An Analysis of Texture in Selected Piano Etudes of Chopin and Scriabin

AN ANALYSIS OF TEXTURE IN SELECTED PIANO ETUDES OF CHOPIN AND SCRIABIN

A Thesis

Presented in Partial Fulfillment of the Requirements for the Degree Master of Arts

by Daniel Dewitt Mickey 111, B.M.

The Ohio State University 1980

Approved by

School of Music CONTENTS

Page LIST OF EXAMPLES ...... iv PREFACE ...... vi

The Purpose of the Study ...... vi The Significance of the Study ...... vi i The Etudes Selected for Analysis ...... vi i The Organizatlon of the Study ...... ix

Chapter I. PROBLEMS IN THE ANALYSIS OF KUSICAL TEXTURE ...... 1 Problems in Defining Texture ...... 1 . Problenis in Determining Linear Independence ...... 5 Specialized Problems in Analyzing Texture in Piano Music ...... 8

11. BASIC TYPES OF MELODIC AND ACCOMPANIMENTAL PRESENTATION ...... 10

The Single Line ...... 11 The Doubled Line ...... 14 Chordal Figuration ...... 17 Arpeggiated Figuration ...... 20 Alternating Figuration ...... 21 Convol u ted Fi gura tion ...... 22 Summary ...... 23

111. DENSITY ...... 27 Densi ty-number ...... 28 Vertical Span ...... 30 Density-compression ...... 32 Spacing-distributisii ...... 33 Density in the Etudes ...... 34 IV. RANGE ...... 39

Range-average ...... 40 Range-averages of the Etudes ...... 43 ii Chapter Page V . CONCLUSIONS ...... 53 APPENDIX: Determi nation of Range-average ...... 58 SELECT BIBLIOGRAPHY ...... 69

iii LIST OF EXAMPLES

Exampl e Page

1. Berry's terms for the description of linear independence . . I 7 2 . Scriabin Etude Op . 8 No . 8. mm . 1-3...... 12 3 . Chopin Etude Op . 10 No . 4. mm . 1-2 ...... 12 4 . Scriabin Etude Op . 8 No . 2. mm . 1-2 ...... 12 5 . Scriabin Op . 8 No . 2. mm . 1-2. with the melody notated .... 13 6 . Chopin Etude Op . 25 No . 6. mm . 27-28 ...... 14 7 . Scriabin Etude Op . 8 No . 10. mm . 58-60 ...... 14 8 . Chopin Etude Op . 25 No. 8. mm . 1-4 ...... 15 9 . Scriabin Etude Op . 8 No . 7. mm . 1-2 ...... 16 10 . Scriabin Etude Op . 8 No. 8. mm . 1-3 ...... 17 11 . Chopin Etude Op . 25 No . 4. mm . 9-12 ...... 18 12 . Scriabin Etude Op . 8 No. 5. mm . 1-3 ...... 18 13 . Scriabin Etude Op . 8 No . 5. mm. 1-3. renotated ...... 19 14 . Chopin Etude Op . 25 No. 1. mm . 1-2 ...... 20 15 . Chopin Etude Op . 10 No. 12. mm . 10-13 ...... 20 16 . Scriabin Etude Op . 8 No. 3. mm . 1-4 ...... 21 17 . Reduction of Example 16 ...... 21 18 . Scriabin Etude 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 . i2; min . 1-2 ...... 25 22 . Chopin Etude Op . 10 No . 2. final measure ...... 28 23 . Scriabsn Etude Op . 8 No . 12. mm . 1-2 ...... 29 24 . Figuration reduction of the left-haqd part of Example 23 ... 29

iv Exampl e Page 25. Synopsis of inflation and contraction of the texture-space as expressed in contra-directional relation of outer components ...... 30

V PREFACE

-The Purpose of the Study

This study examine; three basic characteristics of texture in piano music: 1) types of melodic and accompanimental presentation, 2) density, and 3) range. In selected compositions from the Chopin Etudes Opp. 10 and 25 and the Scriabin Etudes Op. 8 measurements of density and range are compared. These measurements quantify the textural differences among the types of melodic and accompanirnental presentation and also distinguish between the textural styles of the two composers, This study asserts that the texture of nineteenth century piano music, as exemplified by the etudes of Chopin and Scriabin, is lhrgely dependent upon the types of figuration used, and further, that all of the figurations found in 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 that function melodically are labeled single line and doubled line; those that function accompanimental ly are labeled chordal, arpeggiated, a1 twnating, and convol uted. As the study will demonstrate, etudes using the same type of figuration share common textural traits that can be measured according to viirious characteristics of density and range, and these common traits are

1. J, A. Westrup and F. L1. Harrison, "Figuration," The New Colle e Encyclopedia clf Music, (New York: W. W. Norton, -+1960 more strongly linked to the type of figuration used than to the style of the particular composer.

The Significance of the Study

Previous research dealing with texture is very limited, both in quantity and in scope. Typically, studies that do analyze texture are concerned with orchestral or chamber music, placing their emphasis on changes in instrumentation. As a result, the methodology and terminology used in these multi-instrument analyses do not transfer well to the investigation of piano music texture. Considering the importance of texture to musical style, it is hard to understand the neglect that texture, especially that of the piano, re- ceives in theoretical writings. Most writers limit their discussions to broad generalities and a few well-worn terms. This study provides a start- ing point for filling the void by presenting clear definitions of familiar terms, introducing new terms, and presenting a systematic methodology for deal i ng with texture in pi ano musi c.

The Etudes Selected for Analysis

Concert etudes were selected for this study to insure that: 1) the textures to be analyzed are stylistically indigenous to the piano, and 2) each composition exhibits one dominant textural type. The high level of performance technique demanded by concert etudes provides complex textures that are seldom found in any other mediums. Yet, the technical demands of these works are not regarded as compromising their artistic quality or musical value, even though their inspiration stenis from pedagogy. Etudes have the further advantage of emphasizing one principal texture within each vi i piece individually, w1,ile providing a great variety of textures within the coll ections. Composers who wrote concert etudes include Chopin, Scriabi n, Rach- maninoff, Liszt, Mendelssohn, Schumann, and Debussy. Opp. 10 and 25 of Chopin and Op. 8 of Scriabin were chosen for this investigation because their great similarity in style and form afford a good basis for comparison. The later etudes of Scriabin, Opp. 42 and 65, as well as the etudes by Rach- maninoff and Debussy, contain elements that are post-Romantic, or even modern in style, and are therefore less comparable. A1 though the "Transcendental Etudes" of Liszt are comparable in style to the works selected here, the forms arid type of content are quite different. Liszt's forms are larger and often based on variation technique while the Chopin and Scriabin etudes are shorter, generally ternary structures. In terms of technique, Liszt incorporates several. different pianistic devices in each piece, whereas Chopin and Scriabin, normally develop a single principal device. Schumann's "Symphonic Etudes" are actually a theme and variations and are all binary in form except for the last variation which functions as a grand finale. Mendelssohn's "Three Etudes" Op. io4 is too small a collection to allow a fair comparison. There are many similarities between the works of Chopin and the early works of Scriabin despite the sixty years that separate their composition. The similarities are apparently the result of intentional modeling. Scriabin's output is usually divided into three phases of development, the first of which has even been characterized as being "Chopinesque."* The Etudes Op. 8 (1894) fall in this period (1885-1900). Scriabin was fond of

2. M. Montagu-Nathan, Handbook to the Piano Works of A. Scriabin (London: J & W Chester, 19161, 2. viii Chopin'smusic and from the evident similarities in the music (e.g., see page 14 ) it is quite probable that the Etudes Op. 8 were modeled on the Chopin etudes. The individual etudes examined in this study are listed in the following outline accarding to six basic types of melodic and accompanimental presentation. Each of these basic types is described in detail in chapter two. All of the Scriabin Etudes Op. 8 are examined. The Chopin etudes are selected from Opp. 10 and 25 on the basis of their similarity of figuration to the Scriabin etudes.

