analysis of texture in piano etudes of chopin and scriabin.pdf

8/17/2019 Analysis of Texture in Piano Etudes of Chopin and Scriabin.pdf

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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


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CONTENTS

Page

LIST OF EXAMPLES . . . . . . . . . . . . . . . . . . . . . . . . . . i vPREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

The Purpose of the Study . . . . . . . . . . . . . . . . . . .The Significance o f the Study . . . . . . . . . . . . . . . . vi iThe Etudes Selected for Analysis . . . . . . . . . . . . . . . vi iThe 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 . . . . . . . . . . . . . 15

Specialized Problems i n AnalyzingTexture 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. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . 22Summary 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 39Range-average . . . . . . . . . . . . . . . . . . . . .

Range-

averageso f

the Etudes 43

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

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Chapter Page

V . CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . 53 APPENDIX: Determi n a t i o n o f Range-average . . . . . . . . . . . . . . 58SELECT BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . 69

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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 de nc e . . 72. Scr i ab in E tude Op . 8 No. 8. mm . 1-3. . . . . . . . . . . . . . 12

12

4 . Scr i ab in E tude Op . 8 No. 2. mm . 1-2 . . . . . . . . . . . . . 125. 13

6. 1414

15

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

Scr i ab in Op . 8 No. 2. mm . 1-2. w i t h t h e me 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. Scriab in Etude Op . 8 No. 7. mm . 1-2 . . . . . . . . . . . . . 16

10. Scr i ab in E tude Op . 8 No. 8. mm . 1-3 . . . . . . . . . . . . . 1711. Chopin Etude Op . 25 No. 4. mm . 9-12 . . . . . . . . . . . . . 1812. Scr i ab in E tude Op . 8 No. 5. mm . 1-3 . . . . . . . . . . . . . 18

13. Scr i ab in E tude Op . 8 No. 5. mm. 1-3. r e n o t a t e d . . . . . . . . 19Chopin Etude Op . 25 No. 1. mm . 1-2 . . . . . . . . . . . . . .

15. Chopin Etude Op . 10 No. 12. mm . 10-13 . . . . . . . . . . . . 2016. S c r i a b i n E t u d e Op . 8 No. 3. mm. 1-4 . . . . . . . . . . . . . 2 117. 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 . . . . . . . . . . . . . 2219. Chopin Etude Op . 10 No . 9. mm . 1-3 . . . . . . . . . . . . . . 2320. Chopin Etude Op . 25 No . 9. mm . 1-4 . . . . . . . . . . . . . . 2521. Chopin Etude Op . 25 No . i 2 ; min . 1-2 . . . . . . . . . . . . . 2522. Chopin Etude Op . 10 No. 2. f i n a l m e a s u r e . . . . . . . . . . . 2823 . S c r i a b s n Etude Op . 8 No. 12. mm . 1-2 . . . . . . . . . . . . . 2924. 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

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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


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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 fferences 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 p ia no

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 ba sic 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 t s t h a t can be measured according t o

viirious characteris tics o f density and range, and these common t ra i t s are

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


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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, bo th in

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

concerned with orchestral or chambermusic,

placing the i r 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 p iano music texture.

Considering the importance of texture t o musical s ty le , 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 theore tical writings. Most write rs limi t th ei r discussions t o

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

i n g p o i n t for f i l l in g 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 s t y l i s t i ca l ly indigenous t o 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

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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 similari ty i n style and form afford a good basis fo r comparison.

The later etudes of Scriabin, Opp. 42 a n 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

formsarid

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 and 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 too 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 i x t y years t h a t separate their compo-

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

Scr iabin '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.

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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 ted i n the

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

mental presenta tion . 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.

Scr i abinEtudes

Op./No.

I . Melodic presentation

A .Single

l in e 818 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 10/6

2512 2517

2516 2518

25110

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 -

acteris tics of texture i n piano music:

tal presentation, density, and range.

characteris tics i s se t fo r th i n chapter one. The chapte r 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 fo r selecting these three

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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 n d Scriabin a n d classif 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 definitions fo r 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 de ta il and then

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

Chapter five summarizes the methodology of the study and i t s r es u 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 f o r his generous assistance and helpful advice d u r i n g bo th the study's

planning and i t s writing.

X


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Chapter Ia

PROBLEMS IN THE ANALYSIS OF MUSICAL TEXTURE

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

th e 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 definit ion involves considerations

Problems i n Definina Texture

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

3the 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 texture 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 Il texture.

