texture in chopin and scriabin music

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AN ANALYSIS OF TEXTURE

IN SELECTED PIANO ETUDES OF CHOPIN AND SCRIABIN

A Thesis

Presented in Partial Fulfillment o f the Requirementsfor the Degree Master o f Arts

by

Daniel Dewitt Mickey 111, B.M.

The Ohio S t a t e University1980

Approved by

School of Music



CONTENTS

Page

LIST OF EXAMPLES . . . . . . . . . . . . . . . . . . . . . . . . . . i v

PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

The Purpose of the Study . . . . . . . . . . . . . . . . . . .The Significance o f the Study . . . . . . . . . . . . . . . . vi i

The Etudes Selected for Analysis . . . . . . . . . . . . . . . vi i

The Organ iza t lon o f the Study . . . . . . . . . . . . . . . . i x

vi

Chapter

. . . . . . .I . PROBLEMS IN THE ANALYSIS OF KUSICAL TEXTURE 1Problems i n Defining Texture . . . . . . . . . . . . . 1

5Specialized Problems i n Analyzing

Texture in Piano Music . . . . . . . . . . . . . . . 8

. . . . . . .roblenis i n Determining Linear Independence

11. BASIC TYPES OF MELODIC AND ACCOMPANIMENTALPRESENTATION 10. . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . .The Single Line 11

Chordal Figuration 17

Arpeggiated Figuration 20

Alternating Figuration 21

Convol u ted Fi gura t i o n

. . . . . . . . . . . . . . . . . . .The Doubled Line 14. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . 22

Summary 23. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . .11 . DENSITY 27

. . . . . . . . . . . . . . . . . . . .Densi ty-

number 2830

Density-compression 32

Vertical Span . . . . . . . . . . . . . . . . . . . . .

Spac ing-d i s t r ibu t i s i i 33

Density i n the Etudes 34

. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . .IV. RANGE 39

Range-average . . . . . . . . . . . . . . . . . . . . .

Range-

averageso f

the Etudes 43

40. . . . . . . . . . . . .

i i



Chapter Page

V . CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . 53

APPENDIX: Determi n a t i o n o f Range-average . . . . . . . . . . . . . . 58

SELECT BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . 69

iii



LIST OF EXAMPLES

Exampl e Page

1. Berry's terms for t h e d e s c r i p t i o n o f l i n e a r i nd ep en den ce . . I 7

2. S c r i a b i n E t u d e O p. 8 No. 8. mm . 1-3. . . . . . . . . . . . . . 12

12

4 . S c r i a b i n E t u d e O p. 8 No. 2. mm . 1-2 . . . . . . . . . . . . . 12

5. 13

6. 14

14

15

3. Chopin Etude Op. 10 No. 4. mm . 1-2 . . . . . . . . . . . . . .

S c r i a b i n O p. 8 No. 2. mm . 1-2. w i t h t h e m e l o d y n o t a t e d . . . .Chopin Etude Op . 25 No . 6. mm. 27-28 . . . . . . . . . . . . .

7. S c r i a b i n E t u d e Op. 8 No. 10.mm

. 58-

60 . . . . . . . . . . . .8. Chopin Etude Op. 25 No. 8. mm . 1-4 . . . . . . . . . . . . . .9. S c r i a b i n E t u d e O p . 8 No. 7. mm . 1-2 . . . . . . . . . . . . . 16

10. S c r i a b i n E t u d e O p. 8 No. 8. mm . 1-3 . . . . . . . . . . . . . 17

11. Chopin Etude Op. 25 No. 4. mm . 9-12 . . . . . . . . . . . . . 18

12. S c r i a b i n E t u d e O p. 8 No. 5. mm . 1-3 . . . . . . . . . . . . . 18

13. S c r i a b i n E t u d e O p. 8 No. 5. mm. 1-3. r e n o t a t e d . . . . . . . . 19

Chopin Etude Op . 25 No. 1. mm . 1-2 . . . . . . . . . . . . . .15. Chopin Etude Op . 10 No. 12. mm . 10-13 . . . . . . . . . . . . 20

16. S c r i a b i n E t u d e Op . 8 No. 3. mm. 1-4 . . . . . . . . . . . . . 2 1

17. Reduct ion of Example 16 . . . . . . . . . . . . . . . . . . . 2 1

14. 20

18. S c r i a b i n E t u d e Op. 8 No. 7. mm . 1-2 . . . . . . . . . . . . . 22

19. Chopin Etude Op. 10 No . 9. mm . 1-3 . . . . . . . . . . . . . . 23

20. Chopin Etude Op . 25 No . 9. mm . 1-4 . . . . . . . . . . . . . . 25

21. Chopin Etude Op. 25 No . i 2 ; min . 1-2 . . . . . . . . . . . . . 25

22. Chopin Etude Op . 10 No. 2. f i n a l m e a s u r e . . . . . . . . . . . 28

23 . S c r i a b s n Etude Op. 8 No. 12. mm . 1-2 . . . . . . . . . . . . . 29

24. F i g u r a t i o n r e d u c t i o n o f the l e f t - h a q d p a r t o f Example 23 . . . 29

i v



Example Page

25. S ynops is o f i n f l a t i o n and c o n t r ac t i o n o f t he tex tu re- spaceas expressed i n c o n t r a- d i r e c t i o n a l r e l a t i o n o f o u t e rcomponents . . . . . . . . . . . . . . . . . . . . . . . . . . 30

V



PREFACE

-The Purpose o f the Study

This study examine; three basic characteristics of texture i n piano

1) types o f melodic a n d accompanimental presentation, 2) density,music:

and 3 ) range.

25 and the Scriabin Etudes Op . 8 measurements of density and range are

compared. These measurements quantify the textural di ff erences among the

types of melodic and accompanirnental presentation and also distinguish be-

tween the textural styles of the two composers,

I n selected compositions from the Chopin Etudes Opp. 10 and

This study asserts t h a t the texture of nineteenth century piano

music, as exemplified by the etudes of Chopin and Scriabin, i s l h rge ly

dependent u p o n the types of f i g u r a t i o n used, and further, t h a t a l l of the

figurations found i n these collections are derived from six basic types.

In this context, the term "figuration" is defined as "the consistent use

of a particular melodic or harmonic figure." ' The basic types t h a t func-

tion melodically are labeled single line and doubled line; those t h a t

function accompanimental l y are labeled chordal, arpeggiated, a1 t w n a t i n g ,

and convol uted.

As the study will demonstrate, etudes us ing the same type of

figuration share common textural t ra i ts t h a t can be measured according t o

viirious characterist ics o f density an d range, and these common t ra i t s are

1. J , A. Westrup and F. L 1 . Harrison, "Figuration," The New Colle eEncyclopedia clf Music, (New York: W . W . Norton,-+1960



more strongly linked t o the type of figuration used t h a n t o the style of

the particular composer.

The Significance of the Study

Previous research dealing w i t h texture is very limited, both in

quantity an d in scope. Typically, studies t h a t do analyze texture are

concerned with orchestral or chamber music, placing their emphasis on

changes in instrumentation. As a r esu l t , the methodology and terminology

used in these multi-instrument analyses do not transfer well t o the invest-

i g a t i o n of piano music texture.

Considering the importance of texture t o musical s ty l e , i t i s hard

t o understand the neglect t h a t texture, especially t h a t of the piano, re-

ceives i n theo reti cal writings. Most writ ers limi t th ei r discussions t o

broad generali t ies and a few well-worn terms. This s tudy provides a s t a r t-

i n g p o i n t for f i l l ing the vo id by presenting clear definitions o f familiar

terms, introducing new terms, and presenting a systematic methodology f o r

deal ing w i t h texture i n pi ano musi c.

The Etudes Selected for Analysis

Concert etudes were selected for this study t o insure t h a t :

1) the textures t o be analyzed are stylistically indigenous to the piano,

and 2) each composition exhibits one dominant textural type.

of performance technique demanded by concert etudes provides complex textures

that are seldom f o u n d i n any othe r mediums. Yet, t he technical demands of

these works are n o t regarded as compromising their artistic q u a l i t y or musi-

cal value, even t h o u g h the i r i n s p i r a t i o n stenis from pedagogy.

the further advantage of emphasizing one principal texture w i t h i n each

The h i g h level

Etudes have

v i i



piece individually, w1,ile providing a great variety of textures within the

co l l ections.

Composers who wrote concert etudes include Chopin, Scriabi n , Rach-

maninoff, Liszt, Mendelssohn, Schumann, and Debussy. Opp. 10 a n d 25 of

Chopin and Op. 8 of Scriabin were chosen for this investigation because

their great similarity i n style and form afford a good basis for comparison.

The later etudes of Scriabin, Opp. 42 an d 65, as well as the etudes by Rach-

maninoff and Debussy, contain elements t h a t are post-Romantic, or even modern

in style, and are therefore less comparable. A1 though the "Transcendental

Etudes" of Liszt are comparable i n s ty le t o the works selected here, the

forms arid type o f content are quite different. L i s z t ' s forms are larger

and often based on variation technique while the Chopin and Scriabin etudes

are shorter, generally ternary structures.

incorporates several. di ffe ren t pi an is ti c devices in each piece, whereas

Chopin an d Scriabin, normally develop a single principal device.

"Symphonic Etudes" are actually a theme and variations and are a l l binary

in form except for the last variation which functions as a grand finale.

Mendelssohn's "Three Etudes" Op. i o 4 i s t oo small a collection to allow a

I n terms of technique, Liszt

Schumann's

fair comparison.

There are many similarities between the works of Chopin and the

early works of Scriabin despite the s ix ty years t h a t separate their compo-

sition. The similarities are apparently the result of intentional modeling.

Scriabin 's o u t p u t is usually divided i n t o three phases of development, the

f i r s t of which has even been characte rized as being "Chopinesque."* The

Etudes Op . 8 (1894) fall i n this period (1885-1900). Scriabin was fond of

2. M. Montagu-Nathan, Handbook t o the Piano Works of A. Scriabin (London:J & W Chester, 19161, 2.

v i i i



Chopin'smusic a n d from the evident similarities in the music ( e . g . , see

page 14 ) i t i s quit e probable t h a t the Etudes Op. 8 were modeled on the

Chopin etudes.

The individual etudes examined in this study are l i s t ed i n the

following outline accarding t o six basic types of melodic and accompani-

mental presentation. Each o f these basic types is described i n detai l i n

chapter two. The Chopin

etudes are selected from Opp. 10 and 25 on the basis of their similarity

All of the Scriabin Etudes Op. 8 are examined.

of figuration to the Scriabin etudes.

Scri abi nEtudes

Op./No.

I . Melodic presentation

A . Single l i ne 81 8 8/11

B. Doubled line 816 8/98/ 10

11. Accompanimental presentation

A . Chordal figuration 8/ 5

B. Arpeggiated figuration 812 8/4

C . A1 ternating figuration 811 8/3

D. Convoluted figuration 817 8/12

Chopi nEtudesOp ./No.

10/2 10/4 10/62512 2517

2516 251825110

10/11 2514

1018 10112 2511

10 / 10

1019 l o l l 0

The Oraanization of the Study

As stated above, this study is concerned w i t h three basic char-

acterist ics of texture i n piano music:

tal presentation, density, and range.

characterist ics i s se t fo r th i n chapter one. The chapter begins w i t h a

general overview of texture by examining some o f the definitions of the

types of melodic and accompanimen-

The logic for selecting these three

i x



term t h a t can be found in current literature. I t continues with the estab-

lishment of the definition of texture t h a t is used throughout the study and

concludes with detailing of the special problems in analyzing the texture

of piano music.

Chapter two explains the basic types of melodic and xconipanimental

presentation found in the etudes of Chopin a nd Scriabin a n d class i f ies the

etudes accordingly. Examples of each type a n d a discussion of the various

figurations found within them are included.

Chapter three examines the different parameters of textural density

g i v i n g precise de fi ni ti ons for each one. The basic types of accompanimental

figuration discussed in chapter two are then compared according t o measure-

ments o f textural density.

Chapter four discusses the problems concerning the measurement of

range and proposes a modified definition of range t h a t permits more useful

methods for i t s measurement. This method i s explained in detai l and then

is used t o contrast and compare the types of figuration and the styles of

the composers.

Chapter five summarizes the methodology of the study and i t s r esu lt s

and sets forth suggestions for further investigation.

I wish t o acknowledge Dr. Burdette Green of The Ohio State Univer-

s i t y fo r his generous assistance and helpful advice d u r i n g both the study 's

planning and i t s writing.

X



Chapter Ia

PROBLEMS IN THE ANALYSIS OF MUSICAL TEXTURE

One of the most difficult problems i n analyzing text ure i s defining

the term. The word can be defined i n a variety of ways. Three different

views of texture are examined below in order to develop a workable defini-

t ion.

of linear independence which, for the reasons explained in the last twosections of t hi s chapter, i s n o t examined in this s tudy .

