multiple-row serialism in three works by edison denisov

Multiple-Row Serialism in Three Works by Edison Denisov

by

Zachary A. Cairns

Submitted in Partial Fulfillment

of the

Requirements for the Degree

Doctor of Philosophy

Supervised by

Professor Dave Headlam

Department of Music Theory

Eastman School of Music

University of Rochester

Rochester, New York

2010

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CURRICULUM VITAE

Zachary Cairns was born in Champaign, Illinois on July 11, 1978. He attended the

Pennsylvania State University from 1996 to 2000, graduating with a Bachelor of Science in

Music Education with a Performer’s Recognition Certificate in Percussion Performance. He

returned to Penn State in 2001 and graduated with a Master of Arts in Music Theory in

2003. His master’s thesis dealt with rhythmic organization of the music of Edgard Varèse

and was supervised by Dr. Julian Hook. After teaching at Northwestern Lehigh High

School from 2003 to 2005, he came to the Eastman School of Music, University of

Rochester, and began doctoral studies in Music Theory. He has pursued his research on the

music of Edison Denisov under the direction of Dr. Dave Headlam. He will begin work as

Assistant Professor of Music Theory at the University of Missouri-St. Louis in August, 2010.

iii

ACKNOWLEDGMENTS

The completion of this dissertation would not have been possible without the

generous help of many people. First, I must offer deep and sincere thanks to the members

of my dissertation committee, Dave Headlam, Jeannie Guerrero, and Peter Schmelz.

Working with each of them has helped me to fine-tune my ideas and my writing in very

important ways. I would like to thank my advisor, Dave Headlam, for his patient, thoughtful

assistance throughout the entire process. He has allowed me the opportunity to explore my

own ideas, while continually drawing my attention to connections between those ideas and

the work of others. I would also like to thank Jeannie Guerrero for her invaluable

comments on various drafts of this dissertation, particularly in helping me to shape some of

my thoughts in Chapter 3.

I am especially grateful for the willingness of Eastman’s theory department to

support my request to have Peter Schmelz officially act as a member of the committee.

Professor Schmelz has been exceptionally gracious with his time from the earliest stages of

this project, sending thoughtful and thought-provoking responses to my many, many email

queries on various aspects of Soviet music and music theory, as well as my efforts at

translating the Russian language. Having him as a member of the committee has been a true

honor, and I thank him for his willingness to serve in this capacity. I also thank Jonathan

Dunsby, chair of the Department of Music Theory, who helped to make this collaboration

possible.

Over the last several years, I have had many fruitful conversations and interactions

with a number of people that have impacted this work in both direct and indirect ways. I

have been fortunate to be able to communicate with Edison Denisov’s widow, Ekaterina

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Denissova-Bruggeman, and it has been thrilling to read her considerate responses to my

emails which come to her in what I can only imagine to be horribly broken French. She has

been helpful in providing background information on her late husband’s music and

compositional approach.

Professor Truman Bullard deserves special recognition for his help with my

translation of the Kurbatskaya chapter found in Chapter 2. I have fond memories of our

meetings during the summer of 2009, going sentence-by-sentence through that translation

over lunch(es). The experience of working with him has been not only educational, but

deeply rewarding on a personal level as well.

I would like to thank Tuukka Ilömaki, Sebastiano Bisciglia, Justin Lundberg and

Andy Flowers, the members of Dave Headlam’s “Super Computer Club,” for their help with

various aspects of computer programming and for a productive exchange of ideas on twelve-

tone music. Though this dissertation, in its present form, shows little evidence of my

endeavors in C++ programming, our discussions have been very profitable, particularly in

dealing with some of the mathematical aspects of Chapter 3.

My interest in the music of Edison Denisov can be traced back to the two

saxophonists with whom I shared an apartment during my master’s studies at Penn State.

Erik Holmgren and Matt Sisia have always been wonderful friends, and they introduced me

to Denisov’s Sonata for Alto Saxophone and Piano. I never would have thought that a sentence

as simple as, “Zac, I think you’ll like this piece” could be a life-changing thing, but in this

case, it was.

It would be neglectful of me to omit the names of people who have helped me in

acquiring scores and recordings of Denisov’s music. Much of his music is, unfortunately,

not readily available on the shelves of your local public or University library. I would

v

especially like to thank Sibley Music Library’s Special Collections Librarian David Peter

Coppen for helping me to locate Russian music-theoretical sources, and the Interlibrary

Loan staff at Sibley for their tireless efforts in processing my many, many requests to borrow

scores, books, and recordings from other libraries. I also offer my thanks to Elizabeth

Mulhall in the Promotion department at Schirmer, who helped me to obtain perusal scores

and recordings for a large number of Denisov’s works which are otherwise only available

through rental.

Finally, I thank my entire family for their love and encouragement. My parents,

Scott and Ginny, and my wife’s parents, Barry and Trish, have given me constant support

not only through the dissertation writing, but through the entire degree program. And,

above all, I thank my wife Whitney for her immeasurable support in this and all in my

endeavors. I thank her from the bottom of my heart not only for her tireless efforts in

proofreading and correcting problems in the text, notes and bibliography, but more generally

for keeping me motivated and on a forward-moving path. She is the reason that I have

finally finished this dissertation.

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ABSTRACT

The music of Russian composer Edison Denisov (1929-1996) has not been widely

studied by music theorists in the United States. He was one of the student composers who

came of age in the Soviet Union during the period following Stalin’s death. During this time,

young composers began experimenting with some of the modernist approaches to

composition found in Europe and America. In this dissertation, I have chosen to focus on

one specific aspect of Denisov’s approach to serial composition. My goals are twofold.

First, my fundamental objective will be to give analytical attention to what I strongly believe

is an important, though neglected, repertoire. Second, the dissertation explores technical

issues involving multiple-row serialism in general, and demonstrates the utility of my own

analytical approach developed in the study of this music.

The dissertation is divided into two large parts. The first, comprising Chapters 1-3

serves to set up a music-theoretic backdrop against which Denisov’s serial music might be

profitably examined. Chapter 1 gives the reader a sense of the cultural, political and societal

situation in which Denisov and his student colleagues found themselves. This chapter also

provides some general comments about Denisov’s highly varied compositional style over the

course of his career. Chapter 2 presents an annotated translation of a chapter from Svetlana

Kurbatskaya’s book, Seriynaya muzïka: voprosï istorii, teorii, estetiki [Serial Music: Questions of

History, Theory, Aesthetics]. Written in 1996, this book has the interesting distinction of being

the first Russian-language book dedicated entirely to the topic of serial music. This chapter

also uses many of Kurbatskaya’s concepts in an analysis of Andrey Volkonsky’s piece Musica

Stricta (1956-1957). Generally accepted as the first piece of serial music composed in the

Soviet Union, this piece occupies an important place in the history of Soviet music, and is

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one that Denisov knew well. In Chapter 3, I move to a discussion of some of the general

issues of multiple-row serialism. Within this chapter, I introduce a new analytical device, the

interval-class succession graph, which can illuminate Denisov’s music by offering a way of

conceptualizing the structure of a twelve-tone row which heretofore has been unexplored.

Chapters 4 through 7 make up the second part of the dissertation: the analytical

discussion of three specific pieces involving multiple twelve-tone rows. The pieces are the

following: the first of Five Etudes for Solo Bassoon (1983), and the finales of Sonata for Alto

Saxophone and Piano (1970) and Octet for Winds (1991).

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NOTE ON TRANSLITERATION AND TRANSLATION

In this dissertation, I use Gerald Abraham’s system of transliteration outlined in The

New Grove Dictionary of Music and Musicians (1980), as amended by Richard Taruskin and

described at the beginning of his book Stravinsky and the Russian Tradition: A Biography of the

Works through Mavra (1996). Exceptions to Abraham’s system are discussed in some detail in

Taruskin’s book.

The transliteration of Russian names has been carried out literally throughout the

dissertation, with only a few exceptions. The common rendering of Schnittke is used in

place of the more literal Shnitke. I use the Czech spelling of the name Ctirad Kohoutek,

rather than the Russian Kogoutek. Finally, for the sake of consistency, I have rendered the

name of the famous Russian music theorist as Yuri Kholopov throughout, despite the

common Germanic rendering (Iurii Cholopow).

Unless otherwise indicated, all translations in this dissertation are my own, with two

qualifications: 1) I have been fortunate to have had significant editorial assistance with the

Russian translations from Dr. Peter Schmelz and Dr. Truman Bullard; 2) in cases where a

source exists both in the original Russian and an English translation (most importantly,

Kholopov and Tsenova’s monograph on Denisov), I have worked with the two sources side-

by-side, departing from the published English translation where necessary. I have also

approached Denisov’s analysis, published in Russian and Italian in the same journal, of

Webern’s Piano Variations Op. 27 in a similar manner.

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TABLE OF CONTENTS

Curriculum Vitae …………………………………………………………………………. ii

Acknowledgments …………………………………………………………………………iii

Abstract ………………………………………………………………………………….. vi

Notes on Transliteration and Translation ………………………………………………...viii

Table of Contents ………………………………………………………………………… ix

List of Figures and Examples …………………………………………………………….. xi

Chapter 1 Introduction …………………………………………………………………… 1

Introduction ………………………………………………………………. 1

Denisov’s Stylistic Evolution, Piano Variations………………………………5

Denisov’s “Individual Style” ……………………………………………... 13

Chapter 2 The Russian Understanding of Serialism……………………………………… 23

Annotated Translation: Svetlana Kurbatskaya, Serial Music: Questions of History, Theory, Aesthetics (Ch. 2)……………………………………………23 Analysis: Andrey Volkonsky’s Musica Stricta (1956-1957)………………….. 43 Movement 1: Andantino……………………………………………44 Movement 2: Allegretto……………………………………………. 48 Movement 3: Lento Rubato…………………………………………54 Movement 4: Allegro Marcato……………………………………… 59

Chapter 3 On Multiple-Row Serialism…………………………………………………… 65

General Issues of Multiple-Row Serialism…………………………………65

Issues of Structure ……………………………………………………….. 68

Issues of Function………………………………………………………... 70

Issues of Unity ……………………………………………………………76

INTs, INT-Cs, and BIPs…………………………………………………..78

x

The Adjacency Matrix and Interval-Class Succession Graphs…………….. 82

Comparison and Categorization of ICSGs……………………………….. 85

Chapter 4 Analysis: Five Etudes for Solo Bassoon (No. 1)……………………………………. 93

General Observations …………………………………………………… 93

Issues of Structure ……………………………………………………….. 99

Issues of Function………………………………………………………..105

Issues of Unity …………………………………………………………. 112

Chapter 5 Analysis: Sonata for Alto Saxophone and Piano (Mvt. 3)…………………………. 116

Existing Studies of the Sonata ……………………………………………119

Form …………………………………………………………………… 125

Techniques of Serial Modulation in Denisov’s Sonata …………………… 128

The ICSG in Denisov’s Sonata …………………………………………. 132

Chapter 6 Analysis: Octet for Winds (Mvt. 2)……………………………………………… 143

General Observations …………………………………………………... 143

Forms …………………………………………………………………... 145

Multiple Rows in the Octet ……………………………………………….153

Chapter 7 Conclusions and Extensions………………………………………………… 161

Further Research…………………………………………………………163

Bibliography ……………………………………………………………………………. 169

Appendix I: Kurbatskaya Translation……………………………………………………175

Appendix II: Graph Theory Terminology……………………………………………… .187

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LIST OF FIGURES AND EXAMPLES

Example 1.1A, B Webern, Op. 27 and Denisov, Variations – Rows and their INTs 9

Example 1.1A Webern, Op. 27 9

Example 1.1B Denisov, Variations 9

Example 1.2 Denisov, Piano Variations – Excerpts from Variations 1, 3, 6 10

Example 1.2A Variation 1: mm. 10-13 10

Example 1.2B Variation 3: mm. 25-29 10

Example 1.2C Variation 6: mm. 73-78 10

Example 1.3 Webern, Op. 27 – mm. 1-7 12

Example 1.4 Octet for Winds (Mvt. 1) – mm. 1-5 15

Example 1.5 Sonata for Alto Saxophone and Piano (Mvt. 1) – m. 77 17

Example 1.6 The Sun of the Incas (Mvt. 3) – mm. 9-13 18

Example 1.7 The Sun of the Incas (Mvt. 5) 19

Example 1.7A mm. 19-21 (Pianos and Percussion omitted) 19

Example 1.7B mm. 34-38 (Pianos and Percussion omitted) 19

Example 1.8 Sonata for Alto Saxophone and Piano (Mvt. 1) – mm. 17-19 20

Example 2.1 Webern, String Quartet (1905), mm. 1-13 31

Example 2.2 Excerpt from Webern op. 10, no. 3 (from Kurbatskaya) 36

Example 2.3 Peter Schmelz’s “Soviet Serial Bull’s-Eye” Diagram 41

Example 2.4 Musica Stricta (Mvt. 1) – Form 45

Example 2.5 Musica Stricta (Mvt. 1) – mm. 1-9 45



Example 2.8 Musica Stricta (Mvt. 1) – m. 30 47

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Example 2.10 Musica Stricta (Mvt. 2) – Rows A-D 49

Example 2.11 Musica Stricta (Mvt. 2) – ic5 segments in Rows B and D 50


Example 2.13 Forms of Row A in two voices 52

Example 2.14 Forms of Rows B, C and D in three voices 53

Example 2.15 Musica Stricta (Mvt. 3) – Rows E-F 54

Example 2.16 Musica Stricta (Mvt. 3) – mm. 2, 6 56



Example 2.19 Musica Stricta (Mvt. 3) – m. 11 58

Example 2.20 Musica Stricta (Mvt. 4) – Rows G-H 59


Example 2.22 Forms of Rows G and H in mm. 1-13 60

Example 2.23 Triple counterpoint in mm. 28-54 61



Example 3.1 Concerto for Guitar and Orchestra – Form 73

Example 3.2 Concerto for Guitar and Orchestra – Rows 74

Example 3.3 Concerto for Guitar and Orchestra, Guitar, mm. 349-352 74

Example 3.4 Concerto for Guitar and Orchestra, mm. 130-132 75

Example 3.5 Sonata for Saxophone, Row A 79

Example 3.6 Sonata for Saxophone, Row B 79

Example 3.7 Berg, Lyric Suite (Primary Row) 81

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Example 3.8 Adjacency matrix for Sonata for Saxophone, Row A 82

Example 3.9 Sonata for Saxophone, Row A, successions of ic2 83

Example 3.10 Sonata for Alto Saxophone, Row A, ICSG 85

Example 3.11 Three Webern rows and their ICSGs 86

Example 3.12 Webern, Kinderstück (1924) Row and ICSG 87

Example 3.13 Different representations of Kinderstück ICSG 88

Example 3.14 Webern, Drei Volkstexte (Op. 17) Rows and ICSGs 89

Example 4.1 Five Etudes for Bassoon (No. 1) – row chart 95

Example 4.2 Five Etudes for Bassoon (No. 1) – Rows A-J and their ICSGs 96

Figure 4.1 Angle measurements for row pairs in Five Etudes for Bassoon (No. 1) 101

Example 4.3 INTs of Rows C and J (prime forms) 102

Example 4.4 Abstract inclusion relationship between ICSGs of Rows H 103 and Rows A, C, E, and J

Example 4.5 Five Etudes for Bassoon (No. 1) – mm. 1-3 (Row A) 103

Example 4.6 Five Etudes for Bassoon (No. 1) – mm. 5-6 (Row A) 104

Example 4.7 Five Etudes for Bassoon (No. 1) – mm. 3-5 (Row B) 104

Example 4.8 Five Etudes for Bassoon (No. 1) – mm. 6-9 (Row C) 105

Figure 4.2 Invariances in row-form successions in Five Etudes for Bassoon (No. 1) 107

Example 4.9 Symmetry of Invariant Tetrachords 108

Example 4.10 Location of Tetrachords {056e}{349t}{1278} in mm. 6-18 109

Example 4.11 Five Etudes for Bassoon (No. 1) – mm. 18-19 110

Example 4.12 Five Etudes for Bassoon (No. 1) – mm. 17-20 (CP6, X, GP7) 111

Example 4.13A Five Etudes for Bassoon (No. 1) – Small Sets of GP7 112

Example 4.13B Five Etudes for Bassoon (No. 1) – mm. 20-24 112

Example 4.14 Five Etudes for Bassoon (No. 1) – mm. 36-50 113

xiv

Example 5.1 Sonata for Alto Saxophone and Piano (mvt. 3), form 125

Example 5.2 Sonata for Alto Saxophone and Piano (mvt. 3), Row A 128

Example 5.3 RICH and TR-Chain of Row A 129

Example 5.4 Sonata for Alto Saxophone and Piano (mvt. 3), saxophone, mm. 3-7 130

Example 5.5 Sonata for Alto Saxophone and Piano (mvt. 3), piano right hand, 130 mm. 7-13

Example 5.6 Sonata for Alto Saxophone and Piano (mvt. 3), saxophone, mm. 35-37 131

Example 5.7 Sonata for Alto Saxophone and Piano (mvt. 3), piano right hand, 131 mm. 25-26

Figure 5.1 Four Techniques of Serial Modulation 132

Example 5.8 Sonata for Alto Saxophone and Piano (mvt. 3), Rows A and B 133

Example 5.9 Sonata for Alto Saxophone and Piano (mvt. 3), m. 1 134

Example 5.10 Sonata for Alto Saxophone and Piano (mvt. 3), piano part, mm. 17-19 135

Example 5.11 Sonata for Alto Saxophone and Piano (mvt. 3), mm. 34-42 136

Example 5.12 Sonata for Alto Saxophone and Piano (mvt. 3), mm. 53-68 139 (triplet figures only)

Example 5.13 Sonata for Alto Saxophone and Piano (mvt. 3), mm. 76-78 140

Example 5.14 Row C created by left hand in mm. 76-78 141

Figure 5.2 Derivation of Row C 141

Example 6.1 Octet for Winds (Mvt. 2), mm. 1-3, horn 2 – “shooting” 144

Example 6.2 Octet for Winds (Mvt. 2), m. 6, oboe 1 – “pointillistic bursts” 144

Example 6.3 Octet for Winds (Mvt. 2), mm. 20-21, bassoon 1 – “smooth threads” 145

Example 6.4 Octet for Winds (Mvt. 2) – Form 146

Example 6.5 Octet for Winds (Mvt. 2) – Rows A and B, and ICSGs 149

Example 6.6 Octet for Winds (Mvt. 2) – mm. 17-18, Canon #5 150


xv

Example 6.8 Octet for Winds (Mvt. 2) – Row A and B, ICSGs re-drawn 153

Example 6.9 Octet for Winds, Row A & Saxophone Sonata, Row A – ICSGs 154 as non-directed graphs

Example 6.10 Octet for Winds, Row B & Saxophone Sonata, Row B – ICSGs 155

Example 6.11 Concerto for Guitar – Rows A and B, and ICSGs 156



Example 7.1 Octet for Winds (Mvt. 2) – mm. 1-5, horn 2 163

Example 7.2 Octet for Winds (Mvt. 2) – mm. 1-5, horn 2, Beat division 164 succession graphs

Example 7.3 Graph of functional chord successions in major mode pieces 165 Example 7.4 Campion’s Regle de l’octave (1716) presented as a succession graph 166

1

CHAPTER 1 INTRODUCTION

During the rule of Stalin (1929-1953), composers in the Soviet Union lived and

worked within a world of severe restrictions.1 The dogma of socialist realism prohibited

music, literature and the arts from revealing any sort of “formalist” tendencies.2 Music

was expected to play a societal role, one of glorifying the state and the working classes

and promoting the spirit of socialism.3 Without offering much in the way of specific

criteria, a composition was only deemed acceptable by the Soviet authorities if it was

accessible to a general audience, tuneful, optimistic, folk-influenced and fell into a

traditional style.4

Composers during this time had virtually no legal access to scores, recordings, or

books related to avant-garde music of Europe and the Americas; influences of the

modern West had no place in the world of Soviet music. Ideologically, the composition

of serial music in Stalin’s Soviet Union, then, was doubly problematic: first, it was

derided as formalist by the state, and second, the method itself demonstrated an

unacceptable Western influence.

Dmitri Shostakovich is probably the best known of the composers who suffered

under the communist regime; the various facets of his own personal struggles with the

1 The situation faced by Soviet composers during this time period has been addressed in a number of sources. See Hakobian 1998, Schmelz 2002, 2005 and 2009, Schwarz 1972, as well as the various essays from Taruskin 1997. 2 A precise definition of “formalist” was never offered to those composers whose works were publicly denounced as such. In general, though, the word seemed to imply that a composition’s musical language was abstract and complex in some way. See Fay 2000, 87-8 and Taruskin 1997, 517-28. 3 Tertz 1960, 24-26. Tertz takes the phrase “spirit of socialism” from the First All-Union Congress of Soviet Writers. He goes on to describe that socialist realism demands that an artist’s work have a singular Purpose “with a capital P.” On p. 26 he writes, “A poet not only writes poems but helps, in his own way, to build Communism; so, too, do sculptors, musicians, agronomists, engineers, laborers, policemen, and lawyers, as well as theaters, machines, newspapers, and guns.” 4 Fay 2000, 89.

2

Soviet system have been widely discussed.5 We can use the following 1959 statement by

Shostakovich to summarize the Party’s stance on serialism, as, in the late part of his

career, circumstances increasingly forced him to become a “mouthpiece of official Soviet

aesthetic policy.”6

I am firmly convinced that in music, as in every other human endeavor, it is always necessary to seek new paths. But it seems to me that those who see these new paths in dodecaphony are seriously deluding themselves. The narrow dogmatism of this artificially invented system rigidly fetters the creative imagination of composers and deprives them of individuality. It is no accident that in the entire legacy of Schoenberg’s dodecaphonic system there is not a single work that has gained wide acceptance. … Dodecaphony not only has no future, it doesn’t even have a present. It is just a “fad” that is already passing.7

In official Soviet publications such as Sovetskaya musïka, the journal in which this

statement was printed, such polemical statements were common, but it is difficult to

know whether or not they were representative of the author’s true feelings.8 However,

for our present purposes, it is not particularly relevant whether this statement is truly

how Shostakovich, in particular, felt about such music, but rather that this was the

general opinion of the Soviet state on serialism.

Following Stalin’s death in 1953, the situation became somewhat less severe.

During the so-called Khrushchev Thaw, access to Western musical sources was allowed

to varying extents. While completely open access was still an impossibility, the

composers who were studying at the Moscow Conservatory during this time were aware

of the trends that had been developed thirty years prior by Arnold Schoenberg and his

5 Shostakovich’s situation is well documented from a variety of different perspectives. Among the most important are Fay 2000, Ho and Feofanov 1998, the three essays dealing with the composer in Taruskin 1997 and the much-debated publication of Shostakovich’s so-called “memoirs,” Volkov 1979. 6 Fay 2000, 214. 7 Quoted in Fay 2000, 214. While a discussion of the context of this quote and the circumstances regarding Shostakovich’s turbulent relationship with the Communist Party is beyond the purview of the present dissertation, some of the relevant details can be found in Fay 2000, 173-175, 214 and 216-219. 8 Shostakovich himself experimented with aspects of the twelve-tone organization of pitch material. See Child 1993 and Schmelz 2004.

3

pupils, Anton Webern and Alban Berg.9 Though these techniques certainly were not

officially taught within Conservatory walls, composition student Edison Denisov (1929-

1996) and others reportedly sought the aid of their open-minded composition instructor

Vissarion Shebalin to help in their self-study of as much of this music as they could

acquire. Since access to this music was now legal but still not widespread, the scores and

books studied by the young composers were not openly available through the

Conservatory library, and had to be found elsewhere. Unfortunately, it is virtually

impossible to know with any certainty what specific pieces these composers studied.

It was during this time that Denisov’s fellow student Andrey Volkonsky (1933-

2008) composed Musica Stricta (1956-57). This four-movement work for solo piano is

generally considered to be the first piece of Soviet serial music.10 As I will discuss in

Chapter 2, the first movement of this piece is organized around manipulations of an

unordered pitch-class set (pc set), and therefore does not fit into standard Western

definitions of “serialism.”11 It may be described more comfortably by the general label

of “freely atonal” music. On the other hand, the second, third and fourth movements

are serial, as they are based on the transformation of ordered twelve-tone rows.12 But, in

non-Schoenbergian fashion, all three of those movements derive their pitch material

from multiple, simultaneous twelve-tone rows: the second movement features four

distinct rows used in counterpoint, while the third and fourth movement each use two,

and all three movements make use of non-row-based, freely atonal material.

9 Schmelz 2009 provides a great deal of evidence regarding the acquisition of this awareness. See his Chapter 2, especially 28-33, 39-49 and 54-66. 10 Schmelz 2009, 81. 11 To cite just one of these “standard” Western definitions, Dave Headlam defines twelve-tone music as “music in which all pitch events in a piece can be traced, without an unreasonable amount of difficulty, to the common source of the ordered intervals of a twelve-note row, taking pieces like Schoenberg’s Variations for Orchestra op. 31 and Webern’s Symphony op. 21 as examples.” See Headlam 1996, 195. 12 Throughout this dissertation, I will use the word “row” for what should more accurately be called a “row class” – the set of up to 48 row forms related by the basic twelve-tone operations.

4

Peter Schmelz, one of the main researchers of the “unofficial” music of the

Thaw, has speculated that the young Russian composers’ interest in serialism may have

grown from the desire to experiment with a “forbidden fruit.”13 Because they and the

composers of the previous generation had been unable to explore this method in the

past, they may have felt a strong urge to “catch up” with their European and American

contemporaries.14 Schmelz goes on to offer a view of serialism as a symbol of resistance

in the Soviet Union. Having been forced to ignore this compositional opportunity, the

young composers may have felt that Soviet music had been artistically compromised. In

Schmelz’s view, the adoption of serial techniques “became a symbol of intellectual and

moral integrity.”15

A number of young Soviet composers experimented with serial techniques in the

1950s and 1960s. Edison Denisov, Andrey Volkonsky, Alfred Schnittke, Arvo Pärt,

Sofia Gubaydulina, Valentin Sil’vestrov, Nikolai Karetnikov and others were among

those who tried their hands at dodecaphonic writing. However, among these

composers, Denisov appears to be one of the few for whom the twelve-tone approach

found a permanent home in his compositional style. For Denisov and the other young

composers, dodecaphony was used as a compositional technique rather than a

compositional method. Schmelz convincingly argues that “the young composers did not

view [serialism] as a monolithic method…that implied a single style. They were more

13 The phrase “young composers” was used in official Soviet publications to describe these students who were experimenting with new approaches to composition. Though the words translate literally from the Russian molodïye kompozitorï, Schmelz demonstrates that, during the Thaw, this phrase acquired condescending connotations. See Schmelz 2009, 5-6, n. 11. 14 Schmelz 2005, 140-41. 15 Ibid., 143.

5

intent on applying the techniques and integrating them into their own, already

developing styles.”16

It is one particular aspect of Denisov’s serial music that will be the focus of this

dissertation: his use of multiple twelve-tone rows in counterpoint or juxtaposition within

a single composition (or movement). I have two primary goals. First, my fundamental

objective will be to give analytical attention to what I strongly believe is an important,

though neglected, repertoire. To this end, I will examine three pieces in which Denisov

uses multiple, simultaneous twelve-tone rows: Five Etudes for Solo Bassoon (1st etude, 1983),

Sonata for Alto Saxophone and Piano (3rd movement, 1970), and Octet for Winds (2nd

movement, 1991). Furthermore, owing to its importance in Soviet music history, I will

also provide an analysis of the multiple-row serialism of Volkonsky’s Musica Stricta.

Second, the dissertation will explore technical issues involving multiple-row serialism in

general, and demonstrate the utility of my own analytical approach developed in the

study of this music.

DENISOV’S STYLISTIC EVOLUTION, PIANO VARIATIONS

Apart from a few scattered articles, the translation of an important monograph

by Russian musicologists Yuri Kholopov and Valeria Tsenova, and Peter Schmelz’s

work, Denisov’s music has received little attention in the English-speaking music-

theoretic community.17 As such, I shall provide a summary of some aspects of his

musical career and compositional output here.18 As early as June 1948, Denisov began

16 Schmelz 2002, 179. 17 Throughout this dissertation, references to Kholopov and Tsenova’s combined work will be given to show the location of the cited information in the Russian text and in the most recent English translation: 1993 and 2002, respectively. 18 Denisov’s biography is treated more fully in Kholopov and Tsenova 1993, 1-43; 2002, 1-49.

6

corresponding with Shostakovich, in an effort to get the elder composer’s advice and

evaluation of his compositions. Shostakovich’s appraisal was generally positive, but he

indicated in several different letters during the year 1950 that Denisov’s melodic writing

was the weakest aspect of his nascent compositional skill.19 But it is clear that

Shostakovich saw a budding talent in Denisov’s work, and he continued to encourage

him to apply for entrance into the Moscow Conservatory, even after he failed the

required entrance exams in 1950. But this proved to be only a minor setback, as

Denisov was successful in those exams in his second attempt a year later.

From 1951-1956, Denisov studied at the Moscow Conservatory, and he

continued as a post-graduate student from 1956-1959. During the early part of this time

period, Denisov’s music was largely tonal, likely due to the restrictions of the curriculum

and the demands of the Soviet government.20 Soon after graduating from the

Conservatory, however, he began exploring non-tonal and dodecaphonic music.

Denisov himself described the time period from 1959-1969 as his “second

conservatory.”21 During this time, he engaged himself in a personal study of music of

many composers who had been left out of the Conservatory’s official curriculum:

Stravinsky, Bartók, Hindemith, Debussy, Schoenberg, and Webern.22 It will be

immediately apparent that Berg’s name is conspicuously absent from this list, which

includes his Second Viennese School partners. According to Kholopov and Tsenova,

19 Kholopov and Tsenova provide a number of Shostakovich’s letters to Denisov. See Kholopov and Tsenova 1993, 172-183; 2002, 269-282. These letters are also found in French in Denisov and Armengaud 1993, 272-277. 20 Of course, it would be foolish to deny that Denisov’s own personal aesthetic preferences might have played a role in the nature of his compositions. It is impossible to know the extent to which those personal preferences might have been influenced by the music to which he was exposed as a student at the Moscow Conservatory. 21 Denisov and Shul’gin 1998, 22. 22 Kholopov and Tsenova 1993, 20-22; 2002, 19-21.

7

Denisov “failed to have time for [Berg’s music].”23 It is surprising, therefore, that

Denisov’s later music should share several traits with that of Berg: in particular, the use

of multiple rows (both derived from one another, and with no apparent connections)

and material based on a twelve-tone row or rows presented side-by-side with non-row-

based material.24

The year 1961 marked Denisov’s first attempts at twelve-tone composition: Music

for Eleven Wind Instruments and Timpani and Piano Variations.25 The serial writing in these

two pieces contrasts strongly with the first serial efforts of Volkonsky. While

Volkonsky’s Musica Stricta will be discussed in detail in Chapter 2, as mentioned above,

the work is fairly non-Schoenbergian in the approach to twelve-tone composition used

in the piece: in particular, multiple rows, neither of which, separately or together,

accounts for the pitch organization of the entire musical texture. But while Volkonsky

uses his own idiosyncratic style of dodecaphony in his earliest work, Denisov’s earliest

twelve-tone works actually represent the most conventional of any of his works using the

technique.26 Volkonsky’s unorthodox twelve-tone traits may thus be understood as the

result of a young composer experimenting with an incompletely understood technique,

while Denisov’s later unorthodox trespasses may be interpreted as willful transgressions

of a system with which he had already developed a good deal of familiarity and

comprehension.

To demonstrate the awareness that Denisov acquired during the early part of the

1960s, it will be informative to examine one of his early twelve-tone works in

23 Ibid., 21; 20. 24 Headlam 1996, 196-197. 25 Also composed in 1961, the second movement of Denisov’s String Quartet No. 2 is a theme and variations in which the theme is a twelve-tone melody. See Kholopov and Tsenova 1993, 55-56; 2002, 61. 26 For reasons that will be discussed later, I consider Denisov’s “earliest twelve-tone works” to be those written before his 1964 chamber cantata The Sun of the Incas.

8

conjunction with a staple of the Viennese repertoire. That Viennese piece is Webern’s

Op. 27 Piano Variations, which I believe may have provided a model, however informal,

for Denisov’s own Piano Variations.

In 1957, Glenn Gould made a series of concert appearances in Moscow and

Leningrad. Among his performances in Moscow was a lecture recital in the Small Hall

of the Conservatory, where he briefly discussed Schoenberg’s twelve-tone method and

performed, among other works, Webern’s Op. 27.27 Denisov was in attendance at this

recital, and later recalled the impact the performance had by saying, “Ce fut une véritable

révélation.”28 The Webern piece must have made an enormous impression on Denisov,

either at the recital or at some future time, as he published a theoretical analysis of the

work in 1970.

Webern’s overriding concern for symmetry and palindromes in his Op. 27 is not

at all present in Denisov’s Variations. However, the canonic writing in Denisov’s first

and third variations, combined with the fragmented, pointillistic musical surface of the

sixth variation all bear at least a superficial resemblance to the music of Webern. Within

the structure of the row for Denisov’s Variations lies a deeper structural similarity,

though. Example 1.1 shows the two rows, with their respective ordered-interval

sequences (INTs). It is easily seen that the first six entries in the two INTs are identical,

but presented in a slightly different order. There is some evidence that Denisov found

the interval content of row subsets to be an important part of the structure of a twelve-

tone row. In his analysis of Webern’s Op. 27, he discusses the discrete trichords of the

row in the following manner:

27 Schmelz discusses the details of Gould’s visit to Moscow are discussed at some length. See Schmelz 2009, 55-59. 28 “It was a true revelation.” See Denisov and Armengaud 1993, 66.

9

EXAMPLE 1.1: WEBERN, OP. 27 AND DENISOV, VARIATIONS – ROWS AND INTS

A. WEBERN, OP. 2729

B. DENISOV, VARIATIONS

The series is broken up into four three-note segments that constitute intervals of seconds and thirds. The first group is a combination of a minor second and a major third; the second group is a minor third and a major second; the third group is two minor seconds; and finally, the fourth group is, again, a minor second and a major third (but, because of the directional orientation of the thirds, [the first and last groups] are not isomorphic).30

From this description, it is clear that Denisov is thinking of Webern’s row in terms of

unordered interval-class (ic) content. The parenthetical note at the end of the quotation

shows an intervallic intuition similar to modern set theory: even though the first and last

trichords are both made of a minor second and a major third, Denisov says they are “not

isomorphic,” because the major third in the first trichord is descending, while the one in

the final trichord is ascending. Perhaps not coincidentally, three of the discrete trichords

from Denisov’s row can be described in a similar manner: the first and third trichords

are made of a minor second and a major third (enharmonically spelled), with the

29 This is what Denisov considered to be the prime form of Webern’s row, though other authors consider this to be a retrograde-inverted form. See Denisov 1970, 48 and Bailey 1991, 24, 341 and 350. 30 Denisov 1970, 47.

10

direction of both intervals flipped in the third trichord. Additionally, the second trichord

is made of two seconds, like the third trichord of the Webern row, but two major

seconds.

Two notable characteristics of Denisov’s later style are already present in this

early work. As previously mentioned, the first is the close canonic writing of the first,

third, and sixth variations. Excerpts from each of these three variations are shown in

Example 1.2.

EXAMPLE 1.2: DENISOV, PIANO VARIATIONS – EXCERPTS FROM VARIATIONS 1, 3, 6

A. VARIATION 1: MM. 10-13

B. VARIATION 3: MM. 25-29

C. VARIATION 6: MM. 73-78

11

This kind of canonic writing bears a striking resemblance to that found in a number of

Webern’s works: the Five Canons Op. 16, the first variation of the second movement of

his Symphonie Op. 21, the second movement of his Variations Op. 27, and the second

movement of his Cantata Op. 29.31

The second aspect of Denisov’s later style found in the Piano Variations lies in the

row segmentation of the third and sixth variations. As seen in Examples 1.2B and 1.2C,

Denisov is fond of dividing a row into segments, and then manipulating the order of the

pitches within each segment. In the first five measures of Variation 3 (Example 1.2B),

the pianist’s right hand presents the first pentachord of row form I1, forward and

backward, followed by the final pentachord of I1, backward and forward.32 Finally, the

left hand completes the row statement by providing the missing pitches, at order

positions 5 and 6.33 Denisov frequently treats row segments in this manner, blurring the

distinction between P- and RP-forms of the row (as well as I- and RI-forms).34

This technique is not unlike Denisov’s own interpretation of the row

manipulations in the first movement of Webern’s Op. 27. In his article, Denisov writes,

“all the row forms in the first variation are ‘wrapped’ [zavorachiayutsya] (i.e. if one hand

begins a row form from its beginning, the other hand simultaneously begins the same

row form from its ending).”35 Essentially, he is saying that one hand presents the early

order positions of a single row form while the other hand presents the later order

positions, as shown in Example 1.3. This has the net effect of rendering any row forms

31 On Webern’s use of canonic techniques in these and other works, see Bailey 1991, 94-146. 32 Throughout this dissertation, I will label row forms using the letters P, I, RP and RI to indicate which of the standard twelve-tone operators is used. The row form label will be followed by a subscript indicating the first pitch class of the row form. In the case of RP and RI, the subscript will represent the last pitch class of the row form (which is, of course, the first pitch class of the related P or I form). 33 Following the convention in Mead 1985 and Headlam 1996, I will underline order position numbers to visually distinguish them from pitch-class integers. 34 This work is also discussed in Schmelz 2009, 139-145. 35 Denisov 1970, 48.

