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ABSTRACT

A STUDY OF SERIAL-RELATED COMPOSITIONAL
TECHNIQUES PRIOR TO SCHOENBERG'S
METHOD OF COMPOSING WITH
TWELVE TONES

BY

Donna Gartman Schultz

The Problem

The problem of this study was to find compositional
techniques bearing a direct relationship to the serial
method of Arnold Schoenberg in earlier music. Schoenberg's
method is sometimes thought to be revolutionary. The exam-
ination of earlier music, however, reveals that his tech-
niques often had been used by predecessors. Therefore,
music written prior to Schoenberg's dissemination of his

method should be studied for evidence of such techniques.

The Procedure

A definition of serial composition as proposed by
Schoenberg was established in order to ascertain what com-
positional techniques could be considered serial-related.
Two principles were shown to be required in order to have
true serial composition--a use of all twelve notes of the
chromatic scale, and a consistent and pre-determined order-
ing of those twelve notes. Other important aspects of

Schoenberg's method--such as the transposition of the

@556 2..» C? /

Donna Gartman Schultz

series to any pitch level, the use of derived forms of
the series, and the horizontal-vertical use of the series--
were also defined.

The search for serial-related compositional tech-
niques in earlier music involved not only the original
analysis of musical examples, but also a study of analyses
by other music theorists who have attempted to prove that
Schoenberg's method had precedent. Each aspect of serial
composition was considered separately.

Music studied included compositions by Mozart,
Bach, and Beethoven, together with later compositions by
Richard Strauss, Reger, Hindemith, Bartok, Ruggles, Hauer,

Debussy, Stravinsky, and Scriabin.

Conclusions
Each aspect of Schoenberg's serial method of com-
position was seen to have precedent in music written prior
to his discovery of the method. However, none of the exam-
ples studied could be correctly labeled as true serial com-

position.

A STUDY OF SERIAL-RELATED COMPOSITIONAL
TECHNIQUES PRIOR TO SCHOENBERG'S
METHOD OF COMPOSING WITH

TWELVE TONES

BY

Donna Gartman Schultz

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF MUSIC

Department of Music

1975

 

. ——H A

ACKNOWLEDGMENT S

I wish to express my sincere gratitude to the mem-
bers of my committee, Dr. Theodore Johnson and Mr. Richard
E. Klausli, for their interest, their time, and their valu-
able suggestions regarding this study. I am especially
grateful to my major professor and thesis director,

Dr. Russell Friedewald, for his patience, his unerring
guidance, and his concern; his careful approach to theo-
retical study was a most valuable lesson.

Most of all, my love and thanks go to my husband
Paul for his unfailing support, encouragement, confidence,

and love.

ii

TABLE OF CONTENTS

Page

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . ii

INTRODUCTION. . . . . . . . . . . . . . . . . . . . . 1
Chapter

I. SERIAL COMPOSITION DEFINED. . . . . . . . . . 6

II. THE RELATIONSHIP OF SCHOENBERG'S WORK TO
CLASSICAL CONTRAPUNTAL TECHNIQUE. . . . . . . 18

III. MUSIC USING ALL TWELVE TONES. . . . . . . . . 25
IV. MUSIC USING SETS OF NOTES AND OTHER SERIAL-

RELATED COMPOSITIONAL TECHNIQUES. . . . . . . 50

V. CLOSING REMARKS . . . . . . . . . . . . . . . 74

LIST OF REFERENCES. . . . . . . . . . . . . . . . . . 77

iii

INTRODUCTION

The first twenty-five years of the twentieth cen-
tury should no doubt be regarded as years of major signif-
icance in the development of music. Within this relatively
short span of time, tonality, which had dominated the music
of preceding centuries, was, for many composers, replaced
by music that allowed no one tone to predominate, but
rather stressed each of the twelve tones of the octave
equally. The ultrachromatiCism and denial of traditional
harmonic function in the music of the late nineteenth cen—
tury--as seen in the music of Richard Wagner, Richard
Strauss, and Gustav Mahler--led ultimately to a denial of
any existing tonal center in music, or atonality. The
works of the early twentieth-century Viennese school
(Arnold Schoenberg, Alban Berg, and Anton Webern being the
most prominent members) are often regarded as the first
examples of atonal music. Indeed, with Schoenberg's clear
definition in 1923 of his new method of composing wherein
all tones are related to each other, and not to a tonal
center, atonality and serial composition were given de-
cisive recognition. It should be noted that Schoenberg

himself objected to the use of the term "atonality,"

1

instead preferring in its place "pantonality." However,
since the ultimate effect is a denial of any one note as

a tonal center, the use of the word "atonality" would seem
to be appropriate. This is supported by George Perle in
Serial Composition and Atonality;

Schoenberg objected to the use of the term "aton-
ality" to designate a musical idiom.not based on the
traditional tonal functions, recommending in its place
"pantonality." The intended implication, presumably,
is that the new musical language is a consequence of
the merging of all tonalities. But since, according
to Schoenberg and his followers, the immediate effect
of this supposed merging of all tonalities was the
obliteration of the characteristic features of tonality
in general, "atonality" would seem to be a more appro-
priate designation for this language.1

Schoenberg, in a letter to Josef Hauer dated December 1,
1923, stated that he objected to the term "atonality," and
"not . . . the thing itself!"2
Schoenberg occupies a unique position in the an-
nals of music history. In retrospect, his music might be
viewed as the culmination of all preceding Western music.
As already pointed out, Strauss, Wagner, Mahler, and others
were groping for a new harmonic language, one in which the
boundaries of conventional harmonic function would no
longer exist. It was Schoenberg who supplied this new har-

monic language and perhaps exploited it to its fullest

potential.

 

1George Perle, Serial Composition and Atonality,
(Berkeley: University of california’Press, IBGZT} p. 7.

2Arnold Schoenberg Letters, ed. by Erwin Stein,
trans. by Eithne Wilkins and Ernst Kaiser (London: Faber
and Faber Limited, 1964), p. 105.

 

But Schoenberg must also be regarded as a pioneer
of sorts, for it is with his definition and explanation of
serial technique that the means for reaching this new atonal
harmonic language were first achieved. Serial composition,
even to the present day, has found its way into contempo-
rary musical composition, and has served as the springboard
for many composers who have strived to rid themselves of
the boundaries of traditional harmony.

But even though Schoenberg was the first actually
to define the new structural organization upon which atonal
music was based (i.e., serialism), he and his disciples
were not the first to use techniques that are closely anal-
ogous to serial composition.

During recent years several music theorists have
attempted to prove that serial composition began not with
Schoenberg, but with music prior to that of Schoenberg.
George Perle devotes an entire chapter to the subject of
"Nondodecaphonic Serial Composition," in which he exam-
ines music supposedly based upon a series containing less
than twelve tones.l Although Perle includes examples of
music by Debussy and the Russian composer Roslavetz in his
discussion of the use of serial techniques, he gives par-
ticular emphasis to Alexander Scriabin as a forerunner of

Schoenberg. Hans Keller has set the beginning of serial

 

lGeorge Perle, Serial Composition and Atonality.

composition as far back as the time of Mozart and
Beethoven.1 It would appear that, with such a widespread
Opinion regarding its date of origin, the study of serial
composition deserves yet another look to determine just
how much, if any, of Schoenberg's method has historical
precedent.

Josef Hauer's compositional technique has received
due consideration in light of its relationship to Schoen-
berg's serial method. He proposed the use of all twelve
tones of the scale without regard to their fixed order
other thathhe placement of any six notes in one group (re-
ferred to by Hauer as a "trope") which is mutually exclu-
sive of the remaining group. Hauer's theories should be
included in any discussion of the origin of serialism,
regardless of their relationship to Schoenberg's method.

If any true understanding of the term "serialism"
is to be reached, it is necessary for one to examine both
the theoretical writings dealing with the subject of the
origin of serial technique as well as the music which is
purported to contain early examples of serialism. After
such a study one would be able to define more clearly the
compositional techniques that are used, and either be able

to determine their justification for being described as

 

1Hans Keller, "Strict Serial Techniques in Clas-
sical Music," Tempo, XXXVII (Fall, 1955), pp. 12-24.

serialism, or to make clear what, if any, relationship
to the techniques of serialism exists.

The following study, then, attempts to find with-
in music which appeared before 1923 those techniques which
are related to serial composition either directly or in-
directly. It is entirely possible that from this study,
greater clarity of the definition of terms will be
achieved, and that the need for the use of more precise
terminology will be indicated.

The examples of Schoenberg's music (examples 1
through 4 in Chapter I) are used by permission of Belmont
Music Publishers, Los Angeles, California 90049, c0pyright
1952 and 1956 by Gertrude Schoenberg. All other musical
examples which are quoted directly are in the public

domain.

CHAPTER I

SERIAL COMPOSITION DEFINED

Before one can begin to examine the techniques
which are analogous to serial composition in music prior
to Schoenberg's serial works, one must first have a clear
understanding of what serial composition is in its most
strict form.

In A History of Western Music, Donald Grout des-

 

cribes serial composition in this manner:

By 1923, after six years during whichluapublished
no music, Schoenberg had formulated "a method of com-
posing with twelve tones which are related only with
one another." The essential points of the theory of
the twelve—tone (dodecaphonic) or serial technique may
be summarized as follows. The basis of each composi-
tion is a row or series consisting of the twelve tones
of the octave arranged in any order the composer decides.
The tones of the series are used either successively
(as melody) or simultaneously (as harmony or counter-
point), in any octave and with any deSIIGQ rnytnm;
but, in theory at least, all twelve should be heard
before any one recurs. The row may also be used in
inverted, retrograde, or retrograde inverted form,
and in transpositions of any of the four forms.

