COMPOSITION TECHNEQUES EMPLOYED IN THE
FERST MOVEMENT 0F ELLfiOTT CARTER’S
FIANO CONCERTO

Mfg R}? the Degree of Ph. D.
MICHGAN STATE UMVERSITY
ERENE ROSENBERG GRAU
1973

 

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Compositional Techniques Ehployod in the

First Movement of Elliott Carter's
Piano Concerto

Irene Rosenberg Gram

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ABSTRACT

COMPOSITIONAL TECHNIQUES EMPLOYED IN THE
FIRST MOVEMENT OF ELLIOTT CARTER'S
PIANO CONCERTO

BY

Irene Rosenberg Grau

The first performance, recording, and publication

of Elliott Carter's Piano Concerto aroused keen interest.

 

This work, Carter's first composition in this form, was two
years in creation. Despite much discussion in the press,
however, a published technical analysis has not yet
appeared.

The present study investigates the compositional
aspects of the first movement of the two-movement concerto.
The findings indicate in a generalized way the creative
impulse which prevails, however, throughout the entire work.
An analysis in depth has been made of form, melody, harmony, den-
sity, dynamics, rhythmic activity and rhythmic character, tempo,
meter, and metrical modulation, and interpretation and
articulation markings. These aspects offer a comprehensive
frame of investigation, and although in this work they are

treated by the composer in highly original and innovative

Irene Rosenberg Grau

ways they proved open to study by conventional analytic
techniques, expanded and modified as the situation demanded.

The first, and perhaps most significant point of
the present study, is that a systematic and objective
theoretical analysis must be combined with an attempt to
View the philosophy of the composer as it is expressed in
this composition. Carter's apparent purpose in the E1329
Concerto is the creation of an abstract form which experi-
ments with time factors and with structural procedures.
The development of form in this work is removed from
traditional structural considerations of departure and
return, repetition, reconciliation of antitheses in
thematic material or tonality. The form grows out of the
principle of continuous motivic metamorphosis, in this
work of motives comprised of twelve different three-note
combinations.

Carter makes use of the transformation of time
elements through frequent change of meter and tempo,
notated as metrical modulation, a technique in which a
designated note value retains a constant duration although
it changes in its significance within the metrical pattern.
Combined with extreme fluidity of tempo and meter is a
prevailing use of fragmented, dense, and polyrhythmic
patterns.

The motivic three-note combinations which Carter

creates for this composition are non-tertian and give rise

Irene Rosenberg Grau

to chordal sonorities which are predominantly quartal,
secondal, or clusters. When tertian or expanded tertian
chords appear it is usually in a polychordal setting.
Both tertian and non-tertian sonorities are used, juxta-
posed and superimposed.

Figures arising from the kind of harmony employed
permeate the melodic structure.' The voice lines are often
plural and are usually polyphonically complex. The
melodic ambitus is extremely wide. The melodic design is
immensely varied in contour and in intervallic structure.

Melody, harmony, and rhythm do not coordinate to
create phrase structure, cadences, or sectional conclusions.
Density and volume favor high levels, although both fluctu-
ate widely and frequently. They, too, are disassociated
from structural considerations. The independence of each
of theSe compositional aspects, in combination with the
techniques of motivic evolution and metrical modulation,
tends to give the work a continual forward thrust which
makes of the composition's total 348 measures an extra-
ordinarily large one-part form.

It is theorized that the aural challenge in each of
these compositional aspects mabee intended to express an
aesthetic of extreme concentration and intense emotion.
Carter's use of emotive expression markings can be con-
strued as a further indication of his concern for the

communication of musical character.

Irene Rosenberg Grau

The first movement of the Piano Concerto is

 

traditional in that it is non-electronic, non-aleatory,
and conventionally notated in equal temperament. It can
perhaps be called futuristic in its innovative compositional

technique and above all, in its philosophy.

COMPOSITIONAL TECHNIQUES EMPLOYED IN THE
FIRST MOVEMENT OF ELLIOTT CARTER'S

PIANO CONCERTO

BY

Irene Rosenberg Grau

A THESIS

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

DOCTOR OF PHILOSOPHY
Department of Music

1973

ws' ACKNOWLEDGMENTS
GR

My warm thanks go to the faculty of the Music
Department of Michigan State University and especially
to the members of my dissertation committee: Dr. Paul
Harder, Chairman; Dr. Russell Friedewald; Mr. Richard
Klausli; and Dr. Theodore Johnson.

I wish to eXpress my particular gratitude to Dr.
Paul Harder for his generous counselling and encouragement.
His advice in matters of content, procedure, and style
has been invaluable.

Acknowledgments are made to Associated Music, Inc.
for permission to include within my text their publication

of the Piano Concerto by Elliott Carter.

 

ii

TABLE OF CONTENTS

Page
ACKNOWLEDGMENTS . . . . . . . . . . ii
PREFACE . . . . . . . . . . . . . . . . iv
Chapter
I. PURPOSE AND METHOD . . . . . . . . . . 1
II. FORM . . . . . . . . . . . . . . 7
III. HARMONY . . . . . . . . . . . . . 28
IV. MELODY AND COUNTERPOINT . . . . . . . . 55
V. TEMPO, METER, AND METRICAL MODULATION . . . 76
VI. DYNAMIC MARKINGS . . . . . . . . . . 90
VII. DENSITY . . . . . . . . . . . . . 99

VIII. RHYTHMIC ACTIVITY AND RHYTHMIC CHARACTER A . . 106

IX. EXPRESSION AND ARTICULATION MARKINGS . . . . 119

x. SUMMARY AND CONCLUSIONS . . . . . . . . 125
BIBLIOGRAPHY . . . . . . . . . . . . . . 139
APPENDICES

I. Graph of the Occurrence of Events . . . . . 142

II. Graph of Tempo and Meter Change . . . . . 144
III. Graph of Appearances of Eighth Note = 252 . . 155

IV. Classification of Volume Level and
Volume Variation . . . . . . . . . . 157
V. Graph of Density . . . . . . . . . 159
VI. Graph of Rhythmic Activity . . . . . . . 165
VII. Graph of Rhythmic Character . . . . . . . 168
VIII. First Movement of Elliott Carter's
' Piano Concerto . . . . . . . . . . 170

iii

and 1965.

quarter of a century of fruitful creative work.

PREFACE

Eliott Carter wrote his Piano Concerto in 1964

 

Preceding this composition lay more than a

Carter's

published compositions prior to the Piano Concerto

 

include:

1961 Double Concerto for Harpsichord and Piano with
two Chamber Orchestras

1957 String Quartet #2

1956 Canonic Suite for four B Flat Clarinets

1955 Variations for Orchestra

1952 Elegy for String Orchestra

1952 Sonata for Flute, Oboe, Cello, and Harpsichord

1951 String Quartet #1

1950 Eight Etudes and a Fantasy for Woodwind Quartet

1950 Recitative and Improvisation for four Kettledrums

1948 Sonata for Violoncello and Piano

1948 Woodwind Quintet

1947 The Minotaur, Ballet and Suite from the Ballet

1947 Emblems (for Men's Chorus and Piano)

1946 Elegy for String Quartet

1946 Piano Sonata

1945 Musicians Wrestle Everywhere (SATB a cappella, or

with string acc.)

1944 The Harmony of Morning (4 part Women's Chorus and
Small Orch.) '

1944 Holiday Overture (revised 1961)

1943 Dust of Snow (Medium Voice and Piano)

1943 Elegy for Viola (or Cello) and Piano

1943 The Line Gang (Baritone and Piano)

1943 Voyage (Medium Voice and Piano)

1943 Warble for Lilac Time (Soprano, or Tenor, and Piano
or small group of instruments)

1942 Symphony #1

1942 The Rose Family (Medium Voice and Piano)

1941 The Defense of Corinth (Speaker, Men's Chorus, and
Piano 4 hands)

1940 Pastorale for Viola (Eng. Horn or Clarinet) and Piano

iv

1939 Canonic Suite for Quartet of Alto Saxophones

1939 Pocahontas, Ballet and Suite from the Ballet

1938 Heart No So Heavy As Mine (SATB a cappella)

1938 Incidental Music to "The Merchant of Venice"
(guitar and alto voice)

1938 Prelude, Fanfare, and Polka for Orchestra

1937 Harvest Home (SATB a cappella) ‘

1937 Let's be Gay (Women's Chorus and Piano)

1937 To Music (SATB a cappella)

1936 Incidental Music to "Mostellaria" (Baritone,
Men's Chorus, & Small Orchestra)

1936 Tarantella (Men's Chorus and Piano 4 hands)

1933 Incidental Music for "Philoctetes" of Sophocles
(Baritone, Men's Chorus, Oboe, and Percussion)

Although there are works for large orchestra,
Carter's attention seems to have been drawn particularly
to smaller ensembles and to chamber music. He uses piano
as a solo instrument only once; and piano in combination

with orchestra, prior to the present concerto, only in

the Double Concerto for Harpsichord, Piano and Two Chamber

 

Orchestras. The Piano Concerto is a new line of thought

 

 

for Carter in terms of instrumental sound, but upon review
of his total output to date it becomes apparent that each
of his works expresses an interest in a fresh kind of
instrumental circumstance. A free line of inquiry into
many aspects of musical composition is the hallmark of
Carter's creation. As he himself notes:

I began to question the familiar methods of

presentation and continuation, of so-called

"musical logic," based on the statement of

themes and their development. . . . Too, I

questioned the inner shape of "this" and "that"
--of musical ideas-~as well as their degrees of

linking or non-linking. .'. . I was pre-occupied
with the time-memory patterns of music.

The philosophic openness and intellectual strength
which characterize Carter's career reach new expression

in the Piano Concerto.

 

The Piano Concerto was commissioned by the Ford

 

Foundation. The selection of the composer to be commis-
sioned on this occasion was given to pianist Jacob Lateiner,
who turned to Elliott Carter. The first performances of

the Concerto were given by Lateiner and the Boston Symphony,
directed by Erich Leinsdorf, on January 6th and 7th, 1967, in
Symphony Hall, Boston. It was recorded at these per-
formances by RCA Victor (LSC-3001), with the joint

subsidy of the Martha Baird Rockefeller Fund for Music,

the Steinway Foundation, and the National Foundation for

the Arts and Humanities.

Although this event was attended by much publicity
and was widely discussed in the press, a published
technical examination of the compositional techniques
employed in the Concerto has not yet appeared. This lack
is curious in view of the composition's singularity. Both
the Concerto itself and the apparent difficulty of
approaching it represent tantalizing challenges. Hence,

the present study.

 

1Elliott Carter, Jacket notes to Nonesuch Recording
'H-7134, of Carter's Sonata for Flute, Oboe, Cello, and
Harpsichord, and Carter's Sonata for Cello and Piano.

 

 

 

vi

CHAPTER I

PURPOSE AND METHOD

The philosophy underlying this paper is that a
work of art ideally should be understood on its own terms,
as part of its culture, and within an historical perspec-
tive. The sad gap which exists at present between the
contemporary composer and the contemporary listener
indicates that in all three regards understanding is weak.

The personal, social, or historical raison d'étre of

 

contemporary style and content fails to link many musical
creators today to the general public. ‘Contemporary "art"
music may fairly be reported to be considered widely as
enigmatic, isolated, and irrelevant.

It mabee suspectedthat the experimental or
avant-garde composer today is misunderstood because his
work lies in advance of the understanding of his time.
Hopefully, our understanding of the musical trends leading
into the future is being aided by the development of a
methodology of appreciation, of a systematic technique of
analysis, built upon the past but suited to the new
material.

Proceeding from this premise, the present study
involves two main considerations. One is to examine a

l

significant new work, the Piano Concerto, by the highly

 

esteemed American composer Elliott Carter. The second
is to evaluate the applicability to this composition of
the analytic techniques which have been useful up to the
present, and to attempt to devise extensions of these
techniques which may be particularly suitable to music
of our own day.

The Piano Concerto has two movements, the first

 

consisting of 348 measures and the second of 330. Both

movements employ full orchestra of

2 Flutes (Piccolos) 4 F Horns

2 Oboes ‘ 3 B-flat Trumpets

2 B-flat Clarinets 3 Trombones

2 Bassoons Tuba

Contrabassoon Timpani (2 players)

Strings (minimum: 7-6-5-4-3 stands)

There is also a concertino group of Flute, English
Horn, Bass Clarinet, Violin, Viola, Cello, and Bass. The
concertino group sometimes plays alone, sometimes with the
solo piano, and sometimes merges into the larger ensemble.

In the second movement of the Concerto, the con-
certino conducts an extensive dialogue with the solo piano;
there is a dramatic confrontation of distinct musical
personalities. In the first movement there is no comparable

theatrical device. However, in all other major aspects the

two movements are very similar,and the compositional pro-
cedures in regard to rhythm, harmony, density, thematic
process, and formal structure appear to derive from the
same creative impulse. Both movements exhibit a unified
and highly distinctive aesthetic, as well as a composi-
tional technique which is readily identifiable in all
parts of the work.