The most problematic aspect of the definition involves considerations

Problems i n Definina Texture

According t o Wallace Berry, "Changes i n texture. . .are often among

II3the most readily perceptible and appreciable i n the experience of music.

If these changes are so apparent, then one would assume t h a t te xtur e would

be an obvious area for extensive musical investig ati on.

a few wr it er s who have de al t with the area of tex ture i n deta i l . . Most re-

ferences t o 'texture, even i n comprehensive analyses ,are restricted to very

general observations that use descriptive words such as light, heavy, homo-

phonic, and polyphonic.

Yet there are only

Perhaps one reason for the small amount o f significant work i n th i s

important area is the lack of a clear understanding of the concept Iltexture.

I t i s obvious t h a t analyses Snvolving a vague, nebulous concept will f a i l

t o produce meaningful resul ts w i t h any precision or sign ific ance . In the

3. Wallace Berry, Structural Functions i n Music (Englewood C1 iffs, NewJersey: Prentice-Hall, 1976), 189.

1



3

Berry's Structural Functions i n Music contains one of the few i n-

depth discussions of texture t o be found.

t h a t are n o t defined precisely. This practice re su lt s i n the use of

Berry carefully avoids terms

specialized terms that, even t h o u g h they are very precise, make his writ-

i n g style rather cryptic, as one can see in the followirig definition.

The texture of music consis ts of i t s sounding components;i t i s condit ioned i n part by the number of those componentssounding in simultaneity or concurrence, i t s qualit ies deter-mined by the interactions, inter relat ions , and re la ti ve projec-t ions and subs t nces of component lines or other componentsounding factors .7

The most notable feature o f Berry's statement is his division of

texture i n t o quantitative and qual it at iv e charac teris tics . The quanti t a-

t ive characteristics include l ' . . .the number o f concurrent events [commonly

called thickness] as well as the degree of 'compression' o f the events

within a given intervallic space.Il8 He refers t o both thickness and com-

pression as having measurable densities, b u t also states that these measure-

ments do not reflect the subjective impressions o f dissonance and coloration

that he asserts are vitally related t o dens i ty . Berry's "qualitative"

characteristics include the relative independence and interdependence of

the horizantal components within the musical fa br ic as determined by direc-

t i o n a l , intervallic, and rhythmic relationships.

In his G u i del ines for Sty1e Analysis , Jan LaRue places "texture"

under the general heading of "sound." Since he also includes "timbre" and

"dynamics" as separate subheadings under the same category "sound," i t can

be inferred that LaRue does not conceive o f timbre and dynamics as specific

7. Berry, op . c i t . , 184.

8. Ibid.



' 4

characte ristics of texture. He defines texture as a "momentary combination"

and uses the term "fabric" for the whole continuous web of texture and

dynamics. To compl icate matters further, he mentions "range" acd " tess i tura"

under the subheadings of both "texture" and "timbre, I' 1eavi ng the issue un-

decided as t o whether or not they are to be viewed principally as character-

i s t i c s of ' texture. 9

For an analysis of texture to be meaningful , one must clearly under-

stand which of the many possibilities mentioned i n these definitions are to

be considered characteristics of texture.

analytical re su lt s i s dire ctl y connected to the precision of the def init ion,

a singl e c ri te r io n was adopted for deci ding which cha ra ct er is ti cs of tex tur e

are appropriate for the study of these etudes.

the strictest sense should deal only w i t h characterist ics that are princi-

pally associated w i t h ei the r vertical o r horizontal relationships. This

criterion enables us to define the concept of texture according to three

basic characteristics:

Because the validity of the

I believe that texture i n

1) 1inear independence, 2 ) density, and 3) range.

Each of these characteristics involves either horizontal or verti-

"Linear independence" refers to the relat ion-cal factors of the texture.

ships between horizontal components. The degree o f 1inear independence

varies on a continuum from purely homophonic textures or mi n i mu m independ-

ence, o pure1y polyphonic t extures or maximum independence , w i t h any

degree possible between these two extremes. However, the degree of inde-

pendence does n o t easily lend itself to objective measurement.

and other important reasons explained i n the next two sections of this

chapter, 1inear independence was deemed inappropriate as a characteristic

For this

9. Jan LaRue, Guidelines for Style Analysis (New York: W . W . Norton and Co.,1970) 3 23-34.



5

of texture i n this study.

system based on types of melodic and accompanimental presentation.

In i t s place was substituted a classif ica t ion

The second characteristic, "density," refers to the number of

components present a t any g iven moment and the i r arrangcment w i t h i n a

specific vertical span. This concept involves the thickness, compression,

and spacing o f ver tica l components. The t h f r d character is t ic , "range,"

refers t o the changes of pitch as the music progresses through time.

of these char acte ris tic s of texture i s explained i n fur ther deta i l la ter

in the study.

Each

The previously discussed criterion t h a t l imits the definition of

texture enables us to exclude t h e following factors since they are not

normally associated with ei th er vertical or horizontal at tr ib ut es : timbre,

instrumentatioii , dynamics, and ar ti cu la ti on . Indeed, these additional fac-

tors do influence texture to some degree, b u t , according to the limited

definition presented above, they need not be considered i n a textural anal-

ysis. Dissonance or, for that matter, harmonic constructs, are primarily

vertical i n nature, b u t are commonly considered independent areas of inves-

ti ga ti on and have es tabl ished systems for ana lysi s. They therzfo re do not

need to be subsumed under texture. Sini i lar ly , rhythm i s primarily a hori-

zontal component, b u t one tha t i s commonly considered an independent area

of invest igat ion. One cannot deny that components influence each other

ei ther direct ly o r ind i re ct ly. However, fo r the sake of l i m i t i n g the num-

ber o f variables involved and sharpening the focus o f the investigation,

i t i s desirable to examine components independently and selectively.

Problems i n Determining Linear Independence

Generally speaking, the horizontal components of texture result from

the characteristics o f the individual lines and from the relationships that



6

are formed between the lines, I f each l i ne has i t s own melodic and rhyth-

mic identity and i s not subservient t o another line, then the lines are said

t o be independent, and according t o tradition the music i s classif ied as

"polyphonic." Conversely, if the principal melodic and rhythmic interest

centers i n one line, and the remaining parts are merely accompanimental and

function as one unit, then the components are not independent a n d the music

i s c lass i f ied as "homophonic."

I t would be di ff ic ul t t o place all music i n t o one o r the other of

these categories because there are many textures t h a t have a limited inde-

pendence and do not wholly belong t o the class of homophony or polyphony.

For analytical purposes i t i s more useful t o hypcthesize t h a t works f a l l

at points on the continuum described earlier withrn the range from extreme

independence of 1i nes t o extreme interdependence of 1ines .Unfortunately, 1inear independence does no t easily lend i tself t o

objective measurement, and th i s i s probably the reason why Berry designates

1inear indepecdence as a "qualitative" characterist ic of texture." The

number o f variables and the complexity o f the relationships w i t h i n a tex-

ture make placement on the continuum a subjective judymerrt.

the following terms in an apparent attempt t o supply a systematic method

11for descri b i rig 1i near independence .

Berry presents

10. Berry, o p . c i t . , 185.

11. I b i d , 193-95.-



7Ex. 1 Berry's terms for the description of linear independence

homorhythmi c

= hetero-rhythmic

1j=&contra-

1 . 4

I - - contra-JJA-+&d- _ 1

1 1 1 1 I F. I 1 1 1 1 1

I directional

This l i s t provides terminology for three relationships of three

different factors.

systematic means for determi n i ng the degree of 1 near independence for any

work.

two l ines. Any attempt t o label, for example, an eight-measure passage i n

four-part w r i t i n g would require a prohibitive number o f statements, or re-

course t o descrip tive general i t i e s t h a t destroy objectivity.

A t f i r s t glance, his array of terms seem t o provide a

That i s the case, however, only for note-by-note comparisons between



8

Speci a1 i zed Probl ems in Analyzi ng

Texture i n Piano Music

Special analytical problems arise when one deals with texture i n

piano music.

in the medium itself.

mediums i n which all the voices or parts are realized with the same timbre

( i .e. , the same i f we disregard the subtle differences o f tone-color caused

by changes in register o r dynamics). This general lack of tone quality

differentiation makes i t di ff i cul t for a l is tener to isola t e individual ? a r t s

and , as a result, allows the composer more freedom to vary the number c f

parts without d i s r u p t i n g the texture than woul d be possi bl e i n heterogenous

ensemb-ies where entrances and cutoffs art: more noticeable.

These problems can be attributed to several factors inherent

Fi r s t , th e piano i s one of the few instrumental

Second, t he performer i s limit ed by the technical capabilities of

his hands. Consequently coinposers write types of figuration that are known

t o be practical and effective i n performance. T h i s tradition is always be-

i n g modified and extended, b u t regardless o f style changes there has existed

a standard core of performance skills that, can be expected of the pianist.

T h i r d , the piano, due to i t s mechanism, has no capacity t o sustain

a tone a t a constant volume. This deficiency is often compensated for

through use of repeated figures having c o n s t i n t and regular rhythmic impulses

that can either simulate or create the il lusion o f a sustained sound. The

inclusion of this type of textural filligree also facilitates smoother, more

graduai changes i n dynamics since there are, as a result , many more inter-

mediate 1evel s avai 1ab1e between any two dynamic 1evel s.



9

Fourth, and t h i s po i n t i s im po rt ant , m os t n i net een t h- century p iano

mus ic , in c l ud in g th e etudes under cons idera t ion here, f a l l s on the homo-

phonic s ide o f the l i n e a r independence continuum. The reason f o r the

homophonic b ia s i n mus ic o f t he Romantic pe r i od may be l i n k e d t o t h e s p e c i a

a t t r i b u t es o f t he p i ano i t s e l f . I n homophonic m us ic, i t i s d i f f i c u l t enough

t o determine what the hor izonta l components are, l e t a lone t o have t o at temp

t o q uan t i f y t h e i r deg ree o f independence. Because homophonic music i s n o t

as l i n e a r by de f i n i t i on , es tim a tes o f l i ne a r i ndependence seem les s i n f o rm-

at i ve and approp r ia te here than i n po lyphon ic works .

Because o f these fa c t s :

1) measurements o f 1i near independence are inappropr ia te fo rhomophonic music,

2) l i n e a r components a r e d i f f i c u l t t o i s o l a t e i n Romanticera piano music, and

3) methods f o r measur ing l i n e a r independence are no t pre c ise,even fo r po lyphon ic music,

t h e f a c t o r o f l i n e a r independence i s n o t examined i n t h i s s t udy . Th is fac-

t o r s ho uld s t i l l be con sid ere d a l e g i t i m a t e p a r t o f t h e d e f i n i t i o n o f t ex tu r

i n g en er al , b u t f o r t h e purp oses o f t h i s s t u dy and t h e p a r t i c u l a r body o f

music i t examines, i t i s n o t a p p r op r ia te . I n i t s p la ce , we s u b s t i t u t e a

c l a s s i f i c a t i o n s ystem based on t h e t yp es o f f i g u r a t i o n t h a t a r e used t o p r e-

se nt me lo di c and accompanimental components i n homophonic pian o music. T h i s

c l a s s i f i c a t i o n o f components i s n o t inten ded t o measure 1inear independence

a t a l l . I t s o n l y purpo se i s t o p r o v i de a sy st em a ti c s e t o f d e s c r i p t i v e

t erms w i t h w h ic h t o c a t ego r iz e t h e b road v a r i e t y o f t ex t u res i n homophonic

p iano mus ic . Chapter two exp la ins t h i s system f o r c l as s i f y in g p iano f ig ur -

a t i on .



Chapter I I

BASIC TYPES OF MELODIC AND

ACCOMPANIMENTAL PRESENTATION

Etudes are written specifically t o develop performers' competencies

by stressing particular performance skills. As a resul t , a principal text-

ural configuration t h a t involves one o f these sk i l ls i s used throughout

each of the Chopin and Scriabin etudes.

according t o the skills involved also serves t o classify these textural con-

figu ra ti ons. This method of classification i s advantageous because all the

Consequently, classifying the etude

textural configurations i n the etudes can be related t o a small number of

basic patterns.

of each, and explains how the Chopin and Scriabin etudes have been classi-

fied according t o this system.

This chapter examines six basic types, presenting examples

The most basic classification of typical piano texture distinguishes

between the two elementary functions i n homophonic music: melody and

accompaniment. Usually these functions are eas i ly distinguished because

they are delineated by separate components of the figuration, most commonly,

the right hand playing the melody and the l e f t hand i n accompaniment.

rrrarily, melody supplies horizontal content while accompaniment supplies

ve rt ic al content . However, there i s some overlap possible because melodies

often bear some degree of harmonic implication and accompaniments often bear

some degree of voice leading . Occasionally, a sing le component f u l f i l l s

both the melodic and accompanimental functions. A t other times the accom-

paniment will include a fairly independent line t h a t supplies an additional,

t h i r d component.

