© 1979 James Lamb A GRAPHIC ANALYSIS OF BRAHMS, OPUS 118, WITH AN

INTRODUCTION TO SCHENKERIAN THEORY

AND THE REDUCTION PROCESS

by

JAMES BOYD LAMB, B.M., M.A.

A DISSERTATION

IN

FINE ARTS

Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of

DOCTOR OF PHILOSOPHY

Approved

Accepted

December 197 9 ACKNOWLEDGNENT

The author wishes to ackno-'ledge the contribu­ tions of both time and thought from the members of the committee, particularly Cr. Harold Luce, who took time from his administrativi^ duties to chair the committee and to Dr. Lee Rigsby, who came out of retirement to aid in the completion of this project-

Their valuable comments and support are deeply appreciated. It is a difficult task to acknowledge all those who have made this project a reality. I must, however, cite the contributions of my other professors and especially my students at Kansas

State University. I also express gratitude to Gary

Cobb, who often served as a sounding board for the refinement of many ideas. To Pat Stewart for her timely clerical assistance, I extend my thanks.

An.d, of course, I offer a very special, warm thanks to ra>' wife, Lynn and daughter, Kathlyn, for their ceaseless understanding and patience, and many words of encouragement during a time of frequent neglect.

ii CONTENTS

ACKNOWLEDGMENT ii

I. INTRODUCTION 1

II. AN INTRODUCTION TO SCHENKERIAN THEORY 10

III. THE REDUCTION PROCESS 33

IV. A GRAPHIC ANALYSIS OF BRAHMS, OPUS 118 66

Glossary of Graphic Symbols 66

The Work as a Whole 68

No. 1, Intermezzo 69

No. 2, Intermezzo 75

No. 3, Ballade 94

No. 4, Intermezzo 106

No. 5, Romance 114

No. 6, Intermezzo 128

V. CONCLUSION 146

BIBLIOGRAPHY 151

111 CHAPTER I

INTRODUCTION

Analysis, in the words of Allen Forte in his Contemporary Tone

Structures, is "neither composition nor a method of teaching compo­ sition; nor is it perception, or a way of learning to hear. It is a systematic attempt to obtain significant information about a tonal structure." Forte continues by stating that analysis is the work of the theorist and that it "claims to deal more directly and rigorously with music than does any other type of discursive treatment because it is closer to music. [It] is part of music theory and has its roots in the works of the medieval theorists, while music criticism and many phases of musicology stem from literary criticism." What is to be gained from analysis is increased understanding. Through this increased understanding, more artistic interpretations in perfor­ mances, more perceptive listening, and perhaps more inspired creations will result.

Edward T. Cone exhibits a somewhat different:, but similar point of view when he states in his article, "Analysis Today," that the best analysis is the one that "recognizes various levels functioning simultaneously, as when a tone resolves once in the immediate context

Allen Forte, Contemporary Tone Structures (New York: Columbia University Press, 1955), p. 2. but turns out to have a different goal in the long run." Cone,

recognizing more of a dependence on the ear, continues.

The greatest analysts (like Schenker at his best) are those with the keenest ears: their insights reveal how a piece of music should be heard, which in turn implies how it should be played.^

An analysis of any work of the nineteenth century must be able

to deal with one aspect which is of paramount importance--that of

tonality, which was perhaps the prime organizing factor of musical

unity in the music of that century. The tonal events of a musical

work must be investigated in relation to what precedes them and what

succeeds them and in relation to the whole.

A tonal musical work unfolds on various levels--formally, the whole, the movement, the section, the phrase, the motive. The

musician has always utilized the concept of musical hierarchical

structures, as depicted in the diagram of Figure 1.

Tonal relationships exist in hierarchic order as well as formal

relationships. This concept of hierarchic structure or leveled structure, derives preeminently from the analytical approaches of

Heinrich Schenker (1868-1955). Over a period of more than thirty years he formulated an approach whicn has revolutionized the field of musical analysis. He is perhaps the most significant theorist of the

1 "Edward T. Cone, "Analysis Today," Musical Quarterly, 4b, No. 2 (April 1960), p. 178. Edward T. Cone, "Analysis," p. 174. entire composition r movement

section r phrase groups r phrase

motive 1 1 notes

Figure 1. Formal hierarchic structure.

twentieth century. Some evidence of his stature and influence lies in

the following statements (some quite lengthy, but pertinent) by many

of the leaders in the field.

He has been the first modern theorist to find out how the imagination of a composer works, and to differen­ tiate between the raw material itself and the con­ summate art that turns this raw material into a great masterpiece. For some of us at least, Schenker's work has revolutionized the whole conception of music as art.^

In the past thirty years or so, we have witnessed the beginning of a revolution in the theory and analysis of tonal music . . . there seems to be a recognition that many of the concepcs and methods commonly employed are seriously inadequate. Dis­ satisfaction with the misleading results of the old descriptive procedures—the naive associations inherent in the Roman-numeral analysis of harmonic function, the lifelessness of symbolizing form by letters or numbers (ABA, 4-1-4), the trivial results

4 Adelle Katz, "Heinrich Schenker's Method of Analysis," Musical Quarterly, 21 (1935), p. 328. of analyzing melodic "climax" according to curvi­ linear graphs (symmetrical vs. skewed shapes, etc.)—has resulted in a growing appreciation of the work of Heinrich Schenker. . . . His recog­ nition of the importance of harmonic process in tonal music, his symbolization of it through the formulation of the Ursatz and the Urlinie, and particularly his concept of harmonic transfor­ mations on various levels all clearly remain among the most consequential achievements of music theory in this century. ... In our time only Schenker can claim to have created an entirely new system of analysis. . . . The importance allotted Schenker's theory and the enthusiasm surrounding his work seem justified.^

Some writers go so far as to designate his approach as the mainstream;

"Of the numerous analytical systems now applied to music, none has gained more universal recognition than the Schenkerian approach."

Heinrich Schenker's theoretical work was completed as long ago as 1935, with the posthumous publication of Per freie Satz, but only in the last decade or so has its influence grown to the extent that it must be considered the mainstream of musical analysis. . . the hegemony of Schenkerian analysis is virtually total in the current world of the music theorist, certainly for tonal music and often for other repertories as well; it seems to be an idea whose time has finally come.

Cogan and Escot also recognize Schenker as one of the most influential of twentieth-century theorists.

Eugene Narmour, Beyond Schenkerism: the Need for Alternatives in Music Analysis (Chicago: University of Chicago Press, 1977), p. 1, c Charles M. Joseph, rev. of Layer Analysis by Gerald Warfield, The American Music Teacher, Feb.-March 1979, p. 47.

Ruth A. Solie, rev. of Beyond Schenkerism by Eugene Narmour, Notes, 34 (1977), p. 857. The Austrian theorist Heinrich Schenker and his followers revolutionized musician's [sic] views by illustrating in many elegant analyses the linear motion in eighteenth and nineteenth century music (and its relevance for that music's entire structure), . . . For almost two hundred years . . . musical analysis followed Rameau almost exclusively, whereas compositional training and practice were deeply influenced by Fux, Not until the early twentieth century did theorists . . . principally the Austrian, Schenker--openly consider and resolve the contradictions. In the process the two theories emerged as con^lementary, and the nature of spatial motion in tonal music began to be illuminated by analysis.8

The technique of graphic analysis through reduction, is a process developed by Schenker and one which reveals tonal relation­ ships on more remote levels. Schenkerian analysis is, as aptly described by Maury Yeston.

far more than an arhythmic portrayal of long- range voice-leading. It is, primarily, a means of uncovering organic unity within masterwcrks of tonal music, with "organic unity" understood not as an abstract aesthetic norm but rather as a demonstrably concrete relationship of part to whole.^

Of particular interest is his description of the graphic notation system, as he continues.

g Robert Cogan and Pozzi Escot, Sonic Design: the Nature and Sound of Music (Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1977), pp. 153 and 77. 9 Maury Yeston, ed., Readings in Schenker Analysis and Other Approaches (New Haven and London: Yale University Press, 1977), p. 6. What makes the uncovering possible is the spatial mode of presentation that Schenker integrated into his system, since the very medium of discourse about the object under consideration--the work of music—is also music. In this respect an analysis can aspire to the musical elegance of its object much in the same way that literary criticism aspires to the condition of literature.^^

Diverse analytical approaches offer new, fresh insights into a work. No one approach is necessarily the best approach, as each may be a better tool than another to illuminate one aspect of the work, a view held by most analysts, and certainly evident in the following quotation. In discussing the nature of a piece of music and of musical analysis, Charles J. Smith, in his article "The Notations of

Analysis" claims.

The purpose of an analysis of a piece of music is to communicate something about that piece, while ideally reflecting in its own form something of that which it is about. ... A piece of music is^ in as many ways as it can be described, experienced, etc. There is no such thing as "the way a piece is,"--every approach yields a new viewpoint and hence a new "piece," whether that "approach" results from a complex of innate aural prejudices or from the most "sophisticated" analytical theory. An analysis of a piece is an explicit pro­ jection of a structure of relations "heard" in a piece.^^

The aspect of music which Schenkerian analysis is perhaps the best tool with which to gain understanding, as evidenced by Yeston's

Maury Yes ton. Readings, p. 6.

Cliarles J. Smith, '^Tae Notations of Analysis: An Approach to a Theory of Musical Relations," In Theory Only, 1 (Dec.-Jan. 19^*5-76), p. 15. description, is tonality and tonal coherence. However, even staunch

Schenkerians certainly will admit that much is to be gained from other

approaches. Yeston, in the preface to his collection of articles

clearly reflects this attitude as he states.

It is clear that all of the authors of this volume are united by a common passion for musical under­ standing and that no single approach, no matter how all-encompassing, can exhaust a musical master­ piece of its meaning.-^2

That one Schenkerian analysis may differ from another is also 13 a possibility, as evidenced by an occasional "analysis forum" in

recent issues of In Theory Only and other journals. The criticism

that Schenkerian analysis is dogmatic with no room for alternatives

has been leveled against it. However, differences in readings do

occur as in the Rothgeb and Schachter analyses of the Schubert

Impromptu, Opus 94, No. 1, analyses which Yeston describes as "a

fortuitous demonstration of differences that can arise in the context

of two Schenkerian approaches to the same piece.