For this reason, it was felt that the present
study could deal specifically and in depth with an examina-
tion of the first movement and still could be understood
to validly represent in a more generalized sense a way of
viewing the compositional procedures used in the second
movement.

The modus Operandum is to make as comprehensive a

 

list as possible of those aspects of musical composition
whose study has proven fruitful in enriching our under-
standing of the music of earlier periods. This list will
serve as a kind of cultural definition. Each of these
aspects will then be investigated in connection with the
first movement of the Concerto. In view of the complexity
of the material, a minute and systematic categorization of
data will be undertaken. All the information derived from
the various avenues of study will be included in this
report. Some information may, significantly, be of a
negative character. It may appear, for example, in the

early stages of various lines of inquiry, that the

expected results will not be forthcoming; in some cases it
may be that no conclusion can be drawn. However, all the
relevant data will be assembled and reviewed in the hope
of permitting the information to express its own meaning
without suffering from the bias of preconception. It will
then remain to be seen whether these lines of inquiry have
succeeded in providing a viable analytic framework for the
music analyzed, and possibly for other contemporary works
of similar characteristics and prOperties.
The musical aspects investigated include:

Formal structure

Sectional organization

Phrases

Delineation of small units

Motives

Motivic uses

Developmental techniques

Tonality

Key relationships

Harmonic function of the bass

Chord progression

Cadences

Functional harmony

Chromatic harmony

Impressionism

Concepts of Consonance and dissonance

Chord structure

Non-harmonic tones

Twelve-tone technique

Contrapuntal devices

Utilization of pitch area

Melodic structure

Melodic recurrence

Melodic intervallic relationships

Density

Rhythmic intensity

Types of rhythmic motion

Tempo

Meter

Metrical modulation

Dynamics

Interpretation directions

Articulation

Repeats

Bridges and transitions

Interconnectedness of compositional aspects

Use of folk material

These lines of inquiry, with their concomitant

offshoots, will be grouped under the chapter headings of:

Form

Harmony

Melody and Counterpoint

Tempo, Meter and Metrical Modulation
Dynamics

Density

Rhythmic Activity and Rhythmic Character

Expression and Articulation Markings.

CHAPTER I I
FORM
The first movement of Elliott Carter's Piano

Concerto is a striking example of an extraordinarily large

one—part form. Referring to his Variations for Orchestra,

 

Carter said, "As in all my works, I conceived this one as

2

a large, unified musical action or gesture." This concept

appears to be applicable to the Piano Concerto also.

 

The question of the feasibility of extending the
concept of unity through a composition of three hundred and
forty-eight measures duration must be solved in terms of
the special and inherent logic of the structure. In the
Piano Concerto, First Movement, the structural logic does
not depend upon the ordering of the structural parts in
either classic or innovative ways, or upon comparisons of
differences or reconciliation of antitheses. The logic
depends rather upon an unfolding continuity of development
which seems to make manifest a sub-stratum of emotive
continuity. In the large one-part form the original tonal

material presented at or near the beginning of the

 

2Elliott Carter, "Shop Talk by an American

Composer," Problems of Modern Music (New York: W. W.

Norton, 19655, p. 54.

 

composition must be capable of providing for a great deal
of manipulation. It is also necessary that the emotional
tone of the composition as a whole be rich, varied, and_
withal coherent.

Carter's own comments on his compositional pro-
cedure are highly relevant.

The characteristic effort of the serious
composer, as I see it, is not so much in the
invention of musical ideas in themselves, as in
the invention of interesting ideas that will also
fill certain compositional requirements and allow
for imaginative continuations. Serious music
appeals to a longer span of attention and to a
more highly developed auditory memory than do the
more popular kinds of music. In making this
appeal, it uses many contrasts, coherences and
contexts that give it a wide sc0pe of expression,
great emotional power, and variety, direction, '
uniqueness, and a fascination of design with many
shadings and qualities far beyond the range of
popular or folk music. Every moment must count
somehow, as must every detail. For a composer
it is not always easy to find a passage that fits
the particular situation and moment at which it
appears in the composition, that carries to a
further point some idea previously stated, that
has had the apprOpriate expressive quality
motivated by what has been heard and yet is a
passage that sounds fresh and alive.

As far as I am concerned, I am always inter-
ested in a composer's phrases and their shape and
content, the way he joins them, the type of
articulation he uses, as well as the general drift
or continuity of a large section, and the con-
struction of the whole work. The small details
_of harmony, rhythm, and texture fall naturally
into place when one has interesting conceptions
of these larger shapes.3

Carter's usage in the Piano Concerto of composi-

 

tional faCtors such as dynamic markings, density, rhythmic

 

31bid.

activity and rhythmic character, and Some aspects of tempo,
meter, and metrical modulation, all indicate an awareness
of the necessity of generating emotional tone as a
structural principle in an expanded one-part form. In
addition, these factors, although they do not delineate
structure in a traditional sense, do combine with tonal
elaboration and instrumentation to present a patterning

of musical events which gives dimension to the form.

The thrust of these musical events is usually in
the direction of change of some kind. Following is a list,
rather like a kind of relief map, representing some of the
more important configuration changes, or, as Carter
states it above, "general drift," with brief descriptions

pointing out the salient characteristics of each area.

1. From the beginning to m. 18.

 

The original thematic material of a perfect 4th,
diminished 5th, minor 2nd, and diminished 8th, using the
pitches G, F#-C, C#, is presented in a completely
dodecaphonic matrix. (In this paper the term "dodecaphonic"
will mean totally chromatic.) Piano solo, joined by the
concertino, provides adistinctive orchestration, in

contrast to the more usual employment of full orchestra.

Meter is 3/4, quarter note 126.. (See page 10).

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2. M. 18-32.

Here occur changes of meter and texture. The
linear writing refocuses into voice leading in pairs. The
orchestra enters. This area tends to be lyrical in the
orchestral part and figural in the piano part.

(Duration: 14 bars.)

 

12

3. M. 32-40.

 

At this point there begins a series of melodic
phrases in thematic entrances in the piano part and in
clarinet and strings, with thinning of texture and

lessening of rhythmic activity. (Duration: 8 bars.)

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Significant here is the appearance of a rhythmic
figure of triplet 16th notes which will be pervasive in
this area of the work. The use of timpani makes this
figure immediately recognizable as a compositional event.

(Duration: 28 bars.) (See page 13.)

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Rhythmic activity and texture diminish. The

triplet 16th figure disappears for two measures. A new

thought emerges: a motive in clusters with glissando.

This area builds upon the accumulation of everything pre-
ceding, and pushes forward for a longer period than any

of the preceding areas. (Duration: 43 bars.)

 

6. M. 111-124.

The meter and tempo change, activity lessens,

concertino reappears, piano part dissolves. Sonorities

of 3rds and 6ths can be perceived within the lZ-tone

material. (Duration: 13 bars.) (See page 15.)

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7. M. 124-152.

 

The meter and tempo change. Oboe makes a prominent
entrance with a subject consisting of melodic intervals of.
3rds and 6ths, followed by imitative counterpoint.
(Duration: 28 bars.)

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The distinctive feature here is the absence of
piano for fifteen measures. (Duration: 15 bars.)

(See page 17.)

 

 

 

 

 

 

 

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9. M. 167-188

 

 

The piano, abSent since m. 150, makes a vigorous

re-entry. (Duration: 21 bars.)

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10. M. 188-223
‘ Volume, density, and rhythmic activity drop low.
(Clusters, noted at m. 68, are again the main sonority.

(Duration: 35 bars.) (See page 19.)

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ll. Upbeat to m. 223-256

At this point, marked un poco espressivo,

 

p decrescendo to RBI the piano, in a solo entrance,

unfolds a series of 4ths. (Duration: 33 bars.)

M. 222

 

 

21

12. Upbeat to m. 256-270

 

These orchestral entrances use material related
to the firSt statement of the composition, the augmented
4th, minor 2nd, and diminished 8th. The original pitches
C-F# are conspicuous in the cello entrance. (Duration:

14 bars.)

M. 256

 

 

22

13. M. 276-313.

The meter and tempo change. The concertino
reappears in a series of imitative entrances, initiating
the composition's propulsion to its conclusion.

(Duration: 43 bars.) (See page 23.)

14. M. 313-328

 

A distinctive event here is the crashing chord
which embraces the totality of pitches from sub-contra C
to five-line b, an effect used only in this area of the

composition. (Duration: 15 bars.) (See page 24.)

15. M. 328 to the conclusion

 

This event is noteworthy as an extremely rare use
of recall within the work. The original thematic material
is re-used on the original pitches: G, G-flat (= F#)-C,
D-flat (= C#). Further mnemonic reinforcement is offered
by the original tempo, re-affirmed, at m. 329, at quarter
note = 126. The psychological rounding off and sense of
completion, caused by the return of characteristics of the
I beginning, signal the approaching end. (Duration: 21 bars.)

(See page 25.)

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26

The landmarks included on the foregoing "map" are
only the main and most apparent ones. Other parts of the
landscape will of course be perceived and subjectively
evaluated. The compositional landscape preSents a picture
of extreme fluidity and organic self-determination, free
from.arbitrary structuring through the imposition of
historical mores or mathematically oriented aesthetics.
The spacing of events in terms of the numbers of measures
within each area is: 17, 14, 8, 28, 43, 13, 28, 15, 21,
35, 33, 14, 43, 15, 21. The spacing in terms of time-
duration must surely be equally varied, since the tempo
continually changes and the measure lengths are unequal.

It is worth noting that the graph (see Appendix I)
of this study of form-happenings reveals an absence of
meaningful correlation with the graphs of other compo-
sitional factors. The formal aSpect, like all the other
aspects of this movement, is completely independent.

The nature of the events within the work is also
varied. In some cases only a brief effect is noted. In
other instances a change in the on-going situation is
perceived and different emphases will be apparent in the
entire new area. I

The study of the form brings out clearly this
significant finding: ‘it does not seem possible to
designate any of the areas of this composition by pre-

established formal terms such as theme groups, transitions,

27

developments, recapitulations, or the like. Most of the
time it is clear that, while some elements provide change,
other, simultaneous, elements offer such strong lines of
continuity that the elements of change do not bring about
a separation of distinct parts from the structural whole.
The factor which is probably strongest in pro-
ducing unity is the tonal material itself, which is
totally chromatic throughout and which makes use of
tightly organized motivic interval patterning. The
independent functioning of each compositional aspect, as
will be demonstrated further along in this study, also
provides unity through overall characterization.
Finally, the fact that the evolution of thematic,
rhythmic--indeed, all compositional aspects--is pervasive

and continual is in itself a unifying principle.

CHAPTER I I I

HARMONY

Harmony-may be understood in this Study to refer
to three different concepts: (1) harmonic texture or
chordal sonority, (2) cadential forms, and (3) harmony
in relation to formal organization.

The harmonic texture of the first movement of

Elliott Carter's Piano Concerto includes a vast array of

 

chordal sonorities. Some of these sonorities are pre-
sented simultaneously; some occur as arpeggios or chordal
figuration; some can becomprehended vertically or
diagonally as chords accumulated by extension on the time
continuum. Careful analysis indicates that some of the
classic sonorities used in the common-practice period are
included among Carter's chord types. But more prevalent
are innovative sonorities resulting from the intervallic
aggregations typical of dodecaphonic manipulation.

As the variety of chordal sonorities arising in the
Piano Concerto is so great, it may be well to define
further the concept of "chord" as it will be used in this
paper: the co-existence of three or more tones within a

time span sufficiently compact so that their relationship

28

29

may be perceived. This definition permits chordal
sonorities to be classified into eight types.

triads (tertian)

seventh chords (tertian)

polychords, or juxtaposed tertian sonorities

expanded tertian (9ths, 11ths, 13ths, lSths)

tertian with added tones

tertian with cross relations or split chord
members

. quartal-quintal

. secondal-clusters

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There is of courSe some overlapping of chord types and some
variation in analysis does occur.

It should be noted that two-note sonorities occur
only rarely in this work. A study of the density aspect
(see Appendix IV) reveals only seven measures which
contain one to two simultaneous pitches, these arising
only in the first third of the composition.

Chord type I, the tertian triad, hardly exists as
a complete, self-sufficient entity within this work. When
tertian triads or seventh chord structures appear they
almost always form a part of polychords.

ICarter's technique in regard to polychords is
highly original and can be directly linked to the very
distinctive textures prevailing in this composition.

The usage of polychords in the past has often
relied upon wide, juxtaposed spacing. Separation of the
constituent chords by pitch area has been an effective

means by which independent chordal sonorities have been

30

held in aural counterpoise. Carter's use of polychords
departs almost entirely from this traditional method.

Most often his polychords are not distinctly juxtaposed

but are crowded together in a dense and rapidly changing
texture. The existence of tertian triads and seventh

chords can be traced, but their power and distinctiveness

as functioning entities are sacrificed in favor of a sub-
ordination into a richer, more complex web of interrelation-
ships.

