Harmonic Function in the Late Nineteenth-Century Chromatic Tonality of Wagner and Strauss: a Study of Extensions to Classical Prolongational Practices

Home , Chromatic mediant, Diatonic and chromatic, Diminished third, Neotonality, Notturno (Strauss), Predominant chord

Harmonic Function in the Late Nineteenth-Century Chromatic Tonality of Wagner and Strauss: A Study of Extensions to Classical Prolongational Practices

Kyle Hutchinson

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Faculty of Music University of Toronto

Harmonic Function in the Late Nineteenth-Century Chromatic Tonality of Wagner and Strauss: A Study of Extensions to Classical Prolongational Practices

Kyle Hutchinson

Doctor of Philosophy

Faculty of Music University of Toronto

2020

Abstract

That mid-to-late nineteenth-century chromatic tonality challenges diatonic-based prolongational models of tonality is a well-known assertion. Recently, the field has embraced alternative frameworks, especially neo-

Riemannian and transformational approaches, to account for coherence in the works of composers such as Richard Wagner or Richard Strauss. These approaches, however, only occasionally capture the extent to which this repertoire exhibits the prolongational procedures operative in classical tonality despite the unfamiliarity of the chromatic syntax.

My dissertation investigates how this chromatic syntax can be approached as an extension of familiar diatonic models. My broader theoretic basis involves recognizing a proliferation of harmonic polysemy, whereby chords that have commonplace sonorities do not function in ways traditionally associated with that sonority. To account for this disjunction, I develop a model of Functional Interval Progressions (FIPs), which proposes dominant function is a product not of sonority, nor an isolated leading tone, but rather a combination of a univalent dissonance (a tritone or diminished seventh) combined with its conventional resolution: in short, I suggest function is a product of motion.

I apply this principle in various ways. Firstly, I postulate the possibility of chromatically altered diminished-seventh chords: these chords often have the sonority of commonplace tonal chords, such as

ii dominant or half-diminished sevenths, but their behaviour is more consistent with diminished-seventh chords. The presence and resolution of a diminished-seventh interval, I posit, overwrites the centrifugal nature of the chromatic alteration. I then export this principle to triads, arguing that a similar half- enharmonic reinterpretation can explain what Lorenz (1933) refers to as apparent consonances. Contrary to Cohn (2004/2012), I view these triads then as tonal dissonances, rather than as acoustic consonances.

Lastly, I argue for a contextual remodeling of chordal inversion, following Schenker’s (1922) notion of

“the roothood-tendency of the lowest tone,” suggesting that in certain cases inverted chords project the function of their bass, rather than their root. I conclude by applying these principles to larger-scale analysis, proposing that through a more thorough understanding of the surface-level harmonic syntax, deeper-level prolongations— and their relationships to one another—can be adduced with greater certainty and clarity in highly chromatic music.

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Acknowledgments

Seven is an important number for several reasons, and so I want to split the acknowledgments and dedication seven ways:

1. My Parents, Virginia and Ron, whose love and support helped me through these past 23+ years of school, as well as the rest of my family who have also been a source of support. Thank you for everything you’ve done.

2. My advisor, Professor Ryan McClelland, who kept me focused, on track, and offered numerous valuable insights throughout the last six years. Thank you for putting up with me, and fixing all of my run-on sentences: there were many, especially at the beginning, a lot of which had to do with my overuse of the colon construction, but it got better, I think, over the last five years.

3. Don McLean, our incredible Dean, who supported me in numerous ways over the last six years, offered me an abundance of his valuable insight, and made it possible for me to finish this degree.

4. Professor William Marvin (Eastman School of Music), my external reviewer who offered valuable suggestions and insight in this last stage of my dissertation, as well as Professor Steven Vande Moortele and Professor Sherry Lee, my other two committee members, who also offered a wealth of guidance on issues I often hadn’t considered.

5. Tyler my best friend of 23+ years, without whom I may have lost my mind.

6. My friends here at U of T who have been around since the beginning: Matthew, Melissa, Adrian, Massimo. Our discussions about music, Star Wars, puppies, and food have been highlights of my time here (even if we occasionally terrified the people around us with our passionate arguing about harmony…)

7. Finally, all of the students who I taught over the years, many of whom have become good friends. I’ve always said teaching was the best part of every week, and I’m grateful to have met every one of you; you’ve made my time here at U of T better than it otherwise would have been, and I think have made me a better person. Thank you.

Table of Contents

Abstract………………………………………………………………………………………………….ii

Acknowledgements……………………………………………………………………………………..iv

List of Tables….……………………………………………………………………………………….vii

List of Examples………………………………………………………………………………………viii

List of Figures…………………………………………………………………………………………..xi

Introduction. The “Prolongation” Problem in Late Nineteenth-Century Chromatic Music, and the Ontological Implications of Theories of Tonal Music ...... 1

Chapter 1. Dissociating Sonority and Function: Harmonic Polysemy and Chromatically Altered Diminished-Seventh Chords in Late Nineteenth- and Early Twentieth-Century Tonality ...... 45

I. A Theory of Chromatically Altered Diminished-Seventh Chords……………………….....……49

II. Historic Interlude……………………………………………………………………….………...64

III. Analytic Applications……………………………………………………………………….……71

IV. Two Vignettes from Parsifal ...... …97

Conclusion………………………………………………………………………………………105

Chapter 2. When is a Triad not a Triad?: Acoustic Consonance, Tonal Dissonance, and the Dialogue Between Neo-Riemannian and Prolongational Theories of Tonality…………..……...... 108

I. Acoustic Consonance, Tonal Dissonance I: Major Triads……………………………………...113

II. Acoustic Consonance, Tonal Dissonance II: Minor Triads…………………………………….131

III. Three Vignettes Regarding Apparent Consonance…..……………………………………...... 142

Conclusion……………………………………………………………………….……………...156

Chapter 3. The Abnegating-Sixth Chord and its Extensions: Deriving Late Nineteenth and Early Twentieth-Century Harmonic Extensions from Linear Displacements……..…………….159

I. Theoretic Preliminaries and Schenker’s “Roothood Tendency of the Lowest Tone” ...... 161

II. Abnegating-Sixth Chords …...…………………………………….…………………………...167

III. Strauss’ Extensions to Abnegating Chords ……………………………...…………………….182

Conclusion: Elektra, Modernism, and Approaching Tonal Rupture...... 198

Chapter 4. Leitmotivic Auskomponierung : Structural Coherence in Late Nineteenth- and Early Twentieth-Century Music………………………………………………………………..…...…. 214

I. The Schenkerian Ursatz : Organicism, Ontology, and Analytic Viability...... 220

II. The Generative Fundamental...…………………………………….…………………………...229

III. Leitmotivic Auskomponierung …………………………………………………………………242

IV. Parsifal , Prelude…………………………………….………………………………………….249

V. Salome , Scene 1………………………………………………….……………………………..262

Conclusion………………………………………………...... 274

Conclusion ………………………………………………………………………………………….. 278

Bibliography…………………………………………………………………………………………288

List of Tables

1.1. Variants of B-D-F-Af (vii o7 in C), and Polysemic Analyses ……………………………………….57

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List of Examples

0.1. Schoenberg’s Analysis of a Passage from Strauss’ Salome ……………...….………………………….17

0.2. Wagner, Tristan und Isolde , Act I, Scene 2, mm. 24–30……………………....………………………..31

1.1a. Liszt, “Ich möchte hingehn,” m. 125………………………………...…………………………….46

1.1b. Wagner, Tristan und Isolde , mm. 1–4………………………………………………...……………....46

1.2. Strauss, “Befreit,” mm. 1–7……………………………………………...………………………….58

1.3. Strauss, Eine Alpensinfonie , RH32……………………………………………...……………………..69

1.4. Strauss, Der Rosenkavalier , Act III, 6 mm. before RH 285…………………...……………………….72

1.5. Strauss, Till Eulenspiegels lustige Streiche , mm. 46–49…………………………………………………...73

1.6. Strauss, “All mein Gedanken,” mm. 23–31………………………………...………………………..76

1.7a. Strauss, Eine Alpensinfonie , RH88………………...………………………...………………………..79

1.7b. Strauss, Elektra , 2 mm. before RH232…………………………………...…………………...... …81

1.7c. Strauss, “Befreit,” mm. 16–23……………………………………………...………………………81

1.8. Wagner, Götterdämmerung , Act I, Scene 3, mm. 1237–1240……………………………...…………....83

1.9. Wagner, Götterdämmerung , Act III, Scene 3, mm. 1155–1160…………………...... 87

1.10. Strauss, Salome , RH6.2–RH7.2…………………………………………………………...………....89

1.11. Strauss, Guntram . Act I, Scene 1, mm. 1–7…………………………………………..….………...... 91

1.12. Strauss, “Notturno,” mm. 56–67…………………………...……………………………………....92

1.13. Strauss, Salome , Dance, 11 mm. Before RHQ……………………………………………………....93

1.14. Strauss, Elektra , Just Before RH257a………………………………………………………………95

1.15. Wagner, Parsifal , Act I, mm. 1297–1303…………………………………………………………....98

1.16. Wagner, Parsifal , Act II, mm. 67–88……………………………….....………………..…………..101

2.1. Wagner, Tristan und Isolde , Act I, Scene 2, mm. 24–30……………………………………………....109

2.2. Wagner, Das Rheingold , mm. 3833–3836…………………………………………………….....…....117

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2.3. Riemann’s Illustration of Tonalität from Musik-Lexicon ……………………..………………………122

2.4. Strauss, Eine Alpensinfonie , RH40…………………………………………………………………...125

2.5a. Schubert, “Am Meer,” mm. 40–42………………………………………………....……………..126

2.5b. Strauss, Sinfonia Domestica , mm. 19–28……………………………………………………………127

2.6. Strauss, Der Rosenkavalier , Act I, mm. 1–7………………………………………………………….128

2.7. Strauss, Salome , Dance, 11 mm. Before RHQ……………………………………………………....132

2.8. Strauss, Eine Alpensinfonie , 3mm. Before RH29…………………………………………....………..134

2.9a. Strauss, Der Rosenkavalier , RH7…………………………………………………………....………135

2.9b. Strauss, Der Rosenkavalier , Full Score RH6.4–7.6………………………………………………….136

2.10. Strauss, “Ich wollt ein Sträuβlein binden,” mm. 1–8……………………………………………...138

2.11. Strauss, Eine Alpensinfonie , 4 mm. Before RH100…………………………………………………140

2.12. Schubert, Piano Sonata in D major, D.850, i, mm. 1–16…………………..……………………...143

2.13. Wagner, Die Walküre , Act II, Scene 4, mm. 1–3…………………………………………………..146

2.14. Wagner, Parsifal , Act III, mm. 1098–1102………………………………………………………...149

3.1. Triads in Inversion…………………………………………………………………….…………..161

3.2. Schubert, Piano Sonata in A Major, D. 959, iii, mm. 1–8…………………………………………..162

3.3. Strauss, Don Juan, mm. 1–4………………………………………………………………………...168

3.4. Wagner, Tristan und Isolde , Act I, Scene 2, mm. 22–30……………………....………………………171

3.5. Wagner, Götterdämmerung , Act I, mm. 265–267……………………………………………….…….171

3.6. Strauss, Tod und Verklärung , mm. 175–190…………………………………………………………172

3.7. Wagner, Die Meistersinger von Nürnberg , Act I, mm. 139–150………………………………………...175

3.8. Strauss, Tod und Verklärung , mm. 67–79……………….…………………………………………...177

3.9. Wagner, Parsifal , Act II, mm. 824–845……………………………………………………………..180

3.10. Strauss, “Heimkehr,” mm. 1–15………………………………………………………………….183

3.11a. Strauss, Salome , mm. 24–31……………………………………………………………………...185 ix

3.11b. Strauss, Salome , Full Score for mm. 26–30, with voice-leading annotations……………………..187

3.12. Strauss, Der Rosenkavalier, Act III, 5 mm. before RH292…………………………………………189

3.13. Strauss, Eine Alpensinfonie , 5 mm. before RH 141………………………………………….……..191

3.14. Strauss, Der Rosenkavalier , Act III, RH 285.1–285.8………………………………………………192

3.15. Strauss, Also Sprach Zarathustra , mm. 38–49……………………………………………….……...195

3.16. Strauss, Elektra , mm. 10–13……………………………………………………………………...199

3.17a. Strauss, Elektra , mm. 14–26…………………………………………………………………….201

3.17b. Elektra , Full score. 2 mm. before RH1 to 2 mm. after RH1……………………….…….…206–207

3.18. Strauss, Elektra , RH48–RH51………………………………………………….……………...... 209

4.1a. Beethoven, Piano Sonata Op. 14, no. 1: II, 1–38……………………………….………………...232

4.1b. Beethoven, Piano Sonata Op. 14, no. 1, II, Opening of B Section…………….…………………233

4.2. Beethoven, Piano Sonata Op. 13, II, mm. 15–27………………..…………………………………237

4.3a. Schubert, Piano Sonata in B f Major, D. 960, mm. 231–258…………..………..………………….239

4.3b. David Beach’s (2017) Analysis of the Recap of Schubert’s Piano Sonata in Bb, D. 960…….…….241

4.4. Wagner, Götterdämmerung , Act II, mm. 1495–1503………………..……………….………….…….248

4.5. Wagner, Parsifal , Prelude, mm. 1–6……………………………………………………….………..251

4.6. Wagner, Parsifal , Prelude, mm. 39–43…………………………………………………….………..252

4.7. Wagner, Parsifal , Act III: mm. 1077–1087………………………………………………….……...260

4.8a. Salome’s First Motif, m. 1………………………………………………………………….…….268

4.8b. Salome’s Dance, 3 mm. before C………………………………………………………….……..268

4.8c. Salome’s Dance, 8 mm. Before Q……………………………………………………….….…….268

4.9. Strauss, Salome , Final C s PAC (3 bars before RH361)…………………………………….….…….272

5.1. Strauss, Die Frau ohne Schatten , Act III, 3mm. before RH 187………………………………….…...285

5.2. Strauss, Die Ägyptische Helena , Act I, mm. 1–10………………………………….…………………285

List of Figures

0.1. Damschroder’s Figure 1.2 (from Harmony in Schubert )……………………………………………….13

0.2. Schenker, Harmonielehre , Figure 307…………………………………………………...……………..20

0.3. Schenker, Harmonielehre , Figure 285 (Bach, Italian Concerto)………………………………………..24

0.4 William Marvin’s analysis of the Todestrank motif from Tristan und Isolde (Marvin, 2001: 18)….……....31

0.5. David Beach’s (1987) Analysis of a Passage from Beethoven Op. 2, no. 1, IV………………………34

1.1a. Analysis of Example 1.1a…………………………………………………………………………..46

1.1b. Analysis of Example 1.1b………………………………………………………………….………46

1.2. FIPs for Dominant-functioning Chords………………………………………………………...... 52

1.3. FIPs for Chromatically Altered Diminished-Seventh Chords (and sonorities)………….....…………55

1.4. Analysis of Voice Leading in Example 1.2.………………………………………………………….60

1.5. Schenker, Harmonielehre (1906), Figure 321………………………………………………………….66

1.6. Bruckner, Symphony no. 9, IV (Figure 331 from Schenker, Harmonielehre [1906]). Annotations mine…………………………………………………………………………………………….68

1.7. Analysis of Example 1.3…………………………………………………………………………….70

1.8. Analysis of Example 1.5…………………………………………………………………………….75

1.9. Analysis of mm. 27–29 of Example 1.6……………………………………………………………..77

1.10a. Analysis of Example 1.7a…………………………………………………………………………80

1.10b. Analysis of Example 1.7c………………………………………………………………………....82

1.11a. Hunt’s (2007) voice-leading analysis of Example 1.8……………………………………………...84

1.11b. My Analysis of Example 1.8……………………………………………………………………...85

1.12. Analysis of Example 1.9…………………………………………………………………………...88

1.13. Analysis of Example 1.10………………………………………………………………………….90

1.14. Analysis of Example 1.11………………………………………………………………………….92

1.15. Analysis of Example 1.13, second system………………………………………………………….94

1.16. Analysis of Example 1.14………………………………………………………………………….97

1.17. Analysis of Example 1.15……………………………………………………………….………...100

1.18. Analysis of Example 1.16……………………………………………………………….…….…..103

2.1. Schoenberg’s Analysis of Example 2.1 (Quality and Inversion Omitted by Schoenberg)….………..111

2.2a. Voice-Leading Analysis of Example 2.1……………………………………………….………….119

2.2b. Structural Analysis of Example 2.1………………………………………………….……………119

2.3. Analysis of Example 2.4……………………………………………………………….…………..125

2.4. Analysis of Example 2.5b………………………………………………………………….………127

2.5a. Analysis of mm. 1–4 in Example 2.6……………………………………………………….……..129

2.5b. Analysis of mm. 6–7 in Example 2.6…………………………………………………...... ……….129

2.6. Analysis of Example 2.7…………………………………………………………………………...133

2.7. Middleground Analysis of Example 2.8……………………………………………………....……134

2.8. Analysis of Example 2.9a………………………………………………………………………….135

2.9. Analysis of Example 2.10………………………………………………………………………….139

2.10. Analysis of Example 2.11………………………………………………………………………...140

2.11. Analysis of mm. 7–16 in Example 2.12……………………………………..……………………145

2.12. Analysis of Example 2.14………………………….……………………………………………..156

3.1. Differing Analyses of Chords containing the Interval of a Sixth……………………....…………...164

3.2. Analysis of Example 3.2…………………………………………………………………………..167

3.3. Analysis of Example 3.3…………………………………………………………………………..170

3.4. Analysis of Example 3.6…………………………………………………………………………..174

3.5. Analysis of Example 3.7………………………………………….……………………………….176

3.6a. Analysis of mm. 67–78 in Example 3.8…………………………………………………………..177

3.6b. Deep Middleground Reduction of Figure 3.6a……………………….…………………….....…..179 xii

3.7. Analysis of Example 3.9………………………....………………….….…………………....……..181

3.8. Analysis of Example 3.10……………………………………………….………………………....185

3.9. Analysis of Example 3.11a…………………………………………….…………………………..188

3.10. Analysis of Example 3.12…………………………………………….…………………………..190

3.11. Harmonic and Voice Leading Analysis of Example 3.14…………….…………………………...193

3.12a. Deep Foreground Analysis of Example 3.15…………………….……………………………...196

3.12b. Deep Middleground Analyses of mm. 39–42…………….……………………………………..198

3.12c. Deep Middleground Analysis…………………………………………………………………...198

3.13. Deep Middleground Analysis of the first 26 mm. of Elektra ………….…………………………..202

3.14. Analysis of mm. 21–24………………………………….……………………………....………..203

3.15. Analysis of the “Elektra” chord as Derived Through Linear Displacement………....……………204

3.16. Analysis of Example 3.17a……………………………………………………………………….208

3.17. Middleground Analysis of Example 3.18………………....………………………………………211

4.1. Analysis of the opening of Strauss’ Salome (to RH4)……………………………………………….224

4.2. Felix Salzer’s Analysis of Chopin’s Mazurka, Op. 17, no. 2 (Example 499 in Structural Hearing )……227

4.3. Structural Reduction Process to a Generative Fundamental……………………………………….231

4.4. Beethoven Piano Sonata Op. 2, no 1, mm. 1–8 Prolongational Bass Analysis……………....……...236

4.5. Wagner, Tristan und Isolde : Prelude, mm. 44–57 Analysis…………………………………………...238

4.6. Schubert, Piano Sonata in B f, D. 960: mm. 233–255, my analysis.…………………....……………241

4.7. Deeper-level Melodic Analysis of Schubert, Piano Sonata in B f, D.960, bars 215–286…….………243

4.8. Analysis of Example 4.5…………………………………………………………………….……..251

4.9. Wagner, Parsifal , Prelude, mm. 76–79………………………………………………………….…..253

4.10. Voice-Leading Reduction and Analysis of mm. 88–90……………………………………....……254

4.11. Tonal Structure of the D-major Section………………………………………………………….255

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4.12. Deep Middleground Analysis of the Prelude to Parsifal …………………………………………..256

4.13. Analysis of Example 4.7…………………………………………………………………………261

4.14. Foreground Analysis of Scene 1 of Strauss’ Salome ………………………………………….263, 264

4.15. Middleground Reduction of Figure 4.14…………………………………………………………267

4.16. Background Reduction of Figures 4.15………………………….……………………………….267

xiv Introduction The “Prolongation” Problem in Late Nineteenth-Century Chromatic Music, and the Ontological Implications of Theories of Tonal Music

That mid-to-late nineteenth- and early twentieth-century chromatic tonality challenges eighteenth-

and early nineteenth-century diatonic models is a well-known assertion. 1 Joseph N. Straus suggests more

specifically:

Music composed in the first half of the twentieth century is permeated by the music of the past. Traditional sonorities, forms, and musical gestures pervade even works of the past that seem stylistically most progressive. Sonorities like the triad, forms like the sonata, and structural motions like the descending perfect fifth are too profoundly emblematic of traditional tonal practices to meld quietly into a new musical context. As a result, they become the locus of a productive musical tension. They evoke the traditional musical world in which they originated, even as they are subsumed within a new musical context. 2

Straus’ study is directed towards the more atonal-leaning music of Stravinsky, Schoenberg, Webern, and

Berg, a repertoire wherein the disjunction between conventional materials used in unconventional ways is

noticeably pronounced in a way that it is not in the music of Wagner and Richard Strauss. It is not that

Wagner and Strauss use tonal materials in an atonal manner, but rather they extend what it is possible to do with tonal materials, using traditional materials, such as triads and seventh chords, in ways that appear to

contravene traditional tonal-prolongational practice, albeit in a manner far more subtle than Schoenberg and

his other contemporaries. One might indeed suggest that it is the line that Wagner and Strauss’ music toes,

between using conventional tonal materials—albeit in ways perplexing to conventional tonal analysis—and

projecting a clear sense of larger-scale tonal organization on one hand, and the hitherto inexplicable way in which these materials cohere in a tonal sense on the other, which highlights why listeners, analysts, theorists,

and musicologists continue to be drawn to, and captivated by, this music. As David Kopp has suggested,

1 Schenker’s views, in particular, are well-known: that Wagner (and by extension Richard Strauss) were not background composers is a common criticism of the composers in Schenker’s later writings (c.f. Warren Darcy, “A Schenkerian Ursatz : or, Was Wagner a Background Composer After All?” Intégral 4 [1990]). But more than just not conforming to Schenker’s (late) ideal of organic reciprocity between all levels of structure, Schenker saw a fundamental disjunction between the tonality of composers such as Mozart, Beethoven, or Schubert, and that of Wagner and Strauss. Schenker’s concerns are treated in more detail in section III below. 2 Joseph N. Straus, Remaking the Past: Musical Modernism and the Influence of the Tonal Tradition (Cambridge: Harvard University Press, 1990): 1. 1

“the chromatic music of the nineteenth century continues to provide a fascinating and elusive subject for formal theoretical explanation.” 3 But it is also this elusiveness that has led analytic discourse on this music away from organizational models based in tonality. “Of late,” Kopp writes, “the orthodoxies of past decades have given way to freer speculation. Nineteenth-century chromatic tonality as a theoretic entity is developing

an identity of its own, distinct from earlier models, and is attaining the status of a separate system or group

of evolved systems.” 4 Kopp, is, of course referring to a dichotomy between Schenkerian prolongational analysis—when he speaks of the orthodoxies of the past—and the more contemporary field of neo-

Riemannian theory.

The first chapter of Richard Cohn’s 2012 monograph, Audacious Euphony , reprises this dissatisfaction with the applicability of traditional models to late nineteenth-century chromatic music. Cohn engages with

many different aspects of music theory, both historic and contemporary, in his description of a plethora of

problems that plague tonal theory, and, diminish its abilityto function as an analytic system that can both say

and substantiate anything meaningful about the tonal structure of works written in the highly chromatic

idiom of the mid-to-late nineteenth century. Like Cohn, I believe conventional analytic approaches and techniques leave much to be desired in the analysis and understanding of both harmonic function at the musical foreground and the deeper-level tonal-structural underpinnings of highly chromatic works. But where Cohn’s discomfort with the current state of tonal theory lead him to pursue neo-Riemannian, or, as he prefers to see it, pan-triadic, perspectives (which Cohn describes as music that uses triads without recourse to diatonic scales 5) that do not integrate easily into more conventional models of tonality, my approach in this dissertation aims to find ways to more convincingly understand highly chromatic harmonic syntaxes as extensions of, rather than departures from, the organizational principles of classical tonality. 6

3 David Kopp, Chromatic Transformations in Nineteenth-Century Music (Cambridge: Cambridge University Press, 2002): 1. 4 Ibid., 1. 5 Richard Cohn, Audacious Euphony: Chromaticism and the Triads Second Nature (New York: Oxford University Press, 2012): xiv. 6 Steven Rings, for example, equates neo-Riemannian theory with “New Musicology” both in the choice of late nineteenth- century repertoire, and in the post-structuralist ways in which they approach the chromaticism as a form of disunity in the music. He writes: “Riemann analytically constructs chromatic passages so that they show conformance to his tonal theories, which he portrays as universal laws. The neo-Riemannian analyst, by contrast, constructs chromatic passages so that they appear tonally “disunified,” and thus require nontonal explanation. Riemann's theory thus places a high value on order and conformance to putative universals of tonal harmony, while neo-Riemannian theory, it would seem, values crisis and disruption of that order.” 3

Cohn offers three propositions while musing on the reasons regarding why analysis continues to frame itself to “a modified eighteenth-century beat:”

First is the promiscuity of triadic descriptive categories, combined with the illusion that to describe is to explain. Roman numerals are flexible enough to furnish a first-level description of almost any triad in almost any key…Riemannian functions likewise are catchall categories such that ‘a student of Riemann’s system could analyze virtually any chord into any one of the three functions should the occasion demand.’ (Harrison, 1994: 284). Schenkerian approaches allow chromatic triads to degrade into coordinated linear spans, which serve as carpets under which to sweep enharmonic paradoxes. 7

In this paragraph Cohn offers up in a microcosm three of the most pertinent problems facing tonal theory

and analysis when applied to densely chromatic late nineteenth- and early twentieth-century music.

Contemplation of these issues results in a broader issue that binds together Cohn’s observations: what are

the underlying assumptions and ontological claims that music theory makes when it employs a Roman

numeral, or some other analytic nomenclature? Are such labels meant merely to be descriptive, as Cohn

laments seems to be the case, or should the invocation of such labels be understood as suggesting more than

just a surface-level description of a chord’s root and quality? When Riemannian theory suggests that

chromatic chords can be viewed as transformed variants of three diatonic chords, what are the implications

behind such statements?

Matthew Brown writes that “of all issues in music theory, few are more perplexing than explaining

the coherence of highly chromatic tonal music,” and suggests that “often the problems [stem] from the

basic ways in which we think about the tonal system.” 8 I agree with Brown that the basic ways in which we approach and analyze tonality require scrutiny and examination. To this end, the rest of this introduction will be spent questioning a number of assumptions that are inherent in contemporary music theory’s approach to tonality, especially as it pertains to chromatic tonality, while simultaneously engaging with ontological problems and inconsistencies that require acknowledgement and discussion if tonal-

Steven Rings, “Riemannian Analytic Values, Paleo- and Neo-” in The Oxford Handbook of Neo-Riemannian Music Theories , ed. Edward Gollin and Alexander Rehding (New York: Oxford University Press, 2011): 497. 7 Richard Cohn, Audacious Euphony: Chromatic Harmony and the Triad’s Second Nature (New York: Oxford University Press, 2012): 11. 8 Matthew Brown, “The Diatonic and the Chromatic in Schenker’s Theory of Harmonic Relations,” Journal of Music Theory 30, no. 1 (1986): 1. 4 prolongational theory is to move beyond its classical precedents and emerge as a viable analytic method for late nineteenth- or early twentieth-century chromatic tonality. To this end, I will engage with each of the three issues outlined above, drawing on both historical thought and current perspectives to dissect the claims music theory makes when it employs various methodologies, or when it rejects others, and demonstrate the conflicts and problems in the ontological underpinnings of various discourses surrounding tonality. Having examined these differences, I will then return to Cohn’s work, and discuss the ways in which his approach engages with these issues.

Where Cohn’s approach was to create a new system that can map relationships between triads, my

dissertation proposes that there are ways of reconciling the extensive chromaticism on the harmonic surface with common-practice tonal-prolongational techniques that do not involve such a clear disjunction from the

precedents of classical tonality. This, however, requires a willingness to shift our perspectives beyond looking only at chords as static entities with inherent function. I argue that rather than being a product of sonority and root in isolation, function is a product of motion: not transformational motion, which, as

Daniel Harrison has pointed out, is a problematic metaphor, but rather a processual kinetic motion from one object to another, realized through characteristic voice-leading patterns that follow conventional dissonance resolution procedures.9 In short, I argue for a less restrictive approach to analyzing tonal harmony, wherein musical parameters beyond a chord’s root and sonority are more actively integrated into analysis and form part of the ways in which we define harmonic function. A further benefit to this approach, which I will demonstrate throughout this dissertation, is the way in which it appropriates neo-

Riemannian observations and places them within a tonal-prolongational context. Indeed, Cohn’s (among others) neo-Riemannian observations regarding the phenomena of voice-leading parsimony in chromatic music can be seen as an initial, if abstract, step towards the theories I am proposing.

A valid question, at this point, might be: “why prolongational analysis?” My position stems partly from an historic/dialogic argument, and partly from an analytic one. In the historic/dialogic sense, Wagner

9 Daniel Harrison “Three Short Essays on Neo-Riemannian Theory,” in The Oxford Handbook of Neo-Riemannian Music Theories , ed. Edward Gollin and Alexander Rehding (New York: Oxford University Press, 2011): 550. 5 and Strauss were operating in late nineteenth- and early twentieth-century Europe, wherein their models and compositional language would have been shaped by their surrounding aesthetic culture. Both knew the works of earlier composers, and works of their contemporaries as well, most of which were situated in a relatively consistent, if flexible, musical syntax. It seems entirely plausible, likely, even, that Wagner and

Strauss viewed their works within this common practice, even if they extended it. 10 Understanding the extensions in their music can, and I argue should, come through an understanding of the ways in which those extensions function in respect to the common aesthetic practices in which the composers were entrenched. This approach is fruitful on the analytic front as well: rather than devising entirely new systems, or suggesting that tonality in the music of Wagner and Strauss forms some distinct practice from classical tonality, understanding these extensions as derivations of classical tonality allows analysis to posit hermeneutic interpretations through the ways in which these newer chromatic processes relate to the conventional prolongational ones. As such, I argue that more important than the type of local chromatic effects that analysts and theorists have often dissociated from their broader tonal surroundings are the ways in which these chromatic events synthesize with tonal structure. It is through the retention of certain normative features of tonal function, despite the chromatic distortion of others, that these chords and progressions retain their tonal functionality despite projecting sense of cognitive dissonance, or, as Cohn suggests, etherealness.11

Since the music that is the focus of this dissertation has hitherto resisted convincing tonal- prolongational analysis of the sort that is routinely applied to classical tonality with ease, the discourses surrounding these works tend to gravitate either to one extreme or the other. On the theoretic side, harmony is increasingly discussed only in the most abstract terms associated with geometric, transformational, or neo-Riemannian approaches, which have the effect of isolating non-specialists from the

10 This type of dialogic view is currently commonplace in the analysis of form, and is a perspective adopted by James Hepokoski and Warren Darcy, Elements of Sonata Theory: Norms, Types, and Deformations in the Late Eighteenth-Century Sonata (New York: Oxford University Press, 2006). 11 Richard Cohn, “Hexatonic Poles and the Uncanny in Parsifal ,” The Opera Quarterly 22, no. 2 (2006): 232. 6 music, and the music from its tonal basis. On the musicological side, cultural or hermeneutic arguments are often made without the support of the music, which often results in misinterpretation or untenable claims. I

might, then, suggest that in addition to the theoretic and hermeneutic goals, a further goal of this

dissertation is to find a way to weave these opposing approaches together: to understand the late nineteenth-

and early twentieth-century music of Wagner and Strauss in a tonal-prolongational way that has hitherto had

only modest, and not entirely convincing, success. In proposing ways of understanding this music as an

extension of classical tonality without relying on the commonplace crutch of “linear” analysis, my hope is

that this will reopen this music to the analytic lens of prolongational analysis. This in turn will, I believe,

allow for more convincing, interesting, and accurate ways of discussing the ways in which this music

functions in cultural contexts, and ways in which it can be integrated into the vast, changing, tapestry of

nineteenth-century Europe.

Cohn’s first assertion, that Roman numerals are “promiscuously” flexible enough to describe any

type of sonority and ascribe to that structure some position in relation to a tonal center, suggests that even if

it were possible to arrange a vertical simultaneity abstractly into stacked thirds and slap a Roman numeral

analysis onto the resulting construct, it not always analytically sound, nor useful, to do so. In dissecting some

of the more recent scholarship on nineteenth-century chromatic harmony, and the trend towards applying

Roman numerals on a highly descriptive, rather than synthetic, basis, one can sympathize with Cohn’s

disenfranchisement with the tonal enterprise. Cohn also suggests the following:

To view triads against the background of chromatic space is to decline to interpret them in terms of the number of diatonic degrees that separate their root from some tonic. This choice cuts against the multiple denominations of classical tonal theory and their pedagogical offshoots, which all teach that chromatic harmonies are to be understood as transformations of some underlying diatonic one. 12

12 Cohn (2012): 8. 7

This assertion, and in particular the description of pedagogy that adopts an approach to harmony that

espouses the notion that chromatic chords are transformations of diatonic ones, cuts to the heart of what I

see as the issues that prohibit analysis from understanding late nineteenth-century tonality as an extension of

its precedents. Many, if not most, pedagogic streams do exactly what Cohn suggests, though there are some

approaches that, at least ontologically-speaking, do not employ—or, at the very least, do not prioritize—the

transformational process from diatonic to chromatic in the way Cohn suggests. This notion of ontology—of

discussing the reasons and ramifications of what specifically we are saying when we invoke a Roman

numeral, or an alteration symbol—is an area of inquiry that remains relatively undiscussed in scholarly

contexts, but is, I believe, important to consider.13

There exist two competing modes of thought regarding chromaticism in tonal analysis. The first approach takes the extreme monotonal view towards tonality that Cohn describes, and views all chords as transformations of more diatonic precedents. This “transformational attitude” is the ideology that underlies a majority of prominent contemporary approaches to harmonic analysis, either directly or indirectly, and can be discerned in the work of theorists such as Hugo Riemann, Arnold Schoenberg, David Damschroder,

Daniel Harrison, Charles Smith, or David Kopp, and further underlies many of the assumptions and approaches contemporary theory brings to analysis. 14 The second approach, more closely linked with theorists such as Schenker (who more accurately can be said to fall in between the two approaches) and

Kurth (specifically his tripartite division of tonal referentiality), does not prioritize the surface-level transformational relationships between diatonic chords and chromatic ones, but rather prioritizes multiple different levels of tonal relationships and structure, and as such views chromatic chords in a number of different ways: as applied embellishments of more diatonic structures, as modally derived, or in other ways

13 One of the more notable exceptions to my statement is Rings (2011). Here Rings focuses on “assumptions and values that underlie distinct analytic perspectives,” focusing specifically on Roman numeral, Riemannian, and neo-Riemannian approaches to analysis. 14 It also underlies the work of David Lewin and the field of transformation theory (see in particular David Lewin, Generalized Musical Intervals and Transformations [Reprint, New York: Oxford University Press, 2007]). Indeed the approaches that Lewin proposes are similar in the way they perceive chords as transformations of each other. However, Lewin’s approach is more directed towards perception, whereas the approaches under discussion here are more directed towards understanding harmonic structure. 8 hitherto unexplored or undiscussed. I use the terms transformative (to distinguish it from the already common term “transformational,” which usually refers to a specific branch of music theory) or monoreferential to refer to the first approach, and polyreferential to refer to the second.15

As Cohn notes, most often the transformative approach sees chromatic chords as alterations of

diatonic ones, and derives tonal meaning for the chromatic harmonies through this transformational

relationship.16 For example, Charles Smith writes “Of the three [functional] categories, tonic is the most

rigidly defined; it is only the tonic triad that has a direct or primary tonic function. Any other chord that

happens to sound like a tonic is necessarily a substitute for that triad.” 17 Smith’s assertion is that chordal function can be maintained despite a chordal transformation is a common assumption when discussing chromatic harmony, and because of the pervasiveness of these types of transformational claims, and their appearance of explanatory power, the transformative attitude is almost universally accepted without question and rarely scrutinized.

The polyreferential approach—which has been the subject of far less theoretic discourse than the transformative approach—is most succinctly described by Ernst Kurth, who, in Romantisch Harmonik ,

describes three ways in which chords can relate to a governing tonality. Lee Rothfarb summarizes Kurth’s

argument as follows:

According to Kurth every chord has three possible referential modes: tonal referentiality, local referentiality and self-referentiality. As tonal referents, chords have functions supporting a global scheme; this is the case with tonic, dominant, and subdominant harmonies, as well as chords closely related to them (VI, III, VII, II). As local referents chords relate only to their immediate predecessors. Local referentiality may or may not confirm tonal referentiality. When it does not, or does so only indirectly, Kurth speaks of absolute progressions, whose jarring effects set chosen chord pairs in relief against their harmonic environment. The conflict between tonal environment and local referentiality may become so great that a chord becomes isolated unto itself. Such chords are self-referential.

15 In his unpacking of Schenker’s epistemological agenda, Leslie David Blasius likewise suggests that there exist two different types of approaches to music theory: one is systemic, found in the work of theorists such as Riemann, who attempted to codify all types of harmonic progressions under a small number of basic principles; the other synthetic, an approach more associated with Schenker’s early work (such as Harmonielehre ) whose goals are less about codification, and more attuned to synthesizing the ways in which musical materials interact within a given system of relations. While these terms also describe the two camps to which I am referring, I believe transformative and referential to be clearer in their distinctions. Leslie David Blasius, Schenker’s Argument and the Claims of Music Theory (Cambridge: Cambridge University Press, 1996): 90–101. 16 Cohn (2012): 8. “Multiple denominations of classical tonal theory and their pedagogical offshoots…all teach that chromatic harmonies are primarily to be understood as transformations of some underlying diatonic one.” 17 Charles Smith, “The Functional Extravagance of Chromatic Chords,” Music Theory Spectrum 8 (1986): 110. 9

Kurth believes that tonal referentiality reinforces tonality. For this reason, he calls it “constructive.” By contrast, the other two modes, local referentiality and self-referentiality, undermine tonality and are thus “destructive. 18

In this sense chords that are diatonic to a key, as well as their modally-mixed variants, are the chords that most clearly engage in the prolongational processes of classical tonality: their meaning is found directly through their relationship to the tonic. Conversely, applied chords are to be understood as locally referential: they derive their meaning in relation to the tonic only indirectly, through the mediation of the tonally referential chord to which they are applied. 19 Conventional tonal models have, in some sense, domesticated

these types of chromaticism, to the point where their integration into a prolongation does not interfere with

the process of tonal prolongation. Self-referential chords are those whose chromaticism disallows them to

function within a key and who do not have an explicitly apparent local referentiality either. Brown,

Dempster, and Headlam describe this type of chromaticism as invoking the sense of post-tonality, writing

“Post-tonal works, however, tend not only to be densely chromatic, but to employ these chromaticisms in ways often not definable within the hierarchical relationships essential to definitions of mixture and tonicization.” 20 The term polyreferential thus refers to this way of ascribing different levels of referentiality

to chords, and the notion that not all chords need to evince a direct relationship to the tonic.

Ultimately, I will propose that while the transformative and polyreferential approaches share

common ground, and are often applied interchangeably in practice (especially in pedagogic contexts), the

ontological implications of each are striking in their contrast, as well as in what they suggest about the

structure of chromatic tonal music. Consequently I believe it to be worth conceptually separating the two

practices as distinct approaches. As an illustration of this contrast, I will examine Damschroder’s approach,

as elucidated in his Harmony in… series of books. I do not intend to be unfairly critical of Damschroder’s

18 Lee A Rothfarb, Ernst Kurth as Theorist and Analyst (Philadelphia: University of Pennsylvania Press, 1988): 158. 19 Interestingly, Harrison (1995, 187) specifically notes this as a distinction between the term “predominant” and the term “subdominant,” writing “one can be hard pressed not to hear the secondary dominant element ( s4 as 7 of V) and thus not hear some kind of dominant function as a result.” Despite contemporary uses of PD as a substitute for S, I believe Harrison’s approach here demonstrates with great clarity the difference between a diatonic “subdominant” and a chromatic “predominant,” in a manner similar to how I am defining the difference between the two. 20 Matthew Brown, Douglas Dempster, and David Headlam, “The sIV/ fV Hypothesis: Testing the Limits of Schenker’s Theories of Tonality,” Music Theory Spectrum 19, no. 2 (1997): 170. 10 approach, but I focus in particular on his work because of the plethora of analyses in his writings, and because of the ways in which his perspectives operate, or at least appear to operate, in both camps.

While Damschroder situates his approach in what I will refer to as late-Schenkerian approaches (the distinction will become more important in the later stages of this dissertation), meaning a very strict

monotonal orientation, a closer investigation reveals that his approach also has a strong Riemannian-

functional transformative flavour.21 This is most clearly demonstrated in Damschroder’s views on

tonicization. Damschroder writes “I eschew [the practice of tonicization], instead deploying symbols that

account for local transformative processes within the governing key.” 22 Here Damschroder is prioritizing, as he writes, the transformative relationships between chords, rather than the referential ones. Implicitly, the assertion being made is that while a chord such as A–Cs–E–G does not exist in the key of C major, if we understand it as a transformation of an A-minor chord—which according to Damschroder is itself implicitly derived from a C-major chord (via a 5-6 motion)—then the coherence of this centrifugal chromatic entity to

the tonic can be asserted through its association with a more diatonic progenitor.

Damschroder is not alone in this approach: David Kopp likewise suggests that “altered chords must

not be considered as borrowings from other related keys, as other theorists had done, but as chords which draw meaning from Tonalität , through which their chromatic elements are interpreted as variants, or members of, for the most part, the three primary diatonic triads.” 23 Kopp’s statement evinces a striking

kinship with Riemann’s approaches, specifically in the way it prioritizes a monoreferential perspective on chromatic harmony. For example, William Mickelsen describes Hugo Riemann’s approach to harmony as follows:

There are only three fundamental chords: the tonic, and its upper and lower dominants. Therefore, harmonic function (and tonality) basically involves the movement away from the tonic to chords having dominant or subdominant significance, and back to the tonic chord. Chords other than the three primary harmonies are mixtures of notes from these chords and thus may be comprehended as representing two or even three of the primary chords. Yet

21 I am not comparing the two systems in terms of their value or applicability with this comment, but simply noting the strong presence of several Riemannian ideals entwined within the Schenkerian framework. 22 David Damschroder, Harmony in Schubert (Cambridge: Cambridge University Press, 2010): 3. 23 Kopp (2002): 78. 11

one primary chord is always more prominent…thus all chordal formations can be explained as belonging to a key through the concept of chord-representation. 24

Later Mickelsen writes:

The function symbols as a type of designation separable from any particular key constitute a generalization applicable to all keys. They are designed with the idea of clarifying the function of every chord within the key, even chromatic chords not revealing their diatonic origin. 25

Riemann himself notes that “the tenacious relationship of all harmonies to the tonic has found its most

pregnant expression imaginable in the designation of all chords as more or less strongly modified

manifestations of the three main pillars of logical harmonic structure: the tonic and its two dominants.” 26 In

this way, all chords in Riemann’s system are understood, at least ostensibly, to relate to a single governing

tonality through their transformative relationship to other diatonic chords.27 This exists in a stark contrast to

Kurth’s polyreferential approach described above.

Damschroder’s exclusively monotonal approach to harmony is highly reminiscent of Riemann’s, and reflects especially closely Riemann’s intensive transformative nomenclature and the desire of systematizing a way through which all chords, no matter how chromatic, can be related to a single key. Kopp describes

Riemann’s system as “a means to explain how all chords, diatonic and chromatic alike, draw their meaning in a key from their shared membership in one of three functions defined by the three principal triads.” 28

Particularly striking are the ways in which Riemann’s nomenclature resembles Damschroder’s, despite the

latter’s claim to operating within a Schenkerian framework (and with the obvious caveat that Riemann

24 William Mickelsen, Hugo Riemann’s Theory of Harmony: A Study (Lincoln: University of Nebraska Press, 1977): 5. 25 Ibid., 76. 26 Hugo Riemann, Handbuch der Harmonielehre , 6 th ed. (Liepzig, 1912): 214. Quoted and translated in Carl Dahlhaus, Studies on the Origin of Harmonic Tonality , trans. Robert O. Gjerdingen (New Jersey: Princeton University Press 1990): 49. 27 This also recalls David Lewin’s assertion that “An even more basic problem for Riemann was that he never quite worked through in his own mind the transformational character of his theories. He did not quite ever realize that he was conceiving “dominant”…as something one does to a Klang, to obtain another Klang…. [and was led] to conceive “dominant” and the like as labels for Klangs in a key, rather than as labels for transformations that generate Klangs . . .” Lewin (2007): 177. Daniel Harrison, however, questions this transformational attitude, writing “the phrase “something one does to a Klang” in the quotation above should be seen in spotlight. Who, exactly, is doing the doing? Composer? Listener? Analyst? A combination of thereof? The vagueness and misdirection here is essential to the ventriloquist's act.” Harrison (2011): footnote 16. 28 Kopp (2002): 5. 12 employs function symbols where Damschroder uses Roman numerals).29 While Damschroder claims that

“other analytic systems offer a hodgepodge of incommensurate symbols (ii, V/V vii o7 /V, Ger +6 , etc.) that mask commonality among similar chords,” 30 it is difficult to take this claim seriously when his own system,

like Riemann’s, is so systemic in its use of a similar “hodgepodge” of symbols. More importantly though, it

is worth dissecting Damschroder’s claims more fully, first through a number of his examples, then through

comparison to other approaches.

Damschroder notes that any given Roman numeral “is shared by all chords built on the same root, with adjustable components to the right of the numeral noting the chord’s specific constitution.” 31 This

suggests that the root of the chord is the most important—perhaps we might say defining—element or

characteristic of a chord’s prolongational function in Damschroder’s system.32 Figure 0.1 reproduces

Damschroder’s Chart 1.2, in which he shows all of the different chords to which he would assign the II

Roman numeral. Thus E–G–B in D major is, in Damschroder’s view, the progenitor of all the augmented-

sixth chords in D, as well as V 7/V, vii o7 /V as well as the more closely-related variants such as ii ø7 . Worth

noting as well is that there is no single pitch that is consistent throughout the gamut of transformations

Damschroder proposes: E is sometimes present, sometimes absent, G can sometimes be G s, B can

sometimes be B f (or even B s if one admitted a II s5 [V s5/V]). While it is certainly true that one can apply the host of transformations, and their respective symbols, as Damschroder does in order to indicate alterations from a basic E–G–B chord, this approach falls into the trap lamented by Cohn, namely that it succeeds in

describing the chord, but it does not explain a number of other factors regarding the chord’s function or coherence within the tonal-prolongational process. For example, it has been well-

29 Two notable charts for comparison can be found in David W. Bernstein’s survey of tonal theory in the nineteenth century, and in Daniel Harrison’s accounting of Riemann’s system. David W. Bernstein, “Nineteenth-Century Harmonic Theory: The Austro- German Legacy, in The Cambridge History of Western Music Theory , ed. Thomas Christensen (Cambridge: Cambridge University Press, 2001): 798. Daniel Harrison, Harmonic Function in Chromatic Music: A Renewed Dualist Approach and an Account of Its Precedents (Chicago: Chicago University Press, 1994): 286. 30 Damschroder (2010): 5. 31 Ibid., 5. 32 This brings to mind Daniel Harrison’s (1994) concepts of Base, Agent, and Associate. 13

Figure 0.1. Damschroder’s Figure 1.2 (from Harmony in Schubert )

documented that the raised subdominant scale degree does not form a direct part of the diatonic system.

Damschroder offers no explanation as to why this harmonic outsider is accorded identical functional status to the more diatonic subdominant pitch: using V/V suggests the chord has a mediated relationship to the tonic (through its functional dominant relationship to the dominant), whereas II s offers no such distinction. 33 Ultimately, while ii and V/V both usually progress to V, their similarity exists more in the

contrapuntal realm than the harmonic: the F s directs the chord towards V, and away from the tonic key.

One might also question the varying degrees of status Damschroder accords chordal constituents. If,

for example, the root of the chord, per Damschroder’s description of it as being the locus upon which

related chords are built, is so important, and not an adjustable element, does the possibility Damschroder

suggests of analyzing rootless chords contradict this assertion? Another example Damschroder gives: in D

major a diminished-seventh chord spelled Ds–Fs–A–C “extends the opening tonic.” 34 Damschroder suggests that D s–Fs–A–C is a D-major triad that has been subjected to several transformations, both

diatonic and chromatic. Firstly, it is subjected to a 5–6 shift (changing the A to B), making B the root, but retaining the A as well. This “B” chord is then further transformed, and understood as subsequently

33 Louis and Thuille, for example, write “if [the] subdominant is chromatically raised, it loses its consonant relationship to the tonic, i.e. its genuine subdominant character. In other words, a key loses its subdominant, in the ordinary sense of the word, if an ascending leading tone to the dominant is introduced into that key by means of an upward alteration of the fourth scale degree.” Schwartz (1982): 268. David Kopp likewise suggests that alterations of the primary scale degrees are “potentially destabilizing elements” to the tonality. David Kopp, Chromatic Transformations in Nineteenth-Century Music (Cambridge: Cambridge University Press, 2002): 16–17. Harrison (1995) refers to the raised subdominant as a “frequent and honored guest in the diatonic household,” but concedes that it is not native to major or minor collections. Daniel Harrison, “Supplement to the Theory of Augmented-Sixth Chords,” Music Theory Spectrum 17, no. 2 (1995): 176. 34 Damschroder (2010): 6. 14 omitting the new root B, containing a raised third, a seventh, and a ninth.35 The issue that arises in this analysis is similar to the one posited above for altered subdominant pitches. In employing the VI (plus alterations) nomenclature, the claim being made is that this chord relates directly to the tonic, despite the presence of a chromatically altered tonic pitch within the chord. This is a questionable ontological assertion: how can the tonic be chromatically altered and still project the same function? 36 The alteration of the tonic pitch destabilizes the tonic-dominant axis that Stein refers to, forcing the consonant stability of the perfect fifth between tonic and dominant into a dissonant and unstable diminished fifth which, in conventional tonal syntax, requires a resolution through a motion to a consonance. Likewise, Kopp describes the presence of altered tonic and/or dominant pitches as destabilizing elements. 37 As such, I find it conceptually difficult to assign tonic function to such a chord in the way that Damschroder does, a problematization that extends to many of his derivations, and stems from his principle of disavowing the possibility of applied chords. Conversely, using the vii o7 /ii nomenclature again suggests a secondary relationship: the chord does not derive its meaning directly from the tonic, but rather through its relationship—as its leading-tone seventh—to the diatonic supertonic, which acts as an intermediary mediator between the chromatic chord and the diatonic tonic.38

This issue might also be related to Aldwell and Schachter’s notion of double mixture, which they use to explain chromatic mediant chords such as fvi. 39 Firstly, the conventional use of the mixed f6 and f3 in the

35 Certainly it is a well-known perspective that viio7 chords are closely related to Vb9 chords, and in this sense, an analysis that posited this as a derivation of a rootless B 7 or B f9 chord would not be entirely without merit. 36 Matthew Brown, for example, writes that Schenker “rejects any possibility of Lydian mixture on the grounds that the subdominant and dominant must always be available in pure form” (Matthew Brown, “The Diatonic and the Chromatic in Schenker’s ‘Theory of Harmonic Relations,’” Journal of Music Theory 30, no. 1 [1986]: 8). Presumably the tonic must also be available in pure form. Likewise, Deborah Stein writes that classical tonality is “founded upon the premise of a primary structural and inherently cohesive relationship between the tonic and its dominant, the so-called tonic-dominant axis.” Presumably that axis is interrupted or distorted if one were to understand a raised tonic or dominant pitch as having a direct relationship to the tonic (Deborah J. Stein, Hugo Wolf’s Lieder and Extensions to Tonality [Ann Arbor: UMI Research Press, 1985]: 3). 37 Kopp (2002, 16–17). 38 This issue can also be directed towards Charles Smith’s analyses, wherein he allows for even more extravagant Roman numeral nomenclature: chords such as fii ø7 occur frequently, as do III 7s and VI 7s, despite each containing an altered tonic or dominant pitch. While Smith’s use of these Roman numerals is generally a consequence of his thesis that analysis should account for every possible hearing in every possible key, no matter how remote (though of course, a counter-argument exists in regards to the fact that by virtue of the necessity of such extravagant Roman numerals, such keys should not be understood). See Smith (1986): 94– 139. 39 Edward Aldwell and Carl Schachter with Allen Cadwallader, Harmony and Voice Leading , 4 th ed. (Boston: Schirmer, 2010): 595. 15

major mode generate the root and fifth of the fVI chord. They then propose that lowering the third of the fVI chord is a second instance of mixture, borrowing f1 as f3 from the relative minor of fVI. This is

problematic, however; borrowing from the parallel minor is a well-known process, one that Schenker hardly

even considers to be chromaticism. Claiming to borrow f3 from the parallel minor of the submediant, but integrating it into the tonic realm, misses the point of mixture: mixture pitches promote the same tonic as

their parallel mode: C major and C minor have the same tonic pitch, regardless of whether its tonality is

propagated by major-mode scale degrees or minor-mode ones. As such, this might be seen as resulting from

conflating tonal relationships: undoubtedly an A f major triad is related to an A f-minor triad—they share the

same root and fifth. But this transformative relationship does not guarantee that the transformed chord

maintains its relationship to the original tonic of C. Indeed, as Cohn notes, “the derivation freely

interchanges triads and scales as if they were unproblematically identical, and thus partly relies on a sleight of

hand.” 40 The relationship between the A f-major triad and the A f-minor triad is an acoustic one, which does not necessarily translate to a tonal one. It is this type of ontological distinction, dissociating the transformative relationship between chords from their tonal-referential potential, which has rarely been explored in music-theoretic scholarship, yet it is, I feel, one that is of vital importance that distinguishes the underlying assumptions of one system of analysis from another.41

From these approaches, a broader question pertaining the transformative approach—used here in the Riemannian, not the Lewinian, sense—to harmony arises. One difficulty regarding the tenability of such theories is that the transformative possibilities are largely unrestrained. As Daniel Harrison notes of

Riemann’s system, there is “a tremendous flexibility in harmonic interpretation,” which “works radical

40 Richard Cohn, “Uncanny Resemblances: Tonal Signification in the Freudian Age,” Journal of the American Musicological Society 57, no. 2 (2004): 304. 41 Cohn likewise notes that the label fvi, for example, “implies problematic claims about the phenomenological status and dispositional behavior of the individual pitch classes…The first stage of mixture accurately captures the disposition of [ f6 ] as it presses downward toward [ 5]. But the second stage of mixture falsely suggests that [ f1 ], rather than behaving as a leading tone, is similarly disposed toward a flatward fate.” Ibid., 304. 16 effects on the functional triads because Riemann recognizes no limits to the number of additions or chromatic alterations (emphasis Harrison’s).” 42 Harrison further notes:

Even more astounding is [Riemann’s] ability to analyze as tonic-functioned chords that have no tones in common with tonic—indeed, chords that can easily take another functional designation—as is the case with VII and II triads…clearly, there is a way to label any chord with any function. 43

Harrison concludes that “Riemann had…the means to make any harmonic configuration conform to the cadential prototype. An alteration here, an added tone there, an omitted chord tone or two—a procrustean bed could be made for any chord.” 44 While Harrison’s comments all pertain to Riemann’s functional notation, they apply equally well to Damschroder’s conception of alterable chordal constituents and the nomenclature he combines with Roman numeral analysis.

The same arguments can be made of some of Schoenberg’s approaches to harmony that follow similar processes. Schoenberg’s derivation of quartal chords, and the claim that they are functional tonal sonorities, is an example of this approach taken to its extremes. Schoenberg writes, “The four-part fourth chord can even be produced by alteration within the tertian system.” 45 To do so, he alters all three pitches in a triad by semitone (one pitch gets altered twice) to produce such a quartal chord. But more glaring here

than in the more tonal examples above is the arbitrary nature of the alterations Schoenberg applies. One

cannot help but see the same issues Harrison raises in respect to Riemann’s system: anything can generate

anything else if we just change it enough! As Harrison notes, “a [chord] could be so freighted with nonchord

tones, suspensions, and passing tones, and even have its own tones so chromatically altered that one would

be hard put to recognize the resulting monstrosity as having any relationship to the original.” 46 This assessment rings particularly true for Schoenberg’s quartal chord derivations, but applies equally to some of

Damschroder’s harmonic transformations as well.

42 Harrison (1994): 284–285. 43 Ibid., 285–287. 44 Ibid., 288. 45 Arnold Schoenberg, Theory of Harmony [3 rd ed., 1922], trans. Roy E. Carter (Berkeley: University of California Press, 1978): 390– 410. 46 Harrison (1994): 285. 17

The issue with such a system is that if anything can generate or be transformed into anything else, if there are no restraints nor boundaries on a system (of analysis), no effort to explain why certain alterations are permissible and others not, and no intrinsic reason why one transformation should be preferred over another, then such a system, at least as a means of analyzing chromatic music as an extension to classical tonality, is essentially meaningless. 47 And this conceptual problem is immediately foregrounded in the transformative attitude: there is, largely, no effort made to explain how these more complicated chromatic transformations retain the same function of their diatonic precedents.48 Transformations are allowed on an ad hoc basis, regardless of whether or not the effect of such transformations creates, as Kofi Agawu has brought up in regards to Schoenberg’s system of alterations, chords “modified almost beyond aural comprehension.” 49 The passage to which Agawu refers, and Schoenberg’s analysis of it, are given in

Example 0.1. Here, Schoenberg analyzes the downbeat of the third measure (E–Fs–A–C) as an altered III

Example 0.1. Schoenberg’s Analysis of a Passage from Strauss’ Salome

47 Recall Harrison’s questioning of who precisely is generating or understanding these alterations described in footnote 27 above. 48 While he refers more specifically to neo-Riemannian approaches, Kopp too has noted the unconvincing nature of transformational values. He writes, “Since extratonal transformational processes can be identified in chromatic passages where diatonically based functional interpretations fall short, one might suspect the music under analysis must have nontonal content.” Kopp (2011): 400. 49 Kofi Agawu, “Extended Tonality in Mahler and Strauss,” in Richard Strauss: New Perspectives on the Composer and His Work , ed. Bryan Gilliam (Durham, NC: Duke University Press, 1992): 58. Additionally, an example of the extremities of such theories can be found in Schoenberg’s derivation of quartal chords, and the claim that they are functional tonal sonorities. Schoenberg writes “The four-part fourth chord can even be produced by alteration within the tertian system.” To do so, he alters all three pitches in a triad by semitone (one pitch gets altered twice) to produce this quartal chord. But the alterations Schoenberg applies seem arbitrary and it is a questionable claim that in altering all three pitches the chord produced can be understood as related to its tonal precedent, except through the specific transformations under which it has undergone. See Schoenberg (1978 [1922]): 390–410. 18

chord in E f. Certainly the F s might equally be G f, but such an analysis results in a half-diminished seventh chord. Similarly, in the second half of the measure, Schoenberg analyzes an altered II chord. It is here that we can see the challenge to this system more clearly: the pitch F does not occur in this measure at all, and

Agawu’s criticism of Schoenberg analyzing alterations that render the chords incomprehensible rings true. 50

What is missing in the transformative approach to deriving chromaticism from diatonic precedents is some reason, apart from perhaps the very broad assertion of a similarity in absolute note names (i.e. A,

Af, A s all share A), as to why these transformations retain the function of their diatonic progenitors. One aspect of my approach that I develop in Chapter 1 is to suggest that when one posits a transformation, what

is required in order to make that transformation valid is some other means of explaining why the altered

chord retains its tonal function; it must have some mitigating factor that demonstrates that it still remains

referential towards a tonic despite the chromaticism involved. For example, in dominant-seventh chords

7 7 that contain altered chordal fifths, such as V b5 or V s5, the chromatic alteration of the chordal fifth ( 2) does not alter the dominant function of the chord because the univalent tritone and its resolution to a stable consonance, remains present.51 In this case my analysis prioritizes the combination of tonal motion, dissonance resolution, and univalence of the dissonance as defining tonal gestures that override the less diatonic chromaticism of the alterations.

To summarize: the ontological implications of the transformative approach suggests that this type of transformative analysis is not merely charting the ways in which chord B is a transformation of chord A, but that because chord B can be derived by altering chord A in some way (or multiple ways) chord B therefore expresses the same tonal function as chord A, despite the possibility that the chromaticism involved distorts or destroys entirely the possibility of understanding the chord referentially. And such an assertion can be

50 My own analysis—that the chord in question is a chromatic alteration of a diminished-seventh chord applied to the dominant— will be developed further in Chapter 1. While this might initially seem to betray a similar approach to the one I have spent a paragraph questioning, I develop a theory regarding the integration of such chords into the tonal-prolongational system in Chapter 1. 51 Charles Smith, for example, writes that 2 is “the least crucial of the normal members of any dominant chord, and therefore, the most readily modified.” Smith (1986): 124. 19 true in some instances: modally-mixed chords such as IV and iv, or ii 7 and ii ø7 are very often functionally

interchangeable, and are understood as transformations of one another. But in these instances, the music-

theoretic enterprise has a means of explaining how the chords remain functionally equivalent despite being

sonorously dissimilar; in short, the transformational approach in this case is supported by intrinsic musical

factors. These modal pitches (or chords) come from the parallel minor tonality: in that context, they remain

a valid means of prolonging, and thereby making tonic, the tonic pitch. For example, F–Ab–C functions as

iv in C minor, where C is tonic. C is also tonic in C major, and so F–Ab–C can still function as a means of

prolonging the tonic. 52 But there are, as I have discussed above, other instances where the transformative

approach does not explain how the chords remain related to the tonic, except through the transformations themselves. It is like comparing the words “wrong” and “wring.” Obviously the two words are closely related from a transformative perspective, as they differ by only one letter, but they do not have the same, or even similar, meaning. The silliness inherent in positing that the words have the same meaning through transformation can be evinced when a broader context is invoked. For example, in the sentence “The wrong person won the election,” the words wrong and wring cannot logically be used interchangeably, even though they exhibit a structural similarity.

Damschroder’s transformative nomenclature, however, is not so different from the type of analytic symbols that Schenker employs—Roman numerals such as II 7s or I b7 , for example—that indicate the transformed aspects of the chords in question. However, despite his application of these transformationally- informed symbols, Schenker’s nomenclature is often at odds with his prose, an aspect of his theoretic approach that has yet to come under scrutiny. This is particularly prevalent in Schenker’s earlier writings, especially Harmonielehre , in which he writes:

52 As Patrick McCreless, following from unpublished work by Robert Bailey, has suggested that in late nineteenth-century tonality the distinction between major and minor modes becomes obsolete from a structural perspective (though is still important from an interpretive and hermeneutic perspective). Patrick McCreless, “Ernst Kurth and the Analysis of Late Nineteenth-Century Chromaticism,” Music Theory Spectrum 5 [1983]: 60. Schenker expresses a similar approach, suggesting in Harmonielehre that tonalities should be expressed as major-minor, the combination between the scales of parallel modes. Heinrich Schenker, Harmony [1906], ed. and ann. Oswald Jonas, trans. Elisabeth Mann Borgese [Chicago: University of Chicago Press, 1954]: 84–115. 20

Tonicization by descending fifths is effected as follows: The primary object is to find the diatonic dominant as a prelude to the scale step which is to be tonicized. For this purpose the preceding scale-step, the one which is to be used as a dominant, must be defined as such. This can be achieved by transforming the triad under consideration, whether this be a minor or diminished triad, into a major triad by making one or two chromatic changes—according to whether the new dominant is to be gained from a minor or from a diminished triad. 53

Here Schenker refers directly to both the process of transforming diatonic triads into dominants, but

dissociates this process from the more referential aspects of conceiving of them as secondary dominants within a key applied to more diatonic chords. Interestingly, he reinforces the latter point in a passage that

almost contradicts his use of symbols such as II s or I b7 . There he writes:

The significance of the tonic exceeds that of the other scale-steps; and these lose in value the farther they go from the tonic. Thus a scale-step does not aspire to the place of a VI or II in the system, but, on the contrary, it prefers to be a V at least, if not a I… 54

But other passages also demonstrate his thinking in terms of transformed scale-steps, such as when he writes of his Example 307a (reproduced here as Figure 0.2) “In the case of (a) the III step sounds like a dominant seventh-chord, V 7 of A major, which seems…to effect tonicization by a V 7 chord and a downward progression by a fifth.” 55 Here he refers to a III step that merely “sounds” like a dominant of

Figure 0.2. Schenker, Harmonielehre , Figure 307

53 Heinrich Schenker, Harmony [1906], ed. and ann. Oswald Jonas, trans. Elisabeth Mann Borgese (Chicago: University of Chicago Press, 1954): 262. 54 Ibid., 252. 55 Ibid., 271. “Bei a) klingt die dritte Stufe als ein Dominantseptakkord in A-dur, woduch allein schon dieser Fall eigentlich mehr in den Bereich jener Chromatik zu gehören scheint, die mittels des V7-akkord bei quintalen Schritten erzeugt wurde.” 21 another chord, which suggests a prioritization of the transformative over the relational in a way that contrasts with the quotations above that seemingly refer to such chords as dominants of other chords, not as II or VI steps. And again, Schenker’s nomenclature is vague: he analyzes the chord on one level as a III s3 in C, but below places in brackets the V–I analysis in A.

Thus it appears that for Schenker, at least at this early stage in his theorizing, the notion of how tonicization fit within the diatonic framework was not entirely clear. His prose indicates that these were not

to be considered modulations, and speaks to his conception of the ontological basis of these chords as

secondary dominants, but his nomenclature indicates transformed chords on the musical surface. What then

to make of all this? My inclination is that Schenker, like many other theorists, had not entirely unpacked the various implications of what their nomenclature implied on an ontological level, and as such did not engage with the notion that there is a distinction between chords being related by transformation and chords being

referential towards a governing tonic. 56

Deborah Stein’s description of Schenker’s approach offers a little clarification on the matter, but also reinforces the same clash of ontological claims found in Schenker’s writings. Stein observes:

Schenker’s conceptualization of common-practice tonality is predicated upon two fundamental premises. First, common-practice tonality is structurally diatonic; chromaticism functions to elaborate or embellish—on a foreground or middleground level—a diatonic background. Second, common-practice tonality exists within a framework of monotonality wherein one background tonality is embellished by surface modulations that emphasize structurally important scale steps within that singular tonal region. 57

Here we find similar terminology: that Schenker’s system is fundamentally based around diatonicism, and that chromatic chords elaborate the more structural aspects of the diatonic collection, while the term monotonality recalls the more transformative approaches outlined in respect to Riemann, Kopp, and

Damschroder.