Pri-

B u t , i n general, melodic presentation and accompanimental



EXAMPLE 2 Scriabin Etude Op. 8 No. 8, mm . 1-3 12

Lcn t o (Tempr) ru b a t o j Nr.

melody in quicker tempo are commonly called "ve loc i ty s tud ies . " Very

tempos an d an emphasis on scalar passages characterize these pieces.

Chopin etude i n Example 3 has a figuration typical o f many of these p

Etudes belonging t o a second group, having a dist inct s ingle l ine

rapid

The

I;

A l t h o u g h velocity studies are one of the most common types i n

eces.

the

etude genre, Scriabin d i d not include any o f these i n his etudes. Perhaps

Scriabin was leary of this type because of the numerous pieces written for

sheer technical d isp la y since C h o p i n .

One characteristic of melodic presentation t h a t might be overlooked

without careful analysis i s the use of polyphonic melody as i n the case of

Example 4.



13

In polyphonic melody, one "voice"--at l eas t i t i s notated as one

voice--presents two or more related melodic ideas. T h u s , wh a t appears t o

be a single line can actually be regarded as two or more voices a t another

structural level that are combined by an unfolding operation 3r by a motion

t o and from inner voices." Notating the right hand on two separate staves

makes th i s re la tions hip apparent. Notice the simp1 i c i t y of the s tep-pro-

gression t h a t under1 ies this complex sounding melody,

EXAMPLE 5 Scriabin Op. 8 No. 2, mm. 1-2 with the melody renotated.

Although this melody may be derived from two l ines a t some given

level of structure, i t must s t i l l be considered a sing le- line type of

melodic presentation since i t i s perceived as one line a t the most imme-

dia te, surface level. This i s also a practical consideration because o f

the large degree of textural variation that can exist between structural

levels-

-each level can have a different "texture." To be rigorous,

" texture" should only refer t o the actual surface o f the music. After al l ,

12. Felix Salzer and Carl Schachter, Counterpoint i n Composition; TheStudy of Voice Leading (New York: McGraw-Hill , 1969 ) , 153-160.



14we use the phrase " r ough t tex t u re ' ' t o descr ibe an ob je c t whose su r faces a re

rough w i th ou t mak ing any in f e rences as t o i t s i n t e r na l compos it i on. An ex-

ample l a t e r i n th e c ha pt er a l s o i l l u s t r a t e s t h e n e ce ss it y f o r t h i s r e s t r i c -

t i o n (see pp. 21-22).

The Doubled Line

The second basic t y pe o f m el od ic p r e s e n t a t i o n c o n si s t s o f l i n e s

doubled i n s u i t a b l e p a r a l l e l i n t e r v a l s .

e tu d e w i th t h e r i g h t- h a n d p a r t d ou bl ed i n t h ir ds- -Op. 26 No. 6 and Op. 8

No. 10 r e s p e c t i v e l y .

t o a l a r g e e xte n t . The re i s a l so a marked s i m i l a r i t y between th e mo ti ve s

used i n the m idd le sec t ions o f these te r r a r y forms, as seen i n Examples 6

and 7. The resemblance o f these mot ives s t r on g l y suggests t h a t Sc r i ab in

might have consc ious ly imSta ted t h e Chopin Etudes, a t l e a s t i n t h i s case.

Chopin and Scriabin each wrote an

I n b o th o f t h e se th e me lo d i c l i n e s move ch r o ma t i ca l l y

EXAMPLE 6 Chopin Etu de Op. 25 No. 6, m i . 27-28.

EXAMPLE 7 Scr iabin Etude Op. 8 No. 10, mm. 53-60.



15

Each composer a lso wrote etudes wi th the r ight - hand p a r t doubled

*in s i x t h s . Example 8 shows t he opening o f th e one by Chopin.

EXAMPLE 8 Chop in Etude Op. 25 No. 8, mm. 1-4.

,

Not on ly does the r igh t hand p resen t the melody i n s i x th s i n t h i s

example, bu t the l e f t hand a ls o cons is ts o f s i x th s q u i t e o f t e n . The fu n c-

t i o n o f t he l e f t - h a n d s i x t h s i s most o f t e n accompanimental, i .e., i t

prov ides a harmocic scheme. But a t t im es t h e l e f t hand p a r t becomes melodic

as i n t h e second h a l f o f measure fo u r i n Example 8.

Melod ies doub led a t the oc tave abound i n p iano l i t e r a t u r e , mak ing

t h i s d i f f i c u l t f i g u r a t i o n an obvious s u b je c t f o r etudes .

No. 10 and Scriabin Op. 8 No. 9 e a ch g i ve t h e p i a n i s t p r a c t i ce w i t h o c ta ve s

Chopin Op. 25

i n b o th hands. A v ar ia t i on o f t h i s scheme occurs when one o r more notes

a r e f i l l e d b etween the o c tave s. The r i g h t hand o f Sc r ia b in ’ s Op. 8 No. 7

i s a case i n p o in t .



EXAMPLE 9 Scr iab in Etude Op. 8 No. 7, mm. 1-2.16

The question i s whether or not the added middle pa rt 's ro le i s t o

reinforce the melodic function or the accompanimental function. Jus t be-

cause these notes are played in the same register as the melody does not

necessarily mean t h a t their function is likewise melodic. Tt,e middle note

of the right hand i s not linked t o the melody a t any certain interval, nor

does i t always move i n the same direction as the melody.

determined by the harmony and the doub l ings of the accompaniment.

the rhythm and register of this line obviously 'reinforce the melody.

i s an instance where Berry Is termi no1ogy for 1i near independence is useful .He would cl as si fy this l ine as "homorhythmic-heterodirectional-contrain'er-

val l ic , " which provides a concise description, b u t does not clarify the

original problem of determining function.

I t s pitch i s

B u t ,

Here

Since the types of figuration are determined by the technical de-

mands of the music, i t i s logical then t h a t this question should also be

seen from the performer's point of view. The added p a r t , in terms of

performance, belongs w i t h the melody. This decision re sts on th e similar-

i t y w i t h the melody o f the p a r t i n question, and on the basis of factors

such as ar t iculat ion, rhythm, and re gi st er . If a decision must be made,

then this added part can be said t o serve primarily i n a melodic role; i t s

accompanimental characteristics, however, should not be forgotten.

In summary, there are two basic types of melodic presentation:

the single line and the doubled li ne . The former i s divided into legato



17

s tud i es and v e l oc i t y s t ud i es .

doubled t h i r d s, doubled s i x t hs , and doubled octaves. One shoJ ld b ea r i n

m in d t h a t t he se l i m i t e d c a t e g o ri e s a r e a p p r o p r ia t e o n l y f o r t h i s b ody o f

music.

cause o f t h e s t y l i s t i c c o n s tr a i nt s o f t h e p er io d.

may be fou nd i n works i n d i f f e r e n t s t y le s .

The l a t t e r i s d i v id e d i n t o t h r e e types:

D oubled l i n e s a t o t h e r i n t e r v a l s a r e n o t f ou nd i n t he se e tu des be-

However, ot he r doubl ings

13

Chorda l F igura t i on

The most elementary accompaniment s t y l e i s th e s imp le chordal f i gu r-

at io n, such as th e one found i r . S c r i a b i n ' s Op. 8 Nos. 8 and 11.

of these e tudes th e chords a re p re sen t i n both the r i s k t - and left- h a n d p a r t s

I n each

an a rrangement t h a t requ i res t he r i g h t hand t o p l ay t he mel ody and a pa r t o f

t h e accompanifient a t t h e same t ime. i ' h i s p ro ce du re c an r e s u l t i n p i ec es

tha t sound decep t i ve l y easy s ince the l i s tener hears on l y a me lody suppor ted

b y cho rd s, w i t h o u t r e a l i z i n g t h e c o n t r o l r e q u i r e d t o p l a y s i mu lt a ne o us ly

t

co nt ra s t in g dynamics, a r t i cu la t i o n s , and/or rhy thms w i t h one hand.

One should note that the accompaniment i n Op. 8 No. 8 can be div ided

i n t o two p a r t s due t o t h e bass l i n e , which, i n a d d i t i o n t o i t s s ep ar at e

re g i s t e r , has some me l od i c c ha ra c te r i s t i c s o f i t s own. T h i s mel od ic i nde-

pendence r es u l t s i n a tex tu re made up o f th ree separa te s t r a ta as shown i n

Example 10

EXAMPLE 10 Scriabin Etude Op. 8 No. 8 mm. 1-3.

Lento (Tempo r uba t o ) Nr. 8

13. For example, see the l a s t se t o f e tudes by Scr iab in , Op. 65 Nos. 1,2,and 3.



18

In i t s simplest conformation, homophonic music con si st s o f two

strata--one melodic and the other accompanimental . Yet, as later examples

will show, the number of strata can vary greatly, from just one to four or

more.

The Chopin etude in Example 11 i s arranged i n three s t ra ta as was

Example 10, b u t with one major difference: th e chordal stratum i n the

middl e requires two hands to perform.

Example 11 Chopin Etude Op . 25 No. 4 , mn. 9-12 .

As before, the r i g h t hand has both melody a n d chords, and now thel e f t hand has the bass line and chords also. The l e f t hand must skip a

sizable distance i n order t o play both par ts. The major technical d if f ic ul t

of this piece is the accurate extecution o f these large leaps.

occur i n b o t h hands o f the following example.

Large leaps

EXAMPLE 12 Scriabin Etude Op . 8 No. 5, mm 1-3.



19

Here

components:

i t i s possible t o consider the texture i n four different

a me1ody i t s chordal accompaniment, a counter-me1 ody or

and i t s accompaniment.

separate staves.

Example 13 shows the different strata

EXAMPLE 13 Scriabin Etude Op. 8 No. 5, mm . 1-3 renotated.

notated

In a

The constant

separate the

"echo I

on

chordal figuration, large 1eaps can suggest additional strata.

leaping from one register t o another causes the listener to

events int o dis cret e groups. The ef fe ct i s similar to the

polyphoriic melody discussed

easily perceived t h a t i t i s

phoni c me1ody requires some

Because the large change i n

ea r l i e r a l t h o u g h i n this case the effect

apparent on the surface level while the

abstraction o n the p a r t of the l i s t ener .

i s so

P O ' Y -

register can i n effect add another stratum t o

the texture, types of chordal figuration must be further divided i n t o two

subcategories--one simp1e and one w i t h large leaps.



20

Arpegyiated Figurations

The second type of accompaniment is the arpeggiated figuration,

which i s a chordal unit presented in a simple linear fashion, either ascend-

i n g or descending. This type o f presentation can be divided i n t o two sub-categories, distinguishing those t h a t require more t h a n one hand-position

from those t h a t can be played i n a single position, L e . , when all the notes

can be reached without lifting the hand or turning t he thumb under the finge

The left-hand par t o f Chopin's Op. 25 No. 1, the "harp" etude, is an example

of the single hand-position arpeggio. In this figuration there are usually

only four pitches in each arpeggio allowing the hand t o remain in one posi-

tion even t h o u g h the figure covers a large span.

EXAMPLE 14 Chopin Etude Op. 25 No. 1, mrn, 1-2.

The second subcategory of arpeggiated figuration i s shown in the

following example from the "revolutionary" etude.



21

In this example the five or more pitches i n each figu re make i t

necessary for the thumb t o turn under i n every arpeggjo. The passing

motion, c - d - eb - d - c, smooths o u t the figure and rounds off its linear

contour.

A1 ternating Figuration

The t h i r d type of accompaniniental f iguration i s similar t o a tremolo

I t cons ist s of an al te rn at io n between two notes or groups of notes.ef fect .

The t h i r d etude o f S c r i a b i n ' s Op. 8 uses this figuration in both hands.

EXAMPLE 16 Scr iabin Etude Op. 8 No. 3, mm. 1-

4.

I f Example 16 contains accompanimental figures in both hands, then

where i s the melody?

1ines and el i m i n a t i n g octave doubl ings , the texture changes radically, re-

veal i n g the familiar texture o f a four-voice choral e.

By l i n k i n g every other note of the figuration into

EXAMPLE 17 Reduction o f Example 16



Consi dered

presents the 1eve1

the melody and the

22

from the viewpoint o f " layer analysis," Example 17

directly beneath the actual foreground. A t this level

linear nature of the remaining voices become clear. I t

appears t h a t the melody actually exists on a more remote level t h a n the

accompanimental figuration.

surface level due to the alternation. B u t since the actual texture, < . e . ,

the texture a t the most foreground leve l, i s generated by l ine ar motion,

one can easily extract the linear motion of the underlying level. Thi s

example can, a t l eas t a t the foreground level, consist of only accompani-

mental f i gura t i on.

