonic than the paradigmatic illusory seventh progressions, that in comparison, those progressions are less illusory. 5.4.2.2 Introducing the seventh at the middle of the prolongation. The idea that prolongations of the seventh are true if the seventh appears at their beginning, but not if it only arrives at their end, needs refinement when the tone of the seventh appears in the middle of the prolongation. This can happen on two occasions (Ex. 5.16): (a) Arpeggiations or linear progressions in open position and/or scattered contour (upper staff of the example); (b) In close position: inverted arpeggiations

267 The seventh progression takes place in the flute. The violins express the g-fƒ progression directly. This progression also involves a change of harmony. Thus it is a transitive ascending seventh progression (cf. fn. 262).

116 General Overview of Prolongation of Seventh Chords or linear progressions of seventh chords within sixth-spans (lower staff). These inverted arpeggiations or linear progressions may also express seventh chords in root position, even if they occur in the bass,268 or they may take place in the upper voice. The sixth-span contains two thirds and one second, thus giving rise to the familiar problem of two adjacent tones in the same harmony (cf. §2.2, §7.2.2; and Rothstein 1990a, 99).269 In either situation, three possibilities are open to the seventh: (a) The seventh might be a mere passing tone without becoming part of the harmony (Ex. 5.16a); (b) The seventh can become a part of the harmony from its point of initiation (Ex. 5.16b); (c) Arguably, the seventh can be conceptually present even before its actual appearance (Ex. 5.16c). This would be the case when the tone of the seventh is already present in the previous harmony (at least if it is stated at the same or a higher register). In other cases it is usually more difficult to decide between the alternatives. As with the general case, factors that encourage a reading of the seventh as part of the chord are the presence of the seventh in a higher register than the octave, literal retention of the seventh, and special design emphasis on the seventh.

5.4.3 Rhythmic Normalization of Seventh Progressions In rhythmic normalization, as presented by Rothstein (1981, 87–100, esp. p. 96; 1990, 98–101, after MW II, 4 and FC §121), the normalized initiation points of both the initial tone and the goal tone of an arpeggiation or a linear progression occur together; in the upper voice, the hierarchical primary tone is normally the initial tone in descending progressions and the goal tone in ascending progressions. Attempting to apply Rothstein’s rule to seventh progressions demonstrates precisely the difference between genuine and illusory seventh progressions. Illusory seventh progressions such as that in Ex. 5.7a violate the rule: the seventh does not belong to the harmony, and thus does not occur conceptually since the

268 See discussion of prolongation of an apparently inverted V7 (§7.7), and, concerning FC, Fig. 106,3a (from Haydn, Symphony No. 104/II), fn. 442. 269 The seventh may also appear as the initial tone of an arpeggiation of V2 in ascent, or of 6/5 or 4/3 in scattered contour. All the possibilities latent in open position apply also to inversions of seventh chords.

General Overview of Prolongation of Seventh Chords 117 initiation point of the octave from which it is passing; by contrast, genuine seventh progressions such as that in Ex. 5.7b obey the rule, and can even accommodate normalization of the seventh backward (in the cases shown in Ex. 5.14c and 5.16c). It would be an over-simplification to stipulate that descending seventh progressions should be rhythmically normalized, while ascending seventh progressions should not. The actual normalization should follow the more detailed observations shown above. For example, transitive seventh progressions conform to Rothstein’s category of ‘connective’ motion (cf. §1.1.2.2.1.2).

6. PROCEDURES FOR PROVIDING V7 WITH STRUCTURAL MEANING WITHOUT FULL CIRCULAR PROLONGATION

The major-minor seventh chord, which normally functions as V7, is the most common type of seventh chord, and the one that is most frequently and substantially prolonged. As suggested in §5.2, this status derives from its ability to penetrate deep levels, its dominant function, the contrapuntal possibilities latent in the minor seventh, and the relatively soft sonority. In contrast to other seventh chords, V7 can acquire a unique independence. This is best revealed when V7 is approached from a 7–6 series (Ex. 6.1a, after Salzer 1952/1962, Ex. 364b). In such a series, the sevenths are non-harmonic tones, but once V7 arrives, the seventh may be heard as a chordal tone (‘an essential dissonance’), as in Ex. 6.1b, from Haydn’s Piano Sonata Hob. XVI:26/I.270 The drive of the V–I progression is so great that even if the 7–6 sequence continues after the V7, the seventh of V7 is not heard as another

270 Normally, the independent seventh is only resolved with the rest of the chord. In the Haydn excerpt, it fades out into a consonant V (m. 15) and the harmony is only finally resolved at m. 25 (or perhaps m. 27). One of the suspending sevenths produces a major-minor seventh chord, which, however, does not function as a V7. Caplin (1987, 229) quotes the score and provides instructive contrapuntal designations below it. Cf. also Bach, Italian Concerto/II, 8–11 and Handel, Keyboard Fugue No. 6, mm. 6–7 (in FC, Fig. 53,2). In the latter, the seventh of V7 does descend as a 7–6 suspension, but true resolution arrives only at the end of the measure. Eybl (1995, 58) shows a similar pattern as the hypothetical diatonic basis of Chopin, Prelude Op. 28,4, mm. 1–12.

120 Providing V7 with Structural Meaning suspension, but rather as a structural tone before an anticipation (Ex. 6.1c [Brahms]).271

6.1 Analogies between the Structural V7 and Strict Counterpoint

Occasionally, V7 occupies positions that strict counterpoint reserves for consonances. Thus, at a certain level, the tone of the seventh serves as part of the harmony, and is subject to prolongation (albeit not full prolongation) by the tones that relate to it (in terms of strict counterpoint). Cases occur that are analogous to second or fourth species, both with a stationary seventh or with the seventh in the active voice. By analogy with the strong beat in second species (Ex. 6.2), V7 can serve as a point of departure for passing or neighbor motion The former possibility is demonstrated in an example from Beethoven’s Symphony No. 5/IV (in the form 7/5–7/ƒ5). By analogy with fourth species, V7 can serve as either a preparation for or resolution of suspensions. V7 as preparation for a suspension resembles rhythmically the situation of the consonant ¢− as preparation to a harsher ¢¦ suspension (cf. §2.1.1 for Schenker’s insistence that that ¢− remains dissonant) (cf. Ex. 6.3a). The seventh of this V7 may itself be passing; this situation might be called the suspended passing tone (Ex. 6.3b; Cf. Piston 1947, 53). An actual example is suggested by the Roman numerals in FC, Fig. 63,1 (reading of Beethoven, Symphony No. 3/III, 236–8) (Ex. 6.3c). This figure shows a V2 (passing from a consonant V, which is not shown) as preparation for a harsher dissonance. In fact, the harsher dissonance never actually appears, but is a conceptual construct assuming an elided bass (aß at m. 237). This procedure stands in stark contrast to the norms of elision, where the elided tone is a consonance, which is assumed precisely in order to provide a normative point of departure for dissonances. Resolution of suspension is a fruitful procedure for creating V7 with hierarchical priority. Among the suspensions under a stationary tone of the seventh

271 This is a full V7 prolongation. See below, §7.2.8. For the wider context, see the middleground graph by Laufer (1992, Ex. 2-4). When a V7 sonority does not move to I, it is indeed heard as only another suspension. Burstein (1983, 22, Ex. 3c) has shown this in Mozart, Piano Sonata K. 283/I, initial sonority of m. 112.

Providing V7 with Structural Meaning 121

(or, in open position, possibly above it), the most common are 4–3 suspensions, as in the main idea of Beethoven’s Bagatelle Op. 33,7 (Ex. 6.4a). 6–5 suspensions under a stationary seventh are shown schematically by C. P. E. Bach ([1753–1762] 1949, 284) (Ex. 6.4b), either alone or in combination with 4–3. The 6–5 suspension is consonant with the bass, but creates a dissonant lower 2–3 with the seventh.272 Suspending the root itself only introduces the interval of the seventh at the point of resolution. The suspension takes the form of a 6–7 lower counterpoint, with the roles of consonance and dissonance reversed! Such an unusual series of 6–7 suspensions occurs in Mozart’s Adagio K. 540 (Ex. 6.4c). This passage sounds like a chromatic distortion of a diatonic series of seventh chords, where 6–7 suspensions occur in some voices; however, the segmentation into two pairs of chords, each of which functions like II$–V7, highlights the 6–7 suspensions. Here the suspension itself is a conventional seventh chord, which is still subordinate to the V7. I shall discuss this phenomenon below as subordination to V7 (§6.3). Delaying the tone of the seventh itself can occur as either a 6–7 or 8–7 suspension over a stationary bass. This is the type discussed in CP I (280–1) as ‘suspension to seventh chords.’ The ascending appoggiatura 6–7 (Ex. 6.5a) is particularly remote from strict counterpoint. Aldwell and Schachter (1978/2003, 556) show it harmonized as V6/ƒ4/ƒ2–7/5/3 under the title ‘embellishing V and V7’ (Ex. 6.5b, their Ex. 30-23a–b).273

6.1.1 V8–7 with Priority of the Seventh The structural priority of the seventh over a preceding octave reverses the normative interpretation of V8–7 as a structural octave followed by a passing

272 Cf. discussion of ‘Suspension into seventh chords’ in Aldwell and Schachter 1978/2003, 355–6. For 7/4–7/3 suspensions see also Chopin, Mazurka Op. 17,4, m. 7; Beethoven, Piano Sonata Op. 109/III, 42 (m. 10 of variation 2), in combination with reaching-over. The latter case is shown in FC, Fig. 101,3, albeit without the bass. Aldwell and Schachter demonstrate a 7/6–7/5 suspension from Josef Strauss, Dynamiden, mm. 39–40. The 6–5 in this case takes place in a higher register, i.e., 13–12. 273 Aldwell and Schachter refer to Beethoven, Violin Concerto/I, 65–66, where the pattern appears in D major. This is a harmonized version of the unharmonized appoggiatura V7/ƒ4–7/5 at mm. 10– 11 (Kamien 1974, fn. 2). As a result of immediate repetition (mm. 67–68), the appoggiatura diminished seventh chord becomes a complete neighbor (I discuss such neighbors below, §7.3.2.2).

122 Providing V7 with Structural Meaning seventh. Schenker’s student Felix-Everhard von Cube highlighted this problem in a 1933 letter to Schenker (published and discussed in Drabkin 1996b). Discussing graphs of Beethoven’s Piano Sonata Op. 26/I, 17–26, which were later published as FC, Fig. 85 (transcribed by Drabkin, p. 162, not shown), Cube blames Schenker for violating normative structural hierarchy. He comments on the example cited as Drabkin’s Ex. 15: ‘In my view this is not possible! If the neighbor-note is in reality nothing more than a neighbor note, then the original picture would appear thus [Drabkin’s Ex. 16]. It goes against all experience, however, to have a self-sufficient seventh in the Ursatz [actually first middleground]; the 7 is a passing note and must remain so. And so must your 8–7! Thus if the 8 is present, it must be there from the beginning!!!’ (Quoted in Drabkin 1996b, 164). In Op. 26 itself, Cube’s demand to cancel the priority of the seventh is reasonable, since the seventh is very weak and only appears in an inner voice at the last moment.274 As a rule, however, Cube is on the wrong side in adhering to the dogmatic prohibition of dissonance priority (and PD) instead of challenging it.275

274 Beach (1989, 41–42) also reads the seventh at m. 26 as a mere lead-in. An interesting notational detail in Schenker’s analysis is the diagonal line that connects the seventh. Here, the diagonal line ascribes a true vertical character to the seventh, like a normal diagonal line that ‘indicates that the tones are simultaneous at some higher level’ (Rothstein 1981, 79). Similar diagonal lines appear in FC, Fig. 64,1 and arguably in Fig. 154,5b (although there a previous diagonal line connects the octave of IV8, too). By contrast, some diagonal lines that connect sevenths simply indicate the emerging passing interval, and do not endow it with a structural status (see FC, Figs. 100,5, as well as Fig. 76,1, especially the first case [in IV7]). Drabkin (1996b, fn. 26) claims that sevenths connected by a diagonal line are frequent in Forte and Gilbert 1982 (and their supplement), but virtually absent in FC. As I have shown, some instances do appear in FC. In FC, Fig. 100,5 (Beethoven, Piano Sonata Op. 2,2/I) the diagonal line shows a passing seventh (m. 214) within a fourth progression as if it were a primary tone of a third progression. A similar problem is found in FC, Fig. 154,4 (Beethoven, Piano Sonata Op. 57/I), where, before m. 175, V7 is indicated below the staff although the seventh is actually a passing tone in a fourth progression, as shown by the slur in the upper voice. 275 Schenker’s response (Ex. 35 in Drabkin) insists that an octave should precede the more structural seventh, but this would seem to be an instance of having your cake and eating it. Drabkin himself (p. 167) admits ‘a certain paradox’ in Schenker’s response, but ultimately he implicitly accepts Schenker’s argument (p. 171). Copyright for this example not afforded. Cube was perhaps persuaded by Schenker’s response, since in his own analyses he used the same model as a background for several Bach works (Cube [1947–55] 1988, 272–3 and 304–5, reading

Providing V7 with Structural Meaning 123

What makes the priority of the seventh in V8–7 possible is that it provides melodic fluency, since it ‘forms a much closer connection with the fundamental line [or deeper levels in general] than does the octave’ (Schachter [1981] 1999a, 198, commenting on FC, Fig. 23b. Cf. §4.3.2.1).276 The alternative possible interpretation would be that the seventh is a passing tone from a cover-tone octave in an interruption structure (Ex. 6.6), but such a reading is implausible when the music is continuous.277 This is a potential source for analytical dilemmas, especially when the seventh is not reinforced by the surface. For example, the bridge section of Beethoven’s Piano Sonata Op. 53/I (Ex. 6.7) is based on V8–7 of III. In FC, §313 (after commentary to Fig. 154,4), the reduction, which is given in letter-names only, selects the seventh (a2) as the structural soprano tone that connects I and III, with the purpose of finding stepwise motion. However, this seventh only appears at the last moment, 12 measures after a consonant V/III has been established. The reading of a normative V8–7 hierarchy is more faithful to the passage, although it lacks smoothness in the voice leading (see Kamien 1992, 105; Krebs 1980, Fig. I.13; Aldwell and Schachter 1978/2003, 606, Ex. 32-12).278 In these cases of reverse V8–7, the seventh functions at the deeper level as a neighbor tone. This finding is contrary to the claim made by Schachter ([1981] 1999a, 198) that [in the same context] ‘the seventh is essentially a passing tone,’ although ‘it is not always subordinate to the particular octave that precedes it.’

respectively, Inventions in C major and in F major and Violin Partita No. 3, Minuet No. 1). Cube’s objection refers in fact to the general case of unprepared neighbors to the seventh (see §4.3.1). 276 Salzer (1952/1962, 88) describes V7 as ‘often providing for better voice leading.’ The related scheme (Salzer’s Ex. 100), however, inconsistently maintains the lower status of the seventh as a passing tone. Aldwell and Schachter (1978/2003, 90, Ex. 6-12b) simply present the neighbor 34– – 3 (I–V7–I) as deriving ‘from’ the I–V8–7–I. 277 See alternative readings of Brahms, Haydn Variations No. 3 in Jackson 1999a, 257. Jackson contrasts Schenker’s unpublished reading as interruption with his ‘diachronic reading’ where the potential antecedent and consequent are ‘fused.’ The fusion highlights the seventh (m. 93). 278 In a yet different reading, Beach (1983b, 24, Ex. 10) regards the octave (m. 23) as a neighbor to the seventh (m. 34), that is already prepared at m. 20. Additional analyses that highlight the seventh in order to provide better melodic fluency include: Beethoven, Symphony No. 9/IV, theme in Berl [1937] 1990, 3 (the seventh is probably passing); Beethoven, String Quartet Op. 74/IV, first variation, in Marston 1989, 309 (delayed seventh in an inner voice); Liszt, Nuages Gris (deepest level) in Agawu 1989, 294 (the seventh is lacking altogether). The less smooth voice leading seems unavoidable as the correct interpretation in such cases where no actual seventh occurs (see the bridge of Beethoven, Piano Sonata Op. 31,1/I in Krebs 1980, Fig. I.14). For a related dilemma see also the alternative readings of the development of Haydn, Symphony No. 99/I proposed by Webster (1991, 325).

124 Providing V7 with Structural Meaning

This assertion is only valid when the seventh is indeed a passing tone, and nevertheless receives an 8–7 appoggiatura closer to the surface, as happens in the theme of Beethoven's Piano Sonata Op. 10,3/III (Ex. 6.8, after Sadai 1980, 65– 66). In this case, the V8–7 reverse hierarchy is complicated by a momentary inversion. Ex. 6.9 shows appoggiaturas on all inversions of V7: (a) on V#: a sixth resolves into a diminished fifth in relation to the bass, as Oster (1937, 141) shows in an Allemande by Handel;279 (b) on V$. In relation to the bass, the suspension seems deceptively normal (4–3). The case I show (from Mozart’s Piano Sonata K. 284/I) is further complicated by the context; (c) on V2: the suspending sonority is a root position V. This makes the reverse hierarchy even more problematic. It becomes possible through a combination of rhythm, motivic parallelism to other suspensions and voice leading fluency; (d) appoggiatura to the consonant members of V2 (cf. Ex. 6.4b, second case). When the delay of the tone of the seventh is accompanied by a lower third (V§°–∞‡, Ex. 6.10), perceiving the seventh asbeing prior to the preceding octave becomes easier, by analogy with V¢−–£¦. Yet, it still can be read as a 6–5 suspension combined with passing motion from the octave.

6.2 Processes toward V7

In FC, §310,b3, Schenker cites ‘The process of “securing” the seventh whose purpose is to cancel the leading tone to the dominant’—i.e., to reestablish diatonic 4 in order to de-tonicize V—as an optional device to generate three-part form from a more structural binary interruption. In fact, the seventh that de-tonicizes the dominant is not always a product of a process, nor does it necessarily have a deep structural and formal meaning. Rather, it is often a lead-in that appears at the last moment before the return to the tonic, after a consonant V has been reestablished (Ex. 6.11a). However, the reestablished V£¦ may already be de-

279 Handel’s notation shows the sixth as an appoggiatura and the dissonant resolution in large notation, a procedure recalled by Schachter ([1981] 1999a, 198). See also Mozart, Piano Sonata K. 284/II, 12.

Providing V7 with Structural Meaning 125 tonicized, due to the insertion of the diatonic 4 into the preceding V prolongation (Ex. 6.11b).280 A genuine process on the path from V to V7 assumes the seventh to be a boundary tone of a voice-leading procedure, and thus endows it with a certain structural status, even though the seventh is not prolonged. Two situations constitute such a process: gradual transformation and space-filling motion.281

6.2.1 Gradual Transformation of V into V7 The tone of the seventh (4) may be introduced in the middle of a V prolongation on an intermediate harmony. The V begins as a triad, but when it returns, the seventh has already been incorporated. The term gradual transformation derives from its incidental use (as a verb) by Aldwell and Schachter (1978/2003, 577).282 FC shows this process schematically in Fig. 113,3a (reproduced in Ex. 6.12a), in the progression V–ßVII–V7. The text regards the middle sonority as a consonant preparation: ‘the forthcoming seventh first appears as the fifth of such a major triad,’ perhaps in contrast to the diatonic dissonant VII, which is avoided. I have already objected to the idea of preparation for a more structural harmony (§4.3.1). In fact, gradual transformation may introduce the seventh on various harmonies (Ex. 6.12b–e), consonant or dissonant: II in major (FC, Fig. 62,9 [Bach]) or IV (FC, Fig. 154,5 [Beethoven’s Symphony No. 6/I]);283 a passing ¢−

280 The only example of a ‘process’ that Schenker cites is his Fig. 46,1 (Brahms, Waltz Op. 39,2). Even there, the seventh is a mere local event following the return of a consonant V. The retransition is complicated by an additional unique passing motion in the form of V8/3–7/2. For elucidation of Schenker’s idea on this point, see Rothstein 1989, 107. 281 See further discussion below, §6.3, concerning FC, §314. 282 Aldwell and Schachter also refer by this term to transformation of one type of seventh chord into another. 283 This passing IV encompasses the whole development. Interestingly, the recapitulation enters on an apparent tonic within the IV–V7 progression (Rothgeb 1990, 13–14, after Schenker; Laufer 1991, Ex. 18). Alternatively, a structural V might already be heard at m. 262. A seventh progression in the bass transforms it into a V2 at m. 271 (the seventh is connected to the former IV), while the subsequent voice in the soprano supplies a ninth. In the latter interpretation, the tonic at the beginning of the recapitulation is indeed apparent, but not within gradual transformation. Cf. also Beethoven, Piano Sonata Op. 49,2/I, development, in Jonas [1934] 1982, 103. Jonas’s graph is peculiar in that it avoids any interruption in the development.

126 Providing V7 with Structural Meaning

(Aldwell and Schachter 1978/2003, 578, Ex. 31-24 [Chopin]); or ßVII7 (Brahms, Symphony No. 2/IV, 7–24).284

6.2.2 Space-Filling Motion (SFM) toward the Seventh of V7 SFM is the linear filling of a true chordal span that does not nevertheless represent a vertical origin (§2.3.2). This is what usually happens in linear motion from consonant V to V7. The seventh is a true boundary tone, but is nonetheless absent in the underlying vertical harmony, and thus not properly prolonged with the rest of the chord. The principal type of SFM from V to V7 fills the upper third of the seventh chord, as V5–6–7 (see Proctor 1978, 72–74). This pattern often underlies whole development sections in sonata form, connecting the pre-interruption 2 with a lead-in 4285. Ex. 6.13a–e shows this pattern with several harmonizations of the passing tone: I, ßIII–III, IIIƒ,286 VI287 and VIƒ.288 If the goal seventh of V5–7 receives exceptional emphasis, it might become a true structural neighbor rather than an offshoot of an interruption. In that case, the

284 For gradual transformation through VII ß7, see also Chopin, Polonaise Op. 26,1, mm. 33–41. It is misrepresented in FC, Fig. 113,3c. 285 Laufer (1991, 70–72) claims that V5–7 motion constitutes the normal boundaries of development sections, but among his particular paradigms, only paradigms vii, a+b work out this third span. In this situation, the ‘dividing dominant is prolonged as its seventh is worked out’ (Cadwallader 1990, 3). Clark (1982, 248) describes V5–6–7 as a ‘lower-order passing tone on the way to a higher- order passing tone’[8–7], as opposed to a passing tone toward a true goal. He seeks to reconcile the situation with the Schenkerian view, but ignores the normative requirement that a ‘passing tone of a higher order’ must first be transformed into a consonance. 286 The example, from the development of Mozart, Piano Sonata K. 333/I, is based on Beach (1983a, 19). Beach’s study is devoted to this particular pattern in Mozart’s development sections. Beach first endorses the reading that I present as an alternative, i.e., V–IIIƒ–I based on bass arpeggiation, but then (p. 28) admits that ‘the prolongation of the structural dominant must take precedence.’ The analytical dilemma is presented more sharply in Willner 1988, 80–81 and Beach 1993, 6–8, but with regard to the bass alone. Laufer (1991, 92–101) examines several development sections and emphasizes the need for particular decisions in each case. 287 My example, from the exposition bridge of Beethoven, Piano Sonata Op. 110/I, is based on Kamien 1976, 216–7, Ex. 21. 288 My reading of Beethoven’s Piano Sonata Op. 10, 2/III (Ex. 6.13e) diverges from that in FC, Fig. 62,11. Krebs (1980, 58) notes that VIƒ is employed in both outer movements of this sonata. In the first movement, the thematic recapitulation enters on the VIƒ. Schenker (FC, §315) regards the soprano of VIƒ as the primary note, but also expresses unease with his own explanation, as he calls the situation ‘merely . . . a resemblance’ [Anklang]). Laufer (1999, Ex. 15-8) reads the VIƒ as the beginning of an auxiliary cadence. VI or VIƒ within V5–6–7 introduces parallel fifths, which the foreground should eliminate.

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5–7 ascent should be considered as motion from an inner voice (Ex. 6.14).289 Ascending SFM from V toV7 can also encompass larger intervals, e.g., V3–7 as in Beethoven’s Piano Sonata Op. 28/III, 25–48 (Ex. 6.15a).290 When motion toward the seventh begins from the lower root, it coincides with an ascending illusory seventh progression (as in FC, Figs. 62,1–2). An alternative path toward the seventh fills the second 8–7 chromatically (V8–ƒ7–7), as in Haydn’s Piano Sonata Hob. XVI:43/III, 50–56 (Ex. 6.15b). This motion too may be harmonized in various ways and even counterpointed by a bass divider.291 In descent too, SFM toward the seventh need not be restricted to the shortest chordal span. The descending forms V10–7 or V12–7 pass through the tone of the octave, but this tone can be deprived of its normal function as a boundary tone if it is not itself harmonized as V (cf. Ex. 6.15c). Occasionally, even a seventh that initiates motion functions as a mere boundary for SFM, while at the deeper level V appears without the seventh (Ex. 6.16a–b). This happens when the linear continuity is provided by the consonant members of the chord. In the theme of Beethoven’s Piano Sonata Op. 27,2/I (Ex. 6.16c), sevenths even appear at both boundaries of V, but they are not structurally related: the initial seventh is suspended from an incomplete neighbor and the final seventh passes from the preceding octave.292

289 See schematic presentation of this problem in Ex. 4.15. The choice between the interpretations is often influenced by form: according to FC (§312), interruption is obligatory in sonata form but only optional in ABA song form. Accordingly, analytic practice tends—perhaps unjustifiably—to avoid interruption in ABA movements. Cf. discussions of Schenker’s analyses of Chorale St. Anthony (fn. 257) and Chopin, Nocturne Op. 15,2 (§3.2.6, esp. fn. 159). 290 Forte and Gilbert (1982, 240–1) cite this passage as a model for ‘a true middleground progression of a diminished fifth,’ but in fact this it is a SFM toward the tone of the seventh and not a circular linear progression. See also Schumann, Faschingsschwank aus Wien/I, 356–64, in the bass. 291 For a more gradual descent, see Beethoven, Piano Sonata Op. 57/I, 32–34, within full neighbor prolongation of V7 (fn. 354). The descent ƒ4-4 on 7V/V–V7 plays a crucial role in Chopin, Mazurka Op. 30,4 (see FC, Fig. 53,3). This progression opens the introduction and sounds as if it has arrived from an elided V8. When it recurs in the retransition (mm. 97–100), it may be said to stem from the V before the interruption, but the harmony in mm. 65–96 interferes. The commentary in FC, §310,(b)4 hints at the idea that the chromatic motion is form-generating: ‘an unusual beginning, such as the II[7/ƒ3]–V[7]–I in Fig. 53,3, can bring about a three-part form.’ 292 The former seventh chord in the Beethoven excerpt belongs to an even more surface level than the initiation point of the SFM. In this movement, passing motion from an incomplete neighbor has motivic parallels in mm. 7–8 (misrepresented in FC, Fig. 76,7) and in the larger-scale motion

128 Providing V7 with Structural Meaning

6.3 Subordinations to V7

A one-way prolongation in the form of a forward-relating subordination (§1.1.3) applies particularly often to V or V7 (For Schenker’s criteria for subordination toward a consonant V, see Rothstein 1981, 117–20.). The preeminence of the V7 over preceding chords is secured by the participation of the bass in the background tonic arpeggiation (§4.3.1). In terms of conventional harmony, V7 gains priority since its dominant function is more essential than that of the subdominant (possibly consonant) harmonies that might precede it (Lerdahl and Jackendoff 1983, 182). We have already encountered simple appoggiaturas to V7 (§6.2); now I shall discuss subordinate independent chords. In most important subordinations, the tone of the seventh (4) is established before the rest of the V harmony. This prevents the seventh from constituting a simple passing tone. This situation is normally considered as a preparation for V7 (see schematic IV–V7 in FC, Figs. 19a and 32,5), but as I have argued before (§4.3.1), the idea of preparation for a structural V7 misrepresents tonal hierarchy. Reduction should shift the V7 back to the initiation point of 4 (Ex. 6.17), in the same way as it should shift V back to the initiation point of 2 in a consonant II–V progression (cf. Ex. 1.9c).293 The idea of subordination into V7 is discussed in FC (§314, concerning Fig. 154,5 [Beethoven, Symphony No. 6/I]): although the [final] 4 and2 (mm. 272 and 282 respectively) ‘do not appear simultaneously over the V, they must be understood as V∞‡,’ and (end of §314) the activity under the subordinate IV has a task ‘in prolonging V7’ [im Sinne von V7]. (cf. the larger context in Ex. 6.12c).

toward the dominant. I find that the I at m. 27, where Schenker places the primary tone (FC, Fig. 7a, supported by the melodic peak), is actually passing between IV and V, harmonizing inner- voice passing motion from an incomplete neighbor (fƒ1–e1–dƒ1 at mm. 25–28). See also Chopin, Mazurka Op. 17,1, mm. 9–10, according to FC, Fig. 83,2. In this case, however, the tone of the seventh is present in an inner voice (shown within II in the middleground in FC, Fig. 76,5). The boundaries of the dissonance conflict with the surface motive. See Laufer 1981, 166–7 and principal discussion by Cohn (1992a, 157). 293 If the subordinate chord also includes 4 in the bass (IV or 6II), the bass tone is not conceptually synchronized with the following V7. Rather, it is normally a displaced passing tone (see Mozart, Piano Sonata K. 332/I, 10–12 in Jonas [1934] 1982, 121–2, Ex. 188). Subordinations to V7 may be embedded within full neighbor motions (cf. §7.3.1).

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The subordinate harmony can itself encompass huge prolongations. In principle, as long as the prolonged harmony remains subordinate to V7 at a deeper level, the entire prolongation also relates indirectly to the V7. This relation, however, becomes very difficult to grasp when the proportions between the subordinate chord and the following V7 are extreme.294

6.3.1 Specific Types of Subordination to V7 Each specific case of subordination to V7 has its own voice-leading implications. For example, in IV–V7 (and II6–V7), the bass progresses contrapuntally (Ex. 6.18a [Schumann]), while in root-position II–V7 the bass is more harmonic, and involves unfolding (Ex. 6.18b, after FC, Fig. 109,e2, analyzing the theme of Beethoven’s Cello Sonata Op. 69/I).295 Even when no vertical V7 occurs, the progressions IV–V or II–V may merge into a conceptual contracted V7, which gains structural priority (Ex. 6.18c; also Ex. 4.17) provided that 4 appears in the upper voice and that no emphasized5 appears in the same register on either V or I.296 This procedure, where actual consonances are explained as a hypothetical dissonance, is diametrically opposite to the norm that dissonant simultaneous combinations result from displacement of members of consonant harmonies (see §2.3.3.2).297

294 See Mozart, Piano Concerto K. 271/III, 233–304 [minuet of the rondo] (on IV) and 328–44 [episode] (on II), according to Galand 1990, 264, and Schubert, Piano Trio D. 898 (Op. 99)/III, trio on IV followed by a transition on V7. 295 In the exposition of Op. 69, the theme appears monophonic and might be interpreted differently. Schenker’s graph corresponds to the harmonized version in the recapitulation. For II– V7 see also Mozart, Piano Sonata K. 310/I, 24–25. The hypermeter of the progression I–II–V7–I stands in contrast to the feeling of suspension II–V7 (cf. explanation of a similar situation in Aldwell and Schachter 1978/2003, 365, Ex. 21-32). It is instructive to compare the analyses by Beach (1987, 165) and Nolan (1995, 133). Nolan notes only the consonant tenths between the outer voices, while Beach shows the emerging seventh. Schenker’s graph in TW 2 brings II and V to the same level and provides an exceptional interpretation of the II triad as II7. 296 In Mendelssohn’s Song without Words Op. 30,6, mm. 35–38, Schenker reads IV–V as if 4 remains above V (see middleground in TW10 and FC, Fig. 108,3, justified in a footnote to MW I, 39), but in fact, the upper voice proceeds to 5 and disrupts the sense of subordination. 297 In CP I, 111, Ex. 151a, Schenker suggests a similar merging into dissonance in a situation that violates two-part first-species counterpoint. There, however, the dissonance does appear at last. If 4 lies in an inner voice, the merging into 7V is normally avoided. For example, the inner-voice 4 at the final cadence of Mozart’s Piano Sonata K. 330/III (m. 170) is not merged with the following V (the upper voice plays 67– 8– ). My general approach is that the location of the seventh in an inner voice does not rule out its prolongation, but that in marginal cases, its location in the upper voice might be decisive. For example, in Chopin’s Etude Op. 10,6, the inner-voice seventh at m. 33 may

130 Providing V7 with Structural Meaning

As to other subordinate triads, VII–V7 (in major or harmonic minor) is almost a circular prolongation, since all the tones of the VII triad are contained in V7 (Ex. 6.19a; cf. FC, Fig. 111a, first instance). By contrast, VI–V7 is hierarchically ambiguous: 4 is lacking in VI, and might be perceived as an upper neighbor, contradicting the subordination to V7 (Ex. 6.19b).298 Most effective are subordinate degrees that include mixture, especially in major. These usually involve ß6 (e.g.,ß) IV299 or consonant chromatic variants of VII. These altered VIIs are also more distinct from V7 than is the diatonic VII. Ex. 6.19c demonstrates this using Schubert’s Moment Musical No. 2 (after Cadwallader and Gagné 1998, 282). (FC, Fig. 111a shows additional chromatic variants.)300 When the subordinate chord is itself a seventh chord, the seventh of the subordinate chord resolves properly into tones of the V7. VII2–V7 uses motion in a single voice, as a simple appoggiatura to the root of V7 (Ex. 6.20a, from the motto of Beethoven’s Piano Sonata Op. 57/I, m. 238).301 This suspension sounds more independent than appoggiaturas to the third (7/5/4/1–7/5/3/1) or the fifth (7/6/3/1– 7/5/3/1), since it creates a chord of piled-up thirds (cf. §1.2).

be said to resolve only at m. 41, but mm. 33–40 is heard as prolongation of a consonant V, as is correctly indicated in MW I, 84–85. 298 For the latter interpretation, see FC, Fig. 39,1, reading of Schubert, Der Schiffer, D. 694. See large-scale application of this dilemma in Mozart, Piano Sonata K. 576/II, 17–43, where a section on VI is followed by a V7 that connects it to the deeper structure. 299 Cf. the clear effect of IVß6–V7 in Mozart, Piano Sonata K. 576/II, 42–43 (transition from VI, cf. the previous footnote), discussed in Harmony, §173 in conventional terms. The subordination form ßII–V7 involves root tritone relations. See Chopin, Etude Op. 10,12, mm. 65–68. In Chopin, Nocturne Op. 15,2, m. 12, a neighbor ß6 in the bass does not belong to any clear subordinate verticality, since the diminution avoids vertical coordination between the voices, and because of the pedal point in the bass. FC, Fig. 117,1 presents the diminution in detail, but overlooks the subordinate neighbor in the bass. The associated commentary claims that this passage ‘produces the effect of V7,’ albeit without reference to the subordination. 300 The subordination form VIß–V7 in minor (or ßVIß–V7 in major, also VIß–V5/3) is extremely problematic, since the thirds of VIß (ß1) and V(7) ((ƒ)7) are enharmonically equivalent. See the destiny motive in Wagner’s Der Ring des Nibelungen (motive no. 84 in Donington 1974, 303; Kurth 1920/1922, 210, Nr. 114). Cf. Ex. 7.69d. This problem does not derive from the existence of the seventh, and is also present in the form ßVIß–V5/3. Cf. Franck, Symphony/II, mm. 7–8. The same paradox occurs in the opposite direction in the deceptive cadence V8–7–VIß in Brahms, Intermezzo Op. 117,2, mm. 7–8. 301 This Dß-C motion has large-scale implications. Cf. mm. 11–12, 89–93, 123–34. At mm. 11–12 (but not in the parallel passage in the recapitulation, mm. 146–7), VII takes the form of VII6/5 and is itself subject to prolongation by a IV2 neighbor. Theoretically, a series of appoggiaturas may create a series of subordinations IV6/5–II4/3–VII2–V7.

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A two-voice suspension to the root and third introduces II$–V7 (Ex. 6.20b, a variant of the aforementioned motto),302 and IV#–V7 (Ex. 6.20c) emerges from a three-voice suspension to the root, third and fifth. This progression contains parallel fifths, which should be eliminated by the surface. Subordinations to inverted V7s are rather unlikely,303 and can only be established where the subordinate chord is itself local and unstable, normally a seventh chord. The procedures of subordination to an inverted V7 can be described as a general rule, as extrapolated from the specific instance of subordinations to root-position V7. A one-voice appoggiatura to the root of V7 or its inversions results (in the shortest path) in VII7, whose inversion is one lower than that of the V7: VII2–V7, VII7–V#, VII#–V$ and VII$–V2. Similarly, the inversion of the subordinate II7 in a two-voice appoggiatura would emerge two inversions away from that of the V7: II$–V7, II2–V#, II7–V$, II#–V2. Theoretically, a subordinate IV7 would emerge one inversion above that of the V7, but it is very difficult for it to maintain its priority. Ex. 6.21 demonstrates selected possibilities from the literature. The first case (Beethoven, Symphony No. 7/I, 142–51) involves mixture, using VIIº7 in major. (V7 prolongations in general normally use the minor 6, which is diatonic in minor but lowered in major.) Also noticeable is the radical enharmony in the second case (Chopin, Mazurka Op. 24,2, mm. 87–88). Embedded in a retransition from a

302 See also Bach, WTC I, Prelude in C major, 23–24; and Ex. 6.4c (Mozart). The interpretation of m. 23 as II4/3/ß1 rather than a diminished seventh chord is not trivial in the given diminution. See FGA, Jonas [1934] 1982, 88, Ex. 134 and specific discussion in Drabkin 1985, 256–7. 303 Inverted V7s usually function as passing chords or as interpolations that help to avoid parallel octaves. See VI–V6/5–I in FC, Fig. 106,d (Schubert, Waltz D. 969 (Op. 77],5); III–V4/3–I is a recurring pattern in several etudes from Chopin’s Op. 10: the middleground of No. 1 (in the reading of Cinnamon 1994) and No. 8 (where it is even open to debate what inversion is involved), and more locally in No. 3 (V 4/3 of V/V at m. 38). Among other analyses of No. 1, FC, Fig. 153,2 and Forte and Gilbert 1982, Ex. 177 consider VI rather than III as the governing harmony of the middle section, but share the non-structural status of the V4/3 at m. 48. By contrast, FC, Fig. 130,4 converts this V7 into root position and designates its upper voice as a structural neighbor tone, although the note heads and Roman numerals prefer VI over V7. Yet another reading by Ch. Smith (1981, 162) suggests a progression between two dissonances IV6/5–V4/3. Such a variety of readings is made possible by the ambiguity of the opening chord of the section (m. 17). The form IV–V2–I6 is also possible. An explanation of V as an interpolation that avoids parallel octaves between II and I appears in FC, below Fig. 15,6. (cf. also FC, Fig. 54, 10, reading of Bach, Brandenburg Concerto No. 5/II, 7–9). This idea overlooks the structural power that V or V7 usually possesses. Its application to V4/3 is more straightforward.

132 Providing V7 with Structural Meaning chromatic middle section, it wrenches the tonal motion back to the diatonic region.304

6.3.2 Apparent Subordinations to V7 The same harmonic progressions that normally express subordination to V7 may have other structural interpretations, based on rhythmical-metrical or contextual grounds. The influence of rhythmic circumstances is shown in Ex. 6.22a (from No. 15 in Mozart’s Die Zauberflöte). Subordination is avoided here due to the combination of two factors: the metrical position negates the normal placement of a subordinate event on the strong beat (like an ordinary appoggiatura); and the duration of V7 is shorter than that of the preceding chord.305 Context accounts for the avoidance of true subordination when V7 is not related to the preceding chord. This is clearest when the pre-dominant chord belongs to a deeper pattern, while the ensuing V7 is inserted on a more local level. Ex. 6.22b demonstrates such a process in Scarlatti’s Sonata K. 471, mm. 51–54 (after Rothgeb 1975, 276, Ex. 14). This passage is based on the progression II–V, with a passing tone supported by an apparent tonic. A surface V7 leads to this apparent tonic, and is not related to the more structural II that precedes it.306

6.3.3 Filling in of Spaces Created by the Subordination Process Subordinations to V7 include tonal spans that may themselves be filled in by linear motion (cf. the consonant model in Ex. 1.9d). This motion functions as a true, albeit not a full, prolongation of V7 (since its deepest event is the V7), although the subordination process itself counts as a transitive progression. This motion can even be a seventh progression that substitutes for the step in the bass

304 For another reading, see Gibeau 1992, 221, Ex. 280. See also the more dissonant V7/5/2–6/4/2 in Ex. 6.9d (Fauré). Siegel (1990, 23 and 27) shows Schenker’s comments on a 4/2 resolving to a 6/5 in his unpublished annotations of Bach’s Generalbassbüchlein. 305 Everett (1991, 110, Ex. 3) reads the usual V priority here. A similar case: Chopin, Polonaise Op. 26,2, mm. 19–20. Each factor alone is insufficient to override the sense of subordination. For example, the progression I–II2–V6/5–I in duple meter displaces the metrical position of the subordination, but still maintains the priority of V over the preceding II. Cf. above fn. 295. 306 The sense of subordination can be negated even if the V7 maintains its structural priority, provided that the preceding chord does not belong to the immediately subsequent level, but rather is inserted within a deeper progression to V7. See Chopin, Etude Op. 25,5, mm. 7–8, in accordance with FC, Fig. 111,b2 (the seventh in the final V is omitted in the graph).

Providing V7 with Structural Meaning 133 of the IV–V7 progression, as in Ex. 6.23a (Haydn).307 The theoretical status of this seventh progression is intricate: as a transformation of a second, it forms an illusory linear progression; but since 4 is present at the beginning and the 7V belongs to a deeper level than the IV, this illusory progression nevertheless prolongs the final dissonant V7 properly.308 Motion within the progression IV–V7 may also be achieved in the upper voice, by means of descending linear progressions from 4 to members of 7V (Ex. 6.23b–d),309 or through chromatic filling of major seconds either between the roots or (in major) within 65– motion (combined in Ex. 6.23e).310 Within II–V7, connecting the roots involves neither the tone nor the interval of the seventh. Cf. Beethoven, Bagatelle Op. 119,11, mm. 7–9 (Ex. 6.24a after FC, Fig. 100,3h). In this passage, the bass arpeggiation undergoes a pronounced mixture, and the soprano arpeggiates to an upper octave.311 Seventh progressions within II–V7 can arise in the upper voice (similar to Ex. 6.23e) or in the bass from II6, as in the theme of Beethoven, Piano Sonata Op. 14,1/III (Ex. 6.24b). Even IV–V! or II–V! subordinations that merge into a conceptual V7 can embrace linear motion that prolongs the V7. For example, in Ex. 6.24c (Beethoven, Piano Sonata Op. 49,1/I, 12–15), an upper diminished fifth progression is counterpointed by an ascending fourth in the bass. The vertical V7 is latent and realized directly afterward (on the strong measure 16).312 This device

307 In the example, the seventh progression is counterpointed by a diminished-seventh arpeggiation in the upper voice. See also Scarlatti, Sonata K. 501, mm. 69–70. This model serves as the underlying normative paradigm beyond a more sophisticated device, which re-interprets the final V7 as an augmented sixth chord (cf. Ex. 10.6b). 308 See also Beethoven, Piano Sonata Op. 14,2/III, 132–8. The bass is the leading voice; the following voice in the soprano plays a transitive seventh progression. 309 Notice the motivic parallelism in Ex. 6.23c from Mozart’s Rondo K. 485. The origin of this diminished fifth may be traced to the rondo’s main theme. My reading diverges from those by Jonas ([1934] 1982, 102), Rothgeb (Appendix to Jonas, ibid., 167) and Galand (1995, 35, Ex. 5). See also ‘ß5 linie’ in Cube 1988, 300, graph of Bach, WTC I, Fugue in D major, 15–20. 310 Cf. Beethoven, Piano Sonata Op. 2,2/II, 26–31, arriving from IV6. 311 For filling in of II–V7, see also: (1) FC, Fig. 53,5, reading of Bach, WTC I, Fugue in D minor, m. 5, nested within gradual transformation from a consonant V. The diminution is complicated and does not manifest a clear linear progression (cf. schemes in FC, Fig. 72, 1 and 2); (2) Beethoven, Wonne der Wehmuth, Op. 83,1, mm. 9–10, with surface mixture. 312 My analysis follows Jonas (1937, 103). Laufer (1991, 93) also indicates the diminished fifth at mm. 12–15, but shows its middle third to be the main tone. A similar progression occurs in Donna Anna’s aria Or Sai (No. 10 in Mozart’s Don Giovanni), mm. 77–79 (8–10 of the aria). Schachter ([1991b] 1999a, 229–31) shows the diminished fifth in the upper voice and explains the expressive

134 Providing V7 with Structural Meaning enables prolongation of V7 even in Renaissance music, where vertical V7s are foreign to the style.313 Ex. 6.24d shows a more dense realization of the same voice leading, from the first of Schoenberg’s Gurrelieder. In this case, the initial harmony is II7. Motion within VII–V7 actually creates a circular prolongation of a V7, whose root arrives later than the other members of the chord (Ex. 6.25). Simple filling of the lower third-span of V7 offers limited possibilities, but wider motion is feasible through inversion of the third into a sixth,314 or as a fifth-space from VII6. It can also begin with an altered VII, as in Ex. 6.25d (Chopin, Polonaise Op. 26,1 after FC, Fig. 99,2). The upper voice of this excerpt is based on a register transfer of the tone of the seventh and uses reaching-over.315 The fact that VII and V7 (also II and V7) share more than one common tone enables the use of voice exchanges—a technique of circular prolongation—as a means of filling in the subordination. This very procedure is described schematically in FC, Fig. 98,1b (my Ex. 6.25e), where third progressions exchange the third and fifth of V7, while the root arrives only at the goal.316

quality of the deep g–fƒ (43– ) motive. For motion within 6II–V7, see FC, Fig. 100,4b (Bach, 69 chorale melodies No. 11, mm. 5–7), which is said to illustrate ‘descending arpeggiations which develop into four-note harmonies.’ However, 4 is replaced by 5 in the course of the motion. An inner-voice seventh progression within II–V5/3 [in III] appears in FC, Fig. 154,3, graph of Beethoven, Piano Sonata Op. 10,1/I, 40–55. The seventh of V is then reestablished at a lower register. 313 I hear the excerpt from Ave Maria by Josquin des Pres quoted in Salzer 1952/1962, Ex. 273 as being based on a IV–V motion that merges into a structural V7. Salzer’s static reading is presumably closer to the compositional thinking of Josquin. I am aware that my anachronistic interpretation leaves some meta-theoretical questions open. See also the 1601 Hassler chorale discussed above (Ex. 4.13). 314 FC, Fig. 96,4 shows such a motion in Brahms, Waltz Op. 39,4, mm. 5–8, in relation to V. The sixth-unfolding is motivic and reflects the diminutions. The final V (of V) appears first as a consonance; Schenker includes the seventh in the reduction, but does not add the seventh into the Roman numeral designations. Perhaps the initial 4 remains in effect, but is not directly connected to the final seventh, in the form 4 (m. 5)–5 incomplete neighbor-(passing4 )–3 (cf. Ex. 7.61b). 315 I have removed a contradictory inner-voice slur in Schenker’s graph. Laufer (1981, 178) offers an alternative reading as a tonic arpeggiation (of Dß) on the weak beats. However, Schenker’s reading is supported by the articulation of design, including the bass, and by motivic predecessors in mm. 1–5 (on the same pitch classes) and 34–40 (see FC, Fig. 113,3c). 316 The text for FC, Fig. 98 finds that it expresses ‘a single harmony.’ See also Mozart, Symphony No. 39/IV 62–65, according to Kamien (1990, 104, Ex. 11).

Providing V7 with Structural Meaning 135

Subordinations of VIIº7 usually employ maximally smooth voice leading, which offers little space to be filled. However, such a space can be created by several techniques that avoid the smoothest path of voice leading. One technique is the type of voice exchange mentioned above. For example, in Wagner’s Tristan-chord complex (Ex. 6.26a), the third and fifth of V7 are exchanged. The subordinate harmony is VII2 with a raised fifth (VII ƒ6/4/2/1). The alteration’s tendency (its ‘Tonwille’) to proceed upward is negated; hence, my analysis does not explain away the peculiarity of the passage.317 Voice exchanges can even separate the (ß)6-5 motion that resolves the seventh of VII7 into two different voices. The voice exchange uses the appoggiatura (ß)6 as if it were its enharmonic equivalent ƒ5 (an altered version of the root of V). This enables the appearance of voice exchanges where the root of V7 (beginning as a raised root, enharmonically the seventh of VII7) is exchanged with the third of V7 (beginning as the root of VII7). This happens twice in Brahms’s Symphony No. 4/I (Ex. 6.26b). The parallelism between the two voice exchanges is concealed by different thematic diminutions each time.318 More daringly, the (initially altered) root of V7 (ƒ5 to 5) can be exchanged with the seventh of7 (beginningV as the fifth of VII7). This occurs in the opening gesture of the development in Mozart, String Quintet K. 593/I (Ex. 6.26c). The VIIº2–V7 progression in this example is applied to a local ßIII within the V prolongation. The finale of the same quintet offers a simpler device for opening the 6–5 space, namely stretching it over a ninth (Ex. 6.26d). Finally, VII7 may resolve into an inversion of V7 other than that indicated by the smoothest voice leading path. even without voice exchanges. For example, in Ex. 6.26e (Schumann, Novelette No. 3, mm. 42–45),319 VII ß7 proceeds not as a

317 My analysis follows that in Mitchell 1967, 168 (=1985, 244). See also Harrison 1995, 183–4. 318 The former passage (mm. 27–31) is described by Yellin (1998, 58, Ex. 63) as an omnibus progression (see below, §7.2.1.2.1); more accurately, omnibuses are always circular. The latter passage (mm. 114–9) is analyzed in CP I, 25, Ex. 5 as IVƒ–IIƒ (i.e., VII–V in relation to V) via passing chords. Brahms uses an identical configuration in the Tragic Overture, mm. 140–1 (with inner suspensions), but the final V7 is reinterpreted as an augmented sixth chord. (cf. also below fn. 432, on Beethoven, Piano Sonata Op. 54/II, 37–44). 319 The passage recurs at mm. 46–49 and in the last phrase of the work, mm. 82–89.

136 Providing V7 with Structural Meaning smooth appoggiatura to V#, but rather to V2. The emerging space is filled by a non-functional series of diminished seventh chords.320

320 Such remote paths can even create seventh progressions if the smooth subordination VII4/3–V2 is replaced by VII4/3–V7. FC, Fig. 89,1 implies such a seventh progression in the bass of Beethoven, Piano Sonata Op. 109/I, 17–21, in the progression VII4/3–V5/3 (inner voices are not shown). However, the descent in fact begins from the octave and prolongs a consonant V.

7. FULL CIRCULAR PROLONGATION OF V7

This chapter aims to systematically survey the specific techniques involved in full circular prolongations of V7. Some of the ideas proposed here apply to other seventh chords as well. My classification of V7 prolongations is based on a contrapuntal approach, in accordance with Schenkerian thought. I will first comment, however, on the specific harmonies that emerge within V7 prolongations. The end of this chapter also discusses prolongation of the inverted V7, enharmonic prolongation of V7 and large-scale prolongations of V7 in relation to form.

7.1 Harmonies that Emerge within Prolongations of V7

Chords that emerge out of voice leading are not Stufen in the Schenkerian sense, and in Schenker’s own view they lack vertical harmonic significance. Nevertheless, I believe that such chords do include a harmonic ingredient, even where the context is unequivocally contrapuntal.321 It is no coincidence that most prolonging sonorities are themselves based on piled-up thirds, even though voice- leading context enables many additional passing sonorities to appear in tonal

321 Dahlhaus ([1966] 1990, 57) raises a similar argument in relation to another progression: ‘the six-four chord in the progression T–D6/4–T6 is also a passing chord, and yet it still has an undeniably dominant function.’ Cf. also N. Wagner 1986, 39–40. Some passing chords are nevertheless less functional, e.g., the passing apparent seventh chord I–‘II7’–I6. See also consideration of conventional harmonic functions that is ‘compatible with a hierarchical approach’ in Agmon 1995. Rothgeb (1996) refutes.

138 Full Circular Prolongation of V7 music.322 This does not necessarily mean that the immediate root relations are significant. The harmonic sense of passing chords might be revealed by their own prolongation, or by the bass leaping in order to support these chords. Within V7, two intermediate harmonies are particularly interesting: inserted II! creates the harmonic relations of a bass divider (cf. §7.6), and inserted I! creates an illusion of immediate resolution of the initial V7, and challenges the sense of V7 prolongation (cf. Exx. 7.43b; 7.67; 7.95,a1–2). Harmonies within the V7 prolongation can even be tonicized. Contrary to simplistic intuition, a tonicized harmony may serve to prolong a non-tonicized harmony (Schachter [1987a] 1999a, 142–7); it is all the more fascinating that even a PD may encompass various tonicized harmonies.323 Harmonies that prolong V7 in the subsequent level necessarily include tones absent from V7: 36, or 1. Ex. 7.1a shows the harmonies that are created by combinations of these tones: combining all three tones together produces VI, combinations of two foreign tones with one chordal tone introduce IV6 or I¢−, and a single foreign tone combined with two chordal tones creates III6, II¢− and a quartal harmony. All diatonic harmonies are introduced in this way (the exception, VII, is wholly embedded within V7). In smooth voice leading, each chord emerges in the specific indicated inversion; transformation into other inversions is possible via wider voice-leading manipulations. Chromatic variants are possible. Each combination may be achieved in multiple ways, especially when at least two foreign tones are involved. For example, IV6 may emerge through two neighbors, two passing tones, or one neighbor combined with one passing tone (Ex. 7.1b). Paradoxical as it may seem, there is a preference in the literature for triads (rather than seventh chords) as the passing harmonies within V7. Often, the

322 Agmon (1996a, par.7, in reply to Rothgeb [see previous footnote]) makes the same point: passing chords are not ‘some accidental collection of pitches.’ Even seventh chords with a major seventh are generally avoided. Schenker seems to allow any sonority for the passing events. This view derives from his criticism of Schoenberg’s focus precisely on sharp passing dissonances (see §3.2.6). In the same spirit, Jonas (1937, 74–5) ridicules Vogler’s attempt to eliminate non-tertian sonorities in Bach chorales. 323 See below Exx. 7.24d (Chopin, Barcarolle—tonicized II); 7.29d (Chopin, Etude Op. 10,3— tonicized I and II); 7.51 (Schumann, Kinderscenen No. 8—tonicized II and III]; 7.103 (Beethoven, String Quartet Op. 132/I—tonicized VI). The development of Beethoven’s Symphony No. 3/I includes even remote tonicizations, but not on the immediately subsequent level. Enharmonic parentheses introduce additional possibilities for tonicization (see §7.8).

Full Circular Prolongation of V7 139 prolonged V7 appears in an incomplete texture (omitting the fifth or the third) precisely in order to achieve triads as the passing harmonies. In a complete texture, especially in close position, stationary tones clash with the prolonging foreign tones as non-tertian chords or as apparent seventh chords (cf. Ex. 7.1c).324

7.2 Linear Progressions within V7

The following discussion classifies linear progressions within V7 according to three criteria, of which only the third is related to the seventh: (a). Size of the progression. Each of the tonal spans within V7 may be filled by linear motion: major and minor thirds, perfect and diminished fifths, a minor seventh, and their complementary intervals (sixths, fourths and a major second). Besides this, each member of V7 may undergo a complete register transfer. (b). The number of active voices (1 to 4). The more active voices there are, the more independence the prolongation gains.325 (c). Active versus stationary seventh. The tone of the seventh either takes an active role in the prolongation or remains stationary. Both types prolong the seventh chord (as a chord) (cf. §5.3). The presence of the tone of the seventh has an effect even when it is stationary, since it may transform a passing interval into a complete harmony. The presence of dissonant active intervals, i.e., the seventh or the diminished fifth V7–3, is also important. Each type of linear progression may be realized in various ways with various harmonizations of the passing tones and in various contrapuntal combinations. In the following discussion I shall focus on those situations that involve linear progressions alone as the principal voice-leading procedure. (For combinations of linear progressions with neighboring motion, see below §7.3.4).

324 Strictly speaking, the avoided passing seventh chords are only apparent when their true dissonant tone is not their seventh, as in a III6/5 that is the product of a neighbor V7–6–7. For a different case, consider a passing VII2 whose tone of the seventh (in the bass) continues in ascent. V2 prolongation may also include non-apparent seventh chords (e.g., neighbor VII2). 325 The concept of voices here is inaccurate, since linear progressions by their very nature combine conceptually distinct voices. Schenker apparently found the more active motion desirable. He laments the ‘decline of our musical sense’ (FC, comment on Fig. 98a versus b) which is indicated by the less active procedures.

140 Full Circular Prolongation of V7

Linear progressions form genuine prolongations of the seventh chord only if the tone of the seventh is conceptually retained throughout the prolongation. The seventh need not literally appear at both boundaries of the linear progression. In particular, where there is a descent into an inner voice from a primary-tone seventh, the tone of the seventh often need not return in the final harmony. Usually the seventh must be present at the initial boundary. Deeper levels may create exceptions to this rule.326 Occasionally, the seventh arrives after the remainder of V has been established, but then participates in a further prolongation V8–7–. . . –7. This is only possible where the retention of the seventh is especially clear, i.e., when the seventh is a literal pedal point, or serves as the boundary tone for clear activity, as in a voice exchange. Otherwise, the first seventh would sound as a local passing tone that is not structurally connected to the final seventh.327 These observations apply best to linear progression in the upper voice. In the bass, linear progressions connect two literally different inversions of the prolonged harmony (see §7.7.1). In inner voices, linear progressions resemble those in the upper voice, but the conceptual retention here of an initial seventh is questionable.328

7.2.1 Third Progressions within V7 V7 includes three third-spaces. The lower spaces (V1–3 and V3–5) leave the seventh stationary, while the upper one (V5–7) involves the tone of the seventh, and raises the question of whether the seventh participates in the prolongation. The lowest third (V1–3) is major, and, as we shall see, it offers more possibilities for composing out than do minor thirds. In the bass, third progressions connect adjacent inversions of V7 (V7–V#, V#–V$, V$–V2 and vice versa. See §7.7.1). By their nature, third progressions include a passing tone that does not belong to the prolonged harmony (here V7). In order to produce independent chords, the boundary tones of the third progression must not be literally present at the same

326 See Exx. 6.14 (although the seventh arrives late, it nevertheless functions as the primary tone) and 6.17 (the initial seventh does not function as a hierarchical primary tone). Cf. also §8.3. 327 See my remarks on Ex. 7.50 (Haydn) and on Brown’s interpretation of the Eroica (fn. 462). For a more complicated case, see Ex. 7.27c (Mendelssohn). 328 See the inner voice in Scarlatti, Sonata K. 507, 26–33 (at least until m. 29).

Full Circular Prolongation of V7 141 time as the passing tone. Where this occurs, these sounds clash with the passing tone, and the progression sounds like a mere stretching of a single chord.

7.2.1.1 Diatonic third progressions

A single third progression against a stationary chord is rare (Ex. 7.2a–c). Among the three possible third progressions, two produce triadic sonorities, III6 (upper third) and II¢− (lower third), while the middle third results in a fourth-chord (V¢‡; set class 027). Ex. 7.2d–e shows the passing chords with the consonant support of root position (although III6 is itself consonant). Parallel motion can combine three distinct pairs and one triplet of third progressions within V7: (a). Parallel thirds (or sixths or tenths) in the lower pair of third-spaces (Ex. 7.3). This is the case that Aldwell and Schachter (1978/2003, 413, Ex. 24-16b) use as a paradigmatic ‘extended seventh.’329 The passing chord here is IV6, or— with literal retention of the fifth—II$. See both variants in the bridge of Brahms’s Violin Sonata Op. 78/I (Ex. 7.3c).330 The limited space of a third can nevertheless encompass wide prolongations: in Chopin’s Etude Op. 10,5, mm. 23–40 (Ex. 7.3d, after MW I, 90–92), the first step in the lower third progression is augmented (making a II4/3/ß1). This augmented second is transformed into an illusory diminished seventh progression, which allows a rich content on a lower level.331 (b). Parallel thirds (or sixths or tenths) in the upper pair of third-spaces. This pair is more effective in descent, since in ascent, delaying the tone of the seventh to the end might exclude it from the prolonged harmony. The passing chord is

329 Aldwell and Schachter’s corollary illustration (Ex. 24-16a), from Handel’s Flute Sonata, Op. 1,5, Bourrée, 17–18, can alternatively be interpreted as prolongation of a consonant V via VI. 330 The passage has a character of a bridge, but returns to the tonic. Combination of the same pair of parallel third progressions with a pedal point on the root would create a 7/4/2/1 sonority. A pedal point on the root would clash with the passing tones in a 7/4/2/1 sonority. This case has already been shown by Kirnberger (see my Ex. 3.3) in inverted form. See also: (1) Chopin, Scherzo No. 3, Op. 39, mm. 247–9 (after parallel neighbors). The passing motion is prominent since it occupies a full unit of the harmonic rhythm; (2) Beethoven, Violin Sonata Op. 47/II, at the opening gesture of the theme (mm. 1–4) and of most of the variations. 331 The prolonged V6/5 is motivically prepared in mm. 17–22. The text in MW is silent on the PD. Rothstein (1981, 156bis and 159) refers to the passage as V5–7, but the seventh is in fact present since m. 23 in an inner voice. See a similar use of a passing augmented second in Beethoven, Piano Sonata Op. 90/II, 178–80, via IVß6.