A further distinction is that traditional methods
usually deal with clearly recognizable tertian structures,
whereas, through the use of added tones and cross
relations, as well as secondal and quartal sonorities,
Carter's chords often lose the customary means of identifi-
cation as polychords and merge into other categories.

An interesting and typical example of the compli-
cated use of polychords occurs in the orchestral score at
m. 41: the first 16th of the measure is an e minor triad
(C-flat = B), the third 16th is e minor plus a major
seventh (diminished octave), the seventh 16th is E major
plus a major seventh with F major implied on the upper
staff. At the beginning of m. 42 there are three levels:
C-flat major in the middle, A major arpeggio with a
sustained B-flat on the tOp level, and F contra entering

on the lowest level in the piano part at the second 8th.

31

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

32

Diminished triads are rejected. The augmented
triad occurs occasionally, as at m. 328, last beat, where
it appears in conjunction with the interval of a major

third D-flat-F.

M. 328

  
 

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Seventh chords and expanded tertian sonorities
can be found frequently, as in m. 36 and 37 (see page 33)

and m. 231, 232, and 233 (page 34).

33

n .30.;

 

34

 

 

The tertian sonorities are never organized into
successions which resemble functional harmony.

The major-minor seventh chord (dominant seventh
structure) occurs only rarely among the other types of
_seventh chords, as in m. 105, where it appears fleetingly
in a polychordal context (see page 35).

Major-minor seVenth chords have neither the
priority of occurrence which they enjoyed in the music of
the past nor the predictability of usage found in earlier
styles. Most often the interval of a minor seventh will
be left empty, or will be placed upon an interval of a
third, forming a ninth chord (both illustrated in m. 184,

page 35).

35

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36

If the interval of the minor seventh is filled, it is

most likely to contain two fourths, as in m. 227.

 

This is one of Carter's favorite sonorities in the ,
Piano Concerto, as illustrated in m. 3392340 (p. 37).

The diminished seventh chord, like the diminished
triad, is rejected. I

Parallel chord streams and alternations between
polarized harmonies, suggestive of impressionistic tech-
niques, are also absent in this composition. Passages
in which consonant harmony or consonant intervals are
prominent_do sometimes contain streams within the texture,
.for instance in m. 95 throughrm.104 where the lower score
of the piano part is, with one exception, a series of

twenty-four 6ths,while simultaneously the lower score of

37

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38

the orchestral part presents a series of fifths (see pp.
39-40).

M. 156 through m. 165 shows two simultaneous
independent lines, each of which is compoSed almost
exclusively of the melodic and harmonic intervals of the
3rd and the 6th. The relationship between the two lines
is, however, highly dissonant (see p. 41).

There seems to be no concern in the presentation
of any of the chords for such matters as root re-inforce-
ment or sonorous doublings. Registration and voicing.
over the pitCh range is immensely varied, as is shown in
the study of melody (please see Chapter 3), but the guiding
thought does not seem to be the play of sonorities per se.

Tertian sonorities are most frequently blurred by
the addition of non-chord tones, by cross relations at
the chord root as in m. 111, first six notes, or m. 261,
downbeat (see page 42), or by split chord members within
the chord structure as in m. 134 (p. 42).

IThe most prevalent sonorities within the 21332
Concerto are those which contain seconds, sevenths, or
ninths, often in conjunction with perfect or augmented
fourths.. The interval of the fourth is motivic and often

.occurs as quartal harmony, in the form of interlocking

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sometimes tightly bunched with a fourth as the outer
parameter and a third contained, m. 193-194.

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Clusters are sometimes used in expanded form as fistfuls
of sound containingas many as all twelve tones, m. 245-
246 (see page 47).

Carter's harmonic texture in this composition is
immensely varied. There are brief areas where a particular
sonority may prevail, for instance in m. 18 through m. 22,
which is predOminantly quartal, or m. 188 through m. 194,
predominantly clusters, or m. 106 through m. 110, totally
chromatic. Usually, however,the harmonic vocabulary is
displayed in such richness that classification of the area
or even of a group of specific measures by chord type is
impossible. This observation becomes increasingly valid

Lee the composition progresses. An example of a measure

47

 

 

 

 

 

 

 

 

 

 

 

 

 

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48

with a characteristic wealth of harmonic suggestion is
m. 294. This measure is an extreme but typical example ‘
of the aesthetic of dodecaphonic saturation, containing
elements which are atonal, polychordal, triadic and

tertian, secondal and quartal.

Secondal Quartal.

2f

     
 
 
 
 

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Quartal

fl

Tertian

Triadic

Elliott Carter wrote in the program notes to the
first performance of the Piano Concerto:

Technically the work is based on twelve dif-
ferent three-note groups (triads):_ six, used
exclusively by the piano and concertino and six,
by the orchestra. Each triad is associated with
one or more tempi and expressive characters.
Musical ideas are formed out of constantly chang-
ing uses of these fundamental materials.

49

At the outset, the piano and concertino state
ideas derived from the triad shape exemplified by
C, F sharp, G and the three speeds and characters
associated with it. This is answered briefly by
the orchestra using material from one of its triads
(shape: G, D flat, F). Later these two triads,
which are the primary ones for the orchestra and
the piano, each join three others from their
respective instrumental groups to form one twelve-
note chord for the soloists and another of dif-
ferent character for the orchestra, the alternation
of which constitutes the conclusion of the first
movement, summarizing in brief all the various
expressive characters that have been brought into
increasingly sharp focus and contrast.4

Nearly any Small section of this work will reveal
the presence of the two basic three-note groups or their
metamorphoses. In fact it is usually impossible to proceed
beyond any fourteen to sixteen note sequence without having
included therein all twelve tones. M. 1 to 5, or M. 138
to 139, or m. 223 to 224, or the single measures 235 or
302 all illustrate Carter's characteristic technique
of accumulating twelve tones (see page 50).

In view of this typical saturation it becomes
highly debatable whether it can be perceived that the
metamorphosis of these two basic groups into six assigned
to piano and concertino and six assigned to orchestra, as
outlined by Carter, does result in giving clarification to
the texture or dimension to the tonal characterization.
The interrelationship of the basic "triads" is so close

and the means of presentation so dense that a lucid dif-

ferentiation of usage does not seem to result. This

 

4Elliott Carter, "The Piano Concerto." Boston
Symphon Program Notes (Boston, Mass.: The Boston Symphony,
anuary , 67).

50

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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51

conclusion, however, in no way negates the fact that the
concept of such differentiation may have been very
significant in the creative process.

It may be that the framework within which the
composer creates and the framework within which the
listener functions, although agreeing in the main, need
not be congruent in all their parts.

' Cadential patterns do not appear to exist within
the work. Functional harmony employing root progressions
by fifths or fourths is totally absent, as are mediant
progressions. The utilization of harmonic patterns in
'terms of root movement is completely discarded. On the
contrary, roots, where they can be found to exist at all,
are ignored in terms of chord weight.

I Phrase organization is not generated directly by
the harmony. 'It is true, of course, that harmonic usage
is among those compositional factors in thistork which
create increasing or lessening dynamism, but rather than
phrases in the conventional sense there exist undulations
within the texture, such as may be described as fluctua-
tions within the formal scheme. These events are
structured by tonal manipulations, variations in density,
rhythmic activity, changes in rhythmic character, dynamics,
expression markings, and orchestration. They flow very

coherently into one another. There is no consistent use

52

of harmony to produce section endings. The conclusion of
the entire work is brought about by a process of summation
in which the expectation of concluding is partly engendered
by the total duration. I

The absence of clearly recognizable cadences
results in a generally high level of tension throughout
the work. The wish to relax and even to rest is consistently
frustrated; instead the listener is challenged to expand
his concentration span. Tension and extended concentration
are part of the aesthetic of the composition. This
aesthetic concept follows naturally from Carter's remarks,
quoted in Chapter II, £25m, p. 8, about the distinguishing
character of "serious music."

The structural uses of harmony, organizing a large
work and clarifying the framework, can be found in some
instances Within the work; for example,in those areas
mentioned above as having a recognizable type of chordal
sonority for a perceivable duration. However, there is
no master-network of harmonic relationships upon which the
Structure of the entire movement is engineered, no
utilization of relative positions within an harmonic
scheme (either diatonic or chromatic) for sectional
organization, no reference to an underlying focal point

which recurs either as a tonal degree or as a pitch area.

53

There is a significant, albeit slight, tonal recall
in m. 328, where the middle of the measure uses the pitches
G-flat, C, and in m. 330 over the bar line to m. 331,
where the original motivic pitches C, F-Sharp, C-sharp, are
used again in prominent positions. These pitches also occur
in a cello entrance at m. 256 downbeat and are sustained
in a tremolo until m. 258 downbeat, where they are

repeated as the beginning of a figural pattern.

M. 256

 

 

 

54

 

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CHAPTER IV

MELODY AND COUNTERPOINT

Fundamental issues emerge at once in the examination
of melody. Can a definition of melody be formulated which
will be valid for the entire history of music, up to and
including the present?

It is in fact the most basic definition of melody
as motion and rhythm which is applicable to Carter's music.
It may be that the best term to define contemporary usage
of the emotive concept of melody would be simply this
univerSal definition: "A linear succession of tones.“

The new melody or linear succession of tones may be con-
stituted of single notes or of groupings of notes; beyond
this nothing may be specified with validity. However it
may be constructed, the essential quality, and the one
which designates it as a legitimate expression of the
melody concept, is that the constituents are not filler-
tones or color-tones but sequential carriers of an
expressive content. Viewed from this standpoint, even
the most unusual of Carter's lines may be considered

melody.

55

56

 

In the first movement of the Piano Concerto,
Carter's lines tend to consist of a multiple strand,
analogous to a bundle of fibers within a muscle sheath,
sometimes bunched into a muscle knot, sometimes thin as
a lean sinew. His "voices" are treated as orchestral or
choral voices, that is, as aisection capable of divisi.
Polyphony within one voice is common and an abundantly
"freistimmig" texture prevails. The single line
(monophony) occurs only twice in the entire composition,
at m. 17 and at m. 130-133. Several voices are present
almost all the time, resulting in a very complex poly—
phonic web, within which each strand is woven with
equality and independence. The homOphonic concept in
which melody floats upon a chordal support never appears
in this work. The technique used is simultaneous voice-
leading of lines of varying thickness, range, activity,
design, and interval selection, sometimes co-ordinating,
sometimes differing.

An important characteristic is the clouding of
the melodic line through simultaneous major or minor
seconds in the same voice, as in m. 70 (page 57).

As classical melodies were often doubled in
thirds or sixths, or medieval chant in fourths and fifths,

so Carter's lines tend to be adorned by simultaneous

57

 

 

 

 

 

 

 

 

seconds. Other frequent doublings are p. 4ths, aug. 4ths,
7ths, and 9ths, as in m. 56-58 (page 58).' Some

doublings in 3rds and 6ths do exist in this work, for
example at m. 157-165 (page 59), usually however in a
generally dissonant context.

In places where clusters adorn the melodic line
it is not possible to speak of melodic interval progression
but rather of relative placement within the pitch-space
and relative density in filling a pitch-space area, as in
m. 65-71 (page 60).

In areas of thick texture the lines are often a
series of harmonies of fluctuating density, made up pre-
dominantly of quartal chords with enclosed third, quartal
chords with ambitus of a seventh, quartal and quintal inter-
locked, or quintal with ambitus of a ninth, as in m. 170-175

(page 61).

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62

The traditional allocation of voices by pitch
area, historically derived from vocal ranges, does not”
seem applicable in the least. On the contrary, a voice,
indicated as a line by the continuity of its note stems,
may freely range from the highest to lowest pitches and
may proceed by wide jumps, using the G or F clefs without
regard to placement on upper or lower staves. A typical
example of free-ranging writing is m. 238-240. Here both
piano staves, written as two voices (and in one instance,
upbeat of m. 239, three voices), using both treble and
bass clefs, range from contra F-sharp to three-line a and
back to contra E. The three-line a is given to the left
hand. During the same three bars the orchestra, also
written in the reduction as two lines with one extra note
(downbeat of m. 240) as a third voice, ranges from.contra
B—flat to two-line a-flat (see page 63).

Occasional differentiation between voices may
be found in the tendency of the bass line to move more
slowly at times than the upper parts, for example in
m. 12-15, or m. 243-244. However this is rare (see page
64). Generally, differentiation based upon rhythmic
activity and rhythmic character is difficult to discern
within this Work. There is, however, continual differen-
tiation of voices in dynamics, articulation, and

expression markings, as well as in instrumentation.

 

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65

The ambitus of almost any area fluctuates rapidly
and tends to be enormously expansive. Unusual instances
of narrow ambitus occur in m. 188-192 and m. 68-71 (see
page 66). 3

When narrow ambitus occurs it is of relatively
short duration, whereas the expansive ambitus may continue
for considerable time. A typical picture is p. 37,

m. 329-334 (see page 67).