Strictly speaking, there is no melody a t the

Convoluted Figuration

The fourth type of accompanimental presenta tion i s designated here

as the "convoluted" figurat ion . This type cons ist s of any regu lar ly repeat

ing pattern o f chord tones which has a linear contour t h a t changes direction

often.

tones are sounded i n an irregular order, i . e . , i t produces a contour t h a t

cannot be described as ascending or descending, b u t has a specific organi-

zation t h a t controls the contour . The Alberti bass of the Classical era

provides a simple example of this type.

ation i n his etude i n Bb minor, shown in Example 18.

The convoluted figuration can be considered a broken chord whose

Scriabin uses the convoluted f igu r-

EXAMPLE 18 Scriabin Etude Op. 8. No. 7, mm . 1-

2.

Presto tenebroso, a g i t a t o Nr. 7



23

The f i g u r e i n th e l e f t- h a n d p a r t r e pe a ts e v er y s i x t h e i gh th-note ,

i n a pa t te rn th a t can be gener a l l y desc r ibed as lea p ing down-up-down-down-

up-down w i th the upward leaps land in g on th e bea t. Th is p a r t i c u la r pa t te rn

has an ambiguous harmonic rhythm which S c ri a b i n emphasizes t hro ug h t h e beam-

i n g o f t h e e ig hth-notes and the phras ing marks o f t he l e f t hand. The har-

monies change ev er y two beats, w i t h each new harmony beg in ni ng two ei g h th -

notes b e f o re t h e f i r s t and t h i r d be at of t h e measure, r e s u l t i n g i n a ha r-

monic r h yt hm t h a t i s o u t o f phase, o r d i s p l a ce d i n r e sp e c t t o t h e r h y th m ic

i m p l i c a t i o n s o f t h e me te r.

Example 19 i l l u s t r a t e s an i n t e r e s t i n g v a r i a t i o n o f t h e c on vo lu te d

f igurat ion used by Chopin.

EXAMPLE 19 Chopin Etude Op. 10 No. 9, mm. 1-3.

Allcgro, :nolto agitato :to.)

Conta ined w i t h i n the upper pa r t of the accompanimenta l f ig ur e i s

a countermelody. Once again, t he re i s a me lod ic l i n e nes ted w i t h in th e

accompaniment. Th is r e s u l t s i n a t e x t u r e c o n s i s t i n g o f t hr ee s t r a t a l i k e

those i n e a r l i e r examples, except th a t i n t h i s case , the harmon ic suppor t

i s b elow t h e tw o m el od ic l i n e s i n s t e a d o f between them.

Summary

An ou t l i n e i s p res en ted here t o summarize t he t ypes o f f i g u r a t i o n

discussed i n t h i s c h a p t e r .

make use o f t ha t t ex tu re as a pr in c i pa l component o f t he p iece .

F o l lo w i ng each t y p e a r e l i s t e d t h e e tu de s t h a t



24

S c r i a b i n ChopinEtudes Etudes

Op./No. Op ./No.

1. Melod ic p resen ta t i on

A. S i n g l e l i n e

1. Legato study

2. Ve loc i t y s tudy

B. Doub led l i ne

1. Doubled i n oc taves

2. Doubled i n t h i r d s

3. Doubled i n s i x t hs

11. Accompanirnental presentation

A. C h o r d a l f i g u r a t i o n

1. Simple

2. Large l e q p s

B. A r p e g g i a t e d f i g u r a t i o n

1. One hand-pos i t ion

2. More than onehand-posit I on

C. A1 t e r n a t i n g f i g u r a t i o n

D. Conv o l u ted f i gu ra t i on

8/8 8/11 10/6 25/7

--- 10/2 10/4 25/2

8/9 25/10

8/ 10 25/6

8 16 2518

--- 10/11

8 15 25/4

--- 25/ 1

8/2 8/4 10/8 10/12

8/1 813 10/10

8/7 8/12 10/9 l o l l 0



25

Nine of the twenty-four Chopin etudes are not included here i n any

o f the above categories. This is done for two reasons:

contain textures which are combinations or special variations of the above

types. For instance, Op. 25 No. 9 has Ile alternating e f f i x t combined with

a melody doubled i n octaves for the right-hand p a r t , representing a mixture

o f types.

First, these etudes

EXAMPLE 20 Chopin Etude Op. 25 No. 9 , mm. 1-4.

Assai allegro (J=i iz . )

Op. 25 No. 12 uses a variation of the arpeggiated type. The unique

aspect i s the use of repeated notes each time the figure moves an octave.

This allows the constant exchange o f the f i r s t and fi f th finge rs, which

means the hands can transverse the keyboard wi thou t ever t u r n i n g the t h u m b

underneath the other fingers, as i s usual for an arpeggiated figure.

the p i a n i s t , this i s a completely di ff er en t technical s k i l l . Compare

Example 21 t o Example 15.

EXAMPLE 21 Chopin Etude Op. 25 No. 12, mm. 1-2.

For



f

26

These combina tions o r spec ia l v a r i a t i ons o f t he f i gu ra t i on t ypes

i n the n ine rema ining etudes cou ld be inc l uded i n the ca tego ry sys tem by

creat ing new designat ions. Bu t th i s i s no t des i rab le because o f t he second

reason f o r excludi ng these etudes: they have no d i r e c t l y comparable coun ter-

p a r t s i n t h e et ud es o f Sc r i a b in . The puw os e o f t h i s c ha pt er i s t o p r ov i de

l a b e l s f o r t h e t e x t u r e s common t o the two composers i n o rder t o make mean-

i n g f u l comparisons. Although one coul d sp ec if y more and more types, t h i s

procedure wou ld no t benef i t the present s tudy s ince i t would d imin ish the

bases for the comparison o f t ex tu re .



Chapter I I I

DENSITY

As i t is presented i n chapter one, the investigation of texture i n

piano music texture involves three major categories:

mental presentat ion, dens ity, and range. The second of these, density,

concerns the number of components sounding a t one time and the r e l ? , t i v e

spacing of these components. This chapter examines th e Chop in and Scriabin

etudes with respect t o their textural density.

explanation o f the fundamental concepts and terms dealing w i t h density.

Then i t describes the general precedure adopted here for examining the etude

and follows w i t h a comparison of the types of accompanimental presentation

a n d their use by each composer.

Discussions of textural density often contain descriptions such asl ight lheavy or t h i n / t h i c k without p i n p o i n t i n g exactly what is meant o r how

these characteristics are t o be measured.

ambiguous because they can refer t o many different aspects o f texture,

including the number of melodic lines, the tonal color, the instrumentation,

the dynamic levels, and the relative proximity o f the l ines.

terms can connote so many different t h i n g s , the adoption o f a more precise

melodic and accompani-

I t begins w i t h a de ta i l ed

In addition, these terms are

Since these

vocabulary i s essential .

vides some terms t h a t are more precise in their description of textural

components. Those re1 evant t o density incl ude "densi ty-number,I "texture-

space," and "density-compression .

In his Structural Functions in Musics Berry pro-

The following discussion examines

14. Berry op. c i t . , 209, 249.

27



28

these and two new terms, " ve r t i ca l sp a n" and " spac ing- d is t r i bu t ion . ' '

V e r t i c a l span i s s u b s t i t u t e d f o r t h e c on ce pt o f t e xt ur e-space due t o t h e

l a t t e r ' s i na pp ro pr ia te ne ss f o r t h i s s t u d y .

Density-number

Density-num ber r e f e r s t o t h e number o f p i t c h es i n a v e r t i c a l u n i t .

For example, t h e density-number i s f i v e i n t h e f o l l o w i ng c hord.

EXAMPLE 22 Chopin Etude Op. 10 No. 2, f i n a l meas.

m

Obviously, th e densi ty-number i n pc lyphon ic music i s e q u i v al e n t t o

th e number o f vo i ces i n t h e te x t u r e ( p r o v id e d th e r e a r e no systemat ic doub l -

i ngs ) . However, i n Example 22 which i s homophonic, most o f th e ho r i zo nt a l

p a r t s a r e l e s s c l e a r l y d e f i n ed and ten d t o merge i n to v e r t i ca l f o rma t io n s .

The l a c k o f h o r i z o n ta l d e f i n i t i o n causes th e ve r t i c a l u n i t s , i .e . , t h e

chorda: s t ru ct ur es t o tak e on mors prominence -n t h e mus ical s t r u c t u r e .

When density-number no l onger re fe rs t o t he number o f voices, i t mu s t r e fe r

t o t h e number o f p i t ch e s i n each ch or da l s t r u c tu r e .

number i n homophonic music does n o t always c orrespond ex ac t ly t o t h e number

o f "par ts . I'

As a r e s u l t , t h e d e n s i t

A c c w d i n g t o Ber ry, dens i ty-number r e fe rs t o th e number o f p i t c h e s

w i t h i n a v e r t i c a l u n i t which, i n respe ct t o homophonic music: o f t h e n i n e-

teen th cen tu ry, can be de f ined as a pa r t i c u la r chordal u n i t . W ith t h i s i n



29mind, one can see that the notated duration of pitches might not overlap

a t any point, and yet they can function harmonically as par t of the same

chordal u n i t . Consider the left-hand part of the Scriabin etude i n Example

23.

EXAMPLE 23 Scriabin Etude Op. 8 No. 12, mm. 1-2.

All of the pitches i n the lef t-hand part express tonic harmony. When the

horizontal motion o f the accompanimental f igurat ion i n t h i s passage i s r e-

duced to long notes, as shown i n Example 24, the chordal u n i t can be seen

to have a density-number of seven.

EXAMPLE 24 Figuration reduction G f the lef t-hand part of Example 23.

a

71

Notating the pitches of an accompaniment as a block chord makes i t

easier not only to observe the density-number, b u t also the other measure-

ments of density as well. Because the melody functions predominantly i n

the horizontal dimension and only secondarily implies an underlying harmonic

foundation, no attempt will be made t o reduce the r i g h t hand of Example 23

t o a ve r t i ca l s t ruc tu re .



30

Vertical Span

"Vertical span" i s a measurement of density which i s proposed t o

replace Berry's term "texture-space" as a n a1ternative more appropriate to

th i s study. Both refer t o the same characteristic o f texture. To under-

stand the reasoning for this substitution requires examining both ideas.

Berry defines texture-space as

. . .the field enclosed by " l ines" tracing the ? i t c hsuccessions of outer components in addition t o thetwo vertical, or diagonal , "1 ines" 1inking componentsa t " l e f t- r i h t " extremeties a t some 1 w e l of givenstructure. 18

In other words, texture-space is the field delineated by the outer-

most parts. I t i s a two-dimensional shape t h a t points ou t how gradually

o r suddenly the relative changes i n regis ter and range occur. Example 25

shows an analysis of texture-space by Berry of the Handel Prelude from

Suite No. 3 in D minor for Harpsichord.16

EXAMPLE 25 Synopsis of inflation and contraction of the texture-space

as expressed i n contradirectional relation of outer components.

15. Berry op. c i t . , 249.

16. Berry op. c i t . , 254.



31

The concept of texture-space i s most useful i n dealing w i t h "text-

ural progressions'' within a piece and with how these progressions affect

the development o r , i n La Rue's terms, the "growth" of the music. The

emphasis of ' this study, however, i s not placed on the progression of texture,

! ) u t rather on measuring textural density on an absolute scale, in order t o

faci 1i tate comparisons between pieces . I 7 An absol Ute scale permits measure-

ments independent of any arbitrary reference p o i n t . For example, "thick "

chords require a reference chord t h a t is thinner (or "nornial ' I ) for the term

"thick " t o have meaning. The same chord might seem t o be "thin" when ccm-

pared t o a different reference chord. Nevertheless, a chord with a d e r s i t y -

number of seven retains t h a t density-number no matter what the coinparison

might be.

Because i n Berry's scheme, texture-space has a referential nature

that i s quali tat ive rather t h a n quantitative, and its emphasis i s d i rez ted

toward textural progression, this concept will not be useful, as such, i n

this study.

vert*ical s p a n s h ij be used.

Instead the quantitative correlate of texture-space, i .e.,

The term vert ical span i s proposed as a descrip tion of the expanse

of each vertical u n i t measured indiv idual ly. In other words, i t is the span

measured i n terms of the number of semitones from the lowest to 'he highest

pitch i n any particular vertical u n i t . This breaks the texture-space i n t o

discrete units that can be measured quantitatively, similar t o the wayanalog information i s convarted t o d i g i t a l information.

17. For an analysis of textura l progression, see Calvin E. Holden, TheOrganization of Texture i n Selected Piano Compositions of C1 a u d r -Debussy. Dis ser tat ion, Universi ty of Pittsburgh, 1973.