Scri abi n Chopi n Etudes Etudes Op./No. Op ./No. I. Melodic presentation A. Single line 818 8/11 10/2 10/4 10/6 2512 2517

B. Doubled line 816 8/9 2516 2518 8/ 10 25110 11. Accompanimental presentation

A. Chordal figuration 8/ 5 10/11 2514 B. Arpeggiated figuration 812 8/4 1018 10112 2511

C. A1 ternating figuration 811 8/3 10/ 10 D. Convoluted figuration 817 8/12 1019 loll0

The Oraanization of the Study

As stated above, this study is concerned with three basic characteristics of texture in piano music: types of melodic and accompanimental presentation, density, and range. The logic for selecting these three characteristics is set forth in chapter one. The chapter begins with a general overview of texture by examining some of the definitions of the

ix term that can be found in current literature. It continues with the estab- lishment of the definition of texture that 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 and Scriabin and classifies the etudes accordingly. Examples of each type and a discussion of the various figurations found within them are included. Chapter three examines the different parameters of textural density giving precise definitions for each one. The basic types of accompanimental figuration discussed in chapter two are then compared according to measurements of textural density. Chapter four discusses the problems concerning the measurement of range and proposes a modified definition of range that permits more useful methods for its measurement. This method is explained in detail and then is used to contrast and compare the types of figuration and the styles of the composers. Chapter five summarizes the methodology of the study and its results and sets forth suggestions for further investigation. I wish to acknowledge Dr. Burdette Green of The Ohio State Univer- sity for his generous assistance and helpful advice during both the study's planning and its writing.

X Chapter I

a PROBLEMS IN THE ANALYSIS OF MUSICAL TEXTURE

One of the most difficult problems in analyzing texture is defining the term. The word can be defined in a variety of ways. Three different views of texture are examined below in order to develop a workable definition. The most problematic aspect of the definition involves considerations of linear independence which, for the reasons explained in the last two sections of this chapter, is not examined in this study.

Problems in Definina Texture

According to Wallace Berry, "Changes in texture. . .are often among the most readily perceptible and appreciable in the experience of music. II 3 If these changes are so apparent, then one would assume that texture would be an obvious area for extensive musical investigation. Yet there are only

a few writers who have dealt with the area of texture in detail. . Most references to 'texture, even in comprehensive analyses , are restricted to very general observations that use descriptive words such as light, heavy, homophonic, and polyphonic.

Perhaps one reason for the small amount of significant work in this important area is the lack of a clear understanding of the concept Iltexture."

It is obvious that analyses Snvolving a vague, nebulous concept will fail to produce meaningful results with any precision or significance. In the

3. Wallace Berry, Structural Functions in Music (Englewood C1 iffs, New Jersey: Prentice-Hall, 1976), 189.

1 2 minds of some authors, for example Ivor Keys and George Dyson, texture consists of all '!" characteristics of music combined it1 a vague, holistic manner.4 With this kind of broad definition, there is a temptation for analyzers to center their discussions on the area in which they are most secure, i .e. , harmony-discussions having only occasional references to the other characteristics of music. Such a definition is inadNquate. While there are useful definitions of a more specialiied nature, there is, unfortunately, wide divergence of thought concerning the specifics of what tex ture should entail. In order to provide some perspective on the problem, a few of the more useful definitions must be examined. The Ervard Dictionary of Music provides the following definition of texture. Much like woven fabric, music consists of horizontal ( "woof'l) and vertical ("warp") elements. The former are the successive sounds forming melodies, the latter the simul taneous sounds formi ng harmonies . It is these el e- ments that maKe up the texture.5

This is too vague to be a serviceable definition, but Apel does elucidate his concept of texture by listing the different characteristics he would include for consideration: polyphonic-homophonic, polyrhythmic- homorhythmic, and 1 ight-heavy. In this context, 1 ight-heavy ref'ers to 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 to Brahms (London: Dobson Books, 1961)rge Dyson, "The Texture of Modern Music," Music and Letters IV (1923), No.2, 3, and 4. 5. Will i Apel , "Texture," Harvard Dictionarv of Music 2nd ed. , rev. and en1 . (Cambridge, Massachusetts: Bel knap Press , 1969) , 842. 6. Ibid. 3 Berry's Structural Functions in Music contains one of the few in- depth discussions of texture to be found. Berry carefully avoids terms that are not defined precisely. This practice results in the use of specialized terms that, even though they are very precise, make his writing style rather cryptic, as one can see in the followirig definition.

The texture of music consists of its sounding components; it is conditioned in part by the number of those components sounding in simultaneity or concurrence, its qualities determined by the interactions, interrelations, and relative projec- tions and subst nces of component lines or other component sounding factors .7

The most notable feature of Berry's statement is his division of texture into quantitative and qual itative characteristics. The quanti ta- tive characteristics include l'. . .the number of concurrent events [commonly called thickness] as well as the degree of 'compression' of the events within a given intervallic space.Il8 He refers to both thickness and compression as having measurable densities, but also states that these measurements do not reflect the subjective impressions of dissonance and coloration that he asserts are vitally related to density. Berry's "qualitative" characteristics include the relative independence and interdependence of the horizantal components within the musical fabric as determined by directional, intervallic, and rhythmic relationships. In his Gui 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," it can be inferred that LaRue does not conceive of timbre and dynamics as specific

7. Berry, op. cit., 184. 8. -Ibid. '4 characteristics 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 "tessi tura" under the subheadings of both "texture" and "timbre, I' 1 eavi ng the issue un- decided as to whether or not they are to be viewed principally as characteristics of' texture. 9 For an analysis of texture to be meaningful , one must clearly understand which of the many possibilities mentioned in these definitions are to be considered characteristics of texture. Because the validity of the analytical results is directly connected to the precision of the definition, a single criterion was adopted for deci ding which characteristics of texture are appropriate for the study of these etudes. I believe that texture in the strictest sense should deal only with characteristics that are principally associated with either vertical or horizontal relationships. This criterion enables us to define the concept of texture according to three basic characteristics: 1) 1 inear independence, 2) density, and 3) range. Each of these characteristics involves either horizontal or vertical factors of the texture. "Linear independence" refers to the relationships between horizontal components. The degree of 1 inear independence varies on a continuum from purely homophonic textures or minimum independence , to pure1 y polyphonic textures or maximum independence , wi th any degree possible between these two extremes. However, the degree of independence does not easily lend itself to objective measurement. For this and other important reasons explained in the next two sections of this chapter, 1 inear independence was deemed inappropriate as a characteristic

9. Jan LaRue, Guidelines for Style Analysis (New York: W.W. Norton and Co., 1970) 3 23-34. 5 of texture in this study. In its place was substituted a classification system based on types of melodic and accompanimental presentation. The second characteristic, "density," refers to the number of components present at any given moment and their arrangcment within a specific vertical span. This concept involves the thickness, compression, and spacing of vertical components. The thfrd characteristic, "range," refers to the changes of pitch as the music progresses through time. Each of these characteristics of texture is explained in further detail later in the study. The previously discussed criterion that limits the definition of texture enables us to exclude the following factors since they are not normally associated with either vertical or horizontal attributes: timbre, instrumentatioii, dynamics, and articulation. Indeed, these additional factors do influence texture to some degree, but, according to the limited definition presented above, they need not be considered in a textural analysis. Dissonance or, for that matter, harmonic constructs, are primarily vertical in nature, but are commonly considered independent areas of investigation and have established systems for analysis. They therzfore do not need to be subsumed under texture. Siniilarly, rhythm is primarily a horizontal component, but one that is commonly considered an independent area of investigation. One cannot deny that components influence each other either directly or indirectly. However, for the sake of limiting the number of variables involved and sharpening the focus of the investigation, it is desirable to examine components independently and selectively.