142 Full Circular Prolongation of V7

I¢− (Ex. 7.4a), or—with literal retention of the third—I$ (see above Ex. 7.3c, m. 17). The passing I is the subject of root-position support in Mozart’s Piano Sonata K. 280/I, 15–16 (Ex. 7.4b). This instance is used by Gregory Proctor (1978, 74) to demonstrate that PD is possible.332 (c). Parallel fifths in the outer pair of third-spaces (Ex. 7.4c). The parallel fifths should be eliminated nearer to or at the surface. The passing tones do not produce a separate chord without motion in the remaining voice. (d). Three parallel third progressions (Ex. 7.4d). As with the last instance, this configuration includes parallel fifths. The emerging passing chord is VI. In contrary motion, most third progressions within V7 fill a single third in both directions as a voice exchange.333 This creates the intervallic pattern 6–8–10 or vice versa. The passing tones need not be diatonic, but they nearly always coincide on a perfect octave. The emerging harmonies are the same as in one- voice third progressions within an incomplete seventh chord (cf. above Ex. 7.2), but here they are achieved more decisively. Such voice exchanges may be applied to any of the third-spans within V7 (Ex. 7.5).334 Contrary third progressions are not limited to voice exchanges in a single third-space (Ex. 7.6a). Combinations of parallel and contrary third progressions create parallel voice exchanges (Ex. 7.6b–d).335

332 Mm. 7–12 in the same movement are based on similar voice leading. This interpretation is based on the three-measure grouping determined by design (Beach 1983a, 6; Baker 1993b, 279– 80). See also Chopin, Berceuse, 5–6, in Schenker’s deliberately dynamic reading (Ex. 3.19). The seventh starts in the upper voice, and is reestablished in the inner voice after a lower neighbor. Aldwell and Schachter (1978 /2003, 94, Ex. 6–21) present an abstract configuration similar to the excerpt in Ex. 7.4b, albeit with a different inner voice (cf. Ex. 7.66h below). 333 Jonas ([1934] 1982, 103) calls ‘the alignment in contrary motion of two progressions’ voice crossing. Voices may also exchange pitch classes in similar motion (in progressions of complementary intervals) or in contrary motion when one voice moves an additional octave. For the latter technique within V7, see Bach, French Suite No. 4, Sarabande, 1–2. In I8–ß7–IV, the seventh arrives as early as the second beat. This interpretation fits with Rothgeb’s reading of mm. 21–22 (in Jonas [1934] 1982, Ex. 230. See diagonal line). 334 Voice exchange in the middle third appears (inverted) schematically in FC, Fig. 98,1a, quoted from C. P. E. Bach. 335 The passage from Beethoven, Piano Sonata Op. 90/II (in Ex. 7.6b) recurs in expanded form at mm. 49–59, leading to V5/3. Mm. 67–68 from the Handel aria in Ex. 7.6c use a configuration close to that in Ex. 7.6d, but retain the seventh as a pedal point.

Full Circular Prolongation of V7 143

7.2.1.2 Chromatic third progressions

In the upper third-spans of V7 there is room for one chromatic tone, while the bottom third, which is major, can encompass two chromatic tones, although each of them can appear independently of the other. Chromatic insertions can introduce new passing harmonies into the prolongation of V7. Among the single third progressions, the chromatic filling only has a significant potential in the lowest. For example, in Ex. 7.7 (Schubert’s Ecossaise D.781,8, mm. 9–12), this rudimentary motion does sound like a true prolongation (as opposed to a mere quasi-stretching, cf. §§1.1.1.1; Ex. 2.13c), since each passing sonority receives a relatively long duration and some tones have fz dynamics. Each passing tone creates a triadic surface sonority (this also determines details in the enharmonic notation). In this miniature dance, the four measures occupied by the third progression are the sole content of the dominant.336 In parallel motion, the precise adjustment of chromatically filled third progressions is problematic, since the diatonic passing tones within each third do not coincide. Chromatic filling of the lower pair also requires adjustment of the number of chromatic tones, since the bottom third-span includes one extra semitone. The fullest chromatic motion must therefore exceed the boundaries of the third in the parallel (middle) third progression. Schenker addressed this problem in CP I, Exx. 200–1, where he revealed the diatonic basis of a chromatic series of major thirds from Mozart’s Symphony No. 36/I (summarized in Ex. 7.8a). All this motion occurs after a seventh has already been added to the chord.337 The chromatic motion in both voices can be adjusted through either delay or omission. The technique of delay is used in the theme of Schubert’s Piano Sonata D. 960/III (Ex. 7.8,b1) within motion from V# to V$: the chromatic ascent from the root starts (m. 5) before that from the third (the rest of the ascent is diatonic). The delay gives rise to the passing VIIº7/VI, which, however, does not lead to VI

336 Yellin (1998, 37–38) calls this procedure half-omnibus or implied omnibus (named after the usual omnibus, see below §7.2.1.2.1), and finds it in Rossini, Bellini and Verdi. 337 Mozart uses an identical configuration in his String Quartet K. 387/IV, mm. 273–4, and with a change of the last tone in the upper voice in the overture to Le Nozze di Figaro, mm. 101–2.

144 Full Circular Prolongation of V7 in the theme itself. The V7 prolongation crosses the boundaries of the binary phrase rhythm (4+4 measures), which is suggested by the design. (The choice of the primary tone is ambiguous.) Toward the end of the scherzo Schubert alters the theme so that the latent meaning of an applied VIIº7 is realized (Ex. 7.8,b2). In that passage, the theme is located in the lower voice, and transposed: it starts on IV and modulates to the tonic. This makes the applied VIIº7 relate to II, and complicates the understanding of the deeper context. Omission of one chromatic tone in the lower third makes the number of semitones in the lower pair of third spans equal. If the omitted tone is the lower chromatic tone (ƒ1/ß2), the segmentation of the thirds into diatonic steps is also matched in both voices. In the upper pair of third progressions, both thirds are of the same size (three semitones). The locations of the diatonic passing tones coincide in minor, but not in major. Ex. 7.8c, from the introduction to Chopin’s Waltz Op. 34,1, shows both last procedures. The ascending motion starts from the lower pair of third progressions with partial chromaticism (mm. 3–4) and matching segmentation, and continues in the upper pair without matching segmentation.338 Chromatic motion can help to avoid parallel fifths in three-voice parallel third progressions, as in Ex. 7.8d, from Chopin’s Nocturne Op. 27,2. The lowest third progression in this example is expressed as an octatonic tetrachord, with the diatonic passing tone omitted. The descent from the seventh, located in an inner voice, includes the diatonic passing tone, but emphasizes the chromatic one. Among third- voice exchanges within V7, only the lowest (major) third lends itself to chromatic filling (see §7.2.1.2.1). Major thirds contain an even number of semitones, enabling the crossing voices to coincide on a perfect octave. By contrast, in the upper (minor) thirds, the crossing introduces harsh successions of augmented and diminished octaves (enharmonic to a minor ninth and a major seventh) (Ex. 7.9a–b). These opportunities remain infertile, although the clash can be avoided by means of displacement (Ex. 7.9c), or is even actively solicited in

338 For pairs of the lower third progressions with the lower chromatic tone omitted, see also Schumann, Ich grolle nicht [Dichterliebe No. 7], 16–18; Chopin, Piano Sonata No. 2/I, 39–40; Beethoven, Cello Sonata Op. 5,1/I, 31–32; and a modified example in Haydn, Symphony No. 92/I, 160–6 (Ex. 7.78f).

Full Circular Prolongation of V7 145 certain styles. For example, Skryabin inserts chromaticism (albeit in one voice only) into a voice exchange of the middle third of V7 in his Prelude Op. 11,22 (Ex. 7.9d).

7.2.1.2.1 The Omnibus progression

The chromatically filled voice exchange between the root and the third of V7 has almost become a cliché in tonal music. Yellin, who devotes a special study to this phenomenon (1998, after sketches from 1972) calls it the omnibus progression, and attributes the idea and apparently its name to Bernhard Ziehn, who developed ideas of 18th century theorists.339 This model connects V# with V7, or vice versa, and comprises five events (Ex. 7.10a). All the passing sonorities are tertian chords: the middle event is II¢−, as in the diatonic voice exchange. The second and fourth events have a structure of V7. The former functions on the immediate level as an augmented sixth chord (IV ƒ6/5/ß1 of II), while the latter lacks an immediate resolution. The progression is somewhat more common with descending bass, perhaps because it introduces the ordinary augmented sixth rather than a diminished third.340 In real-time listening, especially in a slow rhythm, the omnibus temporarily obscures the tonal directionality, and creates expectation for tonicizations of ßIII or II (Ex. 7.10b).341 Yellin cites many examples, from Mozart to Scott Joplin and beyond, with a special emphasis on opera. His presentation is historical rather than theoretical. Most of his examples are not, in fact, full circular prolongations of V7, since they lack or modify the V7 at one boundary at least. Most examples form transitive progressions, sometimes filling a VII7–V7 subordination (see §6.3.3), and others prolong diminished seventh chords.

339 Yellin 1998, p. xii. Wason (1985, 16–19) provides a concise survey; he calls this progression the classical omnibus, as opposed to the extended ominbus (cf. §7.6.1.1 below). Ziehn’s source cited by Yellin was published posthumously in 1912; Telesco (2001, 134) cites an earlier source by Ziehn, from 1865. See also Devoto’s explanation in his 1978 revision of Piston’s harmony book (Piston/Devoto 1941/1978, 440). See also Gauldin (1997/2004, 711). 340 Another reason: the evolution from the passacaglia progression (the descending lament tetrachord). See Telesco 1998, 255–60. 341 Wason (p. 18, Ex. 2-5) suggests that there is a connection of the second and fourth events, but this segmentation of the omnibus is unusual. The potential tonicizations seem appropriate as motivic preparations for real tonicizations, but I was unable to find a real instance of this procedure.

146 Full Circular Prolongation of V7

Direct, precise and unequivocal realizations of the omnibus appear relatively rarely, in about a dozen of Yellin’s cases, from Meyeerbeer, Verdi, Schumann, Chopin, Brahms, Delibes and popular music.342 The character of the omnibus progression is usually transitory; Brahms is exceptional in using it as a theme in the second trio of his piano Scherzo Op. 4 (Ex. 7.10c; Yellin’s Ex. 61).343 The theme recurs several times transposed, especially in a climatic passage toward the end of the trio (Ex. 7.10c,2). Some of these recurrences modify the omnibus: in the first appearance in the theme, the descending ß3/ƒ2 is missing (see below), and the last one becomes a simple arpeggiation.344 Most occurrences of the omnibus progression modify the basic model. Four types of modification retain the circular prolongation of V7: (a). Omissions (Ex. 7.11). Hybrid situations only partially exploit the chromaticism of the third-space. When the omissions occur in both voices together (Ex. 7.11a), skipping over of the second or fourth events brings the omnibus closer to the diatonic voice exchange. By contrast, omitting the diatonic middle event makes the progression far more daring, and transforms the third into an octatonic tetrachord (cf. below Ex. 7.16). Omitting a passing tone in one voice while its counterpart in the other voice is present (Ex. 7.11b) theoretically produces 24 possibilities (3 * 2 * 2 * 2): Any of the three passing tones, in any of the two active voices, either ascending and descending, can be replaced by either a sustained tone from the former chord or an anticipation of the next chord. In practice, the only possibility in use is the suspension instead of the first descending semitone from the third to the root in the bass. This introduces a diminished seventh chord (VIIº# of VI on the immediate level).345

342 See Yellin’s Exx. 34, 40, 55, 57, 61, 73, 81, 82, 84 and 85. Zajazkowsky (1987, 65–66) cites further examples from Tchaikovsky, including unmodified classical omnibus in Cherevichki, No. 14 (his example 3.22) and in the introduction to Iolanta, mm. 16–19. I have found additional cases in Bizet’s Carmen, No. 7 (duet), 77–79, and in Scott Joplin’s March Majestic, m. 71. 343 Meyer (1989, 124) describes this device of thematization as positional migration. 344 The omnibus in Chopin’s Etude Op. 25,11, mm. 17–19 (Yellin’s Ex. 57) is misrepresented in FC, Fig. 106,2b. Schenker shows the seventh as a passing tone that is delayed until m. 19, but in fact it is present throughout the omnibus, and even before. 345 See also: (1) Ex. 7.10c above (Brahms), m. 302–4; (2) Beethoven, Violin Concerto/III, 253–7: the seventh passes within the 8–5 space, and the dominant governs, mm. 251–60; (3) Mendelssohn, Violin Concerto/I, 459–72: a final phrase of tension, with impressive figuration. The

Full Circular Prolongation of V7 147

(b). Harmonic variants as a result of neighbor motion in other voices (Ex. 7.12). In the basic omnibus, the fifth and the seventh of V7 remain stationary. When one or both of them move to their neighbors, the intermediate harmonies change. Neighbor motion on the middle event may introduce IV6 or (using parallel fifths) VI for II¢−. I have shown the schematic situation and examples from Schubert’s Piano Sonata D. 894 (Op. 78)/I (not fully chromatic), and Verdi’s Otello, act 4 (using chromatic passing motion to the neighbor; Yellin’s Ex. 42). Neighbors on the second or fourth events tend to be less harmonic, but can give rise to a ‘French’ variant of the second event.346 (c). Displacement (Ex. 7.13). This happens when the active voices of the omnibus are not synchronized. Although any dissonant displacement is possible in principle, this procedure is most effective when the voices meet on a perfect octave, albeit not in the middle of the omnibus. One voice makes three chromatic steps before the meeting, and one after it, while the other moves one step before the meeting and three after it. See Ex. 7.13b (from Puccini’s Tosca; Yellin’s Ex. 44), which is further complicated by the addition of a third progression between the fifth and the seventh. (d). Inner and outer expansions. First, any component of the omnibus progression can be subject to an autonomous full circular prolongation. Other inner expansions (insertions) are difficult to achieve, since the smooth voice leading of the omnibus leaves little room for further motion. Passing tones are indeed impossible (unless registral manipulations are used), but suspensions, neighbors and subsidiary linear progressions may be inserted. (d-i) Inserted suspensions. These delay descending tones until after their ascending counterparts. At the immediate level, this results in an

analogous passage in the exposition (210–23) prolongs a diminished seventh chord; (4) Mozart, String Quintet K. 516/III, 64–65: a complete classical omnibus is preceded by an incomplete one. This passage is cited by Seidel (1970, fn. 4), and discussed as expansion by Rosen (1970/1972, 88). The enharmonic notation is inaccurate. 346 Neighbors can also appear as surface appoggiaturas to the passing chords. See Tchaikovsky, Symphony No. 5/III, 57–60 (Yellin’s Ex. 75). Addition of linear progressions is possible too (see below Ex. 7.13b from Tosca).

148 Full Circular Prolongation of V7

enharmonic interpretation of certain tones when they become suspensions (Ex. 7.14a).347 (d-ii) Inserted neighbors in the stationary voices (in the active voices, neighbors would spoil the chromatic drive). Such neighbors are heard as true insertions (rather than as added counterpoint) when all basic five events remain present. In Ex. 7.14b (from Brahms’s Symphony No. 2/I) the insertion of an additional chord before the goal serves as a climax of a local crescendo and reconciles the omnibus with the hemiolic rhythm, which requires six events rather than five.348 This insertion creates harmonic implications, despite its contrapuntal source. The inserted chord, ‘III6,’ relates to its predecessor as V2–I6. This creates the potential to hear the fourth event of the omnibus as V7, a potential which is further exploited in the coda (see below Ex. 7.108b) in a progression which starts as an omnibus but departs from it. (d-iii) Inserted linear progressions that do not form an autonomous prolongation of a specific member of the omnibus. In Ex. 7.14c (from Schubert, Piano Sonata D. 664 [Op. 120]/III), a third progression anticipates the goal in the lower voice, but starts on a subordinate harmony, and thus delays the goal harmonically as well as melodically (misrepresented in Yellin 1998, Ex. 24). The insertion is clearly separated from its environment by means of a stark decrease in dynamic volume and textural density. Locating the insertion immediately before the goal in both last examples seems very effective, since there the chromatic drive is the strongest. (d-iv) Outer expansion of the omnibus. Normally, when the boundaries of the omnibus change, it does not any more form a V7 prolongation. An exception occurs when the third-span between the root and the third is extended into an augmented fourth above the seventh. This procedure connects V# with V2, rather than with root V7. The third, seventh, and

347 This device is used in Schumann’s Cello Concerto/I, m. 61 in invertible counterpoint, where the seventh enters in the middle of the progression (cf. gradual transformation, §6.2.1), and in Liszt’s song Anfang wollt’ ich fast verzagen, 18–21 (Yellin’s Ex. 70), in a truncated manner. 348 See Yellin, Ex. 62. Schachter (1983a, Ex. 5) reduces this omnibus to a single V7/VI. This chord starts on m. 76, and is the subject of neighbors before the omnibus.

Full Circular Prolongation of V7 149

octave exchange positions (see Ex. 7.15 from Mendelssohn’s Reiselied Op. 34,6).349 The various techniques of modifying the omnibus can be combined, as in the trio retransition of Beethoven’s Symphony No. 9/II (Ex. 7.16): the chromatic filling of the third skips over the diatonic element, invoking an octatonic tetrachord; the voice exchange involves displacement that introduces a passing triad sonority; this harmony is internally prolonged by a neighbor chord that creates apparent harmonic V–I relations in ßVI, but the potential local tonic appears as a ¢−. Nevertheless, a remote tonicization is hinted at within this PD. This passage shows that a PD can incorporate lower-level prolongations. Again, dynamic shadings articulate the insertion. 7.2.1.2.1.1 The apparent omnibus. Sometimes, a succession that is identical to the omnibus functions differently, since the genuine grouping of the passage negates the boundaries of the omnibus. For example, in Schubert, Piano Sonata D. 845 (Op. 42)/I, 34–39 (Ex. 7.17a), the music begins to move in chromatic contrary motion several times, but stops after the second event, which functions in retrospect as a neighbor. When the motion finally succeeds in continuing, the chromatic drive pushes beyond the boundaries of the potential omnibus. (Also the rhythmic and dynamic design does not correspond to these potential boundaries). In retrospect, the inner ‘II¢−’ functions as a passing chord in a wider context. In the recapitulation (Ex. 7.17b), the goal V7/III is changed into the primary V7 (leading to Iƒ), and thus the melodic drive is further enlarged.350

7.2.1.3 Altered third-spaces

Third-spaces may move toward a chromatic variant of their goal. In such cases, minor third-spans are used instead of major or vice versa. The prolonged chord remains the diatonic V7, provided that it is re-established at the end of the prolongation. Within the boundaries of the seventh, six altered third-spans are

349 This prolonged chord is highly chromatic (V7/V within III); it appears (as a 5/3) in another function in the former strophe (m. 20) as a promissory sonority. The quasi-omnibus leads to a climax and depicts the rider’s flight to his beloved. 350 Devoto (Piston/Devoto 1941/1978, 440, Ex. 28-27), Yellin (1998, Ex. 26) and Telesco (1998, 243, Ex. 3) regard this passage as a genuine omnibus. I hear as apparent omnibuses also the passages in Wagner, Rienzi, Act 3, Allegro molto, 46–50 (Yellin’s Ex. 46c) and Chopin, Polonaise Op. 71,2, mm. 82–89 (Yellin’s Ex. 56).

150 Full Circular Prolongation of V7 possible (Ex. 7.18a): V1–ß3–1, 3–ƒ1–3, 3–ƒ5–3, 5–ß3–5 (these four under stationary seventh), 7–ß5–7 and 5–ƒ7–5. The inner goal is in most cases a non-tertian sonority, unless additional voices move too. Sometimes, the altered variant is heard as a neighbor, but only enharmonically (in particular, V7 with a raised root is heard as a neighbor VIIº2). The variant V1–ß3–1 is unique in that it introduces without further motion a consonant harmony that provides illusory stability, ßVII major triad.351 The chromatic filling of the 1–ß3 space of V7 is used in a peculiar passage in Beethoven, Piano Sonata Op. 14,2/III, 161–84 (Ex. 7.18b), which expands the content of the preceding passage. Beethoven introduces the beginning of the rondo theme on the ßVII, and achieves the effect of a deceptive recapitulation with a minimum of motion and maximum elegance.352

7.2.1.4 Third progressions that exceed the boundaries of the seventh

Third progressions from the root of V7 (or other seventh chords) downward, or from the seventh upward, exceed the boundaries of the seventh. In the former case, the intermediate chord,‘III9,’ is an apparent ninth chord (Ex. 7.19a, analogous to the apparent seventh chords in Ex. 2.16). The latter case, V7–9–7 (Ex. 7.19b, analogous to Ex. 2.15), forms a full prolongation of the seventh, and may involve SFM toward the ninth. Reading third progressions between the seventh and the ninth assumes that the tone of the octave is passing. When the V harmony is stationary, one might prefer to interpret the stimulus V7–8–9–8–7 as V7–8–7 with a secondary neighbor to the tone of the octave (V7–[8–9–8]–7)(Ex. 7.19c), but this problem is avoided when the passing octave is accompanied by parallel motion, or when the tone of the ninth receives another harmony, e.g., IV or II (Ex. 7.19d).353

351 Theorists describe such prolonging chords in tertian relations to the prolonged harmony as ‘non-stepwise decoration’ (Schachter [1968] 1977, 175), ‘embellishing chords’ (Salzer 1952/1962), or even as special neighbor chords (Cinnamon 1992, 3, fn. 3)—although it is better to distinguish these chords from stepwise neighbor chords. For the related procedure of V8–ßVII–V7 gradual transformation, see FC, Fig. 113,3a (discussed above, §6.2.1) 352 For a straightforward V7–ßVII–V7 progression (with inner prolongation of the ßVII), see Schubert, Trout Quintet/I, 129–43. In that movement, the lowered third has enharmonic motivic relation to ƒ2–3 in both principal themes. Cf. also V7–VIIƒ7–V7 in Haydn, Symphony No. 92/I, Ex. 7.78f, and a more radical chromaticism in Ex. 7.72 (Humperdinck). 353 Other possible harmonizations of the ninth are VI, which introduces parallel fifths that must be eliminated by further levels, or VII7, which is less distinct from V9.

Full Circular Prolongation of V7 151

Ex. 7.19e demonstrates the dilemma between V7–8–7 and V7–9–7 in a more subtle passage from Haydn’s Piano Sonata Hob. XVI:22/I, where the ninth is harmonized as V7/V (Ex. 7.19f).354 Another procedure that guarantees the priority of the 7–9–7 space is avoidance of the diatonic octave (Ex. 7.19g). When the ninth is major, this procedure replaces the 9–7 third by an octatonic tetrachord. A passage from Wagner’s Tristan und Isolde uses this procedure, harmonizing the passing tones with non-functional half-diminished seventh chords (Ex. 7.19h, after Mitchell 1962, 27, Ex. 23d-e).

7.2.2 Inverted Thirds: Sixth Progressions within V7 Each of the three thirds of V7 may be inverted into a sixth (Ex. 7.20a–c shows the ascending form). This device allows for a richer variety of content.355 The segmentation of the sixth progressions according to the arpeggiation of V7 involves adjacent tones (the seventh and the root) that belong to the V7 harmony. This second is absorbed together with an adjacent third into the larger unit of a fourth. In the literature, the only sixth progressions I have found within a circular prolongation of V7 are between the seventh and the fifth.356 These prolong the seventh more unequivocally where the seventh is already present at the beginning. Unlike in seventh progressions, this occurs when the linear progression ascends. Ex. 7.21a shows an extraordinary chromatic instance from the retransition of Brahms’s Symphony No. 1/I (mm. 333–42) (V7 has already been established at m. 321). The sixth occurs in the soprano, completely filled in chromatically. The

354 This bridge (mm. 60–67) expands that of the exposition (mm. 14–16). In TW 7 [1924], 7 [2005, 43], analysis of Beethoven, Piano Sonata Op. 57/I, 23–34, Schenker’s graphs for the succession V7–9–8–7 contain contradictory slurs that suggest both V7–9–(8)–7 and V7–(9)–8–7. The foreground complete graph shows a preference for the neighbor V7–8–7, which is more correct (see below Ex. 7.62d), but the text seems to prefer the connection to the ninth: ‘the possibility of retaining the position [of the seventh] in such cases is afforded by reaching-over technique,’ in contrast to ‘the descent of the seventh’ which ‘must be avoided.’ 355 A similar effect is achieved when one passing tone within a third progression is inverted into a seventh, as in Ex. 7.3d (Chopin, Etude Op. 10,5). 356 Sixth progressions from the third of V7 to its root appear in the form of subordination VII–V7 in Brahms, Waltz Op. 39,4 (cf. fn. 314). A similar sixth-space is outlined as an unfilled unfolding in FC, Fig. 106,2d (Schubert, Waltz D. 969 (Op. 77),5, mm. 9–10). I hear this V7 as continuing until m. 15, but the prolongation is not related to the sixth progression.

152 Full Circular Prolongation of V7 immediate function of the initial V7 (m. 333) is as an augmented sixth chord; it proceeds to a ¢− chord that functions in retrospect as a consonance, since it arpeggiates to the root. When the root arrives, the soprano proceeds in 5–6 motion. This segment recurs four times, with caesuras that consistently articulate precisely the most tense moments, following local augmented sixth chords. The end is adjusted to form closure: the pace slows down, the last sequence in the bass is lowered by one semitone, and the soprano stops ascending. The goal of the linear progression anticipates the return to V7, and is harmonized as V/V. Exact continuation of the sequence might have completed an octave divided into four equal portions (Ex. 7.21b, see §7.6.1).357 In descent, sixth progressions from the fifth arrive at the seventh only at the end (as in ascending seventh progressions), and thus do not prolong the seventh, unless the seventh exists before the linear motion, or otherwise prevails at the deeper level (Ex. 7.22a). In this case, the boundaries of the sixth may themselves be challenged: one might read a fifth progression followed by a passing tone (Ex. 7.22b), unless the V harmony returns only under the seventh, while the preceding 5 occurs within passing motion (for example, a parallel sixth progression, Ex. 7.22c). See a genuine prolongation of V7 by means of a descending sixth progression in Schumann’s Ich grolle nicht [Dichterliebe No. 7] (Ex 7.22d): the seventh is present at the outset of the prolongation in an inner voice, then disappears into consonant V and returns. The consonant V is heard as more local than the V7, mainly because it is achieved in the middle of the descent in the upper voice.

7.2.3 Fifth Progressions within V7 V7 contains one perfect fifth (1–5 space), and one diminished fifth (3–7 space). Diminished fifths are dissonant by themselves, but perfect fifth progressions

357 The unity of this sixth progression is challenged by the textural break after the initial chord; this break might fit an auxiliary cadence (Fƒ in the bass (m. 334)–G (342)–C (343). However, such an alternative interpretation will not provide harmonic coherence.

Full Circular Prolongation of V7 153 within V7 also form PD. Three types of segmentation are possible for each fifth progression:358 Type 1: the fifth-space is divided into two thirds, in accordance with the underlying arpeggiation. The middle tone is harmonized on the surface by the prolonged harmony itself, in our case V(7). Fifth progressions of this type are essentially chains of successive third progressions in the same melodic direction.359 They normally sound very close to the governing harmony. Type 2: the fifth-space is divided into two thirds, but the middle tone receives a different harmony. The effect is to unify the fifth-space. Type 3: the division of the fifth-space does not occur on the middle third, and negates the arpeggiation of the prolonged harmony. This type contradicts the normative assumption that ‘[a] linear progression represents a connection, by means of passing tones, of the tones of an arpeggiation’ (Rothstein 1981, 91).360 In this type, the middle third may lack emphasis, or even be avoided altogether. Such prolongations sound daring, and their governing chord may only be understood in retrospect. This type may create temporary confusion in real-time listening, especially if the segmentation takes place on chromatic tones. When the middle third is present, but not emphasized, the segmentation of the progression is likely to give rise to analytical dilemmas.

7.2.3.1 Diminished fifth progressions (V7–3 or V3–7)

These progressions normally prolong the seventh in descent only, since there the seventh is present from the outset (as in seventh progressions, cf. §5.4). The boundaries of this fifth (47– ) stand in conflict with normative stepwise descent to the tonic (cf. above §§2.1.2.2.3.4 and 4.3.4).

358 This classification may also apply to fifth progressions within consonant chords, and can even be extended to larger linear progressions. It is reminiscent of that for fourth progressions by Schachter ([1990] 1999a, 122). 359 Not every concatenation of two third progression in the same direction combines into a fifth. The exception is when the middle tone is more structural than the boundaries of the fifth (see below Ex. 7.23b). 360 The same assumption is made in Lerdahl’s theory of ‘tonal pitch space’ (Lerdahl 2001, 47 based on Lerdahl 1988, 321–2). Rothstein himself has shown exceptions to the rule he proposed (Rothstein 1999). Cf. also §4.1.

154 Full Circular Prolongation of V7

Type 1 (chain of thirds). This simple model (Ex. 7.23a) gives rise to the tension of the leading-tone tritone (cf. Ex. 2.11). Attempts to adhere to linear descents might lead to a preference of the middle third (2) as the structural tone, and abandonment of the fifth progression (Ex. 7.23b, an extension of the model in Ex. 4.12). An elaborated instance of this type occurs in Bach’s prelude BWV 924, mm. 13–17, within a larger V7 prolongation (Ex. 7.23c, after Jonas [1934] 1982, 134, Ex. 200). When the seventh first arrives (consonant V is already present), it is placed in the top voice and followed by a textural break. This encourages the listener to expect resolution, but such resolution does not arrive until the final measure, after several linear progressions, including two statements of V7–3 fifth progressions. This reading calls into question the existence of a normal Urlinie in the prelude.361 Type 2 (middle third receives a different harmony). The middle third, 2, is most likely to serve as the root of II (or II6) (Ex. 7.24). A simple realization is found in the aria Che faró from Gluck’s Orfeo ed Euridice (Ex. 7.24c). This aria culminates in a climatic fifth progression, with a V7–I–II6–V7 local progression. It is restated twice in hemiolic rhythm, and reappears once in the postlude.362 In Chopin’s Barcarolle, mm. 30–32 (Ex. 7.24d), the passing II is even tonicized, and the bass of V7 prolongation creates a harmonic divider. The final step is delayed by a large register transfer. Although V arrives at first as a consonance, the

361 In TW 4, Schenker indeed reads this prelude with an ascending Urlinie, with the seventh as an inner voice under 7. (For the principal problem, see Neumeyer 1987b and Schachter 1996, 333 and 340, fn. 12). The graph in FC, example for Fig. 43,b, omits the seventh in favor of a normative Urlinie with 2. Laufer (1981, Ex. 21) shows the seventh in the foreground but eliminates it in his reduction, and Forte and Gilbert (1982, sup., Exercise 14.4) resolve the V7 as early as m. 14. For a diminished fifth progression of type 1 within V7 [of V] in Schenker’s analyses, see the bridge in of Beethoven, Piano Sonata Op. 10,2/I, mm. 39–47, in MW II, 26, but not in the later (and better) graph in FC, Fig. 101,4. This type also occurs in Ex. 3.16 (Bach). For a diminished-fifth voice exchange within (an inverted) V7, accompanied by a diminished fifth progression that ascends to the ninth, see Beethoven, Piano Sonata Op. 22/IV, m. 72 (also transposed, m. 73). Schenker has written extended diminuendos for these passages, in order to express these sevenths do not resolve before the next downbeats (Rothstein 1984, 14). 362 The same phrase structure of two groups of three within V7 occurs at the hypermeasure level in Mozart’s Piano Sonata K. 280/I, 7–12. Mendelssohn uses a similar progression over a pedal point in his song Morgengruß, Op. 47,2, m. 6. This transforms the II into a V9.

Full Circular Prolongation of V7 155 seventh participates in the prolongation, due to its higher register and its actual presence at the end.363 Other chords can scarcely harmonize the middle third (2)(Ex. 7.25a–d): as the third of VII, and of course as the fifth of V, harmonic variety would lack, as in type 1 of fifth progressions. The desired variety can be achieved if 2 serves as the seventh of III7 (which is unlikely), or—when the chord involves mixture—as the third of an altered VII, or even as the fifth of minor V. Altering the 2 itselfß 2( or ƒ2, Ex. 7.25e–f) creates a daring variant, in which the division into thirds remains, but the underlying diatonic arpeggiation is absent, and one third is diminished.364 Type 3 (division defies the underlying arpeggiation) (Ex. 7.26). The space of the diminished fifth may be divided as V7–6–4–3, skipping over the fifth of V (2). The passing tones would usually belong to a single chord: ‘I’¢− or !, VI or even VII7/V. I have shown a simple realization from Haydn’s Piano Sonata Hob. XVI:43/I, where descent through type 3 (via I¢−) is followed by a more normative ascent back to the seventh. The inner voices counterpoint in third progressions. The third, fifth and seventh thus exchange positions: V3(–4)–5, 5(–6)–7, 7(–6–4)–3.365 In ascent, diminished fifth progressions V3–7 only reach the tone of the seventh at the end. Therefore, as with ascending seventh progressions, they normally form only SFM to the seventh (cf. Ex. 6.15a), rather than genuine prolongations of the seventh chord, unless the tone of the seventh is present at the beginning of the progression—or before it, as in Ex. 7.27a (Beethoven), (the first V7 arrives by means of II–V! subordination, cf. §6.3.1).366 An ascending fifth

363 In a different reading, Rink (1988, 199–200) prefers the consonant V. The barcarolle contains additional PDs, most remarkable of which is a register transfer within V9 in the introduction. Cf. also prolonged V7s in mm. 90–92 (decorated repeat of mm. 30–32) and 109–10. 364 A possible instance (with ß2) might appear to occur in Beethoven’s Piano Sonata Op. 22/II, 16– 17, but this passage is better read as an auxiliary cadence that negates the fifth progression. 365 The same configuration occurs in Beethoven’s String Quartet Op. 127/II, m. 50. The passing I6/4 occupies a sixteenth note. Even closer to the surface, a 32nd note anticipates the return to V7. TW 7, 39–41 [2005, 69–71] and Jonas 1952 exhaustively analyze this minute example, bearing in mind a letter by Beethoven, in response to prince Galizin who doubted the dissonant sonority that is created under the anticipation. Beethoven himself regarded the anticipation as non-harmonic, but thought of the 6/4 in harmonic concepts, discussing its fundamental tone (root). In Mozart’s Violin Sonata K. 376/III, 18–20, the 7–6–4–3 appears in a voice exchange. The passing function of the inner tonic is only understood in retrospect, since the passage appears after alternating unfolding of V7–I. 366 See also: Mozart, String Quartet K. 465/III, theme (mm. 4–6) and a more complicated passage in Beethoven, Piano Sonata Op. 7/IV, 23–35 (the ascent itself begins at m. 30).

156 Full Circular Prolongation of V7 progression to the seventh may, of course, combine with a descending one to form a voice exchange (Ex. 7.27b, cf. Gauldin 1997/2004, 709, Ex. 39.5). This is the underlying scheme behind Ex. 7.27c from the overture to Mendelssohn’s Die Hochzeit des Camacho. This voice exchange diverges from the basic model in several details, such as the insertion of the octave before the final seventh. Particularly delicate is the status of the initial seventh in the tenor, which is preceded by a consonant V (m. 258), but nevertheless continues a previous seventh. Theoretically, even when the seventh only appears at the end, the diminished fifth ascent can still count as an anticipation of the final V7. Cadwallader and Gagné (1998, 22, Ex. 2.6) read such an anticipation in the theme of Bach’s Fugue in F major from WTC I (Ex. 7.27d), but perhaps the passage expresses a tonic arpeggiation. The former reading sits more easily with the beats, but the latter better suits the meter.367

7.2.3.2 Perfect fifth progressions (V∞‡¡‡– or V¡‡–∞‡)

In V7, perfect fifth progressions connect the root and the fifth. In root position, they ascend from the bass to an inner voice or descend to the bass from an inner voice; the root may already be established at the beginning (Ex. 7.28a–b). Other voices can also contain perfect fifth progressions, involving doublings of the root (Ex. 7.28c, see below). The three types of fifth progressions apply here too: Type 1 is very simple, but even it can be elaborated. For example, the introduction of Chopin’s Waltz Op. 34,3 (Ex. 7.28c includes special chromatic passing and neighbor tones which are themselves decorated. Although the passing tones are not individually harmonized, they would clash harshly with the actual tones of the governing V7 harmony. Chopin avoids this effect by simply leaving off the accompaniment.

367 The tonic reading is unambiguous in a fugue by Johann Kaspar Ferdinand Fischer (his No. 10), which served as a model for Bach’s fugue (cited in Renwick 1995a, 52). Jonas ([1934] 1982, Ex. 144) is not decisive on the micro-hierarchy. See in the same fugue a descending diminished fifth in mm. 30–36 (provided m. 30 is heard as a strong measure). A similar ambiguity in a fugal theme that is based on the leading-tone diminished fifth occurs in the countersubject (imitated in the main theme) of Haydn’s String Quartet Op. 20,2/IV. The dissonant reading is most compelling at the apex toward the end (mm. 152–5), where the harmony of V is established before the leading-tone diminished fifth. The fifth progression, if accepted, is of my type 2.

Full Circular Prolongation of V7 157

In type 2, the middle tone of this fifth progression, which is the leading tone, should have an independent harmony. It may serve as the root of VII7 (VII! is embedded in V7 itself), the fifth of III or perhaps the seventh of I, but not the third of V (Ex. 7.29a–c). Schenker shows an example of a more complicated case, which uses a mixture of the middle third, in FC, Fig. 153,3, graph of Chopin’s Etude Op. 10,3 (paraphrased in my Ex. 7.29,d1). Schenker praises the passage, recognizing the dissonant frame: ‘How imaginatively the neighboring-note harmony II7/ƒ3 is expanded in measures 22–41.’ The suggested PD is impressive indeed, embracing tonicizations and illusory resolutions. However, the passage can be read rather differently (Ex. 7.29,d2). My interpretation hears the immediate resolutions as true, and denies the full PD. Schenker thus suggests, contrary to his ideology, a very daring PD where a more normative reading is possible. I assume he was led by the linear continuity in the bass, which is lost in my reading.368 Type 3, non-harmonic division of the fifth space (5–4–2–1) creates IV (or IV6) with a stationary seventh, or VI with a neighbor to the seventh (Ex. 7.30a–b).

7.2.3.3 Combinations of perfect and diminished fifth progressions

Both fifth-spaces within V7 may be filled simultaneously, in either parallel or contrary motion (Ex. 7.31a–c). One or both fifths can even be filled-in in both directions as a voice exchange (Ex. 7.31d–f, from Beethoven and Chopin). Ex. 7.31g shows a more complicated example from Schubert’s Piano Sonata D. 959/I, which is uncharacteristically located within the first theme itself. Against a prominent ascent in the bass, contrary motion is hidden (and sometimes implicit) within the inner voices. The segmentation of the passage is difficult to grasp, due to chromaticism of the bass and acceleration in the pace of the motion. Although the governing logic of the passage is contrapuntal, an immediate harmonic V–I succession arises. The emerging harmonies are not mere coincidental products of the voice leading: it is also possible to harmonize the same bass within V7 with far less harmonic coherence.

368 Parks (1976, 206–7) agrees with Schenker. His graph also includes an inner prolongation of V7 [of V/V] in mm. 38–41, but it is based on a simple error in the first chord of m. 38. The passage also involves background V8–7 with reverse hierarchy (see above §6.1.1) and diminution of the passing diminished seventh chords (mm. 38–41; see Ex. 8.34c).

158 Full Circular Prolongation of V7

7.2.4 Inverted Fifths: Fourth Progressions within V7 Both fifth-spaces within V7 can be inverted into fourths. Augmented fourth progressions above the tone of the seventh not only prolong a dissonant chord, but also fill a dissonant interval. The unity of this space is challenged by the presence of the octave as a passing tone. As with other linear progressions that involve the tone of the seventh as a boundary tone, the prolongation of the seventh is clearer when it is the initial tone of the progression. In this case, this happens in ascent (Ex. 7.32a). Such an unfolded augmented fourth opens the Allegro from Beethoven’s String Quartet Op. 59,3/I (Ex. 7.32b, after FC, Fig. 148,2). This passage also includes motion between parallel dominant seventh chords, contradicting their apparent resolutions. The extreme durational emphasis on the seventh chords enables this anomaly (cf. also CP I, 50–51 and 285). In descent, augmented fourth progressions to the tone of the seventh pose the same problem as descending sixth progressions: the seventh might sound as a passing tone from the immediately preceding octave (Ex. 7.33a–b). This situation occurs in Brahms’s Fugue on a theme by Handel, mm. 7–8. The melodic diminutions outline alternate augmented fourths and diminished fifths, but the sevenths appear as passing tones from implied octaves (Ex. 7.33c, after FC, Fig. 87,1a).369 Only when the seventh is present at or before the beginning of the progression does the descending augmented fourth prolong the seventh (Ex. 7.33d). Perfect fourth progressions should be possible in both directions (Ex. 7.34a). Perfect and augmented fourth-spaces can encompass voice exchanges, or combine

369 See discussion in Snarrenberg 1997, 23. Even a series of vertical V7s in falling fifths is normatively interpreted with implied elisions (Rothstein 1991, 312–3; see below fn. 468). Bach uses descending augmented fourth progressions in his Preludes BWV 924 and 926 (12 short Preludes, Nos. 1 [see Ex. 7.23c] and 3 [see TW 5] respectively). In the latter, the prolongation of V7 occupies no less than 16 measures out of 42 (mm. 17–32; the seventh is then further suspended over the resolution). The space between the third and the seventh is filled three times, twice as a diminished fifth and once as an augmented fourth. Schenker’s analysis in TW 5 designates the seventh only at the end. The undetailed graphs in FC, Figs. 82,4 and 152,6 ignore the initial seventh. The text of 82,4 (also in §215, cited in Slatin 1967, Ex. 171) presents the prelude only as an instance of illusory seventh (referring to the motion from the opening octave). See a descending augmented fourth progression in Ex. 7.15 (Mendelssohn).

Full Circular Prolongation of V7 159 in parallel or contrary motion (Ex. 7.34b–g). The latter configurations pass through a succession of dissonances unless additional activity is involved.

7.2.5 Seventh Progressions within V7 The space between the root and the seventh of V7 may be filled by illusory or true seventh progressions. I have already discussed the principal criteria for distinguishing true seventh progressions from the usual illusory ones (§5.4). It is worth remembering that most true seventh progressions are descending. Categorizing seventh progressions according to their segmentation is more complicated than the analogous classification of fifth progressions (§7.2.3). Since two points of segmentation (the third and the fifth) belong to the prolonged harmony, whenever these points are treated differently, hybrid situations arise that defy categorization into any of the three types of segmentation: the third can be articulated and even harmonized as V (or V7) while the fifth is not, or vice versa. Ex. 7.35 demonstrates all types of possible diatonic segmentations. Chromaticism by means of either mixture or chromatic passing tones offers further possibilities. An actual case of hybrid segmentation occurs in the sarabande from Bach’s French Suite No. 2 (Ex. 7.36): the fifth is not articulated, while the third receives strong emphasis. The possible alternative reading, without PD, better suits the meter, and to the motivic reaching-over, but ignores the clearly articulated beat level.370 Since any seventh chord includes only one seventh-space, parallel seventh progressions are impossible, at least not in a circular context. Parallel motion can accompany only portions of seventh progression (Ex. 7.37a). Multiple seventh progressions in the same direction become possible in imitation, as in the retransition of Schumann’s Piano Quintet/I (Ex. 7.37b). In this example, the seventh progressions in both outer voices emphasize the tones of the chord, but

370 Forte and Gilbert (1982, 23) endorse the dissonant reading (without providing a full graph), and present the alternative as incorrect. This specific analytical dilemma is extreme, since the competing readings are at odds even as to the identification of the surface chords.

160 Full Circular Prolongation of V7 the accompanying parallel motion in the inner voices defies the simple segmentation.371 In contrary motion, seventh progressions are only possible as a voice exchange. Ex. 7.38a–b compares two Beethoven examples, with different segmentations determined by the meter: in Piano Sonata Op. 101/III, 79–80 the seventh is divided into three thirds, while in String Quartet Op. 18,1/I, 282–4 the seventh is divided into two fourths. However, the apparent voice exchange of the seventh does not guarantee genuine prolongation of the seventh: if the descending line of the contrary motion starts on the octave, the real seventh only arrives at the end of the progression, and the whole progression stands for V8–7 (Ex. 7.38c).372 Seventh progressions within V7 are the kind of PD that most disturbed Schenker. He recognized large-scale seventh progressions that encompass complete development sections of sonata form (see below §7.10.1.2.4).

7.2.6 Inverted Sevenths: Filling the Second-Space 8–7 The motion between the seventh and the octave above it functions in seventh chords as both arpeggiation of a chordal space and neighbor motion (cf. §2.2: violation of the step-skip distinction). The complete motion to the octave and back (V7–8–7) is perceived primarily as neighboring motion (cf. §7.3.1.1). Chromatic filling of the V8–7 space only creates circular prolongation of the seventh if the seventh is literally present at both boundaries.373 It may take place in a single voice if the motion to or from the seventh in another voice takes another path. Ex. 7.39 demonstrates selected possibilities, using either similar or contrary motion. These progressions are reversible: Exx. 7.39b–c, from Schubert and Chopin are basically a retrograde of each other. The latter, from the coda of Chopin’s Scherzo No. 2, Op. 31, is based on FC, Fig. 143,2. It is complicated by

371 This passage is cited in CP I, 116–7 and by Rothstein (1991, Ex. 16) who calls it ‘composing- out of V7.’ The initial boundary is complicated by the existence of an earlier V9. See also Mozart, Piano Sonata K. 533/I, 135–8, with an unusual doubling of the seventh. 372 See also Beethoven, String Quartet Op. 18,2/III, 13–14: the seventh- voice exchange is counterpointed by register transfers, which are completed only after the re-arrival at the seventh. 373 Otherwise, the seventh would form either a passing tone from the octave, or a relatively structural tone with a subordinate octave appoggiatura (for the latter, see §6.1.1). In ascent, a V7–8 filling might be heard as motion into an incomplete upper neighbor.

Full Circular Prolongation of V7 161 local appoggiaturas, the last of which takes the form of V8–7 with priority of the seventh.374 The V7–8 filled step becomes much more conspicuous in voice exchanges (Ex. 7.40). Without further motion, the passing chord is a minor ‘VII¢−,’ which on the immediate level is heard as a cadential ¢− in VII ƒ5, approached from a German augmented sixth chord in the same key. The allusion to a cadence is especially idiomatic when the bass descends through the 8–7 space. This chord succession is identical to the middle of the omnibus progression (§7.2.1.2.1) (Telesco [1998, 259] calls it the small omnibus), but within the omnibus this smaller progression is rarely an independent unit. A unique radical voice exchange of the second-span occurs in Schumann’s Faschingsschwank aus Wien/III, 97–102 (Ex. 7.40b). The area of the prolonged V7 is marked by a distinct break in design: thin texture, quiet dynamics, slow rhythm, chromaticism and lack of skips, in sharp contrast to the prevailing scherzino mood (cf. Goldenberg 2004a). The progression contains five chords, all in a dominant seventh structure. The bass provides a harmonic fifth-divider, which is rare as support for a voice exchange. The daring passing harmonies hint (despite inversions) at V–I relations toward ƒIV, and momentarily obscure the tonal orientation. This passage compensates for the fact that the music stays in the home key throughout the latter half of the movement. The chromatic displacement is reminiscent of tonal relations earlier in the movement: tonicization of A major (VIIƒ, mm. 49–56) after a salient Aß major as a local dominant (V/ßIII).375

7.2.7 ‘Octave progressions’: Complete Register Transfers within V7 Each of the four tones of seventh chords may undergo register transfer. In register transfers of the root, third or fifth, the dissonant seventh remains stationary (Ex. 7.41a–c), but problems of segmentation are still possible. An especially

374 I have corrected the measure numbers. Schoenberg uses a related voice leading in his tonal song Traumleben, Op. 6,1, mm. 1–3 (consult Lewis 1987, 33). In that passage, the motion to the seventh (8–7) and from it (7–5) is identical to that in Ex. 7.39b, but the other voices are less harmonic. The way from the seventh to the octave is also possible by melodic detour. Schachter (1987c, 18, Ex. 8c) shows the motion 7–(8–9)–8 in Bach, Violin Partita No. 3, Gavotte en Rondeau, 80–90. 375 See filling of V8–7 also in Scarlatti, Sonata K. 458, mm. 15–16 (quoted in FC, Fig. 53,1). Only the upper voice fills the second, while the bass descends diatonically. When the upper voice reaches the octave, the bass is already resolved (into local I6).

162 Full Circular Prolongation of V7 interesting use of such octave progressions occurs in Ex. 7.41d, from Wagner’s Tristan und Isolde (the passage immediately after that in Ex. 7.19h). The guiding principle behind the voice leading in this passage is clearly the octave descent in parallel tenths in the outer voices. The boundary tones in these voices are the root and third of V7. The voice leading in the inner voices (including the tone of the seventh) is much less coherent. It is perhaps characteristic of Wagner’s style that the regained V7 only resolves to a remote key after enharmonic transformation into an augmented sixth chord.376 Register transfers of the seventh (4) are more intriguing from a theoretical point of view. In my experience, they are also more frequent, especially in descent. Descending register transfer of the seventh (Ex. 7.42a) gives rise to two interesting problems: (a) its opening seems to temporarily fulfill the tendency of the seventh to resolve, even though in retrospect the succession does not form true resolution of the seventh; (b) its final step is literally V8–7. In a true complete register transfer, the V8 passes within a larger motion, and does not form the source of the final seventh. Alternatively (Ex. 7.42b), one may hear this octave as an incomplete neighbor (transferred through an illusory seventh progression) from which the final seventh passes on a lower level. The latter reading still leaves the initial seventh prolonged, albeit less strictly. Ex. 7.42c applies both readings to Haydn’s String Quartet Op. 76,6/II, 76–78.377 The passing status of the penultimate tone is clearer when it is not harmonized as V (as is also the case with shorter spans that move via the octave). The most effective device is that of adding a parallel register transfer of the fifth (Ex. 7.43a). Bach employs this device in WTC II, Fugue in E major, 38–40 (Ex. 7.43,b(1) after Salzer and Schachter 1969, Ex. 9-67). This passage is complicated through a series of 9–10 suspensions. The inner voice forms a 5–6 series in relation to the bass, but there is ambiguity as to whether the fifths or the sixths prevail in this case. An alternative reading might regard the immediate descent

376 In Beethoven’s Diabelli Variations No. 1, mm. 20–24, the segmentation of the register transfer of the root of V7 is problematic: the penultimate chord within the prolongation is clearly passing, but nevertheless it is tonicized by the preceding chord. 377 Salzer (1976, Ex. 16) reads a complete register transfer. See also Chopin, Nocturne Op. 32,1, mm. 8–12, in motion to the inner voice. In that case, I prefer an incomplete neighbor, which is motivic in the theme of this piece (cf. Salzer 1952/1962, Ex. 216). Rothstein (1989, 229, Ex. 7.14) identifies the passage as ‘a large prolongation of V7,’ but does not read a seventh progression.

Full Circular Prolongation of V7 163 from the initial seventh as a true resolution (Ex. 7.43,b(2)). In that case the register transfer occurs within the tonic.378 The sense of register transfer may be maintained even if the initial and final sevenths belong to distinct linear threads. For example, in Ex. 7.44, from Beethoven’s Piano Sonata Op. 101/II, the line that descends from the seventh is transferred to the bass as a seventh progression, but the arrival at the lower- register tone of the seventh in the upper voice is decisive.379 Register transfer through multiple octaves offers fresh possibilities, provided that the subdivision of the compound space does not simply duplicate single octaves. Even a simple series of thirds alters the meaning of successive octaves (Ex. 7.45a). A more sophisticated procedure is found in Beethoven’s Piano Concerto No. 5/I, 6–9 (recurs 363–4) (Ex. 7.45b). This is an unmeasured quasi- cadenza. Such passages often stretch a single V7 (e.g., ibid. mm. 467–76), but this prolongation is full and imaginative. The segmentation includes a paradox. The passage contains a usually stable progression (I–VI–IV–II–V). The first four chords receive applied V7s, which a simple reduction might have eliminated, but the first of these applied chords is the prolonged V7 itself. It turns out that in the upper octave the emphasized tones are precisely those that do not belong to the prolonged harmony.380

378 Salzer and Schachter (1969, 363) identify the passage as ‘prolonged dominant harmony,’ but ignore the seventh. The prelude to the same fugue prolongs V7 in an analogous location, before the final tonic (mm. 35–45), although there the dissonance is hardly perceived. Cf. also parallel register transfers in the introduction of Chopin’s Barcarolle (within V9), and in Beethoven’s Piano Sonata Op. 14,2/I, 30–32. Concerning the latter passage, Rothstein (1984, 16) shows how Schenker’s tempo indications annotated in his personal copy highlight the register transfer. Register transfer of the tone of the seventh alone also occurs in Johann Strauss Jr., An der schönen blauen Donau, 32–41 (cf. Rothstein 1989, 21, Ex. 2.4). An intriguing chromatic register transfer of all four voices occurs in Grieg’s lyric piece Notturno (Op. 54,4), 47–54. Another device used to avoid the passing V8 is to skip over the 5 altogether. See Bach, WTC I, Prelude in E minor, 34–39 (resolution only at 41), in the inner voice. 379 Schenker (1920/1972, 35, also in Pastille 1990, 76) overlooks this seventh. At mm. 36–43, the passage is repeated varied over three octaves (Krebs 1980, Ex. I.37, ignoring the seventh). See also Haydn, String Quartet Op. 55,2/III, 84–88 (V7 governs since m. 82, perhaps until m. 92). This prolongation occupies a self-contained area, which is articulated also by dynamics and rests. At m. 85, downbeat I5/3 is initially heard as a true resolution. 380 Descending register transfer of the seventh also occurs in Bach’s Violin Partita No. 3, Prelude, 93–98, according to Plum 1988, 152, Ex. 7b. Schenker applies the register transfer to the resolution, but considers the whole passage as part of a larger V7 prolongation (MW I, 40 and 42). The diminution of the descent follows the pattern described in Exx. 2.9b–c.

164 Full Circular Prolongation of V7

Ascending register transfers of the seventh do not delude the listener with temporary resolution of the initial sonority. The ascent from the seventh necessarily involves reaching-over. I am aware of a single but remarkable instance, in Mozart’s Piano Sonata K. 533/II (Ex. 7.46, after Clifton 1970, 182, Ex. 11). This passage includes some striking surface progressions, in a dense texture. The ascending line occurs both in the upper voice and in the tenor in parallel octaves which are not synchronized, due to the harsh suspensions.

7.2.8 Counterpointing Linear Progressions of Different Sizes within V7 Simultaneous linear progressions of different sizes (‘linear progressions in mixed motion,’ FC §229), consonant or dissonant, require adjustment in order to occur within the same time-span. Progressions of any two sizes can be combined in multiple ways.381 Here are selected combinations using diminished fifth progressions. Counterpointing diminished fifth and augmented fourth progressions exchange the seventh and the third in similar motion.382 These progressions share the same absolute size (six semitones), but differ in the number of diatonic steps. They can be reconciled either through elimination of diatonic subdivision altogether, as in the coda of the second of Chopin’s Trois nouvelles Études (Ex. 7.47), or through adjustment. In such an adjustment, if all the diatonic tones of the fifth progression are present, the augmented fourth progression should comprise at least five events. Two methods can provide the missing event: delay and insertion. Adjustment through delay is based on a £− series. Either the initial V7 includes a £− formation as the upper part of V7 in open position, and the final V7 is stated as a £‡ (and provides the additional event) (Ex. 7.48a; cf. Ex. 6.1c [Brahms]), or vice versa, as in Mozart’s Symphony No. 35/I, 56–57 (Ex. 7.48b). Both passages include typical 7–6 suspensions; however, the final 7–6 in the Brahms passage and the initial 7–6 in the Mozart passage are not true suspensions, since these

381 Possible criteria for classifying the combinations: the difference between the sizes of the involved linear progressions, the direction of the motion (similar or contrary), the spatial location (upper and lower counterpoint), the emerging intervals, and the techniques of adjustment. 382 See fn. 333 on voice exchanges in similar motion. The passage in Haydn’s String Quartet Op. 55,2/III, 84–88 (mentioned above, fn. 379) might be understood as a voice exchange in similar motion of the seventh and the fifth (in the two melodic levels of the first violin).

Full Circular Prolongation of V7 165 sevenths are more structural than the ensuing sixths. The opening of Wolf’s song Herr, was trägt der Boden hier explores the latter procedure more daringly (Ex. 7.48c, after Williamson 1996, Ex. 3). In this example, some suspensions violate the linear continuity, and one suspension is transformed into ƒ7–7. The number of events here exceeds the minimum requirement of five.383 Adjustment through insertion of a chromatic passing tone into the fourth progression occurs in Haydn’s String Quartet Op. 64,3/I, 133–5 (Ex. 7.49a). This passage sounds simple enough, as if it hardly departs from the governing V7, but in fact includes a complete diatonic circle of fifths. Each of its four voices is clearly based on a linear progression, but the verticalization of the harmonic progression does not sound sensible. Perhaps this tonal paradox results from a lack of synchronization of two tones in the tenor (Ex. 7.49b). The finale of the same quartet (Haydn, Op. 64,3/IV) includes remarkable passages that combine diminished fifth progressions in different ways. At three points in this movement—in the exposition bridge, the development and the recapitulation bridge—there are enigmatic, slow and quiet passages in a choral texture, which are based on stepwise chromatic motion. All these features contrast with the light character of this movement (cf. Goldenberg 2004a). In both the exposition (mm. 47–53; Ex. 7.50a) and the recapitulation (mm. 173–82, Ex. 7.50b), these passages prolong V7. The initial V7s are established at first by relatively simple means (since mm. 36 and 163 respectively384). In both prolongations of V7, the soprano descends a diminished fifth progression. The bass reaches root position at the end; at the exposition it ascends a fourth from a $ inversion,385 while in the recapitulation it descends a third from a # inversion. The exposition passage creates a more functional impression: the first passing chord, ßIII (Aß major) which is never vertically realized, is heard as a unique sort of a deceptive cadence. In the recapitulation, the voice leading is less complicated (it

383 Cf. also mm. 19–22 of the same song. A similar progression (without local suspensions) is proposed as an interpretation of Beethoven’s Bagatelle Op. 119,8, mm. 9–12 in the repeat, by Cone (1977, 92, Ex. 7) and (with a different context) by Marston (1986, 198, Ex. 2). This reading is based on a problematic hearing of the unaccompanied bß (m. 9) as a seventh. 384 In both passages, V first arrives as a consonant chord (first beats of mm. 35 and 162, second violin). For the reasons for evaluating such passages as prolongations of the seventh, see §5.4.1. 385 See a similar combination of linear progressions in Beethoven, Piano Sonata Op. 49,1/I, 12–15. (Ex. 6.24c). In that case, however, the initial boundary is harmonized as II.