The fullness resulting from active polyphonic
motion over a wide ambitus is examined in Chapter 7,
Density. A brief résumé of the data revealed by that
examination is that two-note sonorities predominate in
sixty-four bars; fouréto five-note sonorities, one hundred
and four bars; five— to six-note sonorities, sixty-nine
bars; and "extremely Opaque" sonorities in thirty-nine
bars. Fluctuations in density are continual, but there
appears to be a general increase in fullness as the work
progresses.

The prevailing rapid motion, as well as the fluid,
diversified rhythms, tend to obliterate any temporal
distinction between the concepts of melody, melodic
figuration, and "passagio." The unification or blurring
of these concepts is furthered by Carter's tendency to use
similar intervallic motion and "freistimmig" texture

throughout. An example is m. 231-237 (page 68).

 

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69

The specific intervallic structure of the melodic
lines is usually difficult to calculate, due to the vari-
ability of texture within the line. It is apparent,
however, that although the interval choices are highly
varied, there is a distinct preference in many areas for
' certain intervals and a rejection of others. An interval
count was made of all of page 1, chosen for its leading,
and hence probably motivic, position (please see p. 70).
The calculations of interval motion in "freistimmig" places,
for instance m. 4, beat 2, were made according to the Vii“
rafifion ofthe note stems. In places where the single line
doubles on the same stem the motion was calculated into
and from both of the notes on the stem. Where a new voice
enters, the motion was calculated from all the existent
notes on the same staff to the new note. Augmented 2nds
were calculated as minor 3rds, diminished 8ths as major
7ths, and augmented 8ths as minor 9ths. Intervals larger
than the major 9th were reduced to within the compass of
the octave. Rests were ignored; the calculations are from
the note preceding the rest to the one following.

i The frequency of occurrence of intervals on page 1

is as follows:

per. 4 35 per. 5 2
aug. 4 27 Maj. 2 l
min. 2 10 Maj. 6 l
min. 7 9 Maj. 3 none
min. 3 8- per. 8 none
min. 9 6 Maj. 9 none
min. 7 3

70

J - 126 (J-

 
 
 

 

 
 
 

73‘9"!

J - 12w. - 42.) fanfash'ca

  

ORCHESY RAL
REDUCTION

bgg/ira

 

.L. J.-as

 

71

The high preponderance of melodic 4ths is signifi-
cant and proves to be motivic. The relatively high count
of minor seconds relates to the opening motive. The
absence of M. 3rds, eSpecially in conjunction with the low
count of p. 5ths, indicates the rejection of triad
formations.

A similar study was made of melodic interval fre-
quency on p. 37, m. 332, in a line of 16th notes including

two clusters. In this case the results are:

per. 4 6 Maj. 7 1
aug. 4 2 min. 2 none
min. 7 2 Maj. 3 none
min. 9 2 per. 5 none
min. 6 2 Maj. 6 none
min. 3 2 per. 8 none
Maj. 2 1

 

72

Although the second study deals with a much
smaller area than the first study, the results are
corroborative. A third study, of m. 231-237, referred
to above (please see p. 68), shows a somewhat different

pattern of interval preference:

per. 4 12 min. 9 4

per. 5 12 min. 2 3

Maj. 7 12 Maj. 2 3

min. 7 11 min. 6 3

aug. 4 9 Maj. 3 2

min. 3 7 per. 8 none
Maj. 6 6

Among the significant differences emerging from
the third study are the prevalence of 5ths, as well as the
higher proportion of minor 3rds and major sixths. The
higher use of fifths and sevenths suggests an expanded
tertian analysis in m. 23l-234.

The principal characteristics which emerge from
Carterls interval choice are a preference for intervals
of high tension, a disregard for traditional resolutions
of these tensions, and a preference for disjunct motion.
The melodic line does not reveal any tendency toward the
use of chains of similar intervals or symmetrical construc-
tions, except for areas where the preponderance of p. 4ths,
augmented 4ths, and minor 7ths is so great that these.
intervals do appear in sequence. Often the melody
reverses direction, returning to the previous pitch. This‘
accounts for some sequential pairs, for instance in m. 99,

piano part (page 73). Often this technique leads into

sbcc.

<puaf.

 

 

 

 

 

 

 

 

 

trill forms as at m. 101.

n. 101
.L-oe
IL.

    

 

 

74

Divisi often results, as at m. 30, sometimes caused by

the harmonic prolongation of one of the paired pitches.

 

When the re-iteration involves more than two pitches, an
unfolding harmony results, as in m. 108 flute part, or

m. 54.

M. 54

/\

M. 108

 

   

3 3
Phgwhm

 

75

The technique of reversal of direction is motivic,
as in the original pitch series the lst, 3rd, 5th, and 7th
notes of the lower voice return to the same pitch: 9,
re-articulated between c-sharp and one-line c; and the pitch
series of the upper voice is lst, 3rd, and 5th notes the
same: f—sharp, re-articulated between one-line c and
c-sharp.

The pitch choice of any melodic line within the
work seems to express the aesthetic of dodecaphonic
saturation. The melodies are not serial, but they are
totally chromatic. It is evident that the entire twelve-
note palette is continually in use.

The aspect of design in the melodic line cannot be
narrowly characterized. VIn fact, the most significant
part of its characterization is that rather than being
stereOtyped the melodic lines are immensely varied, and
this immense and continual variation, being pervasive, is
an integrative, unifying factor. The following criteria
usually do apply, however: a large ambitus; rapid
movement over an outstretched framework: disjunct motion;
frequent quick reversals of direction; jagged and dis-
continuous rhythms. The architecture is not of marble but

of quantum particles.

CHAPTER V

TEMPO, METER, AND METRICAL MODULATION

Most of the tempo markings used in traditional
music are in fact character indications which have come,
over a long period of time, to be associated with rates
of speed. The actual speed suggested by such markings as
Presto, Andante, Grave, etc., varies according to the
interpretation of the content of the music, knowledge of
the traditions relating to the historical period, and
familiarity with the particular tendencies of the individual
composer. Tempo determinants within the content of the
music are inclusive of all aSpects of the composition, so
that sometimes the tempo markings supplied bythe composer
or the editor are found by the thorough student to be
redundant and dispensable. In Baroque music (usually
written without tempo markings), the understanding by the
performer of the "right tempo" is pre-supposed. Nonethe-
less, debates on the subject of tempo arise perhaps more
frequently than on any other musical subject. The issue
is further clouded by the belief held by many musicians
that tempo adjustments should be made for changes in

instrumentation and in acoustical situations. There is also

76

77

the widespread acceptance of the concept of tempo change
without specific instructions from the composer within a
composition of length, as for instance for a variation in
a minor key, for a lyrical second theme inia sonata or
rondo form, or for the trio section in a minuet or scherzo.
There is no doubt that the selection of the tempo for a
short composition, and the handling of tempo changes in
larger forms, represent choices which constitute the heart
of musical interpretation.

Metronome markings can provide an objective measure-
ment for tempo; but their success depends upon the consent-
ing performer's tempo memory, for unless he has the rare
opportunity to consult his metronome before making his
initial tempo choice at the beginning of the composition
and thereafter for each tempo change, he must rely upon
his recollection. -

The discarding of traditional tempo markings in
favor of metronomic indications brings about a separation
of the Speed concept and characterconcept. The cultural
associations which enrich our understanding of the tempo
indications of the music of the past several hundred
years are blocked by the substitution of metronome
markings: and, in a sense, music which uses only metro-
nome markings is disjointed from a meaningful heritage.

Terms like "Allegro con brio" or "Largo e mesto" resonate

78

in the mind of the educated musician like poetic
references--which in fact they are, being part of the
great poems of musical art. They are windows looking
into the meaning and style. .

In the Piano Concerto, Elliott Carter uses as a

 

tempo heading a metronome marking combined with the evoca-
tive word, "fantastico." The use.of'"objective" tempo
indications is carried to its logical extreme. In the
Piano Concerto Carter eschews traditional tempo markings.
The first tempo is established by metronome; thereafter
every new tempo is doubly indicated, by its own metronome
marking and also by metrical modulation, which is the
technique of relating the new tempo to the previous tempo
in terms of some common unit of duration-~an obvious
analogy between the changing of note value function and
the tonal pivot function in traditional harmony. For
example, a note value of an eighth in 6/8 meter at dotted

quarter =‘84 will equal the note value of an eighth in ’

3/4 meter at quarter 126, as occurs at m. 49.

5/3 3/4

1-.., .V

.252 .: ,h= 252, J= 126

79

M. 48

J=126

 

 

g
(A'rWl- b -D

PP

   

In a more Complicated but still typical illustra-
tion, the note value of a triplet sixteenth in 5/8 meter
at quarter plus dotted quarter = 50.4 will equal an
ordinary sixteenth in 9/8 meter at dotted quarter = 126,

as in m. 293 (see p. 80).

/8 3 9/8

A_

5
J+J.= 50.4, .b= 252, $= 756 :fi= 756, $= 373: J= 126

The paradox of great fluidity and freedom requiring
' great precision and discipline is manifest in the area of
metrical modulation as it proves to be in other composi-

tional aspects of this work.

80

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\ «nub R

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

81

It is apparent at first glance that tempo formula-l

tions are extremely important in the Piano Concerto.

 

(Please see Appendix II, Graph of Tempo and Meter Change).
Carter makes use of a sequence of sixty metronome markings,
as well as other indications of meter change and note-
duration equivalencies. He establishes quarter = 126 or
dotted half = 42, as his initial tempo. The movement
concludes at dotted quarter = 126 for the last seven
measures. In between, there are continual fluctuations.
The longest constant tempo is twenty-three measures in
duration. The next longest tempo durations are eighteen
measures, once; seventeen measures, once: fifteen measures,
once: twelve measures, four times; eleven measures, once:
ten measures, five times. The frequency of tempo change is
greatest in the middle section of the work and least at
the end. The manipulation of the tempo durations suggests
an arch form of increasing and lessening activity, with
the composition beginning and ending at the same metronomic
point. The relative lessening in tempo fluctuation from
m. 255 to the end is in contrast to other compositional
procedures within this work where in general activity tends
to increase toward the end.

Frequent changes of meter provide an additional
variable.' In this work, meter and tempo often change

together, so that the metrical beat, whatever it may be

82

at that particular point, changes in actual duration while
at the same time the distribution of accent changes. It
is clear that Carter takes into consideration and generally
makes use of the traditional role of metrical accent. If
he did not intend to distribute emphasis over rhythmic
beats, those places where the eighth note remains constant
but the meter changes could be simply notated as a line of
even eighth notes, perhaps with added accent marks. A
case in point occurs at m. 10, where the quarter = 126 in
3/4 time becomes the dotted quarter = 84 in 6/8 time.

The eighth remains constant, a fact which Carter
meticulously notes by placing an eighth note above the

bar line, with arrows pointing both backward and forward.

Similar situations arise frequently within the
work. Where there is an equivalency of any note value
from the prior to the following tempo or meter, Carter
marks it with a notation of that note value, placed above
the bar line. At m. 28, where there is a change from 6/8
meter to a single bar of 3/16 meter, Carter indicates that
the 16th will be constant (see.page 83).

The presence of the bar line may be attributed to
the need to maintain rhythmic ensemble in the concerto.
However, Carter uses the bar line even in solo passages.

The technique of metrical modulation, i.e.,

expressing each subsequent tempo in terms of the immediately

83

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

84

preceding one, sometimes leads Carter to such extremes as
M.M. 110.25 at m. 129, or M.M. 58.8 at m. 287. However,
the fact that these calibrations do not exist on the
metronome does not invalidate their usefulness in terms

of relationships within the work. For example, the marking
at m. 287 of dotted half = 58.8 in 6/8 meter derives
mathematically from the previous marking of dotted quarter
= 98 in 6/8 meter in that five eighths of the previous
tempo equal a dotted half, or six eighths, in the subse-
quent-tempo.

It is obvious that Carter's metrical modulation
bears a close resemblance to the prOportional system of
the fifteenth and sixteenth centuries, when the "time
signature," often shifting within the composition, would
refer to proportions and equivalencies rather than meter.

Making the metrical modulation successfully
requires great precision and in some instances may demand
greater skills than the player might reasonably be expected
to possess. But the task of remembering a tempo pre-
viously established mentally but unplayed also challenges
the performer. The risk of inaccuracy is therefore no
greater and posSibly less. Furthermore, since the player
in the metrical modulation system does have the precise
metronome marking for each new situation as well as the
pivot unit to guide him, he may avail himself of tempo

recall as well as relying upon the equivalency.

85

At times the equivalencies are hard to express,
as at m. 156 where the duration of a quintuplet sixteenth
note is exchanged for a triplet eighth, changing the tempo
from quarter beat = 110.25 to quarter beat = 183.75.

Measures 221, 290, and 293 are among numerous similar

examples.

M. 290

‘tbjj;J«L-sa4

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M. 156

   
 

 

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7 7° "2.542 I

 

 

 

 

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7 ‘59:.
r 5 , =_,qf :i=—nf

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The relationship between tempo and meter in this
work is a fascinating one. In many places where the
duration of the small unit, for instance the eighth note,
remains constant but the meter changes, there is a kind of
rhythmic phrasing, a play of stress, sometimes duple,
sometimes triple, sometimes asymmetrical, which gives to
the composition a naturalistic motion, a spontaneous
swaying to and fro comparable to the movement of natural
objects, rooted but rarely still.