 

Thus, according to Grout, there are two requisite

principles to the theory of serial composition: (1) the

 

1Donald Jay Grout, A History of Western Music,
(New York: W.W. Norton & Co., Inc., 1960): p. 651.

conscious use of all twelve tones as a structural device,
and (2) a predetermined ordering of those twelve tones.
Each of these two principles must be present in order to

justify a work as having been created serially as defined

 

by Schoenberg.
According to Oliver Neighbour, the first princi-
ple-—the use of all twelve tones--has historical precedent:

The twelve notes are to be found in close proximity
even in Wagner, for as tonality expanded its boundaries
chromatic sequences arose which brought them together.
There is no suggestion of a new constructive princi-
ple in this, and the most that can be said is that the
mere presence of such passages prepared the way for
later developments [i.e., Schoenberg]. Gradually,
however, chromatic variety began to exert an attrac-
tion of its own. This is observable in some of Mahler's
and Reger's melodies which reach out, without recourse
to sequences, almost to the twelve-note limit before
turning back, though they are harmonised within a

tonal framework. Where this tendency became especially
strong, as it did in Schoenberg, it affected every as-
pect If the music so that the framework could not

hold.

 

No doubt the music of Wagner, Mahler, and Reger
was moving toward dodecaphony, but it was left to Schoen-
berg to arrive at the complete organizational principle
of it. Since Schoenberg's objective was to deny any sense
of tonality or tonal function, then the absence of one or
more notes from any statement of the series would tend to
emphasive the remaining notes. The systematic use of all

twelve notes was an attempt, for Schoenberg at least, to

 

1Oliver Neighbour, "The Evolution of Twelve-note
Music," Proceedings of the Royal Musical Association,
LXXXI (1955), p. 50.

 

achieve the atonality toward which the music of the late
romantic composers, with its ultrachromaticism, had been
leading.

The second requisite principle of serial composi-

 

tion--a predetermined ordering of the twelve tones--is !
supported by Perle: '

The specific ordering of the notes is a necessary
consequence of the concept of the set as a unitary
structure whose elements are not functionally differ-
entiated. An unordered twelve-tone set would be
equivalent to the semi-tonal scale, that is, it would
be simply a statement of the available tone material.
The seven-tone scale may be analogously regarded as a
diatonic system, but in addition, certain functional
relations among the elements of the seven-tone scale
are implied. Since the elements of the twelve—tone
set are not thus functionally differentiated, they must
be ordered if the set, conceived as a unitary structure,
is to have any constructive significance whatsoever.

Oliver Neighbour makes a similar observation:
The chromatic scale . . . is a special case since it
represents the complete tonal field of western music
and lacks any limiting factor unless some order is
imposed upon it. It is one of the functions of the
series to do this. . . .2
The predetermined ordering of the twelve tones
appeared to Schoenberg to be the solution to his problem;
with the use of a consistent order of the twelve tones, a
means of logical construction had been found. The neces-
sity for such a constructive principle arose directly from

the disappearance of tonal function in music. Schoenberg

himself states that:

 

1Perle, Serial Composition and Atonality, p. 5.

2Neighbour, "The Evolution of Twelve-note Music,"
p. 58.

The method of composing with twelve tones grew
out of a necessity . . . [of creating a] new procedure
in musical construction which seemed fitted to replace
those formal and structural differences provided
formerly by tonal harmonies.

I called this procedure Method of Composing with
Twelve Tones which are Related Only with One Another.

This method consists primarily of the constant and
exclusive use of a set of twelve different tones.
This means, of course, that no tone is repeated within
the series and that it uses all twelve tones of the
chromatic scale, though in a different order.1

 

Josef Rufer explains how significant the disappear-
ance of tonality was to musical composition:

At the moment when it was no longer possible to
relate harmonic and melodic phenomena to a key-note,
they lost an essential basis of their musical and
logical coherence . . . for with the cessation of
tonality the ordering of the notes produced by
tonality--harmonically by means of the triad, and
melodically by means of the major and minor scales--
no longer applied. This tonal organization is a
hierarchy, set up and ruled over by the key-note,
which drew all the remaining eleven notes toward
itself, and related them to itself. They only existed
through the key-note, as its satellites; as being the
third, sixth, etc., of the key-note.2

 

Without a predetermined and consistent ordering of
the twelve-tone set, the basic structure of serial music
would seem to be undermined. In tonal music all tones
exist only in their relation to the tonic note. Without

this principle, tonal music would have no logical and

 

1Arnold Schoenberg, Style and Idea, trans. by
Dika Newlin (New York: PhilOSOphical Library, 1950),
p. 103, 107.

2Josef Rufer, Composition with Twelvg_Notes, trans.
by Humphrey Searle (Third ed. rev.; London: Barfie and
Rockliff, 1965), p. 79.

10

meaningful construction to support it. In Schoenberg's

serial music, all tones exist only in relation to each

other; Schoenberg called it "composition with twelve

notes related only to one another." Without order, which

is necessary to provide that relationship of tones to each

other, the fundamental constructive principle of Schoen-

berg's method is lacking. The negation of a strict order-

ing would tend to have an effect similar to that of omit-

ting notes as described before--certain notes would begin

to emerge as having greater importance in relation to

others by virtue of their repetition out of sequence. It

is this aspect of order that probably has the greater bear-

ing on the serialism of a composition. As will be shown in

the following chapters, certain techniques described by

various composers and theorists as being analogous to serial

composition deny this fundamental principle of order. Yet

it would seem that, in order to use the word "serial,"

a systematic ordering of notes must be present. According

to George Perle, “In a strict sense the term 'series' de-

notes an ordered succession of elements, such as the Schoen-

bergian twelve-tone set."l
Indeed, the free use of various terms in discussion

of serial music can lead to a great deal of confusion. All

too often different terms are used synonymously, and the

 

1Perle, Serial Composition and Atonality, p. 40.

 

 

ll

precise definition of each separate term is overlooked.
The twelve notes of the chromatic scale, arranged in their
predetermined order, are variously referred to as a

"row," a "series," or a "set." The original German term
Reihg may be translated to mean any of these; but the
choice of the English equivalent, in light of the fact
that the choices have slightly different connotations,
should be determined by the compositional technique found
in the music itself. "Row," the first term to be used in
English writings, is now possibly the least used; as George
Perle states, it "implies a certain regularity, not neces-

1 "Series," popularized

sarily characteristic of the set."
mostly through the writings of Ernst Krenek, is frequently
used; it would seem to be the best choice, for it implies
the use of a consistent order, without which there is no
twelve-tone music as proposed by Schoenberg. "Set," used
first by Milton Babbitt and subsequently adopted by Perle
and others, was originally a term used in mathematics to
refer to a "collection of some kind"--in mathematics, to a
collection of numbers.2 Logically, a set may also refer

to a collection of pitches. But in mathematics where the

term originated, "set" implies no specific order of the

 

lPerle, Serial Composition and Atonality, p. 2.

2Edwin F. Beckenback, Irving Drooyan, and William
Wooton, College Algebra (Belmont, California: Wadsworth
Publishing Company, Inc., 1964), p. l.

 

 

 

 

12

elements of the set. Therefore, its use to refer to an
ordered collection of pitches is somewhat misleading.
The use of the word "set" in discussing compositional tech-
niques would seem to be most appropriate when an unordered
collection of pitches is being used; the use of "series"
would be the preferred term when an ordered collection of
pitches is being used.

Not only are the various words used to refer to
the twelve notes confusing; confusion also arises over
the various names given to the particular style of compo-
sition that Schoenberg developed. "Serial music," "twelve-
tone music," (or "twelve-note music"), "dodecaphonic
music," and "atonal music"--all are frequently used inter-
changeably to refer to Schoenberg's music. Schoenberg
called his compositional technique "a method of composing
with twelve tones related only to one another." The other
terms used to refer to it are inventions of others. The
most appropriate--and the one being used in this study--
is "serialism," for it implies the ordering of the twelve
tones that is a prerequisite of Schoenberg's method. The
other terms are somewhat misleading, for they can also be
correctly applied to music that is not based upon Schoen-
berg's method--for instance, free atonality and free
tonality. Schoenberg's music is certainly not alone in
its use of all twelve tones. Thus the terms "twelve-tone"

and "dodecaphonic" are not restrictive enough. George

"'m.

 

13

Perle refers to this confusion when he notes that "dodeca-
phony" usually means serial music, but ought to refer to
any music based upon a twelve-tone scale.l
To illustrate the process of strict serial compo-
sition as defined by Schoenberg, the following examples,
with serial analysis, are included. These examples illus-
trate both the principle of the use of all twelve notes
and the principle of a prescribed order. By virtue of
this, they may be considered strict serial composition.
For further study, the reader may refer to Ernst Krenek's
Twelve Short Piano Pieces in the Twelve-Tone Technique,

Op. 83 (1938), each of which demonstrates the strict use

of serial technique as described previously.

Example 1: From the Praludium, Suite fur Klavier, Schoen-
berg, Op. 25, measures 1-3.

 

1.2

Though only two things--the use of all twelve
tones, and a predetermined ordering of those tones--are
necessary for serial composition as defined by Schoenberg,

another aspect of the method of serial composition must be

 

1Perle, Serial Composition and Atonality, p. 8.

 

 

14

Example 2: From the Minuet and Trio, Suite ffir Klavier,
Schoenberg, Op. 25, measures 34-38.

 

TRIO 1 5 6. 7 a 9 12.

    

910.fl

 

@125 4' 5'16 7391011121

 

Example 3: From the Gigue, Suite ffir Klavier, Schoenberg,
Op. 25, measures 1-2.

1 [IE

 

 

 

7

considered here because of its relationship to techniques
being used in music before 1923. An analysis of serial
composition that consists merely of counting notes is a

naive one indeed. One must also take into consideration

 

15

Example 4: From Klavierstfick, Schoenberg, Op 33a,
measures 1-6.