Problems in Determining Linear Independence

Generally speaking, the horizontal components of texture result from the characteristics of the individual lines and from the relationships that 6 are formed between the lines, If each line has its own melodic and rhythmic identity and is not subservient to another line, then the lines are said to be independent, and according to tradition the music is classified as "polyphonic." Conversely, if the principal melodic and rhythmic interest centers in one line, and the remaining parts are merely accompanimental and function as one unit, then the components are not independent and the music is classified as "homophonic." It would be difficult to place all music into one or the other of these categories because there are many textures that have a limited independence and do not wholly belong to the class of homophony or polyphony. For analytical purposes it is more useful to hypcthesize that works fall at points on the continuum described earlier withrn the range from extreme independence of 1 i nes to extreme interdependence of 1 i nes . Unfortunately, 1 inear independence does not easily lend itself to objective measurement, and this is probably the reason why Berry designates 1 inear indepecdence as a "qualitative" characteristic of texture." The number of variables and the complexity of the relationships within a texture make placement on the continuum a subjective judymerrt. Berry presents the following terms in an apparent attempt to supply a systematic method for descri bi rig 1 i near independence .11

10. Berry, op.cit., 185. 11. -Ibid, 193-95. 7 Ex. 1 Berry's terms for the description of linear independence

1.4I *- *- JJA-+&d- __ 1 homorhythmi c I - - contra- 1111 IF .I 111 11 I directional

= hetero- rhythmic

1j=& contra -

This list provides terminology for three relationships of three different factors. At first glance, his array of terms seem to provide a systematic means for determi ni ng the degree of 1i near independence for any work. That is the case, however, only for note-by-note comparisons between two lines. Any attempt to label, for example, an eight-measure passage in four-part writing would require a prohibitive number of statements, or re- course to descriptive general i ties that destroy objectivity. 8

Speci a1 i zed Probl ems in Anal yzi ng Texture in Piano Music

Special analytical problems arise when one deals with texture in piano music. These problems can be attributed to several factors inherent in the medium itself. First, the piano is one of the few instrumental mediums in which all the voices or parts are realized with the same timbre (i.e., the same if we disregard the subtle differences of tone-color caused by changes in register or dynamics). This general lack of tone quality differentiation makes it difficult for a listener to isolate individual ?arts and, as a result, allows the composer more freedom to vary the number cf parts without disrupting the texture than woul d be possi bl e in heterogenous ensemb-ies where entrances and cutoffs art: more noticeable. Second, the performer is limited by the technical capabilities of his hands. Consequently coinposers write types of figuration that are known to be practical and effective in performance. This tradition is always being modified and extended, but regardless of style changes there has existed a standard core of performance skills that, can be expected of the pianist. Third, the piano, due to its mechanism, has no capacity to sustain a tone at a constant volume. This deficiency is often compensated for through use of repeated figures having constint and regular rhythmic impulses that can either simulate or create the illusion of a sustained sound. The inclusion of this type of textural filligree also facilitates smoother, more graduai changes in dynamics since there are, as a result, many more inter- mediate 1evel s avai 1ab1 e between any two dynamic 1 evel s. 9 Fourth, and this point is important, most nineteenth-century piano music, including the etudes under consideration here, falls on the homophonic side of the linear independence continuum. The reason for the homophonic bias in music of the Romantic period may be linked to the special attributes of the piano itself. In homophonic music, it is difficult enough to determine what the horizontal components are, let alone to have to attempt to quantify their degree of independence. Because homophonic music is not as linear by definition, estimates of linear independence seem less inform- ative and appropriate here than in polyphonic works. Because of these facts:

1) measurements of 1inear independence are inappropriate for homophonic music,

2) linear components are difficult to isolate in Romantic era piano music, and

3) methods for measuring linear independence are not precise, even for polyphonic music, the factor of linear independence is not examined in this study. This factor should still be considered a legitimate part of the definition of texture, in general, but for the purposes of this study and the particular body of music it examines, it is not appropriate. In its place, we substitute a classification system based on the types of figuration that are used to present melodic and accompanimental components in homophonic piano music. This classification of components is not intended to measure 1inear independence at all. Its only purpose is to provide a systematic set of descriptive terms with which to categorize the broad variety of textures in homophonic piano music. Chapter two explains this system for classifying piano figuration. Chapter I I BASIC TYPES OF MELODIC AND ACCOMPANI MENTAL PRESENTATION

Etudes are written specifically to develop performers' competencies by stressing particular performance skills. As a result, a principal textural configuration that involves one of these skills is used throughout each of the Chopin and Scriabin etudes. Consequently, classifying the etudes according to the skills involved also serves to classify these textural configurations. This method of classification is advantageous because all the textural configurations in the etudes can be related to a small number of basic patterns. This chapter examines six basic types, presenting examples of each, and explains how the Chopin and Scriabin etudes have been classified according to this system. The most basic classification of typical piano texture distinguishes between the two elementary functions in homophonic music: melody and accompaniment. Usually these functions are easily distinguished because they are delineated by separate components of the figuration, most commonly, the right hand playing the melody and the left hand in accompaniment. Pri- rrrarily, melody supplies horizontal content while accompaniment supplies vertical content. However, there is 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 fulfills both the melodic and accompanimental functions. At other times the accompaniment will include a fairly independent line that supplies an additional, third component. But, in general, melodic presentation and accompanimental 10 11 presentation can be considered independently, with each note of a particular texture performing principally one function or the other. After separating melodic from accompanimental functions , the figurations of these two components can be classified into types according to the way they are presented. In the works being considered, the melodic presentation can be divided into two types: the single line doubled in parallel intervals Similarly, accompanimental presentation can be divided into four types: 1) chordal 2) arpeggiated 3) convoluted 4) a1 ternating

These six different types of presentation are defined and explained with examples in the following sections of this chapter. The examples point out the problems of determining how an etude is to be classified and show the great variety that exists within the types. In some cases these types are divided into subcategories in order to provide finer distinctions. The subcategories are explained below as they are encountered in the musical examples, and then summarized in an outline of the types presented on page24.

The Single Line

The simplest type of melodic presentation is the single line melody. Examples of this type can be grouped into two subcategories according to the performance difficulties of the pieces. One group uses slow tempos and requires a very lc-yato style, often with the accompanimental chords or lines written for the same hand, compounding the difficulty of obtaining smooth legato connections. Etudes of this type, which are called "legato studies," have confi gurati ons simi 1ar to Example 2. EXAMPLE 2 Scriabin Etude Op. 8 No. 8, mm. 1-3 12

Lcnto (Tempr) rubatoj Nr.8

Etudes belonging to a second group, having a distinct single line melody in quicker tempo are commonly called "velocity studies." Very rapid tempos and an emphasis on scalar passages characterize these pieces. The Chopin etude in Example 3 has a figuration typical of many of these p eces.

Although velocity studies are one of the most common types in the etude genre, Scriabin did not include any of these in his etudes. Perhaps Scriabin was leary of this type because of the numerous pieces written for sheer technical display since Chopin. One characteristic of melodic presentation that might be overlooked without careful analysis is the use of polyphonic melody as in the case of Example 4. 13 In polyphonic melody, one "voice"--at least it is notated as one voice--presents two or more related melodic ideas. Thus, what appears to be a single line can actually be regarded as two or more voices at another structural level that are combined by an unfolding operation 3r by a motion to and from inner voices." Notating the right hand on two separate staves makes this relationship apparent. Notice the simp1 icity of the step-progression that 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 lines at some given level of structure, it must still be considered a single-line type of melodic presentation since it is perceived as one line at the most imme- diate, surface level. This is also a practical consideration because of 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 to the actual surface of the music. After all,

12. Felix Salzer and Carl Schachter, Counterpoint in Composition; The Study of Voice Leading (New York: McGraw-Hill , 1969), 153-160. 14 we use the phrase "rought texture'' to describe an object whose surfaces are rough without making any inferences as to its internal composition. An example later in the chapter also illustrates the necessity for this restriction (see pp. 21-22).