12

labeled as retrograde or retrograde-inversion virtually indistinguishable from their non-

retrograde counterparts.

EXAMPLE 1.3: WEBERN, OP. 27 – MM. 1-7

Denisov labels all row forms in the first movement with curved arrows like those shown

in Example 1.3. The direction of the arrow is intended to show the path of the row

between the two hands. With this notation, it is clear that Denisov interprets the first

four measures as one statement of P4 which wraps itself from right hand to left hand: the

row’s first hexachord is presented in order in the right hand, and simultaneously the

row’s second hexachord is presented in retrograde in the left hand. Variation 3 from

Denisov’s own Variations (Example 1.2B) seems to involve a similar kind of wrapping,

but on an entirely horizontal plane. Instead of presenting a row segment forward and in

retrograde simultaneously, Denisov’s Variation 3 presents those versions of a given row

segment successively, as indicated by the brackets in Example 1.2B.

An article from 1973 indicates that, for Denisov, the manipulation of subsets of a

twelve-tone row was a standard part of the composer’s serial technique. The article

“The Compositional Process” consists of Denisov’s personal musings on what are more

or less self-evident statements about music composition. But among those musings,

Denisov has the following to say about dodecaphonic composition:

13

In 12-tone and serial technique there are other guiding principles for organizing sound-materials[,] and over the years these have become increasingly sophisticated. Here we work with ‘sets’ in the mathematical sense of the word ‘set,’ and the process of composition lies in (1) the selection of segments from these sets; (2) organizing from these segments a succession of sub-sets (for instance, of harmony); (3) the establishment of definite logical correlations, both between the segments of the chosen sets (the establishment, for instance, of a pattern of consonant relationships) and between those sounds which are included in the complex of sub-sets (the organization of definite patterns of harmonic sequence, or the creation, for instance, of thematic and tonal relationships by intervals); and also (4) the ordering of this complex of sounds, precisely and coherently.36

This statement suggests not only the importance of subsets of a twelve-tone row, but

also touches upon a topic of crucial importance in the present study: “the organization

of definite patterns of harmonic sequence” between the elements of those subsets. A

way of understanding patterns created by organized successions of interval classes will be

presented in Chapter 3.

DENISOV’S “INDIVIDUAL STYLE”

Kholopov and Tsenova single out the year 1964 as the beginning of Denisov’s

“individual style.”37 Composed in this year, his chamber cantata The Sun of the Incas is

cited not only by Kholopov and Tsenova, but also by Susan Bradshaw as the first work

in which the composer’s individual voice can be heard.38 This piece even brought

Denisov his first taste of international recognition.39 Following the premiere

performance in Leningrad, the piece was performed in Darmstadt and Paris, under the

baton of Bruno Maderna. There is also evidence that Igor Stravinsky and Roger

36 Denisov 1973, 9. 37 Kholopov and Tsenova 1993, 51; 2002, 57. 38 Kholopov and Tsenova 1993, 22; 2002, 21; Bradshaw 1984, 3. 39 While an analysis of The Sun of the Incas is not within the scope of this present study, some of its relevant technical aspects have been discussed in Schmelz 2002 and 2009, Kholopov and Tsenova 1993 and 2002, and Bradshaw 1984.

14

Sessions knew and were quite impressed with the work. Predictably, this positive

impression of the piece was not shared by the Soviet authorities. There was a significant

amount of controversy about the piece’s Leningrad premiere, and it was uncertain

whether the performance would be allowed. Additionally, a performance in Moscow

was scheduled and abruptly cancelled.40

From this point until his death in 1996, his music maintained a remarkable

degree of stylistic continuity. As a way of describing aspects of Denisov’s style,

Kholopov and Tsenova catalog a number of characteristic “genres” [zhanrï ]. These

genres are better understood as rhythmic and/or textural gestures, typical of Denisov’s

individual style.41 A general understanding of several of these gestures will prove to be

useful in the analytical portions of this dissertation, particularly in Chapter 6, an analysis

of the Octet for Winds. The most relevant of Kholopov and Tsenova’s genres for the

pieces discussed in the present study include the following:

1) High lyricism [Vïsokaya lirika] 2) Lyrical bands [Liricheskaya vyaz’ ] 3) Shooting, pricking, and sharply rhythmicized points [Strel’ba, ukolï,

ostroritmizovannïye tochki ] 4) Pointillistic bursts [Puantilisticheskiye vspleski ] 5) Rustles, smooth threads [Shorokhi, Gladkiye niti ]

These are five of the nine genres given by Kholopov and Tsenova. Two of the

remaining four (sonorous masses [sonorï-massï ] and sonorous duplications, mixtures and

clusters [sonorï-dublirovki, mikstï, klasterï ]) deal primarily with ways of “thickening” a

melodic line by adding voices to create a series of dissonant, moving clusters.42 The final

two genres not included here are aleatory [aleatorika] and traditional artistic genres

40 Kholopov and Tsenova 1993, 22-24, 29-30; 2002, 22-23, 28-29. 41 Ibid., 61-72; 67-84. 42 Ibid., 66-68; 76-79.

15

[traditsionnïye khudozhestvennïye zhanrï ], which, as their names imply, are not so much

rhythmic/textural gestures as they are indications of broader stylistic attributes.

EXAMPLE 1.4: OCTET FOR WINDS (MVT. 1) – MM. 1-5

Kholopov and Tsenova consider the “lyrical band” gesture-type to be the most

distinctive “calling card” [vizitnaya kartochka] of Denisov’s style.43 Example 1.4 shows a

lyrical band which occurs at the beginning of the first movement of Denisov’s Octet for

Winds. Kholopov and Tsenova note that the term “lyrical band” refers to “strings of

several voices in a quasi-arhythmic and ametrical presentation…It sounds as a ‘thick

melody,’ for the constituent voices merge together without [any single voice] as the

43 Ibid., 64; 70.

16

leading one…”44 In short, Kholopov and Tsenova refer to the entire texture shown in

Example 1.4 as a lyrical band.

The individual lines of a lyrical band are defined by Kholopov and Tsenova as

“rustles” or “smooth threads.” The distinction between rustles and smooth threads is

primarily the tempo and dynamic level of the gesture: rustles are faster, softer gestures

with an “illusory effect” [effekt prizrachnosti ], and are often notated as unmeasured grace

notes. When the gesture is slowed down enough that the figure acquires an identifiable

rhythmic profile, it is termed a smooth thread.45 It is through the combination of these

smooth threads that the texture of a lyrical band results. These smooth threads tend to

consist primarily of small intervals, which combine to create a weaving chromatic line,

which typically results in a chromatically saturated (or nearly saturated) pitch range.46

Any of the individual instrumental lines in Example 1.4 can be seen to represent an

extremely slow smooth thread: the first bassoon part in mm. 2-5, for example, winds

around to chromatically fill in the space between E3 and B3. Often, though, smooth

threads occur in faster rhythms, as shown in Example 1.5.

Though not noted as such by Kholopov and Tsenova, the “shooting” gesture is

found perhaps as frequently in Denisov’s music and is every bit as much a calling card of

his style. Their definition refers to “quasi-unordered pointillistic simultaneous

statement[s] of accented staccato sounds or disjointed chords in all registers in turn…”47

44 Ibid. 45 Ibid., 66; 75. 46 Kholopov and Tsenova suggest that these weaving chromatic lines might be related to the “EDS intonation,” which is the pitch realization of several of the letters of the composer’s name.

We might imagine these smooth threads as fortspinnung-like continuations of the intervallic succession given by either of these two motives. See Kholopov and Tsenova 1993, 83; 2002, 101. 47 Ibid., 65; 72.

17

EXAMPLE 1.5: SONATA FOR ALTO SAXOPHONE AND PIANO (MVT. 1) – M. 77

The examples mentioned in the text reveal, to some extent, the importance of repeated

pitches in this gesture-type. This appears to be the primary difference between shooting

and “pointillistic bursts,” though the authors do not explicitly state this.48 Shooting is

most often found in closely imitative textures, as Examples 1.2A and 1.2B show. The

third and fifth movements of Denisov’s The Sun of the Incas demonstrate two different

realizations of the gesture. In the third movement, the individual rhythms are

syncopated, but they are all based on a uniform subdivision of the beat, as shown in

Example 1.6. The entirety of this twenty-six-measure movement utilizes thirty-second

note beat divisions, in close imitation: a clear example of shooting.49

48 In support of my understanding of shooting as being primarily centered around repetitions of a single note or chord, Kholopov and Tsenova refer to the “broken rhythms” of the finale from Stravinsky’s Rite of Spring. See Kholopov and Tsenova 1993, 65; 2002, 72. 49 This movement also demonstrates Denisov’s penchant for using segments of a single twelve-tone row. While The Sun of the Incas is based on a single twelve-tone row (combined with non-row-based material, particularly in the second, fourth and fifth movements), the third movement derives all of its pitch material from transformations of the first hexachord of this row: the second hexachord is never used.

18

EXAMPLE 1.6: THE SUN OF THE INCAS (MVT. 3) – MM. 9-13

Examples 1.7A and 1.7B show two brief shooting statements in the fifth movement of

The Sun of the Incas. In this movement, as in many of Denisov’s later works (including his

Octet for Winds, as we shall see in Chapter 6), the shooting gesture first appears as part of

an imitative texture, yet is presented later in a homorhythmic texture at the climax of the

movement.

Denisov’s “pointillistic bursts” often have similar rhythmic shapes as the

shooting gestures shown in Example 1.7: highly syncopated, with frequent shifts of beat

division. According to Kholopov and Tsenova, the distinction between the two gestures

is that “‘shooting’ implies an extremely tense rhythm while [the ‘pointillistic burst’] is a

multi-element ‘splash’ [pyatno].”50 It seems that, for the most part, the intensity of

shooting is replaced by the lighter splashing of pointillistic bursts by means of replacing

repeated-note figures with single statements of individual pitches, often at wide melodic

intervals. Example 1.8 shows three measures from the first movement of Denisov’s

Sonata for Alto Saxophone and Piano which demonstrate how these pointillistic bursts (m.

50 Kholopov and Tsenova 1993, 65; 2002, 74.

19

EXAMPLE 1.7: THE SUN OF THE INCAS (MVT. 5) A. MM. 19-21 (PIANOS AND PERCUSSION OMITTED)

B. MM. 34-38 (PIANOS AND PERCUSSION OMITTED)

19) can be used as a tension-releasing eruption to contrast the building intensity of

shooting. In this case, a uniform beat division is used throughout. Kholopov and

Tsenova are not clear on the specific manner in which pointillistic bursts offer a release

of tension, and, certainly, tension in a musical passage can be relieved in a number of

ways. In the particular case of the Sonata’s first movement, the repeated-note gesture is

20

gradually introduced from the beginning of the movement, starting in the piano part in

m. 5, with the repetitions increasing in number from mm. 7-12. In mm. 17-18 (shown in

Example 1.8), the repeated-note figure is divided between the three voices of the musical

texture. With each repetition of a particular single note, there is an ever-greater yearning

for change of pitch. As such, when the repeated notes disappear in m. 19 and are

replaced with large intervallic leaps, this desire is fulfilled, thus suggesting a subtle release

of the tension of the preceding measures.

EXAMPLE 1.8: SONATA FOR ALTO SAXOPHONE AND PIANO (MVT. 1) – MM. 17-19

Kholopov and Tsenova’s taxonomy of characteristic rhythmic/textural gestures

leaves each individual genre broadly defined; they do not analyze thoroughly any single

gesture in great detail. The authors’ primary goal is to provide the reader with a set of

audibly identifiable traits that are particular to Denisov. In Chapter 6, I will take some

preliminary steps toward the goal of attaining a more thorough understanding of the

nature and usage of these gestures, but even my study will focus more on the interaction

between specific gestures.

***

21

A broad description of Denisov’s music is a characteristic that runs throughout

Kholopov and Tsenova’s monograph. The book deals with biographical information,

issues of general compositional style, and some brief analytical observations about a

number of specific pieces. Their research has provided an important foundation for

Denisov scholarship; without it the present study would scarcely be possible.

It is from their work and the work of Peter Schmelz (which will be discussed

further in Chapter 2) that the present dissertation arose. This dissertation divides into

two large parts between Chapters 3 and 4. The first part serves to situate Denisov’s

music within its proper historical context and to discuss the analytical methodology

which will be used in the second part of the study. In the present chapter, I have been

mostly concerned with introducing the reader to broad stylistic issues. Chapter 2 will

provide an annotated translation of a chapter from Svetlana Kurbatskaya’s book Serial

Music: Questions of History, Theory, Aesthetics [Seriynaya muzïka: voprosï istorii, teorii, estetiki].

This book was the first Russian-language monograph devoted entirely to the study of

serial music, published in 1996, the year of Denisov’s death. Though this book’s

circulation appears to have been fairly limited, it was written under the advice of Yuri

Kholopov (1932-2003), the most prominent Russian theorist of his generation. This

book provides interesting insight into a uniquely Russian understanding of what serial

music “is.” In one of the early chapters of the book, Kurbatskaya defines no fewer than

twelve different categories of what she calls “twelve-toneness” (dvenadtsatitonovost’ ).

Between this source and the Russian Musical Encyclopedic Dictionary (Muzïkal’nïy

Entsiklopedicheskiy Slovar’, henceforth MES ), which has different definitions for terms

that Western readers would generally consider to be essentially synonymous (serial

music, serial technique, dodecaphony, twelve-tone music), one can begin to accept the

22

possibility that Russian theorists might be more restrictive in their definitions than their

counterparts in the West. The purpose of Chapter 2 is, thus, to discuss these twelve

brands of twelve-toneness and to demonstrate how they can inform an understanding of

some of the apparently “non-serial” aspects of Volkonsky’s Musica Stricta. In Chapter 3,

I will move to a discussion of some of the general issues of multiple-row serialism. As I

see it, there are three broad categories of issues that arise when considering multiple-row

serialism: issues of structure, function and unity. Within this chapter, I shall introduce a

new analytical device, the interval-class succession graph, which can illuminate Denisov’s

music by offering a way of conceptualizing the structure of a twelve-tone row which

heretofore has been unexplored.

Chapters 4 through 7 make up the second large part of the dissertation: the

analytical discussion of three specific pieces involving multiple twelve-tone rows. The

pieces are the following: the first of Five Etudes for Solo Bassoon (1983), and the finales of

Sonata for Alto Saxophone and Piano (1970) and Octet for Winds (1991). I have selected these

particular pieces because their dates of composition span a full twenty-one years of the

mature period of Denisov’s career. It is important to remember that the use of multiple

rows in a single piece is not the composer’s typical modus operandi. His compositional

output is characterized by the use of a wide variety of methods of which serialism is but

one subset. Furthermore, not all the serial pieces in Denisov’s oeuvre are based on

multiple twelve-tone rows. I must make it clear at the outset of this study that it is not

my goal to “unlock the secrets” of Denisov’s compositional style. My goal, as previously

stated, is to examine the details of one specific aspect of this composer’s wide-ranging

style.

23

CHAPTER 2 THE RUSSIAN UNDERSTANDING OF SERIALISM: AN ANNOTATED TRANSLATION

AND ANALYSIS

Before beginning to examine Denisov’s own idiosyncratic approach to serialism,

we must pause to take account of some Russian theoretical thought about serialism, and

to see how this theorizing might inform analysis. For this purpose, I shall present an

annotated translation of the second chapter from Svetlana Kurbatskaya’s book Serial

Music: Questions of History, Theory, Aesthetics [Seriynaya muzïka: voprosï istorii, teorii, estetiki ].

Following this, I shall demonstrate the relevance of Kurbatskaya’s writing for an

informed discussion of the earliest piece of Soviet serial music, Andrey Volkonsky’s

four-movement work for solo piano, Musica Stricta.

ANNOTATED TRANSLATION: SVETLANA KURBATSKAYA, SERIAL MUSIC: QUESTIONS OF HISTORY, THEORY, AESTHETICS (CH. 2)

As mentioned in Chapter 1, Svetlana Kurbatskaya’s book Serial Music: Questions of

History, Theory, Aesthetics (1996) carries the interesting distinction of being the first

Russian-language monograph dedicated entirely to the topic of serial music.1 Peter

Schmelz’ book Such Freedom, If Only Musical addresses the history of Russian writings on

serialism in some detail, and, while it is not my intent to duplicate his efforts here, a few

notes on the topic are in order.2 In the foreword of her book, Kurbatskaya notes that

there is a large body of significant writings on serialism from outside Russia and

identifies some of the reasons for the apparent delay in the creation of a Russian-

language monograph on the topic.

1 Kurbatskaya 1996, 2 and Schmelz 2004, 353 n. 49. 2 See, especially, the section of his Chapter 2 titled “The Second Conservatory,” Schmelz 2009, 39-66.

24

The doubtless “numerical superiority” of foreign studies speaks of the well known, sad circumstances of the Soviet epoch, when ideological dictates in musical science for a long time seriously prevented the purposeful studying of serial (as well as any other “formalistic,” “incomprehensible”) music. Prior to the beginning of the 1980s, publications on problems of [serialism] were extremely rare and isolated (it was not always even possible to call things by their proper names, for example, Descriptions of Modern Harmony, by Yuri Kholopov, 1974). Sometimes between the writing of a work and its appearance in the press, several years passed, and it is not possible to explain this only by the expensive costs of the publishing process. So Edison Denisov’s article “Dodecaphony and the Problems of Modern Compositional Techniques” is extremely valuable for its time, with its thoroughly developed historical and theoretical base, and the abundance of musical examples. It was published in 1969, only six years after it was written.3

Kurbatskaya goes on to mention three Russian books dealing with the topic to some

degree: Kholopov’s Lessons in Harmony [Zadaniya po garmonii ] (1983), Natal’ya Sergeyevna

Gulyanitskaya’s Introduction to Contemporary Harmony [Vvdenie v sovremennuyu garmoniyu]

(1984), and Anton Webern [Anton Vebern] (1984)4 co-authored by Yuri Kholopov and his

sister, musicologist Valentina Kholopova. While none of these books are exactly

“about” serial music, the first two do contain “special sections”5 on serial techniques and

the third, at least, deals with a single composer’s approach to the serial method.

Kurbatskaya notes that, with the appearance of these works, “the position changed, as if

serial dodecaphony was terra incognita (or musica non grata) for domestic musicologists.”6

The Russian sources on serial music which pre-date Kurbatskaya’s book fall into

three categories: propagandistic articles in official publications, “unofficial” essays, and

chapters in books on the broad category of twentieth-century harmony.7 The first

3 Kurbatskaya 1996, 3-4. 4 This book is better known to Western readers in its 1989 German translation, Anton Webern: Leben und Werk. 5 Kurbatskaya 1996, 4. 6 Ibid. 7 It should be noted, of course, that the present discussion does not deal with the assorted Western sources, legal or otherwise, that the young Soviet composers were able to obtain through various channels.

25

category includes writings like Grigoriy Shneyerson’s On Music Living and Dead [O muzïke

zhivoy i mertvoy] (1960) and numerous articles from the official journal Sovetskaya muzïka.

Schmelz’s book shows that, while the purposes of these writings largely were to deride

the serial method, they often backfired.8 Shneyerson’s book, for example, contained a

number of vitriolic statements such as the following: “[Schoenberg] succeeded in

confusing and destroying much in musical art, but he did not succeed in creating

anything…Such manifestations as dodecaphony, abstract painting, and existentialist

philosophy are natural and unavoidable results of bourgeois decadence and its

reactionary ideology.”9 But alongside such blatantly propagandistic statements were a

wide array of musical examples demonstrating a variety of serial techniques. The same is

true of articles by Johannes Paul Thilman and Marcel Rubin that appeared in Sovetskaya

muzïka. Thilman’s article, especially, contained such a detailed description of the serial

method that it functioned more as a “primer” for young composers.10 Countless articles

in the official press, among them Dmitri Kabalevsky’s “Music and the Present [Muzïka i

sovremennost’ ]” (1960) and Noemi Mikhilovskaya’s “Notes about the Works of the Young

[Zametki o tvorchestve molodïkh]” (1960), while not devoted exclusively to serialism,

provided negative comments on any type of Western-influenced formalist writing within

the Soviet Union, speaking largely in vague generalities rather than displaying any

evidence of close study of specific pieces of music. When specific victims were required,

these types of articles frequently turned their attention to the music of the young

These materials, as well as non-printed influences (such as the impact of Glenn Gould’s 1957 visit to the Soviet Union) are discussed at length in Schmelz 2009, 45-66. 8 Schmelz 2009, 41-45. 9 Quoted in Schwarz 1965, 92. 10 See Schmelz 2009, 42-44.

26

composers of the Moscow Conservatory, offering condescending remarks couched as

words of encouragement.11

The second category is comprised of articles meant as responses to those in the

first category. Denisov’s writings figure especially prominently in this category. Schmelz

notes that he was “the most prolific Soviet writer on the topic, the one who had

obviously contemplated and studied serialism the most thoroughly and the most

sympathetically.”12 A glance at a list of his writings13 reveals the following provocative

titles: “For Objectivity and Fairness in the Evaluation of Contemporary Music [Za

ob’ektivnost’ i spravedlivost’ v otsenke sovremennoy muzïki ]” (1965),14 “Some Words about A.

Webern [Neskol’ko slov ob A. Veberne]” (1966), “The New Techniques Are Not a Fad

[Novaya tekhnika – eto ne moda]” (1966), “Dodecaphony and the Problems of

Contemporary Compositional Techniques [Dodekafoniya i problemï sovremennoy

kompozitorskoy tekhniki ]” (1969), and “On Some Melodic Types in Contemporary Music

[O nekotorïkh tipakh melodizma v sovremennoy muzïke]” (1986).15 Although “Dodecaphony

and the Problems of Contemporary Compositional Techniques” is the only one of the

essays which includes the description of specific serial techniques, one of the primary

purposes of these articles appears to be providing a rebuttal to the official sources that

11 The official criticism of Andrey Volkonsky’s student works is especially relevant here. While the Soviet press often praised him as one of the more gifted of the young composers, other articles condemned his atonal and serial efforts. Often, these condemnations placed more blame on Volkonsky’s liberal teachers (Shebalin), or simply his own youth (and, presumably, naïvety) than on Volkonsky’s own intentions. See Schmelz 2005, 148-157. 12 Schmelz 2009, 147. 13 See Kholopov and Tsenova 1993, 237-239; 2002, 323-329. 14 This “writing” is actually a typescript of the remarks that Denisov made at a conference on contemporary music, held by the Union of Composers of the USSR in 1965. The text is found in Tsenova 1999, 22-33. In her commentary on the remarks, Tsenova notes that many of the ideas in this article are similar to those found in the later “Dodecaphony and the Problems of Contemporary Compositional Techniques.” 15 In addition to these essays, Denisov also wrote analyses of a number of specific Western serial works: Webern’s Variations Op. 27 (as discussed in Chapter 1), Schoenberg’s opera Von Heute auf Morgen, Luigi Dallapiccola’s opera Ulisse, and Luigi Nono’s Il canto sospeso.

27

claimed that serialism was an “unnatural” method of composition.16 On the contrary,

Denisov attempts to build a case for the “naturalness” of the serial method by outlining

a quasi-evolutionary path leading from the extended tonality of late Romanticism

through the dissolution of tonality, to atonality, and finally (and inevitably) to serialism.

In an extremely valuable précis of this article, Schmelz points out that, in addition to the

question of serialism’s unnatural origin, Denisov also counters at least one other official

criticism of the compositional technique:

One of the other official criticisms that he is explicitly countering in his thorough discussion…is the idea that twelve-tone music is modish, something that anyone can do, especially those without talent….Denisov also took pains to discuss the negative situations that confront composers as they employ serial techniques and especially total serialism, especially the resulting problems with perceptibility that frequently

17arise.

Both these explanations bear a remarkable similarity to the way Schoenberg

himself dealt with the same issues. Early in Schoenberg’s 1941 essay “Composition with

Twelve Tones (1)” we find the following claim: “The method of composing with twelve

tones grew out of a necessity,”18 which is echoed by Denisov’s statement that “…the

appearance of this [dodecaphonic] technology was the logical consequence of the

development of some parts of European musical art of the 19th and early 20th centuries,

that dodecaphony was not ‘devised’ by anyone, or ‘imposed’ on art…”19 While Denisov

does not use Schoenberg’s oft-quoted phrase “emancipation of the dissonance,” the

paths to serialism described by the two composers are very similar.

Additionally, Denisov’s refutation of the argument that serial composition

requires no talent is reminiscent of Schoenberg’s stance on the issue:

16 Schmelz 2009, 148. 17 Ibid., 149. 18 Schoenberg 1975, 216. 19 Denisov 1969, 489-490.

28

The introduction of my method of composing with twelve tones does not facilitate composing; on the contrary, it makes it more difficult. Modernistically-minded beginners often think they should try it before having acquired the necessary technical equipment. This is a great mistake. The restrictions imposed on a composer by the obligation to use only one [row] in a composition are so severe that they can only be overcome by an imagination which has survived a tremendous number of adventures. Nothing is given by this method; but much is taken away.20

While Schoenberg’s remarks do not mention total serialism or issues of perceptibility,

the underlying tone is much the same.

Schoenberg’s essay is not directly cited in Denisov’s article, but this does not

necessarily mean that he was unfamiliar with the ideas expressed in it. Certainly, he

could have been exposed to Schoenbergian ideas indirectly, from Western publications

or other sources. Schmelz notes that the path to serialism traced by Denisov begins in

much the same way as did the remarks Glenn Gould made from the stage at the Moscow

Conservatory during a 1957 concert which Denisov attended, as discussed in Chapter 1.

While Gould never uttered the phrase “twelve-tone composition” during his lecture, his

remarks were clearly intended to show the underlying connections between the works he

performed: excerpts from Bach’s Art of the Fugue and Goldberg Variations, Berg’s Sonata

Op. 1, Webern’s Variations Op. 27, and the first and fourth movements from Krenek’s

Piano Sonata Op. 92, no. 4.21 Furthermore, Denisov’s article does cite Schoenberg’s

Theory of Harmony (although it is unclear what version of this book he had in his

possession), Hans Eisler’s Reden und Aufsätzen, and mentions the titles of three books by

René Leibowitz (Schönberg et son école, Introduction à la musique de douze sons, and Histoire de

l’opéra). While it may be impossible to trace Denisov’s familiarity with Schoenberg’s

ideas to one single source, it seems irrefutable that this familiarity did exist.

20 Schoenberg 1975, 223. 21 For a fuller account of Gould’s performance in Moscow, see Schmelz 2009, 55-59.

29

The category of apparently “reactionary” articles has another connection to the

first category: non-Western understandings of what could be considered the

fundamentals of the serial method. Thilman’s article describes “rotation,”

“interpolation” and “substitution” alongside Schoenberg’s traditional three mirror forms

(inversion, retrograde, and retrograde inversion).22 Denisov also observes that, in serial

compositions, the row can be divided into segments which can be used independently,

but will always maintain their connection to the original series.23 Both of these articles

present as primary serial techniques a number of row manipulations which are

fundamentally non-Schoenbergian.

The third category of Russian writings on serialism which pre-date Kurbatskaya’s

book involves monographs with individual chapters devoted to the subject. While a

thorough survey encompassing all such books is beyond the scope of the present

dissertation, I will mention just one representative example.

Natal’ya Gulyanitskaya’s Introduction to Contemporary Harmony (1984) has chapters

devoted to the following topics: chords [akkordika], modality [modal’nost’ ], tonality

[tonal’nost’ ], atonality [atonal’nost’ ], and serialism [seriynost’ ]. At fifty-three pages in length,

the chapter on serialism in this monograph represents the longest treatment of the topic

we have discussed thus far. Most of the chapter, however, treads over already-covered

ground. This chapter is divided into eight sections with the following titles:

1. Preliminary Information [Predvaritel’nïye svedeniya] 2. The Series and Its Purpose in the Composition [Seriya i yeyo naznacheniye v

kompozitsii ] 3. The Structure and Ordering of the Series [Struktura i sistematizatsiya seriy] 4. Serial Forms and Transposition [Seriynïe formï i transpozitsii ] 5. Questions of Texture and Form [Voprosï fakturï i formï ]

22 This information is summarized from Schmelz 2009, 43. Schmelz speculates that these operations may come from a familiarity with Krenek’s writings on serialism as well as his Lamentations of Jeremiah. 23 Schmelz 2009, 149.

30

6. 12-Tone Harmony [12-tonovaya garmoniya] 7. Combinatoriality of the Units of Harmonic Language in Serial Compositions

[Kombinatorika edinits garmonicheskogo yazïka v seriynïkh kompozitsiyakh] 8. Methodological Recommendations [Metodicheskiye rekomendatsii ]

Compared with the writings we have surveyed to this point, Gulyanitskaya’s chapter is

most notable for including a section on combinatoriality.

The preceding survey, albeit incomplete, gives us some sense of the state of

Russian research in serialism prior to Kurbatskaya’s monograph. In the foreword to her

book, Kurbatskaya identifies Webern’s 1905 “C#-C-E” string quartet as “the earliest

experience of the serial organization of musical material.”24

As Example 2.1 shows, Webern’s quartet contains no obvious twelve-tone rows,

does not appear to be organized around any sort of ordered completion of the total

chromatic, and was written at least sixteen years before Schoenberg’s first completely

serial movement.25 This excerpt, at least, appears to be better described as organized

around transformations of the opening “motto,” C#-C-E (labeled x in Example 2.1),

and might find itself comfortably at home in an introductory course on post-tonal

analysis as an example of a composition based primarily on transformations of [014].

While it may seem strange to a Western theorist to call this movement “serial,”

Kurbatskaya’s statement must be understood as representing a more generalized

definition of “serialism.”

This is reflected in a number of entries in the MES for words which Western

theorists would generally use more or less interchangeably: serialism [serial’nost’ ], serial

technique [seriynaya tekhnika], and dodecaphony [dodekafoniya]. All these definitions were

written by Yuri Kholopov. As these terms appear in Kurbatskaya’s book, I will delay

24 Kurbatskaya 1996, 3. 25 Whittall 2008, 31.

31

EXAMPLE 2.1: WEBERN, STRING QUARTET (1905), MM. 1-13

specific discussion of their definitions for the moment, being satisfied for the time being

with the mere observation that these terms are all defined differently from one another

in the MES.

There is an additional Russian term, mentioned in Chapter 1, for which no exact

Western counterpart exists, encompassing all of the terms in the previous paragraph, and

others: dvenadtsatitonovost’, which is most closely translated as “twelve-toneness.” In an

essay analyzing aspects of Volkonsky’s Musica Stricta, Schmelz credits Kholopov with

32

coining this term, which is used to describe “atonal music that sounds twelve-tone.”26 In

the Musical Encyclopedic Dictionary, Kholopov defines the term in a somewhat more global

sense:

Twelve-toneness (dodecatonicism [dodekatonika], twelve-tone harmony [dvenadtsatitonovaya garmoniya]) – a kind of twelve-step sonic system where each sound can function as an independent element. Twelve-toneness is connected with many new types of techniques in the music of the 20th century – symmetrical harmonies (for example, in I. F. Stravinsky, O. Messiaen), “synthetic chords” (A. Roslavets), dodecaphony, tropes (J. M. Hauer), 12-tone rows (…for example in D. D. Shostakovich, R. K. Shchedrin), 12-tone fields, chords…, free atonality and other models of the 12-tone field.27

Kurbatskaya, a former Kholopov student, adopts this term in its broader sense.28

In her book, twelve-toneness is an over-arching concept of which she defines twelve

specific varieties. As defined in Chapter 2, these twelve categories are as follows:

1. “Free atonality” [svobodnaya atonal’nost’ ] 2. Technique of tonal centers [tekhnika zvukovogo tsentra] 3. Technique of “synthetic chords” [tekhnika “sintetakkordov”] 4. Twelve-note chords [12-zvukovïye akkordï ] 5. Technique of twelve-tone rows [tekhnika 12-tonovïkh ryadov] 6. Technique of twelve-tone fields [tekhnika 12-tonovïkh poley] 7. Technique of tropes [tekhnika tropov] 8. Serial technique [seriynaya tekhnika] 9. Dodecaphony [dodekafoniya] 10. Microserialism [mikroseriynost’ ] 11. Total serialism [serializm] 12. Serialism [seriynost’ ]

The general organization of Kurbatskaya’s chapter seems to owe a debt to

George Perle’s Serial Composition and Atonality (the second edition of which is cited by

Kurbatskaya) in regard to two specific issues. The manner in which she proceeds

through the definitions of her twelve categories of twelve-toneness is not unlike the

26 Schmelz 2004, 325. 27 Kholopov 1990, 164. 28 Kurbatskaya and Kholopov also authored a book together which presents analyses of selected pieces by Pierre Boulez and Edison Denisov. See Kurbatskaya and Kholopov 1998.

33

organization of the second and third chapters of Perle’s book. Specifically, the order in

which Kurbatskaya presents her first three topics is the same as in Perle’s book, even

citing several of the same examples, such as Schoenberg’s Erwartung, Skryabin’s Piano

Sonata No. 7 and Roslavets’ Three Compositions for Piano.29 Furthermore, Perle’s manner of

dividing his chapter “Motivic Functions of the Set”30 into subsections titled “The Set As

a Theme,” “The Set As a Melodic Prototype,” and “Segmentation” is echoed to some

degree by Kurbatskaya, who, as we shall see, takes care to note whether the series is

treated as a melodic device or not, and whether or not the series in treated as a single,

whole unit, or as a collection of smaller parts.

***

While a translation of the entire text of Kurbatskaya’s Chapter 2, “On the System

of Terminology [O sisteme terminologii ],” is provided in Appendix 1, a summary with

general notes and commentary is found here.

As the preceding discussion shows, the purposes of Kurbatskaya’s chapter are

first to define twelve-toneness, and second to define the twelve different categories that

fall under its umbrella. Her definition of twelve-toneness does not differ significantly

different from Kholopov’s: “Twelve-toneness is a property of the musical material

according to which each of the twelve tones of the chromatic scale can be used as

29 Erwartung is discussed by Perle on p. 19 and by Kurbatskaya on p. 32, though Kurbatskaya only mentions the work by title (without a detailed musical example), having already directed the reader to Perle’s book in her first footnote of the chapter. Both authors give identical examples from Skryabin’s Piano Sonata No. 7, found on p. 43 in Perle’s book and p. 34 in Kurbatskaya’s. Finally, Perle discusses Roslavets’ Three Compositions on pp. 43-44, and Kurbatskaya cites the same work (again, without a detailed musical example) on p. 34. 30 The reader is reminded that Perle uses the word “set” for what we have been calling a “series.”

34

independent units of the musical fabric.”31 The phrase “musical fabric [tkan’ ]” is one

that Kurbatskaya uses frequently in this chapter, often in relation to whether or not a

particular compositional device is responsible for “the entire musical fabric [vsya tkan’ ],”

or every note on the musical surface.32

In the chapter’s introductory section, Kurbatskaya links the concept of twelve-

toneness with another term from Kholopov’s MES: dodecatonicism. The way the term

is presented in both Kurbatskaya’s chapter and Kholopov’s definition suggests that these

two authors consider this word to be synonymous with twelve-toneness: it is enclosed in

parentheses, with no explanation, after the word “twelve-toneness.” Kurbatskaya writes,

“…twelve-toneness (dodecatonicism, twelve-tone harmony) is the system of thinking

based on the autonomy of each of the twelve pitch classes,”33 associating

dodecatonicism and twelve-tone harmony with twelve-toneness, in exactly the sam

as does Kholopov’s definition (quoted earlier). In an essay titled “After Prokofiev,”

Schmelz provides a bit more detail on the origin of this term. Schmelz’s research traces

this word to a 1965 article by Soviet musicologist Arnold Sokhor titled “On the Na

and Expressive Possibilities of Diatonicism.” Sokhor’s new word was intended to

account for the expanded diatonic features of Prokofiev’s music, which, by having a

similar appearance to the word dodecaphony, allowed Sokhor “to portray Prokofie

fundamentally tonal composer whose works offered either a substitute or complement to

Schoenberg’s system.”

e way

ture

v as a

34 Kholopov and Kurbatskaya’s apparent connection of this word

to twelve-toneness could possibly indicate that these authors allow for an understanding

of twelve-toneness in a tonal context, as well.

31 Kurbatskaya 1996, 32. 32 By “the musical surface,” I am referring to all the notes in the score, without any sort of reduction. 33 Kurbatskaya 1996, 33. 34 Schmelz 2008, 515.

35

Kurbatskaya’s twelve categories of twelve-toneness group themselves as follows:

#3 (technique of “synthetic chords”) is “a version of”35 #2 (technique of tonal centers);

#9 (dodecaphony) and #10 (microserialism) are each “a type of”36 #8 (serial technique).