32Densi ty-Compression

Density-compression i s Ber ry 's term fo r the number of p itches w i t h -

in a particular vert ical span.

w i t h i n the span o f two octaves and a f i f t h .

were spread out over a vertical span o f five octaves, then the density-corn-

pression would be much lower.

octave, then i t would be much higher.

i s t he r a t i o o f density-number to vertical span.

In Example 24 above, there are seven pitches

I f the same number of pitches

I f the vertical-span were reduced to one

Stated precisely, density-compression

In order to make all measurements o f density-compression easy to

compare, all the ratios in this study are converted to a number o f pitches

per one octave span.

number divided by the vertical span measured in semitones multiplied by

twel ve semi tones per octave:

Numerical l y , the densi ty-compression equal s the density

Density-number x 12

Vertical spanDensity-compression =

For instance, in Example 24 there are seven pitches w i t h i n a vertical span

o f 31 semitones.-

Density-compression = x 12 = 2.7131

When measuring density-compression one should realize t h a t the rat io

of pitches per octave span does n o t necessarily represent the subjective

impression o f density. This impression i s a f f ec t ed by the degree o f disson-

ance involved i n the vert ical s tructure, as well as by the regis ter i n

which i t i s heard. For instance , four tones which involve many semitone

relationships might sound more "dense" than four notes involving mostly

tertian relationships, even though the latter i s compressed into a smaller

vertical span. B u t dissonance i s more properly a n aspect o f the harmonic



33domain t h a n i t i s of texture. In addition, the subjective impression of

dissonance is difficult t o quantify. Therefore,

. . . i t i s a convenience t o regard the evaluation of dissonanceas a distinct parameter. . ., considering density [density-coin-pression] as the simple r a t i o of number t o space.18

The same reasoning justifies excluding evaluations of register from

the determination of density-compression.

transposed down i n t o a lower register, i t will sound more dense t han i t

originally did.

i n t o a range t o which our ears are more sensitive. Again however, this

effect can not be quantified i n t o the measurement of densi ty-

compression.

I f an arrangement o f notes i s

This eff ec t i s probably due t o the overtones being shifted

Spacing-di stri butio n

Berry does not provide a term t o designate the vertical arrangement

of the spacing, This component of texture is , nonetheless, an important

factor in the analysis of textural density. For instance, the figuration

shown earlier in Example 23 spans two octaves and a fifth, has a dens i ty-

number of 7 , and a density-compression o f 2.71 pitches per octave.

information does n o t show how the notes are distributed w i t h i n the vertical

space.

centrated a t one extreme. The term spacing-distribution i s proposed for th i

component of textural density. I t may be defined as a description of the

pattern o f pitch distribution w i t h i n a particular vertical unit .

B u t th i s

The pitches could be evenly spaced, o r several pitches could be con-

Spacing-distribution is a component of density that may be more

usefully characterized i n general than as an absolute quanti fic ati on. To

specify the distribution of p-itches within a vertical span precisely would

18. Berry, op. c i t . , 209-10.



34

require a complete li s t i ng of the intervals present. The re su lt s of such

a procedure would be more cumbersome t o cope with than the original nota t ion

of the niusic t h a t was t o be described. Obviously th i s would have l i t t l e

benefit t o any analys is . The more sensible option i s t o generalize the

character of the arrangement by pointing out certain dist inctive f e a t d r e s .

For example, the spacing-distribution o f Example 24 seen earlier could be

characterized as a symmetrical arrangement with open spacing a t the extremes

an d concentrated i n the center.

To summarize, a pa rt ic ul ar vert ical arrangement, a t some given level

has three quantitative parameters:

present i n a vertical structure, 2 ) vertical span--the expanse or space the

ver tica l str uc tur e occupies, and 3) density-compression-- the number of p i t -

ches per octave span.

spacing-distribution, which concerns the pitch distribution pattern within

the vertical span.

1) densi ty-number--the number of pl tches

In a d d i t i o n , there is one "descriptive" parameter,

Density i n the Etudes

Because the vertical structures i n the etudes are typically presented

i n the accompaniment and not i n the melody, though harmonies m i g h t be implied

by linear motion, the rest o f this chapter examines those etudes i n which

the principal textural components have accompanimental functions. A repre-

sentative section o f each of those etudes i s reduced o r abstracted t o i t s

vertical structures. This reduction o f the figuration makes a l l the char-

acter i s t i cs of density read ily apparent. The measurements b k e n from these

reductions are compiled in Table I for the comparison o f various accompani-

mental figuration types and o f the averages for each composer.



Tab1 e I . DENSITY IN ACCOMPANIMENTAL FIGURATION

Etude Density- Vertical Density- SpacingOp/No. Number Span Compression Distribution

Convoluted Figurations

10/9 410 / 10 58/ 7 58/12 7

Average 5.25

Arpeggi ated Figura tions

19192436

2.53 closed a t t o p3.16 closed a t t o p2.50 closed in Riddle2.34 closed -in middle

10/8 12 44

10/ 12 5 245 28

2 18/ 28/4 3

24.50 2.63 - - -

3.27 closed

2.50 open a t bottom2.14 closed in middle1.71 open evenly

Average 4.34. 24.34 2.12 ---

Figurations w i ' t h Large Leaps

25/4 58/ 5 5

Average 5 .OO

A1 ternating Figurations

8/ 1 48/ 3 4

Average 4 .OO

31 1.94 closed a t t o p31 1.94 open in middle

3 1 O 1.94 ---

24 2 .oo open a t bottom19 2.53 open evenly

21.50 2.27 ---

Averages f o r Each Composer

Chopin 4.75 23.25 2.53 closed a t t o pScriaOin 4.71 26.14 2.16 open a t t o p

* Etude 10/8 i s no t averaged ( see below, pages 36-37)



36

With respect t o the measurements i n Table I , one should note that

the density-compression averages can be determined by two a1 ternative

methods which give slightly different results.

is the one used i n this study, the res ult i s obtained by averaging the

various measurements of density-compression of the individual etudes with-

i n the appropriate type.

average densi ty-compression from the average densi ty-number a n d the aver-

age vert ical span. The f i r s t method 5 s used here because i t i s calculated

direct ly from the original measurements and does not; involve any f igures

from previous averaging processes , as does the more indirect,

second method

In t he f i r s t method, which

The second method involves the computation of the

Comparing the averages for the various types of accompanimental

presentation reveals t h a t the etudes with convoluted figurations have the

highest densi ty-numbers and the highest densi ty-compressions. This type

has the second largest vertical spans, b u t i t should be noted t h a t there

i s only a difference of three semitones between three of the four types.

The etudes w i t h arpeggiated figurations include one, Chopin's

Op. 10 No. 8, whose vertical structures are radically different from any

of the others. This etude has a density-number o f 12 and vertical span of

44, which are about twice the magnitude of the other arpeggiated etudes.

Its density-compression is also higher than that of the other etudes. The

reason for this wide discrepancy is t h a t the arpeggios of the etude occur

i n the r i g h t-

h a n d p a r t and the melody i s i n the left-

hand par t. This

reversal of roles places the arpeggios i n a drast ical ly dif ferent regis ter

of the piano.

this register make the validity of any comparison of density questionable.

Another important factor i s the prominence of the arpeggios and the rela-

tive insignificance of the melody i n the le f t hand. Normally melody i s a

The different tonal qualities and faster decay times o f



37foreground event with accompaniment being background. l9 The accompani-

m en ta l f i g u r a t i o n su p p l i e s more co n t e n t t o t h e co m p o s i t io n th a n does t h e

melody and t h e r e f o r e i s n o t l i m i t e d t o t h e s u b s er v i a n t r o l e o f bac kg ro und .

Because o f these substant ia l d i f fe rences Etude Op. 10 No. 8 i s n o t computed

i n t h e averages f o r i t s t y p e o r f o r C h o p i n ' s o v e r a l l a ve ra ge s o f d e n s i t y .

The e t u de ca nn o t be e n t i r e l y d e le t e d f r om th e stud y, however, on , t h e b a s i s

o f the above reasons.

accompaniments w i t h r e sp e c t t o b a s i c t yp e s o f p r e se n t a t i o n ar ld w i th r e sp e c t

t o r an ge .

I t i s s t i l l a l e g i t i m a t e e xample o f a rp eg gi at ed

The re m a in ing t h re e e t u d es w i t h a rp e gg ia t ed f i g u r a t i o n s h ave a n

average density-number o f 4.34. The v e r t i c a l span, as ment ioned above, i s

v e r y s i m i l a r t o t h e c o nv o lu t ed t y pe . The dens i t y -compresc ion l i s t e d f o r

t h e a r p e g g i a t e d t y p e r e v e a l s t h a t Chopin p re f e r s a rpe g gio s wi th r e 1z t i v e l y

c lose spac ing wh i le Scr iab in p re fe rs a more open spac i l ig .

The accompaniments w i th la rge leaps are the onl, : t y p e o f f i q u r a t i o n s

t h a t h a ve a su b s t a n t i a l l y d i f f e re n t a ve ra g e m e a su re of v e r t i c a l s p a n . T h i s

ra d i ca l l y h i g h e r a ve ra g e m u s t b e e xp e c t e d s i n ce t h e co n s t a n t l e a p in g o f t h e

hands w i l l n e c e ss a r i l y in c re a se t h e span o f t h e p i t c h d i s t r i b u t i o n . The

l a r g e r v e r t i c a l spans o f t h i s t y p e p ro du ce lo w er d en si ty- compression becaus

the same number of p i t ches a re be ing sp read ove r a la rge r space .

i n t e r e s t i n g t h a t a1 t ho ug h t h e f i g u r a t i o n w i t h l a r g e l e a ps g en er at es t e x t u r e

w i t h m o re s t r a t a , i t has, a t t h e same t ime, lowe r density-numbers and den-

s i ty- compress ions. Perhaps th e com plex i ty o f numerous t ex tu ra l s t r a t a com-

pensates for reduced dens i t ies .

I t i s

19. F oreg ro un d and b ackg ro un d h e re do n o t r e f e r t o l e ve l s o f s t r u c t u r e ,b u t t o t h e r e l a t i v e d egrees o f i n t e r e s t and c on te nt--perhaps theys h o u l d b e c a l l e d l e v e l s r f perceptual immediacy.



38

The t yp e o f f i g u r a t i o n f ou nd l e a s t o f t e n i n t hes e etudes i s t he

a 1 t e r n a t i n g t yp e. The averages of th e dens i ty-numbers and the vert ical span

su gg est a r ea so n f o r i t s in f r e q u e n t use . The a l t e r n a t i n g f i g u r a t i o n i s t h e

most re s t r i c t i v e ty pe , havi ng bo th t he l owest dens it y-number and the smal l-

e s t v e r t i c a l s p a n .

n o t p e r m i t as much tex tura l complex i ty as do the o ther t ypes .

I t appea rs t ha t t he c ons t ra i n t s o f t h e f i g u r a t i o n do

Di f ferences between the two composers' use o f t e x t u r a l d e n s i t y

ov er a l l are very min imal . One cha rac te l - i s t ic d i f f e r e nc e i s t h e i r p r ef e r-

ences of spacing- d i s t r i bu t i on .

Chopin 's spacing i s r e l a t i v e l y c l c m wh i le Sc r ia b in ' s i s more open. Wi th

regard t o th e d i f fe rences be tween the composers, the o ve r a l l averages f o r

I n t h e t o p p o r t i o n o f t h e f i g u r a t i o n s ,

o the r fac to r s a re s l i g h t when compared t o the amount o f v a r i a t i on observed

between the types of f ig ur at io n. Th is f ind in g suggest; t h a t the two com-

p ose rs d e a l t w i t h t h e t e x t u r a l p o s s i b i l i t i e s o f each t yp e i n approx imate ly

t h e same manner, o r perhaps, were guid ed by th e same c c ms t r a i n t s . I n etudes

composers str ive for t e x t u r a l c om pl ex it y i n o r de r t c j chal lenge the per former

It i s p o s s i b l e t h a t each t y p e o f f i g u r a t i o n h a s l i m i t s o f t e x t u r a l d e n s i t y

t h a t cannot be exceeded wi th ou t compromis ing t he mus ica l q u a l i t y o f t h e

works. These l im i t s , whe ther techn ica l o r s t y l i s t i c , c ou ld account f o r t h e

m a r k e d s i m i l a r i t i e s .



Chapter I V

RANGE

Range, l i k e o t he r a t t r i b u t e s o f t e xt u re , s u f f e r s f ro m a l a ck o f

i nves t i ga t i on . Moreover , no pre c i se o r o b je c t i ve da ta have been p v s e n t e d ,

no r has an adequate termin olog y been developed t o deal w i t h range. These

l i m i t a t i o n s a r e p r o ba b ly due t o t h e a pp ar en t s i m p l i c i t y o f t h e c on ce pt .