The Doubled Line

The second basic type of melodic presentation consists of lines doubled in suitable parallel intervals. Chopin and Scriabin each wrote an etude with the right-hand part doubled in thirds--Op. 26 No. 6 and Op. 8 No. 10 respectively. In both of these the melodic lines move chromatically to a large extent. There is also a marked similarity between the motives used in the middle sections of these terrary forms, as seen in Examples 6 and 7. The resemblance of these motives strongly suggests that Scriabin might have consciously imStated the Chopin Etudes, at least in this case.

EXAMPLE 6 Chopin Etude Op. 25 No. 6, mi. 27-28.

EXAMPLE 7 Scriabin Etude Op. 8 No. 10, mm. 53-60. 15 Each composer also wrote etudes with the right-hand part doubled

*in sixths. Example 8 shows the opening of the one by Chopin.

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

Not only does the right hand present the melody in sixths in this example, but the left hand also consists of sixths quite often. The function of the left-hand sixths is most often accompanimental, i.e., it provides a harmocic scheme. But at times the left hand part becomes melodic, as in the second half of measure four in Example 8.

Melodies doubled at the octave abound in piano literature, making this difficult figuration an obvious subject for etudes. Chopin Op. 25 No. 10 and Scriabin Op. 8 No. 9 each give the pianist practice with octaves in both hands. A variation of this scheme occurs when one or more notes are filled between the octaves. The right hand of Scriabin’s Op. 8 No. 7 is a case in point. 16 EXAMPLE 9 Scriabin Etude Op. 8 No. 7, mm. 1-2.

The question is whether or not the added middle part's role is to reinforce the melodic function or the accompanimental function. Just because these notes are played in the same register as the melody does not necessarily mean that their function is likewise melodic. Tt,e middle note of the right hand is not linked to the melody at any certain interval, nor does it always move in the same direction as the melody. Its pitch is determined by the harmony and the doublings of the accompaniment. But, the rhythm and register of this line obviously 'reinforce the melody. Here is an instance where Berry Is termi no1 ogy for 1 i near independence is useful . He would classify this line as "homorhythmic-heterodirectional-contrain'er- vallic," which provides a concise description, but does not clarify the original problem of determining function. Since the types of figuration are determined by the technical demands of the music, it is logical then that this question should also be seen from the performer's point of view. The added part, in terms of performance, belongs with the melody. This decision rests on the similarity with the melody of the part in question, and on the basis of factors such as articulation, rhythm, and register. If a decision must be made, then this added part can be said to serve primarily in a melodic role; its accompanimental characteristics, however, should not be forgotten. In summary, there are two basic types of melodic presentation: the single line and the doubled line. The former is divided into legato 17 studies and velocity studies. The latter is divided into three types: doubled thirds, doubled sixths, and doubled octaves. One shoJld bear in mind that these limited categories are appropriate only for this body of music. Doubled lines at other intervals are not found in these etudes because of the stylistic constraints of the period. However, other doublings 13 may be found in works in different styles.

Chordal Figuration

The most elementary accompaniment style is the simple chordal figuration, such as the one found ir. Scriabin's Op. 8 Nos. 8 and 11. In each of these etudes the chords are present in both the riskt- and left-hand parts, an arrangement that requires the right hand to play the melody and a part of the accompanifient at the same time. i'his procedure can result in pieces that sound deceptively easy since the listener hears only a melody supported t by chords, without realizing the control required to play simultaneously contrasting dynamics, articulations, and/or rhythms with one hand.

One should note that the accompaniment in Op. 8 No. 8 can be divided into two parts due to the bass line, which, in addition to its separate register, has some melodic characteristics of its own. This melodic independence results in a texture made up of three separate strata as shown in Example 10 EXAMPLE 10 Scriabin Etude Op. 8 No. 8 mm. 1-3. Lento (Tempo rubato) Nr. 8

13. For example, see the last set of etudes by Scriabin, Op. 65 Nos. 1,2, and 3. 18 In its simplest conformation, homophonic music consists of 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 is arranged in three strata as was Example 10, but with one major difference: the chordal stratum in the middl e requires two hands to perform.

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

As before, the right hand has both melody and chords, and now the left hand has the bass line and chords also. The left hand must skip a sizable distance in order to play both parts. The major technical difficulty of this piece is the accurate extecution of these large leaps. Large leaps occur in both hands of the following example.

EXAMPLE 12 Scriabin Etude Op. 8 No. 5, mm 1-3. 19 Here it is possible to consider the texture in four different components : a me1 ody its chordal accompaniment, a counter-me1 ody or "echo 'I and its accompaniment. Example 13 shows the different strata notated on separate staves.

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

In a chordal figuration, large 1 eaps can suggest additional strata. The constant leaping from one register to another causes the listener to separate the events into discrete groups. The effect is similar to the polyphoriic melody discussed earlier although in this case the effect is so easily perceived that it is apparent on the surface level while the PO 'Y- phoni c me1 ody requires some abstraction on the part of the listener. Because the large change in register can in effect add another stratum to the texture, types of chordal figuration must be further divided into two subcategories--one simp1 e and one with large leaps. 20 Arpegyiated Figurations

The second type of accompaniment is the arpeggiated figuration, which is a chordal unit presented in a simple linear fashion, either ascending or descending. This type of presentation can be divided into two subcategories, distinguishing those that require more than one hand-position from those that can be played in a single position, Le., when all the notes can be reached without lifting the hand or turning the thumb under the fingers. The left-hand part of 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 to remain in one position even though the figure covers a large span.

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

The second subcategory of arpeggiated figuration is shown in the following example from the "revolutionary" etude. 21 In this example the five or more pitches in each figure make it necessary for the thumb to turn under in every arpeggjo. The passing motion, c - d - eb - d - c, smooths out the figure and rounds off its linear contour.

A1 ternating Figuration

The third type of accompaniniental figuration is similar to a tremolo effect. It consists of an alternation between two notes or groups of notes. The third etude of Scriabin's Op. 8 uses this figuration in both hands.

EXAMPLE 16 Scriabin Etude Op. 8 No. 3, mm. 1-4.

If Example 16 contains accompanimental figures in both hands, then

where is the melody? By linking every other note of the figuration into 1ines and el iminating octave doubl ings , the texture changes radically, reveal ing the familiar texture of a four-voice choral e.

EXAMPLE 17 Reduction of Example 16 22 Consi dered from the viewpoint of "layer analysis," Example 17 presents the 1 eve1 directly beneath the actual foreground. At this level the melody and the linear nature of the remaining voices become clear. It appears that the melody actually exists on a more remote level than the accompanimental figuration. Strictly speaking, there is no melody at the surface level due to the alternation. But since the actual texture, <.e., the texture at the most foreground level, is generated by linear motion, one can easily extract the linear motion of the underlying level. This example can, at least at the foreground level, consist of only accompanimental f i gura tion.

Convoluted Figuration

The fourth type of accompanimental presentation is designated here as the "convoluted" figuration. This type consists of any regularly repeat- ing pattern of chord tones which has a linear contour that changes direction often. The convoluted figuration can be considered a broken chord whose tones are sounded in an irregular order, i.e., it produces a contour that cannot be described as ascending or descending, but has a specific organization that controls the contour. The Alberti bass of the Classical era provides a simple example of this type. Scriabin uses the convoluted figuration in his etude in Bb minor, shown in Example 18.

EXAMPLE 18 Scriabin Etude Op. 8. No. 7, mm. 1-2.

Presto tenebroso, agitato Nr. 7 23 The figure in the left-hand part repeats every sixth eighth-note, in a pattern that can be generally described as leaping down-up-down-down- up-down with the upward leaps landing on the beat. This particular pattern has an ambiguous harmonic rhythm which Scriabin emphasizes through the beam- ing of the eighth-notes and the phrasing marks of the left hand. The harmonies change every two beats, with each new harmony beginning two eighth- notes before the first and third beat of the measure, resulting in a harmonic rhythm that is out of phase, or displaced in respect to the rhythmic implications of the meter. Example 19 illustrates an interesting variation of the convoluted figuration used by Chopin.