One must remain aware at all times, that the visual, the graphs,

are a result of an aural perception, as evidenced in Milton Babbitt's

statement regarding the method.

^ Maury Yeston, Readings, p. 6,

^"^See "Analysis Symposium: Brahms, Der Tod, das ist die kiihle Nacht, Op. 96/1," In Theory Only, 2, No. 6 (Sept. 1979).

1 A Maury Yeston, Readings, p. 5. [Schenker's] procedures are essentially a descrip­ tion of his own hearing of musical works, and the orderly formulation of the principles derived from such hearing. . . . Within the framework of Schenker's analytical principles, one can arrive at an analysis of a specific work at variance with Schenker's own. There is no authority of ultimate validity beyond the formed, informed, and intelli­ gently experienced musical perception.15

The aural sense is, of course, basic to all musical activity, since music is an art of sound, and as Katz states "The art of hearing in motion—that is the sum total of the Schenker method."

Schenker's musical concepts in general are not simple. Until the forthcoming release in the iiranediate future of Oster's transla­ tion, Der freie Satz, his final and most significant work is available 17 commercially only in the original German. Its complexity and general unavailability is evidenced in John D. White's statement:

"It is a valid method, though a bit con^lex for general use . . . and the beginning analyst should be aware of this method for later study."

Quoted in Sonia Slatin, "The Theories of Heinrich Schenker in Perspective," Ph.D. diss. Columbia University 1967, p. 555.

"^^Adelle Katz, "Heinrich Schenker's Method," p. 528. 17 A translation by Theodore H. Krueger was completed as a doctoral dissertation at University of Iowa in 1960, but was never published commercially. It is available, however, through University Microfilms, Ann Arbor. 18Joh n D. White, The Analysis of Music (Englewood Cliffs, New Jersey: Prentice-Hall, 1976), p. 10. The present work atteii5)ts, in the ensuing chapters, to (1) present the theories on which his analytical method is based, (2) to present the tool of analysis, the reduction technique, and (3) through the applications of (1) and (2) an analysis of Brahms' Opus 118. CHAPTER II

AN INTRODUCTION TO SCHENKERIAN THEORY

The theories of Heinrich Schenker (1868-1935), often obscured by his own obscure language and the difficulties of translation, still remain awesome to more than a few musicians today. Presently, an attenpt will be made to describe his theories in not the technical jargon of the theorist, but, as nearly as possible, in the musical language of the traditionally trained, and practicing, musician.

The core of the study of music theory in Germany as it had developed in the eighteenth century was voice-leading, involving the study of counterpoint as codified by Johann Joseph Fux in his Gradus ad Pamassum (1725) and the study of thorough bass as codified by Carl

Philipp Emanuel Bach in his Versuch uber die wahre Art das Clavier zu spielen (1762). Jean-Philippe Rameau's discoveries of the principles of harmony were developed in his Traite de I'harmonie of 1722, and were introduced in Germany by Friedrich Marpurg in his Handbuch bey 2 dem Generalbasse und der KomiDOsition." As Rameau's influence became

A few such passages are given in Theodore H. Krueger, "'Per freie Satz' by Heinrich Schenker: A Complete Translation and Re- editing. Vol. I: The Complete Text. Vol. II: Supplement of Musical Examples," Diss. University of Iowa 1960, p. Ixix.

"For a thorough discussion of Schenker's predecessors, refer to Sonia Slatin, "The Theories of Heinrich Schenker in Perspective," Diss. Columbia University 1967, and Robert P. Morgan, "Schenker and the Theoretical Tradition: The Concept of Musical Reduction," College Music Symposium, 18, No. 1 (Spring 1978), pp. 72-96.

10 11 widespread, the amalgamation of voice-leading, harmonic center, and scale-step led to a theory of chords. According to Rameau, a triad and all of its inversions generated one and the same fundamental root, a theory whose basis is in the natural harmonic series. Consequently, underlying music was a fundamental, or ground, bass, derived from the roots of all the triads. Since each note of this ground bass was derived from the sounding chord, a mere passing chord could produce the same root as the cadence chord, suggesting equality of the two chords as part of the fundamental bass. The fundamental bass was to progress primarily by fifths, Basic to the fifth progression was the dominant-tonic relationship which created the tonality, and, inherently, modulations abound in chromatic music.

In response to a need for a better means of evaluating notes,

Hugo Riemann provided a theory of functions, which reduced all chords singly to tonic, dominant, or subdorainant. Riemann's contribution allowed for altered chords within the tonality, but still did not allow for the possibility that identical chords might have different meanings according to the context in which they move. This theor>' was concerned with chord to chord relationships.

It was Heinrich Schenker who first revealed a more direct relationship between the horizontal and the vertical and supplied the energy necessary for a broader understanding of the whole. His

3 See particularly Hugo Riemann, Harmony Simplified, or The Tonal Function of Chords, trans. H. Bewerunge (London: Augener and Con^jany, 1895). theories evolved over a period of more than thirty years in various books, articles, and other publications. His Harmonielehre (Harmony) was published anonymously in 1906 under the title Neue musikalische

Theorien und Phantasien (New Musical Theories and Fantasies). 11 .vas the first of a long series in which his theories were revealed as they were developed. Oftentimes these concepts were first revealed in immature, embryonic forms which underwent subsequent development before their final presentation in Der freie Satz (Free Composition), in 1934, a few months after his death. It is this final work which reveals Schenker's ideas in their final form and is his most important work. Schenker's theories are tonal theories. Living at the end of the nineteenth and into the first third of the twentieth centuries, he exhibits in his theories the culmination of tonality as the prime organizing factor of musical unity. Like Rameau and many others before him, Schenker refers to the triad as the only musical entity tied to nature, a relationship that can be seen in the first five

overtones of a harmonic series. He purports that each tonal work

(earlier music was as yet imperfect by his standard, as was modem music) was a unique interpretation of the triad, the tonality, and was an "unfolding" (Auskomponierung) of that triad over the course

of the composition.

^See Heinrich Schenker, Harmony, ed. by Oswald Jonas, trans. Elisabeth Mann Borgese (Chicago: The University of Chicago Press, 1954) and Free Comoosition, ed. Oswald Jonas, trans. Ernst Oster (New York:""Longman', Inc., 1979). For a complete listing of Schenker s works, see David Beach's bibliography in Yeston's Readings. 15 Although this concept is difficult for many to accept, it is little different from saying simply that the tonality is established over the course of the composition and that all sounds relate in one way or another to this tonality. Even the main structural harmonic component of sonata form is supportive of the tonality, or the tonic triad (I—-^v ||«i».uA^v I- H). Using a little of the theories of

Rameau and Riemann, one can say that I-V-I is all that is needed to establish the tonality. Such a totally harmonic explanation is not really what Schenker says at all, as his is a combined contrapuntal and harmonic explanation. It is, nonetheless, what results in the music and is a logical attempt to explain Schenker in functional harmonic thought.

In the course of the unfolding of this tonic triad a structural framework emerges. The harmonic aspect of this framework is referred to by Schenker as the Ursatz, translated by various writers as "pri­ mordial structure," "proto-structure," "archetypal structure." Tliis structural framework is the unfolding of the triad. It is the "hori- zontalization" of the triad. Consequently, it is not difficult to conceive of the triad as being prolonged. Since horizontalization is the concept, one must approach the music in terms of voice-leadings, i.e., contrapuntal principles. The top-most structural voice, not necessarily corresponding to melodic tones, produces a stepwise

^These and other translations are on page 170 of Slatin, "Heinricn Schenker's Theories."

Refer to Adelle Katz definition, page 22. 14 descending line from any member of the tonic triad to the tonic pitch.

Consequently, there are three forms of the Urlinie, as Schenker calls this top line: 321,54321, or 87654321. This Urlinie is st5)ported by a bass voice which arpeggiates among the members of the triad, with a goal of the fifth scale degree imjnediately preceding the tonic. This total structural level (the Ursatz, of which the

Urlinie is the top-most voice) is referred to as the background

(Hintergrund) .

Just as the background is an unfolding and consequently a prolonged tonic triad, any or all of the resultant constituents in the background level can be prolonged through various techniques of prolongation to produce an intermediate level called the middleground

(Mittelgrund). Prolongations of various constituents of the middle- ground will produce the foreground level (Vordergrund), which now very closely resembles the actual surface sound.

.An analogy with architecture may provide a useful illustration for further clarification. Architecture is concerned with filling three-dimensional space with a usable structural entity. Two buildings side by side, one very ornate, the other extremely simple and plain, may seem to be totally different from each other, yet stripped of the finish-work, they could very well reveal identical structural designs and construction. As is the case with any

7 Following the practice of Schenker, the scale degrees of the Urlinie are indicated with carets to distinguish them from other Items indicated with Arabic numbers. 15 structure, the structural framework is usually not visible. Much of what is seen is purely ornamentation.

/ Schenker has often been misinterpreted regarding the Ursatz, tlie ultimate structure. It is not inportant that all music can oe AAA , , 3 2 1 8 . reduced to j y I 1°^ one of the other limited types), but it is important that the structure be secure and adequately support the music which rests on it. It is not of significance to the viewer or user, that there are only a limited number of architectural types

(rectangles, triangles, cubes, pyramids, etc.), but it is vital to the users of the building that it be structurally sound. What probably will have the most immediate appeal to the building's occu­ pants will be the finish-work and extras, the decorations, the usability of the space, etc.

Implicit in this description of music as an unfolding, is the concept of constant motion. Schenker has often been criticized for attributing a static quality to music in the concept of prolongation.

Nothing could be more foreign to the concept. The musical work is in a constant state of motion, with directional goals, both raelodically in the tonic goal of the descending Urlinie, and harmonically in the tonality-defining structural dominant of the Ursatz. Upon reaching A 2 9 y, the most intense motion completes the inevitable return to tonic.

8 A A A A background consisting of an Urlinie of 3 2 1 which is supported harmonically by tonic with a movement to the dominant upon the arrival of 2, coming to a full close on 1 supported again by tonic. 9 '^ As described previously, this symbol represents the Urlinie 2 supported by the dominant in the background level. 16 The motion just described is that effected by the background.

