A theoretical analysis of the symphonies of Aaron Copland


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A theoretical analysis of the symphonies of Aaron Copland
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Hilliard, Quincy Charles, 1954-
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Thesis (Ph. D.)--University of Florida, 1984.
Includes bibliographical references (leaves 216-218).
Statement of Responsibility:
by Quincy Charles Hilliard.
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University of Florida
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Copyrights 1984


Quincy Charles Hilliard


The author is greatly appreciative of Mr. Edward

Troupin for his astute criticism and mature judgment. His

candid comments helped to clarify many of the facts and

concepts in this study. Recognition goes to Dr. William

Hedges for his expert criticism of the manuscript. Much

appreciation goes to Dr. Albert Smith and Dr. Budd Udell for

their counsel throughout the work. The writer is grateful

to Mr. Richard Bowles not only as a committee member, but

also as a composer. His infinite patience, keen insight,

and criticism have been invaluable to me, as has been the

fish scholarship. The author is grateful to Dr. David

Kushner for his wisdom, encouragement, and assistance shown

not only as a professor, but also as a friend. In securing

information, Mrs. Robena Cornwell and Mrs. Barbara Salaman

were most helpful. Special thanks also go to Aaron Copland

for being such a gracious host and allowing time for an

interview, and to Boosey and Hawkes Publishers for granting

permission to incorporate excerpts from the symphonies in

this dissertation. The writer is indebted to his father,


the late Reverend Q. C. Hilliard, whose memory was a con-

stant source of inspiration. Acknowledgment also goes to

the following for their encouragement and support: Laura M.

Hilliard, Alsenia Ashford, Coty Ashford, Deborah James,

Vivian James, and friends. Last, but certainly not least, a

special gratitude goes to his wife, Rubye. Her optimism,

inspiration, and wit were the brightest in the darkest

hours. Without her ceaseless patience, motivation, and

financial support, this degree would be a dream and not a




ACKNOWLEDGMENTS...................................... iii

ABSTRACT........ ..................................... vii

CHAPTER I INTRODUCTION.......................... 1

Statement of the Problem............. 1
Need for the Study.................... 2
Limitations ..... .................... 2
Methodology.................. ........ 3
Data Sources .. ................. ..... 3
Collection of Data................... 3
Analysis of Data..................... 4
Definition of Terms.................. 5
Organization of the Chapters.......... 7


Books Written by Aaron Copland........ 9
Articles Written by Aaron Copland..... 11
Books Written About Aaron Copland..... 14
Articles Written About Copland........ 15
Jazz Elements........................ 16
Folk Music .......................... 18
Short Symphony.................... 18
Third Symphony...................... 19
The Music in General................ 20

CHAPTER III DANCE SYMPHONY ......................... 22

First Movement ........................ 25
Second Movement ...................... 38
Third Movement ....................... 47
General Observations................. 58







FIRST SYMPHONY..........................

First Movement ......................
Second Movement ....................
Third Movement.......................
General Observations.................

SECOND (SHORT) SYMPHONY ..............

First Movement .......................
Second Movement........................
Third Movement ....................... .
General Observations..................

THIRD SYMPHONY ....................... .

First Movement ........................
Second Movement ...................
Third Movement.......................
Fourth Movement ...................
General Observations...................


Melody ...............................
Formal Design .........................
Instrumentation and Orchestration.....


Copland's Melodic Contour.............
Copland's Harmonic Practice...........
Copland's Rhythmic Practice...........
Structural Design.....................
Orchestration Technique...............
Value of These Symphonies to a Young


REFERENCES ...........................................

BIOGRAPHICAL SKETCH......................... ........













Abstract of Dissertation Presented to the
Graduate School of the University of Florida
in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy



Quincy Charles Hilliard

April, 1984

Chairman: Dr. William Hedges
Cochairman: Mr. Edward Troupin
Major Department: Curriculum and Instruction

The primary purpose of this study is to provide a

theoretical analysis of the symphonies of Aaron Copland.

The symphonies analyzed are the Dance Symphony, First

Symphony, Second Symphony (Short Symphony), and the Third

Symphony. The study investigates each symphony with regard

to thematic material, tonality, formal design, rhythm, and

orchestration. A comparison of these elements concentrates

on the differences and similarities among the symphonies,

and the importance of their construction in the development

of Copland's technique and style. His technique and style

are significant examples of twentieth-century musical pract-

ice, and are, therefore, relevant in teaching twentieth-

century music. The study examines the usefulness of the


symphonies as exemplars in the teaching of higher level

music theory courses and the value of the symphonies to a

young composer.

Based on the analysis, the researcher found that a

majority of Copland's melodies are diatonic and do not span

more than an octave. The composer also uses polyharmonies,

polytonality, and clusters. In constructing chords, Copland

sometimes omits tones. There is also an abundant use of

counterpoint throughout the symphonies. With regard to

rhythm, the composer employs such devices as syncopation,

frequent changes of meter, asymmetrical rhythms, ostinatos,

and polyrhythm. The form of each movement is usually based

on some traditional design, and all the symphonies adhere to

the cyclic principle of structural design. Copland's trans-

parent texture can be attributed to the soloistic treatment

of instruments, incomplete chord structure, rare doubling,

and the consistent use of intervals of a fourth, fifth, and

octave for a harmonic background.

The author recommends that the symphonies be used in

music curricula of higher education dealing with harmony,

form and analysis, composition, counterpoint, and orchestra-

tion as examples of twentieth-century stylistic practice.



Statement of the Problem

The major purpose of this study is to provide a theo-

retical analysis of the symphonies of Aaron Copland. In.the

analysis, the study investigates tonality, thematic materi-

al, formal design, rhythm, and orchestration. A comparison

of these elements is made to show the characteristics of each

symphony and the stylistic traits that are common to all.

The devices derived from jazz idioms are also examined in

the analysis. Throughout the dissertation, there is an

attempt to answer the following questions:

1. What relevance do the symphonies have
in the teaching of higher level music
theory courses?

2. How can the study of these symphonies
be helpful to a young composer?

3. What does an analysis of these sym-
phonies reveal about Copland's tech-
nique of composing for the orchestral

4. What are the similarities and differ-
ences among the symphonies?

Finally, this study can serve as a model for analyzing

other compositions from this period.

Need for the Study

Aaron Copland has been called the "Dean of American

Composers."I He has written many compositions, several of

which have been analyzed and others which have been over-

looked. His large works, including his symphonies, fall

into the latter category. Such large works by a major com-

poser should be analyzed to determine the structural make-up

of his symphonic form. The analysis may not only provide

exemplars for the teaching of higher level music theory

courses, but can also be useful in teaching twentieth-

century compositional techniques to young composers.


The present dissertation is subject to the following


1. The works by Copland that are analyzed are
the Dance Symphony, First Symphony, Second
Symphony (Short Symphony), and the Third

2. There is no attempt to supplement extant
biographical material on Copland.

3. No judgment is made concerning the rela-
tive merits of these works.

'Harriett Johnson, "Aaron Copland: Dean of American
Composers," International Musician, LXXV (July, 1976), p. 6.


The following procedure was used in the collection and

analysis of data.

Data Sources

The printed scores of the symphonies were the primary

sources of data. The Dance Symphony (1925) and the First

Symphony (1928) were first published by Arrow Music Press

(originally Cos Cob Press). The Short Symphony (1933) and

the Third Symphony (1946) were published by Boosey and

Hawkes. Another primary source is a personal interview with

Aaron Copland on July 15, 1981.

Secondary sources include books written by Julia Smith

and Arthur Berger. Aaron Copland: His Work and Contribu-

tion to American Music was written by Julia Smith and

published by E. P. Dutton and Company, Inc., in 1955.

Berger's book, entitled Aaron Copland, was first published

by Greenwood Press in 1977.

A majority of the articles that are used in this study

were written by Copland and published in the journals Modern

Music and Tempo. Other critical works, as well as books

written by the composer, were also utilized in the analysis.

Collection of Data

The collection of data was accomplished by purchasing

the scores of the symphonies from Boosey and Hawkes, current

publishers of Copland's music. For the purposes of this

study, an interview was conducted with Aaron Copland to

collect data pertaining to his symphonies and his teaching

philosophy. A methodical search was also conducted through

several magazines and journals, in particular, the journals

Modern Music and Tempo. The books and other historical

material were available in the University of Florida Music

Library in Gainesville, Florida, and the Library of

Congress, in Washington, D.C. The search for data was

conducted from January, 1980, to July, 1981.

Analysis of Data

The symphonies are analyzed through the use of tradi-

tional and contemporary methods. These methods examine

harmony, formal design, melodic structure, rhythm, and

instrumentation. The data from the interview, books, and

periodicals are analyzed to show the usefulness of these

symphonies in the teaching of higher level music theory

courses. The comparative analysis concentrates on the

differences and similarities in the ways Copland has con-

structed his symphonies and the importance of this con-

struction in the development of his particular technique and

style. His technique and style are significant examples of

twentieth-century musical practice and are, therefore,

relevant in teaching twentieth-century music theory and


composition. Charts, diagrams, and musical examples are

shown to aid in a greater understanding of the data.

Definition of Terms

For the purpose of this study, the following

definitions were used:

Augmentation. A proportional increase in note value.

Canonic imitation. A restatement of a melody, theme,
or motive in close succession in a contrapuntal

Cluster. A chord that consists of two or more consecu-
tive intervals of a second.

Col legno. A style of bowing which requires the per-
former to bounce the wooden stick of the violin bow
against the strings.

