UNIVERSITY OF CINCINNATI

Date:______

I, ______, hereby submit this work as part of the requirements for the degree of: in:

It is entitled:

This work and its defense approved by:

Chair: ______

Tonal Mirages: a multifaceted view of tonality in the early transitional pieces of

Alexander Scriabin

A thesis Submitted to the

Division of Graduate Studies and Research of the University of Cincinnati

In partial fulfillment of the requirements for the degree of

Master of Music

In the Division of Composition, Musicology, and Theory of the College-Conservatory of Music

2008

by

Brian D. Hoffman

B.M. University of Michigan, 2003

Committee chair: Steven J. Cahn, Ph.D. David Carson Berry, Ph.D. Catherine Losada, Ph.D.

Abstract

References to the music of Russian composer Alexander Scriabin (1872–1915) abound in

books and articles; dedicated analyses of the music, however, are somewhat rare. The most complete attempt at understanding Scriabin’s musical style comes from the 1986 monograph by

James M. Baker, The Music of Alexander Scriabin. Baker focuses on Scriabin’s “transitional” period, employing a combination of the predominant methodologies of the day: Schenkerian analysis and set-theoretic analysis. This thesis proceeds from the same basic premise that

Baker’s book did over 20 years ago. That is, the balance of tonal and post-tonal elements in

Scriabin’s transitional music gradually shifts from primarily tonal motivations to primarily post- tonal motivations. In order to accomplish an examination of Scriabin’s use of tonality along with a response to Baker’s work, I analyze two preludes from early in his middle period, Prelude Op.

48, no. 4 (1905) and Prelude Op. 49, no. 2 (1905) through the perspective of Schenkerian

analysis and contextual voice-leading analysis. This leads to my titular concept of “tonal

mirages” whereby the presence of tonality in a piece slowly fades as one gets closer to the

piece’s surface.

iii

iv

Acknowledgements

I would like to acknowledge my advisor, Dr. Steven Cahn, for his patience throughout this long process. While his editorial contributions have helped me grow considerably as a writer, our analytical discussions around the piano helped me gain new insights into this treacherous music and solidify old ones. I would like to thank readers Dr. David Carson Berry and Dr. Catherine Losada for their invaluable advice and thoughtful revisions. I would also like to thank my family, whose unending support and confidence aid me in everything I do. Finally, I would like to acknowledge my colleague, Breighan Moira Brown, whose dedication to scholarship unwittingly influenced my own.

v TABLE OF CONTENTS Introduction………………………………………………………………………………………1

Chapter 1: Extending Schenkerian Analysis……………………………………………………..7

Chapter 2: Schenkerian Analysis…………………………………….…………………………..29

Chapter 3: Voice Leading………………………………………………………….…………….67

Conclusions ………………………………………………………………………..…………….98

Appendix ……………………………………………………………………………………….110

vi Introduction

References to the music of Russian composer Alexander Scriabin (1872–1915) abound in

books and articles; dedicated analyses of the music, however, are somewhat rare. The tonally

tenuous nature of his transitional music allows many authors to find examples that illustrate

various analytical concepts. However, the goal of such examples is to make a greater theoretical

point and not to better understand Scriabin’s compositions, themselves.

The most complete attempt at understanding Scriabin’s musical style comes from the

1986 monograph by James M. Baker, The Music of Alexander Scriabin. Baker focuses on

Scriabin’s “transitional” period,1 employing a combination of the predominant methodologies of the day: Schenkerian analysis and set-theoretic analysis. While Baker’s voice-leading graphs

make great strides in capturing the “implicit tonality” contained in Scriabin’s work from 1903–

1913,2 his atonal analyses often amount to little more than locating certain sets melodically and

harmonically. Jim Samson, to whom the term “transitional” music is greatly indebted,3 described these analyses as “an exhaustive taxonomy of set usage.”4

This thesis proceeds from the same basic premise that Baker’s book did over 20 years ago. That is, the balance of tonal and post-tonal elements in Scriabin’s transitional music gradually shifts from primarily tonal motivations to primarily post-tonal motivations. As such, an

1 Baker defines this period from 1903–1910, ending with “an abrupt break with traditional tonal structures and procedures.” James M. Baker, The Music of Alexander Scriabin, (New Haven: Yale University Press, 1986), vii.

2 Baker coins this term in the title of an early Scriabin article, James M. Baker, “Scriabin’s Implicit Tonality,” Music Theory Spectrum 2 (1980): 1–18.

3 Jim Samson, Music in Transition: a Study of Tonal Expansion and Atonality, 1900– 1920 (New York: Norton, 1977).

4 Jim Samson, “Review of The Music of Alexander Scriabin by James M Baker,” Journal of Music Theory, 32/ 2 (1988): 355.

- 1 - understanding of both elements in these pieces requires a combination of methodologies. My

approach differs from his in three meaningful ways:

First, the scope of my thesis is considerably reduced. As such, I use the term

“transitional” not to suggest motion from and to, but rather to express a state of being in

between. Unlike Baker, I am not concerned with the fluctuating balance of compositional

influences between multiple pieces. Rather, I am more concerned with the interaction of these

influences within a single piece.

Second, Baker’s concept of “implicit tonality” factors greatly into his Schenkerian

analyses. As I discuss at length in Chapter 2, this perspective (in addition to his view of these

works as “in transition”) causes Baker to view these pieces in terms of perturbations of a

traditional tonal practice. Not only does Baker compare these pieces to a traditional tonal

background, but he includes elements in his Schenkerian graphs that reflect what he considers to

be latent tonal features. From a conceptual standpoint, my analyses differ by addressing the

elements of tonality present in the work rather than the elements that Scriabin may be alluding

to. My alternate use of “transitional” also accounts for this difference, being less concerned with

changes to former uses of tonality, and more concerned with the state of tonality within a

particular piece.

This distinction is made explicit with Leonard Meyer’s discussion of style and deviance

from Emotion and Meaning in Music.5 Meyer states that once a style has been established, the listener is able to recognize musical elements and moments that deviate from that style.

Ultimately, the deviants become common and are assimilated to form a new style. He goes on to

say: “For in any style the deviants as well as the norms are finite in number; and it is both

5 Leonard B. Meyer, Emotion and Meaning in Music (Chicago: University of Chicago Press, 1956).

- 2 - possible and likely that deviants through constant employment may become so fixed, so common

in its recurrence in particular situations, that the probability relationships of the system become

modified by this recurrence. Consequently a sound term which was once a definite deviant may

become more or less normative within the style and thus lose its potential for expression.”6 Baker seems to consider the post-tonal elements in this music as deviants from a completely tonal style.

I, instead, consider the ubiquity of these post-tonal sonorities as an indication of a new style.

This leads to my titular concept of “tonal mirages” whereby the appearance of tonality in a piece

slowly fades as one gets closer to the piece’s surface. In a direct comparison of terms, Baker’s

“implicit tonality” views the tonal elements of a piece in terms of how it implicates an earlier

style. I view tonality as present in its own right, yet highly evasive.

Third and finally, my thesis represents a change in methodology, using contextual voice

leading in lieu of atonal set analysis. Although the structures used in this compositional period are either close or identical to structures that Scriabin uses later in his post-tonal compositions, I believe that in the case of the two preludes I will examine, each sonority can be understood in terms of tertian harmony. Thus, particular features of the voice leading between such sonorities take precedence over any novelty in their construction.

In order to accomplish an examination of Scriabin’s use of tonality from this perspective,

I analyze two preludes from early in his middle period, Prelude Op. 48, no. 4 (1905) and Prelude

Op. 49, no. 2 (1905). My investigation will proceed as follows:

In Chapter 1, I justify the application of Schenkerian analysis to Scriabin’s music. In order to do this, I review Schenker’s own writings in addition to the various analytical accomplishments and extensions made by previous authors. I conclude this chapter by evaluating

6 Meyer, Emotion and Meaning in Music, 65.

- 3 - both the appropriateness of Schenkerian analysis for my purposes and the type of information gained through such an analysis.

Chapter 2 contains thorough Schenkerian analyses of the two preludes in question. My analysis of Op. 49/2 takes Schenkerian and bass-line concepts from Marian Kelian-Gilbert as its starting point. It incorporates the perspective of multiple interpretations before deciding upon a final view of the piece. Before positing my own analysis of Op. 48/4, I call into question some of the details of Baker’s interpretation. This chapter concludes with a description of harmonic paradigms that occur throughout both preludes. These paradigms result from the limited ways that Scriabin resolves the dominant seventh chord. Iterations of these paradigms can be found both locally and on a large scale.

Chapter 3 examines characteristics of Scriabin’s voice leading that are unreliant upon tonal function. Since such an analysis is necessarily contextual, each prelude is approached from a slightly different perspective, influenced by the contents of the prevailing sonorities of each. In my analysis of op. 48/4, the predominance of dominant-seventh harmonies with altered tertian extensions necessitates an analysis that addresses the voice leading between tritones apart from

their traditional tonal resolutions. While the prior analysis maps elements that are contained

within sonorities, the analysis of op. 49/2 in Chapter 3 creates a voice-leading space within

which entire sonorities can move. The voice-leading distance between the three sonority types

found in this prelude (i.e., altered dominant, major seventh, and augmented triad) is shown

through movement within chains of transformations. Each transformation retains a diatonic third

within the sonority while moving the other members of the sonority chromatically in similar

motion.

- 4 - I conclude this thesis by showing the various ways that our understanding of these preludes is enhanced by multiple perspectives. In addition, I draw conclusions about these preludes as representative of the early part of Scriabin’s transitional period. Finally, with the benefit of concrete analytical results, I return to my concept of the “tonal mirage” and discuss specific elements in my analyses that corroborate this view.

The appendix contains scores for Op. 48 No. 4, Op. 49 No. 2, Op. 48 No. 1, and James

Baker’s voice-leading reduction of 48/4.

- 5 - - 6 - Chapter 1: Extending Schenkerian Analysis

Heinrich Schenker restricted his analytical focus to the repertoire of German music from

Bach to Brahms. Consequently, attempts by theorists to apply his approaches beyond this scope

are often met with varying degrees of skepticism.1 This thesis, which responds to and criticizes

the work of James Baker, applies Schenker’s theories beyond the repertoire in ways Schenker

had not attended. Accordingly, this chapter explores issues that pertain to an extension of

Schenker’s theories. My purpose is to consider the extent to which Schenkerian analysis may

provide information regarding Scriabin’s early transitional music. I begin with Schenker’s own

ideas about analysis to show how those ideas are not abandoned in the Schenkerian analysis of

Scriabin’s music. In addition, I examine literature that offers insight into the theoretical issue of

applying Schenkerian analysis to post-tonal music.

To accomplish my broader goals, this chapter is arranged into five sections. Section 1

examines the conceptual underpinnings of Schenkerian analysis through Schenker’s own

writings. Section 2 takes a brief look at various analytical problems to which Schenkerian

analysis has been applied. This section speculates on the possibility of a flexible use of the

Ursatz in both tonal and non-tonal contexts. Section 3 discusses the issue of prolongation itself

as it is the central issue in deciding whether a composition can be represented through

Schenkerian graphs. Having discussed the issues pertinent to Schenkerian analysis in general, section 4 considers two articles by James Baker that provide insight into the use of Schenkerian

analysis to analyze the music of Scriabin. Finally, section 5 utilizes the various points made

throughout the chapter to corroborate the view that Schenkerian analysis is both beneficial and

1 See, for example, Joseph N. Straus, “The Problem of Prolongation in Post-Tonal Music,” Journal of Music Theory 31/1 (1987): 1–21. This article is discussed in greater detail below.

- 7 - appropriate for Scriabin’s transitional music. In addition, I address certain limitations in the type

of information that can be gained from such analysis.

1. Schenker’s writings

This section looks at both Schenker’s attitude toward analysis itself and considers how his view of the Ursatz may have implications for its extended use. The reader should note that

Schenker viewed his analytical method as a means and not an end. Many times in his writings,

Schenker refers to the responsibilities of the analyst towards the reader/listener/performer. As a criticism of Hermann Kretzschmar’s guide to Beethoven’s Ninth Symphony, Schenker commented “What good is a ‘guide’ if it offers the reader nothing more than what he himself already perceives and knows?”2 This begins to paint the picture that Schenker views his

analytical efforts to show what is otherwise hidden. When commenting on Riemann’s

interpretation of Bach’s Well-Tempered Clavier, he goes so far as to call Riemann an “un-ear,”3 further insinuating his own importance. Schenker gives a further example of the value of his analysis during his explication of the Urlinie early on in his Tonwille. “If this sort of Urlinie is the long-distance hearing of the composer, then it may be of use to the reader, the performer, or the listener whose hearing is only near-at-hand, like a pair of mental spectacles that bring distant things closer to him.” Once again, Schenker sets up a tripartite chain for the analytical enterprise

2 Heinrich Schenker, Beethovens neunte Sinfonie (Vienna: Universal Editon, 1912). trans and ed. John Rothgeb (New Haven, CT: Yale University Press, 1992). Quoted in Robert Snarrenberg, Schenker’s Interpretive Practice (Cambridge: Cambrige University, 1997), 7. In response to Hermann Kretzschmar, Führer durch den Concertsaal. 1ste Abtheileng: Sinfonie and Suite (Leipzig: A.G. Liebekind, 1887).

3 Heinrich Schenker, Der Tonwille Vol. I, ed. William Drabkin (Oxford: Oxford University Press, 2004), 39. In response to Hugo Riemann, Katechismus der Fugen- Komposition: Analyse von J. S. Bachs ‘Wohltemperiertem Klavier’ and ‘Kunst der Fugue’ (Leipzig: Hesse, 1890–1904).

- 8 - featuring himself in a prophet-like position between the composer on high and the average

listener or performer4.

In this respect, Schenker’s view of himself as an analyst resonates with the philosophy of

David Hume. In his attempt to define art, Hume proclaimed that art can only be evaluated by

utopian “true judges” who alone have the requisite knowledge and understanding to decide

whether an object is art or not.5 Hume states that “many men, when left to themselves, have but a faint and dubious perception of beauty, who yet are capable of relishing any fine stroke which is pointed out to them.”6 Schenker viewed himself as uniquely capable of pointing out such “fine strokes.” Even Hume’s view of the objective value of a great piece of art and his invocation of nature resonates with Schenker: “And though prejudices may prevail for a time, they never unite in celebrating any rival to the true genius, but yield at last to the force of nature and just sentiment.”7 In Schenker’s view, this “genius” would refer to a great work and not to Schenker

himself. Such is the fundamental difference between Hume’s view of art and Schenker’s: Hume

places the value of art in the viewer whereas Schenker believes that certain pieces are intrinsically great. Schenker, according to his own view, is merely discovering the natural

greatness of a piece. The concept of a true judge works for both Schenker as interpreter of music

for the masses, and for the presence of a clear Ursatz as the measuring stick by which great music can be judged. It is not a coincidence that late Romantic music, post-tonal music, and

4 Snarrenberg states that Schenker viewed himself as a Moses, “a prophet who would proclaim a monotriadic creed and inscribe the eternal laws of the cultus.” Snarrenberg, xv.

5 David Hume, “On the Standard of Taste,” Reprinted in Aesthetics: the Big Question, Ed. Carolyn Korsmeyer (Malden, MA: Blackwell Publishers, 1998).

6 Hume, “On the Standard of Taste,” 495.

7 Hume, “On the Standard of Taste,” 496.

- 9 - music of other nationalities (Chopin and Domenico Scarlatti excluded) did not receive any merit

with such a measurement.

Thus far, I have suggested that Schenker viewed analysis as a way to inform others of

that which they are incapable of discovering on their own.8 I turn now to the nature of the information that Schenker imparted: the description of tonality as a composing out

(Auskomponierung) of the tonic triad. Schenker’s Free Composition focuses on the interaction

between a two-voice contrapuntal paradigm (or Ursatz) and a fully realized composition. In his

commentary on this work, Carl Schachter discusses the discrepancy between what Schenker says

and what his practice suggests regarding foreground-to-background or background-to-foreground

analysis.9 A foreground-to-background approach to Schenkerian analysis begins with a

completed piece and reduces it to the Ursatz. Contrary to this, a background-to-foreground

approach begins with the Ursatz and traces a generative path towards the completed piece.

Schachter shows that Schenker implicitly favors the latter, or background-to-foreground, direction. He viewed each piece as a different realization of the two-voice Ursatz, which he described as “the horizontal path of tonality.”10 This description of the Ursatz proves to be important in determining how Schenker’s method can be adapted for the analysis of Scriabin.

Acknowledging that the Ursatz is “the horizontal path of tonality” does not preclude two possibilities that are invaluable to the extension of Schenkerian theory. The first of these

8 This view contradicts greatly with Schonberg’s opinion that “[The theorist] knows that the pupil learns most of all through the example shown him by the masters in their masterworks.” Arnold Schoenberg, Theory of Harmony [Harmonielehre], trans. Roy E. Carter (Berkeley: University of California Press, 1978), 8.

9 Carl Schachter, “A Commentary on Schenker’s Free Composition,” reprinted in Carl Schachter, Unfoldings (New York: Oxford University Press, 1999), 190.

10 Heinrich Schenker, “Yet Another Word on the Urlinie,” Der Tonwille Vol. I Ed. William Drabkin (Oxford: Oxford University Press, 2004), 53.

- 10 - possibilites is supported by Schenker’s own writings. Although Schenker believes that an Ursatz

is an indication of tonality, he attempts to analyze post-tonal pieces as well, albeit to show their

inferiority. Temporarily disregarding the prolongational issues that will be addressed in section

3, these analyses, such as that of Stravinsky, indicate that we too, might search for Ursatzen in

untraditional places.11 This begs the question, when an authentic Ursatz is not found, is the

reduction invalid?

Regarding this question, this chapter seeks to disentwine the concepts of the Ursatz and the two-voice background. In this respect, a piece that is not tonal may have a two-voice contrapuntal background that is not an Ursatz. Such distinctions have allowed many analysts to use Schenkerian analysis for various purposes outside of those that Schenker intended.12 I shall call such backgrounds “contrapuntal structures.” By this term, I suggest the presence of a contrapuntal structure that represents a piece much in the same way that an Ursatz represents a piece. However, such structures are contextual, not universal. Thus, the contrapuntal structure of one piece, even in its most abstract form, need not necessarily be found in another. This flexibility is one of the most important distinctions between it and the Ursatz.