56 As Schenker’s theory developed, and moved more towards the contrapuntal approach that is evinced in his later works, these distinctions likely became unimportant to him, as ii or II would have fulfilled the contrapuntal predominant functions regardless of mode. 57 Stein (1985): 3. 22

But Schenker was not the only one to have this ontological and epistemological contradiction between his prose and his nomenclature. Interestingly, Riemann also allows for the possibility of secondary dominants, a notion that is distinctive in the way it departs from Riemann’s otherwise monotonal system, and has important implications. As Alexander Rehding points out:

Riemann can only interpret the relationship [between a C-major triad and an E-major triad] in a rather clumsy fashion as a very indirect relation, namely as the dominant of the relative minor of the tonic, which itself is never sounded. In his function shorthand he usually expresses this relation in the following manner: D[Tp] . This means that what was previously Riemann’s prime example of ‘tonality’ can only be expressed in terms of harmonic function with the greatest difficulty. 58

In other words, the chords in question are not understood as immediately monotonal in the way Riemann derives most of his other relationships; they are in fact not functional—according to Riemann’s description of them as secondary dominants—in the governing tonality, but rather require a different diatonic chord as their point of immediate reference.59 While Rehding does not explore this contradiction in Riemann’s system further, it serves to highlight the differences in approach.

In his discussion on the reception history of Riemann’s system, Ludwig Holtmeier brings up the notion of applied chords in Riemann’s work. Holtmeier suggests that rather than being inconsistent with

Riemann’s monotonal perspective “The notion of the secondary dominant is a central component of the theory of functions and is closely related to Riemann's modern understanding of modulation.” 60 Holtmeier writes that Riemann was critical of what he saw was an “antiquated” view of modulation as happening

“whenever a harmony foreign to the previous key occurs.” 61 One can certainly sympathize with Riemann’s

58 Alexander Rehding, Hugo Riemann and the Birth of Modern Musical Thought (Cambridge: Cambridge University Press, 2003): 58. 59 Alternately, scholars have noted this as an inconsistency in Riemann’s system: various chords can have highly differing interpretations, and there is no means of systematizing which interpretation is the best or most correct. The German augmented- sixth chord, for example, is a good case study: Rings (2011): footnote 31, suggests that Riemann’s “preferred” analysis of this chord is as a rootless alteration of the dominant of the dominant. However, the dominant of the dominant can also be understood as an alteration of the supertonic, which, under Riemann’s system, is itself a transformation of the subdominant S. There is a conflict here: Riemann ascribes dominant of the dominant function to the augmented-sixth chord, but the chord from which that dominant of the dominant is derived is itself an S-functioning chord. 60 Ludwig Holtmeier, “The Reception History of Hugo Riemann’s Music Theory,” in The Oxford Handbook of Neo-Riemannian Music Theories , ed. Edward Gollin and Alexander Rehding (New York: Oxford University Press, 2011): 9. 61 Ibid., 9. 23 criticism that not all chromatic chords create a modulation, which is of preeminent concern in the music of

Wagner, Strauss, and their contemporaries. Holtmeier writes further:

Contemporary attempts to employ classic scale-degree and fundamental-bass theories in the analysis of “chromatic harmony” mostly led to a diagnosis of derisory amounts of “modulatory” processes and a tremendous welter of figures and symbols below the chords. In the eyes of its supporters, function theory was predestined to demonstrate how superficial are judgments that assert: ‘Wagner is always modulating!’ 62

Riemann’s aim, then, was to develop a way of understanding non-diatonic chords in reference to a single tonic so as to avoid this type of analysis that invokes a multitude of micro-modulations. But it seems noteworthy that secondary dominants formed a part of that thinking, despite not being transformations of one of the three tonal pillars, and the conflict that they pose with respect to the rest of Riemann’s systematically monotonal approach.

Schenker likewise did not see applied chords as micro-modulations. Speaking of his Example 285

(reproduced here as Figure 0.3), Schenker clarifies that tonicization should not be considered a type of modulation, that is the governing tonality does not change, but rather secondary, fleeting emphasis is given to a chord within that tonality. He writes:

We would show no more musical sense, however, if, for the sake of this chromatic E-flat, we were to speak of a real change of key, as if the B-flat major generated by this E-flat were a real B-flat major key, which, by a simple modulation, would subsequently be reabsorbed by the F major diatonic system. It would be cumbersome indeed to assume here an independent key and modulation, merely to concede to the E-flat the satisfaction warranted by superficial theory. 63

For Schenker, then, applied chords are not modulations, but temporary embellishments of the Stufe to which they are applied.

But while Schenker and Riemann may have remained unconcerned with, or unaware of, the ontological conflicts between the positions they were asserting, Kurth’s discussion of chordal referentiality discussed above, wherein he suggests that chords can relate either directly to a tonic (tonal referentiality), indirectly to a tonic (local referentiality), or not at all to a tonic (self-referentiality), serves to clarify the

62 Ibid., 11. 63 Schenker (1954 [1906]): 257. 24

Figure 0.3. Schenker, Harmonielehre , Figure 285 (Bach, Italian Concerto)

distinction between the transformative attitude and the polyreferential one. The monotonal approach of transformative perspectives sees all chords as having a direct relationship to the tonic by positing that chromatic chords are transformed variants of more fundamental diatonic chords—for Riemann, these transformations all relate to T, S, or D chords, while for Damschroder, diatonic triads on the various scale degrees serve as the diatonic progenitors. Conversely, the polyreferential approach sees the tonal domain as consisting mainly of diatonic or modally-mixed triads, all of which are referential towards the global tonic, but can also be elaborated by their own applied dominants (or in some cases, applied progressions). In this case, as Kurth outlines, the chromatic applied chords do not find their meaning directly from the tonic, but rather from one of the other Stufen in the key of the tonic, which mediates the relationship of the chromatic chord back to the tonic.

At this point I offer an example to more properly differentiate between the two approaches. Imagine the progression C – d – D – G7 – C. The transformative approach emphasizes the relationship between the

second and third chords: that one need only chromatically raise the third of the d chord to produce the D 7

chord. The polyreferential approach conversely sees the D chord as emphasizing through tonicization the

chord that follows: on a referential level, it relates immediately to V, and only indirectly to the governing 25 tonic. While the distinction may seem almost trivial in this case, the ontological implications of each approach, as I have laid out above, are different. The distinction also becomes more important in cases where the chord in question is not the supertonic. As cited before, the progression I – VI 7s - ii – V – I is far

more problematic, as the transformative approach ascribes direct tonal (and according to Damschroder,

tonic) function to a chord that has an altered tonic pitch in it, whereas the polyreferential approach again

sees it as an embellishment of the subsequent chord.

Another question the polyreferential approach evokes—and this is a question that I will reconsider

in Chapter 1—is whether the term “chromaticism” is adequate as a descriptor for a phenomenon which, as

the previous discussion has certainly evinced, involves a number of different manifestations, some of which

function in ways so dissimilar from others that they can hardly be described as the same phenomenon.

While the transformative approach treats all chromaticism equally, as some variant of a diatonic pitch, the

polyreferential approach invites a reconsideration of chromaticism, that perhaps chromaticism can be viewed as a spectrum of various procedures within tonality. Modal mixture is one type of chromaticism that

is more tonally referential than other types of chromaticism. Applied chords, on the other hand, have a

more local referentiality regarding the way in which they rely on diatonic chords to provide the mediation

that gives them their tonal meaning. Other, more centrifugal types of chromaticism, will be discussed in

Chapters 1 and 2, where this distinction will become more important to the analysis of chromatic tonality in

Wagner and Strauss.

While my views on the two approaches are made relatively clear in the preceding discussion, this is

not to say that the transformative approach is wrong, or even misguided. It still provides an accounting, and

codification, of ways in which chords can be derived from and related to one another at the musical surface.

This is important, as there was undoubtedly an element of this type of transformative process inherent in

the compositional process: one can easily imagine a composer sitting at a piano thinking “what if I just

switch this pitch with that one,” or something similar. The polyreferential approach simply takes what I

believe is a more structural perspective, and views these chords in a more synthetic manner, as part of a 26 tonal tapestry wherein the central tonic is reinforced through its diatonic and modal constituents, who themselves are, at times, reinforced by their own applied chords. The polyreferential approach further avoids the problematic arbitrariness of the transformative approach.

Cohn’s second assertion, regarding the catch-all nature of Riemannian functions, needs little further elaboration, as many of the same topics of discussion that could arise have already been covered in the

above discussion of transformative and polyreferential approaches to tonality. Riemann’s function labels,

and the ways in which he employs them to demonstrate how chromatic chords are transformations of the

three tonal pillars, are fundamentally transformative in their conception. There are, however, some other

important aspects of the functional nomenclature that are worth discussing. Namely, it is worth exploring

further the distinction between harmonic functions and chords, and the ways in which these two concepts

relate to the notion of phrase functions.

Carl Dahlhaus has suggested:

Riemann’s theory of functions is an attempt to explain the tonal connection between chords. Underlying his complicated system is the simple axiom that chords representing a key can be reduced to three functions—tonic, dominant, and subdominant—and that one should seek the reason for the relationships between chords as chords (and not as mere results of voice leading) in the functions that the chords represent. 64

Dahlhaus, however, offers one of the main contemporary critiques of Riemann’s approach. He writes “The metaphor ‘main pillar,’ of which it is uncertain whether it implies ‘function’ or ‘chord,’ conceals an

irresolvable difficulty in Riemann’s formulation of the theory of functions. Riemann leaves undecided the

question of whether ‘tonic,’ ‘dominant,’ and ‘subdominant’ are terms for chordal scale degrees or for

functions.” 65 Dahlhaus describes this problem as the existence of a “fundamental distinction between what something signifies and the form through which it is represented.” 66 Dahlhaus gives the example of F–A–C

64 Carl Dahlhaus, Studies on the Origin of Harmonic Tonality , trans. Robert O. Gjerdingen (New Jersey: Princeton University Press 1990): 49. 65 Ibid., 50. 66 Ibid., 50. 27

(S in C major) and D–F–A (Sp in C major), noting that both occupy subdominant function in Riemann’s system, but the ‘p’ in Sp “indicates a modification of the chord, not the function.” Dahlhaus goes on to suggest that it would be possible, then, to understand function “without a theory of functions,” that S function is obtained by certain types of alterations to the basic, chordal, form of S. 67

Dahlhaus’ concerns may, however, be addressed by reviewing what Riemannian functions designate,

another ontological aspect of music theory, but one that has been more extensively scrutinized. Riemann’s

harmonic functions are perhaps better viewed not as chord functions, but rather they operate more clearly

and convincingly as phrase functions. What I mean by this is that Riemann’s symbols designate the position

of that chord relative to a tonic within the structure of a phrase, or prolongation. As Rehding notes,

cadential succession, which for Riemann involved “a succession of chords that establishes a tonic,” was an

important aspect of Riemann’s approach to harmony. 68 Riemann, of course, had his prototypical harmonic

progression in a phrase: T–S–D–T, which more contemporary theory has replaced with a T–PD–D–T

framework. This alternative became more used due to what William Caplin describes as “a number of

harmonic formulations not directly related to the harmony built on the fourth degree of the scale.” 69

Specifically, Caplin notes that predominant functions “generally relate to one of two main types—those

built above the fourth degree of the scale and those derived from the dominant of the dominant.” 70

Caplin’s divorce of subdominant from applied dominant-of-the-dominant function—and the subsequent necessity of introducing a slight alteration to the intermediary harmonic function between tonic

and dominant—is interesting in relation to the ontological differences between systems outlined in the previous section. As I argued there, there is a referential distinction between diatonic predominant chords such as IV and ii, and chromatic ones such as V/V: the former find their meaning from a direct reference to the tonic, while the latter have a more local referentiality towards the chord to which they act as the

67 Ibid., 50. 68 Rehding (2003): 67. 69 William Caplin, Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven (New York: Oxford University Press, 1998): 23. 70 Ibid., 23. 28 dominant. Replacing S with PD might be seen as necessary not because there was no way of deriving chords from S, but rather, I believe, from the recognition of this distinction, yet wanting to retain a means by which these chords could still be grouped according to their larger-scale function within the phrase. 71 That

Riemann groups these chords together under a single functional designate—S—suggests that his view of S

chords was similar: that Riemann’s S, more broadly conceived, is in fact identical to the more contemporary

PD, save for the different names involved. Thus my contention that Riemann’s functions serve less as

specific chordal designates, but rather more broadly as a classification of the ways in which chords fit as

functions in the cadential, or phrase, model.

Returning to Dahlhaus’ concerns regarding the distinction between ‘chord’ and ‘function,’ I believe

this explanation helps to clarify some of Riemann’s position. The transformational nomenclature that forms

the basis of Riemann’s analytic practice is, as Dahlhaus points out, more geared towards demonstrating

chordal, rather than functional, relationships. As Dahlhaus points out, in Sp the “p” means to replace the

fifth of S with its sixth: understood in this sense, it is most certainly describing a transformation of a chord,

but simultaneously suggesting that the chord serves the phrase function of “S.” But it is likewise impossible

to argue that any chord has an innate “S” (or PD) function in the same way a dominant or diminished

seventh chord invokes a sense of dominant function even shorn of context. S, or PD, functions are only

ever deeper-level functions of the phrase, whereas dominant and diminished-seventh chords have a more

innate dominant pull owing to the conventional dissonances they project. 72 Dahlhaus, then, is correct in assessing a confluence of meaning in Riemann’s symbols, but when his functions are understood not as a

specific harmonic designates, but rather deeper-level phrase functions, then this confluence of roles is

mitigated: the transformational nomenclature acts on chords at the musical surface as a way of relating

chords to one another at a very local, and very abstract—in the sense that these relationships are not always

71 Another possible reason for the proliferation of PD in place of S is the ease with which S can wrongly be associated with only the subdominant harmony, rather than a number of harmonies occupying subdominant (or predominant) function. 72 These, of course, are undeniably products of cultural conditioning. I use the term innate to mean innate with respect to the tonal system and Western listeners, and not necessarily acoustically innate in isolation, nor universally applicable. 29 audible—level, while the functional implications position those chords in the deeper-level confines of the prolongational phrase.

In short, one can imagine that Riemann, like Schenker or any number of other theorists, noticed the tonal convention of musical units beginning with a tonic, and ending with a dominant-to-tonic motion, but

the harmonies in between these two events were less consistent, but remained, for the most part, in the

same position: following the tonic but preceding the dominant. One can easily imagine this approach in

relation to the example from Salome in Example 0.1 above: the beginning and end of the passage are quite

clear in their tonic and dominant-to-tonic functions, it is only the third measure—the intermediary

position—that poses problems. As Cohn notes, “most nineteenth-century passages that can be seen to

juxtapose [chords] according to nonclassical principles exist in close proximity to other behaviors that are

normal under classical diatonic tonality.” 73 In this case, assuming classical phrase or prolongational conventions, this must be some kind of S (or PD) function because it appears between the tonic and the dominant: one can understand, to some extent, Schoenberg’s motivation in calling it an altered II, even if one disagrees with the ontological implications of that analysis. Had he analyzed the passage himself,

Riemann too would have likely assigned to the chord an S designate of some type. In this case I do not

disagree, but also believe there are more detailed and nuanced ways of understanding such chords, which will be the primary focus of the first three chapters of my dissertation.

III

Cohn’s third concern, regarding the way in which linear theory is often invoked as a means of

avoiding engaging with the difficulties posed by chromatic harmony, can in some ways be likened to the

problems approbated in the previous sections. Writing in 1995, Daniel Harrison somewhat sardonically

notes “we could take it as a sign of progress that little remains theoretically uncertain about augmented-sixth

chords. Or we could take it as a sign of complacency.” 74 Harrison’s commiseration that theory has in recent

73 Cohn (2012): 11. 74 Harrison (1995): 170. 30 years become complacent when confronted with understanding harmony, function, and tonal structure is an apt one. Not only has the study of tonality been subordinated in recent years to other approaches—neo-

Riemannian theory, transformation theory, and studies of form spring to mind—but more specifically one could look at the myriad Schenkerian analyses of highly chromatic music from around the time Harrison penned his statement—the 1980s through to the early 2000s specifically—and see a plethora of approaches that are content to write off chromaticism as non-structural, or passing linear prolongations of a more fundamental diatonic structure. 75 While I do not disagree that within a tonal framework chromaticism often

functions as an elaboration of an underlying diatonic structure, understanding it as only a linear feature,

rather than a feature shared between the horizontal and vertical domains has significant drawbacks. Indeed,

in many analyses that take the more linear view it appears analysts are claiming “non-functional,” or

“linear,” status for chords simply because they are unsure as to how to fit them harmonically within a tonal

framework. 76

Take, for example, Figure 0.4 which illustrates an analysis by William Marvin of the passage from

Tristan und Isolde shown in Example 0.2. Here Marvin accounts for the puzzling A-major triad by describing it as a chromatic elaboration of a 5-6 voice-leading motion, but abstains from giving it any sort of harmonic label. He writes:

The voice-leading sketch demonstrates that Wagner’s command of chromaticism is supported by an equally well conceived contrapuntal framework. The graph shows that the direct chromatic succession from A-flat to A major functions within an Auskomponierung of the neighbor note to G within the inner voice; against this neighbor note, an implied ascending third from E-flat to G appears in the tenor, while the main melodic activity consists of a 3–2 motion as tonic harmony moves to the dominant at the end of the phrase. 77

75 Certainly there are certain cases when chromaticism is only passing in nature (such as in voice exchange progressions, or when used melodically), but I am speaking here more specifically of entire chromatic chords being ignored. 76 For example, Kopp laments: “Although [linear] analysis offers a thorough means for contextualizing [chromatic] harmonies within a conventional framework, the potent, dramatic [chromatic harmonies] in this passage merit an explanation truer to their harmonic nature,” rather than subsuming them as linear elaborations of a diatonic framework. Kopp (2011): 404. 77 William Marvin, “Tonality in Selected Set Pieces from Richard Wagner’s Die Meistersinger von Nürnberg : A Schenkerian Approach, PhD diss. (Rochester: Eastman, 2001): 18. Note here as well that Marvin’s analyses both alter the A-major triad. In the score it is presented with the A n in the bass, whereas Marvin’s analysis leaves C in the bass. This is of course to draw attention to his suggestion that the A-major triad results from a linear 5-6 motion, but I feel that the chord exists in root position is of importance. I return to this passage at the beginning of Chapter 2. 31

Figure 0.4. William Marvin’s analysis of the Todestrank motif from Tristan und Isolde (Marvin, 2001: 18)

Example 0.2. Wagner, Tristan und Isolde , Act I, Scene 2, mm. 24–30

Like many Schenkerians, Marvin’s approach to analysis relies heavily on prioritizing contrapuntal procedures as a means of articulating structure in music. While it is undeniable that Schenker’s focus shifted towards the end of his life towards more contrapuntally-oriented schemata, it is important to remember that Schenker

conceived of musical structure as a combination between the vertical and horizontal realms. Linear analysis

is a useful tool for revealing aspects of deeper-level voice leading and motivic parallelisms in music, but when applied in a manner wherein it is used to dismiss harmonies that do not immediately conform to the 32 conventions of classical harmonic syntax, it comes across as too convenient in its avoidance of theorizing or discussing complex harmonies. I am not, of course, advocating that linear analysis be dismissed entirely. As

David Beach notes, “the foundation of Schenkerian thought is the relationship of harmony and voice leading at multiple levels,” and as such I would argue these two domains should be understood to work symbiotically. But this means that linear analysis should not be used as a crutch when the analysis of harmonic syntax becomes difficult. 78 And it is here, in the dismissal of the harmonic dimension, where many

of the more contrapuntally-oriented approaches to highly chromatic music seem to lose some of their

explanatory power: when chromatic chords are written off as mere linear motions without making an

attempt to reconcile them into a harmonic-functional framework.

Ignoring the harmonic surface, or sweeping it away as simply linear, also defeats the notion Beach

brings up regarding multiple levels of structure. Cadwallader and Pastille write that “motives at each level

express the tonal content of the previous level.” 79 The harmonic surface must be intelligible according to tonal prolongational procedures, and in doing so it reinforces and confirms deeper-level prolongational and contrapuntal structures. Indeed, the perceived inability of Wagnerian and post-Wagnerian harmony to achieve these prolongations in a unified and tonally comprehensible manner formed part of Schenker’s own criticism and ultimate dismissal of such music. In Das Meisterwerk in der Music , for example, Schenker lambasts Wagner’s music as being devised more for theatrical effect than for large-scale musical cohesion. 80

Schenker’s specific criticisms of Wagner and Strauss receive a more detailed description in an unpublished manuscript translated recently by William Drabkin and given the title “On the Decline of the Art of

Composition.” There, Schenker contends that Wagner’s music lacked the same type of musical unity— meaning an organic reciprocity between levels of structure that Schenker’s late theories prioritized above

almost all else—that he describes in the music of composers such as Mozart or Beethoven. He further

78 David Beach, “On Analysis, Beethoven, and Extravagance: A Response to Charles J. Smith,” Music Theory Spectrum 9 (1987): 179. 79 Allen Cadwallader and William Pastille, “Schenker’s High-Level Motives,” Journal of Music Theory 36, no. 1 (1992): 134. 80 Heinrich Schenker, “On Organicism in Sonata Form [1926],” in The Masterwork in Music Volume 2 , ed. and trans. William Drabkin (Reprint. New York: Dover, 2014): 29. 33 describes this lack of musical unity—a problem that he lays at the feet of Wagner—in his critique of Strauss, writing:

Not only do his harmonic progressions lack precision, but so much has also been packed into the individual harmonic degree that it is impossible for the ear to gain control of this length. Over long stretches, the fanatical recklessness of this method works all the more banally, since as we know it is not basically a question of a new artistic manifestation that has not yet been overcome, nor is it an erroneous one per se. For so long as a modicum of clarity is brought to the harmony, and the listener is guaranteed each time that it is a question of this harmonic degree and no other, then so far as I am concerned the part-writing can be as reckless as one likes, without causing any damage. It cannot be denied, however, that the enormous expansion of degrees has made harmonic progression in music very unwieldy. The spectacle that we have already witnessed before, with respect to contrapuntal technique, has repeated itself once again: the over-burdening of the cantus firmus in the past, the over- burdening of the harmonic degree today. 81

It is noteworthy that Schenker acknowledges that the question of which harmonic degree is being

sounded in highly chromatic music is a pertinent one, and furthermore one that, at least under the auspices

of classical tonality, often has no clear answer. In short, however, Schenker’s criticisms of Wagner and

Strauss seem to be rooted in an inability to firmly grasp ways in which the chromatic foreground in their works creates and confirms the same prolongational processes that he had identified as being so pertinent to

common-practice tonality.

Indeed, despite Marvin’s assertion that “surprisingly, many later authors have assumed that the

chromatic surfaces in this music presented a problem for the Schenkerian method,” and his subsequent

dismissal of the idea, I believe that the inability of conventional harmonic perspectives to understand what

Schenker refers to as the “chord grammar” in chromatic music is one of the most pronounced challenges to

undertaking tonal-prolongational analysis of this repertoire. My concern is that in refusing a harmonic

interpretation for foreground chords that do not immediately conform to the norms of classical tonality,

and that are not clearly serving any sort of foreground prolongational function (such as a passing chord

effecting a voice exchange), analysis is ignoring an aspect of music that is at least as important as the linear

spans. Certainly not all chords are of equal structural weight, but Beach’s assessment that “not all chords are

81 Heinrich Schenker, “On the Decline of the Art of Composition,” trans. William Drabkin, Music Analysis 24, nos. 1–2 (2005): 118–119. 34 viewed equally, and only those of structural significance are labelled as such,” rings slightly hollow for

densely chromatic music, wherein the number of chords that have structural weight–generally tonic and

dominant chords are those that Schenkerians weight most heavily—is vastly reduced in comparison to

classical tonality. 82

As a demonstration of this conflict, compare Marvin’s analysis above with Beach’s analysis of the

fourth movement of Beethoven’s Op. 2, no. 1, shown in Figure 0.5.83 In his analysis Beach does not give

Roman numerals for every chord, and suggests a linear analysis of the descent from the tonic to the dominant, neighboured by the subdominant pitch. That Beach avoids giving Roman numerals for every chord does not pose a significant drawback here because all of the chords that Beach does not analyze are conventionally tonal in nature, and present no problems in terms of our understanding them as tonally functional. Beach’s analysis occurs at a middleground level and an explicit analysis of the foreground is deemed unnecessary because of its tonal conventionality, but could be easily produced if required. This is not the case with Marvin’s analysis: the chord for which he declines to assign a Roman numeral does not have a simple solution in terms of its harmonic role, and because of this the omission, however well-

Figure 0.5. David Beach’s (1987) Analysis of a Passage from Beethoven Op. 2, no. 1, IV

82 Eugene Narmour, Beyond Schenkerism (Chicago: University of Chicago Press, 1977): 15–17. 83 Beach (1987): 176. 35 supported by appeals to the linear domain, feels slightly misleading, almost as though the exclusion is based on a lack of theoretic precedents for synthesizing such chromatic chords within a tonal-prolongational structure, rather than an analytic necessity for invoking linear theory.

Schenker—at least early in his career—had similar misgivings about appropriating linear explanations for chromaticism, a notion that seems too often to remain forgotten amongst those seeking to demonstrate the applicability of Schenkerian methods to chromatic tonality. Schenker writes of chromatic chords in his Harmonielehre :

Would it do to explain all these phenomena, which certainly are abnormal in a perfect diatonic frame, as merely passing notes or chords? Would anybody believe that such an assumption would relieve us from the duty of explaining their origins? Far from it. But, then, what is really going on in these examples? 84

On the other hand, I am just as inclined to agree with Marvin’s criticism of Charles Smith for relying too heavily on “a conception of chromatic chords rather than chromatic processes (emphasis Marvin’s).”85 Smith’s more metatheoretic argument is similar to the one I have made thus far—that simply relying on linear analysis to explain chromatic harmony without actually giving a harmonic designation to chromatic chords is disingenuous at best. In this regard I agree fully with Smith when he suggests things such as “[the] linear

sketch reflects the assumption that anything that needs to be said about chromatic music can be said in linear terms, and that chromatic sonorities are but the incidental results of voice-leading,” following with “I believe that this assumption is mistaken. The impact of chromatic music results from more than just the

linear patterns that can be found within it.” 86

Ultimately, Smith concludes:

Linear analysis does not tell us much about the harmonic conventions of tonal music whose chromaticisms are not merely decorative or sequential…Linear sketches tell us many valuable and insightful things about tonal pieces, but they fall short of pinning down the precise vertical coincidences of chromatically moving voices; they skim over the functional surface of chromatic music. 87

84 Schenker (1954 [1906]): 71. 85 Marvin (2001): 22. 86 Smith (1986): 103. 87 Ibid., 107. 36

Smith’s approach then takes a questionable turn, in which he suggests: “The assignment of only one label to each chord trivializes and depletes the impact of the music, which should be a machine for generating a multitude of interpretations." 88 Smith thus suggests an analytic methodology wherein a chord is understood

as having potential function in a variety of different keys. This leads to a number of contentious analyses wherein Smith analyzes a short phrase of music in six or more different keys, constantly shifting between

possible understandings of a given chord in the given moment, but rarely showing how the chords relate to

each other or engage in tonal-prolongational procedures on a deeper level that encompasses more than two or three chords.

David Beach’s response to Smith’s article summarizes neatly a number of the criticisms that have been directed at Smith’s approach. Beach writes:

What is the logic, then, of labelling [a C 7 chord in the key of F] as a potential Ger. 6 in E? (Why not V 7 of II in E or V 7 of VI in A, which makes about as much sense?) Though I would not want to argue against the value of understanding the potentialities of any musical event, this label is meaningless within the context of this phrase…It makes little sense to label individual events, as Smith does, according to what their function might be in some other context, as opposed to what they actually are, at least according to a particular interpretation, in this specific context. To do so is to divorce the event from its environment, the part from the whole. This does not mean that we should ignore the potentialities of musical events, but at the same time they should not dictate the analysis. In short, I believe music analysis must be context sensitive. 89

Marvin echoes and extends this criticism in an incisively insightful way. Marvin suggests that “Smith’s multivalent tonal readings, implying multiple keys on the surface of the music, are never adequately interpreted within the domain of the main tonality, backing this up by noting “one does not need to cite studies in music perception to recognize that a crucial aspect of interpreting harmonic motion involves retrospectively correcting an interpretation based on what has come later.” 90

In other words, a chord has a multiplicity of potential functions, some more logical or persuasive

than others. In this regard, Smith’s argument is a useful one, but Beach’s and Marvin’s criticisms point out

the flaws in the overly extravagant application of this type of analysis. They argue, and I concur, that it is

88 Ibid., 100. 89 Beach (1987): 182–185. 90 Marvin (2001): 21. 37 important to understand which function is actually being realized within the context of a passage. Despite all the potential readings ultimately a chord participates in the organized whole of the prolongation of the passage, and must be understood in this manner. Thus while it is problematic to trivialize harmonic processes to linear ones, it is likewise possible, and equally problematic, for one to go too far in the other

direction, focusing far too much on vertical conglomerations in isolation, as Smith’s approach tends to do.

What seems to be lacking, then, is a convincing bridge between the linear and harmonic realms when it comes to analyzing chromatic harmony, and what might be needed is a rapprochement between the two, one that understands harmonic function as a product between the vertical elements and the horizontal ways in which the vertical elements behave. Focusing solely on linear aspects ignores the ways in which harmony and counterpoint interact, while focusing exclusively on harmony as surface-level individualities fails to adequately convey how those harmonies function as part of a tonal-prolongational process. This dissertation will propose theories of understanding chromatic harmony that are both sensitive to the multiple functional potential of chords, while simultaneously proposing a methodology for synthesizing these chords within a larger-scale tonal-prolongational framework.

From the discussions in the three sections above, it is possible, now, to formulate a synthesized articulation of specific challenges facing tonal-prolongational approaches to the chromatic music of the late

nineteenth and early twentieth centuries. Firstly, there is the problem of conflicting ontologies between

approaching chromatic harmony as a fundamentally transformational practice, or approaching it as a

fundamentally polyreferential one. The growing dissatisfaction with simply labeling, or, as Cohn sees it, describing, chords with analytic symbols that are essentially devoid of meaning can be seen as a conflict arising from the ways in which we perceive these diverging approaches. Analyses such as VI 7s, or III, are intended to simultaneously suggest a chord’s position in a scale—in other words, the Roman numeral engages with aspects of referentiality—but the alteration symbols that suggest one chord is simply a 38 transformed version of another reflect a problematic perspective when their meaning is scrutinized beyond the immediate transformational level. Indeed, as I have suggested, in most cases the alterations contradict the referential aspects of diatonic progenitor. Cohn is entirely correct when he writes of the ability of

Roman numerals to furnish a first-level analysis of almost any tertian (or even non-tertian) chord. But surely

music theory must do more than simply describe sonority and root.

Secondly, there is a tendency in music theory to sweep the unexplainable under the proverbial rug.

Schenker himself lambasted this approach, writing:

It follows that the chromatic [pitch] in our example has its own deep justification, of a specifically musical nature; and if we all too often talk away such a chromatic change as a mere passing note or some such thing, this merely proves our general incapacity to follow the real meaning of the tones or, what amounts to the same thing, to hear musically. 91

And yet this tendency exists most often in Schenkerian approaches to chromatic harmony, wherein chords that appear unexplainable with the current tools of tonal harmony are written off as voice-leading phenomena. What is concerning in Schenkerian reductive approaches is that they too often refuse to interact with inexplicable chromatic chords on a harmonic level, and for all intents and purposes simply ignore them. While linear approaches are often able to clarify aspects of the large-scale structure of passages, this comes at the cost of understanding how this larger-scale tonality is constructed and produced through the harmonic roles of the chords at the musical surface, and often renders the analyses unconvincing. As

Cohn sardonically notes, “We can’t just go and pretend that we have made coherent music in B f major. If a tonal theory is to meet its claims of explanatory adequacy, it needs to be able to specify the role, with respect to tonic, of the harmonies that separate the bounding

92 6 tonics.” If we can explain how I–V 5–I prolongs tonic through linear features while simultaneously

acknowledging its harmonic function, then surely if prolongational theory is indeed an adequate tool of

analysis, it must be able to do so for more chromatically complex progressions as well.

91 Schenker (1954 [1906]): 257. 92 Cohn (2012): 2–3. 39

Where Cohn and I share these similar frustrations with the conventional approaches to the analysis of chromatic music, his recourse, as he describes, is to “respond to these questions by adapting a conceptual framework erected…by the field of atonal pitch-class theory, whose great achievement was to develop a systematic approach for exploring the properties, potentials, and interrelations of chords (“sets”) within the

chromatic universe.” 93 In this way, neo-Riemannian theory, and the way in which it catalogues and quantifies inter-chordal units of voice-leading work while simultaneously abandoning the necessity for chromatic chords to exhibit referentiality—directly or indirectly—to a governing tonic, can be seen as adopting an almost entirely transformative perspective. As Kopp notes, “To explain chromaticism in nineteenth-century music that poses challenges to more traditional modes of analysis, neo-Riemannian theory posits mechanisms of structural coherence to which harmonic fifth relations and even the presence of a tonic are extraneous.” 94 In other words, Cohn, and other neo-Riemannians, deal with the tonal-referential problem evinced by chromatic triads (or seventh chords) by simply doing away with the problem altogether.

But, as will be the topics of discussion in the first two chapters, there are progressions wherein the parsimonious voice leading that neo-Riemannian approaches prioritize does little to elucidate coherence or structure between chords. This is most evident in the problems that neo-Riemannian theory evinces when forced to integrate seventh chords (which are often far more prevalent in number than triads in late nineteenth-century music) into its systems, but is also a consideration when dealing with triads that simultaneously do not respond well to either models of parsimonious voice leading nor to conventional tonal analysis. Further, attempts to integrate neo-Riemannian theories into larger-scale tonal analysis raises questions regarding whether shifting between neo-Riemannian parameters and more classically tonal ones constitutes an analytic system that, as Cohn points out, meets explanatory adequacy. Such an approach might, in fact, be considered not a system at all, but rather a continuous slipping between systems when one becomes inconvenient or untenable in an analysis. While some might be content with the assertion that a

93 Ibid., 13. 94 David Kopp, “Chromaticism and the Question of Tonality,” in The Oxford Handbook of Neo-Riemannian Music Theories , ed. Edward Gollin and Alexander Rehding (New York: Oxford University Press, 2011): 400. 40 passage holds some tonal elements, and some disjunct, or non-tonal, elements, my own views are that such a slipping between systems reflects a weakness in current analytic methods.95

This is not to say that I reject Cohn’s approach or find nothing useful in it—far from it. In fact,

Cohn’s perspectives on these types of chords and progressions have had a profound influence on the approaches that I take in developing ways of understanding the chromatic syntax of late nineteenth- and early twentieth-century harmony. I view Cohn’s work, and the ways in which he has pointed out typical voice-leading patterns for a number of these striking chromatic progressions, as a point of departure for my own work, and ways in which the atonal voice-leading relationships he discusses and codifies can be neatly folded back into common-practice prolongational processes when viewed from a slightly different angle.

My approach, then, takes the opposite approach of Cohn’s: rather than prioritizing the ways in which chords can be transformed into each other, I focus on an underlying tonal structure, and the ways in which chromatic harmonies of various types are polyreferential elaborations or enhancements of those processes. As Schenker suggests, “[chromaticism] is an element that does not destroy the diatonic system, but which rather emphasizes and confirms it.” 96 In my view, then, the polyreferential aspects of tonality take

precedence over the transformative ones. This is not to say that chordal alteration is non-existent, but that it

should be understood as a much more restricted practice than current scholarship adumbrates, and one that

further requires invoking other tonal parameters in order to convey why the proposed alterations retain

tonal function, rather than simply allowing for wanton transformative alteration. Chromatic tonality, I argue,

is not a distinct practice, nor a new one, but an extension of previous practice. As Robert P. Morgan notes:

Something as ubiquitous as a common practice does not die easily; and the musical developments responsible for its dissolution, above all in their earlier (nineteenth-century) forms, took shape against an enduring backdrop of stubbornly persisting tonal conventions. The evolution of tonality in the nineteenth century thus did not give rise to an entirely new way of doing things, but to modifications and extensions of what was already being done.

95 Rings, for example, links neo-Riemannian theory and post-structuralist valorization of disunity. He writes: “The valorization of disunity, crisis, fragmentation, and heterogeneity in [the New Musicological] literature finds a curious and distorted echo in neo- Riemannian theory. Indeed, in his introductory article to the Journal of Music Theory issue dedicated to neo-Riemannian theory, Richard Cohn explicitly situates neo-Riemannian analytical approaches with respect to “an evolving post-structuralist critical practice,” suggesting a community of purpose as regards claims of tonal disunity.” Richard Cohn, “Introduction to Neo- Riemannian Theory: A Survey and a Historical Perspective,” Journal of Music Theory 42, no. 2 (1998): 167, cited in Rings (2011): 498. 96 Schenker (1954 [1906]): 288. 41

[This involves] harmonic entities such as augmented triads and diminished seventh chords that at some level can be—and ultimately are—folded back into normal common-practice prolongations according to common-practice procedures…The new tonal procedures, in other words, even the most radical, were dependent upon the persistence of a relatively stable musical language, which provided the necessary crucible for their formation. Only in a few exceptional cases does the diatonic underpinning become irrelevant." No new "practice" coalesced. 97

And this is the aim of my dissertation: to reconcile the difficulties in the analysis of late nineteenth- and early twentieth-century chromatic tonality with tonal-prolongational processes, and thereby demonstrate

that it is possible to understand much of the chromaticism in the works of composers such as Wagner and

Strauss as fundamentally an outgrowth of classical tonal processes. To fold-back, as Morgan puts it,

chromatic harmony into common-practice prolongational procedures, and demonstrate that chromatic

tonality is indeed not an entirely new practice, but an outgrowth of the old. Where Cohn opts for the atonal

approach (though, in fairness, Cohn does often situate his analyses within a tonal backdrop), my approach

attempts to find ways of integrating the abundantly disorienting chromaticism of late nineteenth- and early

twentieth-century music within a tonal framework.

While chromatic chords can be viewed as transformations of diatonic ones, my approach eschews

these somewhat arbitrary ways of generating chromatic chords, and adopts instead a more intensely

referential tack, while maintaining that diatonic tonality forms the basis that underlies chromatic procedures.

In this sense, I adapt Kurth’s tripartite division of harmonic referentiality. Diatonic chords and mode-

mixture chords are categorized as tonal referents, meaning they exhibit a direct relationship to the tonic when being used as prolongational chords on the harmonic surface.98 Conversely, applied chords are understood as local referents, meaning that their point of reference is the tonally referential chord to which they are applied. Thus fVI relates directly to the tonic because it is a modal chord with respect to the tonic, but V 7/ii does not, and instead it is understood as locally referential, requiring the supertonic to mediate its relationship to the tonic. In the final category, self-referential chords are identified as chords that act

97 Robert Morgan, “Are There Two Tonal Practices in Nineteenth-Century Music?” Journal of Music Theory 43, no. 1 (1999): 160. 98 See again footnote 51 above. 42 centrifugally under theories of tonality: chords with altered tonics, dominants, and subdominants, such as fvi, VI 7s, III s, or fiii, for example. 99

Because these types of self-referential chords are the ones whose presence often challenges the norms of classical tonality, investigation of the ways in which they can be understood to participate in prolongational processes will form the basis for the theories I develop in the first two chapters of my dissertation. There, I suggest that harmonic function is not a product of static vertical conglomerations of pitches, scale degrees, or intervals, but rather that tonal function is inherently a product of musical motion.

The creation and understanding of function requires analysis to look beyond the static verticalities we call chords, and investigate ways in which other tonal parameters—specifically, in my view, intervallic valency and adherence to conventional voice-leading behaviours—contribute to the creation of function in tonal music. Chapter 1 proposes a model of tonal function based on the idea that dominant function results when specific univalent dissonant intervals —the tritone and diminished seventh—are sounded and progress according to tonal norms to a more stable consonance. Using this model, I suggest that diminished-seventh chords can undergo chromatic alteration by semitone while remaining functional within a tonality, and I use this approach to explain a number of unconventional seventh chords in prolongational contexts in the music of Wagner and Strauss. Chapter 2 builds on this framework, extends it to similar unconventional triads ( fiii, III s, fvi, VI s), and through voice-leading models similar to those in Chapter 1, hypothesizes ways that these acoustically consonant chords function as dissonances. I then consider how this describes tonally the notion of apparent consonances put forward by Alfred Lorenz, which he discusses mostly in relation to

Wagner’s Parsifal , but never develops further, nor integrates fully into theoretic or analytic models. 100

Chapter 3 develops a methodological framework for understanding tertian sonorities with non- tertian appendages in tonal music. I begin this approach with an overview of early thoroughbass theories,

99 To clarify at this juncture: I differentiate between a chord on the harmonic surface, and a Stufe , or deeper-level key area. I am arguing that chords such as fiii, or VI s cannot function prolongationally at the harmonic surface, but the root of these chords ( f3 , or 6 respectively) can still be a Stufe (which roughly translates to scale-step) at a deeper level of structure. I will explore this distinction in Chapter 4. 100 Alfred Ottokar Lorenz, Das Geheimnis der Form bei Richard Wagner [1924–33], Reprint (Tutzing: H. Schneider, 1966): IV: 89–90. 43 comparing the ways in which they discuss chords containing the interval of a sixth with the perspectives advocated by Rameau, which subsequently became popularized as the theory of chordal inversion. Here I suggest that the thoroughbass approach, wherein the sixth is considered an accidental dissonance (meaning

it displaces the expected fifth) is a fruitful way of conceptualizing certain harmonic progressions in the

tonality of Wagner and Strauss. From here, I investigate a number of extensions to this theory that help

demonstrate Strauss’ tonal language within a prolongational context, such as appendages beyond merely a

sixth. Like the altered diminished-seventh chords and triadic variants, many of these structures also sound

like more commonplace sonorities, but function as different chords when their context and voice leading

are considered.

Having investigated how chromatic chords can contribute to prolongational tonality in the first three

chapters, Chapter 4 proposes modifications to the ways in which we conceive of tonal structure at levels of

structure beyond the harmonic surface. Following contentions by Eugene Narmour, I suggest that the

Schenkerian Ursatz should not be taken as axiomatic at deeper structural levels. Instead, I investigate ways in which Schenker’s earlier theories of tonal structure might be better suited for analyzing tonal structure in

late nineteenth- and early twentieth-century music. Specifically, I suggest that the Ursatz model functions

best as a means of expressing the way tonality—chords interacting to prolong a deeper-level Stufen —

functions at the level of the phrase or section, that is to say, over smaller musical units. It is the interactions

between these deeper-level units, or Stufen , that I propose need not be approached as exhibiting the same

logic of chord progression as the prolongational chords at the harmonic surface do, that deeper level

structure can be understood melodically, as a succession of composed-out tones that find representation as

the tonalities of the various sections of a piece. Where tonalities are often represented by triads, I contend,

again following Schenker’s earlier thinking, that triads are themselves a projection of their own root tone,

and develop this melodic model as a way of understanding harmonic structure in chromatic music. 101

101 See William Pastille, “The Development of the Ursatz in Schenker’s Published Works,” in Trends in Schenkerian Research , ed. Allen Cadwallader (New York: Schirmer Books, 1990): 80–82. 44

The dissertation’s conclusion ties together these various strands by demonstrating how the technical

aspects developed in the preceding chapters can support hermeneutic interpretations of late nineteenth- and

early twentieth-century music. To this end, I undertake prolongational analysis of the first scene of Strauss’

Salome , and describe how the deeper-level prolongations create a tonal structure that supports a reading of

the titular character as the primary focus of the musical and the dramatic domains of the opera. 102 I then compare this to earlier nineteenth-century opera in which the tonalities of female characters, such as Kundry in Parsifal are made tonally subordinate to that of other male characters (Klingsor, Parsifal). Ultimately, I suggest that Hepokoski and Darcy are correct in their assessment that music analysis and theory, despite oftentimes being highly specialized and technical in nature, is a necessary first step to more hermeneutic interpretation, but that hermeneutic, cultural, or any other kind of broader humanistic discussion is the ultimate goal of analysis and the study of music.

102 This view is one that has been highly debated, with scholars such as Lawrence Kramer and Susan McClary suggesting that Salome’s power is ultimately lost to the male characters, while Hutcheon and Hutcheon (2011) suggest that Salome retains power. Chapter 1 Dissociating Sonority and Function Harmonic Polysemy and Chromatically Altered Diminished-Seventh Chords in Late Nineteenth- and Early Twentieth-Century Tonality

A bone of contention exists between Liszt scholars and Wagner scholars regarding which composer conceived of the famous Tristan chord, that is, as Alexander Rehding puts it, “which composer thought of it first ?” 1 While advocating for a digression from questions of authorship, Rehding brings up, almost in passing, a more interesting musical observation: despite the resemblance between the opening of Tristan und

Isolde , and a passage in Liszt’s song “Ich möchte hingehn,” shown in Examples 1.1a and 1.1b respectively, the chords themselves are different sonorities.2 In Liszt’s song, the chord in question is spelled G s–B–D–F, a conventional third-inversion diminished-seventh chord in the key of A that resolves to a V 7 chord. 3 The

Tristan chord, however, is spelled G s–B–Ds–F, but also resolves to a V 7 chord in A (minor): the only difference between these progressions is the D s which creates the tonally-disorienting half-diminished sonority. 4

1 Alexander Rehding, “Liszt und die Suche nach dem ‘TrisZtan’-Akkord,” Acta Musicologica 72, no. 2 (2000): 171. Liszt scholars, motivated in part by Peter Raabe’s assertion that the famous opening passage from Tristan und Isolde appeared in Liszt’s song “Ich möchte hingehn” ten years prior to Wagner even beginning work on Tristan , contend that Wagner plagiarized the progression, copying it from Liszt’s song. Conversely, Wagnerians claim that Liszt’s use of the chord is an allusion to Tristan , with the most damning evidence coming from Rena Charnin Mueller’s study of Liszt’s score (R.C. Mueller, “Liszt’s ‘Tasso’ Manuscript,” PhD diss. [New York State University, 1986]: 123), which revealed that Liszt inserted the Tristan progression long after the song had been written. See Rehding’s article for a more detailed accounting of the various arguments and counter-arguments in this ongoing debate. 2 Rehding (2000): 173. 3 See, for example, Daniel Harrison’s description of the progression as having a subdominant tendency that is “very noticeable,” though he ultimately advocates understanding it as dominant whenever the voice leading concurs (Daniel Harrison, Harmonic Function in Chromatic Music: A Renewed Dualist Theory and an Account of its Precedents [Chicago: University of Chicago Press, 1994]: 66). This progression is relatively ubiquitous and exists even in the confines of the more diatonically-oriented classical tonality of Bach, Mozart, and Beethoven. See, for example, Bach’s C-Major Prelude from WTC I, or the slow introduction to Beethoven’s Piano Sonata op. 13. 4 And yet this one semitone of difference has caused dissention and contention regarding almost all aspects of the Tristan chord over the last 150 years, in what seems like far too great a conflict over such a minute alteration. While many of these perspectives are cited elsewhere in this chapter, a wonderful resource for the myriad interpretations of the Tristan chord is Robert Bailey, Prelude, and Transfiguration from Tristan und Isolde (New York: Norton, 1985), which reproduces in English translation a large number of historic and early contemporary analyses of the prelude, often with a specific focus on the eponymous chord. One of the main contentions in this conflict is whether the G s or the A n is the chord tone. 45

Example 1.1a. Liszt, “Ich möchte hingehn,” m. 125 Example 1.1b. Wagner, Tristan und Isolde , mm. 1–4

Despite the semitonal, and thus sonorous, difference, these two chords are comparable in function and behavior. The voice-leading patterns of both chords, shown in Figures 1.1a and 1.1b, are virtually identical, both resolving to a dominant-seventh chord of A. 5 In such a scenario, the idealized voice-leading

sees b6 in the bass step down to 5, while the other three pitches remain static. In Liszt’s rendering, despite

the voice exchange, this is precisely the voice leading that occurs. Likewise, the Tristan chord’s voice leading follows the conventions of diminished-seventh voice leading, with the exception of the chromaticized note

Ds, which resolves by semitone to D n, a slight deviation from the more prosaic stasis of Liszt’s D n owing to

Figure 1.1a. Analysis of Example 1.1a Figure 1.1b. Analysis of Example 1.1b

5 Patrick McCreless, following Robert Bailey, suggests that in the chromatic tonality of the mid-to-late nineteenth century, it becomes less useful to understand tonal structure from the lens of twenty-four major and minor keys, but rather as twelve tonal centers (C, C s, D, etc.) that can be expressed harmonically as either major or minor tonics. See Patrick McCreless, “Ernst Kurth and the Analysis of Late Nineteenth-Century Chromaticism,” Music Theory Spectrum 5 [1983]: 60. This argument is reminiscent of Schenker’s notion of major-minor keys in which mode is irrelevant to the centricity of a pitch (see Heinrich Schenker, Harmony [1906], ed. and ann. Oswald Jonas, trans. Elisabeth Mann Borgese [Chicago: University of Chicago Press, 1954]: 84–115. 47 the chromaticism Wagner employs. In comparing these two chords not only as vertical objects, but also investigating their behavior as expressed through their voice leading, it is no wonder that these two passages sparked such a lengthy debate and comparison: despite the difference in sonority, the chords behave virtually identically. These parallelisms suggest that there is a functional relationship between the leading- tone diminished-seventh chord and the Tristan chord. 6 What, then, are the features of the Tristan chord that would permit it to be understood as a chromatic alteration of a diminished-seventh chord, despite the centrifugal nature of the alteration?7

This question of chromatically altered diminished-seventh chords forms the topic of this chapter.

Detailed study of the chromatic syntax of late nineteenth- and early twentieth-century composers such as

Wagner and Strauss suggests that chromatically altered diminished-seventh chords became part of the tonal syntax, and are, if not commonplace, then at least common enough to warrant further investigation.

Recognizing the challenges in integrating such chords into common-practice tonal approaches, this chapter

6 There is further evidence for such an understanding. As Rehding, and Alfred Lorenz before him, point out, Wagner uses the unaltered diminished-seventh chord later in the Prelude to harmonize the same ascending line. This version appears in m. 66, still accompanying the same ascending chromatic line, but very unambiguously a fully-diminished seventh chord in third inversion, and, even more clearly, appearing as a neighboring chord between two straightforward iterations of the dominant. See Rehding (2000): 181. See also Alfred Ottokar Lorenz, Das Geheimnis der Form bei Richard Wagner , Vol. 2: Der musikalische Aufbau von Richard Wagners “Tristan und Isolde” [1926], Reprint (Tutzing: H. Schneider, 1966), trans. Robert Bailey in Prelude, and Transfiguration from Tristan und Isolde (New York: Norton, 1985): 212. 7 Among the many different understandings for the Tristan chord that have been proposed, understanding it as a chromatically altered diminished-seventh chord is one over which relatively little ink has been spilled. William Mitchell proposes the idea that o4 the Tristan chord is a variant of the vii 2 chord, but does not develop this into a theory—his suggestion is more passing in nature, in service to his larger goal of analyzing the Prelude using more orthodox Schenkerian techniques (William Mitchell, “The Tristan Prelude: Techniques and Structure,” The Music Forum , vol. 1 (1967): 162–203). Nathan Martin, responding to Mitchell’s analysis, has argued against this interpretation, citing his discomfort (based in aural perception) in analyzing a lack of functional progression between the Tristan chord and the subsequent V 7. Martin instead proposes a new category of augmented-sixth chord as the solution to the Tristan chord (see Nathan Martin, “The Tristan Chord Resolved,” Intersections 28, no. 2 (2008): 10–15, 22). Charles Smith (“The Functional Extravagance of Chromatic Chords.” Music Theory Spectrum 8 (1986): 139) comes close to such a suggestion, concluding that it is “a new kind of dominant chord,” but one he suggests is “a ( fvi ø7 )…” Smith asks the reader to consider carefully what makes a fvi ø7 chord so impactful, before ultimately likewise reverting to the more conventional extended augmented-sixth chord interpretation. While never explicitly referring to the chord as a chromatically altered diminished-seventh chord, Benjamin Boretz employs post-tonal pitch class analysis and language to describe the Tristan chord as a version of the subsequent dominant-seventh chord with a number of semitonally displaced pitches: specifically the D s, which displaces the D, and the F which displaces the E (see Benjamin Boretz, “Meta-Variations, Part IV: Analytic Fallout (I), Perspectives of New Music 11, no. 1 (1972): 159–172). Boretz’ interpretation here might be more susceptible to Martin’s criticism of this view, as Boretz’ claims suggest that the two chords are fundamentally the same. Conversely, Louis and Thuille note the possibility of the diminished- seventh interpretation, but argue against it, writing “the [Tristan] chord does not belong to the seventh scale degree (dominant) but rather to the second scale degree (subdominant).” Their interpretation favors seeing the G s “more correctly interpreted in the manner in which it is actually heard—namely an unprepared ascending suspension” (Richard Isadore Schwartz, “An Annotated English Translation of Harmonielehre of Rudolf Louis and Ludwig Thuille [1913],” Ph.D. diss. [Washington University, 1982]: 282). 48 proposes that chromatically altered diminished-seventh chords form a group, or family, of chromatic chords that are related through their shared dominant function: a function that is not expressed directly through

conventions of vertical sonority, but, as I will argue, through adherence to the conventions of voice leading

and dissonance resolution. In this sense, then, I question some of the traditional notions regarding the

association of sonority with limited types of function in classical tonal theory. 8

I begin the chapter by proposing a functional model of intrinsic factors that create dominant

function in tonal music, suggesting through a series of quasi-transformational figures that this function is the result of a combination between the sounding of dissonant yet univalent intervals, and the motion from

these intervals to more stable intervals upon resolution. 9 As such, I argue that function is a result of a process that chords undertake, rather than an innate property they possess. I then use this model of motion- as-function to argue that diminished-seventh chords can be altered chromatically, yet, as long as certain voice-leading requirements are met, retain their dominant function. The second section of this chapter surveys the limited historic precedents for chromatically altered diminished-seventh chords. Despite a dearth of attention in more contemporary theory, such chords were occasionally discussed in more historic accounts of nineteenth-century harmony. Specifically, brief passages that allude to such chords exist in the works of authors such as Schenker, Marx, Louis and Thuille, Tchaikovsky, and Ernst Kurth, in addition to more vague comments expressed by less well-known theorists such as Kistler. In the final section I demonstrate how the perspectives developed in this chapter can be applied to the analysis of works by composers such as Wagner and Strauss. These analytic vignettes suggest that tonality, and specifically the processes of what Patrick McCreless describes as “classical tonality,” are still operational and understandable in these late nineteenth- and early twentieth-century works, and that incorporating the approaches proposed in this chapter might be a step towards reopening late nineteenth- and early twentieth-century chromatic

8 Obviously triadic sonorities do not share this feature, as a major triad can function as any number of chords: I, V, IV, VI in a minor mode, and so on. Seventh chords, however, are traditionally viewed as more limited in their scope: the half-diminished seventh is usually restricted to ii in minor modes, or vii in major ones, while the major-minor seventh is restricted to V, as is the fully-diminished seventh. 9 I use the term “prolongational dominant” function to distinguish from the more immediately salient cadential dominant function. 49 tonality to analytic insights afforded by tonal-prolongational analysis, which in recent years has been overshadowed by other approaches to chromatic harmony (i.e. neo-Riemannian theory, transformation theory, set-class approaches). 10

I A Theory of Chromatically Altered Diminished-Seventh Chords

The notion of valency is a good point of departure. In conventional discourse, the notion of chordal

univalency suggests that certain chords are highly salient as position-finding chords in classical tonality

because they contain intervals that are exclusive to only a single, or relatively small number of keys. 11 The most common of these chords is the dominant-seventh, owing to its inclusion of the tritone, which only occurs in one place in a given major scale (between 4 and 7), and whose component pitches are present in only two major keys. As Harrison writes, “when confronted with, say, a tritone, one can narrow the choices for a tonic to two…that is, the tritone interval marks the place of either 7 and 4 in C or of 4 and 7 in

Fs/G f…if just one additional pitch class is heard, then a sure assignment of tonic can be made.” 12

While this notion serves the classical repertoire well, it is less useful in the harmonic syntax of the mid-to-late nineteenth and early twentieth centuries, where these valent intervals do not always conform to their common-practice precedents. For instance, if we imagine adding the pitch G to B and F, this does not inherently direct us towards C: the chord in question could be a dominant seventh in C, with an omitted fifth, but what if the F and G both resolve to F s, and the B resolves to A s? In that case the chord is not pointing to C, but to F s, as an augmented-sixth chord. While the enharmonic relationship between the major-minor seventh and the German augmented sixth is endemic to common-practice tonality, this example suggests that it is not necessarily the vertical component of the chord in which the function resides.

10 Patrick McCreless, Wagner’s Siegfried (Ann Arbor: UMI Research Press, 1982): 89. 11 See, for example Richmond Browne, “Tonal Implications of the Diatonic Set,” In Theory Only 5, no. 6 - 7 (1981): 3–21; and Harrison (1994): 73–75. 12 Harrison (1994): 73. 50

Rather, the chord’s function is dependent on the way in which it resolves. This contention grates against a century of function-based theories that contend—as Bryan Hyer notes of Riemann, for instance—that “it is not what a chord does that matters, but what it is .” 13 While this approach serves the common-practice repertoire well, owing to the presence of a relatively stable musical syntax in which chords resolve in a more-or-less consistent manner, I argue that as the enharmonic polysemy of various chords is exploited to greater degrees in the mid-to-late nineteenth century, a focus on the ways in which fundamental dissonances such as the tritone and the diminished seventh discharge onto consonant thirds and fifths (or their inversions, in certain cases) becomes a more precise determinant of harmonic function. 14 While Harrison suggests that “voice-leading in chromatic music is not the colleague of harmony that it is in earlier music but rather its servant since it does not control the choice, progression, or resolution of chords,” and that it is

“useless [to] invoke [voice-leading] rules, difficult [to] speak of consonance and dissonance as principle factors in harmonic progressions,” I would argue to the contrary.15 As this emphasis on harmonic polysemy becomes more pronounced in the syntaxes of composers such as Wagner and (to a greater degree) Strauss, it becomes more important to focus on the ways in which chord’s behave as the primary purveyor of their function. 16 I term this type of univalent, function-projecting interval sequence a functional interval progression

(FIP). Figures 1.2a through 1.2c demonstrate the various FIPs found in the conventional resolutions of

13 Brian Hyer, “What is a Function?,” in The Oxford Handbook of Neo-Riemannian Music Theories , ed. Edward Gollin and Alexander Rehding (New York: Oxford University Press, 2011): 109. Harrison writes, “voice leading structure is subordinated to harmonic structure, [and thus] harmony, and harmony alone, [is] the point of departure for [his] investigations into late nineteenth-century chromatic music.” 14 This is comparable to Hyer’s description of function. He writes, “The tonic triad assumes value only in relation to the dominant and subdominant triads…the tonic triad, however, is actually imperceptible at the moment the dominant or subdominant triad is understood as signifier; at that moment, the tonic triad is signified only as an idea, an abstraction.” Brian Hyer, “Tonal Intuitions in Tristan und Isolde (Ph.D. diss., Yale University, 1989): 28–29. 15 Harrison (1994), 124. 16 One might see here some resemblance to notions of scale-degree qualia and energetics, brought up most recently in Steven Rings’ monograph (see Steven Rings, Tonality and Transformation [New York: Oxford University Press, 2011]: 42), wherein he describes his use—as well as David Huron’s (Sweet Anticipation: Music and the Psychology of Expectation [Cambridge: MIT Press, 2006])—as a description of “scale-degree sensations.” The idea that a scale degree has a particular quality that it expresses is, like other theories discussed previously, more monotonal in its orientation (that scale degree X in a given key always has a certain sensation or has a propensity to resolve a certain way), and function on individual pitches/degrees, whereas the FIPs I discuss are dependent on a number of factors aside from merely a global key, and involve multiple pitches sounding (actually or implicitly) as simultaneities. 51 dominant-functioning chords: the major-minor seventh, the half-diminished seventh, and the fully- diminished seventh. 17

This approach is a notable contrast to the more common perspective in contemporary theory wherein the presence of a leading tone alone is enough for a chord to exert dominant function. Cohn, for instance, suggests, “Our impulse is to seek out leading tones, which channel the energy of one of the triads into the other,”18 while Harrison refers to 7 moving to 1 as dominant discharge. 19 More assertively, Charles

Smith (1986, 110) writes that “any chord containing a leading tone is a dominant.”20 Carl Dahlhaus (1990

[1968], 45), on the other hand, suggests that the leading tone is only part of the story, writing:

The leading tone is undeniably one of the constituent features of the cadence…[but] the leading-tone tendency is only a cofactor in the effect of the dominant, an effect based on the correlation between a leading-tone progression, a descending fifth, and a dissonant seventh. An ascending half step can connect a seventh with an octave, or a fifth with a [flattened] sixth. And while the leading tone is indeed the seventh of a scale, it is not the fifth. The leading-tone effect is thus dependent upon context, upon the system of tonal relationships. Rather than being a basic phenomenon, it is itself based on other phenomena. 21

Dahlhaus here suggests that it is not only the leading tone that creates dominant function, but its combination with other factors, notably the tritone-creating 4.22 The descending fifth, however, may not be

17 I employ the major-minor tonality of a given pitch center as the source of generating tonal meaning. What I mean by this is that chromatic notes such as 3/f3 and 6/f6 , are understood, following Schenker, as simple modal variants of one another (borrowed from the parallel minor). I contrast this with pitches such as s5, s1, or s4, which are not derived from simple mixture, and are thus considered centrifugal to the tonality in question. Thus vii o7 exists equally diatonically in major as vii ø7 . Refer to footnote 5 above regarding McCreless’ suggestion of single major-minor tonalities, as well as Matthew Brown, “The Diatonic and the Chromatic in Schenker’s ‘Theory of Harmonic Relations,’” Journal of Music Theory 30, no. 1 [1986]), who discusses Schenker’s major-minor tonal system. 18 Richard Cohn, “Uncanny Resemblances: Tonal Signification in the Freudian Age,” Journal of the American Musicological Society 57, no. 2 (2004): 307. 19 Harrison (1994): 92–93. 20 This diverges from the original hypothesis of Fétis, who suggests a similar argument to my own: that the notion of ‘tonality’ rests on the dissonance between 7 and 4, and its resolution by semitone to a consonant third (though Fétis seems to ignore that when resolving to minor triad, it is not a semitone between 4 and b3 , but a whole tone). See François-Joseph Fétis, Complete Treatise on the Theory and Practice of Harmony , trans. Peter M. Landy (New York: Pendragon Press, 2008): lxx–lxxv. 21 The descending fifth is more endemic of cadential dominant function, rather than prolongational dominant function wherein o6 6 the descending fifth is less common (progressions such as I–vii 5–I , for instance, include no descending fifth). 22 In this sense too, 4 in an upper line might be seen as an integral part of the tonality of a phrase. While the V triad may express a weak dominant function (such as in cases wherein it prolongs the initial tonic), its cadential dominant function at least in classical tonality, is almost always expressed after a predominant chord containing 4 in one of the upper voices, which creates a deeper- level long-range melodic tritone between 4 and the eventual 7 that materializes in the dominant triad. 52

Figure 1.2. FIPs for Dominant-functioning Chords

a) Dominant Seventh FIP b) Half-diminished Seventh FIP

c) Diminished-Seventh FIPs.

as necessary as Dahlhaus suggests. Certainly the cadential dominant requires such a motion, but prolongational dominant function also arises from inverted dominant chords, and while these chords are not as functionally salient as the cadential dominant, they nonetheless exert dominant function, suggesting 53 that the more important components of dominant function are the leading tone and dissonant seventh—the two components that form the tritone—and their resolution to the tonic and third respectively.

Despite the ubiquity of the tritone, it is not unique in its univalent properties: the diminished

seventh and its resolution to a perfect fifth projects a functional discharge similar to the tritone. Harrison

describes this process: “[the] resolution—to the perfect fifth between 1 and 5—is between the root and fifth

of a major or minor tonic (or tonicized) triad” 23 Further, we might also note that the diminished-seventh

interval is unique to a single common-practice chord—the diminished-seventh chord—which, generally-

speaking, only ever functions as a prolongational dominant chord built on 7 of a given key. 24 Like the

tritone, however, the existence of this interval in isolation does not inherently create function, only the

potential for function. 25 To realize that potential it must discharge in an idiomatic manner, namely, the dissonance must resolve to a consonance, in this case to a perfect fifth (or perfect fourth if it occurs if a chord is voiced in such a way that augmented-second interval resolves to a fourth that remains consonant).

As shown in Figure 1.2c, unlike major-minor and half-diminished seventh chords, diminished- seventh chords contain multiple fundamental dissonances: the tritone between the root and fifth and the diminished-seventh interval between the root and seventh are both suggestive of the same tonic, while the secondary tritone between the chordal third and seventh suggests a possible tonic a third higher. 26 But it is the presence of multiple fundamental dissonances that give rise to the possibility of altering diminished-

seventh chords without the loss of their dominant function. Because these chords contain both the tritone

and the diminished-seventh dissonances, it is possible to subject the more conventional tritone to the

23 Harrison (1995): 173. 24 Looking at FIPs might also suggest why a vii o(7) chord can convincingly substitute functionally for V 7: beyond sharing three common tones, they also share the tritone FIP. Conversely, while the common-tone diminished-seventh includes the same dissonant intervals (tritone, diminished seventh), these do not resolve according to the FIP resolutions, which allows such chords to function as embellishments, rather than dominant-functioning sonorities. 25 This is especially noteworthy in regards to the diminished-seventh interval, which could enharmonically be heard as a major sixth (or minor third in inversion). It is its motion, or behavior, that creates function, not its simple existence. 26 The secondary FIP between 2 and b6 only exists if 2 resolves to 3, however. If it resolves to 1 (as is most common), that FIP does not materialize. When the secondary FIP does materialize, however, it contributes to the sense of ambiguity inherent in diminished-seventh chords and their four possible tones of resolution. 54 machinations of chromatic alteration without sacrificing the ability of the chord to maintain its dominant function. 27

Like the dominant-seventh, which contains the tritone between its chordal third and seventh, thus

7 allowing for the alteration (or omission) of the chordal fifth (giving rise to such constructions as V b5 and

7 V s5), the diminished-seventh chord contains both the tritone and diminished-seventh dissonances. This means that in a fully-diminished seventh chord it is possible to alter the chordal third or fifth (or both) while still maintaining one or both fundamental dissonances, and thereby the potential for a FIP to materialize.