Also present within the music are more immediate, detailed motions, the motions which prolong any or all parts of the background. It is here, in these more immediate levels, that the concept of prolongation becomes paramount. Once again a reference to architecture may aid in the clarification of the concept of prolongation.

As one approaches from a distance, he sees the whole edifice of a church in its rural setting, and realizes the upward projection of space the structure creates. As he comes nearer, he can no longer see the open countryside, but does begin to notice individual windows, doors, and various other aspects of design. As he walks up the steps, he can no longer see the steeple above his head, but notices the beautiful carvings on the huge wooden doors. And, as he turns the door knob, he can no longer see the top of the doors, but focuses very intently on the right wing of the angel in this minute part of the carving.

This same line of thought, from the general to the specific, from the whole to its parts, is partially analogous to that of back­ ground to one prolongation in the middleground, to specifically one chord in the foreground, one that may not even appear in the general, as certainly the wing of the angel does not. However, the analogy is only partially complete. The act of focusing in on the wing tells nothing about the function of that wing in the structure of the church building. To complete the analogy, the function of each part and the relationship of the parts to each other and to the whole must be considered. 17 The door fills a space. Although it is certainly functional, practical, and even aesthetic, it is not structural. The building would not lose any support and coherence in structural design, were the doors not there. What is more, to the solidarity of the structure it matters not what materials are used in the construction of the doors; they could be made of wood, cast iron, chrome and glass, or even papier-mache. Doors of each of these materials, however, would serve a different function, and each would be filling the door-space differently. The door-space is part of a larger space, one that is definitely structural--the wall space. Without a beam at the top of the wall-space, there would be no support for the roof, and conse­ quently no church. The structural framework is on the perimeter of the wall-space and the particular materials and design of the wall could have been of a different sort. However, this wall with this design fills this wall-space. In other words, the carvings are space­ filling in the wood; the actual doors are space-filling in the door- space, and all are space-filling in the wall-space, all of which in turn, is space-filling, but is structural, to the entire edifice.

In music, many of the motions on the surface are space-fillers.

They are unfoldings on the foreground level of an entity which exists on the middleground level, in which that entity may very well be only a part of the unfolding of an even more structural entity on the back­ ground level. It is in this regard--that of the realization of function or significance of an entity or motion to the structure of the phrase, section, or work--that the layered approach offered by

Schenker is vastly different from and, in this writer's opinion, an 18 improvement Lq)on that developed by the Rameau-in flue need theorists. The approach of the latter is seemingly overly concerned with the chord at the moment only in relation to itself, the scale, the harmonic series, and to only the chord immediately before it and after it. This concern is much like examining the angel's wing without realizing its relation and function within its setting and, consequently, its signi­ ficance to the whole structure.

The work of Hugo Riemann was an in^rovement upon the Rameau method. His attempt to delineate the functions of tonality and to carry those functions to increasingly broader areas was certainly an advancement towards understanding the relationships within the larger contexts. However, the primary deficiency in the Riemann approach was the failure to acknowledge variable chord significance. With

Riemann, in a given key, the tonic triad was always tonic function, regardless of its position within the phrase, and hence, carried the same weight at all times.

These comments regarding Rameau and Riemann are in no way meant to underrate the contributions of these two great theorists to the field of music theory. It is highly likely that they were, indeed, aware of the larger relationships within music, as is evidenced by

Riemann's generalized conception of tonality--that all features of a tonal composition must express the content of a single underlying key.

Moreover, it is this conception of tonality, as Robert Morgan so aptly develops in his article, "that forms his [Riemann's] most important contribution to the theoretical atmosphere in which Schenker developed--an atmosphere which Riemann shaped . . . to a remarkable 19 ,,10 extent. Morgan also points out that, although one would be mistaken to contend that Schenker consciously adapted the theories of his predecessors to fit his theoretical framework, there is some indication that he was at least partially cognizant of them. In fact it would have been most unlikely that Schenker's work would have even been possible had these two great theorists not preceded him, for, as

Morgan again surmises, Schenker's contribution is

both more and less original than is generally assumed: less in that it does not offer a totally unprecedented way of looking at musical structure; but more in that it radically transforms inherited theoretical ideas, lending them a totally unforeseen new meaning and unexpected life. Schenker then has maintained tradi­ tion in the very moment of altering it.^l

It should be quite apparent by now that this unfolding is stretched out through time and motion, and that this entity space­ filling is effected through the technique of prolongation. Prolon­ gation is defined by Adelle Katz in her excellent article as "the means by which the genius translates this primordial material [Ursatz] into a Foreground that is the result of his own fantasy and imagi-

1? nation."* Thus prolongation is the means by which the Ursatz under­ goes organic growth. It is the embellishment, the working out, and

Robert P. Morgan, "Schenker and the Theoretical Tradition: The Concept of Musical Reduction," College Music Symposium, 18, No. 1 (Spring 1978), p. 94.

Morgan, pp. 95-96. ^^.Adelle Katz, "Heinrich Schenker's Method of .Analysis," .Musical Quarterly, 21 (1935), pp. 511-529. 20 the heightening to certain significance of various aspects of the basic structure. Prolongation, in the Schenkerian sense, does not

imply making a note or passage temporally longer, but "can be

described as something relatively complex which serves as an elabora­

tion of something that is relatively simple.""^"^ Felix Salzer refers

to prolongation as the "life-giving force" of a conposition, as he states.

It remains futile knowledge unless we recognize the directed motion within the framework with its limit­ less possibilities of variety, detours, and delays called prolongations, and which are the life-giving force of a composition. It is this intricate interplay between the inflexibility of the structural framework and the elasticity and reproductive activity of the prolongations that explains a most significant factor in the art of composition: the purpose and meaning of directed motion. ^^

Several of the means by which prolongation is accomplished are described by Katz. The following examples are offered by her in the previously mentioned article. In Exan^le 1-a the space of the third

(5 to 3) in the C major sonority is filled in with a passing note F. ^

Gerald Warfield, Layer Analysis: a Primer of Elementary Tonal Structures (New York: Longman, Inc., 19 78, first pub. 1976 by David McKay). 14 Felix Salzer, "Directed Motion: The Basic Factor of Musical Coherence," American Musicological Society Journal, 3 (1950), p. 157. .As previously presented, in Schenkerian theory music is the unfolding of a triad. Consequently the various intervals of the triad may be sounded horizontally over a time-span--henee, the concept of 3rd-span, 4th-span, 5th-span, 6th-span. 21 Example 1. Dissonant passing tone harmonized as consonance

h. e. J. ^ -jsn ^^F^ r i^T T 5/1 i r fi 3z: I

In 1-b that passing note is harmonized to become consonant, allowing both melodic and harmonic generation of the C major sonority. Not only are the same conponents present in 1-c as were in 1-b, but also another space filler has been included--the C-sharp chromatic passing note which fills the space from C to D. (The function of the D is that of elaboration of the C.) The harmonic movement of I-II-V-I is as firm and convincing a horizontalization of the C major triad as is possible to effect. The dissonant passing tone C-sharp could be harmonized to become part of a secondary dominant (e.g., V'/ii), in which case another level of prolongation has been effected, as in

(1-d).

Exaii5)le 2. Octave transfer. 22 Another means of prolongation stated by Katz is by changing the register of a note to its octave by horizontalization."^^ In Example

2-a, the beginning pitches have been displaced an octave each by arpeggiation in contrary motion. In 2-b, the space of the upper voice third (3 to 5) and the lower voice fourth (8 to 5) have been filled with passing notes. In the remainder of the arpeggiation, the third

(8 to 3) has been filled in with a passing note, the E (5) splits into two voices to fill with passing motion the fourth (5 to 1), and the lowest voice also fills a third (3 to 1) with a passing note. All is an elaboration of the octave displacement of the initial third--a prolongation with other prolonging motions within.

Example 3. Exchange of voices.

To clarify horizontalization as used by Katz, her Schenkerian definition of tonality is offered: "It is necessary to differentiate between the natural principle, which is Simultaneity (as expressed in the Klang), and the artistic adaptation of that principle, which is Succession. In other words, the triad represents a form of natural Coherence. Tonality then, is the form of Coherence obtained by shifting the raw material—the natural triad--from its vertical position to a horizontal one, and by extending it by means of Succession or Horizontalization. In short, tonality is a transfor­ mation of the triad." (Katz, "Heinrich Schenker's Method of Analysis," u. 313. Caps are Katz'.) Prolongation can also be accoii^Dlished by exchange of voices. I:1

Example 3-a, the top voice moves stepwise 4-3-2, while the bottom voice seems to skip and split. This skip is actually brought about by the transfer (or splitting, in this case) of the C to two octaves. In

3-b the top and bottom voices invert, with the E continuing back to F, the G back to A, producing a sixth inverting to a third, then proceed­ ing on stepwise to the tonic triad which then moves functionally to

the dominant. In 5-b the first two notes of the bottom line, A-G, are continued in the notes of the top line, A-G-F-E-D, producing the

line A-G-A-G-F-E-D, while the other line, F-E-F-E-D-C-G, begins in the top voice and shifts to the lower voice. Through the exchange of voices, the space between the notes of the first and second chords of 1? 3-a is filled in, thus prolonging the 3 upon its arrival.

A final means of prolongation given by Katz is "by the Brechung or skip in the chord line," This particular means she describes as the use of "the tones of the Klang in Succession, thus stretching out 18 the melodic line by means of various intervals of the chord." As an exan^le, she uses the opening measures of Beethoven's Sonata. Opus

2, No. 1, reproduced as Example 4.

In this example, several aspects are revealed. The surface melodic content is that of the intervals of the triad--the triad intervals as the basis for a melodic motive. Very few real functional

17 Note the slur connecting the two E's in 5-b. 18 Adelle Katz. "Heinrich Schenker's Method," p. 516. 24 harmonies are used here--primarily tonic over six measures (embellished

by a neighboring chord and passing through another to the first

inversion) before moving to the SLroertonic which leads to the dominant.