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 i ffs , NewJersey: Prentice-Hall, 1976), 189.

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2

minds of some authors , for example Ivor Keys and George Dyson, t e x t u r e con-

s i s t s of a l l '!" characteristics of music combined it1 a vague, holistic

manner.4

With this kind of broad definit ion, there is a temptation for

analyzers t o center their discussions on the area in which they are most

secure, i .e. , harmony-discussions having only occasional references t o the

other char ac te ri st ic s of music. Such a def ini t ion isinadNquate.

While

there are useful definitions o f a more s p e c i a l i i e d nature, there i s , unfor -

tunately, wide divergence of thought concerning the specifics of what tex

ture should entail. I n order t o provide some perspective on the problem,

a few o f the more useful definitions must be examined.

The Ervard Dictionary o f Music provides the following definit ion

of texture.

Much like woven fabric , music consists of horizontal( woof'l) and vertical ("warp") elements. The former arethe successive sounds forming melodies, the l a t t e r thesimul

taneous soundsformi

ng harmonies . I t i s these el e-ments that

maKe up the t ex tu re .5

This is too vague t o be a serviceable definition, b u t Apel does

elucidate his concept of texture by l is t ing the dif ferent character is t ics

he would include for consideration: polyphonic-homophonic, polyrhythmic-

homorhythmic, and 1ight-heavy. I n this context, 1ight-heavy ref'ers t o both

the number of instruments, and the ,tone color or timbre of the instruments

invol ved.

4. Ivor Keys, The Texture of Music; From Purcell t o Brahms (London: DobsonBooks, 1961)rge Dyson, The Texture of Modern Music," Musicand Letters IV (1923), No.2, 3, and 4.

(Cambridge, Massachusetts: Bel knap Press , 1969), 842.5.

Will

i

Apel , "Texture," Harvard Dictionarv of Music 2nd ed. , rev. and en1 .

6. Ibid.


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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 precise ly. This practi ce 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 cons ist s of i t s sounding components;i t i s conditioned i n part by the number of those componentssounding in simultaneity or concurrence, i t s qualities deter -mined by the interactions, interr elati ons, 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 char act eri sti cs. The quanti t a-

tive characteristics include l ' . . .the number o f concurrent events [commonlycalled thickness] as well as the degree of 'compression' o f the events

within a given intervallic space.Il8 He refers t o bo th 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 hor izantal 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 St y1e 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.


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' 4

charact erist ics of texture. He defines textur e 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 tessi 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 characterist ics of texture.

analytical re su lt s i s di re ct ly connected to the precision of the defi nit ion ,

a sing le c ri te r io n was adopted fo r deci ding which ch ar ac te ri st ic s of texture

are appropriate for the study of these etudes.

the strictest sense should deal only w i t h characteris tics that are princi-

pally associated w i t h ei th er verti cal or horizontal relationshi ps. This

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

basic characterist ics:

Because the validity of the

I bel ieve tha t 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 relation-cal factors of the texture.

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

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

ence, o pure1y polyphonic textures o r 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.


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5

of texture i n this study.

system based on types of melodic and accompanimental presentation.

In i t s place was substituted a class if icat ion

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

components present a t any given moment and t he i r arrangcment w i t h i n a

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

and spacing o f ve rtica 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 thes e char acte rist ics of t exture 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 no t

normally associated with ei th er vertic al or horizontal att ri bu te s: timbre,

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

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 est abl ished systems for analysi s. They therzfore do not

need to be subsumed under texture. Sini i lar ly , rhythm i s pr imarily 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 d irect 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 characteris tics o f the individual lines and from the relationships that


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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 classi f 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 i ed as "homophonic."

I t would be di ff ic ul t t o place a l l 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

a t 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, op .c i t . , 185.

11. I b i d , 193-95.


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

homorhythmi c

= hetero-rhythmic

j= contra-

1 . 4

-

- contra-JJA-+ d-

_

1 1 1 1

I F

. I 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 - pa rt w r i t i n g would require a prohibitive number o f statements, or re-

course t o descriptive 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


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8

Specia1

i zed Probl ems in Analyzi ng

Texture i n Piano Music

Special analytical problems arisewhen

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 subt le differences o f tone-color caused

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

differentiation makes i t di f f i cul t for a l is t ener t o 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, the performer i s l imited 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 cons tant 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 i l 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.


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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 ci a l

a t t r i b u t es o f t he pi 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 qu an 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 appro pr ia t e here than i n po lyphonic 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 p urp oses o f t h i s s t ud y 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 pr 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 1in e a r 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 hi ch t o c a t ego r i z e t he b road v a r i e t y o f tex tur es 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 .