We can also group together the categories which are related to the specific compositional

procedure of an individual composer: #2 (technique of tonal centers) refers to the

technique of Skyrabin, #3 (technique of “synthetic chords”) describes the technique of

Nikolai Roslavets, #6 (technique of twelve-tone fields) references Nikolai Obukhov’s

concept of “total harmony,” and #7 (technique of tropes) is based on the method of

Hauer.

The definitions of several of Kurbatskaya’s categories are self-evident to the

Western reader. Specifically, her definition of “free atonality,” twelve-note chords, and

total serialism are not significantly different than their Western counterparts. Even so, a

few brief comments on these concepts are in order.

In the section on “free atonality,” Kurbatskaya mentions the

“hemitonic…method of symmetrical interval groups.”37 The hemitonic method is

described in Kholopov and Tsenova’s book on Denisov, though it appears to date back

to Valentina Kholopova’s 1973 article “Toward One Chromatic Principle in Twentieth-

Century Music.”38 A full description of the theory of hemitonic groups is neither

necessary for, nor within the scope of the present dissertation, but can be summarized as

an analytical approach which considers combinations of ic1 with itself or with other

interval classes. Kholopov and Tsenova thus define two categories of hemigroups (short

35 Kurbatskaya 1996, 34. 36 Ibid., 37, 38. 37 Ibid., 32. 38 Kholopova 1973, 331-344.

36

for “hemitonic groups”): “1. a semitone with a semitone (coupling: 1+1+…) and 2. a

semitone with other intervals (1+n).”39

This section also lists, by title or opus number, five different pieces which can be

considered as representative examples of music featuring a freely atonal type of twelve-

toneness. Of these five pieces, Kurbatskaya only provides in her text notation and an

explanation for one: Webern’s Five Pieces for Orchestra Op. 10, no. 3. Her example is

reprinted here as Example 2.2.

EXAMPLE 2.2: EXCERPT FROM WEBERN OP. 10, NO. 3 (FROM KURBATSKAYA)

39 Kholopov and Tsenova 2002, 112. This section is not present in the original Russian version of this book. Rather, it appears to have been inserted from Kholopov’s contribution to a Festschrift created in honor of the composer’s 65th birthday. See Kholopov 1995, 84-94.

37

Unfortunately, Kurbatskaya’s verbal explanation of this particular musical

example leaves much to be desired. Her comments are as follows: “…the opening

section of Piece No. 3 (Op. 10) rests on a thirteen-note complex (eleven different pitch

classes), including homogeneous groups which are distributed between a melody and a

chordal ‘background.’”40

This example seems to be getting at the concept of (near) pitch-class

complementation. The bottom staff of the example shows the two primary elements of

the musical fabric: a six-note chord labeled “background” [fon], and a group of seven

quarter-notes, played by violin and horn, labeled “melody” [melodiya]. The melody

contains seven pitch-classes that are almost entirely separate from the six pitch-classes in

the accompanying background (the pitch classes D and Ab/G# are common to both

groups). Though these two musical elements do not form the full aggregate when taken

together, the idea of primarily non-intersecting pitch-class sets appears to be at the heart

of Kurbatskaya’s example.

In addition, the bottom staff of the example shows the generative interval classes

of both the background chord and the melody. Beginning with the background chord

and progressing to the melody, Kurbatskaya labels the eleven distinct pitch classes,

clearly revealing the common pitch classes and makes the absence of pitch class G

obvious. Notes 1-6 are stemmed together and labeled with a “4” above the beam,

which, of course is the interval class formed by G# and E. Within this ic4, this

hexachord is broken up into the interval patterns < 1 4 > and < 4 2 >. Notes 7-10 are

stemmed together and labeled as forming ic5, which is further divided into the interval

pattern < 1 5 1 >. This interval pattern is nearly continued, as the final three notes in

40 Kurbatskaya 1996, 32.

38

the example form the pattern < 1 5 >. With this diagram, Kurbatskaya is trying to make

the point that the background is built primarily out of ic4 and the melody is built out of a

combination of ic1 and ic5.

Total serialism is another of Kurbatskaya’s categories which resonates with

Western musicians. Following Schmelz, I have translated Kurbatskaya’s word seriynost’ as

“serialism,” even though the suffix -nost’ suggests that “serialness” might be a more

literal translation. I have translated Kurbatskaya’s term for this technique, serializm, as

“total serialism,” in order to avoid any confusion with the Western word “serialism.”41

Based on the definitions given, it is clear that Kurbatskaya’s seriynost’ is meant in a more

wide-ranging sense than is serializm. As such, I will refer to these two terms by their

familiar Western counterparts: “serialism” and “total serialism,” respectively.

Category #10, microserialism, deserves some special attention. It is this category

that allows Kurbatskaya to make the claim noted earlier that Webern’s C#-C-E quartet

represents the earliest instance of serial organization.42 She defines a microseries as a

“series of fewer than twelve pitch classes.”43 In addition to the Webern quartet, she also

cites two Bransle dances from Stravinsky’s Agon,44 “In Memoriam Dylan Thomas,” and

Britten’s “Symphony-Concerto” for cello and orchestra.

Perhaps the most notable aspect of Kurbatskaya’s discussion of microserialism is

her advancement of three distinct, but related, terms. The three terms microseries

[mikroserii], incomplete series [nepolnaya seriya], and subseries [subseriya] all relate “to the

41 Schmelz 2004, 353 n. 49. 42 See note 24. 43 Kurbatskaya 1996, 38. 44 Kurbatskaya refers to “two Bransle dances from the ballet ‘Agon.’” It is curious that Kurbatskaya only mentions “two Bransle dances” when there are, in fact, three such dances in Agon: Bransle Simple, Bransle Gay, and Bransle Double. From the musical example she gives of the series of “two Bransle dances,” it is clear that she is referring to the Bransle Simple and the Bransle Gay.

39

ordering of a small number of pitch classes,”45 but all have slightly different meanings.

Of the three, a microseries appears to be the only one which is a complete unit in itself.

Kurbatskaya says that an incomplete series is “part [chast’ ] of a complete twelve-tone

series, which functions independently [of the complete series] in a specific section of the

work.”46 On the other hand, a subseries is a “segment of a series, which functions as a

series on a micro-level.”47 At a glance, these terms appear to be synonymous, but

Kurbatskaya seems to treat the words “part” and “segment” [segment ] differently. In

Kurbatskaya’s use, the former has more of a top-down connotation, while the latter

implies a more bottom-up perspective. Specifically, the concept of an incomplete series

views the whole series as the given entity, and the very existence of the “part” of it which

is used independently depends on the existence of the series as a whole. The concept of

a subseries, however, takes the “segment” as the generative unit, from which a larger

(twelve-note, or otherwise) series is built, through various transformations. Kurbatskaya

cites no particular examples of incomplete series, although the third movement of

Denisov’s The Sun of the Incas is a clear example of this, as the entire movement is based

entirely on transformations of the first hexachord of the row established in the first

movement of the cantata. As an example of a subseries, Kurbatskaya cites the modus

classicus of the technique: the row from Webern’s Concerto for Nine Instruments Op. 24. She

also cites the row from Lutosławski’s Funeral Music in this category.48

As previously mentioned, the most important aspect of Kurbatskaya’s categories

lies in the careful distinction she makes between four concepts that appear to be

essentially synonymous to Western readers. These concepts are her fifth, eighth, ninth,

45 Kurbatskaya 1996, 38. 46 Ibid. 47 Ibid. 48 Ibid., 39.

40

and twelfth categories: technique of twelve-tone rows, serial technique, dodecaphony,

and serialism, respectively. It is in the definitions of these four types of twelve-toneness

that Kurbatskaya’s debt to Kholopov is the most clear: there are no major differences

between Kholopov’s definitions of these terms in the MES and Kurbatskaya’s

definitions in her monograph.

Underlying her discussion of these four concepts is a cautious differentiation of

the following two pairs of terms: “twelve-tone composition” and “dodecaphony,” and

“series” [seriya] and “row” [ryad]. “Twelve-tone composition” is meant as a general term,

referring to a “system of thought,” while “dodecaphony” is a more specific “method of

composition.”49 Kurbatskaya likens this to the German language distinction between

Zwölftonmusik and Zwölftontechnik. Kurbatskaya’s differentiation between “series” and

“row” is based on a similar idea. A series is an organizational principle which

“determines the appearance of relationships in the work.”50 In contrast, a row is

primarily a surface-level phenomenon: a row is a “horizontally presented series.”51

The fifth category, the technique of twelve-tone rows, begins first with a

definition of “row.” In Kurbatskaya’s words, “a row is the horizontal occurrence of

non-repeating pitch classes…which is used as a melodic construction and is not the sole

source of the musical fabric.”52 In a footnote, she notes the curiosity that melodies

meeting her criteria have appeared in pre-20th century music as well, citing the subject

from the B minor fugue in Book 1 of J.S. Bach’s Well-Tempered Clavier and the

introductory theme from Liszt’s Faust Symphony. While it is clear that she is not trying to

imply that these pieces are based on the technique of twelve-tone rows, these pieces

49 Ibid., 37. 50 Ibid. 51 Ibid., 36. 52 Ibid., 34.

41

meet the criteria established in Kurbatskaya’s definition of this technique: the “row” is

found as a melodic construction, and, although transformations of that row may be used

(particularly in Bach’s B minor fugue), the row is “not the sole source” of the musical

material. But she does cite three bona fide examples of the technique of twelve-tone rows:

the last of Alban Berg’s Altenberg Lieder Op. 4, Rodion Shchedrin’s Polyphonic Notebook

and Shostakovich’s Symphony No. 14. The inclusion of these particular examples

demonstrates the significance of her claim that the row is not the sole source of all pitch-

class material. The importance of this claim cannot be overstated for an understanding

of the serial practices of composers like Volkonsky and Denisov.

As mentioned earlier, Kurbatskaya defines dodecaphony (category #9) as a

specific type of serial technique (category #8). Schmelz’s “Soviet serial bull’s-eye”

diagram, shown in Example 2.3, is helpful in understanding the relationship between

these two categories. Dodecaphony, then, is a specific type of serial technique where the

series contains exactly twelve pitch classes.

EXAMPLE 2.3: PETER SCHMELZ’S “SOVIET SERIAL BULL’S-EYE” DIAGRAM53

53 Reprinted from Schmelz 2009, 135.

42

Distinguishing between the technique of twelve-tone rows and serial technique

requires the invocation of Kurbatskaya’s distinction between row and series. Essentially,

one can arrive at Kurbatskaya’s definition of serial technique by starting with the

definition of technique of twelve-tone rows, changing “twelve-tone row” to “series,” and

adding the requirement that the series be the source of the entire pitch fabric. As

Kurbatskaya says, serial technique is “one of the forms of contemporary musical

composition where the entire musical fabric is derived from an invariant [invarianta]

series and its continuous recurrences (in basic and derived forms).”54

Kurbatskaya closes her chapter by discussing “serialism” [seriynost’ ] as category

#12. As she defines it here, serialism is really a different sort of category than the

preceding eleven. It is clear that she considers serialism a wider-ranging phenomenon

than any of the other categories she has discussed. She claims that serialism is “one of

the universal categories of musical thought in the 20th century, applied to a wide range of

genetically related phenomena.”55 She gives a two-part definition for serialism, the first

part of which is not strikingly different from her definition for serial technique. But the

second part of the definition is especially important for the present study of multiple-

row serialism in the music of Denisov: serialism is the “…principle of musical thought

by a series (or multiple series) [seriyami ].”56 While she does not directly discuss her use of

the plural form of series here, it is clear that she is referring to two different ideas. First,

she is allowing for the inclusion of total serialism, in which there may be multiple series

governing multiple musical parameters. Her own example shows the twelve-tone pitch

series, the twelve-unit durational series, the five-unit dynamic series, and the five-unit

54 Kurbatskaya 1996, 36. 55 Ibid., 40. 56 Ibid.

43

articulation series from Oliver Messiaen’s Île de feu. Secondly, by using the phrase

“multiple series” here, she is allowing (or at least, not prohibiting) the use of two or

more distinct series governing the same musical parameter.

This chapter of Kurbatskaya’s book provides insight into the Russian

understanding of serial composition and, more generally, twelve-toneness. The fact that

her work resonates with (and was, in fact, written under the influence of) that of the

prominent Russian theorist Yuri Kholopov, and the fact that its conceptual origins are

based on Denisov’s writings indicates that Kurbatskaya’s point of view is not dismissible

as idiosyncratic or invalid. As the next section of this dissertation will demonstrate, it is

not only intellectually worthwhile to categorize different types of “twelve-toneness” in a

Russian context but it is analytically useful, as well.

***

ANALYSIS: ANDREY VOLKONSKY’S MUSICA STRICTA (1956-1957)

Andrey Volkonsky was one of the “young composers” who developed an

interest in serialism during the Thaw. He and Denisov were students at the Moscow

Conservatory during the same time period. However, Volkonsky was given an academic

leave and eventually expelled from the Conservatory. While it is an oversimplification to

say that he was expelled simply because he possessed scores of modern Western music,

it does seem that this played some role in his removal from the school, though this was

not the official reason given by the Conservatory administrators.57

57 Volkonsky’s biography, including details regarding his expulsion, is thoroughly treated in Schmelz 2009. See Schmelz 2009, 68-77.

44

Composed shortly after the death of Stalin, Volkonsky’s Musica Stricta is generally

accepted as the first piece of Soviet serial music.58 Some general observations about the

compositional techniques in each of the four movements will reveal that this piece

actually provides examples of several of Kurbatskaya’s categories of twelve-toneness.

The first movement is organized around transformations of an unordered pc set, and

therefore does not fit into standard Western definitions of serialism,59 but does fit in

Kurbatskaya’s second category, the technique of tonal centers. On the other hand, the

second, third and fourth movements do fit Western definitions of serialism, as they are

based on the transformation of ordered twelve-tone rows. All three of those movements

derive their pitch material from multiple, simultaneous twelve-tone rows: the second

movement features four distinct rows used in counterpoint, while the third and fourth

movement each use two, and all three movements make use of non-serial atonal

material.

MOVEMENT 1: ANDANTINO

In the opening movement, the A-B-A’ form (see Example 2.4) can be interpreted

as arising from a conflict between two of Kurbatskaya’s categories of twelve-toneness:

the technique of tonal centers and the technique of twelve-tone rows.

58 Schmelz 2009, 81. Schmelz has discussed Musica Stricta in his dissertation, book, and two separate articles. See Schmelz 2002, 84-99; 2004, 323-326; 2005, 160-179; and 2009, 81-89. 59 In a slightly broader sense than Kurbatskaya, the term “freely atonal” is often used by Western theorists to define note groups by their intervallic and/or pitch-class content, rather than by their order.

45

EXAMPLE 2.4: MUSICA STRICTA (MVT. 1) – FORM

A B A’

m. 1 10 17 21 31

[0126] [0126] [0126] dissolves into [014], [013], etc. [0126]

technique of tonal centers technique of 12-tone rows technique of tonal centers

The A and A’ sections of the first movement are saturated with different forms

of set class 4-5, [0126]: literally, every single note within these two sections can be

explained by set-class membership, with the exception of an Eb in the last chord of m.

13.60 In fact, the different forms of 4-5 are actually all transpositions of the unordered

pc set presented in m. 1, {0128}. It is this {0128} tetrachord that functions as the “ton

center” of these two sections, and, as Kurbatskaya’s definition requires, “the entire

musical fabric is worked out by its regular repetitions in specific interval relationships.”

al

61

EXAMPLE 2.5: MUSICA STRICTA (MVT. 1) – MM. 1-9

60 This note could be a misprint. As it is, it forms [0136] with the other notes of the chord. However, were this note an E-natural, rather than Eb, it would form [0126]. 61 Kurbatskaya 1996, 33.

46

The opening nine measures are shown in Example 2.5, with the initial {0128}

labeled as X, and all other occurrences of 4-5 labeled as transpositions of X. Over the

course of the two A-sections (mm. 1-16, mm. 31-35), Volkonsky uses eleven of the

twelve possible transpositions of X; T1(X) is the only transposition that is never used.

The B-section (mm. 17-30) of this movement begins with more transformations

of 4-5, but gradually, that set class loses hold of the pitch structure. The set-class

structure of the B-section is much less consistent, and is dominated by a seemingly freer

interaction between trichords, highlighting 3-3, [014]. Example 2.6 shows this interplay

of trichords in mm. 21-22.


Throughout this section, the use of melodic aggregates appears to be the primary

organizing force. As Example 2.7 shows, the first move away from the transpositions of

X comes in m. 20, where a [0134] is sandwiched between T3(X) and T0(X). Here, the

[0134] represents the complementary pitch classes to the combined {0123458e} of T3(X)

and T0(X).62 By adding this [0134], Volkonsky effectively unites two transformations of

62 As the interval-class vector of 4-5 [210111] indicates, T3 is the only transposition level that can be applied to X without resulting in any pitch-class duplication.

47

X into a single twelve-tone row. As such, it is possible to interpret this melodic line as

representing a transition between the use of the technique of tonal centers to the

technique of twelve-tone rows.


From this point until the end of the B-section, each measure contains one or two

complete rows. There are four exceptions, which occur in m. 21, 25, 26 and 30. All of

these exceptions involve the doubling or repetition of a single pitch class and the

omission of another. Referring back to Example 2.6, the first two beats of m. 21 in the

right hand present a near-aggregate, with Bb omitted, and C occurring twice. Example

2.8 shows a similar case (m. 30), where Ab appears twice, but A-natural is missing.

EXAMPLE 2.8: MUSICA STRICTA (MVT. 1) – M. 30

48

Volkonsky’s use of the technique creates no fewer than fourteen different rows, but

none of these rows are repeated in this movement, or in any of the other three

movements of Musica Stricta. Volkonsky appears to be using the technique of twelve-

tone rows (in exactly the manner Kurbatskaya describes) in order to freely generate a

wide variety of musical material, in contrast with the method of transpositions of a single

“tonal center.”

MOVEMENT 2: ALLEGRETTO

In the second movement, Volkonsky uses four different twelve-tone rows, and

he always uses them in a horizontal manner, with vertical sonorities resulting from

combinations of rows (and row forms) rather than individual row segments or partitions.

The movement’s form evolves as the result of the process of juxtaposing these different

rows, as shown in Example 2.9.


m. 1 4 5 6 7 8 9 10 11 12 13 14 15 16 17 19

AP2 BP3 AP2 CP8 ARP2 BP4 AI2 DPt ARIt CP0 ARP2 BP0 AI2 DP1 ARIt CP9 AP2

DP5 DP8 CP8 BP4

49

I have labeled the four different rows using the letters A-D, followed by a row-form

label.63 The square brackets on the diagram indicate the presence of freely atonal pitch

material, which I will discuss later. These four rows are shown in Example 2.10.

EXAMPLE 2.10: MUSICA STRICTA (MVT. 2) – ROWS A-D

ROW A:

INT: 6 2 1 2 e 3 6 7 1 2 e ROW B:

INT: 3 t 3 7 7 e 5 9 7 6 1 ROW C:

INT: t 1 t 7 1 2 7 e 2 3 2 ROW D:

INT: 4 5 5 6 2 1 2 2 4 t 1

As suggested by the diagram in Example 2.9, the four rows are not presented

with equal emphasis. Clearly, Row A is the primary row of the movement – it is the only

row that is presented in counterpoint with another form of itself. Rows B, C and D

serve to provide contrasting material to Row A, while allowing each horizontal voice to 63 All told, movements 2-4 of Musica Stricta use eight different twelve-tone rows. I will label each of these with a capital letter, A-H.

50

still be serial. The four rows themselves bear little resemblance to each other in terms of

their respective INTs. The most significant such connection seems to be that Rows B

and D both contain two consecutive occurrences of ic5.

XAMPLE 2.11: MUSICA STRICTA (MVT. 2) –IC 5 SEGMENTS IN ROWS B AND D E

Volkonsky makes this connection audible on the musical surface near the very

beginni ng of the movement. In mm. 4-5, BP3 and DP4 both share the trichord {279}.

For BP3, these pitch classes occupy order positions < 3 4 5 >, while in DP4, they occupy

order positions <

1 2 3 >. Both of these trichords are presented with the same rhythm,

one immediately after the other. At no other time in the movement do BPx< 3 4 5 > and

DPy< 1 2 3 > actually state the same pitch classes, although they usually occur with the same

51

rhythmic profile, and in close succession. The four occurrences of these [027] segments

of Rows B and D are shown in Example 2.11. It should also be noted that the initial

statement (mm. 4-5) is immediately preceded by freely atonal material, stating exactly t

same pitch classes, removed from the context of any twelve-tone row (Example 2.12).

These three fast statements of {279} serve to attune the listener’s ears to these short 5-

cycles that will occur at various points throughout the movement, separating the Row A

material from the groups of Rows B, C and D.

he

XAMPLE 2.12: MUSICA STRICTA (MVT. 2) – MM. 3-4

64

E

The kind of inter-row invariance exemplified by the shared {279} described

e

Section 1: AP2 and CP0 share {4579} BP3 and DP5 share {346} and {279}

Section 2: e}

Section 3: in Section 2)

39t}

above also appears to guide Volkonsky’s choice of row-forms throughout the piece,

though not in any systematic way. In the four large formal sections (refer to Exampl

2.9), the following inter-row invariances appear:

CP0 and DP5 share {0te} AP2, BP0, and CP8 share {013} AP2 and CP8 share {0139tARP2 and CP8 share {567} ARP2 and CP8 share {567} (asARP2 and BP4 share {457} ARP2 and CP8 share {013} (as in Section 2) AI2 and DP1 share {09e} AI2 and CP8 share {9et} BP4, CP8, and DP1 share {

64 For more on 5-cycles and cycle theory in general, see Headlam 1996.

52

BP4 and CP8 share {239te}

Section 4:

With the exception of the opening three measures, forms of Row A are always

e

e

nd finally,

t

e

XAMPLE 2.13: FORMS OF ROW A IN TWO VOICES

AI2 t

CP8 and DP1 share {678} AI2 and DPt share {1345} ARIt and BP4 share {3578}ARIt and CP9 share {124te}

presented in pairs. The pairing of Row A forms cycles through AP2, ARP2, AI2, ARIt,

and finally returning to AP2. In each Row A section, there are two row forms: one in th

right hand part of the piano, and the other in the left. These two row forms always

involve one “old” and one “new” form of the row. Volkonsky begins with AP2 in th

opening three measures. In the next Row A section (mm. 6-8), AP2 remains, but this

time it is accompanied by a new form, ARP2. In mm. 11-12, ARP2 remains,

accompanied by AI2. AI2 remains in mm. 15-16, with the addition of ARIt, a

in the final measures of the movement, AP2 returns as the lower voice to the still-presen

ARIt. The choice of forms of Row A is based on the opening pitch of each form; the

forms of Row A alternate between starting on D and F#. The assignment of row form

to linear voice follows a pattern best described as a form of invertible counterpoint.

Each new row form is presented by the pianist’s left hand and is moved into the right

hand when the next new row form enters. This change of voicing is shown in Exampl

2.13.

E RH (old): ---- AP2 ARP2 ARI LH (new): AP2 ARP2 AI2 ARIt AP2 mm. 1-3 6-8 11-12 15-16 19-21

53

Rows B, C and D are presented in a similar manner. As before, each row is

-

,

s

XAMPLE 2.14: FORMS OF ROWS B, C AND D IN THREE VOICES

Freely atonal music is interspersed throughout the movement, between each of

art

restricted to a single linear voice: high, middle or low. As such, the texture of the

movement is constantly changing from the two-voiced Row A sections to the three

voice multiple-row sections. Each time that these three rows are used simultaneously

they are presented in a different vertical alignment. Because there are only four section

in the movement that use these three rows, Volkonsky is only able to present these rows

in four of the six possible vertical arrangements. These arrangements are shown in

Example 2.14.

E High: BP3 CP8 BP4 DPt Middle: CP0 BP0 DP1

65 CP9 Low: DP5 DP8 CP8 BP4 mm. 4-5 9-10 13-14 16-17

the Row A sections and multiple-row sections (specifically, in mm. 3-4, 6, 8, 10, 12-13,

14, 16-17, 19, and 21-22). As I have previously suggested, these brief figures are based

on short cycles of fourths/fifths, clearly derived from the ordered interval content of

Rows B and D.66 These gestures function as transitional signals for the listener, set ap

65 The first pitch of this D-row form is notated as D-natural, but the remainder of the row is clearly from the form beginning on Db. 66 These little fragments cannot easily be categorized as 5-cycles in the Headlam 1996 sense of the term, as the intervals are sometimes presented as perfect fourths/fifths and sometimes as diminished or augmented

ense of “quartal”-ness remains throughout each of these figures. fourths/fifths, which leads to a variety of [027]s, [016]s, and [015]s. Despite differences in the specific interval content, the overall s

54

from the surrounding music by virtue of their accented articulation. As such, the second

movement juxtaposes dodecaphony, multiple-row dodecaphony, and freely atonal, cyclic

elements.

MOVEMENT 3: LENTO RUBATO

sica Stricta functions as an interlude between two

s of

XAMPLE 2.15: MUSICA STRICTA (MVT. 3) – ROWS E-F

The third movement of Mu

predominantly contrapuntal movements. Volkonsky uses two different twelve-tone

rows in this movement, but neither of them bears any strong resemblance to the row

either surrounding movement. These rows are shown in Example 2.15.

E

ROW E:

INT: 4 5 8 5 3 1 4 1 1 3 4 ROW F:

INT: 1 8 6 2 1 1 4 e t 8 t

Volkonsky makes use of only one form of each row, EP5 and FP6, and those two

forms a

each time (sehr kurz, kurz, mäßig lang, or lang). These pauses give the music a fragmented

lternate throughout the movement (one per measure). Each measure is set apart

from the one which follows it by a pause, the approximate duration of which is specified

texture, in which each measure is heard as a complete, finished entity.

55

This movement features a similar conflict between multiple-row dodecaphony

and free atonality as we saw in the second movement. However, this conflict manifests

itself in a different way in the third movement. Noting that there are only four measures

(mm. 1

ulation

ile

f

4-16, 18) of non-row-based music in this movement, one might be quick to claim

that the dodecaphonic material dominates the texture. However, in the dodecaphonic

measures, the strictness of twelve-tone presentation is varied throughout. The first five

measures are presented with few or no order-position exchanges, but beginning in m. 6,

the orderly presentation of pitch classes dissolves to the point of no longer being

“dodecaphonic” in any true sense of the word. In this way, this movement seems to

blur the distinction between what Kurbatskaya calls a “row” and a “series.” A logical,

though ultimately un-answerable question is this: how much order-position manip

can one apply to a row before it is no longer recognizable as a melodic construct? Wh

I do not assume to be able to answer this question, it seems clear that, over the course o

this movement, what began as a clearly presented horizontal twelve-tone row is gradually

“hidden” beneath the musical surface. At certain points during the movement (such as

the four measures mentioned earlier in this paragraph), the row is so completely hidden

that it no longer appears to exert any control over the pitch organization. The row has

been transformed into a series, and the series has been dissolved into freely atonal

material. Example 2.16 shows how Volkonsky sets up this dodecaphonic dissolution in

m. 6 by means of contrapuntally inverting a partition scheme of FP6 which was

presented in m. 2.

56

EXAMPLE 2.16: MUSICA STRICTA (MVT. 3) – MM. 2, 6

In m. 2, the right hand presents FP6 order positions < 0 1 2 4 5 7 8 > while the

left hand presents < 3 6 9 t e >. The two parts interlock rhythmically in such a way that,

with the exception of the simultaneous presentation of 6 and 7, all the pitches occur in

precisely their serial order. Measure 11 maintains this partition scheme, but in opposite

voices: the right hand now presents < 3 6 9 t e > and the left hand presents { 0 1 2 4 5 7

8 }.67 But the actual order of presentation is changed drastically. 0-3 are presented at

the beginning of the measure, followed by the right hand’s < 6 9 t >, the left hand’s < 5

7 >, and the right hand’s 4 occurs at the same time as the left hand’s 7. The measure

concludes with 8, played in the left hand. The consistency of partitioning between m. 2

and m. 6 allows us to understand that the series is still present, but that its original

ordering is slowly being obliterated on the musical surface.

Similar partition schemes can explain the serial underpinnings of the music from

mm. 7-10. Measures 7 and 9 are both based on EP5, but both are missing a single p

class. In m. 7, D# is missing, and in m. 9, C is missing. Ex

itch-

ample 2.17 shows how the

order-p

osition patterns introduced in m. 7 are maintained in m. 9.

67 The order positions 4 5 and 7 are internally rotated.

57


Despite the relative freedom of ordering demonstrated in measure 7, it is clear that the

order position sets {0 1 9}, {3 5 6 7}, {t e} and {2 5} play a role in connecting these two

easures. Example 2.18 shows an analogous situation with the two statements of FP6 in m

mm. 8 and 10.


From mm. 7-20, there are only four measures that present either E- or F-row

with minimal order-position manipulatio ,

with order position 6

ns. Measure 12 is a fairly clear statement of FP6

delayed to occur simultaneously with 9, which connects the interval

58

[11] of {4 5} in the left hand with the interval [11] of {6 9} in the right hand. Measure

11, 17 and 21 present two six-note polychords (the first of which is familiar from m. 1)

as shown in Example 2.19.

EXAMPLE 2.19: MUSICA STRICTA (MVT. 3) – M. 11

s

The sonority {23569t} occupies order positions 0-6 of the row form EP5, and is realized

as an Eb-minor triad above a D-minor triad. In the first hexachord, both hands present

gmental trichords from EP5, producing these two members of set class [037]. The se

second hexachord, however, does not present such segmental trichords. As Example

2.19 shows, the right hand presents order positions {6 7 9} while the left hand presents

{8 t e}, essentially exchanging order positions 8 and 9. While the left hand still produ

a [037], the right hand produces a contrasting set-class, [026]. Despite the fact that [02

is not a subset of Row E, it is a prominent subset of Row F. In this way, Volkonsky is

able to use order position manipulations to create a connection between the otherwise

distantly related Rows E and F.

MOVEMENT 4: ALLEGRO MARCATO

The final movement of M

ces

6]

usica Stricta is, in many ways, similar to the second

ovement. Both movements are primarily contrapuntal, with different rows and row m

59

forms presented in an almost exclusively linear fashion, and formal divisions are marked

by the j is uxtaposition of serial and non-serial techniques. The major difference in form

that, in the fourth movement, the freely atonal sections are expanded into large formal

sections, rather than just acting as transitional signals between formal sections.

EXAMPLE 2.20: MUSICA STRICTA (MVT. 4) – ROWS G-H

ROW G:

INT: 6 e e e e e t t 1 t e ROW H:

Made up of the two new twelve-tone rows shown in Example 2.20, the fourth

movement is cast in an A-B-A’ form similar to that of the first movement (see Example

.21). The serial material is treated in a manner contrapuntally similar to the second

movem

-

INT: 6 t 5 e 6 5 6 t 6 5 5

2

ent. Beginning with GP1 in the upper voice and HPt in the lower voice, the

opening 13 measures state GP1 three times, moving from the upper voice, to the lower,

and back to the upper voice. In invertible counterpoint, GP1 swaps places with the H

rows, HPt, HP5, and HPt again. This is shown in Example 2.22.

60


XAMPLE 2.22: FORMS OF ROWS G AND H IN MM. 1-13

igh: GP HP5 GP1

ow: HPt 1 t

B- triple counterpoint, similar to that of the

o secti f t move is case, however, the row forms do

not change from statement to statement: only their vertical arrangement changes.

A

m. 1 5 9 10 13 15

17 20 25 GP1 HP5 GP6 GP1 GI1 GRP7 HPt HP0 non-row HP7 non-row HPt GP1 GP2 HRP6 HRP2 HP7 clusters HPt

E

H 1

GPL HP mm. 1-4 5-8 10-1368

The section also features a section of

multi-r w ons o he second ment. In th

68 At this point, a third voice (middle) enters on GP2.

B

28 31 34 37 42 44 48 HPt HRP6 HRP2 HP9 GP6 HPt HP9 HP9 HPt HPt HP9 GP6 GP6 HP9 GP6 HPt

A’

55 7 61 64 71 GP0 HRP4 non-row-based material [0157] HP9 HPt HPt

5

61

As in the multiple-row sections of the second movement, this section accounts

for four of the six possible vertical arrangements of these three row forms. The metho

Volkonsky uses to present these four vertical arrangements is virtually identical to th

d

at

which h

GP HPt 9

iddle: HP t HPt HP9 6

GP6 HPt

a ple e second set of three row forms, one row

he ne

ansformations involve moving the row form in the highest voice to the lowest voice,

e used in the second movement.

EXAMPLE 2.23: TRIPLE COUNTERPOINT IN MM. 28-54

High: HPt HP9 6

HP

GPM 9 HP

Low: ---- GP6 HP9 mm.: 28-33 34-36 37-41 42-47 48-54

2.

w

As Ex m 23 sho s, from the first to th

form remains in the same voice, which the other two switch places.69 T xt two

tr

while the other two row forms move “up” one position.


69 To be precise, the stationary voice in the analogous part of the second movement was found in the lowest voice, not the middle voice as is the case here.

62

It is within the A- and A’-sections that the non-row-based material occurs,

nd of m. 19 marks the spot

at which non-row-based music begins to take control of the musical surface. As shown

in Example 2.24, this material makes use of octave doublings and prominent occurrences

of ic3, an interval class that does not occur in either Rows G or H. A varied restatement

of this material, with right- and left-hands inverted, followed by a new, freely atonal bass

melody and fortissimo statement of [0157], also forms the conclusion of the movement,

nd the entire piece. These measures are shown in Example 2.25.

toward the end of each section. In the first A-section, the e

a


Although there are no prominent usages of {2489} in this or earlier movements,

[0157] is the final discrete tetrachordal subset of Row H. In fact, < 8 2 9 4 > does occur

at order positions 8-e of HI7. But, as this row form has not occurred at any prior point

63

in this movement, it does not seem logical to claim that the movement ends on a

nse of finality to the phrase

without being used in a row-based context. The final fourteen measures, in effect, return

the piece to the world of free atonality, while still maintaining an underlying connection

to Row H.

In Musica Stricta, we have seen a somewhat idiosyncratic first attempt at serial

composition. Volkonsky uses not only a variety of row forms, but eight completely

different twelve-tone rows, and juxtaposes them with non-serial musical material.

Despite the fact that six of the eight rows used in Musica Stricta have some sort of

combinatorial properties, Volkonsky never takes advantage of these possibilities.70

Furthermore, it is only in the second movement that he seems concerned with making

other smaller invariances between rows salient features of the musical surface.

That Volkonsky thought he was writing an orthodox twelve-tone composition71

reveals

o view

onsky’s serial “missteps” as the uncertain efforts of a young composer, we

segment of this row form. The use of [0157] here gives a se

that his understanding of Schoenbergian/Webernian serialism was incomplete.

However, his influence on his fellow students at the Moscow Conservatory, and on

future generations of Soviet composers, has in some ways formed a distinctly Russian

brand of serialism. Kurbatskaya’s twelve categories of twelve-toneness permit us t

Volkonsky’s varying compositional decisions through a lens which allows for a finer

distinction between differing degrees of serial-ness, rather than being forced to decide

whether the piece is or is not serial. While it is convenient for Western theorists to

dismiss Volk

x x

are present in the eight rows of Musica Stricta: Row A is combinatorial at APx and AI(x+1); Row B is no

Row E is not combinatorial; Row F is combinatorial at FPx and FRI(x+6); Row G is combinatorial atand GI(x+1); Row H is combinatorial at HPx and HI(x+7).

70 Excluding the trivial case between any row-forms P and RP , the following combinatorial relationships t

combinatorial; Row C is combinatorial at CPx and CRI(x+9); Row D is combinatorial at DPx and DI(x+3); GPx

71 Schmelz 2005, 171.

64

n, we shall see that the case is not always so clear. In the later chapters of this dissertatio

shall return to this idea in the context of three serial works by Edison Denisov, all

composed after he had acquired a reasonably full and well rounded understanding of

“classical” (i.e., Schoenbergian) dodecaphonic techniques.

65

CHAPTER 3 ON MULTIPLE-ROW SERIALISM

GENERAL ISSUES OF MULTIPLE-ROW SERIALISM

Let us begin with a fundamental question: what constitutes a “multiple-row”

scenario? While the answer to this question may seem self-evident, we shall see that it is

not so straight forward, even within the works of the Second Viennese School. Though

Schoenberg spoke against the use of multiple rows (see Chapter 2), he apparently

rejected the idea on a theoretical level, rather than on a practical compositional level. By

the time he wrote his Variations for Orchestra Op. 31, Schoenberg had evolved his

principal technique of developing variation for twelve-tone pieces that is based on

different “partition schemes” – deriving internal, non-adjacent, but relatively ordered,

motivic segments from a row.1 While these derived motives have different interval

patterns, they are usually presented in a row context, with a more-or-less clear derivation.