Example 4. Beethoven's Sonata, Opus 2, No. 1 (mm 1-8)

The triad has been stretched over six measures by moving through the

members of the triad in both soprano and bass (5 to 5 in the soprano

and 1 - 3 - 5 in the bass) while arpeggiating the chords on the

surface level also. One other aspect of the arpeggiation is the

variety in its manner of articulation. In the first measures, the

triad is arpeggiated, stretched out, beginning on C, through F, A-flat,

C, F, until in the fifth measure it is contracted into C as a grace

note plus A-flat. In measure 7, the triad of the tonality is mani­

fested in a broken f minor triad immediately before the move to the

structural dominant. .Arpeggiation is one of the most important _0 prolongational means at work in this passage.

In his textbook. Layer .Analysis, Gerald Warfield refers to three agents of prolongation which he calls "prolongational operators."

These operators are arpeggiation, passing motion, and neighbor motion.

These same motions are discussed in Salzer's Structural Hearing, where they are referred to as interval outlining, interval filling, and ornamental types of motion, illustrated below as Example 5_ 20

Example 5.

•JOH lac Tir~cr la: •JOL I I # in4Ti»\ ySilM^ omfrmfrrt./?/ \t{*r*9\ •tt^/*'*'"'*^

These three types of motion are combined in actual music to produce

layers of prolongations, as in Example 6.

Example 6.

The motion from E to G (A) is an interval outlining motion, while that in (B) from G to E is the interval filling type. All of the

19 Gerald Warfield, Layer .Analysis, p. 4 4

"Felix Salzer, Structural Hearing: Tonal Coherence m Music, 2v. (New York: C. Boni, 1952), v, 1, p, 119, 26 motions, however, depart from and return to E, thus creating an ornamental motion which consists of the other two tv^es.

Based on the previous discussions, one might correctly surmise that Schenkerian theory is predominantly a linear concept. Conse­ quently, its roots are in strict counterpoint. These contrapuntal

lines are best observed in the middleground reduction. (See Chapter

III for a discussion of the reduction technique.)

The contrapuntal element is, however, only half of the theory.

The remaining half is rooted in functional theory. This harmonic aspect is clearly indicated by the concept of the Ursatz, which is a harmonic structure. In the unfolding of the tonic triad, the bass will inevitably reach the dominant, the "octave divider." This

concept is essentially that of a tonality's being established by the dominant, which in functional thought, is the function of the dominant.

Schenker supplies every possible Ursatz formula with all three forms

A A A A A A of the Urlinie (3 - 1, 5 - 1, 8 - 1) in Der freie Satz, according to the application of his rigorous contrapuntal-harmonic principles.

Any harmonic structure within the Ursatz may subsequently be prolonged, thus providing the concept of harmonic prolongation.

Consequently, not only a note may be prolonged, but an entire harmonic entity (chord, or even tonal area) may be prolonged. This concept is based on a principle revealed in counterpoint--"that several tones 21 can stand for the one tone that dominates a group of tones," Thus,

*• Felix Salzer, Structural Hearing, v, 1, p, 106, harmonic prolongation also has as its basis, counterpoint, as evidenced in Salzer's statement:

It is one of the greatest achievements of Western music that the development of the harmonic concept has not overpowered the contrapuntal concept. The former has been applied instead in such a way as to allow the contrapuntal concept to develop fully its own charac­ teristic function, so that it is even possible for whole phrases and units to be dominated by counterpoint and its progressions.22

Oswald Jonas, in the introduction to his edition of Schenker's

Harmony, refers to these two aspects as he describes, "the chief merit of Schenker's early work consists in having disentangled the concept of scale-step [Stufe] (which is part of the theory of harmony) from the concept of voice-leading (which belongs in the sphere of counter­ point)." He further states, "the theory of Auskomponierung shows voice-leading as the means by which the chord, as a harmonic concept, is made to unfold and extend in time." " He then summarizes quite adequately, the dual aspect of music (harmonic/contrapuntal):

The chord is simultaneity. To use a metaphor, it has a dimension in space; and the nature of music, which flows in time, demands its translation into a temporal sequence. This process is . . . "compositional unfolding" or Auskonponierung. It could find its final expression, however, only after an incursion into the field of counterpoint, since the goal of creation in time, of Auskompo­ nierung, can be reached only via voice-leading.^^

*^ Salzer, v. 1, p. 109. 23 Oswald Jonas in Heinrich Schenker, Harmony, p, xvi. 24 Oswald Jonas in Heinrich Schenker, Harmony, p. xvi. 28 And Leo Kraft reflects Schenker's ideas when he states.

The opinion has already been expressed that the term harmony is virtually useless. Supposedly, harmony deals with the study of chords, counterpoint with lines. But such a statement overlooks the basic fact that lines flow together to make chords, and the only reason that chords follow in a certain order is that the lines lead them there. If harmony books make any sense it is because they deal with musical motion--that is, counterpoint. . . . There is much more to learning about chords than writing Roman numerals under them. The way to learn about chords is through learning about the lines that generate the chords.25

Underlying the concept of musical motion or directed motion,

are basically two kinds of chords--structural, harmonic chords (those

which underlie the basic structure) and prolonging, contrapuntal ones.

In discussing chord prolongation, Salzer describes two kinds of motion,

Direct motion he describes as "contrapuntal chords between two

harmonic chords," whereas indirect motion is that created by "contra-

puntal chords prolonging a single chord." Rhythmic position as

such, is not necessarily indicative of a chord's function. The factor

which will actually determine whether a chord has harmonic or contra­

puntal function "will always be its position within the voice-leading

? "7 pattern and the purpose it fulfills within that pattern.""'

25 Leo Kraft, Gradus: An Integrated Approach to Harmony, Counter­ point and Analysis (New York: W. W. Norton and Company Inc., 1976), p. 30. Salzer, Structural Hearing, v. 1, p. 100.

^^Salzer, v. 1, p, 100-101, 29 Example 7, from the Bach chorale, "Der Tag, der ist so freunden- reich," illustrates the difference between harmonic (structural) chords and contrapuntal chords.

Example 7. Bach Chorale No. 158, Der Tag, der ist so freundenreich. n ^^ i «=4 r i 1 iS ^^ m TO 1 r

The first five chords perform a contrapuntal function. They prolong, or spin out the structural tonic triad, as evidenced by the melodic bass line which descends stepwise from tonic in one octave to tonic in another, and by the soprano which moves from the root of the tonic triad to the third during that same time span.

A look at this example from a more traditional, functional approach will reveal the same results. A traditional Roman numeral analysis is given below in Example 7-a.

Example 7-a. r^ \M\m^=^^ i

Vi sL v^'^ -L jr I I ;o Substituting T for all tonic function chords (in the exan^le, I and vi), PD for all pre-dominant function ones (IV and ii) and D for all dominant function chords (V and vii"), the analysis would be that of

Example 7-b.

Example 7-b.

^ f T PD PI PP P T

From the above "reduction" (the passing tones have been omitted), the

first prolongation is revealed. Since, according to the concept which allows the substitution of a secondary triad for a primary one,

the vi chord prolongs the tonic triad, as illustrated in Example "-c.

Example 7-c.

SO Vi 'T

The function of the pre-dominant (subdominant) group of chords is to

lead to the dominant. They provide harmonic movement whose motion is

directed to the dominant. The function of the dominant, of course,

is to establish, or lead to, tonic. Hence, I-IV-V-I, or T-PD-D-T, is

a fully completed motion which begins at tonic, moves into an area

whose function gives direction to complete the motion where it began.

In other words, the motion T-PD-D-T, is a type of prolongation that 51 extends a chord by moving away and back. A more extended view of the above passage provides the analysis of Exanple 7-d.

Example 7-d.

^* ^

ot - IT vn 1 K X I PP J —v PI ?DD I

or KOfi^LlTt)

jv \;(i 1 T 'J n Y 1 EYI

From either of the analytical approaches above (that of the

traditional Rameau-Riemann chord function or that of the Schenkerian

contrapuntal/harmonic) one extremely significant point is revealed:

that all chords are not of equal significance in generating direction

within the music--that is, musical structure exists on various archi­

tectonic levels.

It is perhaps in this realm, that of hierarchic structure, that

Schenker made his greatest contribution to musical theory. Through a

series of reductions, wherein progressively more ornamental, prolonging 52 details are systematically eliminated, the various "layers" of the music are revealed. CHAPTER III

THE REDUCTION PROCESS

Prolongation was previously described as "something rela­ tively complex which serves as an elaboration of something that is relatively simple." One might think of reduction as the reverse

of prolongation. It is something that is relatively sinple which

stands for something relatively complex and elaborate. Reduction

is the sin^lification of a foreground passage to a more fundamental

level. The simplifications are "interpretations of the specific

details of a piece, and thus add to our overall view of the piece.""

The fact should remain clear, however, that reductions are the result

of analysis. They exist by virtue of the conscious and systematic

act of eliminating the ornamentations and elaborations from a passage

or level of music. Reduction is closely akin to variation. In

describing this relationship. Forte states:

In brief, the analytical technique of reduction derives from the compositional technique of variation, as it developed during the tonal period. .At the risk of over simplifying, I point out that reduction is approximately the reverse of varia­ tion. By means of variation techniques a basic structure becomes more elaborate, in terms of increasing number and variety of me Iodic-rhythmic

^See page 20. 2 Gerald Warfield, Layer Analysis, p. 42.

:>j> 54 events. Reduction accomplishes the reverse; detail is gradually eliminated in accord with the traditional distinction between dissonant and consonant tones (made with reference to the tonic triad, the elemental consonance) so that the underlying, controlling structure is revealed. ^

Although Schenker is universally associated with the reduction 4 technique, it is not totally his innovation. He, however, more than any other, refined and developed the technique through its use in his many analyses. Regretfully, Schenker never explained the actual method. However, he left a wealth of examples in his many analyses of musical works.^ He also used the reduction technique as the vehicle through which he articulated his unique conception of tonality as ultimately revealed in Der freie Satz. From these reductions (and to some extent from those of subsequent users of the technique such as Salzer, Forte, Travis, and Berry) the method of reduction in the present work is derived.