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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 skills is 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 classif ication 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 f iguration, most commonly,

the right hand playing th e 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 single component f u l f i l l s

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

paniment will include a f a i r ly independent l i ne t h a t supplies an additional,

t h i r d component.

Pri-

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


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11

presentation can be considered independently, w i t h each note of a particular

texture performing principally one function or the other.

After separating melodic from accompanimental functions , the figura-

tions of these two components can be classified into types according to the

way they are presented. In the works being considered, the melodic presenta

tion can be divided into two types:

the s ingle l inedoubled i n parallel intervals

Similarly, accompanimental presentation can be divided into four types:

1) chordal2) arpeggiated3) convoluted4) a1 ternating

These six different types o f presentation are defined and explained

w i t h examples i n the following sections of this chapter. The examples point

out the problems of determining how an etude is t o be classified and show

the great variety t h a t exis ts w i t h i n the types. In some cases these types

are divided into subcategories i n order t o provide f iner d ist inct ions .

The subcategories are explained below as they are encountered in the musical

examples, and then summarized i n an outline of the types presented on page24

The Single Line

The simplest type o f melodic presentation i s the single line melody.

Examples of this type can be grouped into two subcategories according to

the performance d i f f i cu l t i es of the pieces. One group uses slow tempos and

requires a very l c -ya to style, often w i t h the accompanimental chords or lines

written for the same hand, compounding the difficulty of obtaining smooth

legato connections.

have config u r a t i ons simi 1ar to Example 2.

Etudes of this type, which are called "legato studies,"


22/79

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 and 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 dis t 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 no t 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 disp lay since C h o p i n .

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

wi t h o u t careful analysis i s the use of polyphonic melody as i n the case of

Example 4.


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13

In polyphonic melody, one voice --at leas t i t i s notated as one

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

be a single l i n e 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 ti ons hip apparent. Notice thesimp1 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 sin gle- 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 cons ideration 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 a l l ,

12. Felix Salzer and Carl Schachter, Counterpoint i n Composition; TheStudy of Voice Leading (New York: McGraw-Hill , 1 9 6 9 , 153-160.


24/79

14

we 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 p e o f me lo di c p r e s en 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 sp e c t i ve 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 m o 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 m e lo d i c l i n e s move ch r o m a t i ca l l y

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

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


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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 Chopin Etude Op. 25 No. 8, mm. 1-4.

,

Not on ly does the r i gh 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 melod ic

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

Melod ies doubled a t t he 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 bj ec t f o r etudes .

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

Chopin Op. 25

i n bo 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 th e o ctave s. The r i g h t hand o f S cr i ab i n ’ s Op. 8 No. 7

i s a c ase i n p o i nt .


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EXAMPLE 9 Scr i ab 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. J us t be-

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

necessarily mean t h a t t he i r function i s likewise melodic.Tt,e

middle note

of the right hand i s not linked to 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 BerryIs termi no1

ogy for 1i near independence is useful .He would cl as si fy this l ine as "homorhythmic-heterodirectional-contrain'er-

val l ic , " whichprovides

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 . I f 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 lega to


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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 xt hs , and doubled octaves. One shoJ ld bear 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 r ie s a r e a p p r op r i at 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 t r a i n t s o f t h e p er io d.

may be fo und i n works i n d i f f e r e n t s ty le s .

The l a t t e r i s d i v i d ed i n t o t h r e e typ es:

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 t hese 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 r equ i res t he r i g h t hand t o p l ay t h e me lody and a pa r t o f

t h eaccompanifient

a t t h e same t ime.i ' h i s

p ro ce du re can 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 m ul ta n eo u sl y

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 d iv 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 te x t u r e 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.


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18

In i t s s implest conformation, homophonic music consi st s o f two

strata--one melodic and the other accompanimental . Yet, as later exampleswill 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 th ree s t ra ta as was

Example 10, b u t with one major di fference: 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 be fore, the r i g h t hand has both melody a n d chords, and now thel e f t hand has the bass l i ne 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 di ff ic ul t

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

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

Large leaps

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


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19

Here

components:

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

ame1

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

and itsaccompaniment.

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 in to di scr et 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 cme1

ody 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 t he surface level while the

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

i s so

P O ' Y -

register can i n effect add another stratum t o

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

subcategories--onesimp1

e and one w i t h large leaps.


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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 o r 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 pa r 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.