Range is commonly defined as the extreme expanse encompassed from the low -

e s t t o t h e h i g h e st p i t c h w i t h i n a c om po si tio n.

determined by the two extreme pi tches.

because t h e amount o f i n f o r m a t i o n i t p ro vi de s i s ve ry l i m i t e d .

t h e f a c t t h a t a pi an o p ie c e o f o n l y f i f t y measures may contain over a

thousand notes. A sample o f two o f these notes cannot be expected t o re -

veal much about the piece as a whole. An a l t e r n a t i v e a pp ro ach would be to

c onc e iv e o f r ange i n a manner s im i l a r to the concep t o f tess i tu ra . Accord-

i n g t o t he Harvard D i c t i o n a r y o f M us ic , t e s s i a t u r a ". . .d i f fers f rom range

i n t h a t i t does no t take i n t o accoun t a few i so la te d no tes o f ex t r aor d in -

a r i l y h ig h or low p i t c h . " 2 0 Thus one could s ay t ha t t es s i t u ra c onc e rns

the p i t c h range used most o f t en , i n c on t ra s t t o t he ex treme range . Un fo r tun

a t e l y t he r e i s no c l ea r c u t way t o de te rm ine wh ic h p i t c he s s houl d be e l i m i -

nated because they are " e x t r a o r d i n a r i l y h i g h or l ow." For instance, how

many times should a p i t c h appea r i n a p i ec e t o be c ons ide red " w i t h i n t h e