Although it is beyond the scope of this study to evaluate the various works based on Schenker, it should nevertheless be pointed out that at the present time there exists only one published work whose

^Allen Forte, "Schenker's Conception of Musical Structure," Journal of Music Theory, 3 (1959), p. 18. Reprinted in Yeston's Readings in Schenker Analysis. '^Forte mentions a few prior examples and Morgan develops the history of the technique very thoroughly in his article. ^For a complete listing, see Larry Laskowski, Heinrich Schenker An .Annotated Index to His Analyses of Musical Works. (New York: Pendragon Press, 1978). JO primary purpose is to develop a methodical approach to the reduction process. In most of the older literature, the writers approach the subject of reduction by explaining a Schenker reduction, never by actually reducing a passage of music. Recently, publishers have released several textbooks in which the authors use reduction as a tool in explaining basic theoretical concepts. Even these authors, however, do not separately and systematically approach the technique of reduction.

In a set of reduction graphs, the hierarchic structure of the music is revealed in both harmonic and linear relationships. In the first "level" or "layer," the most obvious ornamentations and arpeggiations are eliminated, revealing a more linear composition. In each subsequent layer more prolongations are replaced with the indivi­ dual notes instead of the stretched out passage, until ultimately the most fundamental structure is revealed, (Schenker's Ursatz). As previously pointed out, Schenker referred to only three levels--the foreground, middleground, and background—each represented by a separate reduction graph. Some analysts today use fewer (or more) reductions to arrive at that level which displays the most basic relationships within the music; the number of reductions or layers is often determined by the complexity of the music. Schenker himself

Leo Kraft, Gradus; William Duckworth and Edward Brown, Theoretical Foundations of Music (Belmont, California: Wadsworth Publishing Company, Inc., 1978); Edward Aldwell and Carl Schachter, Harmony and Voice Leadings (New York: Harcourt Brace Jovanovitch, 1978) ;' Peter Westergaard, Introduction to Tonal Theor>^ (New York: W. W. Norton and Company, Inc., 1975); Robert Cogan and Pozzi Escot, Sonic Design. 56 often used four to five separate reductions in deriving these three levels.

Beyond the foreground level, rhythmic values of notes lose their temporal associations in a reduction and instead indicate relative significance, or structural weight. Rather than the reader's first being referred to a glossary of graphic symbols, in the following discussion he will encounter the symbols as they are needed while realizing several reductions.

Example 1. ^m 3Sfc ¥

:«: i ^m S

The first example for reduction (Example 1) , is a standard four measure phrase length imparting an element of finality in harmonic, melodic, and rhythmic direction. A traditional Roman numeral analysis inplies equality among the constituents: II VI. All are primary triads of equal duration and metric placement. In approaching the phrase, one must realize that the sonority resulting in the second measure is brought about by melodic motion in the bass and soprano through the exchange of tones. Since there is no change of chord in 57 me asure 2 —only arpeggiation of the same chord (3 to 1 in the soprano, 1 to 3 in the bass) , the first two measures combine into the contents of Example 1-a. By the same process, measure 3 results in the contents of Example 1-b.

Example 1 (a, b, c) .

A concept vital to reduction is that octave register is of little consequence and most thought can be in terms of pitch class only. ' .As a result, octave duplications can be eliminated from the contents of

1-a and 1-b. The G in 1-a is doubled as is the F-sharp in 1-b; without the doublings the result is the contents of 1-c,

The two primary con^onents of the voices are the top-most (as expressed in the theory of the Urlinie) and the bass (as expressed in

However, the final Ursatz will be shown in what Schenker referred to as the "obligator>' register," which in a much siiqjlified explanation is that octave register in which the progressions of the Ursatz take place. Excursions into different octave registers result from arpeggiations, outright octave transfers, and a leap of an inner voice into a much higher register into what seems to be the top voice. These concepts will become clearer as the reduction process continues. 58 the theory of the "grundbrechung" aspect of the Ursatz) . The B of

measure 2 (of Example 1) is an inportant tone while its soprano (G)

is not so inportant. The B is more important because it is an aspect

of the tonic arpeggiation in the bass. The top-most voice of the

reduction so far produces a 3-2-1 descending line, one of the Urlinie

forms defined by Schenker. Tlie first reduction now looks like that

in Example 1-d.

Example 1-d.

m I r r

In Example 1-d the descending top voice is indicated in open

note heads where the inner lines are less structurally important;

therefore they are shown in black noteheads. The notes of this bass

are all structurally inportant to the Ursatz form, with the B of

lesser import since it does not si:5)port a new structural chord. This

example cannot be reduced any further; it is one of the Ursatz forms

of Schenker's Per freie Satz. The notation, however, can be inproved

to show more clearly the contrapuntal aspects and specifically the structural weights. The notes of the Urlinie are to be indicated 39 AAA with Arabic numerals and carets (3 2 1) above the corresponding notes.

The G in the inner voice after moving to the leading tone, resolves

to the tonic at j. The other inside voice (the D) merges with the

bass upon its arrival upon the D at y and resolves to G in t.he }. The A presence of the B at the i is superfluous since the whole piece is the horizontal movement through the members of the tonic triad to their convergence upon tonic at the end. The final reduction to the Ursatz form is that of Example 1-e.

Example 1-e.

Ill

It should be pointed out that these four measures were approached

as though they were a whole conqposition. However, since this is more

than likely the first phrase of a more extended work, the Ursatz form

reduction above is only the first reduction of a more extended reduction. The bass notes of the Ursatz are indicated in ooen

g An Ursatz form of a partial composition such as this one is referred to as a "figurative Ursatz." 40 note-heads with stems and beamed together with a balken (broad beam).

The other note values indicate relative significance of weight.

Always the top voice (Urlinie) and bass arpeggiation are the most important. The Urlinie is indicated here in white notes, the lesser

lines in black notes. The B of the bass arpeggiation is indicated in a rather strange way--the flagged half-note. In relation to the other notes, it has almost equal weight with the other three tones of the bass arpeggiation; they, after all, are "flagged" half notes also.

However, it is detached from the others because only the tonality defining roots are connected--i.e., tonic and dominant, and there is no harmonic change over the B.

Tliere are several ways to indicate the same meanings in this reduction. Schenker himself was not consistent, sometimes beaming notes of the Urlinie (as in the above bass, and as that used in

Exan^le 2 and subsequent reductions) and sometimes indicating them as those of this Urlinie above have been indicated, with single white notes. In any case one fact remains — that structural weight and coherence are indicated by the type of note and groupings, respec­ tively. Salzer and many of his followers would indicate the meanings above in the following manner (Example 1-f) . Obviously, in Example

1-f, weight is indicated by length of stem on the white notes.

As a further explanation of the technique of reduction, consider

Example 2. The example will immediately be recognized as a minutely ornamented version of Example 1. Prolongation is at work here.

Reduction is the replacing of the extended passage with that for which the extended passage stands, and in the process reveals the 41 contrapuntal relationships and the structural harmonic framework. In

Example 2 the melodic soprano and bass of measures 1 and 2 have an even greater melodic implication: stepwise motion. The thirds and roots of the soprano and bass have been connected through passing tones, while the tenor has prolonged the G through neighbor note 9 movement. These ornamenting motions are less significant to the structure than the triad members they prolong and are indicated in stemless black notes, as in Example 2-a, (The Urlinie representa­

tional method here is that of connecting the members with broad beams

(balkens) and will be used through the remainder of this work.)

Example 1-f.

h *

pk I n

^Recall the prolongational operators: (1) arpeggiation (only one at work in Example 1) (2) passing motion and (3) neighboring motions (all at work in Exan^jle 2), Exajnple 2.

4- X r'^ l' T 1

Example 2-a.

r 11

As previously cited, coherence is indicated by groupings. In the example above, the "third-span" or "progression through the inter­ val of the third," the Schenker "5-Zug" (3rd span) is indicated by

10 See footnote 15, p. 20. 45 the slurs connecting the B and G in the soprano and the G and B in the bass. They are the outside boundaries of a meaningful musical motion and relationship. A similar type of relationship exists in the motion out of and back into G, implying a retained tone the whole time. The individual relationships within these broader coherences are also indicated: the slurs connecting the small stemless notes to their goals of motion.

Example 2-a can be reduced further to exactly the same Ursatz as Exaji^le 1, through eliminating the most immediate prolongations in the next reduction. When the prolongations of the first coherences are eliminated the arpeggiations can be dealt with. The elimination of those first prolongations results in the level which is the same as that of Example 1 in the beginning.

Example 2-b.

Ill III

Example 3 offers a much more interesting problem of reduction. 44 Example 3.

T' ^' r x^^ t ]!' V{ I," X X

Again its relationship to Example 1 is apparent. The first prolon­ gation is exactly that dealt with above, except that the motions do not stop on the third beat. Instead the top voice reverses direction and ends where it began. It defines the interval of a third (within the tonic triad) while retaining the initial tone. This coherence is notated in such a way as to express these motions, as seen in

Example 3-a.

Example 3-a.

The bass, instead of retaining the initial tone, retains its i^per limit note within the third, the B, but with a neighboring note, C. The "meaning" of the first one and one-half measures is expressed m this reduction (Example 3-b):

Example 3-b.

m ^ n^,,',^•^^ »->F

The notation above requires some further explanations. Retained tones are usually indicated with broken slurs. As a matter of fact, notations connecting any identical pitches (i.e., PC) are indicated in a broken manner, such as the broken beam indicating a retained

A Urlinie tone (the B [3] in the above exan^le). In representing only a portion of a graph, such as above, the partial beam (bass note) is used to indicate that the note is beamed to something which is in the omitted portion. The partial beam is also used to indicate coherences where the solid beam would add to confusion and detract from clarity

(for instance, the absence of the next connected note over the next several staves or even pages). In such a case, the initial note has a forward indicating beam, the next one a backward indicating beam. with a forward one if there is still more to come. 46 Returning to Exanple 3, one finds the remaining melodic line exactly as in Exan^les 1 and 2. However, there are differences in the bass and harmonic structure. At the appearance of G in measure 2, the bass leaps to E and begins a motion whose goal is the C bass tone of the ii cadential material. Consequently, the motions are prolonging motions, which act as a springboard into ii^, and would be indicated as in Example 3-c.