Cuivrt. An effect which is usually found in the French
horn, but is common to all brass instruments. The term
instructs the player to produce a forced and brassy

Cyclic form. A format for a composition with several
movements in which thematic material from the first
movement is used in some or all of the movements,
especially in the last movement.

Diminution. A proportional decrease in note value.

Fugato. A section or passage in fugal style which
occurs in a composition.

Glissando. An effect which requires the performer to
execute a scale passage in a rapid, sliding movement.

Inversion. The changing of a melody, theme, or motive
so that each descending interval becomes the corre-
sponding ascending interval and vice versa.

Jett. An effect which is produced by throwing the
upper third of the bow on the strings so that it will
bounce a series of rapid notes on the down bow.

Neo-classic. A period in twentieth-century music which
uses characteristics and stylistic traits from the
seventeenth and eighteenth centuries.

Ostinato. A recurring rhythm-pitch figure which is re-
peated persistently in immediate succession.

Polyharmony. The combination of two or more chordal
units simultaneously.

Polyrhythm. The simultaneous combination of two or
more metric pulsations.

Polytonality. The combination of two or more key
centers simultaneously.

Retrograde. A melody or theme written backward.

Sonata allegro design. A movement of a composition
written in primarily three sections--exposition,
development, and recapitulation. The exposition may be
preceded by an introduction, and the recapitulation may
be followed by a coda. The exposition consists of two
contrasting themes. In the development section, the
two themes are subject to various treatments, and in
the recapitulation, the two themes are repeated.

Stretto. The imitation of a motive or phrase in close
succession, with the repetition entering before the
first statement is completed. Stretto is a device
commonly associated with the fugue.

Sul ponticello. A style of bowing which requires the
performer to bow close to the bridge.

Sul tasto. An effect which is produced by bowing
slightly over the fingerboard.

Tonal center. The pitch level which serves as a
gravitational pole or pitch focus for a section of a

Organization of Chapters

Chapter II contains a review of significant literature

related to Copland's musical output. The chapter also con-

tains a review of his articles, books and essays, as well as

other literary writings about Copland.

Chapters III, IV, V and VI are devoted to the analyses

of his First Symphony, Second Symphony, Third Symphony, and

Dance Symphony, respectively. These chapters examine each

symphony by movements. There is also a brief section at the

end of each chapter to summarize the important observations.

Chapter VII gives a synthesis of Aaron Copland's

symphonic procedures. The chapter investigates similarities

and differences in melodic, harmonic, rhythmic, and formal

structure. The instrumentation and orchestration of each

symphony are also taken into consideration in this chapter.

Chapter VIII shows the potential utility and importance

of these symphonies as teaching instruments in higher level

music theory courses, and the value of these symphonies to a

young composer.

Chapter IX summarizes and gives conclusions on findings

in relation to their implications in the teaching of theory

and composition. Suggestions for additional research


are also supplied. A comprehensive bibliography is also


Excerpts from Symphony No. 1, Symphony No. 2, Symphony

No. 3, and the Dance Symphony are reprinted by permission of

Aaron Copland, copyright owner, and Boosey & Hawkes, Inc.,

sole licensees.


For the purposes of this study, the review of litera-

ture has been divided into four categories: books written

by Copland, articles written by Aaron Copland, books written

about Copland, and articles written about Copland. The

author believes that Copland's writings and viewpoints about

music are of the utmost importance in the analysis and

understanding of the composer's music.

Books Written by Aaron Copland

Music and Imagination consists of a set of presenta-

tions known as the Charles Eliot Norton Lectures given at

Harvard University during the academic year 1951-52.1 All

the lectures carry the general theme of the role imagination

plays in the art of music. The book is divided into two

parts: Music and the Imaginative Mind, and Musical Imagina-

tion and the Contemporary Scene. The first part of the book

investigates the musical mind in the role of listener (audi-

ence), creator (composer), and interpreter (performer). The

Aaron Copland, Music and Imagination (Cambridge,
Massachusetts: Harvard University Press, 1952).

second part examines the recent innovations and the imagina-

tive mind in Europe and America. Copland also examines the

role and perception of the composer in Industrial America.

What to Listen for in Music was derived from a course

of fifteen lectures that Copland gave at the New School for

Social Research in New York City during the winter of 1936

and 1937. The author not only discusses how people listen

and the importance of listening, but also states that the

listener should "strive for a more active kind of listen-

ing."2 To gain a deeper understanding of music, the com-

poser believes that the listener should become more alert

and aware of what to listen for in music. The importance of

the interpreter, and the effect that he can have on the

listener's comprehension and understanding of a composer's

work are also examined. The book was written for the layman

and not the professional musician. Because of this fact,

Copland acknowledges that his book is restricted to matters

which he feels clarify essential listening problems.

The New Music, as it is called in its revised edition,

was titled in this manner to indicate that it is not just a

reprint of the original edition.3 The book highlights the

main developments in music from the late nineteenth century

Aaron Copland, What to Listen for in Music (New York:
McGraw-Hill Company, Inc., 1957), p. 23.

Aaron Copland, The New Music: 1900-1960 (New York:
W. W. Norton and Company, 1965).

to the mid-twentieth century, and the composers who have

played a significant role in this development. Ideas in

this book are also the result of articles, radio talks, and

lectures presented since 1927. Copland also gives a general

overview of late nineteenth-century and early twentieth-

century music.

Copland on Music contains articles written by Copland

over a period of thirty years on music and musicians.4 Most

of these articles have already appeared in magazines and

newspapers; thus, the purpose of this collection was to make

them available in a collective volume which would summarize

the composer's viewpoints on music.

Most of Copland's writings were the result of lectures

and articles written by him over a period of years. In an

interview with Copland, he explains that the lectures were a

definite source of income. The composer says, "I could make

more money in one afternoon by lecturing to 200 students

than seeing each one of them individually."5

Aaron Copland, Copland on Music (New York: Da Capa
Press 1976).
Statement by Aaron Copland, Composer, in a personal
interview, Peekskill, New York, July 15, 1981.

Articles Written by Aaron Copland

Copland has written many articles, several of which

appear in Copland on Music. Most of these articles are

devoted to:

1. A particular composer's style of composition to
aid in the understanding of his work.

2. American contemporary music.

3. Contemporary music.

For the purposes of this dissertation, only two of the

articles written by Copland have a direct connection with

his symphonic works. Both of these articles give his

viewpoints concerning certain musical elements that are

present in his music.

The first article, "Jazz Structure and Influences,"

published in 1927, gives a brief background of the history

of jazz and its origin. According to Copland, the most

important element of jazz is rhythm. He also states that

early jazz consisted of a slow four quarter note bass line

and is improved by accenting the feminine beats (two and

four). Along with this combination, a new rhythmic element

was introduced in the melody. Jazz, according to Copland,

"contains no syncopation; it is instead a rhythm of four

quarter [notes] split into eight eighths [notes]."6 Because

of these two rhythms (in the bass and melody), whatever

melody is used comes out "jazzy." These two independent

rhythms became known as polyrhythm. In regard to poly-

rhythms, Copland states, "the peculiar excitement they

[polyrhythms] produce by clashing two definitely and regu-

larly marked rhythms is unprecedented in occidental music."7

Copland, therefore, acknowledges that "polyrhythm is the

real contribution of jazz."

In "On the Notation of Rhythms," published in 1944, the

author states that our present-day system is inadequate to

serve the needs of the performer, composer, and conductor.

Notation of traditional rhythmic patterns is not the pro-

blem. The trouble begins when trying to notate combinations

of unequal units of twos and threes. Use of subterfuges by

composers for keeping the strong beat away from the barline

shows the deficiencies in our present-day system. Although

rhythmic freedom seems to be a characteristic of western

music, Copland feels that a more efficient system is needed

Aaron Copland, "Jazz Structure and Influence," Modern
Music, IV (February, 1927), p. 11.

Copland, "Jazz Structure," p. 13.

Copland, "Jazz Structure," p. 13.

"to account for rhythmic subtleties that don't 'get across'

to the interpreter in our old fashioned notational system."9

Books Written About Copland

There have been only two books written about Copland

which pertain to his music. Since the purpose of this study

is not to investigate existing biographical material, those

books that are biographical have been omitted.

Aaron Copland: His Work and Contribution to American

Music, by Julia Smith, may be the most comprehensive book

yet written on Copland.10 Smith has combined biographical

information with a study of Copland's music and writings to

show his contributions to American music. Separate chapters

are given to his two most important teachers, Rubin Goldmark

and Nadia Boulanger. Smith divided Copland's writing style

into three distinct periods. Each section gives a brief

history and a brief analysis of the works in that particular

period. The periods are divided as indicated below:

French-Jazz Period (1924-1929)

Abstract Period (1929-1935)

American Folksong Period (1934-1955)

Aaron Copland, "On the Notation of Rhythms," Modern
Music, XXI (May/June, 1944), p. 220.

J1ulia Smith, Aaron Copland: His Work and Contribution
to American Music (New York: E. P. Dutton and Company,
Inc., 1955).


She also devotes a separate chapter to Copland's critical

works. Smith says that her purpose was to trace Copland's

development as an individual and as a composer because she

felt that "his work was a reflection of his life."1

Smith's book is limited in that it does not include any of

Copland's compositions after 1955.

Aaron Copland, by Arthur Berger, published in 1953, has
a wealth of information about Copland and his music. The

book is divided into two parts--The Man, and The Music.