 

the manner in which the notes, in their respective order,
are being used. An important aspect of Schoenberg's
method was that the notes could be used either as melody
or harmony--"The tones of the series are used either suc-
cessively (as melody) or simultaneously (as harmony or

"1

counterpoint). . . . Note that the preceding examples

of Schoenberg's music illustrate both the successive

 

lGrout, A History of Western Music, p. 651.

 

 

 

16

(melodic) use of notes and the simultaneous (harmonic)
use of notes. This technique can be found in music prior
to that of Schoenberg, as will be shown subsequently.

Any use of notes other than the notes of the pre-
scribed row in their successive order--including the inver-
sion, the retrograde, and the retrograde inverted together
with any transposition of the four forms--must be consid-
ered a deviation from strict serial technique. However,
certain such "deviations" are so common in the music of
strict serial composers that they are considered an inte-
gral part of the technique by composer and theorist alike.
According to rule, no one note may appear before the other
twelve notes have been sounded; but in practice, a note,
or note-group, is often repeated sooner: any one note
may be repeated at the same pitch an indefinite number of
times before the next note is played; two notes may alter-
nate, thereby forming trill or tremelo effects; and larger
groups of notes may be repeated before proceeding to the
next notes of the series. Schoenberg himself admits the
possibility of varying the order of the tones:

. . . It will be observed that the succession of the
tones according to their order in the set has always
been strictly observed. One could perhaps tolerate a
slight digression from this order . . . in the later
part of a work, when the set had already become famil-

iar to the ear. However, one would not thus digress
at the beginning of a piece.

1Schoenberg, Style and Idea, p. 117.

 

"‘9;

17

The preceding discussion and illustration of the
strict use of serial technique serve now as a basis for

the study of serial—related compositional techniques in

music written prior to 1923.

 

CHAPTER II

THE RELATIONSHIP OF SCHOENBERG'S WORK TO

CLASSICAL CONTRAPUNTAL TECHNIQUE

As mentioned earlier, Schoenberg occupies a unique
position in the course of music history in that his work
may be viewed both as a culmination of previous trends,
and, at the same time, as a new, revolutionary style of
composition. All too often greater stress is placed upon
the latter factor. Yet in order to fully understand and
appreCiate serial music, one must be aware of the fact
that Schoenberg drew a great deal of his technique as a
composer directly from his study of classical music. To
quote Oliver Neighbour, "His method evolved in accordance
with his genius for close musical thinking in the tradi-
tion of the Viennese classics and Brahms."1 Perhaps this
is recognized most readily in his use of inversion and
retrograde for derived forms of the series; that he would
conceive the possibilities provided by such transformations
proves that Schoenberg had studied the music of Bach,

Mozart, Beethoven, and Brahms and their use of similar

 

1Neighbour, "The Evolution of Twelve-note Music,"
p. 60.

18

19

transformations of a musical idea. This knowledge of
contrapuntal manipulation displays itself throughout

his music, and its use in his serial compositions will
serve as a comparison to some of the serial-related tech-
niques to be discussed in the following chapters.

Schoenberg's unprecedented achievement was made
possible . . . because he recognized that the great
masters are the ultimate source of learning. Thus,
he assiduously studied the music of Bach, Haydn,
Mozart, Beethoven, Schubert, Brahms, and Wagner,
the masters of the Austro-German heritage. He was
and remained a traditionalist at heart, despite the
musical revolution he brought about. In his teach-
ing, too, he drew his examples from the works of the
named composers, seldom venturing beyond Brahms. His
students all testify to his amazing knowledge to
shed new light on a Bach fugue or Beethoven string
quartet.

. . . The music of Schoenberg and his school
should be looked upon as the last link in a long line
of musical evolution. It represents the crystalliza-
tion and distillation of a long historical process,
and it speaks with the sophistication and differentia-
tion of the accumulated knowledge of many generations.

Schoenberg himself relates that Wagner and Brahms
exerted the greatest influence upon his music: Wagner for
his harmonic freedom, and Brahms for his careful contra-
puntal thinking.2

The phrase "careful contrapuntal thinking" is an
important one, for it perhaps sums up one of the most im-

portant aspects of Schoenberg's composition. The techniques

 

1Otto Deri, Exploring Twentieth-Century Music (New
York: Holt, Rinehart, and Winston, Inc., 1968). p. 271.

2Arnold Schoenberg, "My Evolution," Musical Quar-
terly XXXVIII (1952).

 

20

of conscious contrapuntal manipulation--inversion, retro-
grade, etc.--were used by Schoenberg to obtain the neces-
sary variation while maintaining unity (of the twelve-
tone line). The devices that give coherence and form to
the fugues of J. S. Bach are the ones that Schoenberg
used for the same purpose. I
|
Schoenberg illustrated the classical roots of his ‘
method of composing with one example of Beethoven's music: i
In his only written exposition of his method (Compo-
sition with Twelve Tones, in Style and Idea, New York,
1950, and London, 1951), Schoenberg illustrates its
classical history by a single example from late

Beethoven which shows Beethiven's use of pre-classical
contrapuntal devices. . . .

 

 

The example quoted is from the finale of the F

Major Quartet, Op. 135 (measures 13-20):

Example 5:

 

Schoenberg explained the relationship between the first
four-measure phrase and the second four-measure phrase in

the following manner:

a) Original b) Retrograde c) Retrograde-
Inversion

? ,
EgFZIiE:;;ZZ

d

 

 

‘i A A i

 

 

 

 

1Hans Keller, "Strict Serial Techniques in Classi-
cal Music," p. 12.

21

Thus, the second phrase is a transposed retrograde-inver-
sion, with passing tones, of the original figure in the
first phrase.
In discussing the connection between Schoenberg

and Beethoven, Erwin Stein makes the following observation:

. . . Schoenberg's technique of thematic development--

with its strettos, condensations, and segmentations

into the smallest motivic unit--roots in Beethoven.

. . . The time will come when we shall better under-

stand how Schoenberg's "composition with twelve notes"

too, derives--as a final consequence-~from Beethoven.1

One cannot deny the fact that most of Schoenberg's

music is constructed contrapuntally and contains numerous
examples of contrapuntal manipulation. But the mere ex-
istence of contrapuntal devices is not enough to justify
an assessment of a work as being related to serial music.
If it were, then more music than not would be serial-rela-
ted. Hans Keller has stated that,

In themselves, the mirror forms are old, primarily

contrapuntal devices of thematic economy and by no

means a decisive characteristic of serial technique.
Serial composition, though well-suited to the processes of
contrapuntal manipulation, is something more. Therefore,

in order to find serial—related compositional techniques

in music before Schoenberg's method was developed, one must

 

1Erwin Stein, "Musical Thought: Beethoven and
Schoenberg," in Orpheus in New Guises (London: Rockliff,
1953), p. 95.

2Keller, "Strict Serial Techniques in Classical
Music," p. 12.

 

 

22

look for something that goes beyond merely exploiting
contrapuntal devices.

Hans Keller has given various examples from Mozart
and Beethoven which he claims are directly related to
Schoenberg's serialism.1 Keller bases his claim for the
"strict serialism" of his examples upon the fact that the
"series" (usually only three or four notes long) is not
rhythmically committed, as contrapuntal variations usually
are. For example, a connection is made between the first
subject of the first movement of Mozart's G major Quartet,
K.156, and the beginning of the same movement's development
section. Taking the four-note series D, B, G, F#, one can
see that a transposed form of the same series appears to
be used in the development, and that no ryhthmic relation-

ship is present.

Example 6a: first subject of exposition

#

    

  

Example 6b: opening of development

1. Z

 
   

Lg?

lIbid., pp. 12-24.

 

 

23

However, the transposition of the series is not exact,
but rather a tonal transposition (as opposed to real).

In yet another example, the opening of the develop-
ment section of the first movement of the Quartet in Eb
of Mozart, K. 428, Keller claims that a three-note series
is found in transposed, inverted, retrograde, and retro-
grade—inverted forms. He calls this ". . . a mature ex-
ample of strict serialism . . .” and states that "this is

l

purest Schoenberg." A portion of his analysis is shown:

Example 7:

 

 

'-—Bs-r_-'___.gs

In addition, Keller also marks each statement of a minor

second, calling it ". . . a series in extremest miniature."2
The possibility of so many statements of the series,

including inverted and retrograde forms, is made possible

by the use of the tritone in such a short series. The

question here seems to be one of degree: when does

 

lIbid., p. 15.

21bid.

 

24

contrapuntal manipulation (obviously present in the above
example, even though quite complex) become true serial tech-
nique as prOposed by Schoenberg? The concept of order is
implicit in any example of contrapuntal manipulation; but
to be described as "strict serialism," it would seem that
use of a more extensive and complicated series than is

shown here is necessary. Again, serial composition con-
sists of much more than the eXploitation of contrapuntal

devices.

CHAPTER III

MUSIC USING ALL TWELVE TONES

In order for one to discuss the techniques that
are serial-related in music prior to Schoenberg's serial
writing, the two requisite principles, as described ear-
lier, must be considered separately. The evolution of the
use of all twelve notes, no one being given the function
of a tonal center, is a development independent and exclu-
sive of the evolution of the organizational technique of
arranging a group of notes (not necessarily twelve, but
any number of notes) into an ordered series for composi-
tional purposes. Only in Schoenberg's music did the two
merge to form a SOphisticated and highly intellectual
method of composition.

The evolution of the use of all twelve tones of the
chromatic scale is easily traced up to the dissolution of
tonality in 1923. One must have only a basic knowledge of
tonal harmony in order to understand that atonality was
perhaps inevitable. Early Western music was almost com-
pletely diatonic, with notes outside of the scale being
allowed only as chromatic embellishments, or non-harmonic

tones. Yet as harmony developed, more chromatic tones

25

 

26

were allowed to function harmonically. In the hands of
the romantic composers, chromatic harmony, with its rich
palate of colorful chords, still functioned as tonal har-
mony, despite the high frequency of chromatic tones.