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

Allcgro, :nolto agitato :to.)

Contained within the upper part of the accompanimental figure is a countermelody. Once again, there is a melodic line nested within the accompaniment. This results in a texture consisting of three strata like those in earlier examples, except that in this case, the harmonic support is below the two melodic lines instead of between them.

Summary An outline is presented here to summarize the types of figuration discussed in this chapter. Following each type are listed the etudes that make use of that texture as a principal component of the piece. 24

Scriabi n Chopin Etudes Etudes Op./No. Op ./No. 1. Melodic presentation

A. Single line 1. Legato study 8/8 8/11 10/6 25/7 2. Velocity study --- 10/2 10/4 25/2 B. Doubled line

1. Doubled in octaves 8/9 25/10

2. Doubled in thirds 8/ 10 25/6 3. Doubled in sixths 816 2518 11. Accompanirnental presentation

A. Chordal figuration 1. Simple --- 10/11 2. Large leqps 815 25/4 B. Arpeggiated figuration 1. One hand-position --- 25/ 1

2. More than one 8/2 8/4 10/8 10/12 hand-posi t I on

C. A1 ternating figuration 8/1 813 10/10

D. Convoluted figuration 8/7 8/12 10/9 loll0 25 Nine of the twenty-four Chopin etudes are not included here in any of the above categories. This is done for two reasons: First, these etudes contain textures which are combinations or special variations of the above types. For instance, Op. 25 No. 9 has Ile alternating effixt combined with a melody doubled in octaves for the right-hand part, representing a mixture of types.

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

Assai allegro (J=iiz.)

Op. 25 No. 12 uses a variation of the arpeggiated type. The unique aspect is the use of repeated notes each time the figure moves an octave. This allows the constant exchange of the first and fifth fingers, which means the hands can transverse the keyboard without ever turning the thumb underneath the other fingers, as is usual for an arpeggiated figure. For the pianist, this is a completely different technical skill. Compare Example 21 to Example 15. EXAMPLE 21 Chopin Etude Op. 25 No. 12, mm. 1-2. f 26 These combinations or special variations of the figuration types in the nine remaining etudes could be included in the category system by creating new designations. But this is not desirable because of the second reason for excluding these etudes: they have no directly comparable counter- parts in the etudes of Scriabin. The puwose of this chapter is to provide labels for the textures common to the two composers in order to make meaningful comparisons. Although one could specify more and more types, this procedure would not benefit the present study since it would diminish the bases for the comparison of texture. Chapter I I I DENSITY

As it is presented in chapter one, the investigation of texture in piano music texture involves three major categories: melodic and accompanimental presentation, density, and range. The second of these, density, concerns the number of components sounding at one time and the rel?,tive spacing of these components. This chapter examines the Chopin and Scriabin etudes with respect to their textural density. It begins with a detailed explanation of the fundamental concepts and terms dealing with density. Then it describes the general precedure adopted here for examining the etudes and follows with a comparison of the types of accompanimental presentation and their use by each composer. Discussions of textural density often contain descriptions such as lightlheavy or thin/thick without pinpointing exactly what is meant or how these characteristics are to be measured. In addition, these terms are ambiguous because they can refer to many different aspects of texture, including the number of melodic lines, the tonal color, the instrumentation, the dynamic levels, and the relative proximity of the lines. Since these terms can connote so many different things, the adoption of a more precise vocabulary is essential. In his Structural Functions in Musics Berry provides some terms that are more precise in their description of textural

components. Those re1 evant to density incl ude "densi ty-number ,'I "texture- space," and "density-compression . The following discussion examines

14. Berry op. cit., 209, 249. 27 28 these and two new terms, "vertical span" and "spacing-distribution.''

Vertical span is substituted for the concept of texture-space due to the latter's inappropriateness for this study.

Density-number

Density-number refers to the number of pitches in a vertical unit. For example, the density-number is five in the following chord.

EXAMPLE 22 Chopin Etude Op. 10 No. 2, final meas. m

Obviously, the density-number in pclyphonic music is equivalent to the number of voices in the texture (provided there are no systematic doublings) . However, in Example 22 which is homophonic, most of the horizontal parts are less clearly defined and tend to merge into vertical formations.

The lack of horizontal definition causes the vertical units, i.e., the chorda: structures to take on mors prominence -in the musical structure. When density-number no longer refers to the number of voices, it must refer to the number of pitches in each chordal structure. As a result, the density- number in homophonic music does not always correspond exactly to the number of "parts. I'

Accwding to Berry, densi ty-number refers to the number of pitches within a vertical unit which, in respect to homophonic music: of the nineteenth century, can be defined as a particular chordal unit. With this in 29 mind, one can see that the notated duration of pitches might not overlap at any point, and yet they can function harmonically as part of the same chordal unit. Consider the left-hand part of the Scriabin etude in Example 23.

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

All of the pitches in the left-hand part express tonic harmony. When the horizontal motion of the accompanimental figuration in this passage is reduced to long notes, as shown in Example 24, the chordal unit can be seen to have a density-number of seven.

EXAMPLE 24 Figuration reduction Gf the left-hand part of Example 23.

a 71

Notating the pitches of an accompaniment as a block chord makes it easier not only to observe the density-number, but also the other measurements of density as well. Because the melody functions predominantly in the horizontal dimension and only secondarily implies an underlying harmonic foundation, no attempt will be made to reduce the right hand of Example 23 to a vertical structure. 30 Vertical Span

"Vertical span" is a measurement of density which is proposed to replace Berry's term "texture-space" as an a1 ternative more appropriate to this study. Both refer to the same characteristic of texture. To understand the reasoning for this substitution requires examining both ideas. Berry defines texture-space as . . .the field enclosed by "lines" tracing the ?itch successions of outer components in addition to the two vertical, or diagonal , "1 ines" 1 inking components at "left-ri ht" extremeties at some 1wel of given structure. 18

In other words, texture-space is the field delineated by the outer- most parts. It is a two-dimensional shape that points out how gradually or suddenly the relative changes in register 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 in contradirectional relation of outer components.

15. Berry op. cit., 249. 16. Berry op. cit., 254. 31 The concept of texture-space is most useful in dealing with "textural progressions'' within a piece and with how these progressions affect the development or, in La Rue's terms, the "growth" of the music. The emphasis of' this study, however, is not placed on the progression of texture, !)ut rather on measuring textural density on an absolute scale, in order to faci 1 i tate comparisons between pieces .I7 An absol Ute scale permits measurements independent of any arbitrary reference point. For example, "thick"

chords require a reference chord that is thinner (or "nornial 'I) for the term "thick" to have meaning. The same chord might seem to be "thin" when ccm- pared to a different reference chord. Nevertheless, a chord with a dersity- number of seven retains that density-number no matter what the coinparison might be. Because in Berry's scheme, texture-space has a referential nature that is qualitative rather than quantitative, and its emphasis is direzted toward textural progression, this concept will not be useful, as such, in this study. Instead the quantitative correlate of texture-space, i .e.,

vert*ical spans h i j i be used. The term vertical span is proposed as a description of the expanse of each vertical unit measured individually. In other words, it is the span measured in terms of the number of semitones from the lowest to 'he highest

pitch in any particular vertical unit. This breaks the texture-space into discrete units that can be measured quantitatively, similar to the way analog information is convarted to digital information.