When a graph is made on which the duration of the
eighth note is projected for each tempo and each meter
throughout the entire work, including those sections where
eighths are not used as an actual note value, it is found

that for long stretches the eighth remains constant while

87

the meter plays around it; and it is further discovered
that after disturbances within the middle section of the
work, the eighth returns to its original duration for

most of the final thirty-seven bars. The eighth remains
at 252 for the first forty-nine bars, touches 252 again

at m. 84, m. 101-102, m. 205-221, m. 246-251, m. 311-319,'
and m. 329-348 (the end). (Please see Appendix III, Graph
of Eighth Note = 252.)

No other constant tempo factor has this frequency
or duration. It may therefore be said that in this work
Tempo Primo at eighth note = 252 is the basic tempo. The
composition recalls this Tempo Primo numerous times and
concludes with a recognizable return to Tempo Primo. Most
of the variations away from the constant eighth at 252
occur in the middle section, while the beginning and ending
sections vary in meter rather than in the eighth note
duration. It appears that an arched structural form and
architectonic unity centered upon the eighth note underlie
the extremely varied metrical modulations.

Although Carter makes use of metrical stress, he
is by no means the slave of the meter. Beats are often
replaced by rests. While in many cases this means only
that the beat is felt rather than heard (as in those

measures characterized in Chapter VIII, Rhythmic Activity

 

and Rhythmic Character, as "jagged"), in other instances

88

it does result in obliterating the beat and obscuring the
metrical arrangement (as in other measures characterized

in Chapter VIII as "diverse"). Furthermore, off-beat and
irregular dynamic accents are used frequently.

Carter's manipulation of stress is anything but
simplistic. Tempo and meter change combine with
dynamics, density, and rhythmic activity to offer an
aural picture of the utmost variety.

Motoric rhythm marked by asymmetrical measures
and off-beat accents, such as occurs for instance in £2
Sacre du Printemps and other works by Stravinsky, never

appears in Carter's Piano Concerto.

 

The technique of metrical modulation has no room
for rubato, accelerando, or ritardando. Carter may make
his tempo changes by gradual successive stages of one or
two measures. One such series of gradual changes is
m. 100, marked quarter = 126, going through m. 101-104
marked dotted quarter = 88, and arriving at m. 105 marked
quarter = 73.5. Another example can be found at m. 279
marked quarter = 60, going through m. 285-286 marked
quarter = 90, arriving at m. 287 marked eighth = 180. On
seven occasions a short intermediate measure is employed.
Since the intermediate measure is so brief, there is no
feeling of establishing a level tempo. The effect in
metrical modulation is analogous to a transient modulation

in tonal analysis.

89

Change within the individual measure, on the
minute basis of increasing prolongation from one note to
the next, for instance, is never seen in this work. It
may be, however, that rubato of a very subtle kind is
called for by Carter's frequent use of the term "espressivo."
The possible meanings of "eSpressivo" are discussed in

Chapter IX, Expression and Articulation Markings.

CHAPTER VI

DYNAMIC MARKINGS

Carter's Piano Concerto has an extreme profusion

 

of markings relating to the control of dynamics. A
random sampling shows that page 9 of the two-piano score
has fifty-one markings pertaining to volume level or
volume change. Page 19 has forty-seven; page 29, forty-
seven, page 39, fiftyeeight. Further examination indi-
cates that this wealth of dynamic markings is character-
istic of the entire work. Most often, a single measure
will have several simultaneous or successive markings, of
the same or of contrasting nature.

The dynamic range is extensive and the gradations
subtle. The parameters of volume are ff: and ppp. The
indication ppp occurs four times (m. 194, 198, 225, and
227)?.£££ is used seldom (m. 311 is one instance).

Volume gradations are indicated by ff, f, mi, mp, p, pp,
piuéf, pig_p, poco f, by the words "crescendo" and

"diminuendo, and by Opening and closing wedges. Although
traditionally the words "crescendo" and "diminuendo" are
used for changes from one volume level to another and

wedges are used for small variations of volume within one

90

91

pervasive level, Carter uses these markings interchangeably.
The marking §£_appears frequently and if: occasionally.

It may be expected, in the use of dynamics in
general, that they serve not only to provide variety of
volume but also function as indicators of musical character
and structure, especially if there are correlations between
dynamics and density, tempo, instrumentation, motivic use,
and other compositional factors.

In order to comprehend the meaning of the voluminous
dynamic usage in this work, three criteria were formulated.
One is the volume level during any time period, the second
is the stability of volume during any time period, and the
third is the kind of change which occurs. Six categories
emerge from the application of these criteria to the work:

1. relatively stable, with fluctuations in the
range from pp_to mf, '

2. relatively stable, with fluctuations in the
range from E£.t° ff,

3. very diverse, ranging more widely than
(1) or (2) I

4. predominantly level at p,

5. predominantly level at f,

6. predominantly crescendo.

A category for relative stability within the
middle volume range of p to E, which would complete the
classification system, was not used as this kind of

dynamic usage did not seem to exist within this work.

92

There also seemed to be no place for a category for
"predominantly diminuendo." Since both of these kinds of
dynamic usage are encountered frequently in most music,
their absence in this situation should be noted as two
significantly empty, or non-applicable, categories.
(Please see Appendix IV, Classification of Volume Level
and Volume Variation.)

The validity of this kind of categorizing would
seem to be directly related to the length of the time
period to which the categories are applied. A time period
of one measure or less turned out, upon experimentation, to
be too brief for general use. On the other hand, three or
four bars tended to be insufficiently specific. Two measures
were found to be the smallest unit which was usable for this
investigation. The two-measure unit is not of uniform
size in terms of time elapsed nor of pulses encompassed,
due to frequent changes of both tempo and meter, but it
does have the advantage of being a constant factor which
could be used in measurements of other musical data as
well. All the data derived were placed on a graph in which
the horizontal axis represented one-measure units. This
was done to facilitate comparison with other musical
events which were similarly graphed. Category 3, "Very
Diverse," was not scanned solely in two-measure units but
also represents on the graph various one-measure units

between other categories. Category 6, "Predominantly

93

Crescendo,"

also represents a single measure in two
instances which seem particularly significant (one is the
final measure).

Subjective judgment could not be removed entirely,
but, in order to objectify as much as possible, various
considerations were carefully held in mind in decision
making. These include the number of volume changes and the
frequency of changes within the framework of each category.
Both could be very high without disqualifying the two-
measure unit for placement within either of the "relative
stability" categories, unless the range of fluctuations
exceeded the volume boundaries of the category. In that
case the unit was placed in "Very Diverse." Sections of
low volume punctuated by loud interjections were placed
in Category 1 unless the interjections seemed to prevail
by reason of their duration, frequency, or rhythmic position.
This would have made the section more suitable for 2 or 3.
Rests were considered as tending to reduce the volume
level, unless they were very brief.

The number of notes present at any one time
(density), and the rhythmic activity were studied and
graphed separately. Although,in actual performance,
volume, intensity, and density may frequently be found
to interrelate, the separate investigation of each of
these aspects revealed that a planned relationship among

them is rejected by the composer.

94

In this work, multiple layers, with some strands
marked loud and others soft, occur very frequently. These
sections were placed in the "Very Diverse" category,
unless the dynamic spread did not exceed pp to EE or mg
to ff. Accents and sforzandi were considered to function
with the surrounding volume level. A‘s; in piano, for
instance, was not considered the equivalent of subito
fgrtg, as in this work subito forte, or even £2552 by
itself uses the heavy line over a note to indicate greater
emphasis upon that note. This was assumed to be only a
slight volume modification. Carter does not use the
staccatissimo (') sign to indicate a particularly sharp,
short accent. The word, "marcato," which occurs thirty-
one times throughout the movement, is dealt with under
expression markings rather than volume indications.

When the criteria and categories had been defined and
established, the entire work was scanned repeatedly and each
definable unit was placed on a graph (please see Appendix IV,
p. 158). It then became apparent that the initial impression
Of very profuse and extreme dynamics is in fact true for one
hundred and forty-eight. Category 3, "Very Diverse," was the
one which appeared most often on the graph. It is also the

one which includes some of the longest stretches of any one

' 95

kind. It includes one stretch of twenty-four measures,
one of fifteen, one of thirteen, five of twelve, as well
as various shorter occurrences. Category 3 definitely
prevails in the last third of the work and particularly
at the end.

Category 5, "Predominantly f," is the next most
prevalent category, with fifty-two measures. However, it
is filled by only two appearances, one of twenty-eight
measures and one of fourteen. The twenty-eight measure
stretch is indicated principally in the solo Piano part.

Category 4, "Predominantly p," is least filled,
with only one appearance of thirteen measures at approxi-
mately mid-point in the composition, m. 222. It is evident
that the sections of comparatively level dynamics are the
least frequent, but have relatively long duration.v Perhaps
the implication here is that sufficient time is a requisite
of quietude.

Although Category 4, "Predominantly p," is the
meagerest, Category 1, "Relatively stable from pp to mg,"
is the next in frequency to Category 3. The lower volume
range is indeed used a great deal, although with fluctua-
tions. Category l includes sixty-four measures in twelve
appearances. Significantly, this category begins the
composition with eight bars which offer a particularly

clear-cut example of the type of sonority of that category.

96

Its next appearance is for seven measures, then two,
three, ten, four, six, two, and eight, with the graph
indicating that Category 1 dwindles in importance from
the mid-point of the work.

Category 2, "Relatively stable from mf to if,"
contains only nineteen measures, in five scattered
appearances. Activity in this volume range tends to be
of the upward thrusting type, as Category 6, "Predominantly

crescendo,‘ contains thirty-six measures, in eight
appearances. ’During the first third of the work there is

a five-measure stretch and a six-measure stretch, but
starting at m. 202 there is a five-measure appearance,

then three measures, and then, clustered toward the end,
five measures, ten, one, and one more for the final measure
of the composition. Both Category 3 and the Category 6
become increasingly important as the end of the work
approaches. .

Summary of the data regarding dynamics:

1. Only one place steady at piano (fourteen
measures beginning at m. 223)

2. Two places steady at forte (forty-two
measures beginning at m. 123 and m. 208)

3. More general stability in the lower range
(sixty-four measures) than in the upper
range (nineteen measures)

4. No category for diminuendo, whereas there
are thirty-six measures of crescendo

5. No category for stability in middle range

97

6. Most prevalent, one hundred and seventy-four
measures of very wide and frequent dynamic
fluctuation.

Analysis of dynamics does not reveal that dynamics
are used in this work to illuminate the formal structure or
to indicate any kind of sectional organization. The pro-
gression of the work is marked only very generally by the
appearance at the beginning of "softer stable" and the rise
in "diverse" and "crescendo" toward the end, while both
the piano level and the forte level occur only in the
central portion.

Neither does the analysis reveal any identification
by dynamics of thematic structure, characteristic motives,
or instrumental usage. No significant correlations between
dynamic usage and other compositional aspects were dis—
covered by comparison of graphs.

The ready conclusion is that the use of dynamics
in this work is merely decorative. Further consideration,
however, indicates another, far more SOphisticated,
function.

Decorative dynamics, whose main purpose is to
alleviate tonal boredom, certainly does not require the
immense variety demonstrated by this work. Rather than
comforting the listener's ear, the range, diversity, and
frequency of dynamic change in this work offer an aural
challenge of the highest difficulty. Many listeners will
not be able to meet this challenge. The willingness to

meet the challenge and to function within_such an

98

elaborate framework forces upon the listener an attitude
of the highest concentration. It implies a discipline
requiring a tense emotional state lasting for three
hundred and forty-eight measures. It may be that the
dynamic usage is a means of sensitizing the listener to
all aspects of the composition.

Possibly this is the principal meaning of Carter's
dynamics in this work: the tension level forced upon the
participating listener is itself a vital part of the
message communicated.

Voluminous dynamic markings of the kind found here
are not rare in twentieth-century music, especially in the
works of Schonberg, Webern, and Berg. (See, for instance,
Six Little Piano Pieces, Op. 19, by Schonberg, the Piano
Sonata, Op. 1, or the Chamber Concerto for Piano, Violin,

and Thirteen Wind Instruments by Berg, or Webern's

 

Klavierstuck, Op. Posthumous.) Carter's link to the

 

Viennese atonalists and expressionists, which is also
suggested by other aspects of his compositional technique,
may be further bolstered by his usage of dynamics.

An analogy can be made between Carter's dynamics
and the use of color in certain contemporary paintings,
such as those of Jackson Pollack; non-structural, non-
representational, large scale, often pointillist, ranging

over the entire palette.