166 Full Circular Prolongation of V7 occurs in similar motion), but the emotional impact is stronger, mostly due to the inclusion of several diminished seventh chords among the passing harmonies.386 The analogous passage in the development (mm. 102–11, see Goldenberg 2004a, 107) forms a transitive progression from a diminished seventh chord. Paradoxically, this transitive passage is based on a single tone in the bass, while the circular prolongations of V7 in the exposition and recapitulation connect different tones in the bass. The opening of this movement plants the seeds for the V7 prolongation (Ex. 7.50c): the leading-tone tritone is unfolded throughout the opening gesture (resolving to 8), despite contradicting returns to the tonic pedal point.387 A combination involving a diminished fifth progression in ascent (and the lowest third in similar motion) takes place in Schumann’s Am Kamin (No. 8 in Kinderscenen), mm. 9–16 (Ex. 7.51). Over a V pedal point in the bass (with the seventh at both boundaries), passing II and III are tonicized. The tonicization of the II negates the pedal point; that of the III merges with the pedal point into III6. This feature, together with surface syncopation, weakens the III.388

7.3 Neighbors to V7

Each of the tones of V7 may have upper, lower or double neighbors. Diatonic lower neighbors to the octave or upper neighbors to the seventh pose a problem, since these neighbor tones also belongs to the chord (see violation of the step-skip distinction, §2.2). As with my classification of other prolonging techniques, I distinguish between neighbors to the consonant members of the chord, and neighbors to the tone of the seventh. I will begin by discussing neighbors without

386 The segmentation in of the diminished fifth in the recapitulation is problematic. One might hear the Eº6/5 connected to the Eº7 (dß–bß in the upper voice, g-e in the bass). In that case, a nested prolongation of a diminished seventh chord emerges, and the diminished seventh dß is resolved into an inner voice c at m. 182 (for the principal problem, cf. §4.1 and Exx. 4.3, 4.6 and 4.8). 387 I suggest the 8 as the primary tone, that might suspend to the seventh of 7V, as in the model of Ex. 4.24,a4. The opening unfolding alternates with the tonic tone. This contradicts the well- formedness rules of hierarchy as presented by Lerdahl and Jackendoff 1983. Laufer (1985) describes similar returns to the tonic (on a large scale) as parenthetical. 388 Rothgeb 1999b has a different detailed reading, which was drawn in response to correspondence with the present author (Rothgeb 1999a and then privately).

Full Circular Prolongation of V7 167 additional motion, and proceed to combinations of neighbors with linear progressions.

7.3.1 Neighbor Motion below (or above) a Stationary Seventh

7.3.1.1 Upper neighbors below (or above) a stationary seventh

When the seventh is stationary, upper neighbor motion creates the same voice- leading procedures that produce appoggiaturas (subordinations) to V7, but in a full circular manner (i.e., with the V7 stated before the neighbor as well).389 Thus, they might be called circularized subordinations. The commentary on the specific subordinations (§6.3.1) applies to their counterpart full neighbors as well. As in subordinations, upper neighbors are much more common as semitones, even when the diatonic form requires a whole tone. Thus, in major keys upper neighbors to the root and fifth of V7 would be ß65– andß3 2– respectively. In terms of functional directionality, the neighbor motion expresses a tonal regression (from dominant to subdominant degrees or from V to VII), and then returns to lead forward to the tonic. The following is a description of the particular forms of upper neighbors above a stationary seventh: (a). Upper neighbor to the root alone (Ex. 7.52a–d) creates V7–VII2–V7, or in a thinner texture (omitting the fifth of V7) V7–II¢−–V7. The semitone neighbor VIIº2 became a classical cliché.390 Mozart exploits it more artfully in his

389 For example, VII2–V7 forms subordination to V7, while V7–VII2–V7 forms full prolongation by means of neighbor motion. Every neighbor chord could appear as mere subordination to V7, although not all forms of subordination involve neighbor chords. The distinction between subordination and full neighbor is obscured when the neighbor chord appears twice, once before V7 and then within V7. Such successions sound like a duplication of the single subordination (described as ‘crossing branches’ in N. Wagner 1995). See, for example, the succession IVß6–V7– IVß6–V7 in Schumann’s Die alten, bösen Lieder [Dichterliebe No. 16], mm. 19–23 and 27–31 (applied to structural IV and V). 390 For instances of V7–VIIº2–V7, see: Haydn—Piano Sonata Hob. XVI:22/I, 14–16 (expanded in the recapitulation, see Ex. 7.19f); Mozart—Piano Sonata K. 309/III, 52–57 (+ repeat in 157–61); Piano Sonata K. 333/I, retransition, 87–93; Piano Sonata K. 576/I, 61–62 (within secondary dominant applied to ßVI); String Quintet K. 516/I, 105–6; Beethoven—Piano Sonata Op. 79/I, 36– 38 and 40–42 and Piano Sonata Op. 14,1/III, coda, 112–21, as a climax of expansion of the main theme. In Op. 79, the way from V7 to the neighbor is indirect, through large linear progressions, but the return from the neighbor is direct. Alternative reading: V7 encompasses 108–121. For a

168 Full Circular Prolongation of V7

String Quartet K. 464/I (Ex. 7.52e). The retransition (157–9) emphasizes this neighbor motion through fp dynamics and a long duration. This gesture penetrates the recapitulation, where a similar chord (a passing IVß6) is inserted into the fourth measure of the first theme (m. 165, lacking in the exposition, m. 4) on the same bass tone, with similar dynamic shadings. The smoothest neighbors of the root of V7 always introduce VII7 one inversion below that of the V7 (Ex. 7.53): along with V7–VII2–V7, this creates V#–VII7–V#, V$–VII#–V$ and V2–VII$–V2.391 (a1). An upper neighbor to the octave while the root remains stationary in a lower register creates V¶°–¶·–¶° (Ex. 7.54), often with ß9 (also in major). I also show this neighbor motion accompanied by parallel thirds, as well as a special elaborated example from Chopin’s Scherzo No. 2, Op. 31. (b). Upper neighbor to the root and the third (Ex 7.55): if the V7 is complete, the neighbor takes the form of II$ (possibly II4/3/ß1 with a semitone neighbor in major). In general, the inversion of the II is two phases away from that of the V7: V#–II2–V#, V$–II7–V$ and V2–II#–V2. If the V7 lacks the fifth (2), the emerging neighbor chord is IV6 (or IVß6 with a semitone neighbor in major); the inverted forms would be: V#–IV¢−–V# and V2–IV£¦–V2. (V$ always includes the fifth, since this tone is in the bass).392

diatonic V7–VII2–V7 in major see Mendelssohn, Song without Words Op. 53,6, mm. 3–4. See also V8–VIIº6/5–V7 [of IV] in a composed out manner in Mozart, String Quintet K. 593/IV, 116–31. 391 See recurring V4/3–VIIº6/5–V4/3 neighbors in Haydn, String Quartet Op. 55,1/IV, 100–6 (retransition). The VIIº6/5 is at no time literally present, but is nevertheless unequivocal. Above the neighbor, the first violin plays the largest leaps in the whole movement. 392 Instances of neighbors to the root and the third of V7 include: (1) V7–II4/3–V7, diatonic in minor: Chopin, Scherzo No. 1, Op. 20, mm. 333–7 (see below Ex. 7.101a for context); (2) V7– II4/3/ß1–V7: Mozart, Symphony No. 40/I, 34–37. Schenker (MW II, 67) identifies the V, but not the seventh. Rothgeb (1975, Ex. 16) groups these measures together under V7; Mendelssohn, Die Liebende schreibt, Op, 86,3, mm. 28–33, on V7/IV, in the transition to the last strophe, creating continuity over the articulation point of the design. The resolution takes place on a probably consonant 6/4; after V8/7–9/7–8/7: Schumann, Romance Op. 28,3, first Intermezzo, 152–9 (repeats 160–7). The II4/3/ß1 is approached here as both neighbor and passing; (3) Inverted: V6/5– II ß6/4/2/1–V6/5: Mendelssohn, Song without Words Op. 102,4, mm. 19–20. The V6/5 is stretched until m. 22. This is a thematic retransition, which omits the tonic in its expected location analogous to the opening. This results in a tonal conflict (Schachter [1987b] 1999a, 112–5); (4) In a thin texture: V7–IVß6–V7: Beethoven, Piano Sonata Op. 53/I, 9–11 (V is resolved at m. 14); (5) Inverted, in a thin texture: V6/5–IV6/4–V6/5. Diatonic in a local minor context: Scarlatti, Sonata K. 480, mm. 73–78, with untypical seventh-doubling; Mozart Piano Sonata K. 576/I, 68–69; Haydn, Variations in F minor, coda, 197–9.

Full Circular Prolongation of V7 169

The neighbor itself may have its own neighbor. Secondary neighbors can even negate the diatonic basis, as in Mozart’s Piano Sonata K. 332/III (96–99, recurring in variants four times. See Ex. 7.56). This procedure has a much stronger effect than an ordinary chromatic neighbor.393 (c). Upper neighbors to the root, third and fifth together (Ex. 7.57) produce IV#, and in general, IV7 one inversion higher than that of the V7, i.e., also V#–IV$– V#, V$–IV2–V$, V2–IV7–V2. Three-note neighbors to root V7 or V2 in close position (but not to V#, V$ or open-position V2) create parallel fifths. In the example from the introduction to Wolf’s Mörike song Citronenfalter, mazurka rhythm emphasizes the recurring neighbor chord, until its metrical location is finally transformed into an appoggiatura.394 (d). All other upper-neighbor combinations with a stationary seventh result in non-tertian sonorities, and thus form mere stretchings (§§1.1; 2.3.1). When both the root and the seventh remain stationary, neighbor sonorities necessarily contain the interval of the seventh, whose only chordal harmonization is the seventh chord itself. Similarly, upper neighbors to the root and fifth create the non-tertian 7/6/3/2, 7/5/4/1, 7/6/3/1 or 7/6/4/1. Neighbors to the fifth alone can occur in open position as a ¶ª neighbor to 12/7 (Ex. 7.58).395

7.3.1.2 Other neighbor motion below (or above) a stationary seventh

Lower neighbors to the consonant members of V7 are extremely rare without motion of the tone of the seventh. As Ex. 7.59 shows, the only lower neighbor combinations that produce tertian chords under this condition are elaborations of

393 See also Schubert, Trout Quintet/II, 43–52 (IV6/5/3/ß1 as appoggiatura to the neighbor II4/3/ß1). Beach shows this neighbor as a parenthetical insertion (Beach 1995, Ex. 9) and explains the extraordinary middleground context (Beach 1993, 9; this specific V7 is applied towards IIƒ). The secondary neighbor should be distinguished from 3–4–5–4–3 successions that express third progressions above a 1–(ß)2–1 neighbor. For that procedure, see Mozart‘s song An Chloe, K. 524, mm. 44–47. 394 See V6/5–IV4/3–V6/5 also in Haydn, Symphony No. 100/I, 147–51 (with a further immediate neighbor) and Beethoven, Violin Sonata Op. 30,3/I, 169–70, employing exceptionally a whole tone neighbor. In Haydn, String Quartet Op. 64,3/IV (Ex. 7.50 above), the more daring PDs are prepared by the neighbor motions V4/3–II7–V4/3 in the exposition, V6/5–IV4/3–V6/5 in the recapitulation (and VIIº4/3–IV7–VIIº4/3 in the development). 395 See inverted forms of the upper neighbor to the fifth alone: V6/5 with 3–4–3 neighbor in Chopin, Waltz Op. 34,3, m. 21; V4/2 with 6–7–6 neighbor in Chopin, Waltz Op. 42, m. 238.

170 Full Circular Prolongation of V7 the root and third (via II6), or of all three consonant tones (via IV#). The latter introduces parallel fifths, which are avoided in inversions: V#–IV$–V#, V$–IV2– V$, and in open position V2–IV7–V2. Lower neighbor to the root alone coincides with arpeggiation of the inverted seventh; it creates an improbable diminished VII triad with doubled root. Some combinations of upper and lower neighbors in contrary motion under a stationary seventh also introduce tertian sonorities (Ex. 7.60), while other combinations do not. The effective neighbors usually relate to V7 in an incomplete texture. In a rich texture, the root may be doubled and have both upper and lower neighbors.396

7.3.2 Neighbors to the Tone of the Seventh Itself

7.3.2.1 Upper neighbor to the tone of the seventh

Motion in the space between the seventh and the upper octave (in all kinds of seventh chords, at least with a major or minor seventh) functions both as an upper neighbor and—especially in the absence of additional harmonies—as arpeggiation, violating the normative distinction between leaps and steps (§2.2). Even a direct V7–8–7 neighbor without change of harmony (Ex. 7.61a) is more than a trivial stretching of a single chord, since it means control of the seventh over a point where only the consonant V is literally present, even with the octave in the same register. In certain passages, the final seventh might be heard more as a passing tone from the preceding octave, rather than as a direct continuation of the initial seventh (Ex. 7.61b). Even then, the initial seventh is essentially prolonged, and the octave serves as a lower-level incomplete neighbor.397 Since in V7 the second between seventh and root is major, space is left for chromatic filling in, in either direction or in both (Ex. 7.62a–c). The descending chromatic motion is identical with SFM within V8–7.398

396 This procedure occurs in Beethoven, Piano Concerto No. 4/I, 197–8, without return to the seventh. Cf. contrary neighbors in Haydn, Variations in F minor, 199–201 (cf. fn. 406), and special neighbors that use double alteration in Exx. 7.17 and 7.71. 397 Compare the same problem with descending register transfer, Ex. 7.42 (§7.2.7). The pattern V7– 8–7 as elaboration of the seventh has already been recognized by Heinichen (refer back to Ex. 3.1). The interpretation of the incomplete upper neighbor appears in Kielian-Gilbert 2003, 77. 398 Brahms used the form of Ex. 7.62c as a motto for his Cello Sonata No. 2/II (m. 2; harmonized at mm. 6–7). For filling in of the V8–7 space, cf. also Exx. 7.39–7.40.

Full Circular Prolongation of V7 171

An impressive V7–8–7 true complete neighbor appears in the bridge of Beethoven’s Piano Sonata Op. 57/I (mm. 23–33), applied to III (Ex. 7.62d). The ascent is not chromatic, but uses reaching-over, while the descent moves through several passing chords. The neighbor consonant state is emphasized in the upper register, but as the many existing graphs agree, the seventh governs.399 The neighbor octave may receive a separate harmony, usually a plagal ‘I’¢−, by means of parallel upper neighbors to the third, fifth and seventh together (Ex. 7.63).400 The emerging parallel fifths can be avoided by inverting the upper voices, or eliminated by the surface. The motion to and/or from the harmonized neighbor can be filled chromatically, with or without parallel fifths. This pattern, with chromatic filling of the ascent only, explains most of the exhaustively discussed passage in Bach’s Prelude in C major from WTC I, mm. 24–31 (Ex. 7.64a). In this passage, the seventh is further decorated by surface suspensions. The neighbor motion is preceded by a voice exchange of the fifth with the seventh, which brings the seventh into the upper voice; the passing chromatic tone in the tenor is notated ß6 (eß), as if it leads directly to the final 7V. This excerpt served as proof that a tonal PD is possible (Morgan 1976, 54; Larson 1997, 108–9; Brown and Dempster 1988, 151) and disturbed analysts who wanted to reconcile it with dogmatic Schenkerism (Clark 1982, 222 and 248; Baker 1983, fn. 13). Schenker’s own reading in FGA shows the prolongation of

399 See graphs by Schenker in TW 7 (using parentheses) and in FC, Figs. 119,20 and 154,4; Aldwell and Schachter 1978/2003, 618, Ex. 32-15; Katz 1945, Ex. 53a; and Krebs 1980, Fig. I.5. Several of the graphs refer to different measure numbers, apparently a misprint. Burkhart (1983, 97) explains the influence of Schenker’s reading on the fingering in his edition of the sonata. The earliest and the only detailed graph, in TW 7 (1924), reads a reaching-over to the ninth (cf. above fn. 354) rather than a neighbor, and allots the V8 an improbably low passing rank. Analogous material is absent from the recapitulation, but does appear in the development (94–108, applied to VI). Katz (1945, Ex. 53b) reduces the content of mm. 87–109 into V7 while Krebs omits the seventh in the same boundaries. The actual 4 only arrives at m. 89 and the actual 7V only at m. 90. FC, Fig. 142,2 shows motivic parallelism in the foreground progression in mm. 204–210. Similar cases: (1) Beethoven, Piano Sonata Op. 90/I, 100–9. The initial seventh is weak, and the consonant neighbor V8 is itself internally prolonged (104–8. See FC, Fig. 98,4). Jonas ([1934] 1982, Ex. 174) reads the same boundary events as I do, but refrains from connecting the sevenths; (2) Bach, Violin Partita No. 3, Prelude, 120–8, where the neighbor V8 undergoes register transfer. 400 See Scarlatti, Sonata K. 513, mm. 6–7. This V7 is never resolved properly (it functions in retrospect as VII7/II). It is followed by neighbors to a diminished 6/3 chord (m. 9–10), and has no further parallels in the rest of the sonata. A tendency toward semitonal neighbors is revealed here too (8/6/ß4), although at this point the neighbors do not relate to the root.

172 Full Circular Prolongation of V7 the seventh quite clearly; the presentation in FC (Fig. 62,5) is incomplete and misleading, since it shows the seventh only at the goal (FC does show the initial seventh in Fig. 115,1a). Variants of essentially the same reading as in FGA appear in numerous graphs that exploit this work of simple and steady texture as a case study for testing new approaches (Lerdahl and Jackendoff 1983, 261–4) or for pedagogical purposes (Cadwallader and Gagné 1998, 201–7; with a different ending, Neumeyer and Tepping 1992, 68–71).401 With regard to the prelude’s background, the upper structural tone during the V7 is 2 rather than 4. As to the resolution of this7, Vall existing graphs (except Neumeyer and Tepping) follow Schenker in reading an anomalous delay of the descent to the final 1 until m. 35, after the bass has already arrived at I (m. 32). This situation contradicts the rule of simultaneity of structural points between outer voices (Rothstein 1981, 112–3; also Cadwallader and Gagné 1998, 205–7). This reading is motivated by the background coupling of the upper voice and the return to the obligatory register. It seems to combine two competing interpretations (Ex. 7.64b–c). The prolonged seventh still belongs conceptually to an inner voice under the background 2; otherwise, the entire Urlinie descent must have been read over the final tonic pedal point (Ex. 7.64d), and this is improbable. Besides the ‘I’¢−, the only other tertian harmony that may harmonize the neighbor V7–8–7 with stationary bass is III6 with a doubled third (Ex. 7.65a). In major this chord counts as consonance (in minor it is augmented), so that it does not need ‘consonant support,’ but it can be transformed into more stable positions (Ex. 7.65b–d): I!, III! (in major), or I6. Mixture introduces additional possible harmonizations, e.g., ßIII!. Mendelssohn explores this possibility in Song without Words Op. 53,1 (Ex. 7.65e). The passage starts as a pair of parallel third progressions, but the lower line is not completed. Rather, the last passing sonority

401 See also the graph in Cube [1947–1955] 1988, 275. Drabkin (1985) brings two letters from 1930, written by Schenker to Cube, who was apparently involved in the preparation of the FGA graph. The earlier letter includes a sketch that shows mm. 24–31 as mere 5–7 (as in FC, Fig. 62, 5), but in the later letter, Schenker explicitly acknowledges that ‘the F [the seventh] already appears in the left hand [m. 24]’ (Drabkin 1985, 255). The FGA reading is also discussed by Jonas ([1934] 1982, 88). In Cadwallader and Gagné (1998), Ex. 8.5b invents a consonant source for the seventh of V7, which is in fact lacking (as is accurately shown in their foreground graph in Ex. 8.1).

Full Circular Prolongation of V7 173 becomes V of the ßIII that supports the neighbor. The passage involves chromaticism, but the 7–8–7 neighbor motion remains unfilled. The combination of V7–8–7 with lower neighbors does not produce tertian sonorities. Theoretically, an 8/6/2/1 neighbor might have been perceived as an inverted VI7/3/1, especially when the lower neighbors are altered, but the doublings are implausible. Combining 7–8–7 with a lower neighbor 8–7–8 would bring a voice exchange and retain the V sonority.

7.3.2.2 Lower neighbor to the tone of the seventh (V7–6–7)

V7–6–7 neighbor motion can introduce various harmonies, alone or in combination with other neighbors, in complete or incomplete texture (Ex. 7.66): III#, III6, I$, I¢− and VI2 (along with non-tertian sonorities). Here too, neighbor I or VI may appear in root position and provide consonant support (III or I6 are less likely since 3 is already present in the neighbor tone itself). The nested I3 might be heard temporarily as a resolution of the seventh (rather than a prolongation of it).402 This is a source for compositional subtleties and analytical dilemmas. For example, in Mendelssohn’s Song without Words Op. 30,4 (Ex. 7.67a), the main motivic cell of the theme (mm. 3–6) is based on the harmonic progression V7–I–II6–V7 (the 7–6–7 neighbor lies in an inner voice). It might be heard as a prolongation of the V7, due to rhythmic circumstances: although the V first appears as consonant in the two-measure introduction, the seventh is added before the prolongation begins and is present at both of its boundaries. Nevertheless, I am inclined to hear the tonic at m. 4 as genuine, due to the melodic and dynamic peak. This local dilemma has large-scale consequences, since there is no other true tonic in the piece before the recapitulation. However, even if one hears the initial V as prolonged until that point, perceptually the seventh vanishes long before that even though it is never properly resolved.403

402 In Haydn, Symphony No. 104/IV, 73–80, the neighbor I has such conspicuous root doublings in the timpani and brass that it sounds as if it is in root position, although the lowest tone is its fifth. See interesting neighbor I6/4 in Chopin’s Mazurka Op. 59,1, mm. 17–21. It expands a phrase within V7/IV (Rothstein 1989, 236–7). Gibeau (1992, 133) rejects this IV as a local goal, in order to achieve a motivic e-dƒ-e in the bass, but his reading is contradicted by the foreground. 403 In the retransition (mm. 74–77, repeated 78–81), after 12 measures of V, the potential interpretation of the motive as prolonged V7 is apparently stronger (perhaps only in the repeat). However, dynamic emphasis endorses a tonic reading here too, perhaps as anticipation of m. 83.

174 Full Circular Prolongation of V7

By contrast, V7 prolongation does prevail in Ex. 7.67b (Beethoven, Symphony No. 8/I, first theme). Schenker (FC, Fig. 150) indicates this by means of a dotted slur between the sevenths at mm. 4 and 9 over a 7–6–7 neighbor.404 The decisive criterion that supports Schenker’s reading is the textural contrast: the V7 tutti is left off and picked up again after a neighbor ‘I’ that is played in the wind section only, in p dynamics and without the higher register. In the recapitulation, the analytical dilemma becomes much subtler, due to re- orchestration that avoids tutti in the first phrase. Harmonizing the neighbor as VI creates the momentary effect of a deceptive cadence (V7–VI) (Ex. 7.68a). The neighbor VI may receive an applied dominant (Ex. 7.68b). In Brahms’s Double Concerto/I, 81–83 (Ex. 7.68c), the insertion of VI seems motivated by the enharmonic play of the leading tone toward it (cƒ) and a chromatic passing tone (dß) within the preceding third progression.405 A smoother voice leading is achieved when the leading tone passes in the bass (as part of V6/VI) (Ex. 7.68d), as in Chopin’s Nocturne Op. 9,2, mm. 3–4 (Ex. 7.68e). In this case, the seventh lies in an inner voice. It is therefore not very prominent, and its prolongation is rather subtle; the lower neighbor proceeds a semitone downwards, and perhaps should be regarded as a passing tone toward an implied fifth.406

This is part of a more substantial process in this piece toward stronger assertion of the tonic (m. 3– very weak; mm. 75, 79 and 83; 123 and 130, and the final pedal point). See also the postlude of Mendelssohn’s Song without Words Op. 38,4. Rothstein (1989, 202–4, Ex. 6.11) puts parentheses from the V7 of m. 27 until after that of m. 29. These parentheses may imply prolongation of the V7 (cf. fn. 443). Rothstein regards the original chord as a triad, but in fact, the former seventh remains in effect. 404 The grouping by Lerdahl and Jackendoff (1983, 15) implies the same reading. By contrast, Forte and Gilbert (1982, 116) assert that the seventh is resolved at m. 7, although they seek to emphasize that the resolution does not appear even earlier. 405 The neighbor is obscured by the use of reaching-over. The V/VI governs as early as m. 71. The seventh is already present there, and is prolonged at least from m. 79 (it vanishes in the consonant V/VI at m. 77). Its end is complicated by a 6/4 sonority (m. 88), which at first sounds like a cadential 6/4 within the local dominant, but in retrospect functions as an anticipation of the goal (VI of the overall tonality). See also Schumann, Piano Quintet/I, 103–7, where the V7 is prolonged by the progression V7–V/VI–VI–II–V7. The melodic scheme V7–6–7 is obscured by the fluidity of the actual voice leading. 406 Several graphs exist for this passage. Schenker in MW II, 5 indicates the V7 and a descending third progression from the seventh. FC, Fig. 122,2, groups the end of the diminution under the dissonant boundaries d3-aß2 (arriving at the seventh). Salzer (1952/1962) shows V7 in Ex. 324, but overlooks the dissonance in Ex. 500. The inner dissonance is also omitted by Jonas ([1934] 1982, 65) and by Rothstein 1989, Ex. 7.2 (which is based on Jonas. According to Rothstein [326, fn.

Full Circular Prolongation of V7 175

The neighbor chord itself may be chromatic. First, it may express a mixture of I or VI (Ex. 7.69). One variant deserves attention: V7–ßVIß–V7 (Ex. 7.69d, also V7–VIß–V7 in minor). The enharmonic identity between 7 (third of 7V) and its neighbor ß8 (third of ßVIß) is tonally a paradox (cf. fn. 300). Another chromatic device is inflection of neighbor tones so that they lead closer to the governing V7. In Harmony (§144), Schenker explains such chromatic inflections of non- harmonic tones as ‘microtonicalization’ [miniatur Tonikalisierung], sometimes translated as ‘microtonicization’ (e.g., Proctor 1978, 68–70). This idea is inadequate when the chromatic neighbor is applied to a seventh, since the seventh chord can hardly be tonicized.407 The usual forms of this chromatic inflection of the neighbor are ƒ6/4, 6/ƒ4/3 or 6/ƒ4/ƒ2 (Ex. 7.70a–c).408 In minor, the 6 may be raised too. The chromatic variants avoid the feeling of temporary resolution hinted at by the diatonic neighbors I or VI. A more peculiar effect is achieved by 6/ƒ4/2 (Ex. 7.70d), which might function as V2/II. Schumann plays with this potential in the texturally dense theme of Albumblatt Op. 124,9 [Impromptu] (Ex. 7.70e). If one ignores the pedal point in the bass, the V2/II is resolved immediately, but in retrospect the II is a more immediate event than its applied V is. The upper voices are only reconciled with the bass into a unity when the V7 returns.

7.3.2.3 Unique devices of neighbor chords to V7

(a). Enharmonically chordal neighbors. When a chromatic neighbor above the root combines with one chromatic neighbor below any of the other chord tones (Ex. 7.71a–c), the emerging chords are heard as V7 structures, although a systematic spelling of the neighbor tones as such culminates in non-tertian constructs.

7.3], Rothgeb slightly altered the original Jonas graph in the English edition). One case where VI as a neighbor to V7 does not sound like a deceptive cadence (due to the surface rhythmic pattern) is found in the coda to Haydn’s Variations in F minor (mm. 199–201) in the inverted form V4/3– VI6–V4/3 (preceded by V6/5–IV6/ß4–V6/5). 407 Microtonicization may apply to single tones, ‘regardless of whether or not that note is the root of the harmony to which the tonicization is applied’ (Proctor 1978, 68). 408 For Ex. 7.70a, cf. Mozart, Piano Sonata K. 330/I, 84–86 (without the third) and Chopin, Mazurka Op. 50,2, mm. 61–62 (with the third; the neighbor chord is half-diminished). The Haydn case in Ex. 7.70b is discussed by Proctor (1978, 93) as a common tone diminished seventh chord applied to V7.

176 Full Circular Prolongation of V7

The first case is identical to the beginning of the omnibus progression (Ex. 7.10a) and also of smooth equal division of the octave (Ex. 7.88a below). Its meticulous spelling involves double alteration of the same diatonic tone (V ß2/ƒ2– 3/1).409 (b). Whole-tone non-diatonic neighbors. Normally, chromatic neighbors move a semitone instead of a diatonic whole tone. The opposite procedure, where whole tone neighbors replace diatonic semitones, distorts tonal orientation, especially when these neighbors are themselves filled chromatically. This seems to match ideals of the late Romantic style, as in the stormy Hexenfahrt from Humperdinck’s Hänsel und Gretel (1893) (Ex. 7.72): chromatically filled whole-tone complete neighbors in both directions decorate the seventh, fifth and third, with a shorter neighbor ornamenting the upper octave as well. After that, the pattern changes into a chromatic succession of parallel dominant seventh chords in altered third progressions.410 (c). Neighbor chords to V7 without stationary tones. The effect of neighbor motion to V7 is maximal when all four tones move to their neighbors. The voices may all move in parallel motion (in either direction), or involve contrary motion. In parallel motion, parallel fifths necessarily occur (at least when applied to root position V7). Diatonic neighbors introduce IV7 or VI7 (Ex. 7.73a–b). More often, all four neighbor tones to V7 are semitones. In that case, melodic relations take temporary precedence over harmonic syntax. Schenker identified precisely such a (lower) neighbor in Till Eulenspiegels lustige Streiche by Richard Strauss (CP I, 192, Exx. 268–9. See Ex. 7.73c).411 Upper chromatic four-voice neighbors appear at the climax of Schumann’s Novelette No. 5 at the diminution level (Ex.

409 In his Diabelli variations, Beethoven uses the double alteration notation when the neighbor chord appears as a short ornament (variation 2, m. 21), but when a similar neighbor is slower and endures long enough for the listener to perceive its V7 sonority, Beethoven notates it according to the vertical logic (variation 20, m. 28). See discussion of the Chopin excerpt in Ex. 7.71a in fn. 8 and §3.2.6. See a similar case, applied to a 6/5 inversion, in Schubert, Piano Sonata D. 845 (Op. 42)/I, 34–36 and 194–6 (Ex. 7.17). In the Schumann passage (in Ex. 7.71c), the neighbor has a potential tendency toward G minor, which is realized a few measures later (15–17) within another prolongation of V7. 410 In the Hexenfahrt, further parallel dominant seventh chords divide the octave into three equal portions. The last passing chord then becomes V7 of the ensuing, stable, section. 411 By this stage, Schenker’s reception of Strauss is less negative than later on. He accepts the cited passage as ‘most masterful,’ but criticizes as ‘a complete failure’ the remote voice leading in another neighbor chord to V7-structure (Gƒ7 half-diminished structure within Fß7).

Full Circular Prolongation of V7 177

7.73d), along with variants of four-voice neighbors in contrary motion. The larger progression in this passage is based on a special and enharmonically ambiguous variant of the neighbor (ƒ7/ƒ5/3/2). Four-tone neighbors that employ contrary motion never create complete seventh chords. If the seventh has a lower neighbor, some neighbor tones must meet on an octave. If the octave is perfect, doublings arise, in VI! (Ex. 7.68 above), incomplete IV7 or even an empty fifth. Otherwise, the octave is imperfect, and two variants of the same neighbor tone co-exist: ƒ2 and ß2 (a whole-tone apart), or still harsher, 4 and ƒ4 or 6 and ß6 (a semitone apart). Here we find the explanation for the passage from Mozart’s Symphony No. 40/I that lay at the heart of the Schoenberg-Schenker dispute (cf. fn. 154): it is a four-voice appoggiatura– V ƒ6/ƒ4/4/2–7/5/3/1 (Ex. 7.74a–b). An upper neighbor to the seventh offers additional possibilities of four-tone neighbor chords.412 Neighbors above the seventh and under the root exchange voices when they are diatonic (cf. §7.2.6); as semitones, these neighbors meet at an octave (Ex. 7.74c). This potential normally transforms the seventh itself into an augmented sixth (§7.8.1). One instance where I do not experience such an enharmonic transformation (perhaps due to the indirect voice leading) occurs in Liszt’s Piano Sonata, 414–31 (Ex. 7.74d). The ß8/ß1 neighbor occurs twice; on the latter occasion, the progression back to V7 is expanded in a dreamlike passage.

7.3.3 Double Neighbors to V7

Double neighbors within V7 (Ex. 7.75) may appear with either the upper or the lower component first. In order to introduce tertian neighboring sonorities, they must apply to either the root or the seventh, but they may be accompanied in parallel thirds by double neighbors to the third or fifth. Some double neighbor configurations represent a single neighbor harmony, while others stand for two harmonies that, strictly speaking, perhaps belong to different levels. Double neighbors in a single voice only create tertian sonorities when they apply to the root or seventh of an incomplete V7 (creating II6 or III6). Double

412 Possibilities not discussed here include incomplete variants of IV9 or VI7.

178 Full Circular Prolongation of V7 neighbors in parallel thirds introduce I¢−, IV or II. They are also possible in combination with one-way neighbors or linear progressions.413 According to my findings, double neighbors do not provide a fertile technique for large-scale prolongation of V7 (or other seventh chords), although in principle such prolongations are possible, provided that other voices move too.

7.3.4 Combinations of Neighbors with Linear Progressions The main kinds of prolongation techniques, i.e., linear progressions and neighbor motion, may be combined by means of succession, insertion or counterpoint. Succession of neighbors and linear progressions within V7 is possible in any order. Most effective is the preparation of wide prolongations, which usually employ linear progressions, by a simpler prolongation through neighbors, as in Haydn’s String Quartet Op. 64,3/IV (Ex. 7.50a–b above; the neighbors are not shown). Even mere concatenation of discrete prolongations can be integrated by motivic relations, as in the enharmonic transformation of 5ß6– 5– into 5–ƒ56– 5– below a stationary seventh (see above Exx. 7.68c [Brahms] and 7.71c [Schumann]).414 Insertion means that within the prolongation of V7, another prolongation applies to a subordinate V7-structure. We have already encountered this special procedure as insertion of a neighbor into the omnibus progression (Exx. 7.14b [Brahms] and 7.16 [Beethoven]). Another kind of insertion combines neighbor and passing motion into a single configuration in the contour of a cambiata pattern. For example, in Mozart’s Symphony No. 35/III, 33–35 (in the trio), a simple voice exchange of the seventh and the fifth is transformed

413 Concerning Ex. 7.75,d5 (Beethoven), FC, Fig. 100,5, shows the third progression in the upper voice. §314 refers to this figure as a large-scale V7 composing-out. I take issue with this comment; see fn. 461. See double neighbor to the seventh also in Bach’s Violin Partita No. 3, Prelude, 43– 50. In MW (I,42), Schenker reads this passage as part of a larger V7 prolongation from m. 37. 414 Refer also to fn. 409. See also (1) Brahms, Intermezzo Op. 119,1: the bass of an omnibus progression (mm. 24–30) is restated in a reharmonized and truncated format (mm. 33–34), transforming the last passing tone into a seventh that is resolved into a IV6, which then serves as a neighbor to V7. This observation is absent from the many studies of this piece: Cadwallader (1983) is generally very accurate, but renews V7 only at m. 37; Less precise readings appear also in Salzer 1952/1962, Ex. 477 and Forte and Gilbert 1982, Exx. 183 (middleground graph) and 193 (detailed graph of mm. 24–30). See also Elias’s reading in Oster Collection, item 34/1; (2) Mozart, Symphony No. 40/II, 54–59: cß first appears as a neighbor between V8 and V7, then as a passing chromatic tone in a third progression within V7.

Full Circular Prolongation of V7 179

into 5–6–8–7 in one voice and 7–6–ƒ4–5 in another (not shown). This procedure seems to appear rather infrequently. Counterpoint of linear progressions with neighbors is more common.415 The most basic combinations comprise a third progression against neighbor motion, thus having a single prolonging tone in each voice. Even with this restriction, numerous combinations are theoretically possible: eight neighbors (above or below any of the tones of V7) multiplied by eight passing tones (ascending or descending, in any of the third-spaces, or a chromatic passing tone between the root and the seventh), minus doublings, but including consonant supports for passing chords. Even when the motion in both active voices is synchronized (Ex. 7.76a), various passing chords may emerge, including daring enharmony (case no. 6 [Clara Schumann]). Unsynchronized motion offers additional possibilities (Ex. 7.76b). Significant among these is the fixed cadential formula of pre-tonal origin known as discant clausula (Ex. 7.76,b3). It includes descent from the seventh, and an upper neighbor to the third, usually in the upper voice, whose descent back to the third is delayed.416 The prolongation of the seventh is especially clear in variants where the seventh literally returns in another voice, as in Couperin’s La Favorite.417 A remarkable instance of unsynchronized neighbor and passing motion occurs in the coda of Chopin’s Ballade No. 3 (Ex. 7.77).418 The neighbor in the bass supports ßVI (m. 226), which is momentarily heard as a goal, but is immediately transformed into a German sixth. The passing tone in the upper voice only arrives when the bass of V is re-established, and creates a ¢−, which is itself composed out (cf. FC, Fig. 64,3; I read it somewhat differently). The resolution

415 Salzer (1952/1962, 105 Ex. 148) proposes the cumbersome but precise term ‘neighbor-passing chord.’ For simultaneous combinations of linear progressions with neighbors, see also §7.2.1.2.1 (modified omnibus); Exx. 7.24 and 7.26 (fifth progressions) and Ex. 7.75c (double neighbors). 416 For the term discant clausula, see Renwick 1995b, fn.11. The analytical understanding stems from Schenker himself (annotations from 1917, published in Siegel 1990, 24). A corollary case to Ex. 7.76,a1 occurs in Beethoven, Symphony No. 5/IV, 54–55: V6/5–‘I’–V4/3, including a voice exchange between the fifth and the third, and a lower neighbor to an inner-voice seventh. 417 La Favorite appears in Couperin’s Pièces de Clavecin, book 1, Ordre No. 3. Salzer (1952/1962, Ex. 426) analyzes this example slightly differently. The same excerpt is cited in CP I, Ex. 242. When the last tone in a descant clausula is chromatically lowered, as in FC, Fig. 114,2a, a tonal paradox emerges. This is a specific case of inganno (deception) (Renwick 1995b, 51). For the procedure in Ex. 7.76,a1, see Mozart, Symphony No. 40/I, 59–62 (MW II, 67; Wen 1982, 59). 418 Rosen (1995, 318–9) questions the function of this passage in the overall form.

180 Full Circular Prolongation of V7 back into V7 occurs first in the inner voices, including the doubling of the upper voice, while the upper voice itself is suspended over additional motion. What makes this excerpt so outstanding are the rich texture (employing sixth- unfoldings as diminutions) and the dense motivic relations: the motives of both outer voices appear in a condensed form in the immediately preceding thematic statement (mm. 219–20), and the contour of the six eighth notes of the upper voice within the measure in 219–20 is projected onto complete measures (221–6) (see recomposition at Ex. 7.77b). The seeds of the prolongation of V7 in the coda are planted in the theme itself (Ex. 7.77c). An evaluation of the upper voice’s context in the coda is complicated: the V7 is resolved into the final tonic; the Urlinie descent determines that the opening 4 (m. 221) is an incomplete neighbor and not the primary tone of a third progression; the seventh is retained nevertheless, not least because it is literally stated below the structural 2 . Eventually, the resolution to the final tonic (m. 231) occurs under 3 in the soprano, which normatively counts as a cover tone; alternatively, one might avoid the normative descent to 1 in favor of a3 4––3 middleground neighbor, from which a third descends into an inner voice (43– 2– ) (cf. Ex. 4.13b–c). When neighbor motion counterpoints linear progressions of more than a third, the temporal placement of the neighbor articulates the segmentation of the linear progression. When it coincides with a tone of the governing harmony (here V7), it reinforces this harmony. In fifth progressions, the segmentation on a harmonic tone divides the progression into diatonically equal portions (thirds), but in seventh progressions the equal division of the linear progression occurs on the fourth rather than on a harmonic tone.

7.4 Mixture within V7 Prolongation

Mixture is not a fertile technique for prolonging V7 (or other seventh chords). The stimulus that might function as mixture, e.g., V7/5/3–7ß5/ß3–7/5/3, would be usually perceived as neighbor motion (V7/5/3–7/ƒ4/ƒ2–7/5/3). Ex. 7.78a features an exception from Fauré, where the inner activity forces us to hear mixture. It is more plausible to hear the lowered third (possibly also the lowered fifth) as mixture when it is subject to surface harmonization as a triad (Ex. 7.78b–d):

Full Circular Prolongation of V7 181 minor V, which gains some independence within V7 due to the difference in mode; ßIII; or ßVII (cf. also Ex. 7.18,a1–2 above; possibly also ßVIIß). Mixture of the seventh itself is also problematic. Semitones above or below the seventh are normally heard as chromatic neighbors rather than as variants of the seventh itself. Nevertheless, when the semitone above the seventh is embedded in an altered VII (VII ƒ5 or VII ƒ5/ƒ3), the harmonic third relations force upon this tone the sense of ƒ4 (mixture) rather than5 ß (neighbor) (Ex. 7.78e; cf. Ex. 7.18,a6). Ex. 7.78f shows a particularly convincing use of the digression from V7 to VII ƒ5 from Haydn’s Symphony No. 92/I, 160–6, where the third in the bass is filled linearly. This prolongation develops the motto of the movement (beginning of the allegro), which is based on surface unfoldings of V7. It takes place within a wide expansion in the bridge of the recapitulation. It is surrounded by additional prolongations of V7 (mm. 146–54, 175–9), which are perhaps even connected. The normative explanation of the return from ƒ4 to 4 assumes elision of the octave (5), from which the final seventh passes (Ex. 7.78g). This elision reduces the power of the mixture, but at least in certain cases (as in the Haydn example), direct mixture without elision seems preferable.

7.5 Reaching-Over within V7 Prolongation

In its broadest sense, ‘[t]he purpose of reaching-over is either to confirm the original pitch-level or to gain another’ (FC, §129).419 More precisely, three melodic functions of reaching-over may be distinguished: confirmation of the original pitch, arrival at the same pitch class in a higher register, and establishment of another pitch class. All types can apply to any tone of the V7, including the seventh itself. Reaching-over enables an initial seventh to proceed in ascent. Reaching-over that returns to the original pitch in the same register (Ex. 7.79) descends from the prolonged tone, leaps to a higher tone and then approaches the prolonged tone from above; the procedure may also involve the entrance of a new

419 Today the term reaching-over is used in a more limited sense, but the paradigmatic illustrations of reaching-over in FC, Fig. 41 show it in a greater variety, as an embellishment of neighbors (single or double), linear progressions (including initial ascent) and arpeggiation.

182 Full Circular Prolongation of V7 voice into the texture. Both parts of the reaching-over may occur either through stepwise motion, unfolding or linear progression.420 In the bass, the opposite direction is possible too: a pitch may return from below after it has been left in ascent. This procedure might be called reaching-under (Ex. 7.79e).421 I illustrate it from a Fauré song (after Jackson 1992, Ex. 7b). Reaching-over to the same pitch-class in a higher register can be achieved through a fully worked-out ascending register transfer (cf. Ex. 7.46, from Mozart’s Piano Sonata K. 533/II), arpeggiation or direct superposition (Ex. 7.80).422 Reaching-over that aims at another pitch-class may serve arpeggiation, unfolding or linear progression (Ex. 7.81). The reaching-over may connect tones of the V7 itself (as in Ex. 7.68c [Brahms]), but also intermediate tones, as in Bach’s Violin Sonata No. 1/II, 47–52 (Ex. 7.81c). In addition, the paradigmatic reaching-over that is based on 2–3 suspensions can apply to V7 (under a stationary seventh).

7.6 Arpeggiation of V7

As the normative skeletons beyond linear progressions, arpeggiations of V7 are embedded within many V7 prolongations through linear progressions. Nevertheless, certain arpeggiations, especially in the bass, deserve special commentary. The basic element of bass arpeggiation is the fifth divider, as in the I–V–I bass of the background. Within V7, as within consonant V, a bass divider should take the form of 52– 5– . Even when the harmonization of2 in the bass is not a local dominant, a bass divider endows the prolongation of V7 with a harmonic

420 A chromatic variant of the type V7–6, 8–7 leads from 7 to 7ƒ in Haydn’s Symphony No. 92/I (Ex. 7.78f). Texture can also cause a direct regaining of the seventh to be heard as reaching-over, as happens in Beethoven, Piano Sonata Op. 106/I, esp. m. 55 (see Ex. 5.13), by means of crossing of the hands and musical lines. 421 This is not an accepted Schenkerian concept. Untergreifen is not the opposite of Übergreifen (reaching-over), but rather motion from an inner voice (FC, §§135–9). Plum (1979, 148) presents these terms as opposites (see Eybl 1995, 39–40), but does not suggest the concept I raise here. 422 Ex. 7.80b (Beethoven) follows Beach 1967, Ex. 14b. Cf. also reaching-over in a quasi- arpeggiation in Schumann’s Novelette No. 2, in the bass (Ex. 7.87c). TW 5, 37 [2004, 205] presents another (problematic) example in Beethoven, Symphony No. 5/II, 123–46.

Full Circular Prolongation of V7 183 sense, which eliminates the transitory effect that is characteristic of PDs in general. The harmonic sense of the divider is strongest when the bass 2 serves as a root. The diatonic variant, V7–II–V7 (Ex. 7.82a), may serve as consonant support replacing the more contrapuntal V7–II¢−–V7. The middle II can itself serve as the goal of an applied dominant or even an auxiliary cadence (Ex. 7.82b–c).423 The divider II may itself be a seventh chord, as in Brahms’s Intermezzo Op. 119,1, mm. 25–26 (not shown). Ex. 7.83 details, stage by stage, a more remarkable prolongation of this type in the coda of Beethoven’s Leonore Overture No. 3. It is the way toward II7 that is prolonged, including a chromaticized voice exchange. When the harmony of the divider is altered to form V/V (or V7/V), the affinity with the I–V–I divider of the background is closer (Ex. 7.84a). The chromatic component, ƒ4, is a passing tone between the seventh and the octave of V7. In the complete motion V7–ƒ7–8–7 (Ex. 7.84b), a conflict in the hierarchy arises between the outer voices: in the bass, the most structural tone except the boundary 5 itself is the tone of the divider; however, the tone that belongs with it in the upper voice is a passing tone toward a more structural neighbor.424 This conflict may be avoided if the return to the V harmony is delayed until the seventh is reached once again (Ex. 7.84c), as in Brahms, Haydn Variations No. 7, middle section (Ex. 7.84d). This complex case involves registral manipulations: the immediate continuation of the initial seventh lies in an inner voice. At one stage (m. 306), the seventh seems to be resolved in the bass; however, hearing true tonic

423 Ex. 7.82b shows the transition from the slow introduction of Haydn’s Symphony No. 94/I. The V7 prolongation is avoided in the repeat of the exposition. FC, example 2 for Fig. 110,e provides a different reading, but overlooks the starting point on a strong V7. Suurpää (1999) in yet another reading does show the V7 prolongation. The soprano makes a third progression. For combination of the bass divider with a fifth progression, see Ex. 7.24d above (Chopin). V7 prolongations that pass via II only produce a bass divider if both V7 and II are in root position. For example, in Mendelssohn’s Cello Sonata No. 2/IV, 56–59, the V7 prolongation passes via II (m. 59), but a complete divider is avoided, since the initial V7 is inverted; and in Ex. 7.70e (Schumann) the bass divider is avoided due to a pedal point. 424 The conflict also obtains when the ƒ4 lies in an inner voice, as in Ex. 7.19f (Haydn). See also (with a more complicated harmonization) Ex. 7.40b (Schumann, Faschingsschwank aus Wien/III). This problem is the basis for the still more complicated conflict encountered above in Haydn’s String Quartet Op. 64,3/I (Ex. 7.49), where fifth-relations are extended into a full sequence.

184 Full Circular Prolongation of V7 at that point would contradict the well-articulated formal division of the variation. The passage also includes concealed motivic parallelism.425 The bass divider 2 nearly always serves as a local root. Other possibilities would harmonize the divider as a third of altered VII (ßVII£− or VII6/ƒ3), but not ßVIIß, which avoids the divider itself, or as the seventh of III2 (Ex. 7.85). Only rarely does the bass arpeggiate through all tones of V7. Ex. 7.86 shows an especially bold case of complete bass arpeggiation of V7 from Wagner’s Die Meistersinger von Nürnberg. Most tones of the arpeggiation are harmonized here by V7 itself, except the tone of the seventh itself, which supports a different passing harmony (II6). Passing tones in the bass, combined with lower neighbors and reaching-over in the upper voice, guarantee harmonic variety. The prolongation is prepared through recurrence of its initial melodic gesture (m. 73) on a stationary bass.426

7.6.1 Quasi-arpeggiation: Equal Division of the Octave within V7 Equal division of the octave outlines equally spaced chords in the horizontal dimension: an augmented triad by equal division into three, and a diminished seventh chord by equal division into four. The prolonged chords in these cases are not those outlined chords, but rather the vertical chords that stand at the boundaries of the prolongation. This creates ‘a type of prolongation in which the foreground harmonic relationships that generate it are not referential to the middleground harmony being prolonged’ (Cinnamon 1986, 3).427 In such cases,

425 See motive x, which appears enlarged in the bass and then condensed in the upper voice. The e at m. 304, which does not belong to the motive, is elegantly restricted to the bassoons and avoided in the lower octave in the basses. The background context is probably 54– 5– (cf. Ex. 4.19). 426 Another device that expands the I–V–I relations within V7 is based on harmonic thinking: in Brahms’s Symphony No. 2/I, bridge to third theme 133–55, V7/V is prolonged through I–IV–V–I relations, with a V7 structure on each chord. The prolongation occupies most of a huge expansion (131–55) of the preceding statement (127–30). 427 Cinnamon follows Proctor (1978, 157–8) who speaks of ‘symmetrical division versus arpeggiation.’ The unity of the dimensions is sometimes assumed to be a Schenkerian basic. Perhaps this is what Schenker means by ‘reconciliation of the two dimensions’ (CP I, 54, referring to Harmony, §76). However, dichotomies occur in many situations, e.g., linear progressions whose subdivision is incongruent with the underlying harmony, or arpeggiation via a neighbor, as in the introduction to Chopin’s second Scherzo (FC, Fig. 102, 6). The dichotomy of dimensions seems to define more precisely the paradox that Cohn (1996, 11) points out: ‘Equal divisions are equally paradoxical from a Schenkerian/linear perspective, in part because they erode the fundamental distinction between consonance and dissonance.’ In fact, a crucial difference exists between the

Full Circular Prolongation of V7 185 the truly prolonged chord is usually consonant, as in Beethoven’s Piano Sonata Op. 57/I, 65–87 (cf. FC, Fig. 114,8), but it can also be V7. Thus an apparent arpeggiation (‘quasi-arpeggiation’) of one dissonant chord prolongs another dissonant chord. The simplest realization of quasi-arpeggiation is based on ‘the transposition operation’ (Proctor 1978, 159–70), where all intermediate chords have the same structure (in our case, that of V7) (Ex. 7.87a–b). Aldwell and Schachter (1978/2003, 587, Ex. 31-30) demonstrate the latter progression in Schumann’s Novelette No. 2, 83–90 (Ex. 7.87c). Here, passing tones in the alto create an octatonic scale in the passage. (cf. a more prominent octatonicism in Ex. 7.92b below). Smooth voice leading can produce the same chord progressions. In that case, each of the prolonging chords appears in a different inversion. In equal division into four (Ex. 7.88a), the governing V7 returns at the end of the cycle to the original inversion (since the number of inversions is also four).428 By contrast, in equal division into three (Ex. 7.88b), every cycle reaches another inversion of V7, and the original inversion only returns after four cycles. The mega-cycle can also be divided into three equal portions based on the transposition operation. I have indicated them as shadow cycles. Equal division into three allows smooth voice leading in three out of the four voices (Ex. 7.88c). The immediate successions are smoother with minor-third root relations (division into four). These always preserve two tones (the fifth and seventh become the third and fifth of the subsequent seventh chord, or vice versa). Successive seventh chords in major-thirds relations share only a single tone (the third becomes the root or vice versa). Attempts to exploit correct enharmonic spelling would ruin the notation of the vertical sonorities as V7 structures, and

dimensions in tonal music, due to the distinction between harmony (skips) and voice leading (steps) (Straus 1987, 5; cf. §2.2), while the unity of dimensions motivated much twentieth-century music (Busch 1985–6): Bartók’s fourth-harmonies, twelve-tone serial music, and also music by Skryabin, who described this unity: ‘The melody is dissolved harmony; the harmony is a vertically compressed melody’ (quoted in Morgan 1991, 57). 428 Rimsky-Korsakov brings the same progression in his harmony book (quoted in Taruskin 1996, 306). See Ex. 9.1b for the inversion of the same voice leading, as a prolongation of a half- diminished seventh chord.

186 Full Circular Prolongation of V7 might even lead to the absurdity that the prolonged chord itself returns in a different spelling.429 These progressions may also be used in a partial form. A single phase in minor thirds is fairly common, as a special kind of neighbor (cf. Exx. 7.17 [Schubert], 7.71a [Chopin] and 7.71c [Schumann]). A case closer to the full cycle appears in the introduction of Liszt’s song Blume und Duft (Ex. 7.88d), where only one brick is missing. The voice leading is less smooth here.430

7.6.1.1 Die Teufelsmühle (=the extended omnibus) and its corollaries

Further realizations of the equal division progressions are possible by loosening the voice leading’s parsimony, most notably by means of voice exchanges. Any pair of adjacent tones in any immediate succession may be exchanged. The voice exchanges must be chromaticized in order to match the equal division. One particular type appears in compositional experiments by theorists of the classical era, who aimed to find appropriate harmonization for the chromatic scale. Förster (1805, quoted in Wason 1985, 24, Ex. 3-6) calls it the ‘The Devil’s Mill’ [Die Teufelsmühle] (Ex. 7.89a); the same progression has already been discovered by Vogler (1778, in Wason 1985, 17 and Yellin 1998, 15) who identified it as ‘cyclic progressions through various keys’ [Zirkelmäsige Fortschreitungen mit der im Grunde liegneden vermischten Tonleiter], and indicated only the passing diminished seventh chords. Ziehn (1912 [posth.], 114– 5, class A, quoted in Yellin 1998, 10–11) rediscovered it as ‘canons in the small third and large sixth.’431 This type is based on equal division of the octave into four. The root and third of one V7-structure are exchanged chromatically, and become, respectively, the

429 These observations might expand Neo-Riemannian theory to include seventh chords. One study in this area (Childs 1998) does not cover my ideas. 430 This excerpt is further complicated by context since the prolonged chord does not function as V7. Cinnamon (1982, 14) states that the resolutions of the ‘dominant seventh /augmented sixth sonorities . . . reflect characteristics of either, both, or neither.’ Forte (1987, 215–6) regards the V7 sonorities in this song as non-functional occasions of set 4-27 (in the song, however, all the manifestations of the set are limited to V7 structure, 047T, without inversion). Morgan (1997, 364) argues convincingly against Forte’s denial of functionality in the song. Cf. also Hantz 1982, 6. 431 See also: Ex. 8.31e, after Aldwell and Schachter 1978/2003, 588, Ex. 31-31; Seidel 1970, 448 and 451; Piston/Devoto 1941/1978, 441. Seidel also quotes (p. 448) an 1816 experimental variant of the Devil’s Mill. by Joseph Drechsler, where a 4/4 meter obscures the voice exchanges.

Full Circular Prolongation of V7 187 seventh and root of the subsequent chord. One voice ascends consistently while the other three descend against it in rotation (hence Ziehn’s ‘canons’). The passing tones create octatonic scales in all voices (possibly filled by complete chromaticism), but in two different paces. In the original example, the ascent is located in the bass so that all the chords that divide the octave appear in root position. Placing any other voice in the bass (as in Ex. 7.89b) creates a rotation of #, $ and 2 inversions. In this case, it takes three cycles to arrive back at the original inversion. However, the articulation of the mega-cycle (without additional parameters) does not divide according to the occurrences of V7 (every four chords), but rather according to the cycles of rotation among the other voices (every three chords), and is heard as equal division into four in the opposite direction. Wason (1985, 18, after Yellin) calls this progression in its fully chromatic variant the extended omnibus, since it coincides with a fusion of successive truncated omnibus progressions (Ex. 7.89c). This association seems justified only if the meter stands in conflict with the equal division into four. In the schemes by Vogler, Förster and Ziehn no such conflict arises, but since the extended omnibus produces tertian sonorities on every chromatic step, it might be appropriate for other segmentations as well. Indeed, some variants that sound fairly close to the extended omnibus actually express prolongations of diminished seventh chords or transitive progressions.432 It is also possible to impose voice exchanges on the other spaces within V7 (experimented in Ex. 7.89d–f). Each particular type of voice exchange has another inversion, which is consistent if the bass is the ascending voice, and absent if the bass is one of the descending voices. Ex. 7.90 shows voice exchanges within equal division into three. Here, no mega-cycles are required. Where the chromatic

432 Seidel (1970) in particular blurs together prolongations of V7, of diminished seventh chords (as in Schubert’s Der Wegweiser, cf. below Ex. 8.29) and transitive progressions, as in Beethoven’s Piano Sonata Op. 54/II, 37–44 (cited in Seidel’s fn. 4). The Beethoven passage is a partial cycle of minor thirds (only two phases), which add up to a tritone, but in this case it is equivalent to the progression [in G major] from VII6/ß5/ß1 to V7 (cf. diatonic frame in Ex. 6.25b). In the sketches for this passage, Beethoven explored more extensive options for chromaticism and harmonic digressions (Frohlich 2001, 112–7). A transitive omnibus not cited in Seidel appears in Schubert’s Variations on Ihr Blümlein alle [Trockne Blumen], Op. 160, for flute and piano, Variation No. 7, 33–38 (beginning of a coda). Gauldin (1997/2004, 747) interprets the extended omnibus as a progression between 6/4 chords, and understands the V7 sonorities as passing.

188 Full Circular Prolongation of V7 exchange exploits the lower—major—third-space (as in cases a and b), the exchange requires two passing tones in one direction, transforming the third progression into an octatonic tetrachord.433

7.7 Prolongations of Inverted V7

Inversions in general tend to weaken the structural weight of their chords, and thus make them less appropriate for prolongation. A complementary obstacle is that often the smoothest prolongations of inverted chords move through root position triads, which are not characteristic passing sonorities. Nevertheless, even chords that are both dissonant and inverted may be prolonged; in fact, in dissonant chords, inversions affect the degree of stability less than in consonant triads. Although prolongations of V7 apply most often and in the richest variety to root position V7, all inversions of V7 are amenable to all prolongation techniques that are used with root position V7 (see also Exx. 6.9, 7.53, 7.89b and 7.90b). (a). The # is the most frequent inversion of seventh chords in general and of V7 in particular; prolongations of this chord are also ubiquitous. A daring instance is found in Beethoven’s Fantasy Op. 77, transition to the Allegretto (Ex. 7.91). The V# is formerly stretched (after a lengthy subordinate VIIº7). The rather adventurous prolongation is separated from the fast-paced surrounding material by a starkly contrasting Adagio tempo. Both outer voices outline diminished seventh arpeggiations, but the boundaries of the passage determine that the prolonged chord is V7, while the diminished seventh chord is only its neighbor, expanding the basic scheme V#–VIIº7–V#.434 (b). The $ is in general the rarest inversion, and arguably the least stable one. It is the only inversion that cannot be produced through combined species in strict counterpoint (§3.3.2, on Clark); the very possibility of its prolongation proves the discrepancy between strict counterpoint and tonal hierarchy.435

433 Except case a, each particular voice exchange is based on a permutation of three inversions of seventh chords, and skips over one. Skipping over V2 does not use voice exchange. See Ex. 7.88c. 434 In graphs of deeper levels of this work, Laufer (1988, 129) locates the seventh at the last moment (m. 156), whereas Rink (1993, 20) correctly indicates it at m. 142. 435 See surface prolongations of V4/3 in Beethoven, Piano Sonata Op. 101/I, 12–13. The diminution includes a passing I5/3. The resolution of this V4/3 might already be heard at the last eighth-note of m. 13, or might be delayed until after the V7 of m. 15. Cf. also two songs that share

Full Circular Prolongation of V7 189

A prolongation of (a secondary) V$ that embraces an exceptionally rich content appears in the bridge of Schubert’s String Quartet D. 887 (Op. 161)/I (Ex. 7.92a). The consonant tenth between the outer voices remains in force during an inserted and apparently stable root position VI (II/V), which even contains I–V–I relations. Also included is the recurring passing remote harmony, VIIƒ. According to my interpretation, the occurrences of this VIIƒ are not structurally connected. A possible alternative reading might hear a prolonged VIIƒ and separate the occurrences of V$ of V. At any rate, the oscillation between remote harmonies weakens the sense of tonal hierarchy in the passage (the II–VIIƒ progression may also be heard as IV–V of III).436 The $ prolongation is more certain in the introduction to Liszt’s Sonetto 104 del Petrarca from Années de Pèlerinage (Ex. 7.92b). Liszt enters key signatures only at the end of the prolongation, and for a good reason, since the prolongation is based on an octatonic collection, articulated by equal division of the octave into four (cf. Ex. 7.87; cf. also Cinnamon 1983, 13). (c). V2 is occasionally decorated by diminutions,437 but larger prolongations of this chord are rare, perhaps because it has the seventh in the bass. When the seventh of the prolonged V2 is stationary, it functions as a bass pedal point, in contradiction to Schenker’s assertion that a pedal point on the seventh is not possible (CP I, xxxi quoted at §5.3). This happens in Grieg’s Lyric Piece Op. 38,1 (Ex. 7.93a), where the V2 (of V) is diatonicized into II2, and is never resolved functionally. Ex. 7.93b demonstrates a more active prolongation of

the same topic: Beethoven, L’amante impaziente—Stille Frage, Op. 82,3, 151–3; and Mendelssohn, Frage, Op. 9,1, mm. 1–3 (and perhaps further). 436 In Ex. 7.92a, the prolonged V4/3 harmonizes a passing tone in the bass within a motivic descending tetrachord (Beach 1993, Ex. 12; 1994, Fig. 3; 1998, 98, Fig. 11). It is not entirely clear whether Beach endorses the same 4/3 prolongation that I read here. Webster (1978, 21, Ex. 1) shows only the 24– dyad (and his measure numbers are shifted by misprint). 437 See local prolongations of V2 in: (1) Bach, Cantata No. 60/I, m. 10 (third progression in the upper voices); (2) Bach, French Suite No. 6, Minuet, m. 6 (Neighbor IV5/3, see Cadwallader and Gagné 1998, Ex. 9.11; McKee 1999, 251; Laskowsky 1990, 86); (3) Chopin, Scherzo No. 4, Op. 54, mm. 317–21 and 641–5 (neighbor 7–8–7). This passages exhibits content-expansion [Inhaltstmehrung] without metrical expansion of mm. 45–49 where V2 is merely stretched (these originate from mm. 5–8, where the inversion is 6/5); (4) Chopin, Piano Sonata No. 3/IV, 188–90. The function of this V2-structured chord is itself chromatic, passing between VIƒ and V. An untypical recognition by Schenker of the second as a harmonic interval occurs in TW 7, 15 [2005, 50], in relation to the V2 in Beethoven, Piano Sonata Op. 57/II m. 9: ‘the skip of the third in the lower voice (Gß–Eß) does not cancel the interval of the second between the outer voices.’