17. For an analysis of textural progression, see Calvin E. Holden, The Organization of Texture in Selected Piano Compositions of C1 audr- Debussy. Dissertation, University of Pittsburgh, 1973. 32 Dens i ty -Compressi on

Density-compression is Berry's term for the number of pitches within a particular vertical span. In Example 24 above, there are seven pitches within the span of two octaves and a fifth. If the same number of pitches were spread out over a vertical span of five octaves, then the density-corn- pression would be much lower. If the vertical-span were reduced to one octave, then it would be much higher. Stated precisely, density-compression is the ratio of density-number to vertical span. In order to make all measurements of density-compression easy to compare, all the ratios in this study are converted to a number of pitches per one octave span. Numerical ly , the densi ty-compression equal s the density number divided by the vertical span measured in semitones multiplied by twel ve semi tones per octave: Density-number 12 Density-compression = x Vertical span

For instance, in Example 24 there are seven pitches within a vertical span of 31 semitones. - Density-compression = x 12 = 2.71 31

When measuring density-compression one should realize that the ratio of pitches per octave span does not necessarily represent the subjective

impression of density. This impression is affected by the degree of dissonance involved in the vertical structure, as well as by the register in which it is 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 is compressed into a smaller vertical span. But dissonance is more properly an aspect of the harmonic 33 domain than it is of texture. In addition, the subjective impression of dissonance is difficult to quantify. Therefore, . . .it is a convenience to regard the evaluation of dissonance as a distinct parameter. . ., considering density [density-coin- pression] as the simple ratio of number to space.18

The same reasoning justifies excluding evaluations of register from the determination of density-compression. If an arrangement of notes is transposed down into a lower register, it will sound more dense than it originally did. This effect is probably due to the overtones being shifted into a range to which our ears are more sensitive. Again however, this effect can not be quantified into the measurement of densi ty-compression.

Spacing-di stribution

Berry does not provide a term to 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 density- number of 7, and a density-compression of 2.71 pitches per octave. But this information does not show how the notes are distributed within the vertical space. The pitches could be evenly spaced, or several pitches could be concentrated at one extreme. The term spacing-distribution is proposed for this component of textural density. It may be defined as a description of the pattern of pitch distribution within a particular vertical unit. Spacing-distribution is a component of density that may be more usefully characterized in general than as an absolute quantification. To specify the distribution of p-itches within a vertical span precisely would

18. Berry, op. cit., 209-10. 34 require a complete listing of the intervals present. The results of such a procedure would be more cumbersome to cope with than the original notation of the niusic that was to be described. Obviously this would have little benefit to any analysis. The more sensible option is to generalize the character of the arrangement by pointing out certain distinctive featdres. For example, the spacing-distribution of Example 24 seen earlier could be characterized as a symmetrical arrangement with open spacing at the extremes and concentrated in the center. To summarize, a particular vertical arrangement, at some given level , has three quantitative parameters: 1) densi ty-number--the number of pl tches present in a vertical structure, 2) vertical span--the expanse or space the vertical structure occupies, and 3) density-compression-- the number of pitches per octave span. In addition, there is one "descriptive" parameter, spacing-distribution, which concerns the pitch distribution pattern within the vertical span.

Density in the Etudes

Because the vertical structures in the etudes are typically presented in the accompaniment and not in the melody, though harmonies might be implied by linear motion, the rest of this chapter examines those etudes in which the principal textural components have accompanimental functions. A representative section of each of those etudes is reduced or abstracted to its vertical structures. This reduction of the figuration makes all the characteristics of density readily apparent. The measurements bken from these reductions are compiled in Table I for the comparison of various accompanimental figuration types and of the averages for each composer. Tab1 e I. DENSITY IN ACCOMPANIMENTAL FIGURATION Etude Density- Vertical Density- Spacing Op/No. Number Span Compression Distribution

Convoluted Figurations

10/9 4 19 2.53 closed at top 10/ 10 5 19 3.16 closed at top 8/ 7 5 24 2.50 closed in Riddle 8/12 7 36 2.34 closed -in middle

Average 5.25 24.50 2.63 - .- -

Arpeggi ated Figurations

10/8 12 44 3.27 closed 10/ 12 5 24 2.50 open at bottom 8/ 2 5 28 2.14 closed in middle 8/4 3 21 1.71 open evenly Average 4.34. 24.34 2.12 ---

Figurations wi'th Large Leaps

25/4 5 31 1.94 closed at top 8/ 5 5 31 1.94 open in middle

Average 5 .OO 31.O 1.94 ---

A1 ternating Figurations

8/ 1 4 24 2 .oo open at bottom 8/ 3 4 19 2.53 open evenly

Average 4 .OO 21.50 2.27 ---

Averages for Each Composer Chopi n 4.75 23.25 2.53 closed at top ScriaOin 4.71 26.14 2.16 open at top * Etude 10/8 is not averaged ( see below, pages 36-37) 36 With respect to the measurements in Table I , one should note that the density-compression averages can be determined by two a1 ternative methods which give slightly different results. In the first method, which is the one used in this study, the result is obtained by averaging the various measurements of density-compression of the individual etudes within the appropriate type. The second method involves the computation of the average densi ty-compression from the average densi ty-number and the average vertical span. The first method 5s used here because it is calculated directly from the original measurements and does not; involve any figures from previous averaging processes , as does the more indirect , second method. Comparing the averages for the various types of accompanimental presentation reveals that 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, but it should be noted that there is only a difference of three semitones between three of the four types. The etudes with 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 of 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 that the arpeggios of the etude occur in the right-hand part and the melody is in the left-hand part. This reversal of roles places the arpeggios in a drastically different register of the piano. The different tonal qualities and faster decay times of this register make the validity of any comparison of density questionable. Another important factor is the prominence of the arpeggios and the relative insignificance of the melody in the left hand. Normally melody is a 37 foreground event with accompaniment being background. l9 The accompanimental figuration supplies more content to the composition than does the melody and therefore is not limited to the subserviant role of background. Because of these substantial differences Etude Op. 10 No. 8 is not computed in the averages for its type or for Chopin's overall averages of density. The etude cannot be entirely deleted from the study, however, on, the basis of the above reasons. It is still a legitimate example of arpeggiated accompaniments with respect to basic types of presentation arld with respect to range.

The remaining three etudes with arpeggiated figurations have an average density-number of 4.34. The vertical span, as mentioned above, is very similar to the convoluted type. The density-comprescion listed for the arpeggiated type reveals that Chopin prefers arpeggios with re1ztively close spacing while Scriabin prefers a more open spacilig.

The accompaniments with large leaps are the onl,: type of fiqurations that have a substantially different average measure of vertical span. This radically higher average must be expected since the constant leaping of the hands will necessarily increase the span of the pitch distribution. The larger vertical spans of this type produce lower density-compression because the same number of pitches are being spread over a larger space. It is interesting that a1 though the figuration with large leaps generates textures with more strata, it has, at the same time, lower density-numbers and density -compressions. Perhaps the complexity of numerous textural strata com- pensates for reduced densities.

19. Foreground and background here do not refer to levels of structure, but to the relative degrees of interest and content--perhaps they should be called levels rf perceptual immediacy. 38 The type of figuration found least often in these etudes is the

a1 ternating type. The averages of the densi ty-numbers and the vertical spans

suggest a reason for its infrequent use. The alternating figuration is the most restrictive type, having both the lowest density-number and the small-

est vertical span. It appears that the constraints of the figuration do

not permit as much textural complexity as do the other types. Differences between the two composers' use of textural density

overall are very minimal. One charactel-istic difference is their prefer-

ences of spacing-distribution. In the top portion of the figurations, Chopin's spacing is relatively clcm while Scriabin's is more open. With regard to the differences between the composers, the overall averages for other factors are slight when compared to the amount of variation observed

between the types of figuration. This finding suggest; that the two com-

posers dealt with the textural possibilities of each type in approximately

the same manner, or perhaps, were guided by the same ccmstraints. In etudes,

composers strive for textural complexity in order tcj challenge the performer.