The four primary possible alterations are shown in Figure 1.3. 28 Figure 1.3a and 1.3b show the possibility of lowering or raising the third of a diminished-seventh chord, while Figure 1.3c and 1.3d show the possibility of lowering or raising its fifth. In Figures 1.3a and b the chordal third ( 2) is altered. 2 often plays the least functional role in the FIPs that exert dominant function, which is why it is almost universally recognized as the least crucial, and therefore most easily alterable, pitch in dominant-functioning chords. 29 Conversely, altering the chordal fifth, or 4, as shown in Figures 1.3c and 1.3d, is much less common. 30 Such an alteration erases the tonic-directed tritone, but despite that erasure, the diminished-seventh dissonance remains, and so long as it discharges onto a consonant fifth, can be understood to maintain the dominant

27 Indeed in diminished-seventh chord resolutions, the combination of the 7–4 tritone and 7–f6 diminished-seventh following standard voice-leading practices overrides the other tritone if 2 happens to resolve up by step. In such a case, where 2 does rise by half step, what overrides hearing that pitch as the tonic is the resolution of 7 up by half step as well, rather than as a chordal seventh down by step. This also explains the dual functional role of the half-diminished seventh chord: it is less strongly dominant in function because it has only the single tritone FIP potential, but even that is overridden when the half-diminished seventh chord is functioning as a supertonic, with the root either staying static, or resolving by skip to some chord-tone of the dominant. 28 For the sake of clarity in the exposition of these ideas, I assume the conventional ease with which the diminished-seventh is incorporated in the major mode (i.e. employing the modally mixed 6). As such I do not consider it necessary to include the b7 figure (as Schenker does) in the analysis of vii o7 in major: the o7 symbol already assumes the presence of f6 instead of the diatonic 6. While the presence of altered leading-tone diminished-seventh chords in the major mode could ostensibly be understood as a combination between mixture alteration, and the more radical alteration of 2 or 4, because the mixture of f6 is so common— indeed Schenker does not even consider it chromatic—it seems redundant to describe it as such. 29 Charles Smith, for example, writes: “It is no accident that novel dominant chords are first encountered as a result of apparent alterations to 2. That scale step is the least crucial of the normal members of any dominant chord, and therefore the most readily modified.” See Smith (1986): 124. Louis and Thuille also suggest that 2 is often altered. See Schwartz (1982): 286–291. 30 Smith suggests that “4 participates in the crucial tritone that defines the diatonic collection,” and is thus unsuited for chromatic alteration (Smith [1986]: 124). Likewise, Louis and Thuille write “if [the] subdominant is chromatically raised, it loses its consonant relationship to the tonic, i.e. its genuine subdominant character. In other words, a key loses its subdominant, in the ordinary sense of the word, if an ascending leading tone to the dominant is introduced into that key by means of an upward alteration of the fourth scale degree.” Schwartz (1982): 268. 55

Figure 1.3. FIPs for Chromatically Altered Diminished-Seventh Chords (and sonorities)

a) vii o7 b3 (Mm7/Gr x6 ) b) vii o7 #3 (ø7)

c) vii o7 b5 (Mm7) d) viio7 #5 (ø7)

function of such chords.31 In the nomenclature I employ, the “ s3,” “ f3,” “ s5”, and “ f5” figures refer to

o7 chromatic alterations based on their relationships to the conventional spelling of the chord: vii f5 in C major would therefore be B–D–Ff–Af, with the more normative F n having been lowered chromatically to

31 It might also be worth suggesting then that one fundamental difference between common-practice tonality and the chromatic tonality that proliferated in the mid-to-late nineteenth century is the reliance on the diminished-seventh FIP to exert a weaker dominant function in place of the more tonally-defining tritone FIP that characterizes dominant function through most of classical tonality. 56

Fb. In summary, the presence of the diminished-seventh interval creates the potential for tonal function, a dominant-to-tonic discharge, and the resolution of that interval to a perfect fifth, fulfills this potential. 32

While each of these alterations affects the chord’s sonority and construction in a different manner, altering a single pitch in a diminished-seventh chord also creates the interval of a diminished-third (or

augmented sixth). While contemporary theory often prioritizes the augmented-sixth interval, it is important

to note that despite the presence of this interval in each chord, the specific augmented-sixth interval is not a

property shared among the four types of chords; that is to say in each case the alteration makes an

augmented-sixth interval resolving to a different constituent of the subsequent triad. 33 As can be discerned

in Figure 1.3, the diminished-third interval between 7 and f2 resolves to the root of the subsequent chord,

o7 while the diminished third between s2 and 4 in vii s3 resolves to the third of the subsequent chord, as does the diminished third between 2 and f4 . Finally, the diminished third between s4 and f6 resolves to the fifth of the subsequent chord. In classical tonality, the weight accorded to the augmented-sixth interval exists because it resolves by semitone to the root of the next chord, and as such directs our listening to that root: the same cannot be said for the three latter alterations.

Another point of interest surrounding chromatically altered diminished-seventh chords involves their sonority; when a diminished-seventh chord undergoes a single chromatic alteration, it creates one of two commonplace tonal sonorities, a major-minor seventh, or a half-diminished seventh. Because the major-minor and half-diminished seventh chords have a very limited number of conventional functions

32 In regards to the assertions made above, there is one important caveat, or exception, to my theorizing. As is well-known, the German augmented-sixth chord often progresses to a six-four chord, where the bass is the root of the functional Stufe , but the upper voices are contextually dissonant, allowing for the aversion of parallel fifths. The same, of course, is possible with o7 6 diminished-seventh chords: vii /V is equally likely to progress to V 4 as it is to V. When this happens, assuming a major-mode subsequent chord, the seventh of the diminished-seventh chord steps up chromatically to its major-mode variant (for example in C major, E b, the seventh of vii o7 /V, would step up to E n, the sixth above the dominant bass). Because the modal shift then, conventionally, resolves down by step, this does not interfere with the functional interval progression as I have described it above, it merely delays the resolution. 33 Kurth (1991 [1920], 103–109) discusses these types of alterations as inducing an energetic effect into music from a linear perspective. But Kurth considers this as a type of “shading” that is fundamentally similar to mixture: note particularly that in the same section he discusses an instance of an altered viio7 (p. 104 [Ex. 4.4]) and modal mixture (p. 108, Exs. 4.6 and 4.7). To me, mixture and the type of alteration under discussion in this paper are fundamentally different types of chromatic inflections. 57 associated with them, when they resolve in ways that defy the expectations associated with their function, they exhibit when I term harmonic polysemy. 34 In linguistics, polysemy refers to words, such as “bank,” that have multiple possible meanings despite being spelled or pronounced identically, and whose specific meaning is therefore highly dependent on the context of the sentence or paragraph in which that word is found. Importing polysemy into music theory, I use the term to describe chords that are sonorously identical, but that can exert different functions depending on their context. Thus the Tristan chord, for instance, sounds like a half-diminished sonority rooted on F, but behaves and resolves more akin to a leading-tone diminished-seventh chord in A minor. As shown in Table 1.1, lowering the third or fifth of a diminished-seventh chord creates a major-minor seventh sonority, while raising one of the same pitches creates a half-diminished-seventh sonority. These sonorous relationships are especially interesting, as they suggest that, via enharmonicism, these chords could—and often do—masquerade as more common tonal sonorities that appear to resolve in unconventional ways. The only example of this type of polysemy in conventional tonal practice is the relationship between the German augmented-sixth chord and the dominant-seventh chord. 35 I argue that this practice occurs much more widely in the chromatic harmonic practices of the late nineteenth and early twentieth century.

Table 1. Variants of B-D-F-Af (vii o7 in C), and Polysemic Analyses.

34 Robert Morgan, for instance, describes the dominant seventh as “the one chordal type within the traditional vocabulary whose tonal function is, at least under normal circumstances, unambiguous and which is thus able to define a key-area entirely by itself.” Robert Morgan, “Secret Languages: The Roots of Musical Modernism,” Critical Inquiry 10, no. 3 (1984): 454. Because the major- minor seventh is intrinsically linked to dominant function, it is particularly striking when it resolves in a manner that undermines that function. 35 One might be tempted to include the enharmonic resolutions of diminished-seventh chords in this category as well, though I see this as a slightly different procedure, namely the chord still acts as a leading-tone chord regardless of which of the four potential tonics it resolves to, whereas the German chord is functionally different from a dominant-seventh chord. 58

Strauss’ song “Befreit,” shown in Example 1.2, illustrates this polysemy by placing nearly side-by- side the same chord resolving in two different ways. “Befreit” opens with a tonic chord in E minor that

4 progresses to an apparent V 3 of the modally mixed raised submediant ( svi). This major-minor seventh sonority, and its tritone, suggest a local tonicization of the raised submediant Cs but the raised submediant

does not immediately materialize. Instead of resolving to a C s chord, the major-minor seventh chord returns to the E-minor tonic, acting as a prolongational neighboring sonority despite its seeming direction away from the tonic.36 This second-inversion G s major-minor seventh chord sounds again in m. 5, but this time it resolves following its more conventional tendencies to a triad rooted on the raised submediant. 37

Example 1.2. Strauss, “Befreit,” mm. 1–7

36 And indeed analysis of a more linear persuasion might be content to dismiss this chord as simply a contrapuntally-derived neighboring motion. While this is a valid and true analysis, it does not account for the chord in a harmonic sense. 37 This triad ends up being a major triad rather than the more diatonic minor triad expected, suggesting a function of V/ii rather than the monotonal VI s. 59

What this illustrates is the same major-minor seventh sonority resolving, and thereby projecting function, in

two contrasting ways. In the second usage, it is unquestioningly functioning as an applied dominant of the

4 38 subsequent chord, but is it of analytic value to label this chord V 3/svi when it resolves back to the tonic?

Rather than simply writing off the resolution back to the tonic as an unusual and deceptive progression, or dismissing it as a voice-leading chord, I will explore its behavior more closely.39 As the analysis in Figure 1.4a shows, the first instance of this chord follows more closely the voice-leading tendencies of vii o7 chords: the D s–C (spelled B s) diminished-seventh dissonance is resolved to a perfect fifth

(E–B), a FIP that projects dominant function directed towards E despite the erasure of the tritone FIP by

the alteration to the chordal fifth (A b, spelled G s).40 The voice leading in m.5 is different: there the tritone between B s and F s resolves conventionally to the C s–Es third, creating a tritone FIP that suggests C s as the tonic resolution of the chord, while the D s, which functioned as leading tone in the first iteration, here steps

down to C s, thus not fulfilling its potential to function as a leading tone and eschewing what was previously

a diminished-seventh-to-perfect-fifth FIP. In juxtaposing the same chord with two different resolutions, this

example demonstrates that in a syntax where chordal function is no longer innately tied to sonority, it is

important to consider the chord’s linear behaviour when determining function in highly chromatic music.

38 And this is an instance where Stein’s (1985) notion of prolongation being an elaboration of a chord as opposed to a move away from it is of importance (see footnote 20 above). In the second iteration, the chord realizes the move away from the tonic, but in this instance it does not, inciting my description of this chord as prolongational. 39 Certainly the chord in question is indeed a neighboring chord to the tonic, but since we have the tools and language to describe 6 o7 how most neighboring functions work in more diatonic contexts (i.e. V 5 and vii are understood as prolonging a tonic through neighboring motion as well as through their dominant function in relation to that tonic) it seems fruitful to develop similar understandings for these more chromatic variants. 40 Incidentally, the tritone between F s and C does not resolve as a tritone to G–B, removing the ambiguity of having two FIP’s in play simultaneously. Likewise, the augmented-sixth interval between A b and F s does not resolve as an augmented-sixth, suggesting that that particular interval is not the defining feature of the chord in question. 60

Figure 1.4a. Analysis of Voice Leading in Example 1.2

The value in the approach I advocate for “Befreit” is found in the ways in which it relates this opening progression to the functions and procedures of prolongational tonality. As Richard Cohn has recently observed, “Roman numerals are flexible enough to furnish a first-level description of almost any triad in

almost any key…Riemannian functions likewise are catchall categories such that ‘a student of Riemann’s

system could analyze virtually any chord into any one of the three functions should the occasion demand.” 41

Cohn further problematizes the use of such nomenclature, suggesting that merely describing a chord does

not explain its function, nor the way in which it relates to other chords on various levels of structure. 42 To

4 call the chord in m. 2 of “Befreit” sIII 3, for instance, does not clearly delineate how the chord prolongs tonic. Even more problematically, such nomenclature suggests that the chord expresses an immediate, or direct, relationship to the given tonic. The issue with such a label is that it implicitly suggests that a chord that distorts the fundamental, tonic-defining polarity between 1 and 5—as would be the case with sIII 7, which contains s5 —can relate directly to that same tonic center.43 Kopp, for instance, writes that scale

41 Richard Cohn, Audacious Euphony: Chromatic Harmony and the Triad’s Second Nature (New York: Oxford University Press, 2012): 11. 42 Ibid., 11. 43 In suggesting multi-key analyses, Smith (1986) advocates a plethora of chord symbols such as fii ø7 or fvi ø7 or III 7s, despite each of these containing altered tonic or dominant pitches. In my mind the suggestion of such nomenclature is instead indicative of reasons why these excessive keys are not understood. David Beach (1987, 117–119) responds to this claim, noting that “[while] the E major and B major chords have the potential—at least in the abstract sense—to be dominants of A and E, I question the validity of labelling chords according to their abstract potential as opposed to their real function within the phrase.” Beach 61 degrees such as s1 /f1 or s5 /f5 , if understood as such, “are potentially destabilizing elements,” and further cites the alteration of such tones as “negations of the tonic scale step itself.” 44 Stein likewise problematizes the III s chord, suggesting “the tonality is undermined and thus cannot be prolonged by a III s,” owing to the presence of the raised third of the III s chord as an altered dominant pitch. 45 Reinforcing Cohn’s earlier-

4 mentioned commiserations about the promiscuity of Roman-numeral analysis, III 3 thus describes the root and quality of the chord, but little else. 46

Before concluding this section, I would like to explore further a question I raised in the Introduction to this dissertation: whether fundamentally different types of chromaticism exist within the tonal- prolongational system? I believe the answer to be yes. Especially moving towards the latter portion of the nineteenth century, and into the twentieth century, not all chromaticism can be accounted for by the more conventional theories of mixture and tonicization, both of which allow most chromaticism of the eighteenth and early nineteenth centuries to be easily integrated into a diatonic framework. 47 This, however, does not mean that other types of chromaticism, such as the type employed in chromatically altered diminished- seventh chords, are necessarily destructive to, or incompatible with, tonal analysis, but rather they must be accounted for through a different mechanism. Where tonicization can be understood as a lower-level

continues, “By contrast, everything points to the C7 chord as a real dominant. What is the logic, then, of labelling it as a potential Ger. 6 in E? (Why not V 7 of II in E or V 7 of VI in A, which makes about as much sense?) Though I would not want to argue against the value of understanding the potentialities of any musical event, this label is meaningless within the context of this phrase.” This argument might be extended to the chord in “Befreit.” Labeling it as V 7 of C s does not capture the chord’s function, although recognizing its sonority is important in capturing the phenomenological twist that this resolution presents. Conversely, David Damschroder argues that “other analytic system offers a hodgepodge of incommensurable symbols that mask the functional commonality among chords.” To this end he argues that applied chords do not exist, and instead he employs “symbols that account for local transformative processes within a governing key” (David Damschroder, Harmony in Schubert [Cambridge: Cambridge University Press, 2010]: 3–4). 44 David Kopp, Chromatic Transformations in Nineteenth-Century Music (Cambridge: Cambridge University Press, 2002): 16–17. Kopp writes this in reference to the use of chromatic mediants such as III s or fvi. He suggests that what anchors these chords to tonality is the two common tones they share with the diatonic collection, despite the altered tonic or dominant degree. Recall too Louis and Thuille’s argument cited in Footnote 22 above, where they suggest that alteration of 4 to s4 divests a key of its tonic: logically, a similar alteration of 1 or 5 would remove the tonic or dominant from the key if those alterations were understood as occurring on the same level of harmonic structure as the tonic and dominant. 45 Stein (1985): 107. 46 This type of monotonal approach is what David Damschroder (2010) endorses. 47 Schenker, for example, suggests that “chromaticism does not destroy the diatonic system, [but] emphasizes and confirms it.” Schenker (1954 [1906]): 288. 62 embellishment of a higher-order chord (a diatonic, or modally mixed triad being emphasized through the presence of chords that point towards them by exhibiting local dominant function), and mixture can be explained as simply being a modal shift that remains part of the same tonality of a given pitch, other types of chromaticism do not have recourse to such explanations, especially when forced to function within a previously established system of tonal relations. Indeed, as noted before, Brown, Dempster, and Headlam

(1997, 170) describe such types of chromaticism as invoking the sense of post-tonality, writing “Post-tonal works, however, tend not only to be densely chromatic, but to employ these chromaticisms in ways often

not definable within the hierarchical relationships essential to definitions of mixture and tonicization.” But,

as I have argued, these more extended chromatic idioms do not necessitate the invocation of post-tonality.

As noted in the Introduction, Kurth, in Romantisch Harmonik , describes three ways in which chords

can relate to a governing tonality. To recapitulate, Kurth describes chords as having either tonal

referentiality (direct relations to a tonic), local referentiality, (an indirect relation to a tonic), or self-

referentiality (no relation to the governing tonality). It might be beneficial to integrate Kurth’s categories with more familiar tonal terrain. Kurth’s tonal referents might be seen as traditional diatonic (and modally-

mixed) chords, such as I, vi, iv, fVII, V, and so on, none of which pose any difficulty being understood as

related to, and thereby able to participate in the prolongation of, a given tonic. His notion of local referents

likewise describes very well the process of tonicization: chords whose referentiality towards the governing

tonic requires mediation through a more tonal referent. These chords relate directly through diatonic

processes to one of the tonal referents, and through that relationship find their place in the global tonality.48

Kurth’s final category of self-referentiality might provide a productive way to view the type of chromaticism found in the Tristan and Till chords, and chromatically altered diminished-seventh chord in general, especially when they are viewed in the ways suggested by Cyrill Kistler. 49

48 While V 7/V might be conceived of as an altered II 7 chord, the raised 4 relates it conceptually and diatonically to the subsequent dominant, and its place in the tonal structure is determined based on its relationship to the dominant. Note too that raising 4 forces the global tonic pitch into a tritone relationship, making it locally dissonant and participating in a FIP directed towards the dominant. 49 Kurth divides harmony generally into “sensuous” ( klangsinnlich ) and “energetic” ( energetisch ). Lee Rothfarb describes the former as tertian harmonies that are “harmonically self-preservational” in preserving tonal stability, while describing the latter as tonally 63

In Kistler’s analysis of the Tristan chord, the G s, B, and F are understood in the key of the tonic A, while the D s is drawn from the tonality of the dominant E; D s is in this way an intruder into the system that

distorts the referential potential of the chord in question. 50 The same can likewise be said about the Till

chord (discussed in section 3 below): s2 does not exist in any direct relationship with the tonic, and so might

be understood as an intruder into the system from the key of iii (A). 51 Because these chromatic pitches do not exist functionally within the key of local resolution (A in the case of the Tristan chord, F in the case of the Till chord), they can be understood as centrifugal chromatic pitches that destabilize the key and the tonal-prolongational process considerably, thereby expressing an instance of Kurth’s self-referential category.

This is an important aspect of these chords that should not be downplayed: aside from the commonplace alteration that lowers the chordal third (using b2 of the chord of resolution), the other three

possible chromatic alterations of diminished-seventh chords employ one of s2 , f4 , or s4 , none of which

exist, theoretically, in any kind of direct relationship with a tonic. 52 Their presence thus cannot be accounted for through mixture—though this may explain why the German augmented-sixth chord found a relatively stable home in common-practice tonality, as its chromatic constituents can be explained through the

4 concepts of tonicization and mixture. But where the analysis of a sIII 3 chord discussed above also includes centrifugal elements, using that particular nomenclature does not offer any reason to explain how that centrifugal element—the chromatically altered dominant pitch—can be reconciled into the tonal system.

destructive, employing melodic chromaticism that distorts tonality and pushes such harmonies to more stable chords (Rothfarb, 1988: 113–114). 50 Cyrill Kistler, A System of Harmony [1879], trans. Amanda Schreiber (London: Haas & Co., 1899): 65. 51 Indeed this is similar to the argument Smith makes regarding s2, though Smith simply acknowledges the chromaticism as decorative rather than attempting to find a place for it in the major-minor system. He writes “The s2 in this chord can be regarded as, in some sense, a melodic decoration that intensifies an inner-voice move to 3.” Smith (1986): 122. 52 Technically-speaking, s2 and f4 are enharmonically f3 and 3 respectively, and this could potentially account for their presence, aurally speaking, but functionally they do not act as b3 nor 3. Bribitzer-Stull and Gauldin, for example, write “such a [ s2/f3 ] pitch- class is possible, of course, in equal-tempered pitch space though, in a functionally tonal context, this blending of implied harmonic and melodic functions is highly irregular” (2007: 6). They cite earlier scholarship, such as Gregory Proctor’s 1978 dissertation (Gregory Proctor, “Technical Bases of Nineteenth-Century Chromatic Tonality: A Study in Chromaticism,” PhD diss. [Princeton, 1978]) as proposing such a pitch-class approach rather than a functional one, but, like them, I fall more on the side of a separation of function and melody. 64

All of this, then, points to the need to consider elements of harmonic syntax and function beyond

those analysts traditionally prioritize. As I have suggested, a move away from focusing on presence—in the sense of specific pitches, chords, or sonorities as having an a priori inherent function—to focusing on process might come in the form of the fundamental dissonances and their resolution as FIPs. Because these fundamental dissonances, and their resolutions as FIPs, occur—and I would further argue are central to the tonal language—in the common-practice music of the eighteenth and nineteenth centuries, this approach provides a means of linking the extended chromatic practice of later composers to the conventions of common-practice prolongational tonality. In short, it provides a means of discussing these types of complex chromatic chords in a manner consistent with conventional harmonic syntax without resorting to

“descriptive” or “arbitrary” labels. As such, these chords can be understood as contributing to the prolongation of a tonic in the same way that applied chords and mode-mixture chords have been theorized.

II Historic Interlude

A dearth of discussion and analytic use of chromatic alteration of diminished-seventh chords in contemporary theory may have many causes, and it would, of course, be impossible to pinpoint a single ideological culprit. One factor that may have contributed to this tendency is that there has long been a fascination with the isolated vertical sonority as an object unto itself, rather than understanding such a sonority as a product of its surroundings and a number of musical contexts. Even when chordal behavior is acknowledged, the highest value when determining chordal function remains typically placed on what a chord is rather than what a chord does .53 That being said, a number of historic theorists seem to have already had in mind some sense of the notion that diminished-seventh chords could be chromatically altered without loss of their local dominant function when they wrote about the sonority commonly referred to as

53 Kevin Swinden, “When Functions Collide: Aspects of Plural Function in Chromatic Music,” Music Theory Spectrum 27, no. 2 (2005): 251–252. 65 the German augmented-sixth chord. This section provides a synoptic overview of some of the more prominent suggestions of the possibility of chromatically altered diminished-seventh chords.

In his treatise on harmony, Tchaikovsky, for example, writes that augmented-sixth chords are

“nothing more than the inversions of certain chords resolving into the tonic triad, and having the 2nd degree of the scale chromatically lowered.” 54 He continues to state: “A chord of the augmented sixth on the

6th degree is nothing else than a modulatory digression into the key of the Dominant; this digression is

indeed so unnoticeable, that without the help of a prolonged cadence we scarcely get the impression of a

modulation.”55 According to Tchaikovsky, then, the German augmented-sixth chord is understood as a first-

inversion vii o7 /V chord, with a chromatically-lowered chordal third (in the bass). When he says it resolves into the tonic triad, he does not mean exclusively the global tonic, but rather that augmented-sixth chords have a local tonicizing effect, and as such the chord that follows their resolution is always an immediate- level tonic to the preceding dominant-functioning augmented-sixth. Likewise, both Hugo Riemann and A.B.

Marx proposes a similar derivation. Marx suggests that the diminished-seventh chord “arises from the dominant,” meaning that he sees the diminished-seventh chord as being functionally equivalent to the dominant, in the sense that that both express dominant function. 56 Having allowed for a lowered chordal

7 fifth in the dominant (V b5 ) through a passing motion (5-b5), and seeing dominant sevenths and diminished sevenths as derivations of each other, Marx likewise allows for this to happen on the leading-tone chord, creating the German augmented-sixth chord. 57 David Damschroder writes:

Marx is both exhaustive and contrary in his approach to these chords. He presents all eleven possible bass positionings for B–Df–F, G–B–Df–F and B–Df–F–Af. His resolutions are to tonic—not dominant. He rejects the label übermässige Sext-Akkord because the root positions

54 P.I. Tchaikovsky, Guide to the Practical Study of Harmony , trans. Emil Krall and James Liebling (Leipzig: P. Jurgenson, 1900): 106. http://ks.imslp.info/files/imglnks/usimg/c/c6/IMSLP27753-PMLP61198-Tchaikovsky_HarmonyTextbook_Eng.pdf. 55 Ibid., 108. 56 Adolf Bernhard Marx, Theory and Practice of Musical Composition [1856], trans. Herman S. Saroni (New York: Mason Bros., 1951): 262. 57 Ibid., 262–63. It is interesting that Tchaikovsky arrives at the same conclusions through different means: for Marx, the lowered pitch is a result of a passing motion from the chordal fifth, which suggests that on some level, even if the normal version of the fifth is not present, this is still being viewed as a passing tone, simply displaced to sound simultaneously with the dominant- functioning chord. Conversely, Tchaikovsky does not use the linear dimension to explain the alteration, but rather invokes a more harmonic-based approach in lowering the second degree of the scale with respect to the chord of resolution by simply referring to it as a chromaticization. Though he does not explicitly state it, this might be thought of as invoking the principle of mixture, borrowing this lowered pitch from the Phrygian mode of the local tonic in question, as f2 . 66

of all three chords lack augmented intervals…Marx wonders why one would name any of these chords using an adjective that applies only in the context of inversion. 58

Riemann, according to Steven Rings, likewise preferred “reading the German sixth as an applied

dominant.” 59 Riemann’s interpretation sees the German sixth as a rootless dominant of the dominant with extensive alteration symbols (a lowered ninth, a seventh, and a lowered fifth). As I suggested in the

Introduction, however, the understanding of secondary dominants is an inconsistency in Riemann’s system, as it suggests (rightly, I believe) that the point of reference for the chords in question is not the tonic, but rather the chord to which they are applied.

Schenker, too, writes in his Harmonielehre that “the augmented sixth and diminished third always

indicate that we are dealing with a state of alteration.” 60 Figure 1.5 reproduces Schenker’s subsequent

Example 321 from Harmonielehre , an analysis of the function of the three types of augmented sixth chords as

alterations of dominant-seventh or leading-tone chords. 61 Schenker’s language and subsequent examples suggest that, like Tchaikovsky, he sees the lowered second scale degree as a result of chromatic alteration to dominant-functioning chords rather than a separate class of chords in their own right. 62 Specifically here, his

Figure 1.5. Schenker, Harmonielehre (1906), Figure 321

58 David Damschroder, Thinking About Harmony (Cambridge: Cambridge University Press, 2008): 185. Damschroder also notes that Vogler derived the German augmented-sixth chord from vii o7 (169–170). 59 “Steven Rings, “Riemannian Analytic Values, Paleo- and Neo-” in The Oxford Handbook of Neo-Riemannian Music Theories , ed. Edward Gollin and Alexander Rehding (New York: Oxford University Press, 2011): footnote 31. 60 Heinrich Schenker, Harmony [1906], ed. and ann. Oswald Jonas, trans. Elisabeth Mann Borgese (Chicago: University of Chicago Press, 1954): 279. 61 Indeed Schenker reserves a paragraph in Harmonielehre to note how other textbooks who employ the augmented-sixth nomenclature are “unaware of the origins and correlations of altered chords.” Ibid., 280. 62 Schenker suggests that we “must note, first of all, the effect of V in all these chords.” Ibid., 280. 67 nomenclature suggests that like Marx he understands the German augmented-sixth chord as an inverted

o7 vii b3 , usually applied to the dominant, the French chord in its most common iteration as a second-inversion

7 o V b5 , and the Italian chord as a first inversion vii b3 triad. Schenker, however, takes this thinking a step further than either Tchaikovsky or Marx, and suggests the possibility of altering the chordal fifth of diminished-seventh chords as well. He writes of his Example 331 (reproduced here as Figure 1.6) from

Bruckner’s Ninth Symphony:

We are dealing here most certainly and most simply with a diminished-seventh chord on the VII step in D major/minor (related, by its univalence, to the V step of this same key), whose character is in no way interfered with by the chromatic change of raising the fifth G to G- sharp. 63

However, rather than invoking mixture (which would be impossible for Schenker, since he does not

consider the Lydian-derived s4 as a mixture pitch, but rather as a tonicization of the V step 64 ), he suggests

that “the latter must be considered a passing tone [i.e., 5–s5–6], despite it occupying so much time.” 65

Schenker’s approach here regarding the possibility of a raised fifth in diminished-seventh chords might be equally applied to the passage from Salome problematized by Kofi Agawu and discussed in my Introduction

(Refer to Example 0.1). Where Schoenberg analyzes an altered III proceeding to an altered II, my

understanding of the chord is that it is a vii o7 /V in E b (A–C–E–Gf) with a raised fifth (the raised fifth then

proceeds to the regular fifth E b, before the chord resolves to a B b dominant seventh). Having explained the chromaticism as being simply a form of linear passing motion, Schenker does not contemplate the possibility that such altered chords could exist as chords in their own right, though this may

63 Ibid., 286. 64 Matthew Brown writes that Schenker “rejects any possibility of Lydian mixture on the grounds that the subdominant and dominant must always be available in pure form” (Matthew Brown, “The Diatonic and the Chromatic in Schenker’s ‘Theory of Harmonic Relations,’” Journal of Music Theory 30, no. 1 [1986]: 8). Schenker likewise suggests this in Der Freie Satz when he writes “the chord that has the effect of sIV b7 must have V as the continuation.” (Heinrich Schenker, Free Composition , ed. and trans. Ernst Oster (New York: Longman, 1979): 91). Note that despite his apparent monotonal sIV nomenclature, Schenker does specify that it has the “effect” of that chord, not that it is a sIV chord, as Schenker’s writings suggest that he views such chords as applied chords. 65 Schenker (1954 [1906]): 286. 68

Figure 1.6. Bruckner, Symphony no. 9, IV (Figure 331 from Schenker, Harmonielehre [1906]). Annotations mine

o7 C# -E-G# -Bb = vii #5 of D

come as no surprise, especially given Schenker’s later attacks on Schoenberg for his views on chords created through displaced passing motions. 66

Like Schenker, Louis and Thuille view chromatic alteration of dominant-functioning chords as

essentially a linear feature. They write that “one must realize that chromatic alteration is a completely

66 Schenker criticizes Schoenberg for this view, accusing him of wishing to be the “godfather” of new chords (see Heinrich Schenker, “Further Considerations of the Urlinie : II,” in The Masterwork in Music II [1926], trans. John Rothgeb [Cambridge: Cambridge University Press, 1994]: 15). 69 melodic procedure.” 67 Unlike any of the previously-discussed authors, Louis and Thuille explore an almost exhaustive variety of non-conventional chord sonorities in their Harmonielehre , labeling the chords based on their intervallic construction. 68 Their derivations of the chords, however, take a more Riemannian- transformational approach, and are linked to more consonant precedents than Schenker. For example, they write: “The so-called augmented-sixth chord [their term for the conventionally-termed Italian chord]…[is] obtained from the altered subdominant triad in minor and in major-minor.”69 In this approach they are

employing a highly Riemannian idiom, where all chords are generated from chromatic alterations to one of

three harmonic pillars, and the Italian augmented-sixth chord is thus viewed as a subdominant chord with a

raised root and lowered (or minor-mode) third, Schenker would view the same chord as a chromatically

altered vii o6 chord applied to the dominant.

This notion of passing chromaticism being displaced to become fully centrifugal chromaticism shorn of its original passing nature can be observed in Example 1.3, from Strauss’ Eine Alpensinfonie . Here, as shown in Figure 1.7, C s initially occurs as a displaced passing tone between C and D, filling in the chromatic

o6 6 6 semitone between the two pitches as vii 5 resolves to i in G minor. The i is subsequently prolonged by a

chord spelled F s–A–Cs–Ef. Rather than seeing this as some sort of unconventional half-diminished chord built on the lowered submediant in G, this chord functions as a verticalization, integrating

Example 1.3. Strauss, Eine Alpensinfonie , RH32.

67 Schwartz (1982): 273. I would add nuance to this assertion: chromatic alteration might have its origin in melodic procedure, but that does not mean that once the alteration has occurred the new sonority does not also then project harmonic implications as well. 68 Ibid., 274–278 lists all these possible alterations, some of which align with the views presented herein, some of which do not. 69 Ibid., 274. 70

6 o7 the passing pitch that precedes the initial i chord into a vertical sonority, and thereby creating vii s5. So here one sees the chord being prepared, or generated, through the initial non-chord-tone status of the passing chromaticism, but then used without the diatonic version of the chord preceding it. 70 As Robert

Bailey notes of the Tristan chord, and seems likewise pertinent here, this type of change “reflects the typical

historic process of evolution in musical language: a phenomenon originates as a merely decorative addition

to the prevailing idiom, and is gradually elevated to the level of structural import.” 71 The altered diminished-

seventh analysis here helps bring out this relationship, and further helps clarify and elucidate how this chord

is functioning within the larger-scale tonal-prolongational structure.

While the views of the aforementioned theorists regarding the chromaticism as a result of passing

motion might account for the genesis of chromatically altered diminished-seventh chords, this approach

does not provide a particularly strong or sound accounting for how these chords participate (or fail to do so) in creating prolongational function when sounded as part of a chord independent of existing as a passing pitch. Especially when the unaltered version of the pitch is not present prior to the chromatic variant, it is difficult to argue that the chromatic pitch can be written off as a passing note, as such a view would result in

Figure 1.7. Analysis of Example 1.3

70 o7 And the inversion in which Strauss puts the chord helps avoid the potential parallel fifths inherent in resolving vii s5 to its tonic. 71 Bailey (1985): 117. 71 the chromatic pitch being a consequence of something that does not exist. 72 While their origin may be as chromatic passing tones that were eventually displaced to sound simultaneously with the rest of the chord, thereby replacing the conventional, unaltered version of the pitch in question, as this chapter has already described, a different sort of theorizing is required in order to place the chromaticism in altered diminished- seventh chords into a tonal context.

III Analytic Applications

While the Tristan and Till chords are very recognizable examples of sonorities that push the boundaries of tonality, they are also the most salient examples in contemporary discourse: many other illustrations of these altered diminished-seventh chords exist in less pronounced places. In this final section

I explore some other instances where conventional analysis might struggle in reconciling the harmonies found with traditional tonal approaches. Each of the examples below presents a use of these chords that is

still prolongational, but that has either not hitherto been discussed, has additional complications, or, in the

case of the last two analyses, interacts with existing scholarship.

Example 1.4, from the end of Strauss’ opera Der Rosenkavalier , is a highly localized illustration, but

since it avoids enharmonic spelling, and has an obvious tonal precedent, it provides one of the clearest

examples of an altered diminished-seventh chord exerting harmonic function. The dominant that prepares

the onset of the key of D b for the climactic trio “Hab’ mir’s gelobt” remains a pedal in the bass, but is

elaborated with a chord spelled G–B–Df–Ff. Given that this sonority occurs over the A b pedal, it is nearly

impossible to understand it as anything but a leading-tone harmony applied to that A b. Sounding a

dominant-functioning chord (be it an actual dominant or a leading-tone chord) of a particular

72 Obviously a passing note would require a preceding and succeeding pitch in order to function and be understood as such. 72

Example 1.4. Strauss, Der Rosenkavalier , Act III, 6 mm. before RH 285.

pitch while that pitch is held as a pedal is a common harmonic gesture, but this chord is neither the dominant-seventh nor the fully-diminished seventh of A b. I would suggest that in this case the spelling

of the chord reflects its actual function as a leading-tone chord of A b, confirmed by its voice-leading

behavior. The curiosity here is that despite behaving like a leading-tone chord, the chordal third is raised by

o7 semitone, from what should have been B b to B n, creating a vii s3 (the same alteration as the Till chord) of

Ab over the A b pedal. 73 While this analysis in and of itself does not affect a deeper-level understanding of the

tonal structure at this juncture, its spelling and use over a pedal suggests that chromatic alteration of

diminished-seventh chords was a technique of which Strauss was aware.

The Till chord, shown in Example 1.5, from Strauss’ tone poem Till Eulenspiegels lustige Streiche , also

o7 demonstrates the vii s3 chord. While Matthew Bribitzer-Stull and Robert Gauldin point to a number of

authors who have posited connections between Strauss’s tone poem and Wagner’s operas, they rightly point

out that many of these comments are “generic [rather] than providing detailed analysis.” 74 Bribitzer-Stull and

Gauldin, on the other hand, suggest that there is a more apparent musical connection between the Tristan chord and the Till chord. Like the comparison other authors have made between the Liszt song and

73 While I have used the vocal reduction here for convenience, this particular reduction is problematic in that it visually suggests the F b resolves up by third to A b, which does not follow the full score’s orchestration, where the F b does indeed resolve down to Eb. 74 Matthew Bribitzer-Stull and Robert Gauldin, “Hearing Wagner in ‘Till Eulenspiegel’: Strauss’ Merry Pranks Reconsidered,” Intégral 21 (2007): footnote 6. 73

Example 1.5. Strauss, Till Eulenspiegels lustige Streiche , mm. 46–49.

the opening of Tristan , Bribitzer-Stull and Gauldin note a similarity in the accented rising chromatic half-step

Gs to A, but suggest that more so than this rising melodic gesture, “the most convincing Wagner connection” between the Tristan chord and the Till chord exists in the harmonic realm. Namely they see both chords as half-diminished seventh sonorities that function as augmented-sixth chords, writing:

Although the “Till” chord may be considered a half-diminished sonority with a predominant function, the chordal seventh is notated as G s, suggesting an augmented-sixth (B f-Gs) expanding to the octave thirds of the tonic triad. 75

Indeed, both chords do contain the augmented-sixth interval, and in the Till example it does resolve outward to an octave, as augmented-sixth intervals are wont to do, but it is worth considering whether this

specific intervallic progression deserves the functional importance that contemporary theory ascribes to it,

alongside a number of other contrapuntal factors in this analysis. 76 Firstly, the contention that the G s is the

chordal seventh requires some unpacking: if the G s is truly a chordal seventh, one must then also

acknowledge that its behavior is highly dissonant with the conventions for the treatment of chordal sevenths

in tonal practice. Namely, rather than resolving down by step, it rises by semitone. Although theory “rules”

always have exceptions, it is notable that chordal sevenths in practice almost unfailingly resolve down by

step (there are only two commonplace exceptions to the rule, compared to the relative freedom with which

75 Ibid., 11. 76 The augmented-sixth analysis is also Daniel Harrison’s perspective. See “Supplement to the Theory of Augmented-Sixth Chords.” Music Theory Spectrum 17, no. 2 (1995): 185. Harrison (1995, 188) writes that “dominant function can still be heard to persist in the Till chord—at least in this incarnation—transmitted by E as 7,” but then suggests that the presence of scale degrees b6 and 4 considerable subdominant energy that “largely subdue E, leading to a plagal interpretation. 74 leading tones can be treated, for example). 77 Secondly, as Daniel Harrison has noted, the augmented-sixth interval has no functional valency: it is not found naturally in any single major-minor tonality. 78 This makes

questionable the conventions of music-theoretic discourse on augmented-sixth chords: while the

augmented-sixth interval has a strong tendency to resolve to an octave, when that note of resolution is not

the root of a chord (as in the Till chord), it calls into question whether that particular interval progression

should be isolated as the defining gesture in such chords. Indeed, Louis and Thuille suggest in their

Harmonielehre that “it is difficult for us to hear the interval D s–F, i.e. to relate these two tones separated by a whole-step, such that they resist resolution to the unison,” 79 although they suggest that the augmented-sixth

inversion of the diminished third is better able to be heard as such.

Kevin Swinden, echoing Daniel Harrison’s assertions about the Till chord and the prominence that

the pitch A plays in it, writes:

The chord is an augmented sixth chord whose characteristic augmented sixth (B b–Gs) resolves to 3 (A n) of the following F major tonic triad, over a structural 4 to 1 bass—a sonority that has strong Dominant associations (by virtue of the leading tone, E n) resolving to tonic. The Till Sixth thus combines the Subdominant and Dominant elements necessary to qualify as a SD(4ˆ) chord. 80

Like Bribitzer-Stull and Gauldin, Swinden prioritizes the augmented-sixth interval over the more valent diminished seventh interval (in augmented second inversion) between E and D b, which resolves to F–C, and in so doing, as Swinden acknowledges, provides a strong sense of dominant function. Swinden’s (and

Harrison’s) functional nomenclature that eschews Roman numeral analysis in favor of more abstract

Riemannian-inspired labels such as S, D, and T is, perhaps, too vague: the S D label suggests that this chord is

77 4 6 th The progression I–V 3–I is the major exception, in which the desirability of the parallel 10 that are created by allowing the chordal seventh to rise is cited as the reason for the exception to the rule, is the most commonplace exception. The other exception occurs when a diminished-seventh chord resolves to a six-four sonority: in such cases the chordal sevenths steps up chromatically to sound the sixth above the bass, before resolving down to its expected note of resolution. 78 Harrison (1994): 173. Though Harrison downplays this to allow for his arguments regarding augmented-sixth chords, suggesting that Schenker “cannot discuss augmented-sixths in the same breath as he does diminished fifths and diminished sevenths…” though Schenker’s argument, at least in Harmonielehre , is that augmented sixths are a product of chromatic alteration, and that the eponymous chords are simply chromatically altered dominant-functioning chords (see footnotes 56–59 below). 79 Schwartz (1982): 272. 80 Kevin Swinden, “When Functions Collide: Aspects of Plural Function in Chromatic Music,” Music Theory Spectrum 27, no. 2 (2005): 264. 75 primarily subdominant and secondarily dominant in function, despite the presence of the leading tone and lowered submediant, together forming the tonicizing diminished-seventh interval in the key of F, and suggesting a strong leading-tone function for the “Till” chord.

Might there be analytic value, then, in reassessing music theory’s approach to such chords, and applying the suggestions made above, thereby viewing the chord instead as another chromatic variation of a diminished-seventh chord? 81 Where the Tristan chord’s voice leading retains a degree of ambiguity because it progresses to an unresolved dominant-seventh chord, the voice-leading behavior of the Till chord, shown

in Figure 1.8, is less ambiguous, and matches that of a conventional diminished-seventh chord despite the

chromatic alteration. The proposed leading tone, E, resolves up by semitone, while the chordal fifth, B b, and

seventh, D b, resolve down by step in keeping with the voice-leading practices of tritone and diminished-

seventh FIPs. The chordal third, G, is chromatically raised to G s, which then resolves up by step to the chordal third, A. Thus while the Till chord, like the Tristan chord, sounds like a strangely placed half- diminished-seventh chord rooted on B b, its behavior is identical to that of a diminished-seventh chord rooted on E. 82 What distinguishes the Till chord from the Tristan chord is the chord member that

Figure 1.8. Analysis of Example 1.5

81 Interestingly, despite their insistence that the Tristan chord in not a leading-tone chord in A minor, this is, in fact, the analysis that Louis and Thuille give to the “Till” chord. Schwartz (1982): 285. 82 Conversely, Martin (2008), for example (along with similar comments made by Bribitzer-Stull and Gauldin [2007] and, to some extent, Kevin Swinden [2005]), suggests that the Till chord is part of the new family of augmented-sixth chords that he proposes as the analysis of the Tristan chord, which I see as a relationship focusing on chordal sonority rather than a comprehensive analysis of chordal function and behavior in a tonal-prolongational context. 76 undergoes alteration: the Tristan chord alters the chordal fifth, whereas the Till chord alters the chordal third. In this way, these chords do indeed have a familial association, undergoing the same process of transformative alteration; they are not, however, identical chords, as it is a different chordal constituent that is altered in each case.

o7 Like the chord used in “Befreit” above, another example of vii b5 can be seen in Strauss’ song “All mein Gedanken,” shown in Example 1.6. Unlike in “Befreit,” wherein the altered chord expanded the minor tonic, here the altered chord serves to embellish the dominant at the conclusion of the song as an applied

4 chord. The chord in question in this case resembles V 3/iii (A s-Cs-Ds-Fx), but because of its placement in

6 the phrase between an unfolded supertonic chord (ii 5) and the dominant, coupled with the failure of the

4 mediant to materialize in any way, the label V 3/iii fails at capturing the prolongational function of this

4 83 chord, as does the more monotonal possibility VII 3. As a viable alternative, looking at the chord’s

behavior and voice leading might better accentuate the chord’s function, which could be understood as A s-

Example 1.6. Strauss, “All mein Gedanken,” mm. 23–31.

83 Poundie Burstein (“Surprising Returns: The VII s in Beethoven's Op. 18 No. 3, and Its Antecedents in Haydn,” Music Analysis 17, no. 3 [1998]) notes similar progressions of VIIs resolving to V in the works of Haydn and Beethoven, but in these cases it is almost always with VII as a triad and in root position, rather than inverted version found here in Strauss’ song. As Carl Schachter (The Art of Tonal Analysis: Twelve Lessons in Schenkerian Theory [New York: Oxford University Press, 2016]). notes, this type of VII s to V was understood by Schenker as an unfolding of the dominant, but in this case, given the addition of the seventh, the specific inversion of the chord in question, and its voice leading, the unfolding to the dominant interpretation seems to be less apt in its description of the harmonic process here. 77

o7 Cs-Ef-G, or vii b5 /V. Because of the registral differences between this chord and the subsequent dominant- seventh chord, the voice leading here is rendered in slightly abstract terms, and shown with octave realignment in Figure 1.9. Notably, when the chord in mm. 27–28 resolves, it retains a common tone with the chordal third in the chord of resolution. This type of common tone occurs when lowering the chordal fifth of a diminished-seventh chord and resolving that chord to a major triad, or major-minor seventh chord, and, while unconventional to diminished-seventh voice leading, I maintain that this should not be considered an example of a common-tone diminished-seventh progression, and that the diminished-seventh

FIP maintains the applied dominant function when the chord in question discharges onto the subsequent chord.84

As discussed briefly in the first section, and treated more in-depth in the historical interlude, the

notion of chromatically altered diminished-seventh chords extends to the German augmented-sixth chord.

The perspectives of Marx, Tchaikovsky, Schenker, and Louis and Thuille outlined above all include

references to augmented-sixth chords as being chromatic alterations of either V 7 or vii o(7) chords. While the

Fr4 o7 notion of a V 3 is not new, the notion that the German chord might be also understood as a vii b3 is less commonplace. The perspectives of the aforementioned theorists are, in fact, divergences from the more

Figure 1.9. Analysis of mm. 27–29 of Example 1.6

84 Conventional common-tone diminished-seventh analyses are typically applied to progressions wherein the “seventh” of the apparent diminished-seventh chord is a common tone as the root of the chord of resolution, not the third. 78 normative view of augmented-sixth chords, which sees them as exclusively subdominant-based predominant chords in the key of a tonic a fifth below the chord to which they resolve. 85 While it is true that on a phrase

level augmented-sixth chords, in classical tonality at least, almost universally appear immediately prior to the

dominant, this perspective should not be monopolized as their only function. The more immediate-level

function of German augmented-sixth chords in particular, as expressed by their voice-leading behavior and

the retention of the diminished-seventh-to-perfect-fifth FIP, might more accurately be understood as a

dominant-functioning leading-tone diminished-seventh applied to the chord of resolution, most often the

dominant.

This more localized harmonic function should not be forgotten even if their placement at the level

of the phrase most often coincides with predominant function. Indeed, I am not suggesting that viewing

augmented-sixth chords as having a local tonicizing effect should erase their predominant function; quite

the opposite: the way in which augmented-sixth chords tonicize the dominant enhances their phrase-level

predominant function by creating stronger harmonic propulsion towards the dominant. The distinction

here, however, is that in acknowledging the local-level dominant function of augmented-sixth chords, these

chords can easily be explained when they appear prior to chords that are unequivocally not V: through this

immediate-level dominant function augmented-sixth chords can tonicize chords other than the dominant in

nineteenth-century harmony. I am arguing that the German augmented-sixth chord should be understood in

the same way that vii o7 /V is: at the level of the phrase, vii o7 /V is a “predominant” chord because it occurs

prior to the dominant. Despite this, we still understand that diminished-seventh chords exert dominant function. The placement of a diminished-seventh chord in a phrase as a sonority that happens to come prior to V—and can thus be called a “predominant” at that level—does not dilute this chord’s dominant function

on a more immediate harmonic-relational level. If one approaches that immediate-level dominant function

85 7 Interestingly, using an illustration from Strauss’ Salome Aldwell and Schachter suggest that V b5 in root position should be analyzed as such, but when it gets placed into third inversion, it becomes a different chord altogether (the French augmented- sixth chord). Their discussion vis-à-vis this chord highlights the perplexing way in which analysis applies these identical chords in different functional categories. See Edward Aldwell and Carl Schachter, Harmony and Voice Leading 3rd Edition (New York: Schirmer, 2002): 553. 79 not as an inherent product of diminished-seventh sonorities, but rather as a product of the chord’s voice-

leading behavior, the parallels between diminished-seventh chords and the German augmented-sixth

become apparent.

This view of the German augmented-sixth chord allows the chord to be more flexible in its

application. As mentioned it easily explains their use when resolving to chords other than the dominant, but

this perspective also sidesteps the perennial anxiety that plagues theorists when German augmented-sixth

chords appear in inversions that do not contain the root or third in the bass.86 When understood as alterations of vii o7 chords, inversions that use the chordal fifth or seventh in the bass are far less problematic, and can easily be viewed as the same inversions commonly found in dominants and

o6 ob6 diminished-seventh chords (i.e. vii 43 is unproblematic, so vii 43 should be equally unproblematic). For

instance, the passage shown in Example 1.7a, from Strauss’ Eine Alpensinfonie contains a chord spelled D–

Fs–A–C, a sonority which would traditionally be analyzed as either a dominant-seventh of G, or as the

German augmented-sixth chord in F s, which would necessitate a resolution to the dominant C s-major triad.

A number of factors make either analysis untenable in this passage: the chord that follows (C s minor) is not

G major nor minor, nor any common substitute for G in a tonal prolongation. As such, like the example from “Befreit” above, the dominant-seventh analysis does not

Example 1.7a. Strauss, Eine Alpensinfonie , RH88.

86 There is of course some contention regarding whether augmented-sixth chords have roots. If understanding them, as I have argued, as alterations of V 7 and vii o(7) chords, then they should be understood as having the same roots as those chords. 80

Figure 1.10a. Analysis of Example 1.7a

describe the chord’s prolongational function within the passage, but merely describes a root and sonority.

While the German augmented-sixth analysis more accurately reflects the chord’s function, the chord that follows is unlikely to be a dominant triad—it is both a minor triad and is part of the tonic prolongation of

Cs begun at RH88 and established in the subsequent measures—which complicates this analysis. As such, the German-sounding chord is not functioning as a predominant, but as a dominant built on the leading tone of C s (the B s is spelled enharmonically as C n). This chord uses Fs, the fifth of the chord, in the bass, where either B s or D would be idiomatic of the German sonority. Simply calling this a Gr 6 chord would be somewhat misleading. Conversely, understanding this as a third-inversion chromatically altered vii o7 of C s, as shown in Figure 1.10a, provides a more effective and flexible approach to these types of problems. The four-three inversion is easily accounted for as an inversion of vii o7 , and the difficulty of reconciling the supposed predominant function of this chord with its position as a dominant is rendered unproblematic when it is understood as an applied chord of the subsequent sonority, rather than predominant in function.

A similar circumstance arises in the passage from Strauss’ opera Elektra shown in Example 1.7b.

This passage, locally in C minor (beginning at RH230), depicts a tonic chord over a 6 pedal (or, VI 7)

progressing to the chord B–Df–F–Af over the tonic pedal C. Labelling this an augmented-sixth chord of i

o7 over a tonic pedal does little to elucidate the function of the chord, but understanding it as vii b3 over a

tonic pedal paints a far clearer picture of the chord’s relationship to tonal harmony. Like in the example 81

Example 1.7b. Strauss, Elektra , 2 mm. before RH232

from Der Rosenkavalier above, this chord’s function is that of a dominant leading-tone chord over its tonic

o7 pedal, and, like the example from Eine Alpensinfonie above, the vii b3 chord resolves to a minor chord, meaning that it cannot be predominant in function. Likewise, in Example 1.8c, from later in Strauss’ song

“Befreit,” an apparent German diminished-third chord proceeds to the local B-minor tonic. The alteration, in this instance, is clearly linear in origin, following from an unaltered vii o7 of B minor as shown in Figure

1.10b, but the minor mode of the subsequent chord, and its status as tonic, strongly suggests that this

o7 chord’s role is vii b3 , and unambiguously dominant in its function.

Example 1.7c. Strauss, “Befreit,” mm. 16–23.

Figure 1.10b. Analysis of Example 1.7c

The approaches developed in this chapter are also suggestive of ways in which neo-Riemannian theories of parsimonious voice leading can be integrated into tonal-prolongational analysis. The passage in

Example 1.8, from Götterdämmerung , has been described as “functionally ambiguous,” owing to the idiosyncratic chromaticism. 87 Graham Hunt, following models developed by David Lewin, suggests that

Wagner’s music contains chromatic zones, wherein tonal-functional logic becomes secondary to voice-

leading procedures that can be expressed through neo-Riemannian transformational analysis, citing this passage as one such place where the initial chromaticism is juxtaposed against the more diatonic cadential motion at the end of the phrase. Hunt’s approach and conclusions present a remarkable insight into the relationships afforded by voice-leading parsimony, and depict a number of excellent perspectives on motivic inter-relatedness, but the juxtaposition between chromatic zones and diatonic zones is a particular highlight of his paper, as it clearly delineates the striking difference between passages where rampant chromaticism seems to defy tonal logic, and passages that follow more diatonic norms. A question that might follow,

87 Graham G. Hunt, “David Lewin and Valhalla Revisited: New Approaches to Motivic Corruption in Wagner’s Ring Cycle,” Music Theory Spectrum 29, no. 2 (2007): 180. 83

Example 1.8. Wagner, Götterdämmerung , Act I, Scene 3, mm. 1237–1240

however, is one that has been voiced many times before: namely, can the chromatic zones be functionally integrated with the diatonic zones in a tonal-prolongational sense? Hunt’s suggestion that chromatic and diatonic zones require separate approaches seems to indicate that he believes the answer to be no. I would venture a different view.

My analysis of this same passage suggests that in looking at voice-leading behavior of the chords in

question, and their surrounding context, a possible tonal reading of this passage emerges. As Hunt notes (his

Example 7 is reproduced here as Figure 1.11a) the passage ends relatively diatonically, with an E b minor

chord progressing to a B b dominant creating a half-cadential gesture. Stepping back to the beginning of the

passage, what Hunt has called G so7 might equally be understood enharmonically as vii o7 of E b (D–F–Af–Cf).

However, even if the diminished-seventh chord in question were acknowledged as the leading-tone chord of

Eb, the subsequent chord, which Hunt labels G sø7 , appears to contradict the assertion of an E b tonic.

Understanding this chord as such would require the analysis iv ø7 in E b (which, to be clear, Hunt does not suggest), which is unconvincing for a number of reasons: it is not a conventional sonority found on the subdominant, the motion from a dominant-functioning leading-tone chord to a subdominant is retrogressive and uncommon in tonal practice, and invoking a monotonal Roman numeral suggests a direct

reference to the tonic, which is questionable because of the altered tonic pitch present in the chord. 84

Figure 1.11a. Hunt’s (2007) voice-leading analysis of Example 1.8

It is here where my theory can perhaps clarify the aspects of tonal prolongation that operate in this passage. The half-diminished seventh sonority G s–B–D–Fs can be half-enharmonically respelled as D–Fs–

o7 Af–Cf, or vii s3 of the proposed E b tonic. As such, it can be understood as a chromatic alteration of the

previous diminished-seventh chord; a continuation of dominant function rather than a change of function.

As with other instances of these chords, the F s is understood to be centrifugal chromaticism, though it might also be seen as conforming to Schenker’s description of passing chromaticism, in that the F in m.

1237 rises to F s then moves on to G. In any case, the application of the theory of chromatically altered diminished-seventh chords suggests a more tonal logic to this passage that the neo-Riemannian approach does not entirely elucidate.

But the question of the following G-minor triad remains: even if the half-diminished sonority is enharmonically understood to be an altered leading-tone chord in E b, its resolution to G minor throws into question this function. Firstly, it is important to draw attention to the fact that in the half-diminished seventh chord preceding the G-minor triad there are no pitches that suggest any of the valent intervals in G: while the leading tone F s is present, there is no C n to create a tritone, nor is there an E b to create a diminished-seventh. Because of this the half-diminished seventh chord in m. 1238 cannot be said to have 85 the potential for dominant function in G. Rather than forcing the G to be integrated into the tonal structure as a chord in its own right, I suggest that the G-minor triad here is merely apparent, and acts as the upper third of the E b triad that follows, unfolding to that sonority in the second half of the measure. 88 Voice leading, again, helps to clarify this function: when the half-diminished seventh chord in m. 1238 resolves to

G minor, the F s resolves up to G, as is allowed with chordal thirds, the A b resolves down by step to G, and the chordal seventh, C b (spelled B n) resolves down by step to B b. Up to this point, the voice leading is entirely conventional of diminished-seventh dissonance resolution, except that the D has remained static.

Ultimately the D resolves up by step as a leading tone, but this resolution is delayed, the result of which, combined with the resolution of the other three pitches, is the apparent G-minor triad in m. 1239. While the other three pitches of the half-diminished seventh chord resolve over the bar-line in proper diminished- seventh fashion, as shown in Figure 1.11b, the leading tone D is suspended; when the D does resolve up to

Eb it fulfills its role in the FIP creating a dominant-to-tonic discharge towards E b.89 In theorizing why the G-

minor triad is inserted at all, one might hypothesize that it is simply a voice-leading chord in the most

technical sense: it exists because the

Figure 1.11b. My Analysis of Example 1.8

88 Alfred Lorenz suggests the notion of “apparent” triads in his study of Wagner’s operas, suggesting that in certain cases “a strongly dissonant chord is frequently created, but which is incidentally enharmonically equivalent to a triad.” See Alfred Ottokar Lorenz, Das Geheimnis der Form bei Richard Wagner [1924–33], Reprint (Tutzing: H. Schneider, 1966): 89–90. 89 Notably, the G n is modally altered to G b when the E b triad emerges, but such a modal shift is commonplace by the mid-to-late nineteenth century. 86

Ab in the bass voice is the chordal fifth of the diminished-seventh chord, and in order to fulfill the tritone

FIP, should resolve down by step, which necessitates the G in the bass.

A further illustration of this type of process can be found towards the end of the same opera.

Example 1.9 depicts the passage from mm. 1158–1161 of Act 3. Richard Cohn describes the first chord of

this passage as a “B b-minor triad with G under-seventh in the bass,” and suggests it presents an example of

the uncanny hexatonic pole relationship. 90 To accept this analysis, Cohn writes:

[One] must be prepared to accept two distinct reductive moves. The first asks us to suppress the F s-minor triad on the basis of its intermediate position, both in the event space of the segment and in the tonal space that the segment traverses; F s minor shares common tones with both of its flanking chords, which share none with each other. Perhaps more radical is the interpretation of the {G, B f, D b, F} formation as a minor triad with supplementary under-seventh, rather than as the half-diminished seventh chord universally purveyed by harmony textbooks. 91

Both positions complicate Cohn’s analysis. While the F s triad is indeed intermediate, its role seems more

distinctive than a typical passing or non-functional chord. Similarly, Cohn has offered a defense elsewhere

of the under-seventh reading by appealing to the dualist reading of the half-diminished chord

being generated downward from the top note, thus making the root (G, in this case) the dissonance. 92 While

this position seems acceptable when the pitch in question is in an upper voice, creating an added-sixth chord

(as in the beginning of the third act of Tristan ), it is, as Cohn notes, a harder position to accept when the pitch is the root of the chord. Regardless of whether one accepts the dualist justification for this reading or not, it still requires us to ignore a pitch that is not only sonically present in the music, but occupies often functionally salient bass position. 93

Using the same approach as in the previous example from Götterdämmerung , however, negates these

o7 problems. The half-diminished seventh chord on G can be reinterpreted as C s–Es–G–Bb, or vii s3 of the

90 Richard Cohn, “Uncanny Resemblances: Tonal Signification in the Freudian Age,” Journal of the American Musicological Society 57, no. 2 (2004): 297–298. 91 Ibid., 297–298. 92 Cohn (2012): 142–144. 93 Conversely, it is less challenging to accept that a V 7 chord can be reduced to its triad because the triad shares the same root as the V 7 chord, whereas in the case of the half-diminished seventh chord the two chords do not share the same root. I discuss a further way of justifying the relationship between half-diminished seventh chords and these triadic subsets in the conclusion. 87

Example 1.9. Wagner, Götterdämmerung , Act III, Scene 3, mm. 1155–1160.

D-major chord. The F s triad in this reading then becomes another voice-leading chord, an apparent

o7 consonance that might more readily be understood as a processual step in the resolution from vii s3 of D to the D. As shown in Figure 1.12, the voice leading here resembles that from the example above: the chordal

fifth G resolves down by step, as does the chordal seventh B b. The chordal third E s resolves up by step.

The chordal root, C s, also resolves up by step, but only after remaining held over to create the apparent F s

triadic sonority: it then resolves up to D while the F s and A remain static. Thus both the tritone FIP between C s and G is resolved, as is the diminished-seventh FIP between C s and B b, albeit both in a

displaced manner.

While the voice-leading motions in these passages are semitonal, and the chords themselves highly

chromatic, there remain ways in which the two examples can be viewed from a more tonal-prolongational

perspective without recourse to unconvincing Roman numeral labels such as iv ø7 or fiii. Using the approaches I have suggested, it is possible to note the parsimonious voice-leading behaviors highlighted by neo-Riemannian theory, yet reintegrate these observations into a more thoroughly tonal analysis. In being more sensitive to the tonal implications of more local voice-leading paradigms that emerge in such passages, tonal logic, despite chromatic alteration and ambiguity, can be discerned in instances where simply labeling vertical sonorities based on a root and quality cannot. In this way, the fundamental voice-leading 88

Figure 1.12. Analysis of Example 1.9

observations of neo-Riemannian theory can be reconciled with the more conventional aspects of tonal- prolongational analysis.

I conclude this section with several examples that are suggestive of the possibility of double alteration. There are two different ways that double alteration can occur. Firstly, it is possible to alter one chordal constituent in both directions; that is to raise and lower it by semitone. While this is often referred to as a “split” chord, the voice leading suggests that it can be more functionally understood as a double alteration of a diminished-seventh chord.94 Example 1.10 shows a passage from the first scene of Strauss’

opera Salome . While again a relatively local example, my reading of this particular passage pushes this theory

to what I see as its breaking point, in regard to how much centrifugal chromaticism traditional tonality can

tolerate before breaking. The music concludes a deep-level prolongation of D ( fII of the global C s) in

4 rehearsal (RH) 6.2, moving immediately to a V 3 chord in the tonic. Before reaching the tonic, however,

another chord is inserted. This chord, in RH6.5, is a curiosity for it contains five pitches: D–Fs–A–C–E,

and progresses to the tonic (with a six-four dissonance complex above it, shown in my analysis to be a

4 displaced five-three). Given that the V 3 chord in RH6.3 is dominant in function, under the auspices of tonality the chord in RH6.5 must either prolong or resolve that dominant. Thus the chord in RH6.5 cannot be understood as some extended chromatic variation of fII (such a nomenclature would be fII 9, projecting

94 See, for example, Stefan Kostka, Materials and Techniques of Post-Tonal Music, 4 th Edition (New York: Routledge, 2016): 47. 89

Example 1.10. Strauss, Salome , RH6.2–RH7.2

a dominant-ninth sonority). Given that there is no tonic pitch in the chord (nor is 5 present), and that fII 9 is

counterintuitive to the tonal progression (and more simply a bizarre chord), the former option, that this chord could be an extension, or prolongation, of the dominant in 6.3, is worth investigating.

Enharmonically respelling the chord in 6.5 yields Bs–D–(D x)–Fs–A, which is a diminished-seventh chord with two altered pitches: the normative D s has been both raised and lowered to D x (E) and D n

simultaneously, a type of split-third understanding. As with every other example, the voice-leading helps

guide the analysis. In such a case, the expectation for the diminished-seventh dissonance resolution to create

the FIP would entail the B s rising by semitone, which it does, and the A falling to the chordal fifth, which it

does not do immediately, because the C s chord originates as a six-four chord, with the five-three resolution

displaced over the third progression as shown in

Figure 1.13. Analysis of Example 1.10

Figure 1.13.95 Thus, as the upper voice tracks in Figure 1.13, the diminished-seventh interval does in fact

resolve to a perfect fifth, but this is obscured through linear displacement. The other voices also behave as

expected: the lowered chordal third (D) resolves down by step to the tonic, while the raised chordal third

(D x) resolves up to F s, creating the fourth above C s at RH7, before resolving,

again displaced, to E s (spelled F n) in RH7.1. The chordal fifth F s remains static, but also via displacement

resolves down by step to E s. The voice leading here also further confirms that the chord in 6.5 should not

be thought of as a D-based dominant ninth, as its voice leading follows none of the conventions of such a

chord. The only FIP to be realized is the diminished-seventh resolution between B s and A, while the other

potential FIPs are abnegated.