As I proceed, I do so with full acknowledgement that Schenker intended that his analysis be used for unequivocally tonal music. However, I intend to show in the remainder of this

11 I use the term “traditional” to refer to composers and compositions that Schenker, himself analyzed.

12 For instance, Edward R. Pearsall, “Harmonic Progressions and Prolongation in Post- Tonal Music,” Music Analysis 10/ 3 (1991): 345–55; David Stern, “Schenkerian Theory and the Analysis of Renaissance Music,” in Hedi Siegel (ed.) Schenker Studies (New York: Cambridge University Press, 1990); and James Baker, “Voice Leading in Post-Tonal Music: Suggestions for Extending Schenker's Theory,” Music Analysis 9/2 (1990): 177–200.

- 11 - chapter that one can arrive at a contrapuntal structure of a piece which is not necessarily an

Ursatz.

2. Analytical uses of the Ursatz

The three articles discussed in this section represent three different ways the Ursatz has been incorporated analytically. In the first article, Schenkerian analysis is exploited for its ability to determine the structural and formal necessity of a coda. This represents a traditional use of the

Ursatz that exploits its potential to help define musical structure.14 In the second article, various

Schenkerian analyses are applied to an analytically difficult, yet unambiguously tonal piece by

Chopin. This article shows that even within a traditional tonal context, the Ursatz can be used

with some flexibility. This has important ramifications for the analysis of Scriabin’s music which

often requires flexibility when connecting clear structural points. In the final article, Schenkerian

analysis is applied to pre-tonal music, showing its application in a non-traditional context. This

article ultimately suggests that due to the sophistication of Schenkerian analysis, theorists should

be careful not to disregard its potential to elucidate non-tonal musics. Despite the apparent

flexibility in the Ursatz that these articles seem to exploit, I conclude this section by noting the

importance of its constancy.

John Rink’s article, “Structural Momentum and closure in Chopin’s Op. 9, No. 2,”15 serves as an example of the role of the Ursatz in determining structure. The primary concern in this article is the nature of the coda at the end of the titular Chopin nocturne. Rink distinguishes

14In Chapter 2, I demonstrate to ability of the generative contrapuntal model to similarly determine the structural necessity of the final chord in Op. 49/2.

15 John Rink, “Structural Momentum and Closure in Chopin’s Op. 9, No. 2,” Schenker Studies 2 (Cambridge: Cambridge University Press, 1999).

- 12 - between a “formal coda,” one that extends the form but does not participate meaningfully in the

tonal descent, and a “structural coda,” which does. Rink compares his own graph of this piece with that of Schenker. The two graphs are in direct conflict with respect to the coda. Whereas

Rink divides the coda (i.e., all material following m. 24) into three sections, C1, C2, and the structural coda, Schenker ends his graph at m. 24, suggesting that the remaining measures are tonally superfluous. Schenkerian analysis provides two interesting functions at this juncture.

First, Rink notes that the outer form of this piece (that which is demarcated by external factors such as repeat signs and motives) does not result directly from the inner form or deeper-level voice-leading structure — as this is an interrupted structure, the points at which the descent

ceases and is begun again. Next, Rink is able to show that through linear descents of thirds

occurring throughout the coda, and through motivic parallelisms between the cadenza of the coda

and the bass line of the piece proper, the background descent does encompass the coda. In this

example, both motivic and harmonic elements are utilized to show the structural necessity of the

final measures in the piece to the tonal process.

A 1998 article by Justin London and Ronald Rodman serves as an example of the

variation that can be found in the use of the Ursatz within a tonal context. . In this article,

“Musical Genre and Schenkerian Analysis,”16 they reconsider the often-analyzed Chopin E- minor prelude. This piece provides a particular analytical challenge due to the smooth surface voice-leading and seemingly obvious descent offset by a less well-defined Urlinie. They begin by listing their three goals for the article and their analysis: 1. To describe the problems of linear

coherence and contrapuntal/harmonic support. 2. To show the underlying closed tonal structure.

16 Justin London and Ronald Rodman, “Musical Genre and Schenkerian Analysis,” Journal of Music Theory 42/1 (1998): 101–124.

- 13 - 3. To show that the alterations to the structure should not be viewed as problems but as essential

features of the music. To accomplish their first goal, they present previous analyses by Carl

Schachter and Allen Forte and Stephen Gilbert who posit an uninterrupted structure and an

unorthodox interruption at 4^, respectively.17 After considering the historical role of the prelude,

London and Rodman determine that the prelude’s lack of definite tonal closure could be motivated by its function. The prelude’s traditional placement before a larger piece could cause it to have a tonally open or inconclusive ending. How does Schenkerian analysis play into their argument, however? London and Rodman use the plurality of graphs (including their own suggestion of a gapped line—i.e., one missing ^3) to exhibit Chopin’s skill as a composer. They note that a “remnant” of the fundamental structure exists while retaining a “profound sense of that which is missing.”18 To conclude, they note the issues that result from attempting to measure

a piece against an a priori background. The plurality of interpretations they consider places

emphasis on how a piece relates to the Ursatz as opposed to considering the determination of the

Ursatz an end in itself. Looking ahead to Scriabin, this lends further credence to the value of the

Schenkerian analysis of a piece that contains tonal remnants but not an explicit Ursatz.

In his 1990 article, “Schenkerian Theory and the Analysis of Renaissance Music,”19

David Stern suggests that Schenkerian analysis is potentially useful for the analysis of

17 Carl Schachter, “The Prelude in E minor op. 29 no. 4: Autograph Sources and Interpretation,” in Chopin Studies 2, ed. J. Rink and J. Samson (Cambridge: Cambridge University Press, 1994), 161–182.; Allen Forte and Stephen Gilbert, Introduction to Schenkerian Analysis: Instructor’s Manual (New York, W.W. Norton and Co., 1982).

18 Justin London and Donald Rodman, “Musical Genre and Schenkerian Analysis,” Journal of Music Theory 42/1 (1998): 117.

19 David Stern, “Schenkerian Theory and the Analysis of Renaissance Music,” in Hedi Siegel (ed.) Schenker Studies (New York: Cambridge University Press, 1990).

- 14 - Renaissance music.20 Stern shows that Schenker wrote about the importance of understanding

the origins of the triad. After discussing certain historical examples of composers and theorists

who may have thought vertically as well as horizontally, Stern enters into his main argument. He

claims that since Schenkerian analysis is, at its heart, contrapuntally based, it is quite appropriate

and useful for analysis of contrapuntally based compositions such as those of the Renaissance.

He begins slowly, showing how certain Schenkerian concepts such as hidden repetition can be found in Renaissance music. This is just a small step on the way to his full graph of the Kyrie from Josquin’s Missa de Beata Virgine (1510). Stern uses this graph to show that the upper voice outlines the G –D fifth, similar to an Ursatz on G. Here he notes the major point of incongruence with a fundamental structure in the major-minor system. Due to the structure of the sixteenth century cadence, pieces did not end with 2^ descending to 1^ but rather 7^ ascending to 1^. Stern considers but dismisses the Schenkerian concept of “substitution” at this point.21 Despite this

incongruence, Stern recommends Schenkerian analysis for showing the structure of a

Renaissance composition. More importantly, Stern notes the sophistication of Schenkerian analysis and questions those who would deny it any additional applications.

Although these three analyses use the Ursatz towards different analytical ends, they all

indicate the value of the stability of the Ursatz. While the Ursatz, itself, is intractable, voice- leading reductions vary. Thus, comparing such results to the Ursatz can provide a heightened understanding of form, voice leading procedure, or contrapuntal structure in a non-tonal context.

20 While this particular analytical application of the Ursatz has not been widely adopted, it represents an attempt to apply the Ursatz outside of tonal music. More successful attempts toward post-tonal music are featured in the following sections.

21 With substitution, the leading-tone may appear in place of the traditional ^2 in the Urlinie.

- 15 - As the repertoire under consideration moves farther from the tonality for which Schenker’s theories were developed, the philosophical acceptance of extending Schenker’s methods becomes insufficient. One must develop a system of criteria for accomplishing such analyses. At the forefront of this issue is the extent to which post-tonal music can exhibit prolongation.

3. Post-tonal prolongational issues

There have been two major concerns when theorists have debated the application of

Schenkerian analysis to post-tonal music. The first is an issue that is common to Schenkerian analysis but is amplified when considered in the context of post-tonal music: the problem of strict adherence to an a priori background model. This issue will be addressed through consideration of analyses by Allen Forte, Robert Morgan, and James Baker. The second concern in the application of Schenkerian analysis to post-tonal music is the ability to determine whether a particular note is inherently or contextually consonant or dissonant. Beginning with a quote from Schenker, I look at three seminal publications regarding atonal prolongation from Roy

Travis, Robert Morgan, and Felix Salzer. This section concludes with a look at an article by

Joseph N. Straus who intended to prove that post-tonal prolongation in a strict sense is an impossibility. i. A priori issues

Adherence to an a priori background model proves to be an issue for both tonal and post- tonal analysis. In tonal analysis, the potential problem is at the same time practical and conceptual. Somewhat ironically, both critics and proponents of Schenkerian analysis share very similar views on such issues. Both camps warn of arbitrary note-picking in order to fulfill the necessary background requirement. Some critics are concerned that Schenkerian analysis is a

- 16 - circular exercise intended merely to confirm its own validity. Matthew Brown, Douglas

Dempster, and Dave Headlam speak out about this issue but dismiss it on the grounds that

Schenkerian analysis “makes concrete predictions about the behavior of tonal surfaces and that it

also has clear explanatory limits.”22 In a different vein, Nicholas Cook brings our attention to the

conceptual priority of analysis in music theory. When one loses sight of this, he warns, “the

analyst has come to believe that the purpose of a piece of music is to prove the validity of his

analytical method, rather than the purpose of the analytical method being to illuminate the

music…”23

Since such issues exist in tonal music, in which Schenkerian analysis is generally

accepted, they are only amplified when applied to post-tonal music. Regarding post-tonal music,

unmusically strict adherence to an a priori model can result from an underlying need for

analytical rigor. Such rigor is an attempt to dispel skepticism regarding Schenkerian analysis and

post-tonal music. Forte’s “Linear Analysis” article begins by discussing prior attempts to

describe the voice leading in the often-analyzed Tristan prelude. Part of his criticism of Boretz’s

and Mitchell’s analyses is that “[they exhibit] an overly rigid adherence to a background model

which [determines] virtually every aspect of the interpretation of the foreground.”24 Morgan cites

22 Matthew Brown, Douglas Dempster, and Dave Headlam, “The [Sharp]IV([Flat]V): Testing the Limits of Schenker’s Theory of Tonality,” Music Theory Spectrum 19/ 2 (1997): 182.

23 Nicholas Cook, A Guide to Musical Analysis (New York: G. Braziller, 1987), 2.

24 Allen Forte, “New Approaches to the Linear Analysis of Music,” Journal of American Musicological Society 41/2 (1988): 326. Forte cites Benjamin Boretz, “Meta- variations, Part IV: Analytic Fallout (I), Perspectives of New Music 11 (1972): 159–217; William J. Mitchell, “The Tristan Prelude: Techniques and Structure,” The Music Forum 1 (1967): 162– 203.

- 17 - a similar problem in Schenker’s own analysis of Stravinsky’s Rite of Spring.25 Schenker, whose unstated goal for this analysis was to show that this piece was at best unable to be reduced to a fundamental structure and at worst inferior, attempted to analyze Rite of Spring in terms of a

consonant background. In order to do this, Schenker assumed that the underlying vertical

sonority was a triad. As this was, of course, not the case, Schenker obtained his desired results

without gaining a complete understanding of the piece.26

Baker holds a slightly different perspective of the a priori issue in his discussion of the

Schenkerian analysis of Scriabin’s Enigme. Baker’s solution does not abandon Schenker’s philosophy but rather uses it to its potential but no further. He states: “It is crucial to analyze a transitional composition thoroughly not only in terms of innovative components and procedures but also in terms of its relation to conventional tonal structures.”27 In Chapter 2, I discuss in great detail how Baker employs this philosophy in one of his Schenkerian analyses. I have already mentioned that London and Rodman emphasize how Chopin’s E-minor prelude fits the fundamental structure, not whether it does.28 However, no background can exist without the presence of prolongation, an issue I will now address. ii. prolongational issues

25 Heinrich Schenker, Das Meisterwerk in der Musik, Band II (Munich: Drei Masken Verlag, 1926), 37–40.

26 Morgan, “Dissonant Prolongation: Theoretical and Compositional Precedents,” 52–3. Several decades after Schenker’s analysis, Adele Katz came to a conclusion regarding Stravinsky’s music in general. Critical of some of the ways that Stravinsky had created a new style by moving away from tonality, she conceded that no analyst had yet truly captured the nuances of this style. In contrast to Schenker, she acknowledged her limited analytical means for this style. Adele T. Katz, Challenge to Musical Tradition: a New Concept of Tonality (New York: A.A. Knopf, 1945), 294–349.

27 Baker, “Schenkerian Analysis and Post–Tonal Music,” 168 and 186.

28 This view is expounded upon in the following section.

- 18 - Regarding the issue of prolongation, Schenker states in his Tonwille the crux of many

prolongational debates: “The life of the tone thrives in consonance and dissonance.”29 The reason this statement carries so much weight is both explicit and implicit. Explicitly, this sets up a definition of how a tone is prolonged. Implicitly, it acknowledges a system that must be in place in order to determine the difference between consonance and dissonance. As this relates to analysis, we must decide how a tone is prolonged in a particular piece and whether a sufficient syntax has been established to make prolongational claims. In terms of tonal prolongation, where the syntax issue is practically invisible, Larson has described the process of prolongation as similar to embellishment.30 We perceive that less stable notes require resolution to more stable notes. Larson goes on further to describe the necessary conditions for stability and differentiates between contextual and inherent stability. With contextual stability, we “hear a note as unstable

[by auralizing] a more stable pitch to which it tends to move and a path that would take it there.”31 Larson defines inherent stability simply as consonance.

Early attempts to explicate the nature of consonance and dissonance in post-tonal music

as it pertains to prolongation can be found in Roy Travis’s “Towards a New Concept of

Tonality?,”32 Robert Morgan’s “Dissonant Prologation,”33 and Felix Salzer’s Structural

29 Heinrich Schenker, “The Laws of the Art of Music,” Der Tonwille Vol. I Ed. William Drabkin (Oxford: Oxford University Press, 2004), 51.

30 Steve Larson, “The Problem of Prolongation in Tonal Music: Terminology, Perception, and Expressive Meaning,” Journal of Music Theory 41/1 (1997): 107.

31 Larson, “The Problem of Prolongation in Tonal Music: Terminology, Perception, and Expressive Meaning,” 106.

32 Roy Travis, “Towards a New Concept of Tonality?” Journal of Music Theory 3/2 (1959): 257–284.

- 19 - Hearing.34 Before turning to twentieth-century music, Travis begins with a broad definition of

tonality: “Music is tonal when its motion unfolds through time a particular tone, interval, or

chord.”35 Musical motion is then described in two parts: structure and prolongation, which

elaborates the structure. In order to test the application of this concept to post-tonal music, Travis

considers an octave-traversing passage from The Rite of Spring. Since the passage is clearly

delineated and begins and ends with the same sonority, it is easily separated into Travis’s two categories of motion. In his reasoning, the directed motion between the two sonorities indicates that the sonority is prolonged. This perspective is directly refuted by Straus who warns “Just because event Y fall between two occurrences of event X does not mean that Y prolongs X. 36

Straus’s point locates the main weakness in Travis’s argument. Travis focuses his analyses on the structural sonorities found in pieces by Stravinsky and Bartok but not how the material between them constitutes prolongation, per se.

The problem of how dissonant sonorities might be prolonged is taken up by Robert

Morgan who begins by discussing Schenker’s own analysis of Bach’s C-major prelude. The exception contained in Schenker’s Bach analysis (which has even contradicted his own writings) is that a dominant-seventh chord is shown as being prolonged. In this instance, a harmony that is, by definition, unstable is itself being embellished. Morgan goes on to point out that this section functions on a background level as the primary dominant. This dominant section lies in between

33 Robert Morgan, “Dissonant Prolongation: Theoretical and Compositional Precedents,” Journal of Music Theory 20/1 (1976): 49–91.

34 Felix Salzer, Structual Hearing, vol. 1 (New York: Dover Publications, Inc, 1962).

35 Travis, 261.

36 Joseph N. Straus, “The Problem of Prolongation in Post-Tonal Music,” Journal of Music Theory 31/1 (1987): 7.

- 20 - two consonant sections and therefore is within the realm of traditional tonal hierarchies and not

contextual prolongation.37 However, Schenker’s prolongation of the dominant suggests the possibility that a particular harmony, though dissonant, could be prolonged.

This possibility is presented much more casually in Felix Salzer’s Strucural Hearing.

Salzer’s book deals mainly with triadic tonal music. When he engages the post-tonal repertoire of Ravel’s Jeax d’Eau and Copland’s Piano Sonata, he does not endeavor to alter or augment his theories of prolongation in order to include them. “…we must now mention one of the outstanding revolutionary achievements of contemporary music: the contrapuntal prolongation of dissonant chords, especially polychords... The whole [opening section of Jeax d’Eau] is typical of French impressionistic style insofar as the triad, as an architectonic factor of structure as well as of prolongation, is replaced by seventh chords and altered chords.”38 Instead of putting an

emphasis on chord function, which is essential to Schenker’s theory, Salzer posits that connection through “clearly directed voice leading” is sufficient to portend prolongation.39

A post-tonal perspective on this debate is found in the 1987 Joseph Straus article alluded to in Larson’s 1997 title: “The Problem of Prolongation in Post-Tonal Music” (emphasis mine).40

While Salzer minimizes the prolongational differences between tonal and post-tonal music,

Straus problematizes it. Here, Straus describes four conditions for tonal prolongation to exist:

1. consonance/dissonance which determines structural weight.

37 Robert Morgan, “Dissonant Prolongation: Theoretical and Compositional Precedents,” 56–7.

38 Salzer, Structural Hearing, 193–4.

39 Salzer, Structural Hearing, 193.

40 Joseph N. Straus, “The Problem of Prolongation in Post-Tonal Music,” Journal of Music Theory 31/1 (1987): 1–21.

- 21 - 2. scale-degree which determines the relative weight of a consonance.