190 Full Circular Prolongation of V7

V2 from Liszt’s late piano piece Unstern. This piece is close to the limits of tonality, and ends on the unresolved V2. The seventh is initially exchanged with the octave in an elaborated form of voice exchange, and then prolonged by means of neighbor motion.438 Prolongation of an apparently inverted V7 occurs when both boundaries of the prolonged V7 appear inverted, but the passage is heard as a prolongation of root position V7. This results from the particular tendency of the root to sound like the true bass (especially when the harmony progresses in fifth relations) and is possible provided that at least one stage of the bass arpeggiation emphasizes the root. This happens in Schumann, Piano Trio No. 3/I, 32–38 (Ex. 7.94): both boundaries state V$; the former $ and a passing # are locally elaborated, but the prolonged chord at the deeper level is a root-position V7.

7.7.1 Prolongation of V7 in Changing Inversion Any arpeggiation or linear progression in the bass changes the inversion of the governing V7, as weak circular prolongations (cf. §1.1.2.1). Any motion between V#, V$ and V2 inversions occupies thirds, fifths or their complementary intervals in the bass, and thus resembles motion between inversions of consonant chords. Ex. 7.95 presents selected possibilities.439 Motion from or toward root position V7 is likely to be heard as prolongation of the uninverted V7. It would function as motion from an inner voice to the bass, or from the bass into an inner voice (respectively). The stepwise progression V2– V7 is an exception to this rule (cf. again violation of the skip-step distinction, §2.2). The seventh is not resolved, but nevertheless progresses, creating an impression of resolution; the harmony is sustained, yet the sense of motion remains. The prolongation is most convincing when the second in the bass is filled chromatically. The filling of the step from the seventh to the root of V7 may appear in the same forms that we have encountered in Ex. 7.39 above a bass that guaranteed root position V7. A case in point occurs in Ex. 7.96a from Bach, WTC

438 Baker (1990a, Ex. 6) reads a prolongation of V2 already since m. 89. Mm. 46–52 prolong V2 of E (IV?) by means of a whole tone progression in the bass. Another prolongation of V2 with the seventh as a pedal point in the bass: Tchaikovsky, Symphony No. 5/II, 99–104 (Kraus 1991, 43). 439 Ex. 7.95,a2 (Beethoven, Piano Sonata Op. 2,1/III) is discussed in §3.3.2. We have already encountered motion from V6/5 to V4/3 in Ex. 7.8b (Schubert).

Full Circular Prolongation of V7 191

I, Fugue in A minor. The V2 articulates a significant moment in the fugue, as it occurs at a point of textural break immediately before a General Pause. (It is also played with a fermata). During the chromatic ascent to the root, the upper voice forms a discant clausula (cf. Ex. 7.76,b3 above). The ascent in the bass continues until the third of V7, and the final V appears without the seventh; Nevertheless, the prominence of the seventh is decisive and directs the listener’s focus toward the segment V2–V7 (mm. 80–81).440 Motion from V2 to the lower root V7 opens the space of the seventh, but this need not be realized by simple linear filling. An interesting example takes place in the trio of Mendelssohn’s Symphony No. 4/III (Ex. 7.96b). After the V2 is prolonged by means of ‘apparent resolutions [that] are but the effect of auxiliary [i.e., neighbor] tones’ (Piston 1941/1948, 145), it moves to a local II, by means of a circular voice exchange between the fifth and the seventh (cf. Ex. 1.2b). At this point, the retention of the seventh is weakened, but V7 ultimately returns. The bass in this passage moves a complete octave, after which the root of V7 is approached in ascent (from a local IV).441

440 The resolution appears first in a weak form, as in an auxiliary cadence. However, if the descent at m. 83 is taken as the Urlinie descent, the deeper context becomes problematic. At the end of Bach’s Badinerie from Orchestral Suite No. 2 (mm. 36–37), the seventh is placed at first in the bass, then transferred an octave upward and descends to the root in the original register. 441 See motion from V2 to V7 also in Bach, Violin Sonata No. 2, Andante, 6–7 and WTC II, Fugue in D major, 19–20, and in the bridge of Mozart’s Piano Quartet, K. 493/I, mm. 36–59. In the quartet, the most daring portion is the departure from the dominant before the descent in the bass begins (mm. 36–44). Caplin (1987, 243–6) analyzes the latter passage in a non-Schenkerian manner as an evaded cadence. He regards mm. 36–38 as I6. It is tempting to connect the prolonged V7/V from m. 36 with the modulatory V7/V at m. 27, but m. 28 seems to begin the V area. Salzer (1952/1962, Ex. 383) reads motion from V2 to V7 in Beethoven’s Piano Sonata Op. 13/II, 42–44. In that case, however, the immediate progression from the V2 into I6 is perhaps a genuine resolution, which initiates an auxiliary cadence. The situation is analogous to the appearance of I within V7–6–7 (see §7.3.2.2). Within V2–V7 progressions, inner I6s create analytical dilemmas in several passages from Bach’s violin sonatas: (1) Violin Sonata No. 1, Fugue, 4–5: is the V2 connected with the V7, or is it merely a local suspension that is resolved immediately? At any rate, the structural essence of the fugue’s theme is substantially altered; (2) Violin Sonata No. 2, Andante, 9–10 (but not the parallel passage at 24–25); (3) Violin Sonata No. 3, Largo, 6–7 and 16–17. The V2 inversion even returns. Schenker’s close analysis in MW I (pp. 33–34) engages itself with the legitimacy of the seventh at m. 6, but lacks a precise attack of the problem (for example, it deals with consonant support for a lower-level passing tone while the governing chord is dissonant). Schenker’s background from 8 complicates the meaning. The analogous passages mark a parallelism I–V, IV–I, which challenges the normative background structure. See principal debate on this issue in Laskowsky 1979, Gauldin 1979 and Laskowsky’s response (1980); (4) Bach, Invention in A major, 20–21. The progression from V2 to consonant V5/3 (here via I6)

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Even in prolongations with changing inversions there is one inversion that is more structural than the other. Although in basic theory it is the lowest tone in the setting that determines the inversion, descents below the root can nevertheless represent root position V7.442

7.8 Enharmonic Parentheses (EP) in General and within V7

A prolonged chord may have one function in relation to the broader context, and another function, based on enharmonic re-interpretation, in relation to its inner prolongation. I refer to this kind of prolongation as enharmonic parentheses (EP), since it makes the prolonging passage sound parenthetical: the music tries one tonal path, returns to the crossroads and then adjusts to the true key.443 In a circular EP, two enharmonic transformations neutralize each other, so that by the end of the prolongation the original meaning of the prolonged chord is restored. EP is an elegant device for prolongation, often providing a witty angle, particularly in codas. The gap between conventional wisdom on harmony and Schenkerian concepts is particularly wide in cases of EP. A non-Schenkerian approach would regard the boundary occurrences of the prolonged chord as two modulatory pivot chords on the way to and from another key, and ascribe to the harmonies that prolong the enharmonically transformed chord the force of a goal of one enharmonic modulation and the source of the ensuing one. By its very nature, EP refers to chords (or intervals) with enharmonic potential. The most common forms of EP involve the enharmonic equivalences either between V7 and the German augmented sixth chord (Gr), or between diminished seventh chords and their inversions.

leaves the seventh unresolved. The most coherent way to hear this ending is to consider the V2 as an unstructural chord within a IV [or II]–‘I6’–V progression. 442 See Bach, Brandenburg Concerto No. 1/II, 13–15; and the analysis of Haydn, Symphony No. 104/II in FC, Fig. 106,3a (for the real meaning see Ex. 7.104b). Additional criteria that contribute to the hierarchy between inversions are: which inversion appears at the initial boundary; which inversion creates a deeper linear continuity; and general preference rules. 443 It is not always clear whether parenthesized passages in a Schenkerian graph prolong the preceding sonorities. Schenker himself never addressed the problem. Special focus on parentheses is found in Laufer 1985 and Rothstein 1989 (e.g., p. 88). The term ‘tonal parenthesis’ is also used by Abraham (1939, 91) in a rather similar sense to its Schenkerian usages.

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7.8.1 Enharmonic Parentheses within V7 The enharmonic equivalence between V7 and the German augmented sixth chord (or between V7/3/1 without the fifth and the Italian chord), implies tonally remote keys, a minor second apart (e.g., V7/C=Gr/B). Among the EPs that use this sonority, the vast majority prolong a middleground augmented sixth chord with the local function of a V7, rather than the other way around (cf. §10.3.2).444 The ease of creating the sense of a momentary V7 by means of a minimum of embellishment makes V7 ideal as the governing function in relation to the inner prolongation of EPs, and less appropriate as the function in the wider context, which requires less immediate resolution. EP within V7 is thus not a common state. We have already encountered a rudimentary stage of EP, in the form of voice exchange between the seventh and the octave via a chromatic ¢− chord (Ex. 7.40a). True parenthetical effect involves a return to the original position (perhaps creating elision). Exx. 7.97a–d demonstrate in ascending order ever larger increases in the degree of penetration into the enharmonic territory: the basic form (Ex. 7.97a) implies the enharmonic interpretation through a single nested ¢− chord. In Ex. 7.97b (Chopin, Mazurka Op. 59,2, mm. 97–101) the ¢− chord is major. This requires additional motion, and sounds much more remote. I also present an alternative that avoids the EP (in the spirit of Laufer 1999).445 In Ex. 7.97c (Beethoven, String Quartet Op. 59,3/I, 127– 37), the ¢− actually functions as a normative suspension to the dominant in the enharmonically inserted key. The progression reverts to the ¢−, and then to the pivot sonority, inverted (as a diminished third chord which equals V2).446 Finally, in Ex.

444 According to Aldwell and Schachter (1978/2003, 601), a single enharmonic transformation is more common with chords that are first heard as V7 and then are subject to re-interpretation as augmented sixth chords, than in the other way around. Both their analytic illustrations (Mozart, String Quartet K. 421/I; Beethoven, String Quartet Op. 18,2/IV, retransition) actually employ circular EP. Cf. below, Exx. 10.6b and 7.115c respectively. Properly speaking, the augmented sixth chord should only be labeled German when it functions as an altered dominant preparation. For other possibilities, see fn. 578. 445 The underlying voice leading is similar to that encountered in Ex. 7.74d (Liszt), but there the enharmonic effect is avoided. 446 Arguably, the return to the 6/4 creates a nested 6/4 prolongation within the EP, that defies the interpretation of 6/4–5/3 as a normative resolution. This passage is related to the vague character of the slow introduction (Webster 1980, 114; Kramer 1983, 303–5). Piston (1941/1948, 289, Ex. 555) only shows the modulation at the end of the parenthetical passage. For a similar procedure, see the reading of the development in Haydn’s Symphony No. 55/I by N. Wagner (1986, Ex. 8-5-

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7.97d (Beethoven, Cello Sonata Op. 102,2/transition to III) not only is the enharmonic augmented sixth resolved to V, but this V is further resolved into a local tonic. Although this endows the nested key with a local stability, the wider context suggests an EP, despite the fact that the emphasis on the initial seventh is minimal. The effect of EP seems difficult to achieve when the augmented sixth is resolved directly to a local V, without a ¢−.447 EP within V7 can also be apparent only, if the same chord appears as an augmented sixth chord and afterwards as a V7, but these appearances are not structurally connected. See Ex. 7.98, from Beethoven’s Rondo a Capriccio.448

7.9 Prolongation of Major-Minor Seventh Chords in Functions other than V7

Even without enharmonic interpretation, the major-minor seventh chord can occasionally fulfill functions other than V7.449 Even when the prolongations themselves are concise, the exceptional context makes them notable. The major- minor seventh chord occurs only once in each mode. This location is on V in major (and V is adjusted to this form in minor). In natural minor it is on VII. VII in natural minor normally serves as V7/III, but context prevents this meaning when the VII7 is resolved directly to the tonic, proceeds to V, or serves to prolong V (see Ex. 7.99a–c, respectively). The major-minor seventh chord may

3). This passage (mm. 78–104) includes a false recapitulation on the tonic (97–102). This tonic is surely passing (rather than a true tonic as Burstein [1999, 77] concludes), but perhaps only at a deeper level. In particular, the final V2 is too short and passing to be heard as the final boundary of a large-scale motion. See also discussions in Rosen 1980, 176–80 and Haymo 1995, 104–8. 447 A possible case occurs in the recapitulation bridge of Schubert’s String Quintet/I (mm. 289– 94). The nested V is implied from a bare 5 in all registers. See Beach 1994, 19. 448 The enharmonic ‘contrasting play’ in this passage is recognized in FC, commentary to Fig. 149,6. In Bruckner, Symphony No. 7/II, 176–85, an EP seems to be desired, but since the local nested key is asserted forcefully and the enharmonic pivot never returns, when the resolution of the V7 arrives in the wider-context key, the connection is hardly audible. The passage is analyzed in Louis and Thuille (1907/1920?), 328. 449 Even prolongations of V7 as such might obscure the basic function: prolonged V7 may serve as a secondary dominant to remote harmonies (as in Mozart String Quintet K. 593/I in Ex. 6.26c, directed toward ßIII), or fulfill a linear character (as in the VI–V6/5–I progression in FC, Fig. 106,2d, cited above, fn. 303 from Schubert, Waltz D. 969 (Op. 77), 5.

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(but need not) still function as V7 in relation to the inner prolongation (compare the two cases under a).450 Theoretically, diatonic major-minor chords exist in all natural modes: Dorian IV7, Phrygian III7, Lydian II7, Mixolydian I7, and Locrian VI7. A possible prolongation of Mixolydian I7 takes place in Tchaikovsky’s bizarre piece for the young The Peasant Plays the Accordion (Ex. 7.100), which depicts the primitive performer’s unsuccessful playing. The whole piece is based on a single major- minor chord with local embellishments. A more normative hearing strategy might interpret the prolonged chord as V7, which resolves into an implicit tonic after the piece is over (for the idea of implicit tonic [by Baker 1980, 1986 and 1990], see §3.4). Mixture enables the placement of major-minor seventh chords above any tone. Listeners might initially interpret such chords as secondary dominants. Whenever the continuation does not resolve the seventh chords, these chords might still count as V7 of implied keys,451 but in retrospect they do not function as V7 on any level. The following table lists all major-minor chords on diatonic tones, with all necessary alterations in major and minor, and their potential function as secondary dominants. Chords on non-diatonic tones are excluded from the table, but they too may perfectly well serve as roots to major-minor chords, and be conceived as secondary dominants applied to chromatic chords (e.g., V7/ßV).

450 Schenker analyzes the Handel piece in my Ex. 7.99b in MW I, 16–18 and FC, Fig. 64,1. In both sources, Schenker’s foreground graphs contradict his deeper reductions. The true soprano is based here on an incomplete neighbor, a concept not yet fully grasped in FC. See also elucidation in Aldwell and Schachter 1978/2003, 414. Kassler (1995, 61) reports on errors in the reproduction in the English edition of the graph in MW I. FC, Fig. 113, 3c offers a reduction to the Chopin passage in my Ex. 7.99c, and denotes the VII7 as a ninth from the V root. (This looks like a legacy of traditional theory). See also FC, Figs. 113,3b and d. However, the excerpt in 113,3d (Beethoven, Piano Sonata Op. 22/I, 105–12) includes an actual V ß9 (109–12). For the possible enharmonic meaning of VII7 within V7, see above §7.3.2.3. See also Brahms, Cello Sonata No. 2/I, development, 88–100: VII7/V is prolonged through a chromatic voice exchange with detours. 451 On implied keys, see Rothstein 1991, 314–7, and Schachter [1987a] 1999a, 139–42. Schachter’s apparent centres are to my understanding identical with implied keys.

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Major-Minor Seventh Chords on Diatonic Tones

In Major In minor I ß7=V7/IV I7/ƒ3=V7/IV II7/ƒ3=V7/V II7/ƒ5/ƒ3=V7/V III7/ƒ3=V7/VI III ß7/()5/3=V7/VI IV ß7=V7/ßVII IV7/ƒ3=V7/VII [V7] [V7/(ƒ)3] VI7/ƒ3=V7/II VI ß7=V7/ßII VII7/ƒ5/ƒ3=V7/III [VII=V7/III]

These chords are rare, but in principle all of them may be prolonged. Exx. 7.101a– b show prolongations of III7/ƒ3 and I7/ƒ3 that do not function as V7/VI and V7/IV respectively. In both cases, the prolonged seventh chord is heard temporarily as V7 of an implied key whose tonic never arrives, but in retrospect it functions as a chromatic passing chord and not as a dominant.452

7.10 Large-Scale Prolongation of V7 and Form

Some prolongations of V7 encompass entire sections of the form. V7 is more appropriate than other seventh chords to fulfill this task, since it can participate at the deepest structural levels (see chapter 4). Most of the following examples occupy large portions of the works in which they occur and constitute significant elements of those pieces. Instances of less than a whole section are also included when their location in the formal structure is particularly intriguing.

452 The immediate progression A7–Fß6 in Ex. 7.101b [Schumann] has a precedent in Mozart, Fantasy K. 475, mm. 12–13. Another prolongation embraced by a chromatic major-minor seventh chord: Wolf’s Du denkst mit einem Fädchen mich zu fangen (Italian Songbook No. 10), 2–6: IIIƒ7 which does not function as V7/VI is elaborated three times by upper chromatic four-note neighbors. Even here, the flavor of V7 is invoked (V7–Gr–V7 of a hypothetical VI). See Hantz 1981, 29. I ß7 in major is less independent due to the lack of alterations of the basic triad. Cf. wide stretching of I ß7 (in relation to the major III in minor tonality) in Chopin’s Nocturne Op. 9,1, mm. 52–61. This seventh is cancelled as the chord returns to its consonant position. Not only the dissonant quality vanishes as a result, but also the dominant function of the chord. This change stands in contrast to a normal V7–8, where the dominant function is retained even if the seventh is abandoned (as in Schumann’s Humoresque, mm. 306–13).

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7.10.1 Prolongation of V7 in Dependent Sections The sections most appropriate for basing on prolongation of V7 are those whose formal function is unstable, as either transitions between different harmonic areas, or dominant prolongations: middle section in three-part form; episodes in rondo form; slow introduction, bridges and retransition (arguably also development and occasionally coda) in sonata form. In these cases, the seventh is normally resolved in the ensuing section.

7.10.1.1 Three-part form and rondo form

According to FC (§310), the deep content for the middle section in ABA song form may, among other possibilities, consist of neighbor motion. If the primary tone is 3, its neighbor is4 , and when the bass under the neighbor is a fifth-divider, the combination gives birth to V7. A case in point is the entire middle section of Chopin’s Nocturne Op. 15,2 (see fn. 8; §3.2.6; Ex. 7.71a above).453 Schenker’s systematic discussion of rondo form (FC, §318) views it as a concatenation of three-part song forms. This means that neighbor V7 is also a possible technique for rondo episodes. If one accepts a later assertion in FC (§321), which excludes interruption from the repository of voice-leading strategies available for rondo episodes, the role of the dissonant neighbor as an alternative to interruption becomes even more important for the reduction of rondo episodes. In fact, the two examples used in FC to illustrate rondo form with tonic refrains have a dissonant neighbor V7 as the most structural event in all the episodes.454 However, all these episodes express subordination to V7, rather than a full circular prolongation of V7 (cf. §§1.1.3; 6.3).455

453 Other instances take place in three-part sections of larger works, such as the variations theme of Beethoven, Piano Sonata Op. 26/I (§6.1.1). In Brahms’s Capriccio Op. 76,2, the middle section of a modified ABA consists largely of two prolongations of V7 structures. The former (mm. 46–55) functions in retrospect as an augmented sixth chord, while the latter (mm. 59–66) is indeed the structural dominant of the piece. 454 Beethoven, Piano Sonata Op. 13/II [FC, Fig. 155,1], mm. 28 and 50 and Piano Sonata Op. 10,3/IV [Fig. 155,2], mm. 24, 55 and after 80. See the next footnote. Tonic refrains are a condition for ‘proper rondos’ according to the eighteenth century theorist Kollman (Cole 1970). Non-tonic refrains deprive rondo form of its direct relation to tonal structure, and may even serve within PD. 455 The first episode in Op. 13/II (mm. 17–28) and the first and third episodes in Op. 10,3/IV may be read alternatively as interruptions. The second episode of Beethoven, Piano Sonata Op. 13/II

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An extraordinary large-scale rondo episode that prolongs V7 in the tightest sense is found in Beethoven’s Rondo a Capriccio Op. 129. This work has attracted analytical attention for its non-tonic refrains (Cole 1970; Galand 1990, 84–5), but one refrain on the tonic does divide it into two separate tonal excursions. Both of these are based on neighbor V7; the latter is more remarkable. FC (Fig. 134,6) indicates the structural rank of this V7, which represents the whole of mm. 316–67 (rec: 324–77) in the middleground reduction. Ex. 7.102 details the foreground. V7 itself is achieved at m. 332 (after subordination under the 4); after simple unfoldings (332–42), the seventh is left off, while the root undergoes an ascending register transfer. The end of the ascent passes through the tone of the seventh and continues in order to reach the octave, but at the same time the seventh is preserved in an inner voice.456 Introductions enable V7 prolongation before the initial tonic is stated. These often appear in sonata form, but are possible in other forms too, as in the introduction to Chopin’s Etude Op. 10,12 (this is a V#. FGA describes it as a ‘neighbor harmony,’ ignoring the root).

7.10.1.2 Sections of sonata form

7.10.1.2.1 The slow introduction. V7 prolongation may appear in the slow introduction either before or after the initial structural tonic. For the former procedure I have found no example with V7 (but see a prolongation of a

(mm. 38–50) might be read as a full prolongation of V7, with cß (m. 39) as a passing tone within motion into an inner voice. Salzer (1952/1962, Ex. 383) reads in that episode a sixth progression that obscures the sectionalization of the rondo. Holcomb (1984, 126) follows Schenker’s middleground. Laufer (1981, 182–3) supplies commentary and alternative for the analysis of Op. 10,3/IV. He interprets the last episode as what I call SFM within the 5–7 space (§6.2.2). I hear the whole movement rather differently: the theme begins on IV and arrives at the tonic only at the very last moment (perhaps the first appearance is an exception). When the theme is preceded by V7, this V7 is prolonged throughout the theme. 456 Schenker’s different measure numbering stems from a different version of the work (in the old Universal edition), that lacks mm. 25–32 and avoids the repeated measures at the end of the present prolongation (374–7). The first departure from the tonic in this rondo is based on subordination of VII6 to V7 (241–6). See FC, Fig. 102,2 (designated II–V) and Galand 1990, 84–5. The principles of rondo should also apply to more basic successions of three-part form. See Mendelssohn, Song without Words Op. 53,1, B section of ABABAcoda (Ex. 7.65e), and Schumann, Waldscenen No. 1 (Eintritt), mm. 9–17, as the first episode of ABA’B’A’’ (Ex. 7.82c).

Full Circular Prolongation of V7 199 diminished seventh chord in Ex. 8.27c [Beethoven]); for the latter, refer back to Ex. 7.82b (Haydn).457 7.10.1.2.2 The modulatory bridge of the exposition. The exposition bridge often includes prolongations of the secondary V7 of the subordinate key, as follows: (a). Modulation to V (I–V7/V–V). This scheme fits best when the seventh suspends from the rare primary tone 8 (Ex. 4.24,a4 and b4 above). InMW II, 26, Schenker analyzes in this manner the bridge of Beethoven’s Piano Sonata Op. 10,2/I, but in FC, Fig. 101,4 he abandoned this interpretation. In other melodic positions, the seventh of the prolonged V7/V belongs to an inner voice, possibly below anticipation of the structural pre-interruption 2. (b). Modulations to III (I–V7/III–III). After a primary tone 5, modulation to III requires a seventh in the secondary dominant in order to establish linear continuity (§§4.4.3; 6.1.1). Several piano sonatas by Beethoven exploit this pattern in a variety of ways: in Op. 57/I, the structural V7/III is the subject of full prolongation (Ex. 7.62d above); in Op. 10,1/I (mm. 40–55), it forms the goal of a subordination of preceding harmonies (this is implied in FC, Fig. 154,3); in Op. 53/I [in major], according to Schenker’s reading, it is the more structural element in V8–7 with reverse hierarchy (Ex. 6.7a, alternative in Ex. 6.7b).458 (c). Modulations to other tonal areas (possibly subsidiary goals in a three-key scheme). Any other modulation from the tonic can also include a secondary V7 (consult Ex. 4.24). An extraordinary prolongation of V7/VI within a I– V7/VI–VI scheme takes place in Beethoven, String Quartet Op. 132/I (Ex. 7.103). Morgan (1976, 56) cites this bridge as a proof that even complex PDs are normative as long as they take place in transitory sections (§3.3.2). In fact, this passage is unique in that the dissonance contrives to remain in effect over textural and thematic vagaries: a march changes into a polyphonic gavotte, and back into a march (Agawu 1991a, 123, in terms of Ratnerian topics [Ratner 1980]; and graph of the wider context, p. 119). The most intense tonal

457 In Haydn’s Symphony No. 99/I, the slow introduction is ambiguous. Webster (1991, 325) suggests prolongation of V7 in mm. 9–18 as an optional interpretation. 458 Oster (fn. to FC, §316, p. 139–40) comments on the appearance of I–V7/III–III mainly in minor. His explanation relies on the tonal gravitation of the tritone (cf. §2.1.2.2.3.4).

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activity, however, occurs in the last portion (44–47), whose texture is uniform.459 7.10.1.2.3 The recapitulation bridge. Bridges in the recapitulation must, of course, differ from their exposition counterparts in order to avoid modulation. This necessary change offers a potential for expressive expansions of passages from the exposition bridge. The expanded passages may prolong V7. Haydn explores this potential in two late symphonies, No. 92/I (Ex. 7.78f above) and No. 104/II, 102–21. Schenker’s reading of the latter in FC, Fig. 106,3a outlines a descending # in the bass (reaching fƒ at m. 120), but in fact the root (d) returns. As Rothstein (1981, 156–8) vividly explains, this passage is a foreground expansion (i.e., expansion of a prototype that appears earlier in the work) of the exposition bridge, which in turn expands the main theme. The theme itself prolongs V7 through voice exchange of a fifth. I compare the bridge of the exposition with that of the recapitulation (Ex. 7.104a–b). In the recapitulation, the V is consonant at first (m. 101), but the seventh is highlighted nevertheless, due to its hypermetrical importance, and to its very relation with the model in the exposition bridge. There are further differences between Schenker’s reading and my own; this passage is especially difficult to reduce, due to the emphasis on chromatic chords in remote relations to the governing V7. 7.10.1.2.4 The development section. In normative sonata form, the development either prolongs the consonant V, or (in minor) progresses from III to V. Many development sections are based on motion toward the seventh of V, but the seventh only arrives at the end of the section as an optional lead-in (§6.2.2). If the structural seventh is already present at the outset of the development (or possibly at the end of the exposition), the development prolongs the V7. This seventh still counts as a lead-in in the sense that it is subordinate to the consonant V of the exposition’s second group (The alternative would be to sacrifice the interruption in favor of background neighbor. See Ex. 4.15). The discussion of development sections in FC (§314) is atypically liberal in its approach toward prolongation of V7: ‘In major [i.e., when V is already reached

459 Chua (1995, 91–94, Exx. 3.29–3.30) proposes a similar reading, albeit with a different ending, apparently because he presents a ‘motivic reduction’ rather than pure voice-leading graphs. In his criticism of Chua, Morgan (2003, 34) again considers mm. 30–47 as V/VI (in fact, V7/VI).

Full Circular Prolongation of V7 201 in the exposition] . . . the seventh may be composed-out in various ways (Figs. 62,1, 3, 4, 11; 100,5; 154, 7).’ The term ‘composed-out’ is used here in the strict sense of true prolongation, since it is distinguished from another type, which seems to describe composing-out in the broader sense of SFM toward a final seventh: ‘the seventh may be transferred upward, in accord with Fig. 23.’ Even this latter type assumes that the seventh is form-generating, although this is hardly confirmed in the cited examples.460 Schenker cites six examples of ‘various means of composing out the V7’ in the development. However, among these examples the only genuine cases are two development sections by Beethoven that troubled Schenker for a long time: Symphony No. 3 [Eroica]/I and Piano Sonata Op. 81a [Les Adieux]/I (Figs. 62, 3 and 4 respectively). Schenker reads both developments as being based on descending seventh progressions, the technique which stood at the core of his engagement with PD.461 I shall discuss each case in turn. The Eroica. In the huge essay devoted to this symphony in MW III, Schenker proposed that a genuine seventh progression prolongs V7 throughout the gigantic development of the first movement. The graph in FC, Fig. 62,3 (reproduced in Ex.

460 Schenker cites for this category four graphs of three works: in Beethoven, Symphony No. 6/I (Fig. 154,5), the development is based on gradual transformation of V into V7 via IV (cf. Ex. 6.12c); In Mozart, Piano Sonata K. 545/I (Fig. 47,1), the seventh arrives at the last moment through chromatic motion from V8 (m. 58), and of course, it is located well into the recapitulation; Figs. 47,2 and 154,6 both refer to Beethoven’s Piano Sonata Op. 14,2/I. The seventh arrives only in the retransition at m. 115 in an inner voice (not in the graphs) and then at m. 122. On a lower level, this development includes a progression between V7/III and V6/5 (mm. 69–84. FC, Fig. 114,6 shows the goal as V6; Laufer 1981 suggests alternative; Krebs 1980, Fig. I.28 is indecisive). 461 The other four cases are: (1) Fig. 100,5, for Beethoven, Piano Sonata Op. 2,2/I. The seventh appears only at the retransition, after V has been regained as a consonance, and then undergoes a very brief prolongation (see Ex. 7.75,d5). The seventh arrives through gradual transformation from the octave (m. 211), but the potential tetrachord V8–5 is clearly segmented on the seventh due to the opening of register (see fn. 274, discussion of the diagonal line). Schenker’s background is complicated by the unique reading of the second group as a back-relating dominant (see Oster’s remark in FC, p. 139); (2) Fig. 154,7, for Beethoven, Piano Sonata Op. 10,1/I. It reads a process toward V7 in the unique context of ascent toward a 5 cover-tone above the2 before the interruption (it can be seen clearer in the end of the exposition graph (FC, Fig. 154,3). The seventh is achieved as a passing tone, which is retained under the goal. I prefer the analysis by Laufer (1981, 182) which highlights the consonant V at m. 158. Salzer (1952/1962, Ex. 463) has yet another interpretation; (3–4) The rest of the examples refer precisely to those examples of FC, Fig. 62 (seventh progressions) that take place in development sections. They include an ascending seventh progression, which should count as illusory (Fig. 62,1. See §5.4), and a four-note arpeggiation, which initiates on IV and is reinterpreted as an augmented sixth chord (Fig. 62,11; see Ex. 10.6a), along with the two developments discussed here.

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7.105a) is a slight modification of the relevant portion of the middleground graph in Fig. 3 of the Eroica study. Schenker was troubled by his own reading. His comments (MW III, 23) concern not the PD, but rather the lack of what he considered to be a normative preparation for the structural seventh in the form of IV8–V7 (see Clark 1982, 254 and my reservations here, §§4.3.1 and 6.3). While I accept true seventh progressions and unprepared structural sevenths as valid theoretical models (§5.4; 7.2.5), I take issue with Schenker’s particular analysis. In my alternative (Ex. 7.105b), the initial seventh arrives directly from the adjacent octave.462 It functions as a passing tone within a complete register transfer. The final seventh is not structurally connected with the initial seventh, yet it arrives long before the end of the descent in the upper voice: it is already attached to the fifth of V (m. 374), which returns to the V harmony itself. This seventh arrives even before the fifth itself (which is delayed by means of a local suspension). This prevents any possibility of assuming local (or even elided) consonant V as the immediate source for the final seventh. The final seventh remains in effect throughout most of the descent, but this part of the descent is condensed in the last portion of the development only. Before the descent begins, Schenker’s middleground graph simply omits the tone of the seventh for more than half of the development (152–305), as if it remained as an implied tone, but this does not fit the music. Even according to Schenker’s own foreground graphs, the first step of the descent occurs as early as m. 220, and most of the development takes place under the passing tone 3463. I

462 Brown (1989, 214–8) raises this argument in order to rule out the possibility of true seventh progressions altogether. I reject his conclusion as a general rule, but accept his idea on the Eroica. Schenker’s reading is of course motivated by the conspicuous location of the seventh at the outset of the development. 463 The fifth of V (2) is much less emphasized than3 . In Schenker’s reading,2 is a very local passing tone indeed (m. 374). When FC (§215) claims that genuine seventh progressions ‘emphasize harmonic intervals, at least the third,’ the different status that is applied to the third has no theoretical justification, and seems to reflect the particular situation in the Eroica. On the fallacy of the argument as a whole, see §5.4. In an additional alternative reading of the development, N. Wagner (1986, Ex. 8-2-3) endorses a deeper status for the thematic passages on E and Eß (mm. 284 and 320 respectively). He puts the seventh in an inner voice only, but his reading may be reconciled with the seventh progression. Wagner also indicates a secondary V7 prolonged at mm. 260–84, in contrast to the boundaries suggested by Schenker.

Full Circular Prolongation of V7 203 hear the descent from the seventh even earlier (m. 178, anticipated already at 156), in contrast to Schenker’s graph (MW III, 24, Fig. 18).464 Les Adieux. Schenker discovered the seventh progression in this development in the 1920s (Oster Collection, Reel 64/120–1), and published it in FC, Fig. 62,4 (reproduced as Ex. 7.106a). He expressed his puzzlement at this finding when he called it a ‘harmonic sin’ (unpublished note, cited in Oster’s fn. on FC, 64; see also MW III, 24). This seventh progression is easier to perceive than that in the Eroica, due to the modest proportions, and fairly equal distribution of the descent. Most of the tones in the descent are stated as unaccompanied whole notes (reflecting the motto); this helps to unite a harmonic progression that is otherwise bizarre and lacking in direction. An alternative interpretation might already hear the seventh resolved on the VI chord (m. 72). Such a reading would better match the dynamic shadings and the development of the opening motto. Nevertheless, I still hear a seventh progression. It would seem to me significant that the initial seventh is heard as the highest tone above the previous fifth (structural pre-interruption 2), and is not preceded by a literal octave in the same register.465 The prolongation of the V7 continues after the seventh progression has been accomplished, and penetrates the thematic recapitulation (Ex. 7.106b). This amalgamation of units is prepared, with the same material, in the transition from the slow introduction to the exposition (Ex. 7.106c). Both the exposition and the recapitulation begin on IV6, which is embedded within a V7 prolongation. The upper voice in this progression consists of a ‘stationary tone [4], attained by the motion of a descending and ascending [diminished] fifth’ (FC, remark on Fig. 119,7 in the commentary to Fig. 124,1b). As Fig. 119,7 shows, the ascent proceeds to the consonant octave, but the structural goal is the seventh (the octave is an incomplete neighbor after a diminished fifth progression).466

464 The development contains a passage based on chromatic transformation that is best explained by neo-Riemannian theory: P (parallel), R (relative) and L (leading-tone exchange) motion. Ssee Goldenberg 2007, 82). 465 Forte and Gilbert (1982, 244–5) essentially follow Schenker’s reading. Other citations of this example: Schachter [1981] 1999a, 202, Clark 1982, 254, and Brown 1989, 218, fn. 67. 466 Meyer (1973, 253), Beach (1983b, 23) and Cadwallader and Gagné (1998, Fig. 6.7) share essentially the same interpretation. Different readings: Salzer 1952/1962, Ex. 289, and Agmon

204 Full Circular Prolongation of V7

Development sections that prolong V7 in their entirety seem to be extremely rare. Occasionally, V7 stands at both boundaries of a development section, but in most cases, these boundary V7s are not structurally connected. Rather, they result from local voice leading. An opening seventh (at the end of the exposition or the beginning of the development) might serve as a passing tone in a linear progression that prolongs consonant V (a fourth progression V8–5, a sixth progression V8–3 or a complete register transfer), or pass from V5 to 3 (either diatonic or altered) that belongs to lower-rank chords (apparent tonic, III or VI) within the dominant prolongation. The function of the final seventh is either a local lead-in after the consonant V has been regained, or a goal of a SFM from a consonant V (usually V5–6–7). An example of a highlighted V7 at both boundaries without structural connection occurs in Haydn’s String Quartet Op. 55,1/I (Ex. 7.107a). Although the initial seventh is not immediately resolved, neither is it retained throughout the development. Rather, it leads to ßIII, which returns to the V through a whole-tone progression in the bass. The prolongation of the structural dominant in the bass is thus based on two major thirds (E [m. 30]–C [m. 78]–Gƒ [m. 111]), which divide equally a major sixth, the complementary interval of V1–3. The seventh of the V7 returns in the upper register, but only after V has already returned. In the upper voice, the initial seventh is the Urlinie pre-interruption 4, while the final seventh is a local lead-in.467 I have found only one movement, from the same repertoire (Haydn, String Quartet Op. 55,2/IV, see Ex. 7.107b), where prolongation of V7 is a serious candidate interpretation for the content of the development. The development’s

(1996b, fn. 30). The same material recurs at the beginning of the coda (162–6), but the insertion of an additional measure at that point modifies its meaning. 467 For V7s that stand at the boundaries of the development, but nevertheless lack structural status, see also the following: a V7 at the beginning of the development leads to an apparent tonic: Mozart, Symphony No. 40/II (the local V7 itself prolonged through 54–59); V7 at the end of the exposition leads to IIIƒ (which leads to IV): Mozart, String Quartet K. 575/I; V8 at the end of the exposition becomes V7 which leads to IIIƒ: Beethoven, Piano Sonata Op. 22/I; V7 at the end of the exposition leads to ßVI: Schubert, Piano Sonata D. 850 (Op. 53)/I; to VIƒ: Beethoven, Symphony No. 5/IV. Except for the last case, these movements also demonstrate final non-structural V7. In Haydn, String Quartet Op. 33,3/I, the final V7, in the weak 4/3 inversion, arrives directly from III (within the domain of the recapitulation, m. 109–10), and not from V8, but the initial seventh which ends the exposition is only local. An alternative reading would interpret the development as a V–III–I arpeggiation. See principal remarks in Willner 1988, 80–82 (after Beach 1983a).

Full Circular Prolongation of V7 205 harmonic plan is based on ascending, then descending series of fifths, which begin from V7 at the end of the exposition. The latter half of the development is fairly clear: all the descending fifths are harmonized as dominant seventh chords. The chromatic descent in such a V7-series eliminates the sense of elided octaves as the sources of the sevenths.468 This establishes the feeling that the final seventh is the goal of a large motion. A connection with the beginning of the development is reasonable, since the initial seventh is never properly resolved, but there is no clear voice leading. I will refrain here from making an analytical decision as to whether this development prolongs V7. In a Schenkerian perspective, development sections should not ultimately constitute structurally self-contained areas. If V7 is said to replace the normative structural V as the harmony that is prolonged throughout the development, the seventh must appear in the second theme group. This procedure, however, prevents tonicization of the V. A prolonged V7 could follow a tonicized second group on another harmony (especially III in minor), but I am not aware of any actual work that realizes this procedure. 7.10.1.2.5 Prolongation of V7 in codas (not only in sonata form). When codas include large or significant prolongations of V7 (or PD in general), they adopt the active character of a second development. Both this aesthetic goal and the technical means to achieve it seem to bear the fingerprint of Beethoven’s early period, especially in finale movements, where the effect of ending is the strongest. Johnson (1982, 25) draws attention to the affinity between several such finale codas, which include tonicization of semitonal relations. The nested tonicization of remote harmonies may occur on thematic statements within the V7 prolongation, as in Ex. 7.108a from Piano Sonata Op. 2,3/IV. This creates a

468 In sequences of dominant-sevenths in descending fifths, each seventh arrives from an elided octave that presents the resolution of the leading tone of the former seventh chord (Rothstein 1991, 312–3; fn. 369 above). However, such elided octaves violate the clear chromatic descent achieved through this progression. Schenker, in CP I (Ex. 424) suggests another kind of elision, which resolves each seventh as a 7–6 into an anticipation of the next chord, but this interpretation is hardly compatible with tonal norms. See also ibid., comments on Ex. 427 (Beethoven Piano Sonata Op. 27,2/II, 45–48).

206 Full Circular Prolongation of V7 parenthetical effect, although—at least in this case—without involving enharmonic relations 469 In Brahms’s Symphony No. 2/I, the coda forms the apex of the entire movement, due to a large prolongation of V7 (451–76, Ex. 7.108b). It starts like an omnibus (expanding its prototype from the exposition, see Ex. 7.14b), but then departs from it, and realizes a potential tonicization which is latent in the omnibus (cf. last case in Ex. 7.10b). My interpretation involves consonant 6/4s, whose justification lies in the linear motion of the bass. More problematic are two paradoxes, which I have failed to eliminate: the original seventh in the tenor line behaves as a local appoggiatura (g–f), but it is structurally deeper than its resolution; and at mm. 469–70 a local resolution within ßIII contradicts the sub- boundaries that divide the large prolongation (another reading: Wen 1999, 291).

7.10.1.3 Dependent sections in other forms

Prolongation of V7 throughout dependent sections can also occur in freer forms, as happens in Brahms’s Capriccio Op. 116,1 (Ex. 7.109). The form of this piece is unique, not least because of the unusual proportions between sections; nevertheless, the boundaries between sections are not ambiguous. Prolongations of V7 appear twice in the capriccio, followed by more structural chords whose duration is nevertheless much shorter. The former passage prolongs a 34- measures V7/III, which then resolves into a single-measure III. The entire prolongation recurs almost exactly (with a modified ending); however, it does not appear in a normal recapitulation, but rather within a developmental section that prolongs V. Ex. 7.109b shows (by asterisks) the context of both passages. The latter prolongation is transposed into III ß7, which functions as V7 of the preceding VI, but is never properly resolved (another reading: Dunsby 1983, 177, Ex. 2).

469 Johnson also cites Beethoven’s Piano Concerto No. 1/III, 453–80 (VIIƒ within V7), and an example that does not involve V7 prolongation from Beethoven’s Piano Concerto No. 2/III (passing ßVI between II6 and V7). McCreless (1996, 88–90) quotes Johnson and adds the coda of Beethoven’s Piano Trio Op. 1,3/IV (minor VII in minor within V5/3; cf. Kurth 1920/1922, 293–4, also without prolongation of V7). In fact, the semitonal relations sometimes refer to the tonic (alterations of VII) and at other times to the dominant (alterations of VI). The recognition of the embracing prolongation totally undermines the semitonal relations to the tonic and challenges the recognition of genuine tonicization in all cases. For a similar effect within diminished seventh chords, see §8.5.

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7.10.2 Prolongation of V7 throughout Complete Independent Sections Occasionally, prolongation of V7 can continue throughout an entire section, even within sections whose function in the form is stable. This usually requires resolution within the section in its final chord.

7.10.2.1 Prolongation of V7 in parallel periods as an alternative to interruption

In Schenkerian theory, non-modulatory parallel periods are based on interruption. Occasionally, however, the essential features of such a period can also be achieved without interruption, provided that there is a complete musical statement divided into less stable (antecedent) and more stable (consequent) phrases.470 Among the various forms of non-interruption parallel periods, two types seem to prolong V7: (a). V4–I3–V2, V4–I3–V2–I1. A normative interpretation of this succession would read interruption from 3 with a local neighbor 7V at the opening of each phrase (Ex 7.110a). Often this succession sounds different however (Ex. 7.110b): the initial seventh is prolonged throughout the antecedent by means of motion into an inner voice and the consequent picks the seventh up. An example where the latter, dissonant, reading sounds more convincing is the main theme of Beethoven’s Symphony No. 2/IV (Ex. 7.110c, two variants provided). The opening V7 here is clearly heard like part of the theme. It is emphasized by a unique rhythmic gesture, with loud dynamics and full orchestration over a large diapason; the ensuing I3 lacks all these supporting factors, and is further weakened since it is delayed through motion from an inner voice which starts on a £− inversion.471

470 Schenker himself acknowledges ‘the freest form of interruption’ in FC, §217. The most frequent type of non-interruption parallel periods does not involve PD. It occurs when the antecedent ends on I3 and the consequent on1 I , as Gauldin (1997, 143) demonstrates fromThe Carnival of Venice. Green (1965/1979) discusses such periods and corollary cases with ‘cadential strength determined by goal of melodic line’ (p. 52) but ‘repetition of harmonic movement’ (p. 60). Rothstein (1989, 18) distinguishes between interruption-periods based on an antecedent and a consequent and other periods based on a fore-phrase and an after-phrase. 471 In this theme, the final resolution of 4 is perhaps delayed until an inner voice beneath final1 . (cf. model in §4.1). See also the theme of Beethoven’s Piano Sonata Op. 7/IV (mm. 1–8). The same principle also works in the theme of Mozart’s Piano Concerto K. 459/III. The sevenths at mm. 1–2 and 5–6 are potentially connected. I hear the theme as stable, but when it recurs at mm. 255 ff. after a fermata on V7, the new context alters the structural balance in favor of V7

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(b). I–V7, II–V7–I. When the consequent begins on II, the feeling of a parallel period can be maintained by means of a sectionalized design and surface thematic parallelism, while the abstract tonal structure is continuous, especially in the upper voice. In such periods, the V of the antecedent is prolonged until that of the consequent (Ex. 7.111a).472 When these Vs include the seventh, prolongation of V7 is achieved (Ex. 7.111b). As an alternative to the V prolongation across the division of the period, one might regard the consequent as an auxiliary cadence, in order to achieve closer relations between structure and outer design (Ex. 7.111c, in the spirit of Laufer 1999). However, precisely when the seventh is involved, the reading as a V prolongation sounds preferable. Ex. 7.111d illustrates type (b) in the recapitulation of the first theme of Schubert, Piano Trio D. 898 (Op. 99)/I.473 The upper voice is based in this case on an uninterrupted fifth-line; the seventh appears as a passing tone and is prolonged across the phrase’s division. (The final resolution of the seventh is problematic as always in this pattern; refer again to Ex. 4.3). The initial statement of the theme (in both exposition and recapitulation) is generally similar, but there the continuation of the seventh is avoided by chromatic ascent to V5 before the division point. The V7 prolongation seems latent in the theme itself, but it is realized only in the passage shown here.474

prolongation. More ambiguous variants occur in further recurrences of the theme (mm. 355 and 508). 472 Morgan (1998, 24) refers to I–V, II–I as a legitimate variant of parallel period. Narmour (1977, 55–56) attacks Schenkerian theory for overlooking the sectionalization of such periods. He demonstrates the problem by the main theme of Mozart, Piano Sonata K. 576/I, as analyzed by Salzer (1952/1962, Ex. 277). 473 The thematic recapitulation begins on ßIII (m. 194). The passage under consideration (mm. 207 ff.) might be considered the non-modulatory bridge since it corresponds to the exposition bridge (m. 26 ff.). 474 The upper voice of this theme in the exposition may also be regarded as a fifth-line, but with the seventh delayed until late in the consequent (see Salzer 1952/1962, Ex. 389). Another reading: Beach 1997, 319, Ex. 5. See also Mendelssohn, Song without Words Op. 53,6, mm. 3–18. This non-interruption parallel period does not match either type, but seems to prolong V7 throughout.

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7.10.2.2 Larger stable sections

Stable sections, such as the outer section of three-part form (ABA')—and potentially even complete one-part pieces—may be based on prolongation of V7 with resolution at the last moment. Consider the outer sections of Brahms’s Capriccio Op. 116,3, which has an ABA’ form (Ex. 7.112). The clearest V7 prolongations, which were the first to catch my attention, occur near the end of the sections (mm. 25–28 and 95–98). Where do the V7s begin? In the opening section, the seventh is prepared at m. 24; going in reverse, V is clearly present at several structural points, in mm. 20, 16, 14, 8, 4 and indeed in the very first measure (after subordination). Both boundary events (mm. 1 and 25) include the seventh; actually, the dissonant 4 is already present even before the rest of V is realized, as part of the opening II7. At mm. 4 and 8 the V is consonant, but the seventh seems to remain in effect even there: at these points the soprano states the fifth of V, the goal of motion into an inner voice from the seventh. The final resolution of the seventh is ambiguous, perhaps continuing until the very last chord of the section. The prolongation of V7, I believe, occupies the entire A section of the capriccio. The A' section differs in many details, but prolongs V7 in essentially the same path.475 This impressive prolongation is divided into a series of discrete prolongations, but the sense of organic unity remains due to the non-concurrence with the motivic design. Most notably, m. 13 starts a varied repeat of the opening statement, but this happens under a long suspension to the goal of the preceding linear progression.

7.10.2.3 Prolongation of V7 across sections

While normally the violation of consonance priority requires a design that emphasizes boundaries for PD, occasionally a prolonged V7 can negate the surface design (cf. above Ex. 7.103, from Beethoven’s String Quartet Op. 132/I). An extension of this procedure retains the seventh across sections. A well-known

475 These passages include an excerpt of the omnibus progression (which might have prolonged V7 in F), but the boundaries force another meaning onto it. Laufer (2000) has a completely different reading of the capriccio, which almost entirely avoids the V7 prolongation. He already resolves the initial seventh at m. 3.

210 Full Circular Prolongation of V7 case is Brahms’s Intermezzo Op. 76,4. The large A section prolongs V7 from its beginning and across its inner divisions. The seventh is first resolved deceptively into a tonicized VI; after the double bar, a developmental section leads back to V7. Ex. 7.113a follows Schenker’s unpublished reading with some modifications indicated in my graph.476 Schenker’s intention is not always clear. The various layers in his multi-layer graph are not always consistent with each other and are not graphically synchronized. Schenker understands the final resolution of the seventh as being transferred to the bass,477 and the middle section—the most complex portion of the prolongation—as being based on linear progressions. A particular problem concerns the VI neighbor chord in the repeat on the first section (mm. 1–20). It violates the linear continuity both in the bass and in the inner voice. In fact, Schenker does indicate the bass of VI as relatively structural (Ex. 7.113b), but this leaves the ensuing ß6 in the bass outside the linear path. The alternative by Salzer and Schachter (1969, Ex. 10-18, renotated in Ex. 7.113c) avoids this problem. They replace Schenker’s ascending line in the tenor (where gß functions ultimately as fƒ) with a descending motion from the diatonic neighbor. However, their reading does not always correspond with the emphases in the music itself, especially with regard to the final return to the V7 (m. 31, where they prefer the weak beat). Ex. 7.113d attempts to rectify this alternative reading without sacrificing its main advantage. The seventh’s final resolution is also different in the reading by Salzer and Schachter. Instead of transferring the Urlinie into the bass, they endorse another exceptional structure, where the upper voice is only resolved to 3 and never descends to 4781 .

476 Schenker made this analysis in collaboration with his student Angelika Elias; see Oster Collection, item 34/45–49. Rothstein (1991, fn. 39) cites this analysis along with that by Oster in the same file, nos. 51–52. I also refer to the graph by Forte and Gilbert (1982, sup. 135–6), which essentially agrees with Schenker’s. 477 On the transference of the descent to the bass, see Wen 1999. He refers to this intermezzo on p. 284, fn. 13. 478 The latter view fits the claim by Lerdahl and Jackendoff (1983, 239–40) that this work lacks a normal Ursatz and ‘basic form,’ but yet fulfils a more general normative structure. Additional references to this intermezzo include Frisch (1990, 338–40a)—analysis of the bass alone, in a manner that fits version c (after Salzer and Schachter); Jonas (1934 [1982], 102)—brief comments only, calling the seventh ‘passing;’ Rothstein (1989, 314, fn. 4.12, after Rothgeb)—drawing attention to Schenker’s exceptional differentiation between the two occurrences of the section that precedes the repeat bar; Cone 1968, 25; W. Berry 1989, 45–82. Cf. also: (1) Beethoven, WoO 60. This piece has attracted the attention of Dunsby (1984) as a neglected masterpiece that employs

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At the largest scale of the form, V7 can be prolonged across pieces—or even encompass whole pieces—within multi-movement works that fuse more than one movement into a single tonal plan. For example, in Schumann’s Kinderscenen, the despair expressed in the child’s cry (piece No. 4) and the opposite happiness (piece No. 5) are embraced in their entirety within a single V7 prolongation (Ex. 7.114). The V7 is finally resolved at the end of the fifth piece after several potential resolutions into apparent tonics and cancellations of the seventh in consonant Vs, which are nevertheless subordinate to the wide prolongation. Before the seventh is resolved, the V is modified by means of neighbor motion into VIIº7. Chromatic ascent in the bass introduces a passing VII7, which is internally prolonged as if it were V7/III (cf. Ex. 7.99b).479

7.11 An integrative analysis of a complete movement: Beethoven, String Quartet Op. 18,2/IV (Ex. 7.115)

In the finale of Beethoven’s String Quartet Op. 18,2, prolongations of V7 form an essential motivic feature that penetrates various sections and unifies the movement. There is one place, in the retransition, where the prolongation is prominent and even striking, but I believe it can be understood as the climax of a larger process. (a). Seeds in the theme itself. The initial gesture in the cello ends on the seventh of V. The answer (m. 5) sounds at first like an immediate resolution, but when the seventh is picked up (m. 10), the earlier motion might perhaps be

daring tonal devices. In my view, the whole tonal digressions may be regarded as being embedded within the V7 of the main tonality; (2) Schumann, Waldscenen No. 5 [Freundliche Landschaft]. It opens with an introductory V7 that proceeds to a weak tonic. I hear this tonic as structural nevertheless; the alternative would be a prolongation of V7 until m. 44. 479 In piece No. 5, the V is subjected to its leading tone (ƒ4) on several occasions, which militates toward canceling of the seventh. However, the diatonic seventh appears simultaneously and prevents this possibility. My graph is partly based on N. Wagner (1986, Ex. 6-1-8, with discussion on pp. 133–4); he reads a V7 only from the final event of the fourth piece. See also Schumann’s Dichterliebe. The whole first song prolongs V7 of Fƒ minor, which is finally resolved into the relative major in the second song (Neumeyer 1982). Schenker shows the exceptional resolution of this V7 (at the immediate level) in Harmony, p. 220.

212 Full Circular Prolongation of V7

understood in retrospect as a descent into an inner voice. The second period (m. 21) amends the material in a stabilizing manner.480 (b). Second group. In the region of the dominant, its secondary V7 endures for 40 measures (72–111, transposed literally in the recapitulation 318–57). Most of the time the V7/V is merely stretched, but the prolongation also includes a voice exchange and two third-descents into an inner voice. In the latter of these, the passing tone is altered and supported by the remote harmony of ßIII (of V). The ßIII is preceded by its own prolonged secondary V7. (c). Development and retransition. The exposition ends on V7 emphasized by a fermata (138–9). Even though this seventh functions as a local passing tone that leads to the nested tonality of ßVI, its appearance with such emphasis in such a significant location at least creates an association with the prolonged V7 elsewhere in the movement. The development leads to the seventh through gradual transformation (cf. §6.2.1): 4 arrives as part of a nested IV (m. 179) which then moves to 7V; the second in the bass is transformed into an illusory seventh arpeggiation (196– 203). The seventh that ends the development is not structurally connected with the seventh at the end of the exposition, but is itself prolonged for no less than 54 measures. Again, the V7 territory is first widely stretched (203– 27, employing similar figuration to that in mm. 72–111) and then prolonged more daringly. The intensification begins during the stretching as a result of the increasing involvement of passing tones. The retransition proper is particularly climactic. A neighbor augmented sixth chord recurs three times, the last of which opens a nested prolongation based on EP (§7.8.1; §10.3.2): the augmented sixth chord is momentarily reinterpreted as its enharmonic equivalent V7 in Aß major (ßII of the main key). On Aß, the beginning of the first theme is quoted (235–8). In retrospect, the V7–I relation in Aß major is defied, and the theme functions as a nested

480 Notice that the 3 in m. 6 appears on VI. A stable interpretation would connect it to the I in m. 5. The theme is complicated by additional factors: (1) The second statement (mm. 5–9) is in a higher register than the initial one. The tone of the seventh is thus heard in an inner register; (2) The hypermeter is ambiguous. If m. 1 is heard as an upbeat, the seventh in m. 4 occupies a strong measure. Performances can also influence the perception of this theme: For example, Amadeus quartet emphasizes the 3 in m. 5 much more than Alban Berg Quartet does. In result, it is easier to hear a prolonged seventh chord in the latter recording.

Full Circular Prolongation of V7 213

prolongation of the local (enharmonic) V7, connecting backwards the seventh in the fourth measure of the theme. The return to the main tonality might have been achieved through the same enharmonic pivot, but Beethoven chooses a less direct manner. A neighbor diminished seventh chord (m. 239) serves as the pivot and leads to V7/V (241). The final V7 is regained through voice exchange (239–42), without a preceding octave (as always, the theoretically required elided V8 would have destroyed the chromatic continuity; cf. fn. 468). The retransition involves a tonal paradox: the way out of the enharmonic web involves an ascending octave in the soprano, divided into two tritones. The passing tones in each tritone correspond with the diatonic frame of the surface tonality at work at that moment. The combined ascent as a whole creates a hybrid octatonic scale (set 8-25) that violates the foundations of tonality. As to the overall voice leading context of the passage, the clue might be the consonant V that precedes the enharmonic adventure (m. 227). Even though the harmony of V has not been left after the clear manifestation of the seventh (m. 219), it is unlikely that the seventh could be heard as implied above the V triad here. In particular, the augmented sixth neighbor (228) relates to the triad alone. It is necessary to assume that the seventh at the boundaries of the prolongation (219 and 245–6) moved to an implied octave that might serve as its neighbor. The motion back to the seventh passes through a chromatic passing tone on which the enharmonic adventure takes place (cf. Aldwell and Schachter 1978/2003, 603, Ex. 32-9). (d). Recapitulation. Although the repeat of the first theme in the recapitulation is literal (albeit with added counterpoint), the different context perhaps alters the meaning of the theme. The opening arpeggiation, whose lowest tone is the fifth, has a latent meaning as a ¢− chord. In the exposition, this potential is defied by the normative function of an opening tonic. After an extremely conspicuous V7, however, hearing the opening as a ¢− arpeggiation becomes much more tenable. When the V7 in the fourth measure (250) arrives, it is connected to the preceding V7. This is a clear replica of the precedent in the false recapitulation that was nested in the former V7 prolongation (235–8). This interpretation defies true tonic not only in the theme’s fifth measure (as in the exposition), but in its very beginning as well. Admittedly, the

214 Full Circular Prolongation of V7

prolongation of V7 here is weaker than in the preceding retransition; yet it is at least an optional hearing strategy to delay the tonic resolution until its more affirmative appearance at m. 267.481 (e). Coda. The coda stabilizes the theme and cancels the potential prolongation of the seventh. The statement of the theme on IV is truncated (m. 393), and so the descent from the seventh (V7/IV, m. 391) cannot be read as motion into an inner voice, as in the main representations of the theme. The final statement in the tonic resembles the stable phrase in the exposition (mm. 21-28). The coda thus fulfils its classical task of stabilizing former material.