The second possibility for double alteration involves altering both inner pitches, although it seems to have be used sparingly. The following four examples demonstrate instances of this phenomenon in Strauss’ earliest opera Guntram , in his song “Notturno,” and in what are considered two of his most harmonically adventurous works: Salome and Elektra .

95 One of the drawbacks of conventional nomenclature is that we have no symbol to depict a chordal alteration in the bass when the bass is not the chord root (i.e. here, the D n is a lowered chordal third, but it is impossible to depict that in the Roman numeral/figured bass analysis). In such cases I have adopted the convention of notating the diatonic version as the chord symbol, o6 o7 and including beneath it the altered-version in root position (i.e. vii 5 with vii s3/b3 beneath it) to show the chord’s function, but also its alteration. 91

Example 1.11. Strauss, Guntram . Act I, Scene 1, mm. 1–7

Example 1.11 shows the outset of the first act of Guntram . The chord sounded on the last beat of m. 6 is

spelled C f–Fs–D–A and resolves to a cadential six-four over V of E b.96 The A n and G b (spelled F s) suggest vii o7 of V in E b, and indeed, as shown in Figure 1.14, despite the motion to a six-four chord and a voice

exchange that obscures the resolution, they resolve as is conventional of a diminished seventh. The C b in the

o6 (Gr) bass can be understood as the commonplace alteration of the chordal third that creates the vii 5 of V, but the D n is not part of such a sonority. Here, while it is obvious that the D is more of a displaced neighbour

o6 (Gr) o7 to the E b, which would create a vii 5 if sounded simultaneously with the A, C b, and G b, it creates a vii b5 sonority combined with the lowered chordal third, or what sonorously would resemble a minor-seventh chord. Given that this is a relatively early example in Strauss’ oeuvre, and that the D (or E ff) is clearly a displacement of E b, the origins of this chord is clearly derived in the linear realm, though, as I have argued, its harmonic function should be investigated based at least in part on what it is, not where it comes from. In this case despite the double alteration, the diminished-seventh FIP retains the tonal function of this chord as a variant of an applied vii o7 /V in E b.

96 The deeper-level harmonic progression here is an arpeggiated C chord: the tonicized regions outline C–Ef–G–Bf. 92

Figure 1.14. Analysis of Example 1.11

Another instance of double alteration can be found in Strauss’ 1899 song “Notturno.” The passage, shown

in Example 1.12, is again highly localized, and the alterations are more of a passing nature than an actual

sonority, but it is a progression worth noting, as it reinforces both the origin of these alterations as passing

Example 1.12. Strauss, “Notturno,” mm. 56–67

93 tones that intensify the dominant drive towards the local tonic, as well as the possibility of doing this with both the third and fifth of a diminished-seventh chord. Here, the passage is locally in G minor, and the first

6 two beats in the fifth measures are understood as V 4, followed by a deceptive motion through an applied

diminished-seventh of vi resolving to vi. A similar progression is then occurs down a third, as the tonal

focus shifts away from G to D minor. The vii o7 of D, however, is embellished by two passing chromatic

tones on its way to D: D s and F s, which, coming from C s–E–G–Bb, are understood as E b and G b

respectively, creating a fleeting diminished-seventh chord with a lowered fifth and lowered third, which

sounds like a third-inversion minor-seventh chord rooted on D s, but very clearly functions as an alteration

of vii o7 /D when heard in context.

Example 1.13, from Salome’s dance, employs a similar progression. Kevin Swinden has described

this phrase as “closing with a half cadence,” and although the phrase does conclude on V, it is questionable what the harmony is prior to the V chord that creates a half cadence. 97 In trying to avoid the Schenkerian

Example 1.13. Strauss, Salome , Dance, 11 mm. Before RHQ

97 Swinden (2005): 277. 94

Figure 1.15. Analysis of Example 1.13, second system

trap of ascribing tonal structure because of the presence of a tonic and a dominant, I suggest investigation of the chords that intervene between the initial prolonged C s minor tonic and the cadential dominant is

necessary. In between tonic and dominant there are two chords: an apparent A-minor triad, and a chord

spelled D-F-A-C. Neither of these express tonal-prolongational function in C s minor: understood as they

are written, the former contains an altered tonic pitch, while the latter might be labelled as a minor-seventh

chord built on f2 , also containing an altered tonic pitch. Enharmonic reinterpretation of both yields B s-Dx-(

)-A and B s-D-F-A respectively. In both cases, the diminished-seventh interval between B s (spelled C n) and

A is present, and remains present from the first chord to the second. Thus, I understand this as a processual

o7 o7 unfolding of chromatic variants of the vii chord: in the first case it is an incomplete vii s3 in third inversion, followed by a doubly-altered vii o7 (with a lowered third and fifth), also in third inversion. The

second chord then resolves to V, as third-inversion diminished-seventh chords are inclined to do. My

analysis of this brief passage is given in Figure 1.15, showing a motion from tonic to dominant, neighboured

o4 by the vii 2 chord with fluctuating alterations in the upper voices.

Example 1.14 depicts a passage from Elektra’s dance at the conclusion of Strauss’ opera. In his

analysis of the final scene of the opera, Bryan Gilliam writes that “Strauss composes a scene that is

unremittingly diatonic and consonant,” citing this consonance as a counterbalance to the rampant 95 chromaticism that characterizes most of the rest of the opera. 98 The passage in question, however, diverges

from this analysis of prosaic tonality. At Rehearsal 256a the music is sitting on a dominant seventh of C,

o4 passing through an F s in the bass six measures later to create a vii 3 chord substituting for the more

4 commonplace V 2 that would harmonize the bass descent from tonic to subtonic. This resolves to an apparent C b triad in first inversion, which I understand as a tonic chord in first inversion with a

Example 1.14. Strauss, Elektra , Just Before RH257a

98 Bryan Gilliam, Strauss’ Elektra (New York: Oxford University Press, 1991): 223. 96 suspended fourth above the bass (or sixth above the root). The subsequent chord is spelled E-Gs-B-D, with

o7 D in the bass, functioning as a first-inversion vii b5 of the tonic to which it resolves in the next measure.

Before it resolves, however, the D passes through Db, creating an admittedly fleeting double alteration: B-

Df-Ff-Af. This sounds like a minor seventh sonority (D f-Ff-Af-Cf), but its voice leading places it firmly as a

o6(Gr) diminished-seventh chord, and I have labelled it vii 5f3, to reflect that it has both the German alteration in

the bass (lowered third) and a lowered chordal fifth, which is the third above the bass in this inversion.

o7 From here the bass descends through the leading tone, harmonized as vii f3 of the tonic, and passes

o6 through the subtonic while maintaining the leading-tone diminished-seventh chord, landing on vii 5 of V.

The dominant resolution of this chord appears two measures later, but in between sounds a chord notated

Ds-Fs-Af-Cs. This is not a chord that can easily be defined as a tertian chord if the pitches are understood

as written: perhaps some sort of sII ø7 with a lowered fifth, which, of course, does not express strong tonal-

prolongational coherence. My analysis of this chord is that it is another example of a doubly-altered

diminished-seventh chord: enharmonic respelling yields F s-Ab-Cs-Ef, or a diminished-seventh chord

applied to the subsequent dominant with a lowered third and raised fifth. The voice leading here confirms

the local dominant function I ascribe to this chord: the diminished-seventh interval between F s and E b resolves to the G–D perfect fifth, creating the FIP necessary for dominant-to-local-tonic discharge. Figure

1.16 shows my analysis of this passage as a whole: note in particular the added-note A b I analyze at rehearsal

257a: despite being recast enharmonically as a G s over the first doubly-altered chord, it resolves as an A b to

G once the tonic chord five measures after 257a is reached: thus the A b functions as a dissonant unresolved suspension over the inverted tonic chord, but then turns into part of the tonality-defining FIP progression as it discharges to tonic as part of the diminished-seventh to perfect fifth FIP. As mentioned, double chordal alteration is rare, but as the previous examples show, it does surface on occasion, and follows the same internal logic that I have suggested for single alteration of diminished-seventh chords.

Figure 1.16. Analysis of Example 1.14

IV Two Vignettes from Parsifal

The final two examples in this section each approach a short passage from Wagner’s last opera

Parsifal from the perspectives developed in this chapter. In these vignettes I engage with previous scholarship that suggests that these passages break almost entirely from tonality, and thus implicitly that

prolongational analysis is incompatible. This perspective can be most succinctly absorbed in Brian Hyer’s

description of the harmonic language in the opera. He writes of the second act:

In extreme cases, the motivic chromaticism of late Romantic music negates all reference to the tonic and veers over the precipice into atonality…Wagner loads harmonies with dissonances that render them ambiguous and inoperative: while the music is littered with tonal debris – 7th and 9th chords familiar from more conventional tonal contexts – those harmonies fail to coalesce around a tonic. Sustained bass notes immobilize the harmonies above them and arrest forward momentum: the music wanders between functionless harmonies that neutralize rather than progress to one another, sonorities that seem to float in the music, without a goal, without direction. Dissonant harmonies are either severed from their resolutions or resolve back into themselves. 99

99 Brian Hyer, "Tonality," Grove Music Online. Oxford Music Online (Oxford University Pres), accessed November 9, 2017, http://www.oxfordmusiconline.com.myaccess.library.utoronto.ca/subscriber/article/grove/music/28102 . 98

Contrary to the views expressed by other scholars, my contention is that these passages do in fact retain tonal-prolongational logic, albeit a heavily chromatic and extended version of it, which can be understood through the application of the theories developed in this chapter. I will argue further that the hermeneutic interpretations offered by the atonal analyses are just as viable, if not more so, when these passages are understood as distortions of a more commonplace tonal logic.

The beginning of Amfortas’ lament from towards the end of Act I is shown in Example 1.15. While

William Kinderman has discussed this passage as being unequivocally in E minor, Richard Cohn has suggested a different interpretation. 100 Specifically, Cohn references the G s dominant-seventh chord in m.

1301 that resolves back to the first-inversion E-minor triad in m. 1302. This is a moment that Kinderman

ignores completely in his discussion of the music, despite the G s dominant seventh not

Example 1.15. Wagner, Parsifal , Act I, mm. 1297–1303

100 William Kinderman, Wagner’s Parsifal (New York: Oxford University Press, 2013): 220. 99 being the dominant of the tonality in question. In Cohn’s analysis, under discussion is the prevalence of hexatonic poles in Parsifal : In his earlier work, Cohn writes, “The (hexatonic) progression effaces the border between reality and appearance, between death and life. And it is exactly such effacements that are the mark of the uncanny.” 101

Cohn notes that this move from G s to E minor is one such instance, and he argues that the seventh

on the G s chord is an added dissonance that does not interfere with the more fundamental triadic motion occurring between the G s major and E minor triads. 102 Cohn uses this analysis, which he had previously

suggested invokes a sense of the ethereal, or otherworldliness, to suggest that the music reinforces

Amfortas’ pain. 103 I do not disagree with Cohn’s hermeneutic assessments, but by invoking the notion of hexatonic poles Cohn is suggesting that this progression does not follow the conventions of tonal- prolongational process, while I believe it does, and ultimately suggests that it is the proximity to, but distortion of, tonal processes that create the sense of disquiet and unease that leads to the hermeneutic synergy between music and drama.

Cohn is, of course, right to point out the tonal disjunction between the G s dominant-seventh

sonority and the subsequent E-minor sonority. Given, however, that this event occurs within what is

convincingly an E-minor prolongation, I contend that there is a way of integrating this chord within that prolongation. Indeed, this progression is virtually identical to the opening of “Befreit” discussed above: an

7 6 apparent III s progresses to I (in this case I ). But is the progression here truly from tonic, to dominant, to

(highly dubious) mediant, to tonic? Instead, like in “Befreit” this apparent G s dominant seventh can be

o7 understood as vii b5 of the tonic, in this case with the altered chordal fifth in the bass. In this sense, the

chord in question extends the dominant function of the preceding diminished-seventh and dominant-

seventh chords, but with a chromatic intensification through the distortion of the chordal fifth. The voice

101 Cohn (2006): 232. 102 Cohn (2012): 146. 103 Ibid., 22. 100 leading again helps clarify this function: the D s conceptually (though transferred between instruments)

resolves up to E, while the C (spelled B s) resolves down to B, fulfilling the diminished-seventh FIP requirements, while the A b, spelled G s, in the bass resolves down to G n. This creates, as reflected in Figure

1.17 a deeper-level chromatic neighbour figure around the bass note G, of which the more commonplace dominant-seventh in m. 1300 is an elaboration.

In this context, the altered chord is jarring, and this sonorous disjunction is reflected in Cohn’s approach to the chord, wherein neo-Riemannian transformations that map the G s chord onto the E triad as hexatonic poles seems more appropriate than prolongational analysis. My argument, however, is that the prolongational process in this passage can still be understood through the theory of altered diminished- seventh chords that I have developed in this chapter. Understood from this viewpoint, Amfortas’ pain is reflected in the music not because of a cessation of tonal processes, but through an intensification of it: the chromatic procedure of altering the chordal fifth by semitone creates a disjunction between the chord’s sonority—a dominant seventh—and its resolution as a diminished seventh. This altered chord simultaneously distorts and confirms the tonality, but confirms it in a way that is dissonant with common- practice expectations, and it is, I believe, in this way that it projects the sort of otherworldly etherealness of which Cohn speaks, that it is closely related to, but at the same time different and dissonant from, common practice procedures, rather than a complete departure.

Figure 1.17. Analysis of Example 1.15

101

Example 1.16 shows the opening measures, following the prelude, of the second act of Wagner’s

Parsifal , of which Warren Darcy has written: “95% of this music is harmonically non-functional.” 104 Darcy

goes on to suggest that “despite the Schenkerian appearance of [his analysis], the structural levels are not

recursive: the background level may suggest a functional progression (I–iv–V–I in B minor), but the lower-

Example 1.16. Wagner, Parsifal , Act II, mm. 67–88

104 Warren Darcy, “’Die Zeit ist da:’ Rotational Form and Hexatonic Magic in Act II, Scene 1 of Wagner’s Parsifal ,” in A Companion to Wagner’s Parsifal, ed. William Kinderman and Katherine R. Syer (Rochester: Camden House, 2005): 231. 102 level spans are non-functional and transformative.”105 Darcy’s analysis instead relies on what he describes as interwoven “hexatonic, octatonic, and enneatonic elements.” 106 Rather than viewing the passage as non-

functional or atonal, I suggest instead that analysis using the approaches of chromatically altered diminished-

seventh chords yields a convincing tonal interpretation, though one that differs significantly from Darcy’s.

The broadest outline of this passage is, as Darcy suggests, a move from tonic in mm. 67–68, to half-

cadential dominant in m. 83. The space between these two pillars is, I argue, filled by an extended

prolongation of fII (C) within the global key of B minor, rather than the prolongation of the subdominant

that Darcy suggests, and it is a lower-level prolongation of the diminished-seventh chord, sometimes with

chromatic alterations, that likewise prolongs the fII chord. 107 It is specifically this difference in the intermediary harmony that has a number of significant effects on the claims of understanding complete non-functionality in this passage.

As shown in Figure 1.18, following from the B-minor tonic in. mm. 68–69, m. 70 sounds as though it is moving towards the subdominant, with B–F–A appearing over a subdominant pedal. Because the third is missing from the seventh chord sounding above the pedal, it is unclear whether this is a dominant of E with a lowered fifth (B–Ds–F–A) or a half-diminished seventh chord (B–D–F–A). The subsequent transformation of the A to A b (spelled G s) suggests that the function of the preceding chord is vii ø7 of C

(that the missing note is D n), which then becomes fully diminished before resolving to a C triad in the

subsequent measure. The E pedal, which initially gave the impression of being the subdominant root, ends

up being the third of the lowered supertonic C. 108

105 Ibid., 231. 106 Ibid., 230. 107 For detailed studies on the possibility of prolonging dissonant seventh chords, and the ways in which such prolongations can be realized, see both Robert Morgan, “Dissonant Prolongation: Theoretical and Compositional Precedents,” Journal of Music Theory 20, no. 1 (1976): 49–91; and Yosef Goldenberg, Prolongation of Seventh Chords in Tonal Music (Lewiston: The Edwin Mellon Press, 2008). 108 Having a chordal third as a pedal is certainly less common than the root, but is by no means unheard of. Another example of this can be seen four measures from the end of Schubert’s “Am Meer” from Schwanengesang , where C s–E–G–Bf occurs over an F pedal, but resolves to a first-inversion D-minor triad. 103

Figure 1.18. Analysis of Example 1.16

The chord in mm. 73–74 is a minor seventh rooted on D, whose function can be understood as ii 7

in a deeper-level prolongation of C. This supertonic chord is followed by a chord spelled G s–B–D–F,

whose spelling suggests vii o7 of A, but could equally be vii o7 of C. This chord is then prolonged through a number of voice-exchanges and transformations. From m. 75 to m. 76 B and D undergo a voice exchange, while the A b (spelled G s) migrates semitonally up to A creating a B ø7 chord. Another voice exchange between A and B from mm. 76–78 prolongs the chord further while A returns to A b.109 The chord that results in m. 78 is an example of an altered diminished-seventh, where the E n is enharmonically F b, creating

o7 a fleeting vii b5 sonority, though the lowered fifth acts more as an appoggiatura to the normative fifth that materializes in the subsequent measure. Measure 80 effects another voice exchange, with F moving up to A b through a Tristan-esque ascending chromatic line, while A b moves down to F in the bass. This final chord in

o7 the prolongation is spelled B–Ds–F–Af, or vii #3 .

Rather than resolving immediately into a C triad, an apparent E-major triad is sounded prior to the

C-major triad. Ultimately what I suggest is that the E-major triad is only an apparent consonance; an upper-

109 I have chosen to analyze the chord in m. 77 as a passing chord, despite its occupation of an entire measure, for a few reasons. Firstly, in terms of addressing the issue of duration, it is of the same duration as the chords preceding and following it, and thus, relatively speaking, could ostensibly function as a passing chord (i.e. if mm.76–78 were reduced to quarter-note durations, the notion that the middle quarter note could be passing would not seem obtrusive). Secondly, it continues the voice-exchange figure found in the preceding and following measures. 104 third of C that hides the resolution of the diminished-seventh in a confluence of voice-leading intricacies.

Following the importance I have ascribed to the diminished-seventh FIP, note that it was the B and A b that

created the diminished-seventh interval throughout mm. 75–81. This interval remains imperative to the

analysis at the point of resolution: when B–Ds–F–Af resolves to E, the B and the A b remain static. While it

may be tempting to see the chord in m. 81 as a distorted dominant of E, owing to the presence of D s, I

argue this is not the case, as no tritone nor diminished-seventh interval in the key of E exists in this chord:

Ds to G s is a perfect fourth, while D s to B is a minor sixth, neither of which create functional potential directed towards E. 110 This is the impetus for my analysis of a C-major unfolding here: the B and the G s, which remain static when the apparent E-major triad emerges, ultimately fulfill their FIP potential that was built up over the previous six measures, and resolve as a diminished-seventh interval from the apparent E- major triad into the C-major triad in the second half of the measure. The resolution is, in this case, delayed over a 3–1 unfolding in the bass. 111 The apparent E-major triad might thus be said to function as a voice- leading chord, existing as an accidental conglomeration of pitches sounded in order to effect proper voice

leading from the diminished-seventh chord to its resolution: because the Ab chordal seventh is in the bass

and needs to resolve down by step, the chordal third of C needs to be initially present in the bass. 112

Understood as such, this passage projects a large-scale i–fII–V progression at a deeper level, with the fII Stufe prolonged for a lengthy temporal span by a constantly transforming dominant-functioning

leading-tone chord. The fII expansion begins on the third degree of fII (E) and returns there through an

octave descent in the bass, which then unfolds down to the root-position fII chord before progressing to V

110 Some theorists have suggested that the presence of a leading tone alone is enough to imbue a chord with dominant function. Smith, for example, writes “any chord containing a leading tone is a dominant” (Smith [1986]: 110), while Kopp suggests that upper sharp mediants have “a dominant flavor” owing to the presence of the leading tone which creates a “particularly clear path back to the tonic” (Kopp [2002]: 16]). I would suggest that this approach is too simplistic and open-ended. Such an approach leaves open the possibility of a number of bizarre scenarios, such as a C-minor triad could ostensibly exert dominant function if applied to a D b triad. As I hope this chapter has argued, dominant function is the product of more than just a static univalent interval; by extension, dominant function should likewise not be seen as a product of a single static pitch. 111 The E–C delay here might be seen as a deeper-level parallelism to the more surface-level aspects of the opening measures discussed above, where the E pedal masquerades as the root of IV, but ultimately ends up being the third of fII. 112 Again see Lorenz’ discussion of apparent triads. 105 of B. It is also notable that the stemmed note-heads in Figure 1.18 outline a deeper-level arpeggiation of the leading-tone diminished-seventh chord of C, suggesting that a prolongation of this chord indeed serves as

the structural basis for these measures, which the two chromatic alterations discussed do not functionally

distort.

In this way, the passage can be understood to exhibit functional harmonic prolongations and can be

analyzed in a manner only slightly more elaborate than more conventional tonal-prolongational passages.

The processes in this passage have an identifiable link with classical tonality and its processes, but they are obscured by chromatic alterations. As such, I suggest that tonality—both on the deeper level and also on the musical surface—remains the operative organizing principle in this passage, and that any extended scalar patterns might be understood as a by-product of the chromatic alterations employed. And indeed, as I suggested above, perhaps the magic and mystery of these passages might be better understood as being created through a distortion of, rather than a complete break from, common-practice tonal procedures; it is the relationship of these alterations to tonal precedents that imbues them with an ethereal and otherworldly feel, rather than the use of an entirely new system.

Conclusion

It was in relation to many of the excerpts discussed in this chapter, or other similar ones, that

Schoenberg’s view of music as evincing an “emancipation of the dissonance” developed. 113 In this statement

Schoenberg was noting the tendency for what were previously highly valent chords to function in ways that

defied those functional properties: dominant-sevenths began to exhibit previously-unheard-of resolutions, dissonant pitches like chordal sevenths failed to resolve, leading tones were left to meander about, and the general conventions of voice leading and harmonic syntax were supposedly being abandoned for freer writing. The perspectives I have advanced call into question Schoenberg’s assertion: certainly if one were to

113 Arnold Schoenberg, “Opinion and Insight,” in Style and Idea: Selected Writings of Arnold Schoenberg , ed. Leonard Stein, trans. Leo Black, 258–263 (London: Faber, 1975). 106 place emphasis on vertical sonority, then yes, these apparent dominant and half-diminished seventh chords are resolving in ways that are anomalous to the conventions of tonality. But is sonority the only, or even the ultimate, arbiter of function? As I have argued, viewed enharmonically, or half-enharmonically, the dissonance treatment of the chords studied in this chapter conforms closely to the conventions of tonality, and seen through this light it is not that the dissonance is emancipated, but rather it is re-contextualized and hidden in more complexly chromatic chords masquerading as conventional tonal sonorities. This is not to say that the dissonance was never emancipated, but that perhaps that emancipation happened later than is widely believed: that the move towards emancipation was more processual and incremental.

At first glance, the positions developed in these chapters might seem like an argument for a fairly radical re-envisioning of tonal theory to account for the chromaticism and harmonic syntaxes found in the late nineteenth and early twentieth centuries, particularly in the works of Wagner and Strauss. I would argue that it is not so radical a departure, rather simply a shift in focus, albeit one that grates against the commonly held narratives regarding tonal dissolution in the works of Wagner and Strauss. 114 By stepping away from the

conventional prioritizations of chord classification based on root and sonority, and investigating how other

parameters, specifically the projection of univalent dissonance and its resolution according to tonal

convention, new avenues of harmonic activity and exploration emerge. This is not to say that neo-

Riemannian or other transformational perspectives are not productive. As noted above, neo-Riemannian

observations regarding voice-leading parsimony capture a more abstract version of the voice-leading

motions than my own analyses convey. I argue that these voice-leading processes provide a compelling link

to common-practice tonal precedents, while at the same time pushing this music beyond the conventions of

tonality by using the function of fundamental dissonances to recast conventional sonorities in new ways. As

Joseph Straus suggests, “[Conventional sonorities] are too profoundly emblematic of traditional tonal

114 A similar perspective regarding whether the narrative of tonality being “abandoned” shortly into the twentieth century is entirely accurate forms the underlying conceptual thread of the 2012 volume Tonality 1900–1950: Concept and Practice , ed. Felix Wörner, Ullrich Scheideler, and Philip Ruprecht (Stuttgart: Franz Steiner Verlag, 2012). In the introduction to that volume, the editors question the notion that atonality supplanted tonality entirely in the years around 1910, and suggest that tonality instead continued on in many diverse ways. 107 practices to meld quietly into a new musical context. As a result, they become the locus of a productive musical tension. They evoke the traditional musical world in which they originated, even as they are subsumed within a new musical context.”115 Rather than viewing these chromatic chords as outliers, then, as

Kopp suggests, the question one must ask is how these chords can be understood as tonal; hopefully the positions I have advocated in this chapter, and which will continue to coalesce in subsequent chapters, have begun to provide a solution that shows the ways in which these chromatic chords can be, as Robert Morgan writes, “folded back into normal common-practice prolongations according to common-practice procedures.” 116

115 Joseph N. Straus, Remaking the Past: Musical Modernism and the Influence of the Tonal Tradition (Cambridge: Harvard University Press, 1990): 1. 116 Robert Morgan, “Are There Two Tonal Practices in Nineteenth-Century Music?” Journal of Music Theory 43, no. 1 (1999): 160. Chapter 2 When is a Triad not a Triad? Acoustic Consonance, Tonal Dissonance, and the Dialogue Between Neo-Riemannian and Prolongational Theories of Tonality

One of the benefits of neo-Riemannian approaches to late nineteenth-century harmony is that they provide a means by which triads that appear to be irreconcilable within a given tonality can be viewed as demonstrating coherence—a different type of coherence, to be sure, and as I pointed out in the

Introduction, one that does not require the triad to exhibit a direct or indirect referentiality to a prolongational tonality.1 The drawback to this approach is that neo-Riemannian theory is generally content to operate outside prolongational practice, in the sense that contemporary neo-Riemannian approaches emphasize voice-leading parsimony, depicting in such analyses chords as being very surface-level events related to each other through immediate proximity and minimal semitonal displacements.2 In this sense, neo-Riemannian theory might be understood as a theoretic apparatus designed for dealing with the types of chords described by Kurth as self-referential by making their self-referentiality an asset.

In the Introduction I highlighted several oft-cited drawbacks to neo-Riemannian theory. Its problematic relationship with chords beyond triads is a perennial criticism, as the theory is, in short, idealized to explore exclusively triadic relationships that lie beyond the understanding of conventional tonal

1 In this sense I mean that a triad need to be a primary diatonic triad, nor one derived from the conventional processes of modal mixture nor tonicization. 2 It is interesting to note that Riemannian transformations were only abstractly transformational, whereas current neo-Riemannian transformations are generally transformational in a very visceral sense. Neo-Riemannian transformations map the transformations of one chord into the subsequent chord, and so, in a sense, map a type of hearing that a listener might engage with in order to understand the generation of the chromatic chord in question (see, among others, Richard Cohn’s work in modeling relationships between triads with minimal semitonal displacements [Cohn, 1996; 2000; 2012], or Steven Rings’ (less Riemannian) transformational approaches to tonality [Rings, 2011]). Conversely, Riemannian approaches take Riemann’s three tonal pillars as the only three fundamental harmonic elements, and model any triad, chromatic or otherwise, as a transformation of one of those three pillars, whether that pillar chord is present or not (hence my use of the term abstractly transformational in describing Riemann’s approach). For extensive discussion of Riemannian approaches, see for example David Kopp, Chromatic Transformations in Nineteenth-Century Music (Cambridge: Cambridge University Press, 2002), or William Mickelsen, Hugo Riemann’s Theory of Harmony: A Study (Lincoln: University of Nebraska Press, 1977). Thus one might say that neo-Riemannian theory presents a more phenomenological, or linear, application of Riemann’s theories, while Riemannian approaches suggest at a more structural, or vertical, application of Riemann’s work. 108

109 analysis.3 But there are also some examples for which neither neo-Riemannian theory, nor conventional tonal theory in its current state, is equipped to deal with adequately. Example 2.1 depicts the Todestrank motif from Wagner’s Tristan und Isolde that I cited in the introduction to this dissertation as an example of a passage wherein current theories falter in their explanatory power. The phrase in this example is locally in the key of C minor: it is preceded by V7 of C that resolves to an initiating C chord that sounds with a sixth in place of the expected fifth.4 Looking at the larger-scale trajectory, this phrase moves from the tonic just described to a dominant seventh seven measures later upon which it concludes, thus projecting a tonic-to- dominant prolongation of C. Most of the chords in this progression adhere to the practices of tonal- prolongational harmonic structure and are easily identifiable by conventional harmonic analysis: the chord

Fr4 immediately preceding the final dominant is a V 3/V, a chromatic chord applied to the dominant, whose

Example 2.1. Wagner, Tristan und Isolde , Act I, Scene 2, mm. 24–30

3 A number of attempts at modifying neo-Riemannian approaches to account for seventh chords have been proposed. Cohn, for example, suggests that certain chord members (the seventh in dominant sevenths, and the root in half-diminished sevenths) can be conceptually omitted; the drawback to this approach is that it does extreme violence to the music (see Richard Cohn, Audacious Euphony: Chromaticism and the Triad’s Second Nature [New York: Oxford University Press, 2012]: Chapter 7). Edward Gollin has suggested a model for a three-dimensional Tonnetz (Edward Gollin, “Some Aspects of Three-Dimensional Tonnetze,” Journal of Music Theory 42, no. 2 (1998): 195–206), while a number of scholars have advocated split functions, an approach which benefits from the more precise ways in which it maps the actual voice leading that is occurring (Julian Hook, “Cross-Type Transformations and the Path-Consistency Condition,” Music Theory Spectrum 29, no. 1 (2007): 1–40; Graham G. Hunt, “David Lewin and Valhalla Revisited: New Approaches to Motivic Corruption in Wagner’s Ring Cycle,” Music Theory Spectrum 29, no. 2 (2007): 177–196). 4 This topic will be covered in the subsequent chapter, but it refers to the apparent first-inversion Af-major triad in m. 24, which can be understood, looking beyond inversion theory, as a chord rooted in C with an abnegated (unfulfilled) 6–5 suspension. Conversely, William Marvin, as noted in the introduction, analyzes this chord as a C-minor chord with a (5)-6 motion wherein the fifth is omitted, citing work by Edward Laufer as precedent for his analysis (though Marvin’s text suggests he later reads it as an Ab triad). 110 function serves to provide surface-level emphasis to the final chord through tonicization. This is preceded

by iv 6, also unproblematic as a diatonic predominant preceding the dominant.

The only other chord in the passage, an A-major triad that precedes the inverted subdominant, throws the prolongational unity of the passage into question. From a Schenkerian perspective, one might be tempted to understand this chord as VI s of C, a perspective which, as noted by Matthew Brown, Schenker advocated as a type of mixture. 5 Indeed this is Schenker’s own analysis in Harmonielehre , wherein he suggests

that because the melody is entirely diatonic to C major/minor, it supports the use of the more chromatic

inflection in the harmonic domain.6 This analysis, however, contradicts Schenker’s requirement that tonic and dominant pitches can only be understood as such when used in purely diatonic forms, and thereby results in a questionable ontological claim and calls into question the precise nature of what an analysis using

VI s is saying about this chord. 7 In understanding the chord as VI s, the implied suggestion is that, firstly, this chord has a direct relationship to the tonic, and, secondly, that an altered tonic pitch (C s in this case) can

still be fundamentally understood as functionally equivalent to the unaltered tonic; that is, it can still be

understood as projecting tonic function despite the chromatic alteration. I question the value (and validity)

that such assertions have for a tonal-prolongational perspective: as Brown points out, “[Schenker] rejects

any possibility of Lydian mixture on the grounds that the subdominant and dominant must always be

available in pure form.” 8 If these two pitches, both hierarchically less significant than the tonic, must be available in their purely diatonic form, then presumably the tonic must likewise be only directly intelligible in

5 Matthew Brown, “The Diatonic and the Chromatic in Schenker’s Theory of Harmonic Relations,” Journal of Music Theory 30, no. 1 (1986): 1–12, especially Figure 4. 6 Heinrich Schenker, Harmony [1906], ed. and ann. Oswald Jonas, trans. Elisabeth Mann Borgese (Chicago: University of Chicago Press, 1954): 106–107. As noted in the Introduction, William Marvin conversely analyzes this passage as an extension of the tonic via a chromaticized 5-6 shift. 7 Recall too from the previous chapter the various arguments from Kopp, and Louis and Thuille, regarding the tonally disorienting effects of chromatically altering the tonic or dominant pitches. 8 Brown (1986): 8. Schenker’s prose and analytic nomenclature are often at odds with each other: Schenker will speak of understanding chords (such as VI s) as applied dominants (V/ii), and yet will retain the VI s nomenclature. This is possibly a confluence of level: in classical tonality at the immediate level, A-Cs-E resolving to a D-minor triad would be V/ii, but at a deeper, more contrapuntally-oriented level where tonal harmony is inactive, it might be understood as an expression of the submediant scale degree. 111 a prolongational sense in similar form. 9 Thus it seems illogical to analyze this chord as having a direct relationship to the tonic in the same way that a VI or nvi chord would. This brings up, again, a question I have continued to pose throughout this dissertation: can a chromatically-altered tonic pitch participate in the

prolongational processes of classical tonality?

Schoenberg, it would seem, had similar qualms about understanding the A-major triad in the passage

as VI s, and thereby as directly relating to the tonic of C. His analysis of the passage, from his essay “Brahms

the Progressive,” invokes a micro-modulation to the key of the lowered submediant.10 Schoenberg’s analysis, as shown in Figure 2.1, suggests that the apparent A b-major triad in m. 24 becomes the tonic in the key of the lowered submediant, at which point the A-major triad can then be understood as the lowered supertonic

(fII). 11 This is where I argue Schoenberg’s analysis becomes untenable: his analyzed fII chord then progresses to an inverted vi in the proposed tonality of the submediant, which Schoenberg then uses to return to the key of C minor for the approach to the dominant that materializes two measures later. Thus

Schoenberg’s proposed modulation does not really effect the

Figure 2.1. Schoenberg’s Analysis of Example 2.1 (Quality and Inversion Omitted by Schoenberg)

9 Refer to my argument in the Introduction wherein I suggest that applied chords should not exclusively be understood as chromatic alterations of diatonic precedents, but rather can be viewed on a referential level as embellishments of the chords which they tonicize. Thus V/V, despite resembling a major version of the II chord, has a fundamentally different point of reference. Likewise, it is equally impractical to view vii o/ii as a functional substitute for I: when it is used as such, its purpose is deceptive, not substitutional. 10 Arnold Schoenberg. “Brahms the Progressive,” in Style and Idea , ed. Leonard Stein, trans. Leo Black (London: Faber, 1975): 59. 11 In his analysis Schoenberg uses only upper-case Roman numerals, and does not indicate chordal inversion. 112 sense of a new key: there are no dominant-functioning chords that discharge onto a tonic, and there is a retrogressive progression from fII to vi. This proposed modulation does little to elucidate and explain the tonal coherence of the passage. Instead, it simply suggests a key wherein all the chords in question happen

to make some sense as stacked vertical conglomerations of pitches, the vertical being the musical domain

that Schoenberg the theorist tended to prioritize.

But this is also a passage where neo-Riemannian theory, despite being a theory of chromatic triads, would falter in its explanatory power. One of neo-Riemannian theory’s assets is that it depicts patterns in voice-leading behaviour, often demonstrating that seemingly tonally-incompatible chromatic triads can be

understood as minimal voice-leading perturbations (usually by a single semitone) of the previous or

subsequent triad. This is often demonstrated further to be a replicated pattern in analyses of such minimal voice-leading motions, suggesting that indeed voice-leading parsimony might have been the underlying

framework for such passages.12 This approach, however, seems to generate little analytic insight into the harmonic role of the chromatic A-major triad in this particular passage. In generating the A-major triad from the A b-major sonority, one would need to employ four of the traditional neo-Riemannian operators

(RPLP), and another three (PLP) to move from the A-major triad to the subsequent F-minor triad. These

pairs of triads are thus not related by shared voice-leading patterns, nor are they examples of parsimonious voice-leading. Cohn has termed this relationship a “hexatonic pole,” understanding the relationship between

the two to be a product of hexatonic cycles, but concluding that the signification of the progression is to

project the uncanny. 13 As such, like the conventional tonal theories described above, the neo-Riemannian approach falters in adequately describing the function of the A-major triad in this phrase.

If neither of the two most prominent analytic approaches to tertian chromatic harmony can provide insight into the role of the A-major triad and how it participates in the harmonic structure of the passage

12 I use the term “parsimonious” here to refer to triads with relationships that can be modelled by a single conventional neo- Riemannian function (P, L, R), which means there is only one or two semitones of voice-leading motion. 13 Richard Cohn, “Uncanny Resemblances: Tonal Signification in the Freudian Age,” Journal of the American Musicological Society 57, no. 2 (2004): 285–324. 113

(whether locally or more globally), is this simply a passage that should be written off as incomprehensible, or

perhaps even moving towards the type of neotonality that would burgeon in the early decades of the

twentieth century?14 Given the unequivocally tonal underpinnings that govern the rest of the passage, the

answer would seem to be no, but answering in the negative acknowledges that the theoretic models of

prolongational tonality, neo-Riemannian theory, or both, are at present inadequate to the task of

understanding the harmonic role of the chord in question, and require extension and revision in the same

manner outlined for seventh chords in the previous chapter.

In this chapter I propose extending the theories developed in the previous chapter by applying them

to triadic, rather than tetrachordal, progressions. In particular, I suggest that neo-Riemannian theory’s

observations of minimal voice-leading perturbations between triads is suggestive of a more tonal-

prolongational phenomenon, namely the types of functional interval progressions, or FIPs, that I described

as creating dominant-to-tonic discharge in the previous chapter. Like in the previous chapter, I will develop

the theoretic models required for this type of enharmonic, behaviour-based analysis of harmonic function,

and conclude by presenting a number of analytic examples wherein the proposed theories can be employed

to elucidate tonal-prolongational structure. In this chapter, unlike the previous one, the theoretic portion will be buttressed by a number of musical examples: because this type of analysis is highly contextual, in the

sense that the same conglomeration of pitches could function in different ways depending on the context, it

is more difficult to generalize systematically about the harmonic function of such chords.

I Acoustic Consonance, Tonal Dissonance I: Major Triads

In the previous chapter I proposed that looking at chords as isolated verticalities, even when not

approached as singularities and viewed as part of a larger tonal context, can be restrictive in understanding

their harmonic function, especially in highly chromatic yet tonal music. Function, I argued, is equally a

14 As noted in the Introduction, the question of atonality arises even in passages where neo-Riemannian theory can be applied. 114 product of what a chord does, rather than only what a chord is or sounds like. In that chapter I proposed moving away from a strictly sonority-based vertical approach to harmony, and suggested that in certain cases, a combination between a univalent harmonic interval (the diminished-seventh or the tritone) and its resolution according to common-practice voice-leading procedures, created harmonic function despite alteration to other chord tones that might alter a sonority from its conventional major-minor or fully- diminished seventh sound to another. This same principle—at least in the case of the diminished-seventh to perfect fifth resolution—can be applied to chromatic major and minor triads, further extending the possibility for the types of half-enharmonic reinterpretation introduced in the preceding chapter.

The notion of apparently consonant sonorities being functionally dissonant has been explored only to a limited degree. 15 Most often acknowledgement of non-consonant status for consonant-sounding triads

comes about through an understanding that some chromatic triad does not adequately fit the tonal-

prolongational system (as in the Wagner example above), yet the larger-scale organizational logic of the

passage remains almost unequivocally tonal. In these cases, some theorists have noted that certain aspects of

a triad can, in certain contexts, seem to imbue it with dominant function, although it is neither a major-

minor seventh chord built on the fifth degree, nor a diminished-seventh chord built on the leading tone. 16

As previously mentioned, recognition of this type of latent dominant function usually revolves around the

notion that one of the pitches in the triad in question is a leading tone, and thereby expresses dominant

function, a claim that I have already questioned in the preceding chapters.

Another approach frequently taken with complex chromatic triads is to write such progressions off

as derivations of voice-leading phenomena and ascribe to them the status of non-functional voice-leading

conglomerations. Perhaps the most notable exploration of this possibility, at least within the realms of tonal

music, is found in Alfred Lorenz’ study of Parsifal . In that study, Lorenz suggests that:

When a triad moves to its chromatic change or neighbour-tone adjustment, the ear first hears the leading tone tendency that exists between the changed note and the chord tone. In

15 Steven Rings, for example, suggests the possibility of acoustically consonant triads that can be understood as being contextually dissonant. See Steven Rings, Tonality and Transformation (New York: Oxford University Press, 2011): 86–89. 16 Recall Smith’s analysis of fvi in Chopin discussed in the previous chapter, as well as Swinden’s discussion of a similar chord in Salome . 115

this way, a strongly dissonant chord is frequently created, but which is incidentally enharmonically equivalent to a triad. 17

Lorenz explains this as a number of upper-and-lower leading tones to the subsequent chord being inserted into the music, the conglomeration of which happen to form an acoustic consonance, and suggests that this

consonance is part of the imperative for Wagner’s use of these particular sonorities, as it “tempers” or

“cleanses” the dissonance—especially, he argues, in the harmonic transformations of the Grail motif in

Parsifal .

Ultimately Lorenz does not develop this theory further, and is content to leave his notion of

apparent, or pseudo, consonances explained as inserted leading tones above and below the pitches of the

subsequent chord, and does not link it to any sort of harmonic-functional concept, nor formalize it in any way. Richard Cohn, however, takes up this mantle in his 2006 paper on the uncanny in Parsifal . There he writes of a passage in Act 1 of Parsifal :

Once we understand the E-minor chord at 1482 as diatonic to D major, we no longer have a secure understanding of the G major chord that preceded it. From the standpoint of the D cadence, the G major chord is now retroaudited as Aff , Cf, D, an aggregation of the E minor chord’s chromatic neighbors. 18

Here Cohn is noting the way in which this chord would be heard as a dissonance rather than a consonance,

though he does not explicitly here link it to the diminished-seventh prolongational progression, and retains

Lorenz’ language of neighbour-tone insertions. In his later monograph from 2012, Cohn’s approach has

changed. Writing again about Parsifal , he suggests:

When a consonant triad progresses to its hexatonic pole, its root is displaced down to the raised seventh degree, while its fifth is displaced upward to the flatted sixth degree. The resulting interval ought to be a dissonant diminished-seventh. But if we perceive the new chord as a triad, then we are perceiving the resulting interval as a consonant major sixth. What ought to be dissonant is unaccountably consonant… 19

17 “Wenn ein Dreiklang in seine chromatischen Wechseltöne weiterschreitet oder durch “Nebentoninstellung” vorbereitet wird, hört das Ohr zunächst die Leittonstrebung, die zwischen Wechselnote und Akkord besteht. Auf diese Weise kommen oft stark dissonanten Gebilde heraus, die aber zufallig enharmonisch gleich mit Dreiklängen sind.” Alfred Ottokar Lorenz, Das Geheimnis der Form bei Richard Wagner [1924–33], Reprint (Tutzing: H. Schneider, 1966): IV: 89–90. 18 Richard Cohn, “Hexatonic Poles and the Uncanny in Parsifal ,” The Opera Quarterly 22, no. 2 (2006): 232. 19 Cohn (2012): 148. 116

In this case the specific interval is the hinge upon which the consonance-dissonance interpretation rests: the enharmonic relationship between the diminished seventh and major sixth. This same relationship plays a distinct role in Cohn’s 2004 article on hexatonic poles as well, in which he writes: “Again what is notated as a consonant major sixth, is perceived as a dissonant diminished seventh,” describing this phenomenon as a tonal paradox. 20 Cohn’s observations here regarding the diminished-seventh interval are important: he is noting that the linear aspects of such progressions should invite a hearing of the subsequent chord as a dissonance, but the vertical sonority of the chord in question also simultaneously forces the listener to

perceive the chord acoustically as a consonance. Despite giving an example of an E-major triad

enharmonically spelled as B–( )–Ff–Af in the context of C major, Cohn ultimately prioritizes the

consonance of the triad, and it is from this standpoint that he pursues his neo-Riemannian theory of

hexatonic relationships and voice-leading parsimony.21

But what if one were to instead focus on the linear dissonance inherent in the tonal motion of these progressions, to hear the progression from the dissonant, and univalent, diminished-seventh interval to the perfect fifth as a tonally salient gesture that overrides the acoustic consonances? This is something that

Steven Rings suggests in passing, writing of Example 2.2 from Das Rheingold : “Wagner “teaches” the listener to hear this as a genuine dissonance: the {G, B ♮, F ♭} in m. 3836 is a chromatic inflection of a {G, B ♮, F ♮} chord in the previous bar, both of them acting explicitly as dissonant neighbors to the A ♭-major tonic.” 22

20 Cohn (2004): 307–309. 21 Ibid., Figure 5. 22 Steven Rings, Tonality and Transformation (New York: Oxford University Press, 2011): 77 (footnote 48). Cohn also notes that Marx rejects the notion of hearing the G-minor triad as an altered leading-tone chord, and translates Marx’s thoughts on the matter: “If one wants to explain the progression by transforming the third B b into an A s, then an entity comes into being which is not a chord at all, or is a wrongly named chord. Thereby, one would have just made a bigger enigma out of a smaller one. Or does one want to give weight to the fact that A s points upward as a sharped tone? Then the fifth D would have to become a Cx, and the incomprehensibility would be exacerbated.” But Cohn (2004, 308) also points out that in Riemann’s revision of Marx’s treatise, Riemann rewrites this particular passage to read: “The ear hears the three tight melodic junctions and discovers from the new harmony a reinterpretation of the old. The G-minor chord becomes, via the progression to B major, a ninth chord over F s with augmented fifth ([F s] A s Cx [E] G),” thereby suggesting, as Cohn notes, that the chord is essentially a form of leading-tone chord with a missing pitch. Both Cohn (2004) and Rothfarb (Kurth 1991 [1920], 107) also point out Georg Capellan’s analysis of the chord as similar to Riemann’s, though Rothfarb adds that “a modern view might analyze [the notes] as a contrapuntal chord, neighbors to a governing Ab harmony.” Kurth also discusses the passage, but refers to the F f as a type of harmonic “shading,” a chromatic alteration of the F n from the previous measure (Kurth 1991[1920]). 117

This is, of course, a minor triad—a sonority to which I will return later in the chapter—but the notion of apparent consonance still holds true. Rings does not develop this observation further, but his language suggests that this chord does have some inherent tonal function, and it is notable here that Wagner does not spell what sounds like an E-minor triad as an E-minor triad, but rather as a dissonant seventh chord with a missing pitch.23 Might such an interpretation illuminate a way in which these chords could be more convincingly integrated within a tonal-prolongational analysis? The conflict that Cohn, and Lorenz, note in

the clash between acoustic consonance and functional dissonance remains, but, as I will argue, prioritizing

the tonally salient linear gesture allows for interpretation of these chords in ways that integrate them into the

prolongational processes of classical tonality, rather than requiring an entirely new system to account for

Example 2.2. Wagner, Das Rheingold , mm. 3833–3836.

23 An understanding of this chord as an altered leading-tone diminished-seventh chord reinforces Schenker’s (1987 [1910]: 92) description of the chord as a “neighboring-note harmony,” though goes a step further in an attempt to categorize it more fully than Schenker did. 118 their purpose in tonal structure. This should not be perceived as an attempt at normalization, but rather an attempt to understand how the uncanniness of these salient chords can be understood through extensions of tonal practice, rather than from a complete divergence from it.

As delineated in the previous chapter, I have proposed a different model for understanding chordal function, arguing that such function results from a combination of univalent pitch pairs being both sounded simultaneously, or near simultaneously, and resolving in conventionally tonal ways: specifically under consideration here, the diminished-seventh interval resolving to the perfect fifth, which is a strong projector of dominant function in classical tonality. Because the diminished-seventh interval is enharmonically a major sixth (or a minor third in inversion), the potential for the type of dominant function described in the previous chapter also exists inherently in every consonant triad. But while the potential may exist, it cannot be said to occur unless that potential is realized through voice leading. While this claim may bear some resemblance to similar claims advanced by other scholars, such as the notion that any pitch can be a leading tone, or any chord with a leading tone can function as a dominant, 24 my assertion here retains the more rigorous linear requirements as described in the previous chapter. That is to say, it is not enough simply to sound a diminished-seventh interval—after all, it is enharmonically a major sixth/minor third. Rather, as was the case with the seventh chords of the previous chapter, it is the process of sounding and resolving this

interval as a dissonance that creates dominant function.

Returning to Example 2.1 from above, Figure 2.2a depicts the voice leading of the A-major triad in

relation to the subsequent F-minor triad: the A moves to A b, the C s to Cn, and the E to F. From the

perspective of classical tonality this is a fairly non-standard resolution for the pitches in question, particularly

the C s, which under tonal conventions would be wont to ascend when resolving owing to its chromatically-

raised nature. Instead it falls by semitone, suggesting a revisitation of the tenability of a VI s interpretation.

Employing a similar half-enharmonic reinterpretation procedure as was done for the four-note chords of

o7 the previous chapter results here in E–( )–Bff –Df, which I have analyzed as vii b5 of F in second inversion

24 Again refer to Charles Smith’s (1986) argument. 119

(a chromaticization of E–G–Bf–Df).25 Understanding the pitches in this half-enharmonic manner reveals

tonal logic in this progression: the C s, viewed as D b resolving down to C n creates the diminished-seventh to

perfect fifth FIP when combined with E resolving to F. In observing and prioritizing the linear aspects of

this dissonance resolution over the acoustic consonance, the way in which this chord synthesizes with the

overall tonal contexts becomes more apparent. Because it is functioning as an applied chord of the

subsequent F-minor (iv 6) chord, it is understood as being an embellishment, or elaboration, of that chord.

Figure 2.2b depicts the larger-scale tonal trajectory of this passage afforded by this analysis: it is, structurally,

a motion from tonic through the subdominant, to dominant, with the latter two chords embellished by local

chromaticized dominant-functioning chords. 26 While the sonority sounds like a consonance, that

consonance—specifically the minor third between C s and E—when observed in the context of its

progression to a perfect fourth, rather than resolving inward to an octave D, progresses as though it were a

dissonant seventh, and it is this feature that expresses the applied dominant function of the chord.

Figure 2.2a. Voice-Leading Analysis of Example 2.1 Figure 2.2b. Structural Analysis of Example 2.1

25 As with complete seventh chords, there remains no entirely satisfactory way of notating the chromatic alteration of the chordal fifth when it is in the bass, so my preference is to employ the root-position nomenclature, and clarify in brackets that the chord is in second inversion. 26 A supplementary observation about this passage: Wagner avoids sounding the dominant pitch G until the arrival of the V chord in m. 30. The G is, of course, the missing fourth pitch in my analysis of the A-major triad as E-G-Bff -Df, but it is also omitted from the initial tonic chord, which, as mentioned, I have analyzed as the tonic with an abnegating sixth (i.e. the expectation is for the A b to act as the sixth in a 6–5 suspension figure, but it fails to resolve [to be discussed further in Chapter 3]): this seems to be an intentional attempt at weakening the tonal relationships of this passage by omitting the fifth of the key until the last possible moment—unsurprising given its dramatic content associated with death. 120

Admittedly, the notion that a triad can take on the function of a four-note chord may seem dubious.

Cohn, again, has pointed out however that Wagner, at least, had a propensity to “treat minor triads and their

ø7 supersets as interchangeable in his late music.”27 For instance, if we add C s to the G–B–Ff chord discussed above, a full four-note altered diminished-seventh chord is formed, which has a half-diminished sonority (C s–E–G–B). Cohn is, of course, speaking here of minor triads (which, again, I discuss later in this chapter); more important is his observation on a more general level, that Wagner treats certain triads and

seventh chords as interchangeable. If we were to change the A-major triad that caused the contention in the

passage in Example 2.1 into a dominant-seventh chord, it does not change the function of the chord as I

have analyzed it: reinterpreting A–Cs–E–G as E–G–Bff –Df simply inserts the note that was missing in the

triadic version. Thus while Cohn’s overall claim that half-diminished seventh chords can be understood as

triads with an “under seventh” (i.e. he omits the root of the half-diminished seventh chord in order to

include tetrachordal sonorities into the primarily triadic neo-Riemannian system) remains a contentious

move that primarily serves to counter the criticisms of neo-Riemannian theory’s inability to synthesize

seventh chords into its structure, perhaps the more prolongational approach I am advocating might be seen

as a means of reconciling these difficulties. 28

If we abstract the triadic-dominant functional relationship further, we can state that any major triad whose root lies a root a major third above another triad (of either major or minor quality) has the potential

to act in a dominant-functioning relationship with that second triad. In the Wagner example above, the root

of the A-major triad is a major third above the subsequent triad rooted on F. This relationship results owing

to the presence of the minor third interval in the upper major triad, which can be reinterpreted

enharmonically as a diminished seventh. Under these conditions, it is the chordal fifth of the upper major

triad that is understood as the functional leading tone to the root of the second triad.

27 Cohn (2012): 144. 28 I will explore the relationship between neo-Riemannian claims and prolongational claims further later in this chapter. 121

A major triad which lies a major third above another triad is, diatonically-speaking, an uncommon relationship as it exists nowhere in the major scale: any time the interval of a major third exists between two chordal roots in a diatonic environment, the upper triad is always minor (i.e. IV and vi) or diminished (V and vii o), and thus cannot fulfill the dominant function in the way described above. Interestingly, this

relationship occurs between one set of chords in the minor scale: V and fIII, assuming the leading-tone is

raised in the V chord, and not the fIII chord. This is, however, a very tenuous relationship in the sense that

in classical tonality V rarely resolves to the mediant. If we add the potential for modally-mixed scales into

the equation, then the number of possibilities increases: fII and IV, fVI and I, for example, fulfill the

requirements outlined above, though I would argue against generalizing this type of relationship for these

more conventional associations: it is far more likely reading for IV and fII to be functioning as consonant

prolongational triads in their own right rather than for IV to function as an altered vii o7 of fII (though it may explain the relative ease of moving between these chords, and likewise for I and fVI). Context, as I have argued throughout, determines function.

Also important to this relationship is the voicing of the chords, or the inversions in which they occur. Again referring to Example 2.1 above, it is notable that the subdominant triad is in first inversion, which allows for the bass pitch (B ff ) to move by step in its resolution. This is, however, not always the case,

especially in music composed after Tristan . One of the more common scenarios is to find both triads in root

position, which is problematic from the perspective of the voice-leading models I have hypothesized. For

example, the chord progression presented in Example 2.3—Riemann’s famous example of what he termed tonality. Of this passage David Kopp has written: “In the entry “Tonalität” in his Musik-Lexikon , first published in 1882, Hugo Riemann defined the concept expressly to embrace chromatic as well as diatonic relations to a tonic, in contrast to Tonart , the familiar diatonic conception of key.” 29 Kopp then notes: “How ironic…that the relation between these three chords, cited by Riemann as a fundamental

29 David Kopp, “Chromaticism and the Question of Tonality, in The Oxford Handbook of Neo-Riemannian Music Theories , ed. Edward Gollin and Alexander Rehding (New York: Oxford University Press, 2011): 400. 122

Example 2.3. Riemann’s Illustration of Tonalität from Musik-Lexicon

example of tonality in chromatic music, has come to serve as a fundamental example of nontonal triadic relations in neo-Riemannian theory, when reinterpreted as the product of the hexatonic cycle.” 30 Thus on the one hand, Riemann claims tonal coherence for this progression of chords, while neo-Riemannian approaches imply the opposite. But what is really going on here?

The progression appears as though it sounds the succession of triads I – fVI – I – III s – I in the key of C. The III s chord, however, is somewhat out of place if one prioritizes referentiality over transformation in their approach to tonal harmony: calling this chord III s implies an alteration to the dominant pitch, and thus calls into question whether the chord, and thus progression, exhibit the same prolongational process and logic that govern classical tonality. 31 One might approach this progression from another angle, however.

Obviously the initial I – fVI – I progression is traditionally tonal, using a modally-inflected submediant to prolong the tonic. The III s chord, I believe, prolongs the tonic further, but does so in a manner that I suggest is counterintuitive to the more transformational impulses that generally surround chromatically- altered mediant relationships.32

30 Ibid., 400. 31 This is not to say that one should never analyze III s, far from it. Rather, my argument here is that IIIs cannot adequately participate in prolongational practices at the harmonic surface because of the chromatic alteration to the dominant. There is nothing wrong, for example, with analyzing III as a prolonged scale-step at the deeper level: as a modally-mixed version of the iii Stufe (the conceptual differences between a prolongational chord at the harmonic surface and a deeper-level Stufe will be addressed more thoroughly in Chapter 4). 32 As Cohn notes, it is a type of double mixture procedure that is often called upon when integrating it into a tonal-prolongational idiom. Cohn writes: “The [iii] triad (a) is initially integrated into a diatonic scale (b) for which that triad is presumed to serve as tonic. A first stage of mixture converts that scale to its parallel major (c), from which a [iii] triad is extracted (d) and labeled as siii (or niii). That triad is temporarily reinterpreted as a tonic (e) that sprouts its own diatonic scale (f ). A second stage of mixture converts that scale to its parallel major (g), from which the target [III s] triad (h) is extracted…” Cohn (2004): 307. 123

Kopp, in his survey of chromatic mediant relationships, suggests that in such cases as III s, it is the chord’s root that gives it a connection to the diatonic set, specifically through sharing a common tone with the tonic triad. However, Kopp is also sensitive that this is a tenuous relationship owing to the chromatic third of the chord, which, when the chord is understood as III s, would itself be understood as what Kopp admits is a tonally “destabilizing” s5. The reading of III s as tonally destabilizing is likewise proposed by

Deborah Stein, who argues “the progression I to IIIs does not embellish I, and furthermore, III s does not progress back to I (as IV or V might). Thus [it] seems like more a harmonic structure that departs from I.” 33

Stein also recognizes that the raised third of III s (a chromatic alteration of the dominant pitch) as

“undermining” the tonality. 34 What then, permits III s to function in the way Riemann claims, that is, as a chord that prolongs, or is related to, the tonic?

To begin, Kopp notes that the fifth of a III s chord is the leading tone of its global tonic. While he argues that this gives it “a particularly clear path back to the tonic,” he also suggests that this is not cause to equate III s with dominant function. 35 Kopp further specifies that s5 in the III s chord is “not f6 tending towards 5.” But as Cohn notes, “Its notation as a [ s5] implies a sharpward pressure, yet it is disposed to

discharge flatward, hence an A b representing the flattened sixth degree.”36 Whether the pitch is functioning as s5 or b6 thus depends on context. In most progressions that do not treat III s as V/vi the III s chord

resolves to I or V. When this happens, and the pitch in question resolves to 5, the b6 reading would be more

accurate given the voice leading involved. This is what happens in Riemann’s example: when the apparent

III s resolves to C, the Gs resolves to G n in conjunction with B resolving up to C: this dissonant

combination betrays the notated Gs, revealing its function as A b. Thus I argue that the FIP from a

diminished-seventh interval to a perfect fifth is present in cases where the III s chord progresses to I, leading

33 Deborah Stein, Hugo Wolf’s Lieder and Extensions to Tonality (Ann Arbor: UMI Research Press, 1985): 107. 34 Ibid., 107. 35 David Kopp, Chromatic Transformations in Nineteenth-Century Music (Cambridge: Cambridge University Press, 2002): 16. 36 Cohn (2004): 307. 124

o7 to my decision to assign to such a chord the analysis of a dominant-functioning chord, or vii b5 (E–Gs–B =

B–()–Fb–Ab).

But while this analysis explains the upper-voice motions well, it does not account for the move from the mediant to the tonic in the bass. The explanation I propose for such progressions is that there exists a disassociation between the bass note and upper voices. Here the bass presents an upper-third unfolding of the tonic (E–C in C), while the remaining pitch constituents above it (E–Gs–B) express dominant function through enharmonicism and behavioural considerations. 37 If one were to imagine the idealized voice leading

for a III s chord returning to tonic in C, the B would resolve to C, thereby functioning as a leading tone to

C, the G s would resolve to G n, thereby functioning more akin to an A b, re-envisioned not as the chordal third of an E-major triad, but rather as the diminished-seventh interval “above” (conceptually, though it may be inverted) Bn and resolving down by step as is the functional role of chordal sevenths, while the upper-voice E functions as F b, holding common here, but conceptually “resolving” to E. 38 It is notable that this type of progression has been commonly referred to as a sort of deceptive resolution of the dominant—

Schenker, for example, writes of III 7s (or V 7/vi) resolving to the tonic, that “it could only induce some kind of deceptive-cadence effect.” 39 Riemann, however, uses the term Unterterzen, which translates roughly to

“under thirds,” to describe relationships between an upper triad and one a third below, and the term might thus be useful to import to describe these types of unfolding third relationships. 40 Through this notion of dissociating the root motion down by thirds from the harmonic function of the upper voices, I propose that while the progression certainly sounds jarring and deceptive, it represents an extension to previous practice.

37 This is, in some sense, an extension of the apparent triads discussed towards the end of the previous chapter, where an unfolding bass combined with suspensions from a previous dominant-functioning chord to delay the more stable onset of the tonic. 38 I would like to thank Don McLean for his suggestion here that the F b to E motion might be considered as a sort of deceptive motion, as the expectation for diminished-seventh chords is that they would resolve to a minor triad, not a major, and thus the E n is deceptively standing in for a more expected E b. 39 Schenker (1954 [1906]): 266. 40 See, for instance, Edward Gollin, “From Matrix to Map: Tonbestimmung, the Tonnetz , and Riemann’s Combinatorial Conception of Interval,” in The Oxford Handbook of Neo-Riemannian Music Theories , ed. Alexander Rehding and Edward Gollin (New York: Oxford University Press, 2011): 280. Gollin refers to the term in Riemann’s Musik-Lexicon (5th Edition. Liepzig: Max Hesse, 1900). 125

Example 2.4. Strauss, Eine Alpensinfonie , RH40.

While this disassociation between the chord and the bass may seem jarring, this type of harmonic rupture between the bass and the chord above is commonplace when occurring over a static bass pitch: sounding dominant-functioning chords above their tonic pedal in the bass is relatively ubiquitous in common-practice harmony. The same apparent III s to I progression over a static tonic bass, as shown in

Example 2.4 from Strauss’ Alpine Symphony, would, I imagine, pose fewer conceptual difficulties. The

passage in Example 2.4 depicts what appears to be a chord spelled C–E–Ab–B following from and

returning to a C-minor triad. Notwithstanding the fact that what sounds like an augmented triad with a

7 major seventh is not any type of conventionally tonal sonority, the label I s5 does not really convey a clear

tonal function in this scenario, as this chord is not functioning as tonic, but is rather serving to prolong

tonic. I suggest it does so through the notions of disassociated bass and half-enharmonic reinterpretation

Figure 2.3. Analysis of Example 2.4

126 presented above: the bass pitch C is not part of the chord that sounds above it, nor is the chord above it

o7 functioning as spelled. E–Gs–B, as already noted, can be reinterpreted as vii b5 of C with a missing third, as it is a major triad that lies a major third above said tonic. My analysis of the voice-leading behaviour of the chords in this passage, shown in Figure 2.3, understands this chord as such: a leading-tone, dominant- functioning chord in the key of C, sounded over a C pedal. The voice leading confirms this interpretation, with B resolving up to C in the trumpet part (displaced by an octave), and the A b resolving down to G over the sustained tonic pedal, thereby fulfilling the FIP requirement I have suggested for dominant-functioning chords (in this case, the diminished-seventh to perfect fifth FIP). 41

Although it is more commonplace in classical tonality for dominant-functioning chords to sound

above a static tonic in the bass—most often embellishing that tonic by resolving into the tonic chord—there

are clear instances of similar harmonic progressions occurring over either the third of the chord, or even

more radically, over an unfolding bass—although this procedure is far less common. An example of sounding a dominant-functioning chord over a non-root disassociated bass can be seen in Schubert’s “Am

Meer,” where in the fourth-to-last measure, shown in Example 2.5a, vii o7 /ii is sounded over 4 in the bass, but resolves to a ii chord.

Example 2.5a. Schubert, “Am Meer,” mm. 40–42.

41 The same chord reappears two bars later and also progresses to a C tonic triad: again projecting this type of dominant function over an unfolding tonic bass. 127

An example of the disassociated unfolding bass phenomenon can, however, be seen at the outset of

Strauss’ Sinfonia Domestica , shown in Example 2.5b. Here E (the VII Stufe in relation to the more global tonic

6 of F) is being prolonged, and the local dominant (B), in the form of V 4, is approached by its own dominant seventh (F s). Prior to the V 7/V chord is another chord spelled A s–Es–Gs–B–D. Most immediately

noticeable is that this is not a tertian sonority, as these pitches cannot be stacked cleanly in thirds, and

Example 2.5b. Strauss, Sinfonia Domestica , mm. 19–28

Figure 2.4. Analysis of Example 2.5b

128 neither the A s nor the E s belong tonally or modally in the key of E. My analysis of this chord, shown in

Figure 2.4, suggests that the upper voices (E s–Gs–B–D) form a diminished-seventh that tonicizes Fs (ii, realized on the harmonic surface as a major triad, thus V/V), while the bass pitch A s is disassociated from the other four pitches, and participates in an unfolding of the Fs chord (A s down to F s).

Thus, similar to the unfolding III s–I progression, here a diminished-seventh chord applied to the chord that is being unfolded is sounded over the third of that same chord that is being unfolded, before arriving at the root of that chord in the subsequent measure.

This progression can also play an important role when the apparent triad appears in second inversion, producing what appears to be a six-four chord. Bryan Gilliam, for example, has pointed out that

Strauss in particular had a penchant for six-four sonorities that are non-functional by virtue of “[avoiding] any tonic root as [they] float for quite some time.”42 While many times these are lengthy pedal six-fours that

ultimately function as cadential six-fours, some instances of six-four sonorities, such as those at the outset of

Strauss’ Der Rosenkavalier depicted in Example 2.6, do not. In both m. 2 and m. 6 a conventional Roman

numeral analysis of these chords provides very little explanation of the functional role these chords play. In

Example 2.6. Strauss, Der Rosenkavalier , Act I, mm. 1–7.