Part one, The Man, examines the composer's musical develop-

ment and his relationship to American Music. Part two, The

Music, concentrates on Copland's compositional technique,

his use of folk music, jazz elements, and his method of

chord building. Although brief and generalized, this study

is the only one of its kind that investigates Copland's

music through analysis. The analysis is a consolidated look

at all of Copland's music--ballets, symphonies, film music,

and piano works.

Neither of the two books offers any detailed analysis

of the Copland symphonies. Usually the thematic material

and formal design are the only musical elements discussed.

1Ibid, p. 8.
1Arthur Berger, Aaron Copland (Westport, Connecticut:
Greenwood Press Publishers, 1971).

Articles Written About Copland

A majority of these articles deal with Copland's music

in general. Only four of these articles that the author has

been able to locate deal with his symphonies directly. The

articles in this section of the review of literature are

divided into five subheadings--Jazz Elements, Folk Music,

Second Symphony, Third Symphony, and The Music in General.

Jazz Elements

Fuller reveals that although Copland studied in France,

his music assumed American traits through the infusion of

the sound and rhythms of jazz.13 Goldberg feels that

Copland has managed to use jazz in its purest state. The

use of double and triple rhythms and "their combination in

the same instrumental line," fascinated Copland.14 Goldberg

also found that Copland's chief extension of the use of jazz

has been a "deepening of its emotional range."15 Gold

reveals that Copland found the harmonic limitations of

Donald Fuller, "A Symphonist Goes to Folk Sources,"
Musical America, LXVIII (February, 1948), p. 256.
14Isaac Goldberg, "Aaron Copland and His Jazz," American
Mercury, XXII (September, 1927), p. 64.
15 idi

progressive jazz are more free. The composer described

jazz as having two moods: blues and fast rhythm movement.

In an interview with Copland, he states that he was

attracted to jazz:

First because of the rhythm it was
fresh, different, lively, and exciting. Second,
because it was recognized as a product of America.
My desire to write music that could be recognized
as American was in my mind in the twenties. I
spent three years in Paris as a student and had
become aware of the "Frenchness" of French music
by the comparison of the "Germanness" of German
music. So the jazz boys in America proved that
they could write a music that the whole world
could recognize as American, so I asked myself,
"Why can't we do17it in the field of so-called
classical music?"

In an interview with Don Gold, Copland says, "the wildness

of jazz attracts me--the mood stuff and the colorful stuff.

The let-loose quality is rarely found in 'serious' music."18

The main problem that the composer found with jazz was "a

lack of unity in expressive content, by failing to drive

home a unified idea."19 The composer, however, is quoted in

1Don Gold, "Aaron Copland: The Well-Known American
Composer Finds Virtues and Flaws in Jazz," Down Beat, XXV
(May 1, 1958), p. 25.

1Statement by Aaron Copland, composer, in a personal
interview, Peekskill, New York, July 15, 1981.
Gold, pp. 39-40.

1Gold, p. 16.

the article as saying, "the two fields [contemporary classi-

cal music and jazz] will continue to borrow and perhaps

eventually will overlap. But I don't feel that there ever

will be one form."20

Folk Music

Burns found that Copland's desire to appeal to a larger

audience led him to use folk themes in his music. In Burns'

conclusions, she states that he uses both authentic folk

material and folklikee" material of his own composition.

Burns goes on to state that Copland developed his themes

"instrumentally, durationally, and texturally."21

Short Symphony

Redlich believes that the octave-transpositions in the

opening bars of the theme contribute to the tonal ambitus.22

The narrow intervallic range of the themes in all three

movements lends itself to ostinato treatment. The second


21Mary T. Burns, "An Analysis of Selected Folk-Style
Themes in the Music of Bedrich Smetana and Aaron Copland,"
American Music Teacher, XXV (November/December, 1975), p.
2Ambitus is a Latin word meaning compass or range.
Redlich refers to the fact that the tonal compass or range
of the opening theme is increased through octave-

movement is derived from the "malaguena" motif of a de-

scending fourth, while the third movement is built around a
variety of "rhythmical metamorphoses."2

Evans' analysis of the Short Symphony shows that the

first movement is filled with short jagged motifs. The

motifs are characterized by "not only modified intervals and

octave-transposition but also interpolated notes usually

completing arpeggio patterns."'4 The second movement

centers around an F tonality with a very free rhythmic

motion. He goes on to state that the last movement has a

bi-tonal relationship.25

Third Symphony

Crankshaw says that the tonality in Copland's Third

Symphony is strongly emphasized. The tonal centers of E

major and F major are used throughout the four movements.

The author reveals that the composer uses rhythm and orches-

tral timbres to function as color.26

H. F. Redlich, "Music from the American Continent,"
Music Review, XIX (August, 1958), p. 258.
24Peter Evans, "The Thematic Technique of Copland's
Recent Works," Tempo, LI (Spring/Summer, 1959), p. 4.

2Geoffrey Crankshaw, "Aaron Copland," Chesterian,
XXXII (Spring, 1958), pp. 100-101.


In Berger's analysis of Copland's Third Symphony, he

shows that the first movement contains three themes which

are essentially diatonic. The second movement is a scherzo

and is traditional in form. The third movement is slow in

character and built around a theme that has the elements of

a hymn tune. Copland's Fanfare for the Common Man is also

quoted in this symphony.27

The Music in General

Thomson found that Copland's music is "American in

rhythm, Jewish in melody, eclectic in all the rest."28 The

emotional origin is religious, and tension is created by the

orchestration, which places various instruments into their

extreme high registers. Because of this characteristic,

"the instrumentation is designed to impress, to overpower,

to terrify, not to sing."29 His observations also reveal

that Copland's melodies are "predominantly minor" and chrom-

aticism is used as ornamentation rather than modulation. He

describes Copland's music as coloristicc [with]

harmonic and instrumental elements rather than melodic

devices."30 Thomson states that Copland's music is not

2Arthur Berger, "The Third Symphony of Aaron Copland,"
Tempo, IX (Autumn, 1948), pp. 22-25.
Virgil Thomson, "American Composers: Aaron Copland,"
Modern Music, IX (January/February, 1932), p. 67.
9Ibi d.


polyphonic. His most common contrapuntal device is a "form

of a canon at the octave or unison, everybody doing the same

thing at a different moment."31 Thomson says, "this is

counterpoint but not polyphony."32

Berger suggests that Copland's greatest musical contri-

bution may be the matter of chord spacing. In addition,

some of his harmonies contain tones that are not part of the

diatonic scale.33

Salas characterized the music of Copland's later period

as having an increased use of open harmonies, rhythmic asym-

metry, and a gradual separation from chromaticism. Poly-

tonalism, says Salas, is created by small thematic phrases

built upon triads which disregard traditional harmonic


All of these articles point to the fact that Copland's

music has a distinctive sound. One of the purposes of this

study is to describe the musical elements in the symphonies

which contribute to this result.

Ibid., p. 68.
Ibid., p. 68. The author of this study disagrees
strongly with this last statement, because a canon is a
contrapuntal device with two or more voices, which can be
described as polyphony.

3Arthur Berger, "The Music of Aaron Copland," Musical
Quarterly, XXXI (October, 1945), p. 438.
34Juan O. Salas, "Aaron Copland: A New York Composer,"
Tempo, IX (Autumn, 1948), pp. 8-16.


The Dance Symphony was derived from the ballet,

The symphony was one of the winners of the RCA Victor

The first performance took place on April 15, 1931,

Academy of Music, in Philadelphia. It was performed

Philadelphia Orchestra, under the direction of

Stokowski, in a concert held for the benefit

unemployed musicians of Philadelphia.1

Regarding the work, Smith quotes the Philac




at the

by the


of the


The "Jazz" or "Dance" Symphony of Copland
promptly proved popular and established itself
as modern music of interest and individuality.
It has substantial musical structure, with
considerable diversity of material, and re-
sourcefulness in treatment. The work is orig-
inal and unusual in effect and distinctly
evocative in atmosphere.

Through the analysis, the author of this dissertation

discovered that the Dance Symphony closely resembles the

Julia Smith, Aaron Copland: His Work and Contribution
to American Music (New York: E. P. Dutton and Company,
Inc., 1955), pp. 133-134.

2Ibid., p. 134.

programmatic symphony. The program symphony is a nineteenth

century composition based on an extra-musical idea. There

are three reasons why the author characterizes this symphony

as a program symphony:

1. The Dance Symphony is a large symphonic work
in three movements.

2. The Dance Symphony is based on an extra-musical
idea which is a character named Grogh.

3. Each movement of the Symphony has its own

The first movement is entitled, "Dance of the Adolescent,"

the second movement is entitled, "Dance of a Young Girl Who

Moves as if in a Dream," and the third movement is entitled,

"Dance of Mockery." The entire symphony is based on a

character named Grogh. Grogh is a character that Copland

and Harold Clurman devised, and around whom they invented a

scenario in which magicians, vampires and dead bodies all

participate. Grogh is the title of a ballet from which the

symphony was taken. The ideas from the ballet are carried

over into the symphony. For instance, Copland states that

the introduction "sets the scene for Grogh's domain" (Dance

of the Adolescent), and the last movement (Dance of Mockery)

is where "Grogh is taunted by his victims and servitors."3

Statement by Aaron Copland, composer, in an interview
with Phillip Ramey at the Connaught Hotel in London. The
interview took place on October 3,1967, after Aaron Copland

In addition, the polyrhythms used in the last movement

represent the dancing of the dead bodies. Copland states:

Grogh-like pronouncements appear in the
trumpets and trombones, and then all hell
breaks loose. A sudden pause terminates the
almost hysterical climax while Grogh's com-
manding motto from the opening movement
erupts into shrieking trills--and collapses.