It is possible that each type of figuration has limits of textural density that cannot be exceeded without compromising the musical quality of the works. These limits, whether technical or stylistic, could account for the marked similarities. Chapter IV

RANGE

Range, like other attributes of texture, suffers from a lack of investigation. Moreover, no precise or objective data have been pvsented, nor has an adequate terminology been developed to deal with range. These limitations are probably due to the apparent simplicity of the concept. Range is commonly defined as the extreme expanse encompassed from the lowest to the highest pitch within a composition. In other words, range is determined by the two extreme pitches. Such a definition is inadequate because the amount of information it provides is very limited. Consider the fact that a piano piece of only fifty measures may contain over a thousand notes. A sample of two of these notes cannot be expected to reveal much about the piece as a whole. An alternative approach would be to conceive of range in a manner similar to the concept of tessitura. Accord- ing to the Harvard Dictionary of Music, tessiatura ". . .differs from range in that it does not take into account a few isolated notes of extraordinarily high or low pitch."20 Thus one could say that tessitura concerns the pitch range used most often, in contrast to the extreme range. Unfortun- ately there is no clear cut way to determine which pitches should be elimi- nated because they are "extraordinarily high or low." For instance, how many times should a pitch appear in a piece to be considered "within the

~~~ ~~~~~~ ~ ~ 20. Apel, op. cit., 839. 39 40 tessitura?" Should tessitura be based only on the number of times each pitch appears, or should duration values also be considered? No matter what the answer, this type of concept requires examining every note of the music and applying statistic?l procedures to obtain a meaningful result.

Such an approach would be too involved to be justified, even if an accept- able definition of "extraordinary" could be found.

Range-average

A procedure that would seem to offer a reasonable compromise between examining only two notes and examining every note, involves the use of a sampling process. By dividing a composition into a conveniently large number of segments, the extreme high and low pitches in each segment can serve as representative samples of the whole. These samples can then be averaged to prodwe a "range-average." This averaging process mitigates the effect of extraordinary pitches without having to define criteria with which to identify them. The resulting "range-average" is actually a compromise between the ideas of "extreme range" and "tessi tura." lt has the advantage of being more representative than the extreme range while not requiring an * overly invol ved process for its determi nation.

The following procedure was used to determine the range-averages.

Each etude was divided into from ten to thirteen segments of approximately equal length. The highest and lowest pitches of both the left- and right- hand parts were recorded separately for each segment. The pitches were then converted to numerical values using the standard key-numbers found on pianos

(subcontra A is key number 1, five-line C is key number 88). This operation facilitates the computation of averages. Although the piano has no intervals smaller than a semitone, the averages were indicated within a tenth of a semitone, due to the precision of the computation. With ten or more 41 samples, tenths of a semitone in the average have been regarded as significant figures. This convention also reminds the reader that the range- averages are based on several pitches and do not represent an actual note of the composition. The size of the interval between the low and high averages measured in semitones was also computed. This interval is re- ferred to as the "range-span. I'

For a simple example of the procedure, imagine a piece of music divided into two sections of equal length. The extreme pitches of the first section are C and e 2 . The extreme pitches af the second section are D and #2 g . To find the range-averagey these pitches are first converted to numbers using the key-numbers listed in figure I: C = 16, e2 = 56, D = 18, 9'' = 60. The low pitches are added together arid the sum is divided by the nurnber of samples. The same is done for the high pitch-.s.

The averages can then be converted back into conventional notation: 2 17 = C#, 58 = f# . The span is determined by the interval between the lows and the highs.

First section: C to e2 = 56 - 16 = 40 semitones Second section: D to g#2 = 60 - 18 = 42 semitones 40 ' 42 Average: 2 = 41 semitones

In deriving the average-span, a shortcut method, which gives the same results is to simply find the difference between the low and high numbers of the range-average.

58 - 17 = 41 semitones 42 FIGURE I Key-numbers of the Piano Keyboard 43 Range-averages of the Etudes

The measure numbers and sample pitches for the individual segments of each etude are listed in the tables of the Appendix. The range-averages and span-averages given in the tables of the Appendix are summarized here in Tables 11, 111, and IV. These tables are accompanied by Figures 2, 3, and 4, which represent the pitches of the respective tables in conventional notation. The reader is cautioned at this point to remember that the columns labeled "low" and "high" contain numbers representing pitch or key- number, whi 1 e the col umns 1 abel ed "span" represent interval s measured in semi tones. By comparing tables I1 and 111, one can observe that the leh-hand low note averages of the Chopin etudes vary from GG to E, and average together to give C, while Scriabin's left-hand notes vary from EE to D and average owt to AA. Thus one can see that Scriabin's low notes tend to be about a minor third lower, than Chopin's. Comparing right-hand high notes 4 3 reveals that the Chopin etudes vary from c2 to c and average out to eb , while the Scriabin etudes vary from .;.* to g'3 and average out to c3. Thus one can see that Scriabin's hish notes tend to be about a minor third lower than Chopin's. Also observe that the low averages for both composers are much more consistent than the high averages, which vary over larger spans. The left-hand highs and the right-hand lows vary over a span of slightly more than an octave, and average together at approximately the same pitches for both composers, i .e. within two semitones of each other. There is an overlap of the right- and left-hand ranges of a perfect fifth for Chopin and a minor seventh for Scriabin. It is interesting that both composers' overlaps center on the pitch eb 1 and that the true center of the piano keyboard falls between e 1 and f 1 . Table I1 CHOPIN ETUDE RANGE-AVERAGES

Etude Left Left left Righ t Right Right Hands OP/ No hand hand hand hand hand hand combined 1ow high span 7 ow high span span - _I_ 25/ 10 16.8 45.4 28.7 37.7 67.4 29.7 50.6 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

lo/ 10 20.2 49.5 29.3 44.0 74.8 30.8 54.6 2517 15.3 43.5 28.2 38.2 57.1 18.9 41.8

10/6 19.0 36.2 17.2 35.7 52.2 16.5 33.2

10/12 11 .o 48.3 37.3 37.9 67.6 29.7 56.6

101.8 12.3 52.7 40.4 32.0 76.4 44.4 64.1

2514 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

.b P 45 FIGURE 2 Range-averages of the Chopin Etudes

=IU

I I I II i y7sJ -8-J Table I11 SCRIABI rJ ETUDE RANGE-AVERAGES

Etude Left Left Left Riqht Right Right Hands Op/No hand had hand hand hand hd nd comb incd .1-ow high 2E!.!! ___1ow h!llh spJn. span 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 .@ 17.6 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

mP 47 FIGURE 3. Range-averages of the Scriabin Etudes 48 The most signfficant difference between the two composers can be seen in the average left-hand spans. Scriabin's left-hand parts tend to 90 both higher and lower than Chopin's, and actually span a range an augmented fourth larger than Chopin's. The most striking similarity can be found in the combined span--there is only two-tenths of a semitone difference between the two composers in this respect, Recause the number of keys on the piano had not yet been standard- ized when Chopin was writing, one might ask whether a difference in the size of the keyboard could account for some of the differences in range- averages. To answer this question, one needs only to examine the "extreme ranges" of the etudes. Chopin must have expected that his music would be performed on an Instrument ranging at least from CCC to f 4 (key numbers

4 to 81) since he wrote these pitches repeatedly even in the earliest 4 etudes. Scriabin wrote only pitches from AAA to e (1 to 80) in Op. 8 even though the 88-note keyboard was already standard. Scriabin's use of the lowest three keys is too infrequent to account for his range-averages being lower than Chopin's. In the twelve etudes of Op. 8, Scriabin uses key 1 once, key 2 once, and key 3 less than 10 times. Because range-averages are based on several pitch samples from each etude, they are not significantly a1 tered by such infrequent occurrences. The problem of the additional upper range available to Scriabin, but not to Chopin, is immaterial because: 1) Scriabin never uses this range in ttiese etudes, and 2) the higher range-averages are found in the Chopin etudes.

Table IV and Figure 4 compare and contrast the etudes according to

the types of presentation developed in chapter two. The most obvious result of this comparison involves the legato type of single line figuration.

Its use of high notes in the right-hand part is much more restricted than Table IV RANGE-AVERAGES FOR TIIE FIGURA’TION TYPES

Type Left LQft Ll!f t N I !]h 1; Rlqht Right Hands of hand ha ntl hand hand hand hand comb1 ned 1ow span. yan 1 ow span --a L11Etude - hhh Legs to Studies 17.2 42.7 25.5 37 04 56.4 19.1 39.3 Doubl ed LInes 14 .O 50.6 36.6 39,2 70.2 31 .O 56.2 Arpeggi ated F1 gura tions 13.3 48.5 35.5 36.7 65.5 28,9 52,3

Convoluted Flguratlons 15.1 46.4 31.2 39b1 67.7 28.6 52.6 A1 terna tlng Figura t ions 16.1 48.9 32.8 37.5 C6.8 29.4 50.8 Figurations with Large Leaps 17,O 49.3 32.3 38.7 65.9 27.2 48.9