481 The first movement of Beethoven’s next String Quartet (Op. 18,3) also exhibits a penetration of V7 from the end of the development into the recapitulation. There the effect is more of a fusion via a very weak V7 (in a 6/5 inversion). This reading challenges the existence of interruption, which is preserved in the analyses by both Kamien (1992, 98) and Burstein (1998, 297).

8. PROLONGATION OF DIMINISHED SEVENTH CHORDS (VIIº7)

8.0 General Features of Diminished Seventh Chords and their Consequences

Diminished seventh chords are very common in the tonal literature, despite their absence from the diatonic modes. When they bear a clear tonal function, they serve as VII7. In minor, they are accepted as diatonic, due to the customary raising of the leading tone (harmonic minor); in major, diatonic VII7 is half-diminished, but VIIº7 with a lowered seventh, is more frequent. Secondary VII7s in the literature are overwhelmingly diminished, even when applied to major chords such as V (in major or harmonic minor). Prolongations of VII7 apparently troubled Schenker less than those of V7. Since in VII7 all the voices have linear connection with their resolution (§4.3.4), the seventh is contrapuntally justified as an unfolding of a neighbor harmony in both voices (Ex. 8.1, analogous to FC, Fig. 43e).482 The dissonant character of diminished seventh chords and their prolongations is especially pronounced, perhaps because in diminished seventh chords the seventh is not the only dissonance, and the basic triad is dissonant too. There is a maximum of dissonance: two tones are dissonant with the bass, both fifth intervals are dissonant and every tone is dissonant with some other tone. Another

482 See also ‘n.n.hrm.’ in FC, Fig. 30a (Chopin, Mazurka Op. 17,3), mm. 17–24, accompanied by a question mark. The graph seems to imply subordination of II into VIIº7. See below Ex. 8.9f.

216 Prolongation of Diminished Seventh Chords factor that contributes to the special sound of diminished seventh chords is the diminished quality of the seventh itself. This feature has further consequences: (a). The complementary second is augmented. Its absolute size is equal to that of the minor thirds that comprise the seventh chord. The structure of the chord is thus symmetrical, dividing the octave into four equal parts. Because of the symmetry, all inversions of diminished seventh chords are enharmonically equivalent. This makes diminished seventh chords particularly appropriate as pivots for enharmonic modulations, and also creates opportunities for a variety of enharmonic parentheses (EP, see §§7.8; 8.5). Besides, when the interpretation of the diminished seventh chord is ambiguous, the choice of the prolonging tones may imply the key and thus suggest the particular inversion of the prolonged chord (Lester 1981, 17). Nevertheless, the deeper levels alone determine the true function of the prolonged VIIº7. If the diminutions within VIIº7 conflict with its function in the outer context, a sense of EP arises. (b). The idea that the seventh descends from the (possibly elided) octave above it is hardly appropriate in the case of diminished sevenths. While in V, when the seventh does not arrive until the end of the prolongation the motion is normally explained as V8–7 and the seventh is not itself prolonged (§6.1.1), a similar late arrival of the seventh in the VIIº7 cannot be explained as VIIº8–7. This still does not indicate genuine prolongation of the diminished seventh, since the conceptual retention of the diminished seventh is often avoided by other means (65– resolution. See Exx. 8.18 and 8.26). (c). A direct 7–8–7 augmented second is unlikely, and can scarcely sound as a true neighbor (it might better be interpreted as an arpeggiation).

8.1 Harmonies that Prolong VIIº7

The harmonies that can prolong VIIº7 at the immediately subsequent level necessarily contain tones foreign to VIIº7 (Ex. 8.2, drawn after Ex. 7.1a on V7). The chords that most commonly fulfill this function are I!, IV¢−, VI6, V6 or #, with certain alterations in major. If the prolonged VIIº7 is inverted, the inversions of the prolonging chords change accordingly. When the principal prolonging harmony is V or I, the sense of prolongation of VIIº7 is challenged by a potential alternative that resolves the initial seventh into a true V or I.

Prolongation of Diminished Seventh Chords 217

Prolonging harmonies that deserve special attention are quartal harmonies (¢‡). Within diminished seventh chords, these are enharmonically equivalent to triads (VIß£− in minor, its mirror IIIƒ¢− in major483). This feature derives from the diminished quality of the seventh and of one fourth (the 4–1 in minor, the 7–4 in major). These enharmonic relations might encourage the use of daring harmonic devices within VIIº7 (cf. Exx. 8.3c; 8.4f; 8.9c–d). Ex. 8.2c shows additional enharmonic associations (to ßII and VII ƒ5/3), which involve chromatic foreign tones. This richness of enharmonic devices is related to the enharmonic potential of the diminished seventh chord itself.484

8.2 Subordination to VIIº7

Subordination to VIIº7 is much more rare than to V7 (cf. §6.3), since in the former, no bass divider emerges to provide a built-in structural status for the seventh chord. When a VIIº7 (or VIIº!) nevertheless gains priority, this is principally as a result of its participation in a deeper pattern, through a stepwise connection with its resolution (to either I or V). The subordinate chords ‘prepare’ the seventh, 6 In. terms of non-Schenkerian functional harmony, the VII, which has dominant function, is more basic than the subdominant chords (VI, IV or II). Even simple appoggiaturas under a stationary tone of the seventh are not trivial when the goal is a VIIº7, since they give rise to enharmonic associations latent in the º¢‡ sonority with diminished fourth, as shown above (Ex. 8.2a). º¢‡–º£‡ appoggiaturas (in minor) sound like their familiar enharmonic equivalent, minor £−, or, with the presence of the fifth, a half-diminished $ chord. At the moment of resolution, the enharmonic interpretation becomes deceptively even more persuasive; the immediate progression is heard as IV6 or II$ into VIIº2 in the key of IIIß (Ex. 8.3a–b). Context, however, may cause the subordinate sonority to behave like a ¢‡ appoggiatura. For example, Schubert’s song Daß sie hier gewesen

483 Both VIß in minor and IIIƒ in major are based on Riemannian LP transformation of the tonic. 484 The chromatic tones in Ex. 8.2c can be forced into the main tonality through passing motion (b–cƒ–d and aß–gß–f respectively). They are not possible as neighbors in this context, since they would be heard as diminished thirds from their sources (b–dß or aß–fƒ respectively). For a tonicization of a chord that sounds (enharmonically) like a consonant triad although it functions in the wider context as a non-tertian sonority, see the ßVI in Schubert, Nacht und Träume, D. 827, mm. 15–19, as explained by Schachter ([1983b] 1999a, 218–9). This case does not involve PD.

218 Prolongation of Diminished Seventh Chords

D. 775 (Op. 59,2) opens with two appoggiaturas into inversions of VIIº7 (of II), of which the former is only heard enharmonically as a half-diminished seventh chord, while the latter is a genuine half-diminished seventh chord (Ex. 8.3c).485 The VIIº7/6/3–7/5/3 appoggiatura in its diatonic form does not pose a similar problem. Schenker shows this type of appoggiatura in open position (as VIIº¶ª– 12/7) from Beethoven’s String Quartet Op. 18,1/I (Harmony, Ex. 281 [351]), my Ex. 8.3d). This seventh does not resolve. Semitonal appoggiaturas to VIIº7 sound very odd; 4–3, ß6–5 or å8–7 produce enharmonic allusions reminiscent of those created by VIIº¢‡–º£‡ (Ex. 8.3a above and e–f). Notice how (in the Rubinstein passage in Ex. 8.3e) a very remote enharmonic twist arises at a very immediate level. The keys implied in those three cases (together with the main tonality) divide the octave into four equal parts. Appoggiaturas to the root create the more substantial kind of subordinations, where the subordinate sonorities are true tertian chords (Ex. 8.4a–e). Motion to the root alone introduces IV¢−–VIIº7 or II2–VIIº7.486 These types were encountered above in inversion as enharmonic equivalents for º¢‡–º£‡ and º7/5/4-º7/5/3. Motion to both root and third produces VI6 or IV$, and motion to all three consonant tones of VIIº7 creates VI#.487 These appoggiaturas can also be applied to passing diminished seventh chords that are deprived of functionality. For example, in the overture to Halévy’s La Juive (the passage in Ex. 8.4f), a series of diminished seventh chords in a transitive section is decorated with appoggiaturas to the bass. Due to the context, the boundary seventh chords turn out to be in different inversions (VIIº7 [of I] moves to VIIº# of V). This change also affects the meaning of the appoggiaturas. In major, subordination to VIIº7 normally absorbs the chromatic inflections (ß6 and occasionallyß3 ) in the subordinate chords themselves as well (Ex. 8.5a–e).

485 See discussion in Schachter [1983b] 1999a, 212. Lester demosntrates the same enharmonic allusion in two other examples, from Schumann, Album für die Jugend, No. 28 [Errinerung, m. 20 (the climax of the piece) (Lester 1979, 13) and Franck, Symphony/I, mm. 7–8 (Lester 1981, 16– 17). 486 II5/3 is embedded (in minor) within VIIº7. These relations are analogous to VII–V7. The desired distinction between chords can be achieved by a ßII–VIIº7 subordination. 487 In general, all the types in Ex. 8.4 may be inverted; the relations between the inversion of the subordinate chord and that of the goal VIIº7 remain constant. For II7–VII6/5, see Mozart, Piano Sonata K. 457/III, 230–1 (based on II7/3–VII6/3 in m. 2).

Prolongation of Diminished Seventh Chords 219

This feature can be observed in Ex. 8.5f (from Mendelssohn’s Song without Words Op. 67,1). In this example, the voice leading avoids the smoothest possible path (IVß£−–VIIº2) in order to create a larger span (augmented second in the bass of IVß£−–VIIº#) that may be filled in by further motion.488

8.3 Linear Progressions within VIIº7

The following section classifies linear progressions within VIIº7 along the same lines as in the previous chapter in relation to V7. The conditions for the retention of the seventh, however, are different in the case of VIIº7, due to the anomaly of the diminished seventh.

8.3.1 Third Progressions within VIIº7 Since all the thirds within VIIº7 are minor, single passing tones divide any of them into unequal steps (one whole tone and one semitone). The choice of passing tone normally depends on the underlying key. In minor, the diatonic passing tone lies closer to the lower boundary in the two lower third spans (1–3 and 3–5), and to the upper boundary in the 5–7 third span. Complete chromatic filling is possible too, and obscures the tonal orientation. 8.3.1.1 Single third progressions within VIIº7. Single third progressions over a stationary chord are very rare within VIIº7 (Ex. 8.6a–b). The motion in the two lower third spans behaves similarly in both directions, except that the emerging passing ‘ßII’ is enharmonic in ascent, but not in descent. In the upper third span, a descending progression prolongs the seventh that initiates it, while in ascent the seventh only arrives as the goal of SFM VIIº5–7 (Ex. 8.6c–d, after the analogous cases discussed in §§5.4.1; 6.2.2).489 The span of the augmented second, for Schenker, ‘does not express the motive of a third’ (MW I, ‘The Art of Improvisation,’ 7). Schenker also demonstrates elsewhere how a sequence skips over one chain in Bach’s

488 In this piece, during the time span of VIIº7, resolution into V is expected, but in fact the VIIº7 resolves directly to the tonic. If the lowered seventh is only introduced on the literal VIIº7, after a diatonic chord, the sense of subordination is weakened. See below discussion of Ex. 8.9f (Chopin, Mazurka Op. 17,3). 489 See also Schubert, Der Stürmische Morgen [Die Winterreise No. 18], m. 2. The seventh is added only after the chromatic third progression in the lowest third span.

220 Prolongation of Diminished Seventh Chords

Chromatische Fantasie (m. 31) in order to avoid filling an augmented second as if it were a third (Ex. 8.6e).490 Occasionally, however, passing motion is indeed inserted into an augmented second, as in Ex. 8.6f (Schubert). Only the deeper context determines that the filled interval still functions as a second. 8.3.1.2 Parallel third progressions within VIIº7. Motion in parallel thirds within VIIº7 (Ex. 8.7a–d) can appear in more varied forms than within V7. Four pairs of adjacent third progressions are possible, of which two involve the augmented second as one of the third spans (and also include a vertical augmented second). Although theoretically such parallel thirds are false, they are heard as thirds, especially when they are filled chromatically. See Mozart’s Piano Sonata K. 576/I, 152–3 (Ex. 8.7d), which uses the complementary intervals (parallel sixths and one vertical diminished seventh).491 Motion in the outer pair of third progressions (Ex. 8.7e) is free of the usual problem of parallel fifths, since in VIIº7 the fifths are diminished. The passing intervals may still be perfect fifths, but complete chromatic filling of the parallel motion would avoid perfect fifths altogether. Gliding parallel motion within VIIº7 can even encompass all four voices simultaneously, with or without complete chromatic filling (Ex. 8.7f). In that case, the diminished seventh has an even greater potential for ambiguity, and the diatonic skeleton does not match in all voices. Ex. 8.7g shows an extreme instance from Chopin’s Nocturne Op. 27,1, where such gliding diminished seventh chords fill thirds on two distinct levels. The choice of the passing tones does not derive here from an underlying diatonic key, but rather comprises an octatonic fragment.492

490 ‘[Bach] must give up altogether elaborating the space of an augmented second in the VII7 of D minor, because it could not be translated into a motive of a third.’ In ‘Bach’s Prelude in Eß Minor from WTC I,’ TW 1, 41 [2004, 36]). See similar skips over a chain in a sequence (in the opposite direction) in Beethoven, Piano Sonata Op. 111/I, m. 27 and in Schumann, Cello Concerto/I, 135– 6. In a similar situation, Brahms (in his Cello Sonata No. 1/III, mm. 88–90), replaces the problematic augmented second by a filled-in major third. 491 This VIIº7/V proceeds to a cadential 6/4 (in major). In accordance with the immediate tendency of the soprano toward 3, the diminished seventh chord shouldbe spelt as a 6/5, and the parallel motion involves sixths only. See also the graph in Wen 1990b, Ex. 8.5. See also Mozart, Piano Concerto K. 488/I, 295–7. The spelling, which includes a filled augmented second, is based on the deeper resolution to V, but contradicts the immediate progression to the 6/4 in major. 492 My middleground context follows the reading in Salzer 1970, which is devoted to this nocturne. At the diminution level Salzer’s reading is completely different. Wen (1990a, 109) interprets as a similar gliding of parallel diminished seventh chords the passage in Mozart, Piano Concerto K.

Prolongation of Diminished Seventh Chords 221

8.3.1.3 Third progressions in contrary motion within VIIº7

Most third progressions in diminished seventh chords appear in contrary motion, mainly in voice exchanges: (a). Voice exchange between the fifth and the seventh (Ex. 8.8). The passing harmony, V6, reinforces the dominant function, and might be perceived as resolution of the initial VIIº7 rather than its prolongation. Nevertheless, even when inversion causes the passing V to appear in root position, the VIIº7 can be prolonged, as in Schubert’s Impromptu D. 899 (Op. 90),1 (Ex. 8.8c).493 (b). Voice exchange between the third and the fifth (Ex. 8.9). The passing sonorities are the ¢‡ structures which have enharmonic triadic equivalents, as we have seen above (Ex. 8.2). The precise chords, as well as their enharmonic equivalents depend on the choice of the passing tone. A passing tone half a tone above the third of VIIº7 (as is diatonic in minor) introduces a chord enharmonically equivalent to VIß (£− if the prolonged VIIº7 is in root position; ¢− with motion in the bass—cf. Mitchell [1939/1965, 185, Ex. 332]), and without a wider context, the same third progression can sound enharmonically like a voice exchange between root and third in III (or IIIß) (Ex. 8.9a, analogous to the last chord in Ex. 8.2a); A passing tone half a tone below the fifth of VIIº7 (as is diatonic in major) introduces a chord enharmonically equivalent to IIIƒ (¢− if the prolonged VIIº7 is in root position), and without a wider context, the same third progression can sound enharmonically like a voice exchange between root and third in VI (Ex. 8.9b; analogous to the last chord in Ex. 8.2b). A daring realizations of the latter possibility—in inverted form (within VIIº#), where the passing chord is enharmonically a !—appear in

491/I, 5–8. This reading, however, is in conflict with the melodic sequence, which points to transitive motion starting on m. 4. The famous ‘dodecaphonic’ passage at the beginning of the development of Mozart’s Symphony No. 40/IV can be interpreted as based on an ascending circular series of gliding diminished seventh chords (mm. 127–32). D. Lewin (1987, 222) identifies that ‘the enharmonically equivalent Aß [127] and Gƒ [132] are tied together’ since the harmony ‘implicitly recurs,’ but does not refer to prolongation. 493 In the impromptu, the same material recurs in m. 178 over a V pedal point. See also: Mozart, Adagio K. 540, m. 1 (Aldwell and Schachter 1978/2003, 429, Ex. 25-13); Mozart, Piano Sonata K. 280/II, 26–27, passing through V5/3 due to inversion, using an ascending upper voice; Beethoven, Piano Sonata Op. 10,3/II, 56. For a voice exchange that replaces the passing V by a ‘I’6/4 (through counterpointing neighbor motion) see below Ex. 8.45b (from Mozart’s Piano Concerto K. 595/I).

222 Prolongation of Diminished Seventh Chords

Ex. 8.9c, from Schumann, Davidsbündlertänze No. 6) and Ex. 8.9d from Brahms, Intermezzo Op. 116,6 (discussed in §3.3.2).494 This remote enharmonic allusion can be avoided by modifying the passing chord by means of counterpointing motion. An upper neighbor to the root produces ‘VI6’ (Ex. 8.9e), as happens in Chopin’s Mazurka Op. 17,3, mm. 23–24 (Ex. 8.9f). This passage uses the minor form of passing motion as a mixture within VII ß7 in major. This expands the mazurka’s opening chromatic motive.495 Further motion can also give rise to an apparent root- position tonic (Ex. 8.9g).496 (c). Voice exchange between the root and the third (Ex. 8.10). The vertical interval between the passing tones should form a perfect octave. The diatonic passing chord is IV¢−, as in the prelude from Bach’s Cello Suite No. 4 (Ex. 8.10a).497 When the prolonged VIIº7 is applied to V, the passing ¢− is an apparent tonic in the main key. This particular situation challenges the unity of the prolongation, since in the same chord succession (VIIº7/V–I¢−–VIIº#/V– V) the ¢− can alternatively function as a cadential suspension (Ex. 8.10b). Both interpretations are possible, depending on context and design. Compare Exx. 8.10c (from Haydn’s String Quartet Op. 20,2/I), and d (from Beethoven’s String Quartet Op. 131/I). In the former, the figuration in the inner voices

494 The Schumann passage also includes a voice exchange of the root and third, and in one voice combines the two third spans into a diminished fifth progression. The prolonged chord is VIIº6/5 of V that never arrives: the supposedly cadential 6/4 (in minor form), becomes connected to the ensuing tonic. See also a possible voice exchange in the same 3–5 space in Ex. 8.36b (Chopin). 495 For the same procedure with the same mixture, but in inversions see: Weber, Der Freischütz, prelude to Act 3, 37–40—a prolongation of VIIº2 passes through root-position ßVI; Brahms, Tragic Overture, 37–38—the prolonged VIIº7 (applied to the major diatonic III in d minor) moves from 4/3 to 6/5 inversion via ßVI6/4, a sonority that Webster (1983, 15) claims is ‘unexplained.’ The voice exchange is clearer in the winds, and involves exchange of all voices in the strings. As noted in the previous footnote, the Schumann passage in Ex. 8.9c also implies mixture. 496 See a similar procedure (inverted) in Mozart, Piano Sonata K. 457/III, 21–23. In that case, the seventh of VIIº7 does not return after the passing chord. 497 My reading agrees with Schachter (1994, 62) about the bass; Schachter’s foreground graph interprets the upper strands differently. See also in the same prelude mm. 41–43, and 49–51 (according to Schachter 49–55). See also: (1) Beethoven, Symphony No. 2/II, 41–44; (2) Beethoven, Piano Sonata Op. 10,3/II, 3–4 (Wintle 1985, 156, quoting Federhofer); (3) Mendelssohn, Violin Sonata Op. 4/I, 26–29 (first inverted via a passing 5/3 and then via the normative 6/4). This is a variant of the first theme, which in its initial form (mm. 11–17, also 1–2 in the slow introduction) prolongs VIIº7 by means of simple passing tones.

Prolongation of Diminished Seventh Chords 223

indicates the boundaries for a true voice exchange, while in the latter, the change from crescendo to p marks the cadential ¢− as a boundary point.498 If the voice exchange is not executed through direct crossing, the passing ¢− may be replaced by other sonorities, such as the altered IV$ and IV2 in the coda of Haydn’s String Quartet Op. 71,3/I, exploiting a potential hinted at the end of the exposition (Ex. 8.10e). Finally, Ex. 8.10f, from Chopin’s Scherzo No. 1, shows a freer voice leading, where the boundaries indicate voice exchange but the actual voice leading employs parallel tenths. Further contrary third progressions can occur without voice exchange (Ex. 8.11a); this type can combine with voice exchanges when each direction contains a pair of parallel third spans (Ex. 8.11b). I have only found a partial realization of this procedure (Ex. 8.11c, from No. 13 of Schumann’s Kinderscenen).

8.3.1.4 Chromatic elements in thirds spans within VIIº7

Four devices absorb chromaticism into third spans within VIIº7: (a). Chromatic passing tones which replace diatonic tones. This happens as a result of mixture, normally within VII ß7 in major. Cf. above Ex. 8.9f (Chopin) and the cases cited in the corollary footnote. (b). Chromatic stationary tones that remain during the passing motion. This procedure, too, occurs as a result of mixture within VII ß7 in major. The passing chord is chromatic, although the active motion passes via diatonic tones. For example, in Ex. 8.12 (from Brahms’s Symphony No. 2/I), the diatonic passing tone a merges with the chromatic stationary tone f in the chromatic chord D minor. (In the latter part of the example, the passing tones themselves are chromatic, as in device (a)). This passage forms a motivic enlargement in both outer voices (Schachter 1983a, 61–62, Exx. 3–4). (c). Complete chromatic filling of the third progressions. We have already encountered such complete chromaticism in single or parallel third progressions (Exx. 8.6; 8.7c–f; 8.12). In theory, only the diatonic passing tone participates in the third progression, while the chromatic passing tone lies

498 In the passage from Op. 131, the final VIIº7 is altered into an augmented sixth chord. Mast (1980, 174) reads the voice exchange that I believe is merely apparent. For a true voice exchange of root and third in VIIº7 see also: Mendelssohn, Symphony No. 3/I, 223–36, as a furioso climax. The resolution sounds like V of an elided C in a modulatory context. See also Eybl 1995, 158.

224 Prolongation of Diminished Seventh Chords

even closer to the surface. This distinction is, however, hard to apply: the diatonic steps do not always match in parallel voices (recall Ex. 8.7f); the filling of the augmented second does not include a diatonic tone; and design can emphasize the chromatic rather than the diatonic tone. In voice exchanges, complete direct chromatic filling of minor thirds (as are all the thirds of VIIº7) creates consecutive clashes on a major seventh and a minor ninth (or vice versa). These clashes can be avoided by rhythmic displacement of the passing motion: the exchanging voices should coincide on a perfect octave with separate insertions before and after it (Ex. 8.13a– d).499 The delays are possible in both ascent and descent in any third span, and even within the augmented second; the emerging progressions are reversible and invertible. They give rise to various passing harmonies, some of which suggest enharmonic interpretations.500 The common type of displacement (Ex. 8.13,a1) resembles the classical omnibus within V7, and shares the same passing chords. This passing motion has a functional meaning, which is based on the drive of the augmented sixth outward, as in Ex. 8.13e,501 but the functional meaning also obtains even where the bass ascends, as in Ex. 8.13f (Brahms, Symphony No. 4/I, 9–12).502 Ex. 8.13g (Wagner) shows how such voice exchanges in various third-spans can be combined by means of a sequence (cf. Ex. 8.50 for context). An exceptional technique that avoids the clash without using displacements is found in C. P. E. Bach’s Keyboard Sonata W57,6/I (Ex. 8.13h): the upper voice steers clear of directed melodic motion and creates

499 Each insertion may be used independently. For example, the upper insertion alone appears in Liszt’s song Die Loreley, mm. 2–3 (see discussion in Rosen 1995, 474–5). Aldwell and Schachter (1978/2003, 575, Ex. 31-21c) show a partly-filled voice exchange between the fifth and the seventh of a diminished seventh chord (inversion of Ex. 8.13,c1). Cf. Ex. 7.13 for analogous displacement in the omnibus progression. 500 The emerging passing sonorities are either dominant seventh chords and minor 6/4s (Ex. 813a, d) or their inversions: equivalents of half-diminished seventh chords and major 6/4s (Ex. 8.13b, c). 501 See also Chopin, Scherzo No. 1, mm. 43–44 (immediately after the passage in Ex. 8.10f). 502 The articulation of the boundaries of the prolongation is somewhat vague, since the ascent in the bass is embedded in a larger octave line. My reading deviates from Schenker’s in FC, Fig. 81,2. That graph also contains a certain contradiction concerning the source of the seventh in m. 18. Slurs show it as both a passing tone in a fourth progression and as a suspension from the 4 at m. 15. In other analyses, Boretz (1973/1995, 327–8) and Dunsby (1981, 45, Fig. 10) clearly view mm. 9–12 as a separate unit within a diminished seventh chord.

Prolongation of Diminished Seventh Chords 225

parallel octaves with the bass (another reading: Petty 1999, 59). This device is non-grammatical. (d). Altered third spans. The minor thirds can become either major or diminished. Ex. 8.14 shows those possibilities that produce familiar chords. Cf. also Ex. 8.20g below (Brahms, Double concerto).

8.3.1.5 Additional third progressions within VIIº7

Third progressions that exceed the boundaries of the seventh of VIIº7 (Ex. 8.15) differ from their counterparts within V7. A third from the root downward leads to the kind of relations between VIIº7 and V9 that caused many theorists to identify the former as a rootless form of the latter. The power of the V is so great that it might outweigh the boundary events and be viewed as the true harmony. This situation stands in contrast to the analogous configuration V7–‘III9’–V7, where the ‘III9’ is clearly on a lower structural level than the boundary chord (cf. Ex. 7.19a). The passing tone either creates an augmented second, or uses the melodic minor. A third above the diminished seventh raises unique problems: a minor third would create a diminished ninth, which coincides with the octave; a major third introduces harsh clashes, although motion in additional voices below the ninth can help to avert such clashes. Occasionally, third progressions within VIIº7 are apparent only. The return to the diminished seventh does not necessarily prolong the initial VIIº7, even when the intermediate third-descent is hierarchically inferior. For example, in the coda of Beethoven’s Piano Sonata Op. 57/I (242–5, Ex. 8.16), both VIIº7s take up the voice leading thread from preceding consonances, so that they do not relate directly to each other. Such a procedure seems hardly possible with a V7.503

8.3.2 Inverted thirds: Sixth progressions within a VIIº7 Any of the three third spans within a VIIº7 may be inverted into a sixth. If the segmentation preserves the structure of the prolonged chord, all these sixths contain an augmented second, which weakens the sense of stepwise motion since it is enharmonically equivalent to a skip of a third (Ex. 8.17a–c; see Exx. 8.31–

503 The analysis in TW 7 stops before this passage. The effect of fusion resembles that in Ex. 8.19c (Schubert) below.

226 Prolongation of Diminished Seventh Chords

8.32 for avoiding augmented seconds). Context can force the meaning of a sixth even if the inner prolongation takes the form of a completely linear diminished seventh progression (Ex. 8.17d). In that case, an octatonic scale emerges.504

8.3.3 Fifth Progressions within VIIº7 In diminished seventh chords, both fifths are diminished.

8.3.3.1 Fifth progressions in the VIIº7–3 span

This span actively involves the tone of the diminished seventh. The theoretical problems here differ from those created by fifth progressions to or from the seventh of V7 (cf. §8.0). The tone of the seventh of VIIº7 (6) may come from or resolve into 5 as a cover tone above the tone of the third ()2 (Ex. 8.18). This makes the 62– fifth progression connective (refer back to Ex. 2.14b). The span of the fifth might even be perceived as a combination of a fourth progression within V7 (or #) and a step in the same direction, especially if 5 occupies a strong beat.505 These alternative readings are still dissonant, since they maintain 4 as part of 7V. Practically the only way to guarantee genuine retention of the diminished seventh is to actually have it present at the same time as the third (2) in another voice. The most common technique for achieving this is via a voice exchange (Ex. 8.19a). Here, I show an interesting example from the second of Brahms’s Fest- und Gedenksprüche, Op. 109, for double chorus. The passage is performed by one chorus, then repeated immediately by the other, but with a different ending. The overlapping between the phrases of the choruses guarantees the structural connection to the new VIIº7.506

504 I have found no realization of this procedure in the literature; for an analogous case where a fourth span is internally prolonged as if it were a fifth progression, see Ex. 8.24c. 505 A similar dilemma as to alternative ways of hearing 6 as either a primary tone or as a neighbor also arises in the cases of descending diminished seventh progressions (see §8.3.5) or third progressions. In the latter case, hearing the 6 as a neighbor that resolves into a cover tone5 would destroy the sense of a linear progression altogether. 506 Jonas ([1934] 1982, Ex. 133) uses this excerpt to explain that a local dissonance is merely the product of displacement, but he overlooks the fact that here, the frame itself is dissonant. Interestingly, the embraced progression is based on the primary consonant chords I–IV–V, but nevertheless prolongs the dissonant VIIº7. Additional cases where a statement that descends from the seventh of VIIº7 is repeated with modification, so that the initial 6 is connected with the beginning of the repeat and bridges over the division, are shown in Ex. 8.27b (Brahms) and in the more problematic Ex. 8.19c, first interpretation (Schubert), and the less preferred interpretation in Ex. 8.16 (Beethoven).

Prolongation of Diminished Seventh Chords 227

Other techniques that guarantee retention of the seventh of V7 (4) in analogous cases are less convincing here: (a). ‘Preparation’ of 6 on a preceding harmony before ascending to the seventh (Ex. 8.19b). The preceding 6 might be resolved into 5a cover tone above the 2 that initiates the ascending fifth progression. (b). The opposite procedure, i.e., re-establishing 6 after a descent from the seventh: an implied resolution into 5 might be imagined above the2 , and there need not be a structural connection between the sevenths before and after it. I demonstrate this dilemma with the first theme of Schubert’s Symphony No. 4/I. Ex. 8.19,c1 presents alternative interpretations that differ in respect to the retention of the seventh. In addition, this theme contains a strong harmonic progression (I–VI–II6–V7) at the immediate level. At the first statement of the theme, it is heard as an insertion into the unstable prolongation, but when it recurs and leads to I, it might be heard as a quasi- auxiliary cadence (see my alternative ending). In the development (Ex. 8.19,c2) the theme is cited twice; on the latter occasion it is transferred to the bass and a single tone in the melody is modified (1 replaces 2). This minute change influences the entire passage, since it disconnects the two appearances of the seventh.507 A unique way of unifying the fifth progressions is achieved when the descent reaches ß2 through a perfect fifth, and then corrects it to2 . Over theß2 , the retention of the seventh 6 is more plausible than its resolution to5 (ironically, this happens precisely because it produces a consonance); this also influences our hearing of the diatonic goal. This special device occurs in the Adagio from Bach’s Violin Sonata No. 1 (Ex. 8.19d). Even though 6 does eventually descend when the diatonic 2 appears, the diminished fifth remains in memory. The segmentation of this fifth progression is based on a normative division into thirds, but the temporal distribution of the descent is asymmetric. Along with the techniques discussed here, any factor that reinforces the structural status of the seventh increases the likelihood that it is retained. In

507 One may also hear the descent in the theme as a seventh progression, or as a descending third progression from the fifth under a stationary seventh. For the concept of quasi-auxiliary cadence, which starts from a root-position tonic (at the specific level), see Kamien 2005.

228 Prolongation of Diminished Seventh Chords particular, motivic parallelism with other fifth progressions can help to unify the fifth span as constituting the boundaries of a genuine linear progression. As with other fifth progressions, the division of VIIº7–3 need not emphasize the governing chord. Even if this fifth is divided into two thirds, the middle third (4) can be given another harmony (my ‘type 2’ of fifth progressions, cf. §7.2.3), as a root, third or seventh of the passing chord (IV, ßII or V7 respectively), or even a fifth of an altered VII (Ex. 8.20a–d).508 Alteration of 4 itself offers further possibilities (Ex. 8.20e–f). For example, in Brahms’s Double Concerto/I, 184–8 (Ex. 8.20g), the fifth progression is divided on ƒ4 (cƒ); the bass is based on altered third progressions (moving to aƒ rather than a), and the middle harmony is another diminished seventh chord. If the division into two thirds is avoided (my ‘type 3’ of fifth progressions), the passing 5 and3 are highlighted. If they belong to the same harmony, I, III or VI7 emerge (Ex. 8.21). In the case of III, mini-enharmonicism is produced.

8.3.3.2 Fifth progressions in the lower fifth of VIIº7

The lower fifth progression in VIIº7 can easily prolong the diminished seventh chord under (or above) a stationary seventh (Ex. 8.22). It is invariant with the upper fifth of V7 (47– ), and the procedures for its prolongation are also similar (cf. §7.2.3.1), except that here a V or V7 passing harmony creates variety, and II (in minor) does not (since it is contained in the prolonging harmony). Both fifth progressions within VIIº7 may appear in parallel motion (Ex. 8.23), as in Bach, WTC I, Fugue in Bß minor, 57–8 (Ex. 8.23c, after MW II, 14, Fig. 29). In this example, the broader context is itself a diminished fifth progression IV4- V7 (mm. 57–62). The continuation of the initial4 in the larger motion is made by means of chromatic ascent in an inner voice, but one may hear 6 of VII connected with the second beat of m. 62, which forms the highest melodic peak in the passage. This connection remains tentative, since resolution into V (m. 62) seems to avoid true VIIº7 prolongation. The greatest degree of control over fifth progressions in a VIIº7 prolongation is achieved with a combination of voice exchanges and parallel motion as two

508 I suggest ßII, since in minor, diatonic II is contained within VIIº7. A passing IV was encountered in Ex. 8.19a (Brahms). In that case, a local suspension introduces ßII6 even closer to the surface.

Prolongation of Diminished Seventh Chords 229 parallel pairs of diminished fifth voice exchanges, as in Ex. 8.23d, from Beethoven’s Piano Sonata Op. 90/II.509

8.3.4 Inverted Fifths: Fourth Progressions within VIIº7 Since in diminished seventh chords both fifths are diminished, both complementary fourths are augmented. Their direct expression includes an augmented second, and they are enharmonically equivalent to a diminished fifth which comprises a third-skip and two steps (Ex. 8.24a–b; see Exx. 8.31–8.32 for avoiding direct augmented seconds); when the inner prolongation of the fourth fills the augmented second, it loses its identity even more. Even then, the deeper context can force the tritone span to function as an augmented fourth. For example, in Ex. 8.24c (Chopin, Nocturne Op. 27,2, mm. 40–45), an ascent from the bass into an inner voice is clearly treated as a diminished fifth, divided into thirds on the same harmony (my ‘type 1’), and based on two successive third- voice exchanges reminiscent of the omnibus progression (§7.2.1.2.1). Nevertheless, in context this span functions as an augmented fourth within VIIº2, which serves as a neighbor to V7. This neighbor configuration is based on a 5ß6– 5– chromatic neighbor, which is a motivic element explored throughout the nocturne.510 When all the voices move a tritone in similar motion, some voices express augmented fourths while others prove to be diminished fifths. The inner

509 Ex. 8.23d eliminates registral manipulations. The passing ‘I’ and ‘I6’ refer to the minor V without a raised leading tone. See also fugue BWV 948, attributed to Bach, mm. 79–81 (Rothstein 1991, 312–3, Exx. 22–23). Both outer voices descend a tritone, exchanging the third and seventh, but the linear descent skips over the middle third. See Ex. 8.33b for the preceding passage. 510 Schenker (1916/1971, 7) compares this passage with the introduction to Beethoven’s Piano Sonata Op. 111/I, 5–10 (cf. Ex. 8.33a). He shows how the segmentation in the nocturne corresponds the spaces of the prolonged chord, in contrast to the more problematic case in Beethoven. In the nocturne, Salzer (1952/1962, Ex. 506) ignores the foreground hierarchy (and also the seventh), and indicates only the wider prolongation of V. Yellin (1998, Ex. 58) relates the progression to the omnibus. Another reading: P. Schubert 1993, 296–7. See a similar prolongation of an augmented fourth that is treated in relation to the inner activity as a diminished fifth, albeit without clear segmentation, in the bass of the introductory recitative to Beethoven’s An die Hoffnung, Op. 94, mm. 4–14. This dark PD expresses the existential questions stated by the text, and its resolution depicts the hope at the end of the introduction. Additional augmented fourth progression: Brahms, Rhapsody for alto, male chorus and orchestra, mm. 8–9, upper voice. The augmented second is avoided by means of inserted incomplete neighbor (for that problem, see Ex. 8.32). The insertion creates a temporary impression of resolution; Forte (1983, 260) actually reads such a resolution.

230 Prolongation of Diminished Seventh Chords prolongation must comprise at least five events in order to avoid skips in the filling of the fifth; this requirement might cause a filling in of the augmented second, in which case the augmented second loses its identity. This happens in the theme of Schumann’s Novelette No. 8 (Ex. 8.25). In this theme, all passing chords are themselves diminished seventh chords, and all four diminished seventh chords appear. They do not derive from an underlying diatonicism. The diminutions increase the denial of functionality: they are based on a precise sequence that preserves the exact size of the steps; only the last chain of the sequence adjusts the passing motion to the key.511

8.3.5 Diminished Seventh Progressions In diminished seventh chords, seventh progressions are of course diminished. This anomaly has evident results.

8.3.5.1 Illusory versus genuine diminished seventh progressions

Normally, illusory seventh progressions express incomplete and indirect register transfer. Diminished seventh progressions that function this way represent an augmented second (Ex. 8.26a; cf. Ex. 7.3d [Chopin]), but these are rare.512 This still does not guarantee a genuine retention of the diminished seventh; rather (as was also the case with VIIº7–3 diminished fifth progressions), the seventh (6) may resolve into or arrive from 5 as a cover tone (part of 6V) above the root of VIIº7, which serves respectively as either the goal tone in a descending diminished seventh progression or the initial tone of an ascending one (Ex. 8.26b). Diminished seventh progressions can also be transitive (cf. §1.1.2.1). For example, in Ex. 8.26c (Mendelssohn, Song without Words Op. 62,3, mm. 25–26), the diminished seventh progression in the bass moves from II6 to V# (nested within V7 prolongation). It is neither a genuine prolongation of the seventh nor an indirect register transfer. Meanwhile, the upper and inner voices move in other

511 See also Chopin, Etude Op. 10,3, mm. 38–41 (Ex. 8.34c; see context in Ex. 7.29d). The diminution within each diminished seventh chord is based on similar motion in all voices, complicated by shifts in register. 512 Schenker also presents an augmented second as a step within a linear progression in his schemes of (perfect) fourth progressions (FC, Fig. 87,2). A diminished seventh progression that stands for VIIº8–7 would have to be considered semi-genuine, according to the general case. Cf. §5.4.2.1.

Prolongation of Diminished Seventh Chords 231

(not diminished) seventh progressions which differ in status (as indicated in the graph). As with non-diminished seventh progressions, the span of the seventh may even be deprived entirely of its status as the boundary interval of a linear progression (either genuine or illusory). Successions identical with diminished seventh progressions can mean a step followed or preceded by a sixth in the same direction (Ex. 8.26d–f).513 In this case, the motion to or from the cover tone 5 takes place in the middle of the seventh-motion. The enharmony of the diminished seventh creates an even more radical alternative to the genuine seventh progression when the whole progression serves to prolong its enharmonic equivalent major sixth (Ex. 8.26g).514 The rules that indicate genuine diminished seventh progressions are essentially the same as those concerning diminished fifth progressions from or to the tone of the diminished seventh (Ex. 8.18 above): a diminished seventh progression only forms a genuine prolongation of a diminished seventh chord when this chord stands at both its boundaries. The tone of the seventh in particular should be present at both boundaries, or appear before the beginning of the progression; it can also be indicated through other parameters by means of the familiar preference rules.

8.3.5.2 Descending diminished seventh progressions in various segmentations

Diminished seventh progressions can be segmented with or without correspondence with the underlying harmony (the types of segmentation are explained in §§7.2.3 and 7.2.5). Ex. 8.27a (Haydn) presents a simple and almost direct specimen in the bass.515 When the segmentation does not adhere to tones of the VIIº7, the aesthetic effect depends on the choice of the alternative segmentation. In diatonic diminished seventh progressions, the tones that do not belong to the VIIº7 are those of the tonic. Emphasizing them creates a strong

513 See a problematic passage in Berlioz, Benvenuto Cellini overture, 146–58. Rushton (1983, 214) includes contradictory indications for both seventh- and sixth progressions. 514 This procedure differs from that in Ex. 8.17d, where the space of a sixth that is filled as if it were a diminished seventh nevertheless takes place within a diminished seventh chord. 515 This progression is clearly divided into thirds; while these thirds are not harmonized as VIIº7, their harmonizations are fairly close: V2 (which shares three tones with VIIº7) and VII6/3 (a subset of VIIº7).

232 Prolongation of Diminished Seventh Chords impression of resolution, which only proves to be illusory in retrospect. In Ex. 8.27b (Brahms, Schicksalslied 154–68), such a diminished seventh progression with emphasized passing tonic tones (and sustaining 1 in the bass) is followed by a similar descent where, however, the tonic tones truly resolve the initial diminished seventh. The difference between the passages is articulated in the added string basses, which reinforce 1 in the repeat only. Real-time listening expectations are twice denied: in the first statement, one expects a true tonic resolution, but it proves to be deceptive; in the repeat, the experienced listener awaits a similar deception, but this time the resolution is not cancelled.516 By contrast, in the famous introduction of Beethoven’s String Quartet Op. 59,3/I (Ex. 8.27c, shown in several layers after Katz 1945, 174517), an unusual chromatic segmentation of the diminished seventh progression makes it very daring indeed. This introduction expresses two subordinations to V7: VIIº2–V7/V and VIIº7–V# (of I).518 It is the primary VIIº7 that is prolonged through a diminished seventh progression in the bass. It forms a self-contained area, even though it continues the preceding descent (since m. 1) in the same direction. The precise activity within the seventh progression alludes to several other keys. Most notably, its position as VIIº2 sounds at first as if it is VIIº$/ßIII; the resolution is supposed to acquire a deeper status than its applied VII, but the retrospective hierarchy is reversed. In addition, a nested succession implies a tentative IVß.

8.3.5.3 Ascending diminished seventh progressions

In ascent, diminished seventh progressions are only genuine if the seventh is also included in the initial harmony. This requires a literal presence of the tone of the seventh at the beginning of the ascent (and correct identification of the boundary seventh) (Ex. 8.28a–b). Even stating 6 before the ascent does not preclude the

516 This seventh progression is not entirely diatonic, but the emphasized passing tones are diatonic. Considering the title and character of the work, it is tempting to imbue with programmatic intentions the play with the resolution of the diminished seventh. My interpretation concurs with the reduction in Jackson 1996, 81. See below comment on mm. 317–22 as a neighbor VII7–6–7. 517 Katz’s graph is less detailed than mine, but is accompanied by a detailed text (172–6). Two other graphs, by Webster (1980, 104) and his reviewer Kramer (1983, 304) indicate the entrance of Aß (the tone of the seventh) as a structural event. Green (1965/1979, 224, Ex. 12-5) only identifies the final three chords as a prolongation of VIIº7. 518 The same progression appears in an overt manner in Chopin, Mazurka Op. 30,4, mm. 1–4.

Prolongation of Diminished Seventh Chords 233 possibility of hearing 5 as a cover tone at the initial moment of the ascent (Ex. 8.28c), at least under neutral rhythmic and motivic circumstances.519 Ex. 8.28d presents a remarkable ascending diminished seventh progression in the Benvenuto Cellini overture by Berlioz (mm. 284–99). At the outset, the seventh appears in the bass, as VIIº2 in A minor (a lower bass is left off, and does not have continuation in the voice leading). It proceeds to V7, which is initially heard as its resolution, but in retrospect serves only as a neighbor to the prolonged VIIº7. The VIIº2 already sounds like a boundary event in real-time listening, mainly as a result of the change of orchestration (the recurring pattern in the timpani is especially effective). The hierarchy is clarified when the goal VIIº7 is stated unequivocally and resolves directly to its tonic. The ascent of a seventh is indirect. The insertion might have meant motion from an inner voice, but since the return to the main line (m. 297) is not articulated, the effect of a seventh progression is heard here as the product of two overlapping fifth progressions.520

8.3.5.4 Doubly diminished seventh progressions: the case of Schubert’s Der Wegweiser

The famous progression in the last verse of Der Wegweiser [Die Winterreise No. 20] (Ex. 8.29) is, strictly speaking, a transitive progression from VIIº7/V to V7/V. Nevertheless, the VIIº7 is prolonged throughout most of this passage, and even the ending might count as an alteration of the same chord. The passage is based on three voice exchanges, the last of which is altered. The altered voice exchange transforms the step from 6 to5 step into a diminished third. From this perspective, the actual boundary interval in the bass might be considered a doubly diminished seventh (cƒ–bå), which is filled by a complete linear progression in an essentially circular context. Nevertheless, the goal functions enharmonically as a true V7/V (using a).

519 This strict condition also obtains for ascending diminished fifth progressions to the tone of the diminished seventh (Ex. 8.18); the difficulty is lesser with ascending linear progressions to the seventh of V7. For actual diminished seventh- voice exchanges as in Ex. 8.28b, see C. P. E. Bach, Keyboard Sonata W49,6 [Württemberg No. 6]/III, 112–5, and Mendelssohn, Piano Trio Op. 49/I, 89–91. In the latter, the triple meter causes a subdivision which is incongruent with the chordal tones. 520 Rushton (1983, 220) analyzes the passage with contradictory clues as to its true boundaries.

234 Prolongation of Diminished Seventh Chords

The three voice exchanges refer respectively to the lower, middle and upper third spans of VIIº7. They all pass via minor ¢− chords, of which only the first is a true ¢− in the home key. Spelling according to the wider context reveals that the other two passing chords are, in fact, only enharmonic equivalents of ¢− chords: the passing sonority in the middle third span is an inversion of the usual diatonic º¢‡, while the sonority in the upper third is a unique further altered chord (‘II ƒ5/ƒ3/ß1’) that substitutes for a passing V/V. Interpreting the passing sonorities according to their normative meaning as ¢− chords creates a series of enharmonic re- interpretations of the diminished seventh chord. The ¢−s sound cadential and imply the keys in which they would resolve. Their metrical location is essentially weak, but the arpeggiation (or reaching-over) in the soprano occurs precisely on the passing ¢−s, rather than on the governing VIIº7s. This passage attracted enormous analytic attention in the Schenkerian literature. The existing studies focus on the unifying prolongation and tend to ignore the immediate enharmonic associations, apparently as a reaction to earlier analyses, which interpreted them as a series of modulations.521 I aim to integrate both aspects: the particular third- voice exchanges enharmonically imply specific keys at the surface; viewed the other way around, the choice of specific passing tones in the bass (one semitone above the preceding chord tones) derives from the desired enharmonic associations: the # and $ stages of the prolonged VIIº7 function as an immediate root-position VIIº7/V in relation to the embedded implied keys. As a by-product, the chosen passing tones create an octatonic fragment. Systematic continuation of the sequence (Ex. 8.29b) would complete the octatonic scale by means of an additional voice exchange, and prolong the VIIº7/V in an entirely circular manner. In that case the VIIº7/V would resolve directly to V, and both the prolonged diminished seventh progression and the passing ¢−s (and enharmonic ¢−s) would create cycles that divide the octave into four equal parts.

521 See Everett 1990, 172; Cohen, Wagner and Zur 1985, 106; Wason 1985, 19; Aldwell and Schachter 1978/2003, 579–81, Ex. 31-25; P. Schubert 1993, 294–5. Gauldin 1978 refers to the surface enharmonics, but in a different manner than I do. For a modulatory approach, see Piston/Devoto 1941/1978, 442, Ex. 28-30. For another reading, see Blume 1989. All former studies adhere to Schubert’s enharmonic spelling, even though it does not fit the larger context. Most writers cite the relation to the text, which speaks of ‘a road of no return.’ Wason points the affinity to Vogler’s version of the extended omnibus (which, however, prolongs V7).

Prolongation of Diminished Seventh Chords 235

8.3.6 ‘Octave Progressions’: Register Transfers within VIIº7 Since in VIIº7 all chord tones are dissonant with some other chord tone, register transfer of any of them creates an active PD, even when the registrally shifted tone is not the seventh (or when there is ambiguity as to whether this tone is the seventh). Simple motion of a complete octave (Ex. 8.30a–d) includes the augmented second, which complements the diminished seventh. This interval is virtually always avoided as a direct linear step by either of two techniques (which may also apply within shorter spans than the complete octave): (a). Filling the augmented second. Inserting a single passing tone—it does not matter which of the two—makes this interval sound like a minor third, thus violating the underlying key. If the passing tone divides the augmented second in an analogous manner to the motion within the adjacent third, an octatonic fragment emerges, similar to those found in Exx. 8.7g (Chopin) and 8.29 (Schubert). For example, in Ex. 8.31a (Mendelssohn, String Quartet Op. 13/I, beginning of development), the prolonged chord serves as an enharmonic pivot VIIº2/IV in A minor=VIIº7 of B minor; the enharmonic reinterpretation is expressed in the spelling. By contrast, complete chromatic filling creates a neutral chromatic scale, which does not necessarily contradict the nature of the augmented second. Fully chromatic octave lines can lend themselves to systematic horizontalization of an underlying VIIº7 (Ex. 8.31b–c), in either precise parallel motion in all voices or contrary motion with necessary adjustments to avoid clashes. However, since such chromatic lines sound very undirectional, they are better suited to segmentations that contradict the underlying chord. Ex. 8.31d, from Mozart’s Piano Concerto K. 491/I, demonstrates a case in similar motion where the prolongation even tonicizes a remote area;522 Contrary motion with incongruent segmentation is shown in Ex. 8.31e from C. P. E. Bach’s Rondo W56,5 (after Aldwell and Schachter 1978/2003, 588–

522 Wen (1990a, 122) recognizes the boundary VIIº7, but puts it in parentheses and states that the connection is only associative, precisely because PD is impossible; in fact full prolongation is achieved. The complete register transfer is located in the bass, while the soprano fills the diminished seventh, also contradicting the underlying chord. The choice of Fƒ (Gß) for surface tonicization may result from the main theme.

236 Prolongation of Diminished Seventh Chords

9, Ex. 31-31b). This prolongation follows a systematic division of the octave into four, not in accordance with the VIIº7 but rather according to a chromatic voice exchange that progresses in major thirds between V7-structures (a retrograde form of the ‘devil’s mill;’ cf. Ex. 7.89a). The boundaries of this systematic motion are passing chords within the VIIº7 prolongation, and the equal division is truncated before the completion of the octave within V7. Prominent fermatas do not correspond either to the VIIº7 or the equal division, and form an articulation-hemiola.523 (b). Insertion of incomplete neighbors into the augmented second 67– (Ex. 8.32a– c). The possible insertions are either 8 (normally harmonized as I) or 5 (normally I or V), i.e., 65– 7– or 786–– or their retrogrades. These insertions create a temporary sense of resolution. Ex. 8.32d shows a texturally complicated case from the end of Bach’s Sinfonia in E minor. The primary VIIº7 is retained until the last moment and expresses the structural 2 (if one seeks for a normative background). The prolongation embraces a statement of the main theme, whose internal hierarchy is modified from its tonic interpretation in its earlier appearances (mm. 1 and 25), since here it has no stable point of departure. Notice also the textural break after the initial VIIº7 at m. 37.524

523 Aldwell and Schachter emphasize ‘the great length of time it takes for an intensely dissonant sonority to resolve.’ Yellin (1998, 16, Ex. 12) relates this prolongation to the omnibus progression. For historical context, see Kramer 1985. 524 Jackson (1999b) presented readings after Schenker, his student Oppel and Laufer along with two alternatives of his own. None of these interpretations show a prolonged seventh chord, although Laufer’s and Jackson’s readings include horizontal diminished fifth or diminished seventh in the bass. It seems to be a stylistic feature of Bach to increase tension toward the end of polyphonic works in minor, by using PD at a point of textural break. Aesthetic equivalents may be found in the following arpeggiations of diminished seventh chords: WTC I, Prelude in Cƒ minor, mm. 25, 30–31 (my Ex. 3.13), 35–36 to V7 at m. 37. In this last passage, VII7/V harmonizes 1, and avoids resolution of V (Jonas [1934] 1982, Ex. 112); WTC I, Prelude in Eß minor, mm. 32–35 (cf. also 17–18); within V7: WTC I, Fugue in C minor, 25–26 (MW II, 33 understands this passage as being under 6, which resolves under the course of the prolongation, but this does not remove the need to resolve 4) and Fugue in A minor (see Ex. 7.96a); Sinfonia in B minor 28–31 (Forte and Gilbert 1982, Ex. 205). Cf. also Sinfonia in G minor. 57–64 (perhaps a V9 prolongation) and WTC I, Fugue in D minor, 36–42. Handel makes a similar effect in Concerto Grosso Op. 6,8/I, 48–49. For a register transfer that circumvents the direct augmented second, see also Brahms, String Quintet Op. 88/II, 13–16 (Korsyn 1996, 63).

Prolongation of Diminished Seventh Chords 237

8.3.6.1 Ascending register transfer within VIIº7

So far in my examples of register transfer within VIIº7, I have focused on the more common descending form. As with the V7, ascending register transfers within the VIIº7 raise the problem of proceeding upward from the initial tone of the seventh. Ex. 8.33a analyzes mm. 5–10 from the introduction to Beethoven’s Piano Sonata Op. 111/I. This is a famous case that Schenker (1916/1971, 8) has shown as a prolongation of a diminished seventh chord. If the passage indeed prolongs a diminished seventh chord (VIIº7/IV that never resolves as such), the main underlying voice-leading procedure seems to be an ascending register transfer of the root in the bass. As Schenker himself has pointed out, the segmentation of this prolongation is highly incongruent with the horizontalization of the prolonged chord. The passage includes inner groups of five chords and involves tonicizations of harmonies that are remote from the prolonged diminished seventh chord; the prolonged chord is avoided throughout the prolongation (notice that both e and g are replaced in the upper voice). In fact, I find the factors that compete with the prolongation of the diminished seventh chord strong to the extent that they challenge the interpretation of the passage as a circular prolongation of this chord. In particular, the final boundary is rather weak. The chromatic ascent in the bass continues until it reaches an augmented sixth chord, which often functions as a goal for large-scale motion (cf. §10.1). Perhaps the passage should be better understood as transitive motion toward the Italian augmented sixth chord at the end of m. 10.525 A very interesting case that I do regard as an ascending register transfer fully embraced by VIIº7 occurs in Fugue BWV 948, attributed to Bach (Ex. 8.33b). This is a toccata-like passage with an improvised character; located toward the end of the work it has a formal function analogous to that of a concerto cadenza. Its content, however, seems to derive not only from spontaneous inspiration, but from theoretical experimentation as well. The prolonged VIIº7 embraces minor

525 For Schenker’s discussion of this passage, see also §3.2.3 and fn. 510. Rosen (1970/1972, 442– 3; see also §3.1) and Drabkin (1976, 98 [reduction] and 101 [text]) essentially share Schenker’s view. As Rosen has shown, reading a prolonged VIIº7/IV creates motivic parallelism with the unprolonged VIIº7/V (m. 1) and VIIº7 (m. 3).

238 Prolongation of Diminished Seventh Chords chords over the complete (!) ascending circle of fifths, tonicized by their applied VIIº7s. The articulation of the VIIº7 at both boundaries is very clear, but the voice- leading procedure is less so. The linear motion connects every other diminished seventh chord. Both possible threads create ascending register transfers, one in the bass, the other in the soprano, but each interpretation needs to assume substitutions and creates problems in the other outer voice. It is difficult to understand all the voices simultaneously. The most consistent explanation would interpret the local tritones as a series of unfolded diminished seventh chords, but this reading overlooks the nested consonances to which the inserted VIIº7s are applied. This passage exceeds the limits of common practice in its independence of any diatonic key, but with respect to the voice leading, I would consider it a true prolongation. In other cases, the VIIº7 only governs portions of ascending register transfers. For example, in the coda of Beethoven’s Symphony No. 2/I, the transition from I to II moves gradually, introducing several vertical chords. Most of the motion, however, is carried out under VIIº7/II (Ex. 8.33c), and is based on the same voice leading procedure we have encountered in Der Wegweiser (Ex. 8.29) and even encompasses an entire octave (cf. Ex. 8.29b). (In the present graph I did change enharmonic notation, but also in this example some passing ¢−s are only enharmonically ¢− sonorities.) This diminished seventh chord is passing but nevertheless prolonged. Two tones (a and fƒ) are common to all the passing chords, and in this sense the prolongation is circular. The sense of diminished seventh chord is reinforced (although not determined) by a horizontal diminished seventh arpeggiation in the soprano, used by Schenker to show a ‘four-note arpeggiation’ (FC, §230; Fig. 100,2b).526

526 See also Beethoven, Piano Sonata Op. 13/I, 5–9: most of the ascent takes place within VIIº7, but it culminates on V7 (to which VIIº7 is subordinate). I agree essentially with Katz (1945, 148, Ex. 51), but she regards the passage as a prolongation of the III–V progression through V7 horizontalization, and overlooks the VIIº7. Cook (1987, 25) recognizes that mm. 6–7 ‘are enclosed within a sustained block of [i.e., prolong] a diminished seventh harmony.’ Even during the VIIº7 prolongation, the horizontal dimension emphasizes tones of V7 (hence Katz’s assertion on V7 horizontalization). We have encountered the opposite situation in Ex. 7.91 (Beethoven, Fantasy Op. 77), where a horizontal diminished seventh arpeggiation prolongs V7.

Prolongation of Diminished Seventh Chords 239

8.3.6.2 Non-linear register-transfer and equal division of the octave within a VIIº7

Partial filling of register transfers can be realized through arpeggiation or equal division of the octave. Within diminished seventh chords, both procedures merge into one in the case of equal division into four (Ex. 8.34a); this exceptional feature does not apply for equal division into three (Ex. 8.34b), as happens in the diminution in Ex. 8.34c, from Chopin’s Etude Op. 10,3, in combination with a whole-tone progression in the bass. A more sophisticated procedure is used by Liszt in the introduction to his Piano Sonata (Ex. 8.34d). The octave is divided into two tritones; foreign tones pass in-between, but only as two shorter progressions stemming from inner voices. The latter progression even includes a passing tone of a second order. The ensuing theme (m. 14) states the tonic of the work for the first time, and in a weak articulation as a £−. One might wish to read the PD further (perhaps until m. 31), but the clear statement of the rhythmic theme at m. 14 militates against this opinion and in favor of a large auxiliary cadence.

8.3.7 Counterpointing Linear Progressions of Different Sizes within VIIº7 The VIIº7 is particularly suited to prolongation by a combination of linear progressions, since some linear progressions whose diatonic sizes differ in one step (augmented seconds and minor thirds, augmented fourths and diminished fifths, major sixths and diminished sevenths) share the same absolute size in semitones. This eliminates problems of adjusting the number of events. The perception of some linear progressions can be modified by the imposition of additional simultaneous progressions (this principle may apply to consonances as well), as in Bach’s chorale prelude Puer natur in Bethlehem, mm. 12–13 (Ex. 8.35): diminished fifth progressions that express VIIº7 in the accompanying voices clearly divide into two thirds, but the combination with the third progression in the chorale melody indicates a different, unequal segmentation.527

527 See also Mozart, Symphony No. 38/I, 92–94, within VIIº7/VI. The interpretation of the simultaneous linear progression is ambiguous, and depends on the spelling. The dissonance already begins at m. 88 on V7.

240 Prolongation of Diminished Seventh Chords

8.4 Neighbors to VIIº7

The following discussion generally adheres to the distinction I employed in my classification of neighbors to V7, i.e., between neighbor motion under (or above) a stationary seventh and neighbors to the tone of the seventh itself. However, the application of this classification is problematic in those cases where it is not clear which inversion of VIIº7 is being prolonged, due to the enharmonic equivalence of all inversions of diminished seventh chords, For example, in Beethoven’s Piano Sonata Op. 28/I, 83–86 (Ex. 8.36a), the diminished seventh chord which has chromatic lower neighbors in parallel thirds is notated as a VIIº$, with neighbors to the tone of the seventh; in light of the ensuing chords (within the V region: V$–I) it might be heard as a local VIIº# (i.e., employing f) with a stationary tone of the seventh (Ex. 8.36,a1); nevertheless, since the prolonged chord arrives from IIIƒ, its true function is as notated (Ex. 8.36,a2; see Laufer 1999, 5). The ensuing V$ (mm. 87–90) receives analogous neighbors. In Ex. 8.36b (Chopin), the VIIº7/V does not resolve directly into V (with the seventh dß descending to c), but first proceeds in ascents (as cƒ–d). Thus it is ambiguous whether the chromatic neighbor in the tenor refers to the tone of the seventh, and whether the voice exchange takes place between the root and third of Eº7, or between the third and fifth of Cƒº7.