The author of this study contends that through these de-

scriptive statements, Copland has led the reader to believe

there is a direct correlation between what happens in the

music and the events surrounding Grogh's death. The result

is a symphonic work in several movements with descriptive

titles for each movement. The final conclusion is that the

Dance Symphony is a program symphony adhering to the cyclic

principle of formal design.

The performance time for this symphony is twenty


had finished recording his Dance Symphony with the London
Symphony Orchestra. Aaron Copland, Copland Conducts
Copland, conducted by Aaron Copland, London Symphony
Orchestra, Columbia Records, MS 7223 (jacket notes).


First Movement

The first movement closely resembles the sonata-allegro

design. There are two contrasting themes that return in the

recapitulation, but not in the order in which they are

traditionally found. There is also an introduction with a

very short development section. The tonal levels of this

movement are not consistent, however, with the classical

sonata-allegro format.

Intro 1st Theme 2nd Theme
_I (Trans.)

Meas. 1 26 (70) 78

2nd Theme Ist Theme

(142) 180 176


180 201

Figure 3.1. Tonal Levels of the First Movement

The introduction, marked Lento ( = 48), uses a motive

with the minor third as the characteristic interval, and is

played by the trumpets.


Figure 3.2. Page 1, measures 1-2

In measures three and four, the motive is heard again, but

this time, in a slightly different rhythm pattern.

I S 4.

Figure 3.3. Page 1, measures 3-4

The motive is used throughout the introduction which ends in

measure twenty-five. At measure twenty-six, the tempo

changes to Motto allegro ( = 96). The first theme is

played for the first time by the bassoon:

"'1 -7


Figure 3.4. Page 5, measures 27-36

21 4
5. 3-

The theme is played again beginning in measure forty-four,
and ending in measure sixty-three by the clarinet. The
clarinet plays the theme in a slightly different form;
however, the "dance-like" character is unchanged.

r_ _F


4zz~zL-ilv:V?7 .~~bt; fir,

Figure 3.5. Pages 6-8, measures 44-52

The first theme, played by the bassoon, returns in measures
sixty-six through sixty-nine in its original form. Measures
seventy through seventy-seven serve as transitional material
to the second theme.
The second theme begins in measure seventy-eight. The
theme is played by the oboe and the English horn.




[ W 7dJ

Continued in English horn


I 1,

~V~t#~ALV tjr~'


Figure 3.6. Pages 12-13, measures 78-83

The first theme material is replayed beginning in measure

115 by .the horns, and continues to measure 120. Second

theme material is played in measures 134 through 142. A

short development section begins in measure 146, and ends in

measure 162.

The recapitulation starts in measure 162 in a C tonal

center. Material that was used earlier in the second theme

is repeated beginning in measures 164 through 171. The

viola plays this material.

Figure 3.7. Pages 25-26, measures 164-171

I~~ ny 1-.9 F&~ III

F F- oo



First theme material is heard in the recapitulation begin-

ning in measure 171 and is played by the clarinet in D and

bassoon. The recapitulation comes to a close in measure 179

which also marks the beginning of the coda in measure 180.

There is a stretto between the trumpets and trombones in

measures 179 through 183. The coda ends in measure 200, and

measures 201 through 207 serve as transitional material to

the second movement.

The harmonic implications of this movement are at times

ambiguous, and in other instances, conservative. The first

theme, for example, indicates an E tonal center. The E

tonal center is further reinforced through the accompaniment

material played by the violins. An excerpt from the violin

part is shown below.

Figure 3.8. Page 5, measures 36-37

The E tonal center is never defined as E major or E minor.

There are instances in which a G-sharp is used to indicate a

raised third degree of the E major triad. There are also

times when a G natural is used along with an F-sharp and

D-sharp to indicate the harmonic form of the minor scale.

The type of alternation just described between a major and

minor tonal center is present throughout the first movement.

To complicate the ambiguity between E major and E minor,

Copland uses an F-sharp pedal point in measures thirty-six

through forty-one, and F pedal point in measures fifty-two

through fifty-five, and a B pedal point (which suggests the

dominant of E) in measures fifty-six through sixty-one. The

chord structure during measures fifty-six through sixty-one

suggests an E tonal center with an added fourth degree.

if. / L 1

Figure 3.9. Page 9, measure 56

In measures sixty-two through sixty-five, the piano and

violin play a short transition ending on the dominant of the

E tonal center. The key centers during the transition are

clearly defined. The last center, which is B, is spelled

enharmonically as C-flat in the piano and violin parts.


4 P go P & I KF I 1-IL g

Figure 3.10. Page 11, measures 62-64

In the few instances where Copland has used chords, their

spelling is often incomplete. In measures 184 through 191,

the composer repeats a series of chords which are without




Figure 3.11.

r I

Page 28, measures 184-186

The writing of chords in this manner creates an ambiguity

because without the third, there is no way of determining

the quality of the chord. These types of chords also have

an "open" or "empty" quality which is associated with

Copland's music. Another example of this type of chord

usage can be seen in measures 194 through 196. Overall, the

movement is characterized by the abundant use of counter-

point. This horizontal structure is evident through

1 r.\ I1 F i

8uR.. 1

Copland's linear approach to melodic content and the use of

arpeggiated chords. An example can be seen beginning in

measure 139.

The rhythm of the first movement is very active, except

for the slow introduction. The composer uses the alla breve

time signature beginning in measure twenty-six. The tempo

marking at this point is Motto allegro ( J = 96). The alla

breve time signature is used for most of the movement until

measure 193, where the composer changes to 2/4. Measures

194 and 195 have a 3/4 meter signature, measure 196 has a

4/4 meter signature, and measures 197 through 200 have a 3/4

meter signature. The title of the symphony suggests that

the rhythmic content should be active. Copland reinforces

the active rhythmic feeling in his first theme. The first

theme, because of the new tempo in measure twenty-six, is

very lively and has some syncopation.

I "

Figure 3.12. Page 5, measures 27-31

In measure forty-four, the second theme, although slightly

changed, has even more syncopation than it did the first

time it appeared.

Figure 3.13. Pages 6-7, measures 44-49

Syncopation can also be seen in measures seventy-eight

through eighty-three when the second theme is played.


Continued in the English horn.
Continued in the English horn.

Figure 3.14. Pages 12-13, measures 78-82

In measures 147 through 150, syncopation can be seen in

almost every instrument playing.


Copland also uses ostinato rhythms in the first move-

ment. Measures forty-two through fifty-five show an osti-

nato among the harp, second violin, and the second viola.

.K ^r1 ~R-

2nd Violin

2nd Viola


Figure 3.15. Page 6, measures 42-43

Another ostinato can be seen between measures 112 and 115,

and measures 168 through 171.

With regard to instrumentation, Copland has scored the

symphony for an enlarged orchestra, especially in the

percussion section where he uses a variety of pitched and

nonpitched instruments. The instrumentation for the Dance

Symphony is illustrated below.

1 Flauto piccolo
2 Flauti grand
2 Oboi
1 Corno Inglese
1 Clarinetto piccolo in D
2 Clarinetti in A
1 Clarinetto basso

L. I Ir lP

A1 dA 1 A I:

2 Fagotti
1 Contrafagotto
4 Corni in F
3 Trombe in C
2 Pistoni in B-flat
3 Tromboni
1 Tuba
Tam-Tam, Tamburo Militare, Tamburion,
Legno, Triangolo, Rattle, Zilofone
2 Arpe
Quintuor a corde

With such a large orchestra, the composer is able to produce

some interesting orchestral colors. Perhaps, the most in-

teresting color used during the first movement is the effect

that Copland achieves by scoring for xylophone, woodblock,

piano, and horn in measures 104 through 106, and measures

112 through 116. The composer also utilizes a variety of

instrumental effects. In the strings, for example, these

effects include muted and pizzicato playing, harmonics,

glissandos, col legno, and sul tasto. An example of the

muted strings can be seen in the opening bars of the piece

between the violins and violas.

Con. Sord.

Figure 3.16. Page 3, measures 2-5

The most pronounced use of pizzicato playing can be seen in

measures fifty-six through sixty-one. The effect of produc-

ing harmonics on the strings can be seen in measures forty-

eight through fifty-five in the violins, and in the harp in

measures 203 through 205.

a a p

Figure 3.17. Page 32, measures 203-205

The col legno effect can be seen in the second violins in

measures sixty-two through sixty-five.

.Co legno
Col legno

Figure 3.18. Page 11, measures 62-64

Copland also uses an effect in which half of a group of

strings will play pizzicato and the other half aroo. The

composer labels this effect half pizzicato. There are num-

erous examples of this effect throughout the first movement.

The first violins use this effect in measures sixty-six

through seventy-six. The glissando effect is used in the

first and second violins in measures 157 and 158.


4L _OL






Figure 3.19. Page 23, measures 157-158

The sul tasto effect, which frequently appears in the French

impressionist school of writing, instructs the player to bow

slightly over the finger board. The effect can be found in

measures 201 and 202 in the second violins.

Sul tasto

Figure 3.20. Page 32, measures 201-202

Muted playing for brass instruments is also used. In the

introduction, the opening bars begin with muted trumpets.

The solo for the trombone, in measures twenty-two through

twenty-seven, calls for muted playing as well. The horns

use an effect known as cuivrb. The effect calls for a harsh

and "brassy" tone quality and is commonly found in the horn

section. The effect can be seen in measures 102 and 108.