However, in his book Schoenberg’s Serial Odyssey, Ethan Haimo shows that several of

Schoenberg’s works actually use multiple rows.

The String Quartet No. 3, like several of its predecessors, uses more than one set. However, unlike Opp. 26 and 29 where the subsidiary sets were generated by partitioning out elements from a succession of local statements of the principal set, here Schoenberg begins the composition with clear statements of the different sets. (Schoenberg’s next composition, Von Heute auf Morgen, Op. 32, also uses more than one set.) In the present instance, Schoenberg used three sets – or, more precisely, one principal set with two ordering variants.2

Haimo speculates that Schoenberg’s use of multiple rows in the third movement of the

Wind Quintet Op. 36 “was probably something quite mundane: having used rotation

extensively in the second movement, Schoenberg felt the need for even more melodic

1 See Haimo 1990, 20, 22-26. Haimo’s term for these partition schemes is “isomorphic partitioning.” 2 Ibid., 150.

66

material to provide variety. The extraction of a new twelve-tone set from the original set

must have seemed like a plausible option.”3 In this last sentence, Haimo makes an

important observation about the nature of these multiple rows – they are extracted from

the original row, and therefore may be interpreted as falling within a somewhat larger

concept of the “row class.” Rather than developing this direction (as did his student,

Alban Berg, as described below), according to Haimo, the composition of the String

Quartet No. 3 and the Variations for Orchestra, however, Haimo suggests that “Schoenberg

learned the compositional techniques that would permit him ‘to draw themes’ from the

set with sufficient flexibility that he would have no need of multiple orderings.”4

In place of the use of multiple rows, then, partition schemes applied to a single

row plays an important role throughout the variations of Schoenberg’s Op. 31.5 In the

fifth variation, “the row is decomposed into six semitone dyads,”6 which, as shown by

Tuukka Ilomäki, makes it impossible to indisputably decipher Schoenberg’s progression

of row forms.7 This brings Ilomäki to an interesting question about this particular

variation: “is the variation based on rows or is it based on dyads?”8 For our purposes,

the answer to this question in regard to the specific case of Schoenberg’s Variations is not

particularly crucial. But it does provide an interesting case study of a portion of a work

by Schoenberg in which it is unclear how the row relates to the musical surface.

Certainly, many such passages can be found in Schoenberg’s later works.

3 Ibid., 117. 4 Ibid., 150-151. Haimo’s terminology here is a bit different than mine. When he refers to “multiple orderings” he is referring to multiple orderings of the total chromatic, or multiple twelve-tone rows. 5 Ibid., 169, 171, 175-176, 178-180. 6 Ilomäki 2007, 31. 7 Ilomäki demonstrates that “the same set of ordered semitone dyads can always be drawn from at least two row forms.” See Ilomäki 2007, 34. 8 Ilomäki 2007, 41.

67

In Berg’s music, row partitions are pulled out and used independently of the

original row context, and newly derived twelve-tone rows appear. One major issue in

Berg scholarship is the nature of the derivations of these “new” rows from a principal or

main row.9 It is well known that the three secondary rows used in the Lyric Suite are

derived successively by order position exchanges from the preceding row: the all-

interval row used in the first movement generates a second row by exchanging the pitch

classes at two particular order positions, that new second row generates a third row in a

similar fashion, and the third row generates a fourth row in a similar (but somewhat

more complex) manner.10 The derivational pathway from the first to the fourth row is

clear, but the INTs of the first and fourth rows bear little resemblance to each other.11

This process begs the following question: given a parent row and its derived offspring,

how dissimilar can the two be before the relationship between them is irrelevant?

We can use definitions of degrees of similarity between two rows to consider this

question. Ilomäki’s 2008 dissertation presents a number of different ways of measuring

similarity between distinct twelve-tone rows.12 These different similarity measures

highlight different properties of the rows themselves: 1) similarity may be based on the

coincidence of specific pitch classes at or near specific order positions in two rows; 2)

similarity may be based on shared subsegments between two rows; 3) similarity may be

based on the ordered series of intervals of two rows, and so forth. While these similarity

measures all enable the analyst to assign a discrete value representing how similar two

9 Reich 1936, Perle 1959, Jarman 1979, Hall 1985 and Headlam 1985, 1996 all contribute to a discussion of the relative independence and role of these “multiple rows.” 10 Headlam 1996, 248. 11 This is even more important in Lulu, where a number of rows are derived from a single “Basic Row” but are used independently of each other, representing individual characters in Leitmotif fashion. See Headlam 1985. 12 I am using the word “similarity” in a slightly informal manner. To be sure, some of the so-called “similarity measures” found in the music theoretic literature actually measure dissimilarity. See Buchler 1997, 31 and Ilomäki 2008, 35-36.

68

rows are, they do not provide an answer to the question in the previous paragraph. In

this context, aspects of Ilomäki’s impressive work will be discussed in more detail later in

this chapter.

In the end, it seems impossible (or at least difficult) to provide a definitive

answer to the question of multiple rows in any sort of general way. While we may be

willing to use the label “multiple-row piece” to describe pieces like Berg’s Lyric Suite and

Volkonsky’s Musica Stricta, it seems clear that the nature of the multiple rows in each of

these pieces is substantially different from the other. Whether the pitch fabric of a piece

is taken from two distinct rows or from two rows, one of which is derived from the

other, the characteristics of multiple-row pieces therefore must be addressed on a case-

by-case basis. In beginning to analyze a piece which takes its pitch material from more

than one twelve-tone row, it is necessary to examine the relationship(s) between the rows

themselves. In the course of studying these relationships, the analyst is confronted with

three broad categories of issues specific to multiple-row serialism: issues of structure,

function and unity.

ISSUES OF STRUCTURE

Structural issues of multiple-row serialism involve relationships between the rows

themselves, removed from the context of the specific composition. Do the two (or

more) different rows share any common properties, such as interval successions,

interval-class content, and so forth? I have already mentioned Ilomäki’s work on the

similarity of twelve-tone rows, but it is worth examining certain aspects of it more closely

here.

69

In his dissertation, Ilomäki presents seventeen different similarity measures for

relating any of the 12! twelve-tone rows.13 In so doing, he identifies five different

conceptions of twelve-tone rows, and argues convincingly that each of these conceptions

“brings some aspect to the fore.”14 Ilomäki’s five conceptions are the following: the

twelve-tone row as a vector, as a set of ordered pairs (which is, of course, influenced by

Babbitt), as a set of subsegments, as a set of subsets, and as a sequence of pitch-class

intervals. Of these five, the last appears to be the most useful for the purposes of the

present study of music based on multiple row classes. Simply put, if we are interested in

determining what the abstract relationship is between two distinct row classes, it seems

most appropriate to consider the elements of a twelve-tone row class that remain

invariant (or are varied in a predictable manner) among all members of that row class.15

When comparing two (or more) distinct row classes, we should be most

interested in a method of comparison that allows us to make observations about the

entire row class, rather than making a comparison between a single member of each row

class, and claiming that comparison holds true for all members of each class.16 As the

present dissertation defines a row class as a set of up to forty-eight twelve-tone rows

13 Despite the fact that I have been consistently using the word “row” to mean “row class” in this dissertation, I will not follow that convention in the paragraphs discussing Ilomäki’s work. As Ilomäki’s goal is to measure the similarity between any two ordered sequences of twelve non-repeating pitch classes, his notion of “row” refers to any one of the 12! orderings of the twelve pitch classes. See Ilomäki 2008, 6-7, and Babbitt 1960, 248. 14 Ilomäki 2008, 92. 15 Otherwise, we find ourselves in the potentially awkward position of being forced to find a single row form that can be used as a representative for the entire row class. Of course, this is the case with the most common approaches to pc-set theory. The list of prime forms found as an appendix in Forte 1973 (among a myriad of other sources) does exactly this: it uses a particular member of a given set class as the representative of the entire set class. It is this member which is often used as the “name” of the set class, unless the Forte names “3-1,” “3-2,” etc. are used. It is certainly possible to decide upon such a representative member of any given row class in a particular composition, in a variety of ways. We could choose the first member of that row class used, or the most commonly used member, and so forth. 16 Ilomäki addresses this concern briefly when discussing the spaces formed by different conceptions of twelve-tone rows. His solution is to define the distance between any two finite sets of objects (row classes, in this case) as “the distance between their closest members.” See Ilomäki 2008, 76-77.

70

related by the canonical twelve-tone operations (transposition, inversion, retrogression,

and the combination of those operations), the INT is the only element of all members of

a row class which is varied in a predictable manner for each member, and can be used to

distinguish any row class X from any row class Y. Ilomäki rightly notes that conceiving

of a twelve-tone row as a succession of ordered pitch-class intervals means that we

“abandon the permutational approach”17 pioneered by Babbitt, which has been

fundamental in twelve-tone theory. While I do not wish to suggest that a permutational

perspective is not valid in multiple-row music, it is my belief that viewing a row as an

ordered succession of intervals allows the analyst the ability to conceptualize all members

of a given row class in an easier, more intuitive manner, thus making this approach

useful in distinguishing between multiple row classes.

As such, when examining the structural relationship between two (or more)

twelve-tone rows in a particular piece, we will focus primarily on the similarities between

the ordered succession of intervals and interval classes of the rows in question. Later in

this chapter, I will define one specific analytical tool which will aid us in this kind of

comparison.

ISSUES OF FUNCTION

Functional issues of multiple-row serialism involve questions of how the

different rows are used within a particular piece. Regarding a multiple-row piece like

Berg’s Lulu, the function of the different rows seems clear: the rows function in a

Leitmotif-like manner, with each row being linked to a particular character.18 In this case,

the rows serve a specific dramatic function. But for pieces of absolute music, the 17 Ilomäki 2008, 230. 18 Headlam 1985, 198.

71

function of multiple rows is less clear. It is necessary to examine how the rows

themselves interact during the piece. Are they presented simultaneously? Are they

juxtaposed? Does one row seem to be “primary” and the other(s) serve as contrasting

material, perhaps analogous to traditional themes in tonal music?

A consideration of Soviet composers is especially relevant in this context. In a

2004 essay, Schmelz notes that “[o]nly in Russia was there a pervasive tendency to

construct pieces with multiple twelve-tone rows that in fact obeyed none of the

traditional Schoenbergian ‘laws’ of twelve-tone music (or if they did, did so only

selectively).”19 This does not mean that Soviet serial music was entirely unorthodox,

however. In Chapter 2, we saw that Volkonsky’s serial language involved the use of

multiple rows and the combination of dodecaphonic music with freely atonal material.

But the specific dodecaphonic techniques he applied were not so far removed from

those of Schoenberg: the generation of a large amount of pitch material from the

transformation of these rows, the use of partition schemes, and so forth. Volkonsky’s

early serial efforts were profoundly influential to his peers at the Moscow Conservatory:

Schnittke and Denisov, in particular. As Denisov later recalled, “[p]recisely these

compositions [Musica Stricta and Suite of Mirrors, another of Volkonsky’s early twelve-tone

works] were the ones that exerted a very great influence on us. On all of us.”20

In fact, it was not only the young generation of Moscow composers in the 1960s

who felt Volkonsky’s influence. His influence was felt, at least indirectly, by Dmitri

Shostakovich. Schmelz discusses Shostkovich’s “very personal”21 implementation of

serial techniques in the late 1960s, and shows their connections to the serial techniques

19 Schmelz 2004, 326. Though Schmelz’s comments here refer most directly to the “technique of twelve-tone rows,” they are still relevant in the present context of Soviet serialism in general. 20 Quoted in Schmelz 2009, 67. 21 Schmelz 2004, 305.

72

used earlier by the younger generation of Soviet composers: Pärt, Schnittke, Volkonsky

and Denisov. Schmelz points out that Shostakovich’s use of twelve-note rows in his

Seven Verses of Aleksandr Blok Op. 127 (1967) demonstrates a use of a single tone row as a

melody. In Schmelz’s words, “the ‘row’ retains its identity as a single, unchanging

melodic figure,”22 and states that the use of the row (which occurs, untransposed and

unvaried, in only one of the seven movements of Op. 127) functions “as a catalyst of

harmonic instability and atonality,”23 consistent with the “unclear harmonic language of

the work [which] reflects the apocalyptic text of the poem, which presents images that

are part nocturnal hallucination, [and] part ecstatic vision…”24

In Shostakovich’s Sonata for Violin Op. 134 (1968), String Quartet No. 12 Op. 133

(1968) and Symphony No. 14 Op. 135 (1969), the composer utilizes multiple twelve-tone

rows “to create an effect of long-term shifting instability.”25 But in all these cases,

Shostakovich’s row usage falls more into Kurbatskaya’s category of “technique of

twelve-tone rows” and not the dodecaphony found in the works of the Second Viennese

composers. The rows are occasionally repeated in slightly varied form, but in general,

they each have a fundamental rhythmic profile, as well as a common melodic contour.

In short, these rows are used mostly as melodic or motivic constructions.26 This is

markedly different from Ernst Krenek’s comments that the row not be used as a theme,

but it is fully consistent with Kurbatskaya’s definition of the “technique of twelve-tone

rows.”27

22 Ibid., 306-307. 23 Ibid., 307. 24 Ibid., 306. 25 Ibid., 309. 26 Ibid. 27 Krenek 1940, 3. Krenek’s treatise is one to which Arvo Pärt (in Tallinn, Estonia) evidently had access, as well as a circle of student composers in Kiev. See Schmelz 2009, 51.

73

In Chapter 2, we also saw multiple rows used for a different functional purpose.

The second movement of Musica Stricta uses four distinct rows in a form-generative

manner. To summarize, the movement’s form evolves from the juxtaposition of a

single, primary row with a complex of three secondary rows.

Certainly, the question of whether multiple rows function in a piece primarily as

contrasting themes or as generators of form is not always a clear “either/or” situation. It

is not difficult to imagine a piece of music in which contrasting themes serve the

purpose of also defining large-scale form. The sonata form-like structure of Denisov’s

Concerto for Guitar and Orchestra (1991) provides a representative example. Example 3.1

shows a form chart of this single-movement concerto, taken from Elena Barasch’s article

“The Concertos of Edison Denisov.”28 The Primary and Secondary Rows of the Concerto

are shown in Example 3.2.

EXAMPLE 3.1: CONCERTO FOR GUITAR AND ORCHESTRA – FORM

Exposition

m. 1 38 68

primary theme secondary theme primary theme Primary Row

Development I Reprise Development II Coda

85 193 238 283 Secondary Row Primary Row

28 This essay actually contains two form charts for the Concerto: one with only the largest structural divisions indicated, and a more detailed one, with smaller formal divisions indicated as well. The diagram presented here is a combination of the two: it is essentially the larger-scale form chart, but with a few of the more specific details of the second chart (measure numbers, and smaller divisions in the exposition, in particular). See Barasch 1999, 361 and 366. The indications “Primary Row” and “Secondary Row” are not Barasch’s terms, but the expositional divisions “primary theme” and “secondary theme” are hers (glavnaya partiya and pobochnaya partiya, respectively).

74

EXAMPLE 3.2: CONCERTO FOR GUITAR AND ORCHESTRA – ROWS

PRIMARY ROW

SECONDARY ROW

It must first be noted that neither the Primary nor the Secondary Row accounts

for the entire pitch fabric; there are significant portions of the Concerto which do not

appear to be drawn directly from either row. As such, the presence of the words

“Primary Row” or “Secondary Row” in Example 3.1 should be taken as summarizing the

material of the section in question, rather than being a specific indication of exactly

where a particular row is found. The Primary Row is presented at the Concerto’s opening,

as the first statement by the solo guitar. This row recurs several times during the

Concerto, but is treated primarily as a static melody: rhythmically fixed, and never inverted

or presented in retrograde (but it is transposed at least once, at m. 136). The final

statement of the Primary Row is shown as Example 3.3.

EXAMPLE 3.3: CONCERTO FOR GUITAR AND ORCHESTRA, GUITAR, MM. 349-352

75

The Secondary Row forms the bulk of the pitch material of the Development I

section, where a variety of different forms of the row are used. The opening statement

of the Secondary Row, divided among twelve different instruments, is shown as

Example 3.4.

EXAMPLE 3.4: CONCERTO FOR GUITAR AND ORCHESTRA, MM. 130-132

BPt

These two rows allow us the opportunity to view a potential type of interaction

between the two functional categories identified earlier. The Primary Row functions

76

largely as a recurring melody, as a sort of ritornello which bookends the entire Concerto, and

even invades the presentation of the Secondary Row’s material. The Secondary Row, on

the other hand, is not presented as a theme, per se, but rather, its presence indicates the

beginning of a new formal section.

Often, structural and functional issues of multiple-row serialism go hand in hand.

In Volkonsky and Denisov’s multiple-row serialism, when two rows function as

contrasting themes in a work, those rows are usually differentiated by having different

intervallic characteristics. The same might be true of two rows used in a form-generative

manner, as we will see in the analysis of Denisov’s Octet for Winds in Chapter 6.

ISSUES OF UNITY

Finally, the issues of unity deal with the way in which a composer does (or does

not) achieve a unified musical structure when that structure is based upon a variety of

generative sources. Given that different rows have different characteristics (that may or

may not be measurable in the sense described by Ilomäki), does the use of different rows

destroy the unity of a composition? Though the answer to this question might vary

from composer to composer, or even from composition to composition, it seems that,

as evidenced by his quotations found in Chapter 2, Schoenberg’s answer to this question

would likely be a resounding “yes.”

As it turns out, Denisov himself appears to have had varying thoughts on the

topic at different points during his career. In Denisov’s article “Dodecaphony and the

Problems of Modern Compositional Techniques,” the composer writes the following:

Sometime in addressing dodecaphonic techniques, the following question arises: why is the composer limited to use only one series in a work, rather than using several different series? First, the presence in a work of a new series does not enrich it as all possible sonic combinations can be

77

obtained by the application of the same series. Secondly, the presence of two or more series introduces a certain stylistic differentiation into the work, disrupting the…strength of a single unified thematic basis [however, we see examples of the simultaneous use of several series (A. Berg, I. Stravinsky)]. Usually, even when creating large works, composers are limited to one series, thus giving some monothematicism to the cycle, and if they apply several different series (such as A. Berg’s Lulu), they prefer to use so-called derived series, where the series is brought out in some way from the original.29

Though published in 1969, this essay was written in 1963, while Denisov was in the

relatively early phases of his “second conservatory.” As mentioned in Chapter 1, the

serial works Denisov composed prior to 1964 are much closer to Schoenbergian ideals

than are his later works. At some point between this 1963 article and Denisov’s 1966

Laments and Five Stories of Mr. Keuner (both of which use multiple twelve-tone rows), the

composer seems to have made an about-face on the “disruption” inherent in multiple-

row serial music.

As we shall see in the following chapters, the rows in Denisov’s multiple-row

pieces typically have sharply contrasting intervallic material. In the third movement of

the Sonata for Alto Saxophone and Piano, for instance, the primary row30 is based on T7

transpositions of Dmitri Shostakovich’s D-S-C-H motto, < 2 3 0 e > and < 9 t 7 6 >,

while the secondary row is almost entirely transformations of set-class [037]. In the

second movement of the Octet for Winds, Row A uses mostly ic1 and ic2, while Row B is

made up of the palindromic INT < 6 5 6 e 6 e 6 e 6 5 6 >, which forms four

transformations of [016]. As shown in Example 3.2, in the Concerto for Guitar and

Orchestra, the Primary Row is derived from transformations of [026], while the Secondary

Row has a much less uniform INT.

29 Denisov 1969, 518. 30 I do consider the first row of this movement to be primary, because it, by itself, formed the basis of the pitch material from the first movement as well.

78

In all three cases, we see a similar pattern: one row is of highly regular intervallic

construction (in all cases, these regular rows are made up of only three interval classes),

and the other row has a wider range of interval (or interval-class) content. There is a

sense in which these rows seem to be paired in such a way that they complement each

other. In the passage quoted earlier, Denisov says, “the presence of two or more series

introduces a certain stylistic differentiation into the work.”31 Perhaps Denisov

determined that this thought did not have to be viewed in the negative context in which

it is presented in his essay. This kind of stylistic differentiation does not necessarily

indicate a less unified musical structure.

***

INTS, INT-CS, AND BIPS

The remainder of this chapter will focus on the introduction of a particular

means of examining the structural relationship between multiple rows. The third

movement of Denisov’s Sonata for Alto Saxophone and Piano derives much of its pitch

material from transformations of two distinct twelve-tone rows. Example 3.5 shows the

row from the first movement. As previously noted, this row (Row A), with its frequently

occurring ics 1 and 2, begins with Shostakovich’s famous D-S-C-H (D-Eb-C-B) motto.

The second hexachord of the row begins with the same motto at T7. In the third

movement, this row is joined by a second twelve-tone row, featuring triadic and seventh-

chord subsets. This row (Row B) is shown as Example 3.6.

31 Denisov 1969, 518.

79

EXAMPLE 3.5: SONATA FOR SAXOPHONE, ROW A

BIP: 11111122335 BIP-Vector: [622010] EXAMPLE 3.6: SONATA FOR SAXOPHONE, ROW B

BIP: 33333344455 BIP-Vector: [006320]

In Examples 3.5 and 3.6, each row’s INT is given beneath the row. Below the

INT for each row, I have added an INT-C, which is the ordered succession of interval

classes in the row. While the INT-C is one level of abstraction beyond the INT of a

row, it offers the advantage of representing both the transposed and inverted forms of

the row simultaneously. As is well known, given an INT for row form x, one can

produce the INT of a row form related by inversion to x by substituting each entry of

x’s INT with its mod 12 complement. Because each interval and its mod 12

complement are members of the same interval class, it should be obvious that the INT-

C of row form x is identical to the INT-C of all row forms related to x by transposition

and inversion. Furthermore, reversing the order of all entries of row form x’s INT-C

yields the INT-C for all row forms related to x by inversion and retrograde inversion.

However, it is important to note that the INT-C carries the potential pitfall of not

necessarily defining a single row class. While an INT can unambiguously define a row

80

class, it is possible for two distinct row classes to share an INT-C.32 Despite this

possibility, the existence of non-unique INT-Cs does not concern us presently.

The information in the INT-Cs of Examples 3.5 and 3.6 is also displayed in

unordered fashion by using Allen Forte’s BIPs, or basic interval patterns.33 The BIP-

Vectors in these examples are not something Forte explicitly defines, but their

construction simply displays the information of each BIP in the same format as Forte’s

interval-class vectors. 34 A quick inspection of the two BIP-Vectors shows little in

common between the two rows, in terms of unordered interval-class content. However,

even though the interval classes contained in these two rows are mostly different, their

relative distributions are not so different; each BIP-Vector has one 6, and at least one 2.

One might also entertain the possibility of understanding the 3 in Row B’s BIP-Vector

as having been broken into 2+1 in Row A’s vector.

If we consider different ways of describing the interval content of that row, it is

easy to see the decreasing level of specificity from INT to INT-C to BIP. An INT-C

and a BIP show the same information, but respectively with or without specifying the

order of the interval-classes of a row. If we desire to “fill out” our imaginary continuum,

we might consider investigating partial orderings of the interval or interval-class content

of a row.

Looking at the INT-C of Row A, we can list that row’s interval-class successions

as “protocol pairs,” following the convention established in Lewin (1976)35:

32 This property defines a twelve-tone analog to the Z-related sets of pc set theory. Where Z-related sets are defined as those that share a common interval-class vector, but are not members of the same set class, these “Z-related rows” share a common INT-C, but are not members of the same row class. An examination of the properties of these “Z-related rows” could be an interesting topic for future research. 33 Forte 1973, 63-73. 34 This idea is adopted in Ilomäki 2008, 235. 35 Musical applications of partial orderings are also discussed in Starr 1980, Morris 1987 and 2001, and Ilomäki 2008.

81

Row A = {(1,1), (1,2), (1,3), (2,1), (2,5), (3,1), (5,1)}

While this set of protocol pairs accounts for every pair of successive interval classes in

Row A, it is clear that this set does not constitute a true partial ordering. In a brief but

thorough explanation of the mathematical concept of partially ordered sets, Ilomäki

defines a partial ordering as “a binary relation that is reflexive, transitive and anti-

symmetric.”36 In verbal form, the protocol pair (1,2) states that ic1 precedes ic2. The

set of protocol pairs that makes up Row A includes the contradictory pairs (1,2) and

(2,1), which violates the requirement of anti-symmetry: if ic1 precedes ic2, then ic2 does

not precede ic1.

37

EXAMPLE 3.7: BERG, LYRIC SUITE (PRIMARY ROW)

{(2,3), (3,4), (4,1), (5,2), (6,5), (7,6), (8,9), (9,t), (t,7), (e,8)}

All-interval rows provide the only occasion in which such an account of all of a

row’s interval successions in a row can result in a proper partial ordering. The INT of

the original row from Berg’s Lyric Suite provides a suitable example (see Example 3.7).

In this case, the set of protocol pairs is completely anti-symmetric; there are no

contradictions. This set of protocol pairs can be considered a true partial ordering

because all the intervals are distinct. It should be clear without example that, considered

36 Ilomäki 2008, 284. 37 Lewin 1987 defines a “precedence-oriented” system as one in which “there is no pair of nodes (N, N’) such that N both precedes and follows N’.” See Lewin 1987, 210. Clearly, this is not possible with twelve-tone rows examined in terms of interval class successions; there are 11 positions in an INT-C, but they must be filled with only 6 interval classes.

82

in terms of interval classes, no twelve-tone row (including the Lyric Suite row, and any

other all-interval row) can be described completely by partial orderings.

THE ADJACENCY MATRIX AND INTERVAL-CLASS SUCCESSION GRAPHS

The inability of interval-class successions to produce mathematically correct

partial orderings does not necessarily indicate that a similar concept might not be useful.

Example 3.8 uses an adjacency matrix to show the succession of adjacent interval classes

from the Sonata for Alto Saxophone’s Row A.

EXAMPLE 3.8: ADJACENCY MATRIX FOR SONATA FOR SAXOPHONE, ROW A

1 2 3 5

1 1 1 1 0

2 1 0 0 1

3 1 0 0 0

5 1 0 0 0

The matrix contains the interval classes of the row as both column and row

headers. Every cell in the interior of the matrix is filled either with a 1 or 0, depending

on whether a particular interval-class succession is present in the row. If the interval-

class succession (i,j ) occurs in the row then a 1 is placed in the cell in the i th row and j th

column. For example, the matrix tells us that ic1 is followed by ics 1, 2 and 3 in Row A,

83

but never by ic5.38 The adjacency matrix provides a convenient way of accounting for

the interval-class successions of a twelve-tone row class.

At this point, it is worth reminding the reader that the adjacency matrix has been

filled based on the presence or absence of a particular interval-class succession in a row’s

INT-C. This means that the matrix only accounts for the interval-class succession of the

transposed and inverted forms of the row. In order to account for the retrograde and

retrograde-inverted forms of the row, one must simply “swap” all 0’s for 1’s and 1’s for

0’s. This does not create any serious problems, as the INT-C will refer to the same row

class (or classes) whether it is read forward or backward.

Looking at the adjacency matrix in Example 3.8, we can easily see that ic2 is

followed by either ic1 or ic5, but it is always preceded by ic1. In the matrix’s row (2,j ),

1’s are found in the cells (2,1) and (2,5), but not (2,3). Likewise, in the matrix’s column

(i,2), the cell (1,2) is the only cell that contains a 1. Example 3.9 shows a visual

representation of these relationships.

EXAMPLE 3.9: SONATA FOR SAXOPHONE, ROW A, SUCCESSIONS OF IC2

ic2 ic1 ic5

In this example, a graph has been drawn to show the information about the matrix’s row

(2,j) and column (i,2). As the somewhat clumsy prose of the preceding paragraph

demonstrates, the information in an adjacency matrix might be clear, but difficult to

38 One could easily imagine a different kind of adjacency matrix, which uses not just the numbers 0 and 1, but actually fills the cell in the i th row and j th column with the actual number of occurrences of interval-class succession (i,j ) in the row.

84

communicate efficiently in verbal form. The graph of Example 3.9 provides a more

visually attractive alternative.39

Although the meaning of this graph is intuitively clear, it is necessary to consider

graph terminology from a somewhat more formal perspective. Appendix 2 provides an

introduction to the basic vocabulary of graph theory and demonstrates how that

vocabulary will be used in the present dissertation.

I call the kind of graph depicted in Example 3.9 an interval-class succession graph, or

ICSG. In this graph, each node is labeled with one of the interval classes from the row’s

INT-C, and the directed arrows show the possible interval classes that can occur before

or after ic2. Every ICSG is a connected graph.40

Clearly, the graph in Example 3.9 is a preliminary step toward a complete

visualization of all the interval-class successions of Row A from the Sonata for Alto

Saxophone. It does not tell us all the relationships between ics 1, 2 and 5, and it does not

even mention ic3. However, this information could prove to be useful, as it is a subgraph

of the full graph used to represent the entire set of interval-class successions of Row A –

all of the relationships depicted in Example 3.9 will be present in the full graph, but there

will be additional nodes and arrows as well. As we shall see, subgraphs such as this one

prove to be of special interest.

Example 3.10 shows the complete graph for Row A. This ICSG demonstrates

nearly the full range of interval-class successions in Row A. However, it will not go

unnoticed that there are a handful of successions which may appear to be missing from

this graph, which I will address presently. First, in the interest of maintaining visual

39 On this topic, Robert Morris 2007 has noted that “presenting musical structures by the means of graphs often has an intuitive appeal that verbal or mathematical notation does not.” 40 See Appendix 2 for the definition of “connected graph” and other graph theoretic terms.

85

EXAMPLE 3.10: SONATA FOR ALTO SAXOPHONE, ROW A, ICSG

ic1 ic2 ic3 ic5

clarity, I have not drawn an arrow from ic1 to itself, despite the fact that the row’s INT

has two semitones in a row. While this looped arrow could certainly be added to the

graph, I have chosen only to show successions of different interval classes.41 Second, I

have not taken into account the so-called “cyclic interval” or “wrap-around interval” of

the row: the interval which occurs between the last pitch-class of the row and the first, if

the row were presented in a “looped” or rotated form. Finally, we must be aware that

the arrows only indicate the interval-class successions in transposed and inverted forms

of the row. The directions of the arrows must be switched to accurately account for

retrograde and retrograde-inverted row forms. With an understanding of these apparent

omissions, ICSGs are useful to gain a quick understanding of the interval-class structure

of a row. Furthermore, they can also be used to show structural relationships between

rows that might otherwise go unnoticed.

COMPARISON AND CATEGORIZATION OF ICSGS

There are several ways of comparing ICSGs. Example 3.11 shows the ICSGs for

rows used by Webern in three of his early twelve-tone pieces: the rows from his Op.

41 In a similar manner, my ICSGs do not show multiple arrows connecting the same pair of nodes. While ic1 is followed by ic2 twice in Row A, I have not drawn two separate arrows from ic1 to ic2. A graph which contains such multiple arrows is called a multigraph and a graph which contains loops is called a pseudograph. See Harary 1972, 10.

86

17/iii, Op. 18/iii, and Op. 21. Clearly, these three rows produce identical ICSGs. Identity

is, of course, the closest possible relationship between two graphs.42

EXAMPLE 3.11: THREE WEBERN ROWS AND THEIR ICSGS

WEBERN, OP. 17/III

1 3 4 6

WEBERN, OP. 18/III

1 3 4 6

WEBERN, SYMPHONIE, OP. 21

1 3 4 6

When dealing with non-identical graphs, the concept of isomorphic graphs is useful.

In terms of the underlying structure of each graph, the contents of each node of an

ICSG are largely irrelevant. To compare different graphs abstractly, we are interested

primarily in the relationships between the nodes: which nodes are connected by arrows,

and which direction or directions the arrows point. Frank Harary, author of what is

perhaps the classic graph theory text, states that “two graphs G and H are

isomorphic…if there exists a one-to-one correspondence between their [node] sets

42 While it may seem trivial, it is important to note that these graphs are “identical” rather than “the same graph.” Being derived from three different musical situations, the three graphs of Example 3.11 are three distinct graphs with the same structure of nodes and arrows and the same node labels.

87

which preserves adjacency.”43 Such isomorphisms form a second equivalence relation

on graphs.

EXAMPLE 3.12: WEBERN, KINDERSTÜCK (1924) ROW AND ICSG

1 3 4 5

Example 3.12 shows the row and ICSG for Webern’s earliest serial composition,

the unpublished Kinderstück from 1924. Because the labels of the nodes are not the same,

we cannot say that the Kinderstück row’s ICSG is identical to any of the ICSGs of the

rows in Example 3.11. However, this ICSG is isomorphic to all of the ICSGs of the

rows from Op. 17/iii, Op. 18/iii, and Op. 21.

In this particular case, the visual representation of the ICSGs makes this

isomorphism easy to see: the only difference between the graphs of Example 3.11 and

Example 3.12 is that the node on the far right has as its label a “6” in the former case

and a “5” in the latter. But changing the visual layout of a graph does not change the

structure of the graph. Example 3.13 shows the Kinderstück row’s ICSG presented in

three different but equivalent manners.

Both the representations in A and B show an isomorphic relationship with the

graphs of Example 3.11, despite the rearrangement of nodes 3, 4, and 5. The

relationship between the graphs of Example 3.11 and the representation shown at letter

C is somewhat less obvious, but the isomorphism can be seen by considering the

43 Harary 1972, 10.

88

EXAMPLE 3.13: DIFFERENT REPRESENTATIONS OF KINDERSTÜCK ICSG

A. B.

C.

indegree and outdegree44 of each of the graph’s nodes. Even with the nodes shuffled in

this way, the isomorphism is fairly easy to discern. For the purposes of the graphs in this

dissertation, I will use either a verbal description of the isomorphism when it is not

immediately apparent, or I will re-draw one of the graphs in a way to make the

isomorphism visually clear.

The idea of graph isomorphisms is not new to music theorists; it is probably

most familiar from the writings of David Lewin, dealing with transformation graphs and

Klumpenhouwer networks, in particular.45 When considering a given system of nodes

and arrows, Lewin draws a distinction between “networks” and “graphs,”46 based on

whether or not the underlying “node/arrow system”47 is labeled or not; a “network” is a

labeled “graph.” Although I have not been using his terminology explicitly, it should be

clear that I am invoking the same distinction when I consider isomorphic graphs.48

44 See Appendix 2. 45 See, especially, Lewin 1987, Chapter 9, and Lewin 1990. 46 In this paragraph, I will enclose Lewin’s terms “network” and “graph” in quotation marks in order to avoid confusion with my slightly different definition of graph. 47 Lewin 1987, 193. 48 For the formalism behind Lewin’s “network” and “graph” distinctions, see Lewin 1987, 195-196. In graph-theoretic terms, a network is a graph (with or without labeled nodes) that is associated with a function that provides a numerical value to each of the arrows in the graph. See Harary 1972, 50. Clearly, this is the case for Lewin’s transformational networks (as well as Klumpenhouwer networks, see Lewin 1990).

1 3 4 5 1 4 5 3

3 5 1 4

89

Beyond identity and graph isomorphism, the rows used in the three pieces from

Webern’s Op. 17 provide an example of a third kind of relationship between ICSGs.

Example 3.14 shows the three rows with their ICSGs.

EXAMPLE 3.14: WEBERN, DREI VOLKSTEXTE (OP. 17) ROWS AND ICSGS

A. OP. 17/I

5 1 2 3 4

B. OP. 17/II

61 3 4 5

C. OP. 17/III

1 3 4 6

These three ICSGs are not identical, and they cannot be considered isomorphic because

they do not share a common number of nodes and arrows. But, looking at the structure

of each graph carefully reveals that the ICSG in Example 3.14C is a subgraph of the ICSG

in Example 3.14B: all the nodes and arrows of Op. 17/iii’s ICSG are present in Op.

17/ii’s ICSG, but the latter contains additional nodes and arrows. Conversely, the ICSG

in Example 3.14B is a supergraph of the ICSG in Example 3.14C.

There are two types of subgraph relationships: abstract and literal. If we

consider these three graphs without their respective node labels, we can see that the As none of the graphs in the present dissertation involve labeled arrows, I will use the word “graph” for all cases, specifying whether the graph is labeled, or unlabeled (or abstract) if necessary. See Appendix 2.