CHAPTER VII

DENSITY

f Density, or the "thickness" of sound, is a compo-
sitional factor which has grown greatly in significance
during the late 19th and 20th centuries. Density is
related to harmonic texture and chord structure, contra-
puntal delineation and linear integrity, acoustical
reinforcement and tonal diversification, spacing and
utilization of pitch areas. In orchestral writing,
density is related to tone color.

Density may be consistent, stable in the number of
voices used andperhaps also in their assigned ranges, or
fluctuating in number and pointillist in allocation of
pitch area. The organization of density can be useful in
establishing formal structure. The deliberate evocation
of well-established hiStorical associations in density
usage, such as four-part chorale writing or melody with
figural accompaniment, for example, may offer clues to
thematic characterization and interpretation. In a
concerto or concerto grosso, density is concerned with the
massing of instrumental forces into tutti, solo, or

concertato groups.

99

100

In view of the striking complexity of material in

Carter's Piano Concerto, a minute and systematic classifi-

 

cation of data regarding density may be essential. In

this study, density is investigated in regard to both

(1) the degree of thickness and (2) the consistency of

texture. First it is necessary to define density in such

a way as to eliminate confusion from related consideration

of volume (acoustical reinforcement), rhythmic activity,

and orchestration. Orchestral doublings of the same pitch ‘\

do not come under consideration because the composer's piano{\, 3
reduction of the orchestral score is used for this study. Kéhfifl'
Carter states in a prefatory note to the published two-
piano score that his reduction of the orchestration is
fairly literal except for a few octave transpositions and

some very densely composed passages. Volume is considered

separately in Chapter VI, Dynamic Markings, and rhythmic

 

activity in Chapter VIII, Rhythmic Activity and Rhythmic

 

Character. Those instances within this work where density

 

seems to have increased simultaneously with the building up
of volume are studied from both vieWpoints. Similarly,
closely arpeggiated figures are measured under both

Density and Rhythmic Activity.

 

The strictest and most precise definition of density
would be simply the number of pitches present at any one
time. A problem immediately arises in the interpretation '

of "one time." Does this mean occurring simultaneously

101

(beginning together), or perceived as related and compre-
hended as a chordal structure which is extended over a
relatively brief duration, as an arpeggio or an accumula-
tion of chord tones? Another approach would be from the
durational aspect, without, if possible, infringing upon
the concept of rhythmic activity. This approach would
require choosing a suitable time unit and measuring the
thickest and thinnest of sonorities during that time span.
Should priority be given to the most prevalent density
within the time unit, or to the density of rhythmically
significant chords? If the time unit is not precise
simultaneity, how minute should it be?

A suitable, although often rather large, time unit
is the measure. This choice facilitates graphing in the
same way as is used for other compositional aspects and
offers ready comparison with other data by making use of
the measure as the same constant factor in each case.

A sliding scale of density measurement was devised,
with overlapping of boundaries. Subjective judgment was
used to determine those sonorities which were likely to be
perceived as chordal although not simultaneous. Rhythmic
placement of thick sonorities, and the most prevalent
density within the measure were taken into consideration
as tending to raise the density level. Ambitus was also
considered; sonorities which were either very broad and

expanded or very narrow and concentrated were rated higher

102

where it was feasible to do so. To illustrate, let us
take a measure where the highest number of pitches which
seemed to form one sonority was four, but where only two
notes were also present at one time. According to the
scale of classifications below, this measure could be
placed in one of three categories, depending upon the
concomitant considerations. In all decisions, aural
perception was taken as the principal guide. In this
connection it is noteworthy that Carter's dodecaphonic
tonal matrix has nothing to do with the traditions of
doublings and spacings for full sonority within a chord.

The classifications which developed as useful
categories in this work are:

l. l to 2 notes

2. 2 to 4 notes

3. 4 to 5 notes

4. 5 to 6 notes

5. 6 or more notes

6. extremely opaque.
The spread within each category is required by the length
of the one-measure time unit and is adjusted in the way
which seems suitable for this particular composition.

Category 1 is significant for its meagerness and
its placement. The composition begins with one of the rare
appearances of the single note, in this instance a note

lasting for an entire measure, which is a unique occurrence

103

within this work. In all, the single note occurs only

three times: at the beginning, marked piano espressivo,

 

for a whole measure of the piano part; in m. 223, last

quarter, again in the piano part, marked piano un poco

 

espressivo; and in m. 285, downbeat, the lowest C, in this

instance actually a doubling between the piano and the

 

double bass, marked fortissimo. The single line is also
extremely rare. It occurs in m. 17 in the piano part and
in m. 130-133 in the orchestral part.

The other appearances of Category 1 are predomi-
nantly two-note sonorities: m. 17, 113, 130, 131, 132, 160,
and 166, seven in all. They are conspicuously absent from
the second and third sections of the composition.

Category 2, "2 to 4 notes," has sixty-four
measures, scattered throughout the work but appearing,
least in the third section.

Category 3, "4 to 5 notes," has one hundred and
four measures, beginning in m. 4 and appearing without
apparent pattern throughout.

Category 4, "5 to 6 notes," does not begin until
m. 31, and contains sixty-nine measures.

Category 5, "6 or more notes," begins in m. 28
and has sixty-four measures. This category is absent
-from m. 107 to m. 173. A lowering of density results as
it is replaced by sparser categories, Category 3 in

particular.

104

Category 6, "extremely opaque," has only thirty-
nine measures, but as it merges into Category 5 we do not
get the impression of meagerness in that category as we
do in Category 1. On the contrary, the combination of
5 and 6 reveals the very important usage of thick density.
The denser categories begin later and occur more frequently
as the composition progresses. Category 6 occurs for
longer stretches later in the work and is the concluding
sonority.

In the entire movement, only seventy-two measures
contain sonorities of less than 4-5 notes and these
measures occur mostly in the earlier sections, while the
denser sonorities, first appearing in m. 25, increase in
significance until the end. Some of the sonorities of
Category 6 are tone clusters including almost all the,
notes throughout the pitch range of the piano, as at

m. 316 (see page 105).

Summary of findings regarding density:

There does not appear to be a systematic use of
different leVels of density, different concepts of con-
sistency or variety of texture, or different kinds of
density change, such as the addition of voices. Neither is
density used for sectional organization or thematic
characterization. The soloistic role of the piano is not

marked by a particular kind of texture. In studying the

105

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

fir),

 

graph of density, for which a classification decision has
been made for each measure, it proved impossible to
discover any meaningful pattern. It would seem that the
artistic purpose is the expression of extreme variety and
freedom, with much use of very thick sonOrities challenging
the perceptual capabilities of the listener. The aesthetic
is of non-structuring and fantasy. The general growth in
density throughout the work tends to reinforce the onward
progression in much the same way as was found true for
other compositional aspects. This growth is rendered less

than obvious by the wide and continual fluctuations.

Please see Appendix V, Graph of Density, p. 159.

CHAPTER VIII

RHYTHMIC ACTIVITY AND RHYTHMIC

CHARACTER

Elliott Carter's Piano Concerto is extremely complex

 

in regard to rhythm. The spacing of the sounds in time and
in relation to one another displays fantastic variation.
In the hope of achieving greater awareness in this area,
a classification and graphing system was attempted along
the lines of previous chapterS. (Please see Appendix VI,
Graph of Rhythmic Activity, p. 165). V

The concept of rhythmic activity may be described
as a horizontal view of density. Instead of measuring the
number of simultaneous sounds, the measurement applies to
'the number of successive sounds within a given duration.
Again, in this study as in others, one measure was taken
as the unit of duration and each measure was classified
and graphed on a scale of

l. l to 3 notes per measure

2. 4 to 7 notes

3. 8 to 11 notes

4. 12 to 20 notes

5. more than 20 notes.

106

107

Although the disparity in the lengths of measures
within the work is in this case a factor which may tend to
lessen the validity of this means of considering the data,
some conclusions can be drawn.

Rhythmic practices throughout the work appear to
adhere to a fairly uniform concept. A careful perusal of
the entire movement indicated that the first 120 measures
of the composition could, in fact, offer a sampling which
would be ample, characteristic, and representative of the
method of investigation. This in itself constitutes one
of the most important findings: stability of usage.
Undoubtedly this stability functions as a significant
factor in creating unity in this composition, a very help-
ful consideration in such an extraordinarily large one-
part form. 1

Immediately apparent is the correlative fact that
rhythmic activity, like "dynamics" and "density," is
extremely free, fluid, and wide-ranging. There is no
observable pattern.

Complications of notation often obscure the true
number of successive musical occurrences, for instance when
a note tied to the next beat must be written twice.

In cross rhythms, some notes share time slots. For example,
a five-note group juxtaposed upon a two-note group results
in only six sequential sounds.

The third important conclusion, drawn from examining

both the music itself and the graph, is that in this

108

composition rhythmic activity is a completely independent
aspect. It is free from either positive or negative cor-
relations with other compositional factors. Increased
rhythmic activity may be used at times to aid in building
volume, but in general this is not the case. Thicker
sonorities may be relatively more widely spaced in time,
as in the last few bars, but sparser spacing also occurs
in areas of meager density.

Rhythmic activity in this work is used to express
scope, variety, frequent change, high levels of rhythmic
density, conceptual independence, and dynamic propulsion.

In listening along a time continuum, it is not
only the relative frequency and duration of successive
notes which is perceived, but also, and more importantly,
the kind of rhythmic motion which prevails in any area.
The use of gradations of rhythmic density offers one means
of expression; the kind of rhythmic motion employed by
the composer offers another. The rhythmic character of any
area depends upon the total number of notes, their fre-
quency or relative speed, and their relative placement.
In this work, rhythmic character types can be sorted into
five categories:

1. smooth

2. uneven

3. jagged

109

4. diversified

'5. extremely diversified.

It is of interest to note that in the study of
this compositional aspect, as well as of several others, it
is necessary to include a superlative classification. The
classifications are also appropriate to the work analyzed
in that the homophonic and polyphonic considerations are
studied together.

The study of rhythmic character types proved
rewarding in clarifying the concept in general and the
specific usage within this work. "Smooth" implies that
most notes are of equal duration or similar subdivision,
or fit easily upon the meter. Examples are m. 17, 23, 232,
258, 282-284 (see page 110). It is not necessary that
these measures contain relatively few notes. On the
contrary, if the rhythmic activity is very high the
impression may be "smooth" because all the time slots are
filled. Polyrhythms may therefore lose their effect, as
for instance, in m. 109 (page 111), unless the integrity
of each rhythmic strand is clearly delineated in other
ways, as in m. 207 (page 111), where the orchestration
clarifies the rhythmic counterpoint. Carter's technique
in dealing with this sensitive concern is one of the more

debatable aspects of this composition.

110

M.r_1_7__-7’. = J

fl*J

 

111

M. 109

 

finance fiss.

*Tpt
I—a-L?‘

“final/am

 

’9'

112

"Uneven" describes those places where notes are of
similar but not equal duration, where the subdivision
changes, but where the metrical placement remains undisturbed,

as in m. 6, 22, 45, 76-78.

M. 76

 

f

Tp.‘

    

"Jagged" refers to an irregular rhythm that sur-
prises by missing beats. Some kinds of syncopations and
anticipations would be included in this category,
especially those which place events narrowly off the beat.
The dotted eighth followed by the sixteenth sometimes falls
into this category, as does the pattern which places very
disparate note values in sequence. This type of rhythmic
character is of particular interest, because, although it
may seem very active due to the alertness required of both
listener and performer in perceiving and effectively
playing the disproportionate values, it does not necessarily

contain many notes. Rather, it is of importance to guard

113

the significant space between the notes. From this view-
point, "jagged" may be considered an expansion of the
concept of Monteverdi's "stile concitato." Examples are

m. 49, 114, 106-107, 145, 150, 189, 251, and 339.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-h_.,J.-73.s M. «339461

VA -"

 

 

114

The classification "diversified" requires many
notes--12 to 20 or even more than 20, comparable to
Categories 4 and 5 of Rhythmic Activity.’ There is usually
great variety of note values and of subdivisions within the
single line, as well as a high degree of contrapuntal
complexity. "Smooth," "uneven," or "jagged" lines may be
contained within the texture; however, the overall
impression is of rhythmically independent lines made up
of different note values. Examples are m. 75, 212, 230,

and 327.

M. 212' ~ I‘":

 

"Extremely diversified" will probably contain.
polyrhythms and irregular groupings. In this study the
term is reserved for measures which are so complex that

they tend to be interpreted as a sound effect, similar to

115

the "special effect" interpretation of the measures of
highest density. These saturated areas occur with con-

spicuous frequency, as in m. 81, 99, 215, 248, 249,

313-315, and 343.

u. 215’"

    

memn

'..-.-..---00.

ill :7 E [:1 «J

    
  

L1

 

3___.I I.”

 

116

The first ninety measures of the Piano Concerto

 

' were systematically classified and graphed in terms of
rhythmic character. (Please see Appendix VII, Graph Of
Rhythmic Character, p. 168.) As in the graphing of rhythmic
activity, this sampling offered sufficient data to serve

as a visual representation of the kind of use of this
compositional factor in the entire work.