3. embellishment which denotes an established syntax for prolongation.

4. harmony/voice-leading which describes prolongation as the horizontal manifestation

of a vertical harmony.

Straus’s argument here is that since post-tonal music does not satisfy all of these conditions, prolongation cannot exist within such a piece. Of course, Straus does not mean to claim that there is no sense of coherence in a post-tonal piece. Instead, he describes the process of

“association” in post-tonal music. Here, structural pitches are determined in a more contextual manner through criteria such as register and gesture. Such an idea was subsequently taken to a highly detailed level in Lerdahl’s “Atonal Prolongational Structure” in which he gives a numerical weight to each type of association in order to develop a hierarchy.41

Although intended to prove the inability of post-tonal music to contain prolongation,

Straus’s specific criteria for prolongation ultimately belies his seemingly diametric view of the issue. Straus’s four conditions are intended to exclude all post-tonal music as such music does not satisfy all of those conditions. However, my description of “transitional” music indicates a shifting balance of influence between tonal and atonal elements. It is therefore possible that the balance in a particular piece could be such that it satisfies Straus’s conditions without being devoid of atonal elements. Thus, Straus’s rules allow for the determination of prolongation on a case-by-case basis and do not constitute the dismissal of all post-tonal music. This possibility

aids Baker’s assertion that it is more important to address how, not whether, a piece is tonal.

Since the ultimate goal of this chapter is to determine the validity of a Schenkerian approach to

the music of Scriabin, we need not accept prolongation in Schoenberg in order to propose a

41 Fred Lerdahl, “Atonal Prolongational Structure,” Contemporary Music Review 4 (1989): 65–88.

- 22 - Schenkerian view of Scriabin. Instead, since tonal elements in Scriabin adhere to Straus’s conditions, those conditions help confirm the presence of prolongation.

In the next section, the writings of James Baker indirectly address how these conditions relate to the music of Scriabin. Since Straus discusses the lack of prolongation in Schoenberg

Op. 19/2, the next section begins by discussing Baker’s view of Schoenberg, Op. 19/1.

4. James Baker

The first Baker article, “Voice Leading in Post-Tonal Music,”42 concerns itself with the music of Schoenberg, not Scriabin. Baker notes several elements that belie prolongation in

Schoenberg’s Op. 19/1. First, the lack of fifth-related bass motion and the chromatic saturation prompts Baker to conclude that “it seems totally improbable that a Schenkerian Ursatz-form

supports the structure, and questionable whether any sort of prolongational technique accounts for closure and overall coherence.”43 In addition, he notes the lack of octave doubling in much

post-tonal music such as Schoenberg’s since octave doubling creates an undesirable hierarchy

among the tones. These comments have indirect implications for the application of Schenker’s

method to the music of Scriabin. When considering the pieces under scrutiny in this thesis—

Scriabin’s Opp. 48/4 and 49/2—Baker’s comments regarding Schoenberg’s music do not apply.

Scriabin’s transitional music does involve fifth-related harmonies and octave doubling. The

contrast between Scriabin and Schoenberg highlights the overt tonal elements in Scriabin as

compared to the latent ones in Schoenberg. In contrast to Schoenberg’s music, these overt tonal

42 James Baker, “Voice Leading in Post-Tonal Music: Suggestions for Extending Schenker's Theory,” Music Analysis 9/2 (1990): 177–200.

43 Baker, “Voice Leading in Post-Tonal Music: Suggestions for Extending Schenker's Theory,” 179.

- 23 - elements such as a predominant, dominant, and tonic hierarchy and tonal melodic closure help

align Scriabin’s music with the conditions set by Straus.44

Whereas Baker’s earlier article only suggests the use of Schenkerian analysis for the music of Scriabin, a later article, “Schenkerian Analysis and Post-Tonal Music,”45 explores it explicitly. In this article, after reviewing much literature, Baker presents a dichotomy: one can allow prolongation that is not based on tonic and dominant elements, or one can not. Taking the former view, Baker notes the compromise that many analysts (particularly of Schoenberg’s and

Berg’s music) have made: don’t ask “is it tonal or atonal” but rather “in what way is this piece tonal?”46 Baker proceeds to apply this philosophy to Scriabin’s quintessential transitional piece,

Enigme, which is Scriabin’s first to end on a dissonant harmony. Much like Stern, who suggested that analysts focus on the elements of Schenker’s theory that inform non-tonal music rather than the elements that are not compatible, Baker urges the analyst to think of the piece holistically and to focus on how Schenkerian analysis can aid our understanding of a piece.

Thus, both Baker and Straus have shown that assuming certain conditions, it can be beneficial to apply Schenkerian analysis toward a transitional piece of music that retains multiple tonal elements despite a) being ambiguously tonal and b) not containing a traditional Ursatz.

44 See Chapter 2 for a discussion of harmonic relations in the two Scriabin preludes under consideration.

45 James Baker, “Schenkerian Analysis and Post-Tonal Music,” in David W. Beach (ed.), Aspects of Schenkerian Theory (New Haven, CT: Yale Univ. Press, 1983), 153–86.

46 Baker, “Schenkerian Analysis and Post-Tonal Music,” 168.

- 24 - 5. Applications to Scriabin

Having discussed Schenker’s original intentions, previous applications of his method, and

prolongational issues, it is appropriate to turn to the broader goal of this chapter: the benefits and

limitations of Schenkerian analysis for Scriabin. There are two types of limitations that are

pertinent to this chapter. One type questions whether it is appropriate to apply Schenkerian

analysis to Scriabin at all. The other type questions what type of knowledge is gained from the analysis.

In terms of applicability, the earlier discussion of Schenker’s own writings helped frame the issue. If we accept the fact that a proper Ursatz is the signpost of tonality, then is it possible to use the Ursatz as a measuring stick, not a litmus test? On the other hand, regardless of how a piece measures up to this standard, is it beneficial to determine a contrapuntal structure for that piece?47 We have already seen that Baker answers these questions in the affirmative. Straus’s

negative answer to these questions brings to light the potential semantic issue of this debate. By

setting conditions for prolongation that are stylistically non-specific but tonally biased, Straus

makes the argument that since prolongation can only truly occur in tonal music, and Schenker’s

theory is based on the concept of prolongation, post-tonal music cannot be analyzed with a

Schenkerian methodology. Although it is difficult to argue against the notion that, unaltered,

Schenker’s theory can only apply to tonal music, much of the debate seems to surround the

question of whether an altered form of the theory can still be considered Schenkerian. It is in this

respect that this debate is semantic. While no one denies that the concept of the Ursatz is central

to Schenker’s theory, no one (that has not been rebuked by later theorists) claims that post-tonal

music contains an Ursatz! In other words, if the question is whether we can call the extension of

47 The next section will address the ways in which it might be beneficial.

- 25 - Schenker’s theory truly “Schenkerian,” my answer is that it doesn’t necessarily matter. What

matters is the next issue: what does such an analysis tell us?

It is with this question that the “transitional” nature of Scriabin’s middle period from

1903 –1910 is pertinent. The beginning of this period is marked by a move away from the traditional sonorities and harmonic syntax of late-nineteenth-century Russian tonality. The end is marked by an abandonment of a clear tonal center in favor of symmetrical pitch-collections and an atonal sense of harmonic progression. As I said in my introduction, I am not concerned with the dynamic view of such “transitional” music as presented by both Samson and Baker. Thus my interest in Schenkerian analysis is not to assess a piece’s distance from tonality or proximity to atonality. Rather, I seek to better understand the manner in which tonality is utilized within these pieces.

The nature of tonality in a transitional piece may be shown through a a Schenker- influenced reduction, or what I have called a generative model. This model allows one to view traditional tonal elements in terms of the piece itself and not necessarily in comparison to an abstract background structure. Once such a graph is compared directly to a tonal Ursatz, a judgment of distance is made by both Baker and Schenker. Although Baker revels in this distance while Schenker abhors it, their conclusions both indicate motion away from tonality. By avoiding such explicit comparisons, I do not fall into the trap of treating this highly sophisticated music as either a deformation of an earlier style or a primitive version of a future one. This does not imply a denial of tonal allusions in this music. Such allusions (in addition to actual tonal motion) are essential for my concept of “tonal mirages.” However, I make the distinction between acknowledging the tonal elements in these pieces while treating them as part of an

- 26 - autonomous style and treating the pieces as essentially tonal with foreign elements that

foreshadow a later style.

I now turn to the limitations of this type of analysis. To begin with, the a priori nature of

Schenker’s methodology has been often cited in this chapter but always dismissed. As I contend

that this is a feature of Schenkerian analysis that can be effective, it would be hypocritical to list

it as a limitation. Therefore, it is a limitation for those who let it be one. Note that “limitation” is

not merely a euphemism for “flaw.” Schenker’s famous dictum, semper idem sed non eodem

modo (always the same but not in the same manner), addresses this very concern. The Ursatz is

not an inevitability that confines tonal composers but rather a basic framework within which

their artistry flourishes. Despite this, those who believe that only traditional tonal backgrounds

can exist with Schenkerian analysis will only use it for pieces with tonal backgrounds.

What does Schenkerian analysis not reveal, then? Schenker is reliant upon oppositions.

Whether one uses tonic and dominant, consonant and dissonant (or even salient and less salient as Lerdahl has),one is constantly creating a hierarchy of pitches based upon some criteria.

Although Schenker considers surface-level events in his analyses, the extreme foreground is “the piece.” Following that, there is typically a graph that looks almost identical to “the piece” with stems and slurs instead of rhythmic notation.50 And although all pitches may remain present at this level, the presence of stems and slurs already indicate the criteria being used. It is in this respect that a necessary and useful complement to this analysis is one that regards all pitches equally in order to observe contextual voice-leading phenomena. Following the next chapter, which contains Schenkerian analyses, Chapter 3 presents an analysis that views voice leading outside of a tonal context. By temporarily ignoring any latent tonality, characteristic movement

- 27 - between tones can be observed. As the conclusion to this thesis states, the interaction of the two analyses can help reinforce or deepen the conclusions given by either analysis separately.

- 28 -

- 29 - Chapter 2: Schenkerian Analysis

The goal of the previous chapter was to explore theoretical issues surrounding the application of Schenkerian analysis to the music of Scriabin. It was concerned with both the values and limitations of such analysis and with evaluating whether or not Schenkerian analysis should be applied to this repertoire. In this chapter, I will present analyses of two Scriabin preludes, Op. 49/2 and Op. 48/4. These analyses accomplish three goals. First, they reveal the ways in which a piece without a traditional tonal Ursatz can be reduced to a contrapuntal structure with tonal elements. Second, they show how Scriabin uses non-traditional sonorities within a tonal syntax. Third and finally, they bring to light idiomatic features of Scriabin’s compositional practice in his early transitional period, concentrating specifically on recurring harmonic and formal issues.

Op. 49/2

The Op. 49/2 Prelude contains three elements typical of Scriabin’s transitional preludes.

First is an opening chord formed by an altered dominant seventh chord built with the tonic bass

note. Second is the clear authentic cadence at the end of the prelude. Third is a frugal use of

musical materials such that most of the prelude is derived from the opening measures. This

particular prelude contains an AA’ form in which the A’ section consists of an almost exact

transposition of the A section. An important feature of such preludes is the point at which either

the transposition becomes inexact or our interpretation of similar musical material shifts. Since

the Urlinie descent must be different in each half of the piece, so that the second half ends on 1^

while the first half does not, either a literal or an interpretational change must exist. In the case of

this prelude, the level of transposition is up a perfect fourth, creating the sense that the first

- 30 - section ends on a half-cadence. While in the Classical period, one might assume that this

indicates a I–V/IV–I harmonic scheme, the ensuing analysis shows that the beginning of each

formal section does not contain the tonal clarity to support such a scheme.1

Issues found in the work of James M. Baker and Marian Kielian-Gilbert are particularly relevant to the analysis below. Baker’s monograph, The Music of Alexander Scriabin,2 makes an important allowance due to the idiomatic textures of Scriabin’s compositions. First, Baker notes that although the top voice appears to be melodically and registerally disjunct, this is often the

result of an inner voice doubled at a higher register.3 As a result, the true upper voice descent can

be concealed. Additionally, Baker allows an Urlinie to exist on multiple registral levels, an idea

that Schenker prohibited with his notion of the obligatory register but occasionally employed in practice. Although Baker’s concessions are practical, they require a modicum of restraint in that they allow the analyst to search high and low (literally) for Stufen (scale-steps). It is in this respect that the a priori nature of Schenker’s theory, discussed in the previous chapter, becomes a factor. One must be vigilant against convenient note-picking. As Rothstein has warned, if one enters an analysis with a preconceived idea of what he or she will find then “theory wins, music loses.”4

1 This issue is taken up further in the analysis of 48/4 where I discuss similarities between the analysis of near-identical musical passages in Scriabin’s preludes and the analysis of secondary themes in the exposition and recapitulation of sonatas.

2 James M. Baker, The Music of Alexander Scriabin (New Haven: Yale University Press, 1986).

3 Baker, The Music of Alexander Scriabin, 24.

4 William Rothstein, ‘Letter to the Editor: “The Americanization of Schenker Pedagogy?,”’ Journal of Music Theory Pedagogy 4/ii, 297, quoted in Marianne Kielian-Gilbert, “Interpreting Schenkerian Prolongation,” Music Analysis 22 (2003): 67.

- 31 - Kielian-Gilbert has written two articles that have relevance to both my methodology and

this particular piece. In “Interpreting Schenkerian Prolongation,”5 she discusses the apparent need that many theorists have to come up with one single “solution” to the analysis of a piece, rejecting other competing graphs. Instead of this practice, Kielian-Gilbert proposes that an

analyst can allow multiple interpretations to exist simultaneously. This alternation is similar to

the experience of an observer viewing a Necker Cube.6 With this in mind, my subsequent analyses benefit from the perspective of multiple interpretations. In some cases, one graph will be chosen in favor of another. I will allow two competing graphs to be equally viable if they each present an important aspect of the music not accounted for by the other graph.

A second article by Kielian-Gilbert directly relates to issues regarding this prelude’s bass- line.7 In it, she looks at cyclic bass patterns. She is particularly interested in bass lines that move in thirds, and differentiates between two types of cycles and two subcategories. In her terminology, a bass cycle is harmonic-linear if it supports a functional chord progression, and

transpositional if it supports a consistent cycle of intervals that suspends harmonic direction. In

addition to these considerations, Kielian-Gilbert distinguishes between directional and axial

(circular) patterns. Directional patterns move away from their point of origin while axial patterns

return to where they began. These distinctions are pertinent to the Op. 49/2 prelude due to the

5 Marianne Kielian-Gilbert, “Interpretting Schenkerian Prolongation,” Music Analysis 22 (2003): 56.

6 This particular imagery is employed by Philip Rupprecht in his article, “Tonal Stratification and Uncertainty in Britten’s Music,” Journal of Music Theory 40/2 (1996): 316. In his example, he shows how a listener might alternate between embracing tonal clarity and tonal uncertainty. In my adoption of this graphic allusion, I show how a listener might alternate between a harmonic and melodic view of the upper voice.

7 Marianne Kielian-Gilbert, “The Functional Differentiation of Harmonic and Transpositional Patterns in Liszt’s Consolation No. 4,” 19th-Century Music 14/1 (1990): 48–59.

- 32 - cycle of descending diatonic thirds found in both of its sections. Although these thirds cycles are

unquestionably directional according to the above criteria, it will be left to the analysis to

determine whether they are harmonic-linear or transpositional. In simpler language, we must

determine whether the pattern repetitions are the result of pure transposition, or if they create a

functional harmonic progression.

My analysis, which will proceed in three stages, will: 1) interpret the upper voice motion,

2) interpret the bass voice motion, and 3) create a complete voice-leading graph that takes into

account the results of stages 1 and 2. In the first two stages, the location of structural bass and

soprano notes are considered separately because each functions melodically as well as

harmonically. When combining analyses that were derived independently of one another, the

composite must represent the music as accurately as each constituent part does.

Precedent for this approach to analysis comes from Schenker’s analysis of the Austrian

National Anthem by Haydn as interpreted by Joseph Lubben.8 Schenker’s aim in this analysis is to show the “incomparable artistic synthesis” Haydn demonstrates in order to represent the political synthesis of the anthem itself.9 Although Schenker does present an Ursatz, Lubben remarks that Schenker’s analysis “illustrates the consequences of admitting multiple independent parameters into a context in which Stufen and Ursatz are conceptually fused in a unified

background.”10 Most relevant to my analysis is Lubben’s description of two successive levels in

Schenker’s graph. He notes that the two levels are not hierarchically linked. Instead, Lubben

8 Lubben discusses this analysis in “Schenker the Progressive: Analysis in ‘Der Tonwille’,” Music Theory Spectrum 15/1 (1993): 70–4. Schenker’s analysis can be found in Heinrich Schenker, “Haydn: Austrian National Anthem,“ Der Tonwille Vol. II Ed. William Drabkin (Oxford: Oxford University Press, 2005),135–6.

9 Schenker, “Haydn,” 135.

10 Lubben, “Schenker,” 70.

- 33 - posits that this example “focuses on the working-out of a melodic strategy rather than on the

composing-out of a harmonic-contrapuntal structure.”11 Lubben notes that Schenker puts emphasis on his concept of synthesis [Synthese] over the generative power of the Ursatz by using non-hierarchically related graphs with respective melodic/motivic and harmonic emphases.

Thus, the Ursatz becomes only one of many parameters that Schenker attributes to the total musical effect. As such, he “did not feel completely compelled to maintain the primacy of the

Ursatz by relegating all musical phenomena which neither belonged to it nor were derived from it to the status of irrelevancies.”12

There are multiple benefits to considering the upper and lower voices independently. The

independent upper-voice analysis allows me to focus on analytic challenges specific to Scriabin’s music. As in Schenker’s Haydn analysis, I also weigh the virtues of competing motivic influences. The independent bass analysis, which is more unconventional, allows a detailed look at the descending third pattern the bass contains. When I ultimately present a generative contrapuntal model, that model benefits from the extensive consideration of the melodic and bass parameters while retaining rigorous contrapuntal criteria.