8.4.1 Neighbors under a Stationary Diminished Seventh As within V7, most normative neighbors under a stationary seventh are upper neighbors, and they produce neighbor chords whose roots lie a third, fifth or seventh below that of the prolonged seventh chord (Ex. 8.37a–e): II2 (or IV¢−) through an upper neighbor to the root; IV$ (or VI6) through neighbors to the root and third; and VI# through neighbors to all consonant members of VIIº7.528 When the embracing VIIº7 is applied to V, the plagal ¢− neighbor becomes ‘I¢−,’ which enables an interplay with its more usual function of a cadential ¢− (for the same problem with passing ¢− within VIIº7, see Ex. 8.10b–d). This happens in Ex. 8.37f (Mendelssohn): the succession VIIº7/V–I¢−–V (within the area of VI) is stated

528 For an altered version of the neighbor chord to VIIº7, see below Beethoven, Allegretto WoO53 153–9 (Ex. 8.39b).

Prolongation of Diminished Seventh Chords 241 twice. The normative interpretation of a cadential suspension only makes sense in the case of the latter statement. In the former, the ¢− is a neighbor to VIIº7/V, and the V is a passing chord which is even closer to the surface than the ¢− itself. It appears with a seventh, which passes from a reached-over octave in the upper voice. Lower neighbors are unlikely under a stationary diminished seventh; in particular, the augmented second under the root is inappropriate for neighbor motion. Among the other possibilities, no lower neighbor motion can construct a tertian sonority, but several neighbor sonorities are enharmonically equivalent to tertian chords, and some even invoke an enharmonic interpretation of the diminished seventh chord itself (Ex. 8.38). Chopin, in his first Ballade, uses an ingenious device which combines the lower neighbor to the root and the stationary seventh with additional passing motion in the 5–7 space (Ex. 8.38f). The spacing of the chord makes the passing tone a thirteenth. The passing chord is very exceptional indeed, and is motivic in this work: it is enharmonically equivalent to V¶ª, a chord which is used in the ballade very saliently, even at the same pitch.

8.4.2 Neighbors to the Tone of the Diminished Seventh Lower neighbors to the seventh are a source of ambiguity, since they provide an illusory temporary resolution to the initial seventh (cf. §7.3.2.2). Even an unsupported neighbor (Ex. 8.39a) produces this effect: the emerging neighbor V6 or # might resolve the initial VIIº7. When it does not, there is a reversal of the normal hierarchy, i.e., V serves as a neighbor to VIIº7, whereas usually (inverted) VIIº7 decorates V or V7 (cf. §7.3.1.1). Juxtaposing the opposite hierarchies one after the other highlights the interplay between them. For example, at the end of Beethoven’s Allegretto WoO 53 (Ex. 8.39b), VIIº7 first decorates V (m. 143), then V decorates VIIº2 (which serves in turn, however, as a neighbor of V7 at a deeper level). This prolongation continues with other neighbors, with a stationary seventh: a three-voice neighbor with alteration that transforms the neighbor into a V7 structure; and larger motion, apparently fifth- and seventh-linear progressions, which represent a more

242 Prolongation of Diminished Seventh Chords concealed neighbor.529 Ex. 8.39c (Beethoven, Piano Sonata Op. 78/I, 20–24) presents an even more intricate hierarchy between alternate VIIº7 and V (or V7): VIIº$, itself prolonged by V2 neighbors, sounds at one moment (m. 24) as if it is subordinate to a more structural V2 that resolves into I6; in context, however, the V2–I6 progression is merely passing within a chromatic voice exchange between the prolonged VIIº7/V and IV ƒ6/5 of V.530 Additional motion in the harmonization of the VIIº7–6–7 neighbor may create an even stronger sense of resolution, as VIIº7–I (Ex. 8.40a), in combination with an upper neighbor to the root. Other harmonizations of the VIIº7–6–7 neighbor (Ex. 8.40b–e) sound daring. Some of them create enharmonic associations, possibly transforming the neighbor motion into mixture. Upper neighbors to the diminished seventh are also problematic (Ex. 8.41). A diatonic neighbor would have to be an augmented second; other neighbors, as either major or minor seconds, violate the tonal orientation. In order to produce a separate harmony on the neighbor, motion in additional voices is necessary.531 The most comprehensible form is a four-voice neighbor diminished seventh chord. A semitone above the diminished seventh can also function as mixture.

8.5 Enharmonic Parentheses within Diminished Seventh Chords

Diminished seventh chords are especially appropriate for prolongation by means of enharmonic re-interpretation. In each interpretation, another interval of nine semitones functions as a diminished seventh, while the other three function as major sixths.

529 Reading a normative Urlinie here requires us to assume that substitution has taken place. See my comments and alternative in §7.2.3.1 [concerning Ex. 7.24c]. See VIIº7–V6/5–VIIº7 also in Chopin, Waltz Op. 64,3, mm. 59–60 and 63–64; and inverted as VIIº2–V7–VIIº2 in Brahms, Schicksalslied, mm. 314–24. The harmonic boundaries are somewhat ambiguous, but the chorus highlights the VIIº2 as a frame chord. 530 Beethoven’s enharmonic spelling is inaccurate throughout the passage: the prolonged diminished 4/3 is notated as root position º7 and the augmented sixth chord as a V7 structure. The notated spelling suggests mixture instead of the perceived neighbor. The voice exchange connects a circular interval prolongation in a transitive chord progression (cf. §1.1.2.1). One might perhaps read a deeper voice exchange from the initial tonic to the augmented sixth chord at m. 26. I am not certain about the consequences of such a reading upon the passage which I have shown here. 531 For an upper non-harmonic neighbor VIIº7/5–8/6–7/5, see Beethoven, Violin Sonata Op. 96/I, m. 32.

Prolongation of Diminished Seventh Chords 243

In any EP, the prolonged chord has one function in context and another function in relation to the inner prolongation (§7.8); in the case of diminished seventh chords, three different relations are possible between the two functions since any inversion can be re-interpreted as any of the three other inversions, i.e., VIIº7=VIIº#/ƒVIm=VIIº$/ƒIVm(ßVm)=VIIº2/ßIIIm. Accordingly, the difference between the true resolution and the nested allusion to resolution are either of a minor third in either direction, or of a diminished fifth. The actual implied keys can vary much more, since the seventh chord may be applied to chords other than the tonic. Single semitone neighbors are sufficient to introduce simple EP within VIIº7. Lower semitone neighbors tend to sound as embellishing the tone of the seventh (7–6–7, as VIIº7–V#–VIIº7), since this is the only diatonic location for a semitone below a member tone of VIIº7. Whenever the tone that the neighbor decorates is not the seventh in the wider context, rudimentary EP occurs (Ex. 8.42a–c). For example, in the introduction of Brahms’s Symphony No. 1/I, m. 12 (Ex. 8.42d), the diminished seventh chord functions as VIIº# in the wider context, but the lower neighbor makes it sound locally as VIIº7 that goes to V# within ßIII.532 The same surface chord succession can mean only apparent EP when the occurrences of the diminished seventh chord are not structurally connected. For example, in Beethoven’s String Quartet Op. 59,3/II, 184–92 (Ex. 8.42e), enharmonically equivalent VIIº7/VI (repeated inverted as VIIº2/VI) and VIIº#/IV (VIIº7/IV) are separated by one strongly articulated chord (V7/VI, former time inverted) into which the initial diminished seventh chord is resolved.533 The complementary procedure is generated by upper semitone neighbors to tones of VIIº7 (Ex. 8.43a). Such neighbors tend to be heard as decorations of the

532 M. 11 too occupies EP (see below §10.3.2.1). FC, Fig. 121,3a, cites this passage as an illustration of enharmonic restatement, but does not put it in the conceptual framework of EP. The passage has motivic implications in the Allegro theme (mm. 15–19, 53–55). See also Brahms, Piano Trio Op. 8 (revised version)/IV, 304–5: VIIº7 of Fƒ as the V of B minor in the wider context serves at the surface as VIIº2 of A minor. This is a detail within an expansion of the cadential 6/4 (cf. Nivans 1992, 167). The notated spelling does not imply the EP, but rather shows the V7- structured neighbor as VII7 (product of mixture). 533 For cases where there is ambiguity as to whether the EP is genuine, see Brahms, Symphony No. 2/II, 55–56 and 60–61, and Beethoven, Piano Sonata Op. 53/II, 23–26 (unit starts at m. 21). The latter passage can be interpreted as motion toward V7, which separates the surrounding diminished seventh chords and avoids EP.

244 Prolongation of Diminished Seventh Chords root; 3–4–3 neighbors too would be diatonic in the key of the wider context, but they produce a non-tertian sonority with enharmonic potential.534 Upper neighbors of a whole tone (Ex. 8.43b) sound as relating to the fifth of the diminished seventh chord (the only diatonic location), and thus produce a similar enharmonic effect. This configuration is likely only in an incomplete texture, where it is possible to avoid a non-tertian clash on the neighbor. The enharmonic spelling of the incomplete VIIº7/5/1 is a diminished ¢−. Linear progressions can generate EP within diminished seventh chords in more elaborated forms (Ex. 8.44), provided that the diminished seventh chords outline true boundaries. In the last example (8.44d, after N. Wagner 1987, 64), from Mendelssohn’s Hebrides overture, the local tonic is the relative major of the main key, and the EP embraces its VI, which is the main tonic of the work. This tonic reference is emphasized by a motivic quotation which also causes a deviation from the smoothest possible voice leading. The four enharmonic interpretations can even be exploited in a single EP, as my hypothetical version for Der Wegweiser (Ex. 8.29b above) demonstrates. The multiplicity of enharmonic interpretations enables also open EP. In this procedure, the prolonged diminished seventh chord serves as a pivot between two enharmonic interpretations, while its inner prolongation invokes a yet different interpretation. For example, in the coda of Beethoven’s Violin Sonata Op. 30,1/III, a variations movement in major (Ex. 8.45a), the prolonged chord is approached as VIIº7/VI, left as VIIº2(/I), and in relation to its inner prolongation it serves in the yet more remote interpretation of VIIº#/ƒIV(ßV).535 In this case, the

534 Consult Ex. 8.3. See also Schumann, Romance Op. 28,3, mm. 44–48: an upper semitone neighbor is inserted between the passing VIIº2 and its goal V7. This makes the VIIº2 sound temporarily like a root-position VIIº7. No circular PD is involved. 535 This passage expands the preceding foreground prototype (mm. 186–203). Notice also the motivic parallelism between incomplete neighbors on two levels. The continuation in both the prototype and the expanded passage is complicated by de-alteration, i.e., motion an altered chord to its diatonic variant (violating the chromatic tendencies of the final diminished seventh chord). I use the term ‘de-alteration’ for what is known in Russian as dezalteratzia (Balter 1976, 292–3). I thank Boris Plotnikov for the reference. This term must not be confused with disalteration in the sense of simultaneous sharpened and flattened alteration of the same scale degree, as used by Kurth ([1913] 1973, 130–146). Enharmonic prolongation of a pivot chord through an additional function also occurs in miniature in Schubert, Symphony No. 8/I, m. 16. The pivot is VIIº7=VIIº7/III (inversions are difficult to determine because of a pedal point), and the inner passing motion lends it a flavor of

Prolongation of Diminished Seventh Chords 245 passage is anchored in a single key, since the initial VIIº7 is secondary. Open EP can, however, serve true modulatory purposes. For example, the passage in Ex. 8.45b (Mozart, Piano Concerto K. 595/I, beginning of the development, 179–83) is based on a sequential pattern, but stops after two statements in order to connect keys a tritone (!) apart. Admittedly, the sense of parentheses in such a modulatory context is weakened.536 EP in a weaker sense happens when a diminished seventh chord has different functions at two different levels, but this chord is stated only once. For example, in Beethoven’s Symphony No. 6/IV, 68–78 (Ex. 8.46), VIIº7/G retains conceptually at the deeper level until it is replaced by its true resolution (into G). The best way to understand the inner motion, which resolves the diminished seventh chord as if it were VIIº2/Bß is as analogous to a ‘back-relating dominant’ (cf. fn. 15); it might be called ‘back-relating resolution’ into a ‘back-relating tonic.’537

8.6 Prolongation of Diminished Seventh Chords in Special Contexts

Most prolonged diminished seventh chords serve in the ordinary function of diatonic VII7 in harmonic minor. Others form VII ß7 in major, as in Ex. 8.9f (Chopin) above, or serve as pivot chords in modulations, as in Ex. 8.31a (Mendelssohn). The passing tones within the prolonged chord determine whether

VIIº7/VI. The miniature relations III–VI adumbrate the key relations of the second theme in the exposition and recapitulation. Ironically, FC (Fig. 56, 2f) uses that very measure to show consonantization of the passing tone. The graph notes a p.t. (passing tone) on the second diminished seventh (which is dissonant, and also placed above a dissonant pedal point). The lower-level passing tone within the diminished seventh is transformed into a 6/4, which forms a consonant 6/3 with the pedal point. 536 Each statement is based on third- voice exchanges that are heard as exchanging the local fifth and seventh. They pass through 6/4s that imply the transitory keys (for the enharmonic potential of such 6/4s, see discussion of Ex. 8.29). Melodically, the sequence includes one additional statement before the arrival at the diminished seventh chord. 537 Schachter ([1995] 1999a, 178) discusses this passage as a ‘detour to Bß minor,’ but does not offer the interpretation suggested here (see also his graph, p. 162). In the movement discussed, dissonant progressions also govern mm. 95–118, including passing motion within a diminished seventh chord at mm. 106–10. For ‘Back-relating resolution’ within EP of an augmented sixth chord, see Exx. 10.17 and 10.18b and fn. 606.

246 Prolongation of Diminished Seventh Chords the function which obtains during the prolongation matches the preceding or the ensuing key,538 or a third function, as an open EP (see above Ex. 8.45). Diminished seventh chords hardly ever serve other functions. Even when they are enharmonically transformed, the new interpretation coincides with inversions of the same VIIº7. Non-enharmonic possibilities (analogous to dominant seventh chords as VII7, §7.9) are unlikely either: on any scale degree, diminished seventh chords are likely to eventually function as VIIº7 (resolving the interval of the diminished seventh into a perfect fifth) usually applied and/or inverted. Since any diminished seventh chord can appear as VIIº7 in any key (relating to I, IV or V), it is never necessary to interpret these chords as other scale degrees. For example, in minor, II ß7 would sound as VIIº7/III, and IV ß7/ƒ1 would sound as VIIº7/V. Exceptions occur in two situations: (a). Prolongation of a diminished seventh chord that proceeds to another dissonance. In the lack of resolution, diminished seventh chords lose their functional character, even if they are themselves prolonged. They may pass in a wider dissonant context, possibly prolonging in turn another dissonance, even another diminished seventh chord (cf. Ex. 8.7g above). At other times, non-functional diminished seventh chords pass within a transitive context or within a prolongation of consonance. For example, in Ex. 8.47 (Chopin), the diminished seventh chord which embraces the voice exchange is only a chromatic link within I–II motion by means of an illusory seventh progression in the bass. It lacks any resolution at a more immediate level, and defies any consistent spelling. Even here, the inner prolongation creates a flavor of a local VIIº7 (of V), but this function does not derive from the larger context.539 (b). Common-tone diminished seventh chords.540 Such chords are difficult to prolong: they normally serve as neighbors to their immediate surrounding chord (a consonant triad on the same root); once the ensuing chord does not

538 The situation can also be ambiguous. For example, in No. 6 of Schumann’s Davidsbündlertänze, mm. 12–15, the prolonged chord is VIIº4/3 of Eß major = VIIº2 of A minor, but neighbors in the bass and in the inner voice give contradictory clues. 539 For a different analysis, see Lewis 1996, 128–9. For a prolonged diminished seventh chord in a special context, see also Ex. 8.50 below. 540 Common-tone seventh chords are actually apparent seventh chords, since the tone that is spelled as their seventh is not the dissonant tone.

Prolongation of Diminished Seventh Chords 247

sound as true resolution, the function of the diminished seventh chord as a common-tone chord is questioned too. For example, in the theme of Brahms’s Piano Trio Op. 87/IV (Ex. 8.48a), it is possible to hear the diminished seventh chord as either a common-tone chord which resolves immediately and whose appearances are disconnected, or as a prolonged VIIº7/V that proceeds to V in spite of the tonic pedal point on the beginning of V. 541 Nevertheless, true prolongation of a common-tone diminished seventh chord is possible. In particular, prolonged common-tone chords to the tonic can be perceived as distinct from the synonymous VIIº7/V when no V follows them. A tentative case occurs in Die Wolfsschlucht scene from Weber’s Der Freischütz (Ex. 8.48b). The common-tone chord is the principal motive of the number, and is clearly prepared in an unprolonged form. The motivic significance of the common-tone chord is decisive, since both the identification of the diminished seventh chord as the boundary chord of the prolongation and its interpretation as a common-tone chord are complicated by inversions of both the diminished seventh chord and the surrounding tonic. The prolonged chord proceeds to a ¢− which I hear as consonant, principally because the return to the tonic is approached without any V.542

8.7 Large-scale Prolongations of Diminished Seventh Chords

Large-scale prolongations of diminished seventh chords seem to be very rare, perhaps because these chords hardly penetrate the deepest levels (in contrast to V7, see chapter 4 and §5.2, factor a). Although I have not found many examples of such prolongations, there is no essential reason to prevent them, and they even seem aesthetically appropriate for tense passages. A rare case where a complete section might be read as a prolongation of VIIº7 (of V) occurs in the secondary theme of Beethoven’s Piano Sonata Op. 2,2/I (Ex. 8.49); even there this reading is not straightforward. A straightforward reading

541 Schenker hints at the latter reading in CP I, 58 when he presents the harmonies of the passage as I–ƒIV–(I–ƒIV)–V. The ‘ƒIV’ means VII/V, which here appears as VIIº7/V. The notated meter supports a tonic reading, but the rhythmic emphasis justifies a rebarring of the first measures. 542 Yellin (1998, Ex. 29) cites approximately the same passage with other boundaries as a kind of transitive omnibus. See also earlier in the same scene (mm. 8–11) a third- voice exchange within a VII7–V7 progression (applied to V).

248 Prolongation of Diminished Seventh Chords would consider the initial boundary of the theme (and of the structural V) at m. 58 on minor V, after 16 measures of V/V. Although the Vß is approached by a strong cadence, it serves immediately as a point of departure for unstable sequential excursions. Stable V (in the expected major mode) only arrives on the less thematic material at m. 84 (first as a £− chord, more firmly at m. 88). An ordinary Schenkerian representation would resemble a huge quasi-auxiliary cadence (i.e., connect the Vß to the later stable V, but show the priority of the later event). This reading explains the bass ascending motion, and seems to reflect Beethoven’s compositional ideas.543 Yet, the salient sustain on VIIº7/V (mm. 76–83) makes the whole passage sound as nested within VIIº7/V (Ex. 8.49b). Factors that support this reading are the dynamic gesture which precisely corresponds with the boundaries of the PD, and the reappearance of the witty motto of the movement at the final boundary. The inner structure of the theme remains essentially the same. The prolonged chord recurs several times during the passage, but these additional occurrences remain passing (cf. Ex. 8.49c).544 A more problematic example occurs in the prelude to Act 3 of Wagner’s Parsifal. Morgan (1976, 62–72) reads there in great detail a complex prolongation of a diminished seventh chord that lacks a clear harmonic function (it leads from VIIº#/V to VIIº7/V in the notated key). The deepest passing chords are themselves diminished seventh chords; Morgan shows two alternative variants which differ in relation to their inner hierarchy (Ex. 8.50a). On a still deeper level both are based on a single passing diminished seventh chord (Ex. 8.50b); redistribution of the voices in the passing chord reveals a smooth voice leading, cf. Ex. 8.7f). While the final boundary of the prolonged diminished seventh chord (mm. 38–43) is stated clearly (cf. Ex. 8.13g), the initial boundary is problematic. The prelude begins with an ascending perfect fifth, a stable tonic according to the notated key. Rothstein (1989, 284), who follows Morgan and studies in greater detail the first 11 measures of the prelude, shows the initial tonic as a weak sixth chord, which forms an appoggiatura into the prolonged diminished seventh chord (cf. Ex.

543 Tovey (1956, 219) recognizes the ascending bass as the most prominent feature of this unstable section. Churgin (1992, 45) cites Tovey in her study of unstable secondary sections in sonata form. 544 Suurpää (2000, 197) presents an essentially similar reading to that proposed here, although he places the 2 earlier. He shows this exposition as kinda of continuous exposition (p. 195).

Prolongation of Diminished Seventh Chords 249

8.50c). However, the bass appears after the rest of the chord has been established; I find it difficult not to hear a stable tonic as the point of departure for the prelude (Ex. 8.50d). In my reading, the huge unstable progression nevertheless begins with a stable point of departure. The stable beginning weakens the diminished seventh chord, although it does not rule out the possibility that it is prolonged.545

545 Some shorter excerpts in the passage surely prolong diminished seventh chords on lower levels, e.g., the one-measure prolongation in m. 12, shown by Morgan (1976, 69, Ex. 8 [first excerpt]). Although this excerpt only lasts a single measure, its slow pace makes it sound as a complete prolongation (§2.3). The passage is complicated by incongruent segmentation of the diminution in the various voices. Another large-scale projection of a diminished seventh chord is shown by Parker and Brown (1985, 52) in the first act of Verdi’s Otello, but it connects tones that do not in fact structurally belong together. For a diminished seventh chord that is passing but nevertheless prolonged, see Ex. 8.33c.

9. PROLONGATION OF THE REMAINING SEVENTH CHORDS

9.0 General Considerations

The remaining seventh chords may be classified according to their harmonic function (based on their scale degree location) or according to their chord structure; these classifications do not always match (cf. §5.2). This chapter is organized according to the former criterion, proceeding from the relatively common II7 to those seventh chords that are more rarely prolonged. The latter criterion is used mostly as a secondary parameter within each scale degree. This method of organization de-emphasizes the importance of the seventh chord structure, which is a crucial factor by itself. The chord structure determines to a large extent which seventh chords are appropriate for prolongation, since chords with a major seventh are hardly ever prolonged (§5.2, factor (c)). Properties of the chord structures themselves may even determine some potential prolongations. For example, half-diminished seventh chords are the set-class inversion of dominant seventh chords (set class 036T, see Ex. 9.1a). This means that some prolongation procedures that apply to V7 may also prolong half-diminished seventh chords. This will probably work only where the prolongation is not highly functional, e.g., in prolongations based on equal division of the octave. For example, Ex. 9.1b prolongs a half-diminished seventh chord by precise inversion of the prolongation of V7 shown in Ex. 7.88a.546

546 Bass (2001, 48) shows three cyclical octatonic systems, each of which comprises four half- diminished seventh chords whose roots divide the octave into four. These cycles are realized in Ex.

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The harmonic factor, however, seems more important. It explains why certain seventh chords are prolonged far more easily than others in the same chord structure. For example, in major, both II7 and III7 are minor-minor seventh chords, but only the former is usually used. This difference derives from the insignificance of III in major in general. Also important is the fact that different chord structures may share the same scale degree in major and minor. For example, in Grieg’s National Song (Lyric Piece Op. 12,8) (Ex. 9.2), similar fifths- voice exchanges prolong II7 in both the principal major key and the tonal area of the minor degree III.547 For many of the theoretical possibilities of prolonging the remaining seventh chords I have found no genuine examples. I shall not attempt to fill the lacunas with original excerpts of my own, although I regard such a task as feasible. I shall, however, comment on selected possibilities for which I have not found realizations.

9.1 Prolongations of II7

In both modes, the seventh of II7 is minor, which makes it relatively appropriate for prolongation. Its harmonic function (as well as that of II!) is almost always subdominant, but this has important ramifications: When the II7 is pre-dominant (proceeding to V or VII) it forms a genuine seventh chord, but when it is plagal (embellishing the tonic) the seventh chord is apparent, i.e., the tone of the seventh is a common tone with the embracing chord, while the dissonant elements are the root (and perhaps the third too). Another reason for regarding the root of II7 as its real dissonance is based on the chord’s relations with IV: the upper members of II7 produce IV, and the included IV is the prototypical harmony of the subdominant function, to which II7 belongs (cf. Agmon 1995, 200–1). This case is different from the analogous situation with VII and V7: the upper members of V7 produce VII, and both usually have the same function (dominant), but in that case

9.1b. In fact, the same cycles also create octatonic systems with dominant seventh chords. The inversional symmetry between dominant and half-diminished seventh chords has already been used by Ziehn in his canonic studies (published1912), quoted in Yellin 1998, 12. See also discussion in Telesco 2001, 134. 547 See also Chopin, Etude Op. 25,5, mm. 1–9.

Prolongation of the Remaining Seventh Chords 253 it is the chord with the lower root (V, also V7) that is the prototypical harmony of the function. The IV–II7 relation points to the possibility of regarding II# as IV with an added sixth. This concept stems from Rameau and contradicts the normal identification of the root as the lowest tone of a stack of thirds. The present study refrains from delving into this problem.548 Ex. 9.3 presents the harmonies that prolong II7 (in both modes), according to the procedures that I have applied to other seventh chords (Exx. 7.1 and 8.2): III, I6, V¢−, VI¢− and VII6. When the II7 is inverted, as is often the case (especially as a #), the inversions of the prolonging chords change accordingly. The same chords would also result within a prolongation of V7/V; the chromatic difference between diatonic II7 and V7/V only affects the wider context. Appoggiaturas to II7 stand at the limits of legitimate subordination (Ex. 9.4. Cf. §§1.1.3; 6.3). Appoggiaturas to the root (‘IV2’, if the goal II is in root position) or to the root and third (‘VI$’) obey functional directionality and sound like true subordinations, but when the subordinate sonority produces I(£− or #), the suspension is likely to be sustained from a more structural harmony and the feeling of subordination is only evident in the sense of a rhythmic reduction. In the three-note appoggiatura ‘I#,’ 7 is an accented (shifted) passing tone and not a real appoggiatura.

9.1.1 Prolongation of Half-Diminished Seventh Chords as II7 in Minor

9.1.1.1 Linear progressions within half-diminished II7 in minor

* Third progressions within half-diminished (HD) II7 (Ex. 9.5a–c) usually occur in the middle third, especially by means of voice exchanges, as demonstrated in Beethoven’s Piano Sonata Op. 27,2/I, m. 58.549 This finding deserves

548 Rameau recognized the two possibilities of interpreting such 6/5 chords as double emploi. See Lester 1992, 132–5. For a prolonged II7 in Rameau, see Ex. 3.2b. 549 This measure is reduced into a vertical II6/5 in FC, Fig. 54,3. The manuscript reveals that this measure is a late interpolation that creates melodic fluency in the middle voice (Rothgeb 1990, 8– 11). On the resolution, see Wen 1999, 279. See also: Mozart, Piano Concerto K. 491/I, 112–4 (without voice exchange); Chopin, Scherzo No. 3, Op. 39, m. 536 on a stationary bass, within wide stretching of II 6/5 (526–40); Tchaikovsky, Symphony No. 5/II, 39–41, moving from 4/3 to 6/5 via a quartal sonority. The local function of the HD as II is distorted by the continuation; Mendelssohn, Song without Words Op. 30,4, mm. 115–6. The voice exchange starts on V6/5 of V (analogous to a former V 6/5 of IV that resolves into IV), but undergoes de-alteration (see fn. 535)

254 Prolongation of the Remaining Seventh Chords

explanation, since the filling of this third moves via a quartal sonority, and for this reason it is usually avoided within V7 and VIIº7. Two possible and complementary explanations are: (a). The other third progressions are less appealing. Filling the lower third via a ¢− (the only inversion that conforms normatively to the doubling of the fifth) creates the impression of an untypical HD VII/V in the relative key; in the upper third, which is major (and actually offers more space to be filled in), the expected passing tone in harmonic or melodic minor creates an augmented step, although division into two major steps is possible (see Ex. 9.5c); (b). II7 mostly appears as an inverted # or $ in order to lead more effectively to V. Motion between these inversions fills the middle third in the bass (and voice exchanges in general occur more often between outer voices). Occasionally, the quartal passing motion within the middle third of HD II7 is replaced by tertian harmonization (by means of motion in additional voices), thus creating a fuller sense of prolongation. Most convincing is a passing ‘I’¢−, as in the retransition of Mendelssohn’s Piano Trio Op. 49/I (Ex. 9.5,d1).550 This prolongation intensifies the expectation of the structural dominant. In the coda of the same movement, the voice exchange appears in its non-harmonized version with a unique neighbor embellishment of the quartal passing sonority (Ex. 9.5,d2).551 * Fifth progressions within HD II7 are prominent in Mahler’s Nun will die Sonn’ so hell aufgehn [Kindertotenlieder No. 1], mostly in the lower, diminished

into its real subdominant function as II. The Schumann example in Ex. 9.5c is unusual to my experience. This measure is identified as II7 in Piston 1941/1948, 230, Ex. 430. For parallel third progressions within II7, see Ex. 3.2b. 550 Aldwell and Schachter (1978/2003, 311, Ex. 19-10a) cite this passage as an illustration of a normative use of a passing 6/4. See also Beethoven, Piano Sonata Op. 28/II, m. 3 and its counterparts in the variations. In the coda, mm. 85–86, the climax of these voice exchanges appears in enlargement via a quartal sonority. (Mm. 87–88 repeat within V6/5 of V). 551 The seeds for this motion may be identified in the passing tone above II6/5 in the theme, m. 10. In Brahms’s Auf dem Kirchhofe, Op. 105,4, a 42– third within ‘II2’ (II over tonic pedal point) occurs without a voice exchange in the introduction (mm. 2–3) and in the first strophe (mm. 5–6). Schenker has indicated this as the mini-appoggiatura ‘I 11/9/6’ in a graph published in 1988 (see also FC, Fig. 63,3). The general tension of the excerpt seems even stronger: the 3 in m. 4, which Schenker’s graph indicates as the primary tone, is not harmonized as a tonic, and probably serves as a passing tone from V to II over a tonic pedal point. Among the commentaries attached to the publication of the graph, Braus (1988, 22) emphasizes the prominence of the ß6 during the C minor portion of the song; the ‘II2’ is part of that prominence.

Prolongation of the Remaining Seventh Chords 255

fifth span. Some of them involve voice exchanges. The prolongations are simple, but they vary with every strophe (Ex. 9.6a–d). The initial sonority is always an unharmonized sixth over the tonic tone (perhaps VI), which usually becomes II2, and then proceeds to other inversions. In the outer strophes, the prolonged II7 proceeds to V, while in the inner strophes it returns plagally to the tonic (thus functioning as an apparent seventh chord).552 * Seventh progressions (and seventh arpeggiations) within HD II7. The rules that distinguish genuine seventh progressions should be adjusted to the HD II7 as follows: in descent (Ex. 9.7a–d), genuine prolongation of the seventh only occurs when both boundary tones (8 and2 ) are stated literally at the boundaries of the linear progression. In the absence of 2 in the initial harmony, the primary tone 8 would serve within I (or VI or IV), and the motion would be either a transitive illusory seventh progression that reaches II7 only at its end, or a sixth progression within I;553 in the absence of 8 in the goal harmony, the goal is heard as V or VII (8 replaced by7 , either literal or implied), and the seventh progression is again illusory and transitive.554 In ascent (Ex. 9.7e–f), the linear progression may be genuine if 8 is sustained from a preceding I. Otherwise, the seventh-ascent is illusory, representing a registrally transferred passing tone. This situation is the same as with illusory seventh progressions within V7, except that in HD seventh chords, the triad that serves as a point of departure for the dissonant passing seventh, is itself dissonant (diminished).

552 In this song, recurring neighbor leading tones create a flavor of VIIº7, which is, however, negated by the true harmony. Salzer (1952/1962, Ex. 445) provides a tonic interpretation of the theme (strophe 1). His reading overlooks the accentuation of the dissonant tones on longer tones on the strong beats, and the distribution of the text. 553 Seventh-descents from I8 to II are reminiscent of the seventh-descents IV4–V7 or II4–V7 (or even to V5/3) [§6.3.3]. However, the hierarchy in this case is reversed: while the descents to V form subordinations to the hierarchically prior dissonance, in motion from I to II7 the prior event is the opening consonant tonic, and the II7 is deprived of any structural status. 554 See, however, the beginning of Ex. 9.11 (Wagner): the initial seventh 6 remains in effect during the opening descending and then ascending arpeggiations, even though 5 appears at the bottom of the arpeggiation in a lower register.

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9.1.1.2 Motion in the 7–8 space in half-diminished II7

Filling in the major second above the seventh of HD II7 produces (in voice exchange) a passing ßII (Ex. 9.8a). The tendency to interpret the passing chord as a vertical triad works against another potential hearing strategy, according to which the minor seventh before the ascent functions as an augmented sixth. Spelling according to this principle entails interpreting the HD II7 as a Tristan chord (the analogous situation within V7 gives rise to the more familiar German-type augmented-sixth chord, see Ex. 7.40a).555 This potential is revealed in my recomposition of Wagner’s original Tristan complex (Ex. 9.8b), where I have transformed the Tristan chord into a true HD II7 using an 8–7 voice exchange. A real instance from the literature appears in Schubert’s Piano Sonata D. 958/IV (Ex. 9.8c). The thin texture of this passage, where the third is missing from the HD seventh chord, brings about an empty fourth as the passing sonority.

9.1.1.3 Neighbors to the half-diminished II7

Neighbors to the HD II7 are rare. Where they involve the 7–8 space, diatonic neighbors would coincide as usual with motion between chord tones (cf. §7.9). Chromatic neighbors avoid this problem. Ex. 9.9a uses both neighbors in contrary motion. The neighbors meet at an octave (cf. §7.3.2.3 and Ex. 7.74c), or more genuinely at a diminished ninth (8–ƒ7–8, 7–ß8–7) (in order to arrive at an octave, the seventh should be interpreted as an augmented sixth, and this is difficult to hear in the present configuration). The emerging neighbor chord is thus only enharmonically equivalent to ßII. Dense neighbors to a HD II7 are demonstrated in Ex. 9.9b, from Chopin’s Mazurka Op. 17,2: Chopin prolongs a HD II7, which is itself a neighbor chord (an apparent seventh chord that embellishes IIIƒ plagally). It is heard locally as an altered plagal embellishment of V/VI, but even from this perspective the configuration is essentially the same. This chord receives its own neighbors, motion to which is filled chromatically. The overall contour outlines a third,

555 This procedure inverts that which occurs within V7. The inversion results from the relation of set-class inversion shown in Ex. 9.1.

Prolongation of the Remaining Seventh Chords 257 which does not, however, mean a third-span. As the gesture recurs, added mixture further blurs the identity of the secondary neighbor.556

9.1.1.4 Special contexts of the prolonged half-diminished II7

II7 can be half-diminished in major too, through mixture, as in Beethoven’s Symphony No. 7/III, 41–44 (Ex. 9.10). Initially, the passage sounds like a recurring appoggiatura II4/3/ß1–V7 that continues the pattern established by the previous eight measures. However, a sudden and extreme intensification of dynamics and orchestration (and long held tones) modifies this pattern so that the inner grouping changes and the altered II$ is heard as being prolonged by V7 neighbors. This procedure reverses the usual hierarchy between these chords.557 In a highly chromatic context, the very function of the HD as II7 is attenuated. A case in point occurs in the Norns’ scene from Wagner’s Götterdämmerung (Ex. 9.11). This passage appears toward the end of the scene, when the third norn sings about Alberich. It is based on the ring/destiny motive (cf. Donington 1963/1974, 280–1, motives 8–12).558 The prolonged HD seventh chord is both approached and left through remote modulations; in the foreground it is heard as II7 of Eß minor (Wagner’s accidentals indicate Eß major), since the prolonging harmonies are heard as VIIº2 and V$ in that key. Inversions guarantee that these harmonies are structurally inferior. The chord structures match diatonically the expected chords in their specific relations. This procedure implies a key, although neither its tonic nor its true dominant ever arrive. At the end of the scene, the same material recurs in a modified form, with V7—longer and in root position—as the true resolution of II7. The voice leading is even further complicated by parallel second relations between the voice part and the orchestral upper voice (mm. 271– 3) and by reaching-over characteristic of the ring/destiny motive.559

556 For neighbors to HD II6/5, see Gluck, Orfeo ed Euridice, Act 1/I, 7–8. 557 For the normative II4/3–V7 relations, see §§6.3.1 and 7.3.1. For an analogous reverse in hierarchy where V7 prolongs VIIº6/5, see Ex. 8.39a–b. For passing motion within HD II7 in major see also Brahms, Violin Sonata No. 2/III, m. 47. 558 According to McCrelees (1989, 280), the scene constitutes three rounds of the norns’ speeches: narratives of Wotan, Loge and Alberich, each divided into three for each norn. McCrelees provides a graph of the complete scene (pp. 292–5) until shortly after our excerpt. He identifies the II7 prolongation but his foreground interpretation is problematic. 559 For a prolongation of HD II7 in a special context, see also Katz 1945, 364–5, Ex. 118, reading of Schoenberg, Verklärte Nacht, 19–26 .

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9.1.2 Minor-Minor as II7 in Major Schenker recognizes this chord as a true harmony twice, once in a # and once in a 6/4/2 inversion. He addresses the non-harmonic character of further dissonances that appear within II7, rather than the harmonic character of the II7 itself, but nevertheless his recognition of the harmonic II7 is inconsistent with his strict prohibition on harmonic seventh chords.560

9.1.2.1 Linear progressions within minor-minor II7

Third progressions within minor-minor II7 usually move in the outer third-spans. The goal of the motion in the upper span is II!; by contrast, the lower span moves to IV, as in Ex. 9.12a (Beethoven), where II# moves to ‘IV6’ and back. When the seventh is not stated in the boundary, motion from IV to II7 and back prolongs IV, not II7 (Ex. 9.12b). This case of space-filling motion resembles the problem encountered by V5–(6)–7–(6)–5 (§6.2.2), and indeed, the same intervals emerge here too, but the sense of a seventh chord as piled up thirds is negated, as the root of II7 is achieved through a piled down third from its upper triad, and the constant tone is the seventh rather than the root. Ambiguous cases would arise when the seventh is stated at only one boundary (see above §9.1 and Ex. 3.2b from Rameau),561 or when II7 and IV alternate (Ex. 9.12c).562 Third- voice exchanges within minor-minor II7 are generally similar to those in HD II7 in minor, except for one notable difference: the upper third- voice exchange moves via a diminished triad (VII6) (Ex. 9.13a, cf. Ex. 9.5c in minor). Unlike the analogous situation in HD II7, the problem of the augmented second below the leading tone is avoided here, but another problem emerges, that of undesired doubling. I also present voice exchanges of the middle third (Ex. 9.13b,

560 In CP I, Ex. 260, an ultra-focused description of real-time perception of a detail from Schubert’s song Der Kreuzzug, D. 932, mm. 3–4, shows II6/5 as the resolution of 7–6 motion, with anticipation of the resolution. This suspension is an inversion of a IV2–II7 true subordination; The commentary on FC, Fig. 122,3 (C. P. E. Bach, Arioso con variazioni, variation 7) claims that ‘there is no doubt [kein Zweifel] [!] that the chord in the second measure is to be understood as [II]6/4/2.’ This measure includes a 5–4 suspension, which of course contradicts strict counterpoint. The text explains a foreign tone e2 as being part of an independent chord e2–g2–d3, without mentioning that it is also dissonant (VII7). 561 Inversion of the same constellation (II6/5–IV6) takes place in Chopin, Scherzo No. 4, Op. 54, mm. 65–73. The continuation, mm. 81–96, prolongs V7/V. 562 This kind of ambiguity is described as ‘crossing branches,’ forbidden by Lerdahl and Jackendoff (1983), but see N. Wagner 1995.

Prolongation of the Remaining Seventh Chords 259 from Mozart; a harmonized version appeared in Ex. 9.12a [Beethoven]) and the lower third (Ex. 9.13c–e). In the latter, a simple passing ¢− tends to sound like an apparent tonic, which gives the prolonged II7 the impression of being a IV7 (in the key of VI); in the counterpart situation in minor, the prolonged HD might be heard as VII7. These associations can be avoided by means of additional motion to the passing harmony, which introduces ‘VI6’ (Ex. 9.13d, after Aldwell and Schachter 1978/2003, 181, Ex. 12-13b–c).563 In a real example from Brahms’s Violin Sonata No. 2/III, 3–4 (Ex. 9.13e, after Forte and Gilbert 1982, 76, Ex. 73), the voice exchange is slightly concealed by an appoggiatura that modifies the contour of the violin part.564

Larger linear progressions in minor-minor II7 are rare; a voice exchange of the lower fifth was shown in Ex. 9.2 (Grieg).

9.1.2.2 Neighbors to minor-minor II7

The only neighbors to minor-minor II7 I have found are simple, and move under a stationary seventh. These neighbors may be either chromatic or diatonic. For example, Ex. 9.14 compares two excerpts from Mozart piano sonatas. In both, neighbors embellish an apparent ‘II#’ that connects I6 with a consonant I¢−. In K. 332/III, m. 4, the neighbor is diatonic and harmonic, while in K. 284/I, m. 30 (quoted in Harmony Ex. 223 [289]) the chromatic lower neighbor to the root clashes with the diatonic seventh.565

563 Ibid., Ex. 12-12a, from Chopin, Etude Op. 10,11, m. 15, shows gradual transformation of II into II7. 564 An alternative reading might regard the I6 as the beginning of an auxiliary cadence. See also Schubert, Piano Sonata D. 959/IV, m. 7; and voice exchanges between different types of seventh chords that involve de-alterations (cf. fn. 535) into II7: de-alteration from a German augmented- sixth in Mendelssohn, Song without Words Op. 85,4, m. 31; and de-alteration from V7/V in Joplin, Bethena, mm. 69–76 in a far-reaching modification of the omnibus progression (Yellin 1998, Ex. 83). 565 See also: Scarlatti, Sonata K. 502, mm. 60–63 and again 64–67 (upper neighbor to the root); Bartók, For Children No. 32, mm. 3–5. Plagal II2 receives neighbor embellishment here lasting a full beat, with both the root and the seventh stationary (see Salzer 1952/1962, Ex. 186). This feature might be unique to twentieth-century tonality.

260 Prolongation of the Remaining Seventh Chords

9.1.2.3 Bass divider within minor-minor II7

Since the fifth of minor-minor seventh chords is perfect, such chords are amenable to prolongation by means of a true bass divider. Within II7, a straightforward realization of this creates the progression II7–VI–II7, and sounds like a modal I–V–I progression under a seventh pedal point. Such an arpeggiation appears in Skryabin’s Prelude Op. 11,9 (Ex. 9.15a), first tentatively in the main idea, then in the climax of the work, as a culmination of a larger prolongation of II7. The prolonged II7 may create root fifth-relations with the subordinate harmony (VI), even when inversions prevent the fifth-divider in the bass. This happens in the most famous prolongation of II# in the literature: the opening of Schumann’s String Quartet Op. 41,3/I (Ex. 9.15b). The II# is retained throughout the slow introduction, and resolves only after the beginning of the allegro. This is an auxiliary cadence, which is based on the opening idea of Beethoven’s Piano Sonata Op. 31,3/I. The passage is based on two voice exchanges between the outer voices, that return to the initial # sonority, but the exact procedure of retaining the seventh is not very clear. The final seventh might even be heard as approached from the consonant II at m. 5; The initial seventh is perhaps transferred to the bass (aƒ at m. 4), but it is unclear how this fits the larger voice exchanges. Nevertheless, the salience of both boundary #s seems decisive in favor of genuine prolongation of the seventh in this case.566

9.1.2.4 Large-scale prolongation of minor-minor II7

In the last movement of the same quartet (Schumann’s Op. 41,3), the main theme is based on a II#–V–I auxiliary cadence, no doubt related to the first movement. Toward the end of the movement, the theme is developed for the first time, and includes a remarkable prolongation of II# (Ex. 9.16). The main linear voice leading takes place in the bass: it begins to ascend, ‘reaches under’ a third (m. 242; cf. Ex. 7.79e), then ascends further into a lengthy ‘I’¢−, which sounds first like

566 Schenker analyzes this passage in FC, Fig. 110,e4 in an essentially correct manner, but overlooks the dissonance altogether (he designates the prolonged harmony simply as II). The motivic structure of the passage signifies the structural tonal points (II6/5–VI6–II8–6/5), but the meaning of the motivic leaps does not always match these points.

Prolongation of the Remaining Seventh Chords 261 a normative cadential suspension, but in retrospect moves back to II#. The ensuing progression to V includes nested EP (mm. 263–7) within an augmented sixth chord, cf. §10.3.2.1), and one harmony with an association to the prolonged II#.

9.2 Prolongation of Half-Diminished Seventh Chords in Other Functions

9.2.1 Half-Diminished VII7 in Major Diatonic (HD) VII7 in major is fairly rare. In particular, VII7/V appears almost invariably diminished, rather than in diatonic HD form. Ex. 9.17a presents a rare case of a local voice exchange between the root and third of a HD VII7/V; as in the similar situation within a diminished VII7/V (Ex. 8.10b–d), the passing chord is ‘I’¢−. In minor, VII7/III is more commonly diatonic. A prolongation of a diatonic VII7/III occurs in Schumann’s Piano Quintet/I, 51–56 (Ex. 9.17b). This material prepares the second theme; it consists of a motive that is stated three times: twice within VII7/III, and the third time resolving into V#/III. The inner diminution is based on motion from an inner voice that emphasizes a chromatic tone. Since the other voices provide an independent harmony only to this chromatic element, and since it lies just below the seventh (6), it might also be perceived as a neighbor.567 This neighbor is enharmonically a HD chord (homonymic with altered II2). In fact, the bass of V remains, so that the prolonged chord can be regarded as a V9. The bass even provides the missing root, although never as a vertical V9. The context is thus a gradual transformation V°–¶·–¶°/III. A primary HD VII7 is prolonged in a passage from Richard Strauss’s Der Rosenkavalier (Ex. 9.17c) by means of equal division of the octave into three. It is based on the transposition operation (cf. §7.6.1), i.e., the harmonies which divide the octave are themselves half-diminished and in the same setting. The passing harmonies are remote; the entire passage was described as based on ‘semi-random chord progressions’ (Shir-cliff, Jay and Rauscher 1965, 158).

567 For a less unequivocal instance, see Tchaikovsky, Symphony No. 5/I, 140–9. It is tempting to hear the linear bass as a sixth progression within VII7 (of D major), which continues to V 6/5 when completing the octave. However, the initial VII7 might better be heard as VI7 of melodic minor in a mini-auxiliary cadence (140–1), whose immediate goal is consonant.

262 Prolongation of the Remaining Seventh Chords

9.2.2 Half-Diminished Seventh Chords as Altered IV7 HD seventh chords can appear on additional scale degrees as the product of mixture. On IV, they can appear as IV7/ß5 in minor or the more remote IV ß7/ß5/ß3 in major. Both variants share the pre-dominant tendency of the diatonic HD seventh chords. Both are prolonged in the development of Schubert’s Piano Sonata D. 279/I (Ex. 9.18): within a sequence of descending minor thirds, each chain contains an auxiliary cadence from a HD IV (which embraces a voice exchange) through V or VII, but in a slightly different way each time. Most auxiliary cadences are applied to minor chords, but one of them is applied to a major chord, which requires more substantial alteration. The first statement includes an additional dissonance. The organization of the passage as a whole seems to be based on an equal division of the octave, but the final boundary of the division is not structural. This peculiar harmonic device is generated from the descending third- successions, since each HD chord is first heard as II# of the preceding tonicized degree, and only in retrospect is it understood to have a rather more rare function. The progression IV7/ß5–V (or IV7/ß5–VII) brings about a problematic situation (already encountered in the progression ßVIß–V, see fn. 300 and Ex. 7.69d), where the tertian construction of IV7/ß5 assumes ß1 as the fifth, while its resolution into V assumes the same tone as (ƒ)7. This may lead us to hear the HD sonority as a non-tertian enharmonic equivalent, but I believe that the IV–V functional progression still holds true.

9.3 Prolongation of Minor-Minor Seventh Chords in Other Functions

9.3.1 Minor-Minor Seventh Chords as IV7 in Minor IV7 is in principle a true seventh chord when it moves to the dominant, but only an apparent seventh chord when it functions as a plagal embellishment of the tonic. This chord is prolonged far less than one might expect. A rare case is found in Wolf’s Mörike song Auf ein altes Bild (Ex. 9.19a), where the main motive is based on the lower third- voice exchange within IV7. A straightforward voice exchange would pass via I¢−, but here additional motion introduces a natural V6 as the passing sonority. The modal flavor—which contributes to the archaic character of the song—also governs the tonic, which should be minor according to

Prolongation of the Remaining Seventh Chords 263 the key signatures, but invariably appears with a picardy third. The IV7 might count as the product of mixture (IV ß7/ß3) in relation to the major tonic, but Wolf notates the IV7 as the diatonic element. One graph in FC (Fig. 149,5) hints at the more intriguing idea of a true seventh progression within IV7. In Beethoven’s String Quartet Op. 59,2/IV, 5–7 (Ex. 9.19b), Schenker identifies the seventh progression as unfolding, i.e., as representation of a vertical entity. Verticalization assumes the progression VI– IV#–V–I in E minor (Real-time listening might lead one to perceive the progression as I–III in C major). In fact, the descent begins on consonant VI, and only becomes dissonant by the end of the seventh progression (analogous to Ex. 9.7b). True unfolding assumes that the root is conceptually present from the initial point of the descent, but such a rhythmic normalization is dubious here. Rather, the root passes from the lower g1 and the seventh progression is illusory, standing for an ascending second (VI5–6) based on an 8–7 lower counterpoint (cf. Ex. 5.2b), a situation that is sharply opposed to the ordinary rules of seventh progressions.

9.3.2 Minor-minor Seventh Chord as VI7 in Major VI7 is hardly ever prolonged, even in the most basic forms. On a single occasion, Schenker indicates a reduction into VI7, in his analysis of the Fƒ major prelude from WTC I, m. 2 (‘Die Kunst zu hören,’ TW 3, pp. 22–3 [2004, 118–9]. See Ex. 9.20,a1). This strange interpretation uses the model of ornamented suspension, which is not a common technique of prolonging the seventh (cf. §2.1.2.2.1). Clearly, Schenker himself is aware of the counter-intuitive nature of his suggestion: in the attached text, which is detailed and vehemently polemical, he vividly describes the confusion of a composer to whom he has shown this interpretation, and refutes two alternative interpretations proposed by that composer, reading either a IV6–V7 progression in mm. 2–3 (I regard it as subordination into V7), or a retention of I throughout m. 2 (Ex. 9.20,a2–3). I cannot help but agree with the unidentified composer’s confusion and alternative interpretations. I am aware of a single passage, composed as late as 1899, which is probably based on a true prolongation of VI7, in Skryabin’s Mazurka Op. 25,6 (Ex. 9.20b). The fore-phrase embraces plagal ‘arpeggiation’ via a II7, which supports a complete octave motion in the upper voice; the after-phrase repeats the VI7–II7

264 Prolongation of the Remaining Seventh Chords motion, but this time continues to form a normative cadence.568 The VI7 is obscured by further surface non-tertian dissonances, which are typical for Skryabin, even in the same early opus (especially in no. 4). The prolongation contains overlapping voice exchanges of II7 and VI7; this enables an alternative reading as a less unusual II7 through minimal motion (quasi-stretching). The recurring 6 in the bass reinforces the reading as a VI7 prolongation, but does not rule out the alternative (an intermediate interpretation would highlight the inverted form II$).

9.4 Prolongation of Seventh Chords with a Major Seventh

9.4.1 Non-tonic Seventh Chords with a Major Seventh Theoretically, prolongations of seventh chords with a major seventh should be possible. In fact, they hardly ever occur, probably due to the special difficulties caused by major sevenths (lack of space in the 7–8 step and special harshness. cf. §5.2, factor c). Major seventh progressions are rare even as melodic constructs. When they appear, they are usually not even illusory progressions that stand for 8–7 on the same bass, but merely transitive connections between distinct harmonies, especially from the root of I (8) to the third of V7 ( 569). The least dissonant type of seventh chord with a major seventh is the major- major chord, which appears twice in the diatonic system: I7 or IV7 in major, III7 or VI7 in minor. IV7 is given a high structural status in Schenker’s deep middleground schemes (FC, Figs. 15,2c; 16,2c(1); 16,3c; 16,5(1); refer back to Ex. 4.9), which are presented in major. However, these schemes do not actually indicate particularly fertile possibilities within the tonal system; indeed IV7 is infrequent even in surface harmonic progressions. This perhaps derives not only from the chord structure, since as we have seen, even the minor form of IV7 is rarely prolonged.

568 Here, I avoid the terms antecedent and consequent, since this is not a true parallel period. See Rothstein 1989, 18. 569 For transitive major-seventh ascents from I8 to 7V , see: major-major form: Haydn, Symphony No. 84/I, 20–26 (Rothstein 1989, Ex. 5.19); minor-major form: Mendelssohn, Song without Words Op. 30,6, mm. 21–29 (TW10; FC Fig. 106,3c and 112,2; Cf. above, fn. 262). See also remarks on V4–I3 in Beethoven, Symphony No. 4/I, mm. 212–7 (Ex. 5.15c).

Prolongation of the Remaining Seventh Chords 265

In fact, I am not aware of any genuine full prolongation of IV7 in major. Due to their rarity, even simple embellishments of this chord are noticeable, as for example, the neighbor and the motion from the ninth in Ex. 9.21a from Chopin’s Scherzo No. 2. This IV7 appears twice, first plagally (as an apparent seventh chord) and then leading to V.570 Mini-prolongation of III7 in minor appears in Schenker’s reading of Bach’s prelude BWV 942 [12 Short Preludes No. 12], mm. 6–7 (MW I, 62–65, my Ex. 9.21b). Schenker reads m. 6 as C7–(8)–7 (i.e., III7–(8)–7 in A minor). This interpretation is problematic; the very existence of a vertical III7 chord is dubious. However, this is not an incidental mistake on the part of Schenker: Schenker defends his reading in great detail. As with the VI7 prolongation in Bach’s Fƒ major prelude (Ex. 9.20), Schenker argues in favor of certain dubious prolongations of seventh chords (rudimentary as they are) in the same vehement tone that he adopts elsewhere to attack the very possibility of their existence. I have not found even the most fleeting prolongation of a major-major VI7 in minor, although improvisation immediately reveals that simple voice exchanges and neighbors can be easily applied to this chord (as well as to IV7 in major).

9.4.2 Prolongations of I7 Normally, tonic function creates repose and resolves the tentative dissonance of harmonic motion. How can the tonic itself absorb dissonance? Throughout my work I have assumed that the true kernel behind the idea that dissonances cannot be prolonged is their inability to be tonicized. Louis and Thuille ([1907/1920?, 8) even define consonant chords as those chords that might serve as tonics.571 Nevertheless, exceptions to this rule exist. A rudimentary precedent from the common-practice repertoire appears in Schumann’s Humoresque Op. 20, ‘noch rascher’ section, 130–1 (Ex. 9.22a). In the basic progression of V7–I (in the key of V), I appears first with a seventh, which later vanishes. A surface V2–I# progression recurs twice, and on the latter occasion the V2 becomes a complete neighbor chord to I#. The clear source of the added dissonance is the imitation of

570 Jackson (1990, 122, Ex. 5) presents a major-major ßIV8–7 with priority of the seventh as an optional reading in Bruckner’s motet Vexilla Regis, mm. 29–30. 571 ‘Consonierend (im harmonische Sinne) heißt ein accordliches Gebilde eben dann, wenn es fähig ist, als Tonica zu fungieren.’

266 Prolongation of the Remaining Seventh Chords the normative neighbor to V# in the preceding passage. Even though the continuation of the imitation omits the seventh on I (although it has appeared on V), and although the tonic phrase is also repeated without the dissonance, this little neighbor to I# is important because it is so exceptional.572 In twentieth-century music, Salzer (1952/1962, Ex. 415) shows a prolonged I7 throughout the opening section of Ravel’s Jeux d’eau. Ex. 9.22b is a further reduction of Salzer’s reading with some modifications. Added dissonances to the tonic are common, I would suggest, in impressionistic works and even more so in jazz repertoire. Further research is needed to explore whether the compositional procedures in these repertoires really prolong I7 by the techniques shown here with regard to the other seventh chords.573 The major seventh makes the prolongation of major-major chords problematic, but even in this case the intervallic characteristics can be overridden. Schubert’s song Aufenthalt [Schwanengesang No. 5] provides a tiny but instructive example (m. 52; look ahead to Ex. 10.24b). An inverted major-major seventh chord is further weakened: it appears in inverted form (as a #); its root is chromatic to the key; it actually functions as an apparent seventh chord. Nevertheless, it is subject to an appoggiatura that forms a consonant root position triad! That this is possible at all demonstrates the extent to which the dissonance can be overridden.574 I have not found any traces of prolongations of either minor-major chords (I7 in harmonic minor) or the augmented seventh chord (III of harmonic minor). There is a low probability of finding them prolonged in pre-twentieth century tonal music. Only unequivocal situations that are without potential for contradictory readings could force the listener to hear a prolongation of such chords.

572 Also Schenker’s example from Bach of an embellished III7 (Ex. 9.21b) is tonicized by an applied V7. 573 It is my impression that a I7–V–I7 divider under a stationary 7 is a frequently used device, where the V is consonant, but the I is not. See also Schoffman 1982, 49, concerning ‘seconds as tonics’ in Bartók. 574 The same appoggiatura has already occurred at m. 48.