Carter's ingenuity in devising and manipulating
rhythms seems inexhaustible. Rhythmically identical
measure-groupings hardly exist. Although repeated figures,
chains of triplets, for example, do sometimes recur,

Carter usually manages to eschew the use of repetition or
sequential patterning. There is no rhythmic motive.
Rhythmic recall is not practised. There is no correlation
of rhythmic character with any other compositional aspect.
Interpretive mood is evinced by rhythmic character only in
an oblique way. Significantly, ostinato is not used.
Rhythmic patterning of an organizational nature, such as
augmentation, diminution, or "divisions," is also completely
absent.

Carter's rhythmic aesthetic is striking in its non-
affiliation with other considerations. Perhaps its most
important quality, in addition to the astOnishing level
of its imagination, is that it is a selfécontained means

of expression.

117

So many areas within this work can be described
as "diversified" or "extremely diversified," with more
than twelve or even more than twenty successive sounds
per measure, that questions of aural judgement arise. Are
the more complex measures intended to be clearly and
accurately perceived, or is a sound effect of overwhelming

activity the desired objective? In Chapter VI, Dynamics,

 

aural strain in regard to the perception of fluctuating
dynamics was presumed to be part of Carter's aesthetic
in this composition. Perhaps the rhythmic activity and
complexity, amounting at times to a shock wave, may be
adjudged similarly.

If confusion, as an expressive phenomenon, is in
fact part of the conceptual framework of mid-twentieth-
century music, it can be observed in measures such as
239-242. Confusion certainly must be admitted to its
place on the extreme Dionysian side of the aesthetic
continuum. In this work Carter demonstrates that if con-
fusion is to be communicated purposefully, it cannot be
assigned with surety to the possibly obvious happenings of
aleatory means, but requires meticulous structuring by

the composer.

118

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CHAPTER IX

EXPRESSION AND ARTICULATION MARKINGS

Carter is extremely specific in every aspect of the
music analyzed. Dynamic markings are precise, tempo is
measured to minute metronomic calibrations. It would not
seem as if there were need for many interpretive directions
or "expression markings." However, Carter does make use
of an extensive vocabulary of "expression markings," and,
surprisingly, many are of a subjective, non-specific
nature.

A complete list of expression markings found in the
first movement of the Piano Concerto and the places where
they are used follows (when the marking occurs at an
upbeat, the numbering is of the following measure):

1. espressivo, m. 1, 8, 28, 35, 50, 94, 124, 133,

—_I38T—ITU, 141, 144, 146, 162, 228, 236, 258,
259, 264, 270, 271, 277, 279, 322, 329, 330,
331, 339 (this is the final marking)
2. un poco expressivo, m. 223

3. espressivo sempre, m. 281

4. molto expressivo, m. 54, 105, 125, 126, 276,
299,‘3l8

5. molto espressivo e ben legato, m. 301

6. cantabile espressivo, m. 5, 175, 179, 231

119

11.

12.

13.

14.

15.

16.’

17.
18.
19.
20.

21.

120

espressivo ben cantando, m. 32

cantabile, m. 24, 49, 216

 

ben cantando, m. 140, 304

 

ben sentito, m. 319

 

delicato, m. 69

1e iero, m. 6, 54, 72, 80, 98, 128, 130, 199,
20I, 225, 253, 329

sempre leggiero, m. 81

 

marcato, m. 22, 23, 24, 30, 34, 37, 39, 61, 102,
147, 168, 169, 174, 178, 184, 204, 205, 212,
215, 219, 247, 248, 249, 253, 293, 308, 327.
Marcato mano sinistra, m. 27

 

ben marcato, m. 209

 

marcatissimo, m. 207, 310

 

sonoro, m. 216

brillante, m. 290

 

sempre staccato e pesante, m. 302

giocoso, m. 123, 185

accompagnato, m. 105

 

Very often, different strands within the texture

have different markings (m. 252 is one instance among many),

presumably to indicate linear balance in terms of tonal

pre-eminence.or placement within simultaneous independent

phrases.

Sometimes Carter will repeat an expression marking

as if to reaffirm its validity in the face of conflicting

markings for simultaneous parts. Often he will meticulously

place the same marking in simultaneous parts. In general,

121

expression markings occur at the beginning of phrases and
indicate tonal character or solo position.

Articulation markings are also highly specific and
numerous. The word "legato" appears often and there are
many legato slurs as well as longer, phrase, slurs. Carter
'uses staccato dots, but not under slurs. Sometimes he will
pair staccato dots with a heavy line over each note,
achieving the same kind of "portato" effect which is often
the interpretation of dots under a slur. .In m. 17 he uses
the word "détaché."

. It is clear that the expression markings which
Carter considers most important in this work are "marcato,"
"espressivo," and "cantabile." These are all terms of
considerable ambiguity. If "marcato" is interpreted in
its literal sense, one may wonder why a slightly higher
dynamic level was not Specified.e The implication is either
that "marcato" is too subtle a volume gradation to be
named as such, or that the meaning is principally of
psychological import, referring to the portentious presenta-
tion of each note within the phrase. "Cantabile" may be
related to "marcato," referring to tonal prominence or to
similarity of sound within a phrase. The familiar term
"dolce" is conspiCuously absent.

Enigmatic, too, is the use of the term "espressivo."
Possibly the usage goes beyond the exact definition and

means a flexibility in phraSe dynamics and phrase rubato.

122

What does "sensibile" (upbeat of m. 257), mean in regard
to a single sound, the diminished third A - C-flat?
"Giocoso (subito)" at the upbeat of m. 185 is
correlated significantly with a change of articulation
from "legato" to "staccato." "Giocoso" at m. 123 is

_particularly interesting.

M. 123

    

~J-no.25-.

- J-uo.25-¥ (“99)

(as)

 

123

It is not a performance direction, but a descrip-
tion of the musical character at that moment, an evocation
of the empathy and psychological involvement of the player
(oboe). The specific verbal communication of this joyful
mood serves to indicate Carter's awareness of the inten-
sity of feeling and emotional participation of the per-
former. It also makes explicit his wish and expectation

in terms of human communication between composer, performer,

and listener.

It may be taken as an expression of Carter's
philosophy that he makes use,in this work,of terms which
indicate to the player not only what he should do, or what
he should try to make the listener perceive, but also what
he himself might feel if he were internalizing the emo-
tional progression of the composition. The emotive con-
tinuity which is the life line of a free form (as this
work appears to be) may well call upon the sympathetic
partnership of the performer to a degree analogous to
that practised by some schools of acting.

The freedom of the lines of internal coherence
within this composition are signalled by the use of the
term "fantastico" at the beginning. This word appears
above the staff, next to the metronome indication in the.
solo piano part and in the same position above the
orchestral reduction, which is tacit at this point. There

is no indication in the positionusually allocated to the

124

title of the moVement or to the principal tempo.

Although "fantastico" is written in lower case italics
without an initial capital, it may be that the meaning of
the term extends in a general sense to all aspects of the
composition. Certainly there is no specific meaning which

could apply at this point.

CHAPTER X

SUMMARY AND CONCLUSIONS

Elliott Carter (b. 1908) has had a long career as
composer, teacher, and lecturer. His critical success and
frequent performances place him in a position of leadership
in the world of music. He not only influences the progres-
sive movement in contemporary music, but in his personal
and unique way he may be considered one of its true
representatives. Each of Carter's new works is therefore'
extremely interesting in itself, and also may prove helpful
in illuminating some of the conceptual trends and composi-
tional techniques of today. The first movement of the

Piano Concerto poses serious challenges to the listener

 

and analyst; hopefully, in studying these challenges, per-
ceptual skills may be developed which will be rewarding in
understanding not only Carter but other composers of our
time.

The principal difficulty in undertaking the present
study lay in finding a way to begin (a far from rare
problem in analysis and of significance in itself). The
first impression is of a work of great complexity and

innovation, very active, thick, long, aurally overwhelming,

125

126

apparently formless, the creation of which may have been
governed to a high degree by an intuitive process. It

was helpful at first to define the composition by determining
what it is not. It is a work without themes or tunes, with
no distinction between statements and transitions, no
scenario even in the sense of area-distinction by emotional
content, no tonality, no modulation, no identification by.
pitch-space area, no returns or repeats, no cultural or
folkish allusions.

Casting aside false expectations in regard to these
considerations brought out the fact that some traditional
and even conservative criteria remained. The work is non-
aleatory, non-electronic, and makes no use of mixed media
or experimental acoustical effects. There are no micro-
tones or deviations away from the locked-in pitches of the
tempered scale. Traditional instruments are employed and
’used in traditional, albeit sometimes very virtuosic, ways.
(The virtuosic element may also be regarded as traditional
in a concerto.) Pitch notation, rhythmic notation,
expression markings, and dynamics are employed in the
classic tradition. The six basic attributes which define
most Western music are all present in some way--rhythm,
structure, melody, harmony, timbre, and volume. In
addition there are directions to the player. These basic

attributes turned out to be quite sufficient as points of

127

departure for a comprehensive analysis. All the investigable
elements of composition listed earlier in Chapter I, Purpose

and Method, could be grouped into these attributes.

 

The study of rhythm required two kinds of inquiry,
one into rhythmic activity and rhythmic character, and
another into tempo, meter, and metrical modulation. The
study of melody included a consideration of the counter-
point. Timbre was deemed a Specialized tOpic somewhat
outside the area of this paper; however, the thickness of
sound was investigated under Density. Volume comes under
Dynamic Markings, and directions to the player under Expres-
sion and Articulation Markings. Harmony, in its three
aspects of chordal sonority, cadential form, and structural
organization, formed a chapter in itself. Form, although it
is presented first in this paper, was actually investigated
last, as it required bringing together sufficient knowledge
of all the other attributes or aspects of the composition.

Procedure, in the sense of evolution over a time-
span, is the particular philosophical inquiry in which we,
together with Carter, are involved in this work. In
studying each attribute it seemed important to consider
both the character of the element itself and the kind of
prosedure in which it was engaged, whether, for instance,
the melodic lines were of the same type throughout or, if
they varied, in which way they did so. Wherever possible

a statistical method was employed, measuring the attribute

128

in its various presentations and measuring the procedure
in which it was involved. Each new aspect studied was
scrutinized for possible clues regarding other aspects.
A brief recapitulation of findings follows.

In form, the first movement of the Piano Concerto

 

is less like a structure with members, connecting tissue,
and organized parts expressing a genetic lineage than it
is like protoplasm moving toward its fulfillment. The
concept of structure in this work is not one of "being"
but "becoming." Apparently one long evolving form, its
forward movement is marked by a series of interconnected
changes of various kinds, some relating to the harmonic
texture, or to the rhythm, density, orchestration, or
motivic usage. There are no pauses. The 12-tone matrix
is always used and the motivic three-note chords of C,
F—sharp, G and G, D-flat, F are always present in their
original form or metamorphosed. There is a slight recall
of the original pitches toward the end of the work, but in
no sense a recapitulation.

The movement is headed by the indication

"fantastico, which is perhaps a reference to an intuitive
approach to the unfolding of the motivic possibilities.
The emotional level is high throughout, due to the absence
of sectionalization, obvious phrase endings or cadences,

as well as to the particular kind of usage of other compo-

sitional aspects. The overall impression is of an

129'

immensely dynamic forward propulsion in one Sweep from
beginning to end.

The harmonic texture is based upon the use of the
two motivic three-note chords. As these three-note chords
are not tertian triads but are atonal in implication, it
is therefore not surprising that even in their furthest
metamorphosis they rarely exhibit tertian formation. The
diminished triad never appears; neither does the diminished
seventh chord. ”The augmented triad is seen seldom, but
major and minor triads do appear as part of polychords, as
do sevenths, ninths, elevenths, thirteenths, and
fifteenths. Tertian sonorities with cross relations or
added tones are frequent. Most prevalent, again a natural
consequence of the motivic material, are quartal and
secondal harmony. Although the harmonic vocabulary is
proquely varied, the favorite and characteristic
_sonorities are sevenths or ninths combined with fourths,
or clusters which may be expanded to include all twelve
tones. -

7 Movement in block chords is not used, nor are
sustained harmonies. Chordal figuration, free expansion
'of the number of voices present, extension of some pitches
within afigure to form a harmonic constellation are the
techniques prevailing.' Chord streams are not used, but
occasionally a Stream of a particular interval may appear

within the texture.

130

Although Carter writes (see p. 48) of tonal
organization by the method of allocating the three-note
chords to soloists or to orchestra, the aural impression
is of dodecaphonic saturation throughout.‘ The harmonies
are not generated serially, but all twelve tones are
always present in close juxtaposition.

Cadences in the usual sense of the word cannot be
discerned. The tension level of the harmony is consistently
high. Although there are some fluctuations to a lower
tension level, these periods are brief and do not appear
to have Significance in defining the structure of the
entire composition.

Organization by pitch-Space area, or by tonal
reference, for example to a special pitch emphasized by
frequent repetition or prolongation or rhythmic placement,
are techniques unused by Carter in this work.