Examples 2.1a and b show two considerably different interpretations of the upper line of the Op. 49/2 prelude. Example 2.1a gives preference to notes made salient by register. In general, the highest appearing voice in a chord is used. There is one notable exception to the selection to the highest voice. When considered without the lower voice, the three-note anacrusis featured throughout the upper voice (mm. 1, 3, 9, and 11) strongly suggests the structural role of the boundary pitches (C and Eb in the opening gesture). This view of the upper voice is crucial to

11 Lubben, “Schenker,” 71.

12 Lubben, “Schenker,” 74.

- 34 - recognizing the structural weight of Eb in the face of the registrally higher Cb in m. 1 and G in m.

2. Despite the disjunct musical surface, the graph of the first half of the piece is relatively static.

Once Ab is obtained in m. 3, it is prolonged through arpeggiation until the final chord of the A section, where it resolves to G to form the melodic motion to ^2 of a typical interrupted

13 ^ ^ structure. Ab is then reobtained in m. 9 and descends through b2 in m. 19 to 1 in m. 23. The C reached in m. 4 cannot be a Kopfton in this interpretation because its connections to other structural notes in the first section is only through arpeggiation, not stepwise descent. Were Bb to be considered structural, perhaps as part of a descent from C, a gap between 4 and ^2 would be created in the final measures. The possibility of this C as the Kopfton will be considered below.

Example 2.1a:

Example 2.1b:

13 Upon listening to multiple recordings of this prelude, I have determined that the A– naturals in the right hand at m. 5 should in fact be Ab’s. Within the sonority itself, one can easily see that an A–natural would contradict the Ab in the left hand in that harmony. In addition, if Scriabin had intended the pitch A, it would function as a flatted ninth and thus would likely have been written as a Bbb.

- 35 - Example 2.1c:

As noted above, this prelude follows an AA’ form where A’ (mm. 9–23) is a transposed form of the first A (mm. 1–8).14 Since the first section ends in a cadence on V, Scriabin transposes the second section up a fourth to result in a cadence on I. As exact transpositions do not necessarily result in identical tonal structures, one analytical concern will be to highlight corresponding moments in the two sections that do not prolong the same pitch. The hierarchical stems and slurs of Schenkerian analysis provide a way to determine exact differences between transposed repetitions. Parallel points in the first and second sections that do not serve the same function are stemmed differently.

This is seen most notably in Example 2.1a with the stemmed Bb in m. 10. This Bb, which locally appears to be an anacrusis, is revealed to be structural due to its prolongation through m.

17.15 The corresponding pitch in the first section to the Bb in the second section is the F in m. 2,

which appears unstemmed. The different stems can be accounted for by difference in how the

tones are prolonged. The Ab from the first section is prolonged through arpeggiation and

reactivated just before the half cadence. In contrast, the F, which would correspond to the

stemmed Bb in the second section, cannot be prolonged for two reasons. First, the tonal motion

clearly ends on the G at the end of the first section. This G is reached through descending motion

14 For this prelude, I will follow the following formal diagram: A (mm. 1–9)— A’ (mm. 9–23).

15 Although Bbb seems to be operative in mm. 11–12, my subsequent graph in Example 2.5 shows that this pitch is part of a chromatic inner voice descent.

- 36 - from the Ab that precedes it. In order to claim that F steps up to G would require F to be

prolonged through octave displacement to the high F in m. 6. Following that, however, it is

difficult to meaningfully connect the higher register back to the lower one. Although there are

two F’s in the same middle register of mm. 6–7, which might be sufficient for Baker, Example

2.1a endeavors to find an Urlinie in the highest notes. The subsequent Example 2.1b considers how an upper voice can be created from retained pitches that are not necessarily the top note on the surface. Second, while the fact that F locally moves up to Ab could be seen as prolongation

by upper third, Ab never structurally moves back down to F before G is reached. In the second section, it is the Bb that is prolonged by arpeggiation. In fact, the arpeggio reaches up to the Bb an

octave above before descending. Once rearticulated in its original register, the Bb immediately

^ ^ ^ descends to 1 through a potential candidate for structural 2, the Gb in m. 19. The lack of 3

following the prolonged Bb will factor greatly upon consideration of the final graph.

Having explained the prolongational differences between the two sections, I will now

examine the upper-voice descent as suggested by 2.1a. Discussions such as this one help

illustrate the value of an independent upper-voice analysis. The Gb in m.19 appears to be the best

candidate for ^2 due to its presence in the final dominant harmony and the preponderance of

altered dominant chords in Scriabin. Example 2.1c does not take the harmonic context into

account and presents a continuation of the parallel sixths begun at m.13. Viewed in this manner,

the coupled F/Db sixth is stated three times during this two-octave descent and the Gb to F

resolution is abandoned in favor of the continuation of parallel sixths. This mirrors the same

event in mm. 5–8. In order to decide whether Example 2.1a or 2.1c more accurately represents

- 37 - the voice-leading, durational information must be taken into account as well. Specifically, the long duration of the dissonant sonority at mm. 21–22 emphasizes the difference between itself and the F major triad at m 23. After this augmented triad is sustained, the presence of a perfect fifth above the bass sounds like a resolution of the augmented dissonance and not a melodic continuation. In other words, the Gb from m. 19 resolves to an F which begins as an inner voice but emerges in m. 23 as the final note in the upper voice. Thus, the melodic Db shown as the final melodic pitch of Example 2.1c is actually an inner voice that resolves to C in m. 23.

Example 2.1b arises out of Baker’s idea that in an idiomatically pianistic texture, inner voices in the texture may be more structural than the actual upper voice. Such a texture is readily seen in Chopin’s C-minor Prelude, Op. 28/20. Illustrating this idea, the anacrusis figure that begins Scriabin’s Op. 49/2 is used as the primary indicator of the structural upper voice due to its use in this prelude as a recurrent rhythmic and melodic motive to begin phrases. Once the goal of this anacrusis is reached, it holds sway until either a new anacrusis appears or a new tone is prolonged. When viewed in this manner, the upper voice of Example 2.1b is more static than the one found in Example 2.1a. In some ways, this is due to the graph’s design, which specifically avoids extraneous upper voice motion. However, pre-analytical decisions are not solely responsible for the static nature of the graph. This increased stasis is also due the persistence of successive chords with common tones.

According to this view, the piece begins with an initial ascent to C that is immediately followed by a rapid descent back to F and a subsequent move to E, which is melodically incompatible with the upper-voice of a typical interruption. After the half-cadence in m. 8 there is an ascent to Bb, the next Stufe. Bb is prolonged through motion to its upper fifth and then reobtained in m. 17. The nature of the gapped descent will be discussed below in the context of

- 38 - my completed graph. Note that Bb is prolonged in both Examples 2.1a and 2.1b, albeit by

different means.

Any further decisions regarding the upper voice must follow a similar examination of the

structural bass movement of the prelude. In consideration of the melodic aspects of the bass line, the descending bass motion in thirds from mm. 1–5 makes a purely linear view pertinent before a harmonic one. Confirmation of this linear view comes in m. 2. Harmonically, this measure remains static. An extended Db dominant-seventh chord is followed by a less dissonant

incomplete Db dominant-seventh chord. However, the octave leap in the bass marks an important

division. First, it coincides with the transposed repetition of the opening anacrusis figure. More

importantly, it indicates a division within the descending thirds of the first four measures (Ab

down to Gb). This division, then, suggests that the bass line should be segmented into two sets of

triadic outlines a fourth apart. Example 2.3a shows the result of viewing the final pitch of each

triadic descent as a goal. In order to realize this latent idiomatic progression, a linear view of the

bass is required. In contrast to this graph, Example 2.3b shows that a purely harmonic view of

this section makes mm. 1-4 a consistent drive towards a goal of Gb. As Example 2.2 shows, m. 2

contains both an arrival on a Db chord and a subsequent departure from a conceptually new Db

chord.

Example 2.2:

- 39 - Example 2.3a: 3b: 3c:

According to Marian Kielian-Gilbert’s criteria for various types of bass patterns, this bass line represents a tonal transpositional pattern because it preserves key-orientation through an asymmetrical division of the octave.16 If the pattern were not tonal, the quality of thirds in the descent would be consistent and divide the octave through either minor thirds (Ab – F – D – B –

Ab) or major thirds (Ab – E – C – Ab). Kielian-Gilbert uses the designation “tonal” much in the

same way one would designate a fugal answer tonal. In the case of mm. 1–4, the tonality implied

is Db major.

There are two reasons that Kielian-Gilbert’s categories are beneficial at this early stage of

analysis. First, they allow the piece to be seen exclusively in terms of sequential and non-

sequential sections. Second, they place the focus of the bass line on the beginning and the goal of

those sequences. Regarding the first reason, both the A and A’ sections are primarily made up of

a diatonic third sequence. When the sequence ends, it resolves by descending half step to ^4 of the

ensuing cadence. Instead of viewing the entire descending thirds sequence from mm. 1–5 as a

single unit, we can also view the sequence as a 3+3 division, split by the octave leap in the bass

line. In this view, we find that Scriabin foreshadows the transposition up a fourth between the

first and second sections by transposing mm. 1–2 up a fourth to form mm. 3–4. This provides a

16 Kielian-Gilbert, “The Functional Differentiation of Harmonic and Transpositional Patterns in Liszt’s Consolation No. 4,” 49.

- 40 - good example of the type of multiple interpretations called for in the other Kielian-Gilbert article mentioned here.17 As analysts, we can acknowledge the two-part division of mm. 1–4 while still noting that these measures are unified by means of a sequential bass. Regarding the second reason (i.e., viewing the sequence in terms of where it begins and ends), the focus can shift from the nature of the descending thirds themselves to the pitch that is attained as a result of them. In other words, it enables the interpretation of the bass line as passing from Ab through Gb into F. In

this view, Ab and F form a double-neighbor about G. (See Example 2.3c). In a typical

Schenkerian phenomenon, the anacrustic nature of the opening Ab sonority does not effect its

viability for prolongation.

The careful analysis of the melodic aspects of both upper and lower voices now allows a

sensitive voice-leading analysis of the entire piece. Example 2.4 presents the combination of

Examples 2.1 and 2.2. Note that the upper voice greatly favors the interpretation of Example

2.1b. There are two justifications for this decision. First, Example 2.1a presents a largely

arpeggiated view of the upper line. While arpeggiated upper-lines are capable of prolongation,

the Urlinie must progress by step. Second, Scriabin’s penchant for the retention of pitches

between subsequent harmonies suggests that in places such as mm. 5 and 6, the highest notes

according to register, Ab and F, merely double inner voices at a higher octave.

This choice of upper voice also effects the decision between an interrupted and

uninterrupted structure. Although the harmonic and gestural evidence around m. 8 suggests an

interrupted structure, the melodic C has no means to descend linearly to G prior to the

interruption. Thus, Example 2.1b which favors an uninterrupted structure is further supported.

17 Kielian-Gilbert, “Interpretting Schenkerian Prolongation”.

- 41 - Upon stating my methodology for this analysis, I suggested that alterations might be required once the two voices were considered in counterpoint with each other. As such, there are two significant issues with Example 2.4. I have already noted the motivic importance of the opening melodic triplet and how that might lead an analyst to consider the boundary pitches of the anacrusis figure more prominent than the middle pitch. However, the consonant C above Ab in the anacrusis to m. 1 belies the actual harmony formed by the mutual presence of C and D. If we consider the C and D together, they form a Mm7 sonority with flatted fifth, which is ubiquitous in this prelude. Corroborating this, D, not C, resolves up to Eb and C resolves down to

Cb. The resulting graph of the prelude is shown in Example 2.5a. As this example shows, this change has no effect on the upper-voice descent and thus addresses issues of harmonic clarity.

A second issue is found in Example 2.4 and clarified by Example 2.5a: the seemingly unresolved harmonic seventh formed by F and Eb in m. 1 and Bb and Ab in m. 3. While these sevenths appear to resolve up, this is a case of the Schenkerian concept of Übergreifen

(overlapping). As example 2.5a shows, the retained Eb above Db does not move up. Instead, it resolves into the Db of the ensuing harmony while a previously inner voice appears above it simultaneously. This is seen once more with Ab resolving to Gb as the melodic Bb appears.

Examples 2.5b and 2.5c show progressively deeper levels of interpretation. The deep middleground and background graphs further clarify the uninterrupted structure. Apart from the gapped Urlinie descent which is discussed in the following paragraph, an unusual feature of the harmonic structure of the piece is that it does not begin with a structural tonic. While one might presume that the F-rooted chord in m. 1 functions as a structural tonic, my graphs show that this

F is subsumed within larger progressions. In addition, the graph reveals that the first eight

- 42 - measures of the piece move toward an authentic cadence in C and not a half cadence typical of

an interruption.

As discussed above, it is debatable whether the melody stays on A as it did in the

corresponding point of the first section or descends to F. In Schenkerian terms, this means the

difference between an incomplete Urlinie from ^5–3^ or a gapped Urlinie: ^5–4^–3^–( )–1^. Once again drawing on the analytical “prework,” the extended duration between the attack at m. 21 at that at m. 23 provides grounds for seeing this as a genuine melodic shift. Lending further credence to this interpretation is Schenker’s predilection for giving an open notehead to the brief ^2 that occurs at a final cadence. This practice indicates the great structural weight that Schenker gave to the final cadence, superseding any of its temporal properties. In light of this, it is reasonable to interpolate a brief dominant bridging m. 21 and m. 23 instead of the coda-like lingering on the tonic harmony. I am not suggesting that there is an implicit ^2 to complete the descent. Rather, I suggest that instead of the melodic descent ending on ^3, we are aware of the conceptual space between ^3 and 1^, resulting in a legitimate gap in the descent and not a prolongation of A.

Example 2.4:

- 43 -

Example 2.5:

Example 2.5b:

Example 2.5c:

- 44 -

Op. 48/4

In this second half of the chapter, I will focus on an analysis of Op. 48/4. Whereas the

preceding analysis took as its point of origin two competing upper-voice graphs, this one

compares my analysis with one from James Baker,18 whose book on Scriabin set the precedent

for the Schenkerian analysis of Scriabin. Not only does this comparison help highlight the

particular issues that surround the application of the type of analysis to the music of Scriabin, but

it gives an indication of the differences between my approach and Baker’s to the music of

Scriabin.

There are three questions vital to the analysis of this prelude: 1) Is there an Urlinie and (if so) how is it realized? 2) Do formal repeats exhibit identical tonal function? 3) As in the previous analysis, how is the return of the opening material altered to enact a final cadence on C? Baker concentrates his analysis on the determination of the Urlinie. I take issue with his determination of the Kopfton, his view of harmonic prolongation in the B section, and his analysis of the final measures of the prelude. After discussing these issues, I specify his answers to the three questions and then answer them myself. To conclude, I describe three voice-leading paradigms that arise out of my analysis. Through these paradigms I show a structural link between the two preludes discussed in this chapter.

Baker’s analysis takes place on two levels.19 First, he reduces the musical surface to its

essential vertical sonorities. On a deeper level, Baker leaves only the sonorities that perform primary prolongational functions in the piece. Baker ultimately traces an incomplete descent

18 Baker’s graph is reproduced in its entirety in the appendix.

19 Baker, The Music of Alexander Scriabin, 76–9. A reproduction of this graph is found in the appendix of this thesis.

- 45 - from 5^ to 3^. Baker’s 5^, which is prominently featured in the upper voice of the prelude, is

contrasted greatly with his ^4 and 3^, which occur both registrally distant from the upper voice and

in the left hand. At the opening of the prelude, Baker posits an implied C-major triad with a G in

the upper voice. Although it is not unprecedented to posit implied tonics at the outset of pieces, it

seems that the normalization of such an idiomatic Scriabin opening circumvents rather than

confronts the issue. As noted in Chapter 1, Baker has said that the goal of such an analysis

should be to determine the particular ways that a piece, as written, exemplifies tonality. Such

implied chords have the connotation of “correcting” an off-tonic opening, even if correction was

not the express intent of the analyst. In addition, implying not only the initial chord, but the

Kopfton in a situation where there are an ample number of G’s to use later in the piece is

unnecessary.

A second issue occurs in the B section from mm. 9–16. Baker asserts that the Db sonority

in m. 10 functions to prolong the dominant throughout the bridge. However, the use of m. 10 to

prolong the dominant requires viewing the Db sonority completely out of context. The bridge

represents a large-scale auxiliary cadence to Ab.20 Each member of the IV–V–I is preceded by its own dominant. The Db chord in m. 10 functions as a IV chord in Ab. Therefore on a background

level, it should be the Ab sonority that is retained, not the Db. The prolongational implications of

20 The auxiliary cadence is discussed extensively in: L. Poundie Burstein, "Unraveling Schenker's Concept of the Auxiliary Cadence," Music Theory Spectrum 27/2 (2005): 159–178. In his summary at the beginning of the article, he describes the auxiliary cadence as follows: “Schenker created the term ‘auxiliary cadence’ along with the synonymous term "incomplete transference of a form of the fundamental structure" to refer to a progression that begins on a non-tonic Stufe and is closed off from the preceding harmonies. In most cases, only the final chord of the auxiliary cadence functions on deeper structural levels, so that this progression tends to yield a sense of expectancy and forward momentum. Schenker valued these progressions for their dramatic potential and their ability to aid in creating a sense of harmonic fluidity.” (159).

- 46 - this will be presented when I discuss my own analysis. Here, Baker seems to ignore the context

of m. 10 in order to show a long-term V–bII–V progression. This indicates the functional status

Baker attributes to bII. He considers such chords to be dominant substitutes, anticipating the

dominant harmony.21 This should not be confused with the function of a predominant (either in

the form of ii or IV or in the form of V/V) which leads to a dominant. bII harmonies, in Baker’s

view, already contain dominant function. This is somewhat problematic as these “substitutes”

never, in fact, stand alone in place of a dominant harmony. The determination of the exact nature

of a bII harmony is considered in various ways throughout this chapter, culminating in the

labeling of harmonic paradigms that conclude the chapter.

The final two issues that I have with Baker’s analysis relate to the very end of the piece.