90

ICSG in Example 3.10C is an abstract subgraph of the ICSG in Example 3.14A. Because

the relationship described in the previous paragraph is true based not only on the

relationships between nodes and arrows, but also based on the specific label assigned to

each node, that relationships is a literal subgraph relationship.49

Two of the three graphs in Example 3.14 also provide an example of a particular

kind of graph: the star graph. A star graph is a graph in which exactly one node is

adjacent to or from all other nodes, but none of the other nodes are adjacent to or from

each other. In other words, a star graph contains a single nexus node which is the only

node to or from which all remaining nodes are adjacent. The ICSGs from Example

3.14B and 3.14C are both star graphs.50

This definition allows us to make a similar, but more specific, observation to the

type made by Kathryn Bailey about Webern’s general intervallic preferences in his

earliest twelve-tone works (Op. 17, Op. 18 and the unpublished Klavierstück and

Kinderstück). Bailey discusses the abundance of ic1 in these early rows, while stating that

many of the later rows “rely less on semitones between adjacent notes as symmetry and

invariance become the significant concerns.”51 A quick glance at the INT-Cs of

49 It is worth noting that Kathryn Bailey notes that the first of the three Op. 17 Lieder “consists of twelve-note fields rather than linear statements” (Bailey 1991, 14), and that it “is not really constructed from a row. It presents a succession of twelve-note fields” (Bailey 1991, 33). Interestingly, even though the row shown in Example 3.14A (which is the row Bailey assigns to this movement) only appears on the musical surface in a more or less strict ordering during mm. 1-3, the majority of the vocal line forms a non-serial ICSG which is, itself, isomorphic to the ICSG shown in Example 3.14A. The only portion of the vocal line of this piece which does not form such an isomorphic ICSG is at the piece’s climax, mm. 10-12. 50 This definition is based on that which is found in Harary 1972, 17, and Wilson 1975, 18. Both authors define a star graph as a graph in which the nodes can be divided into two non-intersecting sets, V1 and V2, in such a way that every edge in the graph joins a node from V1 to a node in V2. This is called a bipartite graph. A special type of bipartite graph exists when every node in V1 is adjacent to every node in V2 (a complete bipartite graph). The definition of a star graph, then, is a complete bipartite graph in which either V1 or V2 is of cardinality 1. The examples provided by Harary and Wilson reveal that both authors are referring to a star graph as a type of (non-directed) ordinary graph. Because my definition of star graph applies to directed graphs, it might be more accurate, if less clear, to say that a star (di)graph is a directed graph whose underlying ordinary graph is a star graph. 51 Bailey 1991, 13-15.

91

Webern’s rows supports this observation, but the use of ICSG technology allows us to

put his early use of ic1 into a larger context. Rather than simply counting the number of

ic1’s in a particular row, we can use the ICSG to examine how these interval classes are

used with the other interval classes of the row. By noticing that the ICSGs for the rows

used in Op. 17/ii and iii are both star graphs, and that the node labeled ic1 is, in both

cases, the nexus node, it becomes clear that, in these rows, Webern uses this abundance

of ic1’s in a very specific way. In addition to these two rows, the rows from Op. 18/iii,

the Klavierstück, and the Kinderstück all form ICSGs which are star graphs, and they all

have ic1 as the nexus node. This adds a deeper level of understanding to Bailey’s note

about the preference for ic1 between adjacent pitch classes in Webern’s early rows.

Bailey also implies that sequential intervallic construction plays a significant role

in these early twelve-tone works.52 The preponderance of a single type of ICSG

supports this claim. While star graphs are not found in many of the ICSGs for Webern’s

later dodecaphonic works, the ICSGs of the rows for the Op. 20 String Trio and the Op.

21 Symphony are both also star graphs. So, where Bailey sees Op. 20 as the culmination

of these “early experiments,”53 the analytical use of ICSGs allows us to see a point of

coincidence and an additional thread of continuity between these early rows and

Webern’s later twelve-tone rows.

***

In this chapter, I have attempted to engage three general issues of multiple-row

serialism. To begin, we have seen some of the ways in which issues of structure, 52 Ibid., 16. 53 Ibid.

92

function and unity play a role in the understanding of compositions which use more than

one single row as the foundation of their pitch material. This led to a discussion of some

of the ways one might choose to explore the relationships between the rows of a piece,

and it provided a new analytical device, the interval-class succession graph, which can be

used to this end. The chapters to follow make up the second large part of this study: the

analytical discussion of three pieces by Edison Denisov. First, we will examine this

composer’s use of ICSG-equivalent and ICSG-isomorphic row in the first of his Five

Etudes for Bassoon. Second, we will examine the choice of rows with notably different

ICSGs in his Sonata for Alto Saxophone and Piano and his Octet for Winds.

93

CHAPTER 4 ANALYSIS: FIVE ETUDES FOR SOLO BASSOON (NO. 1)

In this chapter, I will examine Denisov’s use of multiple rows in the first of his

Five Etudes for Solo Bassoon.1 I will begin by making some general observations about the

piece’s composition, form, and row content. The analysis to follow will then revisit the

three broad categories of multiple row serialism discussed in Chapter 3. First, I will

examine the structural relationships between the ten rows which appear in this piece,

using an ICSG-based method to describe the similarity in unordered interval-class

content among these rows. Second, I will discuss the functional use of the rows,

focusing particularly on row-chaining procedures, which Denisov refers to as “serial

modulation.” Finally, I will turn my attention to questions of unity in this composition,

which is based on a wide array of rows and uses little repetition of individual row forms.

GENERAL OBSERVATIONS

Composed in 1983, these etudes are dedicated to the famous Russian bassoonist

Valeriy Popov.2 As one might expect by the title, the Five Etudes appear to have been

composed with a pedagogical purpose in mind. Jeffrey Lyman notes that “[i]n listening

to the Five Etudes, one realizes that the standard etude books of the nineteenth century

1 I am aware of only two writings about the Five Etudes, neither of which deals with the work in any length. The first is Jon Beebe’s annotated bibliography Music for Unaccompanied Solo Bassoon (Beebe 1990), which has three paragraphs of descriptions of performance concerns of the piece (range, duration, some brief analysis). The second is Jeffrey Lyman’s article “After Shostakovich, What Next? New Russian Soviet Music for Bassoon,” from the International Double Reed Society Journal (Lyman 1996). This article gives a paragraph-long description of the overall shape of each of the Etudes, which would be suitable for recital program notes. 2 Beebe 1990, 24. The published score (Deutscher Verlag für Musik, Leipzig) does not indicate a dedicatee. According to the website of the Moscow Conservatory, Popov studied at the Conservatory during the early 1960s, and was appointed to teach there in 1971. He has been on the wind and percussion faculty at the Conservatory ever since, and, in 2007, he was named the head of that department. http://www.mosconsv.ru/english/teachers/about.phtml?65 accessed October 16, 2009.

http://www.mosconsv.ru/english/teachers/about.phtml?65

94

could not have been far from the composer’s mind during their creation.”3 In fact,

Denisov’s widow, Ekaterina Denissova-Bruggeman, has written a brief note about this

piece based on the composer’s own explanation of his work.4 This note indicates that he

had the student bassoonist in mind when composing this piece. Because, to the best of

my knowledge, this particular note is not available in any published form, I will quote it

here in full:

This work was composed at the request of the publisher Deutsche Verlag für Musik and is dedicated to the Russian bassoonist Valeriy Popov. The publisher Deutsche Verlag für Musik made an entire series of pedagogical books for various solo instruments. To this end, they commissioned compositions from various 20th-century composers in order to have works of [not only] high musical quality but also aesthetic variety. Their idea was also to introduce a maximum number of innovative techniques for each instrument. This is why Denisov composed several works of the same design for Deutsche Verlag für Musik in the mid-1980s: Winter Landscape (1987) for harp, Two Pieces for Solo Flute (1983), a piece for vibraphone,5 Dead Leaves (1980) for harpsichord, and Five Etudes for Bassoon (1983). The composer writes: “I think that this type of collection, devoted specifically to a chosen instrument and its new technical procedures, is very useful. There should be as many of these [collections] as possible. It is evident that they are indispensable for performers. But [they are] also [indispensable] for composers who, through this work, have the opportunity to study the instruments in greater depth, exploring their potential technique and expression. Furthermore, as the composer knows that his music will be published with the works of other composers (often already well known, and even famous), he is well obliged to apply [his best effort] to not appear weaker and be ashamed of his work.”6

3 Lyman 1996, 55. 4 Ekaterina Denissova-Bruggeman, email correspondence with the author, February 6, 2008. 5 Though she does not give a specific title here, Denissova-Bruggeman is referring to Black Clouds (1984) for vibraphone. This piece is more commonly known as the first of Denisov’s Three Pieces for Percussion, published in 1989 by Deutsche Verlag für Musik. 6 Unpublished note “Cinq Etudes pour basson seul, 1983,” from the composer’s personal archive, in possession of Ekaterina Denissova-Bruggeman. The note was originally written in Russian by Mme. Denissova-Bruggeman. I am deeply grateful to Mme. Denissova-Bruggeman not only for sharing this note with me (email correspondence, October 16, 2009), but also for translating it from Russian to French. The translation from French to English is my own.

95

Jon Beebe characterizes the Five Etudes as “atonal and non-serial, with free use of

twelve-tone rows,” and states that the first movement, in particular, “is based on

continuous development of two motives[: o]ne consisting of a P4 and a tritone, the other

a chromatic neighbor-note figure.”7 Beebe’s observation is accurate, yet incomplete.

The pitch fabric of this Etude is derived from no fewer than ten distinct twelve-tone

rows, and is a clear example of Kurbatskaya’s “technique of twelve-tone rows,” as

discussed in Chapter 2. The two motives cited by Beebe are actually built into the

structure of the rows used: of the ten rows used in this brief, 50-measure Etude, only

three of them are not made up exclusively of ics 5, 6 and 1. The three remaining rows

each make use of these interval classes as well, but with the addition of a few

occurrences of ics 2 and/or 4. We shall examine the structure of each row shortly.

EXAMPLE 4.1: FIVE ETUDES FOR BASSOON (NO. 1) – ROW CHART

1 2 3 4 5 6 7 8 9 10 11 12

AP9 ------------------------------ AP8 ---------------- DP7 ------------------------------------ FP1

BP1 ----------------------------- CP0 ---------------------------- EP5 -----------

13 14 15 16 17 18 19 20 21 22 23 24

(FP1)-------------- AP1 ------------ NR ------ GP7 --------- NR ----------------------------------------------- (EP5) CP6 ------------------------- CP6 -------- 25 26 27 28 29 30 31 32 33 34 35 36

CI8 -------------------------------- CP8 ------ HP8 --------- NR -----------------------------------

CP1 ------------------------ CP1 --------------------------

37 38 39 40 41 42 43 44 45 46 47 48 49 50

IP9 ------------------------------------------------- NR --- FP8 -----------------------------

JP0 --------------------------------------- NR

7 Beebe 1990, 24.

96

Example 4.1 shows the organization of rows and row forms in the first Etude. In

this diagram, each of the ten row forms is assigned a letter, A-J, and the label “NR” is an

abbreviation for “no row”: a succession of notes which, with or without pitch-class

duplication, does not present all twelve tones.

Although this piece contains no simultaneous pitches, I have listed the

succession of row forms in Example 4.1 along two lines. Listing the row forms as such

is intended to show that one of the major organizational principles of this Etude is the

chaining of various rows and row forms. Thus, in Example 4.1, when two rows appear

to be indicated simultaneously, row chaining is occurring: the last few pitches of one row

are simultaneously functioning as the first few pitches of another row. I will have more

to say about this feature shortly. The ten rows used are shown in Example 4.2, along

with their respective ICSGs.

EXAMPLE 4.2: FIVE ETUDES FOR BASSOON (NO. 1) – ROWS A-J AND THEIR ICSGS

ROW A:

1 5 6

BIP-Vector: [300053] ROW B:

1 5 6

BIP-Vector: [500033]

97

EXAMPLE 4.2, CONT’D ROW C:

1 5 6

BIP-Vector: [300035] ROW D:

1 5 6

BIP-Vector: [500033] ROW E:

1 5 6

BIP-Vector: [500024] ROW F:

1 5 6 4

BIP-Vector: [300134] ROW G:

1 5 6


98

EXAMPLE 4.2, CONT’D

ROW H:

1 5 6 4 2


ROW I:

2 5 6


ROW J:

1 5 6


The three primary formal divisions in this Etude occur at mm. 12, 25 and 35;

these divisions are articulated by changes in texture, register, dynamics and rhythm.

However, the formal divisions generally do not coincide with the changing row forms.

The opening section, from mm. 1-11, presents a number of somewhat isolated gestures,

separated by silences of various durations. The bassoon’s large leaps force the

instrument to cover a wide range: from C2 to Ab4. After m. 11, registral expansion (A4

in mm. 12, 15 and 19; D5 in m. 20; and finally E5 in m. 21) is accompanied by increased

rhythmic activity and much shorter silences between individual gestures. This section

also features the introduction of a small number of new interval classes and interval-class

99

successions, most notably the introduction of ic4 in m. 13. The arrival of E5 is followed

by a rapid descent and decrescendo, forcing the third section (mm. 25-34) to begin with

apparent uncertainty, with a return to the isolated gestures of the opening section. This

time, however, the gestures themselves are shorter: mostly single staccato notes, or two-

or three-note slurs. The final section (mm. 35-50) presents a series of five short phrases,

played successively louder. Each phrase begins with a rep

eated staccato pitch, played in

regular rhythms, followed by a series of slurred notes.

SUES

e

has a single occurrence of ic 2, and Row H has single occurrences of both ics 2

d 4.

air

my

values

ir

IS OF STRUCTURE

As previously mentioned, ics 1, 5 and 6 are at the heart of the intervallic structur

of nearly all of the twelve-tone rows found in this Etude. Example 4.2 reveals that only

Rows F, H and I involve additional interval classes: Row F has a single occurrence of ic

4, Row I

an

To be more precise, one might desire to measure the similarity between each p

of rows. In Chapter 3, I briefly discussed Tuukka Ilomäki’s work on the similarity of

twelve-tone rows, but unfortunately, none of the methods proposed by Ilomäki serve

present purposes. Of his seventeen similarity measures, two are based on intervallic

structure: intervallic distance, and intervallic displacement. The former is concerned

with the ordered pattern of intervals in a row form, and I am primarily concerned with the

unordered interval-class content of the rows in the Etude. While the latter is concerned

with examining row forms as sets of unordered intervals, it only returns numerical

when the row forms being compared share the same set of unordered intervals.8

8 Ilomäki 2008, 230-241.

100

Furthermore, neither of these similarity measures examines the interval classes of a

twelve-tone row. Anticipating this issue, Ilomäki notes that “all set-class similarity

measures based on the interval-class contents of set classes could be…adapted with little

effort.”

ontent

e

y to use a row’s

BIP-Ve

J, and Rows E and G). Figure 4.1 shows the Angle measurements

t,

9

To pick just one such similarity measure, Damon Scott and Eric Isaacson’s

“Angle” can be adapted to measure the similarity of the unordered interval-class c

of two twelve-tone rows.10 In its original conception, the Angle measurement is

designed to measure the similarity between two pc sets by considering the entries of their

interval-class vectors as coordinates indicating a location in a six-dimensional space. Th

similarity between two pc sets, then, is determined by measuring the angle between the

locations of both of the pc sets. Results for Angle are returned in degrees, ranging from

0o to 90o, with larger Angles indicating a greater dissimilarity between the two pc-sets.11

In adapting this measure for use with twelve-tone rows, it is necessar

ctor in place of the traditional pc set interval-class vector.12

Of the ten rows in Denisov’s Etude, three pairs have identical BIP-Vectors (Rows

B and D, Rows C and

for each pair of rows.

The information in this table provides concrete support to my earlier casual

observation that these rows are generally quite similar not only in interval-class conten

but also in relative distribution. Considering all the results in Figure 4.1, the average

9 Ibid., 236. 10 Scott and Isaacson note that their Angle measurement “has a very high correlation (over 0.90) with some ‘favorite’ measures, namely Lewin’s REL2 and Castrén’s %Rel and his RECREL,” suggesting that their measurement is, at least, as good a choice as any of these other methods of measuring pc-set similarity. See Scott and Isaacson 1998, 118. 11 Scott and Isaacson 1998, 107-108. The formula for calculating Angle is given on p. 110. 12 Because all twelve-tone rows are members of set-class 12-1, they all have the same interval-class vector [12 12 12 12 12 6]. As such, any calculations using the interval-class vector will return meaningless values, and, thus, the BIP-Vector must be used.

101

Angle for all the rows of Denisov’s Etude is 26.9o. The largest values are 51.1o and 5

both of which are pairs involving Row I. As can be gleaned by looking at the BIP-

Vectors shown in Example 4.2, Rows H and I appear to have the least in common w

the other eight rows, and correspon

5.0o,

ith

dingly, the highest Angles are all measurements

volving one of these two rows.13

FIGURE 4.1: ANGLE MEASU R ROW PAIRS IN TUDES FOR BASSOON (NO. 1)

A

in

REMENTS FO FIVE E

ROW PAIR NGLE

Row A – Row B/D 24.9o Row A – Row C/J 24.9o Row A – Row E/G 32.7o

Row A – Row F 21.9o Row A – Row H 16.5o Row A – Row I 28.4o

Row B/D – Row C/J 24.9o Row B/D – Row E/G 12.2o

Row B/D – Row F 21.9o Row B/D – Row H 31.9o Row B/D – Row I 51.1o

Row C/J – Row E/G 21.2o Row C/J – Row F 11.6o Row C/J – Row H 25.3o Row C/J – Row I 37.3o

Row E/G – Row F 21.2o Row E/G – Row H 36.6o Row E/G – Row I 55.0o Row F – Row H 19.8o Row F – Row I 37.9o Row H – Row I 24.1o

We can also seek to discover structural connections between the various rows in

the Etude by examining the ICSGs of those rows, which are given in Example 4.2. Some

inter-row relationships can be seen easily with these graphs. Most obviously, Rows C, E,

13 However, Rows H and I are not terribly dissimilar from each other, as suggested by an Angle of 24.1o.

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and J all yield identical ICSGs. Rows C and J, therefore, can be said to have the clo

relationship of any pair of rows: not only are their BIP-Vectors identical, but their

ICSGs are identical as well. Furthermore, Example 4.2 also reveals that the prime forms

of Rows C and J have nearly the same INT (and, thus, INT-C). The last seven entries of

the INTs of these two rows are identical, and, in fact, the first four are identical, except

for the reversal o

sest

f the second and fourth entries.14 These INT relationships are shown

Example 4.3.

XAMPLE 4.3: INTS OF RO

of

its associated arrows) from

s C,

ow

nd

makes this abstract inclusion relationship clear: node a x, d z and e y. These

in

E C AND J (PRIME FORMS) WS

The identical ICSGs of Rows C, E and J are also literal subgraphs of the graph

Row F. Removing the node which contains ic4 (and both

Row F’s ICSG results in the ICSGs of Rows C, E and J.

Examination of the ICSGs also reveals a close connection between these three

Rows and Row A: though Row A’s ICSG is not identical to the ICSG shared by Row

E and J, it is related by isomorphism. Though it is the least visually similar to all the

other ICSGs, Row H’s ICSG is seen to be an abstract supergraph of the ICSGs of R

A and Rows C, E and J. Example 4.4 shows the ICSGs of Rows H and C with the

specific interval-class content of their nodes removed. Removing the nodes b and c (a

their associated arrows) in Row H’s ICSG (which represent ics 2 and 4, respectively)

Row J: 6 e 6 5 6 e 6 e 5 6 7

Row C: 6 5 6 e 6 e 6 e 5 6 7

14 Though distinctly different in purpose, this swapping recalls Forte’s R1 relation. See Forte 1973, 47-48.

103

graphs are each one arrow shy of being a complete graph, in which every possible path is

allowed.

EXAMPLE 4.4: ABSTRACT INCLUSION RELATIONSHIP BETWEEN ICSGS OF ROWS H

AND ROWS A, C, E AND J ROW H: ROWS A, C, E AND J:

In a row with three distinct interval classes, there are six possible interval-class

successions. Example 4.2 shows that Row A uses five of those six possible successions:

ic1 ic5; ic5 ic1; ic5 ic6; ic6 ic5; ic6 ic1. The only interval-class

succession lacking from Row A is the succession ic1 ic6. However, this interval-class

succession is only lacking from Row A in a structural sense. Example 4.5 shows the

music for mm. 1-3, the first occurrence of Row A. As this example shows, a single

pitch-class repetition on the musical surface results in the completion of Row A’s ICSG.

EXAMPLE 4.5: FIVE ETUDES FOR BASSOON (NO. 1) – MM. 1-3 (ROW A)

In this example, the pitch C4 is found in two places: at order position 5 and again

following order position 6 (B3). By repeating C4 in this way, Denisov uses the one

missing interval-class succession: the ic1 between order positions 5 and 6 (and again

a d e x y z b c

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between order position 6 and the repeated 5) is now followed by an ic6 between the

repeated order position 5 and 7. In this light, we can see how the “chromatic neighbor-

note figure”15 observed by Beebe serves a deeper purpose: the exhaustion of all possible

interval-class successions involving ics 1, 5 and 6.

EXAMPLE 4.6: FIVE ETUDES FOR BASSOON (NO. 1) – MM. 5-6 (ROW A)

After its initial presentation, Row A returns in mm. 5-6, as seen in Example 4.6.

In this realization of Row A, we also find that the repetition of order position 5 serves to

present the single interval-class succession which is lacking in the Row’s unrealized

structure: that of ic1 ic6. A statement of Row B occurs between these two Row A

passages. Shown in Example 4.7, this presentation of Row B involves no pitch

repetition. But such a pitch repetition is unnecessary in this case: Row B’s ICSG (see

Example 4.2) indicates that all six possible interval-class successions are present in the

unaltered row.

EXAMPLE 4.7: FIVE ETUDES FOR BASSOON (NO. 1) – MM. 3-5 (ROW B)

15 Beebe 1990, 24.

105

Continuing in the same vein, let us now examine the first appearance of Row C,

which uses as its initial pitch the final pitch of AP8 (Example 4.5). This statement of CP0

is shown in Example 4.8.

EXAMPLE 4.8: FIVE ETUDES FOR BASSOON (NO. 1) – MM. 6-9 (ROW C)

Row C’s ICSG (see Example 4.2) shows that, again, five of the six possible interval-class

successions are present in the structure of the row. In this case (and also the case of

Rows E and J, since they share identical ICSGs), the missing interval-class succession is

ic 5 ic 1. But, in a manner similar to that shown in Examples 4.5 and 4.6, the

repetition of order position 3 (after 4) forms an ic5 with the Bb of order position 5,

which in turn is followed by an ic1 between 5 and 6. These examples suggest that the

different rows used in the opening section of Denisov’s Etude (mm. 1-11) all are realized

in particular ways to bring the full range of possible interval-class successions to the

fore.16

ISSUES OF FUNCTION

The primary functional issue in this Etude is the way in which the different rows

and row forms are linked from one to the next. In his 1970 essay on Webern’s Piano

16 Although I have not explicitly discussed Row D’s role in this A-section, it is obvious from its ICSG shown in Example 4.2 that Row D, in its natural state presents all six possible interval-class successions.

106

Variations Op. 27, Denisov uses the term “serial modulation” (seriynaya modulyatsiya) to

describe Webern’s practice of row chaining, where the last note or notes of one row

form becomes the first note or notes of a new row form.17 I will adopt this term here, as

it seems especially appropriate for Denisov’s method of linking together not only

different row forms, but even different rows. I will also use the term “modulating area”

to refer to the notes shared between two row forms.

Throughout the Etude, every time two row forms are presented successively,

without any intervening non-row material, Denisov uses the technique of serial

modulation to connect one row form to the next. These connections are shown by the

overlapping lines of Example 4.1. The size of the modulating area is not entirely

consistent throughout the Etude; some pairs of rows are linked by three pitches, others

are linked by four, and still others are linked by a single shared pitch.

Denisov’s selection and presentation of specific row forms appears to be guided

by invariant pitch-class segments. Clearly, the common notes in the modulating area are

one type of invariance, but each successive pair of row forms features additional

invariant dyads, trichords, tetrachords, or pentachords. Figure 4.2 presents a list of all

successive pairs of row forms in this Etude to highlight these invariances. In this list, the

common notes found in the row forms’ modulating area are enclosed in circles, and the

other invariant pitch-class segments are indicated with brackets.18

While several different invariance schemes are employed throughout the Etude, it

is clear that the maintenance of tetrachordal content is the most common method of 17 Denisov writes, “By coupling the row forms by means of one or more common notes, a transition from one pitch level to the next is carried out, or in other words, serial modulation is achieved.” Denisov 1970, 51 (italics original). 18 In many cases, there exist a variety of ways of identifying invariant pitch-class segments. For example, in the second row of Figure 4.2 (mm. 3-6), we could also bracket the trichord {017}, and the dyads {56}, {te} and {34}. In these cases, I have chosen to prefer the most “regular” partitioning: if invariant pitch-class segment of equal size can be identified, I will label those segments.

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FIGURE 4.2: INVARIANCES IN ROW-FORM SUCCESSIONS IN FIVE ETUDES FOR BASSOON (NO. 1)

mm. 1-5 Row A: AP9

9 3 t 4 5 0 e 6 7 2 8 1

Row B: BP1

1 0 7 6 5 e t 4 3 8 2 9

mm. 3-6 Row B: BP1

1 0 7 6 5 e t 4 3 8 2 9

Row A: AP8

8 2 9 3 4 e t 5 6 1 7 0

mm. 5-9 Row A: AP8

8 2 9 3 4 e t 5 6 1 7 0

Row C: CP0

0 6 e 5 4 t 9 3 2 7 1 8

mm. 6-11 Row C: CP0

0 6 e 5 4 t 9 3 2 7 1 8

Row D: DP7

7 1 8 2 3 t 9 4 5 6 0 e

mm. 8-13 Row D: DP7

7 1 8 2 3 t 9 4 5 6 0 e

Row E: EP5

5 6 0 e t 4 3 9 8 1 7 2

mm. 11-14 Row E: EP5

5 6 0 e t 4 3 9 8 1 7 2

Row F: FP1

1 7 2 8 4 3 9 t e 6 0 5

mm. 12-16 Row F: FP1

1 7 2 8 4 3 9 t e 6 0 5

Row C: CP6

6 0 5 e t 4 3 9 8 1 7 2

mm. 14-17 mm. 16-18

Row C: CP6

6 0 5 e t 4 3 9 8 1 7 2

Row A: AP1

1 7 2 8 9 4 3 t e 6 0 5

mm. 25-29 mm. 27-30

Row C: CI8

8 2 9 3 4 t e 5 6 1 7 0

Row C: CP1

1 7 0 6 5 e t 4 3 8 2 9

mm. 30-33 Row C: CP1

1 7 0 6 5 e t 4 3 8 2 9

Row H: HP8

8 2 9 t 4 e 3 5 6 1 7 0

mm. 45-50 Row F: FP8

8 2 9 3 e t 4 5 6 1 7 0

Row J: JP0

0 6 5 e 4 t 9 3 2 7 1 8

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connecting the various successive row forms in this piece. Nine of the thirteen row-

form pairs19 shown in Figure 4.2 are related by tetrachordal invariance. To be even more

specific, all of the row-form pairs with shared tetrachordal content feature the same

relationship between those shared tetrachords. In every case, the tetrachords are related

in the symmetrical manner shown in Example 4.9.

EXAMPLE 4.9: SYMMETRY OF INVARIANT TETRACHORDS

Row form X: {ABCD} {EFGH} {IJKL}

These tetrachordally invariant row-form pairs are found exclusively in the first,

second and third formal sections of the piece; tetrachordal invariance is not a feature of

the final section. In fact, it is precisely this tetrachordal invariance that runs as a

common thread between the first two sections. The first section makes use of this

relationship in its second pair of row forms (BP1 and AP8 ) and again in its last pair of

row forms (CP0 and DP7). But as row form DP7 is ending, the pitch-class segment

< 5 6 0 e > allows this row form to modulate to row form EP5. This particular

modulation features the largest modulating area of any successive row forms throughout

the Etude : an entire tetrachord is shared between DP7 and EP5. This shared tetrachord

makes up the final four pitches of the Etude’s first section.

As the second section moves through row form EP5 to FP1, from FP1 to CP6,

from CP6 to AP1, and from AP1 back to CP6, each pair of rows utilizes the same three 19 Although there are only eleven distinct row pairs listed in Figure 4.2, two of these pairs are used twice each (CP6 and AP1; CI8 and CPe).

Row form Y: {IJKL} {EFGH} {ABCD}

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sets of tetrachords: {056e}{349t}{1278}. As Example 4.9 shows, every pair of

tetrachordally invariant row forms switches the placement of the first and third

tetrachords while keeping the second tetrachord in the same place. As such, from the

beginning of the second section of the Etude until the introduction of non-row-based

material at m. 18, the tetrachords {056e} and {1278} are found alternating between

placement at the beginning and end of each row form, while {349t} is continually found

at order positions 4-7 of each row form. The exchange of tetrachord placement is

shown in Example 4.10.

EXAMPLE 4.10: LOCATION OF TETRACHORDS {056E}{349T}{1278} IN MM. 6-18

Row CP0, m. 6: 0 6 e 5 4 t 9 3 2 7 1 8

Row DP7, m. 8: 7 1 8 2 3 t 9 4 5 6 0 e

Row EP5, m. 11: 5 6 0 e t 4 3 9 8 1 7 2

Row FP1, m. 12: 1 7 2 8 4 3 9 t e 6 0 5

Row CP6, m. 14: 6 0 5 e t 4 3 9 8 1 7 2

Row AP1, m. 16: 1 7 2 8 9 4 3 t e 6 0 5

Row CP6, m. 17: 6 0 5 e t 4 3 9 8 1 7 2

A brief, eight-note pitch segment occurs between m. 18’s row form CP6 and m.

19’s row form GP7. This segment, labeled as X, is shown as Example 4.11, with a bit of

the C- and G-rows surrounding it.

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EXAMPLE 4.11: FIVE ETUDES FOR BASSOON (NO. 1) – MM. 18-19 X

Initially, the segment X sounds like a repetition of a small portion of CP6, featuring the

same < 4 3 4 9 8 > motive from the beginning of m. 18, with pc9 placed an octave

higher. This pitch segment can be seen as a portion of yet another ordered aggregate,

overlapping with the surrounding rows. However, this overlap produces a pitch-class

duplication which prevents listing this as a row. Although we have seen repetitions

within rows earlier in this Etude, the duplication here is of a different sort. Prior to m.

18, all of the repeated pitches have occurred as part of a neighbor-note motive: they have

been repetitions of a given row’s order position segment < n n+1 n >. In the present

case, pc7 is presented two times: once during the modulating area between CP6 and X,

and once in the modulating area between X and GP7.

This passage also features a similar type of invariance as was found in the earlier

portions of the Etude. While neither the invariance pattern between CP6 and X nor the

invariance pattern between X and GP7 have the consistent sharing of pitch-class

segments of uniform sizes that we saw in mm. 6-18, they do share the same kind of

symmetrical relationship between those same row forms. The relationship between

these three units is shown in Example 4.12. In this example, repeated pitch classes are

shown in parentheses.

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EXAMPLE 4.12: FIVE ETUDES FOR BASSOON (NO. 1) – MM. 17-20 (CP6, X, GP7)

CP6, mm. 17-18: 6 0 5 e t 4 3 (4) 9 8 1 7 2

Each pair of pitch-class units (CP6 and X; X and GP7) shares three invariant subsets, two

of which are shared among all three units. In moving from one unit to the next, the

invariant pitch-class segments feature a similar kind of symmetrical exchange as we saw

in Example 4.9. Even though, in this case, the invariant segments are not of the same

size, nor do they account for every pitch class in the three units, the principle remains

the same among these invariant segments: the first invariant segment becomes the last,

the last becomes the first, and the invariant segment between these two remains in the

middle.

The next phrase, from the anacrusis to m. 21 through m. 24, represents the

longest non-row-based passage of the entire Etude. But even this passage shares a

connection with the row form (GP7) that precedes it. As if deconstructing the invariant

relationships established in the first 20 measures of the piece, Denisov chooses an

ordering of pitch classes which highlights several small sets (mostly dyads) from GP7.

Example 4.13A shows the relevant division of GP7, with each small set labeled with a

letter from a-e. Example 4.13B shows the placement of those small sets within the non-

row-based passage.

X, mm. 18-19: 1 7 2 4 3 (4) 9 8 e t 6 (7)(6)(7) 0 5 GP7, mm. 19-20: 7 6 (7) 0 5 e t (e) 4 3 (4) 9 8 1 2 (1)

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EXAMPLE 4.13A: FIVE ETUDES FOR BASSOON (NO. 1) – SMALL SETS OF GP7

a b c d e GP7, mm. 19-20: 7 6 0 5 e t 4 3 9 8 1 2 EXAMPLE 4.13B: FIVE ETUDES FOR BASSOON (NO. 1) – MM. 20-24

d c b a b d c e d e c e d mm. 20-24: 8 9 4 3 t e 6 5 0 t e 8 9 7 5 3 4 2 1 8 9 7 1 2 3 4 2 1 0 t 8 9 ISSUES OF UNITY

In a fifty-measure composition, does the presence of ten distinct twelve-tone

rows allow for sufficient unity? The following section will serve to conclude the present

chapter by addressing this issue.

While it seems unlikely that a relatively short piece of music could project a

unified musical whole when it is built on the structure of ten different rows, both the

nature of the rows themselves and the motivic construction of the musical surface act to

contradict this hypothesis. The web of inter-row relationships outlined in the earlier

section of this chapter titled “Issues of Structure” certainly provides ample evidence that

these rows, though distinct from each other, have a great deal in common. At the heart

of this is the relationships made clear by the ICSGs of each row, and, even more directly,

the shared unordered interval-class content (ics 1, 5 and 6) of the majority of the rows

used.

Regarding the motivic construction of this Etude, we have already seen that at

least one commentator has noted two unifying motives; Jon Beebe has identified the

frequent uses of ics 5 and 6, as well as the chromatic lower-neighbor figure as the basis

of the pitch organization of the piece. While I have labored to show that these motives

fall directly out of the piece’s twelve-tone organization, the presence of an underlying

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fabric of rows certainly does not render these motivic connections moot. The chromatic

lower-neighbor figure is an obvious audible motive, used throughout the piece, most

frequently found as pitch-class segment < 4 3 4 >, though it is not restricted to this pitch

level. I have discussed the lower-neighbor motive earlier, in the context of < n n+1 n >

order position repetitions in several row forms throughout the piece. Beebe’s

consideration of ics 5 and 6 seems to miss the mark slightly, however. The melodic

motion of this Etude is not a haphazard string of ics 5 and 6, but rather the combination

of the two intervals to form members of set class 3-5, [016].

EXAMPLE 4.14: FIVE ETUDES FOR BASSOON (NO. 1) – MM. 36-50

Example 4.14 shows the music for the closing section of the Etude. In this

example, I have labeled the occurrences of this pc set throughout. The overlapping

brackets indicate that nearly every pitch in this fifteen-measure section can be explained

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as a member of multiple members of set class 3-5. This is somewhat reminiscent of the

way set class 4-5, [0126], saturated the musical surface of the first movement from

Volkonsky’s Musica Stricta, as seen in Chapter 2.

By using rows of similar construction, and by bringing these structural

relationships to the fore by using them to create salient motives, Denisov is able to

provide his Etude with two levels of unity: the deep-level unity given by similarity of the

structural material (the interval-class content of the various rows) and the surface-level

unity given by instantly audible and identifiable motives.

This observation leads to a potential question: why consider this piece to be row-

based at all? Couldn’t one analyze this piece without recourse to a discussion of any

twelve-tone rows? Certainly, it is easy enough to interpret this Etude as a realization of a

kind of game of intervallic manipulations. While it is not my intention to hypothesize

about the precise manner in which Denisov might or might not have gone about

composing this piece, it is not unreasonable to imagine a composer setting up the system

of limitations in which Denisov appears to be operating in the majority of this Etude:

using only three interval classes, complete the aggregate with minimal pitch-class

repetition.

The distinction here is subtle, and ultimately is little more than a chicken-and-egg

dispute. Is the piece based on the transformations of several rows which feature ics 1, 5

and 6? Or is the piece based on manipulations of ics 1, 5 and 6 which happen to form

several ordered aggregates? While I suspect that both interpretations have some validity,

it seems unlikely that the use of a variety of twelve-tone rows was not a conscious part of

the compositional act. Given that there are 1,392 twelve-tone rows that use only ics 1, 5

and 6, it is improbable that Denisov would ever stumble upon a different member of a

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previously used row class. While he does not repeat the same row class very often,

members of Rows A and C are both used multiple times in this Etude. Furthermore, the

third Etude in this set of Five Etudes is based exclusively on transformations of Row C.

This evidence makes it difficult for me to dismiss the underlying row structure as merely

incidental, or the result of intervallic manipulations.

***

In this chapter, we have seen Denisov’s use of highly similar rows in the first of

his Five Etudes for Solo Bassoon. I have demonstrated the nature of the relationships

between these rows by using the ICSG and adapting Scott and Isaacson’s similarity

measure, Angle. I have also demonstrated Denisov’s technique of serial modulation

between the different row forms in this Etude, and I have tried to show how the

underlying structural connections between the different rows manifest themselves as

motives on the surface of the music. In the next chapter, we shall see a different kind of

multiple-row piece: Denisov’s Sonata for Alto Saxophone and Piano. Where the Etude made

use of ten closely related rows, the Sonata makes use of two widely contrasting rows.