10. PROLONGATION OF AUGMENTED-SIXTH SEVENTH CHORDS

Altered seventh chords can absorb diminished thirds or the more common, complementary interval of the augmented sixth. Prolongation of augmented sixths raises the general problem of PD, but does not derive directly from the presence of the seventh. In principle, augmented sixth chords need not include a seventh (e.g., the Italian £−), and the theoretical source of dissonance in augmented sixth chords is neither passing motion nor accumulation of more than two thirds but rather a change in the quality of the thirds themselves (cf. fn. 104). Nevertheless, in practice, augmented sixth chords usually include a seventh. A discussion of the prolongation of these chords belongs to the present study. Augmented and diminished intervals in general distort the correlation between the sizes of diatonic and absolute intervals: one interval (e.g., an augmented second) can be larger than another interval (e.g., a diminished third) in terms of absolute size, and at the same time, smaller than it in terms of diatonic size. A consistent application of Schenker’s rejection of dissonances as true intervals (e.g., in MW II, 9. cf. §3.2.6) would also deny that diminished thirds form a genuine space that is appropriate for composing out. Schenker never addresses this issue directly, but at least one remark in his writings indirectly involves recognition of diminished third progressions: the commentary for FC, Fig. 83,1 (Ex. 10.1) refers to what (in Chopin’s Etude Op. 10,12, m. 28) is ‘only seemingly a third-progression,’ but is actually a notational enharmonic convenience for a chromatically-filled major second. Since the apparent third-

268 Prolongation of Augmented-Sixth Seventh Chords progression is diminished, it turns out that had the notation shown the genuine tonal relations, the diminished third progression would have been genuine too.575 However, the common scenario of a melodic diminished third, ß27– in descent into an inner voice before resolving into 1 does not present a vertical diminished third, since the ß2 changes into a diatonic (and consonant)2 in an inner voice below the 7. Schenker does not take intoccount a the possibility that the ß2 will not be rectified (Consult again Ex. 4.22), a situation that at the deepest level would also destroy the diatonic character of the Urlinie.576

10.1 Problems in the Ordinary View of Augmented Sixth Chords

Augmented sixth chords usually, but not necessarily, lead to the dominant. This is the case with the common ‘geographic,’ or better, ‘ethnic,’ chords: IV ƒ6/3/(ß1) (Italian), IV ƒ6/5/3/(ß1) (German = Gr) or II ƒ6/4/3/(ß1) (French).577 I will only use the ethnic titles of these chords in these particular functions; when they serve another function (without enharmony), I will refer to them as chord-types, e.g., VII# (in minor) with lowered bass belongs to the Gr type.578 Occasionally,

575 The whole-tone space (set class 02) allows an additional interpretation as a doubly-augmented prime. For example, in Beethoven’s Leonore Overture No. 3, mm. 12–19, ß2 in the bass (m. 9) seems to become ƒ2 (m. 18) by means of voice exchange (the passage is graphed in FC, Fig. 62,2). 576 The discussion of the ß2 in FC takes place in the section on the background (§§104–5 and Fig. 31) and therefore does not address the characteristic diminished-third descent into an inner voice. The remarks should be applicable, however, to all levels. For example, the aß–g–fƒ third progression proposed by Laufer (1981, 167, commentary on FC, Fig. 100,3f) for Schubert, Impromptu D. 899 (Op. 90),3, mm. 159–66 [= in urtext editions aßß–gß–f, mm. 80–83], does not represent a vertical diminished third. Of course, a genuine diminished third must be perceived as a third in the first place, rather than as a combination of upper and lower neighbors. A relevant, ambiguous case is the opening theme of Brahms’s Piano Trio Op. 8/IV (both versions). According to both Nivans (1992, 158) and P. Smith (1997, fn. 5), the diminished third reflects two neighbors to the tonic. A tempting and daring alternative interpretation would hear diminished third progressions. Brahms plays with this ambiguity, e.g., when m. 6 defies tonic interpretation. An unambiguous realization of the diminished-third progression appears at mm. 108–10 of the revised version. 577 Before a cadential 6/4 in major, the Gr can be heard as an alteration of II 4/3 (e.g., aß–c–dƒ–fƒ rather than aß–c–eß–fƒ in C major). This view does not suit the Schenkerian idea that the cadential 6/4 is a local insertion that is not the true resolution of the preceding Gr (see discussion in Proctor 1978, 119). Nevertheless, the 4/3 spelling has found its way into the textbook by Aldwell and Schachter (1978/2003, 575, Ex. 31-20b). 578 Augmented sixth chords of the German type that do not lead to the dominant include II ƒ6/5 in major keys (e.g., aß–c–eß–fƒ resolving to Eß major), or, in harmonic minor, VII6/5/3/ß1 (e.g., aß–c– eß–fƒ resolving to G minor) or VII4/3/ß1 (e.g., aß–c–dƒ–fƒ resolving to E6 minor). Harrison (1995)

Prolongation of Augmented-Sixth Seventh Chords 269 augmented sixth chords appear in other inversions, possibly as diminished third root-position chords. The problems involved are essentially similar; the following discussion applies to other such inversions too. The textbook explanation of the augmented sixth (at least in its normal pre- dominant function) presents it as a surface chromatic passing tone from a more structural diatonic sixth (Ex. 10.2a from Aldwell and Schachter 1978/2003, 514). However, Schenkerian analyses often afford augmented sixth chords a structural status that is deeper than that of their preceding diatonic variants. This structural power derives from their location as final boundary chords immediately before the arrival of a structural V. In particular, the augmented sixth often serves as a goal of a voice exchange with chromatization, e.g., I into Gr/V (Ex. 10.2b, after Kamien and Wagner 1997, 3), and can preserve this sense even if a diatonic sixth precedes it (Ex. 10.2c). Even though those augmented sixths are not fully prolonged, their very participation in the deeper pattern does not square with Schenker’s restrictions on dissonance behavior. They form a chromatic kind of apparent passing tones (cf. §2.1.2.2.3.3). The model of a chromaticized voice exchange into an augmented sixth chord is rare in Schenker’s own analyses; perhaps this reflects reservations concerning the structural status of the augmented sixth.579

10.2 Structural Priority of the German Augmented Sixth chord

10.2.1 Priority of the German chord (Gr) over a preceding (ß)VI When the Gr augmented sixth is approached from ßVI (in major, or diatonic VI in minor), the augmented sixth does not function as a simple chromatic passing tone as when it passes from a diatonic sixth. Since all the tones of (ß)VI are included within the Gr, it is possible to regard this progression as an arpeggiation. (Motion

studies augmented sixth chords other than the ethnic ones, both in the same chord structures with other harmonic functions and in other chord structures. This area of theory is much more developed in German writings from Schenker’s generation, e.g., Louis and Thuille (1907/1920?), 220–39. It was apparently preserved in the Russian school. As an undergraduate, I studied it with Dr. Bela Berginer-Tavger, who was educated in the U.S.S.R. 579 I have come across a single instance in FC of a voice exchange into an augmented sixth (Fig. 115,2), but even there a contradictory slur is found (cf. Laufer 1981, 170; N. Wagner 1995, 154). Concerning the theoretical status of voice exchanges into augmented sixth chords, see §1.1.2.1.

270 Prolongation of Augmented-Sixth Seventh Chords to the diatonic IV6 or # is in principle similar, but there the sixth is heard as a passing tone, see Ex. 10.3).580 The hierarchy in the (ß)VI–Gr progression is not always the same. The Gr may be interpolated so as to eliminate parallel fifths within a (ß)VI–V progression, possibly including SFM (cf. §§2.3.2; 6.2.2) or gradual transformation (cf. §6.2.1).581 What interests us are those cases where the Gr is hierarchically deeper than the (ß)VI. This derives from the participation of the tone of the augmented sixth in a deeper pattern than the other members of the chord, which are also present in the (ß)VI. Sometimes, the (ß)VI serves as anticipation to the Gr. This happens in modulations where the (ß)VI, which is subordinate to the Gr in relation to V, is the (ß)III of the main key. This situation is common where the Gr/V is the

580 The augmented sixth appears as a passing augmented step in FC, Fig. 154,2 (Beethoven, Piano Sonata Op. 2,3/I), m. 42, where it is approached from an apparent tonic rather than from ßVI. Laufer (1981, 181, Ex. 35) criticizes this reading and highlights the augmented sixth. In principle, the structural status of the Gr might be caused by a deeper pattern that also embraces the preceding chord. See FC, Fig. 154,6 (Beethoven, Piano Sonata Op. 14,2/I, 105–6 [ßVI from m. 99]). In the alternative reading by Laufer (1981, 180, Ex. 34), the Gr is a non-structural boundary tone, as the goal of SFM (see below). The following discussion might illuminate the well-known feature of ßVI as a host for tonal adventures or ‘purple patches’ in Tovey’s terminology (see Rothstein 1989, 91). 581 The Gr is usually heard as an insertion when it is approached from above as a diminished third below the root of VI. Cf. Beethoven, String Quartet Op. 18,1/III, m. 24 (Krebs 1980, Fig. I.51). A case where the diminished-third space is filled in through a SFM appears in Beethoven, Piano Sonata Op. 10,3/I: bß (m. 133)–a (163)–gƒ (165) (other readings: Salzer 1952/1962, Ex. 458; Krebs 1980, Fig. I.40). The diminished third can also be inverted into a melodic augmented sixth, or another third in the chord can be inverted into a consonant sixth. Harrison (1995, 189) presents an example from the opening of Brahms’s part-song Im Herbst, Op. 104,5, where bass arpeggiation arrives at a 4/3 inversion of the Gr. (The second strophe [m. 20] even modifies the tonal function, since it leads to the relative major). Harrison describes this passage as a ‘horizontalized German- sixth chord’ using ‘unfolding of a melodic diminished third’ in the upper voice, and makes the more general observation that ‘the very notion of such a horizontalization destabilizes the idea of the augmented sixth chord being a mere passing verticality.’ When the Gr is weakened, it might serve as insertion into the (ß)VI–V progression, even when the augmented sixth is approached as an augmented second above the fifth of (ß)VI. See, for instance, Beethoven’s Piano Sonata Op. 7/II: the Gr chord at m. 36 is a lower-level insertion between the tonicized of ßVI (m. 25) and the following V (m. 37). The augmented sixth is approached via SFM—the melodic ascent Eß–F–Fƒ. In this passage, what weakens the augmented sixth is its placement in an inner voice. FC, §317 cites the tonal plan of the exposition as ßVI–IV–V. The IV stands for the Gr, and thus Schenker reveals his sensitivity to the power of the Gr. (Another reading: Krebs 1980, Ex. I.41). A more daring interpretation might deny the resolution at m. 37 and regard it as passing within a further diminished third. For gradual transformation from (ß)VI to a non-structural Gr, see Chopin, Impromptu No. 2, Op. 36, mm. 39–72. The tone of the augmented sixth bƒ first appears as c in a consonant triad (m. 67). Cf. Aldwell and Schachter 1978/2003, 605, Ex. 32-11; the bass in Burkhart 1983, 105, Ex. 8.

Prolongation of Augmented-Sixth Seventh Chords 271 goal of a chromatic voice exchange from the opening tonic. Ex. 10.4a–b presents two Mozart examples (after Kamien and Wagner 1997, 8 and 10): they show the augmented sixth approached from below (in an inner voice) and from above (arriving from an incomplete neighbor).582 The anticipation to the Gr is illusory if the unfolding of the augmented second starts on another harmony, which also contains tones that do not belong to the Gr, namely (apparent) Iß instead of (ß)VI (i.e., Vß instead of ßIII in a similar modulatory context) as in Ex. 10.4c.583 According to the rules of arpeggiation (and unfolding) (Rothstein 1981, 89– 90; 1990, 92), if the (ß)VI is not an anticipation, the Gr is conceptually present as far back as the initiation point of the preceding (ß)VI, and thus should be shifted in the reduction back to this point. Schenker applies this method in TW 3, in his reading of Haydn’s Piano Sonata Hob. XVI:52/I, m. 50 (reproduced with annotations in Ex. 10.5a). He places the Gr (ƒIV ß7/5/ß3) at the beginning of the measure, although a consonant ßVI occupies the whole of this measure except the last eighth note. The reason lies in the linear continuity, which forms an embellished repeat of the surface motive that opens the development section (mm. 44–45). This motivic relationship is emphasized in Schenker’s text. In a thin texture, the literal harmonization of the augmented sixth that follows the (ß)VI can be a £− Italian chord. The unfolding of the augmented second indicates that when the Italian chord is approached from ßVI, the tones of the augmented second conceptually combine to produce the effect of a Gr (Ex. 10.5b).

582 My graphs essentially preserve the readings by Kamien and Wagner, but notate the anticipation to Gr in a more precise manner. See also Mozart, String Quintet K. 515/IV, 118–34 (repeated 375– 90). The augmented sixth continues a linear ascent that preceded in the ßVI. In this case, the ßVI is not tonicized, but nevertheless lasts much longer than the structurally superordinate Gr. 583 Such a problematic usage of the unfolding symbol (rejected in Ex. 10.4c) appears in Laufer (1981, 181, Ex. 35), reading of Beethoven, Piano Sonata Op. 2,3/I exposition. This case differs from my scheme in that the inserted Vß is not prepared by its dominant and the passing 2 is supported by Vß from the beginning. This challenges the sense of anticipation to the passing 2. For an analysis by Schenker that shows the structural significance of the Gr in the progression I–Gr–V, see FC, Fig. 30b (Schubert, Waltz D. 365 (Op. 9),2, mm. 9–13). The graph shows the middle section as a bass arpeggiation that seems to anticipate the Gr (indicated as IV ß7), including one diminished third. In the music itself, however, the augmented sixth appears in an inner voice, and is perhaps better understood between ßVI and V. This graph raises a further problem: it is intended to illustrate middleground mixture in the upper voice, but the return to 3 is a low-level cadential 6/4 (even if Gr is taken as being more structural); see discussion in fn. 577. The structure of the second part of the Waltz is thus as follows: Iß–ßVI–(Gr)–V(6/4–)5/3.

272 Prolongation of Augmented-Sixth Seventh Chords

A daring application of the priority of the augmented sixth might suggest its participation in the deep middleground. Consider Haydn’s Symphony No. 104/III (Ex. 10.5c). This movement comprises a minuet in I, trio in ßVI, transition leading to Gr–V, and the minuet repeated in I. Can the Gr in the transition be more structural than the ßVI that governs the entire trio as a local tonic? This idea might seem implausible, but it reflects the conflict between the particular tonal plan and the dictations of the fixed background. This conflict is also present here without Gr priority, since the short untonicized V is more structural than the ßVI that serves as the tonic of the trio. The transition provides the essential connection between the voice leading of the trio and that of the main section. Each section has its own 5 as a primary tone, but it is the transition that unifies them into a whole. More difficult to accept is that rhythmic normalization should already place the Gr in the reduction at the beginning of the trio. Such a procedure would obscure the tonicization of ßVI throughout the trio.584

10.2.2 Motion from the Tone of the Augmented Sixth The relationship of augmented sixth chords to V7 influences the perception of this chord even when it does not display any genuine enharmonic transformation. The true seventh (fifth above the bass) sounds as if it is indeed a consonance, and motion toward the Gr, which starts on another harmonization of the tone of the augmented sixth, sounds similar to the so-called preparation of the seventh (which is, however, not a true preparation. See §4.3.1), although theoretically the augmented sixth above the bass serves as a root. Augmented sixth chords can win structural priority over preceding chords in retrospect, but the function of the tone of the augmented sixth as ƒ4 (in the usual location) is not revealed in real-time listening from the beginning. My conception

584 W. Berry (1980, 28) claims that in this movement ‘second-order status is established for the submediant major . . . rather than the dominant or subdominant.’ He thus overlooks the transition that unifies the movement as a whole. My observations on this movement also apply to the minuet in Haydn, String Quartet Op. 77,1/III. Another Haydn minuet with trio on ßVI is found in String Quartet Op. 74,2/III, but there the situation is different. The three minuets are cited by Krebs (1980, 54) as large-scale ßVI followed by V, without reference to the Gr. For a smaller instance, see Schubert, Piano Sonata D. 845 (Op. 42)/I, coda, 262–8. Other melodic positions enable a ßVI–I connection even without transition: 5ß/()VI = (ß)3/I (mixture in major ordiatonic in minor) or 3VI/ß =8/I. In such situations, even thepresence of V in the transition might be heard as an insertion. For the problem of a short structural transition after a lengthy tonicized area, cf. §6.3 and fn. 294.

Prolongation of Augmented-Sixth Seventh Chords 273 of this situation derives from Schenker’s treatment of Beethoven’s Piano Sonata Op. 10,2/III, 33–62 (see my synthesis in Ex. 10.6a). FC, Fig. 100,4a clearly presents the Gr as the deepest harmony that results from an arpeggiation; The text admits ‘arpeggiation which develop[s] into [a] four-note harmon[y].’585 The arpeggiation itself is presented as the enharmonically equivalent dominant seventh structure, and in FC, Fig. 62,11, the same passage illustrates a ‘descending arpeggiation . . . 7–5–3–1’ (see commentary before Fig. 62,5).586 As Rothstein (1981, 131–2) has pointed out, the location of the deeper Gr in Schenker’s reduction is not shifted back. Rothstein describes this state as ‘Rhythmically, . . . analogous to an auxiliary cadence. . . in that the previous harmony remains in effect at the level shown (Fig. 100,4a) until the actual appearance of the passing augmented sixth chord.’ This means that the foreground consonant harmonies that support the intermediate tones in the arpeggiation anticipate the Gr. In this particular movement, I doubt whether the four-tone arpeggiation really indicates the true boundaries (see my alternative), since the Gr is weakened by three factors: (a). The drive into V only leads to a relatively weak secondary V (of VI), which resolves after six measures; (b). The goal of the Gr (V/VI) continues in an equal pacing a descent in fourths that starts earlier (m. 51). Schenker indicates a succession of three fourths that express a tenth, which stands for the middle third in the seventh arpeggiation (in retrospect, motion from the true seventh of the Gr), but in fact there is a succession of four fourths; (c). The tone of the augmented sixth is not literally sustained throughout all the foreground harmonies of the arpeggiation, since the D minor chord at m. 59 implies a rather than aß. My alternative admits the enharmonic transformation of the single tone ß3ƒ4/ , but not of the whole chord. The retrospective re-interpretation of an arpeggiated seventh as an augmented-sixth Gr can be startling, especially where the embraced space of an augmented second is linearly filled as if it were a third. In the opening of the development in Mozart’s String Quartet K. 421/I (Ex. 10.6b), the enharmonic

585 Oster’s translation of Vierklang as ‘four-tone harmony’ in this case, rather than ‘seventh-chord’ might well have to do with the enharmonic transformation of the arpeggiated chord. 586 This description might create the impression that the enharmonic transformation into an augmented sixth is a local matter of no structural significance, since the arpeggiation is not presented as ƒ6–5–3–1.

274 Prolongation of Augmented-Sixth Seventh Chords transformation is all the more surprising, since the junctures of the linear progression (filled arpeggiation) are lowered by mixture: 7–ß5–ß3–1. The lowered tones enharmonically foreshadow tones of the resolution of the Gr, rather than tones of the Gr itself. The status of the seventh progression is similar to that of a diatonic descent IV–V7: it is an illusory seventh progression that expresses a second, but also expands the content of a subordination into its dissonant goal. The second, however, turns out to be a diminished third realized as its complementary augmented sixth.587

10.3 Full Circular Prolongations of German-Type Chords

10.3.1 Prolongations of German-Type Chords without Enharmonic Association Although augmented sixth pre-dominant chords often gain structural importance, their full circular prolongations usually remain restricted to basic contrapuntal devices. They often exploit only a single embedded chord in the next level, and tend to avoid significant elaboration on further levels. This is especially true when they function as augmented sixth chords in relation to their inner content and not only in relation to the wider context.

10.3.1.1 Third progressions within the Gr-type augmented sixth chord

Gr-type chords contain three thirds: one diminished (between the root and the third), one major (between the third and the fifth) and one minor (between the fifth and the seventh). The span between the seventh and octave is an augmented second, which is enharmonically equivalent to a minor third, and under certain circumstances can be filled too. (a). The diminished third progression in the lowest third span displays the alteration most characteristically. This span does not appear in the usual Gr # inversion. Without further motion, the passing harmony is a ¢− (‘I’¢− within the

587 This passage has been subject to attack by Mozart’s contemporary Sarti (cf. Mitchell 1969, with graphs of the whole development). Mitchell emphasizes the unifying elements of the passage as a normative procedure, as do other Schenkerian commentaries on this passage (Federhofer 1956, 78, in response to a 1924 article by Gerber; Aldwell and Schachter 1978/2003, 602, Ex. 32-8). Allanbrook (1996, 152) correctly observes that Sarti’s complaints are no longer taken seriously by the present generation. For the diatonic model behind this progression, see Ex. 6.2a

Prolongation of Augmented-Sixth Seventh Chords 275

ordinary pre-dominant Gr). Filling this third-span in a single voice only produces a full circular prolongation if both boundary tones are literally present at both boundaries, as in Ex. 10.7a (Beethoven).588 More characteristic are diminished third voice exchanges (Ex. 10.7b). The passing ¢− might be replaced by V, with the aid of additional neighbor motion, as in Ex. 10.7c (Tchaikovsky). This passing V creates ambiguity, as it might be taken as the true resolution of the Gr. Wolf’s Mörike-song Seufzer (Ex. 10.7d) provides an extraordinary example of this kind of third progressions,589 remarkable not only for its thematic significance, but also for the extreme dissonant quality caused by surface displacements, which help to create the effect of a sigh (Seufzer). Included are prolonging sonorities with a major seventh (a major-major seventh chord) and with a minor ninth. The former even becomes a vertical motive when it recurs at the vocal entrance (m. 9). The prolonged augmented sixth chord only resolves to V after a large non-directional transition in parallel sixths.590 The genuine spelling of the augmented sixth is problematic. The notated function as VII7/ß3 is possible and indicates a de-alteration of the lowered third (f) into the diatonic fifth of V (fƒ); spelling according to normal alterations into V would create the non-tertian sonority c–dƒ–eƒ–a; on a more immediate level, the progression into V (in the first strophe) is based on a descending motion that assumes eß (moving to dß–c–b at mm. 8–10) as if the augmented sixth is on the bottom line V7. Where such ambiguities prevail, the inner prolongation as an augmented sixth chord is decisive. (b). The major third progression in the middle third span of Gr-type chords would introduce, if filled diatonically, a passing harmony that is enharmonically equivalent to a minor £− (the same as within VIIº7) (Ex. 10.8a). The only real

588 This problem does not derive from the alteration. It is basically the same with a diatonic VI– IV7, which is not usually reduced into IV7. This rule also applies to IV–II7 relations, but not to VII–V7 relations (cf. §9.1). 589 This passage has already attracted analytical attention from Kurth 1920/1922, 198, translated with a further analysis by Williamson 1996, 217–8 and 229. Williamson also analyzes most of the song (pp. 231–3). Our readings diverge considerably. 590 In the repeat (mm. 13 ff.), the path to V is different but the general plan is similar. The identity of the augmented sixth chord becomes questionable since it lacks a clear resolution, and the same motion can occur within V7 (voice exchange 7–8). Kurth claims that there is an enharmonic transformation, relying on Wolf’s notation.

276 Prolongation of Augmented-Sixth Seventh Chords

filling of this span I have found, however, is different (Ex. 10.8b, a quasi- cadenza from a Chopin nocturne). It takes place in a single voice over a stationary bass of a root position diminished-third chord. (c). In the minor third progression in the upper third-span of Gr-type chords, the stationary tones state the interval of the augmented sixth. The passing sonority might be the French augmented sixth. In a voice exchange (as in Ex. 10.9a, from Beethoven’s song Vom Tode) it is literally ‘II ƒ6/4,’ which can be regarded as a French chord without a seventh (analogous to the Italian in relation to the German). The choice of the passing tone, a semitone below the upper boundary, derives from the underlying diatonic key. This tone differs from that which would pass within the enharmonically equivalent middle third of V7.591 (d). Parallel third progressions within augmented sixth chords are possible in a variety of combinations between the major, minor and diminished thirds. Ex. 10.10a–d shows all pairs of third progressions. The most unique combination simultaneously states a diminished third and a filling in as a third of the augmented second. Ex. 10.10e shows a realization of this procedure from Bruckner’s Symphony No. 1/III, 36–40. The Gr (of V) is followed by a ¢− chord which is emphasized by the entrance of the trombones. It is initially heard as a cadential suspension to the resolution of the Gr, but in retrospect it is proved to be a passing chord. The passing harmonies have V–I root relations, but the inversions guarantee priority to the Gr.592

10.3.1.2 Larger linear progressions within the Gr-type augmented sixth chord

Fifth progressions, both perfect and diminished, can in principle occur within Gr- type chords in several forms of segmentation (Ex. 10.11a–c show the three types of segmentation proposed in §7.2.3.1). Ex. 10.11d presents the only case I am aware of, from Tchaikovsky’s piece A Winter Morning [Album for the Young 2].

591 Third progressions in the upper third of a Gr also occur in the following passages: in a single voice–Beethoven, Bagatelle Op. 33,4, mm. 24–25 and Bruckner, Symphony No. 3/III, 39–42; via a voice exchange–Haydn, String Quartet Op. 20,2/I, m. 42 (after neighbors to the Gr); within a common-tone Gr-type chord over a pedal point–Fauré, Piano Quartet Op. 15/IV, m. 145. 592 For another reading, see Kraus 1996, 282, Ex. 11. Perhaps another case is Chopin, Prelude Op. 28,4, mm. 20–23, where, however, the initial sonority might be heard as a surface 7–6 suspension.

Prolongation of Augmented-Sixth Seventh Chords 277

After extensive diminished third voice exchanges, the bass descends a diminished fifth. Its basic segmentation is in rapport with the prolonged harmony, but the third g is altered into gƒ (transforming the Gr into a diminished seventh chord) and back into g. My interpretation draws upon my perception of the hypermeter, according to which the Gr at m. 18 occupies a strong measure that opens the entire section after one upbeat measure. This hypermetric interpretation derives from the retention of the harmony from m. 16 to 17 and from the longer duration at m. 18; it counters the basic symmetrical sectionalization into groups of 16 measures (1– 16, 17–32).593 Although no linear progressions of more that a fifth within augmented sixth chords are known to me, there is no theoretical obstacle to creating such progressions, analogous to those used within other seventh chords (especially in VIIº7).

10.3.1.3 Neighbors to Gr-Type Augmented-Sixth Seventh Chords

Ex 10.12a–d shows selected possible neighbors to augmented sixth chords. Neighbors to the genuine seventh of these chords (a fifth above the bass in the ordinary inversion) sound as if they relate to a consonant component of the chord, even when the enharmonic function of the Gr as V7 remains latent.594 As in diminished seventh chords, upper neighbors to the seventh or lower neighbors to the root cannot be confused with arpeggiation (§8.0, consequence (c)), since the 7–8 second is augmented, while such neighbors will only move in minor or perhaps major seconds (e.g., in Ex. 10.12b).595 The dissonance is highlighted in neighbors to the altered tones of the chord, i.e., the raised root (normally the augmented sixth) and, in major, the lowered third (normally the bass) as well. When contrary simultaneous neighbors to both altered tones coincide on an octave (or a unison), the immediate continuation of the initial augmented sixth interval fulfills the chromatic expectations of the

593 The subsequent material (m. 33 ff.) continues the chromatic line in the bass. This conflicts with (but does not override) the interpretation of the augmented sixth chord as a common-tone chord. 594 See surface lower chromatic neighbors to the genuine fifth and seventh of an augmented sixth chord in Haydn, String Quartet Op. 20,2/I, m. 42 (mentioned fn. 591 above). 595 Theoretically, the diminished third space might be perceived as a major step, but this would have to involve enharmony.

278 Prolongation of Augmented-Sixth Seventh Chords participating tones. The embedded chord, V or more idiomatically a ¢− (Ex. 10.12d), might alternatively be perceived as the resolution rather the prolongation of the Gr. Mendelssohn elaborates an augmented sixth chord with such a neighbor ¢− in his Piano Trio Op. 49/IV, 236–8, and then brings the neighbors to the enharmonically equivalent V7 (of ßII) (Ex. 10.12e).596

10.3.1.4 Potential for Larger Prolongation of Gr-Type Augmented-Sixth Seventh Chords

Prolongations of augmented sixth chords can become more substantial where the interpolated sonorities (either neighbor or passing) receive consonant (or at least harmonic) support. Ex. 10.13a–d shows selected possibilities. The third of these hints at an enharmonic potential (compare Ex. 10.13c and 10.15d). The last configuration is realized in Ex. 10.13e (Tchaikovsky) according to one reading (based on N. Wagner 1986, 99 and Ex. 3-4-6). I also suggest an alternative, where the augmented sixth is relegated to the surface level, and the emerging I becomes more structural (albeit still an apparent tonic at the deeper level). I have not found any wider prolongations of augmented-sixth seventh chords without enharmonic transformation. A single case where a Gr might be read as embracing a compound linear progression of a diminished twelfth appears in Beethoven’s Piano Trio Op. 1,3/I, 294–8 (Ex. 10.14a).597 However, it is already possible to hear a resolution at the first appearance of V (Ex. 10.14b). Reading a Gr-prolongation must assume that m. 294 (occupied by the initial Gr) is a strong measure. The melodic contour of the upper voice in the piano and the location of dynamic change into ff (m. 294) support such a reading, but the regular four- measure units (as established previously) determine a different hypermeter (strong measure at m. 295) so that the descent prolongs the resolution (Ex. 10.14b). The prolongation of the Gr is nevertheless latent here, and can be brought to the fore through simple recomposition of the rhythm alone (Ex. 10.14c). This

596 This is a re-harmonization of a motive from the end of the motto of this movement, appearing after many former re-harmonizations. The neighbors to the Gr first appear at mm. 232–3. For a lower neighbor to the tone of the lowered third (the bass) alone, see Mozart, Piano Sonata K. 282/I, m. 19. The embellished chord is an Italian 6/3, with no seventh. 597 This passage takes place in the recapitulation. Its counterpart in the exposition (mm. 91–95) has VIIº7/V instead of the Gr. In both exposition and recapitulation, the alteration appears first as VIIº6/V (mm. 86 and 289, respectively).

Prolongation of Augmented-Sixth Seventh Chords 279 recomposition proves that the augmented sixth chords are capable of remarkable prolongation, even without resorting to the enharmonic V7.

10.3.2 Enharmonic Parentheses within German-Type Augmented-Sixth Seventh Chords The most significant means of prolonging augmented sixth chords interprets the augmented sixth of the outer context as a minor seventh in relation to the inner prolongation. In the ordinary pre-dominant function, a prolonged Gr behaves as V7; and potentially, also as a French chord = V7/ß5 and an Italian chord = V7 with a missing fifth. Enharmonic parentheses (EP) within augmented sixth chords is the most common type of EP in general (cf. §7.8).

10.3.2.1 Enharmonic parentheses within Gr via ßII

When the Gr # is interpreted as V7, the tonic of the inserted passage is the ßII of the main tonality.598 The simplest technique for introducing this prolonging harmony maintains the bass without consonant support. Aldwell and Schachter (1978/2003, 535) have identified this procedure as ‘The ‘Neapolitan ¢−’ as embellishment of the German #.’ The ‘ßII¢−’ is most easily achieved through a combination of neighbors, of which the semitonal neighbor below the augmented sixth (the root) accounts for the enharmonic transformation (Ex. 10.15a). In Schubert’s Piano Sonata D. 845 (Op. 42)/I, 20–24 (Ex. 10.15b, cf. Proctor 1978, 135), this procedure brings to a climax the neighbor configuration 56– 5– (V8–9–8), which is worked out through much of the first group. This enharmonic neighbor itself appears three times; it is questionable whether each of these neighbors is separated.599 ßII¢− within an EP can also derive from passing motion, in either of two related forms: (a) passing motion into an inner voice within the prolonged enharmonic chord, which only afterward regains the augmented sixth, as in Ex. 10.15c from

598 EP within a Gr might explain many vague passages (‘purple patches’) on the ßII (cf. Rothstein 1989, 91), especially in codas. 599 See also: Schumann, String Quartet Op. 41,3/IV, 263–7 (Ex. 9.16). The function of the augmented sixth chord in this case is complicated, possibly embedded in a large II 6/5 prolongation; Brahms, Symphony No. 1/I, m. 11 (Ex. 8.42d). The augmented sixth chord serves as an alteration of VII7.

280 Prolongation of Augmented-Sixth Seventh Chords

Beethoven’s Piano Sonata Op. 109/III, variation No. 4;600 (b) the ßII passes directly into another soprano position of the prolonged chord itself (Ex. 10.15d).601 The nested ßII may receive consonant support. When it appears in root position, there is a strong illusion of ßII tonicization. A good example is found in the coda of Beethoven’s Piano Sonata Op. 10,1/III (mm. 106–13) (Ex. 10.16a). In this movement, seeds for the digression might be perceived in the theme itself, which includes an embellished Gr #.602 A traditional approach to tonality would identify in the coda a modulation into ßII (cf. Kerman 1982, 155). The tonal plan I–ßII–I, however, lacks the harmonic coherence provided by the EP. Paradoxically, a Schenkerian approach enables an appreciation of a prolonged dissonance, which is otherwise difficult to grasp.603 The temptation to hear the ßII as tonicized is weaker where it appears as a £−. It is easiest to approach this ‘ßII6’ from its V2, enharmonically equivalent to a diminished third chord, as in Ex. 10.16b from Beethoven’s Piano Sonata Op. 109/II. This EP is approached via a modulatory sequence, which departs from the key. The interpretation as an augmented sixth chord serves to re-establish the tonal frame. This sequence is based on alternating sevenths and sixths, but they do not function as an ordinary series of 7–6 suspensions, but—strange as it may seem—on a progression between the seventh chords with the sixths as passing tones. (This is due to the rhythmic circumstances and to chromatic motion in the bass).

600 See also in the same movement variation No. 2, 39–40 and 47–48, and variation 5, mm. 7–8 (the latter only reaches the altered tones at the end). Proctor (1978, 133–5) analyzes these passages in a context similar to that of the present study. When the root position arrives after the ßII is stated as a 6/4, the ambiguity disappears. See Meyerbeer, overture to L’Africaine, 43–45. 601 A similar sequence of chords occurs in Schubert’s Gefror‘ne Thränen [Die Winterreise No. 3], mm. 46–47, but they do not form a genuine prolongation. See below apparent EP in Ex. 10.20. In Haydn’s Symphony No. 100/I, 157–66, it is ambiguous whether there is an EP within Gr via ßII, or the initial boundary is passing from a consonant VI (as V8–7 of ßII). 602 The details of the prolongation are somewhat ambiguous. I understand the interpolated ßII as a connected harmony at mm. 107–11, but regard it as a passing chord at m. 109. Possible alternatives would either connect 109 to the ßII or disconnect 107 from 111. 603 At the end of Schubert’s String Quintet/II (mm. 91–93), the progression ßVI–ßII–Gr–V–I, is not a completely closed EP, but the ßVI–...–Gr is heard as V8–7 in the key of ßII.

Prolongation of Augmented-Sixth Seventh Chords 281

In case the usual inversion (with the augmented sixth) is employed, either the Gr or the ßII should involve their own arpeggiation in order to achieve the ßII6. The latter procedure occurs in Ex. 10.16c (Mendelssohn).604 As we have seen with EP within diminished seventh chords (cf. Ex. 8.46), EP in a weaker, retrospective, sense can occur when the prolonged chord is stated only once, but nevertheless has different functions at two different levels. This happens with the Gr chord in Schubert’s Moment Musical No. 6 (Ex. 10.17). The chromatic chord is first heard as V7/ßII, but eventually deeper voice-leading continuity is based on the resolution of the enharmonic interpretation as an augmented sixth chord. In retrospect, the ßII functions as what I have called a ‘back-relating tonic’ (cf. §8.5) of the preceding chord. It is easier to achieve this effect with the augmented sixth as the ultimate interpretation than the other way around.605 The content of the EP may be expanded by means of linear motion. When the ßII is reached immediately, and only the way back to the enharmonically prolonged chord is composed out, the temporary illusion that the embedded ßII truly solves the preceding Gr is particularly strong. The nested line would normally stem from the embedded ßII. For example, in Mendelssohn’s Piano Trio Op. 49/III, 90–98 (Ex. 10.18a), the bass is filled by a fifth progression, supporting a partly-filled ascending seventh in the upper voice. In retrospect, the whole passage serves to circularly prolong the Gr of a local tonic (III, mm. 65–106). Ex. 10.18b shows a much more unusual procedure from Mozart’s Horn Concerto K. 447/I, 85–104. This EP should be regarded in relation to VI, although this VI never arrives (V/VI turns out to be IIIƒ of the main tonality). ßVII (Dß; could be ßII/VI) is subject to an impressive prolongation and establishes the impression that the preceding chord is merely its applied V7 (this local V7–I progression even imitates the preceding V7/V to V). Nevertheless, it is from this applied V7 that the ensuing linear voice leading continues. The chromatic line in the bass composes

604 This passage is rhythmically distinct from its environment. It stands at the end of the recapitulation, before a large coda. Its counterpart in the exposition includes no Gr, but emphasizes instead a half-diminished seventh chord (II 6/5 of III = VII 6/5 of V) without genuinely prolonging it. 605 My analysis essentially agrees with that by Laufer (1985, 20, Ex. 25). Cone (1982, 239) simply refers to ‘a tonicized Neapolitan,’ and offers a hermeneutical interpretation (p. 241), according to which in this passage Schubert’s horror from his syphilis breaks out.

282 Prolongation of Augmented-Sixth Seventh Chords out its lower third and returns transformed into an augmented sixth # (Gr of VI). In retrospect, the ßVII forms a parenthetical interpolation (in the sense of Laufer 1985) and functions as a ‘back-relating tonic’ to the augmented sixth chord that serves as the frame of the EP.606 The situation is different when the motion connects both boundaries of the enharmonically prolonged Gr (Ex. 10.18c). In this case, the tone of the augmented sixth itself is embellished by neighbor motion (as in Ex. 10.15b), but the bass moves from the usual # Gr to an uncharacteristic $.607

10.3.2.2 Enharmonic parentheses within the Gr without involving ßII

A prolonged Gr can be temporarily heard as its enharmonically equivalent V7/ßII even if this secondary V7 never actually resolves. Even the mere choice of passing tones that match the key of ßII can indicate enharmony, as in Ex. 10.19a from Beethoven’s Cello Sonata Op. 102,1/I, where the enharmony is even evident in Beethoven’s notation.608 This example also includes a lower neighbor to the root; an upper neighbor is even more effective since it introduces the familiar cliché V7–VIIº2–V7 in the nested enharmonic chord. Weber uses this device (albeit with an incorrect spelling) at a crucial moment in Der Freischütz (Ex. 10.19b). Max expresses his joy following his rescue from the tragic fate that Samiel had planned for him through the dictated tendencies of the magic bullets (latent resolution of the ordinary V7 function into dark E minor). He is saved by Agathe’s love that redirects the trajectory of the magic bullets and forces them to travel in the

606 See a related procedure in the same repertoire and key in Mozart’s Horn Concerto K. 417/I, 98– 111. The voice leading continues from the ßII until it reaches the raised sixth. The boundaries of the EP in this case are problematic. An apparent back-relating resolution occurs in Beethoven’s Violin Sonata Op. 47/I, coda, 510–29. The ßII is approached from its applied V and later progresses to V, but the initial V/ßII continues a sequence of descending thirds (I–VI–IV–ßII) with applied dominants, and is not an augmented sixth chord. 607 In making this configuration, I was inspired by a passage in the recapitulation bridge from Haydn’s String Quartet Op. 64,1/I, mm. 133–47. This passage is discussed by Rosen (1970/1972, 134; see also here §3.1) as an expansion of V7 of Dß (i.e., of ßII), and this V7 is ultimately transformed into an augmented sixth chord. However, in the Haydn passage a strong consonant ßVI (m. 139) challenges the reading of mm. 133–47 as a structural unit. 608 In Mozart’s Fantasy K. 394, m. 45 (before Primo Tempo), the spelling of a stretched Gr is modified into a V7-structure and back, but since the figuration is based solely upon arpeggiation without passing tones, the enharmonic transformation remains latent.

Prolongation of Augmented-Sixth Seventh Chords 283 opposite direction (enharmonic interpretation as an augmented sixth leads to the bright Eß major).609 A more radical alternative to the formulaic patterns of EP is found in Tchaikovsky’s Orchestral Suite No. 3/II, in the coda (which forms an expansion of the theme) (Ex. 10.19c). Immediate descent from the initial augmented sixth negates its tendency to ascend, and achieves the enharmonic effect. However, this descent is located in an inner voice, while the uppermost voice systematically continues an ascent that has begun previously. Even more importantly, the nested chords do not create clear functional relations, certainly not in the key of ßII. At best, there is a rare variant of a deceptive cadence.610 Finally, when prolonged Gr-type chords do not function as the ordinary pre- dominant IV ƒ6/5, the local tonic implied by their enharmonic interpretation as a local V7 changes accordingly. For example, in Brahms’s Symphony No. 1/I (refer back to Ex. 8.42d), The prolonged chord in m. 11 is VII# with a lowered bass (inversion of VII7/5/ß3), which is internally prolonged as V7 of ßV (not of ßII).

10.3.2.3 Apparent enharmonic parentheses within augmented sixth chords

As is also the case with other EPs, successions that are identical to those of EP within a Gr occasionally function in a different manner. When the ßII is more structural than its embracing chords, it disconnects them and cancels the EP. In such a case, the initial sonority is really V7/ßII, and only the final sonority is a true augmented sixth chord (Ex. 10.20a). Possible factors that weaken the EP are ambiguity in the function of the initial V7/Gr, or the presence of ßII before the initial V7/Gr.611

609 See also EP within a Gr through one-voice neighbors in Mozart, Piano Sonata K. 310/I, 54–56 (cf. TW 2; Beach 1987, 175). Unlike the Freischütz passage, here the function of the prolonged chord as a Gr 6/5 is only revealed in retrospect. 610 Spelling the Gr enharmonically according to the immediate voice leading creates a non-tertian chord (c–fß–g–bß). The EP is further weakened by an unusual suspension to the final resolution. Another unique case of EP within an augmented sixth occurs in Schubert’s Piano Trio D. 929 (Op. 100)/II, 84–114. No structural vertical augmented sixth is found, but the prolongation is latent in the consonantly supported progression I–ßVI–ƒIV–V (of C) (cf. §1.1.2.2.1.1). The augmented sixth Aß–Fƒ is divided into two fourths, as if it were its enharmonical equivalent, a minor seventh. 611 Cf. analytical dilemmas in Mozart’s Piano Sonata K. 457/I, 121–5 and Piano Trio K. 496/II, 30–33 (Kamien [1986, fn. 12] draws attention to these passages) as well as String Quintet K. 515/I, bridge, 48–54, and expanded in the recapitulation, 232–9; Schubert, String Quintet/II, end, 92–93. The inserted harmony, ßIIß, is a reminiscence of the main subsidiary tonal area of the

284 Prolongation of Augmented-Sixth Seventh Chords

The EP might be apparent even when the embedded ßII is in 6/4 inversion. Such a ¢− need not be consonant: it can be a dissonant passing chord at a deeper level than the V7/Gr. I find this to be the case in the very passage that serves Aldwell and Schachter (1978/2003, 535) as a textbook example of embellishment of the Gr, from Schubert’s Einsamkeit [Die Winterreise No. 12] (Ex. 10.20b). Notice that the initial V/ßII appears first consonant, that the sevenths at both boundaries are short, and that the ¢− chord is emphasized.612

10.3.2.4 Combinations of various types of enharmonic parentheses

I have presented three types of EP, based on the enharmonic relations between V7 and Gr (in both directions) and between different interpretations of the diminished seventh chord. These types do not exhaust all theoretical enharmonies of seventh chords (cf. for example the identity of the HD seventh chord with the Tristan Chord). My presentation has shown the different types as distinct, but music can combine EPs of different sonorities in a single passage. Beethoven’s Piano Sonata Op. 2,2/IV uses two related devices of combination in two almost adjacent passages. At mm. 140–44 (Ex. 10.21a), the boundaries of the EP include both types of sonorities in reverse order, so that it is uncertain on which chords the enharmonic transformation occurs (FC, Fig. 121,1 [and the attached commentary] analyzes this passage as an illustration of prolongation through enharmonic restatement and indicates the outer, diminished, seventh chord as the carrier of enharmonic transformation, thus overlooking the peculiar situation). In a later

movement. The augmented sixth is only added at the end. See also Beethoven, Piano Trio Op. 1,3/I, 138–52. If this passage is regarded an EP, the inner function is normal (V 4/3 of B; actually the initial boundary is VII6), but the outer function is complicated, as it leads to VIIº7=VIIº2 of F. In relation to this F, which is the next tonal center, the outer context of the enharmonic chord would be an appoggiatura to V7 (V7/ƒ4/3/ß2). The boundaries of this potential EP are questionable. For an apparent back-related resolution, see above fn. 606. 612 Die Winterreise also includes a similar apparent EP in its third song, Gefror’ne Thränen, 41– 49. Graphs of both songs appear in Everett 1990, 161–2, Exx. 5–6. Everett’s graphs are correct but lack detail (the ‘IV6’ that he indicates in Gefror’ne Thränen is ßII6/4). For an apparent EP on a larger scale, see Chopin, Bolero, 176–87. M. 177 opens a whole section on ßIIß, perhaps chosen for the possible modulation back to the tonic via Gr 6/5. The approach to the ßIIß is heard as V7/ßII and constitutes the last sonority of a truncated omnibus (the last in a sequence of modified omnibuses). The approach to the final Gr 6/5 from VI6 passes through an apparent tonic (186–7). For the opposite direction of an apparent EP, see Ex. 7.98.

Prolongation of Augmented-Sixth Seventh Chords 285 passage (mm. 157–65, Ex. 10.21b), the initial boundary is a Gr while the final boundary alters it into a VIIº# of V.613

10.4 Prolongations of Other Augmented-Sixth Seventh Chords

10.4.1 Prolongation of the French-Structured $ The structure of the French chord (set class 0268) has symmetrical features: it is a subset of the whole-tone scale, includes only three interval classes and maps onto itself once under transposition (T6) and twice under inversion (I2 and I8). This symmetry limits the variety of first-level prolongations of this chord. As a stack of piled-up thirds, it includes two major thirds and one diminished third; the complementary second is major, sharing the absolute size with the diminished third. In filling the middle, diminished, third without further motion, the passing sonority is a non-tertian ¢¦ sonority (when voice exchange is employed), as in Ex. 10.22a (Grieg); filling the 7–8 major second would be similar. Moving through the major thirds between root and third or fifth and seventh (Ex. 10.22b) would pass via an augmented triad (two different augmented triads emerge).614 Larger linear progressions within the French $ chord are possible, but weaken the tonal identity of the chord. The clearest technique is to fill a tritone by means of parallel French-structured chords until the chord maps onto itself (Ex. 10.22c).615 As to other devices, FC shows on one occasion an unfolding of a sixth within a French chord in Beethoven’s String Quartet Op. 59,3/I (FC, Fig. 148,3, renotated in Ex. 10.22d with corrected measure numbers). Even if one accepts the unfolding, it is immediate without passing tones; in fact, the sixth does not

613 The pre-dominant augmented sixth chord can be regarded as an alteration of VIIº7/V. In major, VIIº7/V = IV ƒ7/ß1 and the inverted form VII 6/5 of V = IV ƒ6/ß5. Lowering the root makes the Gr chord IV ƒ6/ß5/ß1. This interpretation is plausible when the sharpening of the sixth precedes the flattening of the bass. On the relations between VIIº7/V and Gr, see also below, end of §10.4.2. Another relevant example is found in Chopin’s Tarantelle. M. 90 is first heard as VIIº2/V–Gr2 in Aß (probably minor), then transformed into VIIº6/5 of V–V4/3 of A minor (ßIIß); however, here the EP is never circularly completed. The context is a parallel period, which fuses the antecedent (84– 91) with the consequent, due to the fact that both parts of the sequence begin on V (Chopin also uses this device in the opening period of his Mazurka Op. 6,1). 614 Chromatic filling of Ex. 10.22b would create a ‘French omnibus,’ where the middle chord is an augmented triad, rather than a 6/4 chord as in the classical omnibus (cf. §7.2.1.2.1), and the chromatic passing chords are minor-minor seventh chords rather than V7/Gr sonorities. 615 This configuration, with added registral manipulations, forms the basis for the opening phrase (mm. 1–4) of Berg’s song Schlafend trägt man mich in mein Heimatland, Op. 2,2.

286 Prolongation of Augmented-Sixth Seventh Chords represent a single verticality, but rather results from an anticipation of V that resolves a Gr (see my alternative). Neighbor motion within the French chord is possible too. The constant problem of distinguishing neighbor motion from arpeggiation is at least latent here, not only in the 7–8 space but in the 3–5 diminished third space as well. Such a neighbor makes ‘a short prolongation of the French sixth’ at the close of Mussorgsky’s song Be Bored, according to Russ (1996, 31 and 35, See Ex. 10.22,e1). The ‘French sixth’ here is actually V ƒ6/4/3 (inversion of V7/ß5), i.e., the same sonority untransposed with dominant function (the ordinary French chord can be regarded as II ƒ6/4/3/ß1). For the actual song, Russ’s reading seems imprecise, but a slight recomposition can force an unequivocal reading of the passage as neighbor motion to the French-structured chord (Ex. 10.22,e2). As to large-scale prolongations of the French-structured $, Baker (1983, 169– 85) claims to find one throughout an entire piece from the transitional period to post-tonal music: Skryabin’s Enigme Op. 52,2 (Ex. 10.23 quotes Baker’s reading of the deep middleground [from his p. 185]). According to Baker, the entire piece prolongs V7/ß5, which resolves either into an implicit tonic in the listener’s imagination (after the piece is over) or within the next piece of the opus. Enigme also serves as the final and most daring example in Morgan’s seminal 1976 essay on dissonant prolongations (pp. 79–86), but Morgan regards this piece as prolonging a ‘dominant seventh chord’ structure, using (e2 ß) rather than ß(e2 å). That Morgan and Baker, who both provide detailed graphs of the piece, can disagree even as to the identity of the deepest prolonged chord seems to derive from the lack of sufficient clues about the music’s hierarchy. Enigme is hardly amenable to Schenkerian analysis in any meticulous sense; perhaps as Morgan claims (p. 84), Enigme ‘approached a condition in which it is no longer a matter of composing out a basic vertical sonority . . . as of composing out a basic set of pitches.’616

616 Among the foreground techniques in Enigme, most intriguing is the tritone-arpeggiation (a true arpeggiation for Baker but not for Morgan) in the bass of mm. 6–8. For a comparison between the readings by Baker and Morgan, see Dunsby and Whittall 1988, 111–2. In general, members of one whole-tone system can pass within the other whole-tone system (e.g., passing members of set 02468T in set 13579E).

Prolongation of Augmented-Sixth Seventh Chords 287

10.4.2 Prolongation of Rare Types of Augmented-Sixth Seventh Chords

Simple third- voice exchanges at least can be applied within any diminished-third space, and so prolong any kind of augmented sixth chord. For example, the famous augmented sixth chord from Richard Strauss’s Till Eulenspiegels lustige Streiche (VII ƒ6/4/ß3, inversion of VII ƒ7/ß3) can encompass just such a third- voice exchange (as recomposed in Ex. 10.24a). Subordinate appoggiaturas to such rare chords are possible on rhythmic grounds. For example, in Schubert’s song Aufenthalt [Schwanengesang No. 5], m. 53 (Ex. 10.24b), an appoggiatura is given to a very unusual passing sonority: IV ƒ6/5/3/ß1 (inversion of IV7/5/ß3/ƒ1) in major, where the fifth above the bass is augmented. This type of hierarchy is absolutely independent of tonal factors (consonance priority and diatonic priority) and points to the possibility of post-tonal diminution, if not of wider prolongation. A more substantial prolongation opens the scherzo of Bruckner’s Symphony No. 9 (Ex. 10.24,c1). The prolonged chord is VII(ƒ)6/5/ƒ3, an inversion of VII7/ƒ5 in harmonic minor. The diminished third lies here neither between the root and the third (as in the ordinary Gr-type and Italian), nor between the third and the fifth (as in the French type), but rather between the fifth and the seventh. The passage is based on linear progressions in similar motion: four voices ascend, expressing four different progressions (perfect and diminished fifths, perfect and augmented fourths). A lower bass provides contrary chromatic dissonant passing motion, which enables the tonic to arrive in root position. The distribution of the passing tones is highly asymmetric; the passing motion includes augmented seconds although the number of the prolonging chords is sufficient to avoid them. The circular prolongation is guaranteed by the return to the initial chord in the last chord before the resolution. The sense of the chord as an altered VII7 only becomes evident with the resolution to the tonic; in real-time listening, the prolonged chord is heard rather differently, as the enharmonically equivalent Cƒ minor triad with an added sixth. This is due to the unusual subdivision, to the passing tone in the bass (which creates V7/V in Cƒ minor) and to the fact that the diminution within the initial chord itself emphasizes the consonant elements of the chord and passes via dƒ, which belongs to the key of Cƒ minor but not to D minor. As Schenker observes in Harmony (286) this is a ‘creation . . . of the tonic

288 Prolongation of Augmented-Sixth Seventh Chords yearning of the root tone C-sharp.’ The allusion to Cƒ minor causes the introduction to sound quite stable, perhaps too stable for a PD. The opening chord has already attracted analytic attention. Schenker’s aforementioned discussion belongs to an early stage (Harmony, 285–7) and does not grasp the prolongation.617 The first to recognize the introduction as a self- contained prolongation is Laufer (1996, 212), who, however, claims that since ‘a dissonance cannot itself be composed out . . . [w]e must understand . . . an initial V-chord as being conceptually present . . . and elaborated.’ Laufer’s argument expresses, of course, the very idea over which the present monograph takes issue. He therefore must assume elision not only of the opening V, but also of a subdivision on (e2 ) in the soprano. Laufer’s reading overlooks the identity of the first and last chords in the introduction, and does not take into account the ‘tonic yearning’ of the Cƒ about which Schenker has commented. Laufer also shows the tonal space of the upper voice in the introduction as a sixth, but due to the change of harmony, it is better to regard it as an unfolded fifth that continues in the same direction. Finally, it is possible for a prolonged seventh chord to only reach its altered variant (usually the raised sixth) at the end of the prolongation, most commonly through voice exchange. The prolonged chord in such cases is the diatonic original, and the alteration counts as a passing chromatic tone in the wider context. More occasionally, the prolonged seventh chord regresses from the altered variant that appears at the outset of the prolongation to the diatonic variant. In this kind of prolongation, the tone of the seventh is subject to circular melodic prolongation, but the chord prolongation is only loosely circular, due to chromatic differences between the initial and final boundary chords. I have shown a sample instance in the context of EP, which does not return precisely to the same chord that has been quitted (Ex. 10.21); a more comprehensive survey of such semi- transitive configurations remains beyond the scope of the present study.

617 Schenker already refers to the chord as ‘much discussed,’ and presents his interpretation as innovative. Louis and Thuille (1907/1920?, 31–2, Ex. 233) and Kurth (1920/1922, 201–2) explain this chord as an alteration of VII.

11. CONCLUSIONS

11.1 Theoretical-Analytical Conclusions

Prolongations of seventh chords are not only possible but quite common. They can embrace any sonority, even apparent tonic triads in root position; the subordinate harmonies may even be tonicized.618 All prolongation techniques can be applied to seventh chords and most prolongations of seventh chords are based on ordinary prolongation techniques. Schenker’s system is, after all, surprisingly compatible with the conception and representation of prolongations of seventh chords. One useful device for prolongation of seventh chords that Schenker does not fully explore is that of enharmonic parentheses (§§7.8; 8.5; 10.3.2). The only valid argument against prolongation of seventh chords is that such chords can hardly be tonicized (§9.4.2). There is a considerable difference between the various types of seventh chords as far as their prolongation is concerned (§5.3): prolongations of V7 are by far the most common and varied and occasionally adventurous. Second to V7 are diminished seventh chords. By contrast, seventh chords with a major seventh are hardly ever prolonged. Such a crucial difference between the various types of sevenths is impossible to explain by strict counterpoint. Indeed, the control of strict counterpoint over free composition turns out to be less complete than Schenker believed. Any prolonged seventh chord violates the

618 See Exx. 6.19c (Schubert); 7.18b (Beethoven), 7.24d (Chopin), and discussion of the more problematic case in Ex. 10.5c (Haydn).

290 Conclusions basic assumption of strict counterpoint that no absolute dissonance, not even V7, can ever function as a contextual consonance (§2.1.1). Perhaps prolongation of seventh chords should count as one of the freedoms of free composition, although Schenker certainly did not conceive it as such. It must be concluded that there are additional forces at work in tonal music alongside strict counterpoint. Schenker himself has acknowledged one such independent force in MW and TW: the power of scale degrees (§§3.2.5–3.2.6); in his final theory, however, he abandoned this idea (§3.2.7). In this respect, Schenker’s stance in the 1920s is more convincing than the one he adopted in his later, fully developed theory. There are, however, other independent forces that I consider to be even more important: in relation to scale structure, it is the driving force of the leading tritone (§2.1.2.2.3.4). Another principle that Schenker vehemently denied but emerges even in the formation of seventh chords (prior to their potential prolongation) is the idea of piled-up thirds (§1.2). This is the basis of Schenker’s early and essentially correct notion of harmonizability in Harmony (see §3.2.1).619 The prolongations of seventh chords involve another set of competing factors that work against the natural tendency of the seventh to be resolved immediately. In particular, the melodic fluency provided by the seventh, especially that of V7 (§§2.3.3.1; 6.1.1), can cause the seventh to participate in a melodic pattern at a relatively deep level, so that everything between the seventh and its resolution becomes its prolongation. Other factors can define the seventh as a boundary event through its separation from its environment. This effect has been demonstrated in various realizations: change of registration, orchestration and dynamics (Ex. 7.67b), tempo (Ex. 7.91); or a more radical break of texture (Exx. 7.40b and 7.50a–b). Many parameters can thus influence the perception of prolongations of seventh chords, as in the multi-parametric approach by Lerdahl and Jackendoff (§3.3.1.4). Nevertheless, the difference between consonance and dissonance remains more central than other factors, since it derives from strict counterpoint, on which Schenker’s entire system is founded.

619 However, the other idea that Schenker attacked in this context—that of the seventh as a remote overtone—plays indeed hardly any role in tonal music.

Conclusions 291

11.1.1 Recurring Theoretical Problems Occasionally, alternative interpretations are possible for passages that, according to one reading, prolong a seventh chord. Analyzing these cases reveals recurring patterns that result from recurring theoretical problems, which challenge the boundaries of the prolongation or its unity. As always, the decision between the alternatives—in our case between a prolongation of a seventh chord and a competing interpretation—must be taken on an individual basis for any particular piece, according to general preference rules that do not have a direct bearing on the problem of the seventh. (a). A seventh chord can be prolonged even if the seventh itself appears at only one of its boundaries, either at the beginning of motion into an inner voice (see models in Exx. 4.8b and 4.12b–c) or, occasionally, at the end of motion from an inner voice (Ex. 6.14). When this happens, the seventh must be more structural than the other boundary or the content between the boundaries would constitute only SFM rather than genuine prolongation (cf. Exx. 4.12a; 6.13). The other cases assume a literal statement of the seventh at both boundaries. (b). If the seventh is not stationary, the initial seventh must be conceived as the initial tone of a tonal motion on some level, e.g., the primary tone of a linear progression. This is simplest to achieve when the seventh functions as an upper neighbor at the deeper level (cf. Exx. 7.102; 7.109a; 8.28d). When this seventh is itself passing from the octave above it (e.g., Exx 7.31e [inner voice]; 7.38c; 7.48b), the situation is most intricate, although such a seventh can be truly prolonged under some conditions (Ex. 5.13). (c). The initial seventh must not be resolved before the end of the prolongation. When the immediate continuation of the initial seventh is in stepwise descent—as either a lower neighbor (Exx. 7.67; 7.76,a1; 8.39a–b, 8.40a), a passing tone (within motion into an inner voice [Exx. 7.26; 8.18c], register transfer [Ex. 7.43b], a compound linear progression [Ex. 10.14] or motion in the bass [Ex. 8.27c]), or even an interpolation on a more surface level (Exx. 7.29d; 7.32)—it might be taken as the resolution of the initial seventh (especially when harmonized as an apparent tonic after V7). Occasionally, the seventh chord might be thought to resolve immediately even with a stationary seventh (cf. Ex. 8.10b and d).

292 Conclusions

(d). A final seventh, if it exists, must form a structural continuation of the initial seventh. When the immediate predecessor of the final seventh is the octave above it, this octave might be perceived as the true source of the final seventh (cf. Exx. 7.22; 7.33; 7.42; 9.15b). (e). The prolongation must not continue after the final seventh (This condition is less problematic than the former ones). If the final boundary is denied, the prolongation continues. A true prolongation of the seventh is still possible until the arrival of a later, final boundary (cf. Ex. 7.17a). The source of some of these problems (especially b and d) is the violation of the distinction between skips and steps in the 7–8 space, a problem that does not derive from the dissonant quality of the seventh (§2.2). The double meaning of the 7–8 space can also raise a dilemma between two alternative interpretations where both readings admit the prolongation of the seventh chord, in particular between an upper neighbor to the seventh and arpeggiation (§§7.2.6; 7.3.2.1).

11.1.2 Locations in the Form Most of those prolongations of seventh chords that occupy a large portion of a certain form take place, not surprisingly, in those sections that are traditionally unstable (§7.10.1). This does not mean that such prolongations are insignificant: they can be very expressive or even bear extra-musical meanings.620 The retransition seems an especially common and effective location, enabling an intensification of tension before the resolution to the recapitulation (see especially Exx. 7.21; 7.37b; 7.115c).621 The thematic use of prolongation of seventh chords is a special device that attracts attention whenever it appears in a piece. In opening themes, this can be found in Schubert (Ex. 7.31g) and Brahms (Ex. 7.10c); perhaps the dislocation

620 See the introductions to Beethoven’s song An die Hoffnung (cf. fn. 510), and to Mendelssohn, Cello Sonata No. 2/IV. 621 Retransitions that are based on prolonged seventh chords may also occur in concerto movements, as we have seen in Ex. 7.45b (Beethoven, Piano Concerto No. 5), or before rondo refrains, as in the fairly more simple passages in Beethoven, Piano Concerto No. 4/III, 132–59 and 402–15 (FC, text to Fig. 151). See also the retransitions of Mendelssohn's Sextet for Piano and Strings, Op. 110/I and of Mozart’s Piano Sonata K. 330/I).

Conclusions 293 expresses a Romantic virtue. The prolongation itself can embrace thematic quotations, as a false recapitulation or a false refrain (Exx. 7.18b; 7.115c).622 There seems to be a slight preference for locating prolongations of seventh chords toward the end of pieces, as a last twist in the music before the final fulfillment of tonal directionality is achieved, not unlike the prolongation of the cadential ¢− in classical concerto cadenzas. This tendency is especially strong with diminished seventh chords and enharmonic parentheses. The former are located toward the end, mainly in pieces in minor by Bach (cf. fn. 524), but also by Mozart (Piano Concerto K. 488/I, cf. fn. 491) and Beethoven (WoO 53, Ex. 8.39b). The latter appear mainly in codas, and is typical of early Beethoven (cf. §7.10.1.2.5). An increase in the prolongation of seventh chords can itself create a kind of directionality. This happens when large prolongations of seventh chords expand analogous, earlier passages (cf. Exx. 7.45b [Beethoven] and 7.104 [Haydn]). In general, multiple prolongations of seventh chords in one work often create rich relationships. These normally occur within one movement (cf. Ex. 7.115 from Beethoven’s String Quartet Op. 18,2/IV), but can even give rise to motivic relationships between different movements, as between the outer movements of Schumann’s String Quartet Op. 41, 3 (Exx. 9.15b–9.16).