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21

In this example the five or more pitches i n each figure 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 igurat ion i s s imilar t o a tremolo

I t con sis ts of an al te rn at io n between two notes or groups of notes.effect .

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

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

4.

I f Example 16 contains accompanimental figures in bo th 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


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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. T hi s

example can, a t l ea s 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" figur at ion. This type con si st s of any regul ar 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 igur -

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

2.

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


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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 beat. 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 m ete 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 co nv ol ut ed

f igurat ion used by Chopin.


Allcgro :nolto agitato :to.

Conta ined w i th in t he upper pa r t o f t he accompan imenta l f i g ure 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 h r e e 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 harmonic suppor t

i s below t h e t w 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 y pes o f f i g u r a t i o n

discussedi n

t h i s c hap t e r .

make use o f t ha t te x t u r e 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


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24

S cr i a b i n ChopinEtudes Etudes

Op./No.

Op ./No.

1. Melod ic presenta t ion

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

1. Legato study

2. Ve l oc i ty s tudy

B. Doub led l i ne

1. Doubled i n octaves

2. Doubled i n t h i r d s

3. Doubled i n s i x t h s

11. Accompanirnental presentation

A. Ch 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 te d f i g u r a t i o n

1. One hand-posi t ion

2. More than onehand-posit I on

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

D. Co n vo l u te d f i g u r a t i o n

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


35/79

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 f i f th finge rs, which

means the hands can transverse the keyboard without 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.


For


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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 e tudes cou ld be inc l uded i n th e ca tego ry sys tem by

creat ing new designat ions. Bu t th i s i s no t d es i r ab 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-

in gf u l comparisons. Al though one could 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 .


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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 presentation, densi ty , 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 Ch o p 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 igh t lheavy or t h i n / t h i ck 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 ings , the adoption o f a more precise

melodic and accompani-

I t begins w i t h ade ta i l ed

In addition, these terms are

Since these

vocabulary s essential .

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

components. Thosere1

evant t o density incl ude densi ty-number,I "texture-

space," and "density-compression .

In his Structural Functions inMusics

Berry pro-

The following discussion examines

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

27


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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 n g c hord.

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

m

Obviously, th e densi ty-n um be r i n p c l y p h o n i c music i s e q u i va l en t t o

th e number o f vo i ces i n t h e t e 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 lp 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 rm a 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 m us ical s t r u c tu r e .

When density-number no l onger r e f e r s t o t he number o f voices, i t m u s t r e f e 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 y

A c c w d i n g t o Ber ry, densi ty-number r e fe rs t o t he 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 centu ry , can be de f ined as a pa r t i c u la r chordal u n i t . W i th t h i s i n


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

a t any point, and yet they can function harmonically as pa r 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 p itches i n the lef t-hand par t express tonic harmony. When the

horizontal motion o f the accompanimental f igura t 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 Figurat ion reduct ion G f the lef t-hand part of Example 23.

a

71

Nota ting the p i tches of an accompaniment a s a block chord makes i t

easier not only to observe the densi ty-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 .


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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 a1 ternative more appropriate to

t h 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 i ne s 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 reg is 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 inflat ion 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.


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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

tha t i s qualitative rather t h a n quantitative, and i t s emphasis i s d i r ez t ed

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 ver ti ca l span i s proposed as a descr ip tion of the expanse

of each vertical u n i t measured individual 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 tex tural progression, see Calvin E. Holden, TheOrganization of Texture i n Selected Piano Compositions of C1 a u d r -Debussy. Disse rtat ion, University of Pittsburgh, 1973.


42/79

32Densi ty-Compression

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

in a part icular 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 12Vertical span

Density-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 = 12 = 2.7131

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

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

impression o f density. This impression i sa f f e c t e d

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


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

dissonance is diff icult 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 ofnumber

t ospace.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.

in to 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 ef fe ct 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 t ex ture i s , 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 no 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 t h i

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

pattern o f pitch distr ibution w i t h i n a part icular vertical unit .

B u t t h 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 qua nt if icat ion. To

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

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


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34

require a complete l i s t i n g of the inter val s present. The re su lt s of such

a procedure would be more cumbersome t o cope with than the original no ta t ion

of theniusic

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 sens ib le option i s t o generalize the

character of the arrangement by pointing out certain distinctive f ea td re 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

and concentrated i n the center.

To summarize, a pa rt icu lar v er ti ca l 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 tic al st ru ct ure 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 l inear 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 -

ac te r is t ics of density readi ly apparent. The measurementsb 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.