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CHAPTER 5 ANALYSIS: SONATA FOR ALTO SAXOPHONE AND PIANO (MVT. 3)

From Denisov’s use of multiple twelve-tone rows with highly similar intervallic

construction in the Five Etudes for Solo Bassoon, we now turn our attention to the analysis

of a piece in which the multiple rows have contrasting intervallic material. In this

chapter, I will discuss the third movement of Denisov’s 1970 Sonata for Alto Saxophone

and Piano, which is probably his most frequently performed and recorded work, and a

staple of the modern saxophone repertoire.1 This piece takes most of its pitch material

from two distinct twelve-tone row classes, but also contains a fair amount of non-row-

derived material. We begin with some general observations about Denisov’s writing for

the saxophone and discuss five existing published studies of the piece. The ensuing

analysis has two main objectives: to examine Denisov’s use of serial modulation in the

Sonata, and to demonstrate how the interval-class succession graph can inform an

understanding of the relationship between the two rows, and also the relationship

between the dodecaphonic and non-dodecaphonic sections of the composition.

The Sonata is the second of six works including saxophone written by Denisov

during his career, and the first to use the instrument in a soloistic capacity. The 1966

Five Stories of Mr. Keuner for tenor and seven instrumentalists uses the alto saxophone as

well, but the instrument’s role in this piece is almost exclusively supportive, filling the

role of low woodwind the piece’s instrumentation, which is similar to that of Stravinsky’s

The Soldier’s Tale.2 Furthermore, the saxophone part does not involve any significant

technical challenges for the performer.

1 Helton 2000, 16. 2 Denisov and Stravinsky’s pieces each make use of one “high” and one “low” representative from woodwind, brass, and string families (though Denisov’s piece uses a piano in place of a high string instrument). The instrumentation for Five Stories of Mr. Keuner is as follows: Eb clarinet, alto saxophone,

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The Sonata marks a new phase in Denisov’s interest in the saxophone, in

particular, as a solo instrument. In the years following 1970, the composer wrote Two

Pieces for Alto Saxophone and Piano (1974), the Concerto Piccolo (1977) for a solo saxophonist

playing successively soprano, alto, and tenor saxophones with the accompaniment of six

percussionists, a transcription for alto saxophone of his Concerto for Viola (1986), a Quintet

for Four Saxophones and Piano (1991), and the Sonata for Alto Saxophone and Violoncello

(1994). This new phase appears to have been brought about by Denisov’s interaction

with the famous French saxophonist, Jean-Marie Londeix, to whom the work is

dedicated. Through the encouragement of Dmitri Kabalevsky, Londeix gave six

performances and several public lectures in Moscow during March, 1970.3 During this

visit, Londeix apparently made quite an impression on the Soviet music world in general,

and on Denisov specifically. Before this visit, the saxophone was not taken seriously in

the Soviet Union as an instrument of serious artistic merit, and, in fact, it was not even

taught in the Moscow Conservatory.4 Denisov was so impressed by Londeix’s

remarkable performance abilities that he asked the performer to make a recording

demonstrating the unique sonic capabilities of his instrument, which he did upon his

return to France. It appears to have been this recording that helped Denisov to discover

a number of extended saxophone techniques (quarter tones, multiphonics, timbre-

altering fingerings, etc.) which were incorporated into the Sonata.5

The impact that this work has had for the saxophone community is

immeasurable. Londiex himself has noted that Denisov’s Sonata “has become one of the

trumpet, trombone, piano, double bass and percussion. Stravinsky’s The Soldier’s Tale uses the following instrumentation: clarinet, bassoon, trumpet, trombone, violin, double bass and percussion. 3 Londeix 2000, 222. 4 Umble 2000, 100. See Umble 2000, 97-101 for a more detailed account of the impact that Londeix’s visit to Moscow had on the contemporary music scene in general. 5 Ibid., 101.

118

most significant works in the saxophone’s repertoire.”6 It is interesting, then, that

Denisov himself has said that he does not consider this work to be one of his most

successful pieces.7 Ekaterina Denissova-Bruggeman has written a brief note about the

Sonata, based on her late husband’s own thoughts about the work, which would be

suitable for use as program notes for a performance of the composition. As was the case

with the note about the Five Etudes for Solo Bassoon, which we saw at the beginning of the

previous chapter, this note comes from the composer’s personal archive, maintained by

his widow, Ekaterina Denissova-Bruggeman. Because, to the best of my knowledge, this

note is not available in any published form,8 I will quote it here in full:

The Sonata for Saxophone and Piano was written at the request of the French saxophonist Jean-Marie Londeix and is dedicated to him. Denisov had a great deal of love for the saxophone, because it possesses considerable expressive and technical possibilities, both in the domain of jazz and classical [music]. Furthermore, Denisov had great esteem for the saxophone’s very large, sonorous, and dynamic amplitude. Sonata form is not present here. It is more a cycle of three movements, which have an analogous meaning to the three-part cycle of the 19th century sonata. The first movement has the function of the allegro of the sonata-cycle. Very energetic, it alludes to a jazz improvisation. The syncopations, the uneven rhythms found in the swing [style], disrupt the regular beat. The meters are constantly changing: 6/32, 4/32, 11/32, 17/32, etc. The principal theme is constructed in the manner of jazz: the melodic line is almost improvised, syncopated. The piano accompaniment is also typical of jazz: the chords which occur in the gaps left by the soloist sound isolated and heavily accented. The second movement is a monologue for solo saxophone. It is only at the end [of the movement] that the piano emits some very delicate

6 Londeix 2000, 222. 7 Helton 2000, 16. James Umble also notes that “[t]wenty-five years later the composer paradoxically stated he didn’t totally identify with this work, as he found it too ‘aggressive.’” See Umble 2000, 223, n. 332. 8 There are similarities between this note and two other sources: the liner notes Denisov wrote for Claude Delangle’s recording of the piece, on the CD The Russian Saxophone, BIS CD-765 (1996), and the discussion of the work found in Denisov and Shul’gin 1998, 208-211. It seems that Denissova-Bruggeman has compiled the present note from at least those two sources.

119

chords, bringing a new sound. This movement is very free in its development, which gives the impression of improvised music. It also acts as a long prelude to the third movement. In the finale, all the musical material becomes imprinted with the jazz element that takes center stage at the beginning, when the piano imitates the movement of the boogie woogie. Here, a concertante and virtuosic style dominates the writing. Denisov’s Sonata is very popular among saxophonists throughout the world. It appears as a required work in the majority of saxophone competitions, and has been recorded about fifteen times.9

EXISTING STUDIES OF THE SONATA Denisov’s most frequently performed piece is also the piece about which the

most has been published. Four essays have been published dealing with particular

aspects of the Sonata, all in English, and all primarily concerned with performance issues.

In addition, there is a short discussion of the piece in Kholopov and Tsenova’s book on

Denisov, and I will discuss that as well.

The first of these articles is the brief essay by the work’s dedicatee, Jean-Marie

Londeix, published as part of James Umble’s important reference book about the

renowned saxophonist, Jean-Marie Londeix: Master of the Modern Saxophone. The

introduction to this essay provides some background on the composition of the Sonata,

most of which has been cited earlier in the present chapter. Following this, Londeix

describes some of the technical concerns found in each movement of the composition.

Most of these observations are either purely descriptive or provide some sort of

seemingly self-evident advice to the performer: “[t]he atonal and rather chromatic

language [of the first movement] is Boulezian in its general character, especially in regard

9 Unpublished note “Sonata pour saxophone alto et piano, 1970,” from the composer’s personal archive. The note was written in Russian by the composer’s widow, and I am deeply grateful to Mme. Denissova-Bruggeman not only for sharing this note with me (email correspondence, October 9, 2009), but also for translating it from Russian to French. The translation from French to English is my own.

120

to accentuation and dynamics,” and the suggestion that the performer should “clearly

and consistently present each dynamic gradation throughout each movement.”10

Londeix describes the third movement as “a jazz trio for saxophone, piano, and

string bass, with the piano assuming the two latter roles.”11 He also mentions a number

of “jazz characteristics” found in this movement: “a strong rhythmic pulse, dominant

seventh and blues chords, the pizzicato of the string bass at the outset…”12 Londeix

does provide a description of the form of the movement. He argues for an

interpretation that divides the piece into four large sections (with divisions at m. 21, 43

and 53) and a coda (beginning at m. 76), which he refers to as “a stretto recalling elements

from the first two movements.”13

The author refers to the Sonata’s first and third movements as being based on a

twelve-tone row, and identifies the two transpositions of the D-S-C-H motive which

begin each of the row’s hexachords. In a footnote, he cites the suggestion of one of his

students that these two four-note groups (D-Eb-C-B and A-Bb-G-F#) can be re-ordered

diatonically (G-A-Bb-B-C-D-Eb-F#) to demonstrate “a kind of altered blues scale.”14

This observation, unfortunately, is not explored any further. It is unclear, for example,

why G has been selected as tonic in this scale, since that particular pitch class does not

appear to have any significant structural importance throughout either the first or the

third movement.; if anything, the consistent presence of the pitch class C at the

beginning of the piano’s ostinato in m. 1 and the pitch class D at the beginning of the

saxophone’s repeated statements of the primary row immediately following suggests that

10 Umble 2000, 223. 11 Ibid., 224. 12 Ibid. 13 Ibid., 225. 14 Ibid., 223.

121

a more likely tonal hearing of the beginning of the third movement, at least, would likely

identify either one of those two notes as the primary pitch center.

Regardless, Londeix correctly identifies the primary row of the movement (and

of the Sonata as a whole), but he neglects to even mention the presence of a second row.

Instead he refers to the “dominant seventh and blues chords”15 used in the third

movement, without mentioning that those purported jazz elements have a deeper level

of organization as part of a twelve-tone row, which is constructed precisely to highlight

those specific characteristics.

Denise Dabney’s 1995 article seeks to provide “diverse analytical insights” by

taking a “multicultural approach” to Denisov’s Sonata.16 The over-arching argument in

this essay is that Denisov represents the music of a different culture in each of the

movements of the composition. The first movement is labeled “Russian” because it

“suggests a possible element of anarchy” by using “violent rhythms, extreme dynamics,

[and] textural and dissonant sonorities.”17 Furthermore, she claims that the repeated-

note patterns “depict…Soviet oppression” by representing machine gun firing.18 The

second movement, on the other hand is labeled “East Asian” because of the use of

quarter-tones and unmeasured time, and the final movement is deemed “American”

because of the influence of jazz music.19 While these labels may or may not be helpful in

evoking a particular approach to performance, they are likely intended to be understood

in a rather informal, casual manner, and therefore I will not explore them in any detail

here.

15 Ibid., 224. 16 Dabney 1995, 10. 17 Ibid., 12. 18 Ibid. 19 Ibid., 13.

122

Dabney notes in passing that the third movement “begins with a 12 tone row in

the saxophone part,”20 but while she makes frequent reference to a three-note motive

which “is heard throughout the [first] movement,”21 she does not recognize the motive’s

source in the first three notes of Shostakovich's D-S-C-H motto, which begins the

twelve-tone row that governs much of the pitch-class material of the movement.

In 1999, Joren Cain published an article comparing stylistic aspects of Denisov’s

Sonata for Alto Saxophone and Piano with his Sonata for Alto Saxophone and Violoncello (1994).

Cain is the only author surveyed thus far who not only notes the presence of jazz-like

triads and seventh chords, but also recognizes their origin from a second row used in the

third movement. Additionally, he makes at least a passing reference to the interaction

between the two rows, noting how the two instruments “begin to exchange the rows”

between mm. 53-69.22 Unfortunately, the article’s primary goal does not allow Cain to

explore the movement in greater depth.

Finally, Jonathan Helton’s 2000 article presents some more detailed analytical

observations of the pitch structure of the work. Like Londeix, he also proposes an

outline of the movement’s form, interpreted in three large sections with an additional

coda (with divisions at m. 21, 53 and 76).23 While he also fails to identify the second row

as the source of many of the third movement’s “jazz harmonies”24 and “intermittent

chordal material”25 he goes to great lengths to analyze the structure of the piece’s

primary row. He notes that the row’s INT does not contain any occurrences of ics 4 or

6, and shows how these interval classes can be formed by simply exchanging the notes

20 Ibid. 21 Ibid., 11. 22 Cain 1999, 37. 23 Helton 2000, 31. 24 Ibid., 30. 25 Ibid., 33.

123

found at order positions 4 and 5, 7 and 8 (to form ic4), or 7 and 8 simultaneously with 9

and t.26 Helton makes the claim that these particular order position manipulations do

“occur in the piece,”27 although he never identifies precisely where in the piece they

occur.

l, but

ng

for

53,

ter of the main part is imparted to the material of the subsidiary

n

In their book on Denisov, Kholopov and Tsenova devote three pages to the

Sonata. Again, the comments provided are largely descriptive rather than analytica

the authors make special note of the two rows present in the movement, and the

intervallic dissimilarity between them. They mention that Denisov’s serial method

generally involves “working with the series as [one would work with] a theme, allowi

for its fragmentation, incomplete statement and repetition of separate segments.”28

From this thematic perspective, which resonates with Kurbatskaya’s definition of the

“technique of twelve-tone rows,” they are able to draw an analogy to sonata form

this movement. The two rows are comparable to primary and secondary themes,

presented in mm. 1-20, developed in mm. 21-53, and recapitulated beginning in m.

“where the charac

second series.”29

All five of the writings discussed here mention jazz influences in the third

movement only on a rather superficial level. While this might appear to be evidence of

incomplete analysis, it actually resonates with Denisov’s own writing on jazz music. I

1968 he published the article “New Music and Jazz” in the multi-lingual journal The

World of Music. In this article, he attempts to show ways in which jazz music (and folk

26 Ibid., 17-18. These are not exhaustive lists of the order position exchanges that can produce ics 4 or 6. For example, exchanging order positions 2 and 3 or 5 and 6 also will produce ic4 in this row. 27 Ibid. 28 Kholopov and Tsenova 1993, 119; 2000, 159. 29 Ibid. Helton also suggests a tentative sonata form reading of this movement, based on the recurrence of particular row chaining devices. See Helton 2000, 38.

124

music) might provide new musical structures for use in concert music. As he says in the

introduction to the article, “…we should not become snobs and, merely because m

people regard folk music and jazz as primitive forms of art, shut the door on their

natural penetration into serious music.”

any

ains

t

ecially

isov

e

of typical characteristics of his own music, and thus being

nmistakably by Denisov.

30 But throughout the article, Denisov rem

relatively vague on the specifics of the jazz influences that can be adapted for this

purpose. He mentions a prevalence of the use of ostinato as a formal device in the ar

music of the 20th century (citing specifically Stravinsky, Shostakovich and Orff), and

suggests that “jazz provides us with new forms of ostinato, not all of which (esp

those in the finest works of avantgarde [sic] jazz) have yet been investigated by

composers.”31 But Denisov’s discussion of these forms of ostinato ends here; at no

point is the topic engaged in any more detail. While it is clear that, for Denisov, the use

of ostinato can be seen as a jazz influence, it is unclear whether the ostinato walking bass

sections of the third movement of the Sonata are among these “new forms of ostinato”

or not. Additionally, he discusses connections between the general idea of improvisation

and various components of musical form which are left “unfixed.”32 In a sense, Den

appears to be primarily concerned with broad, general characteristics of jazz music,

rather than with specific features of a particular jazz style or performer. As a result, th

third movement of Denisov’s Sonata is able to sound “jazzy” in a general sense, while

still incorporating a number

u

30 Denisov 1968, 31. 31 Ibid., 31-32. 32 Ibid., 33. Denisov experimented with aleatoric techniques in a number of works, perhaps most famously the 1965 Crescendo and Diminuendo for Harpsichord and Twelve Strings.

125

F

Example 5.1 shows the form of the third movement. In this diagram, all the row

forms from this movement are labeled, and the non-row-based sections are identified by

the use of boxes, with some of the most prominent pc sets labeled inside these boxes.

The layout of the diagram shows that this movement primarily features a linear, three-

voice texture made of saxophone, piano right hand, and piano left hand. This texture,

course, corresponds with Londeix’s interpretation of the movement as “a jazz trio f

ORM

of

or

saxophone, piano, and string bass, with the piano assuming the two latter roles.”33

R ALTO SAXOPHONE AND PIANO (MVT. 3), FORM

on-serial material

OSTINATO 1

EXAMPLE 5.1: SONATA FO

* = incomplete row form † = out-of-order row form = n

1 2 7 8 9 10 11 12 3 4 5 6

Sax: AP ------------------------- AP --- AP AP -- AP --------- AP -------------- AP --------- AP ----- AP ---------- 2 4 2 4 6 8 t 0 2H: BP2 --------- BRI1 ----- BP9 -------- BRI8 ------- BP4 ----------------

-------- R

LH: *AP0 (+Eb) ------------------------------------------------------------------------------------------------------------------------

13 14 15 18 19 216 17 0

SaR

x: AI ------------------ AI7 ----- AI5 -------------- AI3 ------ 1 --- *AIe --- [0369] [0258] H: BPe ---------- BRI3 ----------------- *BRI9 *BRI7 *BRI5 *BRI3 [048][037][014]

-------- [016] ------- †*BP1 †*BPe †*BP9 †*BP7 [036][037][014]

----------------------------------

BP4 *BP3 BP2 *BP1 BP0 BRIe BP4

LH: (AP0) -------- OSTINATO 2

Sax: AI4 ------------------------- AI0 ---------- *ARP9 --------- ARIe ------------------------------ AIe ------------ AIt -------

33 See note 11.

RH: AI4 -- AI2 --------AI0 -- APe -- AP1 ---AP4 ---------- AI7 ----- AI5 --- ARP0 --- ARPt ----------- *AP 9 -----------

21 22 23 24 25 26 27 28

LH: 6 ------------------------ *BRP1 -- BRP7 ---------- BP3 --------- BRI2 ---- BPt --------------- BRI

29 30 31 32 34 35 36 33

Sax: (AI ) ---------- -------------- BRP ------------- AP ----- t 1 7 4 5 5

6 ------ARP4 --- AP2 ------- AP4 -- BRI7 †BI1 ---------------------------L *AI2 -------------------------- AI2 ----------- †BP4 --------------------------- BP1 ----- BP0 -------

*AP --- BP ------- BIRH: ARP8 - ARP

H: BP5 ----------

126


WHISPER CHORUS

OSTINATO 3

CODA

SaR

x: BP --------- *AP --- AP ----- *AP --------- *AP *AP -- AI --- AP ---- 3 2 2 4 4 4 7 7H: BP3 --------- *AP2 --- AP2 ----- *AP4 ----------- BI2 *AP4 *BRP6 *AP4 --- AI7 -- AP7 ----

LH: BP3 --------- *AP2 --- AP2 ----- *AP4 ----------- BI2 *AP4 *AP4 --- AI7 -- AP7 ----

45 46 47 48 49 50 51 52

Sax: (AP ) --- BP ----------- BRI ----------- BP ------ BRI -------- *BRI ------------- [0125]

5 7 6 7 6 7 1 - ---------- -- ---------- ]

- ---------- -------------

38 39 40 41 42 43 44 37

RH: BI0 ---- BRP - BI0 ------ BP9 BI9 ------ [0147] BRIt --- [0147LH: *BP9 --*BP5 BRI4 -BP5 -BI3 - BP3 ------- [0258] BRIe [036]

53 54 55 56 57 58

SaR

x: (AP ) --- BI ---------------- *BRP --------- *AP ----- AP ----- AP ----- AP ------- 7 7 8 9 4 6 8H: *BP2 *BP2 [0147] [036] [0258] [0147] -------------------- *BP2 *BP4

*BP2 --------- *BP2 --------------------------- BP2 -------------------------------------------------- *BP2 --- BP0 ------ LH:

59 60 61 62 63 64 ax: (AP ) -------------- AP ----------------------------- *BP -------AI ------------------------------------------- S 8 t 5 7 *BP9 [0369][0147][0258] [037][0258] BP2 ------ [0147]----------------------------------- H: *BP9 ---------------------------------------------------------------- BP2 ----- [0258]------------------ *BP2 -------- RH: L

Sax: *AI t ------- AIe -------------------------------------------------------- RH: [0147] [0258][037] [0147] ------------------------------------- BP8 ------------- 3 ---------------------------------------- [0258] -------------[0358] ------ [0258] BP0 ------------- LH: BP

65 66 67 68 69 (1st half)

69 (2nd half) 70 71 72 73 74

Sax: *ARIt -------------- ARI6 -------- AP8 ---------------------------- A ---------------------------------------------- Pt 6]

RH: [016] *AI7 ------ *AIe [016] LH: [016] *AI5 ------ [01AI9 ---------

75 76 77 78 79 80

Sax: [0369] -------------------------------------------------------------------- ------------------- *AI0 [0369] *AIt RH: *AIe ------------- [0369] -------------------------------------------------------------------- [0147][0258] ----------------- [0258] ------------------------- BP 3 BP4 LH: *AI8 [016] [0369] --------------------------------------------------------------------

SaR

x: [0369] --------------------------------------- H: [016] ----------------------------- [0127] [0147] [015] -----------------------------------------

LH: [016] ----------------------------- [0147] [0258] [016] -----------------------------------------

AP2

81 82 83 84 85

127

of

as

o

.

a

iece prior to this point. I shall have more to say

out this [0369] sonority shortly.

ECHN

v’s

ng

are four primary

As seen in Example 5.1, my interpretation of the form of this movement is

similar to that of Londeix and Helton. Both authors place structural divisions at m. 21,

53 and 76, but Londeix offers an additional division as well, at m. 43. I propose a formal

model that casts the movement as a succession of three ostinati, the second and third

which are separated by a series of soft unison gestures I call a “whisper chorus,”34

these unison figures are reminiscent of a big band “shout chorus,” but at a pian

dynamic. Like Londeix and Helton, I recognize the presence of a coda in this

movement, but I argue that the coda begins in the second half of m. 69, rather than at m

76, due to the reprise of material from the first movement. Measure 76, however, is

significant point of articulation within this coda, as it introduces the [0369] sonority

which has not played a role in the p

ab

T IQUES OF SERIAL MODULATION IN DENISOV’S SONATA

One of the primary organizational forces of the third movement of Deniso

Sonata for Alto Saxophone and Piano is his use of serial modulation. In the previous

chapter, we saw serial modulation used as a method of moving between different rows,

but in the Sonata Denisov’s modulation techniques are limited primarily to connecti

different forms of the same row. As we shall see presently, there

techniques of serial modulation found in the third movement.

The most widely known technique of serial modulation is undoubtedly David

Lewin’s RICH operation. RICH is the operation which connects a twelve-tone row

34 Helton calls this section the “jazz riff” section. See Helton 2000, 35.

128

form to the retrograde-inverted form whose first two elements are order positions t and

e of the original row form.35 Additionally, Lewin defines TCH as the successive

application of two RICH operations, and he defines MUCH as the operation which

connects a pitch or pitch-class segment to the retrograde-inverted form of that segment

which o

question. One such property is found in the

Sonata’s Row A, as shown in Example 5.2.

5.2: SONATA FOR ALTO SAXOPHONE AND PIANO (MVT. 3), ROW A

ROW A:

verlaps “to the maximum possible extent.”36

Any ordered series of pitches (or pitch-classes) can be linked to another form of

that series by RICH or TCH. Additional serial modulation techniques can be defined,

based on specific properties of the series in

EXAMPLE

As its INT shows, Row A begins and ends with the same interval. This property allows

for chain

ing together two row forms that are related by transposition, which I call TR-

hain.37

C

35 RICH is not restricted to twelve-tone rows. The operation can be applied to any pitch or pitch-class segment, regardless of whether or not that segment uses all twelve pitch classes. 36 See Lewin 1987, 180-183. 37 Care must be taken here not to confuse TR-Chain with Lewin’s TCH, as they both deal with “transposition chains,” but in different manners. Moseley 2009 also discusses something similar. His PCH is also a chain of transpostionally related row forms, but it only requires that the two row forms share a single pitch class. Moseley also introduces the labels RECH and ICH for retrograde-chain and inversion-chain, respectively. While these operations are useful in the repertoire Moseley investigates (as well as for the sake of theoretical completeness), they do not appear in Denisov’s Sonata, and, as such, I will not deal with them here.

129

EXAMPLE 5.3: RICH AND TR-CHAIN OF ROW A

arrows represent RICH operations, and the horizontal arrows represent TR-

s

P4

, completing a full T-Chain

ycle. The beginning of this cycle is shown in Example 5.4.

AP2 AP4 AP6 AP8 APt AP0 AP2

ARI7 ARIe ARI3

Example 5.3 shows the relationship between RICH and TR-Chain in Row A, starting

with AP2, the first complete row form found in the movement. In this Example, the

diagonal

Chains.

RICH and TR-Chain are two of four different serial modulation technique

featured in the third movement of Denisov’s Sonata. Their presence is especially

noticable at the beginning of the movement. The saxophone’s opening gesture is a clear

statement of row form AP2, repeated three times. Each repetition adds a portion of A

at the end of AP2, using AP2’s last two pitches as the first two pitches of AP4, as a T-

Chain. Once AP4 has been stated in its entirety, Denisov uses the last two notes of that

row form as the first two pitches of AP6. Similarly, AP6 modulates to AP8 by T-Chain,

which in turn modulates to APt, AP0, and finally back to AP2

c

130

EXAMPLE 5.4: SONATA FOR ALTO SAXOPHONE AND PIANO (MVT. 3), SAXOPHONE, MM. 3-738

During this process, the pianist’s right hand supports the saxophone’s TR-Chain with a

succession of RICH operations on forms of Row B, moving through BP2, BRIt, BP9,

BRI8, BP4, BRI3, and BPe before the pattern in m. 14. The beginning of this process is

shown in Example 5.5.

EXAMPLE 5.5: SONATA FOR ALTO SAXOPHONE AND PIANO (MT. 3), PIANO RIGHT

HAND, MM. 7-13

38 The irregular beaming in this Example is Denisov’s. Additionally, there is a clear misprint in the score in m. 6: the concert G4 on the sixth 16th note of the measure is notated as Ab4. This misprint has been corrected in Example 5.4.

131

The third technique of serial modulation found in this movement involves

chaining row forms together based on sharing a single pitch class. I call this technique

PC-Chain. As this technique requires no shared interval content, it is possible to link

together any two types of row forms. Furthermore, PC-Chain is the only modulation

technique which is used to link a form of Row A with a form of Row B. An occurrence

of this type of modulation is found in the saxophone part between mm. 35-37, as shown

in Example 5.6.

EXAMPLE 5.6: SONATA FOR ALTO SAXOPHONE AND PIANO (MT. 3), SAXOPHONE, MM. 35-37

The fourth and final technique of serial modulation is one that involves the

manipulation of one row form in order for the modulation to take place. I refer to this

technique as MANIP-Chain. This occurs in two different ways: as the result of an order

position exchange involving either the first or last two pitches of one row form, and as

the result of omitting a particular order position of one row form. This occurs in mm.

25-26, where the pianist’s right hand modulates from AP4 to AI7 by switching the order

of the first two pitches of AI7, as shown in Example 5.7.

EXAMPLE 5.7: SONATA FOR ALTO SAXOPHONE AND PIANO (MT. 3), PIANO RIGHT

HAND, MM. 25-26

132

Figure 5.1 shows the occurrences of each of these four techniques of serial

modulation in the third movement of the Sonata.

FIGURE 5.1: FOUR TECHNIQUES OF SERIAL MODULATION

RICH TR-CHAIN mm. 7-14 (RH: BP2 BRI1 BP9 BRI8 BP4 BRI3 BPe) mm. 25-30 (LH: BRI7 BP3 BRI2 BPt BRI9 BP5) m. 27 (RH: AI5 ARP0) mm. 34-35 (Sax: BI4 BRP5) mm. 37-40 (Sax: BP7 BRI6 BP7* BRI6) mm. 38-39 (RH: BI0 BRP1 BI0*) mm. 38-39 (LH: BP5 BRI4 BP5*)

* = MUCH operation

mm. 3-13 (Sax: AP2 AP4 AP6 AP8 APt AP0 AP2) mm. 13-18 (Sax: AI7 AI5 AI3 AI1 AIe) mm. 21-24 (Sax/RH: AI4 AI2) mm. 24-25 (RH: APe AP1) mm. 26-27 (RH: AI7 AI5) mm. 27-31 (RH: ARP0 ARPt ARP8 ARP6 ARP4)

PC-CHAIN MANIP-CHAIN mm. 24-26 (RH: APe AP4) mm. 24-27 (Sax: ARP9 ARIe) mm. 35-38 (Sax: BRP5 AP5 BP7)

mm. 30-31 (RH: omitted note, ARP4 AP2) mm. 25-28 (Sax: op exchange, ARIe AIe) mm. 25-27 (RH: op exchange, AP4 AI7)

THE ICSG IN DENISOV’S SONATA

The first and third of the Sonata’s three movements are based on transformations

of a twelve-tone row or rows. The first movement uses only a single row, which is

brought back at the beginning of the third movement. In the third movement, however,

this row is joined by a secondary row. As mentioned in Chapter 3, these two rows share

little in common in terms of intervallic content. The two hexachords of Row A begin

with transpositions of D-S-C-H, 39 which, when coupled together, create a weaving

39 The Sonata for Alto Saxophone was not the first piece Denisov wrote which used Shostakovich’s musical monogram. A year earlier (1969), Denisov composed a piece titled DSCH for clarinet, trombone, cello and piano. On the surface, this piece appears to be a tribute to the young composer’s mentor, who played a major role in the early part of his career. See Kholopov and Tsenova 1993, 8-12; 2002, 4-9. However, Schmelz 2007 argues that this piece might be better understood as a “stylistic and generational critique” (p. 309) of Shostakovich’s music, perhaps brought on by the disappointment the younger generation of Soviet composers felt when Shostakovich joined the Communist Party in 1960. In addition to

133

chromatic line, typical of a great deal of Denisov’s music, both dodecaphonic and non-

dodecaphonic.40 On the other hand, Row B makes use of no semitones or whole tones,

featuring instead “tonal” intervals which are linked together in such a way that makes a

variety of triads and seventh chords available to the composer. These rows and their

respective ICSGs are shown in Example 5.8.

EXAMPLE 5.8: SONATA FOR ALTO SAXOPHONE AND PIANO (MVT. 3), ROWS A & B

ROW A:

1 2 3 5

ROW B:

3 4 5

While Example 5.8 clearly shows that Row B’s ICSG is an abstract subgraph of

Row A’s ICSG, the subgraph relation also reveals an important connection between

Row A and the pianist’s non-row left hand part at the beginning of the Ostinato 1

section: a literal subgraph of Row A occurs in the opening measures of the Sonata’s third

movement. The left hand alone begins the movement with the six-note ostinato pattern

shown in Example 5.9, which supports the saxophone’s TR-Chain of forms of Row A.

Shostakovich’s motto, DSCH features a quotation from his Eighth String Quartet, which Schmelz says is “deformed” (p. 309) when it is combined with Denisov’s serial musical language. In this respect, DSCH can be seen as indicative of “the tenuous relationship between Shostakovich and the next generation of ‘unofficial’ composers…” (pp. 305-306). 40 As discussed in Chapter 1, this is an example of what Kholopov and Tsenova call “smooth threads.”

134

EXAMPLE 5.9, SONATA FOR ALTO SAXOPHONE AND PIANO (MVT. 3), M. 141

1 2 5

The INT and INT-C of the left hand part show the presence of Row A’s

intervals, but neither series of interval successions is found in the row as such. Cain has

identified this ostinato as the first five notes of row form AP0 with an interpolated Eb:

< 0 1 Eb 2 3 4 >.42 The addition of Eb to this partial row form allows for the presence

of ic5 in this ostinato, and produces an ICSG which can be seen as a literal subgraph of

Row A’s full graph.43 As it turns out, Eb is the only non-duplicating pitch class that does

not violate at least one of the paths of Row A’s ICSG when placed between Db and

Bb.44

Example 5.10 shows the piano part for mm. 17-19 of the third movement. This

passage marks the first point in the movement where the pianist’s two hands appear to

be working in conjunction with each other, rather than as two distinct voices. In the

second half of m. 18, the two hands present a melodic line in parallel minor ninths. The

INT of this line is < t 7 1 1 9 e >, which is not part of any form of either Row A or Row

B. However, we can see by examining the INT-Cs of the two rows that the interval-class

41 The repeat sign is not found in the actual score, but I have added it to the notation in Example 5.9 to demonstrate the motive’s ostinato function. 42 See Cain 1999, 36. Cain’s actual words are as follows: “…the ostinato is based on the first five notes of the piece’s tone row (with an added D-flat).” Given that there is no form of Row A that contains the pitch-class segment < 3 t 9 e >, I can only assume that the reference to D-flat in Cain’s article is a misprint, and should be replaced by E-flat. 43 To confirm this, one need only to look back at Example 5.8 and notice that, if the node labeled 3 (and that node’s associated arrow) is removed, what remains is the graph shown in Example 5.9. 44 Ab is the only other pitch class that comes close. While the interpolation of Ab would not add any new interval classes to the ICSG, it would force the arrows from ic2 to ic5 and from ic5 to ic1 to be reversed.

135

EXAMPLE 5.10: SONATA FOR ALTO SAXOPHONE AND PIANO (MVT. 3), PIANO PART, MM. 17-19

17

segment < 2 5 1 1 3 1 > is present between order positions 3-9 of Row A. As such, this

phrase produces an ICSG which is a literal subgraph of Row A’s subgraph: all the nodes

of Row A’s ICSG are present in the mm. 18-19 ICSG, but without the double-ended

arrow connecting ics 1 and 2.

In the first half of Example 5.10, which features a sixteenth-note sequence of

descending triads, the pianist’s right hand presents an ordered sequence from the second

hexachord of four RI-forms of Row B, each relating by T10 to the preceding row form.

The pianist’s left hand follows a similar pattern of T10-related P-forms of Row B.45 But

unlike the right hand’s passage, the left hand hexachords are presented out of order.

Specifically, order positions 1 and 2 have been exchanged, as have order positions 4 and

5. The ICSG shown below the example shows that these order-position exchanges do

not result in any significant alterations of Row B’s ICSG; the exchange of these

particular order positions does not result in any “new” interval-class content. If, for

45 These partial T10 cycles seem to be motivated by the T2 cycle formed in mm. 3-13 by the saxophone’s TR-Chained forms of Row A.

1 2 3 5 3 4 5

(ic 4 found only in RH)

136

example, order positions 0 and 1 were exchanged, a new interval-class succession would

result: ic4 would be followed by ic5.

At this point, it might be instructive and perhaps compositionally suggestive to

examine what I believe to be the four-step derivational process by which a third row,

Row C, is created. Example 5.11 shows the music of part of the Ostinato 2 section, mm.

34-42.

EXAMPLE 5.11: SONATA FOR ALTO SAXOPHONE AND PIANO (MVT. 3), MM. 34-42

INT-C: 4 3 4 3 4 3 5 3 5 3 3 4 3 3 3 4 5 3

137

EXAMPLE 5.11, CONT’D.

5 3 3 4 3 3 3 4 3 3 3 …

INT-C: 3 3 3 3 4

3 3 5 3 3 5 3 3 5 5 4 3 3 5 5 3 5

4 3 3 5 3 3 3 3 3 3 3 3 3 3 3 3 5

With the exception of a few measures of non-row-based music and one brief

statement of AP5 in the saxophone, this section is largely dominated by forms of Row B.

This fulfills the first step of the derivational process by which Row C is created: establish

Row B as an important aspect of the structural organization of the piece.

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From the end of m. 35 until m. 41, the piano part presents a two-voice inversion

canon, three sixteenth-notes apart. Throughout this canon, Row B briefly loses control,

and the musical material is non-row-based in m. 37 and the first half of m. 38. However,

each of the slurred segments here produces the same ICSG as Row B. This brief section

thus maintains the same set of interval-class successions, but has removed the

dodecaphonic requirement of aggregate completion without pitch-class duplication.

A similar event takes place in the saxophone part from the end of m. 40 through

m. 42. While the saxophone no longer presents different forms of Row B, it does

present interval-class successions that have already been heard as part of that row. The

saxophone uses ics 3 and 4 at the end of m. 40, ics 3 and 5 after an eighth-note rest, and

finally ics 3, 4 and 5 after yet another eighth-note rest.46 Both the piano part in mm. 37-

38 and the saxophone part in mm. 40-42 serve to fulfill the second step of the derivation

of Row C: separate Row B’s ICSG from its serial context.

After the whisper chorus, the second half of m. 53 finds the left hand beginning

the third ostinato pattern, based on row form BP2. Of interest here are the cascading

sixteenth-note triplet figures found variously in the saxophone and piano right hand

parts, shown in Example 5.12. Some of these sixteenth-note triplet figures are portions

of different forms of Row B, and some of them are not. Of those that are not forms of

Row B, every figure here features only ics 3 and 4, forming the ICSG that will soon be

associated with Row C. But in the present situation, this passage demonstrates the third

step of the derivational process: eliminate one of the interval classes from Row B (and

consequently, remove one of the nodes of Row B’s ICSG).

46 Notice that this final grouping does contain two “illegal” interval class successions: ic5 is followed by ic4 in two places.

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(TRIPLET FIGURES ONLY)

1 2 3 m. 56 m. 58m. 54

4 5 m. 60 6

m. 59 m. 61

7 8m. 62 m. 62

10m. 64 9 m. 65

m. 66

13m. 66 12 11 m. 66

m. 6815

m. 67 14

140

The final step of this process involves returning the new ICSG to a serial

context. This step is precisely what occurs at mm. 76-78, shown in Example 5.13.