42 Bryan Gilliam, Rounding Wagner’s Mountain: Richard Strauss and Modern German Opera (Cambridge: Cambridge University Press, 2014): 26–27. 129

6 the first case, calling the chord in m.2 III 4 is almost pointless: it does not function as a mediant chord, and

its inversion further weakens the case for calling it such. Likewise, giving a Roman numeral analysis to the

6 second instance in m. 6 would require VII 4, again, a highly dubious analysis, given that VII is rare enough in root position, let alone second inversion. In both cases there is, I believe, a more compelling solution. The

o7 first chord can be half-enharmonically reinterpreted from E f–Af–C to D s–( )–Af–C, vii b5 in the tonic E major. Figure 2.5a shows the voice leading from this chord, through the cadential six-four and its ultimate resolution to the dominant seventh in m. 4. As depicted in Figure 2.5b, the reinterpreted triad in m. 2 is participating in a dominant prolongation that initiates the opera, and acts as an upper third to the bass,

6 7 stretching out the dominant function of the V 4 before it resolves to V in m. 4. The chord in m. 6 is spelled

o7 Bf–Ef–G, but can be half-enharmonically reinterpreted as A s–( )–Ef–G, or vii b5 of V, resolving into the subsequent cadential dominant-seventh chord, as per the voice leading in Figure 2.5b.

It is interesting that neo-Riemannian approaches to such progressions highlight, in a roundabout way, the FIP that I am suggesting provides the functional discharge from these chords to their chords of

resolution. Take the progression in Example 2.1 under further consideration: under neo-Riemannian

perspectives, transforming A major into F minor requires three neo-Riemannian transformations: the

Figure 2.5a. Analysis of mm. 1–4 in Example 2.6 Figure 2.5b. Analysis of mm. 6–7 in Example 2.6

130

Parallel transformation, which takes C s to C n, the Leittonwechsel transformation which takes E to F, and a second Parallel transformation which takes A to A b. Likewise, the same logic can be applied to Example

2.6b if we momentarily disregard the seventh of the subsequent dominant chord. Here, E f–G–Bf and the

dominant B–Ds–Fs are related by the compound operation PL. 43 Looking at the specific operations in

question, the P operation takes G to F s, while the L operation then takes B b up to B n, and the E b is enharmonically realized as D s. These two transformations highlight the importance of the voice-leading conventions that I have previously described: this type of contrary motion in the voice leading is part of

Cohn’s systemization of the hexatonic cycles that he develops as a unifying alternative to Roman numeral- based approaches to tonality, and this property, when viewed as transformations of specific tonally- functional pitches, can be seen here as playing a large role in the claims that I am advocating. Although I have broken it down into individual motions from specific pitches in a tonal space, the neo-Riemannian perspective is often more generalized in nature, and concerns itself more with voice-leading motion as a cumulative magnitude, rather than with the specific functional roles of the pitches undergoing transformation. 44 Thus most neo-Riemannian approaches would be more concerned with the number or

type of semitonal displacements highlighted above, and systematizing them within a voice-leading space

rather than engaging with the specifics of voice-leading relationships. That being said, it is noteworthy that

neo-Riemannian theory has, perhaps unknowingly, mapped these types of relationships and the importance

of the semitonal voice leading between such chromatic triads as an important feature of such progressions.

My approach here simply attempts to integrate this parsimonious voice leading into a more tonal-functional

framework better able to depict the functional role of these chords in prolongational contexts.

43 Cohn (2012) prefers to understand PL as a single operation that happens to have a multisyllabic nomenclature. 44 For example, neo-Riemannian theory would see this as voice-leading motion of three semitones, rather than investigating the functional role of those semitones. 131

II Acoustic Consonance, Tonal Dissonance II: Minor Triads

If this type of relationship is true for the major triad because it contains a minor third, it may be natural to wonder whether it is possible to say something similar for the minor triad, which also contains a minor third. Where the major-triad version proposed a dominant-functioning leading-tone chord relationship between a major triad a major third above another major or minor triad, a minor triad a major third below another triad can be conceptualized as expressing a similar dominant function. Take for example an Ab minor triad in the context of a C-major tonic. Understanding this Af chord as fvi poses similar ontological problems to those previously discussed: such an analysis proposes that a chord containing a chromatically altered tonic can still directly relate to and prolong the tonic. But because C b is enharmonically B n, there exists the potential for reinterpretation. Example 2.7 shows the passage in

Salome’s dance for which I have already discussed the prolongational processes in the first phrase in

Chapter 1. Its repetition, nine measures later, begins with a similar, yet functionally different harmonic progression. Here, instead of an A-major triad, the tonic is prolonged by an A-minor triad in first inversion, making the 5–6 analysis less plausible, given that the bass pitch changes. As Kevin Swinden has pointed out:

Careful analyses of this behavior must separate the apparent vertical spelling and acknowledgment of a triadic sonority from the linear behavior and clear authentic functional discharge that characterizes the sense of double-function afforded this striking progression. 45

Swinden’s warning to separate the vertical sonority, which sounds unequivocally like a minor triad built on

A, from linear behaviour is important, but equally important is to consider the vertical and linear domains in respect to each other. Swinden proposes a plural function, suggesting that the enharmonic 7 in the bass expresses dominant function, while “the essential plagal aspect of the progression is embodied in the resolution of s2 to b3 in tonic, exhibiting the linear behavior of a common-tone b3 alongside the

45 Kevin Swinden, “When Functions Collide: Aspects of Plural Function in Chromatic Music,” Music Theory Spectrum 27, no. 2 (2005): 277. 132

Example 2.7. Strauss, Salome , Dance, 11 mm. Before RHQ.

subdominant b6 resolving to 5.” 46 As I have previously argued, a leading tone alone is not sufficient to create dominant function in the way Swinden implies, and what Swinden sees as a subdominant inflection into a dominant-functioning chord I see alternately as an integral part of a FIP that projects unequivocal dominant function: the upper-voice A n (f6 ) forms a diminished-seventh with the bass’ enharmonically-spelled B s which then resolves to a perfect fifth (C s–Gs), creating a dominant-to-tonic discharge, and what I analyze as

o7 47 a vii s3 chord. The common-tone resolution of s2 /b3 is unconventional for diminished-seventh chords, but, as I have mentioned, is occasionally a product of modal choice in the chord of resolution, and is overridden by the more tonally salient FIP. With this in mind, the function of this chord is then easily

46 Ibid., 277. 47 This is not to say that Swinden’s perspective is wrong—the lowered submediant pitch combined with the subdominant certainly creates subdominant qualities—but rather simply stating that there is subdominant inflection in this chord does not do enough to advance our understanding of how the dominant function is created and projected into the prolongational framework: indeed, diminished-seventh chords traditionally contain the subdominant and lowered submediant pitches. 133

Figure 2.6. Analysis of Example 2.7

discernible: as an altered diminished-seventh chord it prolongs the tonic in a conventional way, shown in

Figure 2.6, despite the chromatic alteration and missing (or delayed via unfolding) pitch. 48

Like the major triad, the inversion of the apparent minor triad matters in regards to the way in which the chord resolves. When found in root position, it is much more difficult to discern as a chromatically- altered diminished-seventh chord, owing to the inherent stability found in a root-position triad. In such cases, voice-leading convention would require the root to step down chromatically. Because these triads

o4 resemble fvi chords, this means that the root-position variant of this chord must function as vii 2 and resolve to a root-position dominant. Because this is also a valid harmonic motion for the submediant, it can occasionally become difficult to say whether the enharmonic diminished-seventh interpretation is better than the triadic one. Example 2.8, from Strauss’ Eine Alpensinfonie , illustrates this dilemma. Here, the fVI

Stufe is prolonged over a number of measures, and is first realized as the conventional major triad, then subsequently as a minor triad. This larger-scale prolongational context suggests a case where the concept of a modal inflection of the prolonged local fVI Stufe provides a better analysis than does that of an altered diminished-seventh chord. Ultimately, fVI acts on a deeper level as a contrapuntal passing tone in the bass between the preceding first-inversion dominant chord and the root-position dominant that follows the fVI

48 This progression is almost identical to the one Charles Smith (1986) points out at the outset of Chopin’s Sonata in Bf Minor, Op. 35. Smith’s analysis suggests the chromatically altered pitch is a displaced chromatic neighbour to the third of the chord of resolution, and highlights the resolution of 7–1 and b6 –5. Ultimately, Smith opts to stick with the fvi analysis, but qualifies it with parentheses to indicate that the spelling of the triad somewhat misrepresents the chord’s function. 134

Example 2.8. Strauss, Eine Alpensinfonie , 3mm. Before RH29

expansion, as shown in Figure 2.7. 49 In this sense, it is a tonicized projection of the lowered submediant

pitch, and whether it is harmonized as major or minor is less important than its contrapuntal role in the

expansion of the dominant.

When the apparent triad is found in second inversion, this chord can also be functional, but such

cases place the third of the enharmonically-respelled diminished-seventh in the bass, meaning that the

subsequent chord is often found in root position, but possibly in first inversion. An illustration of this

particular inversion can be found in the passage from the prelude to Der Rosenkavalier shown in Example

Figure 2.7. Middleground Analysis of Example 2.8

49 This of course creates a deeper-level augmented second between G and F b, which is mitigated on the musical surface by the intermediary V of fVI. 135

Example 2.9a. Strauss, Der Rosenkavalier , RH7

2.9a. On a mid-level scale, shown in Figure 2.8, this progression is a prolongation of the dominant initiated

in m. 48 (RH7.4) through a third progression from B up to D s, which then unfolds back to the cadential B 7 chord in m. 51. As noted, the Ds bass note is part of an inverted B 7 chord that unfolds the dominant.

6 Spelled D–G–Bf (with the G delayed by a retardation and passing note), a fIII 4 analysis of the preceding

6 chord does not imbue much functional understanding into the way in which the apparent fIII 4 prolongs the

dominant in its motion up to its first inversion. Enharmonically respelling this chord, however, yields A s–

o7 7 Cx–( )–G, or vii s3 of the subsequent B chord: here the C x (enharmonically spelled D) in the bass moves

up to D s, completing the upper-third progression

Figure 2.8. Analysis of Example 2.9a

136 from B through C s to D s and back to B that prolongs the dominant. I also want to draw attention to

Example 2.9b, which presents two measures from the full orchestral score. The vocal score in this case is

not entirely clear regarding the voice leading of my proposed diminished-seventh chord: while it is true that

in the upper voice the B b leaps down to F s, in an apparent circumvention of the voice-leading rules for

diminished-seventh chords, the same pitch resolves more conventionally in the inner voices. Specifically, the violas and the bassoons resolve A s to A n in an elided leading-tone

Example 2.9b. Strauss, Der Rosenkavalier , Full Score RH6.4–7.6

137 resolution to become the seventh of the following chord. While this does not form part of my current argument, it is well worth noting that Strauss’ voice leading might at times seem unwieldy or careless, but it is often the case that in some part the voice-leading will occur in accordance with tonal practice. 50

With these preliminaries in mind, a number of questions linger. Firstly, why not simply write these as

full four-note chords? Secondly, if these are indeed functioning as altered diminished-seventh chords, why

not make them apparent through proper spelling, rather than notating them as triads? The easier of these

questions to answer is the one regarding spelling: in short, the spelling is most likely a product of readability.

Composers tend to favour keys and spellings that avoid unnecessary double flats and double sharps or use fewer sharps and flats. Regarding writing consonant triads instead of four-note chords, a likely explanation may revolve around the phenomenological contradiction that results from employing a consonant sonority in a dissonant manner. As outlined above in the discussions of Cohn and Lorenz, the acoustic consonance of these chords clashes with their dissonant nature. In some cases, there are dramatic reasons for this phenomenological disjunction: when depicting the unnatural or ethereal, as Cohn has suggested for chords that are hexatonic poles, for example. 51 But while this acoustic disjunction has often been noted, analysts continue to favour the triadic interpretations, despite being unable to reconcile these triads into a prolongational framework. My approach here has, I hope, extended that research and formulated a way in which the observations of scholars like Cohn and Lorenz can be integrated into a prolongational context

through observing their behaviour, rather than their vertical attributes.

In addition to Example 2.2 above, wherein Wagner spelled an E-minor triad as G–B–Ff, two further

examples support the notion that composers might have at the very least been aware of the potential of

these chords to function enharmonically as incomplete diminished-seventh chords. The passage shown in

Example 2.10 is from the opening of Strauss’ song “Ich wollt ein Sträuβlein binden.” The opening measures

50 I use the term voice to mean a registral line in this case: another anomaly of Strauss’ orchestral writing is a tendency to leap the registral line around between instruments, but still maintain the melodic line in a given register. 51 Cohn (2014), for example. 138

Example 2.10. Strauss, “Ich wollt ein Sträuβlein binden,” mm. 1–8

sustain an F tonic triad, which then progresses to a supertonic chord in m. 4, followed by a passing mediant triad that promotes a voice exchange between the supertonic and the chord that follows the mediant. That subsequent chord, an A b-minor triad in first inversion, is highly jarring against the mediant triad, and, like

many of the triads under discussion herein, has dubious harmonic-prolongational function in prolonging the

tonic owing to the chromatic alteration of the tonality-defining fifth scale degree (C b). 52 What is most

interesting about this example is that Strauss notates C b in the upper voice, but enharmonically spells this pitch as B n in the bass voice. Almost certainly this has to do with the voice-leading motion, which moves from A to B to C in the bass, and from C through C b down to B b in the upper voice, but it also highlights the unlikelihood that Strauss conceived of this chord as a fiii chord. If he did, there would be no notational problem with using C b in the bass: this is not a clear case of enharmonic respelling to avoid notational excesses (since Strauss is content to use C b in the upper voices), but seems rather to be a case of a

combination between linear continuity and functional importance. Note, too, as shown in Figure 2.9, that

the upper voices adhere to conventional voice-leading for a diminished-seventh chord: the A b resolves down to G, completing the FIP, the E b functions as D s rising to E, and the C b in the upper voice elides its resolution to 1 and passes down to the seventh of the subsequent chord in conventional fashion. This

52 In short, can this triad truly be perceived as prolonging tonic when the chromatic alteration distorts the tonic-dominant relationship so integral to tonality? 139

Figure 2.9. Analysis of Example 2.10

notation and the way in which the chord resolves suggest that Strauss was at the very least aware of the

dominant-functioning potential of this triad and was exploiting that potential here as an embellishment of

the subsequent dominant. 53

The passage in Example 2.11 comes from the “Elegie” section of Strauss’ Eine Alpensinfonie , where

Fs minor is established as the local tonic leading into RH100. Three measures later, on the third beat of

RH100.4, is a chord spelled B s–( )–Es–A.54 Enharmonically-spelled, this should be understood as B s–( )–

o7 F–A, or vii b5 of the dominant, as shown in Figure 2.10. Here the altered fifth (F

o6 sounds. Here the pitch F is a neighbour tone to the F s chord tone (which creates a vii (5) of fII), but the

initial impression of the F-major triadic sonority—the same sonority in RH100.4, b.3—is present (this is

53 I would like to thank Ryan McClelland for pointing out that Strauss subsequently orchestrated this set of songs, and, indeed he retains the B n spelling in the basses, but the C b spelling in the descending upper voice. 54 In the organ part, this pitch is spelled as a C n as before, but in the strings it is spelled as a Bs. 55 And as I have mentioned previously, should not therefor be construed as a common-tone diminished-seventh progression, as such progressions should only be analyzed under specific parameters (namely that the common tone is the root of the chord that is being embellished, and is likewise the “seventh” of the apparent diminished-seventh chord. 140

Example 2.11. Strauss, Eine Alpensinfonie , 4 mm. Before RH100

Figure 2.10. Analysis of Example 2.11

141 then repeated in condensed form in the first two beats of RH100.4). As in Example 2.10, this double spelling suggests that Strauss was at the very least aware of the dominant-functioning potential inherent in such triads.

Because major and minor triads each have a single minor third interval in their construction, their

o7 o7 reinterpretation only ever yields vii b5 or vii s3: the other two possibilities for altered diminished-seventh

o7 o7 chords, vii b3 and vii s5, accordingly do not have corresponding triadic variants. While these sonorities are distinctly triadic, and thus are able to convincingly masquerade as more conventional chords, they are, I

believe, merely apparent consonances as Lorenz has suggested. Discerning the harmonic function of

extravagant chords in chromatic music comes down to context and perspective. What I am advocating here is a perspective that sonority need not be the sole arbiter of harmonic function in the manner in which it is in more diatonic music. In earlier music, a triad is a triad, diminished-seventh sonorities occur almost exclusively on the leading tone (save for common-tone diminished-sevenths), and major-minor seventh sonorities are almost exclusively dominant. As the potential for enharmonic reinterpretation became more widespread—such that major-minor sevenths could function as German augmented sixths, while the

symmetrical constructs of the diminished-seventh chord encouraged deceptive resolutions—this certainty of

linking sonority with function began to ebb, and sonority could no longer be the sole determinant of

function: it was, rather, the way in which the chords behaved that determined function. What I have

suggested above, as well as in the previous chapter, is that this enharmonic uncertainty may pervade more than just the major-minor seventh/German augmented sixth relationship in tonal music. Appealing to chordal behaviour, or, as Swinden puts it, what a chord does, rather than simply a chord’s vertical dimensions

(or what a chord is ), demonstrates that even highly chromatic music long thought to be bordering on

atonality retains a strong relationship to prior tonal-prolongational practices, despite the very surface-level appearance of pervasive and diatonically-distorting chromaticism. 56 In unearthing the behavioural

56 Swinden (2005): 251–252. 142 relationships these chromatic triads and seventh chords have with common-practice tonality, we can begin to discern tonal structure in passages and works that generally appear to eschew common-practice tonal conventions, and begin to redress the notion that prolongational analysis is inadequate to the task of analyzing tonal structure in these works.

III Three Vignettes Regarding Apparent Consonance

The final section of this chapter presents three larger analytic vignettes. The passages under

consideration have all been discussed and analyzed as projecting a sense of tonal disruption, or even

borderline atonality, by previous scholarship. I propose that the reinterpretation of apparent triadic

sonorities as chromatically-altered diminished-seventh chords in these passages elucidates ways in which

analysis can understand the more tonal-prolongational logic of these passages.

1. Schubert, Piano Sonata in D, D.850, I: mm. 1–16

Of this passage, shown in Example 2.12, Kopp writes, “[it] contains an unusual, highly chromatic passage near the opening…that appears to breach the key at an unusually early point.”57 Kopp then describes this breach in detail, writing:

From subdominant G minor in measure 7, the music spirals first through an insistent, cadential-sounding F major six-four at measure 8, then into a surprising C ♯ major harmony at measure 12, before landing back in diatonic territory on dominant A major at measure 14 on its way to the tonic in measure 16. Conventional harmonic analysis falls short in explaining the coherence of this particular progression; F major and C ♯ major, along with A major, define a descending major-third cycle outside typical cadential and sequential process. 58

While Kopp then suggests that a linear analysis could account for these chromatic abnormalities, he believes

this approach—which essentially suggests coherence for the passage based on a linear ascent in the bass—is

57 Kopp (2011): 404. 58 Ibid., 404. 143 not convincing, and proposes “the potent, dramatic triadic juxtapositions in this passage merit an explanation truer to their harmonic nature.” 59 Kopp proposes the integration of chromatic mediants into the diatonic syntax, an elaboration of the thesis of his 2002 monograph, but, as I have argued, this approach evinces an ontological strain by proposing understanding altered tonic and dominant pitches as directly related to the tonality of the passage. Furthermore, the descending cycle of roots a major third apart does

Example 2.12. Schubert, Piano Sonata D.850, I, mm. 1–16

59 Ibid., 404. 144 not account for the fact that the first of these chords (F) appears in inversion while the other two appear in root position, a detail which seems suggestive of the importance of these details, and not simply the abstract triadic sonority.

Up until the surprising resolution of the vii o7 /V chord in m. 7, the tonal logic of the passage is easily discernible. Measure 5 presents the minor tonic, which progresses to the subdominant, which is itself prolonged through a tonicization and middleground level 6-5 motion. 60 From there, the vii o7 /V suggests impending dominant onset, but is thwarted through a common-tone resolution to an inverted F-major sonority. This chord initially appears in second inversion, but unfolds quickly down to first inversion, suggesting A (the global dominant) as the structural bass, with suspended non-chord tones above it as shown in Figure 2.11.61 The C s-major triad, which Kopp highlights as the most tonally disorienting aspect of this passage, arpeggiates this bass A up to its third, and, in m. 14 back down again. The C s triad, while seeming to be acoustically consonant yet tonally disjunct, might be understood as an example of the

o7 dissociated bass concept discussed above. Here C s–Es–Gs can be reinterpreted as G s–()–Df–F, or vii b5 of the dominant A, to which the chord ultimately progresses. When the chord change happens, G s resolves up to A (and chromatically down to G n) while the E s functions as F, resolving to E n, and in this way projecting the diminished-seventh to perfect-fifth FIP. The bass, as noted, arpeggiates back down to the dominant. 62

This moment, then, can be understood as an extension of the harmonic process Schubert used in “Am

Meer” cited above: he sounds a dominant-functioning chord

60 This type of middleground 6-5 melodic elaboration is the subject of the subsequent chapter, but serves to conceptually link the ø6 apparent ii 5 in m. 6 with the subdominant in m. 7. 61 These type of suspended non-chord tones that form apparent inverted triads will be explored further in Chapter 3. 62 Schenker, and others, have discussed the function of the VII s chord as unfolding to V. Carl Schachter, for example, suggests: “This represents a reasonably common situation in tonal music, where VII functions as an upper-third of the dominant,” but ultimately suggests that this is a colouristic effect, and does not discuss how it achieves function apart from unfolding to the dominant (Carl Schachter, The Art of Tonal Analysis: Twelve Lessons in Schenkerian Theory [New York: Oxford University Press, 2016]: 247–48). My discussion of the Schubert example above, and the apparent VII s chord (C s) might suggest how these chords can be more readily explained within a prolongational process: not only an unfolding of 7 to 5, but the specifics of the voice leading also lend a level of applied emphasis to the dominant through the resolution of the diminished-seventh interval. 145

Figure 2.11. Analysis of mm. 7–16 in Example 2.12

mm. 7 8 12 14 16

over the third of that dominant-functioning chord’s tonic, but instead of resolving it with the third remaining static in the bass, the third unfolds down to the tonic at the moment of resolution, much like in the example from Strauss’ Sinfonia Domestica .

While the progression is, and remains, aurally striking, it retains a level of tonal-functional logic as well, which, as I have previously suggested, is where the interest in these progressions resides. That their acoustic consonance overwhelmingly implores the listener to hear these chords as such, their tonal dissonance simultaneously grates on the ear, and forces the listener to call into question the tonal stability of the passage. What I hope this approach shows is that there is a way to account for these disjunct moments in terms of tonal structure, while avoiding “normalizing” them entirely: viewed as an extension of tonal practice, these progressions are placed in a dialogue with classical tonality, rather than breaking off from the practice entirely, and it is that dialogue which allows for these processes to be folded back into prolongational procedures while maintaining their stark sense of distinction and disjuncture.

146

2. Die Walküre, Act II, Scene 4

My second analysis engages with the passage that begins the fourth scene of the second act of

Wagner’s Die Walküre , shown in Example 2.13. This passage came to my attention through Kurth’s mention of it as an instance that juxtaposes two apparently “remote” chords. Kurth writes:

The two chords in the following "Fate-Motive" from Walküre , for example, are also apparently, i.e., according to the sound, very remote: according to the external form, a D- minor chord preceding a dominant seventh on C s.63

In his translation and annotation of Kurth’s work, Lee Rothfarb notes of this passage that it has been

“discussed extensively.”64 He notes that the prevalent analysis, with which Kurth’s views coincide, is that the

first chord is a transformed version of the second. Kurth himself suggests:

The first chord is a tension distortion of the second one, is in fact tonally identical with it. D is a neighbor-note insertion, from above, to C s; likewise A in the uppermost voice is a neighbor-note insertion to G s, so that here too the first melody note of the motive appears as a dissonant, non-chordal tension tone. Thus the only new note joining the second chord is the seventh, B. 65

Example 2.13. Wagner, Die Walküre , Act II, Scene 4, mm. 1–3

63 Ernst Kurth, Ernst Kurth: Selected Writings, ed. and trans. Lee A. Rothfarb (Cambridge: Cambridge University Press, 1991): 117. 64 Rothfarb discusses extensively analyses by Bruckner, Josef Schalk, and Georg Capellen. Capellen, Rothfarb writes, suggests that “once the shift to C s7 occurs, we reinterpret D–Es–A retroauditively as a suspension chord delaying the V 7 in the key of F s minor.” Ibid., 118 (footnote 14). 65 Ibid., 118. 147

Notably, this view is similar to the one Benjamin Boretz proposes for the Tristan chord: that it is essentially the same chord as the dominant seventh that follows it, with the D s and F n understood as neighbour tones

to the D and E respectively. 66 As with the Tristan chord, which I suggested in the previous chapter was an

o4 7 example of the vii 2–V progression combined with a chromatic alteration, here too I believe the theory of chromatically altered diminished-seventh chords, combined with the notion of apparent consonance serves to help explain this jarring progression. 67

While referring to it as an apparent D-minor chord, Kurth is noting the consonant nature of the

sonority in question. But approaching it as a consonance fails in terms of understanding its role in the

tonality of the passage: the label fvi, as I have argued, poses ontological complexities. Instead, I argue that

this chord can be better understood according to its functional behaviour: as a chromatic alteration of a

os4 o7 diminished-seventh chord, specifically as vii 2 (an inverted vii s3). As in the passages from Das Rheingold and

“Ich wollt ein Sträuβlein binden” discussed above, Wagner likewise spells this chord, at least partially, as a

diminished seventh: E s–A(Gx)–( )–D, rather than as a triad. While I am uncertain as to whether the

chromatically-altered diminished-seventh chord is the best analysis for this passage—one might equally posit

that the A is simply an unprepared suspension or other lengthy non-chord tone—the analytic interest of this

interpretation lies in its suggestiveness regarding how composers began to perceive the potential possibilities

of chromatic alteration.

That the A is subordinate to the G s is easily argued from a harmonic perspective, but the relative

length of their respective durations calls into question this assertion: the A (or Gx) receives the metric

accent and is three times the length of the G s.68 On the other hand, understanding the A as a G x also

66 Benjamin Boretz, “Meta-Variations, Part IV: Analytic Fallout (I), Perspectives of New Music 11, no. 1 (1972): 159–172. 67 A long-held perspective is that vii o7 is a rootless V b9 chord, so in this sense Kurth’s analysis is in some ways synergistic with the prevalent analytic perspectives of the time. As Rothfarb notes, Josef Schalk suggests an analysis of this passage wherein the D in the bass is understood as the chordal ninth of an inverted and incomplete dominant ninth. This is not far from the analysis I advocate below, though I avoid analyzing extended tertian chords in inversions, and am more prone to cite a proximity, rather than identity, relationship between vii o7 and V b9 . Kurth (1991): 118 (footnote 14). 68 It would be unsurprising if alterations of diminished-seventh chords came about in just such a fashion, through the gradual increasing of the length of chromatic neighbour notes, which is, incidentally, what Kurth suggests is the function of the A. 148 requires acknowledging that it does not resolve immediately as such, but instead resolves in a manner very similar to the Tristan chord. 69 In the Tristan chord I argued that it was the chordal fifth that underwent chromatic alteration, whereas in the case under discussion here it is the chordal third. Like the Tristan chord’s raised fifth, which moves by chromatic descent to the diatonic 4 when the Tristan chord progresses to the V 7 chord, the G x resolves down chromatically to the normal version of 2; the difference here is that it

does so in an anticipatory manner within the predominant chord, rather than as the chord changes. Without

trying to explicitly make a case for a teleological progression of Wagner’s chromatic-harmonic syntax, this

progression plays out almost as a simpler, more subdued precursor to the Tristan chord that flirts with

similar tonal boundaries as the latter progression, but ultimately retreats from it at the last minute.

I believe my analysis here clarifies with more theoretic precision what Kurth is attempting to convey.

Kurth’s analysis seems to fluctuate between wanting to hear a D-minor triad, and wanting to understand it

as some version of the dominant constructed with neighbour-note insertions. While I am attempting to

move away from the idea of the D-minor sonority as a mere function of inserted neighbour tones, which

seems to be somewhat ad hoc in its explanatory power, I nonetheless agree with Kurth that there has been an alteration of a more fundamental chord tone. To this end, I suggest that the D-minor triad is functioning as a chromatic alteration of a diminished-seventh chord. The conventional spelling of such a chord, given the dominant-seventh nature of the subsequent C s chord, would be E s-Gs-B-D, but Wagner omits the B and

o7 alters the G s to Gx, creating a vii s3 of F s initially, but transforming the raised third into the normal version

as an anticipation of the subsequent dominant-seventh chord. Using a combination of chromatically-altered

diminished-seventh chords and enharmonic sleight-of-hand Wagner’s harmonic language here creates a

progression that has startling sonorous qualities but that through a careful examination of its voice leading

69 It is notable that if the B were included in this progression, it would create a half-diminished seventh sonority of the polysemous type described in the previous chapter: namely an apparent half-diminished seventh but in a nonfunctional scale step. In this case it would resemble iv ø7 of F s, but such an understanding contains a chromatic alteration of the local tonic, and should thus be avoided. 149 and behaviour can also be understood as conforming to the practices and conventions of common-practice tonal syntax.

3. Parsifal, Act III

The last vignette involves a passage from near the end of Wagner’s Parsifal that has become a

favourite for music theorists, with commentary regarding colouristic effects coming from more historical theorists such as Kurth and Lorenz, to more contemporary transformational and neo-Riemannian perspectives from theorists such as David Lewin and Richard Cohn. Despite the concurrence between many of these commentators that the passage is tonal in some manner, describing exactly how the chords support tonality has been a subject of contention, with little consensus reached.

Of Wagner’s harmony, Kurth writes broadly that:

Shifts of harmonies whose roots lie a major or minor third above or below one another, unlike those previously discussed mediant progressions that belong to one key, direct our attention to their harsh and multi-faceted appeal. The Romantic delight in color also extends to unmediated harmonic progressions whose roots are separated from one another by diminished fifths, augmented fourths, and other altered intervals. Such shifts appear early, often like a wedge driven abruptly into an otherwise straightforward series of harmonic connections. Hence a rift opens up on the series, a rift that is then bridged by a returning progression or by broader coherence. 70

More specific to the passage shown in Example 2.14, he writes that the harmony herein is “based on the unmediated, absolute effect of tonally remote progressions.” 71 Cohn, noting a kinship between his own

Example 2.14. Wagner, Parsifal , Act III, mm. 1098–1102

70 Kurth (1991): 123. 71 Ibid., 123. 150 approach and Kurth’s, describes Kurth’s perspective as implying that “many chromatic progressions, particularly those that involved root relations by third, introduced rifts, wedges, and fissures into the fabric

of tonality. The identity and function of these chords are found in their internal structure and in their local

connections to their immediate antecedents and successors.” 72 Cohn further notes “When concatenated with sufficient intensity and persistence, such absolute progressions bring about the ‘total disruption of the

original embracing tonal unity.’” 73 Kurth, like Lorenz and subsequent theorists, then links these types of

progressions, especially in Wagner, to the magical or otherworldly, citing similar passages found depicting the Tarnhelm in Wagner’s Ring cycle, as well as the magic potion from later in the cycle. 74

While the ethereal nature of the passage is well noted, I would draw on Schenker’s assertion regarding the association of “exotic” elements with the conventional tonal system. Citing a number of examples, from Haydn or Beethoven’s Schottische Lieder to Hungarian Dances by Brahms, and Rimsky-

Korsakov’s Scheherazade , Schenker argues against analyses that invoke non-tonal parameters (often in the form of allusions to pentatonicism, or octatonicism), maintaining instead that these elements should be

understood as an enhancement of the tonal system.75 As I noted in Chapter 1, the same holds true of these otherworldly or magical progressions: they are understood as such because they are being incorporated into the major-minor system, and are expressive because of both their juxtaposition against the conventions of that system, but also because they fit within that system. The otherworldliness of the objects in question (the

Grail, the Tarnhelm, the magic drink) are further rooted in the worldly: while possessing of magical

elements, these objects are not completely foreign, and are understandable as magical extensions of normal

objects (a cup, a helmet, a drink). As such, I would argue that analysis of these progressions should not

72 Cohn (2012): 10. 73 Ibid., 10. 74 Kurth (1991): 124. Though I would digress from Kurth here and suggest that the Tarnhelm motif juxtaposes a minor tonic and its modally-mixed mediant before concluding on V. Richard Cohn alternately suggests that the two triads that form the Tarnhelm motif are reciprocal in that “each Tarnhelm triad contains the others leading tone, and hence signifies the other as tonic” (Cohn [2012]: 23). As I have argued previously, a leading tone alone is not enough to create dominant function (and thereby suggest tonic function for the subsequent chord), though Cohn’s point is well-noted that the progression in question is difficult to discern functionally in isolation. 75 Heinrich Schenker, Counterpoint [1910/1922], ed. John Rothgeb, trans John Rothgeb and Jürgen Thym. 2 vols (New York: Schirmer Books, 1987): I, 28. 151 simply be content with marvelling at the their ethereal nature, but should also be able to convincingly incorporate them into the major-minor tonality necessary in creating the conditions for these chords to achieve the otherworldly effects that have been claimed.

In his analysis, Kurth suggests that the tonal logic and structural impetus of this passage is derived

from a larger scale partitioning of the octave into equal major thirds. “The Grail-Motive,” he states,

“harmonized tonally at first…is intensified to yield harmonic progressions whose colors diffract into the

most glaring spectrum.” 76 Where Kurth is content to avoid discussing specific tonal chord relations and appeals instead to coloristic effects and the supernatural to drive his analysis, more contemporary theory seeks to codify and understand how these triads relate to one another. Cohn’s analysis posits that the E b

major and B-minor triads exist in what he terms an H, or hexatonic-polar, relationship. This means that

these two triads share the same hexatonic cycle, but exist as far away from each other in that cycle as

possible, requiring three units of voice-leading work to transform one into the other—more specifically, all

three voices in the first triad move by semitone to yield the second triad. 77 I will return to this analysis

momentarily.

David Lewin has also investigated this passage in a more classically Riemannian analysis that likewise

integrates questions of more prolongational approaches to make an overall point that “the nature and logic

of Riemannian tonal space are not isomorphic with the nature and logic of scale-degree space.78 He writes

that on a larger scale this passage outlines a I–V–IV–I scale-step progression, a larger-scale version of the

type of progression Wagner seemed to favour in concluding his operas. The initial E b major triad of the

passage in question is thus understood as V of A b, though locally it is tonicized as I of E b. Lewin then takes

his readers through four different readings of the passage, citing the inadequacies of each. Rejecting the

understanding of the second and third triads as Dp and S functioning chords respectively, Lewin writes:

76 Kurth (1991): 124. 77 Cohn (2012): 31–32. 78 David Lewin, “Amfortas’ Prayer to Titurel and the Role of D in Parsifal : The Tonal Spaces of the Drama and the Enharmonic Cf/B,” 19 th -Century Music 7, no. 3 (1984): 345–347. 152

“We hear too strongly that the "A bb " of the third harmony…is the same pitch-class as the G that appeared as the third of the opening triad. Hence the third harmony prolongs the (function of the) first harmony; it is not a subdominant for it.” 79 He later concludes:

The passage as a whole begins by prolonging the opening D-function; the passage then pivots on the fourth harmony and moves on to tonicize the closing S-function. The analysis recognizes the D-function of the pivotal fourth harmony, a triad involving the same root and fifth as the opening D-function harmony. The Riemann analysis (of Dp and S) was oblivious to that aspect of the progression. On the other hand, in order to do minimal justice to the passage as an object of Riemann space, the analysis must do violence to the passage as an object in motivic Stufen space: the degree distances between the outer voices of the opening two chords are changed. 80

Cohn, on the other hand, posits that the unity of this progression can be found in the hexatonic

relationships between the chords. He writes that the passage:

[Begins] in E f major, moves to E f minor via three moves within the 'Western' hexatonic system, then exits that system at the arrival of D f major. The overall T1 motion from E f major to E f minor is composed of three separate moves: (i) E f major moves to its hexatonic pole of B minor via T3; (ii) B minor moves by T1 to G major; (iii) G major moves to its hexatonic pole, E, minor, again via T3. The composition of the transposition operators reflects addition modulo 6: i.e., 3 + 1 + 3 = 1. 81

Thus Cohn is noting the overall move from E b major to E b minor: his assertion that this represents a single

(T1) move in the hexatonic cycle, which equates to a single semitonal displacement, highlights this. By

invoking the hexatonic system, however, Cohn is, I believe, implicitly acknowledging a discomfort with

fitting this progression into a conventional tonal framework. 82

Steven Rings has also investigated this passage, approaching it from a transformational but tonal

GIS perspective. In regards to Cohn’s chromatic/neo-Riemannian approach Rings argues that “the formal elegance of [non-functional] arguments has been a principal attraction of much work in neo-Riemannian theory. The elegance exacts a cost, however, turning the B-minor chord into a collection of inert pitch

79 Ibid., 346. 80 Ibid., 346. 81 Richard Cohn, “Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of Late-Romantic Triadic Progressions,” Music Analysis 15, no. 1 (1996): 23. 82 Indeed Cohn cites Kurth’s analysis of this progression’s “supernatural strangeness” in a footnote (Ibid., footnote 32). 153 classes, indistinct from any other [037] chord.” 83 Rings’ approach investigates how the various pitches in the

B-minor chord interact with the tonality of E b major, and the various ways in which these pitches can be

interpreted as scale degrees, or alterations thereof, in that key. He suggests that it is difficult to interpret the chord in E b since only one of the pitches existing in E b major, namely the D n (this is of course mitigated by the fact that C b, the enharmonic spelling of B n is also functional in E b major-minor). Rings suggests a number of possible interpretations: that the apparently consonant triad is in fact a dissonant, non-tertian chord made up of scale degrees 7, b3, and b6 in E b, that it is a minor submediant chord ( fvi) or the less enticing sv. 84 Ultimately Rings argues that the B minor chord has a diatonic home in the key of D major, but that that key is offset by a semitone, and justifies this assertion by comparing it to the diatonic version of the grail theme heard in the prelude—among other places—where the chord used at this parallel moment is indeed a vi chord, and suggesting that “far from lessening the magic of the moment, the tonal adjustment increases it.” 85

Both Lewin and Cohn imply that this passage cannot be understood coherently using conventional

prolongational approaches to tonal harmony, yet at the same time both note that there are unifying

relationships at play. Rings’ analysis is somewhat of an outlier, positing a tonal understanding but in a key

that is not perceptible in the prolongational span. But Rings, too, recognizes something inherently tonal about this chord; he writes that “whatever this chord may be, it is far from inert: it thrums with energy. The

system of tonal norms becomes more conspicuous, not less in its seeming violation…” 86 Even more

specifically, Lewin explicitly brings up the notion that the first four chords are part of a prolongation, noting

that the first and fourth chords are different modes of the same triad. Cohn also implicitly invokes a type of

83 Steven Rings, Tonality and Transformation (New York: Oxford University Press, 2011): 88. 84 Rings also notes that a fourth possibility, taken by Alfred Lorenz, is understanding the pitches as a dissonant D-Fs-Cf. Lorenz’ argument is that some of these triads are merely what he terms apparent, or pseudo, consonances. Thus he reads the B-minor triad as noted above, but he then reads the G-major triad as a G-major triad, while reinterpreting the E b-minor triad that follows as F s-As-Ef, which then morphs into E b-minor. See Lorenz (1966 [1933]): 90. As mentioned, he does not suggest a function for these conglomerations, except to note that “the psychological impact of these processes is magical.” In his discussion, it is apparent that he does not see these as functional entities, but rather a dramatic conflation of consonance and dissonance. 85 Rings (2011): 88. 86 Ibid., 88. 154 prolongation, though his analysis suggests the prolongational aspect is one of a group, namely that these chords all fall into the same hexatonic cycle. If, however, a T1 operation on the larger scale can prolong a single triadic function (E b in this case), should it not do the same on a local level? That is, does the T1 Cohn posits between the B-minor and G-major triads, noting the single semitonal displacement, suggest some form of functional proximity or relationship between these two chords, and is it possible to use this relationship in order to make a more functional argument for this passage?

I argue that there is a way to integrate these observations regarding prolongation into a more conventional tonal-prolongational analysis, while remaining conscious of and addressing the wariness both

Lewin and Cohn express in regards to such an integration. As Lewin states, there is a prolongation occurring

here, reflected by the shared root of the first and fourth chords. The problem, then, is in figuring out the way in which the intervening chords—B minor and G major, prolong E b. Neither of these chords is

conventional in the key of E b: understanding the B-minor triad as such requires the use of the nomenclature

sv, which is merely descriptive, and does not carry with it any actual functional connotations; and while the

G-major triad might be understood as III s, this label, again, is descriptive only, since (as I have already

argued) III s cannot function as a prolongational chord. Strict enharmonic reinterpretation is of little help

here: the B-minor triad might be reinterpreted as a C b minor triad, but this would simply generate the label

fvi, and replace the chromatically-altered dominant pitch with a chromatically-altered tonic pitch.

But this reinterpretation opens the door to a suggestion made in this chapter: both fvi and III s are

only apparent triads that I have argued can be enharmonically understood as projecting dominant function

as chromatically-altered diminished-seventh chords, and in this manner their ontology and role in the tonal

prolongation can be more clearly understood. Where analyzing fvi and III s pose such ontological problems

owing to the implications that they relate directly to the tonic on a similar structural level, the chromatically-

altered diminished-seventh chords as I have theorized them pose far fewer problems in this regard. The

o7 apparent B-minor triad can be reinterpreted as D–Fs–( )–Cf, or vii s3 of E b, while the G-major triad can 155

o7 likewise be respelled as D–( )–Aff –Cf, or vii f5 of E b. Because these two chords are sounded consecutively, we might think of the second as a continuation of the first, simply with a different inversion and a shift in chromatic alteration: indeed, this is precisely what Cohn’s T1 analysis notes. Notably, as Figure 2.12 indicates, understanding the B n as C b makes sense on the melodic level as well: the upper-voice B b is prolonged by its chromatic upper neighbour C b, which resolves back to B b when the prolongation of the E b chord returns to E b minor. When the resolution to E b happens, as noted, it is now Eb minor, functioning as

the supertonic of the local D b tonic—IV in the global key of A b. One might posit then that the goal of this

prolongation is to take E b major as dominant and transform it into to E b minor as supertonic.

Admittedly, such a reading is slightly complicated by the bass voice in the progression (if one

decides to abstain from understanding the contrabass’ E b as being conceptually, if not sonically, present

throughout these two measures), but, in disassociating the bass from the harmony above it proves fruitful in

such an analysis. The bass sounds B–G–Eb, or, viewed in a slightly different manner, it arpeggiates an E b

chord with a raised fifth, confirming the larger-scale dominant function of E b.87 Thus if we see the bass as

an arpeggiated E b chord (and this actually synthesizes well with the thought of E b being the conceptual, if

not sonically present bass for this passage), the chords above it are functioning as dominant-functioning chords above an unfolded pedal point, much in the same way some of the examples above do: in this case the arpeggiation cycles through the entire triad. 88 Thus Kurth’s view of the equal division of the octave is

indeed helpful, and, when combined with the possibility of reinterpreting the triads above the bass and

divorcing them from the bass, helps explain the prolongational aspects of this passage from harmonic,

contrapuntal, and voice-leading perspectives. My overall analysis, combining the disassociated bass, the

chromatic reinterpretation of the triads with their conventional voice leading FIP, and the concluding

87 Augmented triads most typically express dominant function, as either V, or less often V of IV, which resembles an altered tonic. 88 Though I do not have the space to investigate this technique in more detail here, outlining tertian chords via an arpeggiated bass that is disassociated from the harmonies that sound above it is a common strategy Wagner employs, especially in his later music. Further illustrations of this technique can be found in Kundry’s monologue, “Ich sah das Kind,” in Act II of Parsifal , and in the final scene of Götterdämmerung . 156

Figure 2.12. Analysis of Example 2.14

harmonic progression in D b are shown in Figure 2.12, including Lewin’s deeper-level suggestion that this passage moves on a deeper level from V to IV in A b.89

Conclusion

This chapter extends the methodological approaches and perspectives of the previous one by further developing the idea that in highly chromatic music, when tonal-prolongational function cannot be easily ascertained from static objects, the linear realm, and retention of conventional voice-leading motion therein, becomes important in articulating function. Here the disparity between sonority and the functions that I am

advocating becomes even more pronounced: not only are triads regarded as the fundamental building blocks

of tonal music, but they are also the locus of the notion of harmonic stability in conventional theoretic

89 This was not an uncommon larger-scale process in Wagner’s music at this point—see Tristan und Isolde , for example, as well as Götterdämmerung , which does not have any sort of convincing authentic cadence at its conclusion, but rather concludes with a plagal gesture. See Warren Darcy, “The Metaphysics of Annihilation: Wagner, Schopenhauer, and the Ending of the “Ring,” Music Theory Spectrum 16, no. 1 (1994): 1–40. While Darcy notes an unfolding V–I immediately prior to the sequential ascent of the Valhalla motif at the conclusion, this is almost certainly not to be understood as achieving a convincing cadential closure. 157 discourses. As such, I can imagine a number of initially skeptical reactions to the suggestion that they not be understood as such, but rather express the functions of four-note chords. Part of this problem, I believe, comes from music theory’s insistence on function being a product of singular static objects in singular domains. Harrison’s theory of harmonic function, for example, posits that scale-degree pitches are inherent signifiers of function. I do not disagree that this is true in certain cases: when tonic or dominant is in the bass, for example, it is often difficult to hear anything other than those respective functions. But Harrison’s argument that pitches themselves have inherent function almost plays out as an extension of the idea that dominant function can be understood if only there is a leading tone somewhere in the chord. 90 In such approaches, which remain relatively commonplace in contemporary theory, the leading tone is not required to do anything, and is simply noted as a beacon of dominant function. And it is this that I take issue with.

Function, I have argued—especially in the highly chromatic music of Wagner and Strauss, wherein various diatonic scale degrees are, almost as a matter of course, transformed into dissonant, rather stable, elements—cannot be approached a priori as an inherent feature of a pitch, or chord. This perspective, which tends to work so well for classical music, loses its traction in the more chromatically complex music of the

late nineteenth century.

Joseph N. Straus summarizes this disparity with remarkable acuity:

90 Notably Swinden (2005) points out that Harrison’s theory also eventually steps away from this approach when it begins to suggest the notion of functional discharge, and Swinden too attempts to pull the focus away from pitches with inherent function to pitches doing things and thereby exuding function. 91 Joseph N. Straus, Remaking the Past: Musical Modernism and the Influence of the Tonal Tradition (Cambridge: Harvard University Press, 1990): 1. 158

While Straus’ study is directed more towards composers of a later style than Wagner or Strauss, his

argument holds just as true when discussing tonality in their music, especially from the perspectives

advocated in this chapter and the preceding one.

Function in this music is more sensitively viewed as a product of musical material doing things, not

of musical material being things. While the tritone, which is often lauded as a univalent interval that clearly

delineates key, it is worth remembering that it can resolve in either of two ways, and it is the resolution which clearly expresses the function of that interval. When it resolves as a diminished fifth, to a third, we

understand it expressing dominant-to-tonic function in that key. If that same tritone resolves as an

augmented fourth, we understand dominant to tonic function in a key a tritone away. The diminished-

seventh interval, I have argued, is similarly univalent in relation to a tonal center, and performs in the same

manner as the tritone: on sounding, it suggests the potential for dominant function, and upon resolving to a

perfect fifth, it realizes that potential and creates that dominant-to-tonic discharge.

In classical tonality it is far simpler to understand chords as objects, because the music employs a

more limited set of pitches and chords in a generally consistent syntactic way. What I am arguing in this

chapter, and the preceding one, is that the extended chromaticism of the late nineteenth and early twentieth

centuries negates that simplicity. It forces us to look beyond identifying vertical conglomerations of pitches

as objects that simply are. Instead, I have argued that in this highly chromatic idiom, identification of

chordal function, and larger-scale tonal structures, comes through an understanding of tonal motion in

music, realized as a synthesis between the vertical and the horizontal domains of music, and further through

understanding that despite the chromatic alteration present, there is a dialogic process with the conventions

of classical tonality. As mentioned in the introduction to this dissertation, my overall goal is to demonstrate

that classical tonality is still prevalent in these works, and I believe the processes I have outlined in this

chapter and the previous one, are a step towards reconciling this music with the tonal-prolongational

practices of its classical precedents. Chapter 3 The Abnegating-Sixth Chord and its Extensions Deriving Late Nineteenth and Early Twentieth-Century Harmonic Extensions from Linear Displacements

The last two chapters have focused on the aspect of late nineteenth-century harmony that has

received the most attention in the last hundred years, namely the role chromaticism plays in the

prolongational processes of chromatic works. This focus on chromaticism is idiomatic of the study of late

nineteenth- and early twentieth-century harmony, where analytic and theoretic inquiry prioritizes the

increase in chromaticism and acoustic dissonance, noting the ways in which these dimensions push tonality

up to, and eventually past, the point of atonal rupture. Less often studied are other dimensions of music that

extensions to those dimensions play in the dissolution of tonality. While it is certainly well-noted that

increased surface-level activity—such as a proliferation of suspensions, passing tones, chromatic neighbour

notes, and a variety of other non-chord tones—was idiomatic to many late nineteenth- and early twentieth-

century composers, there are, I will argue, instances where such surface-level melodic, or linear, idioms can

take on harmonic roles. 1

This chapter argues that in certain contexts, non-chord tones can undergo processes of linear displacement or abnegation that pull the pitches in question from existing solely in the linear-contrapuntal realm, and force them into the harmonic one as well. As in the previous two chapters, this process does not create new sonorities, but rather in the same way that the half-enharmonic reinterpretation of seventh chords and triads demonstrated that conventional sonorities can function in ways that differ from their traditional roles, the same type of revisionist thinking can be applied to inverted chords in certain contexts.

Thus, again, I argue that recognizing the potential of the familiar to operate in ways that are unfamiliar is a useful strategy in approaching late nineteenth- and early twentieth-century tonality.

1 Schoenberg, for example, cites displacements of linear events, rather than harmonic alterations, as a potential generator of new chords and chromaticism. See Arnold Schoenberg, Theory of Harmony [3 rd ed., 1922], trans. Roy E. Carter (Berkeley: University of California Press, 1978): 319–322. 159

160

I begin by outlining an alternative to the theory of chordal inversions, with a specific focus on chords that contain the interval of a sixth, which I suggest need not be exclusively understood as first- inversion triads, but instead could be understood as dyads with a non-tertian sixth appended in an upper voice. Following Schenker, I term this conceptual perspective the “roothood tendency of the lowest tone” and link the ideas to early conceptions of chords with sixths, such as those described by Zarlino or

Albrechtsberger. After developing a theoretic model and framework to account for how such chords can still be understood as a derivation of the syntax of classical tonality, I use examples from the works of

Wagner and Strauss to demonstrate instances where substituting the theory of chordal inversions with the theory of the roothood-tendency of the lowest tone produces analyses that more clearly elucidate the prolongational processes of the passages in question. Combined with the perspectives adopted in the preceding chapters, these approaches, I contend, help discern the prolongational practice that Schenker, and others, proclaimed to be lacking in the works of composers such as Strauss and Wagner.

The focus of this chapter then narrows specifically on ways in which Strauss further extends the uses of linear displacements and abnegations to distort chords with additional appendages. I categorize these instances of harmonic reinterpretation, including those pertaining to the sixth chords described above, under the broader label of “harmonic polysemy” discussed in Chapter 1. Like the major-minor and half- diminished sonorities discussed in that chapter, the chords under scrutiny here likewise sound and appear to be one type of chord under the conventions of tonality, but, owing to their context, arguably function in a manner entirely different from what their sonority would suggest under the auspices of conventional theoretic approaches.

I Theoretic Preliminaries and Schenker’s “Roothood Tendency of the Lowest Tone”

In a relatively unremarkable, and oft-overlooked passage from the second volume of Kontrapunkt ,

Schenker writes that “the lowest tone in each case seeks above all to be the root of a 5/3 sonority…we are 161

always first inclined to assume root-value for each lowest tone.” 2 This is a curious statement, especially given

that he softens this position shortly thereafter, writing that “our sense is forced to overcome the initially

intrusive assumption of roothood-tendency of the lowest tone in order to attend [to the] artistic labor of

inversion.” 3 These two quotations in some ways summarize two competing ways in which music theory approaches and professes to understand chords that do not contain the chordal root in the bass: either as an inversion of a chord wherein the root has been displaced by an octave, or as a chord containing one or more contextual dissonances that materialize when non-tertian pitches occur in conjunction with a chord whose construction should be tertian in nature. While claiming the bass always seeks to be the root of a five-three sonority should be read as an overstatement on Schenker’s part, nevertheless the bass pitch remains highly salient, and this engenders investigation into ways in which this might have been used to extend common- practice tonality in the late nineteenth and early twentieth centuries.

Example 3.1 depicts one of the most common identity relationships in tonal music: the triad in inversion. First presented in the early seventeenth century, and subsequently popularized by Rameau, this has been one of the foundational principles of tonal theory through to the present day. 4 As David

Damschroder writes, “Though chords could be compared in ways that emphasize their differences, pitch

Example 3.1. Triads in Inversion

2 Heinrich Schenker, Counterpoint [1910/1922], ed. John Rothgeb, trans. John Rothgeb and Jürgen Thym, 2 vols. (New York: Schirmer Books, 1987), II: 8. 3 Ibid., 9. 4 Lippius, for example, thought of triads in inversion in the early 1600s. See Joel Lester, Between Modes and Keys: German Theory 1592–1802 (New York: Pendragon Press, 1989): 47–61. Lester also observes that Campion in 1613, Burmeister in 1599 and 1603, Otto Siegfried Harnish in 1608, and Johann Magirus in 1611, in addition to Lippius, each conceived of triadic inversion prior to Rameau. See Joel Lester, “Root-Position and Inverted Triads in Theory Around 1600,” Journal of the American Musicological Society 27, no. 1 (1974): 110–119. 162

content is here proposed as their defining feature. E–G–C is more closely allied with C–E–G than with E–

G–B.” 5 But although inversion theory explains a vast majority of cases, it cannot be relied on exclusively.

For instance, the passage in Example 3.2, from the opening of the third movement of Schubert’s Piano

Sonata in A major, D.959, contains in m. 6 a chord spelled B–D–G. Conventional harmonic analysis might label this fVII 6 in the key of A, but this label does not really account for the chord’s function in the passage, and seems to merely describe the chord’s root and sonority. What follows this curious entity—a dominant seventh of B-minor resolving to a B-minor triad—sheds some light on a second possible reading of the function of the chord in m.6: rather than read as an inverted G-major triad, it might be understood as a B- minor chord with a sixth appended to the dyad below in place of the conventionally expected fifth.

What we now term chords in inversion was not always the standard practice. Joel Lester writes that in the sixteenth century Zarlino’s view was that “the first-inversion triad is explained as a chord in which the fifth over the bass has been replaced by a sixth.” 6 Even after Rameau popularized the theory of inversions, it was not universally accepted: two centuries after Zarlino, Austrian theorist Johann Georg Albrechtsberger’s

Example 3.2. Schubert, Piano Sonata in A Major, D. 959, iii: mm. 1–8

5 David Damschroder, Thinking About Harmony (Cambridge: Cambridge University Press, 2008): 1. 6 Lester (1974), 111. 163

(1736–1809) thoroughbass treatise, Kurze regeln des reinsten Satzes , adopts a similar approach. In Kurze ,

Albrechtsberger calls five-three sonorities perfect, and six-three sonorities imperfect. Albrechtsberger does not see five-three and six-three chords as related by inversion, but understands them rather as derived through the substitution of a sixth for the more normative fifth. 7 These perspectives contrast with the fundamental bass approach advocated by Rameau in his Traité sur l’harmonie and subsequently adopted into

contemporary thought as the theory of chordal inversion. 8 Rameau’s view proposes that the sixth above the bass is understood as maintaining its status as the chordal root, despite the lack of a stable five-three sonority that results from the root’s displacement from the bass. Even though the older perspective espoused by Zarlino and Albrechtsberger pertained to much earlier music, it might be a useful tool to import into the study of late nineteenth-century tonality. 9

Thus the older perspective, shown in Figure 3.1a, suggests that a chord with a sixth above the bass is more closely related to a five-three chord that shared the same bass, while the more pervasive Ramellian perspective shown in in Figure 3.1b is that a chord with a sixth above the bass is more closely related to a five-three chord that shares the same root when abstractly stacked in thirds. Thus B–D–G, under the theories of Zarlino and Albrechtsberger is still fundamentally a “B chord,” with the sixth displacing the expected fifth, either momentarily, or for the duration of the chord, while under the theories of Rameau and chordal inversion, it is fundamentally a “G chord,” with the root having been moved from the bass to one of the upper voices via octave displacement, destabilizing the five-three sonority. Both perspectives suggest that chords containing the interval of a sixth above the bass are less stable than five-three sonorities, and are generated via a displacement of some pitch. The difference lies in which dimension of music that displacement is understood to belong: the horizontal or the vertical.

7 Robert Wason, Viennese Harmonic Theory from Albrechtsberger to Schenker and Schoenberg (Ann Arbor: UMI Research Press, 1985): 8. 8 Lester (1974): 112. 9 See also the opening of David Damschroder’s Thinking About Harmony (Cambridge: Cambridge University Press, 2008, 3–9), wherein he discusses various perspectives on the differences between 5/3 and 6/3 sonorities that share the same root. Damschroder writes, “Even past the middle of the twentieth century, Carl Dahlhaus questions the importance of differentiating between ‘5/3 and 6/3 sonorities that share the same bass pitch. Chordal connection is based on the actual bass pitch, not on the abstract basse fondementale .’” 164

Figure 3.1. Differing Analyses of Chords containing the Interval of a Sixth

a) Zarlino/Albrechtsberger: The sixth replaces the fifth

b) Rameau: The sixth is the root of the chord

The perspective adopted by those with a more horizontally focused perspective wherein the sixth functions as a substitute for the fifth, might be seen as exhibiting a kinship with what theorists such as

Johann Kirnberger or Gottfried Weber termed an incidental , or non-essential, dissonance. 10 Such dissonances arise when an unexpected pitch, in this case the sixth, substitutes for a more expected pitch, here the fifth. When this happens, a sense of contextual dissonance is created when the sonority with a sixth grates against the expectation of a fifth.11 If aligned with more contemporary analytic systems, this older

10 Gottfried Weber, The Theory of Musical Composition: Treated with a View to a Naturally Consecutive Arrangement of Topics [1832], trans. James F. Warner, ed. John Bishop [London: R. Cocks, 1851]: 649; and David W. Beach and Jürgen Thym, “The True Principles for the Practice of Harmony by Johann Philipp Kirnberger: A Translation” Journal of Music Theory 23 (1979): 163–225. See also William Caplin, “Moritz Hauptmann and the Theory of Suspensions,” Journal of Music Theory 28, no. 2 [1984]: 255; William Caplin, “Review: The Art of Strict Musical Composition by Johann Philipp Kirnberger; David Beach; Jurgen Thym,” Journal of Music Theory 8, no. 1 (1984): 124–128. 11 This in some ways reflects the views of Karl Mayrberger, who viewed only thirds, the perfect fifth, and octave as real consonances. Other pitches could sound like consonances, but were dissonant against the fundamental. Here, Mayrberger is still restricted to inversion theory, but acknowledges the sixth as being less consonant in a manner similar to my own suggestions. See Karl Mayrberger, “The Harmonic Style of Richard Wagner, Elucidated with Respect to the Leitmotifs of Tristan und Isolde [1881], 165

perspective of the sixth being understood as a non-essential dissonance might be seen as having a close link

to the 6–5 suspension, a similar case wherein the sixth above the bass substitutes for the fifth prior to the

fifth materializing through the linear resolution of the sixth. Indeed, in such cases, as William Caplin writes,

“Kirnberger asserts that both the chords of suspension and resolution have the same harmony,”

highlighting the view that the sixth is simply displacing, or standing in for, the fifth. 12

Conversely, Rameau and triadic inversion theory see the sixth in such suspension figures as akin to an essential dissonance, meaning that it does not replace another expected note, and exists more independently. Caplin further indicates that in opposition to Kirnberger’s view, Rameau, via his fundamental and interpolated basses, saw the chord of suspension and the chord of resolution as two distinct harmonic entities. 13 It is worth noting, however, that even Rameau was not entirely consistent in his application of chordal inversion theory. Most notably, his theory of the double emploi juxtaposes the perspective of the sixth

6 as a displacement note with the theory of chordal inversion. Rameau argues that the ii 5 chord can be rooted on the supertonic, which is necessary for it to progress to the dominant by root motion of a fifth, but can

also be rooted on the subdominant, which avoids a root progression by step—something Rameau’s system

6 forbade—when the ii 5 chord is approached from the tonic. Rameau writes that “there are two ways of hearing [to inform the ear] in this case: one by the fundamental succession of the bass, the other by the fundamental [root] of the harmony.” 14 Thus in his subdominant understanding of the chord, Rameau is,

essentially, analyzing the supertonic pitch as an added dissonance, which diverges from his theory of chordal

inversion, but allows him to dismiss the possibility of root motion by the interval of a second.

Contemporary theory, such as that found in the work of Richard Bass, and more prevalently in the field of

popular music, would term this subdominant understanding of the chord as IV (add6) , further reinforcing the

in Music Analysis in the Nineteenth Century Volume One: Fugue, Form and Style , ed., trans., ann. Ian Bent, 221–252 (Cambridge: Cambridge University Press, 1994). For a discussion of Schoenberg’s views on the dissonance of the sixth-three chord, see also Matthew Arndt, “Schoenberg on Problems; or, Why the Six-Three Chord is Dissonant,” Theory and Practice 37/38 (2012–2013): 1– 62. 12 William Caplin, “Moritz Hauptmann and the Theory of Suspensions,” Journal of Music Theory 28, no. 2 [1984]: 255. 13 Caplin [1984]: 257. 14 “Il y a dans cette occassion deux moïens de prévenir l’Oreille, l’un par la succession fondamentale, l’autre par l’Harmonie fondamentale.” Jean-Phillipe Rameau, Génération harmonique, ou traité de musique theorique et pratique (Paris: Prault fils, 1737): 117. 166

understanding of the supertonic pitch not as a root but rather as an added dissonance that is not generated

by stacking pitches in thirds. 15

Thus, like the juxtaposition of Schenker’s two perspectives as outlined above, Rameau’s double emploi highlights concurrently these two perspectives on chords with sixths above the bass. On one hand, the sixth can be viewed as the chordal root, simply displaced by an octave, while on the other hand, the bass voice retains the designation of root, and the sixth is viewed as a dissonance that displaces, or delays, the expected fifth. Rameau’s reasoning for this interchangeability boils down to one thing: context. There must be contextual reason to promote one analysis over the other. In classical tonality, almost without fail, the prevalence and salience of clear tonal relations motivates the use of inversion theory, to the point where it has become the de facto mode of analysis for almost all tonal music. But perhaps this perspective needs to be reconsidered. Think, for instance, of how in early twentieth-century tonality, such as the music of Debussy or Ravel, the bass becomes linked almost inexorably as the sole arbiter of function, or, likewise, a similar phenomenon in popular music studies. Based on the alternate mode of understanding sixths above the bass that I have described above, one might see the music under discussion in this chapter as a sort of transitional phase between the predominantly inversion-based approaches to classical tonality, and the bass- oriented perspectives that came to be associated with twentieth-century tonality. In this transitional period, I contend there are contexts in which supplementing the theory of chordal inversion with the proposed theory of the roothood-tendency of the lowest tone produces not only more nuanced and interesting analyses than a strict devotion to inversion theory, but also more readily accounts for the role that peculiar chords play in tonal-prolongational processes. But again, context must be the impetus for the use of one or the other system, not simply tradition or desire.

Applying this perspective indeed helps clarify the tonal language of the Schubert example shown above. Looking at the larger context, rather than understanding the chord in m. 6 as an inverted G-major triad, the progression invites the analysis of a B-minor chord with a sixth in place of the conventional fifth:

15 See, for example, Richard Bass, “Half-Diminished Functions and Transformations in Late Romantic Music,” Music Theory Spectrum 23, no. 1 (2001): 41–60. 167

Figure 3.2. Analysis of Example 3.2

the G, which should resolve down to F s, instead remains suspended over the B-minor chord. B-minor’s centricity in this local progression is then made clear by the sounding of the F s cadential six-four to dominant-seventh chord, and its subsequent resolution to a complete B-minor sonority. The sixth I have analyzed in m. 6 can thus be understood as projecting a delayed resolution to the expected F s over the prolongation of B-minor between mm. 6–8, as shown in Figure 3.2. These few chords project a brief tonicization of the supertonic, resulting in a progression that I analyze as i 6 – – (V 7) – i – 5 of the supertonic.

From a hierarchical perspective, the most fundamental chord in this local progression is the B-minor chord, and so, on the deepest level, the progression is simply ii 6 – 5, but the resolution of the sixth is delayed by the dominant seventh chord that separates the two iterations of ii.

II Abnegating-Sixth Chords

Example 3.3 shows the opening of Strauss’ tone poem Don Juan . The tonal center of the work is E

(first major, ultimately collapsing to the minor mode at the end), but it begins on a curious first-inversion C-

major triad. James Hepokoski has described this chord as an E-major triad “subjected to a n6-

168

Example 3.3. Strauss, Don Juan, mm. 1–4

n3 shift.” 16 This language suggests that even though the chord resembles and sounds like a conventional

first-inversion C-major triad, it has a function different from that suggested by its sonority. Hepokoski’s

language, however, is also emblematic of the conventional way in which the field discusses such six-shift

chords. Like Hepokoski’s reference to a n6 shift, Damschroder, for example, refers to such chords as being

in their “six-phase,” meaning that the sixth above the bass has been generated—explicitly or implicitly—

from a fifth above the bass. 17 Likewise, Edward Laufer refers to this process as elision, writing that it

consists of “an omission of notes that are due,” and gives an example from Brahms’ Ballade Op. 118 no.3 wherein a C dominant-seventh chord resolves to what appears to be a first-inversion D b-major triad. 18

Laufer thus suggests “in bar 19 a 5-6 motion must be understood, with the 5 (C 2) elided.” 19

The issue I take with the ontology of these approaches is that under such a view the existence of the

sixth, which is sonically present in the music, is predicated on the existence of something that is oftenabsent:

in the conventional 5–6 motion the sixth exists as a consequence of the fifth, but if the fifth is absent, the

sixth cannot logically result from it. To take a biological analogy, a child cannot exist if the parents do not

exist. To circumvent this ontological challenge, I propose instead that such chords might be better

16 James Hepokoski, “Fiery-Pulsed Libertine or Domestic Hero? Strauss’s Don Juan Reinvestigated,” in Richard Strauss: New Perspectives on the Composer and His Work , ed. Bryan Gilliam (Durham, NC: Duke University Press, 1992): 144. 17 David Damschroder, Harmony in Schubert (Cambridge: Cambridge University Press, 2010). 18 Edward Laufer, “On the First Movement of Sibelius’ Fourth Symphony: A Schenkerian View,” in Schenker Studies 2, eds. Carl Schachter and Hedi Siegel (Cambridge: Cambridge University Press, 1999): 127–28. 19 Ibid., 128. 169

understood as the result of a 6–5 suspension. While the act of a suspension implies a resolution to a

consonance, the actual suspension occurs, and thus can exist, regardless of whether it fulfills its implications.