First, in m. 19, the upper two voices of Baker’s middleground are very clear. He notates a line descending from G in the soprano, indicating that the high C and F in the score are inner voices displaced an octave for textural purposes. However, an examination of the tenor line of his graph indicates an inferred Bb (such a pitch does not occur anywhere in the sonority) followed by a

displaced Ab, and then a completely implied G. This problem is further complicated when the

fabricated G, and a second G an octave above it, end up in the background graph. The purpose of

the G is to aid Baker’s interpretation of this Db chord as a dominant prolongation. In the

middleground, both the Db and G are said to be retained in the ensuing G dominant harmony. As

opposed to their appearance in the background, their presence in the middleground is mitigated

by parentheses.

21 Baker, The Music of Alexander Scriabin, 77.

- 47 - My second issue with Baker’s analysis of mm. 19–23 involves the transition from middleground to background in the last two sonorities. Baker’s middleground shows that the pitch F from m. 19 becomes an E in m. 21. Baker takes this E despite a) its being the thirteenth of the G dominant chord, b) that F is one of the multiple common tones between the Db and G

dominant chords22 and c) that by showing this resolution of F, Baker completely leaves that pitch out of the G dominant chord. Even if we accept the voice-leading of the middleground, the background contradicts this reading by reintroducing an F in the upper register that doesn’t resolve to E until the final chord. Baker surreptitiously attempts to show two subtly different voice-leading events simultaneously. Here the difference, though subtle, is important largely

because of the stress Baker, himself, puts on the prolongation of V via bII.23

Before proceeding to my own analysis, answering the three prior analytical questions

from Baker’s point of view will enable a more explicit comparison of our views of the piece.

Overall, Baker’s answer to my first question regarding the Urlinie involves a long prolongation

of ^5 and descent to 3^ at the final cadence. Baker gives no explicit answer to my second question regarding the tonal reinterpretation of formal repeats. However, an examination of his voice- leading graph reveals an ambiguous answer. At first glance, Baker seems to indicate that the opening material continually serves the same harmonic function by leaving blank space in the middleground and background under mm. 5 and 17. This would normally indicate that the graph

22 Referring to the use of bII to prolong V, Baker says that this “highly idiosyncratic prolongational procedure…depends upon the retention of pitches” which seems to contradict this analytical choice. James M. Baker, “Scriabin’s Implicit Tonality,” Music Theory Spectrum 2 (1980): 16.

23 In order to remain consistent with Baker’s labels, I will use the designation “bII” as Baker does. However, below I will designate such a harmonic event as part of a ∆ paradigm, avoiding the implications of an altered Roman numeral.

- 48 - of this material should be the same each time. This graphic omission obscures a vital aspect of

Baker’s analysis and introduces a final issue with his implied tonic triad. The same material that

prolongs tonic in m. 1 prolongs the dominant in subsequent iterations. Although Schenker spoke of “apparent tonics” that can occur in the midst of dominant areas without challenging the local governance of the dominant, such tonics do not occur within a functional return, which mm. 5

and 17 are. Since Baker indicates that the initial tonic harmony “is implied by the tonic root in

the bass” in m. 1,24 he must either continue to consider this motive a sign of tonic prolongation or

justify the change in his interpretation. So, despite a lack of reinterpretation on the surface of his graph, Baker implicitly shows that the opening motive prolongs tonic at first, but prolongs the dominant upon subsequent returns.

Baker’s answer to my third question is brief and uncomplicated. He writes that “The most significant deviation is the use of the chord on Ab in m. 19 as V/bII (compare m. 3), which

progresses precipitously to bII.”25 In the conclusion to this chapter, I will show that this reinterpretation of the chord on Ab is established by the varied manner in which Scriabin treats dominant harmonies, and not simply through comparison with m. 3.

The preceding discussion should serve to show some of the difficult, yet recurring issues encountered in a Schenkerian analysis of Scriabin’s music from this period. Although I stand by my critique of Baker’s decisions, his were the types of decisions that analysts must make in such rough analytical terrain. In the ensuing analysis, I will develop my answers to the three questions

asked above: 1) Is there an Urlinie and (if so) how is it realized? 2) Do formal repeats represent

identical tonal function? 3) How is the return of the opening material altered to enact a final

24 Baker, The Music of Alexander Scriabin, 78.

25 Baker, The Music of Alexander Scriabin, 79.

- 49 - cadence on C? The reader will find that, for the most part, these are the same questions that are

answered in the Op. 49/2 analysis, showing the consistency of certain analytical issues in this

music.

The difficulty of positing an Urline in pieces that exhibit high degrees of formal

repetition is that identical musical passages may require different interpretations26. A very common example of this occurs in the recapitulation sections of major-key sonata forms. When the secondary material appears in the tonic key, it must be interpreted differently from its appearance in the dominant during the exposition. This difference can be accounted for by their respective roles in the path of tonal motion.27 In my analysis below, the interpretation of mm. 1–

2, 5–6, and 17–18 will rely on two factors. First I will consider what has transpired until the point of repetition. Because music exists temporally—even in the Ursatz, as Schachter has reminded us28—an event is understood in terms of its place in the tonal scheme and not necessarily in terms of where it has occurred previously. Second, I will consider where the music is headed. This is to ensure that the upper voice is in fact prolonged until the next Stufe. As the

interpretations of mm. 1–2, 5–6, and 17–18 are so dependent on context, ideas regarding

subsequent interpretations of similar material will be answered as the relevant sections appear in

my analysis.

26 This, of course, is similar and certainly related to the reinterpretation found in the A’ section of 49/1. I revisit this concept here because unlike the similar sections in 49/2, music returns untransposed in 48/4.

27 Multiple compositional solutions to this issue can be found in David Robert McGuire, “Revisiting the Return: The Structural Dilemma of the Recapitulation in the Schenkerian Account of Classical Sonata Form.” Ph.D Diss, 1996 where he describes this as a critical dilemma of sonata form.

28 Carl Schachter, “Rhythm and Linear Analysis: A Preliminary Study,” Music Forum 4 (1976): 281–334.

- 50 - Regarding the Urlinie, Example 2.6 shows a voice-leading graph of the entire piece. The

A section, comprising mm. 1–8, supports an Urlinie descent from ^5–3^. This A section contains both a harmonic challenge idiomatic to Scriabin’s music and a formal repeat of the opening material.

Example 2.6:

Harmonically, the challenge of this A section is interpreting the tonic triad with added

dominant seventh that begins the prelude. This initial sonority functions locally as V7/IV.

However, the situation is further complicated when the IV chord, also given a dominant seventh,

- 51 - moves directly to bII, and then the dominant.29 The fact that a chordal seventh is added to the subdominant harmony suggests that a Mm7 chord may be contextually consonant30 and we are presented with a simple I–IV–V progression. This helps clarify my issue with Baker’s implied tonic triad. Baker’s interpretation suggests that the opening sonority is not sufficient to initialize the path of tonality and avoids engaging in the ambiguity contained in the opening sonority. In this light, I would assert that only when ^3 replaces F in m. 7 does the piece confirm tonic. Until this point, C major is implied by the presence of its dominant.

Mm. 5–6 represent the first repetition of the opening material. In contrast to the upper- voice G that was prolonged in mm. 1–2, F is now prolonged. The reader will recall that my two points of consideration when reinterpreting similar material were the nature of the motion leading up to the repetition and the nature of its continuation. Although I don’t assume the a priori concept of the Urlinie, these conditions implicity favor a stepwise descent in the upper voice. In m. 1, G has not yet been prolonged. Although G appears in m. 1, it is still weakly supported locally with a Db and only gains legitimacy through its prolongation from mm. 1–4 where it gains local structural support over the G dominant harmony. Only on a deep level does the G in m. 1 receive structural support from the opening C in the bass. Therefore, without a prolonged G to precede it, it is premature to consider the upper-voice F in m. 1 structural. This is

not the case in m. 5 where G is reattacked and steps down to F.

An interpretation of F must also consider where F leads. In contrast, the prolonged F in

mm. 5–6 resolves to E in m. 7. The F from m. 1 does not receive the same resolution in m. 3.

29 Baker, The Music of Alexander Scriabin, 77.

30 Robert P. Morgan, “Dissonant Prolongation: Theoretical and Compositional Precedents,” Journal of Music Theory 20/1 (1976): 49–91.

- 52 - Instead, the F from m. 1 is transferred to the bass in m. 2 where it serves as a passing tone from

G to Eb. This descending motion from G to Eb contrasts with the bass in m. 6, which remains on

G, leaving the melodic F lingering above until the E in m. 7 provides it respite. The bass G is reattacked on beat 3 of m. 6 to hold the rhythmic place that F held in m. 2, highlighting the change. I will return to this critical change below when I discuss some experiential aspects of the prelude.

Continuing with the discussion of the Urlinie, the B section consists of mm. 9–16. On

Baker’s view, both ^5 and the dominant harmony are prolonged through this entire span. He asserts that this is accomplished harmonically through the Db harmony in m. 10. In my analysis, this section contains directed harmonic motion to Ab, not G as Baker suggests. Once Ab is reached, it is reinterpreted as bII/V, tonicizing G. It is important that this is indeed viewed as a reinterpretation, however. The Db chord in m. 10 is clearly subsidiary to this Ab. In C major, Ab is a tonic, not dominant, prolongation.

The B section is marked melodically by the motive found in mm. 10, 12, and 14. This three-note chromatically descending motive is derived from inner voice motion found in mm. 4 and 8. In the B section it is given additional prominence through doubling at the octave. At the conclusion of the B section, this chromatic motive is returned to a single inner voice at m. 16.

Additionally, it is on the same pitch level (E–Eb–D) at which it was initially stated in m. 4.

However, the structural upper voice continues from the E in m. 8. Prepared as an augmented fifth, it is retained in m. 10 and resolved upwards to F in a combination of the opening melodic gesture, where an augmented fifth resolves upward, and an inversion of the appoggiatura motive discussed above. Continuation of this resolution pattern in the upper voice reveals a hidden

- 53 - motivic parallelism between the end of the B section and the end of the piece. Shown in Example

2.7, Scriabin achieves melodic closure on C in m. 14 in a completely different harmonic context

from that which is found at the very end of the prelude. The C achieved in m. 14 is immediately

moved down to an inner voice in m. 16. The E is restated in mm. 15–16 in an unstable context despite being the tone that is prolonged in this section. This unstable statement of E structurally

steps down to D at the end of m. 16, concluding the B section. The up-stemmed D in m. 16 of the

score corroborates this interpretation. Although surface features do not necessarily effect

middleground voice-leading, the alternate stemming of measures 4 and 16 suggests that a

performer might direct a listener’s attention toward G in m. 4 but toward D in m. 16.

Example 2.7:

With 2^ reached at the end of the B section, an important decision must be made.

Typically, when there is a descent to 2/V followed by a repeat of opening material, an interruption occurs and the descent begins once again from the Kopfton. Therefore, we must

decide whether ^5 is reattained in m. 17 or whether ^2 is prolonged until the final cadence. The first

option can be seen in Baker’s reading from m. 17. Recall that unlike my graph, Baker’s graph

prolongs G from the outset. Using G in m. 17, Baker’s Urlinie is only able to descend to E.

Above, I discussed several issues with the connection of Baker’s middleground to his

background in the final measures of the prelude. If we consider only his surface-most graph,

where F steps down to E in the final chord, we note that in the actual voice-leading of the prelude, the high F in m. 19 is transferred to an inner voice in m. 22 before resolving. This

- 54 - certainly follows Baker’s claim in both his 1980 Spectrum article31 and his book that the clearest descents often occur in inner voices. By connecting inner voices, Baker is no longer showing how the outer voice might be derived from a contrapuntal background, but is selecting the inner voices that create the smoothest descent. In my analysis of Op. 49/2, this distinction was more explicit with inner voices occasionally appearing suddenly above the true outer voice and then returning in the subsequent chord below it. In that analysis, my two interpretations of the upper line afforded an opportunity to discuss moments in which the registrally highest voice should not be considered structural. Such decisions were not based on the creation of a smooth descent but rather on determination of the likely melodic voice.

If ^2 is to be prolonged through the formal return, the analyst must justify yet another reinterpretation of the same musical event. Harmonically, no reinterpretation is necessary to distinguish mm. 17–22 from mm. 1–4. In my description of the opening four measures, I noted that C major is represented by its dominant and is not confirmed until m. 7. At the formal return, the dominant is similarly prolonged. In terms of voice-leading, my graph shows that D is prolonged through a descending third progression before resolving to C in m. 23. This interpretation accounts for both the local B–C resolution at the final cadence and the structural resolution of the D from m. 16. The high G in the final chord is likely a residual echo of the high

G in m. 1. Baker finds such an event common in Scriabin, and observes that “The initial tone of the Urlinie is frequently restated at the conclusion of Scriabin’s works as an overlapping of ^1.

This gesture does not reinstate the initial tone structurally; rather, it is a codalike reminder of the origin of the fundamental melodic progression.”32 It is interesting to note that D in m. 18 is

31 Baker, “Scriabin’s Implicit Tonality,” 13

32 Baker, The Music of Alexander Scriabin, 50.

- 55 - upstemmed as was the D in m. 16, marking a deliberate change from the two previous

appearances of this passage in m. 2 and m. 5. As before, note-stemming provides salience to this

D in a sensitive performance that would not have been heard in previous iterations.

There is one final example that implies a structural resolution of D to C at the final

cadence. One of the more important motivic gestures in this piece is the appoggiatura. In

measures 4, 8, and 16 the appoggiatura figure appears as 9–8 over the bass. In measures 2, 4, 6,

8, 15, 16, and 18, the same figure is seen as 13–1233 (6–5) over the bass. Sometimes this figure is obscured by melodic diminution as in m. 2, or chromatic passing tones as in m. 4. It is also relevant that the majority of these appoggiaturas not only occur above G, but contain an E descending to D. Due to the ubiquity of this gesture, it is reasonable to posit that D is elided between mm. 22 and 23. This implicit D results from an implied appoggiatura involving the E above G in m. 22. The use of such an implied pitch is not crucial to my analysis. The very essence of prolongation is that a pitch is conceptually exerting its influence even when not being sounded. However, it is important that this is the only G dominant harmony in the entire prelude that does not move its E down to D. See Example 2.8.

The final question about this prelude concerns the alteration to the opening A section that brings about the final cadence. This can be accounted for by the difference between mm. 3 and

19. This is the distinction between the function of a dominant II chord (V/V) and a bII chord in

Scriabin’s harmony that was mentioned at the outset of this analysis. In m. 3, the V/V is used and

G is tonicized. This cadence on G in m.4 ends the first phrase. Along with the obvious melodic

33 My use of 13–12 is to indicate that the initial pitch functions as the true thirteenth of the dominant sonority, conceptually above the seventh. Such labeling represents the nature of the chord tone more accurately than would the more common 6–5 designation.

- 56 - repetition, the cadence in m. 4 emphasizes the idea of formal repetition in m. 5 as opposed to the sense that the dominant resolves to C in m. 5. This bII–V–I progression on the level of the

dominant foreshadows the same progression in mm. 14–16. In m. 19, V/V is replaced with bII.

Here, bII does not prolong V as much as it temporarily stands in for it, according the Baker’s

concept of “dominant substitution.” This Db chord is followed by measures of rest. As m. 19

represents the third time that this material has been heard and the third different variation of its

original statement in m. 3, the prolonged silence emphasizes the ambiguity that the listener

experiences. This ambiguity is the focus of the next section. When the dominant occurs, it is not

an arrival as in m. 5 but a continuation from the previous chord. As such, the dominant requires a

tonal resolution. For a second explanation of the difference between mm. 3 and 19, see Chapter

3.

Example 2.8:

Harmonic Paradigms

In the conclusion to the previous section, I noted the ambiguity caused by motivic

similarities placed in different harmonic contexts in mm. 3, 7, and 19. To a listener, repetition of

musical material will not be regarded as functionally different until a clear harmonic change is

- 57 - detected. This is a similar concept to Fred Lerdahl and Ray Jackendoff’s assertion that “once a

clear metrical pattern has been established, the listener renounces it only in the face of strongly

contradicting evidence.34” I will locate such a shift or point of reinterpretation through a series of bass-line reductions arranged into a paradigmatic analysis. My conclusions from this analysis will be utilized to form a theory of three voice-leading paradigms that address the various possible resolutions of a dominant seventh chord.

Example 2.9 is organized like a traditional paradigmatic analysis with the similarity of events shown through their mutual alignment within a column. As this chart represents an experiential (i.e., temporal) view, differences in similar events can not be recognized until a clear change is present. An interpretation that is eventually abandoned by the listener will be placed in brackets with a downward arrow pointing to the listener’s new, retrospective interpretation. I am proceeding on the premise that a listener will interpret recurrences of the same music in the same way until a change forces reinterpretation.

According to Example 2.9, mm. 1–2 and 5–6 (excluding beat three) are interpreted identically. C locally tonicizes F which subsequently acts as a predominant of G. In mm. 2–3, G slips through F to Eb; while in mm. 6–7, G resolves directly to C. The implications of this difference are discussed briefly below. The third instance of this progression at this same pitch level, mm. 7–8, is somewhat disguised by the absence of G# in the upper voice. However, the second sonority (on F) is aurally identical to all previous versions35. Therefore, it is not until the third beat of m. 7 that the listener reinterprets the first two beats, recognizing an affinity to mm.

3–4 and not mm.1–2. Some may assert that a listener would grasp on to and even anticipate the

34 Fred Lerdahl and Ray Jackendoff, A Generative Theory of Tonal Music (Cambridge: MIT Press, 1983.)

35 The respelling that indicates a reinterpretation to the analyst is unknown to the listener.

- 58 - motivic unity of mm. 7–8 with mm. 3–4 more than the harmonic affinity of mm.7–8 to mm.1–2

and 5–6. In fact, one could describe this point as an assimilation of the antecedent and

consequent phrases found in mm. 1–4. Regardless of whether one gives preference to the motivic or harmonic connections, it is the B dominant sonority on beat three that marks a change away from C major for the listener. This causes a reinterpretation of the C sonority as an upper neighbor to B, relinquishing the V/IV status of C. This reinterpreted version of the four-chord progression from mm. 7–8 is then reduced to a three-chord progression and repeated four times

(with the last two progressions overlapping on Ab) to form the B section. When the A section returns in m. 17, the harmony functions as it did in mm. 1–2; i.e. the listener’s rhetorical expectations of a formal return are confirmed. As I showed above, it is not mm. 17–18 but m. 19 in which an alteration occurs. Here my graph indicates that a listener expects m. 19 to be harmonically similar to m. 3. Although an alteration to create a final cadence is not unexpected, upon the repeat of A, a listener can only expect what he or she has heard before. Instead, beat three forces a reinterpretation in which Ab is treated much in the same manner as Eb in m. 3 and

C in m. 7.