Example 5.13 shows an excerpt from an extended passage, near the beginning of

the Coda, at m. 76. This section is based entirely on transformations of set class [0369].

The linear voices in this passage can be seen to have ICSGs that are subgraphs of the

ICSG of Row B: simple manipulations of ic3 and ic4. Though [0369] does not exist as

an ordered subset of either Row A or Row B, it is presented here through repetitions of

ic3, which is Row B’s most frequently occurring interval class, as well as one of only two

interval classes that Rows A and B share. The T1, T11, and T10 forms of the pc set

marked X on Example 5.13 result by connecting interval-class segments < 3 3 3 > by a

single ic4. Repetition of this pattern results in a new row, as seen in the left hand part:

< 0 9 6 3 e 8 5 2 t 7 4 1 >. Example 5.14 shows the INT and its ICSG. Simple

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inspection shows that this ICSG is a literal subgraph of Row B’s ICSG.47 Figure 5.2

summarizes the derivational procedure I have just demonstrated.

EXAMPLE 5.14: ROW C CREATED BY LEFT HAND IN MM. 76-78

3 4

FIGURE 5.2: DERIVATION OF ROW C STEP 1: Establish Row B’s importance in structural organization STEP 2: Maintain Row B’s ICSG, but remove the requirement of aggregate completion without pitch-class duplication STEP 3: Remove one interval class from this ICSG STEP 4: Re-apply the requirement of aggregate completion to this new ICSG.

Throughout the present discussion, as well as in Example 5.14, I have referred to

this row as Row C. But it must be remembered that Row C is of a notably different

structural importance than Rows A and B. Where those two rows govern large sections

of the movement, Row C’s influence seems to be limited to the section shown in

Example 5.13. Thus, Row C appears to function in a manner more like many of the

non-recurring rows of the Five Etudes for Solo Bassoon examined in Chapter 4.

***

In this chapter, I have used the third movement of Denisov’s Sonata for Alto

Saxophone and Piano to demonstrate an important extension to the use of the ICSG in 47 Returning the ICSG from Example 5.14 to a serial context shown in Example 5.13 involves a compositional choice – there are, in fact, 185 rows which have this as their ICSG. Speculations on the reason why this particular row was chosen as Row C are beyond the scope of the present study.

142

analysis. After examining the existing writings about Denisov’s best known

composition, I have used the ICSG in the same way as I employed it in the preceding

two chapters: to examine the structural relationships that exist between the movement’s

two rows. In addition to this examination, we have seen how subgraph relationships can

inform an understanding of the manner in which Row B relates to several of the non-

row-based passages of the Sonata. Finally, I have endeavored to explain the process by

which Denisov appears to derive a third row for limited use in the Coda of this

movement.

143

CHAPTER 6 ANALYSIS: OCTET FOR WINDS (MVT. 2)

To this point, we have considered music based on multiple twelve-tone rows,

and developed the ICSG. Then, Chapters 4 and 5 each presented analyses of multiple-

row pieces from Denisov’s oeuvre in order to demonstrate practical applications of the

concepts. In the present chapter, I will turn my attention to the second movement of his

Octet for Winds.

GENERAL OBSERVATIONS

Because, to the best of my knowledge, the only published writing dealing with

the Octet is the exchange between Denisov and Dmitri Shul’gin, a brief note about the

piece will provide some useful background on the general nature of the composition.1

As with the notes from Chapters 4 and 5, this note was written by, Ekaterina Denissova-

Bruggeman, and is based on Denisov’s own description of the piece.2

The Octet for Winds was composed at the request of the clarinetist Sabine Meyer, for the ensemble that she founded.

Regarding its form, it is a cycle in two movements, a configuration dear to Denisov, found in many of his works, beginning with the Wind Quintet (1969), Sonata for Solo Clarinet (1972), and later in the Sonata for Clarinet and Piano (1993) and the Symphony No. 2 for large orchestra (1996).

The first movement is a type of extended introduction, while the second is based on entirely different thematic material. It makes use of the technique of groups, where an ostinato of a single note plays an important role. Denisov finds the opposition of the cantilena in the first movement and the pointillism in the second particularly interesting as a dramatic idea. [This opposition] makes an allusion to the pictorial contrast between lines and points. In many of Denisov’s works, and particularly in his Octet, the lines of the first movement become the points of the second.

1 See Denisov and Shul’gin 1998, 373-375. There are also some brief remarks on the Octet in the liner notes to Sabine Meyer’s recording of this piece (EMI 7235 5 57084 2). 2 Ekaterina Denissova-Bruggeman, email correspondence with the author, February 6, 2008.

144

Furthermore, in the “singing” first movement, the voices are never synchronized with each other. Here, the actual instrument group is very homogenous, [and] polyphony is present everywhere. Conversely, in the second movement, where one could easily believe that everything is scattered or even “disorganized,” the sounding material being very pointillistic, the tendency is actually toward synchronization. At the end, all the voices gather together in chords. However, the rhythmic pattern of his chords is so complex that one almost wonders if the composer did not have the malicious idea to test the ability of the musicians to play as an ensemble…In fact, septuplets within which the beats there are multiple, scattered points, and rhythmic figures like 9:8, 11:8, etc.—all of this is singularly difficult to assemble. Thus, this work requires a large number of rehearsals.3

The second movement of the Octet is organized around three primary rhythmic

and textural gestures, featuring a series of different imitative textures. These gestures,

defined by Kholopov and Tsenova and discussed in Chapter 1, are “shooting,”

“pointillistic bursts,” and “smooth threads.” As a reminder to the reader, Examples 6.1-

6.3 show instances of these three gestures as they occur in the Octet.

EXAMPLE 6.1: OCTET FOR WINDS (MVT. 2), MM. 1-3, HORN 2 – “SHOOTING”

EXAMPLE 6.2: OCTET FOR WINDS (MVT. 2), M. 6, OBOE 1 – “POINTILLISTIC BURSTS”

3 Unpublished note “Octour à vent, 1991” from the composer’s personal archive, in possession of Ekaterina Denissova-Bruggeman. The note was originally written in Russian by Mme. Denissova-Bruggeman. I am deeply grateful to Mme. Denissova-Bruggeman not only for sharing this note with me (email correspondence, February 6, 2008), but also for translating it from Russian to French. The translation from French to English is my own.

145

EXAMPLE 6.3: OCTET FOR WINDS (MVT. 2), MM. 20-21, BASSOON 1 – “SMOOTH THREADS”

As Denissova-Bruggeman’s note indicates, the movement ends with the eight

players presenting complex shooting figures in rhythmic unison. But prior to that point,

the bulk of the movement features imitative textures, with very little homorhythmic

playing. In fact, through the first seventy measures, all shooting patterns are presented

in strict four-, seven- or eight-voice canons, with imitative entries placed at constant

quarter-note intervals.

While shooting patterns are found fairly consistently throughout the movement,

the pointillistic bursts and smooth threads appear to be used in different portions of the

piece. Specifically, pointillistic bursts dominate the first thirty measures, are seemingly

replaced by smooth threads from mm. 31-60, and return to the foreground during mm.

61-88. The final twelve measures (mm. 89-100) are made up almost entirely of

homorhythmic shooting, with the exception of a single measure of smooth threads, at m.

98.

FORM

Example 6.4 presents a form chart for the second movement. This chart shows

the interaction of the three different gestures and the different transformations of the

movement’s two twelve-tone rows. I shall have more to say about the rows themselves,

146

and their specific relation to the movement’s form shortly. But, for the sake of

reference, Example 6.5 shows the two rows and their respective ICSGs.

EXAMPLE 6.4: OCTET FOR WINDS (MVT. 2) – FORM NR = non-row-based material

SECTION 1:

Gesture: Shooting (S) -------

SECTION 2:

SECTION 3:

----------------------------------------------------------------------- Pointillistic bursts (P) ---------------- Rows: AP2 ---------------------------------------------------- AP6 ------------------------------------------

ARI9 -------------------------------- BPt/BRPt ------------------------------

1 2 3 4 5 6 7

Canon #1Canon #2

Gesture: S --------------------------------------------------------------------------------------------------------------- P ---------------------- Rows: APt ----------------------------------------- AP1 ----------------------------------------------------- ARI5 ------------- AP4 --------------------------------------------------------

8 9 10 11 12 13 14 15 16 17 18 Canon #3 Canon #4

Canon #5

19 20 21 22 23 24 25 26 27 28 29 30 Canon #6 Canon #7

Gesture: Smooth threads (T) ----------------------------- P ---------------------------------------- Unison P ------- Gesture: S -------------------------------------------- Ob 1: AP4 -------------- AP3 --------------- BP2 ------------- Ob 2: AI7 -------------- AP3 ------------ NR ------- Cl 1: AI9 -------------- AP3 --------------- BPt ---------- Cl 2: AI9 ----------------------- AP3 ----------- BP9 ---------- Bsn 1: AI4 ----------------- AP3 ------------ BP4 ---------- Bsn 2: ARP0 --------------- AP3 ------------ BP2 ---------- Hn 1: AI2 --------------- AP3 ---------- BP0 ---------- Hn 2: ARP6 ----------- AP3 ---------- NR ------------

BP2 BP0

Gesture: S --------------------------------------------------------------------- T ---------------------------------------------------------------- Rows: BIt -------------------------------------------------------------------- (Bsn 1: AI5)------------------

31 32 33 34 35 36 37 38

Canon #8

147


Gesture: S ------------------------------------------------------------------------------- Gesture: T --------------------------------------------------------------------------- Rows: Ob 1: BP4 ----------------------- NR ---------------------------------------- Ob 2: BP0 --------------------------------- NR ----------------- Cl 1: NR ------------------------------ Cl 2: NR --------------------------------------- Bsn 1: BP0 -------------------- NR -------------------- Bsn 2: BP0 -------------- NR ------ Hn 1: BI7 ----------------------

39 40 41 42 43 44 Canon #9

BP2 BP8 BP3

Gesture: S/T ------------------------------------------------------------------------------------------------------------------------------------- Rows: BI8 ---------------------------------------------- BP4 --------------------

45 46 47 48 49 50 51 52 53 54 55

Canon #10

Gesture: S (with multiphonics) ----------------------------------------- (silence) Rows: BP2 ----------------------------------------------------------------

56 57 58 59 60 Canon #11

SECTION 4:

Gesture: Unison S ------------------------------------------------------------------------------------------------------------------------------- Rows: BP2 ---------------------------------------------------------------------------------------------------------------------------------------

61 62 63 64 65 66 67

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68 69 70 71 72 73 74 75 76 77

Gesture: P -----------P/S -------------------- P ------------------------------------------------------------- Gesture: T ------------------------------------------------------------------------------ Ob 1: BPt -------------- NR --------------------------------- NR ----- BP0 ------ Ob 2: BPe -------------- NR ---------------------------- NR ----- BP0 ------ Cl 1: BI0 ------------------------- NR ---------------------------------------- BP7 -------- BP6 ---- Cl 2: BI5 --------------------- BIt ----- NR -------------------------- BP7 ------------ BP6 -- Bsn 1: BPe -------------- NR ------------------------- NR ----- BP3 ------ Bsn 2: BIe ---------------- NR -------------------------- NR ----- BP3 ------ Hn 1: BI5 -------- BIt ----- NR ------------- NR ------- BPt ------ Hn 2: BI5 ---- BIt ----- NR -------------- NR ------ BPt ---

Canon #12 Canon #13

78 79 80 81 82 83 84 85 86 87 88 89 90 91

Gesture: Ob 1

C

BB

H

Gesture: P (some unison BP2 chords) ------- Unison P --- Unison P -------------------------------- T ----------- T ------------------

: BP9 ------------- BI2 ------------ Ob 2: BI8 -------------- NR ------------

l 1: BI6 -------------- NR ------------ Cl 2: BI5 -------------- BP6 ---------------------

sn 1: BI7 -------------- NR --------------------- sn 2: NR ------------- NR ---------------------

Hn 1: BI8 -- BI2 ----- NR --------------------- n 2: BI9 ------------- BP2 ----------------------

92 93 94 95 96 97 98 99 100

Gesture: Unison S ---------------------------------------------------------------------------- T ---------- Unison S/TrillRows: NR -------------------------------------------------------------------------------------- BP5 (Cl 1) NR ---------------

149

EXAMPLE 6.5: OCTET FOR WINDS (MVT. 2) – ROWS A AND B, AND ICSGS

ROW A:

1 2 3 5

ROW B:

1 5 6

In terms of large-scale form, most of the movement’s five large sections are

separated by a quarter-note unison silence, with a three quarter-note silent duration

between sections 3 and 4. Within sections, phrases are defined by points of imitation

but with overlap blurring the phrase boundaries (in Example 6.4, the crossing arches

indicate the overlap).

Throughout the second movement, one can trace a process whereby a simple

phrase structure is gradually altered. The following discussion of the movement’s form

will focus on the development of the initial seven measures, paying particular attention

to the interaction between shooting gestures, pointillistic bursts, and smooth threads as

previously discussed.

Section 1 (mm. 1-18) features a large sort of period structure. The first seven

bars form a unit made of two canons, one utilizing shooting gestures, the other utilizing

pointillistic bursts. As Example 6.4 shows, the shooting canon presents two separate

forms of Row A, and the pointillistic canon presents several statements of a single form

of Row B. Measures 8-18 follow a similar basic structure, providing a consequent phrase

150

to mm. 1-7: the section begins with shooting canon material based on forms of Row A,

and concludes with canonically presented pointillistic bursts. This final statement of

pointillistic bursts (labeled as Canon #5 in Example 6.4) is shown as Example 6.6.

EXAMPLE 6.6: OCTET FOR WINDS (MVT. 2) – MM. 17-18, CANON #5

This section is not based on a particular row form, nor is the ICSG produced by any of

the individual instruments related by identity, isomorphism or inclusion to the ICSGs of

Rows A or B. However, ics 1 (presented as ±11 or ±13), 5 and 6 feature prominently in

mm. 17-18, giving it at least a similar overall sound to the statements of BPt in mm. 6-7.

151

Section 2 (mm. 19-30) features the first stage of development of this initial

phrase structure. While the first four measures introduce the lyrical band gesture in free

imitation, the bulk of this section is made up of another alternation between a shooting

canon based on a form of Row A (AP3) and a pointillistic canon based on several

fragmentary forms of Row B. The section concludes with the first homorhythmic

figures of the movement: a brief burst of pointillism followed by a long trill from the

entire ensemble. Though it might be possible to understand Section 2 as a continuation

of Section 1 because of the similar canonic structure, it seems clear that the primary

purpose of Section 2 is the introduction of new gestural elements: the smooth threads

which will be brought to the fore in Section 3, the idea of homorhythmic playing of

somewhat unpredictable rhythmic patterns, and the full ensemble trill which will

eventually conclude the entire piece.

Section 3 (mm. 31-60) is divided into four subsections, mm. 31-38, 39-44, 45-55

and 56-60. Each of these sections recasts the structure of the different parts of Section

1, by allowing the smooth threads of the beginning of Section 2 to replace the

pointillistic bursts of Section 1. The shooting canons remain constant, but are

contrasted in each statement by increasingly long smooth threads. The angular

pointillistic bursts have disappeared entirely. This pattern of shooting smooth

threads plays out in three of the four subsections, and is expected when the fourth

subsection begins in m. 56. But this expectation is not realized, as the addition of

double-reed multiphonics bring Section 3 grinding to a rather alarming halt.

At the beginning of Section 4 (mm. 61-77), the homorhythmic material which

was introduced at the end of Section 2 returns. By this point in the piece, the earlier

pointillistic bursts have completely lost the inclination to change pitch and, instead, form

152

the homorhythmic shooting gestures that play such an important role in Sections 4 and

5. These two sections have a recapitulatory function, bringing together all the primary

gestures of the piece. After the opening homorhythmic passage, a freely imitative stretto

brings the pointillistic bursts into close contact with smooth threads and a shooting

canon as shown in Example 6.7.


As the end of the piece approaches, we are confronted with the fiendishly difficult

ensemble shooting patterns to which Denissova-Bruggeman referred in her writing

about the piece. These shooting rhythms are interspersed with brief canonic smooth

threads, before finally concluding with a long, forceful trill from the entire ensemble.

153

MULTIPLE ROWS IN THE OCTET

As can be seen in Example 6.5, the two rows of Denisov’s Octet for Winds share

little in common in terms of interval-class content and subset content. Row A itself

forms a weaving chromatic line, featuring primarily ics 1 and 2, with a single occurrence

each of ic3 and ic5. On the other hand, Row B is derived entirely from [016] trichords,

using exclusively ics 1, 5 and 6.4 While the two rows both share ic1, the realization of

those interval classes on the actual surface of the music is notably different: Row A’s five

ic1s are always realized as ±1, while the three ic1s in Row B are always realized as ±11 or

±13. This different treatment of the same interval class produces an audibly different

effect.

Despite the dearth of common interval-class content, the two rows share a

similarity in the successions of their respective interval classes: Row B’s ICSG is an

abstract subgraph of Row A’s ICSG. Because the visual presentation of the ICSGs in

Example 6.5 does not make this relationship immediately obvious, the two graphs are re-

drawn in Example 6.8, with the nodes of Row B’s ICSG rearranged to make the

connection clearer.

EXAMPLE 6.8: OCTET FOR WINDS (MVT. 2) – ROW A AND B, ICSGS RE-DRAWN

ROW A:

1 2 3 5

6 5 1

ROW B:

4 Not only are Row B’s discrete trichordal subsets members of set class 3-5 [016], but every trichordal subset from this row are members of set class 3-5.

154

The two rows share several notable features with Rows A and B of the Sonata for

Alto Saxophone and Piano. Each piece’s respective “Row A” is a winding chromatic line,

made up of mostly ics 1 and 2, with a few occurrences of ics 3 and 5. They share very

similar BIP-Vectors as well: [622010] is the BIP-Vector of the Sonata’s Row A, and the

Octet ’s Row A has BIP-Vector [631010]. Furthermore, their ICSGs are very closely

related. Though not identical, they do share identical underlying ordinary graphs.5

Although they can be visualized easily by imagining the ICSGs in Example 6.5 above and

Example 5.9 with their arrows removed, Example 6.9 shows these two underlying

graphs.

EXAMPLE 6.9: OCTET FOR WINDS, ROW A & SAXOPHONE SONATA, ROW A – ICSGS

AS NON-DIRECTED GRAPHS OCTET, ROW A:

SONATA, ROW A:

In addition, each piece’s respective “Row B” is made up of larger intervals. The

Sonata’s Row B is made up of leaps of ics 3, 4 and 5, and the Octet’s Row B is made up of

leaps of ±11, ±13, and ics 5 and 6. While the trichordal subsets of the Sonata’s Row B

5 As discussed in Appendix 2, an “ordinary” graph is a non-directed graph, or a graph without arrows. Although I have not explored the analytical uses of ordinary graphs in the present study, they can be used to show possible connections between interval classes, without the specificity of actual interval-class successions; an ordinary graph can only show that node x might follow and/or might be followed by node y.

1 2 3 5

1 2 3 5

155

are certainly not as regular as those of the Octet’s Row B, the Sonata’s row does at least

feature [037] subsets as three of its four discrete trichords (and three additional non-

discrete trichordal subsets, as well). The two rows yield isomorphic ICSGs, as shown in

Example 6.10. Furthermore, both ICSGs are abstract subgraphs of their corresponding

Row As.

EXAMPLE 6.10: OCTET FOR WINDS, ROW B & SAXOPHONE SONATA, ROW B –

ICSGS OCTET, ROW B:

1 5 6

SONATA, ROW B: 5 4 3

Some comparable relationships can be seen between the rows of the Sonata, the

Octet, and the Concerto for Guitar and Orchestra. The two rows from the Concerto are

reprinted here as Example 6.11, accompanied by their INT-Cs and their ICSGs. From

this Example, it can be seen that Row A’s ICSG is an abstract subgraph of that of Row

B.6 Clearly, the ICSG of the Concerto’s Row A is isomorphic to those of the Sonata and

the Octet’s Row Bs.

Composed in the same year as the Octet, the Concerto for Guitar also involves the

use of a derived row: all the discrete trichords of Row A are members of set class 3-8

[026]. In both pieces, the regularity of construction of the derived row provides a

6 There are, in fact, six different mappings that can relate Row A’s ICSG to Row B’s ICSG. 1) 1 2, 4 4, 6 1; 2) 1 4, 4 2, 6 1; 3) 1 2, 4 6, 6 1; 4) 1 6, 4 2, 6 1; 5) 1 4, 4 6, 6

1; 6) 1 6, 4 4, 6 1.

156

contrast to the other, more intervallically varied row. As suggested in Chapter 3, this

contrast can be viewed as analogous to the primary and secondary themes in a piece of

EXAMPLE 6.11: CONCERTO FOR GUITAR – ROWS A AND B, AND ICSGS

Row A:

1 4 6

Row B:

tonal music. In the Concerto, Row A is treated as a static melody, with an apparent

ritornello function, while Row B is used at specific formal junctions as a sort of

transitional signal.

In the Octet, the case is somewhat different. Initially, the rows are attached to

specific gestures: Row A makes up the pitch material of the shooting canons, while Row

B (or intervallic material related to Row B, as previously discussed) is used as pointillistic

bursts. The consistent association between the rows and their respective gestures allows

2 1 3 4 6

157

us to view these rows as thematic, in the sense described by Kurbatskaya in her

definition of the “technique of twelve-tone rows.” But these rows are used in two

different ways: 1) through transformation, as the sources of pitch material of large parts

of the musical fabric, and 2) in a form-generative manner.

Regarding the first type of use, one can observe from the form chart shown in

Example 6.4 that these two rows are used in a variety of transformations throughout the

movement, and they are never used simultaneously. This allows for large sections of the

movement to have the unity provided by the use of manipulated forms of a single row.

As discussed in Chapter 2, Kurbatskaya makes a careful distinction between the concepts

of “row” and “series,” where the former is treated somewhat like a melody, and the latter

is treated like the background source of pitch material. In the Octet, Rows A and B walk

a fine line between these two concepts: they are attached to a specific rhythmic/textural

gestures in a manner similar to that which Kurbatskaya describes, but they also are used

in a variety of transformations which recalls Kurbatskaya’s definition of “serial

technique.”

Secondly, the interaction of these two rows with each other and with the three

primary gestures of the movement plays an important role in defining the composition’s

form. Overall, this piece traces a path from multiple-row serialism, to single-row

serialism, to freely atonal. The first two sections of the piece establish a conflict between

the two contrasting rows, each assigned to its own particular type of gesture. At the

beginning of Section 2, smooth threads are heard for the first time, and each instrument

presents a truncated form of Row A. These fragments of Row A are shown in Example

6.12. Eventually this gesture gives way to the familiar shooting canon, which features

row form AP3. At this point in the piece, Row A seems to be asserting itself as the

158

primary row of the movement; Row A is not only continuing to dominate the shooting

gestures, but also dominates the new gesture-type, smooth threads.


This situation changes abruptly in Section 3. Canon #8, which begins this

section, provides the expected return to the shooting gesture, but this time, the pitch

material of this canon is taken from row form BPt. When the smooth threads return in

m. 35, only the first bassoon presents a statement of a form of Row A; all the other

instruments have moved to freely atonal material. However, given the presence of small

intervals and frequent direction changes, this freely atonal music has at least a similar

aural stamp to Row A.

Following this last brief statement of AP5 by the bassoon, Row A disappears

completely. Row B establishes its own dominance by taking over the shooting gestures

and even involving itself in the smooth threads of mm. 42-44. This dominance appears

to be confirmed in Section 4: from mm. 61-67, the entire ensemble presents a unison

159

pattern of irregular rhythms which project row form BP2,F

7F a portion of which is shown

in Example 6.13; pointillistic bursts return in mm. 68-69 and 74-77, with each instrument

playing fragmented forms of Row B; a brief shooting canon based on BIt occurs in mm.

70-71.


As was the case with Row A, once Row B appears to have established its primacy

over the pitch material of the movement, the focus shifts. During the first six measures

of Section 5, Row B gradually loses hold over the musical fabric, until it disappears

7 As Example 6.13 shows, mm. 61-67 only present order positions U4U – Ue U of BP2. The first four pitches are not shown here, but they are found in mm. 56-59 with the last note of horn 2’s lyrical band (U0U), and the four-voice shooting canon in clarinet 1 (U1U), clarinet 2 (U2U), horn 1 (U3U), and horn 2 (U4U). The horn 2 pitch is carried through from the shooting canon (mm. 57-59) to the phrase shown in Example 6.13.

160

entirely in m. 84. The remainder of the movement alternates between freely atonal

homorhythmic shooting figures and smooth threads. The final set of smooth threads

presents the interval classes involved in Row B, and even presents a fragmented version

of row form BP5 in the first clarinet, but, before this row is allowed to reassert itself, a

fortissimo statement of the unison shooting gesture shuts the door and ends the

movement.

***

In this chapter, I have demonstrated the role played by three distinct rhythmic

and textural gestures, defined by Yuri Kholopov and Valeriya Tsenova, in the second

movement of Denisov’s Octet for Winds. I have continued to use the ICSG developed in

the earlier chapters of this dissertation, but have limited my use of it to a discussion of

the relationships between the two rows of the Octet, and also to provide insight into

some larger connections between the rows of the Octet, the Saxophone Sonata, and the

Concerto for Guitar. These connections have revealed some general trends in Denisov’s

multiple-row serialism. Specifically, I have demonstrated the composer’s predilection for

using pairs of rows with contrasting intervallic content, but with similar arrangements of

interval-class successions. The remainder of this chapter focused on the interaction

between the previously defined textural gestures and the changing row structure of the

piece.

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CHAPTER 7 CONCLUSIONS AND EXTENSIONS

The primary goal of this study has been to formulate theories for and to present

analyses from the multiple-row twelve-tone pieces in Edison Denisov’s compositional

output. Though multiple-row serialism makes up only a small segment of Denisov’s

oeuvre, it has been present in his music throughout his career. Furthermore, the use of

multiple rows is noted by Peter Schmelz as a distinctly Russian trait.1 The combination

of the cultural and political separation of the young Russian composers, and Denisov’s

unique vision, resulted in works which simultaneously follow some of the Second

Viennese School’s lead, but which move in new directions in the treatment of serial and

non-serial elements.

As a prelude to this discussion, it was first necessary to address some general

issues. First, in order to gain an understanding of the Russian concept of serialism,

Chapter 2 presented an annotated translation of a chapter from the first Russian

monograph on serialism, Svetlana Kurbatskaya’s Serial Music: Questions of Theory, History

and Aesthetics. The terms, definitions and concepts presented in Kurbatskaya’s work were

then applied in an analysis of the first known piece of serial music to have been written

in the Soviet Union, Andrey Volkonsky’s Musica Stricta.

Second, Chapter 3 served two purposes: initially, to suggest three aspects of

multiple-row serial music as fruitful points of inquiry for the analysis of such music, and

subsequently to introduce the interval-class succession graph (ICSG). The first part of

the chapter suggested that the analysis of multiple-row serialism should address

structural and functional issues between the rows involved, and the ways in which an

underlying unity might exist, despite the use of multiple rows. In the second part of 1 Schmelz 2004, 326.

162

Chapter 3 the ICSG was presented, with the intent of making clear its potential use in

examining structural relationships between pairs of twelve-tone rows (or, indeed, any

ordered pattern of pitch classes). The second part of this chapter, in combination with

Appendix 2, presented terminology adapted from mathematical graph theory which can

be used to describe the structure of the graphs formed by different twelve-tone rows.

With these necessary preliminaries in place, the study presented analyses of three

works from various points during Denisov’s “mature”2 period: chronologically, the

third movement of the Sonata for Alto Saxophone and Piano (1970), the first of the Five

Etudes for Solo Bassoon (1983), and the second movement of the Octet for Winds (1991).

The Etude provided an appropriate opportunity to work through the tripartite approa

to the analysis of music based on multiple twelve-tone rows. In the analysis of the

Sonata, I used the ICSG to show not only the relationship between the two rows used in

the third movement, but also to show the connections between the intervallic structur

of the rows and some of the non-row-based sections of the movement. Finally, the

analysis of the Octet focused primarily on the interaction between the row structure and

the use of various rhythmic/textural gestures. Additionally, Chapter 6 endeavored

show commonalities between Denisov’s multiple-row procedures in these two pieces,

and in the Concerto for Guitar and Orchestra (1991), discussed briefly in Chapter 3.

Specifically, we saw that Denisov tends to favor row pairs related by abstract inclusio

which share relatively little common interval-cla

ch

e

to

n

ss content.

2 Kholopov and Tsenova refer to the period from 1964-1977 as Denisov’s “individual style,” and the time period from 1977-1996 as “stabliziation,” stating that the works prior to his 1964 cantata The Sun of the Incas represented a “prenatal” (predrodovomu) state in his compositional development. See Kholopov and Tsenova 1993, 51 and 58; 2002, 57 and 65.

163

FURTHER RESEARCH

This dissertation has opened up several new avenues for potential exploration.

First, the ICSG, as an analytical tool, is flexible enough to offer any number of

extensions. The general concept of a succession graph can be adapted to account for

successions in non-pitch domains. Example 7.1 shows the subject of an eight-voice

canon (Canon #1, see Example 6.4) at the beginning of the second movement of

Denisov’s Octet.

EXAMPLE 7.1: OCTET FOR WINDS (MVT. 2) – MM. 1-5, HORN 2

Phrase 1 Phrase 2…

Beat 7 8 6 10 8 6 8 4 8 6

Divisions:

Phrase 3

8 10 6 7 10 8 6 10 6

From a performer’s standpoint, the most difficult aspect of this passage certainly

must be the constant shifting of beat subdivision required: the first beat is divided into

seven parts, the second beat is divided into two parts, the first of which itself is divided

into four and the second of which is divided into three. Below the example, I have

placed the numbers 4, 6, 7, 8 and 10 based on the divisions of the quarter-note beat

throughout the passage.

Example 7.2 shows a rhythmic adaptation of the ICSG, which captures the

succession of beat divisions in each of the three phrases of Example 7.1. In this case,

164

the beat-division succession graphs for the second and third phrases prove to be

isomorphic to each other. Furthermore, these two graphs appear to be closely related to

the graph of the first phrase. Specifically, the direction of the arrow connecting the first

and last nodes has been reversed, as has the direction of the arrow connecting the two

nodes at the extreme right of the graph. These three graphs all share the same

underlying non-directed graph. It is not difficult to imagine using these graphs as a

practice tool to be used by performers of this piece in order to practice the range of beat

division successions required.

EXAMPLE 7.2: OCTET FOR WINDS (MVT. 2) – MM. 1-5, HORN 2, BEAT-DIVISION

SUCCESSION GRAPHS PHRASE 1: 6 7 8 10

PHRASE 2:

6 4 8 10

PHRASE 3:

6 7 10 8

The concept of “underlying non-directed graphs” has come up twice in this

study: once near the end of Chapter 6, and once here. We might consider exploring the

relationships between succession graphs which, though not equivalent or isomorphic,

share identical underlying non-directed graphs. It would be possible to define a variety

of “arrow operations” on such graphs. We might say that, in Example 7.2, the beat-

165

division succession graphs of Phrase 1 can be transformed to the graph of Phrase 2 by

two applications of an operation called arrow reversal: moving 10 8 to 8 10 and 6

10 to 10 6. Three such operations could be defined. Arrow reversal is the operation

that converts the adjacency (x,y) to (y,x). Arrow addition adds an element to the set of

adjacencies in the graph: if adjacency (x,y) exists, then arrow addition allows a new graph

to maintain that adjacency but also to add the adjacency (y, x). Finally, arrow deletion takes

a symmetric adjacency, where (x, y) and (y, x) are both members of the set of the graph’s

adjacencies, and eliminates one of these adjacencies.

From adapting the concept of an ICSG to showing successions of different beat

divisions, it is easy to imagine other generalizations of this basic idea. In fact, any series

of musical events which can be described by saying “this can be followed by that” can be

represented by a succession graph. One pedagogically useful example is presented as

Example 7.3.

EXAMPLE 7.3: GRAPH OF FUNCTIONAL CHORD SUCCESSIONS IN MAJOR MODE

PIECES

This familiar diagram from Stefan Kostka and Dorothy Payne’s textbook Tonal Harmony

represents “the normative harmonic functions in major keys.”3 Though the visual

presentation of this diagram is quite different than the graphs I have used throughout

this paper, it should be clear that the principle is the same: arrows connect certain “legal”

chord successions, and the lack of an arrow connecting two Roman numerals indicates 3 Reprinted from Kostka and Payne 2009, 113.

166

an “illegal” chord succession. As another example, we might even attempt to represent

the harmonization of different bass scale degrees from François Campion’s 1716 Regle de

l’octave in a graph like the one shown in Example 7.4.4

EXAMPLE 7.4: CAMPION’S REGLE DE L’OCTAVE PRESENTED AS A SUCCESSION

GRAPH

A second area of inquiry opened up by this dissertation lies in the area of the

INT-C, as introduced and discussed in Chapter 3. In that chapter, it was noted that an

INT-C does not necessarily define a single row; it is possible for two distinct rows to

share an INT-C. This property defines a situation analogous to the Z-relation of Forte’s

pc-set theory. An abstract study of “Z-related rows” might prove to be a fruitful area of

future exploration. In fact, Sebastiano Bisciglia and Jeremiah Goyette, fellow graduate

students at the Eastman School of Music, are in the early stages of writing dissertations

dealing with these and other related issues.5

Third, I hope that this dissertation represents a significant step in Denisov

scholarship. Even so, there is still important work to be done. Most obviously, I have

only addressed one specific area of his musical style. Considered in its entirety, his

4 Campion’s Regle de l’octave (Rule of the octave) was one of many ways of harmonizing ascending and descending bass scales (and scale fragments) during the 18th century. See Christensen 1992, 91. 5 Sebastiano Bisciglia, personal correspondence with the author (email, November 27, 2009).

^

5 3 ^ 1

6 4 3 2 ̂

6 3 3 ̂

6 5 4 ̂

6 4 2 4 ̂

5 3 5 ̂

6 3 6 ̂

6 4 3 6

6 5 7 ̂

6 3 7 ̂

167

compositional output involves a wide array of different approaches, many of which are

themselves worthy of further exploration. In particular, the twelve-tone works of

Denisov’s so-called “second conservatory” demonstrate a far more “traditional”

approach to dodecaphonic composition than the works examined in this dissertation.6

An in-depth examination of these works might provide some insight into the composer’s

increasing familiarity with and growing understanding of Western styles of music. It

would also be worthwhile to investigate in more detail the taxonomy of different

gestures defined by Kholopov and Tsenova. Specifically, the concept of “smooth

threads” could be analyzed in detail and clearly codified, as this gesture is one found in

virtually all of Denisov’s music, regardless of its stylistic orientation.

Finally, the relative inaccessibility of Russian-language writings on 20th-century

music has severely limited the ability of English-speaking music theorists to deal with

much of the music of this time period. Denisov himself was a prolific author, with

essays about the music of Webern, Lutosławski, Debussy, Schoenberg, Nono,

Dallapiccola, Bartók’s string quartets, Shostakovich’s orchestration, Prokofiev’s use of

sonata form and many other topics. Of these essays, only “New Music and Jazz” and

“The Compositional Process” have been published in English, and the article “On Some

Melodic Types in Modern Music” has been published in German. Two writings in

particular, seem to demand English translation: his analysis of Webern’s Piano Variations

Op. 277 and his study “On Dodecaphony and the Problems of Modern Compositional

Techniques,” which has many points in common with the Kurbatskaya chapter

6 These second conservatory works include not only the Music for Eleven Wind Instruments and Kettledrums (1961), the Piano Variations (1961), mentioned in Chapter 1, but also the Concerto for Flute, Oboe, Piano, and Percussion (1963), the Sonata for Violin (1963), and the Italian Songs (1964). 7 This article was published for the first time in 1970 in the Italian music journal Collage, in Russian and Italian.

168

translated in this study. Translations of many of these sources (or portions of those

sources) would prove to be important contributions to the historiography of Soviet and

Russian twelve-tone theory, and the history of twelve-tone theory and non-tonal music

in general. I believe that these translations would represent an important step toward the

goal of beginning a productive dialogue on the topic of Soviet serialism between

English- and Russian-speaking music theorists.

169

BIBLIOGRAPHY Babbitt, Milton. “Twelve-Tone Invariants as Compositional Determinants.” Musical

Quarterly 46/2 (1960), 246-259. Bailey, Kathryn. The Twelve-Note Music of Anton Webern: Old Forms in a New Language. New

York: Cambridge University Press, 1991. Barasch, Elena. “Kontsertï Edisona Denisova.” In Svet–dobro–vechnost’: Pamyati Edisona

Denisova, stat’i, vospominaniya, materialï, ed. by Valeriya Tsenova, 343-368. Moscow: Moskovskaya gosudarstvennaya konservatoriya im. P. I. Chaikovskogo, 1999.