As chromatic chords became more and more accepted,
they began to be used more by composers--such as Mahler
and Wagner--often without regard to their harmonic func-
tion in a key. Debussy carried this even further in his
use of unresolved chromatic, active sonorities and a vague-
ness of tonality involving quickly shifting modulations.
That atonality came about as a further consequence of the
use of chromaticism in music, is supported by Oliver
Neighbour's comment: "We may fairly conclude that the
tendency towards total chromaticism was a natural histor-

1 All twelve notes were seen more and

ical develOpment."
more frequently, and the necessity for a key center was no
longer apparent. The problem facing composers of the early
twentieth century was one of organization: with the organ-
izational principle of tonality no longer present, some
means had to be found to give coherence and unity to music
using all twelve tones.

Schoenberg's ultimate solution to this problem
was to put the twelve notes into an ordered series.

Other composers chose different solutions for the organi-

zation of the twelve tones.

1Neighbour, "The Evolution of Twelve-note Music,"

ED. 50.

 

27

With the adoption of [the twelve-tone system] as
an exclusive basis for atonal composition in the works
of Schoenberg and his immediate disciples, the period
of "free" atonality was seen as a closed historical
epoch that necessarily and inevitably had been super-
seded by a new stage of development. But the twelve-
tone system has its source in only a few of the seem-
ingly inexhaustible implications of the music of that
period. It is conceivable that viable structural
principles other than those of the twelve-tone system
may still be discovered in this music.

One of the most often-mentioned composers, other
than Arnold Schoenberg, who attempted to organize all
twelve notes for compositional purposes, is Josef Hauer.
One of Schoenberg's student-colleagues, Egon Wellesz, has
described Hauer, his music, and his influence upon Schoen-
berg:

It was in 1916 that I received the visit of a sol-
dier who was sent to me by my friend, Rudolph Reti.. ..
This soldier was an elementary-school teacher whom
the military medical authorities considered too high—
strung for active service. His name was Josef Matthias
Hauer. He showed me some of his works. I had never
seen such a mixture of amateurish writing, without any
training in harmony and counterpoint, and of passages
of undisputed originality. He told me that he wanted
to write music like the ancient Greeks. He showed me
his compositions. All were very short. Each piece
represented a Nomos, and the Nomos consisted of twelve
tones. . . . This meant that each melody represented
the whole compass of the chromatic scale, but the tones
were chosen in such a way that the layout of a row
sounded almost diatonic. The music was easily sing-
able. Hauer's compositions became known in our small
circle and were brought to Schénberg, who, at that
time, had occasionally made use of the serial tech-
nique. But undoubtedly Hauer's twelve-tone composi-
tions showed him the way out of his crisis; they came
to him as the right impulse at the right moment.

lPerle, Serial Composition and Atonality, p. 34.

 

 

28

. . . He [Hauer] provided Schanberg with the principal
idea, the row of twelve tones as a new principal of
composition.1

Hauer's technique consisted of dividing the twelve
notes of the chromatic scale into two groups of six notes
each, called "tropes." No note was repeated in each seg-
ment, and no note was common to both segments. Unlike
Schoenberg's serial method, Hauer suggested no prescribed
order for the notes in each segment; his only restriction
was that each segment be used in alternation with the
other segment of six notes. Hauer's method, as compared
to that of Schoenberg, allowed much more freedom of choice
in twelve-note composition in that neither harmony nor
melody were predetermined by any concept of series. Had
Hauer had the skill to handle his concepts in a manner that
would have produced music of great value, he, rather than
Schoenberg, might have been the composer to be credited
with originating a new method of composition.

Hauer's method did not provide for the conscious
contrapuntal manipulation whose value Schoenberg had the
foresight to realize. If the notes in each trOpe or hexa-
chord do not have a prescribed order, then the possibility
of systematic transposition, inversion, and retrograde has

no significance. Transposition and inversion of a trope,

¥

1Egon Wellesz, "The Origins of Schoenberg's Twelve-
5Tone System," a lecture delivered in the Whitehall Pavil-
Lon of the Library of Congress, Washington, D.C., 1958,
pp. 7-90

 

 

 

29

while possible, would more frequently than not produce
'duplication of notes within the following hexachord. Re-
trograde has no meaning at all since the order of the six
notes is not predetermined. Although Hauer's method lacks
the close-knit organization of serialism, it does neverthe—
less present a method for composing with twelve tones.

How Hauer first conceived the possibility of
using all twelve notes in his composition is not known,
but his first theoretical concept of twelve-note music was
of a melodic line--the Melos--in its purest form, devoid
of rhythm or harmony. Rhythm, supposedly, would develop
from the suggested stress and nature of the intervals.
Harmony was to be a result of notes still sounding after
they had served their melodic function; this would be sim-
ilar to the process in tonal music where a melodic figure
consisting of an arpeggiated triad is harmonized by the
chord itself. This concept of the Melos is, in part, re-
sponsible for the weakness in Hauer's music. Since har-
mony and rhythm are determined only by the implications of
the melody itself, Hauer's music tends to contain an over-
abundance of stagnant harmony which moves in relatively
regular rhythmic patterns.1

The following examples, with analysis, illustrate

the typical compositional technique of Hauer.

 

lNeighbour, "The Evolution of Twelve-note Music,"
pp. 53-54.

 

Example 8:

 

30

From "Fantasie," Op. 37.

 

 

 

 

 

 

 

Example 9:

 

From Vom Melos zur Pauke.

 

 

31

Example 10: From "Fantasie," Op. 37.

 

Wellesz's account of Schoenberg's knowledge of

Hauer's work supports the supposition that Schoenberg was
influenced by Hauer. How important that influence was must
be left to speculation. Perhaps Schoenberg was influenced
to some degree by Hauer's conscious attempt to manipulate
all twelve notes of the chromatic scale in some sort of

systematic fashion; but conceivably, Schoenberg would have

 

32

reached the same conclusion with regard to his own method
of composition had he never heard of Hauer or his music.
Josef Hauer is not the only one to be credited with
anticipating Schoenberg's discovery. Desire Pacque, a
Frenchman born in 1867, traces twelve-tone music back to
the beginning of the nineteenth century, and is supposed
to have written three atonal violin sonatas by 1911. And
the Ukranian composer Jef Golysheff in 1914 wrote a string
quartet showing dodecaphonic characteristics, as well as
an orchestral piece in 1919 which further develOped his
style of twelve-note composition. However, neither of
these works by Golysheff was ever published, and the writ-
ings and work of Pacque have subsequently been lost.1
The conscious use of twelve notes (or almost twelve
notes, in many cases) as a melodic idea is not restricted
to the late nineteenth and early twentieth centuries.
Numerous examples from earlier periods are to be found
that use many notes within a few measures, though the
usage is most often melodic and is harmonized within a
tonal framework.
J. S. Bach used all twelve tones of the chromatic
scale in the three-measure subject of Fugue No. 24 in

B minor in the first volume of The Well Tempered Clavier:

 

lMdsco Carner, A Study of 20th-Century Harmony,
Vol. II: Contemporarngarmo y (London: Joseph Williams
Limited, 1942), p. 65. Also see Neighbour, "The Evolu-
tion of Twelve-note Music," p. 49.

 

33

Example 11:

 

The idea here is a sequential one, of course; and the sub-

sequent treatment of the subject is within the structure

 

of tonality. But this, as well as several other subjects
in similar Bach fugues, is remarkable for its use of many
notes.

Heinrich Jalowetz, in an article on Schoenberg,
observed that the beginning of the development section of
the last movement of Mozart's G minor Symphony (K. 550)
contains a "genuine twelve-tone line, . . . a series of
ten tones of the chromatic scale that are treated as of
equal value and therefore not as in traditional chroma-

ticism."1

Example 12:

125 ‘

   
 

 

 

lHeinrich Jalowetz, "On the Spontaneity of Schoen-
berg's Music," Musical Quarterly, XXX (October, 1944), p. 387.

34

In yet another example taken from Mozart, eleven
of the twelve notes appear; the following line is from

the beginning of the develOpment section of the first

movement of the String Quartet in Eb, K. 428:

Example 13:

83456789 10 1.1

(91 1

           

 

The missing note, A, appears in the viola and Violoncello
parts in the fourth measure.

Both of the Mozart examples seen above also employ
a sequential idea, however briefly, as did the subject of
the Bach fugue in Example 11. It is, of course, impossible
to determine whether the inclusion of so many notes of the
chromatic scale was a conscious effort. The effect becomes
one of a momentarily-suspended tonality, which is often
typical at the opening of a classical development sec-
tion.

The use of twelve-note melodic ideas became much
more prevalent, however, in the late nineteenth century.
Various passages in the music of Richard Strauss are re-
markable in their use of a11--or most of--the notes of
the chromatic scale. It seems that each time Strauss has
included as many notes as possible, within as short a

Space as possible, resulting in a lack of any strong sense

35

of tonality. Even in as early a work as the symphonic

poem Also sprach Zarathustra (1896), the following theme,

 

using all twelve notes, appears:

Example 14:

 

Several years later, in Salome (1905), Strauss

used similar themes even more frequently. In one line sung

by Jochanaan, eleven of the twelve notes appear:
Example 15:

12545 67 8 9

   
   
  

 

The twelfth note, C7, appears in the accompaniment played
by the cellos and double basses in the fourth measure; the
accompaniment, on the whole, here merely elaborates upon
the vocal line, so that the complete texture uses most of
the notes of the chromatic scale.
In another place, eleven notes appear in even
b

closer succession in a line sung by Salome; only B is

missing.