11.2 Historical Conclusions

The initial assumption of this work was that PDs in general, and perhaps also prolongations of seventh chords, become more frequent, various and adventurous toward the end of the tonal era. In retrospect, this assumption looks like a compromise between Schenker’s total denial of PD and the recognition of some prolongations that I have encountered.623

622 In Beethoven’s Symphony No. 6/I, the thematic recapitulation begins in the middle of a prolongation of V7 (see fn. 283). A further manipulation of the formal location of prolonged seventh chords occurs when apparently stable sections turn out to be parenthetic islands between seventh chords. Most daring is the transitive motion in Chopin’s Fantasy, mm. 119–54; Jonas ([1934] 1982, 74) presents a structural progression between seventh chords, while the consonant large stable passages do not belong to the structure. Another reading: Schachter [1988b] 1999a, 277. 623 For a presentation of the historical evolution of PDs, see §3.3.1.4 on Katz (1945). Laufer apparently thinks of tonal and post-tonal practices as being more strictly separated with regard to

294 Conclusions

The findings of my work are somewhat different. The historical evolution of prolongation of seventh chords corresponds to a large extent to that of prolongation in general. Significant examples appear as early as Bach, the climax occurs in the works of Beethoven, and among late nineteenth-century composers, prolongation of seventh chords seems more significant in Brahms than in Wagner. I have looked for examples in representative works by Wagner, Bruckner, Wolf, Liszt, Grieg, Richard Strauss, Reger, Skryabin and Mahler. I have provided some examples from these composers, but on the whole, I found it difficult to locate clearly defined circular prolongations in their works. I feel fairly certain that this ‘nineteenth-century second practice’624 eschews circular prolongations, although it could be the case that I failed to grasp some examples in this rather more complicated style. Those circular prolongations of seventh chords that I was able to detect in this late repertoire are often highly innovative, and sound beyond the bounds of what is acceptable in common practice (e.g., Ex. 7.72 [Humperdinck], Ex. 10.24c [Bruckner]). They have special significance in prolonging rare types of seventh chords. However, they do not seem to explore the entire range of possible prolongations in the same ingenious variety that Beethoven uses to prolong V7 or VIIº7. In one sense, it is even easier to achieve prolongation of seventh chords in pieces with a classical and well-established form, since the clearly defined boundaries of unstable sections can remain valid even where they are occupied by large prolongations of seventh chords. By contrast, in works whose structure is ambiguous, it is more difficult for seventh chords (or other dissonances) to control large sections that may also include foreground consonances. There is more justification for viewing the early history of prolongation of seventh chords as an evolution. Many Baroque works (except by Bach) seem to avoid prolongations of seventh chords altogether. Having scanned representative works by Telemann, Vivaldi and even Handel, it is my impression that the potential for prolonging the seventh remains unrealized in this repertoire.625

the possibility of PD: his studies of post-tonal music (1986, 1991a) show PDs which he prohibits in tonal music (e.g., 1996, 212). 624 This is the title of a collection of essays (from which I referred to Williamson 1996 etc.). 625 See again exceptional PDs in early music, fns. 44 (Neusiedler) and 314 (Josquin des Pres).

Conclusions 295

Geographically, my study focused on the great German tradition. I have included some examples from Russian and French music, as well as from Italian opera, but in these repertoires too, I have encountered considerable difficulty in tracing circular prolongations, including those of seventh chords. The historical and geographical limitations do not necessarily contradict the general character of my theoretical observations: in those styles where circular prolongations exist, seventh chords are prolonged by means of the techniques I have shown. Prolongations of seventh chords, it seems, are mainly to be found in the works of those composers that Schenker himself admired and studied. Since the history of prolongations of seventh chords largely corresponds to that of prolongations of triads, it cannot serve as a significant technical basis for understanding the evolution of tonality. My findings might perhaps reaffirm Schenker’s claim that other composers are composers of the foreground alone, a claim that Schenker intended as derogative (e.g., in his attack on Wagner in MW II, 29). This condemnation might be applicable to passages where a seventh initiates a large tonal motion, but then never resolves but rather fades away.626 Within common-practice tonality, prolongation of seventh chords (and perhaps prolongation in general) offers only a limited tool for stylistic analysis beyond very large generalizations. The same techniques appear in similar manners in various styles,627 so that it is principally the unity of the tonal language that can be observed.

11.3 Aesthetic Observations

As a rule, prolongation of seventh chords preserves the tension of the seventh, and the very delay of the resolution actually serves to heighten that tension. As a result, such prolongations can be used as a means of ‘painting’ tense emotions, as shown in songs by Beethoven (Vom Tode, Ex. 10.9a), Mendelssohn (Reiselied,

626 One possible listening strategy might expect that a specific seventh chord that has previously been heard is being prolonged, and that after its reappearance it will be resolved, but then the sense of prolongation is violated and the tension of the initial seventh is lost. For example, in Berlioz Benvenuto Cellini overture, m. 20, V2 is followed by a G. P., but the ensuing material simply leaves it unresolved. 627 This may be different with other dissonances (prolongations of augmented triads, for example, might be revealed as being unique to Liszt).

296 Conclusions

Ex. 7.15) and Wolf (Seufzer, Ex. 10.7d) (cf. also fn. 620). The expressive character is most effective when it is reinforced by more explicit musical parameters, e.g., abrupt breaking of a lively texture for a choral passage (Exx. 7.40b; 7.50). Not all prolongations of seventh chords share this character, however; in general, prolongations of V7 are less expressive than those of diminished seventh chords (this seems true for the unprolonged chords too). Precisely because prolongations of V7 fit so well into the tonal system, they are not always marked as special. Particularly diatonic prolongations of short spans tend to minimize the tension (e.g., Exx. 7.2; 7.4–7.6). Even in such passages, however, it is not the prolongation that prevents the feeling of tension. The idea that prolongation equates with stability (cf. §§1.1.1.3; 1.3.1) must be refuted then, at least with regard to prolongation of seventh chords. The experience of prolonged tension by no means leads to the emancipation of dissonance: on the contrary, its very expressiveness derives from the basic difference between dissonance and consonance. Structural analysis, which is often blamed for overlooking the expressive qualities of music, thus becomes an effective tool for analyzing the expressive tension where the object of prolongation is a seventh chord (or presumably another dissonance).628 Aesthetic effects similar to those achieved by prolongation of seventh chords can be created by other means, such as stretching of a seventh chord (§2.3.1) or a quantitative abundance of seventh chords at the surface (§2.3.3.2). On the other hand, no single effect is shared by all the various prolongations of seventh chords. Even if more specific aesthetic effects can be described, their precise classification will not correspond to the classification of prolongations that I have presented here. The extent to which prolongation determines certain expressivity is ultimately somewhat limited.

628 Cone (1968,25) makes the same point without using rigorous Schenkerian terminology. He is referring to Brahms’s Intermezzo Op. 76,4 and Schumann’s Fantasy Op. 17.

Conclusions 297

11.4 Areas of Future Research

This study has attempted to fill gaps in the understanding of the prolonged seventh, but there is still room (as well as new opportunities) for future research on the topic. First, while I have explored the topic systematically, I have refrained from statistical and rigorously historical investigation. A quantitative study of prolongations is problematic, but even entering the data that is presented here into a database would enable a more accurate detection of the historical development and stylistic distribution of prolongations of seventh chords in general and of specific patterns. I am not sure whether this would lead to significant results, but it is certainly worth exploring. While I have surveyed all the voice-leading techniques, I found it impossible to discuss all of their potential combinations. This might require calculations using mathematical methods. I have chosen to study a relatively narrow topic in considerable depth. I have excluded from this study the discussion of prolongations of other dissonances in tonal music: diminished and augmented triads, the dissonant 6/4, ninth chords and higher stacks of thirds, and occasional prolongations of non-tertian sonorities. I have gathered plenty of material relating to these issues, which has not ultimately been included in this study. My focus on circular prolongation has left unexplored transitive progressions between seventh chords or unresolved sevenths in transitive contexts. Expanding the subject of study to include transitive progressions as well would also expand the repertoire where examples are found. One would probably find significant instances in the works of Wagner and other late Romantic composers, where my original expectation of finding prolonged sevenths was unsatisfied. Jazz music, where the tonic appears with added dissonant tones (cf. §9.4.2), should be explored in the light of my observations by scholars who know it and love it. Expanded tonality can now also be examined with more precision than in the existing literature (§3.4). As to the study of true post-tonal music, the findings and conclusions of this study are admittedly less relevant than might have been hoped. In truly post-tonal music, not only is the distinction between consonance and dissonance destroyed, but so is the principle of piled-up thirds, which serves as the basis for harmonizability and for recognizing the seventh as a

298 Conclusions chordal tone. The ubiquity of prolonged sevenths still does not prove, then, that prolongation in non-tertian, post-tonal music is possible. I do believe that it is indeed possible, but my study does relatively little to prove this. Another kind of future research can be generated from concepts that have been introduced during the course of my work, which are not directly related to the study topic. Distinctions between prolongation and composing out (§1.1.2.2) are useful for sharpening the theoretical understanding of many marginal cases; The classification of prolongations according to the emerging passing sonorities (§7.1) or to their inner segmentation (§7.2.3) can be applied to prolongations of triads as well. These concepts are not entirely new, but they are rarely used; the latter stems from Schenker himself, but the former would apparently meet Schenker’s objections.629 The most radical potential for future research derives perhaps from my ideas on the seventh at the deepest levels. I have hinted at the possibility of alternative background and deep middleground configurations, which highlight V7 and the tritone above the leading tone instead of the consonant V. These possibilities should be explored in depth; if they are accepted, our understanding of the structure of many pieces might be modified. Last but not least, the examples I present from the literature contribute to the understanding of those individual works that are analyzed here; fresh insights into each piece in its entirety may result from my own observations on specific passages in those works.

629 Further innovative concepts proposed in this work include reaching-under (§7.5) and back- relating resolution (§8.5).

Appendix: Prolongation of Dissonance in Schenker’s Free composition

Fig. No./§ Location/ Type of PD /Issue under discussion mm. §9 + fn. 3 normative view, refuting Schoenberg’s ideas §16 normative distinction between perfect and diminished 5th 7b 40–55 tritone unfolding §18 triad (rather than consonance) as basis of tonality §§35–6 dissonant ‘unsupported stretch’ in the background §66 formulation of the normative view 16,3c IV7 at the deep middleground 19,a-c subordination to V7, cf. 32,5 23b+§111 conflict between dissonant neighbor and interruption 30a 17–24 II–V7 subordination 30b 3–4 diminished fifth progression ibid. 10–13 apparent bass arpeggiation of dissonance 32,5 subordination to V7; struggle against background V7 32,7 conflict between dissonant neighbor and interruption §110 contradictory remarks on the seventh as neighbor §111 working-out of the seventh as form-generating 39,1 retransition harmonic V7, deprived from structural status (cf.130b) 41, 1,3&4 dissonances as product of reaching-over

300 Appendix: Prolongation of Dissonance in Schenker’s Free Composition

Fig. No./§ Location/ Type of PD /Issue under discussion mm. 41,1-Ex. 26–60 subordination to V7 42,2 11–18 signed as V7 since 11. middleground dissonant neighbor, not interruption 43,d1-2 tritone unfolding 43e tritone unfolding 43b-Ex. 7–17 stationary seventh in the music (not in the graph) 47,1; 47,2 middle §314 claims that achieving the seventh is form- section generating 50,2 (consonant?) ¢−s receive applied VIIs. 53,1 voice exchanges from dissonances 53,3 3–4 subordination to V7 54,6 subordination to V7 (in the analysis only). §§169–70 main formulation of normative prerequisite of transformation into consonance 57,2a middleground tritone as a series of whole-tone steps 59,4 parantheses keep the tension of (=prolong?) an augmented triad §§176–7 main discussion of seventh progressions, including contradictory remarks. A footnote by Oster on direction of the progression and on ‘preparation’ 62,1–11 main examples of seventh progressions and seventh arpeggiations 63,3 delayed suspension §181 composing out of suspensions 64,3 arpeggiation of a cadential ¢−, actually nested within V7 73,3 9–16 unfoldings within V7. doubtful text to diminished third progression as a normative model 74,3

Appendix: Prolongation of Dissonance 301 in Schenker’s Free Composition

Fig. No./§ Location/ Type of PD /Issue under discussion mm. 76,1(c) + diagonal line connects a seventh §196 §206 normative explanation of illusory seventh progressions 82,3b 20–35 dissonant unfoldings 82,4 17–32 see 152,6 83,1 diminished third progression as a normative model 85 26 neighbor seventh instead of interruption 87,1a tritone unfoldings in diminution level 88,3 schematic diminished fifth progression 89,1+text true seventh progression. doubtful. §215 illusory vs. genuine seventh progressions. The criterion is emphasis on harmonic intervals 90,4 reduction into V7 95,8 diagonal line connects a seventh 96,4 5–7 subordination VII–V7 (in V) composed out 98,1 schematic voice exchange within V7 99,2 7–8 chromatisized subordination to V7; local tritone unfolding §230 recognition in arpeggiation, also of a four-note chord 100,2a [illusory] four-note arpeggiation 100,2b arpeggiation of a diminished seventh chord (begin with V7) 100,4a four-note arpeggiation as a middleground German chord 100,4b four-note arpeggiation connects II–V 100,4c four-note arpeggiation (real) 100,5a 214 diagonal line connects a seventh 100,6b&c equal division of the octave 102,2 240–52 subordination to V7

302 Appendix: Prolongation of Dissonance in Schenker’s Free Composition

Fig. No./§ Location/ Type of PD /Issue under discussion mm. 102,7 31–34, diminished fifth progressions 39–50 103,2a illusory diminished fifth progression 106,2a&b tritone unfoldings 106,2d 9–10 unfolding under stationary seventh 106,3a 102–20 arpeggiations within V7, involving inversions (I read neighbor motion) 108,3 35–38 subordination to V7 109,e2 explicit presentation of subordination to V7 109,e6 schematic cadenza: ¢− prolongation 110,a4 vertical V7 110,e4 prolongation of II# 111a & c schematic subordinations to V7 113,3 gradual transformations into V7 113,5+text recognition of vertical diminished seventh 114,5b apparent diminished fifth progression 114,6 harmonic progression between dissonances (seventh omitted in the graph at m. 84) 115,1a 23 a harmonic space of a second + text ibid. 24–26 voice exchange within V7 115,1c diminished fifth-progression + text 115,3b vertical dissonant support (diminished seventh) 117,1 the seventh as incomplete neighbor: alternative to + text subordination 119,4 V9 expanded without other harmonies 119,7 V7 arpeggiation 119,20 23–34 V7/III as middleground event

Appendix: Prolongation of Dissonance 303 in Schenker’s Free Composition

Fig. No./§ Location/ Type of PD /Issue under discussion mm. 121,1&3a 140–5 prolongation of augmented-sixth chords (in 121,1 perhaps diminished seventh chord) through enharmonic transformation text to diminished fifth progression 122,2 122,3 suspension resolves into II2 text to Mozart, unfolding within a seventh chord 124,1b Symphony 40/I, 44–47 124,2a tritone unfolding 130b 48 middleground V7 (root position only implied) with contradicting hints to its status (cf. 39,1) 134,3 third progression with double neighbor in bass within V7 134,6 316–67 V7 as middleground event 134,9 145–69 middleground arpeggiation of a diminished triad (supported in the foreground by consonances) §283 normative distinction between perfect and diminished 5th 143,2 unfoldings within V7 148,2 tritone unfolding within V7 149,4 diminished fifth progression in the bass 149,5 5–7 true seventh progression 150 3–9 neighbor apparent tonic within V7 152,6 17–32 V7 prolongation through tritone unfolding and register transfer of the seventh §310,(b)3 [V]8–7 as form-generating 153,3+text 41–62 structural V8–7 with priority of the seventh; arpeggiation within V7/V 154,3 dev. deep V7 as passing toward cover tone over V.

304 Appendix: Prolongation of Dissonance in Schenker’s Free Composition

Fig. No./§ Location/ Type of PD /Issue under discussion mm. §313: Waldstein V7/III as a middleground event (implied by letters) p. 135 35–42 §314 direct statement: ‘the V7 may be composed out’ 154,5 deep subordination to V7, nested within gradual transformation V–V7. End of §314 describes as prolongation. 154,6 115–22 text: deep middleground V7. In fact only a lead-in 155,1 41–48 bass dissonant arpeggiation ibid. 28 & 50 V7 as the structural event of both episodes 155,2 24, 55 & 80 middleground dissonant neighbor; V8–7 with priority of the seventh 155,3 36–37 passing motion towards V7 (V5–6–7)

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INDEX

Bach, Carl Philipp Emanuel Riem. 81—Christus, der uns Arioso con variazioni, Var. 7 258 selig macht, m. 9 32 Keyboard Sonatas Chromatische Fantasie for W48,1/I 53–54 Ex. 8.40e Keyboard, m. 31 W48,4/I 3–6 Ex. 9.4a 7, 54, 220, 317, Ex. 8.6e W49,6/III 112–5 233 English Suites W57,6/I 58–62 224, Ex. 8.13h No. 2/Bourrée No. 2, m. 1 Rondo W56,5 mm. 140–54 40, Ex. 2.15b 235, Ex. 8.31e No. 4/Sarabande Ex. 7.95b2 BACH, JOHANN SEBASTIAN No. 6/Gigue Ex. 3.9 Brandenburg Concertos French Suites No. 1/II 13–15 192 No. 2/Sarabande, mm. 1–5 No. 5/II 7–9 131 159, Ex. 7.36 Cantatas No. 6/Allemande 103 No. 60/I m. 10 189 ____/Sarabande, mm. 13–20 No. 61/V 2–3 32 92, 105, 125, Ex. 6.12b No. 86/V 32 ____/Gavotte, mm. 6–8 96 Chorales ____/Minuet, m. 6 189 69 melodies, No. 11—Auf, auf! Fugue BWV 948 for Keyboard die rechte Zeit ist hier 134 (attributed), 65–83 ___, No. 30—Gott, wie gross ist 229, 237, Ex. 8.33b deine Güte 39, Ex. 2.14b Inventions (2-part) Riem. 4—Es ist das Heil uns C major, background 123 kommen her, m. 1 32 F major, background 123 Riem. 59— Herzliebster Jesu, A major, mm.20–21 191 was hast du 26, Ex. 2.2a Inventions (3-part) Riem. 64—Freu’ dich sehr, o E minor, 37–44 236, Ex. 8.32d meine Seele 33 F minor, m. 1 20, Ex. 1.12 Riem. 80—O Haupt voll Blut und Wunden 32, 73, Ex. 3.21

330 Index

BACH, J. S.—contd. St. Matthew Passion/Chorale—O Italian Concerto for Keyboard/I Haupt voll Blut und Wunden, 60–63 108 m. 1 32, 73, 307, Ex. 3.21 ___/III 17–22 258, Ex. 9.12c Suites for Cello Magnificat. Esurientes (end) 44 No. 4/Prelude, mm. 1–10 32 Motet No. 5—Komm, Jesu, ____, 15–27 222, Ex. 8.10a Komm, m. 14 63, 154, Ex. 3.16 ____, 41–43, 49–51 222 Orchestral Suite No. 2/Badinerie, No. 5/Prelude, 27–30 36–37 191 32, 108, Ex. 2.9c Organ Works The Well-tempered Clavier, Allabreve, BWV 589, Vol. 1 mm. 29–32 27, Ex. 2.3c Prelude in C major, 23–24 Das Orgelbüchlein. No. 5— 105, 131 Puer natur in Bethlehem, ____, 24–31 71, 75, 105, 131, mm. 12–13 239, Ex. 8.35 171, 172, Ex. 7.64 Partita for Violin, No. 3 Fugue in C minor, 25–26 236 /Prelude (background) 114, 171 Prelude in Cƒ minor, 30–31 ___, 43–50 178 56, 236, Ex. 3.13 ___, 93–98 163 Fugue in D major, 15–20 13 ___, 120–128 171 Fugue in D minor, m. 5 133 /Gavotte en Rondeau, theme 95 ___, 36–42 236 ___, 80–90 161 Prelude in Eß minor, /Minuet No. 1 (backgr.) 123 17–18, 32–35 236 ___, m. 7 32 Fugue in Eß minor [Dƒ minor], Preludes for Keyboard theme 88 BWV 894, 77–85 54 147 Prelude in E minor, 34–39 163 BWV 924 (12 short preludes, Fugue in F major, 1–4 No. 1), 3–5 32 156, Ex. 7.27d ___, 7–18 154, 158, Ex. 7.23c Prelude in Fƒ major, 1–4 BWV 926 (12 short preludes 61, Ex. 9.20a No. 3), 17–32 61, 158 Fugue in A minor, 80–83 BWV 942 (12 short preludes 190–1, 236, Ex. 7.96a No. 12), 5–7 265, Ex. 9.21b Fugue in Bß major, 55–63 63 Sonatas for Violin Fugue in Bß minor, 55–62 No. 1/Adagio 227, Ex. 8.19d 228, Ex. 8.23c ____/Fugue 4–5 191 The Well-tempered Clavier, ______47–52 182, Ex. 7.81c Vol. 2 No. 2/Andante 6–7, 9–10 191 Prelude in E major, 35–45 163 No. 3/Largo 6–7, 16–17 191 Fugue in E major, 38–40 St. John Passion/Chorale— 138, 162–3, 291, Ex. 7.43b Christus, der uns selig macht, Fugue in D major, 19–20 191 m. 9 32 Fugue in B major, theme 32 ___/Chorale—O grosse Lieb, m 10

26, Ex. 2.2a

Index 331

Bartók, Béla ______/IV (complete) For Children/No. 32, 3–5 259 193, 211, 293, Ex. 7.115 Mikrokosmos/No. 131: Fourths 82 Op. 18,3/I retransition 214 ___/No. 132: Major Seconds… 82 Op. 59,2 (Razumovsky 2)/IV BEETHOVEN, LUDWIG VAN 1–9 106, 263, Ex. 9.19b Ah, Perfido!, Op. 65, 118–21 Op. 59,3 (Razumovsky 3)/I 157, Ex. 7.31d introduction 1–29 ____, 156–60 275, Ex. 10.7a 199, 232, 291, Ex. 8.27c Allegretto for Piano, WoO 53, _____ 30–43 158, Ex. 7.32b 141–69 240,241,293,Ex. 8.39b _____ 126–37 193, Ex. 7.97c Bagatelles for Piano _____ 150–70 285, Ex. 10.22d Op. 33,4, mm. 24–25 276 ___/II 183–194 243, Ex. 8.42e Op. 33,7 theme 121, Ex. 6.4a Op. 74 (Harfe)/IV theme 90 Op. 119,1 mm. 25–29 ______Var. 1 123 70, 133, Ex. 3.20 Op. 127/I 7–10 131, Ex. 6.21c Op. 119,8 mm. 9–12 165 ______/II m. 50 155 Op. 119,11 mm. 7–9 Op. 131/I 18–20 222, Ex. 8.10d 133, Ex. 6.24a Op. 132/I bridge Op. 126,1 beginning 34 75, 138, 199, 209, Ex. 7.103 Concerto for Violin/I Rondo a Capriccio for Piano, Op. 10–11, 65–68 121 129, 149–62 194, 284, Ex. 7.98 ______/III 251–60 146 ___, 260–379 198, 291, Ex. 7.102 Concertos for Piano Sonatas for Cello and Piano No. 1/III 453–80 206 No. 1, Op. 5,1/I 24–34 49, 144 No. 2/III coda 206 No. 3, Op. 69/I 1–5 No. 4/I 197–98 170 129, Ex. 6.18b ____/III 132–59, 402–15 292 __/III 47–49 258,259,Ex. 9.12a No. 5 (Emperor)/I 6–9, 363– No. 4, Op. 102,1/I 128–135 364 163, 292, 293, Ex. 7.45b 282, Ex. 10.19a Fantasy for Piano, Op. 77, No. 5, Op. 102,2/transition to III transition to Allegretto (142–57) 194, Ex. 7.97d 188, 238, 290, Ex. 7.91 Sonatas for Piano Overtures Op. 2,1/III 1–4 Leonore No. 2, 4–31 111 78, 138, 190, Ex. 7.95a2 Leonore No. 3, mm. 9–12 99 Op. 2,2/I 42–92 247, Ex. 8.49 ______, 12–19 268 ______retransition 215–24 ___, 570–614 183, Ex. 7.83 178, 201, Ex. 7.75d5 Piece for Piano (Klavierstück), ____/II 26–31 133 WoO 60 210, 305 ____/IV 139–46, 157–65, Quartets (Strings) 284, 288, Ex. 10.21 Op. 18,1/I 14–15 218, Ex. 8.3d Op. 2,3/I exposition ______282–4 160, Ex. 7.38b 205, 270, 271 _____/III m. 24 270 ___/IV 282–308 205, Ex. 7.108 Op. 18,2/III 13–14 160

332 Index

BEETHOVEN, Sonatas (piano)–contd. _____/II m. 3 254 Op. 7/II 25–37 270 _____/III 25–49 127, Ex. 6.15a ____/IV 1–8 207 Op. 31,1/I bridge 123 ______23–35 155 Op. 31,3/I theme 260 Op. 10,1/I 40–55 134, 199 Op. 49,1/I 12–17 ______development 97, 201 133, 165, Ex. 6.24c ____/III coda 280, Ex. 10.16a Op. 49,2/I 51–52 87 Op. 10,2/I exposition bridge Op. 53 (Waldstein)/I 9–11 168 90, 154, 199 ______bridge ______m. 111 64, Ex. 3.17 123, 199, Ex. 6.7 _____/III 23–85 126, 201, 273, ______/II 21–26 243 Ex. 6.13e, Ex. 10.6a Op. 54/II 37–44 135, 187 Op. 10,3/I 133–65 ______130–3 Ex. 8.13e 124, 197, 270 Op. 57 (Appassionata)/I ______/II 1–9 42, Ex. 2.17a exposition bridge, 23–33 ______3–4 222 61, 199, Ex. 7.62d ______m. 56 221 _____ 54 131, Ex. 6.20b ____/III 1–8 124, 199, Ex. 6.8 _____ 65–87 12, 185 ____/IV 197 _____ 238 130, Ex. 6.20a Op. 13 (Pathétique)/II _____ 242–5 225, 227, Ex. 8.16 17–28, 38–50 197–8 ___/II m. 9 189 _____ 42–44 191 Op. 78/I 20–27 242, Ex. 8.39c Op. 14,1/III 1–4 133, Ex. 6.24b Op. 79/I 36–38, 40–42 167 ______coda 112–21 167 Op. 81a (Les Adieux)/I Op. 14,2/I 30–32 163 transition from introduction ______99–106 270 12–21 203, Ex. 7.106c ______development 201 ______47–49 Ex. 7.79c ____/III 160–89 150, Ex. 7.18b ______development ______132–8 133 66, 111, 203, Ex. 7.106a-b Op. 22/I beginning of Op. 90/I 100–9 171 development 68–75 204 _____/II 41–43 142, Ex. 7.6b ______105–12 195 ______49–59 142 ______/III 1–8 96 ______178–80 141 ______/IV 1 and 3 43 ______221–9 37 ______72–73 154 ______261–7 229, Ex. 8.23d Op. 26/I theme, esp. 17–26 Op. 101/I 12–13 57, 188 42, 93, 122, 197 ______/II 1–7 163, Ex. 7.44 _____/III 1–18 42, Ex. 2.17b ______4–6, 58–9 57 Op. 27,2 (Mondlicht)/I 1–5 _____/III 79–80 160, Ex. 7.38a 127, Ex. 6.16c ______/IV 17–24, 236–7 (=/III, ______48–49 Ex. 7.95a1 49–56, 268–9) 57 ______m. 58 253, Ex. 9.5b Op. 106 (Hammerklavier)/I _____/II 45–49 205 bridge 113, 182, Ex. 5.13 Op. 28/I 77–91 240, Ex. 8.36

Index 333

BEETHOVEN, Sonatas (piano)– _____/III 236–8 120, Ex. 6.3c Op. 109/I 1–4 114 No. 4/I 203–17 ____ 17–21 136 113, 115, 264, Ex. 5.15 ______/II 42–57 No. 5/II 123–46 61, 182 280, Ex. 10.16b _____/IV 54–55 179 ______/III 7–8, 39–40, 47–48 ______265–6 120, Ex. 6.2c 280 ______development 204 ____ 42 121 No. 6 (Pastoral)/I development ____ 102 56 125, 128, 201, Ex. 6.12c __ 103–4 279, 282, Ex. 10.15c ____ retransition 293 Op. 110/I bridge 126, Ex. 6.13d ____ 468–70 182, Ex. 7.80b ______/II 45–47 56, Ex. 3.14 __/IV 68–78 245, 281, Ex. 8.46 ______/III m. 169 93 No. 7/I 142–51 131, Ex. 6.21a Op. 111/I 5–11 ____/III 1–10 112, Ex. 5.10b 49, 56, 229, 237, Ex. 8.33a ______33–45 257, Ex. 9.10 Sonatas for Violin and Piano No. 8/I theme No. 6, Op. 30,1/III 198–220 174, 290, 291, Ex. 7.67b 244, Ex. 8.45a No. 9/I 142–43 55, 56, Ex. 3.12 No. 8, Op. 30,3/I 169–70 169 __/II 117–26 55, Ex. 3.11 No. 9, Op. 47 (Kreutzer)/I ____ trio 466–75 149, Ex. 7.16 510–529 282 __/IV theme 123 ___/II 1–4 141 Trio for Piano and Strings, __/III 100–52 96, 129, Ex. 4.17 Op.1,3 /I 138–52 284 ____ 317 157, Ex. 7.31f __ 294–99 278, 291, Ex. 10.14 No. 10, Op. 96/I 32 242 _____/IV coda 206 Songs Variations for Piano An die Hoffnung, Op. 94 4–14 Diabelli Variations, Op. 120 229, 292 /No.1 20–24 162 L'amante impziente [Stille /No.2 m. 21 176 Frage], Op. 82,3 151–3 189 /No.20, m. 28 176 Mit einem gemalten Band, Op. 32 Variations in C minor, 83,3 21–24 155, Ex.7.27a WoO 80, Var. 9 Ex. 3.8. Vom Tode, Op. 48,3 15–17 Berg, Alban 276, 295, Ex. 10.9a Schlafend trägt man mich in mein Wonne der Wehmuth, Op. 83,1 Heimatland, Op. 2,2 285 9–10 133 Berlioz, Hector Symphonies Benvenuto Cellini overture, No. 1/I m. 1 84 m. 20 295 No. 2/I coda 238,249,Ex. 8.33c ____ 146–58 231 ____/II 41–44 222 ____ 284–99 233, 291, Ex. 8.28d ____/IV theme 207, Ex. 7.110c Bizet, Georges No. 3 (Eroica)/I development Carmen/No. 7—duet 77–79 146 65, 111, 138, 140, 202, Ex. 7.105

334 Index

BRAHMS, JOHANNES Rhapsody for alto, male chorus Concerto for Violin and Cello, Op. and orchestra, Op. 53 8–9 229 102/I 71–89 Schicksalslied 152–72 174, 178, 182, Ex. 7.68c 226, 232, Ex. 8.27b ____ 180–93 225, 228, Ex. 8.20g ______314–24 242 Fest- und Gedenksprüche, Op. Sonatas for Cello and Piano 109. No. 2, mm. 36–41 No. 1, Op. 38/III 88–90 220 226, 228, Ex. 8.19a No. 2, Op. 99/I, development Piano Works 88–100 195 Op. 4 (Scherzo), trio No. 2 ______/II theme 170 146, 292, Ex. 7.10c Sonatas for Violin and Piano Op. 5 (Sonata no. 3)/V 9–10 No. 1, Op. 78/I m. 10 160, 161, 161, 193, 256, Ex. 7.40a 170, 190, Ex. 7.39f Op. 24 (Variations and Fugue _____ bridge 141,142,Ex. 7.3c on a theme by Handel) No. 2, Op. 100/III 3–4 /theme 92 259, Ex. 9.13e __/Var. 1 92 ______m. 47 257 __/Var. 5 92 Symphonies __Fugue, mm. 7–8 No. 1/I 9–13 99, 158, 292, Ex. 7.33c 243, 279, 283, Ex. 8.42d Op. 39 (Waltzes)/No. 2 125 ____ 327–9 12, 110, Ex. 1.8b ____/No. 4 5–8 134, 151 ____ retransition 151, Ex. 7.21 Op. 76,2 (Capricico) middle No. 2/I 14–41 223, Ex. 8.12 section 197 ______78–82 Op. 76,4 (Intermezzo) 148, 178, 206, Ex. 7.14b 69, 103, 210, 296, Ex. 7.113 ______127–55 184 Op. 79,1 (Rhapsody), theme 42 ____ coda 148, 206, Ex.7.108b Op. 116,1 (Capriccio) ____/II 55–56, 60–61 243 206, 291, Ex. 7.109 ____/IV 7–24 126, Ex. 6.12e Op. 116,3 (Capriccio) outer No. 4/I theme 224, Ex. 8.13f sections 209, Ex. 7.112 ______27–31, 113–17 Op. 116,6 (Intermezzo) 42 135, 187, Ex. 6.26b __13–14 49, 78, 222, Ex. 8.9d ______81–85 53 Op. 117,2 (Intermezzo) 7–8 130 ____/II 96–97 86 Op. 118,3 (Ballade) 15–17 Tragic Overture. background 90 120, 164, Ex. 6.1c ______37–38 222 Op. 119,1 (Intermezzo) 24–37 ______140–1 135 178 Trios for Piano and Strings ____ 25–26 183 Op. 8/IV (both versions) theme Quartet (Strings), Op. 51,2/II end 268 87 __ (rev. version) 304–5 243 Quintet (Strings), Op. 88/II 13–16 Op. 87/IV theme 247, Ex. 8.48a 236

Index 335

BRAHMS, JOHANNES—contd. ______40–55 99 Variations on a Theme by Haydn ______73–75 87 Var. 3 123 Op. 10,11 m. 15 259 Var. 7 183, Ex. 7.84d Op. 10,12 introduction Wie bist du, meine Königin 26, 99, 198, 267 (song), Op. 32,9, mm. 15–20 ______m. 28 267, Ex. 10.1 87 Op. 25,3 background 100 Bruckner, Anton Op. 25,5 1–9 132 Symphonies Op. 25,5 7–8 132 No. 1 [Linz version]/III 25–44 Op. 25,11 17–19 146 276, Ex. 10.10e Trois nouvelles Études No. 2 No. 3/III 39–42 276 coda 61–63 164, Ex. 7.47 No. 7/II 176–85 194 Fantasy, Op. 49 119–54 293 No. 9/II 1–43 Mazurkas 84, 287, 294, Ex. 10.24c Op. 6,1 theme 285 Vexilla Regis (motet) 29–30 265 Op. 17,1, mm. 9–10 128 Carnival of Venice (traditional tune) Op. 17,2, mm. 43–49 207 105, 256, Ex. 9.9b CHOPIN, FREDERICK FRANCISZEK Op. 17,3 17–25 215, 219, 222, Ballades 223, 245, Ex. 8.9f No.1, Op. 23 27–28, 68–71 Op. 17,4 theme 77 241, Ex. 8.38f ______m. 7 121 No.3, Op. 47 theme Op. 24,2 75–88 180, Ex. 7.77c 131–2, Ex. 6.21b __ coda 95, 179, 180, Ex. 7.77a Op. 30,4 1–4 127, 232 No.4, Op. 52 92–99 ______retransition 127 222, 240, Ex. 8.36b ______end 91 Barcarolle, introduction 155, 163 Op. 41,3 background 84, 90 ______, 28–33 Op. 50,2 1–8 141, Ex. 7.2b 138, 154, 183, 289, Ex. 7.28d ______61–62 175 Berceuse 3–7 65, 142, Ex. 3.19 Op. 59,1 17–21 173 Bolero Op. 59,2 82–84 6 155–72 102, Ex. 4.23b _____ 97–101 193, Ex. 7.97b 176–87 284 Nocturnes Etudes Op. 9,1 52–61 196 Op. 10,3 3–4 12 ______end 100 ______22–42 Op. 9,2 3–4 138, 157, 230, 291, Ex. 7.29d 65, 174, 177, Ex. 7.68e ______38–41 Op. 15,2 m. 12 130 157, 230, 239, Ex. 8.34c ___ middle section 64,127,170, Op. 10,5 23–40 186, 197, Ex. 7.71a 41, 151, 230, Ex. 7.3d Op. 27,1 m. 17 Op. 10,6 33–41 129 100, 268, Ex. 4.22c Op. 10,8 middleground 93 ______65–83 220, Ex. 8.7g

336 Index

CHOPIN, Nocturnes—contd. Chorale St. Anthony (previously Op. 27,2 18–25 144, Ex. 7.8d attributed to Haydn) 11–15 __38–46 57,226,229,Ex. 8.24c 93, 111, 127, 314 Op. 32,1 m. 62 276, Ex. 10.8b Couperin, François Op. 62,2 1–7 81, Ex. 3.23b Pièces de Clavecin 1, Ordre 3. La Polonaises Favorite m. 3 179, Ex. 7.76b3 Op. 26,1 33–41 Dvořak, Antonin 126, 194, 195, Ex. 7.99c Silhuoutte for Piano, Op. 8,5 40 ______54–56 Ex. 6.25d Fauré, Gabriel Op. 26,1 58–65 246, Ex. 8.47 Quartet for Piano and Strings, Op. 26,2 19–20 132 No. 1, Op. 15/IV 145 276 Op. 71,2 82–89 149 Songs Preludes Arpège, Op. 76,2 Op. 28,4 background 98 180, Ex. 7.78a Op. 28,6 5–14 43 Chanson, Op. 57,1 Ex. 7.95b1 Op. 28,9 m. 6 Ex. 6.12d La fleur qui va sur l'eau, Op. Op. 28,23 end 45 85,2 32–34 182, Ex. 7.79f Scherzos Mirages, Op. 113. No. 1–Cygne No. 1, Op. 20 37–44 sur l'eau m. 10 132, Ex. 6.9d 223, 224, Ex. 8.10f Fischer, Johann Kaspar Ferdinand _____ 112–27 Ex. 8.6a Fugue No. 10 156 _____ 332–41 168, Ex. 7.101a Franck, Cesar No. 2, Op. 31 introduction 184 Symphony/I 7–8 218 _____ 53–56 168, Ex. 7.54c ______/II 7–8 130 _____ 265–74 Ex. 9.21a Gluck, Christoph Willibald _____ coda 736–55 160, 170, Orfeo ed Euridice 190, Ex. 7.39c Act 1/I 7–8 257 No. 3, Op. 39 247–9 141 /Aria: Che faró 154, Ex. 7.24c ______526–40 253 Grieg, Edvard No. 4, Op. 54 317–21, 641–45 Lyric Pieces 189 Op. 12,8 (National Song) 1–8 ______65–73 258 252, 259, Ex. 9.2 Sonatas Op. 38,1 (Berceuse) 51–61 No. 2/I 39–40 144 189, Ex. 7.93a ______122–25 291, Ex. 7.31e Op. 54,4 (Notturno) 47–54 163 No. 3/IV 188–90 189 Stimmungen, Op. 73. No.5– Waltzes Study, 8–15 285, Ex. 10.22a Op. 34,1 1–17 144, Ex. 7.8c Halévy, Jacques François Fromental ______second section 65 La Juive. Overture 107–29 Op. 34,3 9–17 217, 218, Ex. 8.4f 108, 156, Ex. 7.28c Op. 42 m. 238 169 Op. 64,3 59–60 and 63–64 242 Op. 69,1 55–6 Ex. 7.76a2

Index 337

HANDEL, GEORG FRIEDRICH ______74–80 162, Ex. 7.42c Fugue for Keyboard, No. 6, Op. 77,1/III background 272 mm. 6–7 119 Die Schöpfung. Die Vorstellung The Messiah. No. 3—Every Valley des Chaos 3–5 28, Ex. 2.4 Shall Be Exalted, m. 39 Ex. 7.6c Sonatas for Piano _____ 67–68 142 Hob. XVI:22/I 14–16 167 No. 13—Pastoral Symphony, ______60–67 m. 7 32 151, 167, 183, Ex. 7.19f Sonata for Flute and Piano, Op. Hob. XVI:26/I 6–8 40 1,5 Bourrée 17–18 141 ______11–14 119, Ex. 6.1b Suites for Keyboard (collection 1), Hob. XVI: 32/III 147–50 Suite No. 3/Prelude Ex. 7.99b 133, Ex. 6.23a ______/Allemande m. 18 Hob. XVI: 43/I 28–32 124, 188, Ex. 6.9a 155, Ex. 7.26a ____ (collection 2), Suite No. 1/ ______/III 50–56 Prelude 39, 194–5 127, 140, Ex. 6.15b Hassler, Leo Hob. XVI: 52/I 44–51 Lustgarten. Chorale No. 24 1–12 271, Ex. 10.5a 25, 40, 94, 96, 134, Ex. 4.13 Symphonies HAYDN, JOSEPH No. 55/I development 193–4 Quartets (Strings) No. 84/I 20–26 264 Op. 20,2/I 42 276, 277 No. 92 (Oxford)/I rcp. bridge ______64–76 155–70 181, Ex. 7.78f 222, 240, 261, Ex. 8.10c No. 94 (Surprise)/I transition _____/II 23–26 231, Ex. 8.27a from slow introduction _____/IV countersubject 156 183, 199, Ex. 7.82b Op. 33,3/I retransition 204 No. 99/I slow introduction 199 ______/IV 59–62 Ex. 6.25c ______development 123 Op. 55,1/I dev. 204, Ex. 7.107a No. 100 (Military)/I 157–66 ______/IV 100–6 (retr.) 168 280 Op. 55,2/III 84–88 163, 164 No. 104 (London)/I retransition ______/IV dev. 204, Ex.7.107b 97–98 177, Ex. 7.75d4 Op. 64,1/I 133–47 49 ______/II theme 9–14 6 Op. 64,3/I 132–8 165, Ex. 7.49 ______exposition. bridge Op. 64,3/IV theme 1–2 200, Ex. 7.104a 166, Ex. 7.50c ______rcp. bridge 114, 116, ____ 35–59, 162–96 114, 165, 192, 200, Ex. 7.104b 169, 178, 290, Ex.7.50a-b ______/III background, Op. 71,3/I coda 284–300 272, 289, Ex. 10.5c 223, Ex. 8.10e ______/IV 73–80 173 Op. 74,2/III background 272 Trio for Piano and Strings, Op. 76,4/I 128–9 175,Ex. 7.70a Hob. XV:28/II m. 5 39 ______/II 70–71 Ex. 8.38a Variations for Piano in F minor Op. 76,6/II 64–86 11 coda 197–201 168, 170, 175

338 Index

Humperdinck, Engelbert Quintet (Strings), Op. 18/I end of Hänsel und Gretel. Hexenfahrt exposition 240, Ex. 8.37f 47–50 150, 176, Ex. 7.72 Sextet for Piano and Strings, Joplin, Scott Op. 110/I retransitions 292 Bethena 69–76 259 Sonata for Cello and Piano, No. 2, March Majestic m. 71 146 Op. 58/IV introduction 292 Liszt, Franz ______56–59 183 Faust Symphony/I introduction 75 Sonata for Violin and Piano, Op. Piano Works 4/I 26–29 222 Années de Pèlerinage. 2nd year. Songs Sonetto 104 del Petrarca 1–5 Die Liebende schreibt, Op. 86,3 185, 189, 303, Ex. 7.92b 28–33 168 Bagatelle ohne Tonart 75 Frage, Op. 9,1 1–3 189 Nuages Gris background 123 Morgengruß, Op. 47,2 m. 6 154 Sonata in B minor introduction ______m. 30 168, Ex. 7.54b 239, Ex. 8.34d Reiselied, Op. 34,6 45–48 ______415–31 177, Ex. 7.74d 149, 158, 295, Ex. 7.15 Die Trauer-Gondol No. 1 75 Songs Without Words Die Trauer-Gondol No. 2 75 Op. 30,4 theme 173, Ex. 7.67a Unstern 75, 190, Ex. 7.93b Op. 30,6 21–29 113, 264 Songs ______35–38 129 Anfang wollt’ ich fast verzagen Op. 38,4 postlude 174 18–21 148 Op. 53,1 1–24 Blume und Duft 1–4 172, 198, Ex. 7.65e 186, Ex. 7.88d Op. 53,6 3–4 168 Die Loreley 2–3 224 ______3–18 208 Mahler, Gustav Op. 62,1 99, Ex. 4.21 Kindertotenlieder. No. 1—Nun Op. 62,3 21–26 230, Ex. 8.26c will die Sonn’ so hell aufgehn Op. 67,1 18–23 219, Ex. 8.5f 105, 255, Ex. 9.6 Op. 102,2 8–9 11, Ex. 1.6b MENDELSSOHN, FELIX Op. 102,4 19–20 168 Concerto for Violin/I 210–23, Symphonies 459–72 146–7 No. 3 (Scottish)/I 223–36 223 Overtures No. 4 (Italian)/III trio 77–92 Die Hebriden 69–77 191, Ex. 7.96b 244, Ex. 8.44d Trio for Piano and Strings, Die Hochzeit des Camacho, No. 1, Op. 49/I 89–91 233 247–63 140, 156, Ex. 7.27c _. retransition, coda 254, Ex. 9.5d Quartets (Strings) ___/III 65–106 281, Ex. 10.18a Op. 13/I beginning of dev. ___/IV 236–40 278, Ex. 10.12e 85–99 235, 245, Ex. 8.31a __234–6 Ex. 6.21d Op. 44,2/I 228–35 281, Ex. 10.16c

Index 339

MOZART, WOLFGANG AMADEUS _____/IV theme 89 Adagio for Piano, K. 540 m. 1 221 K. 575/I development 204 ______m. 30 121, Ex. 6.4c Quintets (Strings) An Chloe, K. 524 44–47 169 K. 515/I bridge 283 Concertos for Horn _____/IV 118–34, 375–90 271 No. 1, K.412/I 86–89 Ex.7.75c1 K. 516/I 105–6 167 No. 2, K. 417/I 81–112 _____/III 64–65 147 282, Ex. 10.18b K. 593/I transition to dev. No. 3, K.447/I 85–104 245,281 194, Ex. 6.26c Concertos for Piano _____/IV 104–12 89 K. 271/III minuet (=233–304), ______116–31 168 episode (=328–44) 129 ______128–32 135, Ex. 6.26d K. 459/III 255 ff. etc. 207 Rondo for Piano, K. 485 53–95 K. 488/I 295–7 220, 293 (esp. retransition) 97, 133, K. 491/I 5–8 221 320, Ex. 4.19c, Ex. 6.23c ______112–4 253 Sonata for Violin amd Piano, ______220–40 235, Ex. 8.31d K.376/III 18–20 155 K. 595/I 38–40, 56–59 43 Sonatas for Piano ___ 157–60 259, Ex. 9.13b K. 280/I 7–12 154 ___178–84 221, 245, Ex. 8.45b ______13–17 142, Ex. 7.4b Eine kleine Nachtmusik, K.525/IV _____/II 26–27 221 14–32, 91–99, 127–31 98 _____/III theme 97 Fantasies for Piano K. 282/I m. 19 278 K. 394 m. 45 282 K. 283/I m. 12 120 K. 475 mm. 12–13 196 K. 284/I 29–34 Operas 124, 259, Ex. 6.9b, Ex. 9.14b Don Giovanni. No. 10—Or Sai _____/II m. 12 124 77–79 (=8–10 of the aria) 133 K. 309/III 52–57, 157–61 167 Le Nozze di Figaro, Overture. K. 310/I 24–25 129 101–102 143 ______54–56 283 Die Zauberflöte. No. 3—Dies ______70–73 111 Bildniss 1–6 111, Ex. 5.6a K. 311/II 3–4 12 ___ No. 15—In diesen heil’gen K. 330/I 84–86 175 Hallen 1–2 132, Ex. 6.22a ______112–7 43 Quartet for Piano and Strings, ______retransition 292 K. 493/I 36–39 191 _____/III 169–70 129 Quartets (Strings) K. 331/I theme 40 K. 387/IV 273–4 143 ______10–12 128 K. 421/I beginning of dev. ______41–48 32 133, 193, 273, Ex. 10.6b ______132–45 43 _____/II 31–50 114 ____/III 3–4 259, Ex. 9.14a K. 464/I 1–37 271, Ex. 10.4a K. 332/III 96–101 169,Ex. 7.56 ____ retansition 168, Ex. 7.52e K. 333/I dev. 126, Ex. 6.13c K. 465/III theme 155 ______retransition 87–93 167

340 Index

MOZART, Sonatas (piano)—contd. Ravel, Maurice K. 333/I 147–8 Ex. 7.95a3 Jeux d’eau 1–7 266, Ex. 9.22b K. 457/I m. 8 87 Rubinstein, Anton ______230–1 218 Das fallende Sternlein 29–34 _____/III 21–23 222 218, Ex. 8.3e ______121–5 283 Scarlatti, Domenico K. 533/I 135–8 160 Sonatas for Keyboard _____/II 63–71 K. 458 15–16 161 98, 164, 182, Ex. 7.46 K. 471 51–54 132, Ex. 6.22b K. 545/I development 201 K. 480 73–78 168 K. 576/I 61–62 167 K. 483 29–36 37 ______68–69 168 K. 501 69–70 133 ______152–3 220, Ex. 8.7d K. 502 60–67 259 _____/II 17–43 130 K. 507 26–33 140 ______42–43 130 K. 513 6–7 171 Symphonies Schoenberg, Arnold No. 35, K. 385 (Haffner) Piano Piece Op. 19,1 82, 84 ____/I 1–13 87, Ex. 4.4b Songs ____ 56–57 164,291,Ex. 7.48b Das Buch der Hangenden ___/II 21, 27 38 Garten, Op. 15. No. 2—Hain ___/III 33–35 178 in diesen Paradiesen 82 ___/IV 71–79 87 Gurrelieder. No. 1—Nun No. 36, K. 425 (Linz)/I dämpft die Dämmerung jeden 161–3 143, Ex. 7.8a Ton 134, Ex. 6.24d No. 38, K. 504 (Prague)/I Pierrot Lunaire. No. 8— 92–94 239 Nacht, m. 8 83, Ex. 3.24 _____/II 1–35 271, Ex. 10.4b Traumleben, Op. 6,1 1–3 161 No. 39, K. 543/IV 62–65 134 Verklärte Nacht, mm. 19–26 257 No. 40, K. 550/I theme 1–9 SCHUBERT, FRANZ 111, 113, Ex.5.6b Dances for Piano _____ 34–37 168 Ecossaise D, 781,8, mm. 9–14 _____ 59–62 179 38, 143, Ex. 7.7 ____ 150–52 63,177,Ex. 7.74b German Dance D. 783 (Op. ____ /II 54–59 178 33),11 5–8 17, Ex. 1.11 ______development 204 Valse Noble, D. 969 (Op. 77), 5 ____/IV 125–32 221 131, 151, 194 Trio for Piano and Strings, Waltzes, D. 365 (Op. 9)/No. 2 K. 496/II 30–33 283 9–13 271 Mussorgsky, Modest _____/No. 4 65 Be Bored 28–29 286 _____/No. 11 end 65 Puccini, Giacomo Tosca. Act 1, scene 1 37–39 147, Ex. 7.13b

Index 341

SCHUBERT, FRANZ—contd. _____/II 73–83 Impromptus for Piano 160, 161, Ex. 7.39b D. 899 (Op. 90),1 18–20 _____/IV m. 7 259 221, Ex. 8.8c D. 960/III 1–8, 77–84 ______,2 38, Ex. 2.13a 143, 190, Ex. 7.8b ______,3 40–46 220, Ex. 8.6f Songs D. 935 (Op. 142),3 theme 99 Daß sie hier gewesen, D. 775 Moments Musicaux for Piano, (Op. 59,2) mm. 1–2 D. 780 (Op. 94) 217, 218, Ex. 8.3c No. 2 1–36 130, Ex. 6.19c Der Alpenjäger, D. 588 113 No. 6 65–70 245,281,Ex. 10.17 Der Kreuzzug, D. 932, Quartet (Strings), D. 887 (Op. mm. 3–4 258 161)/I bridge 189, Ex. 7.92a Der Schiffer, D. 694 130 Quintet (Strings), D. 956 (Op. Die Wintereise, D. 911. No. 3 – 163)/I 289–94 194 Gefror‘ne Thränen 41–49 _____/II 91–93 280 280, 284 Quintet for Piano and Strings _____. No. 12—Einsamkeit (Forelle), D. 667 (Op. 114) 29–34 280, 284, Ex. 10.20b _____/I 129–43 150 _____. No. 20—Der Wegweiser ______/II 43–52 169 41–67 187, 233, 234, Sonatas for Piano 238, 244, 245, Ex. 8.29 D. 279/I 104–13 262, Ex. 9.18 Nacht und Träume , D. 827 (Op. D. 575 (Op. Posth. 147) 43,2) 15–19 217 ______/II 77–79 87 Schwanengesang, D. 957. No. _____/III middle section 28–51 5—Aufenthalt 51–55 291, Ex. 6.13b 105, 266, 287, Ex. 10.24b D. 664 (Op. 120)/III 67–79 _____. No. 11—Die Stadt 148, Ex. 7.14c 38, Ex. 2.13b D. 784 (Op. 143)/I 158–60 Wandrers Nachtlied, D. 224 Ex. 7.5b (Op. 4,3) m. 2 142, Ex. 7.5a D. 845 (Op. 42)/I 10–24 Symphonies Ex. 10.15b No. 4 [Tragic]/I theme 30–39, ____ bridges 149, 186, Ex. 7.17 156–60 227, Ex. 8.19c ____ coda 262–8 272 No. 8 [Unfinished]/I m. 16 244 D. 850 (Op. 53)/I development Trios for Piano and Strings 204 No. 1, D. 898 (Op. 99)/I D. 894 (Op. 78)/I 52–54 207–18 208, Ex. 7.111d 147, Ex. 7.12b ___/III trio and retransition 129 D. 958/IV 145–69 9, Ex. 1.4 No. 2, D. 929 (Op. 100)/II ______323–49 256, Ex. 9.8c 84–114 283 D. 959/I theme 1–13 Schumann, Clara 157, 292, Ex. 7.31g Romance Op. 11,2 179, Ex. 7.76a6 ____ retr. m. 197 146, Ex. 7.11 ____ coda 350–53 101

342 Index

SCHUMANN, ROBERT ___. No. 5—Freundliche Concerto for Cello/I m. 61 148 Landschaft 211 ______135–36 220 Quartet (Strings), Op. 41,3/I 1–11 Piano Works 260, 292, 293, Ex. 9.15b Albumblätter for Piano, Op.124. ____/IV 236–81 No. 9— Impropmptu, 260, 279, 293, Ex. 9.16 mm. 1–4 175, Ex. 7.70e Quintet for Piano and Strings, Op. Album für die Jugend, Op. 68. 44/I 50–57 261, Ex. 9.17b __. No. 3—Trällerliedchen _____ 103–7 174 m. 1 40, Ex. 2.16 ____retransition 53,159,Ex. 7.37b __.No. 28—Errinerung Songs m. 20 218 Dichterliebe, Op. 48. No. 7— __.No. 41—Nordisches Lied Ich grolle nicht 9–11 m. 13 43 152, Ex. 7.22d Davidsbündlertänze, Op. 6. Frauenliebe und -Leben, No.6, mm. 12–15 246 Op. 42. No.2—Er, der ______41–48 222, Ex. 8.9c herrlichster von Allen 28–31 Fantasy Piece, Op. 12,2— Ex. 7.39g Aufschwung 1–2 130, Ex. Liederkreis, Op. 39. No. 8—In 6.18a der Fremde 1–17 Ex. 7.101b Faschingsschwank aus Wien, Symphony No. 1/II 10 Ex. 9.5c Op. 26/I 356–64 127 Trio for Piano and Strings, No. 3, ___/III 97–102 Op. 110/I 32–38 190, Ex.7.94 161, 183, 290, 296, Ex. 7.40b Skryabin, Alexander Humoresque, Op. 20 121–31 Enigme Op. 52,2 background 75, 265, Ex. 9.22a 286, Ex. 10.23 ______306–13 196 Mazurka for Piano, Op. 25,6 7–15 Kinderscenen, Op. 15 263, Ex. 9.20b __. Nos. 2–5 211, Ex. 7.114 Poems for Piano __. No. 8—Am Kamin 9–16 Op. 32,1 implicit opening 84 138, 166, Ex. 7.51 Op. 32,2 implicit opening 84 __. No. 13—Der Dichter Preludes for Piano spricht 10–12 223, Ex. 8.11c Op. 11,9 260, Ex. 9.15a Novelettes, Op. 21. No. 2, mm. Op. 11,22 5–6 145, Ex. 7.9d 83–90 182,185,Ex. 7.87c Strauss, Josef __. No. 3 42–45 135, Ex. 6.26e Dynamiden 39–40 121 __. No. 5 222–8 176, Ex. 7.73d Strauss, Richard __. No. 8 1–4 230, Ex. 8.25 Elektra 1–2 after no. 27 81 Romance, Op. 28,3 44– 48 244 Der Rosenkavalier. Act 1, 1–5 ______152–167 168 after no. 42 261, Ex. 9.17c Waldscenen, Op. 82. No. 1— Till Eulenspiegels lustige Streiche Eintritt 8–17 198, Ex. 7.82c 46–49 287, Ex. 10.24a __. No. 4—Verrufene Stelle 12– __ 67–68 176, Ex. 7.73c 13 176, 178, 186, Ex. 7.71e

Index 343

Stravinsky, Igor Parsifal. Prelude to Act 3 Concerto for Piano and Winds/I 1–4 and background rehearsal number 11 64,Ex. 3.18 75, 224, 246, 248, Ex. 8.50 Le Sacre du Printemps. 38–43 224, 248, Ex. 8.13g Introduction 1–9 81, Ex. 3.23a Rienzi. Act 3. Allegro molto Tchaikovsky, Pyotr Il’yich 46–50 149 Album for the Young Tristan und Isolde No. 2—A Winter Morning 21– Prelude, mm.3–4 135, Ex. 6.26a 38 276, Ex. 10.11d ______79–89 83, Ex. 3.25 No. 7—The Doll's Burial Act 2, Scene 2, mm. 546–550 theme 40 151, Ex. 7.19h No. 12—The Peasant Plays the ____ 554–77 162, Ex. 7.41d Accordion 195, Ex. 7.100 Prelude to Act 3, 30–31 73 No. 19—Nursery's Tale Act 3, Scene 1 51, Ex. 3.7 275, Ex. 10.7c Weber, Carl Maria von Iolanta. Introduction 16–19 146 Der Freischütz Orchestral Suite No. 3/II coda No. 9—Terzett 180–92 278–321 283, Ex. 10.19c 282, Ex. 10.19b Symphony No. 5/I 140–9 261 No.10 (Act 2, Finale) /Die ______/II 18–20 261, Ex. 9.17c Wolfsschlucht scene 13–35 ______39–41 253 247, Ex. 8.48b ______/III 57–60 147 _____/Melodram. 108 The Seasons. No. 1—January Wolf, Hugo 47–53 278, Ex. 10.13c Italian Songbook. No. 10–— Verdi, Giuseppe Du denkst mit einem Fädchen Aida. O Terra Addio 106 mich zu fange 196 Otello Mörike songs Act 1, Storm Scene up to No. 18—Citronenfalter in victory chorus 249 April 1–4 169, Ex. 7.57b Act 4 23–26 147, Ex. 7.12c No. 22—Seufzer 1–10 ____ Finale 37 48, 275, 296, Ex. 10.7d Wagner, Richard No. 23—Auf ein altes Bild 1–4 Die Meistersinger von Nürnberg. 262, Ex. 9.19a Act 2, scene 3 184, Ex. 7.86 Spanish Songbook. Spiritual Song Der Ring des Nibelungen. Destiny No. 9—Herr, was trägt der motive 130 Boden hier 1–6 165, Ex. 7.48c Das Rheingold. Scene 4, 62 ______9–12, 19–22 165 measures from the end 22 Götterdämmerung. Prologue (Norns’ scene) 259–77 255, 257, Ex. 9.11 __. Act 3. Immolation scene 9