Beebe, Jon P. Music for Unaccompanied Solo Bassoon: An Annotated Bibliography. Jefferson, North Carolina: McFarland and Company, Inc., 1990. Bradshaw, Susan. “The Music of Edison Denisov.” Tempo 151:2 (December 1984), 2-9. Buchler, Michael. “Relative Saturation of Subsets and Interval Cycles as a Means for

Determining Set-Class Similarity.” Ph.D. dissertation, University of Rochester, 1997.

Cain, Joren. “The Saxophone Sonatas of Edison Denisov: A Study of Continuity.” The

Saxophone Symposium 24 (1999), 26-40. Chartrand, Gary, and Linda Lesniak. Graphs and Digraphs, 4th ed. Boca Raton, FL:

Chapman & Hall, 2005. Child, Peter. “Voice-Leading Patterns and Interval Collections in Late Shostakovich:

Symphony No. 15.” Music Analysis 12/1 (March 1993), 71-88. Christensen, Thomas. “The ‘Règle de l'Octave’ in Thorough-Bass Theory and Practice.”

Acta Musicologica 64/2 (July-December 1992), 91-117. Dabney, Denise. “A Multicultural Approach to Edison Denisov’s Sonata for Alto

Saxophone and Piano: Diverse Analytical Insights.” The Saxophone Symposium, 20 (1995), 10-13.

Denisov, Edison. “New Music and Jazz.” The World of Music, 10/3 (1968), 30-37. __________. “Dodekafoniya i problemï sovremennoy kompozitorskoy tekhniki.”

Muzïka i sovremennost’ 6 (1969), 478-525. __________. “Variatsii op. 27 dlya fortepiano A. Veberna.” Collage 9 (1970), 46-71. __________. “The Compositional Process.” Tempo 105 (June 1973), 2-11.

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__________. “O kompozitsionnom protsesse.” In Sovremennaya muzïka i problemï evolyutsii kompozitorskoy tekhniki, 10-18. Moscow: Sovetskiy Kompozitor, 1986.

__________. Sovremennaya muzïka i problemï evolyutsii kompozitorskoy tekhniki. Moscow:

Sovetskiy Kompozitor, 1986. __________. “Novaya tekhnika—Eto ne moda.” In Svet-dobro-vechnost’: pamyati Edisona

Denisova, stat’i, vospominaniya, materialï, ed. by Valeriya Tsenova, 33-38. Moscow: Moskovskaya gosudarstvennaya konservatoriya im. P.I. Chikovskogo, 1999.

Denisov, Edison, and Grigori Pantijelew. “Edison Denissow im Gespräch mit Grigori

Pantijelew.” In Sowjetische Musik im Licht der Perestroika, ed. by Hermann Danuser, Hannelore Gerlach, and Jürgen Köchel, 242-247. Laaber: Laaber-Verlag, 1990.

Denisov, Edison, and Jean-Pierre Armengaud. Entretiens avec Denisov: Un compositeur sous le regime sovietique. Paris: Edition Plume, 1993. Denisov, Edison, and Dmitriy Shul’gin. Priznaniye Edisona Denisova: Po materialm besed.

Moscow: Kompozitor, 1998. Fay, Laurel. Shostakovich: A Life. Oxford: Oxford University Press, 2000. Forte, Allen. The Structure of Atonal Music. New Haven: Yale University Press, 1973. Gulyanitskaya, Natal’ya. Vvedeniye v sovremennuyu garmoniyu. Moscow: Muzïka, 1984. Haimo, Ethan. Schoenberg's Serial Odyssey: The Evolution of His Twelve-Tone Method, 1914-

1928. New York: Oxford University Press, 1990. Hakobian, Levon. Music of the Soviet Age. Stockholm: Melos Music Literature, 1998. Hall, Patricia. “The Progress of a Method: Berg’s Tone Rows for Lulu.” Musical Quarterly 71/4 (1985), 500-519. Haray, Frank. Graph Theory. Reading, MA: Addison-Wesley Publishing Company, 1969. (Third printing, 1972). Headlam, Dave. “The Derivation of Rows in Lulu.” Perspectives of New Music 24/1

(Autumn-Winter 1985), 198-233. __________. “Row Derivation and Contour Association in Berg’s Der Wein.” Perspectives

of New Music 28/1 (Winter 1990), 256-292. __________. The Music of Alban Berg. New Haven: Yale University Press, 1996. Helton, Jonathan. “Edison Denisov’s Sonata for Saxophone and Piano: An Analysis for the

Performer.” The Saxophone Symposium 25 (2000), 16-38.

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Ilomäki, Tuukka. “Aspects of Pitch Organization in Schönberg’s Variations for Orchestra, op. 31.” Lietuvos Muzikologija 8 (2007), 30-43.

__________. “On the Similarity of Twelve-Tone Rows.” Ph.D. dissertation, Sibelius

Academy, 2008. Ho, Allan and Dmitry Feofanov. Shostakovich Reconsidered. London: Toccata Press, 1998. Jarman, Douglas. The Music of Alban Berg. Berkeley: University of California Press, 1979. Kholopov, Yuri. “Andrei Volkonsky the Initiator: A Profile of His Life and Work.” In

Underground Music from the Former U.S.S.R., ed. by Valeriya Tsenova, 1-20. Amsterdam: Harwood Academic Publishers, 1997.

Kholopov, Yuri, and Valeriya Tsenova. Edison Denisov. Moscow: Kompozitor, 1993. In

English as Edison Denisov: The Russian Voice in European New Music. Translated by Romela Kohanovskaya. Studia Slavica Musicologica 28. Berlin: Ernst Kuhn, 2002. There is an earlier, less complete translation of this book: Edison Denisov. Translated by Romela Kohanovskaya. Chur, Switzerland: Harwood Academic, 1995.

Kholopova, Valentina. “Ob odnom printsipe khromatiki v muzïke XX veka.” Problemï

muzïkal’noy nauki 2 (1973), 331-344. Kostka, Stefan and Dorothy Payne. Tonal Harmony, 6th ed. New York: McGraw Hill, 2009. Krenek, Ernst. Studies in Counterpoint Based on the Twelve-Tone Technique. New York: G.

Schirmer, 1940. Kurbatskaya, Svetlana. Seriynaya muzïka: voprosï istorii, teorii, estetiki. Moscow: Sfera, 1996. Kurbatskaya, Svetlana, and Yuri Kholopov. P’yer Bulez-Edison Denisov: Analiticheskiye

ocherki. Moscow: Sfera, 1998. Lewin, David. Generalized Musical Intervals and Transformations. New Haven: Yale

University Press, 1987. __________. “Klumpenhouwer Networks and Some Isographies that Involve Them.”

Music Theory Spectrum 12/1 (1990), 83–120. Londeix, Jean-Marie. “Sonate for Alto Saxophone and Piano by Edison Denisov.” In

Jean-Marie Londeix: Master of the Modern Saxophone, ed. by James C. Umble, 222-225. New Jersey: Roncorp, 2000.

Lyman, Jeffrey. “After Shostakovich, What Next? New Russian Soviet Music for

Bassoon.” International Double Reed Society Journal 19/4 (1996), 53-67.

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Morris, Robert. Composition with Pitch Classes: A Theory of Compositional Design. New Haven: Yale University Press, 1987.

__________. Class Notes for Advanced Atonal Music Theory. Lebanon, NH: Frog Peak

Music, 2001.

__________. “Some Musical Applications of Minimal Graph Cycles.” Paper presented at the annual conference of the Society of Music Theory, Baltimore, 2007.

Moseley, Brian. “Getting RICH: Chains and Space in Webern’s Op. 22, ii.” Paper

presented at the annual conference of the Society of Music Theory, Montréal, 2009.

Perle, George. “The Music of Lulu: A New Analysis.” Journal of the American Musicological

Society 12/2-3 (1959), 182-200. Reich, Willi. “Alban Berg’s Lulu.” Musical Quarterly 22 (1936), 383-401. Robinson, David and L. R. Foulds. Digraphs: Theory and Techniques. New York: Gordon

and Breach, Science Publishers, Inc., 1980. Schmelz, Peter. “Listening, Memory, and the Thaw: Unofficial Music and Society in the

Soviet Union, 1956-1974.” Ph.D. dissertation, University of California, Berkeley, 2002.

__________. “Shostakovich's ‘Twelve-Tone’ Compositions and the Politics and Practice of Soviet Serialism.” In Shostakovich and His World, ed. by Laurel Fay, 303-354. Princeton: Princeton University Press, 2004.

__________. “Andrey Volkonsky and the Beginnings of Unofficial Music in the Soviet

Union.” Journal of the American Musicological Society 58 (Spring 2005), 139-207. __________. “What Was ‘Shostakovich,’ and What Came Next?” Journal of Musicology

24/3 (Summer 2007), 297–338. __________. “After Prokofiev.” In Sergey Prokofiev and His World, ed. by Simon

Morrison, 493-529. Princeton: Princeton University Press, 2008. __________. Such Freedom, If Only Musical. Oxford: Oxford University Press, 2009. Schoenberg, Arnold. “Composition with Twelve Tones (1).” In Style and Idea, ed. by Leonard Stein, 214-245. Berkeley: University of California Press, 1975. Schwarz, Boris. “Arnold Schoenberg in Soviet Russia.” Perspectives of New Music 4/1 (Fall-

Winter 1965), 86-94. __________. Music and Musical Life in Soviet Russia, 1917-1970. London: Barrie and

Jenkins, 1972.

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Scott, Damon & Eric Isaacson. “The Interval Angle: A Similarity Measure for Pitch-

Class Sets.” Perspectives of New Music 36/2 (1998), 107-142. Starr, Daniel Victor. “Derivation and Polyphony in Twelve-Tone Music.” Ph.D.

dissertation, Princeton University, 1980. Taruskin, Richard. Defining Russia Musically: Historical and Hermeneutical Essays. Princeton:

Princeton University Press, 1997. Tertz, Abram. On Socialist Realism. New York: Pantheon Books, 1960. Tsenova, Valeriya. Prostranstvo Edisona Denisova: K 70-Letiiu so Dnia Rozhdeniia: 1929-1996:

Materialy Nauchnoi Konferentsii. Moskva: Moskovskaia gos. konservatoriia imeni P.I. Chaikovskog, 1999.

Tsenova, Valeriya, ed. Svet–dobro–vechnost’: Pamyati Edisona Denisova, stat’i, vospominaniya,

materialï. Moscow: Moskovskaya gosudarstvennaya konservatoriya im. P. I. Chaikovskogo, 1999.

Umble, James C. Jean-Marie Londeix: Master of the Modern Saxophone. New Jersey: Roncorp,

2000. Volkov, Solomon, ed. Testimony: The Memoirs of Dmitri Shostakovich. New York: Harper

and Row, 1979.

Whittall, Arnold. The Cambridge Introduction to Serialism. New York: Cambridge University Press, 2008.

Wilson, Robin J. Introduction to Graph Theory. London: Longman Group, Ltd., 1975. Yakub, Roman. “An Interview with Edisson Denisov.” Ex Tempore 20/1 (Spring-

Summer 2002), 112-118. BIBLIOGRAPHY FOR APPENDIX 1 (KURBATSKAYA TRANSLATION) Babbitt, Milton. “The Function of Set Structure in the Twelve-Tone System.” Ph.D.

dissertation, Princeton University, 1992. [Cited by Kurbatskaya as Babbitt 1946] Brindle, Reginald Smith. Serial Composition. New York: Oxford University Press, 1966. Denisov, Edison. “Dodekafoniya i problemï sovremennoy kompozitorskoy tekhniki.”

Muzïka i sovremennost’ 6 (1969), 478-525. Forte, Allen. “A Theory of Set-Complexes for Music,” Journal of Music Theory 8/2

(Winter, 1964), 136-183. Gershkovich, Filipp. O Muzïke: stat’i, zametki, pis’ma, vospominaniya. Sovetskiy

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Kompozitor, 1991. Gulyanitskaya, Natal’ya. Vvedeniye v sovremennuyu garmoniyu. Moscow: Muzïka, 1984. Kholopov, Yuri. Zadaniya po garmoniy. Moscow: Muzïka, 1983. Kohoutek, Ctirad. Tekhnika kompozitsiy v muzïke XX veka. Moscow: Muzïka, 1976. Leibowitz, René. Schoenberg and His School: The Contemporary Stage of the Language of Music.

New York: Da Capo Press, 1975. Perle, George. Serial Composition and Atonality; An Introduction to the Music of Schoenberg, Berg,

and Webern, 2nd ed. Berkeley: University of California Press, 1968. Peyser, Joan. Twentieth-Century Music: The Sense behind the Sound. New York: Schirmer,

1980. Rognoni, Luigi. The Second Vienna School: Expressionism and Dodecaphony. London: Calder,

1977. Schäffer, Boguslaw. Klasycy dodekafonii. Kraków: Polskie Wydawnictwo Muzyczne, 1964. Schoenberg, Arnold. Style and Idea, 1st ed. New York: Philosophical Library, 1950. Wellesz, Egon. The Origins of Schönberg’s Twelve-Tone System. Washington DC: Library of

Congress, 1958. Webern, Anton. The Path to the New Music, ed. by Willi Reich. Translated by Leo Black.

Bryn Mawr, PA: Theodore Presser Co., in Association with Universal Edition. Reprinted London: Universal Edition, 1975.

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APPENDIX 1: KURBATSKAYA TRANSLATION

Serial Music: Questions of History, Theory, and Aesthetics Svetlana Kurbatskaya

[Notes on the translation:

- I am deeply indebted to Dr. Peter Schmelz and Dr. Truman Bullard for their careful readings of this translation, the suggestions they offered, and the insight they provided into the mechanics of Russian translation.

- The phrase vïsotnaya organizatsiay translates literally as “pitch organization,” but I have modified this to “pitch-class organization,” as I believe this Western theoretical term more accurately conveys Kurbatsakaya’s intended meaning. Likewise, I have also translated the word vïsota as “pitch-class” rather than the more literal “pitch.”]

[pg. 32]

Chapter 2: On the System of Terminology

The terminological system of serial and twelve-tone music evolved just as the

methods of composing with the twelve-tone system did. Existing studies have

developed the fundamental concepts of “serialism” [seriynost’ ] as an independent musical

area and in the context of a more encompassing phenomenon (“twelve-toneness”)

[dvenadtsatitonovost’ ]. When summarizing musical material from the end of the 20th

century, it seems possible to encompass twelve-toneness, dodecaphony, and serialism as

a unified whole, represented with an appropriate terminological system.

Twelve-toneness is a property of the musical material according to which each of

the twelve tones of the chromatic scale can be used as independent units of the musical

fabric. Accordingly, twelve-toneness (dodecatonicism [dodekatonika], twelve-tone

harmony) is a system of thinking based on the autonomy of each of the twelve pitch

classes. It includes a wide spectrum of variously organized contemporary stylistic

phenomena and techniques:

176

1) “Free atonality” – a special type of pitch-class organization [vïsotnaya

organizatsiya] that does not reflect the standards of classical major and minor tonality, or,

in general, to the centralizing action of a single foundation pitch [yedinoye ustoy – i.e., tonic

pitch]. New structural laws governing harmony are based on the equality of all pitch

classes [vïsota], and the emancipation of dissonance.1 As examples, consider the

Erwartung of A. Schoenberg, along with the Five Pieces on texts of Stephan George and

the instrumental cycles Op. 6, Op. 9 and Op. 10 of A. Webern. The hemitonic (twelve-

semitonal) method of symmetrical interval groups is the principle of atonal harmony, for

example, in Webern’s Op. 10.2 Thus, the opening section of Piece No. 3 (Op. 10) rests

on a thirteen-note complex (eleven different pitch classes), including homogeneous

groups that are distributed between a melody and a chordal “background”:

1 For definitions of the concept of “atonality” and the analysis of some structural types of atonal harmony see Perle 1968 (Ch. 1); Kholopov 1983/1 (225-236), Gulyanitskaya 1984 (160-193), Filatova 1990. 2 This principle is specific to the twelve tone harmony of Webern.

177

[pg. 33]

2) Technique of tonal centers – systems fashioned from the functional

connections between dissonant sonic elements on the basis of an individually selected

simultaneity [sozvuchiye]. One of the examples of such a pitch-class system (vïsotnaya

sistema) is the dissonant tonality of Skryabin’s late works (Op. 56) - the Skryabin scale, in

which the Prometheus chord figures as the tonic, and the entire musical fabric is worked

out by its regular repetitions in specific interval relationships (as in the Seventh Piano

Sonata).

[pg. 34]

3) Technique of “synthetic chords” (N. Roslavets’ term) - a version of the

technique of tonal centers (#2), where a chord [gruppa zvukov] functions as the source of

vertical and horizontal material (in the work, or parts thereof). It is a predecessor of the

dodecaphonic series, but is distinguished from it: it uses fewer than twelve notes, allows

for octave doubling, and allows for changing “synthetic chords” during the course of the

piece (N. Roslavets’ Three Compositions for piano, and vocal cycle Sad Landscapes).

178

4) Twelve-note chords – independent chords (polychords) made up of all twelve

pitch classes with or without repetitions (A. Berg, Five Orchestral Songs, Op. 4, no. 3; A.

Webern, Orchestral Piece Op. 6, no. 5).

5) Technique of twelve-tone rows [12-tonovïye ryadï ] – A row is the horizontal

occurrence of non-repeating pitch classes (or, at least, with minimal repetitions), which is

used as a melodic construction and is not the sole source of the musical fabric.3

Consider the twelve-step rows [12-stupennïye ryadï] in the last of the Five Orchestral Songs

(Op. 4) of A. Berg, No. 16 from The Polyphonic Notebook of R. Shchedrin, and the 14th

Symphony of D. Shostakovich (respectively, Examples 4a, b, c.)

[pg. 35]

6) Technique of twelve-tone fields (Nikolai Obukhov, Liturgical Poems on texts by

K. Balmont; A. Webern Six Bagatelles, Op. 9). A twelve-note semitonal field [12-zvukovoye

3 It is curious that melodic occurrences of twelve pitch-classes (with or without repetitions) appeared in music long before the development of the twelve-tone system. For example, the subject from the B minor fugue in Book 1 of J.S. Bach’s Well-Tempered Clavier, and the introduction of F. Liszt’s Faust Symphony.

179

polutonovoye pole] is “the set of twelve pitch classes (without or with repetitions),

distributed vertically and horizontally” (Kholopov 1983/1, p. 216). It concerns a special

type of a twelve-tone harmonic system, where the sonic structures are formed in a mixed

measurement (along a vertical line, horizontal, and also diagonal), systematically filling in

the chromatic space.4 For example, the beginning of Webern’s Op. 9, No. 1 Bagatelle:

[pg. 36]

7) Technique of tropes (in the music theoretical system of J.M. Hauer) – a form

of twelve-tone composition based on dividing the twelve pitch-classes into two

hexachords (all in all, there are 44 possible tropes).5

8) Serial technique [seriynaya tekhnika] – one of the forms of contemporary

musical composition where the entire musical fabric is derived from an invariant series

and its continuous recurrences (in basic and derived forms).

A series is: 1) a specifically structured and constantly reproduced set of twelve

(or fewer) pitch classes out of which all the sonic material is derived6; 2) the ordered

4 The chromatic field can be incomplete – that is, it can contain fewer than twelve pitch classes. 5 For the basic conditions of the system, and examples from Hauer’s compositions, see Appendix 2. [Kurbatskaya’s Appendix 2 is not included in this translation.] 6 Let us give some existing definitions of “series”:

1) “A series is the ordering of sonic material; the linear sequence of tones, which determines their mutual relations.” (Schäffer 1964, cz. 2, s. 6)

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sequence of elements at various (including non-pitch) levels of a twelve-tone

composition, fulfilling the role of the repeated invariant.

This definition of “series” considers both a narrow and a wide-ranging concept

which were uncovered in the course of the evolution of serial thinking (see below

“serialism,” #12): narrow – the series only as the basic pitch class structure; wide – the

series as the invariant model of sonic order at a different level (or on all levels) of a

musical whole. When speaking about a pitch class series, it is necessary to note two

crucial points. First, the basic value for the process (and result) of a composition does

not have as much to do with the initial linear ordering of pitch classes as it does with the

content of their intervallic relations. Specifically, they [the intervallic relations] realize

themselves in the sonic fabric, creating the foundation for the logic governing the

arrangement of pitch classes [vïsotnaya logika] and, to a large extent, creating musical sense

in serial works. Secondly, in the process of development of serial techniques, the regular

repetition of a complete series has lost importance as an underlying principle (which is

essential, for example, in the strict dodecaphony of the Schoenbergian/Webernian type).

It became possible to derive the entire musical fabric from a single series by other

methods – in particular, by the repeating of small segments or other interval structures,

which are genetically connected to the series but not taken directly from it.

2) “A series is a group of sounds (row) from which, through its repetition, the entire fabric of the

work is derived. The term “series” indicates the row itself (with its repetitions) and its function.” (Kohoutek 1976, c. 107)

3) “A series (from Lat. ‘series’ is a ‘row,’ Fr. ‘serie,’ German ‘Reihe’ or ‘Grundgestalt’) is a row of twelve (sometimes fewer) different pitch classes, the repetition and transformations of which forms the entire musical fabric of a work.” (Yuri Kholopov, article in MES 1990, s. 494)

4) “A series is a set of all twelve pitch classes from which, through its recurrence, the entire musical fabric of a piece is derived.” (Kholopov 1983/1, s. 218)

5) “A series is a basic sound group which contains twelve non-repeating tones of equal importance in a strictly ordered sequence.” (Gulyanitskaya, 1984, s. 196)

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The horizontally presented series takes the form of a row (as in the theme of

Edison Denisov’s Variations for Piano):

[pg. 37]

Hence, some foreign theories treat the definitions of “series” and “row” (see Example 6)

synonymously.7 However, there is a fundamental difference between the two terms: a

series does not appear as a surface element (like a row), but determines the appearance

of relationships in the work.

9) Dodecaphony – a type of serial technique in which the entire musical fabric is

derived from a twelve-tone series.8 “Dodecaphony” (from the Greek δωδεкα meaning

twelve, φονη meaning sound) literally indicates “twelve sounds” [dvenadtsatizvuchiye], and,

7 In German, the different phenomena (row and series) are designated by the word “Reihe” (row) and “Reihentechnik,” respectively. In English and American usage, before the term “series” appeared, beginning with M. Babbitt (1946), the term “set” was used (see Babbitt 1946, also Forte 1964). Being borrowed from mathematical set theory, this term has two meanings in music theory: “row” and also “formalized collection” [formalizovannaya obshchnost’]. The creator of musical set theory (M. Babbitt) has combined in it the theory of sets and the “morphology” of the serial-dodecaphonic method (see Tsaregradskaya 1988, p. 14-18). In the works of R. Brindle and G. Perle the terms “series” and “set” are used interchangeably (see Brindle 1966, Perle 1968. 8 In our national [Russian] literature, one encounters instances of definitions of dodecaphonic serial technique. For example, in N. Gulyanitskaya’s “Introduction to Modern Harmony,” the use of “dodecaphony” and “serial” is thought of as synonymous (see Gulyanistkaya, 1984, p. 194). The discussion, however, deals with two concepts – the specific and the general. This distinction is provided for in Russian and foreign terminology: “Dodecaphony” and “serial composition”; “Zwölftontechnik” and “Reihentechnik” makes sense here, as it places dodecaphony and serial composition in opposition, where “Reiche” [misprint: certainly must be “Reihe”] indicates not only “twelve-tone row” but also “series.”

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at first glance, it coincides with “twelve-toneness.”9 We confront the well known

terminological problem of the divergence of the meanings of the two concepts, very real,

not only for Russian-language studies. Thus, in foreign theory, there are pairs of

corresponding terms: “Zwölftonmusik” and “Zwölftontechnik” (Ger. “twelve-tone

music” and “twelve-tone technique”)10; “Twelve-tone composition” and

“dodecaphony.” It is logical to distinguish the two concepts in the Russian

terminological system (instead of equating them through a literal translation): “Twelve-

tone composition” as a system of thought, “dodecaphony” as the method of

composition based on the synthesis of twelve-toneness with serialism.11 As an example

of deriving the musical material from an initial twelve-tone series (in the course of its

transformations [vidoinzmeneniye]), consider the beginning of one of A. Webern’s Drei

Lieder (op. 23) on poems by Hildegard Jone.

[pg. 38]

9 This coincidence is present, for example, in B. Schäffer’s definition of dodecaphony: “Dodecaphony is the 12-tone technique…which is the basis of the music, founded on the material of twelve (different!) sounds.” (Schäffer 1964, cz. 2, s. 5). 10 N.B.: In E. Krenek’s work “Studies in Twelve-Tone Counterpoint” (“Zwölfton-Kontrapunkt-Studien”) and J. Rufer’s “Composition with Twelve Tones” (“Die Komposition mit zwölf Tonen”), the discussion does not deal with twelve-toneness in general, but with dodecaphony. 11 Concerning this distinction, we mean, for example, the definition of “dodecaphony” in the Russian translation of Ctirad Kohoutek’s book, which includes techniques of twelve-tone serialism, techniques of an incomplete series under the conditions of the twelve-tone system, and also the technique of twelve-tone rows in complete and incomplete chromatic fields. (see Kohoutek 1976, p. 108)

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10) Microserialism – a type of serial technique in which the source (invariant) of

the musical fabric is a microseries, that is, a series of fewer than twelve pitch classes. For

an example, consider the “C#-C-E” quartet of A. Webern, two Bransle dances from the

ballet “Agon” (Example 7a) and “In Memoriam Dylan Thomas” by I. Stravinsky, and

the “Symphony-Concerto” for violoncello and orchestra by B. Britten (Example 7b):

It is appropriate to compare the concept of “microseries” with two other concepts, also

relating to the ordering of a small number of pitch classes, but displaying other shades of

meaning.

An incomplete series is part of a complete twelve-tone series that functions

independently [of the complete series] in a specific section of the work. A subseries is a

segment of a series that functions as a series on a micro-level.

[pg. 39]

All methods of serial development can be applied to a sub-series: horizontal and vertical

reflection [obrashcheniye – horizontal reflection is retrograde, vertical reflection is

inversion], transposition, permutation. The classic examples are found in the works of

A. Webern (for example, the Concerto for Nine Instruments, op. 24) in which isomorphic

interval groups/sub-series are derived from one intonational “kernel” [zerno] which

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effectively fulfills the role as sole source of the pitch class fabric (more about this in

Chapter 3). Here, consider also the series from W. Lutosławski’s “Funeral Music”:12

The distinction is that a microseries exists as an independent “unit,” but a

subseries is a component of a more powerful structure (a full series).

11) Total Serialism (serial technique) [serializm] – the method of creating music by means

of a series of two or more parameters (see: Kogoutek 1976, p. 107, MES 1990, p. 493).

For example, Messiaen’s Île de feu uses not only a twelve-tone pitch class series, but also a

series of rhythms (also twelve units), dynamics (five units) and articulations (five units):

12) Serialism [seriynost’ ]

12 In Example 8, small letters designate the interval forms of the subseries, similar to the forms of a series (p – prime, ri – retrograde inversion). As the initial subseries quite often acts in relation to other groups as the prime form of the series acts to derivative forms, we use the corresponding labels: p, i, r, ri.

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1) In the twelve-tone system, the principle of pitch class organization in which all

music, without exception, is derived from an initial sequence of non-repeating pitch

classes.

[pg. 40]

2) The principle of musical thought by a series (or multiple series) [serii].

The wider meaning of serialism (and of “series” as a “formalized order”

[formalizovannïy poryadok]) is connected with the principle of [total] serial organization

[serializatsiya] on non-pitch musical parameters.13 Having been born during the crisis of

major/minor harmonic systems, serialism was considered as an alternative to the tonal

thinking of the 18th-19th centuries (hence, the comparison of a series with harmony, the

theme; hence, the tendency to write with the aid of a series as with the aid of

major/minor melodies and chords).14 Examination beyond the narrow framework of

pitch class organization makes it possible to reveal the influence of serialism as one of

the universal categories of musical thought in the 20th century, applied to a wide range of

genetically related phenomena. Depending on the sphere of application, the concepts of

“series” and “serialism” display different levels in their meaning. So, in speaking about

Schoenbergian serialism, we primarily mean the entire complex of serial methods then

available to the composer (i.e., his serial techniques in the realm of pitch organization).

Speaking about the “post-classical” serialism of the second half of the 20th century, we

no longer mean so much concrete techniques of structural organization, as much as 13 Both aspects of the concept of serialism (broad and narrow) are contained in the definition of Kohoutek: “Serial technique is 1) a method of music composition, based on the repetitions (and development) of a series; 2) a method of music composition which uses only a pitch-class series. (Kohoutek 1976, 107). Schäffer’s definition is an example of a limited treatment: “Serial music is music based on material of a series of twelve…or fewer than twelve pitches.” (see Schäffer 1964, 2, 5). 14 See Schoenberg 1950, Wellesz 1958, Denisov 1969, Webern 1975, Leibowitz 1975, Rognoni 1977, Peyser 1980, Gulyanitskaya 1984, Gershkovich 1991.

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different manifestations of serial thought in general. The following chapter is dedicated

to the consideration of the broad sphere of questions connected with serialism.

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APPENDIX 2: GRAPH THEORY TERMINOLOGY

This appendix serves to introduce the basic terminology used in graph theory. The

vocabulary used in graph theory is large and, in many cases, varies idiosyncratically with

individual authors. For example, the words “node,” “vertex,” “point,” “element,” and

“dot” have all been used to describe the same concept. For the most part, I will use the

terminology established in Harary (1972). However, I will depart from his terminology

in the most basic of terms: where Haray uses the words “point” and “arc,” I will use the

words “node” and “arrow,” respectively, owing to the familiarity of these terms to music

theorists, due in no small part to the pioneering work of David Lewin.1

DEFINITION A2.1: GRAPH

A graph consists of a finite, non-empty set N of nodes and a collection A of ordered

pairs of distinct elements of N. The elements of A are visually represented by arrows

connecting the indicated nodes.2

I am using the word “graph” here for what should more strictly be called a

“digraph.” In terms used by graph theorists, a graph is a set of nodes connected by lines.

A digraph is a directed graph: a set of nodes connected by arrows. Because my examples

deal almost exclusively with directed graphs, I will adopt the convention established in

Morris (2007) and use the word “graph” for purposes of simplicity. In the even that I

need to refer to a non-directed graph, I will use the term “ordinary graph.”

1 See Lewin 1987, particularly chapter 9. 2 Harary 1972, 10. This is also what Lewin calls a “node/arrow system,” though Lewin does not require that the ordered pairs of A be distinct elements. See Lewin 1987, 193.

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DEFINITION A2.2: LABELED AND UNLABELED GRAPHS

A labeled graph is a graph in which the nodes represent concrete musical objects (interval-

classes, in most cases, though this need not necessarily be the case), and the nodes are

labeled with names describing the objects they represent. An unlabeled graph shows a

system of relationships between abstract musical objects.

David Lewin has proposed a similar distinction between “networks” and

“graphs.”3 While it should be clear that I am invoking a similar distinction, I will not

explicitly use Lewin’s terminology presently. In graph-theoretic terms, a network is a

graph (with or without labeled nodes) that is associated with a function that assigns a

numerical value to each of the arrows in the graph.4 While this definition does apply to

Lewin’s transformational networks, none of the graphs I am considering here involve

such a function. In most cases, the term “labeled graph” will be implied when the word

“graph” is used.

DEFINITION A2.3: ADJACENCY

For all elements (n1,n2) of A, we say that node n1 is adjacent to node n2 and that node n2 is

adjacent from node n1.5 If A contains both (n1,n2) and (n2,n1), then both n1 and n2 are

adjacent to each other, and we say that the adjacency is symmetric.

3 Lewin 1987, 195-196. 4 Harary 1972, 50. 5 Harary 1972, 198. Other authors define adjacency in digraphs differently. In the present example, Chartrand/Lesniak 2005 would say that node n1 is adjacent to n2, but n2 is not adjacent to n1. Robinson/Foulds would say that nodes n1 and n2 are adjacent if either (n1,n2) or (n2,n1) is an element of A. See Chartrand/Lesniak 2005, 26 and Robinson/Foulds 1980, 19. When dealing with ordinary graphs, all authors are consistent in saying that if (n1,n2) is an element of A, then we say that n1 and n2 are adjacent to each other.

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DEFINITION A2.4: INDEGREE AND OUTDEGREE

The number of arrows beginning at (pointing from) a given node is that node’s outdegree

and the number of arrows ending at (pointing to) a given node is that node’s indegree.

Example A2.1 shows a three-node graph, similar to the ICSGs introduced in

chapter 3, which will serve to put these terms into context.

EXAMPLE A2.1

ic1 ic2 ic5

In the labeled graph shown in Example A2.1, the non-empty set N of nodes are

labeled interval class 1, interval class 2, and interval class 5 (ic1, ic2, ic5). The collection

A consists of the following ordered pairs of nodes: (ic1,ic2), (ic2,ic1), and (ic1,ic5). The

adjacency between ic1 and ic2 is symmetric, but, while ic1 is adjacent to ic5, ic5 is not

adjacent to ic1. In Example A2.1, ic1 has an outdegree of 2 and an indegree of 1. Both

ic2 and ic5 have an indegree of 1.

DEFINITION A2.5: SINK AND SOURCE

A node with an outdegree of 0 is called a sink, and a node with an indegree of 0 is called

a source.

Sources and sinks only exist in interval class succession graphs for twelve-tone

row’s which do not graph the row’s cyclic interval, as described in Chapter 3 (page 79).

A source is found when a row only has one occurrence of a particular interval class, and

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that interval class is the first entry in that row’s INT-C. When a unique interval class is

the last entry in a row’s INT-C, the row’s ICSG will have a sink. These two special types

of nodes only occur under these particular circumstances.

DEFINITION A2.6: WALK

A walk is an alternating sequence of nodes and arrows, n1, (n1,n2), n2, …, (nx,ny), ny. There

are three types of walks: a closed walk is a walk in which the first and last nodes are the

same,6 a spanning walk is a walk which contains all the nodes, and a path is a walk in which

all the nodes are distinct.

DEFINITION A2.7: REACHABLE, CONNECTED GRAPH

If there is some path from n1 to n2, then we say that node n2 is reachable from node n1.

Furthermore, a graph is connected if, for every pair of nodes, nx and ny, there is either a

path from nx to ny, or from ny to nx, or both.7

DEFINITION A2.8: SYMMETRIC GRAPH

A graph is called symmetric if, for every (nx,ny) in A, (ny,nx) is also in A.

A few examples of some Second Viennese School rows will serve to acquaint the

reader with the terms from Definitions A2.5 – A2.8. Example A2.2A shows the ICSG

6 Robert Morris refers to this as a cycle, but a cycle is usually defined as a specific kind of closed walk within a digraph. Harary 1972 defines a cycle as a “nontrivial closed walk with all points distinct (except the first and last)” (emphasis mine). Morris 2007 does not observe this requirement. 7 This definition essentially considers the digraph as an ordinary graph, with lines connecting nodes instead of arrows. Harary actually defines three different types of digraph connectedness: strongly connected, unilaterally connected, and weakly connected. My definition corresponds to Harary’s definition of weakly connected digraphs. See Harary 1972, 199.

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for the primary row of Berg’s Lyric Suite. This is an example of a symmetric graph: all

the arrows are double-ended.

As can be seen in Example A2.2A, the INT-C for the Lyric Suite row forms a

palindrome. It may seem that this palindromic INT-C is the reason for the symmetric

nature of the ICSG, but this is not precisely the case. Example A2.2B shows the ICSG

for the row of Schoenberg’s Violin Fantasy, Op. 47. Like the Lyric Suite ICSG, this graph

is also symmetric, but the INT-C associated with this row is not a palindrome. While it

is true that every row with a palindromic INT-C has a symmetric ICSG, Example A2.2B

has shown that it is not true that every row with a symmetric ICSG has a palindromic

INT-C. The primary row from Berg’s Lulu is shown in Example A2.2C. The ic4 node

in this ICSG is a source. Example A2.2D shows the row and ICSG for Schoenberg’s

Wind Quintet, Op. 26. In this graph, the ic3 node is a sink.

EXAMPLE A2.2: VARIOUS ICSGS

A. BERG, LYRIC SUITE (PRIMARY ROW) Row: < 5 4 0 9 7 2 8 1 3 6 t e > 1 2 3 4 5 6

INT-C: < 1 4 3 2 5 6 5 2 3 4 1 > B.

1 2 4 6SCHOENBERG, VIOLIN FANTASY, OP. 47 Row: < t 9 1 e 5 7 3 4 0 2 8 6 > INT-C: < 1 4 2 6 3 4 1 4 2 6 2 > C. BERG, LULU (PRIMARY ROW) Row: < 0 4 5 2 7 9 6 8 e t 3 1 > INT-C: < 4 1 3 5 2 3 2 3 1 5 2 > D. SCHOENBERG, WIND QUINTET, OP. 26 Row: < 3 7 9 e 1 0 t 2 4 6 8 5 > INT-C: < 4 2 2 2 1 2 4 2 2 2 3 >

1 2 3 4

1 2 3 4 5

multiple-row serialism in three works by edison denisov

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