 

36

Example 16:

.1A2 545 67 991.0 1.1

   
 

This is followed immediately by another similar melody,

again using eleven of the twelve tones; here, G is the

missing tone:

Example 17:

      

12345 4.7 89 1.0 11

Though the harmonization here is basically triadic, the
use of eleven of the twelve tones suggests that Strauss
was making a conscious effort to exploit their use.

In yet another instance, the twelve notes are used
vertically as well as horizontally within a span of only
five measures. Their use here is even more related to
Schoenberg's method in that there appears to be a conscious
effort to let twelve notes, and not tonality, control the

organization of the music, however briefly.

 

37

Example 18:

 

Eleven notes are found in the top staff, with few repeti-
tions; and the twelfth note, Bb, can be found in the chords
underneath both in the first and last measures. However, if
one looks for all twelve notes in the complete texture

# in the fourth

here, they occur even sooner; by the E
measure, all twelve notes have been heard, again with few
repetitions.

Strauss's use of the twelve notes of the chromatic
scale hardly constitutes true serial music. But close
analysis has revealed that he was perhaps consciously
attempting to employ the twelve tones in some manner that
tonality would not admit.

Max Reger uses all twelve notes with even greater
frequency, and in perhaps a more controlled manner, than
does Strauss. In the first movement of the String Quartet

#

in f minor, Op. 121 (1911), the following is found:

 

 

38

Example 19:

 

1

 

The missing note, F7, appears in another instrument just

before the G. in the last measure.

 

Later in the same movement, there is a passage very
similar in style to Schoenberg's use of one series in two

voices:

Example 20:

12 345 8

    

ha.

The String Trio in d minor, Op. 141b (1915), opens

with the following theme containing all twelve notes:

Example 21:

1.25 45’: 79 91011 12

     

   

And from the Violin Sonata in e minor, Op. 122

(1911), comes this theme:

39

Example 22:

 
  

  

19

 

4799

  

  

1z545

  
 

5456 78 91.0 “'11

    

In the previous example, the first statement of
eleven notes is immediately followed by another statement
of eleven notes, though in a different order. In each

#

group of eleven notes, the missing twelfth note (D in the

#

first group, A in the second) can be found in the accom-
paniment near the beginning of each group.

Paul Hindemith also used themes containing most or
all of the twelve notes in his music. The Third String

Quartet, Op. 22 (1922), opens with this theme played by

the first violin:

Example 23:

i 2 5 4 5 6 7 8 9 ‘0

    

The two remaining notes--F and Bb--appear in the fifth

measure in an imitative entry of the viola. Then in the

 

40

very next measure the violin begins a statement of eleven

notes in which only one is repeated:

Example 24:

@411

   
 

The twelfth note, C, appears in the following measure.
And in the first measure of the third movement of the
Second String Trio (1933),1 ten notes are present; the re-

maining two follow in the next measure:

Example 25:

 

Numerous other examples of the use of all twelve

notes both thematically (melodically) and as harmony can be

1In including a very few examples of music composed
after 1923, the author is assuming that Schoenberg's devel-
<3pment of his serial method was of no influence on the
(composition of these particular examples.

41

found in the music of Strauss, Reger, and Hindemith, as
well as the music of other composers contemporary with
them. But there is little evidence that any viable organ-
izational method based on twelve tones exists in their
music, other than perhaps briefly.
This is not true of Bela Bartok, however. In at
least one piece there is justification that the piece--
in its entirety--is organized and controlled by twelve
tones, though in a manner quite different from that of
Schoenberg. "Bartok . . . was, as far as I know, the first
composer to use a group of twelve notes consciously for a
structural purpose."1
The third one of Bartok's Fourteen Bagatelles,
Op. 6, for piano, composed in 1908, is clearly organized
for the purpose of employing all twelve tones. Throughout

the entire piece the right hand plays an ostinato of five

notes:

Example 26:

 

When the left hand enters with the melody in the third

measure, it introduces four more notes in the first phrase:

 

lNeighbour, "The Evolution of Twelve-note Music,"
p. 53.

 

 

42

Example 27:

 

The phrase is repeated; then the third phrase introduces 1

yet a tenth tone, C#:

Example 28: 1‘

 

And, finally, in the fourth phrase, the eleventh and

twelfth notes, F and D, are heard:

Example 29:

 

The piece then concludes with a phrase recalling the melody
of the first phrase. To call this particular piece any-
thing other than a conscious effort to employ all twelve
tones structurally would seem inconceivable.

Other examples of Bartok's use of twelve tones are
perhaps not so well-organized, but yet bear some resem-
blance to Schoenberg's method. All twelve notes occur

within the opening statement of the first movement of the

43

First String Quartet, Op. 7, also composed in 1908, in a
two-part contrapuntal setting which could easily be mis-

taken for Schoenberg's:

Example 30:

 

   

‘Several places in The Wonderful Mandarin, Op. 19 (1919),

use all twelve notes in a similar manner:

Example 31:

-1 9 1° 12

 

44

Example 32:

   

Example 33:

 

Another composition, the First Sonata for Violin
and Piano, written in 1921, begins with the piano playing
an arpeggiated figure based upon ten notes; when the

violin enters, its melody adds the two remaining notes.

45

Numerous other examples of Bartok's use of all
twelve notes may be found in music written prior to 1923.
But he never really used the twelve notes as consciously
for constructive purposes as did Schoenberg. A definite
method for organizing the twelve tones for compositional
purposes was either never arrived at, or perhaps even
searched for. As Oliver Neighbour observes:
So many passages of an extremely chromatic nature were
not easily to be brought within a structure of tonali-
ties. Bartok was faced with a choice. Continuing in
the same direction he would have abandoned tonality
and reached a position not essentially different from
that of Schoenberg in Herzgewachse (1911), a work in
which the twelve notes are almost continuously present,
though it is perhaps not intentional here. A new
problem of organization would have then presented it-
self, as it did to Schoenberg. Instead he hesitated
until he had finished his Second Violin Sonata . . .
and then gave up the twelve-note idea.1
An American composer, Carl Ruggles, also sought
to use as many of the twelve tones as possible in his music.
Ruggles, born in 1876, did not begin to compose until he
was forty years old. His compositions, relatively few in
number and usually quite short, were subjected to many re-
visions. But analysis of his music reveals that he, too,
was using techniques closely related to Schoenberg's
method even before 1923.

Ruggles technique was based upon his own idea that

no tone should be repeated until a number of tones--at

 

lNeighbour, "The Evolution of Twelve—note Music,"
pp. 54—55.

 

46

least nine, usually--had been heard. No predetermined

and consistent order was used; in fact, the opposite

idea--that no two notes should be adjacent in separate

but closely spaced statements of notes--was often employed.
As George Perle observes,

. . . there is the self-imposed rule, applied freely
and with exceptions that have their own evident logic,
that within the melodic line no note is to be repeated
until eight or nine have intervened. Assuming that the
ideal is a perfectly balanced texture based on the
equivalent function of all twelve notes, as it seems

to be, there should be no repetition until the remain-
ing eleven notes have been sounded, but such a formula
can be applied strictly only through the constant re-
iteration of a single arrangement of the twelve notes--
a twelve-note row, in other words. Schoenberg himself
has suggested that this principle of non-repetition

is the source of his concept of twelve-note serial
composition. Since Ruggles often tends to avoid
literal motivic repetitions and, within a phrase, some-
times even the return of adjacent pairs of notes, it is
impossible for a single pitch element to remain in a
constant ordered relation to the remaining eleven
notes.l

Henry Cowell analyzed Ruggles' style of composition
as early as 1930.

Carl Ruggles has developed a process for himself in
writing melodies for polyphonic purposes which embodies
a new principle and is more purely contrapuntal than a
consideration of harmonic intervals. He finds that if
the same note is repeated in a melody before enough
notes have intervened to remove the impression of the
original note, there is a sense of tautology, because
the melody should have proceeded to a fresh note in-
stead of a note already in the consciousness of the
listener. Therefore, Ruggles writes at least seven or

 

lGeorge Perle, "Atonality and the Twelve-Note
System in the United States," The Score, July, 1960,
p. 56.

 

 

47

eight different notes in a melody before allowing 1
himself to repeat the same note, even in the octave.

And Charles Seeger made similar observations in
1932:

The determining feature or principle of the melodic
line [in Ruggles' music] is that of non-repetition of
tone (either the same tone or any octave of it) until
the tenth progression. This applies rigidly to the
leading melody and characterizes the other parts to a
surprisingextent.2

 

Perle observes that, "The principle of non-repe-
tition is applied harmonically as well as melodically, in
the avoidance of octave doublings apart from the occasional
consistent doubling of a single line for the sake of
sonority."3

The Opening measurescfi'Carl Ruggles' Portals, for
string orchestra, composed by 1930, reveal the use of all
twelve notes. The second statement of ten notes is here
numbered in the analysis to correspond to the first state-
ment of twelve notes, for the purpose of showing that only
notes 9 and 10 (Eb and B) are adjacent in both statements

of the twelve.

 

1Henry Cowell, New Musical Resources (New York:
Alfred A. KnOpf, 1930), pp. 41-42.

2Charles Seeger, "Carl Ruggles," The Musical
Quarterly, XVIII (1932), p. 582.

3Perle, "Atonality and the Twelve-Note System
in the United States," p. 57.

 

 

48

Example 34:

1 2» 34 5

    

‘ 12.
357 4": 9 LR:

 

Perle points out that the first B, in the second

bar, in a later edition was changed by Ruggles to Bb in

order to avoid repeating the two adjacent notes.1
The following example, also taken from Portals,
demonstrates that Ruggles also used as many as ten notes,

without repetition, harmonically as well as melodically:

Example 35:

 

 

lPerle, "Atonality and the Twelve-Note System in
the Unites States," p. 56.