The difference between the ends of these two A sections relies on multiple interpretations

of dominant sonorities.36 Such multiple interpretations allow dominant sonorities to behave in ways other than the typical resolutions by fifth or by ascending step. A parallel example of this type of pluralistic harmonic treatment is seen in the fully diminished seventh chord in the

eighteenth and nineteenth centuries. The term dominant, itself, can be problematic since it can

36 Scriabin often alters his dominant harmonies in various ways such as adding extensions and augmenting or diminishing the fifth of the chord. In my present discussion, all variant forms are considered equal. A detailed discussion of the contextual voice leading resulting from these alterations can be found in Chapter 3.

- 59 - refer both to a function and a specific type of seventh chord containing a major triad and minor

seventh. In traditional tonal music, this distinction is often negligible since chords formed with a major triad and minor seventh almost exclusively serve a dominant function as well. In this prelude, I contend that Scriabin expands the role of such sonorities. As such, references to dominant sonorities in this section do not assume traditional function unless specifically noted.

Instead, such references imply only the quality of the sonority itself. Example 2.10a shows three options found in this prelude for movement from a dominant sonority, labeled α, β, and ∆. Note that ∆ provides an alternate view of Baker’s bII–V progression.

The ubiquity of the ∆ progression requires further explanation. The fact that the first two

sonorities of the ∆ progression often contain complete pitch invariance does not indicate the

presence of inversion. Instead, this is an actual change of root. Support for one sonority as a

functional predominant and the other a tonally functional dominant comes in the sonorities’

mutual inclusion. The enharmonic shift that often occurs, as in the final two harmonies of m. 3,

indicates that Scriabin likely viewed this in terms of root movement and not inversion. This is

corroborated by Scriabin’s consistently deliberate spelling of chord tones. He has said of his

compositional process as a whole, “I compose in a strict style … there is nothing by accident.37

In Example 2.10b, a longer progression is represented, which is characteristic of

progressions found in the prelude; I will refer to such a progression as a meta-progression. One

notes quickly that in longer progressions, the three paradigms overlap greatly. In fact, α

concludes both the β and ∆ paradigms. In this regard, we are reminded that the characteristic

element of each paradigm is the way that the initial dominant harmony is interpreted. The third

37 Faubion Bowers, The New Scriabin; Enigma and Answers (New York: St. Martin’s Press, 1973), 128.

- 60 - chord functions similarly in each, completing the tonal trajectory. In a similar fashion, we do not refer to ii–V

Example 2.9:

- 61 -

Example 2.10a:

α β ∆

Example 2.10b:

Example 2.11:

Example 2.12:

progressions but rather ii–V–I despite the fact that the resolution to I is implied by the dominant.

The interaction among the three paradigms can be seen in mm. 7–8, shown below as Example

2.11. My paradigmatic analysis of these two measures favors an elaborated β paradigm over “∆

- 62 - with a dominant prefix.” Gesturally, this is a four-chord progression and should be treated as

such. This high level of relation suggests the possibility of viewing the first two chords of β as an

elision of a complete ∆ progression. This possibility is shown below in Example 2.12. In this

view, the entire B section can be seen not as a repetition of β progressions but as a series of elided versions of mm. 7–8.

To illustrate further how mm. 7–8 influence the B section, Example 2.13 shows nested β progressions connecting the C sonority in m. 7 to the C sonority that signals the return of the A section. Apart from the ubiquity of β, there are two other important implications of this graph.

First, it shows a second way of understanding the prolongation of tonic throughout the B section.

Second, it shows the structural use of the meta-progression involving α, β, and ∆. I have already

discussed how the progression in mm. 7–8 is elided and repeated to form the B section. This

same four-chord progression points toward G to end the B section.

Example 2.13:

In the course of defining these harmonic paradigms in Scriabin, I have surreptitiously included the bII–V–I progression that was featured prominently in Baker’s analyses. In this context, this so-called bII harmony neither points to nor stands in for the functional dominant.

Instead, its move to the functional dominant is but one of three options. Scriabin’s harmonic

- 63 - vocabulary would allow a Db dominant sonority to move to G on the way to C, to Gb, or to C on the way to F interchangeably38.

A broader theory of harmonic progression in Scriabin would require the analysis of several pieces before being able to claim validity; and such a study far exceeds the scope of this thesis. However, I will conclude this chapter by briefly discussing how these local harmonic paradigms function on a larger scale in Scriabin’s op. 49/2. Example 2.14 shows a deep-level reduction of the bass-line from op. 49/2. Each of the two sections features the same meta- progression from Example 2.11. In the first section the progression leads to C while in the final section it leads to F. It now becomes clear that the descending thirds from that piece serve as diminutions of a larger progression idiomatic to the music of Scriabin. This connection between the two preludes begins to illuminate the highly consistent harmonic language found in

Scriabin’s music at this time. While the larger progression from Example 2.11 moves about the circle of fifths, note that the exact location of the tritone bass movement within this progression

(from F to B in this case) is important. In other words, if the progression had begun on B, creating the bass progression B–E–A–D–G, the progression idiomatic to Scriabin would not be produced.

Example 2.14:

38 In other words, the three progressions obtained if one transposed the progressions of Example 2.10a to start on Db.

- 64 -

- 65 - Chapter 3: Voice leading

One of the major points of discussion concerning Scriabin has been his ability to achieve

a highly chromatic and seemingly complex surface while retaining, at least locally, traditional

tonal relationships. In Scriabin’s earlier compositions, tonal sensibilities pervade both the

melodic and harmonic structure; his later compositions can be understood in terms of the

manipulation of particular pitch-class sets. However, in the period of roughly 1903–1910,

Scriabin achieves a balance between these two manners of tonal organization. While the Baker- based Schenkerian analyses in the previous chapter focused on the underlying tonal aspects of these works, this chapter focuses on characteristic local voice leading that is found within these

pieces. The voice-leading aesthetic in these two pieces favors invariant pitches between adjacent

harmonies and the smooth voice-leading of the moving pitches.

Voice leading in Scriabin has received its most thorough treatment by Clifton Callender

in the 1998, Neo-Riemannian issue of the Journal of Music Theory. Beginning with Scriabin’s

“mystic chord,” Callender sets out to examine the pitch collections that are ubiquitous in

Scriabin’s late writing and their relationship to this chord. The two relations on which Callender

focus are the P and S functions.

In this chapter I will describe two methodologies to model the voice-leading found in

Opp. 48/4 and 49/2, respectively. In Op. 48/4, I examine the voice leading caused by the ubiquity of tritones that result from extended tertian sonorities. There are often two tritones found in a single harmony: one formed between the major third and minor seventh above the root and an additional tritone formed between the augmented fifth and the ninth of the chord. I will show that the voice leading between tritones in these sonorities motivates the harmonic movement and can

- 66 - demarcate formal divisions. In Op. 49/2, I consider the entire content of sonorities rather than focusing on a common feature within them. Creating a voice-leading network that includes altered dominant seventh sonorities, major seventh chords, and augmented triads, I adapt Adrian

Childs’ S-transformation (where S refers to the similar motion of the non-invariant pitches between two chords) in a manner that retains a common third while moving the other two voices chromatically.1

* * *

A common feature of Scriabin’s harmonic language is his use of altered dominant seventh sonorities. These alterations, including alterations of the fifth and extended tertian chord- tones, introduce additional tritones apart from what Kirnberger would term the “essential”

dissonance of the third and seventh.2 Example 3.1 represents the first measure of Op. 48/4.

Brackets indicate the multiple tritones found within each chord. In the first chord, for example,

an additional tritone is formed between the ninth and raised fifth. Such harmonies contrast an

efficient use of pitch classes with a liberal use of doubling. Texturally, the voicings are full but

they contain only pitches with tritone pairs. The bass note occasionally provides an exception as

it is the chordal root.

Due to the prominence of tritones in Scriabin’s vertical structures, it is necessary to

understand how he moves horizontally between them. Example 3.2 shows three types of motion

that engage these tritones. These types are 1) retention, 2) slide, and 3) resolution.

1 The reader should recall that in this chapter, use of the term “dominant seventh sonority” does not imply any harmonic function within the context of the piece. This term is used to describe any Mm7 chord with or without additional pitches.

2 This concept is introduced in Johan Phillip Kirnberger, The Art of Strict Composition [Kunst des reinen Satzes in der Musik], trans. David Beach and Jurgen Thym (New Haven: Yale University Press, 1982), 44–46.

- 67 - Example 3.1: tritones found in m. 1 of Op. 48 no. 4

Example 3.2: three types of tritone movement

Retention Slide Resolution

The first type, tritone retention, occurs when two adjacent harmonies have (at least) two invariant pitches that are a tritone apart. This is typically accompanied by a move in the bass by the interval of a tritone and enharmonic reinterpretation of one member of the tritone. This provides a second description of the harmonic paradigm described as ∆ in the previous chapter.

In the second type, the slide, both voices of the tritone move in similar motion. This is often accompanied by a fifth descent (fourth ascent) in the bass. Because such a slide often moves one dominant harmony to its expected chord of resolution, this might seem like a superfluous category. However, the ubiquity of dominant seventh sonorities in this prelude makes it necessary to distinguish between dominant chords that move to other dominant chords and those that achieve resolution (a separate category of movement). In addition, tritone slides can occur outside of the essential tritone of a dominant chord, such as in Example 3.1, suggesting that this is a legitimate voice-leading strategy and not tonally trivial. The third type, resolution, involves

- 68 - the chromatic contraction to a third, or expansion to a sixth, typical of a tritone resolution. As

with the slide, it is accompanied by a fifth descent in the bass. Significantly, the resolution type

is used as a formal marker, signaling the end of a section. This use further distinguishes it from

the slide and aligns it with my α harmonic paradigm. In my conclusion I will discuss ways in

which these three tritone movements inform the harmonic paradigms discussed in Chapter 2.

Example 3.3 traces the voice leading of tritones in mm. 5–8 of 48/4 and establishes a

notation system for modeling tritone motion. Pitches within the same sonority are listed

vertically and the succession of harmonies is shown from left to right. Between tritones, the

following symbols are used: a dotted line indicates tritone retention; a solid line indicates a

tritone slide; and an arrow indicates a tritone resolution. Adjacent tritones that do not adhere to

any of these motion types will not be connected with a symbol. A vital aspect to this theory is that the voice leading described occurs in pitch space. The tritones shown in my reductions are not simply contained in adjacent harmonies, but move directly to one another. In the conclusion to this section, I have included a reduction of Scriabin’s Etude, Op. 49/1, to show how this reduction technique could be misused to represent tritones that do not connect registrally. This counter-example indicates the significance of pieces in which the voices do connect, sometimes in multiple registers simultaneously.

As shown in Example 3.3, m. 5 starts out with a sonority containing two tritones: Bb/E

and D/G#. However, both of these tritones slide in contrary motion to a single tritone, A/Eb.

Immediately, this disturbs the one-to-one correspondence indicated by my three types of tritone

motion. This “two-into-one” slide (and its inverse, the “one-into-two” slide) can be understood in

- 69 - terms of the fuse and split functions described by Clifton Callendar in his article on voice-leading

in Scriabin.3

Example 3.3: tritone movement in mm. 5-8

According to Callender, a voice can exist in one of two states: split or fused. The fused

state exists as a single pitch while the split state exists as two pitches a semitone higher and

lower than that pitch. Callender’s figure 5 is reproduced below as Example 3.4. In my adaptation

of Callender’s terms, a tritone can similarly exist in a split or fused form. When a single tritone

splits, it creates two distinct tritones a semitone higher and lower than the original tritone. When

two tritones fuse they slide inwards to the same tritone. These motions are shown in Example

3.5. As this example illustrates, the split and fusion of tritones require that the tritones exist in

multiple registers simultaneously.

Example 3.4: Callender’s split and fuse functions

3 Clifton Callender, “Voice-Leading Parsimony in the Music of Alexander Scriabin,” Journal of Music Theory 42/2 (1998): 219–33.

- 70 - Example 3.5: fuse and split of tritones

Applying this concept to Example 3.3, the two tritones of the first harmony, D/G# and

Bb/E, move in contrary motion to form two separate statements of the Eb/A tritone an octave

apart (i.e., they fuse). This motion is shown in Example 3.6. However, this is not the only tritone

contained in the second sonority. The A/Eb tritone is joined by a B/F tritone. The introduction of

the B/F tritone in this context is particularly important. In my previous chapter, I argued that this piece should be understood as C major. As such, the B/F tritone plays a vital tonal role

throughout the prelude. The introduction of this tritone within a subdominant harmony has two

implications. First, it uses a sonority typically found in dominant chords as a functional

predominant chord. This follows immediately after a sonority with a root of C—which would

normally be considered tonic—also contained pitches commensurate with a dominant chord.

This early destabilization of tonal function is indicative of many Scriabin preludes and suggests a

further need for mapping tritones independently from their traditional tonal functions. Thus we

see that the movement of tritones in this music transcends the resolution of tendency tones in

fifth-related harmonies. Second, the inclusion of the B/F tritone in a subdominant harmony

creates a connection between the subdominant and dominant harmonies in this prelude. From a

tonal perspective, this lends credence to the idea that the entire opening section prolongs the

dominant, as described in Chapter 2.

- 71 -

Example 3.6: tritone fuse in m. 1

After the B/F tritone undergoes a slide to Bb/E in m. 7, this sonority moves to a chord

with two tritones in it. One tritone, A/D#, is the result of a slide. The other, F/B, results from the

bass movement by fifth and the splitting of the pitch Bb into B and A. A acts as part of one

tritone, and B acts as part of the other. This motion is shown in Example 3.7a with marked open

noteheads. If an additional F had occurred in an inner voice, this would exactly follow my

definition of a tritone split. This hypothetical version is shown in Example 3.7b, with marked

open noteheads. Due to my concern for motions that occur in pitch-space, I must be rigorous in

my use of terminology and not call this a tritone split, even though half of the second tritone is

the result of such a split. Continuing my summary of these measures, the next two chords result

from retention of the A/D# tritone. Finally, to end this formal section, the tritone A/D# resolves

to the dyad E/G#. This moment represents both the end of a formal section and the first sonority

in the prelude that does not contain a tritone. This reinforces the designation of the tritone

resolution as formal divider.

Although similar voice leading occurs in the B section, the remainder of this analysis will concentrate on the slight differences between the three statements of primary material which occur at mm. 1–4, 5–8, and 17–23. In Chapter 2, I sought to understand alterations made to recapitulated material that brought about a final cadence. Similarly, this analysis describes how each formal section ends and the subtle yet important differences

- 72 - between m. 3, m. 7, and m. 19. As was discussed earlier, these particular measures are important because mm. 1–2, 5–6, and 17–18 are all identical, forming the beginning of each respective phrase. However, each phrase ends very differently. The changing path that each phrase takes can be attributed to mm. 3, 7, and 19, respectively.

Example 3.7: real and hypothetical versions of tritone movement in m.7

a b

Example 3.8: tritone movement in mm. 3-4, 7-8, and 19-23

Example 3.8 compares mm. 3–4, 7–8, and mm. 19–23. The difference between the three

can be accounted for by the movement of the tritones. Not shown in this example is the fact that

B/F is the prevailing tritone going into all of these excerpts. In mm. 3–4, there is a slide down

followed by a retention and second slide down, this time to B/F, the ultimate goal of this phrase.

In terms of tritones, m. 7 represents a transposition of m. 3 but contains an important difference

- 73 - in its motion to m. 8: instead of the slide found between mm. 3 and 4, mm. 7–8 contain a

resolution—one of only two in the prelude. Mm. 19–23 represent a combination of the two previous phrases. Similar to mm. 3–4, this third section begins on a G/Db tritone and moves through slides to B/F. An important difference is that compared to mm. 3–4, the second slide occurs one chord early. The effect of this is that the B/F tritone comes earlier and thus is no longer a destination as in m. 4, but a stop along the way to C/E. It is in this resolution that this section is similar to mm. 7–8. This similarity between the second and third excerpts is particularly important. Mm. 8 and 23 represent important formal and tonal moments of the prelude, defining the ends of the ternary form’s A sections. These two moments contain the only instances of tritone resolution and the only triads in the prelude. With this observation, it can be seen that the mapping of tritones in this prelude is not a frivolous exercise made possible by traditionally functioning dominant-seventh chords in circle-of-fifths progressions. Instead, my analysis shows that Scriabin used the tritones contained in his harmonies to generate harmonic movement. Due to this constant stream of tritones, he is able to create salient points of formal articulation through rare tritone resolutions. The effect is not that of a single tritone resolving to a diatonic third. Instead, these resolutions allay the combined weight of the long chain of tritones that precede them.

Although this chapter is intended primarily to provide a contextual voice-leading analysis of Opp. 48/4 and 49/2, it is important to show that the distinction between tritone slide, retention, and resolution is prominent in Scriabin’s other works. I do not mean to suggest with these examples that this method of voice leading is pertinent to all of Scriabin. A quick glance through the opening chapters of Baker’s monograph, in which he lists numerous tonal strategies or idiosyncrasies that appear in various Scriabin works, makes it clear that there is no single

- 74 - compositional method that encompasses all of Scriabin’s works. Similarly, examining the voice

leading between tritones, is only relevant for certain pieces. Examples 3.9 and 3.10 show pieces

in which tritone movement is an important feature, as above, in both voice leading and formal

divisions. In these and in my previous analyses, I have taken great care to discuss voice leading

between registrally adjacent voices. Registral adjacency, I believe, is particularly important when

describing tritones as sliding back and forth due to the physical metaphor that it evokes. Example

3.11 is from an Etude, Op. 49/1, in which the sonorities are also governed by tritone movement.

In this example, the tritones do not move to registrally adjacent pitches in the next chord.

Instead, they often move via voice exchange or through octave transfer. This example will serve to emphasize the restrictive conditions within which the tritone movement happens in the other examples.