Ho rn

+ Cuivrt



Figure 3.21. Page 15, measure 102

Second Movement

The second movement has a much slower tempo than the

first. Andante moderato ( = 88) is the tempo marking.

This movement is built around two themes linked together by

transitions. The second movement does not follow any

traditional design and is characterized by subtle hints of

polytonality. During the first theme, for example, F and D

tonal center are suggested; whereas, during the second

theme, C-sharp and D tonal centers are implied. The tonal

levels of this movement are diagrammed below.

IF (Trans.)

D/F D/C-sharp
Meas. 208 (253) 264

1st Theme 2nd Theme
I (Trans.)_ (Trans.)
D/F D/C-sharp
289 (306) 323 (330)

Figure 3.22. Tonal Levels of the Second Movement

The first theme, which enters in the English horn,

begins in measure 209.

Figure 3.23. Page 33, measures 209-212

A close examination of the first theme shows that it is

comprised of descending chromatic half steps.


Figure 3.24

The theme is played again in measures 213 through 220;

however, this time, an extension has been added.

lst Theme

2nd Theme


i Ia

Figure 3.25. Page 33, measures 213-220

There are various treatments of this theme, using the

chromatic half step concept, beginning in measure 221. One

such treatment is played by the oboe in measures 221 through


Figure 3.26. Pages 33-34, measures 221-224

Another example can be seen in measures 228 through 230 and

is played by the clarinets.

Figure 3.27. Page 34, measures 228-230

The first theme is played the final time, before the

transition, by the English horn in measures 241 through 244.


Another repetition of the theme is also played between
measures 245 and 249. The transition begins in measure 253,
and finishes its statement in measure 264.
The second theme is played in measures 264 through 266
and consists of only four notes.

I' uu I II

Figure 3.28. Page 37, measures 264-266

The second theme is played again in measures 266 through
272. During this time, a different rhythm pattern is used,
and two more notes are added to give a total of six tones.


19 m lmiilin 99
L ..........

Figure 3.29. Page 37, measures 266-272

A close examination of these six tones shows the formation
of a whole tone scale on D.

7' C


-p --


9~ ?t:

Figure 3.30

The use of the whole tone scale represents Copland's determ-

ination to move away from the feeling of centralization or

stability which is associated with traditional scales.

Measures 280 through 289 show an expansion of the second

theme and are played by the bassoon.


Figure 3.31. Page 38, measures 280-289

The first theme returns in measure 289 in the English horn.
The second theme completes its statement in this section in

measure 301. There is another transitional section begin-

ning in measure 305 that concludes in measure 322. During

the transition, there is a melodic sequence that is built on

the notes B, C, F-sharp, G, C-sharp, A, and D. A majority

of this sequence is played by the violins with various other

instruments entering occasionally and playing parts of the

sequence. The climax of this movement, in measure 322,

marks the end of the transitional section. The second theme

returns in measures 323 through 330. Measures 331 through

340 serve as transitional material to the final movement.

With respect to harmony, the movement has some implica-

tions of polytonality. The celesta, for example, plays a

figure which implies an F tonal center in measures 208

through 215.

Figure 3.32. Page 33, measures 208-215

The cello, however, has suggested a D tonal center.

A I 1 ) 1 I F i I v I I \ I

Figure 3.33. Page 33, measures 209-217


Thus, the result of these two tonal centers, sounding

simultaneously, is polytonality. These same two tonal

centers can be seen again in measures 225 through 228

between the bass clarinet and cello, and in measures 241

through 248 between the celesta and cello. Beginning in

measure 265, Copland has established C-sharp and D tonal

centers. This is accomplished through the C-sharp arpeggios

in the harp and the melodic whole tone scale on D.

141 1- / I i "

Figure 3.34. Page 37, measures 265-268

The same polytonality previously mentioned can be seen on

the repeat of each theme throughout the movement. Within

this movement, as with the first movement, Copland has taken

a horizontal approach to writing. Chordal harmonies are all

but eliminated, and when they do occur, it is because of the

interplay of melodic lines.

With a tempo marking of Andante moderato ( J = 88),

the rhythmic activity of this movement is very conservative.


Except for a few instances where the 2/4 meter signature is

used, the entire movement has a 3/4 meter signature. At

times, Copland does manage to escape a strong metric pulse

through the use of ties. The second and third measures of

the first theme are good examples of this phenomenon.

Figure 3.35. Page 33, measures 209-212

With reference to orchestration, the composer has used

a variety of solo instruments and as little doubling as

possible. The entire movement is built around one large

climax. The composition begins softly (ppp), and builds to

a triple forte (fff) at the climax in measure 323. Copland

also uses many orchestral colors, some of which are for

strings. Muted playing for strings can be seen in measured

209 through 212 in the violins, along with the production of


i Con Sord.



Con Sord.

Figure 3.36. Page 33, measures 209-212

The violas illustrate the half arco and half pizzicato

effect in measure 211. In measure 221, the second violins

are instructed to play half with mutes and half without

mutes. There is also the use of a glissando in the harp in

measures 328 through 330.

Figure 3.37. Page 45, measures 328-330

Trills can also be observed in the upper woodwinds in

measures 323 through 329. The cuivrt effect is used in the

horns in measure 330. During the transition, Copland has

used a surprisingly new effect. The effect calls for the

viola to play a quarter-tone.

*) = tone

Figure 3.38. Page 46, measures 339-340

The composer uses the quarter-tone effect several times in a

composition entitled Vitebsk. When asked whether or not

his quarter-tone is to be interpreted as a jazz inflection,

Copland is quick to point out that this is not the intent.5

Third Movement

The third movement is built around the development of

three themes. In regard to form, this movement does not

follow any strict mold of formal design. The tonal levels

and thematic material are diagrammed below.

1st Theme 2nd Theme
(Buttress) (Trans.)
Meas. 341 (366) (374) (400)

3rd Theme 2nd Theme

416 440

1st Theme 1st Theme Prime
(Buttress) (Buttress)
(453) 472 (480) 500

2nd Theme Ist Theme



1st Theme Prime 2nd Theme Coda

542 548 571

Figure 3.39. Tonal Levels of the Third Movement

Statement by Aaron Copland, composer, in a personal
interview, Peekskill, New York, July 15, 1981.

+~3* 5




Figure 3.40. Page 46, measures 341-345

The first theme implies a G tonal center. The theme is

repeated in measures 346 through 351. In measures 352
through 357, the theme is played by the trumpets. Although
the theme is changed somewhat from its original statement,
the essential character still remains the same.


F I I I I I P"

Figure 3.41. Page 48, measures 352-357

Measures 360 through 365 mark the final time the theme is
heard in this section. Although the new theme does not
enter until measure 374, measures 366 through 373 serve as
linking material between the first theme and the second
theme. The connecting link will be called a buttress



i rr A


I % -Z I

k I r-N-1 11%
i U. I
!:3 j


because of its return later in the composition to serve the

same purpose. The second theme enters in measure 374 and

immediately establishes an F tonal center.

Figure 3.42. Page 52, measures 374-375

The theme is heard again in measures 376 through 382.

Beginning in measure 382, the second theme undergoes a

slight change.

Figure 3.43. Page 53, measures 382-385

The second theme is played twice between measures 382 and

393. Measures 394 through 399 lead into a transitional

section which begins in measure 400. The transition is

based on material from the second theme, and is concluded in

measure 415. In measure 416, the third theme enters in the

oboe and English horn.

Figure 3.44. Pages 57-58, measures 416-420

The third theme is played in a variety of forms until

measure 439. At this point, the second theme returns in

measures 440 through 453. In measures 454 through 471, the

buttress returns in a slightly different form; however, the

essential character remains unchanged. The first theme

material returns in measures 472 through 479 and the

buttress is heard again in measures 480 through 499. In

measures 500 through 513, the first theme material returns

at a slower tempo and with a change in rhythm. The theme is

played by the first violins while excerpts from the buttress

are played in the background by various other instruments.

)i -C






a-~ Z



Figure 3.45. Page 67, measures 500-503

The original tempo is resumed in measure 514, and the second

theme, with its various treatments, is played between mea-

sures 514 and 533. In measures 534 through 541, the first

theme is heard again and is played by the trumpets in a

different rhythm pattern.

7< M

14, I ,I
I Aw 11

r->> >i Ii Y U L

Figure 3.46. Pages 71-72, measures 534-541

The first theme material returns once again at a slower

tempo in measures 542 through 547. In this statement, only

the ostinato from the buttress is used as background materi-

al. Statements of the second theme material continue until

measure 570. During the coda, there are several statements

of thematic material from this movement and the first move-

ment. The listing below shows the occurrence of these


First Theme First Movement 571-675
First Theme First Movement 595-604
First Theme Third Movement 606-631
Second Theme Third Movement 632-635
First Theme Third Movement 636-648
Second Theme Third Movement 638-648

The movement begins with hints of polyharmony. The

first theme implies a G tonal center. The pedal point,

however, implies a D tonal center. The D tonal center is

further reinforced by a C-sharp leading tone. The G tonal

center over a D tonal center implies a tonic/dominant (I

over V) relationship. The polyharmony is used throughout

the statement of the first theme. In the first statement of

the buttress in measures 366 through 373, a D tonal center

is emphasized through the ostinato rhythm in the bassoon,

contra-bassoon, cello, and double bass.

4- O

y > 7 "

Figure 3.47. Page 51, measures 366-369

The harp and piano play some very traditional harmonies in

measures 396 through 399. These harmonies include the

B-flat, and A-flat triad.