The figural writing which is employed almost
continually tends to bring together the concepts of harmony
and melody. The harmony is definitely implied by the
melodic movement, and the prevailing contrapuntal treatment
of the melodic lines causes the harmonic sonorities in most
instances. Melodic voices are treated as choral or instru-
mental "sections" which divide and reunite continually.

The fluctuation of texture is one of the most identifiable
characteristics of the work. Voices frequently move in

paths of seconds, or in clusters. Occasionally streams of

131

parallel sixths or thirds appear, or sometimes a stream of
fifths. The twinning of the melodic line into seconds may
be motivic in that the original three-note chords contain
seconds. Since the line is often thickened in this way
into two or more concurrent notes, it is usually not
possible to speak of the precise intervallic motion which
comprises the melodic movement. In the few instances where
the linear flow is of single notes, the intervals chosen
clearly indicate a preference for leaps of fourths,
sevenths, and fifths. This correlates with the harmonic
analysis of the most prevalent chordal sonorities.

In design, the lines often reverse direction,
repeating the previous pitch. Chains of identical or
similar intervals appear rarely. Small interval pattern-
ing is used, but expansive movement, noted above as fourths,
sevenths, and fifths, is preferred. There seems to be no
preference for direction of movement, but swift and fre-
quently reversing motion, ranging over a very wide
ambitus, is a conspicuous style-characteristic, as is
rhythmic fragmentation. Short rests are often interjected
and there seems to be no deliberate manipulation of phrase
length in terms of the duration of melodic continuity.
Legato slurs and staccato markings are used as articulation,
not as phrasing indications. Variety of phrase length and

definition of phrase character through articulation are

132

not utilized as deliberate techniques in this work.
Melodic phrasing is not supported by harmonic usage.

Although bunches of sound frequently group upon
the line, the prevailing texture is polyphonic. All the
voices share the characteristics mentioned above, but they
are differentiated by rhythmic patterning, dynamics,
articulation, and by the occasional tendency of the lowest
voice to move more Slowly. The clarity of the voice
leading, however, is obscured by the "freistimmigkeit,"
by the frequent crossing, fragmentation, and the pointillism
in the orchestration. There is little, if any, polarization
of soprano and basses. "Companioning" of two or three voices
within the texture is rare. The counterpoint is freely
dissonant at all times and the lines are completely
independent. The impression is of varying degrees of
concurrent activity, usually rapid and dense.

Elliott Carter's writing is frequently associated
with a new technique of tempo change called metrical modu-
lation. A considerable amount of publicity has been given
to this innovation. In the composition analyzed, metrical
modulation is evidenced by Sixty metronome markings and a
comparable number of meter changes, indicating that Carter
is deeply involved in the procedure of shaping events in
time. This concern is extremely enlightening as to
Carter's meaning in creative circles today, for it is both

sophisticated in its technical application and profound

133

in its confrontation with basic musical truths. The
philosophy of music conceived as aural experiences on a
time continuum creates the vieWpoint which illuminates all

the aspects of the first movement of the Piano Concerto.

 

Carter's continual manipulation of the time element
expresses his aesthetic involvement with matters of
procedure and "becoming." All the compositional aspects
of the work are in flux and the time element itself is
extremely fluid.

The time element in music is by nature dual, both
objective and subjective, lying within the twin concepts of
duration and pulse or tempo and meter. Carter plays with
the time element by varying the duration of his beat, the
subdivisions of his beat, and the distribution of accent
over the group of beats.v He uses bar lines and meter
indications, but, going further, he controls the time
element by means of a specific interchange unit which may
be a beat or may be a portion of a beat. The interchange
unit functions rather as a coin whose buying power or
"real value" changes in altered cirCumstances, although
its assigned numerical value is consistent. A large array
of coins may be used by Carter; their meaning changes.

To expedite this fluidity, Carter makes use of
extremely specific directionsas to both the particular
'interchange unit, or metrical value which "modulates,"

and also the objective duration of the beat. The

134

interchange unit is indicated as a note value over the bar
line at the point of tempo change: the duration of the beat
is indicated by a metronome indication in each instance.

The technique of metrical modulation results in
precise control over the time element. Presumably, there-
fore, extreme finesse over the Shaping of aural events on
the time continuum can be achieved. .On the other hand,
this system disregards two time concepts which are of
limitless interest: (1) rubato, accelerando, and
ritardando (that is, progressive change within minute
units), and (2) complete change Without a ready interchange
unit (as, for instance, from one system of coinage to
another totally unrelated). It would seem, then, that
metrical modulation alone does not provide complete control
of all the elements that pertain to time.

Carter's further explorations along these important
lines will probably be of the highest interest. It may be
that a change in his entire aesthetic would reSult from
either greater control over the time element, or renuncia-
tion of the presumed present objective of very tight
control.

The entire movement is shaped by time considerations.

The original tempo is quarter note 126. This can be sub-
divided into eighth note = 252. Carter calls attention
to the eighth value at m. 10 by shifting from 4/4 meter

to 6/8 meter, keeping the eighth constant. If we grasp

135

this clue and keep in mind the impliedvalue of the

eighth note throughout the work, it can be seen that,
despite many wide fluctuations, the eighth often re-asserts
itself at 252. This metronome marking provides a touching-
down place at intervals through the work and becomes a
settling-down place at the end. This circumstance may, of
course, be unintentional. It does provide a thread,
however tenuous, through what appears at first to be a
maze of changes of both tempo and meter.

The first movement of Carter's Piano Concerto

 

offers a challenge to the listener's comprehension through
the sheer number of sounds employed. Extreme density and
extreme activity prevail. A statistical method was
employed in the hope of giving definition to the somewhat
overwhelming impression of the ear and eye. Each measure
was counted, classified, and graphed in terms of the
number of simultaneous sounds (density). Large areas of
the work were graphed in terms of the number of successive
sounds (rhythmic activity). It emerged that prevailing
density is so high that only seventy-two measures out of
the total of three hundred and forty-eight contain con-
sistently fewer than four to five notes at the same time.
Density increases through the middle of the work and is
'highest at the end. Except for the gradual upward shift,
no purposeful patterning appeared. Similar findings

emerged from a note-count of successive sounds. Rhythmic

136

activity, like density, is generally very high, very
varied, and tends to increase slightly toward the con-
clusion of the composition. Here again, a purposeful
patterning, related perhaps to other compositional aspects,
could not be found.

The rhythms employed were classified in terms of
character implications such as smooth, jagged, and the
like. Here, too, the findings were, typically, of great
variety, ingenuity, and complexity, tending in many
instances, due to the activity of each line and to the
contrapuntal diversity, toward aural saturation and
hyperactivity.

The meaning of the challenging thickness is
uncertain. One hypothesis is that the listener of the
future may be expected to reach higher comprehension
levels than at present. Or it may be that the listener
today, by effort and careful attention, can outreach his
present self. Or it may be that the listener's effort and
careful attention is in itself the goal of Carter's com-
positional thrust in these areas. The aural saturation
and hyperactivity may be designed to sensitize the listener
to higher emotional and intellectual states. Or it may be
that turbulence is indeed the prevailing message in this
composition.

If the last two hypotheses are correct, they supply

a raison d'étre to the profusion of dynamic markings and

137

expression markings. A typical page of Carter's score
may include forty to sixty such markings, some concurrent,
some sequential. No doubt many of these markings are
intended to give clarity to the texture, but many others
are probably designed to provide variety and richness of
expression to the on-going aural experience and to
challenge the listener's involvement with the composition.
The dynamics do not identify structural areas.

The findings for each measure in terms of density,
rhythmic activity, dynamics, and tempo and meter were-
placed on a graph to facilitate comparison. It is note-
worthy that purposeful correlations do not appear.

Perhaps the two most significant findings which
emerge from the study of all the compositional aspects of
the work analyzed are the intensity of functioning of
each aspect and the apparent disassociation between them.

It may be fruitful to look for analogies between '
the techniques of this composition and some of the
techniques of twentieth-century painting. In the use of
dynamics, harmony, and rhythm, we have a brilliant,
profuse, and diversified palette of color. In density, a
generally thick application of paint, with the surface in
high relief. In rhythmic activity and rhythmic character,
the uSe of a complex web of design with many planes of

super-imposed and conflicting perspective.

138

Harmony and melody both emerge from compositional
choices predetermined by the creator and motivic in the
sense that they can be perceived by the listener and also
in the sense, more important, that they provided guidance
in creation. These choices are innovative and, to a high
degree, intuitive.

In his concern for the time element, perhaps the
most sensitive matter of all, Carter may be compared to the
painter who realizes that his picture may be seen as a
whole, as a Gestalt, but may also be viewed in part: and
as the eye peruses the picture and makes its own path
between the parts, a subjective reproduction of the
picture is created by the viewer. So, the pulling
together of the parts of Carter's composition by the
memory of the listener creates the form. It may therefore
be possible in music, as in painting, to create a totally
abstract form.

From this vieWpoint it can be seen that while many
of the techniques and honored traditions of the past are

discarded in Carter's Piano Concerto, the basic purpose of

 

the art-work remains the same, and eternally true: the
communication of an emotional state through the ordering

of sound.

BIBLIOGRAPHY

139

Carter,

BIBLIOGRAPHY

Elliott. Jacket notes to Nonesuch Recording
H-7134, Sonata for Flute, Oboe, Cello, and
Harpsichord, and Sonata for Cello and Piano.

 

 

 

. "Shop Talk by an American Composer." Problems
of Modern Music. New York: W. W. Norton, I960.

 

. "The Piano Concerto." Boston Symphony Program.
Notes. Boston, Mass.: The Boston Symphony,
January 6, 1967.

 

140

APPENDICES

141

APPENDIX I

GRAPH OF THE OCCURRENCE OF EVENTS

142

APPENDIX II

GRAPH OF TEMPO AND METER CHANGE

144

APPENDIX II

GRAPH OF TEMPO AND METER CHANGE

This graph offers a visual representation of the
tempo and the meter used in each measure throughout the
work analyzed. The numbers running from left to right
across the top of the graph are measure numbers. The
numbers running from bottom to top along the left side of
the graph are metronome indications. Numbers in paren-
theses within the graph area are metronome indications
which differ from the customary calibrations. The note
values drawn on the graph are those which equal the metri-
nome indication. The numbers which appear as fractions
on the graph area indicate the meter at that point.

The duration of any tempo can be determined by
position on the measure number line. The longest duration
is twenty-three measures, which occurs only once. The next
longest durations are eighteen measures, once; seventeen
measures, once; fifteen measures, once: twelve measures,
four times, eleven measures, once; and ten measures, five
times. The longest durations occur in the final third of
the work; and the largest number of changes of tempo and
meter occur in the middle third. The metronome indication

of 126 occurs at the beginning and at the end of the work.

145

146

 

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APPENDIX III

GRAPH OF APPEARANCES OF EIGHTH NOTE

155

252

156

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APPENDIX IV

CLASSIFICATION OF VOLUME LEVEL

AND VOLUME VARIATION

157

 

158

 

 

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APPENDIX V

GRAPH OF DENSITY

159

160

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APPENDIX VI

GRAPH OF RHYTHMIC ACTIVITY

165

166

 

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GRAPH OF RHYTHMIC CHARACTER

168

169

 

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APPENDIX VIII

FIRST MOVEMENT OF ELLIOTT CARTER'S

PIANO CONCERTO

170

 

Note

The reduction of the orchestra for a second piano is fairly literal except for a few octave
transpositions and some very densely composed passages. A compromise between playability and
cueing to give the main orchestral material was sought.

In many passages the piano part should be performed not emphasizing the upper line of a
series of chords but as a sequence of chords or intervals evenly balanced. This is particularly true
of mm. 1224-139, Fifi-151, l79-18l, 223-2'25, 25l-269. 321-327, 339-340, 543-607 (wherever
simultaneous groups of two or more notes occur), and in 669 to the end. As is indicated in the
score, the two passages that emphasize the perfect fifth —- mm. 393-410 and 505-521 ——- depend
for their character on this sonority.

Pedalling is suggested in many passages to clarify the chordal intent. but need not be
followed literally, and may be used in many other passages at the soloist’s discretion.

Pasagos marked A‘ “‘x or R’” “x (which occur only in the con-
certino) are to be played as a continuous accelerando or ritardando; the note values indicated
are only approximate.

A note to mm. 522-529: Beginning at m. 522 the soloist should accelerate gradually while
the orchestra maintains a strict, regular tempo. The dotted arrows indicate approximately what
points the piano should have reached in its relation with the orchestra. This relationship can be
somewhat free, but at m. 529 the soloist must reach the beginning of his tremolo somewhere
between the limits indicated. Once there, he must continue his accelerating and fading tremolo.
reaching the maximum speed and lowest dynamic level at the point indicated at the end of the
bar. The length of this tremolo is determined entirely by the time it takes the orchestra to arrive
at this point playing in strict tempo.

Elliott Carter

171

'K—i'

Piano Concerto

Reduction by the composer “0’ Elliott Carter

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