Example 3.9 shows a voice-leading model of mm. 1–12 from the Prelude Op. 48/1. The score of this prelude is found in part iv of the appendix. In general, the emphasis of this piece is on tritone retention as exhibited by its frequent bass movement by tritone. Once B/E# moves to

A#/E in m. 5, this tritone is locked onto, due to an oscillation between C and F# in the bass. At m. 9, the beginning of the B section, the existing tritone E/A# does not quite resolve as it did at the outset of the B section in Op. 48/4. Although the repeated bass descent from F# to B in mm.

9–11 foreshadows the expected harmony of resolution, B major, there is a long retardation that latently retains the E/A# tritone. It is not until the first half of m. 12, the end of the B section, that this tritone is truly resolved. Note that this resolution appears in the same register as the tritone that was leaped away from and unresolved in m. 8. The final A section, beginning with the pickup to m. 13, represents a transposition of the opening three and a half measures up an octave.

- 75 - The final cadence begins with the G dominant harmony reached in m 16, which acts as part of a

∆ paradigm leading to a cadence on F#.

As in my previous analyses, an important analytical concern is the alteration that brings

about a cadence in the return of the A section. In this piece, this alteration is found through the

comparison of m. 4 with mm. 16–18. Looking at these moments from the perspective of tritone

movement, the corresponding points in the music differ in terms of the succession of tritone

slides and retentions. In m. 4, the tritone that ends the first A section, E#/B, slides to E/A# to begin the next A section.4 In mm. 16–18, instead of a slide moving the music forward in m. 4,

there is a tritone retention followed by a resolution, marking the end of the piece. Therefore, as in

the prior analysis, the music adheres to three general principles. First, the majority of the music

features tritone slides and retentions. Second, formal divisions can be located through the presence of tritone resolution. Third, altered repetitions in the music can often be explained by the difference of tritone slide or repetition.

Example 3.9: tritone movement in Op. 48 no. 1

4 Since the second A section begins in a lower register to match the opening of the piece, this slide remains in the same voice but not the same register.

- 76 - Scriabin’s Ironies from Op. 56 provides an additional example of a piece in which a change in tritone movement creates a key structural difference between two otherwise identical sections of music. Example 3.10a models the tritone movement in the opening seventeen measures of this piece. As in previous examples, motion is primarily determined by slides and retention. In this example, the transition from mm. 8–9 and 16–17 are most worthy of note.

These measures from the score are compared in example 3.10b. The rolled chord in m. 8 at the ritard. is the last chord before a repeat of mm. 1–8. This chord enables the repeat via the retention of the Cb/F tritone. Eight measures later the music reaches the same chord. This time, instead of retaining the tritone, it slides up a semitone to begin a transposed repetition of the opening eight measures. Once again, identical sections of music differ largely due to a change in the voice leading of certain tritones.

Example 3.10a: tritone movement in Ironies

Example 3.10a: a comparison of mm. 8–9 and 16–17 of Ironies

- 77 - To conclude the first section of this chapter, it is important not to take for granted an

essential aspect of the voice leading described thus far: it has all occurred between registrally

adjacent pitches. In order to show that tritones in consecutive chords do not necessarily connect to each other through registerally adjacent voice leading, the final example models the tritone movement from mm. 11–13 of the Etude, Op. 49/1, in two different ways. First, in Example

3.11a, the tritone movement alone is shown graphically as it has been in the remainder of the chapter. Then in Example 3.11b, the reality of the voice-leading that Example 3.11a represents is indicated by lines connecting adjacent tritones. Whereas 3.11a seems to suggest that each voice of the tritone is connected to an adjacent voice, 3.11b reveals this to be false. Tritone movement,

even when the same tritone is retained, is often accomplished through voice exchange in this

excerpt as indicated by the crossed lines in 3.11b. This counter-example shows that the presence

of tritones in successive chords does not necessarily guarantee voice leading in pitch space. By

excluding examples in which the mere presence of tritones, and not their motion in pitch space,

is taken into consideration, examples such as Op. 48/4 become more meaningful.5 Example 11c represents the tritone motion in the last measures of Op. 48/4 in the same way that 11b represents

Op. 49/1. Note that in contrast to 11b, no lines in this example cross, indicating that each voice of the tritone moves to an adjacent note in pitch space.

5 Not all voice leading theories depend on relations in pitch space. Through the use of both dotted and solid lines, Matthew Santa has used examples similar to my 3.11b to explicitly show registrally displaced common tones and stepwise voice leading examples of his parsimonious voice-leading concept. Matthew Santa, “Nonatonic Systems and the Parsimonious Interpretation of Dominant-Tonic Progressions,” Theory and Practice 28 (2003): 9.

- 78 - Example 3.11a: tritone movement in Etude Op. 49 no. 1

Example 11b: voice leading in Etude Op. 49 no. 1

Example 11c: voice leading in the final measures of Op. 48 no. 4

* * *

A theory of voice-leading for Op. 49/2 must include two aspects of Scriabin’s writing.

First, it must address the voice leading between harmonies. Second, it must acknowledge the importance of the altered dominant-seventh chord in its own right. In fact, this dominant-seventh chord with a flatted fifth is one of three sonorities that are found prominently in this prelude; the other two are the augmented triad and the major-seventh chord. A model must contain these sonorities, which are often neglected in parsimonious voice-leading graphs, and reconcile the disparity among chords with different cardinalities.

- 79 - One previous article that has addressed parsimonious voice-leading from the augmented

triad is Richard Cohn’s, “Weitzman’s Regions, My Cycles, and Douthett’s Dancing Cubes.” The

initial titular name is that of Carl Friedrich Weitzman, whose 1853 treatise addressed the voice-

leading between augmented triads and consonant triads, as from C–E–G# to C–E–A or B–E–G#.

Cohn refers to this voice-leading as SSD (Single Semitone Displacement). Taking this concept a

step further, Cohn derives his graphic representation, “cube dance,” from Weitzman’s graphs.

This is shown in Example 3.12.

Following Cohn, Adrian Childs notes that SSD is an allusion to Lewin’s concept of

minimal perturbations, expressed as a Pn transform. Here, n represents the number of

perturbations from (i.e., semitone changes to) a starting pitch-class set. Childs is primarily interested in P2 transforms so he can model voice-leading between half-diminished seventh

chords and dominant seventh chords. He creates two more specific variants of P2

transformations, in which two pitches are held constant while two other pitches move in either

similar motion (Sa(b)) or contrary motion (Ca(b)). In this terminology, “a” is the interval between the stationary voices and “b” is the interval between the moving voices. Childs then creates

“double S-transforms” in which S is performed twice on a given sonority. For example, to get from C7 to C#7, Childs uses S3(2) and S2(3). Thus, C–E–G–Bb becomes C#–E–G–B and then C#–

E#–G#–B. Using a double S-transform, one can derive all twelve dominant seventh chords from

a single dominant seventh chord. This property of the double S-transform is shown below as

Example 3.13.

- 80 - Example 3.12: Cohn’s Cube Dance

Example 3.13: Child’s chart of double-S transformations

In order to create a model that is useful for my current purposes, I have expanded the

SSD (or P1, after Lewin) voice-leading from augmented triads to P2 transforms. Adapting

Lewin’s P-transforms into S-transforms, Childs strives for flexibility by allowing different members of the seventh chord to be held constant. This flexibility is exemplified by Childs use of variable a and b labels. As I am tailoring this analysis to Scriabin’s voice-leading, my aim is to show consistency rather than variability in the voice-leading. As such, I exclusively use S3(3) transformations6, in which one third is held constant while the other moves chromatically in

6 Since an S3(3) transformation of a single harmony contains two possible outcomes, it is not a mathematical function like Childs’s S-transforms are. Although all outcomes are presented in my graphs below, the lateral movement throughout the space does not link each chord with

- 81 - either direction. Above, I noted that there are three essential sonority types that are utilized in

Scriabin Op. 49/2: augmented triad, major seventh chord and dominant seventh (b5). All three of these chords contain two major thirds. These three chords can be linked by using successive S3(3)

transformations in which one third is held constant while the other moves chromatically in either

direction. If one begins with the altered dominant sonority, the same augmented triad is derived

after two S3(3) transformations regardless of whether the moving third ascends or descends. This

is shown in the figure below, Example 3.14. Note that the stationary voices are written only once, but are present in every chord. I call this an “S3(3) chain.”

An important aspect of this chain is that it contains chords of multiple cardinalities. A

similar attempt at connecting seventh chords and triads can be found in Matthew Santa’s

nonatonic system whereby dominant seventh chords are connected to major triads

parsimoniously. However, in order to deal with the different cardinalities of the two chords,

Santa considers dominant seventh chords that omit the fifth, creating a three-note chord.7 Going a step further, Santa inverts this trichord to form a corresponding half-diminished seventh chord that omits its third.8 In order to demonstrate this final step, Santa uses a musical example in which the third omitted in his voice-leading model appears only in the right hand while the remainder of the chord is in the left hand.

Returning to my S3(3) chain, the inversionally symmetrical nature of its generative chord

(the dominant seventh sonority with lowered fifth) could be used tonally in two different ways.

Example 3.14 holds the dyad C–E stationary while the dyad Gb–Bb is transposed chromatically. both possible outcomes of the double S3(3) operation. As such, the resultant graphs below can not be derived mathematically.

7 Santa, 11.

8 Santa, 12.

- 82 - If we hold the dyad Gb–Bb stationary, major seventh chords and an augmented triad are produced that are tritone-related to the chords derived in Example 3.14. This is shown below as Example

3.15.

Example 3.14: a single S3(3) chain

G# A Bb B C or C–E–G#, F–A–C–E, C–E–G–B E F Gb G G# E C

Example 3.15: a second S3(3) chain

D Eb E F Gb or Gb–Bb–D, B–D#–F#–A#, Gb–Bb–Db–F, Bb B C Db D Bb Gb

Example 3.16: three chains combined into a cycle

- 83 - Since there are only four augmented triads, we can link S3(3) chains by common

augmented triads, creating a cycle. Such a cycle is found in Example 3.16. The point at which

different chains overlap is notated by a vertical line. Note that in order to create links through

common pitches, there is only one way to connect the chains into a cycle. This can be seen by

looking at the cycle in Example 3.16. For example, the first link between two F/A dyads could

not be created between any other chains other than the two used.

While chains are connected horizontally, cycles can be connected vertically. One can move from one cycle to another using a common generative chord which I will call a “ladder” because it allows vertical movement between two cycles. I call the vertical combination of two cycles a “multi-cycle.” One of two possible multi-cycles is shown below as Example 3.17. For example, I can move from Gb–Bb–Db–F in the lower cycle to F–A–C–E in the upper cycle in two

moves: 1. Gb–Bb–Db–F to Gb–Bb–C–E and 2. C–E– Gb–Bb to C–E–F–A. These sonorities are

highlighted in the multi-cycle below. I do not consider the move from the lower cycle to the

upper to contain any voice-leading distance. In terms of voice-leading, movement through the

“ladder” is similar to an enharmonic reinterpretation since no pitches change. As such, it is not

counted as one of the two moves between Gb–Bb–Db–F and F–A–C–E. This also engages the ∆

paradigm from the previous chapter which contains two altered dominant seventh sonorities

rooted a tritone apart.9 From a harmonic perspective, the reorganization of the constituent thirds

creates two tritone related chordal roots (Gb and C, to take an example from the multi-cycle

below.)

9 The harmonic paradigms can be found in example 2.10a on p. 64.

- 84 - Example 3.17: two cycles combined into a multi-cycle

There is only one other multi-cycle that can be created. This multi-cycle contains the

other three dominant seventh (b5) chords and the other two augmented triads. Since the cycle

above exhausts all major seventh chords, these harmonies are repeated in the cycle below, an

aspect that will become essential to the relation of the two different multi-cycles. See Example

3.18.

Example 3.18: the second possible multi-cycle

Graphically, movement within a multi-cycle is intuitive. One moves laterally without restriction and vertically only through three “ladders.” It is important to remember that these are

continuous cycles despite their linear appearance on the page. Although certain chords are

- 85 - centered and may appear at a glance as generative (such as G–B– Db–F above), they hold no

special priority. In the past, parsimonious voice-leading models, even cyclical ones such as the

Tonnetz have been laid out in a Cartesian grid, allowing unhindered vertical and horizontal

movement as on a checkerboard. An expanded treatment of use of Cartesian space that allows

not only vertical and horizontal movement, but reflections about horizontal, vertical, and

diagonal axes is Stephen Brown’s “dual interval space.”10 In contrast to these, my model allows

unrestricted horizontal movement but vertical movement only through ladders.

While moving within a multi-cycle is somewhat intuitive, movement between multi-

cycles is graphically more cumbersome. In order to move from one multi-cycle to the other, we

must use the common major seventh chords that occur once in each multi-cycle. Example 3.19

below shows the how the major seventh chords in one multi-cycle can be connected to the same

major seventh chord in the other multi-cycle. Similar to moving up a ladder from one cycle to

another, “moving” from one sonority at one part of the cycle to that same sonority at another

place of the cycle is not counted when determining the number of steps required to get from one

sonority to another. This is justified by the fact that there is no change in pitch. The move is a

conceptual reorientation within the graph. Conceptually, we enter the sonority at one point on the

graph, but exit it from the same sonority at a differnet point.

Having established both a space to move within and a protocol for movement, I can now

make analytical use of this model. Each harmony in Scriabin Op. 49/2 can be reduced to one of

the three harmonies mentioned above, with two exceptions that must be noted. First, the final

harmony of the prelude is a consonant F triad. However, the final cadence resolves to an

augmented triad before becoming a consonant triad. Therefore, the structural voice-leading from

10 Stephen C. Brown, “Dual Interval Space in Twentieth-Century Music,” Music Theory Spectrum 25/1 (2003): 35–57.

- 86 - the dominant to tonic harmonies can be appropriately modeled. Second, some of the augmented

triads that I have found represent the upper three notes of a four or five-note chord. In these cases the extra note—which is always in the bass—moves while the augmented triad remains constant.

I discussed in the previous chapter the independent nature of the descending bass-line of this piece. Due to this bass-independence, I feel justified in considering only the upper structure, excluding the bass, in my model.

The fact that each harmony can be placed on this graph, and that there is a traceable path of voice-leading from one to the other, does not provide insight into Scriabin’s music as much as it exhibits the utility of the model itself. It is the manner in which these harmonies move about the space that provides insight into Scriabin’s use of these harmonies. To move from any one harmony to the next requires a maximum of two moves within or between multi-cycles.11 When discussing P2 transformations, Callender similarly states that in order to get from one pitch collection to another, it must “pass through” a sonority.12 The motion between two multi-cycles is shown in three excerpts below. In Example 3.20a, I show a progression that requires a single move; in Example 20b, the final cadence is shown which requires two moves; Example 3.20c shows a complete phrase from mm. 5–8. Each chord that appears in the music (and is not merely part of a double move) is labeled by a boxed number representing the measure in which it appears. While the limited number of moves from one harmony to the next suggests an efficiency of voice-leading, Example 3.20c brings it out visually. In this example, shifts from one multi-cycle to the other that do not contain any voice-leading distance are set apart by a dashed line; finally, Example 3.20d shows a map of the first eight measures of the prelude. In light of

11 Since the first A section ends in a consonant major triad, the two major formal sections cannot be linked to each other.

12 Callender, “Voice-leading Parsimony,” 225.

- 87 - the previous three examples, the continual use of arrows to show each voice-leading move is

both unwieldy and unnecessary. In this extended example, chords that appear in the music are

labeled with ascending Arabic numerals that correspond to the numbers above the score excerpt.

Chords that do not exist in the music but are necessary to connect two actually sounding chords

are given the suffix “a.” E.g. the imaginary chord that appears between chords 1 and 2 is labeled

1a. Furthermore, moves that do not contain any actual voice-leading distance (from a major

seventh chord in the upper multi-cycle to the same major seventh chord in the lower multi-cycle,

for example) are given identical labels and connected with an arrow to avoid any confusion

regarding their proper orders. One sees that similar paths are taken throughout the excerpt. Such

common paths indicate a voice-leading proximity between the chords used. This proximity is

examined below.

Building on this idea, my final example shows the location of each chord in the piece. In

contrast to Example 3.20, this example shows only sounding harmonies, and not the harmonies

that are traversed conceptually along the way. The highlighted chords appear in small clusters

indicating that the piece takes place in a highly confined harmonic space. Thus a second utility of

these multi-cycles is to show not only the path these sonorities take, but to show the voice-

leading proximity or distance among all of the sonorities.

- 88 - Example 3.19: the connection of major seventh chords between multi-cycles

- 89 - Example 3.20a: a progression requiring a single move

- 90 - Example 3.20b: the final cadence, requiring a double-move

- 91 - Example 3.20c: movement between mm. 5–8

- 92 - Example 3.20d: movement between mm. 1–8

- 93 - Example 3.21: location of all sonorities in op. 49 no. 2

* * *

On the surface, the two methods of modeling voice-leading discussed in this chapter are different in terms of what aspect of voice-leading they are concerned with and how they show them. What is important to gain from both of them is the underlying voice-leading aesthetic that

they represent. Underlying the sometimes dissonant and often disjunctive musical surface is a

highly controlled efficiency of voice-leading.

- 94 - In the first analysis, I showed that Scriabin was very aware of each tritone that was created by altering dominant seven harmonies. Each of these tritones followed a long path until finally being resolved at select formal junctures. In the second analysis, I showed Scriabin’s controlled use of specific types of sonorites rather than the behavior of a common interval among multiple types of sonorities. An important reason for this (which I have seldom discussed in this thesis) is his use of complete whole-tone collections in this prelude. Specifically, Scriabin uses chords derived from whole tone collections such that each subphrase in both the A section and its transposed repetition contains a single whole tone collection. Therefore, when placed together, the first four measures of each A section complete the twelve-tone aggregate. This is shown in

Example 3.22. Thus, Scriabin’s use of a particular type of altered dominant and augmented triads is to be expected. In addition, the idiosyncratic way of moving between sonorities helps obtain the specific pitch-classes needed to remain within the whole-tone collections. Thus, if we consider that Chapter 2 provided an insight into why Scriabin’s harmonies progress in certain ways for tonal reasons, this chapter has shown how one harmony progresses to another.