In other words, under this view, fifth is a consequence of the suspended sixth, not the progenitor of it, and

as such can be omitted without changing the understanding of the preceding sixth as an accidental

dissonance.

Because the implication of the suspended sixth is that it will resolve to a fifth, if it fails to do so, or fails to do so immediately, it has denied its expected outcome. Robert Hatten refers to such cases where an outcome is denied as “abnegation,” using as an example the slow movement of Beethoven’s Piano Sonata,

Op. 7, where a V 6/V chord proceeds first to ii 6 before the structural dominant is sounded. Hatten writes

that “a reversal (F s–F) displaces the goal and creates a denial, or negation , of the implication of the bass F s.” 20

This notion of a denial of implication is the same type of phenomenon I am discussing, and as such, I use the term abnegating-sixth chord to describe such scenarios: abnegating because this is often a processual abnegation, and is only understood as such in retrospect. Phenomenologically speaking, the sixth above the bass in these cases creates the expectation for the fifth: in some cases the fifth materializes (suspensions), in some cases it does not (complete abnegation), and in some cases the suspended pitch is delayed over the course of the prolongation of a Stufe before resolving (delayed resolution). The latter two of these are where my interest lies in regards to their role in late nineteenth-century harmony.

If we examine more broadly the opening of Don Juan , and place Hepokoski’s assertion into a

broader context, we might then see this as an example of a delayed resolution of a(n unprepared) 6–5

motion. My analysis in Figure 3.3 suggests that the C-major triad, as Hepokoski notes, is in fact a triad

rooted on E, with an appended sixth C n above the bass. Given that these first measures are easily

understood as a prolongation of the E tonic, I suggest that this might instead be viewed as a deeper-level

20 Robert Hatten, Musical Meaning in Beethoven (Bloomington and Indianapolis: Indiana University Press, 1994): 59. 170

Figure 3.3. Analysis of Example 3.3

Ef6-5 motion, with a dominant chord inserted between the resolution of the sixth to the fifth. 21 This type of

f6 o7 5 contrapuntal-prolongational procedure I am describing might best be likened to the V 4–vii /V–V 3

progression that can be found relatively often in the music of the early-to-mid nineteenth century. In such

progressions, the pitches that create the sixth and the fourth above the bass are non-chord tones that defer

the stability of a five-three chord, but eventually resolve to the fifth and the third. Most often, they do so

immediately, but in the abstract progression shown above they are suspended over the intermediary applied

diminished-seventh chord, which also lends tonicization support to the dominant Stufe . In the case of Don

Juan , it is not a suspended sixth and fourth, but rather only a sixth. Thus instead of deriving this chord from a non-existent E-major triad prior to the apparent C-major sonority, I consider its function as part of the process of establishing the tonality of the piece.

Another example of this process can be found in the Todestrank motif from Tristan und Isolde , whose interior chromatic procedures were discussed in detail in the previous chapter (see Example 2.1). In my previous analysis I glossed over the first chord, which despite my assertion of a prolongation of C, is acoustically an A b-major triad in first inversion. Example 3.4 shows the passage with the measures preceding

21 While a sixth is not inherently a dissonance, as Damschroder (2008, 22) notes, Rameau saw the “chord of the added sixth ( accord de la grande sixte ), [as having] the sixth serving as a sort of dissonance to propel the chord onward.” 171

Example 3.4. Wagner, Tristan und Isolde , Act I, Scene 2, mm. 22–30.

os6 7 it included: a progression that sounds vii 42 (Tristan chord) to V in C prior to the first-inversion A f triad.

The dominant function of the V 7 chord suggests the possibility of a tonic arrival, which I argue does indeed happen. Instead of the anticipated five-three sonority, however, the A b displaces the expected G. This A b is

then neighboured by the A n (B bb as discussed in Chapter 2), before being transferred to the bass, where it

resolves to the expected G at the onset of the dominant harmony. Using this trick, Wagner creates a

continued suspension of stability, while maintaining the prolongational processes of common-practice

tonality.

Indeed, what I view as this type of long-range dissonance suspension and resolution is the more

common of the two approaches: singular chords with appended notes that fail to resolve at all occur far less

frequently, although illustrations of this do exist. For instance, the passage in Example 3.5, mm. 265–267 in

Example 3.5. Wagner, Götterdämmerung , Act I, mm. 265–267

172

the prelude to Götterdämmerung, uses a i +6 chord but does not resolve the appended sixth The passage is

ø7 o6 +6 locally in E b, with the progression ii –vii 5–i . Here the C b in the vocal part, the seventh of the diminished-

seventh chord, remains suspended over the tonic chord that follows, rather than resolving down by step to

Bb as expected. This is, in every sense of the word, an abnegation of the expectation of the chordal seventh, and, I believe, can be heard as such given the passing B b in the orchestral part at m. 267.

A second example, from Strauss’ Tod und Verklärung , likewise does not resolve its appended note over a prolongation: the chord in question occurs at a structurally salient moment—the predominant prior to the medial caesura—whereas the chords in question above usually occurred in the midst of a prolongational passage. Shown in Example 3.6, here Strauss uses the B b major-minor seventh as an applied

o6 (GR) vii 5 , which in turn leads to a chord that initially appears to be a D-major triad in second inversion, which in turn proceeds to a D major-minor seventh chord as the cadential goal of the medial caesura that precedes the secondary theme in G major.

Example 3.6. Strauss, Tod und Verklärung , mm. 175–190

175

180

187

173

To label the chord in m. 180, which I mentioned appears to be D-major triad in second inversion, as

6 V 4—not the cadential six-four, but a dominant triad of G in second inversion—would, I feel, be inappropriate in this context. Instead, given that the music reaches a V:HC MC in G a few measures later, this chord might be more accurate described as V +6 of V in G. Notably, the fourth above the bass, D, does eventually make its way, through an ascending chromatic line, to C s, a third above the bass. The sixth above

the bass—Fs—however, does not manage to find its way down to the E n that would be expected. In this

case this confluence of linear processes pushes this example slightly beyond the confines of the previous

ones, in the sense that the added note appears in tandem with a 4–3 suspension figure that is obscured on

the musical surface.

Approaching the chord in m. 180 with the reinterpreted Bb major-minor seventh helps to clarify that

the root of the chord should be taken as A. Respelled, B f–D–F–Af can be understood as Gs–Bf–D–F, or,

o6 (Gr) vii 5 of A: and indeed, Strauss does respell the chord to reflect this function. As discussed in Chapter 1, I

o6 (Gr) prefer the nomenclature vii 5 , which absolves the augmented-sixth chords of their supposedly rigorous predominant function, and allows them to be understood instead as local dominant-functioning chords applied to their chord of resolution. Here the altered Gs diminished-seventh chord, with all its intendent voice leading, as shown in Figure 3.4, suggests that A is the very local tonic resolution that receives the discharge of the seventh-chord’s dominant function. There exists one exception here, discussed above: namely that the chordal seventh of the diminished-seventh chord steps up chromatically to become the sixth above the bass. This voice leading is entirely normative when progressing from a diminished-seventh to a six-four sonority: it is this sixth that fails to resolve down to the fifth above the bass that interrupts the norms of tonal voice leading.22 Thus I suggest that the chord in m. 180 is not, in fact, an inverted D chord,

22 o7 6 When vii /V resolves to V 4, the convention is for the chordal seventh to step up chromatically to the major-mode variant of the pitch ( f3 steps up to n3), before ultimately resolving down by step as expected. Sometimes, for the sake of visual aesthetics, o7 o6 o7 the vii /V chord is thus respelled to resemble vii 5/iii, though its function remains unchanged. Conversely, if vii /V resolves to f6 V 4 (i.e. a minor-mode tonic), the seventh remains static. 174

Figure 3.4. Analysis of Example 3.6

as it first might appear, but rather it is a distorted A chord: depending on one’s preference of nomenclature,

either V (+6) /V or II (+6) in G.23

A final example that displays an even more extended use of this idiom, can be seen in Example 3.7,

from the first act of Die Meistersinger von Nürnberg . Here, D has been the unquestionable tonic for some time,

6 ø6 7 and Wagner sets up the expectation for a cadence with a i –ii 5–V progression, but, instead of resolving the

dominant to a D-major or D-minor triad, he resolves it to a B b major triad in first inversion, concurrent with a shift into the key of B b major. In viewing this as fundamentally a D-related chord, Wagner’s tactic in overriding the cadence becomes apparent: this is not simply an inverted deceptive resolution, but can instead be viewed as the displacement of the chordal fifth A, anticipated by the sixth B b. It is noteworthy that this sort of gesture is relatively common in Die Meistersinger von Nürnberg , possibly hearkening back to the older, more contrapuntally-oriented procedures being employed.

In addition to being a relatively straightforward example of a chord with the sixth in place of the fifth, the chord in question acts as the pivot to the new key of B b, functioning therein as I 6. Thus the situational and prolongational context preceding the chord suggests I (+b6) as an analysis, meaning that the B b

23 This has a relationship to the dominant-thirteenth chord, although V 13 is usually reserved for chords that also contain a seventh, which this illustration does not. 175

is an accidental dissonance anticipating the chordal fifth A, but the context that follows retrospectively redefines this chord as an inverted B b triad, highlighting the interchangeability of these two theories in more contexts than Rameau’s double emploi . Incidentally, it is worth noting that the sixth does eventually move to

4 the fifth, as shown in my analysis in Figure 3.5, but only after the chord has changed to V 3 in B b.

Example 3.7. Wagner, Die Meistersinger von Nürnberg , Act I, mm. 139–150

139

143

147

176

Figure 3.5. Analysis of Example 3.7

I conclude this section with two vignettes demonstrating how this perspective can be extended to apply to

the analysis of larger-scale passages. The passage in Example 3.8, drawn from the onset of P-space in Tod

und Verklärung , begins on a C-minor tonic, but moves quickly to a chord spelled F f–Af–Df. Perhaps this

might be considered the minor lowered supertonic in first inversion in the key of C, but, aside from

questions that arise from the relative scarcity of that chord as a surface-level prolongational triad,

considering the tonal trajectory suggests a different interpretation. 24 As shown in Figure 3.6a, the overall

motion of this section is a move back to a prolonged dominant of C, the ultimate goal of this trajectory.

6 Along the way there is an intermediary goal, the B 4 chord in m. 76. At a middleground level the function of

6 this chord is to unfold to the global dominant G, but on a more surface level this chord functions as V 4 of

E. The function I suggest for this chord is supported by the tonal trajectory that precedes it: as shown in

Figure 3.6 these chords express an expansion of E.

The only issue one might take with viewing this as an expansion of E is that no E tonic triad ever materializes, and even the dominant only occurs as a six-four chord before moving on to the chords that

preempt G. This, is, I believe, a valid concern: how can a Stufe be expanded if its root fails to materialize in

some way? In looking at the D b-minor triad that occurs in first inversion immediately after the initiating C-

24 Mark Ellis suggests that it appears in mm. 29–30 of the first movement of Beethoven’s String Quartet Op. 132. A closer analysis suggests that this chord is not bii, but rather, owing to the piece having already modulated, iv of F. See Mark Ellis, A Chord in Time: The Evolution of the Augmented-Sixth Chord from Monteverdi to Mahler (Burlington: Ashgate, 2010): 187. 177

Example 3.8. Richard Strauss, Tod und Verklärung , mm. 67–79

Figure 3.6a. Analysis of mm. 67–78 in Example 3.8

178

minor tonic triad, I suggest it may be fruitful to understand this chord not as a D b-minor chord, but rather as an E triad with a sixth in place of the fifth. Thus the trajectory from the outset of the Allegro section to

6 7 ø7 6 the B 4 chord would express a I–IV –vii /V–V 4 progression in the major mediant (E): an example of what

Felix Salzer refers to as an “incomplete” harmonic progression, wherein the prolongation of a Stufe occurs

as projecting outward from a tonic triad, but does not return there, and concludes instead on the

25 6 dominant. In this case, Strauss takes things a step further: rather than resolving the B 4 chord to a five-

three, it steps up in the bass, mimicking a deceptive resolution wherein the submediant chord is substituted with a supertonic half-diminished seventh chord in second inversion. This chord simultaneously functions

ø4 as vii 3 of G, the dominant, and subsequently proceeds to the dominant of G which resolves to a dominant-

lock on G again.

Here I am arguing that surrounding contextual factors, most notably the prolongation of the major-

mode mediant, suggest that instead of understanding the inverted D b-minor triad as such, it is beneficial to step away from the confines of inversion theory and understand that chord as an E major dyad with a sixth appended to it, what I will henceforth refer to as an appended-sixth chord . This is slightly different than the

abnegated sixth I describe above: where in the illustration given earlier, the sixth failed to resolve at all, here

6 the sixth does eventually resolve down to the fifth, over the B 4 chord, which, my middleground analysis in

Figure 3.6b depicts as part of the arpeggiation of the E triad. Essentially, a tonic chord with a sixth

appended to it functions as the initiation point of a long-range 6–5 suspension: the sixth does not resolve

immediately over the surface-level triad, but rather resolves over the course of the prolongation of that

harmony, creating a deep-level E 6–5 motion. These perspectives are all detailed in Figure 3.6b. Likewise, in reviewing Figure 3.6a, the same type of motion occurs, with the appended sixth F s passing through F n to

resolve down to the E over the i 6 chord at the end of the measure.

25 Felix Salzer, Structural Hearing: Tonal Coherence in Music [1952] (Reprint. New York, Dover, 1962): 153. 179

Figure 3.6b. Deep Middleground Reduction of Figure 3.6a

A final, more elaborate example from the second act of Parsifal , is shown in Example 3.9. Here, one

finds conflict between the more local context in m. 830 and the deeper-level prolongational and

contrapuntal contexts that follow in mm. 831–834. Kundry’s aria-like passage “Ich sah das Kind” begins with a prolonged tonic moving to a dominant that eventually culminates as a V b9 resolving to I 6. The

preceding dominant strongly confirms this as a I6—the local resolution to the V b9 chord—but what follows suggests that the chord acts almost as a pivot, becoming the mediant with an appended sixth. I base this claim in the harmony of the following measures, which presents a chain of applied dominants leading to the

mediant in m. 834. As shown in Figure 3.7, my reading of this passage is that the inverted G triad then

becomes a B-major triad with a 6–5 suspension whose resolution to the expected fifth is delayed over the

course of four measures. Wagner then repeats this motion, using the more diatonic B-minor triad instead,

before moving to a tonicization of V resulting in a half cadence. This creates a local middleground I-III-V

outline, the type of which proliferates the harmonic middleground structures of Parsifal .26

Traditionally, chords with additional non-tertian pitches—whether added sixths or what I have

termed abnegating sixths—were, at least in the confines of the understanding of tonality prior to Debussy or

Ravel, confined almost exclusively to a pitch that was the interval of a sixth above the bass being added to

the subdominant, creating the supertonic-subdominant double emploi discussed previously. What I suggest

26 It forms the large-scale background of the Prelude, but also the more local deep-level progressions in various sections of the Prelude. 180

Example 3.9. Wagner, Parsifal , Act II, mm. 824–845

824

830

835

840

here is that this type of non-tertian added-note analyses can be recognized beyond the confines of the supertonic-subdominant relationship given the proper contextual factors. Thus through the addition of a sixth above the bass, whether to a complete triad, or to a dyad resembling the omission of the downward resolution of the sixth to the fifth, relatively basic harmonic progressions can be obscured at the musical surface and made to seem more exotic.

181

Figure 3.7. Analysis of Example 3.9

Thus I would argue that the theory of the roothood-tendency of the lowest tone need not be

relegated exclusively to the category of a competing method of analysis, waiting to supplant conventional

inversion theory, but rather it can be defined as an extension of the more commonly-employed theories of

inversion and of suspension. As the examples from Parsifal and Die Meistersinger von Nürnberg make clear, when dealing with contextual factors such as these, elements of interpretation and analysis come into play. I am not suggesting that there are necessarily hard-and-fast rules for determining when to employ inversion theory or when to employ the theory of the roothood-tendency of the lowest tone, but rather elucidating instances wherein momentarily placing aside the confines of inversion theory leads to insightful analyses that suggest that harmonic extensions in the late nineteenth and early twentieth centuries were not exclusively products of chromaticism and rampant acoustic dissonance, but could be created by simply displacing or abnegating simple suspension or non-chord-tone figures.

The above discussion and analyses have, I hope, laid out much of the groundwork describing the ways in which the two competing modes of analysis can work, either in tandem or at odds with each other.

The above examples represent what I view as less tonally intrusive uses of the roothood tendency of the lowest tone, as they mostly operate through the abnegation or displacement of a single pitch, almost always a sixth. Because the sixth is not a dissonant interval, and the 6–5 suspension is idiomatic to common practice tonal music, it is not too far a stretch of the analytic imagination to understand an upper-voice sixth 182

as a contextual dissonance, replicating the suspension figure but remaining unresolved, or resolving only

over the course of a prolonged Stufe .

This brings up the larger-scale function of this type of analysis. In conventional Schenkerian theory, most, if not all, of the chords I have hitherto described would be viewed as some kind of dissonant contrapuntal sonority. The analyses I have presented above suggest that, quite to the contrary, these chords form part of deeper-level Auskomponierung of Stufen . Take the Schubert sonata, for example: there, the bizarre chord that appears to be a fVII 6 chord, can, through this theory, be viewed as participating in the harmonic middleground, as part of a deeper level ii 6–5 motion prolonged by its own dominant. Thus while the notion of simply popping a sixth on top of an otherwise stable sonority may not be new, analyzing their function and usage in works prior to Debussy or Ravel yields fruitful insight, not only about the harmonic surface and the ways in which chords can be malleable and undergo extensions, but also to the deeper-level structures of a phrase, or section, or even of an entire piece.

III Strauss’ Extensions to Abnegating Chords

In the remainder of this chapter, I will present a number of analyses that employ the theories

outlined above, but press them into even deeper extended-tonal territory in a number of works by Richard

Strauss. I contend that these progressions, which would seem bizarre and perhaps outlandish from the

perspective of strict classical tonality, can be, as Robert Morgan suggests, “folded back into common-

practice prolongational procedures,” through a rigorous application of the theories I have developed.

Example 3.10, shows the opening of Strauss’ song Heimkehr (Op. 15, no. 5). The first phrase begins

in E major, and concludes with a IV–V–I progression in that same key; some of the intervening harmonies,

however, are difficult to relate to that tonic. Specifically here I suggest a prolongation of the subdominant

occurs in mm. 4–10. The chord in m. 4 is E s–Gs–B–D, spelled as a diminished seventh chord of F s (ii) but 183

equally plausibly understood as an applied leading-tone chord of A (IV). The chord that follows is a second-

6 inversion D-major triad, which under the traditional harmonic lens might be fVII 4 in E. This analysis,

however projects little clarity: the harmony subsequently shifts to a root position D-major triad (which would as least be more convincing as fVII in root position) followed by a B b-major triad. Here, as noted previously, the sIV/ fV analysis does not particularly convey the function of the chord, but its context

4 reveals another possible interpretation. The following chord is E–Gs–B–D, or V 3 of IV in the

Example 3.10. Strauss, “Heimkehr,” mm. 1–15

184

key of E. This allows the reinterpretation of the preceding chords as possibly being only locally referential,

meaning that they relate to the home key through the mediation of the locally tonicized subdominant.

Viewed in this context, the D-major triad would be IV in the key of IV, and the B b-major triad would be fII,

4 which creates an extremely conventional progression of IV–fII–V 3–I in the key of the subdominant. But how to account for the second-inversion D-major chord?

o6 The chord in m. 4 points the way. Its function as vii 5 of IV suggests that the next chord can be understood as an iteration of the subdominant. 27 In this case, it is a subdominant with not only a sixth, but a

fourth as well, appended to it, what I term an abnegating six-four chord. And indeed the two appended

pitches—D and F s—are suspended over the entire prolongation of the subdominant, resolving down by

4 28 step as suspensions only when the penultimate V 3 of the subdominant resolves to its local tonic. An analysis of this passage is given in Figure 3.8, illustrating the voice leading of the D and F s in

particular, but also how a combination between understanding local referentiality as well as the possibility

for appended pitches beyond the sixth provides an account of this passage that highlights its relationship to

classical precedents.

Likewise, Example 3.11a, from Salome , contains a similar phenomenon, one that has confounded

previous analysts. Ernst Kurth, for example, describes this triad as an isolated and absolute harmonic effect, whose coldness is explained by its dramatic context harmonizing the word tot .29 Building on Kurth’s

description of the chord, however, I suggest that this passage illustrates another example of the abnegating

six-four chord, albeit one that extends beyond the clear contrapuntal procedures shown in the previous

27 The chord in m. 3 is also curious. I understand it as a chromatically altered diminished-seventh chord applied to V of IV (D s– 4 Fs–Af–C) in third inversion. This should resolve to V 3 of IV (E–Gs–B–D), but the dominant seventh is replaced by its leading- tone substitute, yielding G s–B–D–F in first inversion. The voice leading reinforces this interpretation, with each of the chordal constituents behaving in the manner expected of the described analysis. 28 4 Technically speaking the F s resolves down to F n in the fII chord, and then F n resolves to E in the V 3 chord, but the consonant 4 resolution of that F s only materializes once that V 3 chord resolves to its tonic. 29 Ernst Kurth [1920], Ernst Kurth: Selected Writings , ed. and trans. Lee A. Rothfarb (Cambridge: Cambridge University Press, 1991): 127. 185

Figure 3.8. Analysis of Example 3.10

Example 3.11a. Strauss, Salome , mm. 24–31

186

example. At rehearsal 4, there is a cadence to D minor—at the deep middleground a manifestation of the

lowered supertonic scale degree, realized on the surface in the minor mode—preceded by a V b9 chord. That

6 chord in turn is preceded by what appears to be an A 4 chord. The chord prior to that is an F minor triad

that concludes a middleground prolongation of the F Stufe , functioning as biii of D. Again here the six-four

chord is perplexing: it might be understood as the minor dominant in second inversion, but, much like in

the example from Tod und Verklärung , such an understanding undermines the cadential potential of the

subsequent root-position dominant chord.

As an alternate reading, I propose understanding this chord as a further extension of the concept of

chords containing abnegating linear elements as part of their harmonic function. Where previously there was a bass pitch with a third and sixth above it, which I understood as the root and third of a dyad while the sixth above said root failed to resolve, here, I suggest that the sixth and the fourth above the pitch E are not chord tones, but are both unresolved suspensions, creating what appears to be a minor dominant in second inversion, but that actually fulfills the predominant function. I claim this mostly by virtue of it occurring in

the predominant position (read: literally right before the cadential dominant), and the bass progression from

3–2–5–1, one of the more common cadential bass progressions. 30 This analysis is depicted as part of Figure

3.9, which shows the tonal outline of this passage.

Admittedly, unlike the previous examples, there are fewer immediately discernible tonal contextual cues, apart from the tonal progression itself, to suggest that this chord is functioning as a supertonic.

However, I wish to point out one more aspect of this progression that might provide further substantiation for this claim: the subsequent Vb9 chord. While this sonority is not unheard of, it is likewise not one that is

common in Strauss’ syntax. The presence of the lowered ninth in this chord might be explainable as part of

this strange cadential progression. The voice leading, which as shown in the excerpt from the full score in

Example 3.11b, occurs between groups of instruments. The two abnegating pitches in what I have called the

30 William Caplin, Classical Form: A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven (New York: Oxford University Press, 1998): 26–29. 187

ii+6+4 chord do ultimately resolve in a linear sense; that is to say, they resolve as suspensions should,

though this does not occur as part of the supertonic chord, but rather when the harmony changes to the

dominant over the bar line. The suspended sixth C resolves down to B b, the lowered ninth in the dominant chord, while the suspended fourth A likewise resolves down by step to the G, the seventh of the dominant chord. 31 I have shown this in Figure 3.9 as a displacement: that the seventh and the lowered ninth above the dominant function as such, but also as the resolutions to the displaced fourth and sixth above the

E bass in the previous measure. This careful voice leading, despite occurring between different instrument

Example 3.11b. Strauss, Salome , Full Score for mm. 26–30, with voice-leading annotations

31 The A also rises chromatically to B f as part of the ostinato-like ascending chromatic line present throughout most of the first part of this scene, while the C also rises to C s, a type of split resolution for both pitches. 188

Figure 3.9. Analysis of Example 3.11a

groups (though in the same register and timbre), lends support to the characterization I have suggested for this chord.

This type of six-four sonority, wherein the bass is better understood as the functional root of the chord in question, and the upper voices dissonant suspension figures, appears frequently in Strauss’ other works. For instance, as shown in Example 3.12, in the climax of the trio “Hab’ mir’s Gelobt” from Der

Rosenkavalier , a chord spelled E–Gs–B appears at RH292, immediately prior to the cadential dominant-

seventh chord. This is certainly a jarring chord in the context of D b major, which would entail, under the

6 traditional root-quality analysis, a Roman numeral of fIII 4 (enharmonically respelled). It is approached, however, by a diminished-seventh chord spelled G–Bf–Df–Ff, which can be likewise understood

o6 enharmonically as A s–Cs–E–G, or vii 5 of fVII. I thus argue that the function of this apparent second-

inversion triad might be better understood as fVII, with an abnegating sixth and fourth above its root. The voice-leading from the diminished-seventh chord lends credibility to this analysis, as the B b (in Sophie’s part, as well as the first violins) resolves up to B n, which the C s in the bass (spelled D b) resolves down to D n. The other voices behave conventionally in the way they step up chromatically to the sixth and fourth above the

189

Example 3.12. Strauss, Der Rosenkavalier, Act III, 5 mm. before RH292

190

Figure 3.10. Analysis of Example 3.12

bass: traditionally these would resolve down to the fifth and third, thus completing the diminished-seventh voice leading, but because the upper voices abnegate, this resolution fails to materialize. That the chord progresses to a dominant further reinforces this analysis, and that the applied diminished-seventh chord is

6 7 +6 preceded by a I and ii further confirms the phrase-function of the VII +4 chord as shown in Figure 3.10.

The passage in Example 3.13, from near the end of Eine Alpensinfonie , uses a similar process with a

fVII chord, though the approach to the chord is more complicated than in the previous example. Here the music is moving towards the deceptive cadence in RH141.2 (later a PAC at RH142), and the cadential dominant at RH141 is preceded by what appears to be a second-inversion G b triad that could be labeled

6 fIII 4. Such a label, however, would be just that, and would elicit very little meaning beyond the descriptive; it is the context in which this chord appears that provides the impetus for a different interpretation. Four measures prior to RH141, the E b tonic shifts to a chord spelled A–C–Ef–G, which is prolonged through the subsequent measure, with a D n passing tone on the last beat understood as E bb . A–C–Ef–G can be half-

o7 enharmonically reinterpreted as C–Ef–G–Bff , or vii s5 of fVII in E b major. The bass Ebb might be seen as creating an instance of double alteration, or might simply be understood as passing between Eb and Db. The applied diminished-seventh function of this chord resolves by discharging onto D b, with the C resolving up 191

Example 3.13. Strauss, Eine Alpensinfonie , 5 mm. before RH 141

to D b, and the B bb (spelled A n) resolving to B b, which is expected when resolving an applied diminished- seventh to a major six-four sonority. This suggests that the chord two measures before RH141 should indeed be understood as a fVII chord, despite the sixth and fourth sounding above it. These pitches resolve down to the fifth and third in the second half of the measure, but then step down a second time to return to 192

the six-four figuration. That the chord resolves to V further supports the reading of this chord I propose

since fVII to V is a relatively common progression in nineteenth-century harmony.

Example 3.14 presents the beginning of “Hab’ Mir’s Gelobt.” The third through fifth measures present a curious harmonic progression following the initial dominant to tonic gesture: a diminished-seventh chord spelled D-F-Ab-B in m. 3 proceeds to what initially appears to be a second-inversion dominant- seventh chord in m. 4, in turn progressing to the dominant in the subsequent measure. At first glance, one might be tempted to simply write this off as an idiosyncratic instance of a common-tone diminished-seventh embellishing an inverted dominant: certainly this analysis is possible, but the combination of the bass progression, context, and voice leading suggests the possibility of a more nuanced interpretation.

4 I argue that this progression presents an instance of what I term the predominant V 3 chord , which I

define as a chord that appears to be a second-inversion dominant-seventh chord, but whose function is

more closely aligned with that of supertonic. This is, of course, a more radical version of the appended-sixth

chord discussed previously, though here there are multiple non-chord tones. In Der Rosenkavalier , the use of

4 the predominant V 3 is made even more radical by both multiple non-chord tones that resemble suspensions

Example 3.14. Strauss, Der Rosenkavalier , Act III, RH 285.1–285.8

193

but fail to resolve at all, and the absence of the supertonic triad in any conventional form. 32 Despite this, what suggests supertonic function in this case is the combination of the placement of the chord in question prior to the root-position quasi-cadential dominant, the quasi-cadential bass progression of s1 –2–5–1, and the function of the preceding chord, which, as mentioned, could simply be an embellishing common-tone chord, but is also vii o7 of the supertonic. Thus I contend that this presents a further instance of Strauss

elaborating the supertonic chord, the theoretic baggage of which I will unpack in the following discussion.

Firstly, the preceding diminished-seventh chord. This chord is vii o7 /ii, and functions this way in

4 most respects, despite resolving to an apparent V 3 chord. As depicted in Figure 3.11, in relation to the supertonic E b, the local leading tone D resolves up to E b, the chordal third F resolves up to G, the chordal fifth, A b is suspended (and both remains suspended but also resolves down to the chordal third G on the

subsequent beat), while the chordal seventh C b (spelled B n) rises to C n—as mentioned previously, a perfectly

common when resolving a diminished-seventh chord proceeds to a chord with a sixth above the bass in

place of a fifth. Thus the D diminished-seventh chord does indeed function according to the conventions of

Figure 3.11. Harmonic and Voice Leading Analysis of Example 3.14

32 Unresolved suspensions over a functional bass becomes a harmonic motif in this trio, culminating in a rather unusual approach 6 7 to the cadential dominant in the form of a fVII 4 to V unfolding in which the six-four over the fVII chord remains unresolved in most voices, but Octavian’s vocal line, doubled by the lower strings, emphasizes the missing five-three resolution. This emphasis on unresolved dissonances over the bass suggests a harmonic realization of the emotional uncertainty inherent in the scene, as both Octavian and the Marschallin attempt to come to terms with their impending separation, their emotions for each other, and, in Octavian’s case, his feelings for Sophie: in short, a parallelism between the music and the drama exists in regards to a large amount of indecision and a lack of clear resolution. 194

functional harmony: because the A b is suspended, it gives the impression of having a common tone, and thus projects an illusory common-tone resolution.

The bass progression of 1, s1 , 2, 5, 6 is highly suggestive of the supertonic reading I am arguing.

Specifically here, the leap of a fifth/fourth, from the supertonic scale degree to the cadential dominant

(resolving deceptively) very much indicates what Daniel Harrison might term a supertonic to dominant

discharge. 33 In terms of reconciling the C b/C n resolution, which remains suspended all the way into the

deceptive resolution of the cadential dominant, it is worth noting that over the tonic-substituting

submediant chord, the C does finally resolve down to B b: odd, certainly, since at this point it is functioning as the leading tone, but it also resolves simultaneously up to D b. In resolving the C to both the D b and the

Bb, both of the pitch’s acquired tendencies as dissonances—one as the seventh of the applied diminished- seventh chord, one as the leading tone—are fulfilled.

Thus I believe that the contextual factors surrounding this curious chord and progression strongly suggest a supertonic function, despite the chord resembling the global dominant-seventh on the musical surface. To this end, I have employed as nomenclature the Roman numeral ii, to indicate the chord’s supertonic function, and include a six-four-three figured bass complex above the numeral to indicate the suspended voices, complete with their various resolutions and movements within the chord itself.

My next illustration, shown in Example 3.15, is taken from the second section (“Von den

Hinterweltlern”) of Strauss’ tone poem Also Sprach Zarathustra . Here too, I argue that Strauss employs the

4 above-described predominant V 3 chord, but further clarifies its function as a supertonic through the use of the contrapuntal dimension. In short, this passage presents an extended use of the 6–5 suspension that occurs over an elongated span of music with a number of tonally-orienting chords inserted between the chord with dissonant suspensions and the consonant chord that resolves those suspensions. Where the

33 Daniel Harrison, Harmonic Function in Chromatic Music: A Renewed Dualist Theory and an Account of its Precedents (Chicago: University of Chicago Press, 1994): 36–39. 195

Example 3.15. Strauss, Also Sprach Zarathustra , mm. 38–49

example from Der Rosenkavalier above used a similar extension (the 6/4/3 complex), that chord only

resolved the fourth, leaving the sixth unresolved prior to moving to the cadence. Here the sixth and the

fourth, likewise viewed as suspensions, resolve only after a succession of intervening chords, much like the

example from “Heimkehr” above.

This section begins in A b, but quickly moves to, I argue, an extended tonicization of the submediant,

F, from mm. 39–49. Measure 39 contains what appears to be a C major-minor, or dominant, seventh chord

in second inversion: at this point there is no reason to believe it is anything but that. What follows, however,

is not a progression that fits monotonally in either F or as a tonicization of its dominant. An Fs half- diminished seventh chord is followed by a B major-minor seventh, an E-minor triad, an A diminished triad in first inversion, and finally a D major-minor seventh chord that resolves as a dominant to G in m. 32, which itself is first realized as a major triad then redirected to the more diatonic minor-triad version.

Conventional tonal practices generally do not see a half-diminished seventh chord on the lowered 196

supertonic, nor are fvii (E minor in the key of F) or iii o6 commonplace. 34 Even if we were to accept the absolute roots of these chords (F s, E, A), the progression from bII to bvii to iii is still bizarre by tonal standards.

The diminished triad on A provides a guide to the harmonic center of these chords. The root of diminished triads generally acts as one of two scale degrees: either the supertonic or the leading tone in a

given key. 35 Thus the A diminished triad could be either the leading-tone chord of B b, or it could be the supertonic of G: given the subsequent dominant-seventh to tonic gesture in G, the latter option seems to fit

the context more so than the former (an E-minor triad in B b poses similar tonally-interpretive difficulties).

Note too that the B major-minor seventh tonicizes E, and the F s half-diminished

Figure 3.12a. Deep Foreground Analysis of Example 3.15

34 As expressed in the introduction, I disagree vehemently with Charles Smith’s arguments that such chords are possible, and am more tonally conservative in my predilection to not open up tonal analysis to allowing any sonority on any scale degree. See Charles Smith, “The Functional Extravagance of Chromatic Chords,” Music Theory Spectrum 8, no. 1 (1986): 94–139. 35 It is also possible, though statistically less common, to have a diminished triad occur with the submediant as its root, with 3 modally-mixed (i.e. in C: A–C–Ef). See Edward Aldwell and Carl Schachter, Harmony and Voice Leading 3rd Edition (New York: Wadsworth, 2002): 546. 197

seventh—vii ø7 in G—is also the supertonic in E. Thus we are dealing with a heavily layered structure of tonicizations. I depict this in Figure 3.12a, a middleground view (Middleground A) of the passage, which omits the more localized intermittent harmonies in favour of showing the deeper-level expansion of G that

I am arguing.

With this in mind, I suggest that the initiating C major-minor seventh chord does not function in this context as a dominant seventh chord, but rather it functions as a chord with G as the root (and bass),

4 another example of the “predominant V 3” discussed above. Unlike in Der Rosenkavalier , here Strauss does

resolve the dissonant tones above the bass over the course of the prolongation. In some ways this example is very similar to the way in which Schubert elaborated the supertonic in D.959 discussed previously, but made much more elaborate. The upper line in Figure 3.11a depicts the contrapuntal motions of the various voices over the course of this prolongation. C, the dissonant fourth above the bass G, is neighboured locally

(not pictured) but remains active until the resolution of the D dominant seventh, where it resolves as the

local chordal seventh down by step to B n then B b. The sixth above the bass, E, undergoes a similar trajectory, though it resolves to D (passing through E b) over the dominant chord, anticipating its continuation when that resolves to the G tonic. The B b, already a chord tone, also undergoes a contrapuntal

journey, moving down to the tonic in order to allow the C to resolve as described above.

Thus at a more middleground level, I suggest that this passage presents a G six-four to five-three motion: as depicted in Figure 3.12b, a contrapuntal prolongation of the Stufe (Middleground B and C). What follows this G expansion is a half-diminished seventh chord in F, which is prolonged through a similar usage of the tonic chord with displaced upper voices, eventually reaching a stable root-position iteration in m. 49, preceded by a first-inversion dominant. This entire analysis is shown in Figure 3.12a, but, while interesting to develop new and nuanced means of understanding Strauss’ harmonic language, there is a deeper-level point to be made regarding this passage. Figure 3.12c depicts a deep-middleground reading from the beginning of this section: monotonally in A b, the expanded G, understood as such through the analysis above, acts as a passing note in this contrapuntal line, creating a linear motion from the tonic A b 198

Figure 3.12b. Deep Middleground Analyses of mm. 39–42 Figure 3.12c. Deep Middleground Analysis

down to the submediant F that expresses a series of deeper-level motion in parallel tenths. This further

enforces my contention throughout the dissertation that a thorough understanding of surface-level

harmony—even in this highly chromatic idiom—through common-practice prolongational procedures, or

extensions thereof, is indispensable in discerning the deeper-level structures of music.

Conclusion Elektra , Modernism, and Approaching Tonal Rupture

Broadly speaking, the preceding three chapters have argued that the comfort we find in the familiar is disadvantageous in the analysis of late nineteenth- and early twentieth-century tonality, and indeed the need to retain these conventions has in some ways impeded research into ways in which tonal syntax around that time exists as an extension of classical tonality. The theories I have developed over the course of these

chapters have, I hope, addressed some of the perennial issues inherent in the analysis of this music—

especially those discussed in the Introduction of this dissertation. All of my proposed perspectives, however,

share a common feature: their syntactic functions are derived from the linear displacement of what were in

earlier music melodic dissonances. The chromatic alterations of diminished-seventh chords, as noted in

Chapter 1, arise from chromatic passing motion between the diminished-seventh chord and its resolution, while the abnegating chords in this chapter arise from a melodic suspension wherein a sixth above the bass

displaces the expected fifth. 199

The examples of abnegating chords given in this chapter are mostly predicated on the notion that there are

intrinsic cues in the music that point to the abnegating analysis as one that better integrates the chord into

the prolongational processes of classical tonality, as opposed to the more conventional root-quality analysis

that often merely describes the chord’s structure. But as the nineteenth and twentieth century moved on,

these intrinsic cues became less common. For instance, the first scene of Elektra makes heavy use of dyads with an added sixth that are almost entirely unprepared. Where these chords in the above examples were usually the subject of local tonicization, or were given contrapuntal emphasis, here, Strauss eschews any such necessities. Example 3.16 depicts one such occurrence. At Rehearsal 1 (RH1), and again at RH3, the local tonic has shifted to B minor: it is never sounded in root position, and the dominant is always projected with a sixth above the bass in place of a fifth. Instead of F s–As–Cs–E, a D s is present in place of the C s,

and does not resolve to the C s.36 What makes this progression more radical than those seen previously is the lack of any sort of tonal preparation for the added-note chord: V is not preceded by an applied chord, nor even by a predominant, but rather occurs as part of an oscillation between the dominant and tonic, both in non-stable figurations. Unlike in many of the previous examples, here there is no contextually-driven impetus to immediately hear or understand these chords as being in a tonic-dominant relationship, and thus no strong phenomenological necessity to hear the abnegated-sixth chord. But, I argue that the single deeper- level context that is present—the local prolongation of B minor—

Example 3.16. Strauss, Elektra , mm. 10–13

36 Though in both instances the seventh of the V chord, E, only appears briefly, its role in creating the tritone is important. While not explicit in the vocal score, the full score clarifies that E does indeed resolve down to D in the inner parts: at RH3, for example, it is transferred between the bassoons and violas to resolve in the same register in the first and second violins. 200

is enough to suggest this as a possible reading, while acknowledging that such a reading is likely only possibly retroactively, and not phenomenologically.

I want to conclude my discussion of these surface-level displacements, abnegations, and chromatic alterations with a final example that does not fit neatly into any one of the chapters discussed herein, but which displays the same type of processes that I have been discussing. The chord boxed in Example 3.17a is the famous “Elektra chord,” which has received a number of analytic descriptions over the years. Bryan

Gilliam refers to it as “a polytonal combination of E major and D-flat major.” 37 Thethys Carpenter, whose

approach is more atonally-based in set-class notions, also refers to the chord as bitonal, though notes that it

“can be adapted to suit a wide range of tonal situations or assume their own pseudo-tonal function.” 38 The

tonal functions that Carpenter suggests are mostly sequential passages and instances where common-tone

retention “softens” the otherwise harsh sonority. 39 Lawrence Kramer describes this chord as “both monomaniacal and polymorphic,” and “is treated by turns as a colour chord, a voice-leading chord, and

(with varying degrees of fictitiousness) as a functional chord.” 40 While not going into any technical detail about the chord’s genesis, nor how it projects its function, Kramer’s description here appears to be an appropriate characterization of this chord: specifically regarding how it expresses different functions in different contexts, despite often being sounded as the same absolute pitches (E–B–Df–F–Af, or enharmonic variants thereof).

In relation to the specific instance depicted in Example 3.17a, Carpenter accounts for the chord by suggesting that it is indeed the common-tones found in the approach and dissolution of the chord that give it its intelligibility in the progression. Gilliam, on the other hand, writes that it is here a “static, unstable chord.” 41 Richard A Kaplan’s description of the most common analysis is useful to cite here. He writes:

37 Bryan Gilliam, Richard Strauss’ Elektra (New York: Oxford University Press, 1991): 71. 38 Tethys Carpenter, “The Musical Language,” in Richard Strauss: Elektra , ed. Derrick Puffett (Cambridge: Cambridge University Press, 1989): 85. 39 Ibid., 78. 40 Lawrence Kramer, “Fin-de-siècle Fantasies: "Elektra", Degeneration and Sexual Science,” Cambridge Opera Journal 5, no. 2 (1993): 153. 41 Gilliam (1991): 83. 201

The Elektra chord is generally described as "bitonal," "polytonal," or "polychordal"; it is clearly an example of what I call a compound chord. To my knowledge, every previous analysis of this chord describes it as the union of two triads, those of E major and D f major; in this interpretation, the fifth of the upper triad also functions enharmonically as the third of the lower. 42

Kaplan’s explanation for the chord ascribes to it the label of a “compound chord”: specifically, he suggests that it is a German augmented-sixth sonority over an E pedal completely dissociated from the upper four pitches (that is, the chord above the E does not bear dominant function in relation to the pedal note). This explanation, however, does not entirely suggest how the chord plays a prolongational role in the music,

Example 3.17a. Strauss, Elektra , mm. 14–26

42 Richard A. Kaplan, “The Musical Language of Elektra : A Study in Chromatic Harmony” (PhD diss. University of Michigan, 1985): 98. 202

implicitly suggesting that while it bears similarities to common-practice tonal sonorities, it does not have a

function in the same way those sonorities do. 43

A number of surrounding tonal contexts, however, suggests that the chord does function within a prolongational idiom, through it is a fairly radical one bordering on the cusp of the more modernistic atonality for which Elektra was celebrated. In understanding the function of this chord, the first thing to

note is the background structure of the first part of this scene. Shown in Figure 3.13, I suggest that on a

middleground level, the opening part of the scene composes-out a D 5–6–5 motion. The B-minor middle

section of this middleground figure receives its own local tonicization, but the local B-minor tonic only ever appears in first inversion (save for an elusive half of a beat, and there its presence is more of a melodic unfolding in the voice), thus creating the long-range continuation of the D bass. It is within this expansion of B minor, from m. 8 to m. 26, that the first occurrence of the “Elektra” chord occurs. In looking more closely at this section, and ignoring the “Elektra” chord momentarily, the tonal trajectory can be summarized as a motion from tonic to an unfolding dominant-functioning complex (2 measures before

RH3), back to the B-minor tonic at RH3.

Figure 3.13. Deep Middleground Analysis of the first 26 mm. of Elektra

43 While space restraints prohibit extensive elaboration, one way in which Kaplan’s analysis might be extended is to understand o7 the Elektra chord as vii f3 over the chordal third of its tonic acting as a pedal. Schubert’s song “Am Meer,” from Schwanengesang , in which he sounds vii o7 /ii (Cs–E–G–Bf) over a 4 pedal but resolves the leading-tone chord in the upper voices to ii 6 might be cited as precedent (as in Chapter 2). The Elektra chord could be understood as a similar phenomenon, without the resolution (and o7 indeed, later in the opera at RH232, as discussed in Chapter 1, Strauss uses the same vii f3, but now over its actual tonic pedal, C). The problem with this approach is that it only seems to describe the Elektra chord: without the resolution of the upper voices its function is left suspended (which, indeed, may be the intention), and the pedal note could adopt virtually any harmonic designation in virtually any key.

203

Figure 3.14. Analysis of mm. 21–24

As a brief aside, though one that is integral to the tonal trajectory I am analyzing, the unfolded

dominant complex is unconventional by traditional means. The V 7 of fVII chord in m. 24 resolves deceptively to V (with an abnegating sixth) in m. 28, but, as shown in Figure 3.14, the dominant triad is unfolded in the bass before reaching its vertical representation in m. 28. This unfolding progresses through a

six-four-three sonority (mm. 26 and 27, first beat), followed in mm. 26 and 27 (second beat) by what is

4 spelled in the score as B f–Df–Ef–G: at first glance V 3 of A b. A b, however, does not emerge in any sort of

functional capacity in this passage, and I suggest a half-enharmonic respelling of the chord as A s–Cs–Ef–G,

an altered leading-tone chord in the key of B minor which then unfolds down to the dominant in m. 28. In

this sense, then, the harmonic progression here is a more complex variant of the relatively common VII–V

unfolding, wherein the third and fifth of the dominant are sounded in the bass, harmonized with their own

sonorities as they unfold down to V, itself obscured through the presence of the abnegating sixth. This

dominant then resolves to a first-inversion tonic chord at RH3. 44

44 A number of surface-level chord progressions undergo repetition in this scene. By this I do not mean simply they are repeated—that alone is not of interest, but rather in these cases the function of the second chord is unrelated–or only minimally related—to the first chord, but the repetition suggests a functional relationship. I suggest that in reality, these repetitions are harmonic illusions, and can, for the purposes of analysis, simply be condensed into one iteration of the progressions in question (see, for example, three measure before RH2, the case at RH3, and RH7). 204

Where then does the “Elektra” chord fit into this framework? I suggest that in this specific instance,

it functions as a version of the supertonic preceding the tonicized unfolding of the dominant chord

described above.45 The pitches of the Elektra chord are C s–E–Es–Gs–B, which, when spelled and stacked as such suggest a type of chord often referred to as having a split third. In this case the split third creates a clash between a minor seventh chord—ii 7 in the key of B minor—and a dominant-seventh chord—V7/V in the key of B minor—as depicted in Figure 3.15a. These two chords share three out of four pitches, the divergent pitch being the chordal third. Conventional Schenkerian approaches to the progression from ii to

V/V usually regulate the chromatic pitch (s4 ) as a passing tone between the subdominant pitch and the

Figure 3.15. Analysis of the “Elektra” chord as Derived Through Linear Displacement

a) Proposed derivation of the “Elektra” Chord.

b) and c) Linear Displacement of Passing Tone s4 to create Elektra Chord.

45 This is not to say there it cannot function differently in other situations. 205

dominant. Here, as shown in Figure 3.15b, that passing tone is understood as being displaced in a linear

fashion, much in the same way that chromatically altered pitches of diminished-seventh chords were,

sounding concurrently with the ii 7 chord to create this sonority. 46 Functionally-speaking, this clash does not

in any virulent way destroy the tonal logic of the progression: ii 7 and V 7/V often occupy the same tonal function, and indeed often occur one after the other as part of a drive towards the dominant. What it does achieve, however, is to introduce a modicum of referential doubt into the chord: ii 7 finds its reference

directly from the tonic, while V 7/V, as I have discussed in the Introduction to the dissertation, finds its reference indirectly from the dominant. The raised s4 introduces the potential for a FIP directed towards the dominant, which clashes with the more diatonic predilections of the normal 4. In this sense, the chord is still polytonal, but not in the way those who describe it as two juxtaposed triads see it. Rather, its polytonal flavour comes from this clash between its modes of referentiality. 47

This understanding also helps to account for the F-minor sonority that precedes the Elektra chord.

The three measures preceding the onset of the Elektra chord oscillate between the first-inversion B-minor

tonic triad and a chord spelled A f–C–F: this chord does not have any strongly, nor easily, articulated

function in B-minor, but respelled as G s–Bs–Es can be understood as a further usage of the abnegating-

sixth chord prevalent in this scene. Under that spelling, it can be understood as V+6 of C s, Cs being the root

of the Elektra chord in my proposed analysis. While the voice leading here is difficult to pinpoint with

precision because of the number of instruments that either drop out or enter upon the sounding of the

Elektra chord, tracing pitches registrally, as shown in Example 3.17b—an excerpt from the full score—

provides some evidence for this reading. The B s (spelled C n), is sounded in the same register in the trumpet

in D (and also an octave higher in the third violas). The second and third violas take over the resolution of

46 Whether this was or was not the method by which Strauss arrived at this sonority I cannot say, but its function certainly suggests this as one possible reading. 47 This reading, in turn, may have hermeneutic implications for the opera, and more specifically for the titular character. One possible interpretation is that her quest for revenge pushes her forward, the way the V 7/V chord would push more forcefully towards the dominant, while some part of her conscience—perhaps personified by her sister Chrysothemis and her own desires for a normal, peaceful, life—conflicts with those desires. 206

this pitch: the seconds have a D b (C s) while the thirds have a B n. Thus the leading tone B s resolves in both of the conventionally tonal ways a leading tone can resolve: up by step to the root of the local tonic, and

Example 3.17b. Elektra, Full score. 2 mm. before RH1 to 2 mm. after RH1

(continued)

207

down by semitone in a frustrated resolution, but one that is entirely conventional when resolving a

dominant-functioning chord to a subsequent chord with a seventh. In this sense, then, the entire passage,

6 6 beginning at RH1, can be seen as a prolongation of B minor. As shown in Figure 3.16, a deeper-level i –ii 5–

6 6 V–i progression underlies this passage, where the ii 5 chord is embellished by its own applied dominant

(with an abnegating sixth) and is further obscured by the displacement of the chromatic passing tone s4 which sounds simultaneously with it. Likewise, the dominant is obscured through the complex variation of

the VII–V unfolding described above.

208

Figure 3.16. Analysis of Example 3.17a

While its function may not always assume this type of displaced ii 7 + V 7/V combination, a second instance in which the Elektra chord can be seen to express this function occurs in Elektra’s monologue.

Locally prolonging a C-minor tonic, the passage beginning at RH48, shown in Example 3.18, redirects towards the dominant of C, G. 48 The A-minor triad at RH48 can be viewed as the pivot, both vi in C, but

also ii in G, progressing to the Elektra chord two measures before RH49. This Elektra chord is prolonged

for nine measures, resolving to a chord spelled G b–Bb–D–Ab. While I understand this as a dominant chord of G, like in the passage at the outset of the opera discussed above, this dominant is also obscured. Here my analysis divorces the bass from the upper voices. I understand the bass in this progression as participating in an unfolding from b3 to the tonic, while above this unfolding the augmented dominant of G (D–Fs–As) sounds. But in addition to the raised chordal fifth A s (spelled B b), Strauss also sounds the lowered chordal fifth A b. This dominant, then, like the Elektra chord, can be understood as a juxtaposition of what in earlier

48 My broader analysis here generally corresponds to Kaplan’s analysis: his analytic graph of RH50 and onward begins with G as the structural pitch, preceded by a prolonged Elektra chord. See Kaplan (1985): 135–142. 209

Example 3.18. Strauss, Elektra , RH48–RH51

(continued)

210

tonal practice were understood as linear embellishments: the genesis of both the A s and the A b is

understood to be the linear displacement of passing tones emanating from the (absent) diatonic A n.49 What

distinguishes this case from the more common practice is the use of both the raised and lowered chordal

fifth simultaneously. My analysis, shown in Figure 3.17, thus suggests an expanded ii–V–I progression in G

(within a larger C-minor). The A-minor chord at RH48 begins as ii of G, a seventh is added two measures

later and the chord is placed into first inversion, but when this happens s4 also appears: what should be a

6 chromatic passing tone instead sounds simultaneously with the ii 5 chord. Here the function is clarified due to the presence of the unaltered supertonic chord prior to the Elektra chord; it is easier, in this case, to

49 A similar instance of double alteration in Strauss’ work can be found in Strauss’ 1905 opera Salome (Scene 1, 2 mm. before Rehearsal 7), in which Strauss alters the chordal third of a viio7 chord, both raising and lowering the chordal third chromatically (the same scale degree as the chordal fifth of a V chord). Daniel Harrison notes a similar instance of double alteration in Schoenberg’s Chamber Symphony from 1907. Daniel Harrison, “Supplement to the Theory of Augmented-Sixth Chords, Music Theory Spectrum 17, no. 2 (1995): 186. 211

Figure 3.17. Middleground Analysis of Example 3.18

understand the Elektra chord as being generated through linear displacements and additions to this initial

supertonic triad.

Elektra is frequently cited as Strauss’ most modernist work, and his apparent step back from this

syntax in subsequent operas was at times considered a disappointment. 50 And yet, as I have shown above, tonality—a rugged, strained, and nearly broken tonality to be sure, but tonality nonetheless—remains, I believe, the cornerstone on which even Elektra is built. 51 But it is in truth a very tenuous tonality: the

abundance of abnegating sixths, chromatically-altered diminished-seventh chords used without any sort of

preparation and in more contrapuntal manners (i.e. as part of the unfolding of V), and the Elektra chord

itself all push the tonality of this opera close to the point of atonal rupture. Indeed, some might argue it goes

beyond that. But, as I hope the previous discussion has shown, the tonal processes that underlie these

extensions remain present, if not entirely apparent: it is merely a codification of the syntax of this harmonic

language that scholarship lacks.

50 Michael Kennedy, Richard Strauss: Man, Musician, Enigma (Cambridge: Cambridge University Press, 1999): 4. 51 Lukas Hasselböck has argued that even though Strauss stuck to tonality, even his mid-period Lieder (ca. 1900) display instances of chord progressions that do not appear to adhere to the conventions of tonality. He thus argues that Strauss was no less modernistic than his contemporaries such as Schoenberg, but rather his syntax was simply less grating on the ear, couched as it was in the familiarity of tonal process. Lukas Hasselböck, “Beiträge zur Untersuchung der Harmonik in den Strauss-Liedern (Der Einsame – Im Spätboot – An die Nacht),” Richard-Strauss-Blätter 43 (2000): 179–186. 212

Over the last three chapters I have argued for a fairly radical re-envisioning of tonal theory to account for the chromaticism and harmonic syntaxes found in the late nineteenth and early twentieth centuries, particularly in the works of Wagner and Strauss. I would, however, argue that it is not so radical a departure, but rather represents a shift in analytic focus, albeit one that grates against the commonly held historic narratives regarding tonality and its dissolution in the works of Wagner and Strauss leading into the twentieth century.52 In classical tonality it is far simpler to understand chords as objects because the music

employs such a limited set of pitches and chords in a generally consistent syntactic way. The extended

chromaticism of the late nineteenth century negates that simplicity. Objects that appear to be conventional

and recognizable, such as dominant-seventh chords, are easily understood as those things if we are resigned

to seeing them only as inert objects that are something. But it is often the case that such apparent objects

occupy spaces wherein understanding them as such does little to explain how they function tonally, and amounts to little more than a description of sonority and root. Instead, I have proposed that analysis must take a step back and divest itself of the comfort it finds in the familiar. It is easy to say that a triad is a triad, or that a half-diminished seventh sonority is a half-diminished seventh chord, but such labels, outside of the safety of classical tonality, do little to elucidate how the processes of tonality and prolongation occur in the harmonically complex works of Wagner and Strauss. Instead, I have argued that function is a product of

both sonority—in the form of specific univalent intervals—combined with motion, in the form of resolving

these univalent intervals according to the norms of classical tonality. This approach offers a synthesis

between the vertical and the horizontal domains of music that reveals a remarkable dialogic relationship

between the extended chromatic idioms of the late nineteenth and early twentieth centuries and classical

tonality. As mentioned in the Introduction to the dissertation, the overall goal is to demonstrate that the

processes of classical tonality are still prevalent in these works, despite the misgivings of contemporary

52 As noted in Chapter 1, several scholars have described sections of Wagner’s Parsifal as expressing atonality. Likewise mentioned in Chapter 1, a similar perspective regarding whether the narrative of tonality being “abandoned” shortly into the twentieth century is entirely accurate forms the underlying conceptual thread of the 2012 volume Tonality 1900–1950: Concept and Practice , ed. Felix Wörner, Ullrich Scheideler, and Philip Rupprecht (Stuttgart: Franz Steiner Verlag, 2012). 213

discourses, and I believe the processes I have outlined are a step towards reconciling this music with the tonal-prolongational practices of its classical precedents.

Chapter 4 Leitmotivic Auskomponierung Structural Coherence in Late Nineteenth- and Early Twentieth-Century Music

The previous three chapters focused on understanding tonal prolongation on the musical surface and proposed ways in which the abundant chromaticism and dissonance that forms part of the late nineteenth-and early twentieth-century tonal syntax could be integrated into prolongational processes and procedures established in classical tonality. What I proposed in those chapters—that function in late nineteenth-century music is not an inherent property of chords or scale degrees, but rather a product of how

they behave—applied almost exclusively to the musical surface. With these new tools available to

demonstrate how Stufen , or more broadly tonalities, are prolonged, this chapter now turns to applying these

concepts in investigating relationships between tonalities, or what is more commonly referred to as middle-

or deep-level structure. As Cohn notes, analysis must “consider how the local keys (or, from a different

perspective, the triads prolonged by local spans) relate to one another.”1 But while the previous chapters argued that harmony on the musical surface can be understood as generally consistent with classical precedents, albeit in a more chromatic manner, this chapter suggests that the ways we understand deeper- level structure in late nineteenth- and early twentieth-century music can differ significantly from the commonly held structuring principles of eighteenth- and early nineteenth-century music.

Deeper-level relationships in the lengthier, larger, and more chromatically complex music of the late nineteenth and early twentieth centuries have been a source of some consternation for scholars. The different types of larger-scale tonal structures that begin to emerge in the late nineteenth century challenge

the assertions of the monotonally oriented Schenkerian approach to analysis, although as David Kopp

notes, “this has often been interpreted as a sign of weakness or inferiority in the music itself rather than due

to any inappropriateness of the model[s].” 2 Julian Horton likewise addresses the appropriateness of

1 Richard Cohn, Audacious Euphony: Chromaticism and the Triad’s Second Nature (New York: Oxford University Press, 2012): 2. 2 David Kopp, Chromatic Transformations in Nineteenth-Century Music (Cambridge: Cambridge University Press, 2002): 1. 214

215

Schenkerian approaches for analyzing late nineteenth-century music, and Bruckner’s in particular. Horton writes:

But what exactly is the status of works, or materials within a work, standing outside the Schenkerian ‘index of common practice’? Do they inhabit a different, chromatic tonal practice? [If] the non-Schenkerian aspects of the music form part of a different kind of tonal practice, then the question arises as to what the basis of this practice is, and we are left with the problem of theorising a common-practice chromatic tonality before we are fit to the task of analysing Bruckner’s music. 3

Because Wagner scholars and Schenkerian theorists, as Darcy writes, “appear to have tacitly agreed that the

complete Schenkerian model is inapplicable to Wagnerian [or Straussian] opera,” scholars have been forced

to find other ways of discussing this music. 4

Robert Bailey’s notions of different types of tonalities in Wagnerian opera form some of the most commonly cited methods of analysis. 5 In his monograph on Wagner’s Siegfried , Patrick McCreless develops

Bailey’s ideas in further detail. Bailey/McCreless propose that there are four categories of tonal strategies

operative in late nineteenth-century repertoire. The first is what they term “classical tonality.” McCreless says:

Classical tonality is epitomized in the works of the Baroque, Classical, and early Romantic composers, and is codified theoretically in the works of Heinrich Schenker. [Classical] tonality, as extended by Wagner, is operative most prominently at the foreground and middleground levels, for it constitutes the measure-to-measure tonal language of many of the essentially diatonic sections that prolong a single tonal center. In such passages all the trappings of classical tonality are usually present: diatonic, though (although not necessarily exclusively diatonic) harmonic progressions, prolongation of diatonic scale degrees, and often closure through dominant-tonic cadences and 3-2-1 melodic progressions. 6

The second category is termed expressive tonality, which involves taking large musical units and transposing

them up or down to increase dramatic tension. Bailey describes it as “an outgrowth of sequential melodic

3 Julian Horton, Bruckner’s Symphonies (Cambridge: Cambridge University Press, 2004), 94. 4 Warren Darcy, Wagner’s Das Rheingold (New York: Oxford University Press, 1993): 54–55. 5 See Robert Bailey, “The Structure of the ‘Ring’ and its Evolution,” 19 th -Century Music 1, no. 1 (1977): 51–55, and Robert Bailey, "An Analytical Study of the Sketches and Drafts, in Richard Wagner, Prelude and Transfiguration from "Tristan und Isolde," ed. Robert Bailey (New York: Norton, 1985): 113-46. 6 Patrick McCreless, Wagner’s Siegfried (Ann Arbor: UMI Research Press, 1982): 89. 216 construction. The repetition or recall of a passage is transposed up to underscore intensification, or shifted down to indicate relaxation. These shifts are usually made by a semitone or a whole tone.” 7

The remaining two categories are more pertinent to deeper-level structural considerations.

“Associative” tonality refers to the choice of tonality as not necessarily having an internal tonal coherence, but rather as being associated with a particular dramatic significance. McCreless suggests: “The actual musical means of expressing the relevant emotion…[is through] the establishment of a tonality appropriate to the desired emotion.” 8 He continues: “The emotional content of a passage is thus symbolized by the choice of tonality. The development of dramatic action and the calling forth of other emotions suggest corresponding changes of key…” 9 McCreless ultimately concludes that tonal structure in Wagner’s operas is a result of a dramatically referential array of keys operating as the background structure, and he asserts that most of the keys are “associatively determined” through their relationship to the drama. 10 The drawback to

this approach is that it shears the music of independence, and forces musical structure to be seen as a by- product of the dramatic situations in the libretto, rather than the two co-existing in a synergetic manner. 11

The final strategy is directional tonality, which applies to units of music that begin in one key and end in another. McCreless describes this process as “the construction of a formal unit not as a prolongation of a single key by means of the elaboration of its tonic-dominant polarity, but as a progression from one structural key at the beginning and another at the end.” 12 Deborah Stein’s description of this process, in her

study of extensions of tonality in Hugo Wolf’s Lieder , extends this definition further. She describes directional tonality as two keys that are used as follows:

One key functions as an opening tonality; and after the first key is clearly established as a tonic, a transformation occurs whereby the initial tonic becomes a nontonic function within

7 Bailey (1977): 51. 8 Patrick McCreless, Wagner’s Siegfried (Ann Arbor: UMI Research Press, 1982): 87. 9 Ibid., 87. 10 Ibid., 95. McCreless’ assertions regarding dramatic associativity should be noted as coming about through their use in the opera. That is to say D f becomes associated with Wotan and Valhalla in the Ring cycle through its initial associations. My concern is that simply understanding musical structure as based on this principle relegates the musical structure to merely a by-product of the drama, unable to exist on its own. 11 As Carolyn Abbate and Roger Parker suggest, “Analyzing opera should mean not only ‘analyzing music,’ but simultaneously engaging, with equal sophistication, the poetry and the drama.” Carolyn Abbate and Roger Parker, “On Analyzing Opera,” in Analyzing Opera: Verdi and Wagner , ed. Carolyn Abbate and Roger Parker (Berkeley: University of California Press, 1989): 4. 12 McCreless (1982): 89. 217

a second tonality. The piece then concludes in the second key. The ultimate effect of directional tonality is twofold: first, the original tonality loses its identity as a tonal focus in deference to the second tonality; and second, the piece is heard as beginning and ending in two different keys. 13

Though she notes the distinctions can often be subtle, Stein suggests a number of criteria for differentiating directional tonality from works that are monotonal but simply begin off-tonic. Most important for the present study are her requirements that “the opening tonality must be adequately defined as a tonic,” and

“the functional transformation itself must involve a change from tonic to nontonic, to distinguish that process from simple reinterpretation, where the function of a harmony is merely reconsidered.” 14

It is this last category of directional tonality which is of interest, as it represents one of the greatest

challenges to the Ursatz -based Schenkerian approaches to tonality. 15 While some attempts have been made to find ways of adapting Schenkerian approaches to account for works that begin in one key and end in another, one might rightly question these approaches from two different angles. Firstly, as William Marvin suggests:

According to McCreless’ definition, the extended uses of tonality are all defined against the traditional Schenkerian conception of a tonic-dominant axis. Therefore, it seems logical that a prerequisite to the reasonable application of these tools is a complete Schenkerian reading of the music; only when classical tonality breaks down is it appropriate to invoke expressive, associative, or directional explanations.” 16

Secondly, one might suggest that any approach attempting to fit such works into a Schenkerian monotonal framework runs the risk of normalizing, or even trivializing the uniqueness of the music in question. As

Marvin points out, “given the monotonal nature of Schenker’s theories, double-tonic analyses, as well as most expressive tonality, cannot exist within the Schenkerian universe without modifying fundamental aspects of the theory.” 17 By extension, doing the opposite, and fitting pieces exhibiting such properties into the Schenkerian mold is likewise untenable. But how, then, to determine, analyze, and discuss larger scale

13 Deborah Stein, Hugo Wolf’s Lieder and Extensions to Tonality (Ann Arbor: UMI Research Press, 1985): 143. 14 Ibid., 144. 15 Stein (1985): 145, for example, suggests that there is a disparity between Schenker’s monotonal schemata and directional tonality, though she argues that the difference is not as vast as some believe, though she admits it requires a number of extensions to Schenker’s ideas, or applying Schenker’s ideas idiosyncratically (not that this is a bad thing). 16 William Marvin, “Tonality in Selected Set Pieces from Richard Wagner’s Die Meistersinger von Nürnberg : A Schenkerian Approach” (PhD diss., Eastman School of Music, 2001): 25–26. 17 Ibid., 27. 218 structure? On the one hand, we gain nothing from simply stating that no structure exists because it does not

conform to the orthodox Schenkerian models; on the other hand, forcing a piece that is not monotonal into

a Procrustean bed of monotonality leaves little room to discuss the nuances of the piece. As Cheong Wai-

Ling notes:

[Bailey’s] concept of ‘directional tonality’, in contrast to Schenkerian theory, specifies little more than that the music begins and ends in different well-defined tonal areas, leaving questions as to how the different tonal areas are composed-out (‘diatonic tonal space’? ‘chromatic tonal space’?), how the transition between them is achieved (‘mediating harmonies’?), how coherence is provided (‘dyadic unification?’), etc., largely unanswered. If, as William Benjamin has pointed out, Bailey’s concept of ‘directional tonality’ represents only one of the manifold alternatives to monotonality, it should be stressed further that Bailey’s hypothesis—being of a very different nature from Schenker’s theoretical framework—is not an alternative to the Schenkerian analytic approach. 18

Of particular interest is Cheong’s assessment that despite the directional nature of the deeper-level structure,

the tonalities in question remain “well-defined,” meaning that they exhibit their own internal tonal

coherence. While I hope that the preceding chapters have made progress in addressing the first of Cheong’s

concerns—regarding the ways in which these tonalities are constructed on the harmonic surface, or what

McCreless refers to as the “measure-to-measure tonal language”—the question of how coherence between these areas is understood remains largely unanswered in nineteenth-century works, and will be the focus of this chapter.19

Further complicating the matter is the diffusion of structural diatonicism, and with it the clarity with which analysis can relate highly chromatic tonal centers to a global tonic via traditional Schenkerian methodologies. In Audacious Euphony Cohn presents an excerpt from Schubert’s B f-major Piano Sonata

(D.960) as an example of a piece in which he claims coherence on a middleground level “is not entirely determined by the logic of classical diatonic tonality.” 20 Cohn’s claims arise from what he views as an inability to coherently “locate” each key—represented as a triad—within the tonality of B f. Cohn’s reasons

18 Cheong Wai-Ling, “Conference Report: Alternatives to Monotonality,” Music Analysis 8, no. 3 (1989): 357. Cited in Marvin (2001): 27–28. 19 Some authors, such as Stein (1985), Bailey (1985), or Krebs (1996) have proposed ways of extending conventional Schenkerian concepts so as to reconcile Schenkerian monotonality with the directional nature of the tonality of certain nineteenth-century works. 20 Cohn (2012): 4. 219 for this stem in large part from the inability of conventional deeper-level analysis to relate the G f-major, Fs- minor and A-major tonalities to B f simultaneously. And his claim is entirely logical: if F s is understood as a minor-mode inflection of the preceding G f—itself fVI in B f—then, Cohn claims, the A must be heard as

Bff in order to relate it to Bf. But understanding A as B ff requires hearing the subsequent B f as C ff , which

Cohn rightly notes is irrational since this is certainly the tonic. Cohn uses this assertion as a launching point for a discussion of the rationale behind gauging triadic distance through measurements other than classical diatonic methods, and the necessity for the neo-Riemannian system he proposes. However, as has been a thread throughout this dissertation, breaking from tonality seems an overreaction, when there remain, in my view, other ways of discussing deeper-level tonal structuring than conventional Schenkerian monotonality.