> ^

Figure 3.48. Page 55, measures 396-397

In the statement of the third theme, the cello outlines a D

tonal center.

Figure 3.49. Page 58, measures 417-422

When the buttress is stated a second time, the ostinato

rhythm that accompanies it implies an F tonal center.

Figure 3.50. Pages 61-62, measures 454-457

The same type of harmonic structure is used to imply an F

tonal center at the Meno messo in measure 500. A different

tonal center is emphasized in measures 522 through 533. The

new tonal center is E-flat. The polyharmony of I over V can

again be seen in the return of the first theme in measures

534 through 541. In general, a majority of the harmonies

throughout this movement remain clear and well defined. The

last chord of the movement, however, has a very harsh sound.

This is partly due to the fact that the tones in the cluster

are separated by no more than a whole step.

cluster contains the notes G, A, and B-flat.

The chord

Figure 3.51. Page 87, measure 655

In regard to rhythm, the movement is very active. The

tempo marking is Allegro vivo ( ) = 200). With such a fast

tempo, syncopated rhythms, and polyrhythms, Copland is able

to achieve a striking rhythmic effect. The first example of

syncopation can be seen in the first theme.


Figure 3.52. Page 46, measures 341-345

Beginning in measure 366, Copland uses an ostinato rhythm in

a 6/8 meter signature. This rhythmic ostinato is character-

ized by the use of shifting accents.

-i~ .

IF R~-

r G4

10 so Mr


f m

>> >>

Figure 3.53. Page 51, measures 366-370

In measures 396 through 399, Copland uses a 3/8 time signa-

ture, but has shifted the accents to give a 2/8 pulsation.

Figure 3.54. Page 55, measures 396-399

Beginning in measure 472 and ending in measure 479, Copland

uses the first of his polyrhythms. Although still writing

in a 3/8 meter signature, the composer manages to achieve

three different meter signatures or pulsations by shifting

accents. The first, played by the upper woodwinds and

piano, gives a 3/16 metric pulse feeling. The second,

played by the violins, indicates a 2/8 meter pulsation. The

third, played by the viola and cello, indicates a 3/8 meter





K #Iii I5>l~b

I. 74

ip )~ I.

Figure 3.55. Page 64, measures 472-477

The horns and trumpets, in measures 534 through 541, play
two different meter pulsations. The horns are playing in a
3/8 meter signature while the trumpets are playing in a 3/16
meter signature. In measures 552 through 558, the horns are
again playing a 3/8 rhythmic pulse; but, the violin and
viola are playing a 2/8 meter pulsation. Another example of


r0000; r0o;

t /I

-Y i
C, 1 or

N *Aj

> l

the polyrhythmic effect can also be seen in measures 606

through 614.

The use of incomplete chords is still prevalent

throughout the movement to give the "open" or "empty"

quality associated with Copland's music. The composer also

manages to use a variety of instrumental effects. The

violin and xylophone give an example of the trill at the

beginning of this movement. In addition to the trill, the

second violins are instructed to play sul ponticello. An

example of the cuivrg effect can be seen in the horns in

measures 352 through 360. Muted playing for brass instru-

ments is shown in measures 366 through 374. In measures 374

through 377, pizzicato playing in the strings can be ob-

served. The glissando can be seen in measures 559 and 600

in the viola, violin, and trombone.

General Observations

The analysis of the Dance Symphony shows that the tonal

levels of each movement are not consistent with any classic

design. The first movement has some resemblance to the

sonata-allegro design. The second movement is also uncon-

ventional in design. The third movement is the most uncon-

ventional of all. Since thematic material from the other

movements occurs in the last movement, this would qualify

the overall symphony for the cyclic principle of structure.

The tonal levels of the first movement center around E;

whereas, in the second movement, there is a strong tendency

toward polytonality. Although the tonal levels in the last

movement are often well defined, no consistent pattern is

found in the order of their occurrence. In regard to har-

mony, the tonal levels of each movement tend to be ambigu-

ous. The first movement, for example, has an ambiguity

which is created between E major and E minor. The ambiguity

is also carried over into the chord structure. When Copland

does use chords, they are usually constructed with one or

more of the tones omitted. The third of the chord, in some

cases, is omitted. This phenomenon serves two purposes.

The first is the ambiguity that results in chord quality,

and the second is the "empty" effect that results from a

chord built around this principle. The symphony also shows

indications of polyharmony. A majority of the polyharmony

is built around a tonic-dominant (I over V) relationship.

In the second movement, the harmonies center around two

tonal centers. These two centers are D/F and D/C-sharp.

Copland also utilizes the whole tone scale in the second

movement. The implication of this scale is the destruction

of a stabilization or key center which can be associated with

other scales. Thus, the result is an even further move away

from conventional tonality. In every movement, Copland has

taken a linear approach to writing. Through the linear

approach, chordal harmonies as such are mostly eliminated.

Several of the harmonies that do occur, however, are the

result of the interplay of melodic lines.

Copland's themes vary from short fragments to long syn-

copated ones. The themes in the first and last movements

are longer and more syncopated. The themes in the second

movement are built around descending half steps and whole

steps. There is also the use of the whole tone scale as

thematic material in the second movement. Although the

composer manages to change his themes rhythmically or inter-

vallically, the overall character of the themes remains the

same. An example can be seen in the second movement.

There, Copland has applied the half step and whole step

idea, of which the first theme is composed, in a variety of

melodic statements. In almost every case, the first theme

is not quoted exactly, but the essential character remains

the same because of the intervallic relationship of whole

and half steps used in the melodic statements. Copland also

uses stretto in the first movement. The composer has linked

the entire symphony together, without pauses between move-

ments, through transitional material.

Syncopation can be observed in the rhythmic content of

this symphony. The syncopation adds to the "dance-like"

character of the work. The composer also uses ostinatos in

this composition. One of the ostinatos in the third move-

ment is characterized by shifting accents. The most impor-

tant aspect about rhythm is the use of polyrhythms. By

shifting accents, Copland is able to change the pulsation of

a given meter. In the third movement, for example, Copland

uses a 3/8 meter signature. Along with a 3/8 meter pulsa-

tion, the composer, by shifting accents, manages to achieve

a 2/8 meter pulsation and a 3/16 meter pulsation simultane-

ously. It must be pointed out that the composer does not

combine more than three meters at any given time. Copland

makes the following statements regarding Boulanger's atti-

tude toward his use of polyrhythms.

She made much of their appearance in my
own work, and rather pointed them out
to me as one of the new features of the
music in the '20's, different from what
the typical young French student would
be producing. She showed great inter-
est in my rhythmic experiments, and
made me more conscious of my own6
potentialities as a rhythmicist.

Copland also gives conductor's notes, directly on the score,

for subdividing the beats in the polyrhythmic passages.

In orchestrating this work, the composer tends to treat

the instruments in a soloistic fashion in the first and

second movements; whereas, in the third movement, he uses a

Smith, p. 65.

lot of doubling. There is also the use of many instrumental

effects. For the brass, the composer utilizes muted and

cuivrt playing. For the strings, Copland uses such effects

as half arco and half pizzicato playing, glissandos, muted

playing, cot legno, sul tasto, quarter tone, and sul ponti-

cello. The composer does not use more than two of these

effects together at any given time. The symphony also calls

for an expanded percussion section. Through the use of

these instrumental effects, and an expanded percussion

section, the composer is able to achieve a variety of


The Dance Symphony is a program symphony which adheres

to the cyclic principle of design. Through the use of such

elements as polyrhythms, polyharmonies, and polytonality,

Copland is able to attain some very interesting sounds and

effects from the orchestral medium.


The First Symphony was originally written for organ and

orchestra. The symphony, entitled, Symphony for Organ and

Orchestra, was dedicated to Nadia Boulanger. The Symphony

for Organ and Orchestra received its premiere performance on

January 11, 1925, by the New York Symphony Orchestra under

the direction of Walter Damrosch. Copland completed the

orchestral version, without the organ, in 1928. The new

version was called the First Symphony.2 A study of the two

works indicates that this was not a difficult task, the

reason being that during the original version of the work,

the organ was treated not as a solo instrument with accom-

panying orchestra but as an integral part of the orchestra.

There is a difference of opinion between Smith and

Berger regarding the first performance of the First Sym-

phony. Smith is of the opinion that the first performance

took place in Berlin, by the Berlin Symphony Orchestra, in

December, 1931. She also states that the Scherzo movement

was performed on November 4, 1927, by the Philadelphia

Julia Smith, Aaron Copland: His Work and Contribu-
tion to American Music (New York: E. P. Dutton and Company,
Inc., 1955), p. 75.

2Ibid., p. 77.

Orchestra in Carnegie Hall.3 Berger contradicts Smith by

stating that the first performance took place on January 18,

1934, by the Chicago Symphony Orchestra. Berger does,

however, agree with Smith on the performance of the Scherzo


The performance time for the symphony is twenty-five


First Movement

The first movement, entitled Prelude, is built around

one theme. The tonal level of this movement centers around

G-sharp. Since there is no standard format for a "prelude,"

this movement could be regarded as being in free form.

Copland states that free form is the "absence of a tradi-

tional strict form or design."5 The tonal levels are

diagrammed below.

lst Theme - - ->
I i I I I
G-sharp B/F G-sharp D-flat G-sharp
Meas. 1 29 43 51 62

Figure 4.1. Tonal Levels of the First Movement

3Ibid., p. 77.

Arthur Berger, Aaron Copland (Westport, Connecticut:
Greenwood Press Publishers, 1971), p. 101.