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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 Figurat ions

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/ 2

8/4 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

Chopi n 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 not averaged ( see below, pages 36-37)


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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 ul t 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 figures

from previous averaging processes,

as does the more indirect,

second method

In t h e 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 highes t 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 abou t 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-

hand 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


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37

foreground event with accompaniment being background. l9 The accompani-

menta l f i g u r a t i o n supp l i es more con ten t t o the compos it i on than does the

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 ubs e rv i an t r o l e o f bac kg round.

Because of these substant ia l d i f ferences Etude Op. 10 No. 8 i s no t computed

i n t h e a verages f o r i t s t y pe o r f o r C h o p i n ' s o v e r a l l ave rages o f d ens i t y .

The e tude canno t be en t i r e l y de l e tedf r om

th e study , however,on,

t h e b a s i s

o f the above reasons.

accompaniments w i t h resp ec t t o bas i c t ypes o f p res en ta t i ona r l d w i t h

respec t

t o range .

I t i s s t i l l a l e g i t i m a t e example o f a r pe gg ia te d

The rema in ing th ree e tudes w i th a rpegg ia ted f i gu ra t i ons have an

average density-n um be r o f 4.34. The v e r t i c a l span, as mentioned above, i s

v e ry s i m i l a r t o t he c onvo l u ted 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 pre fe rs a rpegg ios wi th r e 1z t i v e l y

c lose spac ing wh i l e Sc r iab in p re fe rs a more open spac i l ig .

The accompaniments wi th large leaps are the onl, : t yp e o f f i q u r a t i o n s

t ha t have a subs tan t i a l l y d i f fe ren t average measure of v e r t i c a l s pan . T h i s

rad i ca l l y h igher average mus t be expec ted s ince the cons tan t l eap ing o f t h e

hands w i l l n e c e s s a r i l y i n c re a s e 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 spread over a l a rger 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 p s ge ne ra te s t e x t u r e

w i t h more s t ra ta , i t has, a t t h e same t ime, lowe r densi ty-numbers and den-

s i ty- compressions. Perhaps th e com ple xi t y o f numerous te x t ur a l s t r a t a com-

pensates for reduced dens i t i es .

I t i s

19. F oreg round and bac kg round he re do n o t r e f e r t o l e v e l s o f s t ru c tu r e ,b u t t o t h e r e l a t i v e degrees o f i n t e r e s t and co nt en t--perhaps theys hou l d be c a l l ed l ev e l s r f perceptual immediacy.


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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-

es t v e r t i c a l s pan .

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

I t appears t h a t t he c on s 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 rence s be tween the composers, the ov er 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 gui ded by t h e same c c ms t r a i n t s . I n etudes

composers s t r i ve for t e x t u r a l c om pl ex it y i n o r de rt 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 t hou t compromising th e 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 .


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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 ac k o f

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

no r has an adequate term inolo gy 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 gh e st p i t c h w i t h i n a c o mp os it io 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 r e -

veal much about the piece as a whole. An a l t e rna t i v e app roac h would b e t o

c on ce iv e o f r an ge i n a manner s im i l a r to the concep t o f t ess i tu ra . Accord-

i n g t o t heHarvard

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 rangei n t h a t i t does no t take i n t o account 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 t imes 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 t h e r words, ra ng e 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


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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 th e 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 involved 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 ch e s w i t h o u t h a vi ng 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 the 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 na t i on .

*

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 semi tone, due to th e pre c is ion o f th e computat ion. Wi th t e n o r more


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41

samples, ten ths 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

of 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 h e " range-span. I

For a s imp le example o f t he procedure , imag ine a p i e ce o f m us ic

d i v i d e d i n t o two s e c t i o n s o f e q ua l l e ng t h. 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 andg To f i n d t h e r a n g e-averagey t he se p i t c h e s 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 c ti on :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


52/79

42

F IGURE I Key-numbers o f t h e Piano Keyboard


53/79


54/79


55/79

4

FIGURE 2 Range-averages o f the Chopin Etudes

I

I I

I I I i

y7sJ - 8 - J


56/79

Ta b le I

S C R I A B I

ETUDE RANGE-AVERAGES

EtudeOp/No

L e f thand1ow.-

L e f th a d

h i g h

L e f thand

2E .

R i q h t

hand

1ow__

R i g h thand

h llh

R i g h thd

nd

spJn.

Handscomb

i

ncd

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 36.440.8 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 .@

17.6 44.8 27.2 39.1 59.5

analysis of texture in piano etudes of chopin and scriabin.pdf

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