Exan^le 3-c,

3E V*,g g m ^ ^

I ii 11 The final reduction, Exanqjle 3-d, produces the same Urlinie as Examples

In a Schenkerian reduction only the structurally important harmonic planes (his scale-step) are indicated with Roman numerals, and not the lesser chords within prolongations. Schenker's Roman numerals did not indicate the type (major, minor, etc.) of the triad; all were indicated with the same capital Roman numeral. Today, however, many analysts indicate various other harmonic constituents and use both i^per and lower case Roman numerals. In addition, variable physical size of numerals are used to indicate relative harmonic significance, a practice in which Schenker sometimes engaged. In Example 5-c the only Roman numerals Schenker would have indicated are I II V I. 1 and 2 but is a different Ursatz.

Example 3-d.

-^4- ^^w=p^

1 iitr

An examination of the first phrase of Bach's Chorale No. 158,

Der Tag, der ist so freundenreich (first encountered in Chapter II, provided again now as Example 4) will further clarify the reduction process.

Exan^le 4,

2=?: ={=?=• T=T=T I ,51 i raj mm - zz * • 48 The extended tonic triad (through the whole first measure) is brought about through two directions of motion within the bass G prolon- 12 gation. The first is the passing note motions, filling the third space between the consonant notes as can be seen in Example 4-a.

Exan^le 4-a.

The second is the resultant neighbor motion, G-A-G, through octave transfer, as shown in Exan^jle 4-b.

Example 4-b.

L_„J

A new representational symbol is encountered in the middleground reduction of 4-c--the curved arrow. The extended tonic is intensified at the end of the first measure to create a dominant relationship to the structural IV in measure 2, which consequently adds even more en5)hasis to the pre-dominant IV. The understanding of the G

12 This prolongation, as such, is discussed more fully in Chapter II, pp. 29-52 49 major-minor seventh in measure 1 is dependent upon the IV chord m the next measure. The arrow relates this dependence.

The next problem in reducing Example 4 occurs in the final measure. Since the Urlinie is a descending stepwise line, a question

arises regarding the C on the first beat of the measure in the soprano.

One might be inclined to accept the C as the most structural tone here

rather than the B. Admittedly a C is structural--the bass root of the

IV leading directly to the dominant. Regarding the top voice, however,

one must remember that the theory of the Urlinie arose from Schenker's

concept of tonality: that a composition is an unfolding (or horizon­

talization) of the tonic triad. The spaces between the members of

the tonic triad are filled in as passing notes which are harmonized

to become consonant to produce the harmonic structure, the Ursatz.

If the C in the top voice were considered structural in the final background reduction with the B having previously been eliminated as

a passing motion from C to A, the Urlinie concept is violated. (A step-wise voice connecting a member of a tonic triad to the final tonic would not exist.) Consequently, a more orthodox view (in the

Schenkerian sense) is that the B (the 3) is prolonged through 7 neighboring motion as it becomes the seventh of a IV , which m turn 2 moves properly to y, as in Exan^le 4-c. Elimination of all the prolongations results in the Ursatz of 4-d.

As the final exaii5)le for reduction. Example 5 is an extension of Example 2. lO Example 4-c.

T T' T I Example 4-d.

A A A 3 2 I

^ If ^

lE'E^ TT?? I Exaii5)le 5.

4; jr*i' T r -• :?% X ' Example 5 cont'd.

(0 ^'^ 1 X' r VI It 1/ r i

The Ursatz form of Exaii5)le 2-c is now understood as only another

prolongation since more music follows. The space ber^een the 3rd and

root, over the first two measures, has been filled in with passing

motion, and has been harmonized in the foreground level to produce a

consonance, 13 resulting in the reduction of 5-a. The motions of measure 3 are obviously moving to a goal of the

dominant, the 5, in measure 4, which actually is the first note of

the Urlinie. The motion prior to the 5 is considered "space-opening"

motion. (Schenker's German term is Anstieg.) The presence of the

C-sharp leading tone and the secondary dominant relationship elevates

the stature of the D to that of the Urlinie note seen in the reduction

of 5-b.

^•^This "consonant passing tone" is an aspect of the concept referred to as "dissonant prolongation," i.e., a dissonance of a more remote level is prolonged while being harmonized with consonance and is often even "tonicized," which is Schenker's explanation of what is traditionally conceived as modulations. O.- Exan^le 5-a.

rn a^'^f-,^ff. a ^

Example 5-b

U'^f, • ft L

Were the C-sharps of measure 3 only C-naturals, the inner voices would

only be rising from within to produce a long i as in 5-c.

An interesting question at hand now is which C is the next

structural Urlinie note? Considering the voice-leadings in measure 3,

it soon becomes apparent that this C performs a linear function

connecting the D to B, supported by the same type motion in the bass, O J resulting in a totally contrapuntal passage (Example 5-d)

Example 5-c, tA

^ ^1- '*

f)^ d^^^^^

Example 5-d.

The motions produced by the vi chord in measure 6 are of the same function as those in Example 3, a springboard into the structural bass ii , which in turn becomes basic to the structure as dominant preparation. It is the C of the supertonic triad that resumes the descending motion from 5 to I of the Urlinie, as in Example 5-e. 54 Exan^Jle 5-e.

A ^ 3 ft I

\.* g>"^-K£»^ ^' J g-i ^

,<, /* t»» /If ,p i

T- • \tt-^l

Example 5-e, which is actually a middleground reduction, reveals many aspects of organization. The prolonged tonic triad at the beginning, which encon^asses five and three-quarters measures,--in fact all the music up to the cadential ii I4 V I--is organized in parallel tenths resolving to octaves between the outer voices, resulting in a contrapuntal line. This principle, tenth between the voices, surfaces again at the cadence (G-B) as if to unify the whole.

Just as the tenths during the first are created by an "inner voice"

(since the top-most voice is on D the entire time), the B at the end is also created by a rise from the inner voice while the structural voice is the G. The most remote level, the Ursatz, is shown in

Example 5-f. DO Example 5-f.

The preceding examples have been approached from the point of view that there are coherencies within music, which when recognized both conceptually and particularly perceptively, give direction and produce sound, secure, and unified structure. The coherencies are related and effected by tonality. The ultimate structure will be the tonality defining entity and such structure exists on a remote level in all tonal music. All pitch occurrences within the music perform either a structural function or a prolonging function, or both, alw.iys projecting towards the tonic--the one and only tonic.

As a final example in which the concepts of tonicization

(tonicalization) and interruption will be revealed, the first part, the minuet portion, of Schubert's Moments Musicaux, Opus 94. No, 6

(D, 780) is presented as Example 6 (p, 57). .At first perusal, a o 6 modulation to E major seems to take place within the middle of the work. Upon further analysis, through reduction, other explanations are offered.

The initial four measures are, in effect, an extended tonic triad which over this period of time, is arpeggiated from root position with the third in the soprano to the first inversion with the fifth in the soprano. During this arpeggiation, the chord and individual members of the chord are embellished by a neighboring ii^6 upon resolving a suspension. This tonic triad in first inversion, after an octave transference in the bass through arpeggiation, returns to its initial position in measure 5 after passing and neighbor note motions. In measure 6, the dominant is actually arrived upon and embellished by its dominant during the arpeggiation from first inversion to root position. In retrospect, the first eight measures are a linear movement from tonic to the functional dominant.

An immediate problem lies in the meaning of the E-flat soprano note in measure 8. Is the initial C the first Urlinie note, or is all the initial motion merely space-opening motion to the E-flat as the first Urlinie note? Several factors SL5)port the choice of E-flat, not the least of which is the secondary dominant immediately preceding it. However, the tonic prolonging motions were completed in measure

6 and the dominant was reached in the next measure with 2 in the soprano and the third of the V in the bass, which then filled the space to the root with passing motion. Upon reconsidering, the secondary dominant is a contrapuntal chord, not a harmonic one, a Example 6: Schubert, Moments .Musicaux, Opus 94, No. 6 (D. "80)

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•Ji a >:V-t—r-;—)—TTT:—^^ t»—:i-i—t—SLi - \ s ^ ^Me SE-: es 5^ —* —. "i"^* •9 •*• - 59 factor strongly supporting C as the first Urlinie note. The first reduction would be that of Example 6-a.

Example 6-a.

^^ ' • I" *^I 1 ^ ^ T

Tlie second phrase begins like the first. Hence, a return to

A the initial 3 is quite expected. A question here might have to do with the descending Urlinie concept. Is this concept violated? The answer is no, for in its descension the Urlinie may experience inter­ na ti on when supported by the "octave divider," the dominant, after which there is a return to a tonic triad tone and a resun^tion of its descent. One should realize that for this interrtqption to occur, this dominant must be extremely inportant structurally, such as the half cadence here, after which is a second parallel-constructed phrase. A 2 (When describing this y as an interruption, consideration is given only to these first two phrases. These phrases will be reinterpreted presently in relation to what follows.) The interriqDtion is often an f^ 60 14 - agent m delineating form, such as the V at the end of the develop­ ment section of the sonata-form in which the recapitulation begins ^ A A again with 8, 5, or 3. The interruption is indicated with two parallel vertical lines as seen in Example 6-a.

In considering the second phrase, measures 9-16, one notices more chromaticism. This chromaticism is actually the result of even more ornamented prolonging motions. In the arpeggiation of the two positions of the tonic triad, the B-flat neighbor note passes through a B-natural passing note in returning to C; the F neighbor note passes through an F-flat (written as E-natural) in returning to E-flat. The

C is, of course, also embellished with an upper neighbor D-flat and the A-flat, a neighbor G.

In measure 13, rather than the soprano returning to C, here, it remains on the E-flat that was brought into the top by an exchange of voices; it came from an inner voice and merges with the Urlinie note only at the end of measure 14, These motions are shown in Example 6-b.

The Roman numeral III is indicative of the fact that the chromatic mediant is en^loyed here in a rather structural position.