- 95 - Example 3.22: whole-tone collection in Op. 49 no. 2

- 96 - - 97 - Conclusions

The aim of this thesis has been to examine two of Scriabin’s middle-period preludes from

two analytical vantage points. As with any combination of methodologies, insight is gained both

through the individual analyses and their resultant whole. Referring specifically to tonal music,

David Beach has written, “To me, the process of analysis implies, among other things, a

thorough investigation of harmony and voice leading, and their interaction at all levels.” 1 In his analysis, the harmonic aspect of analysis was represented essentially by an examination of local chord function while the voice-leading aspects were represented by Schenkerian analysis. My analysis has also been concerned with harmony and voice leading. However, Schenkerian analysis has primarily served to determine harmonic function in these preludes while more contextual analyses have been used to examine voice-leading. Such a combination of techniques, as compared to the techniques espoused by Beach, befits Scriabin’s idiomatic use of tonality in his transitional period.

The goals of the present conclusion are threefold. First, I will provide a brief summary of the analyses from the previous two chapters. Second, I will illustrate what has been gained from the combined use of these analyses. Third and finally, I will draw conclusions regarding

Scriabin’s compositional style during this period.

In the Op. 49/2 prelude, I determined that the descending thirds found in each section of the piece can be broken up into two descending trichords. This is important for two reasons.

First, the resulting reduction revealed a latent harmonic progression common to both the Opp.

49/2 and 48/4 preludes, among others. Second, the role of the F dominant harmony in m. 1 is shown to be subsumed in the first descending third pattern. Without such an analysis one might

1 David Beach, “Harmonic and Linear Progression in Schubert’s Music,” Journal of Music Theory 38/1 (1994): 2.

- 98 - presume, considering Scriabin’s penchant for using dominant harmonies in places typically

reserved for consonant harmonies, that this F harmony serves a tonic function despite its

dominant façade. The fact that the F chord does not serve a tonic function is corroborated by the

contrapuntal structures presented in Examples 2.4 and 2.5. The Kopfton that appears in m. 6 is

clearly forward-related to the ensuing dominant harmony and not back-related to the opening F

harmony. We can be sure of this as the Kopfton first appears above a subdominant harmony en

route to a cadence on V. In a similar situation at the opening of Op. 48/4, Baker inferred a

consonant triad at the beginning of the piece. Chapter 2 presents my critique of that analysis.

Thus, the model of this piece shows that the dominant is prolonged until the final cadence of the

piece.

In my subsequent analysis of this prelude, I addressed the fact that Scriabin’s music

employs a limited number of sonority types and exhibits similar voice-leading between them.

This resulted in a voice-leading model that connected sonorities via successive S3(3)

transformations that held one diatonic third constant while transposing the other by semitone.

This model has the effect of verifying analytical intuitions of Scriabin’s smooth voice-leading. In

addition, the attention to each sonority’s pitch content instead of tonal function reveals that

Scriabin uses a very limited number of pitch collections in addition to the already limited scope of sonority types employed. This is accomplished largely through the respelling and inversion of certain harmonies. Finally, by locating each sonority within my model, the proximity of the sonorities to each other is revealed. Whereas one might assume that this indicates a limited number of pitch-classes, the conclusion of Chapter 3 noted that each A section systematically completes the twelve-tone aggregate through the alternation of whole-tone collections. Thus, the

- 99 - voice-leading proximity of Scriabin’s harmonies is the result of a compositional aesthetic and not

of limited pitch-selection.

Certainly, the particular information provided by these separate analyses is valuable for

the greater understanding they impart. However, multiple methodologies are particularly useful

when they resolve ambiguities that exist after only a singular analytical perspective is attempted.

There are two Schenkerian issues that are corroborated by the consideration of local voice- leading issues. First is the decision to treat the F harmony in m. 1 as passing rather than structural. I noted in Chapter 3 that due to the common tones in the upper-voice structures in mm. 1–2 and the salience of the descending third in the bass, the voice-leading in these measures can be reduced to a static augmented triad over a dynamic bass. In this view, the F is necessarily unstable. Thus, a contextual, but not tonal view of the voice-leading helps corroborate an analytical choice made for tonal reasons.

A second Schenkerian ambiguity occurs at the very end of the piece. In my analysis, I posited a conceptual gap between the augmented triad in m. 21 and the major triad in m. 23. The reason this gap is important is that if the final triad is viewed simply as an echo of the augmented triad that preceded it, the Urlinie could not descend from ^3–1^. In my Schenkerian analysis, I suggested that the length of time that the augmented triad is held supports the idea that the change in sonority in the final triad represents a new Stufe. In light of my additional analysis in

Chapter 3, we can see that this final chord stands out for reasons other than the duration of the chord before it. This final harmony represents one of only two consonant triads in the entire

- 100 - prelude. Thus, this triad not only resolves the tension of the preceding augmented triad, but

represents a resolution of the tension contained in the sonorities of the entire piece2.

My Schenkerian analysis of Op. 48/4 proceeded out of three questions and an evaluation of Baker’s analysis of the same prelude. Whereas the AA’ form of Op. 49/2 required an analyst to examine a transposed repetition of the first section, the AA’BA form of Op. 48/4 required an analyst to examine music that reappeared at the same pitch level, but in different tonal contexts.

This need for reinterpretation led to a phenomenal account of the prelude in the form of a paradigmatic analysis. From this, I concluded that new interpretations of repeated musical events could be explained through a syntax established within the prelude. This syntax provides three

options for the resolution of dominant seventh sonorities in this prelude. These harmonic

paradigms, as I termed them, are not only ubiquitous in this prelude, but are also found in the

middleground graph of Op. 49/2. This indicates a harmonic vocabulary that extends beyond the

single prelude in question.

The voice-leading analysis of this prelude arose out of the multiple variations of

dominant seventh chord (as described in Chapter 3) that appear throughout. Specifically, the

analysis established three ways in which the multiple tritones contained in these dominant

harmonies moved between each other and resolved in form-defining ways. In addition, an

2 If one employs Morgan’s concept of contextual consonance, (Morgan 1976) one might create an alternate view in which the augmented triad is established as a “dissonant tonic” and the final consonant sonority leaves the prelude open-ended, not resolved. Further support for this view is found in London and Rodman’s reminder that preludes were historically intended to be followed by full pieces. Thus, it is logical that a composer would leave the ending of a prelude inconclusive or ambiguous. Since London and Rodman make this point in reference to Chopin’s E minor prelude, it is apt to apply the same concept to a Scriabin prelude considering the multiple biographical and stylistic similarities that exist between the two composers. This alternate analysis further emphasizes the transitional nature of this prelude as each interpretation relies on the presumption of or denial of traditional tonal relationships, respectively.

- 101 - adaptation of Callender’s split and fuse functions allowed me to voicelead between successive

harmonies that contained different numbers of tritones.

The most meaningful commonality between these two analyses occurs between the

harmonic paradigms and types of tritone movement. In Example 4.1 below, these two concepts

are shown in connection with one another. This comparison reveals that there is a one-to-one

mapping of types of tritone movement and harmonic paradigms. In this manner, the three ways

that Scriabin establishes to resolve a dominant sonority can be understood in terms of specific changes in voice-leading. In Op. 49/2, the two analyses interacted on equal ground. They mutually benefited from each other to create stronger support than either analysis contained

individually. In the Op. 48/4 analyses, the two perspectives interact within a hierarchy. At one

level, events are described in terms of harmonic function and an altered tonal syntax. This syntax

can subsequently be viewed at a more local level in terms of the movement of tritones.

Example 4.1:

α β ∆

Resolution Slide Retention

While the various analyses all take slightly different approaches, there are many common

issues that require similar attention. Such overlapping concerns reveal a discernable

- 102 - compositional style. Until this point of the thesis, this style has been described generally as the

interaction of tonal and post-tonal elements. Having benefited from the process of multiple

analyses, more specific observations are now possible. The tonal elements within these preludes

are most prominent at points of formal articulation. Cadences continue to reflect the tonal notion

that bass motion by descending fifth creates the strongest type of closure. More specifically, the

interaction among tonic, dominant and subdominant harmonies is firmly rooted in nineteenth century chromatic harmony. In addition, Scriabin retains exclusively tertian harmonies.

Scriabin’s manipulation of these harmonies gives the most salient indication of the purely atonal compositions to come. Many of the altered dominant seventh sonorities of these preludes are utilized in an exclusively atonal context in later compositions. Thus, the term transitional in this context does not imply movement forward so much as it indicates a state of being in- between. In Op. 48/4, these dominant seventh sonorities are used in place of traditionally consonant harmonies. At the same time, the fact that we have expectations as to what harmony

“should” go in their place reveals an active syntax, however latent it may be. In the Op. 49/2 prelude, harmonies simultaneously served tonal functions while residing within clearly stratified whole-tone collections. In later compositions, these same sonorities are stripped of their tonal implications and used exclusively for their pitch content. This prelude more clearly illustrates the qualities I define as “transitional.” This prelude does not have a sense of moving away from tonality or towards atonality. Rather, it comfortably contains elements of both.

Scriabin’s tendency to use harmonically clear motion at cadences and uncomplicated forms allow a tonal listener to remain oriented despite the inclusion of less familiar sonorities.

The cumulative effect is of a mirage. From far away, many of the signposts of tonality are present, temporarily superseding the presence of unfamiliar sonorities and tonal functions.

- 103 - However, as one approaches the surface of the piece, the formerly clear tonality is now difficult to reconcile. Even moments of tonal and formal clarity are not as vivid as they once seemed.

- 104 - Bibliography

James M. Baker. The Music of Alexander Scriabin. New Haven: Yale University Press, 1986.

______. “Post-Tonal Voice-Leading.” In Jonathan Dunsby (ed.), Models of Musical Analysis: Early Twentieth-Century Music, 20–41. Oxford: Blackwell, 1993.

______. “Schenkerian Analysis and Post-Tonal Music.” In Aspects of Schenkerian Theory, ed. David W. Beach, 153–186. New Haven, CT: Yale Univ. Press, 1983.

______. “Scriabin’s Implicit Tonality.” Music Theory Spectrum 2/1 (1980): 1–18.

______. “Voice Leading in Post-Tonal Music: Suggestions for Extending Schenker's Theory.” Music Analysis 9/2 (1990): 177–200.

Bass, Richard. “Half-Diminished Functions and Transformations in Late Romantic Music.” Music Theory Spectrum 23/1 (2001): 41–60.

Beach, David. “Harmonic and Linear Progression in Schubert’s Music.” Journal of Music Theory 38/1 (1994): 1–20.

Benjamin, William E. “Models of Underlying Tonal Structure: How Can They Be Abstract, and How Should They Be Abstract?” Music Theory Spectrum 4/1 (1982): 28–50.

Bent, Ian. Analysis; with a glossary by William Drabkin. Basingstoke: Macmillan, 1987.

Berry, David Carson. A Topical Guide to Schenkerian Literature: An Annotated Bibliography with Indices. Hillsdale, NY: Pendragon Press, 2004.

Bowers, Faubion. The New Scriabin; Enigma and Answers. New York: St. Martin’s Press, 1973.

Brown, Matthew; Dempster, Douglas; Headlam, Dave. “The [Sharp]IV([Flat]V): Testing the Limits of Schenker’s Theory of Tonality.” Music Theory Spectrum 19/2 (1997): 155–83.

Brown, Stephen C. “Dual Interval Space in Twentieth-Century Music.” Music Theory Spectrum 25/1 (2003): 35–58.

Burstein, L. Poundie. "Unraveling Schenker's Concept of the Auxiliary Cadence," Music Theory Spectrum 27/2 (2005): 159–178.

Callender, Clifton. “Voice-Leading Parsimony in the Music of Alexander Scriabin.” Journal of Music Theory 42/2 (1998): 219–233.

- 105 -

Childs, Adrian P. “Moving Beyond Neo-Riemannian Triads: Exploring a Transformational Model For Seventh Chords.” Journal of Music Theory 42/2 (1998): 181–193.

Cohn, Richard. “Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of Late- Romantic Triadic Progression.” Music Analysis 15/1 (1996): 9–40.

______. “Neo-Riemannian Operations, Parsimonious Trichords, and Their ‘Tonnetz’ Representations.” Journal of Music Theory 41/1 (1997): 1–66.

______. “Square Dances With Cubes.” Journal of Music Theory 42/2 (1998): 283–296.

Cone, Edward T. “Beyond Analysis.” Perspectives of New Music 6/1 (1967): 33–51.

Cook, Nicholas. A Guide to Musical Analysis. New York: G. Braziller, 1987.

Debellis, Mark. “The Paradox of Musical Analysis.” Journal of Music Theory 43/1 (1999): 83– 99.

Douthett, Jack and Steinbach, Peter. “Parsimonious Graphs: A Study in Parsimony, Contextual Transformations, and Modes of Limited Transposition.” Journal Of Music Theory 42/2 (1998): 241–264.

Epstein, David. Beyond Orpheus: Studies in Musical Structure. Cambridge, MA: MIT Press, 1978.

Forte, Allen. “New Approaches to the Linear Analysis of Music.” Journal of the American Musicological Society 41/2 (1988): 315–48.

Haimo, Ethan. “Atonality, Analysis, and the Intentional Fallacy.” Music Theory Spectrum 18/2 (1996): 167–199.

Hume, David. “On the Standard of Taste.” Reprinted in Aesthetics: the Big Question. ed. Carolyn Korsmeyer. Malden, MA: Blackwell Publishers, 1998.

Hyde, Martha M. “Neoclassic and Anachronistic Impulses in Twentieth-Century Music.” Music Theory Spectrum 18/2 (1996): 200–235.

Jackendoff, Ray Jackendoff and Lerdahl, Fred. A Generative Theory of Tonal Music. Cambridge: MIT Press, 1983.

Kielian-Gilbert, Marianne. “The Functional Differentiation of Harmonic and Transpositional Patterns in Liszt’s Consolation No. 4.” 19th-Century Music 14/1 (1990): 48–59.

- 106 - ______. “Interpreting Schenkerian Prolongation.” Music Analysis 22 (2003): 51– 104.

Larson, Steve. “The Problem of Prolongation in Tonal Music: Terminology, Perception, and Expressive Meaning.” Journal of Music Theory 41/1 (1997): 101–36.

Lerdahl, Fred. “Atonal Prolongational Structure.” Contemporary Music Review 4 (1989): 65–88.

London, Justin; Rodman, Ronald. “Musical Genre and Schenkerian Analysis.” Journal of Music Theory 42/1 (1998): 101–24.

Lubben, Joseph. “Schenker the Progressive: Analysis in ‘Der Tonwille’.” Music Theory Spectrum 15/1 (1993): 59–76.

McGuire, David Robert. “Revisiting the Return: The Structural Dilemma of the Recapitulation in the Schenkerian Account of Classical Sonata Form.” Ph.D. diss, 1996.

Meyer, Leonard B. Emotion and Meaning in Music. Chicago: University of Chicago Press, 1956.

Morgan, Robert. “Dissonant Prolongation: Theoretical and Compositional Precedents.” Journal of Music Theory 20/1 (1976): 49–91.

Pearsall, Edward R. “Harmonic Progressions and Prolongation in Post-Tonal Music.” Music Analysis 10/3 (1991): 345–55.

Perle, George. “Scriabin’s Self-Analysis.” Music Analysis 3/2 (1984): 101–122.

Reise, Jay. “Late Skriabin: Some Principles Behind the Style.” 19th-Century Music 6/3 (1983): 220–231.

Rink, John. “Structural Momentum and closure in Chopin’s Op. 9, No. 2.” In Schenker Studies 2. Cambridge: Cambridge University Press, 1999.

Rothstein, William. ‘Letter to the Editor: “The Americanization of Schenker Pedagogy?”’ Journal of Music Theory Pedagogy 4/2 (1990): 297–301.

Salzer, Felix. Structual Hearing vol. 1. New York: Dover Publications, Inc., 1962.

Santa, Matthew. “Nonatonic Systems and the Parsimonious Interpretation of Dominant-Tonic Progressions,” Theory and Practice (2003), 1–28.

Samson, Jim. Music in Transition: a Study of Tonal Expansion and Atonality, 1900–1920. New York: Norton, 1977.

- 107 - ______. “Review of The Music of Alexander Scriabin by James M Baker.” Journal of Music Theory 32/2 (1988), 353–356.

Schachter, Carl. “A Commentary on Schenker’s Free Composition.” Reprinted in Carl Schachter, Unfoldings. New York: Oxford University Press, 1999: 177–202.

______. “Aspects of Meter.” Music Forum 6 (1987): 1–59.

______. “Rhythm and Linear Analysis: A Preliminary Study.” Music Forum 4 (1976): 281–334

______. “Rhythm and Linear Analysis: Durational Reduction.” Music Forum 5 (1980): 197–232.

Schenker, Heinrich. Der Tonwille Vol. I Ed. William Drabkin. Oxford: Oxford University Press, 2004.

______. “The Laws of the Art of Music.” Der Tonwille Vol. I Ed. William Drabkin. Oxford: Oxford University Press, 2004.

______. “Yet Another Word on the Urlinie.” Der Tonwille Vol. I Ed. William Drabkin. Oxford: Oxford University Press, 2004.

______. Beethovens neunte Sinfonie. (Vienna: Universal Editon, 1912). Trans. and Ed. John Rothgeb. New Haven, CT: Yale University Press, 1992.

Snarrenberg, Robert. Schenker’s Interpretive Practice. Cambridge: Cambrige University Press, 1997.

Stern, David. “Schenkerian Theory and the Analysis of Renaissance Music.” in Heidi Siegel (ed.) Schenker Studies. New York: Cambridge University Press, 1990.

Straus, Joseph N. “The Problem of Prolongation in Post-Tonal Music.” Journal of Music Theory Vol. 31, No. 1 (Spring 1987): 1–21.

Travis, Roy. “Towards a New Concept of Tonality?” Journal of Music Theory Vol. 3, No. 1 (1959): 257–284.

van den Toorn, Peter. “What Price Analysis?” Journal of Music Theory Vol. 33, No. 1 (1989): 165–189.

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- 109 - Appendix i. Scriabin Op. 49, No. 2

..

- 110 - ii. Scriabin, Op. 48, No. 4

- 111 - iii. Baker’s graph of Scriabin, Op. 48, No. 4

- 112 - iii. cont.

- 113 - iv.

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