Why is it necessary to relate every tonal event to a single tonic as a type of enlarged chord progression?21

This chapter investigates ways in which the difficulties inherent in analyzing structure in late

nineteenth- and early twentieth-century works outlined above can be reconciled within a tonal-

prolongational analytic framework that is based in, but loosely adapts, Schenkerian methodology. I begin with a discussion of the Schenkerian Ursatz , and scrutinize both Schenker’s organic claims to unity in his formulation of the Ursatz concept, and the applicability of the Ursatz on the larger scale to both classical and nineteenth-century tonal analysis. Ultimately, I propose that while the Ursatz works well as a general outline for many works in the classical style, and is an excellent tool for modeling phrase-level tonality, it is not an axiomatic aspect of large-scale tonal structure, and should not be considered a defining feature of what is or is not tonal.. Instead, I suggest that some of Schenker’s earlier conceptions of tonality, namely a succession of smaller scale composed-out secondary tonalities that relate to one another as Stufen , is a more engaging lens through which to discuss tonal structure; one that does not rely on the same questionable ontological assertions on which Schenker’s Ursatz axiom rests.

Having suggested this move away from the Ursatz , I contend that analysis must recognize that there exists a critical difference between the logic that governs chord progressions at the harmonic surface whose

21 I will return to the Schubert example later in this chapter. 220 function is to prolong deeper-level Stufen , and the logic that governs the ways in which these deeper-level

Stufen interact; that the Stufen being prolonged do not necessarily exhibit the same logic of harmonic progression that chords at the foreground do. 22 I propose that rather than viewing middleground-level

tonalities as composed-out triads, another way of viewing these units is as composed-out fundamentals,

reducing the concept of a key even further to the generating fundamental of its scale. As such, I argue that

prolonged, deeper-level Stufen are representations of the tone that is their generative fundamental, and when

reduced to that fundamental pitch the succession of tonalities can be viewed as creating a melodically

oriented succession of tones that often project an enlargement of some important surface-level melodic

motif. In this sense, the relationships of the secondary tonalities to the tonic of a given work exist in what

Leonard Ratner defines as a more solar, rather than polar, relationship. 23 I conclude by proposing that one way of understanding coherence—which, to clarify, I do not use as a synonym for “unity,” but rather as a way of describing that a work has some kind of logic that governs its construction at various levels—within certain late nineteenth- and early twentieth-century works comes from understanding this deep-level progression of generative fundamentals as a composing-out of a prominent motif, or Leitmotif , found at the musical foreground. To demonstrate this concept, I undertake deeper-level analysis of both the Prelude to

Wagner’s Parsifal , and the first scene of Strauss’ Salome . In this sense, these works, as well as others that

often defy the traditional tonal criteria for “unity” or “coherence,” can be understood as expressing an

internal logic that does not require the extrinsic notions of the Ursatz , nor organic unity, in order to be

described as coherent.

I The Schenkerian Ursatz : Organicism, Ontology, and Analytic Viability

Novel to Schenker’s approach was his assertion of organic unity across all levels of structure. One

might view Schenker’s perspective as one which took the syntactic norms for a smaller musical unit, such as

22 Carl Schachter likewise problematizes this approach. See “Analysis by Key [1987],” in Unfoldings: Essays in Schenkerian Theory and Analysis , ed. Joseph N. Straus (New York: Oxford University Press, 1999): 143. 23 Leonard Ratner, Classical Music: Expression, Form, and Style (New York: Schirmer Books, 1980): 51. 221 the phrase or section, and exported them onto larger-scale structure. This resulted in a conceptual parallelism between foreground, middleground, and background structures: where most tonal units exhibit some sort of T–(PD)–D–T structure at the foreground, so too, according to Schenker, did the deeper levels of musical structure. As such, Schenker concluded that each successive level of structure must be understood as a transformation, or elaboration, of that deep-level background structure in order for a work

to exhibit organic unity. While it is true that a high percentage of tonal music begins on tonic, and ends with

a dominant-to-tonic progression, does this truly imply that the deep-level structure of all tonal music can be

fundamentally reduced to the Ursatz , and, even more importantly, should it? Does Ursatz -based analysis

encapsulate the dynamic and intricate relationships between the secondary tonal centers, or is the Ursatz

merely an interpretive step that Schenker takes in order to create the organic unity that he valued so highly

in music?

Schenker’s proclamation of the Ursatz as Urform , as Eugene Narmour has pointed out, is a

problematic one because it suggests that the goal of analysis is to demonstrate a preconceived structural

unity. As such, it turns Schenker’s theory into a proscriptive approach, exalting the Ursatz as an a priori

unifying imperative, a procrustean mold into which all musical structure can be shoehorned. 24 Narmour

suggests that “to permit I and V to operate [as privileged elements] is to allow certain favoured relations to predetermine structural features of certain individual works of art.” 25 And, if the music cannot be so described,

and does not follow these predetermined features, then the implication is that it is bad music. 26 In his later works Schenker is very clear in his insistence that every aspect of tonal music stems from the Ursatz : “my theory shows that music is a self-contained unity in every respect…the [ Ursatz ] constitutes a unity; [this]

24 Eugene Narmour, Beyond Schenkerism (Chicago: University of Chicago Press, 1977): 15. 25 Ibid., 15. Emphasis Narmour’s. Narmour overstates this somewhat: certainly I is a privileged element as it is the primary point of reference. On a more local level V is also privileged as it is a syntactic norm in creating a cadence, though Narmour’s point is accurate when it pertains to deep-level structure. 26 Abbate and Parker, for example, write: “Many critics assume a priori that the musical object, to be of value, must be unified in certain conventional ways.” Abbate and Parker (1989): 3. Adorno likewise takes Schenker to task for his axiomatic approach, writing: “Schenker repeatedly attacked Debussy in a very shabby manner, and accused him (and others, including Richard Strauss) of the destruction of the Fundamental Line, without being able to see that…there are criteria for inner consistency and musical cohesion which are entirely different from the requirements of what he called the Fundamental Line.” T. W. Adorno, “On the Problem of Musical Analysis,” trans. Max Paddison, Music Analysis 1, no. 2 (1982): 175. 222 unity alone makes it possible for voice-leading transformations to take place in the middleground and enables the forms of the fundamental structure to be transferred to individual harmonies.” 27 Richard Cohn writes that when “Schenker crowned the Ursatz as the sole source of all compositional unity, [all] other compositional parameters lost their autonomy as independently functioning modes of organization,” and instead they were turned towards serving the ideal of the Ursatz .28

This differs from Schenker’s initial perspective. As Cohn suggests:

Schenker [around 1905] began also to view the Stufe as a source of unity for all of the events falling within its span. Here, for the first time, Schenker considered unity as the product of the relationship between an included smaller part and an including larger part. The subsequent stages of Schenker's development were marked by a detailed exploration of the relations between smaller and larger part (via an intensive study of counterpoint); by recognition of the recursive potential of these relations, and the multilevelled design yielded thereby; and eventually (in the early 1920s) by an immense expansion of the scope of the larger including part. 29

Cohn’s description implies that Schenker’s earlier view did not recognize a single overarching structure on one level over an entire work, but instead related a sequence of smaller units of music (phrases, sections) which displayed the syntactic prolongational procedures on this more local level. Ultimately Schenker,

desirous of relating the prolongations of secondary tonalities in some way, came to subsume them as

products of the whole, rather than constituents that created the whole. In this sense, in deeper-level analysis

of musical structure, a secondary tonality of a piece—a B section in vi, for instance—can be, and often is,

subordinated to a single dominant chord—itself more often than not part of a prolongation of I, and not a

tonality in its own right—at the end of a piece, simply because that dominant chord fulfills the overarching

harmonic structure that Schenker required for his theories of organic unity. 30 While the vi, like anything else, is necessarily subordinated to I, and in a more local prolongation would likewise be subordinate to the

dominant, it is not clear that such parallelisms need to exist at the deepest levels of structure. Indeed, it

27 Heinrich Schenker, Free Composition [1935], ed. and trans. Ernst Oster (New York: Longman, 1979): 9. 28 Richard Cohn, “The Autonomy of Motives in Schenkerian Accounts of Tonal Music,” Music Theory Spectrum 14, no. 2 (1992): 153. 29 Ibid., 152. 30 To clarify, I am speaking here of structure on the deepest level. Again, prolongation on the harmonic surface, or near-surface, is different: there, a vi chord—even one prolonged by its own dominant—still functions in a relatively subordinate role to functional dominant chords (this becomes more and more difficult to disentangle in late nineteenth-century syntax, as chords on the harmonic surface take on characteristics of prolonged Stufe , expanded as they can be by their own internal tonal progressions). 223 remains a strangely bizarre mindset of music theory that a single chord can be promoted to a hierarchically superior role than a tonality that receives emphasis through its use as a key area (often reinforced with a cadence). Yet this is precisely what Schenkerian analytic methodologies argue, namely that at deeper structural levels, “in contrast to the structural arpeggiation of III and V, tonicizations of other scale steps have only subsidiary, contrapuntal functions.” 31 But this perspective is entirely determined a priori to any

analysis or hearing of the work.

And indeed, one of the challenges of late nineteenth- and early twentieth-century tonality is a general

increase of proportion in musical units, such that it becomes difficult to determine what is a chord, what is a secondary tonality, and where to place analytic weight. Where in classical tonality a local progression of I – vi – ii – V – I is commonplace, late nineteenth- and early twentieth-century syntax might take such a progression, and prolong the vi, the ii, the V, or any combination thereof for large spans via tonicization, such that each begins to seem like its own tonal center. Ultimately there is no definite methodology for determining what is or is not part of a deep-level structure: such considerations must be left to the analyst, though things like relative cadential articulations, strength of the prolongation, and phrase structure can all

offer guidance as to whether something is its own structural key, or whether it is a discursive expansion of a

more local chord. For example, in the analytic graph of the opening of Scene 1 of Strauss’ Salome , shown in

Figure 4.1, following the opening C s chord D becomes a secondary tonality. It is prolonged via an

arpeggiation through its mediant F, which is in turn prolonged through its own mediant. This nesting of

common tonal structures within larger tonal structures is challenging when determining which is more

important in terms of tonal structure. While F receives its own prolongation, the cadential articulation at

RH3 is undermined by the continuity of the vocal line which ultimately closes with the V b9 – i progression in

D at RH4, suggesting that the prolongation of F is a structure nested within the prolongation of D, despite its length (and likewise the brief tonicization of A is weaker and short-lived compared to the F prolongation in which it is nested). Ultimately over the course of the scene the D itself becomes a nested structure,

31 Stein (1985): 142. 224

Figure 4.1. Analysis of the opening of Strauss’ Salome (to RH4)

functioning as a deep-level neighbour tone to C s, and creating a deep-level double-neighbour structure around C s with the subsequent tonality of C (B s), an example of at least four different levels of musical structuring within a prolonged tonic. 32

The above-mentioned C s–D–Bs–C structure is certainly not of the conventional Ursatz variety, and yet the music in the first scene of Salome remains, in my view, unassailably tonal. Such issues call into question the value of the Ursatz as a foundational, or unifying, principle in analysis, especially that of late nineteenth- and early twentieth-century chromatic tonality. Understanding relationships between keys on deeper levels is restricted by the necessity of fitting these keys into the Ursatz schemata, and ultimately such analysis is only able to make statements regarding how the same structure is transformed in different ways in every piece of music, rather that understanding each work as having its own mode of expression and construction related to its intrinsic motivic properties. To this end, I concur with Narmour’s assessment that the Ursatz should not be taken as axiomatic:

Instead of seeing a descending series of transformations generated from a postulated organizing original whole (the Ursatz ), we might view a given system as generated from the

32 Analysis of this scene is continued below. 225

bottom up. In that case, the characteristic implications of the individual parameters would be taken as the postulates , instead of the combining action of the realized whole, and we would look for rule of dynamic structuring rather than for rules of dynamic wholes (italics belong to Narmour). The whole would therefore be conceived as a by-product of this structuring, rather than the organizing activity of the whole. 33

What Narmour describes is the notion that deeper-level structure arises from the various activities of the

musical surface and middleground, rather than understanding the surface and middleground as

consequences of a predetermined background structure. 34 This is not to say that the more general notion that a tonality can be prolonged over a large musical and temporal span is faulty; indeed most tonal understandings of music are predicated on the notion that a tonality remains operative at some level. Rather,

I am suggesting that if deeper-level tonal relations need not be defined in terms of the spinning out of a single tonality over the course of a piece, other approaches to tonal relationships at deeper levels of structure become possible. And this move away from the Ursatz as the governing axiom behind deep-level tonal logic proves especially useful, as I will demonstrate in this chapter, when applied to the music of

Wagner and Strauss in the mid-to-late nineteenth and early twentieth centuries.

Unlike many Schenkerian analyses, Felix Salzer’s approach is notable in how it describes the relationships between these units at various levels of structure:

In recognizing that a certain passage or section of a composition, if separated from the total organism, has its own basic direction or structure, we at the same time acknowledge that it has its own tonality. This passage, when linked up again with the complete composition and heard in relation to the whole, loses any individual status and becomes a prolongation of an organism of a higher order. 35

Salzer’s recognition of the ways in which secondary tonal areas—either chords that undergo tonicization at

the musical surface, or secondary keys at a middleground level—can be constructed independently and then

link-up to deeper-level structures, is similar to the approach I am advocating. However, like most

Schenkerian approaches, despite Salzer’s position as expressed above, his analyses—at least those of the

conventional Schenkerian canon—often remain mostly entrenched in the Schenkerian Ursatz concept, in the

33 Narmour (1977): 122. 34 Narmour’s work ultimately moves away from tonal structure and into phenomenological (almost cognitive) approaches to analyzing music, which I do not follow. 35 Ibid., 227. 226 sense that the highest-order organism is always the I–V–I Ursatz , and as such everything is ultimately a by- product of this structure. For example, Salzer’s analysis of Chopin’s Mazurka Op. 17 no. 2, reproduced as

Figure 4.2, assigns to identical dominant chords in the A and A’ sections different levels of structural weight, despite their occurrence in identical musical contexts prolonging the tonic Stufe . Owing to the organic impetus that drives Schenkerian theory, and through this the necessity of understanding the deeper-level structure as the progenitor of all other levels of structure, including the harmonic surface, Salzer’s analysis accords the penultimate dominant in the A section only a local structural weight (as evinced by the solid note head), whereas the identical dominant in the A’ section is elevated beyond the local level and given structural weight at the level of the entire piece (as evinced by the open note head). But this poses a problem: why are two identical dominants in virtually identical contexts seen as exhibiting two different functions? Rather, I would be inclined to understand both in the manner Salzer analyzes the first: as the dominant of the local tonic prolongation: it is not a structural chord, but a prolongational one, part of the tonic expansion of the A’ section. As such, I would argue that the deep-level structure of this piece is not I–

V–I, but rather i–VI–i. Each section (A, B, and A’) has its own tonality, which is composed out in the form of a basic structure prolonging that tonality.36 These deeper-level prolonged chords—Stufen —are products

of the prolongational functions of the chords at the harmonic surface.

In this sense, then, I argue that it is not a requirement for prolonged deep-middleground-level Stufen

to replicate identically the syntactic norms that govern prolongational harmony on the musical surface. 37

Carl Schachter likewise problematizes the assumption that “key successions are simply chord progressions writ large,”38 yet this remains a compelling perspective in the analysis of tonal music. Stein, for example, writes that “tonal progression on the middleground is an expression of the Bassbrechung ,” equating the

36 The middle C-major section does not have a cadence in that key, but C governs the tonal logic of the section, and ultimately concludes on a cadence in G (a deeper-level half-cadence in C). 37 Leonard B. Meyer writes of the “fallacy of hierarchic uniformity,” suggesting that it is a methodological mistake to assume that the same processes that govern one level of a hierarchy must function in the same way at all other levels of structure. See Leonard B. Meyer, Music, the Arts, and Ideas: Patterns and Predictions in Twentieth-Century Culture (Chicago, University of Chicago Press, 2010), 96–97. 38 Schachter (1999 [1987]): 143. 227

Figure 4.2. Felix Salzer’s Analysis of Chopin’s Mazurka, Op. 17, no. 2 (Example 499 in Structural Hearing )

elaboration of the Bassbrechung with the ways in which chords create prolongations at the musical surface. 39

And this is where I believe things become challenging in discerning tonal structure solely within the Ursatz

framework. In needing the deeper-level key structure to conform to the same “logic” as surface-level

harmonic progressions, the succession of possible keys becomes very limited, to the point where everything

must ultimately reduce to I–V–I if the demands of unity required by this approach are to be maintained. But

this does not always provide an accurate, or convincing, analysis of what is happening in the music.

What I am suggesting in this regard should not seem radical, in the sense that many scholars have

questioned the importance of the Ursatz, and have likewise proposed alternatives, to varying degrees of

success. And yet the shadow of the Ursatz still looms in the background of most Schenkerian approaches to

tonality in the late nineteenth century; it remains, in short, a system that has prioritized the structural role of

the dominant on all levels. Prolongational harmonic functions that are found at the harmonic surface are

required to function in such a systematized manner—the syntactic prolongational progressions we associate with classical tonality—because their role is to prolong these deep-middleground level Stufen . Because this process so clearly confirms a given tonic, it is thus not necessary to have this replicated at a deeper level between prolonged Stufen . Schenker likewise saw the need to observe a distinction between the logic that

39 Stein (1985): 142. 228 governs the ways in which chords function prolongationally at the foreground, and the ways in which prolonged tonal centers interact at a deeper level of structure:

I call the content of the fundamental line, counterpointed by the bass arpeggiation, diatony …in contrast, tonality , in the foreground represents the sum of occurrences from the smallest to the most comprehensive—including the illusory keys and all the various musical forms. 40

In this sense, if the deeper-level Stufen are divorced from the requirement that they act in a syntactically

identical manner to the chord progressions that function on the musical surface, they can exist in what

Leonard Ratner refers to as a more contrapuntally-oriented “solar” layout, rather than the polar layout that

has been reinforced through Schenker’s Ursatz approach. 41

Ratner describes tonal polarity as an arrangement that “sets the dominant against the tonic (in minor-key movements the relative major is the opposing key). This opposition is potentially dramatic, as the dominant takes over from the tonic…and the tonic eventually reasserts itself.” 42 Solarity, on the other hand,

is described as “a circular arrangement of keys…[that] represents a modification by cadential reinforcement

of the older system of church modes, in which the tonic was a “sun” surrounded by a constellation of

closely-related degrees.” 43 The solar layout is described as being more common in Baroque forms, while the polar approach began to appear in the sonata forms of the classical style. One can certainly understand, and see, how the dominant often plays an important and active role in the tonal structure of classical sonata forms, but, as I have argued already, this need not mean that the dominant is a proscriptive element in a deep-level tonal structure: one can even infer this in Ratner’s comment regarding minor-mode movements

40 Schenker (1979 [1935]): 5. Nicholas Cook has also suggested that part of the impetus behind Schenker’s position lies in more social-cultural rationale, namely that Schenker’s conception of the Ursatz and tonality was meant as a sort of foil to the Wagnerians of Bayreuth, and their anti-Semitic ideologies (Nicholas Cook, The Schenker Project: Culture, Race, and Music Theory in Fin- de-Siècle Vienna [New York: Oxford University Press, 2007]: 88). Holly Watkins extrapolates further that “As a Jew excluded from the pan-Germanist, Wagnerian circles of his adopted hometown, Schenker fought back by endeavoring to answer Wagner’s polemical question ‘What is German?’ once and for all. To do so, he turned the composer’s own aesthetic principles against him, devising a ‘properly theorized definition’ of Wagner’s woolly metaphysics, as Cook aptly remarks. By the 1920’s, Schenker had essentially written [Wagner] out of music history as he understood it. The Masterwork in Music hammered the last nail into the coffin with a pronouncement best left in German: “Wagner war kein hintergründiger Musiker!.” Holly Watkins, Metaphors of Depth in German Musical Thought from E.T.A. Hoffman to Arnold Schoenberg (Cambridge: Cambridge University Press, 2011): 164. 41 Ratner (1980): 51. 42 Ibid., 51. 43 Ibid., 48. 229 above—that it is the relative major that exists as the “key of opposition” suggests that i and III are the more important structural tones.

If one is open to a more constructional approach at the deepest levels of tonal structure, rather than the proscriptive downward-transformational approach of the Schenkerian Ursatz , the more solar understanding of deeper-level structure, rather than enforcing the strictly polar view, allows the deep-level i to VI to i as a valid tonal plan. As surface-level harmonic chords this would not necessarily be a strong

prolongational progression, in the sense that i–VI–i on the harmonic surface does not adequately establish a

key on its own, but at a more structural level this type of relationship does not divest the work of its tonic.

Thus in the case of the Mazurka above, the A’ section should be analyzed as fundamentally the same

prolongation as the A section: the dominant chord at the end should not be seen to have recursive deeper-

level function, but rather it is part of the A’ section’s tonal prolongation of E.

II The Generative Fundamental

William Pastille writes: “The two voices of the Ursatz form what Schenker calls an Aussensatz —that

is, a contrapuntal setting of outer voices.” 44 Of this Aussensatz , Schenker writes that “in prolonged form [it]

is actually a setting of [two voices] above a conceptual lower voice which carries the fundamental, or scale

degree, notes.” 45 Schenker’s prose here is somewhat vague, and Pastille clarifies that Schenker is referring to

“the fundamental of the generative triad of which the Ursatz is the first elaboration,” or, in other words, the tonic pitch of a given prolongation.46 What this suggests is that Schenker, in some sense, perceived that it was the root of a triad that generated the third and the fifth of that same triad.

44 William Pastille, “The Development of the Ursatz in Schenker’s Published Works,” in Trends in Schenkerian Analysis, ed. Allen Cadwallader (New York: Schirmer Books, 1990): 81. 45 Heinrich Schenkner, “Further Consideration of the Urlinie I” in The Masterwork in Music vol. 1 [1925], trans. John Rothgeb, ed. William Drabkin (Cambridge: Cambridge University Press, 1994): 105. 46 Pastille (1990): 81. 230

Essentially what I am proposing is that while the tonal structure for a unit of prolongation can be understood as a composing-out of a triad, this can be reduced a step further. One conventional view of a major triad is that it is derived from its root combined with that root’s first four overtones. Rameau, for example, writes: “It must not be forgotten, however, that all properties of the octave, of sounds in general, of intervals, and of chords rest finally on the single, fundamental source, which is represented by the undivided string or unit.” 47 Likewise, Schenker suggests that “every tone is the bearer of its generations and…contains within itself its own major triad, I: 5: 3.” 48 If a triad can be understood as generated from a root tone, one might thereby say that a triad can be thought of as, to invoke a Schopenhauerian term, a representation of a single pitch: the root of that triad. 49 Indeed, it was not only Schenker who subscribed to this notion. As Carl Schachter describes it, a number of eighteenth-century theorists suggest a similar view through the ways they describe tonalities. Schachter summarizes:

Schenker praises C.P.E. Bach for conceiving of ‘keys’ as prolonged Stufen , drawing this inference from Bach’s referring to the goals of modulation as scale degrees in the main key…Both Rameau and Kirnberger do so [as well]: and Kirnberger even uses Roman numerals to indicate the scale degrees in the main key on which the new ‘tonics’ fall. 50

Note how the reference here is to scale degrees, not chords. A schematic of this type of reductive process is provided in Figure 4.3, depicting the move from a prolongational structure to a triad, to a single pitch as the deepest-level reduction. 51

47 Jean-Phillip Rameau, Treatise on Harmony [1722], ed. and trans. Phillip Gossett (New York: Dover, 1971): 13. 48 Heinrich Schenker, Harmony [1906], ed. and ann. Oswald Jonas, trans. Elisabeth Mann Borgese (Chicago: University of Chicago Press, 1954): 25–29. Likewise, Wagner refers to the static E f of the Prelude to Das Rheingold as expanding a “fundamental note” rather than as expanding a triad (Richard Wagner, “On the Application of Music to the Drama,” in Richard Wagner’s Prose Works , trans. William Ashton Ellis [London: Keegan Paul, Trench, Trübner & Co. Ltd., 1897]: 185). 49 As Martin Eybl notes, Schopenhauer was “one of the most widely read authors in fin-de-siècle Vienna.” Eybl further notes that Schenker makes references to Schopenhauer, and a number of Schenker’s terms evince clear Schopenhauerian underpinnings (such as Der Tonwille ). See Martin Eybl, “Schopenhauer, Freud, and the Concept of Deep Structure in Music,” In Schenker- Traditionen: Eine Wiener Schule der Musiktheorie und ihre internationale Verbreitung/A Viennese School of Music Theory and Its International Dissemination , edited by Martin Eybl and Evelyn Fink-Mennel (Vienna: Böhlau, 2006): 56–57. Schopenhauerian thought is well- known to have been highly influential on both Wagner and Strauss as well, and one of the threads that pervades this dissertation, which has hitherto been unmentioned, is the notion of structure in music echoing the Schopenhauerian notions of the Will, and its Noumenal and Phenomenal aspects. This is something I will explore briefly at the end of this dissertation. 50 Schachter (1999 [1987]): 143. 51 In regard to the minor triad, Patrick McCreless, following work by Robert Bailey, has suggested that “in the late nineteenth century we have moved from a tonal universe in which there are twenty-four diatonic major and minor keys to one in which there are twelve keys with interchangeable mode…a tonic performs the same role, regardless of modal choice.” (Patrick McCreless, “Ernst Kurth and the Analysis of Late Nineteenth Century Chromaticism,” Music Theory Spectrum 5 [1983]: 60). I would suggest 231

Figure 4.3. Structural Reduction Process to a Generative Fundamental

With this proposition of the triads as a representation of a generative fundamental in mind, I

propose another way of considering key relationships, one that is particularly useful in later nineteenth-

century works. Since, as mentioned above, seeing key relationships as larger-scale replications of harmonic

progressions becomes untenable in late nineteenth-century music, another way we might perceive key

relationships is as a melodically conceived progression of the fundamentals of the structurally salient

tonalities. This approach is a different type of organizing principle for musical structure than the axiomatic

monotonality of the Ursatz . Instead of prioritizing a secondary key’s position in the tonic scale as its main

defining feature, this approach prioritizes the specific way in which keys unfold over the course of the work;

in other words, it prioritizes what makes a work unique. 52 This is not to say that one cannot still understand these keys as having a position in a tonal scale, but rather that position need not be understood as their sole, or even primary, source of analytic value.

Let us take as an example the second movement of Beethoven’s Piano Sonata Op. 14 shown in

Example 4.1a. While this is obviously a piece that can still be easily analyzed from a more conventional perspective, the relationships that form from the approach I am proposing are likewise of interest. The form of this movement is ABA’, with the A sections in E minor and the B section in C major. Each of these

that in structural analysis, the same principle holds true in earlier music as well, even though the dichotomy between major and minor modes is more pronounced. 52 Felix Salzer, Structural Hearing: Tonal Coherence in Music [1952] (Reprint. New York, Dover, 1962). 232 sections can be understood as a middleground-level prolongation of its respective tonics. 53 It is thus possible

to suggest that the juxtaposition of the E minor and C major triads forms the tonal backbone of this

movement. If we further understand these tonalities as projections of their fundamentals, or roots, we can

understand the structure of the section as a melodic motion from E, to C, back to E. This contrasts with a

more traditional Schenkerian reading which would likely have the dominant at the end of the B section

understood as creating a divided structure, and give the dominant chord in m. 50 (on the repeat) the onus of

Example 4.1a. Beethoven, Piano Sonata Op. 14, no. 1: II, 1–38

53 The B section does not have a cadence in C, though it does have a tonicized cadence on G, V of C, a deeper-level half cadence (see below for a discussion of different types of prolongations: this fits into what Salzer describes as an “incomplete progression”). 233 structural dominant. Like in the Chopin example above, however, this dominant is a chord : it is participating

in a prolongation of a tonic, and is no different from the same dominant that occurs the first time the A

section is played. This is, of course, a relatively simple example, but one that serves to demonstrate the

perspective that I am advocating, namely a more versatile and dynamic process of composing-out a

sequence of fundamental tones in a quasi-melodic manner, rather than an axiomatic, governing Ursatz into which all progressions, key areas, and tonalities must be shoehorned. Notable in this deeper-level melodic

interpretation of the tonal structure is the replication of this figure at both the middleground in the A

sections (mm. 1–45, and their repetition), which themselves move from E to C back to E, and at the musical

surface in the B section of the movement, whose melodic outline begins with an embellished skip of a third

from E down to C (Example 4.1b).54 In the sonata’s first movement, the pitch C is also the prominent tonal center of the development section, and intrudes into the recapitulation, again highlighting the important E–

C relationship.

A tonal prolongation is, in this way, understood as a means of elaborating and expanding a generative fundamental, rather than a triad, across a unit of music (a phrase, a section, a theme, etc.). As

Example 4.1b. Beethoven, Piano Sonata Op. 14, no. 1, II: Opening of B Section

54 Schachter discusses this movement in his essay on durational reduction (“Durational Reduction,” in Unfoldings: Essays in Schenkerian Theory and Analysis [New York: Oxford University Press, 1999]: 65–70), focusing specifically on the A section, which he analyzes as I – VI – V in E minor. In this case I agree with this reading, as the VI is half the length of the two periodic A themes that it divides, and contains no strongly articulated cadence in C (assuming R = ½N, the G-major arrival is very quick to be considered a strong half cadence) and C never really establishes itself as a key in the way it does in the B section of the movement (there is likewise no melodic motion at a deeper level of structure in this section: G remains the primary melodic tone, and does not move throughout the section). 234 described above, I believe that Schenker’s generalization of tonality as following the principles of composed-out Stufen is an analytically viable and useful methodology when applied to these smaller-scale units, in the sense that chords on the musical surface prolong deeper-level tonalities. Where I believe

Schenker’s interpretive step hinders this approach, however, was his induction of the Ursatz , and the monotonality it demands, as an organizing principle at the deepest level. Schachter describes this trend in analysis: “in…modern harmonic analysis, theorists attempted to relate secondary keys—at least those most frequently employed—to the whole piece rather than regarding them as separate, self-contained entities.” 55

Why can they not be thought of as both? Secondary tonalities could be described as a prolongation of the V step, or the II step, or so on, while still being understood as their own self-contained units. But what I am advocating is that while relating large-scale harmonies to a central tonic as a type of enlarged I–(PD)–V–I chord progression may be effective in classical tonality, it is less so in late nineteenth-century tonality. As

Carl Dahlhaus writes:

The tonality characteristic of Wagner, unlike that of Brahms, is not an ‘expanded’ centripetal one, integrating remote degrees and regions in one secure tonic to which modulations can always be related, but a ‘wandering,’ or ‘floating’ tonality. The fragmentation of classical tonality into brief tonal particles which follow each other in a line, connected like links in a chain rather than assembled around a common center, by no means represents aesthetic weakening, [nor] the relinquishment of harmonic function. 56

Dahlhaus’ description of the deeper-level relationships in Wagner’s music possesses a similar outlook to the

solar layout described above.. Instead of exporting the conventions of how chords prolong a local tonic and

using them to describe the deeper-level relationships between prolonged units, if we reconceive a prolonged

tonality as a representation of a single pitch, we might effectively reconsider Dahlhaus’ description of a

chain of tonal particles as being an essentially melodic event: if the succession of key areas can be reduced to

their generative fundamental, then we can discuss the ways in which their specific progression mirrors other

tonal events in the same piece. . One can, of course, still relate these pitches to a global tonic (i.e. in the

Beethoven example above, I – VI – I), but it is important to my approach to note the distinction between

55 Schachter (1999 [1987]): 143. 56 Carl Dahlhaus, Between Romanticism and Modernism: Four Studies in the Music of the Later Nineteenth Century, trans. Mary Whittall (Berkeley: University of California Press, 1978): 68–69. 235 these deeper-level objects that are prolonged, and the harmonic processes that create the objects that are prolonged.

At this point it is worth diverting from this train of thought, momentarily, to observe that not all

prolongations of Stufen are clear-cut in positioning a tonic at the outset and conclusion of the prolongation.

In this sense, it is useful to digress here for a moment to clarify different types of prolongations, especially as the less common variants become more commonplace in the late nineteenth- and early twentieth-century repertoire I am studying. As a point of departure, Salzer describes tonality as “prolonged motion within the framework of a single key-determining progression.”57 This is most easily discernible at the level of the

phrase, and Salzer describes two different types, or methods, of tonal prolongation. The first, which he calls

a “complete harmonic progression,” is the most common and most stable. A tonic is sounded at the outset of the prolongation, moves through several intermediary chords following the conventions of prolongational practice (in this sense, the tonic is often prolonged initially, before moving on to predominant harmony), and concludes with a dominant-to-tonic gesture that closes off the prolongation.

The second type of prolongation Salzer terms “incomplete” and divides into subcategories described as “more complicated” owing to the missing tonics either at the beginning or end of the prolongation. The first subcategory is similar to a complete harmonic progression, but instead of concluding on the tonic, it concludes on dominant harmony. An example of this can be found in the opening sentence of Beethoven’s

Piano Sonata Op. 2 no. 1, where the Primary theme concludes on V, and the transition begins immediately after, moving the music towards the secondary key of the relative major. This prolongation is slightly weaker in that the tonality is not reconfirmed at the end of the prolongation; the tonic, however, remains the structural foundation as shown in Figure 4.4.

57 Salzer (1962): 227. 236

Figure 4.4. Beethoven Piano Sonata Op. 2, no 1: mm. 1–8 Prolongational Bass Analysis

Another subcategory is what Schenker terms an auxiliary cadence. Salzer describes this type of

prolongation as “a drive towards [the tonic].” 58 Like the previous type of prolongation, these are also not as clear or strong as the first type since the tonic does not appear in a stable position until the prolongation concludes (though it could appear in inversion prior to that). For example, the first episode in the second movement of Beethoven’s Piano Sonata Op. 13, shown in Example 4.2, is a prolongation of the dominant tonality (E f), but does not sound an E f chord at the outset. This type of prolongation is more common in late nineteenth-century music, though it also occurs frequently in transitional and developmental passages in

eighteenth and early nineteenth-century music.

Salzer also describes a third subcategory, which he terms “dominant prolongation of the tonic.” 59

Salzer does not provide a detailed description of what he means here, though the two examples he gives suggest that he is referring to cases where he understands the tonic to be in effect even when it is never actually sounded in root position, and is only ever represented by its dominant. In this particular case I disagree with Salzer’s contention. While it is true that a dominant signifies in some abstract way the existence of its tonic, if the tonic is not sonically present in a prolongation, it is impossible to state that it is being prolonged, or exists in the musical structure as a prolonged Stufe . For example, this question comes up

58 Ibid., 153 59 Ibid., 153. 237

Example 4.2. Beethoven, Piano Sonata Op. 13: II, mm. 15–27

in the middle section of the Prelude to Tristan und Isolde : as shown in Figure 4.5, I argue that B functions as the prolonged bass pitch, approached by its own dominant at two points of phrase articulation. The challenge here, however, is that in both cases the harmony is a dominant-seventh chord built on B, rather than a stable triad (my graph notates this as “I”). While this might initially suggest that E is the tonal center,

E plays a minimal role in this passage, finding expression only once, in first inversion, following its own leading-tone seventh chord. While this could be understood as I 6 in E, as Figure 4.5 shows, it could likewise be interpreted as IV 6 in B, an interpretation that makes far more tonal sense given the subsequent chords in the progression. As Robert Bailey notes, “Another innovation in the musical language of Tristan is the

treatment of the V 7 chord as a temporary local consonance.” 60 Although Bailey does alternatively argue that certain V 7 chords are also used to represent their tonic, even in absentia , this notion that a V 7 chord can serve

60 Robert Bailey, “An Analytical Study of the Sketches and Drafts,” in Prelude and Transfiguration from Tristan und Isolde, ed. Robert Bailey (New York: W.W. Norton & Company, 1985): 125. 238

Figure 4.5. Wagner, Tristan und Isolde : Prelude, mm. 44–57 Analysis

as a consonance on the same level as a tonic suggests that this section can be perceived not as prolonging an

E Stufe that never materializes, but rather as a prolongation of a B Stufe —whether B is understood as the

local tonic with what Bailey suggests is an “[expanded] concept of consonance,” or as V of a phantom E

does not detract from the fact that it is B, not E, that exists as the prominent prolonged bass pitch in this

section. 61

Let me return now to the excerpt from Schubert’s B f-major Piano Sonata mentioned at the outset,

and shown here in Example 4.3a, which engages with many of the issues presented above. As mentioned,

the challenge Cohn sees in analyzing deeper-level tonal structure in this excerpt is the disjunction between

Gf major, F s minor, and A major, and relating them all to B f major consecutively as chords in B major.

David Beach’s recent monograph on Schubert’s instrumental music presents a Schenkerian interpretation of

this movement, though it is one that justifies Cohn’s concerns. Beach’s analysis of this section, reproduced

in Example 4.3b,62 does not clearly articulate how these tonalities relate to the tonic B f, but is instead content to let them exist as the type of “tubs,” to use Cohn’s expression, that are “bounded by the B f

61 Ibid., 125. 62 David Beach, Schubert’s Mature Instrumental Music: A Theorist’s Perspective (Rochester: University of Rochester Press, 2017): 145. 239

Example 4.3a. Schubert, Piano Sonata in B f D. 960, mm. 231–258

240 shores,” but do not explicitly elicit any type of coherence. 63 And Cohn’s metaphor is an apt one: in such an

analysis of the music, these so-called “keys” of G f, F s, and A seem to float listlessly and without purpose.

Of the two tonal centers (G f and F s being parallel enharmonic equivalents), A major is the most clearly defined as a tonality: complete tonal progressions sound above the persistent A pedal (I–IV–I and I–IV–V–

I). Conversely, the G f/F s tonal center is, comparatively, weakly defined and fleeting in nature: no similar harmonic progressions occur, save for some neighbouring figures in m. 235 and a tonic six-four in m. 237.

As such, I would propose that Gf major/Fs minor is not a tonality in and of itself, but rather it represents

an expansion of the submediant of the subsequent A-major tonality, which itself can be understood as a

prolongation of the VII Stufe in B f. This analysis is given in Figure 4.6, which also shows how the VII Stufe

then transforms to become V 7 of D (which is either iv of A or iii of B f), resolving deceptively to lead back into the tonality of B f.

While this may initially seem to contradict my earlier assertions regarding the infeasibility of relating chords with altered tonic pitches directly to a tonic (i.e. G f major, understood as F s major relating to A major), those assertions were made regarding prolongational chords whose function is to expand a tonic.

Here, the F s is understood as a thing being prolonged, and relates at a deeper level as a subordinate Stufe to

the subsequent A triad. As such, the tonality of A does not begin on A, but rather on the submediant, an

example of a deeper-level auxiliary progression described above. Cohn is, of course, correct in his

assessment that relating all of these tonalities directly to B f under the classical Schenkerian regime is a

challenge, but, as I hope this brief discussion has demonstrated, this does not necessarily imply that there is a lack of coherence in the work. Rather, that coherence results from a more polyreferential approach than the more Ursatz -based approach allows; the G f/F s material does not need to be related directly to the tonic, but instead can be seen as part of the prolongation of A major. This has further hermeneutic implications that will be discussed below.

63 Cohn (2012): 2. 241

Example 4.3b. David Beach’s (2017) Analysis of the Recap of Schubert’s Piano Sonata in B f, D. 960

Figure 4.6. Schubert, Piano Sonata in B f, D. 960: mm. 233–255, my analysis

242

III Leitmotivic Auskomponierung

In the Schubert example discussed above one might also see this approach as revealing a deeper- level parallelism between tonalities and melody, one that also helps to account for the strange B-minor section that follows. The deeper-level structure of the opening of the recapitulation that I have proposed here is a move from B f, to A (initiated by its submediant), to B f again. If these keys are reduced to their

fundamentals, then the succession of fundamentals that ensues is B f–A–Bf, which is an enlargement of the

first three pitches of the prominent melody that saturates this movement. 64 This type of parallelism is often referred to as “enlargement,” which Alegant and McLean describe as a process where “a surface (or near- surface) object (usually an ordered string of notes) is subsequently "enlarged," or re-presented in temporally expanded form.” They note that “in this way a small and comparatively modest musical object can develop into a larger entity of considerable structural and expressive consequence.” 65 One might take this notion of

enlargement in the Schubert example a step further, and suggest that the subsequent B-minor/D-major

complex of the recapitulation’s S-space—again refer to Beach’s graphic analyses above—continues this

deeper-level composing-out of the movement’s main motivic gesture, albeit in a chromaticized manner, as

shown in Figure 4.7.

The chromatic nature of this enlargement might in turn suggest that G f has not yet relinquished its grip on the tonality of the piece: B is enharmonically C f, the subdominant of G f, and D is enharmonically

Eff , the lowered submediant of G f. While, as Charles Fisk writes, “By Schubert’s time, the use in the major of the sixth scale degree borrowed from the parallel minor

had become one of the most common of chromatic inflections,” 66 Joseph Kerman also notes that the

manner in which Schubert introduces the G f is as a “mysterious, impressive, cryptic Romantic

64 This neighbour figure further permeates the melodic material for the remaining movements of the sonata as well. 65 Brian Alegant and Donald McLean, “On the Nature of Enlargement,” Journal of Music Theory 45, no. 1 (2001): 31. 66 Charles Fisk, “Schubert’s Last ‘Wanderer:’ The Sonata in B f Major, D. 960,” in Returning Cycles: Contexts for the Interpretation of Schubert’s Impromptus and Last Sonatas (Berkeley: University of California Press, 2001): 241. 243

Gesture.” 67 And indeed, the G f pedal trill that has proliferated throughout the movement and is, as Fisk describes it, “something outside or beyond what is implied in the theme itself, something fascinating in both its allure and its danger,” is never entirely vanquished in this movement, and sounds one last time prior to the final dominant-to-tonic gesture. 68 No matter what lengths the music goes to in order to more fully integrate the G f into its structure (as fVI, as vi of A, and so on), the G f resists this integration and continues to function just as Fisk describes, as something external to the tonality of the work, despite the ease with which it could be integrated. 69

Figure 4.7. Deeper-level Melodic Analysis of Schubert, Piano Sonata in B f, D.960, bars 215–286

67 Joseph Kerman, “A Romantic Detail in Schubert’s ‘Schwanengesang,’” in Schubert: Critical and Analytical Studies , ed. Walter Frisch (Lincoln: University of Nebraska Press, 1986): 59. Kerman notes that “the figure does not develop, certainly not in any Beethovenian sense,” though I disagree with this assessment to some extent, as G f as a pitch continues to inspire much of the tonal drama of the movement. 68 Fisk (2001): 242. Fisk likewise notes that the G f has a strong distorting effect within the Primary theme space of the sonata, writing “Schubert not only emphasizes the G b through a trill, as soft and low as possible, but he introduces it into a subtly disoriented thematic complex, one that has already begun to lose its way, rhythmically and melodically.” 69 Joseph Straus’ discussion of the role of G f in the movement corroborates these claims. He writes: “After exploring (or perhaps indulging in) unusual harmonies and keys to which the G-flat gives rise, the music of the first movement makes an effort to heal that breach. Specifically, at the end of the movement, the music makes a number of attempts to create a convincing final cadence in B-flat major, each of which dissipates in silence. Finally, the music provides two strong perfect authentic cadences, both featuring a normatively resolving G-flat. The disruptive potential of the G-flat would seem to be fully contained at this point— now it is presented as a simple chromatic upper neighbor—and its abnormality would appear to be fully normalized. But the movement continues with a three-fold reminiscence of the opening theme. As the third of these concludes, the ominous trill on G-flat returns, in virtually every respect just as it was in the beginning. The tonal problem has not been solved—its imbalance and unrest resound right through the end of the movement. Certainly there is no sense at all of heroic overcoming in the Beethovenian manner. If the G-flat can be understood metaphorically as a wound of some kind…then the wound remains open, unhealed at the end of the movement.” Joseph Straus, Extraordinary Measures: Disability in Music (New York: Oxford University Press, 2011): 65–66. 244

Combining this notion of enlargement with the perspectives outlined above regarding the relationships between tonalities and the ways in which they can form a deeper-level tonal structure that is melodically oriented is a way in which I propose to examine tonal structure in mid-to-late nineteenth- and early twentieth-century works. What I suggest, and will demonstrate in the two subsequent analyses, is that one way of viewing structural coherence in some late nineteenth-century music is to understand the progression of secondary tonal areas as a composing-out of a surface-level motif or Leitmotif .

The study of the Leitmotif , however, has fallen on hard times. Matthew Bribitzer-Stull writes, “critics

have disparaged its effectiveness and value as a compositional device, but also leitmotivic analysis has been attacked as a puerile, descriptive mania akin to collecting.” 70 Bribitzer-Stull suggests that these types of

approaches that simply collect or tally the themes, are misguided, principally because they “ignore or downplay the themes’ musical attributes.” 71 As Deryck Cooke notes, these types of analyses imply that such music is simply made up of “a patchwork of short ideas,” in which “the interrelationships between themes are neglected in all but the obvious cases.” 72 Theodor Adorno likewise has naught but scathing criticism for

this approach, writing “It may be noted in passing that this kind of analysis contradicts its own aim, and serves, in fact, to further that external, superficial type of listening which so characterizes the old-style

Wagner listener, proud if he is able to recognize the 'Curse Motif' in the Ring every time somebody gets murdered…while in doing so [misses] what is really happening in the music.” 73 Bribitzer-Stull observes that even Wagner himself expressed disappointment in a shallow approach that prioritized the dramatic aspects

of Leitmotif s above their musical ones::

The studies of one of my younger friends [Wolzogen] have viewed the characteristics of what he calls my ‘Leitmotife’ rather in the light of their dramatic significance, than that of their bearing on musical construction. 74

70 Matthew Bribitzer-Stull, Understanding the Leitmotif (Cambridge: Cambridge University Press, 2015): xix. 71 Ibid., 23. 72 Deryck Cooke, I Saw the World End (London: Oxford University Press, 1979): 38–44. 73 Adorno (1982): 178. 74 Richard Wagner, “On the Application of Music to the Drama,” in Richard Wagner’s Prose Works , vol. 6, trans. William Ashton Ellis (London: Keegan Paul, Trench, Trübner & Co. Ltd., 1897): 182–183. Quoted in Bribitzer-Stull (2015): 26. 245

Schenker takes further the critique of Wagner’s Leitmotif technique, citing Wagner’s inability to “achieve

diminutions like those of the masters [which] made it necessary for him to turn away from diminution and,

in the service of the drama, to make expressiveness, indeed overexpressiveness, the guiding principle of his

music.”75 Marvin’s dissertation undertakes an extensive discussion of the role of the motif in Schenker’s writings. In a survey of the ways in which Schenker’s views on the motif evolved, Marvin notes a major change in Schenker’s perspective evinced in his study of Beethoven’s Piano Sonata Op. 101. Where previously, in Harmonielehre , Schenker held a “a very traditional view, relying on foreground pitch shapes that define themselves as motives through immediate repetition,” that view changed in Schenker’s later writings:

“motives are no longer limited to appearances on the surface of the music,” Marvin writes, “but now appear

at higher levels in connection with voice-leading transformations.” 76 Marvin continues to warn, however,

that it “is important to note that motivic figures are still present on the surface of the music, and are not

excluded by the emphasis on motives at the higher transformational levels.”77 This changed further by the

time of Der Freie Satz . Schenker writes:

Great composers trust their long-range vision. For this reason, they do not base their compositions upon some “melody, ” “motive, ” or “idea. ” Rather, the content is rooted in the voice-leading transformations and linear progressions whose unity allows no segmentation or names of segments. Every linear progression, provided it does not quickly pass by in sixteenths or thirty-seconds, presupposes a certain extended vision, and has nothing to do with “melody ” or “idea. ”78

This is a particularly polemic passage from Schenker, and reinforces the notion that his conception of the background was the unifying force behind compositions. 79 As Marvin notes, “In [his] later writings,

Schenker recognized surface motives as musical entities, but he strongly preferred that they be generated by the earlier levels.”80 Indeed, Schenker instills this view in his continued polemic, writing:

75 Schenker (1979 [1935]): 106. 76 Marvin (2001): 69–70. 77 Ibid., 71. 78 Heinrich Schenker, Free Composition , ed. and trans. Ernst Oster (New York: Longman, 1979): 26–27. 79 Marvin (2001, 72) notes that this polemic is directed towards Schoenberg, and his conception of the ‘basic idea’ of a motif that shapes an entire composition. 80 Ibid., 72. 246

It is certainly not out of place here to distinguish ‘fundamental structure’ composers from ‘idea’ composers. The latter must always be concerned with the effect of the moment; they ramble constantly instead of deriving higher entities from the background or middleground. If only they would once attempt to create a truly organic work! 81

Again, for Schenker everything must be derived from the preconceived background. As Marvin notes, this

may be rooted more in polemics than in actual musical practice: “[Schenker] rejects the explanations offered

by theorists (Schoenberg, Réti, Leichtentritt) that these surface entities can generate material that comes later in the composition.”82

Marvin further notes that a commonly held view of Wagner’s music sees the “ Leitmotive as the primary form-generating force…with tonality acting in an important supporting role. This view is in direct opposition to Schenker’s own position on the form-generative role of tonality and the extraneous nature of motives as outlined above.” 83 Here Marvin is referring to scholars, such as Thomas Grey, who speak of

Wagner’s music as a continuous musical fabric of Leitmotif s, as described by Bribitzer-Stull above. In short,

Leitmotif s, and approaches to analysis that focus on them, are thus regularly regarded as musically inane,

something that a listener can grasp aurally and that provides a direct one-to-one connection with some

sentiment or idea in the drama, but that is often regarded as having little musical value and rarely participates

actively in the creation of deeper-level tonal structure.

The problem here is not that Schenker does not recognize motifs, or Leitmotif s, as viable musical

entities, but rather he takes a stance in direct opposition to those who claim that surface-level motifs

generate form and structure in musical works. One can sympathize to some extent: as noted above, a

tendency to take this approach too far exists, wherein analysts claim that the constant presence and web-like

interaction of motifs generates a coherent form; this is certainly an approach of which to be skeptical. But,

as Marvin likewise suggests, one can also recognize that Schenker occasionally, in the depths of his

polemics, overstates his case. For instance, one might indeed look to the Leitmotif as having a generative role in Wagnerian, and post-Wagnerian opera; not in the sense that the opera’s forms are created by a network of

81 Schenker (1979): 27. 82 Marvin (2001): 77–78. 83 Marvin (2001): 81. 247 leitmotivic utterances, but rather in the sense that the pitches of an important motif could be composed-out to become the main tonalities of a section of music, and in this way generate a type of coherence that does not rely on the Ursatz to define its musical logic.

Despite Schenker’s disdain for the leitmotivic technique, the notion of composing-out a melodic motif is not a new one, and has been expressed elsewhere in more Schenkerian idioms. 84 These approaches,

however, all posit relationships between relatively conventional (one might say mundane) motivic content of

the Schenkerian type (that is to say linear progressions), where the notion of composing-out a Leitmotif

engages in a less restrained process. While the examples I present below posit that this process unfolds on a

deeper level of structure, this notion of composing-out more dynamic, rather than strictly linear, motifs,

particularly in Wagner, has been explored by Carolyn Abbate. In a study of the concluding scene of Act II in

Götterdämmerung Abbate notes of the passage in Example 4.4, that it projects a “long-range bass motion from

the initial note rising in thirds [sic]: C–D–E (mm. 1495–1508) in the first variation, C–D–Ef (mm. 1512–

1519) in the second, and G f–Af–Bf (mm. 1522–1531) in the third.” 85 Abbate then describes how this motif undergoes diminution, appearing in faster and faster iterations as the section progresses, “until it finally breaks to the surface of the music (m. 1535) to become a sound heard only once before: the bizarre unison motif in the Act I ‘Brotherhood Oath.’” 86 Abbate concludes: “This is an extraordinary moment: we realize

the apparently neutral sounds, the harmless ascending thirds twisting slowly beneath this passage, were not

neutral at all, but known and sinister,” and links Hagen’s text at this moment to the earlier scene. 87 Abbate’s argument here implies that there is an aspect of coherence to what initially appears to be a number of simple, droning, bass notes, in the way that they enlarge the “Brotherhood Oath” motif from Act I, as

Gunther, Hagen, and Brünnhilde plot to break that oath.

84 See for example Charles Burkhart, “Schenker’s ‘Motivic Parallelisms,” Journal of Music Theory 22, no. 2 (1978): 145–175; or Leslie Kinton, “Motivic Enlargement in Dvořák’s Symphony Op. 70,” in Explorations in Schenkerian Analysis , ed. David Beach and Su Yin Mak (Rochester: University of Rochester Press, 2016). 85 Carolyn Abbate, “Opera as Symphony: A Wagnerian Myth” in Analyzing Opera: Verdi and Wagner , ed. Carolyn Abbate and Roger Parker (Berkeley: University of California Press, 1989): 116. 86 Ibid., 116. 87 Ibid., 116. 248

Example 4.4. Wagner, Götterdämmerung , Act II, mm. 1495–1503

What I am suggesting here is that the importance of the Leitmotif spans beyond simply a surface-level

melodic notion of dramatic associativity. 88 If, as I have argued, analysis moves away from defining musical

structure in late nineteenth-century tonality as being exclusively tied to the Ursatz , and allows other

processes and procedures to generate musical coherence at deeper levels of structure, analyzing the

composing-out, or enlargement, of Leitmotifs over the course of a large span of music, such as an entire

prelude, becomes one such possibility. It is worth clarifying that my argument here is not that all mid-to-late

nineteenth-century music follows this

88 Abbate’s example still exists towards the musical surface, but projects the notion that a melody can transfer to the bass to become part of a more prolonged tonal structure. 249 procedure—it is, hopefully, well-known at this point that the eclecticism and sheer volume of music produced in the nineteenth century disallows the assertion of a monopoly on any single compositional approach—but rather that it is one possible procedure that is used to great effect in certain cases.

To this end, the following in-depth analyses argue that both the Prelude to Parsifal , as well as the first scene of Salome exemplify this type of procedure, the former composing-out the more complex initial

“Communion” motif, the latter the double-neighbour figure associated with the opera’s titular character.

This approach suggests an internal logic for the specific succession of tonal areas in the preludes that does not derive its value from the associating of pitches directly to a tonic, but rather specifically for the unique way in which the tonalities presented are used. 89

IV Parsifal, Prelude

Schenker’s claims that Wagner was only a foreground composer, unable to achieve deeper-level coherence for reasons of theatricality, extended to Wagner’s preludes, about which he wrote:

One should indeed not be deceived by the construction of lengthy preludes, interludes, or postludes. These, too, do not represent any group constructions, since in most instances they consist of just a few immensely extended harmonic degrees, with which length–and therefore the illusion of an adding together–is achieved where in fact only a single thought is expressed. To these belong, for example, the prelude to The Rhinegold, which is based on a single harmony; the postlude to the second scene of the same opera, which is likewise supported by a single bass note; and the prelude to The Valkyrie with the usual progression of I–II–V. 90

89 The Prelude to Tristan und Isolde initially formed part of this discussion as another example of this process of Leitmotivic Auskomponierung in music of the late nineteenth century; the discussion was ultimately excised for reasons of length. To give a brief summary, the Prelude, I argue, moves from A to C (as Bailey [1985] suggests), but does so through the intervening middle section, which I suggested above prolongs B (whether as a tonic with additional dissonance or as V of an E that never materializes). This deep-level succession of tonalities, reduced to their generative fundamentals, creates the succession of pitches A–B–C (with C being anticipated earlier on). This can be seen as a composing-out of the “Glance” motif that forms the motivic material for the A section of the Prelude (first heard in mm. 17–18). This composing-out is also replicated on more middleground levels within the Prelude, specifically mm. 1–24 (A), 25–28 (B), and 30–37 (C). Given that the Prelude is often referred to as the spinning out and transformation of the same motif, that the motif itself can be understood as being enlarged as the succession of deep-level fundamentals over the course of the Prelude should not be surprising. Allen Forte suggests a similar approach to analysis of the Prelude, especially in questioning any analysis that is “mono-tonal [in] orientation.” Forte ultimately focuses more on the role of the Tristan chord in the prelude, employing more atonally oriented set-class approaches to claim inversional equivalence, and suggesting that the Tristan chord is prolonged in various linear (melodic) forms throughout the Prelude. See Allen Forte, “New Approaches to the Linear Analysis of Music,” Journal of the American Musicological Society 41, no. 2 (1988): 324– 338. 90 Heinrich Schenker, “The Decline of the Art of Composition: A Technical-Critical Study,” trans. William Drabkin, Music Analysis 24, nos. 1–2 (2005): 99. 250

Schenker’s observations that Wagner’s Preludes consist of just a few extended harmonic degrees seems to suggest—implicitly, since it is unlikely Schenker would have conceived of it as such—the possibility for the

type of Leitmotivic Auskomponierung that I am suggesting. The most convincing manifestation of this can be

found in the Prelude to Parsifal , whose deep-level tonal strategy is, I will demonstrate, a composing-out of

the initial “Communion” Leitmotif. In this way, not only does the prelude project a sense of internal

coherence, albeit one that does not conform to conventional tonal models, but that its structure is

distinctive: a chromaticized composing-out of the initial three measures of the prelude. 91 Unlike the analyses

in previous chapters, which focused on the details of the harmonic surface, in this analysis I will support this

claim through analysis of the harmonic surface at key points where the tonality being projected is

questionable, but otherwise will mostly engage with middleground- and background-level considerations.

Having outlined this deeper-level structure, I engage in a broader discussion regarding the chromaticization

of the motif that occurs as the motif is composed-out, suggesting that these processes link the prelude to

the drama of the opera. Specifically, I argue that harmonic and motivic elements within the Prelude project

musically the initiation of one of the primary conflicts of the opera, namely the inability of Amfortas to

perform in his role as the leader of the Grail-Knights due to the wound he suffers at the hands of Kundry

and Klingsor.

The motivic material heard at the prelude’s outset, commonly referred to as the Communion motif,

can be subdivided into two parts: I designate mm. 1–3 as “Communion,” followed by a combination of the

Spear and “Suffering” motifs in mm. 4–6. 92 The full six measures are presented in Example 4.5, while Figure

91 In a more orthodox Schenkerian fashion, Carl Schachter suggests a similar interpretation of Mendelssohn’s Song Without Words , Op. 62, no. 1. Schachter writes “[the] initial bass motion points out a path through the piece’s tonal field, a path that the rest of the piece will traverse.” Carl Schachter, “The Triad as Place and Action,” in Unfoldings: Essays in Schenkerian Theory and Analysis , ed. Joseph N. Straus, 161–183 (New York: Oxford University Press, 1999). 92 There are a variety of labels used for these six measures. Some scholars, such as William Kinderman, consider the entirety of the six measures as the Communion motif, though differentiate a head and tail between the first and last three measures (William Kinderman, Wagner’s Parsifal [New York: Oxford University Press, 2012]: 77–81). Others, including Hanz von Wolzogen, who published initial leitmotivic guides to Wagner’s late operas, suggest that the initial six measures, which he calls the “ Liebesmahl ” be divided in two. For Wolzogen the first six measures (up to the E f) constitute the “ Schmerzenfigur ” and the last three measures are the Spear motif, though he later characterizes a descending line similar to that at the end of the motif as “cries of woe,” which I have in turn labeled “suffering.” (Hans von Wolzogen, A Key to Parsifal , trans. Roger Ashton Ellis [London: Chapel & Co., 1889]: 16, 33). 251

Example 4.5. Wagner, Parsifal , Prelude, mm. 1–6

Figure 4.8. Analysis of Example 4.5

4.8 provides a reductive analysis. As much as it is possible to infer a tonal structure from an unaccompanied melodic line, the analysis in Figure 4.8 suggests that the motif arpeggiates the tonic triad, with an upper neighbour note embellishing the dominant pitch. This arpeggiation is replicated at a deeper level, and incorporates the emphasized mediant in m. 3, with the subsequent D n passing between the mediant—

emphasized by its own upper fifth—and dominant pitches.93 Here the C–D–Eb progression of pitches sounds locally like a prolongation of C minor, but when the E f resolves to A f in the next measure, it takes

on a dominant quality in the A f tonic owing to the descending fifth motion. Walter Frisch notes this ambiguity, writing:

[The G in m. 3] shifts its identity from that of leading tone in A f to the dominant in C minor. Moving resolutely down to C, by fifth, it generates the first real cadential gesture, towards C minor, or iii of the initial A f. The D n on the second beat is the first nondiatonic note to be heard. It lies outside the scale of Ab and confirms the motion of the theme

93 Here the C–D–Ef progression of pitches sounds locally like a prolongation of C minor, but when the E f resolves to A f in the next measure, it takes on a dominant quality in the A f tonic owing to the descending fifth motion. Walter Frisch notes this ambiguity, writing “[the G in m. 3] shifts its identity from that of leading tone in A f to the dominant in C minor. Moving resolutely down to C, by fifth, it generates the first real cadential gesture, towards C minor, or iii of the initial A f. The D n on the second beat is the first nondiatonic note to be heard. It lies outside the scale of A f and confirms the motion of the theme towards the realm of C minor. But the final E f begins to lead us back to the sound world of the opening. It serves at once as an implied iii, but also as V of A f. 252

towards the realm of C minor. But the final E f begins to lead us back to the sound world of the opening. It serves at once as an implied iii, but also as V of A f.94

The material in mm. 1–19 is repeated in the next section up a major third, in the key of C minor.

This section expands the C Stufe , or iii of the global A f tonic and the second note of the prelude’s opening motif. The A section of the prelude concludes with the first sounding of the “Dresden Amen,” or Grail motif, shown in Example 4.6. Harmonically, this section initially suggests a move back towards

Af, but instead of closing on A f it concludes on the dominant. This analysis can be found in the analytic annotations to Example 4.6, which suggest that while A f is initially tonicized, in the larger context of the phrase, and in conjunction with the move to the dominant that follows, the E f found at the end of the second ascending line is the harmonic goal of these four measures. The A f sonority can thus be understood at a deeper level as the subdominant of E f progressing to E f’s dominant and concluding on the Ef tonic, in a manner Schenker would term an auxiliary cadence.

Example 4.6. Wagner, Parsifal : Prelude, mm. 39–43

The B section of the prelude is predominantly constructed of multiple repetitions of the “Faith” Leitmotif .