I n o the r words, range i s

Such a d e f i n i t i o n i s in ad eq ua te

Consider

~~~ ~~~~~~ ~ ~

20. Apel, op. c i t . , 839.

39



40

t e s s i t u r a ? " Should te ss i tu r a be based o n ly on the number o f t imes each

p i t c h appears , o r should dur at i on va lues a l so be considered? No m at t e r

what t he answer, t h i s t ype o f concept r eq u i r es examining every no te o f t he

music and apply ing s t a t i s t i c ? l procedures t o ob t a in a mean ing fu l r e su l t .

Such an approach would be too invo lved to be jus t i f ied, even i f an accept-

a bl e d e f i n i t i o n o f " ex t raord inary " could be found.

Range-average

A procedure t h a t would seem t o o f f e r a reasonable compromise betwee

examining on ly two notes and examining every note, inv olv es t h e use o f a

sampling process. By d i v i d i ng a c ompos it i on i n t o a c onv en ien t l y l a rge num-

ber o f segments, th e extreme h i g h and low pi tch es i n each segment can serve

as re pr es en ta t i ve samples o f the whole. These samples can the n be averaged

t o p r o d w e a "range-average." This averaging process m i i g a t e s t h e e f f e c t

of e x t r a o r d in a r y p i t c h e s w i t h o u t ha v in g t o d e f i n e c r i t e r i a w i t h w hi ch t o

id en t i f y them. The re su l t in g " range-average" i s a c tu a l l y a compromise be-tween th e ideas o f "extreme range" and " t e s s i t u r a ." l t has the advantage

o f being more representat ive than the ex t reme range whi le

o v e r l y inv ol ved process f o r i t s determi n a t i o n .*

The fo l lowing procedure was used t o de te rm ine the

Each etude was d i v i de d i n t o from te n t o t h i r t e e n segments

equal le ng th . The hig hes t and l owes t p i t c h e s o f bo t h t he

n o t r e q u i r i n g an

range-averages.

o f approx imate ly

l e f t - a n d r i g h t -

hand parts were recorded separately f o r each segment. The pi tches were the

conver ted t o numer ica l va lues us i ng th e s tandard key-numbers found on piano

(subcontra A i s key number 1, f i v e - l i n e C i s key number 88). T h i s ope ra t i o

f a c i l i t a t e s t he com pu ta ti on o f av erages . A lt hough t he p iano has no i n t e r -

va ls sm al l er than a semitone, the averages were ind ic ate d w i t h i n a te n th

o f a semitone, due t o th e pr ec is io n o f t he computat ion. Wi th te n o r more



41

samples , t en t hs o f a sem i tone i n the average have been regarded as s ign i f i -

ca n t f i g u r e s . T h i s co n ven t i on a l so re mind s t h e r e a de r t h a t t h e r an ge-

averages a r e based on severa l p i t che s and do no t repre sent an act ua l no te

o f th e composi t ion . The s i z e o f t h e i n t e r v a l b etween t h e l o w and h ig h

averages measured i n semi tones was a l s o computed. T h i s i n t e r va l i s re-

f e r r e d t o as t he " range-span. I'

For a s imp le example o f t he procedure , imag ine a p i e ce o f m u si c

d i v i de d i n t o two s e c t i o n s o f e qu al l e n g th . The e xt re me p i t c h e s o f t h e f i r s t

s e c t i o n a r e C and e . The extreme pi tches a f t h e second s e c t i o n a re D and

g To f i n d t h e r a n g e-averagey t he se p i t c h es a r e f i r s t c o nv er te d t o num-

bers us ing the key-numbers l i s t e d i n f i g u r e I :

9 = 60. The low p i tches are added together arid t h e sum i s d i v i d e d by t h e

nurnber of samples. The same i s done f o r th e h i gh p i t ch - . s .

2

#2 .C = 16, e2 = 56, D = 18,

The averages can then be conver ted back i n t o convent iona l no ta t i on :

17 = C#, 58 = f# . The span i s determined by t h e i n t e r va l b e t w e e n t h e l o w s2

and the h ighs.

F i r s t s e ct io n:Second sect ion: D t o g#2 = 60 - 18 = 42 semitones

C t o e2 = 56 - 16 = 40 semitones

40 ' 2= 41 semitonesAverage: 2

I n d e r i v i n g t h e a ve ra g e-span, a sh or tc u t method, wh ich g ives t he

same resu l ts i s t o s imp l y f i nd th e d i f f e re nc e between the low and h igh num-

b e r s o f t h e r ange-average.

58 - 17 = 4 1 semitones



42

F IGURE I Key-numbers o f t he Piano Keyboard



43Range-averages of the Etudes

The measure numbers and sample pitches for the individual segments

of each etude are listed i n the tables of the Appendix. The range-averages

and span-averages given i n the tables o f the Appendix are summarized here

i n Tables 11, 111, and IV. These tables are accompanied by Figures 2 , 3,

and 4, which represent the pitches of the respective tables i n conventional

nota t ion .

columns labeled "low" a n d " high" contain numbers representing pitch or key-

number, w h i 1e the col umns 1abel ed " s p a n" represent interval s measured i n

semi tones.

The reader i s cautioned a t t h i s p o i n t t o remember t h a t the

By comparing tables I1 and 111, one can observe t h a t the l e h - h a n d

low note averages of the Chopin etudes vary from GG t o E, and average to-

gether t o give C, while Scriabin's left-hand notes vary from EE t o D and

average ow t t o AA. Thus one can see t h a t Scriabin's low notes tend t o be

about a minor t h i r d lower, t h a n Chopin's. Comparing right-hand h i g h notes

4 3reveals t h a t the Chopin etudes vary from c2 t o c and average out t o eb ,

while the Scriabin etudes vary from .;.* t o g'3 and average out t o c3. T h u s

one can see t h a t Scriabin's h i s h notes tend to be about a minor t h i r d lower

t h a n Chopin's. Also observe that the low averages for both composers are

much more consistent than the h i g h averages, which vary over larger spans.

The left-hand h i g h s and the r i g h t- h a n d lows vary over a span of

s l ight ly more than an octave, and average together a t approximately the

same pitches for b o t h composers, i .e. w i t h i n two semitones of each other.

There i s an overlap o f the r i g h t- and left-hand ranges o f a perfect f i f t h

for Chopin and a minor seventh for Scriabin. I t i s interesting that b o t h

composers' overlaps center on the pitch eb and t h a t the true center of the

piano keyboard f a l l s between e and f .

1

1 1



Tab le I 1

CHOPIN ETUDE RANGE-AVERAGES

EtudeOP/No

L e f thand

1ow-L e f thand

h igh

l e f thand

span

28.7

R i ghthand

7 ow_I_

Righ thand

h igh

R i g h thand

span

Handscombined

span

50.625/ 10 16.8 45.4 37.7 67.4 29.7

2516 15.5 50.2 34.7 41.4 74.4 33 .O 58.9

2518 16.7 47.2 30.5 42.3 68.9 26.6 52.2

10/9 19.7 44.6 24.9 41.5 69.6 28.1 49.9

l o / 10 20.2 49.5 29.3 44.0 74.8 30.8 54.6

2517 15.3 28.243.5 38.2 57.1 18.9 41.8

10/6 19.0

11 o

36.2 17.2 35.7 52.2 16.5 33.2

10/12

101.8

2514

48.3 37.3 37.9 67.6 29.7 56.6

12.3 52.7 40.4 32.0 76.4 44.4 64.1

20.1 44.8 24.7 42.6 63.6 21 o 43.5

Average 16.7 46.2 29.6 39.4 67.2 27.8 50.5

.

P



4

FIGURE 2 Range-averages o f the Chopin Etudes

= I

I I

I I I i

y7sJ -8-J



Tab le I 1 1S C R I A B I J ETUDE RANGE-AVERAGES

EtudeOp/No

L e f thand1ow.-

L e f th a dh i g h

L e f thand

2E!.!!

R i q h thand1ow__

R i g h thand

h!llh

R i g h thdnd

spJn.

Handscombinc d

s p a n

7.9 53.7 45.8 32.6 71.6 39 .O 63.7

12.1 55.6 43.5 40.4 69.5 29.1 57.4

14.8 51.2 36.4 40.8 69.2 28.4 54.4

8.5 50.0 41.5 37.7 69.2 31.5 613.7

12.1 41.3 29.2 33.3 57.1 23.8 45 [email protected] 44.8 27.2 39.1 59.5 20.4 41.9

16.7 46.2 29.5 36.5 56.9 20.9 40.2

11.4 46.6 35.2 38.0 57.3 19.3 45.9

18.3 46.5 28.2 38.8 60.8 22.0 42.5

13.8 53.7 39.9 34.8 68. I 33.3 54.3

16.6 49.7 33.1 36.8 63 .O 26.2 46.4

11.4 47.4 36.0 31.6 C2.7 31.1 51.3

Average 13.5 48.9 35.5 36.7 63.8 27.1 50.3



47

F IGURE 3 . Range-averages o f the S c r i a b i n Etudes



48

The most s i g n f f i c a n t dif ference between the two composers can be

seen i n the average le f t - han d spans. Sc r iab in ' s le f t- h a n d p a r t s t e nd t o

90 bot h hig he r and lowe r than Chopin' s , and ac t u a l l y span a range an aug-

mented f ou r t h l a r ge r t han C hop in ' s. The m ost s t r i k i n g s i m i l a r i t y can be

found i n th e combined span-- t he re i s o n l y t wo- t enths o f a semitone d i f f e r -

ence between the two composers i n t h i s r esp ect ,

Recause th e number o f keys on the piano had no t ye t been standard-

i z ed when Chopin was wr i t in g , one might ask whether a d i f fe re nc e i n the

s i z e o f t he k ey board c ou ld acc ount f o r some o f t he d i f f e renc es i n r ange-

averages. To answer t h i s quest ion, one needs on ly t o examine the "extreme

ranges" of the e tudes .

performed on an Ins t rument ranging a t l e a s t f rom CCC t o f

4 t o 81) s inc e he w ro te t hese p i t c hes repea t ed l y even i n t he ea r l i e s t

etudes.

even though the 88-note keyboard was alr ea dy standard. Sc r i ab in 's use o f

the l ow es t t h ree k eys i s t oo i n f r equen t t o ac coun t f o r h i s r ange-averages

being lower than Chopin 's . I n t he t w el v e e t udes o f Op. 8, S c r i a b i n uses

key 1 once, key 2 once, and key 3 l e s s t han 10 t imes. Because range-aver-

Chopin must have expected t h a t h i s music would be

4 (key numbers

4S c r i a b i n w r ot e o n l y p i t c h e s from AAA t o e ( 1 t o 80) i n Op. 8

ages ar e based on sever al p i t c h samples f rom each etude, they a re n ot

s i g n i f i c a n t l y a1 t e red by such in fr eq ue nt occurrences. The problem of th e add

i t i o n a l upp er r an ge a v a i l a b l e t o Sc r i ab in , bu t no t t o Chopin, i s im m at er i

because:

h igh er range-averages are found i n the Chopin etudes.

1) Sc r i ab in nev er uses t h i s r ange i n t t iese etudes, and 2) t h e

Table I V and Figure 4 compare and co nt ra st t h e etudes accordin g t o

the t ypes o f p rese nta t i on developed i n chapter two.

s u l t of t h i s comparison i n v o l ve s th e l e g a t o ty pe o f s i n g l e l i n e f i g u r a t i o n .

I t s use of h i g h no te s i n t h e r i g h t- h a n d p a r t i s much more r e s t r i c t e d t h a n

The most obvious re -



Type L e f t

L11Etude -o f hand

Legsto Studies

1ow

17.2

Doubled L Ines14 .O

Arpeggiated F1 gurat ions13.3

Convoluted Flgura t lons15.1

A1 terna t lng F igura t ions16.1

Ta b le I V

RANGE-AVERAGES FOR TI IE FIGURA’TION TYPES

L Q f thantl

hhh

42 .7

50.6

48.5

46.4

48.9

Ll!f thandspan

25.5

36.6

35.5

31.2

32.8

N !]h 1;

hand1ow

37 4

--a

39,2

36.7

3 9 b 1

37.5

Figurat ions w i th Large Leaps17 ,O 49.3 32 . 3 38.7

Average o f Al l Etudes15.0 47.7 32.8 3769

R l q h thand

56.4

70.2

65.5

67.7

C6.8

65.9

65.3

Righthandspan.

19.1

31 .O

28,9

28.6

29.4

27.2

27.4

Hands

comb1ney a

39.3

56.2

52,3

52.6

50.8

48.9

50.4



50

FIGURE 4, Range-averages for the F igurat ion Types

Legatostud ies

Doubled1 inc

Arpeggiatedf igurat ions

*E l

Convol u t e d

F igurat ion

I

A 1 t e r n a t i gFigure i o n

be- 1

F i g u r a t i o n wi thLarge L e a p s

a.- 1

Average o f Al l Etudes

h



The range-a ve ng es o f t h e type s of f i g u ra t i o n w i t h a l t e r n a t i o n and

la r g e l ea p s re ve a l n o th in g s ig n i f i ca n t l y d i f f e r e n t fro m what a ppears t o be

normal f o r the etudes i n genera l . The i r averages co r respond ve ry c los e ly

to the range-averages o f a l l th e etudes taken toge ther as a group.

The arpegg ia ted f igu ra t ions use the lowest ranges o f a l l t h e types

i n bo th the r i g h t and l e f t hands. However, the d i f fe rence between any of

the t ypes i n respec t t o the average lows i s marg ina l . The average-spans

o f t h e i n d i v id u a l hands i n t h i s t yp e a re a l so w id e r t h an most type s, p a r t i c

u l a r l y f o r t he l e f t hand, which i s only exceeded by one other type, L e . ,

the doubled 1ine type.



Chapter V

CONCLUS IONS

The most problematic aspect o f any analysis of texture involves

the de f i r , i t i on of the term. There * is no concensus among theoretical or

analytical writers concerning which musical parameters are encompassed by

" tex ture ." This study adopts a definition 1imited t o characteristics t h a t

have definite vertical or horizonta l components--basic types of melodic

and accompanimental figuration, density, and range.

reasons, the study examines only homophonic piano music, an analysis of

1inear independence was inappropriate.

system which categorizes f igura t ion i n t o basic types according t o the

function i t per foms (melodic or accompanimental) and t o the performance

technique i t requires t o be realized.

Because, among other

I n i t s place was substituted a

The proposed definition of texture can be evaluated i n two ways--

according t o its precision and i t s usefulness in practice. I t i s precise

i n t h a t i t relegates characteristics such iis instrumentation and dynamics

t o separate areas of investigation, thus reducing the number of variables

t h a t can complicate the inves tigation. The usefulness of the definition

can be supported by the many quantitative measurements t h a t are shown

t o be available i n this study for the objective analysis of style and

structure i n homophonic piano music.

The system proposed for classifying melodic and accompanimental

I t provides

I t provides a

presentation can be evaluated from several p o in t s of view.

new terminology for the description of piano figuration.

53



54

p ro ce du re fo r c l a s s i f y i n g complex f i g u r a t i o n i n t er ms o f e x te n si o n, va r i -a t i o n , and co mb in a ti o n o f s i x b a s i c typ es o f f i g u r a t i o n . From th e s tan d-

p o i n t o f c om po si ti on al s t y l e , c h ap t er two p o i n t s o u t t h e c l o s e r e l a t i o n s h i p

between the p iano mus ic o f Chopin and Scr iab in t h a t r es u l ts f rom the use o f

s i m i l a r f i g ur a t io n s .

t h a t m ig ht n ot be apparent i s i t s f l e x i b i l i t y . The system i s open-ended-

the c a teg or ies can be d iv id ed o r combined i n a number o f ways t o prov ide

t h e d eg re e o f d i s c r i m i n a t i o n a p p r o p r i a t e f o r a p a r t i c u l a r body o f mu si c.

One f a c e t o f t h e f i g u r a t i o n c l a s s i f i c a t i o n system

The examination o f t e x t u r a l d e n s i t y p r ov id e s s u pp o rt f o r t h e d e c i s io

t o c l a s s i f y t h e va r i o u s f i g u r a t i o n s i n t o b a s i c typ es . The measurements o f

d e n s i t y r e ve a l t h a t c e r t a i n t yp es have p a r t i c u l a r a s so c ia t ed c h a r a c t e r i s t i c

Fo r * ins tance, the convo lu ted ty pe o f accompaniment has t he h ig hes t dens i ty -

numbers and density-compressions.

l a r g e s t v e r t i c a l spans. A 1 t e r n a t i n g f i g u r a t i o n s h a v e t h e s i t i a l l es t d e n s i t y-

numbers and smal lest ver t ica l spans. The d i f fe rences be tween the s ty les o f

Chop in and Scr iab in w i th rega rd to de nsi ty were min imal . One d i f f e r en cet h a t was observed was the ch a r ac te r i s t i c sp ac ing - d is t r ibu t ion used by each

composer. The Chop in e tu de s e x h i b i t c l o se d sp ac i ng a t t h e t o p o f t h e v e r t i

c a l u n i t s wh i l e the Sc r ia b in e tudes have open spac ing a t th e to p and c losed

spacing i n t h e m id dl e o f t h e v e r t i c a l u n i t s .

Di f f e ren ces between Chop in 's and Sc r i ab in 's use o f range are a l so

F i g u r a t i o n s w i th l a r g e l e a p s h a ve th e

minute . There a re more s i m i l a r i t i e s than d i f f e ren ces . Moreover, the on ly

a p pa r en t ly s i g n i f i c a n t d i f fe r e nc e s a r e Ch op in 's use o f s l i g h t l y h i gh e r