 

49

Carl Ruggles developed his own method for using
as many notes of the chromatic scale as possible, if not
all twelve, in his compositions. The relationship of
his method to that of Schoenberg lies mainly in the aspect
of non-repetition of tones before a certain number of others
had intervened.

The fact that many composers were using twelve, or
most of the twelve, tones in their music with great fre-
quency--sometimes consciously, more often perhaps uncon-
sciously--brought about the need for an organized method
of composition. Bartok, Ruggles, Hauer, and perhaps others
demonstrated in their music that, for themselves at least,
they had each developed some systematic method of control
over twelve tones. Their methods were not the methods of
Schoenberg; but perhaps had they been developed as exten-
sively as Schoenberg's serial method has been, they would
offer equally viable solutions to the problem of composing

with all twelve tones as serialism ultimately did.

ti

.‘Ilu A

CHAPTER IV

MUSIC USING SETS OF NOTES AND OTHER

SERIAL-RELATED COMPOSITIONAL TECHNIQUES

The origin and the use of the term "set" was dis-
cussed in some detail in Chapter I (pp. 11-12). Having
originated as a mathematical term to denote a collection
of numbers, it has subsequently been adopted by Milton
Babbitt, George Perle, Allen Forte, and others, to refer
to compositional techniques related to serial composition.
In the ad0ption of this mathematical term "set" into mus-
ical terminology it would seem logical simply to substi-
tute the word pitches for the word numbers: a "set" is a
collection of pitches. When used in referring to mathe-
matics, "set" denotes only a collection of elements (num-
bers) without implying any specific order of those elements.
If a predetermined order is imposed upon the elements of a
set, then that set becomes a special kind of set--i.e.,
an ordered set. Though the term "set" may be used to refer
to an ordered collection of pitches, that, too, is a
special kind of set--an ordered set. The term "series,"

which implies a predetermined and specific order of

50

 

51

elements, would seem to be most apprOpriate in referring
to an ordered set. This is supported by George Perle:

In a strict sense the term "series" denotes an ordered
succession of elements, such as the Schoenbergian
twelve-tone set. Hauer's "tropes" are only partially
ordered, while in the works of Scriabin and some other
composers the set is a collection of pitches the
specific ordering of which is purely compositional.1

 

In an effort by this author to avoid any confusion,
the use of the term "set" in this study will denote only
an unordered collection of pitches; the term "series" will
denote a colleCtion of pitches used in an ordered manner.

The use of a set as the basic structural material
of a composition is a technique closely related to Schoen—
berg's method. Schoenberg used a twelve-tone, ordered
set--i.e., a series; other composers prior to Schoenberg
used unordered sets of notes from which they selected
their musical material.

For the moment let us regard a "set" as any collection
of notes. If we seek historical precedents to justify
such arbitrary sets as basic musical components there
is no lack of material. Leaving aside the most ob-
vious examples, the traditional chords of tonal music,
we find the notion of the set implicit in the late
experimental works of Liszt, in the nonfunctional
chords of Debussy's music, in the "constructivist"
works of Scriabin, and in the iconoclastic atonal music
of Schoenberg and his eminent pupils.2

If a set is defined simply as any collection of un-

ordered pitches, then all music must be considered to be

 

lPerle, Serial Composition and Atonality, p. 40.

2Allen Forte, "A Theory of Set-Complexes for Music,"
Journal of Music Theory, VIII (1964), p. 136.

 

 

52

based upon sets. In order to draw a parallel between the
use of any set as a compositional device and Schoenberg's
use of a series, one must look for a specific manner

in which the set is being employed that bears a relation-
ship to Schoenberg's serial technique.

One of the most important ways in which a set may
bear a relationship to Schoenberg's method lies in the
property of a set to be used both successively--as melody--
and simultaneously--as harmony. Schoenberg developed
this idea into an integral facet of his serial method.
When the same technique is applied to a set, one can see
the relationship between the techniques being used.

In his Harmonielehre Schoenberg already pointed
out that a note can be understood in both its
vertical and horizontal implications: that is to
say, its overtones can be presented simultaneously
in a chord or arranged one after another in a

scale. The simultaneity of the notes of a chord
can be changed into consecutiveness.l

 

Schoenberg again commented upon this prOperty of
a set in "Composition with Twelve Tones:"

The elements of a musical idea are partly
incorporated in the horizontal plane as successive
sounds, and partly in the vertical plane as simul-
taneous sounds. The mutual relation of tones
regulates the succession of intervals as well as
their association into harmonies; the rhythm
regulates the succession of tones as well as the
succession of harmonies and organizes phrasing.2

 

lRufer, Composition with Twelve Notes, p. 48.

2Schoenberg, Style and Idea, p. 109.

 

53

The application of this concept, as Rufer has
summed it up, can be seen as easily in compositions based
upon unordered sets as it can in Schoenberg's serial
works:

The perception of these facts had decisive
results for composition with twelve notes; for it
made it possible to use a basic series of twelve
notes, as a whole or in parts, in either dimension--
that is to say, allowing its notes or note-sequences
to appear both vertically in a chord and horizontally
in a melodic formation.1

A second way in which music based upon sets bears
a relationship to Schoenberg's method is apparent when
transposition of the basic set forms an important aspect
of the compositional technique. If a set is unordered,
then the concepts of inversion and retrograde do not apply.
Therefore, the use of transposition becomes an even more
important means of achieving a sense of development.

The presence of compositional devices related to
Schoenberg's method--such as the horizontal and vertical
use of the set, or the transposition of the set--makes it
possible to relate music based upon unordered sets to that
of Schoenberg. However, a further parallel may be drawn
when the construction of an unordered set is seen to be
similar to the construction of a twelve-tone series. The

diatonic scale or chords of major-minor tonality may be

considered, in the simplest sense, a set. But the basic

lRufer, Composition with Twelve Notes, pp. 51-52.

 

 

54

construction of the major or minor scale is diametric to
that of Schoenberg's series; the diatonic scale is based
upon a functional relationship of each tone to the tonic
note, whereas in the twelve-tone series no functional re-
lationship exists other than through the relationship of
one adjacent tone to another. The construction of a set
is said to be similar to the construction of a twelve—
tone series only when the various pitches of that set
bear no functional relationship to each other.

George Perle has described the properties of sets
that are related to twelve-tone series by content or con-

struction in the following manner:

The overextension and consequent weakening of
the traditional tonal functions gave rise, prior
to Schoenberg's formulation of his "twelve-tone
method," to a number of attempts to base a total
musical structure upon a complex [or set] of
functionally undifferentiated pitch elements.

Perle, in describing such a pitch collection, or set, has

said that it

. . . cannot be regarded as analogous to a "mode" or
"scale," since (1) its elements are functionally equiv-
alent, (2) transpositions are freely used so that there
is a constant circulation of all twelve notes, and (3)
there is no special criterion of simultaneity, such

as the triad in the major-minor system or the limited
consonant intervallic relations of the modal system.
The unordered content of the set is the sole general
basis of both simultaneity [harmony] and succession
[melody].2

 

1George Perle, "An Approach to Simultaneity in
Twelve-Tone Music," Perspectives of New Music (Fall-Winter,

1964), p. 91.

21bid.

 

55

Some of the earliest and simplest examples of such
sets can be found in the music of Hindus in which a £333
or mode--a certain combination of various tones--is used
as the entire basis of construction, both melodic and har-
monic, of a piece. Egon Wellesz observed the relationship
between the £3333 use as sets and Schoenberg's work:

The principle of the series of tones and the twelve-
tone row is not an entirely new system, which Schén-
berg or Hauer invented, but the revival of the tech-
nique of formulas which originated in the East, came
to the West with plain-chant, and is one of the basic
principles of early medieval polyphonic music.

Debussy's use of whole-tone scales and pentatonic
scales provides a similar use of a set. Each comprises a
group of pitches which are used in an unordered manner.
There are no functional relationships inherent in the
whole-tone scale, and functional relationships in the penta-
tonic scale are limited. These scales, or sets, function
equally as both melody and harmony. However, the trans-
positions are limited by the nature of these particular
scales, causing a lack of any real sense of progression
or development. Voiles, from the first book of Preludes,
is based entirely upon these two sets. For the major por-
tion of the piece, the whole-tone scale (Bb C D E F# G#)

forms the basic set; six bars within the piece are based

upon a set comprised of a pentatonic scale. Even the one

 

lWellesz, "The Origins of Schoenberg's Twelve-Tone
System," p. 10.

 

56

available transposition of the whole-tone set is not used,
thus giving the entire piece an overall static quality.
Perle's analysis of Voiles is consistent:

The tone material of each of the three sections of
this work is rigorously derived from a restricted sel-
ection of the notes of the semitonal scale, defined
only with regard to content, not order. The only
tonal contrast in the work results from the fact

that the set upon which the middle section is based
[i.e., the pentatonic set] is not the same as that of
the two outer sections [based upon the whole-tone
set]. Each set functions both as chord and as scale,
that is, as the sole criterion of both simultaneity
and linear succession. Since both sets are extremely
limited in harmonic content, there is an absence of
tension and movement, and the texture is excessively
homogenous. As an example of serial composition the
work is admittedly naive, but as an isolated adumbra-
tion of later musical developments it is worthy of
attention.1

A similar, yet different, use of a set as scale
and chord was made by Stravinsky. The first of Three
Pieces for String Quartet (1914) uses a ten-tone set by
assigning to each instrument a sub-set of these tones:
the first violin plays only the notes G, A, B, and C; the
second violin, F#, E, D#, and C#, always in a descending
scale pattern; the viola plays a D only; and the 'cello
plays a three-measure ostinato built on the notes C, Db,
D5, and Eb (duplicating the two notes of the second violin's
sub-set). The piece consists of repetitions of these sub-

sets at different intervals causing them to ". . . coin-

cide in almost every possible combination. It is as though

 

1Perle, Serial Composition and Atonality, pp. 40-41.