As often occurs in the B sections of ternary designs, this section expands the V Stufe, though in mm. 68-69 the progression ii 7 – V – vi is sounded in A f major, signaling that E f is beginning to resume a chordal

94 Walter Frisch, German Modernism: Music and the Arts (Berkeley: University of California Press, 2005): 32. 253 dominant-functioning role. This deceptive gesture is repeated in mm. 72–73, and, I would argue, in mm. 75–

78. There, as shown in Figure 4.9, the deceptive progression is obscured by surface harmonic details: the ii 7

– V7 motion from the previous two deceptive gestures is repeated, but in m. 76 the dominant seventh

sustains over a tonic pedal: the final beat of the measure sounds an apparent A f-major triad, but the

function of the upper voices A f and C in this chord are anticipatory, and the E f in the lower voice functions

as the root of the dominant chord, not the fifth of the tonic. This detail is important, as the resolution of

this dominant is to an incomplete dyad made up of Af and C. This initially suggests an A f triad, until the

chord is completed in the next measure by the addition of F in the bass. The large-scale motion is thus a

third iteration of the same deceptive gesture, resolving V to vi in A f.

In terms of the deeper middleground structure, the implication of the deceptive resolution is that the

A’ section of the prelude begins over an F minor triad. Much like the initial motif (refer back to Example

4.5), which saw the pitch F preceded by an anticipation, one might similarly understand the two previous deceptive gestures at mm. 68–69 and 72–73 as larger-scale harmonic anticipations of this emphasized F that materializes at the outset of the A’ section at m. 79. The A’ section itself is not a strict reprise, but is fragmentary with a considerably different tonal trajectory. Instead of repeating the Communion motif in C minor, as happened in the opening section, the next sounding of the motif at m. 84 occurs in C f, which is

Figure 4.9. Wagner, Parsifal , Prelude, mm. 76–79

254

Figure 4.10. Voice-Leading Reduction and Analysis of mm. 88–90

prepared by its own dominant seventh in m. 83. I accord these occurrences a prominent place at the deep middleground, as they seem to function as analogous to the opening progression from A f to C.

In m. 89 there is a sudden shift into the key of D which, via conventional tonal theory, seems unprepared, as there is no explicit link from the preceding Bf half-diminished seventh chord in m. 88 to the dominant seventh on A in m. 89.95 However, using the theories discussed in this dissertation, the chord B f-Df-Ff-Af

o4 can be half-enharmonically reinterpreted as an altered vii 2 (C s–E–Gs–Bf) in the key of D, progressing much like the Tristan chord, to V 7. Figure 4.10 shows the voice leading here is consistent with a third- inversion leading-tone chord, despite the chromatic alteration, and the chord of resolution, the dominant of

D, is indeed typical of such a resolution.

D is subsequently expanded as a Stufe : the dominant seventh chord on A resolves to a D minor triad, which harmonizes a third entry of the Communion motif, repeated sequentially up a minor third from the

95 One might also consider the B f half-diminished seventh chord as fvi ø7 in D, although as I have argued is not a convincing chord analysis given that it includes an altered tonic pitch ( f1). A second possibility is to allow for more than the traditional three types of augmented-sixth chords (here one that contains the augmented-sixth interval, but with two common tones with the subsequent dominant), as Daniel Harrison suggests in “Supplement to the Theory of Augmented-Sixth Chords,” Music Theory Spectrum 17, no. 2 (1995): 170–195. I believe, however, that rather than introduce a completely new chord construction loosely- based on so-called augmented-sixth chords (which themselves are simply chromatic alterations of dominant-functioning chords), recognizing the chromatic alteration that occurs within diminished seventh chords is a more convincing solution. This is especially pertinent when the voice leading functions in a manner entirely consistent with a diminished seventh chord but for the chromatic alterations. A third option is the use of neo-Riemannian theory, especially as suggested by Cohn in Audacious Euphony . Cohn’s notion that a move from B f half-diminished seventh to a dominant seventh on A consists of two semitonal slides is correct, but I am hesitant to switch systems in the middle of an analysis on the basis of one chord, and prefer a tonal, albeit chromatic, solution to the problem. 255

Figure 4.11. Tonal Structure of the D-major Section

previous entry on C f. Figure 4.11 provides an analytic outline of the harmonic structure of this passage, which projects a similar triadic arpeggiation that has figured so prominently in the prelude: 1-3-5 expanding a given chord, this time D major. 96 As with previous iterations of the arpeggiation, the fifth steps up deceptively, this time to a B f triad. The subsequent progression B f-g7-C7 suggests a IV-ii 7-V7 progression

leading towards F, but is ultimately used to revert (again deceptively) to the supertonic of A f, unfolded in m.

97. This supertonic is expanded, and eventually gives way to the dominant, which is expanded through to the end of the prelude.

Instead of attempting to relate the prolonged D to an Ursatz -like structure, the perspectives I have

proposed in this chapter solicit a different way of interpreting the deeper-level structure of the Prelude. 97 If we follow the path of the expanded tonal areas through the Prelude, this D expansion occurs at an interesting juncture, between the C f preceding it, and the prolonged E f dominant that eventually follows it.

Figure 4.12 presents a graphic depiction of the progression of deeper-level fundamentals. Observe the

parallelism between this progression and the Communion motif shown above: the secondary tonalities of

the Prelude correspond to the pitches of the Communion motif first sounded at the outset of the prelude,

albeit sometimes in a modally chromaticized manner. In this sense, the larger-scale coherence of the Prelude

96 This obviously poses a conflict between the musical surface, which presented D minor as the key, and the deeper level of structure, which suggests D major through the arpeggiation. As noted previously, for the purposes of musical structure and the expansion of Stufen the modal quality is a moot point: Schenker would simply classify such a conflict under the umbrella of modal mixture. See also Patrick McCreless, “Ernst Kurth and the Analysis of the Chromatic Music of the Late Nineteenth Century,” Music Theory Spectrum 5 (1983): 56–75. 97 Indeed, some theorists have posited that sIV is inadmissible into tonal structure. See Matthew Brown, Douglas Dempster, and David Headlam, “The sIV( fV) Hypothesis: Testing the Limits of Schenker’s Theory of Tonality,” Music Theory Spectrum 19, no. 2 (1997): 155–183. 256

Figure 4.12. Deep Middleground Analysis of the Prelude to Parsifal

does not necessarily need to be a product of a deep-level replication of local syntactic function, but might be seen, as I have described, as projecting an enlargement of the Leitmotif that initiates the Prelude. Such a reading not only serves to suggest a principle for understanding the specific ordering of tonalities in the

Prelude, but also carries hermeneutic significance and interpretive potential.

We learn from the plot of Parsifal that prior to the point where the drama begins the leader of the

Grail Knights, Amfortas, had gone to Klingsor’s domain to confront the sorcerer. Amfortas, we learn, failed

in his mission, and was instead seduced by Kundry, which allowed Klingsor to gain control of Amfortas’

magical Spear and use it to deliver a wound to Amfortas that causes him unending anguish and never heals.

This event might also be thought of as a loss of purity for Amfortas, and by extension the Grail Knights,

and forms one of the primary conflicts within the opera. Because of the wound, Amfortas is unable to

perform in his role of leader of the Grail Knights, and it ultimately falls to Parsifal to defeat Klingsor,

reclaim the Spear, heal Amfortas, and save the Grail Knights. As William Kinderman describes it, “The

central dramatic tension consists in the threat to the Order of the Grail posed by the plight of Amfortas, whose festering wound opens afresh when he reveals the Grail at the communion service.” 98 Kinderman suggests that this conflict is represented in the juxtaposition of A f and C, which he describes as already being inherent in the Prelude. 99 However, as I have noted, C minor is not so outlandish in the key of A f:

98 William Kinderman, “Dramatic Recapitulation and Tonal Pairing in Wagner’s Tristan and Parsifal ,” in The Second Practice of Nineteenth-Century Tonality , ed. William Kinderman and Harald Krebs (Lincoln: University of Nebraska Press, 1996): 106. 99 Ibid., 106–107. 257 there are many more tonalities at work in this opera that pose tonal conflict with the key of the Grail

Knights: Klingsor’s B minor, Kundry’s G major/B minor, and the Spear’s D major.

Looking at the A’ section of the Prelude, and the way in which it chromatically inflects the G and C of the initial motif to G f and C f suggests an allusion to the aforementioned antagonists. G f is enharmonically F s, while C f is enharmonically B n, which then progresses to the prolonged D tonality. The

A’ section of the prelude, in this sense, composes-out Klingsor’s B-minor triad, as though the destructive tendencies of the sorcerer’s machinations—which have already injured Amfortas in such a way that could lead to the undoing of the Grail Knights entirely—are seeping into the musical fabric of Grail Knights as well. Bribitzer-Stull refers to this type of transformation as “harmonic corruption” of a Leitmotif , describing it as a more intense version of a modal shift. He writes, “Harmonic corruption, in particular, seems to be a

favorite of Wagner’s for suggesting stygian alterations in thematic association. Notable examples occur in all

[Wagner’s] operas after Rienzi in conjunction with a dramatic corruption of a theme’s original meaning.” 100

This type of tonal relationship, the chromatic inflection of the composed-out Communion motif, is not

something traditional Schenkerian theory would necessarily value, or bring to the fore of an analysis, and yet

the hermeneutic significance, that it represents musically Amfortas’ wounding and the subsequent onset of

deterioration into the Grail Knights, is of great importance. Indeed, Wagner himself suggests the motif is

laden with this potential, that “the pain of Amfortas is contained in [the motif].” 101 That the prelude is

unable to find its way back to the tonic after the violence of this chromatic intrusion is perhaps further reinforcement that the music here is depicting musically the primary dramatic problem of the opera, a problem to which the opera itself provides the answer.102

The tonal drama that I suggest is a product of understanding the prelude’s tonal structure as a

deeper-level composing-out of the Communion motif, and the association with the Grail Knights it entails.

100 Bribitzer-Stull (2015): 176–177. 101 Kinderman (2005, p. 167) writes that Wagner expressed this to Cosima. 102 David Lewin (1984, pp. 342–343) suggests that the role of D (part of the B-minor triad) is important to the tonal drama of Parsifal , and, specifically, suggests that D becomes an important element in returning to the tonic at the end of the opera, where he suggests the music does, finally, reaffirm the tonic of A f (with a lengthy plagal section afterward). 258

The relatively diatonic deep-level tonality of A f, the tonality of the order of the Grail Knights of which

Amfortas is the leader, and which is represented by the Communion motif, is distorted by the violent intrusions of the B-minor-related tonalities associated with Klingsor, Kundry, and the Spear. This intrusion does not destroy A f entirely, as the ending on V of A f suggests the possibility of returning to the stability of

the tonic, just as the wound does not kill Amfortas. Like Amfortas, after the violent intrusion of the

composed-out B-minor triad, A f can no longer easily fulfill its role as the tonal center. This suggests an

importance in understanding the deep-level structure as a composing-out of the Communion motif: the

chromatic inflections do not simply distort the tonality of A f but are enlargements that stem from a

chromatic problem that exists within the Communion motif itself, one that ultimately requires the

subsequent opera to resolve.103

Thus a more compelling conflict seems to center around these tonalities, and, more specifically, Dn, which, as David Lewin points out, is associated with the Spear. 104 Tonally, D n is the raised subdominant

pitch, which as I have suggested throughout can induce a strong level of tonal disruption into a progression,

especially when its use is not as the leading tone to the dominant. In this way, the Prelude might be seen as

setting up one of the tonal conflicts that I understand as forming part of the musical drama of the opera: the

role of D in respect to the tonality of A f. The Communion motif at the outset is almost entirely diatonic, with the exception of the raised fourth scale degree D n. Here we have what would otherwise be an entirely diatonic theme with a single intruding chromatic pitch, but one that proceeds in a tonally conventional manner, namely it functions as the leading tone to the dominant pitch. As such, I would argue that the D within the context of this initial presentation of the motif represents only a potential for disruption, one that

103 Frisch likewise (although for different reasons) notes that “within [the opening six measures] Wagner manages to convey much of the essence of Parsifal , especially the opposition of its two worlds—the realm of the grail and that of Klingsor.” Frisch (2005): 32. 104 David Lewin, “Amfortas’ Prayer to Titurel and the Role of D in Parsifal : The Tonal Spaces of the Drama and the Enharmonic Cf/B,” 19th-Century Music 7, no. 3 (1984): 336–339. B and F s are, enharmonically, C f and G f respectively, which can be fairly easily integrated into the tonality of A f as f3 and f7 respectively, whereas D cannot. 259 exists within the Grail Knights, but is kept suppressed by its function as a secondary leading tone to the dominant.

While the A f–D pairing is only one of the tonal conflicts in the opera, it is one that is highlighted by how it reaches a resolution in the opera proper.105 The moment at the end of the opera, shown in Example

4.7, in which Parsifal heals Amfortas with the spear, and then ascends to his new position as leader of the

Grail Knights, is the moment that David Lewin has cited as the “obligatory structural gesture of the opera,” which implies the structural close. 106 It is here where A f is re-attained

as the structural tonic, and where D n is diverted from distorting A f, and instead forms part of the

prolongational process that reaffirms A f as tonic. The following paragraphs will examine that passage in

more detail.

Firstly, leading up to the sounding of the dominant of A f in m. 1079, D is prolonged as tonic, but

transforms into a diminished-seventh chord immediately prior to the E f dominant, resolving up by step as

s4 should. This dominant is then prolonged for seven measures before resolving in a cadence on A f,

although Lewin writes of this moment:

I am puzzled by the harmonies of mm. 1084- 87, the measures that span this D-to-Af progression. Why should the huge A f arrival, so strongly plagal on a large scale, be approached locally from its dominant, Eb in m. 1087? And why should that Eb be preceded by its own dominant in m. 1086? 107

The approaches I have presented in this dissertation may help to account for this passage, and Lewin’s

puzzlement. Lewin’s struggle in this passage I believe stems from viewing the E f dominant in m. 1079 not

as the onset of the structural dominant, but rather as a continued prolongation of D.108 Indeed Lewin

105 For example, Lewin (1984) ascribes significance to the role of the enharmonic C f/B, as well as to the pitch D in a transformational perspective. Patrick McCreless conversely ascribes significance to the E/F dyad prominent in the opera: see Patrick McCreless, “Motive and Magic: A Referential Dyad in Parsifal ,” Music Analysis 9, no. 3 (1990): 227–265. 106 Ibid., 342. 107 Lewin (1984): 342. 108 Lewin suggests that “From this [D] chord in m. 1084, a chain of Liebesmahl incipits leads directly to the tonic A f downbeat four measures later. The stage action concomitant with this obligatory structural D-to-Af progression is the obligatory structural gesture of the opera: Parsifal, firmly in command of the office, discharges his foreordained duty by directing the unveiling of the Grail,” which suggests that Lewin views this not as E f to A f but D to Af. Ibid., 342. 260

Example 4.7. Wagner, Parsifal : III: mm. 1077–1087

suggests that the only dominant in the passage is the one in m. 1086, writing “unless…the solitary E f harmony of [m. 1086 is] to carry the structural dominant weight for the entire second half of Act III.”109

Understanding the onset of dominant function in m. 1079 might thus assuage Lewin’s reservations

regarding dominant function in this passage, while also further allowing the E f dominant to serve as the

resolution of the preceding D-based harmony.

109 Ibid., 343. 261

This E f dominant can then be understood as prolonged for the seven intervening measures (see Figure

4.13). What I suggest is that this passage exhibits similar logic to a number of passages discussed in previous

chapters. The dominant in m. 1079 resolves deceptively to fVI, embellished by what appears initially to be

7 o7 the tonic substitute V /IV, but which resolves as vii f5 of fVI, with a dissociated bass unfolding. The two

chords in m. 1082 can be thought of as vii o7 of the supertonic (B f): F s–A–Cs–Ds is enharmonically A–Cs–

os4 Ef–Gf, or vii 2 of B f. This is followed by a D major chord in m. 1083, which can also be enharmonically

o7 respelled, and understood as A–( )–Eff –Gf, or vii f5 of B f. This becomes D-minor in m. 1084 which then

progresses to, as Lewin notes, the dominant of the dominant, a B f7 chord. Figure 4.13 illustrates the tonal process I analyze here, where the D-major triad functions as an altered leading-tone chord of B f, and the D- minor triad is a voice-leading chord: the G f (spelled F s) from m. 1083 resolves to F n, while the A is held

over and resolves to B f in m. 1085. In this way, the transgressive D is also brought into the prolongational process of A f, functioning as an applied chord to the B f that prolongs the global E f dominant. 110

Figure 4.13. Analysis of Example 4.7

110 Indeed, this is how Alfred Lorenz analyzes the D major and D minor chords: essentially, he sees them as rootless variants of the B f dominant seventh, although this explanation is precarious, given that both employ A n, which makes it difficult to argue that they have dominant function in relation to E f. Instead, my argument suggests that their dominant discharge is towards B f, which then discharges its own dominant function onto the deeper-level dominant E f. See Lewin (1984): 343. Lewin disagrees with Lorenz’ analysis, suggesting it “goes too far” in asserting a large-scale structural weight for the E f chord of m. 1086. 262

V Salome , Scene 1

Like the Prelude to Parsifal , the tonal structure of the first scene of Strauss’ Salome can also be seen as an example of Leitmotivic Auskomponierung . Analyses of tonality in Salome are few and far between, but those

that do exist are generally oriented towards deep-level structure. Tethys Carpenter’s chapter in the 1989

collection of essays edited by Derrick Puffett, for example, uses a McCreless-esque scheme of dramatic

referentiality to guide her analysis. 111 Her analysis of the first scene exists only as a bass line sketch, and while it recognizes most of the same structural points as I do – she likewise sees the scene as a large-scale prolongation of C s – our analyses also differ considerably.112 Jean-Michel Boulay’s analysis is slightly more nuanced, but, desirous of demonstrating that the opera writ large is a “two-part structure,” Boulay does not recognize the return to C s at the end of the scene. 113 Like Carpenter, Boulay’s analysis also glosses over

much of the music, representing large sections with a single bass note. More extreme than either Carpenter’s

or Boulay’s readings is Bryan Gilliam’s assertion that the scene is tonally unstable. 114 He writes: “Strauss

suspends tonality…Although the scene begins and ends in C s...the only tonal stability is the pious,

disembodied voice of Jochanaan in C major.” 115 While the tonality is certainly not the clear diatonicism of

classical tonality, to characterize it as suspended tonality, is, I believe, an unfortunate product of the paucity

of research into Strauss’ more local harmonic-syntactic processes.

My analysis of the musical surface is presented in Figure 4.14. While I do not want to engage in a

chord-by-chord description, I would offer some short analytic commentary in order to clarify some of the

decisions. The first graph shows the analysis up to RH4. Following the opening C s chord, D becomes a

111 Tethys Carpenter, “Tonal and Dramatic Structure,” in Richard Strauss: Salome, ed. Derrick Puffett (Cambridge: Cambridge University Press, 1989): 89. 112 This is especially in the area from RH9 onward where she suggests a fuzzy sort of A f with an “echo” rather than understanding the passage all in relation to the overarching C tonality of the passage. 113 Jean-Michel Boulay, “Monotonality and Chromatic Dualism in Richard Strauss’ Salome ” (Ph.D diss. Eastman School of Music, 1992): 41. Boulay devotes only a single paragraph to the scene. 114 Bryan Gilliam, Rounding Wagner’s Mountain: Richard Strauss and Modern German Opera (Cambridge: Cambridge University Press, 2014): 82. Carpenter’s “echo” analysis, however, is likewise suggestive of a similar conclusion regarding stability. 115 One might also question what “stability” means. Does tonal stability result from merely the presence of cadential formulae (there are many)? From strictly diatonic harmonies? Or is it possible to project tonality even if the chords being used push it past the boundaries of what has hitherto been theorized? 263 secondary tonality and is prolonged via an arpeggiation through its mediant F, as well as a melodic descent from A to D. F, in turn, is prolonged through its own 1–3–5 arpeggiation. These features are important aspects in determining what should be considered a secondary tonality versus what is understood as a tonally emphasized, or prolonged, chord within a tonality. 116 While F receives its own prolongation,

complete with an IAC, that IAC happens mid-phrase in terms of the vocal line, which ultimately closes with the V b9 – i progression in D at RH4. The more strongly cadential PAC in D, combined with the closing of the vocal line, suggests that the prolongation of F is a structure nested within the prolongation of D, despite its length (and likewise the tonicization of A is weaker and short-lived compared to the F prolongation in which it is nested). Ultimately, over the course of the scene, the D itself becomes recognized as a nested structure, functioning as a deep-level neighbour tone to C s.

Figure 4.14. Foreground Analysis of Scene 1 of Strauss’ Salome

116 This nesting of common tonal structures within larger tonal structures within even larger ones poses analytic challenges when determining which is more important in terms of tonal structure, but, as Julian Horton (2015) notes, is also a recognized feature of formal structures in nineteenth-century music. 264

265

The second graph mostly depicts the reaffirmation of C s after the D-minor section through a multi- layered tonicization of the dominant. Here the main harmonic thrust is a tonicization of V. The half- diminished seventh chord just before RH8 functions as ii of V, moving to what I have analyzed as an altered diminished-seventh unfolding to the root-position V7/V through a passing six-four and an applied chord of

V/V (RH8). 117 Despite its complex presentation on the musical surface, the underlying process is relatively conventional: a move from one dominant-functioning chord to another, with an intermediary tonicization of the dominant to prolong the dominant function. Although Strauss spells the chords using the more performer-friendly flat-side notation, I have opted to re-spell them with sharps to more clearly show their

o6 (Gr) 7 harmonic function. From here, a vii 5 chord of C s pivots to become V /V in C major, which is confirmed through a V 7–I cadence. 118

The third graph details the first part of the C-major prolongation. Having confirmed C as the tonal

center, the music then expands A f through a progression that tonicizes its mediant, followed by its supertonic, and finally the tonic (RH10–11). Despite its length, the A f expansion should not be viewed as a deeper-level tonal center. I base this claim on two criteria: the A f prolongation beginning with an auxiliary progression – a weaker form of prolongation than the C-major tonality in which it resides – and the lack of a PAC in A f. As such, I believe it does not express the same level of tonal prolongation and closure as the deeper-level C tonality, and should be viewed instead as a prolongation of the fVI Stufe in C, eventually

progressing to the dominant, which resolves to the C major tonic (RH12). A similar process recurs at RH13,

117 While the notion of chromatically altered diminished-seventh chords has as yet not entirely made its way into contemporary discourse on tonality, Schenker discusses the possibility of chromatic alteration of leading-tone diminished-seventh chords in his Harmonielehre , citing a passage in Bruckner’s Ninth Symphony as an illustration of vii o7 with a raised fifth. He writes: “We are dealing here most certainly and most simply with a diminished-seventh chord on the VII step in D major/minor (related, by its univalence, to the V step of this same key), whose character is in no way interfered with by the chromatic change of raising the fifth G to G-sharp.” (Schenker 1954 [1906]: 279–86). Schenker understands such phenomena as linear displacements: the chromatic tone in question, E f, is passing conceptually from the normative E n, even though the E n is not sonically present. 118 Contrary to more conventional North-American understandings of the German augmented-sixth sonority as an exclusively predominant chord, I espouse the views of theorists such as Riemann and Schenker, who both view augmented-sixth chords as alterations of dominant-functioning sonorities. Riemann, according to Steven Rings (2011: footnote 31), preferred “reading the o7 o German sixth as an applied dominant.” Likewise, Schenker’s (1954 [1906]: 279) Figure 321 in Harmonielehre , gives vii b3 , vii b3 and 7 V b5 as his analyses of the German, Italian, and French augmented-sixth chords respectively. Thus the German chord of C s is o6 understood as a chromatic embellishment of vii 5 progressing to I in C s. 266 wherein an auxiliary progression in A f prolongs the dominant of C as a neighbour tone (RH14–RH17

[beginning of the fourth graph]). Again, there is no cadence in A f, and it is weakened by its auxiliary nature,

suggesting that it is better viewed as a prolongation of fVI in A f rather than its own tonality. This

neighbouring fVI ultimately returns to the dominant (RH17), which, in turn, is prolonged via its own

tonicization (as my analysis indicates, V is the ultimate goal of this tonicization, and is preceded by an

unfolding of fVII), before resolving to a C-major tonic at RH19. After this cadential confirmation, the C- major tonic then becomes a diminished-seventh sonority on the same root (C => C o7 ), in order to function on a more local level as vii o7 of C s and serving as a pivot to the original key for the conclusion of the scene.

Space constraints prohibit a more in-depth discussion of the specifics of the musical surface, though the graphs in Figure 4.14 are, I feel, sufficiently detailed to demonstrate the syntactic processes of the harmonic surface. The middleground analysis derived from the preceding foreground analysis is given in

Figure 4.15, and is itself further reduced to the background bass-line structure in Figure 4.16. My analysis understands the three prominent tonal centers of the scene as C s, D, and C n, the latter two of which Boulay notes “are keys of secondary importance.” 119 Using the notion of tonalities as composed-out elaborations of their fundamentals, this scene can be understood as a deep-level unfolding of a chromatic double-neighbour motion, from C s to D, to B s, back to C s. While this particular structure does not conform to Schenker’s Ursatz schemata, this does not mean that the music is inherently incoherent, or that it is not tonal.

Interestingly, Schenker took particular umbrage with Salome , writing “Strauss’ music, through its motives (one bar long or even less!) always resorts to the same trick, the trick of projecting neighbor motions – in the wider context of a trivial, irredeemably poor [process of] development, etc.” 120 Certainly if the Ursatz was Schenker’s point of reference for what makes for good processes of development, this might

119 Boulay (1992): 36. 120 Tgb. 25.V.1907 in Helmut Federhoffer, Heinrich Schenker: Nach Tagbüchern und Briefen (Hildesheim: Georg Olms Verlag, 1985): 258. Translated in Matthew Brown, “Polyphony and Cacophony?: A Schenkerian Reading of Strauss’ ‘Dance of the Seven Veils,’” in Explorations in Schenkerian Analysis , ed. David Beach and Su Yin Mak, 283–302 (Rochester: University of Rochester Press, 2016). 267

Figure 4.15. Middleground Reduction of Figure 4.14

Figure 4.16. Background Reduction of Figures 4.15

be true; one might, however, question the appropriateness of the model. Indeed, the coherence and design of this scene finds its brilliance in the way in which Strauss uses the double-neighbour figure not only as a surface-level Leitmotif , but enlarges it to generate the deeper-level structure of the scene, and uses this deeper-level tonal design as an expression of the scene’s dramatic content. The chromatic double-neighbour figure is, of course, of great importance in the opera: the first motif heard, that of Salome herself, is constructed from an incomplete double-neighbour figure around 5 in the tonic chord, as shown in Example

4.8a. Another of Salome’s motifs, this one heard prominently in her dance, is shown in Example 4.8b, and likewise deploys the chromatic double neighbour figure at a number of levels. Schenker’s analysis of a third motif, shown in Example 4.8c, depicts another instance of a surface-level double-neighbour figure. 121 Thus

the deeper-level structure of the scene can be viewed as an enlargement, or Auskomponierung , of this more surface-level motif.

121 Heinrich Schenker, Counterpoint [1910/1922], ed. John Rothgeb, trans. John Rothgeb and Jürgen Thym, 2 vols. (New York: Schirmer Books, 1987), I: 67. 268

Example 4.8a. Salome’s First Motif, m. 1

Example 4.8b. Salome’s Dance, 3 mm. before C

Example 4.8c. Salome’s Dance, 8 mm. before Q

But what can this analysis say about the music, the drama, or other aspects of Salome ? It illuminates, in my view, that relationships between the various characters in the opera has a level of musical nuance often overlooked in discussions of the opera. Cs is often described in this opera as the tonal center. As

Boulay notes, “notwithstanding a very high level of complexity, the tonal structure of Salome is organized around C s.” 122 Carpenter likewise writes: “Salome’s music has at its center C sharp,” indicating that this is

the key most strongly associated with the titular character. 123 The keys of D and E, peripheral tonalities in this first scene, are likewise associated with peripheral characters. D, at least in the first scene, seems to be

122 Boulay (1992): 36. 123 Carpenter (1989): 95. Boulay also notes that when Salome first enters in Scene 2, she does so in A major, the key in which that scene begins. Of this Carpenter writes: “Here is Strauss’ first attempt at ‘progressive’ tonality, for Salome’s character develops from naivety through frustrated desire to satisfaction of that desire, mirrored by A major, C s minor, and C s major” (1989: 95). While Carpenter’s claim is slightly inaccurate – this is not Strauss’ first instance of progressive tonality: his choral song “Der Abend” (1897), for instance, begins in G major and ends in E minor – the relationship between C s and A is a notable one: using a more transformational lens, A major is a single semitone displacement from C s minor, suggesting a very close proximity between the two. 269 initially adopted by Narraboth (the music shifts to D when he begins his first line), though as he becomes more enraptured with Salome his utterances fluctuate more towards C s. C, as Carpenter describes, is used

more as “an abstract symbol on which everything that opposes or conflicts with Salome [may be built].” 124

For instance, C (in various modal inflections) comes to be used most prominently by both Herod and

Jochanaan. Indeed this occurs in the first scene: the portion of the scene where Jochanaan is speaking from the cistern, or being discussed by the guards, is guided by an overarching C tonal center, as shown in Figures

4.15 and 4.16.125 Gilliam reflects on the C s-C relationship further, citing the semitonal opposition as one

Strauss had explicitly exploited before, in Also Sprach Zarathustra .126 Gilliam’s analysis of the first scene posits a deep level C s–C–Cs outline, similar to my own analysis, except he does not accord D the same level of tonal weight. 127 One might, then, see this opening scene as structured in a way that reflects the dramatic content of the interpersonal relationships between characters: Salome exists as the central locus around which the actions of the rest of the characters hinge. Both Herod and Narraboth are drawn towards Salome,

just as the two chromatic neighbours are drawn towards the tonic. 128

More than simply being a clever parallelism between the music and the drama, uncovering these

types of relationships might also be used to further engage with certain dialogues that surround the opera

Salome , and specifically the nuances of the relationships between characters and notions of power. Lawrence

Kramer, for instance, castigates Strauss, and his music in particular, as “[contributing]…to the masculine

projects of scopic triumph,” and being “deliberately theatrical in the debased sense of the term.” 129 But

Kramer goes even further, writing of Strauss’ music:

124 Carpenter (1989): 94. 125 The expansions of the fVI (A f) and fIII (E f) chords occur most prominently when other characters (i.e. the guards) are speaking about Jochanaan. 126 Gilliam (2014): 81. Gilliam describes the two keys as representing the sensual (C s) and the ascetic (C), reflecting the tonal antagonism between I and VII. 127 Ibid., 81. 128 Carpenter further suggests that Herodias adopts the key of E more often than not, which has no particular gravity or strong function in relation to a C s tonic (1989: 95). One might also suggest that while Jochanaan is able to control his own desires, he refuses to look at Salome because it would break his resolve. Indeed, as Hutcheon and Hutcheon (2000: 219) note: “Jochanaan too knows the power of the visual and refuses to look at the staring Salome. The power is in the one beheld and not in the beholder. Jochanaan refuses to give Salome the power that would result from his gaze.” 129 Lawrence Kramer, “Culture and Musical Hermeneutics: The Salome Complex,” Cambridge Opera Journal 2, no. 3 (1990): 285. 270

Densely contrapuntal, elaborately and often thickly orchestrated, it sounds more like a vertical mass of sound than a purposeful movement in time. 'Ranting and raving', to use Strauss's own description, the music is also impossible to dominate vocally, however 'Isolde- voiced' the singer may be. Its chief effect is to hold Salome in place: to situate her more for the eyes than for the ears of the audience. As a result, what the audience encounters is less a character singing than a woman, as woman, acting out a multiple debasement: scopic, erotic, artistic, linguistic. What Jochanaan's head does to Salome, Strauss's music does to the singer who embodies her. Strauss exacts this punishment in a style that Salome herself has seemed to create: sensuous, reiterative, highly wrought, resistant to closure. Strauss, too, endorses the fin-de-siècle style by reshaping its 'effeminacy' as anti-feminine. 130

Contrary to Kramer, Carolyn Abbate is slightly more ambivalent in her assessment, suggesting that while Salome is the constant object of visual attention, she also transcends that role through her voice, before being ultimately silenced. 131 But Linda and Michael Hutcheon challenge the views of both Kramer

and Abbate. The conventional view, they write, is that:

Through distancing, the observer has the potential power of objectifying what is observed, of mastering and controlling it. Because of this connection between power and the act of seeing, the privilege of vision has been linked to sexual privilege: the gaze has thus been gendered male, leaving women as the objects of the gaze… 132

They argue, however, that “Salome the character and Salome the opera turn this now widely accepted theory

on its head. Here, to be the object of the gaze is to have ultimate power; it is the position of being looked at

that conveys mastery and control.”133 Thus they conclude that Salome recognizes the power of vision, and turns that power to her own uses, as she “alters the power dynamics of the gaze itself.” 134

These various perspectives are notable in the ways in which they conflict with each other. On the one hand, Salome is viewed as an object: mistreated, demonized, and destroyed by Strauss’ orchestration and musical machinations. Conversely, she is viewed as a subject: sympathetic, powerful, and whose strong centric role in the drama drew Strauss to composing the opera. The perspectives of all three authors also share another commonality: analysis of the music beyond surface-level observations plays virtually no role in

130 Ibid., 281–282. 131 Carolyn Abbate, “Opera, or the Envoicing of Women, in Musicology and Difference, ed. Ruth A. Solie (Berkeley: University of California Press, 1993): 254–256. 132 Linda Hutcheon and Michael Hutcheon, ““Staging the Body: Strauss’ Salome, ” in Siren Songs: Gender and Sexuality in Opera , ed. Mary Ann Smart (Princeton: Princeton University Press, 2000): 217. 133 Ibid., 219. 134 They also note that the power of the gaze is reinforced through Jochanaan’s refusal to look at Salome, who even laments in her final monologue that he would have loved her had he only looked at her. 271 their assessments. As Blair Johnston observes, “few accounts…provide detailed analysis in support of or instead of vivid interpretive claims.” 135 In the 2002 forward to a reprinting of Feminine Endings , Susan

McClary asks “that the field allow for cultural interpretations.” 136 I could not agree more, and indeed the plethora of new vistas that have arisen since McClary penned her forward (and even more since Kerman’s

1985 publication of Contemplating Music ) is indicative that these types of interpretation have indeed found

their place within the field. But what I hope the above discussion has reinforced is that these perspectives

are symbiotic with analysis, and one must engage with both in order to produce a convincing argument. 137

My analysis of the tonal structure described above supports the notion that Salome is indeed the recipient of the male gaze within the opera. The tonalities of Herod and Narraboth surround Salome’s own tonality, drawn towards the C s much as the two men surround and are drawn toward the princess herself.

But it also supports the assertions of Hutcheon and Hutcheon that the power dynamics here are not of the

conventional sort: C s, Salome’s key, is the point of tonal reference in the opera. The other keys of D and C are subordinate to C s in a tonally hierarchical sense, and find their structural meaning as neighbour tones through their relationship to the C s tonic. This likewise suggests that the characters associated with these tonalities derive their meaning in the context of the drama through their (periphery) relationship to Salome, but she remains central to the drama, and, in many ways, controls the actions of the other characters.

This is further reinforced at the end of the opera. Like the first scene, the climatic monologue, which

Craig Ayrey has described as “recapitulatory,” prolongs C s, sometimes cast in the minor mode, sometimes the major. 138 While space constraints preclude a full analysis of the monologue here, important for the

135 Bair Johnston, “ Salome ’s Grotesque Climax and its Implications,” Music Theory Spectrum 36, no. 1 (2014): 34. 136 Susan McClary, Feminine Endings: Music, Gender, and Sexuality (Minneapolis: University of Minnesota Press, 2002): xiv. 137 Others too, such as Adorno, Abbate and Parker (1989: 4), and Kerman (1981: 53) have all pointed to the necessity of analysis in the study of music, with Adorno’s statement being one of the most eloquent. He writes: “The signs and the music which they signify are never directly one and the same thing. And in order to read notation at all, so that music results from it, an interpretative act is always necessary – that is to say, an analytical act, which asks what it is that the notation really signifies. Already in such elementary processes as these, analysis is always essentially present. The façade – i.e., the score as 'picture' [ das Notenbild ] – has to be unraveled, dissolved, [ aufgeloast ] (and this as reliably as possible) in order to arrive at that which is indicated by the score” (Adorno 1982: 172). 138 Craig Ayrey, “Salome’s Final Monologue,” in Richard Strauss: Salome, ed. Derrick Puffett (Cambridge: Cambridge University Press, 1989): 111. 272 current argument is the conclusion of the opera. The final cadence, shown in Example 4.9, is an unequivocal

PAC in C s major, as Salome proclaims that she has kissed Jochanaan’s mouth, an action she swore she would accomplish earlier in the opera. C s major, then, might be seen to reflect

Salome’s perception of the events, rather than that of other characters. 139 That Salome achieving her stated goal coincides with this moment of structural and rhetorical closure further confirms the importance of C s as the tonal center of the opera. C s is then undermined, as Herod watches the scene unfold in horror, and orders his guards to kill Salome. As they carry out this order, the orchestra bellows out what Alex Ross has described as “noise.” 140 The opera, as such, does not end in C minor, but rather ends more simply on a C- minor chord: no tonal progression occurs in C, and the proliferate chromaticism obscures any sense of key or tonal center until the final C-minor hammer blows once the curtain has fallen. This C-minor passage, then, might be likened more to a coda, or what form-functional theory might

Example 4.9. Strauss, Salome , Final C s PAC (3 bars before RH361)

139 If one were to impose a Schopenhauerian reading of this, one might suggest that the triumphant C s-major conclusion underscores and reflects Salome’s psyche and view of events, while the C imposes an outside force that cuts off and destroys that particular point of view. Strauss’ relationship to Schopenhauer is somewhat more ambiguous: at one point he was, like Wagner, heavily entrenched in Schopenhauerian doctrine, but he more-or-less abandoned it early in his career. Charles Youmans (2005) offers an accounting of Strauss’ intellectual development, including his flirtation with Schopenhauer. Youmans cites a letter from Alexander Ritter, one of Strauss’ early mentors of a Wagnerian-Schopenhauerian disposition, who, upon Strauss’ veering away from Schopenhauerian beliefs sent a letter castigating the composer that “nothing of Wagner’s worldview remains in you. What alone of Wagner has survived in you? The mechanics of his art.” This suggests that despite abandoning the intellectual backdrop in which Wagner’s own harmonic language developed, Strauss did not abandon entirely the technical aspects of that language. 140 Alex Ross, The Rest is Noise: Listening to the Twentieth Century (New York: Farrar, Straus and Giroux, 2007): 9. 273 describe as something that happens after the end. 141 Acoustically the opera concludes on C minor, but structurally, and, I believe, tonally, C minor should be understood as more of a codetta-like appendage rather than a structural imperative. 142

Thus it is Salome’s tonality that carries the weight of being the central tonic of the work, and the

center that receives the final tonal closure as Salome achieves her goal (if, perhaps, not entirely how she

planned) of kissing Jochanaan’s mouth. Far from the music destroying, marginalizing, or negating Salome, it

supports and confirms her key. Likewise, the first scene composes out her motivic content in the form of a

deep-middleground double-neighbour tonal structure. These analyses further support the documentation

left to us from Strauss’ correspondences and writing. While Kramer’s arguments indict Strauss’ music as

complicit in Salome’s subjugation and de-powering, Strauss’ own comments suggest that he viewed the

character of Salome as sympathetic. “Salome,” Strauss writes, “must be played with the simplest and most

restrained gestures, unless her defeat by the miracle of a great world is to excite only disgust and terror

instead of sympathy.” 143 Conversely Strauss seemed to have had the most antipathy towards the male characters. In a letter to Stefan Zweig Strauss describes Jochanaan as “a clown,” noting that a preacher who

“lives in the desert, especially one who feeds off locusts, seems infinitely ridiculous to me.” 144 In the same letter he notes how his setting of the play “pokes fun at Father Herod.” The analysis I have presented reinforces that there is a level of ambiguity present in the opera regarding the interpersonal relationships and

power dynamics in the opera that needs to be acknowledged. It is not quite as simple as picking a side and

141 William Caplin (2009: 23), for example, refers to coda functions as “after-the-end.” The idea that the music can continue after what is the more structural end of a piece is commonplace in discussions of music. Codas in sonata-form movements are perhaps the most common examples, but even in opera, scenes such as the final prolongation of A f in Parsifal strike as a sort of musical unwinding. 142 Susan McClary suggests that “Salome’s pathology is signaled by her slippery chromatic deviations from normative diatonicism. In this she is a sister to Isolde and Carmen, who likewise play maddeningly in the cracks of tonal social convention.” But McClary also writes that Salome is “crushed to death beneath [the guards’] C-minor shields” because “the monstrosity of Salome’s sexual and chromatic transgressions [demand] extreme violence for the sake of social and tonal order.” What McClary fails to acknowledge is that the C-minor section is just as, if not more, chromatic than what precedes it. This is an important point, that chromaticism and diatonicsim are not so easily separated into binaries, and there should be a certain caution exercised regarding hermeneutic readings of chromaticism as transgressive and diatonicism as order. 143 Richard Strauss, Recollections and Reflections , ed. Willi Schuh, trans. L. J. Lawrence (London: Boosey & Hawkes, 1953): 151. 144 144 Richard Strauss, Letter to Stefan Zweig, May 1935. In A Confidential Matter: The Letters of Richard Strauss and Stefan Zweig, 1931–1935 , trans. Max Knight (Berkeley: University of California Press, 1977): 90. 274 claiming Salome is or is not misogynistic or explicitly masculine: a closer investigation of the musical structure adds a further layer of nuance to any arguments one wishes to make about the opera and its role in various facets of early twentieth-century European culture.

Conclusion

This approach, to understand a tonal structure as being generated through the enlargement of the

melodic contour of a prominent motif, does not, as noted, necessarily conform to traditional conceptions of

tonal structure, nor is it meant to be understood as an assertion that this is the only way to analyze deeper

level structure.145 That being said, I hope that my arguments regarding the understanding of tonality as

mostly a product of surface-level chord progressions that compose-out middleground-level Stufen provides a

contrast to the more conventional, but questionable, assertions of deeper-level “unity” or coherence as a

product of an axiomatic background schematic . While this approach does not allow for a deeper-level

parallelism between these deeper-level prolonged tonalities and the way in which foreground chord

progressions function, such an approach is, and always has been, tenuous at best, often, as Morgan describes

it, “[offering] a ready handle with which to grasp the form but [distorting] its most original and distinctive

features.” 146 Instead this approach posits a parallelism between deeper-level structure and melodic-motivic aspects of individual works.

The idea of Leitmotivic Auskomponierung suggests that there exists more than a single way of deploying

Schenkerian analytic procedures to understand musical coherence in a work and that this idea of internal

coherence versus external unity is an important one. One might see Schenker’s Ursatz , and the various

proliferations of its use through the decades, as a way of imposing an external view of unity onto music,

145 Certainly other tonal-structural strategies exist: for example, one might see the secondary tonalities that Strauss’ tone poem Don Juan employs as an outgrowth of the prominent (i.e. given some degree of emphasis) non-tonic pitches (B, G n and C n) in that work’s P-space (itself a more complex version of a common tonal strategy in earlier works in which a surface-level chromatic pitch inflects the deeper-level structure). See James Hepokoski, “Fiery-Pulsed Libertine or Domestic Hero?: Strauss’ Don Juan Reinvestigated,” in Richard Strauss: New Perspectives on the Composer and his Work , ed. Bryan Gilliam (Durham and London: Duke University Press, 1992): 144–145 especially for a discussion of the piece’s tonal areas. 146 Morgan (2000): 69. 275 namely the axiomatic approach that many scholars have questioned. 147 This external view of unity suggests that there is some ‘thing’ music must do, a certain set of criteria that it must fulfill in order to be viewed as good or worthwhile. But as Abbate and Parker note, “analysis is at its worst when trapped in a cage of tautological value judgements predicated on musical unity, for then it has no devices for coping with music

that is ambiguous…with the enigmatic.” 148 Conversely, I see the approach I have advocated here, one that

engages in a more internal view—prioritizing the unique ways in which a piece or movement unfolds

tonally—rather than a function of an axiom, as a way of understanding what makes a piece coherent. As

mentioned above, I use the term coherent as a means of describing the ways in which a piece follows some

sort of discernible logic, be it tonal, transformational, or otherwise. A “discernible internal logic” is, of

course, a fluid concept, but one that I think is a productive way in which to view the nature of theory,

analysis, and the roles they play in the broader discourse of musicology; that is, to speak about music. One

of the roles of theory and analysis is, in my view, to discern these internal logics, and the beauty in analysis is

that the internal logic can vary from piece to piece, composer to composer, but can also be traced through

several different pieces, or can be related as extensions of earlier practices, thereby suggesting a

compositional trend, or process. Indeed, this is one of the currently popular approaches to the analysis of

form, viewing it as a dialogic process between works; presumably the same approach could be adopted in

the study of harmony and tonal structure. 149

And this approach further responds to some of the criticisms or discomfort that have been raised regarding analysis and hermeneutic interpretations. Lawrence Kramer, for example, projects a discomfort with analysis that prioritizes deep-level relationships, citing specifically that “most analytical practice devalues—normatively devalues—the communicative action of the foreground,” and the ways in which the

Ursatz “supplies the underlying vital principle…on which the expressivity of the foreground ultimately

147 For example: Narmour (1977), Abbate and Parker (1989), Cohn (2012). 148 Abbate and Parker (1989): 3. 149 James Hepokoski and Warren Darcy, Elements of Sonata Theory: Norms Types and Deformations in the Late Eighteenth-Century Sonata (New York: Oxford University Press, 2006) adopt this approach as their methodology for discussing sonata forms. 276 depends.” 150 When Kramer uses the term foreground, it is worth noting he is speaking not of individual harmonies so much as foreground musical effects, such as melodic devices, contour, or sonorous qualities.

Kramer suggests elsewhere 151 that these aspects of the musical foreground are in fact worth prioritizing over any such structural considerations, and while I would not go so far as to agree, I do think, as I have outlined in this chapter, that analysis depends on the interplay between syntactic foreground elements—chord progressions that prolong various local tonics—and the ways in which these prolonged local tonics interact with each other at a deeper level of structure. One cannot make tenable, meaningful claims for one without the other, and the strongest analyses are those that are supported by both. As suggested in my analysis, there is a case to be made for the hermeneutic claim that in composing-out the “Communion” motif, yet corrupting it chromatically, the Prelude to Parsifal projects musically the initiating dramatic elements of the plot that occur temporally before the opening scene: this is not a product of the musical surface, but the musical surface plays a role in understanding the unfolding of the deeper-level tonal sequence of events and the stories it tells.

In short, my proposition is that there is never any single way to understand structure and coherence in music. Rather, a multiplicity of approaches is conceivable, so long as they are grounded in relatively consistent and defensible analysis. As much as I have argued against the Ursatz as a tonal-structural

imperative in this chapter, it too has value in certain situations and cases; I simply caution against adopting it

as a requisite ontological or epistemological value in undertaking analysis of coherence or structure in tonal

music. And here we find ourselves back almost where we started, with the questions of ontology and

epistemology that underlie music theory and analysis, of what motivations, desires, or priorities we bring

into analysis. I am not, as I see it, arguing so much for an “out with the old!” approach that seems inherent in some of the more contemporary manifestations of analysis, but rather to approach some of music theory’s tried and tested traditions with a conscious apprehension. The most interesting observations—be

150 Lawrence Kramer, “Haydn’s Chaos, Schenker’s Order: or, Musical Meaning and Musical Analysis: Can they Mix?, in Critical Musicology and the Responsibility of Response: Selected Essays (Burlington VT: Ashgate, 2006): 243. 151 See Lawrence Kramer, “Culture and Musical Hermeneutics: The Salome Complex,” Cambridge Opera Journal 2, no. 3 (1990): 269–294. 277 they musical, hermeneutic, or cultural—come, in my view, from the ways in which musical relationships unfold in this music in a reflection of previous practice: the ways in which they interact in ways that are similar, yet subtly different from the syntax with which music scholarship deals far more comfortably. That the pitches in a particular passage might form an octatonic collection, or that a few triads exhibit parsimonious voice leading, or that the prolonged tonalities in a piece do not conform to conventional

Ursatz analysis all relate isolated technical details about the music, but they are often incapable of suggesting much in terms of musical dialogues and relationships beyond “this is not tonal,” where instead, as David

Kopp suggests, we should instead be asking how such passages can be understood to exhibit tonality. 152

152 David Kopp, “Chromaticism and the Question of Tonality,” in The Oxford Handbook of neo-Riemannian Music Theories , ed. Edward Gollin and Alexander Rehding (New York: Oxford University Press, 2011): 401. Kopp also reflects on the predisposition of music theory to engage in “presentism,” which he partially defines as “an inclination…to find evidence in earlier music or music theory of a concept not articulated until later,” citing in particular the predilection to observe in music written in a tonal style elements of atonality and non-tonality. Conclusion

The impetus for this dissertation was what I viewed as a distinct lack of any sort of codification of

the principles of the harmonic syntaxes of composers such as Wagner and Strauss in the same way that the

harmonic syntaxes of the common practice era have been understood, particularly as extensions of that

preceding practice. As such, this dissertation has focused on understanding ways in which the harmonic

syntax of composers in the mid-to-late nineteenth and early twentieth centuries extends the conventions of

classical tonality. My approach to this endeavor, however, has strayed from some of the more common

approaches: rather than deriving a syntax a priori from the vertical objects themselves, or from their position in an abstract tonal phrase structure, my focus has engaged with the ways in which unconventional vertical

objects behave on a more immediate level. While Schenkerian theory has never been bereft of a focus on linear and contrapuntal elements—indeed these are sometimes given overemphasis—observing the interaction between not only harmony and counterpoint, but moreover the specific details of of voice leading and dissonance resolution, provide a means of reconciling what often appear to be tonally disjunct sonorities within a larger prolongational framework, without resorting to ad hoc labels of chromatic alteration.

Indeed, if this dissertation responds to anything, it is to the notion of chromatic alteration, and perhaps, as an extension of that, an attempt to more clearly articulate where the boundary of tonality and atonality might lie. It is, as I have expressed throughout, a somewhat fallacious concept to expect that chromatic alteration can simply happen, that something can have an equivalence relationship with something else without a rigorously defined rationale behind what elements foster that relationship. As mentioned at the outset, in some cases there is a convincing link. IV and iv, for instance, can be explained as equivalents through the concept of modal mixture and the notion that they both are tonally referential to the same tonic pitch. The link between ii 7 and V 7/V is slightly less clear: they are both chords built on 2, and both conventionally progress to V. The former, however, is referential to the tonic, while the latter derives

278

279 its referentiality to the tonic through the mediation of the dominant. In this sense they have a surface-level similarity, but their deeper-level point of tonal reference diverges. But other cases, many of which I have presented throughout this dissertation, are far less convincing. III s and VI s are particular points of interest for me, because I find it impossible to conceive of these chords as able to contribute directly to promoting, or prolonging, a tonic when they employ chromatic pitches that alter the fundamental polarity between tonic and dominant pitches that define a tonal center. 1 But these are still relatively tame alterations in comparison to some of those proposed by writers such as Schoenberg, or Riemann. My qualms with these approaches are not that one cannot derive chromatic triads from diatonic ones, but rather I find such an unrestricted process to be unfulfilling in its explanation of the ways harmonic syntax is extended in the late nineteenth and early twentieth centuries, especially in the music of composers like Wagner and Strauss, whose music

seems to be grounded unflinchingly in tonality. As I have noted previously, if there exist no restrictions on what can be altered, then the concept of alteration ultimately proves hollow and meaningless. If anything

can be anything else than everything is an identity relationship.

This is not to say that this notion of alteration did not play any role in late nineteenth- and

twentieth-century tonality, but, as I have suggested the possibility of alteration, at least in the works

discussed herein, seems to have been informed by other musical parameters. Under these considerations,

Schoenberg’s famous proclamation of the emancipation of the dissonance, or Webern’s assessment that

tonality was “in its last throes,”2 might require reassessment. As my study of the tonal language of Wagner

and (pre-Ariadne auf Naxos ) Strauss suggests, the use of what Daniel Harrison refers to as “fundamental

dissonances,” (the diminished fifth and diminished seventh) and the continued resolution of these intervals

according to classical convention remained one of the prevalent factors in their tonal language, even if the

presence and behaviour of the aforementioned intervals were masked behind veils of enharmonicism or

apparent consonance.3

1 Recall Deborah J. Stein’s similar argument that the III s, understood as such, would necessitate a projection away from the tonic, and thus be unable to—directly, I would add—prolong a tonic. 2 Anton Webern, The Path to the New Music , ed. Willi Reich, trans. Leo Black (Bryn Mawr: Presser, 1963): 47. 3 Daniel Harrison, “Supplement to the Theory of Augmented-Sixth Chords,” Music Theory Spectrum 17, no. 2 (1995): 171–173. 280

It is these veils of convention under which composers like Wagner and Strauss were able to subtly

extend the conventions of tonality. The apparent sonorities of the chords in question—chords with a

diminished-seventh function that sound like dominant or half-diminished seventh chords in the wrong

places, triads whose presence defies the conventions of tonality if understood as triads, or chords with

added notes—invoke a type of conventional hearing and reading which, at first glance, gives the impression of random or wanton alteration. To recall Joseph N. Straus’ argument:

The harmonic syntaxes that I have identified in this dissertation are emblematic of Straus’ argument. And, as

I argued in the introduction, where conventional tonal materials used in unconventional ways are often apparent in the more atonal works of other composers, in this repertoire the subtlety in which they are integrated into the tonal fabric that gives the music the sensation of being something different without creating a complete break from tonality.

Beyond the technical aspects of music, however, this work has three broader continuations that I intend to pursue in the future and will sketch out in summary below. The first involves the philosophic underpinnings of Wagner and Strauss’ music. Both, as has been adequately noted, found inspiration in the works of Arthur Schopenhauer. 5 For Wagner, this was relatively late in his career, for Strauss relatively early

(and short lived). Indeed, Strauss’ relationship to Schopenhauer is somewhat more tenuous, and, without

claiming to be in any way encompassing, a short summary of his interactions with Schopenhauerian

4 Joseph N. Straus, Remaking the Past: Musical Modernism and the Influence of the Tonal Tradition (Cambridge: Harvard University Press, 1990): 1. 5 For instance: Bryan Magee, The Tristan Chord: Wagner and Philosophy (New York: Holt, 2000), Warren Darcy, “The Metaphysics of Annihilation: Wagner, Schopenhauer, and the Ending of the “Ring,” Music Theory Spectrum 16, no. 1 (1994): 1–40, or Deryck Cooke, I Saw the World End (London: Oxford University Press, 1979). Similarly: Charles Youmans, Richard Strauss’ Orchestral Music and the German Intellectual Tradition (Bloomington: Indiana University Press, 2005), Charles Youmans, Mahler and Strauss: In Dialogue (Bloomington: Indiana University Press, 2016). 281 philosophy might be of use. Like Wagner, Strauss was at one point heavily entrenched in Schopenhauerian doctrine, but he more-or-less abandoned it early in his career. Charles Youmans offers an accounting of

Strauss’ intellectual development, including his flirtation with Schopenhauer in his monograph Richard

Strauss’ Orchestral Music and the German Intellectual Tradition . Youmans cites a letter from Alexander Ritter, one of Strauss’ early mentors of a Wagnerian-Schopenhauerian disposition, who, upon Strauss’ veering away from Schopenhauerian beliefs sent a letter castigating the composer that “nothing of Wagner’s worldview remains in you. What alone of Wagner has survived in you? The mechanics of his art.” 6 This suggests that

despite abandoning the intellectual backdrop in which Wagner’s own harmonic language developed, Strauss

did not abandon entirely the technical aspects of that language. Indeed, Bryan Gilliam notes this as well, writing:

Adorno recognized in Strauss’ unique modern attitude the protean composer’s desire to undermine a transcendent and metaphysical worldview, even as the latter used Wagner’s own technical and musical apparatus of a massive orchestra, chromatic harmonies, a system of leitmotifs, and the like. 7

While many scholars have noted the influence of Schopenhauer on both composers, and have suggested that the influence extended to their music and compositional practices, Gilliam’s quote above is emblematic of the ways in which the harmonic domain is treated in these studies. Few have noted the ways in which the syntax can be understood to express such a philosophic underpinning beyond relatively surface-level observations such as the scarcity of cadential articulation in Wagner. The work in this dissertation, I believe, suggests that there are other ways in which the musical syntaxes of both composers can be understood through the influence of Schopenhauerian metaphysics and philosophy.

The most explicit example of this, in my view, is the concept of apparent consonances developed in

Chapter 2. When a triad is sounded, the effect (phenomenal) is one of consonance since listeners entrenched in the Western classical style are conditioned to hear triadic constructions, but the function of the chords, at least as I have described them, is one of extreme dissonance. Thus a conflict arises between

6 Letter from Ritter to Strauss, Jan. 17 th , 1893. Quoted in Youmans (2005): 68. 7 Bryan Gilliam, “The Great War and Its Aftermath: Strauss and Hoffmansthal’s ‘Third-Way Modernism,” in Modernism and Opera , ed. Richard Begam and Matthew Wilson Smith (Baltimore: Johns Hopkins University Press, 2016): 130. 282 hearing the chords as the consonances that they appear to be—as has been the case with most analyses of such repertoire in the past—and hearing them in terms of their voice-leading function, which one might suggest is a more noumenal reading of the chords. The consonant aspects of the chord suggest a place of rhetorical stability, but the dissonant aspects force the chord to push forward and resolve into the more stable consonance. A similar, though less extreme, claim can be made for altered diminished-seventh chords: acoustically they project a certain function, often dominant of some other key, but when they resolve, that apparent dominant function is revealed to be illusory, and the key suggested fails to materialize. Likewise, my notion of apparent prolonged, less consonant appendages such as sixths and fourths above a functional bass, projects a very apparent Schopenhauerian underpinning. For Schopenhauer, life was constant striving towards goal after goal. Once one goal was attained, there was no—or very limited—satisfaction, as another goal simply took its place and the striving began anew. 8 The consonance function of the abnegated chords

remains, and in this way one can understand some sort of tonal stability, but the appended pitches also

propel that harmony forward; as more dissonant displacements of the expected consonances, these

appendages elicit a propulsion towards the consonances they displace. In this sense, one goal (tonal

consonance) has been attained, but it is not an end, and a new goal (a deeper level of acoustic consonance)

replaces it in the form of the sixth (or whatever other appendage arises) needing to resolve. With these

illustrations in mind, it may be profitable to future research to reexamine some of the previous thinking on

the relationships between Wagner and Schopenhauer, and Strauss and Schopenhauer, from the perspective

of their musical languages.

Secondly, there remains (and likely will always remain) other ways in which this music can be

approached, analyzed, and discussed, and the approaches developed in this dissertation are not meant to

stifle other approaches to the music. Indeed, as I have suggested, I feel that many of the approaches I have

developed herein complement a number of other approaches, especially those of neo-Riemannian theory

and Schenkerian analysis. While I have already elaborated at length in Chapter 2 on the ways these

8 Again this is not meant to be a comprehensive study, and I offer only the briefest of summaries of Schopenhauerian philosophy. 283 approaches integrate with neo-Riemannian perspectives, the ways in which it influences Schenkerian studies

has remained somewhat underdeveloped. In short, I believe the approaches suggested herein allow for a

more convincing reading of many of these pieces from a Schenkerian perspective. Where in the past these

chords have been often overlooked as voice-leading chords, the perspectives I have developed suggest

specific ways in which they fulfill both that particular linear function while still exhibiting a harmonic

4 function as well. As I have mentioned, if we can understand the linear function of a V 3 chord while still

understanding its harmonic role as a prolongational dominant, then a similar dual linear-harmonic

understanding should be possible for almost any chord that we wish to integrate into a tonal structure. 9

Even within the confines of the system that I have appropriated for this study there remains more work to be done: the concept of the Unterterzen discussed in Chapter 2, for instance, could be elaborated further and with broader application. The notion of double alteration, and its consequences, could likewise be further studied—it received what I feel was only the briefest of expositions in Chapter 1. Likewise, the relationship between abnegating chords with various appendages could be further studied as an intermediary state between the triadic and inversion-theory dominated classical syntax and the syntax of early twentieth- century composers like Debussy, in whose music the bass is typically the strongest signifier of function.

Beyond even this, the concept of added, less-consonant appendages also suggests a comparison with contemporary pop harmony, wherein chord symbols employ figurations such as SUS, or ADD regularly, suggesting an understanding of harmony similar to the one I am advocating for isolated instances in the music of the late nineteenth and early twentieth centuries, namely that these notes are added, in a non- tertian sense, to the function of the bass.

Thirdly, this study gives a grounding for further investigation of Strauss’ post-Elektra operas, which have in general received far less scholarly attention than Salome or Elektra . With a framework of tonality for late Wagnerian and early Straussian tonality in hand, I believe it would be a fruitful undertaking to

9 This is not to say that purely linear, or passing chords (such as passing chords in a voice exchange), do not exist, merely that it is too often the case that chromatic harmonies that are difficult to integrate conventionally into prolongational analyses are simply written off as linear phenomena. 284 investigate how (or if) Strauss further extends his tonal language in later operas. This possible project also gives rise to another project, namely the question of Strauss and modernism after Elektra , discussed briefly

in Chapter 3. As Michael Kennedy notes, “throughout his long composing career—a total of seventy-eight years—[Richard Strauss] remained true to a belief in tonality as the cornerstone of musical craft.” 10 Indeed

Strauss’ adherence to tonality in the atonal- and serial-dominated landscape of the first half of the twentieth

century, led to accusations of “betraying modernity,” especially after his more harmonically adventurous

Elektra . Strauss, however, demurred. Shortly before his death in 1949, he wrote: “Why don’t people see what is new in my works, how in them, as is found otherwise only in Beethoven, the human being visibly

plays a part in the works?” 11 But the attitude of understanding most of Strauss’ post-Elektra works as

artistically stagnant, even retrogressive, in their clearly tonal framework remains entrenched in contemporary

scholarship. 12 Indeed, as both Gilliam and Walter Frisch argue, it is not so much the musical language of

Strauss’ later operas that is modernistic, but rather their focus on the individual and a “rejection of collective redemption.” 13

But despite the accusations of betraying modernity, as Hasselböck argues Strauss’ musical syntax was simply less jarring to the ear than that of other composers owing to its framing in tonality: but this does not mean that Strauss’ artistry was stagnant, nor retrogressive. Indeed, as Example 5.1 and 5.2 demonstrate, instances of questionably tonal procedures continued to form part of his later operas. Example 5.1, from the

third act of Die frau ohne Schatten , illustrates a pentachord that is, in my view, more tonally perplexing than

the famous Elektra Chord. Example 5.2 shows the opening of Die Ägyptische Helena . Here it is difficult to give any sort of functional analysis to the succession of chords leading up to the arrival on D at RH1, and even at this point of arrival the bass and upper voices seem to be divorced from each other: the D in the

10 Michael Kennedy, Richard Strauss: Man, Musician, Enigma (Cambridge: Cambridge University Press, 1999): 4. 11 Richard Strauss, Betrachtungen und Erinnerungen , ed. Willi Schuh [Zürich, 1949]: 182. Quoted in Kennedy (1999): 5 (Kennedy further notes that this is not included in the English translation Recollections and Reflections ). 12 A notable exception, Lukas Hasselböck—using examples from Strauss’ Lieder from ca. 1900—argues that Strauss’ harmonic language employed highly chromatic and tonally disjunct chords, and, as such, was just as innovative as other composers in the early twentieth century, if less jarring to the ear. See Lukas Haselböck, “Beiträge zur Untersuchung der Harmonik in den Strauss- Liedern (Der Einsame – Im Spätboot – An die Nacht),” Richard-Strauss-Blätter 43 (2000): 179–186. 13 Gilliam (2016): 30. See also Walter Frisch, German Modernism: Music and the Arts (Berkeley: University of California Press, 2005). 285

Example 5.1. Strauss, Die Frau ohne Schatten , Act III, 3mm. before RH 187

Example 5.2. Strauss, Die Ägyptische Helena , Act I, mm. 1–10

286 bass is approached by C s and E, giving the bass progression a weak quasi-dominant projection towards D, which is obscured by the tonicization of E-minor (Ds–Fs–A–C one measure before RH1) and the subsequent E-minor triad sounded above the bass D at RH1. It is too simple an overstatement to state one way or the other whether Strauss’ post-Elektra operas were modernist, or relics of the past, without undertaking a detailed study of the mechanics and processes of their musical language.14 I believe further study, armed with a clearer understanding of the tonal practices that prefigure these operas, can help add nuance to this debate, and contribute further to discourses surrounding the historiography of tonality in the early twentieth century.

Fortunately, this idea that tonality, atonality, and the concept of musical modernism are not so clearly defined and require further research, analysis, and consideration—especially in the case of Strauss— links back with one of the less explicit points of this dissertation, namely that it is important to avoid the complacency, as Daniel Harrison aptly refers to it, of accepting the ways things are without questioning them simply because they appear to follow tradition. 15 This is true of most of the approaches that I have

advocated in this dissertation: that conventional tonal materials, such as triads and seventh chords, can be

repurposed as other, slightly less conventional versions of other tonal materials, that the concept of the

augmented-sixth chord requires re-evaluation, that the deeper-level structure of a work can be informed by

the musical surface, rather than the other way around. Each of these perspectives grates against the

conventions of contemporary analytic practice, against the conventions of Schenkerian views of tonality and

structure, and in some cases against the historic narrative of music history around the turn of the twentieth

century. And yet grating against these conventions has, I believe, proven to generate insight into music

14 Citing “Brahms the Progressive,” an essay in which Schoenberg undertakes a technical study of Brahms’ musical syntax in order to combat the image of Brahms as conservative in his musical syntax, as a model, Leon Botstein suggests that “the comparable argument for Strauss would have to show that Strauss prefigured the aesthetics of postmodernism; that beneath the surface of seemingly stylistically regressive music aspects of innovation, which have been the hallmarks of a new movement, were apparent.” Botstein argues that “if one were to approach the catalogue of Strauss’ work not from a historical and chronological perspective, but methodologically in retrospect, one might come to a set of novel conclusions.” See Leon Botstein, “The Enigmas of Richard Strauss: A Revisionist View” in Richard Strauss and his World , ed. Bryan Gilliam (Princeton: Princeton University Press, 1992): 16– 17. 15 Harrison (1995): 170. 287 previously isolated by a syntax that likewise appeared to grate against the conventions of tonality. And yet adopting these approaches also, I believe, helps us understand with greater clarity some elements of that same transitory period, and gives us a more precise tool through which to examine the multitude of musics happening at that time. If we can begin to understand the relationships between the musical languages of

Wagner and Strauss and their predecessors, as well as their contemporaries and successors, then we can begin to more accurately, and with greater nuance and clarity, discuss the changing musical landscape of in the culture of late nineteenth- and early twentieth-century Europe. Bibliography

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