p i t ch e s a n d S c r i a b i n ' s use o f wi de r l e f t- ha nd spans. These f ind ings add

more suppor t to the assumpt ion s t a te d i n the P re face t h a t t he two composers

w r o t e i n a v er y s i m i l a r s t y l e w i t h re s pe c t t o t e x t u r e . More s i g n i f i c a n t

f indings were observed between types of f igurat ion than between the compose



5

s ty les . This f a c t justif ies the attention given the distinction i n

chapter two concerning basic types of figuration. In general i t can be ob-

served that the low range-averages of both hands tend to remain constant i n

a l l the basic types while the upper range-averages vary. I t would seem l o g i -

cal t o assume t h a t increases i n range would occur equally i n both directions,

b u t the evidence suggests t h a t th i s i s not the case.

Etudes t h a t have a predominance of parallel doublings contain higher

Etudes w i t h convoluted figurationspitches and wider spans t h a n the others,

tend t o limit the span of the left hand--perhaps the constant motion of the

part precludes larger intervals due t o technical 1imitations, or perhaps the

large s k ip s would tend t o polarize the accompaniment i n t o separate bass and

middle register parts t h a t can no longer function as an entity. Legato

single line etudes have much more limited ranges t h a n other types and do not

venture int o the upper re gi st er s nearly as much. Perhaps the legato ef fe ct

i s hampered by the piano's i n a b i i i t y t o sustain volume in the higher registers

Some care must be taken i n drawing conclusions based on these results.

Several factors should be kept i n mind. First, the methods used for averaging

ranges i s arbi trary in certain respects, since the number and the size of the

units sampled var ies somewhat. Second, the resu l ts , s t r i c t l y speaking, apply

only t o these two collections o f etudes and do not necessarily reflect upon

other genres, other composers, o r piano texture i n general. However, the

etudes were, i n part, selected as being representative of the complex, i d i o-

matic texture of nineteenth century concert pieces. Third, the composition of

these etudes was separated by s ix ty years. A lthough the piano of Chopin ' s

time was fairly advanced technically, certain developments i n the construction

and design of the piano migh t have been responsible for some of the difference

between composers. The changes t h a t occurred d u r i n g this time include:



c a s t i n g t h e i r o n f ra me i n one s o l i d p i ec e i ns tea d o f us i ng c omposi te f rames

o f t h r ee o r more s epa rate pi eces , i nc rea s i ng t he s t r i n g t ens i on (now pos s i b l e

due t o th e s t r on ge r f rames and improved p iano wi re ) f rom a t o t a l o f 10.9 t ons

t o a bo ut 30 t ons , ov e r s t r i ng i n g and f ann i ng ou t t he bass s t r i ngs , and re -

l o c a t i o n o f t he s oundi ng board br idge . * ' Changes o f t h i s k i n d c ou l d poss-

i l b y acc ou nt f o r S c r i a b i n ' s use o f l ower reg i s te rs , s ince these improvements

c hanged t he qua l i t y o f t h e bass notes .

The ques t i ons ra i s ed i n t h i s d i s c us s i on abou t t h e c oncl us i ons s uggest

m a n y p o s s i b i l i t i e s f o r f u r t h e r i n v e s t i g a t i o n u s i n g t h e c o n c e p t s a n d m e t h o d-

o l og y p r e s en t ed i n t h i s s tu dy .

o f f i gu ra t i on and dens i t y and range f ound he re Frcbab1.y ex tend t o genres

o ther than e tudes . A s tu dy s i m i l a r t o t h i s one c ou l d be des i gned t o i nv es t i -

ga te s ho r t " c ha rac te r p i ec es" 1 i k e those found i n Schumann's "Carnaval , ' I

For example, th e re la t i on sh ip s between types

s i nc e t hey , l i k e t he e tudes, a re each s t r uc t u re d a round one p r i n c i pa l t y pe

o f f i gu r a t i o n . A l a rger s tudy could examine the homophonic p iano m u s k o f

severa l composers, t he reby in vo l v i n g a g r e a t e r v a r i e t y of s t y 1es , and c o u l d

h i g h l i g h t t h e t e x t u r a l d i f f e r en c es of var iou s composers and/or s t y l es . Such

a s tudy migh t p rov ide use fu l i n f o r m a t i o n c on ce rn in g s t y l e i d e n t i f i c a t i o n and

t h e p a r t i c u l a r c h a r a c t e r i s t i c s o f m usi c b y i n d i v i d u a l composers. An i n t e r e s t -

i n g s t u dy a lo n g a d i f f e r e n t l i n e o f t h ou gh t c o u l d examine t h e i n t e r n a l , f or m al

s t ru c t u r e o f l a rg er works such as th e Beethoven sona tas us ing these methods

o f a na ly s i s.

a work t o de te rmi ne what t y pes o f pa t t e rns a re p res ent . A l t h o u g h t h e d e t a i l s

o f methodo logy p res en ted he re a re t a i l o re d t o meet t he p a r t i c u l a r requi rements

One c o u l d a l s o i n v e s t i g a t e t h e p r o g r e s s i o n o f t e x t u r e t h r ou g ho u t

21. A r t h u r Loe sse r. Men, Women and Pianos: A So c i a l Hi s t or y (New York : S imoand Schuster, 1954) , 494-96, 564-65.



o f t h i s s tudy , th e concepts and te rm ino logy a r e conce ived on a l a r g e r s ca l e.

I t i s hoped t h a t o t h e rs w i l l f i n d t hese id ea s f r u i t f u l i n a g r ea t v a r i e t y o f

s i t u a t i o n s .



APPEND1X

DeterrninatIon o f Range-averages

Sc r ia b in E tude Op. 8, No. 1 Scr iab in Etude Op. 8,No. 2

Measurenumbers

1-5

6-10

11-15

16-20

21-25

26-30

31-35

36-40

4?.-45

46-52

Averages

Lef t-hand R iqh t-hand Measure Lef t-hand R i sh t-handLow

16

17

16

9

16

22

20

16

17

17

16.6

- High Low-

46 36

46 36

49 36

48 33

55 40

46 38

41 40

52 36

49 40

65 33

49.7 36.8

High

57

58

63

62

65

58

57

64

65

ai

63.0

nu i1bers

1-2

3-4

5-6

7-8

9-10

11-12

13-14

15-16

17-18

19-20

21-22

23-24

25-26

Averages

Low

22

22

22

15

6

4

6

6

5

10

10

10

10

11.4

- -i&

40

48

48

48

47

50

43

42

48

51

51

53

29

46.6

-Low"

41

42

41

37

34

37

35

32

41

37

41

38

38

38 O

High

5860

58

53

56

59

61

52

58

63

63

54

50

57.3



APPEND1X

DetermJnaLion o f Range-,averages

S c r i a b i n E tu de Op. 8, No. 3 Sc r i ab in E tude Op. 8, No. 4

Measure Left- hand Right-hand Measure L e f t-hand Ri ah t-handnumbers

1-1112-22

23-33

34-44

45-55

56-66

67-77

78-88

89-99

100-110

111-122

Averages

Low

2217

3

3

8

13

13

22

18

3

3

11.4

- High

4850

63

35

46

37

39

48

50

63

42

47.4

Low

3434

27

25

35

34

33

34

38

32

22

31.6

-- Hiqh

615

78

51

61

51

56

61

65

78

63

62.7

--nurrihe r

1-23-4

5-6

7-8

9-10

11-12

13-14

15-16

17-18

19-20

21-2223-24

Averages

Low

1420

14

15

24

26

29

17

14

21

1510

18.3

- H iqh

4646

44

43

46

48

52

46

46

46

4451

46.5

-Low"

3839

38

34

40

43

48

39

38

39

3931

38.8

H b k

6260

57

55

56

58

65

60

62

60

6075

60.8



APPEND1 X

Dete rm ina t i on o f Range-averages

Scr iab in E tude Op. 8, No. 5 S c r i a b i n Etude Op. 8, No. 6

Measurenumbers

1-67-12

13-18

19-24

25-30

31-36

37-42

13-48

49-54

55-58

Averages

Left-hand Rig ht-hand Measure L ef - t iand Riqht-handLow

1510

15

18

10

15

12

10

13

20

13.8

- H i & 5-

53 3655 32

51 36

56 36

51 36

51 36

55 34

51 32

51 34

63 36

53.7 34.8

High

6870

63

68

65

65

70

67

65

80

68.1

nutribers

1-56- 10

11-15

16-20

21-25

26-30

31-35

36-40

4 1-45

46-50

51-55

56-60

6 1-65

Averages

Low

1815

13

22

22

15

13

15

20

13

13

13

1

14.8

- High low"

49 4256 48

51 42

53 41

53 45

53 37

49 34

49 42

53 42

53 38

48 44

49 46

49 29

51.2 40.8

t i i

6873

72

69

68

68

70

73

68

68

68

68

66

69.2

m0



S c r i a b i n Etude Op, 8, No. 7

Measurenumbers

1-7

8-14

15-21

22-28

29-35

36-42

43-49

50-56

57-63

64-70

71-77

Averages

Lef t-handL O W cH i &-14

16

14

13

11

10

9

14

16

14

2

50

43

50

33

33

30

37

50

45

50

33

12.1 41.3

APPEND1X

D e t c m i n a i o n o f Range-ave%*ages

S c r i a b l n Etude Op, 8, No, 8

R 1gh t-handLow

38

36

33

29

29

28

33

38

36

37

29

33.3

_y

-Hi&

62

57

62

53

53

53

57

62

57

62

50

57.1

McasureIn-1-1n)bers

1-6

7- 12

13-18

19-24

25-30

31-36

37-42

43-48

49-54

55-60

Averages

Lef t - handLow t t iqh--17 41

12 41

10 50

30 57

32 53

17 55

17 4 I.

13 37

12 37

16 36

17.6 44.8

Right-handLow

38

33

35

48

48

38

40

36

.I-

C ) -

J J

40

39.1

H i g h

58

62

60

62

61

60

62

58

58

54

59 * 5



APPEND1X

Dete rm ina t ion o f R sngc-averages

S c r i a b i n Etude Op. 8, No. 9 S c r i a b i n Etude Op. 8, No. 10

Measure Left-hand I1i ht-hand Measure Le ft - hand Rictht-handnumbers

1-1011-20

21-30

31.-40

41-50

51-60

61-70

7 1-80

81-90

91-100

101-103

Averages

Low

53

8

12

7

12

7

8

7

6

12

7.9

- High &-

56 3656 27

49 22

56 41

51 31

59 31

52 33

53 36

56 35

55 30

48 31

53.7 32.6

High

7277

61

77

75

72

62

76

77

79

60

71.6

-7nurnbers

1-1011-20

21-30

31-40

41-50

51-60

61-70

7 1-80

81-9G

91-100

101-110111-122

Averages

Low

1717

12

9

14

17

17

22

5

5

55

12.1

L_

H i q h

6052

60

47

45

57

60

57

60

60

4267

55.6

1.-Low"

4040

41

40

41

40

40

45

40

56

2933

40.4

High

7468

74

64

57

69

74

73

68

74

6277

69.5

mN



APPENDIX

Dete rm ina t ion o f Range-averages

S cr iab in E tuqe Op. 8, No. 11 S cr iab in E tude Op. 8, No. 12

Measure Lef t-hand R igh t- hand Measure L e f t-hand Right-handnurn ber

1-5

6-10

11-15

16-20

21-25

26-30

31-35

36-40

4 1-45

46-50

51-54

Averages

Low

26

19

12

12

2 1

14

14

19

19

14

14

16.7

- High

46

46

46

47

50

50

46

48

46

33

50

46.2

-Low-

37

32

32

33

37

38

32

33

38

33

57

36.5

H i g h

57

57

53

63

57

58

55

57

55

45

69

56.9

n urn be r s

1-5-

6-10

11-15

16-20

21-25

26-30

31-35

3 6 - 4 0

41-45

46-50

51-55

Averages

Low

19

7

7

10

13

3

7

7

6

7

7

8.5

- High m-

5 1 38

55 38

55 39

46 41

43 39

42 34

51 38

51. 39

48 45

46 38

62 26

50.0 37.7

High

67

70

70

72

70

6 1

65

70

70

67

79

69.2

mw



Measurenumbers

1-6

7-12

13-18

19-24

25-30

31-36

37-42

43-48

49-54

55-60

61-65

APPEND1X

Dete rmina t i on o f Range-averages

Chopin Et ud e Op. 25, No. 4 Cho pin Etud e Op. 25, No. 6

Le f t- handLow High

20 45

20 46

20 45

24 45

19 45

19 47

20 45

20 46

18 45

16 46

25 38

-

Right-handLow High

44 68

47 68

44 64

40 61

43 60

43 64

44 68

44 64

40 68

40 61

40 54

- Measurenumbers

1-67-12

13-18

19-24

25-30

31-36

37-42

43-48

49-54

55-60

61-64

Averages 20.1 44.8 42.6 63.6 Averages

Lef t-handLow High-1912

10

18

2 1

19

19

17

12

12

12

45

53

63

48.

5 1

65

55

5 1

4 1

4 1

36

15.5 50.2

Right-hand-Low -

5048

38

50

45

4 1

5 1

35

36

33

28

41.4

High

75

80

80

75

8 1

77

79

80

72

79

40

74.4



Measurenumbers

1-7

8-14

15-21

22-28

29-35

36-42

43-49

50-56

57-63

64-69

Averages

APPENDIX

Dete rmina t i on o f Range-averages

Chop in Etud e Op. 25, No. 7 Chop in Etude Op. 25, No. 8

Le f t- hand-Low -iCJtl-

17

15

25

9

7

15

17

10

21

17

44

44

44

52

43

43

44

44

48

29

15.3 43.5

Right-hand MeasureLow

40

36

39

42

43

40

39

36

36

3 1

38.2

- High

56

56

60

62

60

6 1

56

56

56

48

57.1

--numbers

1-3

4-6

7-9

10-12

13-15

16-18

19 -21

22-24

25-27

28-30

31-3334-36

Averages

Le f t- hand-Low High

12 48

17 50

21 53

12 46

24 36

24 36

17 57

17 50

12 55

17 53

10 36

17 46

Right-handLow

45

45

46

40

40

44

45

45

46

4 1

33

38

-

16.7 47.2 42.3

High

67

67

74

64

58

76

74

69

70

67

64

77

68.9



Measurenumbers

1-10

11-20

21-30

31-40

41-50

51-60

61-70

71-80

81-90

91-100

101-110

111-118

APPENDIX

Determina t ion o f Range-averages

Chopin Etude Op. 25, No. 10 Chopin Etude Op.10,No. 6

L e f t-hand-Low High

9 39

21 53

8 60

17 46

22 47

20 43

22 47

20 43

22 47

17 35

14 39

10 46

Averages 16.8 45.4


33

43

a4

36

37

38

38

38

38

38

38

41

37.7

- High

63

75

78

67

67

61

67

61

67

65

63

75

67.4

numbers

1-5

6-10

11-15

16-20

21-25

26-30

31-35

36-40

41-45

46-50

51-53

Averages

L e f t -hand-Low High

27

24

24

14

10

12

15

13

27

24

19

41

41

38

37

29

36

35

26

41

41

33

19 o 36.2

Right-handLow High

43 55

35 50

35 55

33 50

34 51

36 56

36 58

33 48

43 55

34 53

31 43

52.2 52.2

_I_



APPEND1X

Chopin Etude Op. 10, No 8

Determi n a t i o n o f Range-averages

Measure Le f t- hand Right-handnumbers -Low High & High

1-78-15

16-23

24-31

32-39

40-47

48-55

56-63

64-71

72-79

80-8788-95

89

8

6

5

13

13

9

8

i5

3321

42 2845 28

45 28

45 25

58 25

56 35

59 50

61 28

45 28

45 29

62 4769 33

7478

74

78

76

73

76

74

74

8 1

7881

Chopin Etude Op. 10, No 9

Measure Left- hand Right-handnumbers Low Hig h Hi gh

1-67-12

13-18

19-24

25-30

31-36

37-42

43-48

49-54

55-60

61-67

2121

19

12

11

28

21

21

21

21

21

4 141

4 1

36

50

48

4 1

4 1

46

4 1

65

4040

40

36

4 1

48

40

40

45

43

44

6460

64

58

77

77

64

72

72

77

8 1

Average s 19.7 44.6 41.5 69.6

Ave rag es 12.3 52.7 32.0 76.4



Measurenumbers

1-78-14

15-21

22-28

29-35

36-42

43-49

50-56

57-63

64-70

71-77

Averages

APPEND1X

Determi n a t i o n o f Range-averages

Chopin Etude Op. 10, No. 10 Cho pin Et ude Op. 10, No. 12

Lef t- hand-Low High

2419

20

17

24

25

19

19

19

24

12

4950

47

45

44

50

59

59

48

50

43

20.2 49.5


4343

39

41

44

50

43

48

43

54

36

44.0

- High

7072

76

70

72

75

80

77

74

81

76

74.8

numbers

1-78-14

15-21

22-28

29-35

36-42

43-49

50-56

57-63

64-70

71-777884

Averages

Le f t- handLow High

1116

11

14

10

9

11

12

11

14

94

6043

43

47

47

48

60

43

43

42

43

60

11 o 48.3

Right-handLow

2828

28

25

25

35

50

28

28

29

47

33

32 .O

- High

7478

74

78

76

73

76

74

74

8 1

78

8 1

76.4



SELECT BIBLIOGRAPHY6

Apel, W i l l i . "Texture", Harvard Dictionary o f Music, 2nd ed. rev. and enl.Cambridge, Massachusetts: Bel knap Press, l F 6 T

Berry, Wallace. S t r u c t u r a l Functions i n Music. Englewosd Cliffs, NewJersey: Prenti ce-Hal 1, 1976.

Bowers, F a t h i o n . The New Scriabin; Enigma a n d Answers. New York: S t . MartinPress, 1973.

. Scr i ab in ; A Biography of the Kuss-ian Composer 1871-1915, 2 vo l s .

Chopin, Frederic . EtGden, ed. by Herrnann Schol tz . Frankfort : C . F . Peters,

Tokyo: Kodansha In te rn at io na l 1969.

n.d.

Dyson, George. "The Texture of Modern Music," Music and Letters IV ( 1 9 2 3 ) ,Nos. 2 , 3, and 4.

Ganz, Peter Fel ix . " T h e Development of the Etude for Piano f o r t e . "Disser ta t ion , Northwestern University, 1960.

Garvelmann, Donald. Sc ri ab in : Complete Piano Music, boo kle t for the recordalbum o f the same t i t l e , perf. by Michael P o n t i . SVBX 5462, 5463, and5474 (1974).

Holden, Calvin E. "The Organizat ion of Texture i n Selected Piano Compositionsof Claude Debussy. I' Disse r t a t i on , Un ive r s i t y of Pit tsburgh, 1973.

Keys, Ivor . The Texture o f Music; From Purcell t o Brahms. ondun: DennisDobson, 1961.

LaRue, Jan. Guidelines for Sty le Analys is . New York: W . W . Norton and Co.,1970.

Loesser, Arthur. Men, Women and Pianos; A Social History. New York:Simon and S c h u s t e r , 1954.

Nordgren, Quentin R. "A Measure of Textural Pat terns and St reng ths , "Journal of Music Theory IV/1 (April 1 9 6 0 ) , 19-31.

texture in chopin and scriabin music

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