57

the piece were based on a single chord which is never
heard in its entirety but from which any selection may
be made."1
Stravinsky's use of repeated patterns as basic
sets from which both melody and harmony are derived occurs
frequently in The Rite of Spring. Taking as one example
the "Dance of the Youths and Maidens" in Part I, one can

observe the use of the basic set Eb, Eh, g, G#, Bb, B ,

and Db. At the beginning it occurs as a complete sonority;
after eight bars the melodic material begins to be drawn
from the same set, with the addition of an eighth tone, C,
to the overall pitch content of the set. From here on,
the section is based upon different patterns built from
the notes of this basic set; other notes occur, but are
used primarily in an embellishing role.
In the music of Alexander Scriabin is perhaps to

be found the most consistent and highly structured use
of sets (composed of notes containing no functional rela-
tionships), along with the use of these sets in a manner
closely related to Schoenberg's serialism.

Along with Schoenberg (Three Piano Pieces, 0p. 11,

1908), Webern (Five Pieces for String Quartet, 1909),

and Charles Ives (Three-Page Sonata, 1905), Skryabin

(Fifth Sonata, 1908, and onwards) is exploring atonal-

ity and providing structural principles to replace
traditional tonality.

 

lNeighbour, "The Evolution of Twelve-note Music,"
p. 55.

2Peter Dickinson, "Skryabin's Later Music," Music
Review, XXVI (1965): p. 19.

 

58

A similar observation is made by Reti:

The search for a new musical style was not carried
on solely by the two great antipodes, Debussy and
Schoenberg. There were a few others who, though their
influence did not prove so far-reaching, nevertheless
contributed greatly to the evolution. One eminent
figure in this respect . . . was Alexander Scriabin.
Scriabin's artistic path was somewhat blocked by inner
and outer obstacles. His aesthetic vision and the
practical realization of his musical ideas were not as
balanced, clear and unified as were those of Debussy,
nor as definite, bold and revolutionary as Schoenberg's
work. Yet Scriabin's influence on both these composers
and on the whole musical world cannot be overlooked.
Though his talents were somewhat dissipated, he was
still more than a mere experimenter. In some of his
most mature works he developed musical structures of
real strength and beauty which have not yet been fully
exploited. In the present intensified search for the
origins of the new musical style Scriabin's music may
still experience a revival.1

Scriabin, born in Russia in 1872, was a well-known
concert pianist (performing almost exclusively his own
works), up until his untimely death in 1915. The music
that he wrote for piano and for orchestra follows a clear
line of development from nineteenth-century romanticism.
The earliest works are in imitation of the piano music of
ChOpin; after these comes a period of extreme romanticism
in which Scriabin was influenced by the chromatic writing
of Liszt and Wagner. The develOpment of this highly
chromatic style soon evolved into music that approaches
the brink of atonality. This last period (beginning as
early, perhaps, as the Fifth Sonata, Op. 53, and clearly

present in the Seventh Sonata, Op. 64) contains many

 

1Rudolph Reti, Tonality, Atonalityl Pantonality
(London: Barrie and Rockliff, 1958), pp. 59-60.

 

59

examples of the use of sets that are closely analogous to
Schoenberg's serialism.

The similarity of Scriabin's music to the later-
developed serialism of Schoenberg has been observed by more
than one person. In 1967, Eric Salzmann wrote,

Already over a period of years a number of Soviet com-
posers have been working with twelve-tone and other
contemporary materials . . . whose twelve-tone chro-
matic styles suggest roots in Scriabin as well as
Schoenberg and Berg.

Otto Deri has made a similar observation:

We find evidence in his [Scriabin's] later piano
sonatas of an attempt to replace tonality by a rigid
harmonic scheme, which can be considered the first
explorations in serialism. In this system, a chord
[whose notes form the members of a set] may serve as
the foundation of a work, such as the famous "mystic"
chord to his Prometheus, from which all melodic and
harmonic material is derived.2

 

The previously-mentioned "mystic" chord of

Prometheus is built in fourths--augmented, diminished, and

E?

Scriabin, using as his basis the overtone series, derived

 

perfect:

the notes of this chord from the eighth through the six-

teenth partials, omitting only the twelfth and fifteenth

 

1Eric Salzmann, Twentieth-Century Music: An Intro—
duction (Englewood Cliffs, New Jersey: Prentice-Hall, Inc.,
1967), p. 137.

2Otto Deri, Exploring Twentieth-Century Music, p.

 

 

150.

 

60

partials. Harmonically, this one chord is quite produc-
tive, for different combinations of its notes produce all
four qualities of triads: a major triad with a root of

D, a minor triad with a root of A, a diminished triad with

#, and an augmented triad with a root of Bb.

a root of F
This "mystic" chord is the structure which Scriabin fre-
quently used as a basic set for his composition. By the
addition of other notes of the chord to the triads to form
seventh, ninth, eleventh, and thirteenth chords, by the
occasional alteration of notes in the chord or addition of
another note to it as a part of the basic set, and by the
frequent inversions and transpositions of the basic set,
Scriabin had at his disposal a veritable wealth of material
within the set. These factors enabled him to take the
basic set and use it as the basis of an entire composi-

tion. The set has become, according to Neighbour, ". . .

a tonal field which is equally chord and scale. . . ."1
The Seventh Sonata, Op. 64, composed in Switzer-
land in 1912, is based upon the same chord as that used

in Prometheus. However, Scriabin allowed both the D and
#

 

the F to be lowered a half-step and permitted the

addition of a fifth (G) above the root, forming a basic

set of nine notes:

1Neighbour, "The Evolution of Twelve-note Music,"
p. 56.

 

61

 

 

The first four measures of this sonata are based entirely
upon this basic set, used both melodically and harmoni-
cally. The following four measures have a transposition

of the same material (and set) a major second higher.

Example 36:

 

In an effort to define further the compositional
technique using this basic set which Scriabin has employed
in the Seventh Sonata, Perle has developed a system of
analysis whereby he extracts the following chord--used as

a sub-set--from the basic set:

 

62

 

 

 

1%

This sub-set and its transposition at the interval of a

minor third above,

 

D

are, according to Perle, ". . . derivable from a single

 

 

 

statement of the set, a possibility that permits the es-
tablishment of a closed system of transpositions and a
principle of progression."1 By transposing only these
four notes of the sub-set to other pitch levels, Perle

is able to offer an analysis of the Seventh Sonata by using
different transpositions of only this four-note segment:
"T-l" is used as a symbol to indicate the transposition

of the set up one half-step, "T-2" is its transposition

up two half-steps, etc.2 By using such a system of trans-
position of the sub-set, Perle has eliminated the neces-
sity of transposing the entire set; but actually trans-
positions of the basic set do occur, with Scriabin elect-
ing to use only certain pitches from the set as his com-

positional material in the given examples.

 

lPerle, Serial Composition and Atonality, p. 41.

21bid., pp. 41-43.

63

Example 37:

 

The Sixth Sonata, Op. 62, also composed in 1912,
is based on a set similar to that of the Seventh Sonata.
Here, the root of the chord used as the basic set is G in-
stead of C; again, the fifth above the root frequently

appears, as does the lowered secpnd degree:

 

The same set, arranged in a linear manner, is as follows:

 

 

 

 

The use of this set as basic compositional material
is shown in the Opening of the Sixth Sonata. The notes are
numbered, corresponding to the set given above, in order

to show their use; it should be observed that no concept

 

 

 

of order is implied by this method of analysis. (The
only exceptions to the exclusive use of notes from the
basic set, as indicated, function much in the manner of

nonharmonic tones in earlier music.)

Example 38:

 

The next measure (m. 10) is based upon the same

set transposed up a minor third (Bb - B - C - D - E - F -

G - Ah); the following four measures (ll-14) use the basic

set transposed up yet another minor third (Db — D - Eb -

F - G - Ab -'Bb - B), after which there is a return, in

measure 15, to the original pitch level of the set.

 

65

Example 39:

   

:2?"-
The second theme of this sonata is composed from

the basic set again transposed to Db:

Example 40:

39 Li ALA

    

The third theme appears to be built from the

following transpositions of the basic set:

66

S-2*: A‘Bb '(B)" C# -D# -(E)-F# -G
s-s : c - Db -(D)- E,- F# - (G)- A - Bb
s-a : Eb - E -(F)- G - A -(Bb)- c - Db

Example 41:

 

 

5'2”: 5'5 j "3—7 5"“ j

      

 

 

In the examples given from both the Seventh and

the Sixth Sonatas, Scriabin has used the interval of a
minor third for adjacent transpositions of the set. Though
other intervals of transposition of the set occur in
Scriabin's music, he does seem to indicate a particular

fondness for the minor third transposition.

 

*
The designation 8-2 is used to indicate the
transposition of the basic set up two half-steps.

67

As further illustration of this same principle,
one may observe the construction of the opening of

Scriabin's Vers la flamme, Op. 72. Because of its chordal

texture and use of repetition when the basic set (E - A# -

# # #

 

D - G - C - F ) is transposed, the transposition of the
set up a minor third in measure 5, and the transposition
of the set up yet another minor third in measure 11 can
easily be seen.
An interesting feature of Scriabin's frequent use
of the minor third as the interval of transposition of
his basic set is the fact that each time the set is trans-
posed, two or more notes are always common to both trans-
positions of the set. For example, taking as a basic set
the previously-discussed "mystic chord," which forms the
basis of most of Scriabin's sets, along with transpositions
by minor thirds of that set, one can see that each trans-
position of the set has two notes in common with the same
set a minor third removed:
S-O: C - F# - Bb

S-3: Eb - A - Db - G - C - F

S-6: Gb - c - Fb - Bb - Eb - Ab

- E - A - D

Perle describes such notes which are common to two differ-
ent statements of a set as ". . . invariant segments that
function as pivotal elements among the various transposi-

tions."1 Scriabin Often employed such notes in common to

 

1Ibid., p. 41.