Statement by Aaron Copland, Composer, in a personal
interview, Peekskill, New York, July 15, 1981.


The movement begins with the tempo marking Andante

( = 108). Immediately, the first theme is heard as it is

played by the flute.

Figure 4.2. Page 1, measures 2-5

The theme undergoes a different treatment in its next state-

ment. The first three notes are in retrograde, and the

theme can be heard in the clarinet.

K / k 4- 4- .-^- h h /,

SI -1 II *r I


Figure 4.3. Page 1, measures 10-13

There is another treatment of the thematic material in

measures eighteen through twenty. In measure twenty-nine,

the tonal center has changed to B and F. There is also an

ostinato rhythm which accompanies the change in tonal

center. The intervallic content of the ostinato theme is

the intervals of a minor third and a perfect fifth.

_ __ 1_ _I C


in F



Figure 4.4. Page 3, measures 29-30

Julia Smith calls this ostinato theme a motto. The motto

can be heard in measures twenty-nine through thirty-nine.

Even though the motto seems insignificant at this time, it

will soon become the unifying force for the entire symphony.

The G-sharp tonal center is resumed in measure forty-three.

The thematic material in measures forty-three through fifty

is identical to that in measures ten through seventeen; how-

ever, this time, the melody is played by the horn. The

opening melodic material can be seen in measures fifty-two

through fifty-four, and is again played by the flute.

A+K ;7F -I I I I

Figure 4.5. Page 4, measures 52-54

The motto theme can be heard in measures sixty-three through

sixty-five, and is played by the trumpet. In measures

Smith, p. 78.

sixty-seven through sixty-nine, the motto theme can be seen


I S*

Figure 4.6. Page 6, measures 67-69

The movement ends with the statement of the first theme by

the flute.

Copland has begun this movement in a G-sharp tonal

center. Both the ostinato accompaniment and melody, in

measures six through twenty, indicate the G-sharp center.

Measures twenty-nine through thirty-five indicate a poly-

tonality. The motto theme displays a B tonal center,

whereas, the cello and viola suggest an F tonal center.

in F


Figure 4.7. Page 3, measures 29-32

Measures seventy-two through seventy-four also lend them-

selves to polytonality. The tonal center suggests D and

G-sharp centers. The G-sharp center is played by the second

violin, while the D center is played by the cello and




Figure 4.8. Page 6, measures 72-73


Id I


The entire movement has a 6/8 meter signature, except

for measures eighty-one and eighty-nine, which are in 3/8.

On one occasion, Copland changes the 6/8 meter pulsation to

that of a 4/8 meter pulsation by shifting accents through

the use of grace notes.

I Mb. ho I ;MN, I L

L j

Figure 4.9. Page 5, measures 64-65

There are also several rhythmic ostinatos in this movement.

One such ostinato can be seen in measures six through

twenty. Another ostinato can be seen in measures twenty-

nine through thirty-five. The latter consists of four

chords which are repeated for seven measures. Occasionally,

the motto theme is treated with an ostinato rhythmic pat-

tern. An augmentation of the motto theme and its original

rhythm pattern are presented in measures twenty-nine through


The instrumentation for this symphony is listed below.

1 Flauto Piccolo
2 Flauti Grandi
2 Oboi
1 Corno Inglese
2 Clarinetti in B-flat
1 Clarinetto Basso in B-flat
2 Fagotti
1 Ccntrafagotto

1 Alto Saxophone in E-flat
8 Corni in F
5 Trombe in C
3 Tromboni
1 Tuba
Tambour Militare, Tambour de Basque,
Wood Block, Piatti, Tam-Tam, Cassa
Zilafone, Glockenspiel
2 Arpe
Violine I
Violine II

For the most part, the orchestration of the first movement

only calls for a portion of the orchestra. The composer has

used such instrumental effects as muted, pizzicato, and sul

ponticello playing. Muted playing, by the strings, can be

seen throughout this movement. One such example is seen in

measure five. Pizzicato playing can be observed in mea-

sures fifty-one through fifty-three.

pizz. arco pizz.

;/n/I "u I I v JE7 u

Figure 4.10. Page 4, measures 51-53

Sul ponticello playing is presented in measures fifty-one

through fifty-seven. Measures sixty-three through sixty-

five show an example of muted playing for trumpets. In this

movement, Copland has treated the instruments in a soloistic

fashion; thus, there is little doubling except for emphasis

or color.

Second Movement

The second movement, entitled Scherzo, has a tempo

marking of Molto allegro ( ) = 160). The word scherzo has

a specific meaning with regard to formal design. The

scherzo is usually the third movement of a sonata, symphony,

or quartet. In some instances, this form was used as a

replacement for the minuet. Scherzo is an Italian word

meaning "joke." Much like the minuet, the scherzo is

followed by a trio after which the scherzo returns. The

Harvard Dictionary of Music reveals that, "the distinguish-

ing features of the scherzo are rapid tempo in 3/4 meter,

vigorous rhythm, a certain abruptness as though involving

elements of surprise and whim, and a kind of bustling humor

that ranges from the playful to the sinister."7 The second

movement does have some of these qualities, and also has a

Willi Apel, Harvard Dictionary of Music (Cambridge,
Massachusetts: Belknap Press of Harvard University Press,
1972), 2nd ed., p. 755.

close resemblance to the scherzo design. The trio is re-

placed with a blues section; thus, the element of surprise

is introduced. With regard to tonal levels, the scherzo and

trio have a mediant relationship. The tonal levels of this

movement are shown below.

1st Theme

2nd Theme

I (Dev.)
Meas. 92 128 (171)

Blues Ist Theme 2nd Theme

215 (266) 274 301

1st Theme Coda
i I
C 340

Figure 4.11. Tonal Levels of the Second Movement

The first theme is introduced by the oboe over an osti-

nato figure.

9-m F I IF a I ir I I I

Figure 4.12. Page 8, measures 94-100


For the next twenty-two measures, there are various treat-

ments of the ostinato and first theme material. One such

treatment is played by the alto saxophone in measures 111

through 117.

>1 7 / \I 7 >>

K -

I' I 1 I I I ]' I .. II
ag / "7 r -

Figure 4.13. Page 9, measures 111-117

The second theme enters in measure 128; however, in contrast

to the first theme, the second theme has a lyrical quality.

The theme also closely resembles a French folksong entitled

Au Clair De La Lune.

I .^ I | | I | o="

Figure 4.14. Page 10, measures 128-132

During the statements of the second theme, the ostinato

rhythm is still present. Immediately following the state-

ment of the theme by the flute, there is another statement

> >


of the theme by the first violin in augmentation. The same

rhythm is used in all the statements of the theme by the

flute; whereas, a different rhythm is used in the statements

of the theme by the first violin. The second statement of
the theme has a different melodic pattern.

Figure 4.15. Pages 11-12, measures 137-141

The melody is echoed in the violin as follows.

I r I I I I II I I I

Figure 4.16. Pages 12-13, measures 141-147

The third statement of the theme acts as the second phrase
of the theme.


Figure 4.17. Page 13, measures 146-150

The second phrase is again repeated in the violin.

}7 1- .7=- 11 1 1
1 I F F i

Figure 4.18. Page 13-14, measures 148-153

Measures 154 through 170 show various treatments of the

second theme material. The flute and oboe, for example,

illustrate one such treatment in measures 154 through 164.

The development section can be seen in measures 171 through

214. In measures 199 through 214, the motto theme, from the

first movement, returns in a B-flat key center. The motto

theme is used in an imitation in which four instruments are

involved--horn, trumpet, bassoon and flute. Measures 204

through 207 show a return of the first theme material before

the trio begins in measure 215. The trio or middle section

introduces new material. The new material is the blues, and

the alto saxophone is used to add to the overall timbre.

1 [ '> r9 I I h i WF I=

Figure 4.19. Page 24, measures 215-221

The blues theme is heard again in measures 222 through 228.

I -~ L-
L.. I W IC IF f

I-rn 11n~

Figure 4.20. Page 25, measures 222-228

A close examination of the tones will show that the composer

had used the flatted third, fifth and seventh degrees of the

major scale. Thus, the alteration of the tones in this

manner will result in a blues scale.

5 4 5

Figure 4.21.

There are various treatments of the blues melody by the alto

saxophone (measures 229 through 235) and by the clarinet

(measures 237 through 241). The original blues melody

returns in measures 249 through 252, and the motto theme

returns in the horns in measures 255 through 258.

Figure 4.22. Pages 28-29, measures 255-258





Measures 266 through 273 serve as transitional material to

the return of the first theme material. First theme materi-

al is heard in measures 274 through 300. At this point, the

second theme returns in augmentation as it has earlier. The

section, measures 301 to 331, is almost identical to the

previous statements of the second theme material in measures

332 through 339. The coda begins in measure 340, and ends

in measure 390.

The composer manages to maintain a C tonal center

throughout the first section of this movement. An example

of the C tonal center can be seen in measures 92 and 93. It

should also be mentioned that the C tonal center is implied

through an ostinato rhythm.

> >a

Figure 4.23. Page 8, measures 92-93

On occasions, Copland uses the C tonal center as a pedal

point, and above this center, he will use a variety of im-

plied chords. In measures 118 and 119, the C center is

played by the bassoon, whereas, intervals of a fifth are


played by the flutes above this center. The intervals above

the center imply an E-flat and a D-flat chord; thus, the

result is polyharmony.

k t ) I I L

Figure 4.24. Page 9, measures 118-119

During the middle section of this movement, the tonal center

changes to A. The E (in the cello) serves as a dominant

pedal point; whereas, the B in the upper voices suggests an

added second.