The bass drops the octave; it is harmonized as a root, not a third, as in the first phrase. It is part of a tonic arpeggiation in the

At the time of his death Schenker was working on a study of form. 61 bass: I III ii^ v I. 15 (1 3 [4] 5 1)

Example 6-b.

mm^

(i'll

The remainder of the minuet is graphically notated in Example

6-c. The German Augmented sixth chord appears in measure 16 to begin the second section or the digression. With the resolution of this chord, the minor third scale degree is retained to effect a change of mode. The effect of the German Augmented sixth chord as an inten­ sified pre-dominant chord is weakened by a retrogression to a weaker pre-dominant within this context, iv , as the embellished dominant is transferred to an inside voice in measure 20. From this point until the last beat of measure 41, where it is transferred back to the bass

Notice that another relatively important factor in bringing about the structural significance of the III is the French Augmented sixth chord which precedes it. The voice leadings of the upper and lower leading tones are resolved in a most intense way in a strategic position within the phrase. 62

Example 6-c. Schubert: Moments Musi caux No. 6

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T 64 where the German Augmented sixth function returns, the dominant and its upper leading tone, F-flat (most of the time spelled enharmoni- cally as E), remain in the middle voice, only occasionally emerging as the bass (but always at strategic points). These twenty-five measures are, in effect, a prolonged German Augmented sixth upper

leading tone to the dominant as it is moving to the dominant towards the end of the digression. After its resolution to the dominant in measure 42, the dominant is embellished again by its other neighbor,

the subdominant over the dominant pedal. The pre-dominant functioning

submediant leads into the leading tone diminished seventh chord, which

"thins out" into a first inversion dominant triad in measure 52 where

the digression ends. The seventh is added to the dominant in measure

53 where the resolution begins the return to "A" after what can be

viewed now as a digression "around" the dominant, not as a modulation

to the chromatic submediant key of E major, as is most frequently the

analysis of this work.

Through voice-leadings, one can now view these measures as an

intense movement to the dominant through the German Augmented sixth

embellishment. In the process of moving to the dominant, the aural

root of the German Augmented sixth chord, the upper leading tone to

the dominant, is prolonged through a tonicization brought about by its

own dominant and extended usage. There is no new tonic; there is but

one tonic in a tonal work because, according to Schenker, all the

music is an unfolding of the tonic triad, the tonality. The function

or significance of E major in this work in these measures is to

prolong and heighten the significance of the dominant E-flat; and in 65 the process becomes prolonged itself through tonicization.

A similar but much less extended situation exists in measures

65 through 73, except here the pre-dominant function is being prolonged, specifically the Neapolitan chord on its way to the dominant (six-four, five-three figuration). These motions too, are shown in Exan^le 6-c.

The examples in this chapter have been provided as a presen­ tation of the primary tool with which the Brahms Opus 118 has been analyzed. The presentations of the analyses and findings from these analyses comprise the remainder of this work and will be found in the section following the glossary of graphic symbols. CHAPTER IV

A GRAPHIC ANALYSIS OF BRAHMS, OPUS 118

Glossary of Graphic Symbols

The various rhythmic values of notes have no rhythmic associations. Structural signifi­ cance of a pitch is relative to the indicated rhythmic values. Decreasing rhythmic values represent decreasing structural significance.

Upward stemmed, open noteheads connected by a broad beam indicate the notes of the top structural line, or Urlinie. Arabic numbers with superimposed carets are placed above those notes. (Uncapped Arabic numbers indicate an Urlinie motion of the same sort on a more immediate level.)

Downward stemmed open noteheads connected by a broad beam indicate the structural bass.

The slur denotes contexts of structural relationships (for example, the third-span). It is used when beginning and ending pitches of the context are of different pitch classes. The first and last notes are structural, there fore some kind of stemmed note. Sometimes the slur is in the form of an ess, when octave transfer is employed.

The broken slur is used to connect notes of the same pitch class in a context, and denotes the return to or the retention of a '•,.• single pitch. It, too, may be in the form of an ess.

66 Tlie beam often replaces the slur when indicating more intermediate and remote relationships. As with the •,!.•• slur, the beam may be solid or broken,

Over an extremely long context, the middle portion of the beam may be omitted. Often a direction is inter­ r 1 polated in the omission (for example, to meas. 80).

# #^# Crossed lines indicate exchange r-f of voices.

Curved arrows indicate dominant fif relations, with the arrow pointing to the referential tonic.

Roman numerals denote areas and/or I -E-E'J points of harmonic significance. Rela­ tive size denotes relative structural significance.

r IT r JT A horizontal brace denotes a succession of local harmonies essen­ tially prolonging and embellishing one of broader, structural significance. The same aspect may also be shown by an » T- J arrow following a single Roman numeral.

Figured bass type .Arabic numbers £-'(0' S-'L, ite. denote the employment of techniques of voice-leading, or the linear or contra­ puntal functions of a series of sonor­ ities.

Parallel lines indicate the loca­ tion of a break or interruption in the structure. 68

The Work as a Whole

The six pieces of Opus 118 exhibit a remarkable degree of unity within each and are unified as well as a whole. Each reveals a mastery of tonal organization with utmost economy.

Each of the six projects an Urlinie of 3 2 1, resulting in

compatible structures. The tonalities also contribute to the sense of unity in that they are related by step, as demonstrated in Example

1 below.

Example 1,

I g^ »' 4" * « j. ^ &a- ^" a J j"" a ^ ia r.^ » L J L J L J L J L J L

Additional aspects of unity revealed in the diagram above are shown in Figure 2.

1. An element of palindrome:

I—?=^—1 m M m m .M m 2. Step progression:

A G^_^F^^^^-flat

3. Repetition:

a. A, g moved down a 3rd = f, F, e-flat

4. Change of mode:

a - A and F - f

Figure 2. Aspects of unity in Brahms, Opus 118. 69 These facets are also supported by expressive aspects. The pieces flanking either end, Nos. 1 and 6, are the most harmonically oriented, whose piano textures are basically arpeggiation, and whose tonalities are most ambiguous. The two major tonalities, Nos. 2 and

5, are the most lyrical, whose substructures involve submediant prolongations. The interior ones, Nos. 3 and 4, are the most unsettled, and end with the coimnon rise of the dominant tone from an inner voice, a prominent aspect of each.

The motivic connection of the perfect fourth and a long extended structural dominant are prominent. The voice-leading graphs reveal organization and tonal coherence within a work whose contrapuntal and expressive qualities have long been recognized. They also reveal aspects of overall structure, aspects which contribute to the under­ standing of a truly remarkable work of unity.

No. 1, Intermezzo

The Commentary

The first "Intermezzo," only forty-one measures in length, is perhaps the least complicated of the set. The first ten measures are a mediant prolongation effected by a top voice movement from C (5) through parallel constructed sonorities (chords of the sixth) to its octave transfer prior to the tonicization of C (III) in measure 8.

Problematic in this passage is the B-flat of the second measure. The sound is that of a major-minor seventh chord. However, the chord does not resolve as such, and upon examining the voice-leadings, it becomes apparent that parallel sonorities are at work in this passage, rather than functional movements. These chords of the sixth are 70 articulated through the occurrence of an appoggiatura.

The middle portion of this work, measures 11 through 2 8, is the

-> structural dominant prolongation, rising from the y in measure 13 to

G as part of the C major sonority and bearing the same material as the opening measure. This material is attained after three measures of chromatic bass motion up to the dominant E, The effect of all this rise out of the chord is that of an upper neighbor embellishment.

The real cadence, that is, the resolution of this eighteen- measure dominant, is in measure 28. From here until measure 39 is 9 tonic prolongation. Measure 31 appears to be vii/V resolving to V in measure 34. One might believe this progression is preparing the final cadence to tonic. However, the directed melodic activity reached its goal in measure 28, and the tonic chord of resolution becomes a secondary dominant headed towards the subdominant embellish-

•7 ment of tonic (vii° /iv over dominant pedal). The bass arrival upon tonic is not so strong as might otherwise be because of the subdorai­ nant triad above, first major then minor, with obvious melodic activity producing the embellishment shown in the middleground graph.

The basic material of this "Intermezzo," is harmonic arpeggia­ tion. An inportant aspect of the harmonic-tonal structure is the beginning of the bass arpeggiation on 3 rather than on 1, creating an impression as though the work begins between tonic and dominant, progressing immediately to dominant, as indeed it does. (Refer to the commentary of No, 6 regarding the initial ambiguity of that piece.)

The melodic span of the perfect fourth is also of importance, as it is in numbers 2, 3, and 5. hc_j\n ajj^ sis

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% 74 No. 2, Intermezzo The Commentary

The second of Opus 118, also an "Intermezzo," is structured on A a background of a prolonged x foi" forty-eight measures before a submediant (and consequently, continued tonic) prolongation until measure 76. At this point, with the obvious return of the beginning material, the prolongation continues only until measure 84, where the structural dominant is heard. The resolution of the structural domi­ nant is heard at measure 106, after which is a final tonic prolon­ gation.