 

68

a set and its transposition as a sort of pivot between
them, in much the same manner that Schoenberg would fre-
quently use one or more notes common to two forms of a
series. To quote Oliver Neighbour,

Where the usage is strict, the flexibility and mobility
Of the technique are reminiscent of Schoenberg. One

of Skryabin's favourite devices is particularly so:

his use of a group of notes as a pivot between two
transpositions of his chord. His Seventh Sonata, for
instance, is based on the commonest of his scales:

C, Db, E, F#, A, Bb [the notes from the same chord

used earlier in this study]. The main subject of the
work makes great use of the triad with both major and
minor thirds. .. . It can be derived in two ways from
the scale I have quoted [i.e., using as roots the

notes F# and A, triads with both major and minor thirds
can be obtained], so that one such chord can be in-
terpreted as belonging to two transpositions, and can
be heard with two different pairs of notes to make up
the complete forms. There is a striking parallel here
with Schoenberg's habit of punning on a group of notes
common to two forms of his basic series.

This use of notes as pivotal elements between
transpositions of the set can again be seen in measures
12-14 of Scriabin's Seventh Sonata. By taking the basic
set containing the notes C, Db, E, F#, A, Bb, and these
transpositions,

A, Bb, Db, Eb, F#, G

F#, G, A#, B#, D#, E

D#, E, G, G#, C, C#,
one is able to see both the application of transposition of

the set as a compositional device and the use of certain

 

lNeighbour, "The Evolution of Twelve-note Music,"
p. 57.

 

69

notes as pivotal elements between the transpositions.

The four notes in common to any two transpositions a

minor third apart are the notes which form a triad with
both major and minor thirds; these notes form the pivotal
elements between the transpositions. (The transposition
of each set is indicated by the first note of each as
given before, and the pivotal notes between transpositions

are indicated by arrows.)

Example 42:

 

In all the examples of Scriabin's music given pre-
viously, both harmonic and melodic content have been gen—
erated from the same basic set of pitches, with transposi-
tion of that basic set being used as the principal means
of providing a sense Of progression. This practice of
deriving both melodic and harmonic material from a basic
set was soon to become an important principle of Schoen-

berg's method.

 

 

70

According to Perle,

The set [as used by Scriabin]--consisting of notes
selected out of the possible twelve--is employed not
only as the basis of linear association but even more
consistently as the basis of vertical association.
Since in these instances the set is not ordered, the
concept of adjacency does not appear, but only that
of content. The total content of the set is here
the sole general criterion of harmonic propriety.1

 

Otto Deri further observes that,

[Scriabin's] derivation of both melody and harmony
from the same vertical arrangement of notes, fore-
shadows the two-dimensional musical Space of Schoen-
berg. . . . Schoenberg bases his claim for historical
necessity on two considerations: first, that the
motivic use of the twelve half steps of the chromatic
scale was in the air in the second half of the nine-
teenth century; second, that during the same period
attempts were already made to view the horizontal
(melodic) and vertical (harmonic) aspects as a
unified field.2

In this practice of deriving all of the notes of a

musical texture--both those used in vertical association

and those used in horizontal association--from only one

given set of notes which have no functional relationship

with each other, is to be found one of the basic concepts

of Schoenberg's serial composition. Looking at still

another passage taken from the Seventh Sonata of Scriabin,

and numbering the notes so that they correspond to the set

transposed,

1 z 3? 14 5' 6 7

 

 

 

.EA
6
i

 

PP-

lPerle, Serial Composition and Atonality, p. 83.

2Otto Deri, Exploring Twentieth-Century Music,
165, 110.

 

 

 

71

one can observe that both melody and harmony are derived
from the same limited set. (Again, the numbering of the

notes indicates no implication of a strict order.)

Example 43:

 

Every set used by Scriabin discussed previously
has been derived primarily from his "mystic chord."
Though this particular set figures prominently in Scriabin's
works, examples are also to be found which use yet a dif-
ferent type of set. One such example is the third of Five
Preludes, Op. 74 (his last work), which is based upon a set
of eight notes Often referred to as an "octotonic scale,"
a scale derived from the interlocking of two diminished

seventh chords:

 

 

 

 

 

 

 

According to an analysis by Charles Burkhart, this piece
". . . adheres strictly to the notes of the scale [set]
except for a few short, rhythmically-weak passing tones."1

The first three measures are given here:

Example 44:

 

By using sets without functional relationships

among their elements, along with systematic transpositions
of those sets, as the basic structural material for much
of his music, Scriabin has, in essence, used procedures
closely related to the serial techniques of Schoenberg
more than ten years before Schoenberg defined them.
Scriabin, in his employment of a more complicated set
[i.e., more complicated than that used by Debussy in
Voiles], of transpositions of the set, of invariant

segments that function as pivotal elements among the
various transpositions, and of consistent variants

 

lCharles Burkhart, Anthology for Musical Analysis
(2nd ed.; New York: Holt, Rinehart & Winston, Inc., 1972),
p. 448.

 

73

of the set, may be considered the first to exploit

serial procedure systematically as a means of com-

pensating for the loss of traditional tonal functions.

The use of sets whose elements generally bear no

functional relationship to each other, together with the
use of procedures--such as transposition of the set, and
horizontal-vertical use of the set--which are related to
Schoenberg's serial method, constitutes a valid example of
one more aspect of Schoenberg's method that had precedent.
Debussy, Stravinsky, and Scriabin all used procedures re-
lated to serialism prior to 1923; but in no case were
their procedures ever so well-defined as those of Schoen-

berg were soon to be.2

 

lPerle, Serial Composition and Atonality, p. 41.

2For further study of Scriabin's use of sets, the
reader may wish to refer to a dissertation study entitled
Quasi-serial Techniques in the E3te Piano Works of Alex-
ander Scriabin by John—Everett Cheetham (University of
Washington, 1969). Mr. Cheetham's analysis, while dif-
fering in some respects from that given here, discusses
many more examples Of Scriabin's use of sets, though the
use of the contradictory term "quasi-serial" seems objec-
tionable.

l

 

 

CHAPTER V

CLOSING REMARKS

Schoenberg's serial method, as proposed by Schoen-
berg himself after 1923, is considered by many to be one
Of the major musical innovations of the twentieth century.
According to Oliver Neighbour, "From the technical point
of view, Schoenberg emerges . . . as the central figure of
his time."1 Donald Grout claims that

Schoenberg has exercised a far-reaching and profound
influence on the music of the twentieth century, not
only through his compositions but also through his
work as a teacher and his intellectual stature as a
philosopher and interpreter of the age.
And Leon Dallin states that, "The twelve-tone method or
tone-row technique is one of the most significant musical
innovations of this century.3

To look for evidence of procedures related to

Schoenberg's method in music prior to his own serial com-

position is not to negate Schoenberg's accomplishment.

In order for his method to have gained such wide acceptance

 

lNeighbour, ”The Evolution of Twelve-note Music,"
p. 59.

2Grout, A History of Western Music, p. 652.

3Leon Dallin, Twentieth Century Composition (3rd.
ed.; Dubuque, Iowa: Wm. C. Brown Company, 1974), p. 189.

74

 

 

75

so quickly after its emergence, there would have to have
been a develOpment of related procedures in earlier music.
Musical developments are seldom isolated phenomena; they
are most often an evolutionary process.

Definition of the most important aspects Of serial
composition was necessary before evidence of techniques
related to serial composition by composers prior to Schoen-
berg was sought. The music of various composers was then
studied for examples of the use of serial-related tech-
niques before Schoenberg's influence. Many examples were
found which gave evidence of some precedent for the differ-
ent aspects-~such as the use of all twelve tones, or the
use of systematic transpositions of a set--Of serial com-
position. However, in no case could any example be labeled
as true serialism as prOposed by Schoenberg; for no example
prior to Schoenberg's serial works revealed the simultaneous
use of the two things necessary to serial composition--the
use of all twelve tones combined with a consistent and pre-
determined ordering Of those tones.

Schoenberg's accomplishment was to bring together
all of the various aspects of serialism and combine them
to form a logical and coherent method of composition which
has proved useful to many twentieth-century composers. No
other Composer prior to Schoenberg used all twelve notes
with a consistent, predetermined order, and a systematic

method of transposed and derived forms of the series,

 

 

76

together with a derivation of both melody and harmony from
the series. Other composers used some of these procedures
in their music, and Schoenberg might possibly have been
aware of such procedures; but only Schoenberg conceived
the possibility of uniting every aspect of his method into

what is now known as serial composition.

 

 

REFERENCES

77

LIST OF REFERENCES

Burkhart, Charles. Anthology for Musical Analysis. 2nd
ed. New York: Holt, Rinehart and Winston, Inc., !

1972. I :F

ii

 

Carner, Mosco. A Study of 20th-century_Harmony. Vol. II:
Contemporary Harmony. London: Joseph Williams
Limited, 1942. d“

Cheetham, John Everett. "Quasi-serial Techniques in the
Late Piano Works of Alexander Scriabin." D.M.A.
dissertation, University of Washington, 1969.

Cowell, Henry. New Musical Resources. New York: Alfred
A. Knopf, 1930.

Dallin, Leon. Twentieth Century Composition. 3rd ed.
Dubuque, Iowa: William C. Brown Company, 1974.

 

Deri, Otto. Exploring Twentieth-Century Music. New York:
Holt, Rinehart, and Winston, Inc., 1968.

Dickinson, Peter. "Skryabin's Later Music." Music Review.
XXVI (1965). pp. 19-22.

Eschman, Karl. Changing Forms in Modern Music. 2nd ed.
Boston: E.C. Schirmer Music Company, 1968.

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