Figures 4.25. Page 24, measure 215

Beginning in measure 227, the tonal center has changed to B.

The same type of chord structure, used previously in the A

center, is also used in this center. In the second return

of the first section, the composer, in measures 289 and 290,

has used several different triads over an implied C tonal

center. These triads include D, C, B, A and G.

> > > > >

Figure 4.26. Page 32, measures 289-290

In measures 292 and 293, the composer used a D major triad

over a C center and, in measure 295, a B major triad over a

C center. The use of these triads over the C center results

in polyharmony. Beginning in measure 379, Copland has used

a series of major triads with an added second and a flatted


(4A I' I
,I A I

Figure 4.27. Page 43, measure 379


The composer uses the 3/4 meter signature for a major-

ity of the movement. In the middle section, Copland uses

the 4/4 meter signature. At the beginning of this movement,

there is an ostinato that is used mostly in the first and

third sections of the Scherzo.

L i

L i

10 f I f AV~1

I1 PI F)

461 ff

-.f. V

Figure 4.28. Page 8, measures 92-94

In measures 97 and 98, the directions call for the performer

to play the notes freely, accelerating.

(ad lib faster and faster)

k A& J 0 10

S0S 0 '0 '0

IX I :t7 I I I I I I

Figure 4.29. Page 8, measures 97-98

Measures 108 through 110 illustrate the shifting of accents

in a 3/4 meter signature to give the pulsation of a 3/8

meter signature.

k r--ft


*f O -A 0

Figure 4.30. Page 8, measures 108-109

Copland uses the 3/8 meter pulsation simultaneously with the

3/4 meter pulsation; thus, the result is polyrhythm. During

the statements of the second theme, Copland uses augmenta-

tion to increase the note values of the melody. In each of

the three statements of the melody by the flute, the violin

echoes the same melody, but in augmentation. In measures

344 through 351, the composer, by shifting accents, manages

to achieve a 2/4 meter pulsation while writing in a 3/4

meter pulsation.

Figure 4.31. Page 37, measures 334-347

In measures 289 and 290, accents have also been used to

change an 8/8 meter pulsation to a 3/8 meter pulsation.

k 0 >16 t. A- .0

Figure 4.32. Page 32, measures 289-290


The composer also creates an ambiguity between the 3/4 and

6/8 meter signatures. Although the melody is written in a

6/8 metric pulsation, it can also be played in a 3/4 metric


Copland uses a variety of orchestral effects during

this movement. Measure 92, for instance, shows the col

legno effect used by the violins. Although the symphony

calls for an alto saxophone, the composer has written the

part so that it can be played by the English horn if no

saxophone is available. Measures 112 through 114 illustrate

muted playing for the trumpets, while pizzicato playing for

the strings can be found in measures 117 through 183. Muted

passages for strings can be seen at the beginning of the

blues section in measure 215.

Third Movement

The third movement, entitled Finale, has a tempo mark-

ing of Lento ( ) = 60) for measures 391 to 450, and another

marking of Piu mosso (Allegro moderato, J = 112) for meas-

ures 431 through 656. The movement is built around two

contrasting themes, and is similar to the sonata-allegro

design. In the exposition, the two themes remain in the

same tonal center which conflicts with the classical sonata-

atlegro idea where two contrasting themes are used in


different tonal centers. The tonal levels of this movement

are shown below.

1st Theme
1st Theme 2nd Theme 2nd Theme

B B B-flat
Meas. 391 431 468

2nd Theme 1st Theme

B G-sharp
(494) 571 594



Figure 4.33. Tonal levels of the Third Movement

The first theme is played by the viola in measures 391

through 402.

r---- "-- F --j --1 1 g
... .i

Figure 4.34. Page 45, measures 391-402


Beginning in measure 403, there is a stretto occurring

between the strings in which the motto theme is used as

material. In measure 418, the trombones play the first of

several treatments of the first theme material.

Figure 4.35. Page 46, measures 418-422

During the treatments of this theme, the motto material is

played by the cello and bass in measures 420 through 430.

The second section begins at the Piu mosso in measure 431.

However, the second theme does not enter until measure 433.

The second theme is played by the violins and viola.

Figure 4.36. Page 49, measures 433-439

The motto can also be heard in an ostinato rhythmic pattern
beginning in measure 436. The second theme is played by the
horns (measures 451 through 457) and by the trumpets and
trombones (measures 458 through 461). Beginning in measure

468, the first theme is presented in a fugato by the oboe
and English horn. The fugato is heard for fifteen measures.
Along with the fugato, second theme material is played by
the bass. The first theme ends in measure 483, and the
second theme continues until measure 493. The development
section begins in measure 494, and ends in measure 570. In
measure 571, the second theme returns in diminution.

Figure 4.37. Page 66, measures 571-573

The motto theme is also played in diminution.

&0 L., ) C0

Figure 4.38. Page 66, measures 571-572

The second theme is treated in a fugato manner in measures

571 through 585. The first statement of the theme is by the

cello and has a C tonal center. The second statement of the

theme is by the viola and has a G center. Hence, the tradi-

tional statement of the second entrance is on the fifth de-

gree of the scale. The third statement of the theme is by

the violins and has a C center. The first theme material

returns in measures 594 through 603.

Figure 4.39. Pages 68-69, measures 594-603

The coda begins at measure 604, and the movement ends in

measure 656. In measures 627 through 629, there are three

different statements of the motto theme.

k >

Figure 4.40.
Figure 4.40.

1ii ~ e-q -`

L1 I I i1 1 I I 1 ILU I

Pages 73-74, measures 627-629

There is also an augmentation of the first theme material in
measures 627 through 639. The augmented theme is played by
the trumpets and trombones.

kL > 1a b >I |
(^ z===^^==^^=l00

I >


Figure 4.41. Pages 73-77, measures 627-639

I 1w1

r A
A U 1 I T
*r~ I F r sFf f^--fIrS ff^

r^ F 41 t-_ : .

Copland has used many indications of polytonality.

Measures 451 through 455, for instance, show an example of

polytonality. During these measures, the composer uses

three tonal centers simultaneously. The first, an F tonal

center is the bass, contra-bassoon, and trombones; the

second, an A tonal center in the horns; and the third, an

F-sharp center in the woodwinds, trumpets, and strings.




>i i


Figure 4.42. Page 50, measures 451-455

!- > <^ 11 -y. wrr 1'-r e; I ~rjir ~
74 FJ -p7

70-1 | 4 1


More often than not, Copland utilizes the motto theme in an

ostinato rhythm to establish a tonal center or centers. The

idea can be seen in measures 468 through 489 where a B-flat

center is established, measures 431 through 450 where a B

tonal center is established, and various other places

throughout the movement. Measures 494 through 497 show

still another indication of polytonality. In this instance,

the bass and cello indicate an F-sharp center, and the viola

and violin indicate a C center. Beginning in measure 571,

another example of polytonality can be found between the

bass and cello. The bass has established a B tonal center

while the cello has established a C tonal center.

>i^ n- >i
t~h+ '444A -0



Figure 4.43. Page 66, measures 571-574

UI I 7A Ud A( 1 1 Li AL F; 'Cf I 7 I
F ; '11

AV --Ar r r

F 21


Perhaps the final example of polytonality can be seen in

measures 594 through 603. In these measures, the cello and

glockenspiel indicate a G-sharp center, and the viola and

bass clarinet indicate an F tonal center.
Copland also utilizes polyharmony. An example of these
polyharmonies can be observed in measures 428 through 430

where there are two different triads sounding simultaneously

over a C tonal center. The example below is a reduction of

the triads that occur in measures 428 through 430.
F* F B C Ff F D E ~F FF E E


G G F F b A A

G A1W A 8 A BI
'r 1 o A
I 1,

Figure 4.44. Page 48, measures 428-430

Another example of polyharmony is found in measures 425

through 427. These harmonies also occur over a C center.

The following example is a reduction of the triads that

occur in measures 425 through 427.

F F F F* F F G ,A

.* JOL

Figure 4.45. Page 47, measures 425-427

The last two examples of polyharmony used major triads. The

bottom triadic unit of the polychords is in second inver-

sion. Persichetti states why this is important:

The resonance of a polychord is determined
by the intervallic structure of the bottom
chordal unit and the power of its separate tones
to generate overtones. The second inversion of
the major triad as a bottom unit is the most re-
sonant chordal unit upon which polyharmony can
be erected, because its internal spacing is
closest to that of the harmonic series; the

major third of the fundamental triad in close
position is not as close to the size of the
perfect fifth of the overtone series as is the
perfect fourth of the six-four chord. When the
tones of the bottom triad are spread apart, the
fundamental position is most sonorous.

There is also another series of polyharmonies in measures

509 through 514; however, these chords do not adhere to the

intervallic spacing described by Persichetti.

Copland also uses quartal harmonies. In measures 451

through 461, there are a series of quartal harmonies over an

F center which changes to a B center in measure 458. The

intervallic arrangement of the three note chords is aug-

mented fourth and perfect fourth.

Figure 4.46. Pages 51-52, measures 460-461

The quartal harmonies from measures 451 through 459 imply an

A tonal center while the harmonies in measures 460 and 461

are used to modulate to a different tonal center.

In measures 607 through 609, and measures 610 through

612, the composer uses two different chord clusters.

Vincent Persichetti, Twentieth-Century Harmony (New
York: W. W. Norton and Company, 1961), p. 138.