The initial tonic prolongation reveals a substructure of AA3 2 A1 parallel construction to the overall structure, i.y.j. Following this prolongation is that of the submediant during which time the descending perfect fourth (the melodic material of measure 1) is essentially the only material. Brahms presents this material in counterpoint, change of mode, and invertible counterpoint during this prolongation. This same fourth, which both opens and closes the

"Intermezzo," also serves as the material for the high points of measures 1 through 48 and measures 76-end, The climax occurs within a dominant prolongation on the middleground level, within a neighbor­ ing subdominant ornamentation. It is further enhanced by the use of hemiola (the only instance of such rhythmic use on the foreground level in the "Intermezzo.") (See measures 29 and 97.) At work within this piece is extensive use of prolonged, and consequently significant, subdominant and supertonic harmonies, (See measures 50 through 37.) TIic Analysis

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^ _ •_ ^- - 'f 94 No, 5, Ballade

The Commentary

The "Ballade," the third piece of Opus 118, has a somewhat extraordinary prolongation within the center of the work, after a A3 ^2 1A complete structural prolongation of i_y_x> of the opening tonic (measures 1-37). At this point (measure 38) the bass arpeggiates to the major third scale degree, which is then prolonged for thirty-two AAA measures, producing its own substructure 3j.y.j 2 1, after which is a restatement of the first prolongation (measure 77), The bass arpeggiation is that of a major tonality while the Urlinie is that of a minor tonality embellished by the upper neighbor major 5. An interpretation is that the tonality of G is unfolded in both its major and minor forms, as indeed the foreground modalities do fluctuate between major and minor. Also of interest is the inner voice D, 5th, that rises to importance by its ornamented prolongation at the end, a characteristic common to No. 4. Tlie Analysis

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t) fc ^ 5= 106 No. 4, Intermezzo The Conmientary

The "Intermezzo," Opus 118, No, 4, is a virtual canon from beginning to end. It is not as harmonically adventurous as the other five in that the only structural prolongations are those of tonic and dominant. (There is, however, an interesting aspect to the structural dominant prolongation beginning in measure 16.) Although there appears to be a section in A-flat, upon further examination and listening, the ear is led through a motion out of and back into the dominant, effecting part of the dominant prolongation shown in the voice-leading graph of measures 5 3 through 85. The structural dominant is reached in measure 16, followed by an ornamentation through the German Augmented sixth (measure 35) with a not so obvious resolution to the tonic six-four at measure 39 which finally becomes dominant five-three in measure 47. The music following is the pro­ longation of measures 53-84, discussed above. Following these measures is motion out of V, to 14 in measure 98, through the Italian

Augmented sixth in measure 109, back to the tonic six-four with its A 2 five-three resolution in measure 109 as the y, which resolves to the structural tonic prolongation in measure 110. This tonic is prolonged through subdominant ornamentation, finally effecting what is commonl.yV called a plagal cadence, which is obviously a final tonic prolonga­ tion sending a middle voice to the top for a 5th to rise from the inner voices. (See discussion of No. 5.) Tlie Analysis IC

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^^^^^^^^ *^* _ - -

^^^^^^S * 114 No. 5, Romance The Commentary

Although all of these pieces are very tightly-knit, economically constructed works, the "Romance," No. 5 of the Opus is perhaps the most economical. The initial tonic prolongation is created through the statement of four phrases. The initial halves of these four phrases are identical, with the second halves resulting in a half cadence in F major in the first and third phrases and a half cadence in d minor in the second and fourth phrases. Variety is created through a technique of "invertible counterpoint" where the first

Urlinie tone is actually revealed as the top-most voice in measure

9, after its previous occurrence as an inner voice in the preceding two phrases.

The middle section is not only a prolonged submediant, but also, and more importantly, a prolonged 5 (Urlinie note) reharmonized and suspended over the V/vi. This middle section is the ornamentation of a three-voice structure through rhythmic variation, which becomes increasingly complex and active. These phrases, like those of the first section, are basically a repeated four-measure phrase. They are "circular" in nature in that they move to a V'/V which resolves to a V melodically and often harmonically, but all over a D pedal.

Particularly interesting in this piece is the rise from the inner voice which occurs repeatedly in measures 40 through 44. Also of interest is the ornamentation pattern of the neighbor note figure, a pattern whose basis is in the first notes and is the whole manner of ornamentation in the middle section. 115

Thc__An^j.2^^is

Ursatz:

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\f X J 128 No. 6, Intermezzo The Commentary

The most tonally unusual of the set is tne "Intermezzo," No. 6.

The tonality of E-flat minor is not substantially established until

towards the end. The most prevalent soinid during the first part is

that of the diminished seventh chord, A-C-E-flat-G-flat., Four reso-

lutions of this chord'are explored within the work. The first is to

tonic six-four, which then becomes absorbed as a passing chord into

the C half diminished seventh chord, as in measures 3 through 8. The

second resolution is that found in measure 11.. Here the chord is not

really resolved at all but is extended downward to become a dominant

ninth chord. The F dominant ninth chord resolves to a B-flat minor

triad which becomes prolonged through measure 19. It is at the end

of this prolongation that the third and fourth resolutions are

encountered. The diminished seventh chord of measure 17 resolves as

though it were an apparent C diminished seventh, resolving to what

appears to be a D-flat major triad. By the end of the measure, however, the ear has realized that the chord was an A diminished

seventh chord all along and did resolve to B-flat minor. It is this

ambiguity of root that enables the ear to hear these two resolutions, one an apparent resolution, the other perhaps the real resolution.

Although one might expect to hear a tonicization of G-flat from measure 41 on, B-flat minor is heard as the tonal area for this entire section, revealing a continuation of the prolongation of the struc­

tural dominant. This B-flat minor evolves into a B-fiat dominant

thirteenth chord which resolves into the final tonic prolongation in 129 measure 55, after which is a return to the nebulous tonal implications of the A diminished seventh chord. These nebulous qualities, however, are not exploited now, for there is a movement to the embellishing subdominant side--to the submediant, then to the Neapolitan before arriving iq)on the dominant, which is weakened througli the retrogression to the supertonic half-diminished seventh before moving to tonic.

There then follows a double statement of the motivic top third of the beginning diminished seventh chord, this time, however, without its

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^^ *J ( T^ CHAPTER V

CONCLUSION

Schenker's conception of tonal music--that a tonal work is a unique interpretation of the triad and is an unfolding of that triad over a period of time--has profound implications for the teaching of music theory in the college curriculum. Since music theory is con­ cerned with developing avenues of understanding for the entire art of sound, it is responsible for developing a framework within which one can expectantly approach all music. Tlie framework should be fashioned from related or compatible parts, from parts that grow out of or con^lement each other--not from those of such total diversity that each piece of music or each style period has to be approached from such a totally new direction that any sense of coherence or inter­ relationships is lacking. The Schenkerian concept of structural levels can provide a basis for approaching all music.

Although Schenker never intended for his concepts to apply to music other than tonal music through the nineteenth century, these basic concepts regarding tonality are applicable to all tonal music-- tertian, triadic, or otherwise. The emergence of tonality in music stands as a milestone in the history of the development of music, much as the emergence of perspective in the development of painting.

Perspective may be at work in a painting regardless of whether or not the painting is representational. Likewise, tonality may be at work

146 14' within a musical composition, regardless of whether or not the music is in a "key." Through the elimination of non-essential tones by considering such factors as repetition, doubling, duration, dyna^mcs, register, recurrence, rhythmic position, position within motion, etc., a reduction of a post-tonal work may reveal a manner of growth and elements of unity, whose presence otherwise might not have been revealed. The results will not be an Ursatz of the Schenker variety, but it is just such a result that might illuminate another aspect of style. Several theorists are presently expanding these theories in this direction. (Notable are the works of Forte, Katz, Travis, and

Morgan.)

These concepts are equally compatible with pre-functional modal music. Since their basis is partially in counterpoint, they are as easily applied to that music in the reduction process as to post- tonal music. The reductions will reveal backgrounds of types other than Schenker's Ursatzen, but again, it is this very fact that validates the application of the principles.

Admittedly, Schenker's concepts are difficult for the beginning freshman to fully comprehend and appreciate. But is it necessary to know the source of the gift in order to use it? .An investigation of recent undergraduate theory textbooks will reveal Schenker's wide­ spread, inescapable influence. The result of his influence can be seen in works as early as Piston's Harmony, through Salzer's

Structural Hearing, Kliewer, et al. (Materials and Structure of

Music), Forte's Tonal Harmony in Concept and Practice, and numerous others until finally his influence is openly acknowledged in such 148 publications as Kraft's Gradus, and Aldwell and Schachter's Harmony

_gnd Voice-Leading, and is the foundation from which they spring.

The study of music has traditionally been approached on the freshman level from primarily a harmonic standpoint. After a cursory study of melody (often within the span of three to six weeks if undertaken at all), the long and bewildering study of chords is begun.

This study commences with the memorizing of rules of part writing

(not_ voice-leading) through the application of those rules to four- voice structures and ends with the frustration resulting from the seeming irrelevance of those rules to the styles of the late nineteenth and twentieth centuries. How much more excited the students (and teachers, for that matter) would be if the music could be approached first from a broad view—a view point which allows the use of terms applicable to virtually all music. Most music creates a sense of tension and release, with tension sometimes created through instability during tonal movement to a directional goal, such as the movement to a half cadence, the movement to the related key area during the bridge passage, or the virtually constant movement in a Wagnerian passage.

Sometimes that movement is rather strong and/or abrt^t (as in some

Schubert songs), other times rather weak and/or subtle (as in some

Debussy Preludes). During this broad-view approach, the student could become familiar with terms such as linear, vertical, spatial, dimensional, prolongation, background, etc., terms applicable to all music.

To support the students' conceptual growth, the aural work must be aimed in the same direction. It is here—in the area of the 149 aural ski lis--that much innovation, experimentation, and research are needed. Schenker's theories were based in his perception of musical works, and by implication can be the basis for others' perception.

In an investigation into the aural aspect of harmonic rhythm in an earlier study, the author found that students seemingly heard the

overall tonal direction of a phrase more clearly than the individual

harmonic changes within. It is highly probable that most listeners' perception of music is more in line with Schenker's middleground than

that of the surface harmonic rhythm anyway. There is already some

activity in this direction with the recent publication of Gerald

Warfield's Layer Dictation. This work is, admittedly, only a

beginning, and paves the way for more investigation.

A program so structured would require that the instructor be

able to hear and discuss music from these vantage points. Although

Schenker's concepts have influenced most theoretical studies, there

is still some theoretical thought which has co-existed virtually

untouched. It is this author's opinion that although Schenker's

theories are not without flaws, they do offer a way of understanding

a musical work in its entirety and its constituent relationships and

consequently should be at the core of all graduate studies in theory.

One final conclusion and area for further investigation should

be rather obvious —that an understanding of a work derived from a

^James Lamb, "Aural Harmonic-Rhythmic Perception of Theory Students at Sam Houston State University," Master's Thesis, Sam Houston State University, 1970, p. 100. 150 reduction process yielding a background structure will have definite performance implications. Being cognizant of the structural dominant can only heighten the projection upon its arrival with a resultant response in the listener.

Heinrich Schenker developed a theory of tonality and a method of comprehending and perceiving tonality within music. His method involves reducing the surface articulations to reveal the underlying structural design and coherence. Applying the method based on those principles to the six pieces of Brahm's Opus 118, one discovers organic unity and interrelationships. Also discussed is the possibility that Schenker's theories have far-reaching implications which can affect theoretical study and should be the source of

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