Average of All Etudes 15.0 47.7 32.8 37 69 65.3 27.4 50.4 50 FIGURE 4, Range-averages for the Figuration Types

Legato Doubled Arpeggiated studies 1 inc figurations *El

Convol uted A1 ternat ing Figuration with Figura t ion Figure tion Large Leaps be a. I -1 -1

Average of All Etudes

h 51 those of the other types, The average high pitch of the legato single line etudes is almost an octave lower than the others. This restriction results in a much smaller right-hand span also, sirice the right-hand low average is approximately the same. The left-hand highs are also more restricted in this type, being approximately an augmented fourth lower than most of the types. Likewise, the span of the left hand is restricted accordingly. The lower boundary of the range-averages for the legato single line etudes are typical of the other types as well. In fact, the low ranges of all the types do not vary more than two or three semitones, suggesting that the lower range of each hand is relatively set while the upper range fluctuates.

The etudes with the melody doubled in parallel intervals have in both hands the wides spans of the various types. This characteristic concerns the average highs since the lows tend not to vary. The combined span is dlso wider than the other types, exceeding them by about a perfect fourth. Just because the spans of the individual hands may both be wider than those of another type, it does not necessarily follow that the span of the two hands combined will also be wider. Even though Scriabin uses larger left-hand spans and almost the same right-hand spans of Chopin, it is still the case that the two composers use combined spans that are almost identical.

The left-hand span of the convollited type of figuration is slightly smaller than the doubled-line type or the arpeggiated type. This is e3pec- ially true if we disallow Scriabin's Op 8 No. 12, which appears to have an exceptionally large span compared to the other etudes of its type. Aver- aging only the remaining three etudes produces a span of 27.8 semitones, which is smaller than all the types except for the legato single line etudes. 52 The range-avenges of the types of figuration with alternation and large leaps reveal nothing significantly different from what appears to be normal for the etudes in general. Their averages correspond very closely to the range-averages of all the etudes taken together as a group. The arpeggiated figurations use the lowest ranges of all the types in both the right and left hands. However, the difference between any of the types in respect to the average lows is marginal. The average-spans of the individual hands in this type are also wider than most types, partic- ularly for the left hand, which is only exceeded by one other type, Le., the doubled 1i ne type. Chapter V CONCLUS IONS

The most problematic aspect of any analysis of texture involves the defir,ition of the term. There *is no concensus among theoretical or analytical writers concerning which musical parameters are encompassed by "texture." This study adopts a definition 1 imited to characteristics that have definite vertical or horizontal components--basic types of melodic and accompanimental figuration, density, and range. Because, among other reasons, the study examines only homophonic piano music, an analysis of 1 inear independence was inappropriate. In its place was substituted a system which categorizes figuration into basic types according to the function it perfoms (melodic or accompanimental) and to the performance technique it requires to be realized. The proposed definition of texture can be evaluated in two ways-- according to its precision and its usefulness in practice. It is precise in that it relegates characteristics such iis instrumentation and dynamics to separate areas of investigation, thus reducing the number of variables that can complicate the investigation. The usefulness of the definition can be supported by the many quantitative measurements that are shown to be available in this study for the objective analysis of style and structure in homophonic piano music. The system proposed for classifying melodic and accompanimental presentation can be evaluated from several points of view. It provides new terminology for the description of piano figuration. It provides a

53 54 procedure for classifying complex figuration in terms of extension, vari - ation, and combination of six basic types of figuration. From the stand- point of compositional style, chapter two points out the close relationship between the piano music of Chopin and Scriabin that results from the use of similar figurations. One facet of the figuration classification system that might not be apparent is its flexibility. The system is open-ended- the categories can be divided or combined in a number of ways to provide the degree of discrimination appropriate for a particular body of music.

The examination of textural density provides support for the decision to classify the various figurations into basic types. The measurements of density reveal that certain types have particular associated characteristics.

For *instance, the convoluted type of accompaniment has the highest density- numbers and density-compressions. Figurations with large leaps have the largest vertical spans. A1 ternating figurations have the sitiallest density- numbers and smallest vertical spans. The differences between the styles of Chopin and Scriabin with regard to density were minimal. One difference that was observed was the characteristic spacing-distribution used by each composer. The Chopin etudes exhibit closed spacing at the top of the vertical units while the Scriabin etudes have open spacing at the top and closed spacing in the middle of the vertical units.

Differences between Chopin's and Scriabin's use of range are also minute. There are more similarities than differences. Moreover, the only apparently significant differences are Chopin's use of slightly higher pitches and Scriabin's use of wider left-hand spans. These findings add more support to the assumption stated in the Preface that the two composers wrote in a very similar style with respect to texture. More significant findings were observed between types of figuration than between the composers I 55 styles. This fact justifies the attention given the distinction in chapter two concerning basic types of figuration. In general it can be observed that the low range-averages of both hands tend to remain constant in all the basic types while the upper range-averages vary. It would seem logical to assume that increases in range would occur equally in both directions, but the evidence suggests that this is not the case. Etudes that have a predominance of parallel doublings contain higher pitches and wider spans than the others, Etudes with convoluted figurations tend to limit the span of the left hand--perhaps the constant motion of the part precludes larger intervals due to technical 1 imitations, or perhaps the large skips would tend to polarize the accompaniment into separate bass and middle register parts that can no longer function as an entity. Legato single line etudes have much more limited ranges than other types and do not venture into the upper registers nearly as much. Perhaps the legato effect is hampered by the piano's inabiiity to sustain volume in the higher registers. Some care must be taken in drawing conclusions based on these results. Several factors should be kept in mind. First, the methods used for averaging ranges is arbitrary in certain respects, since the number and the size of the units sampled varies somewhat. Second, the results, strictly speaking, apply only to these two collections of etudes and do not necessarily reflect upon other genres, other composers, or piano texture in general. However, the etudes were, in part, selected as being representative of the complex, idio- matic texture of nineteenth century concert pieces. Third, the composition of these etudes was separated by sixty years. Although the piano of Chopin's time was fairly advanced technically, certain developments in the construction and design of the piano might have been responsible for some of the differences between composers. The changes that occurred during this time include: 56 casting the iron frame in one solid piece instead of using composite frames of three or more separate pieces, increasing the string tension (now possible due to the stronger frames and improved piano wire) from a total of 10.9 tons to about 30 tons, overstringing and fanning out the bass strings, and re- location of the sounding board bridge.*' Changes of this kind could poss- ilby account for Scriabin's use of lower registers, since these improvements changed the quality of the bass notes.

The questions raised in this discussion about the conclusions suggest many possibilities for further investigation using the concepts and methodology presented in this study. For example, the relationships between types of figuration and density and range found here Frcbab1.y extend to genres other than etudes. A study similar to this one could be designed to investigate short "character pieces" 1 ike those found in Schumann's "Carnaval ,'I since they, like the etudes, are each structured around one principal type of figuration. A larger study could examine the homophonic piano musk of several composers , thereby invol ving a greater variety of sty1es , and coul d highlight the textural differences of various composers and/or styles. Such a study might provide useful information concerning style identification and the particular characteristics of music by individual composers. An interesting study along a different line of thought could examine the internal, formal structure of larger works such as the Beethoven sonatas using these methods of analysis. One could also investigate the progression of texture throughout a work to determine what types of patterns are present. Although the details of methodology presented here are tailored to meet the particular requirements

21. Arthur Loesser. Men, Women and Pianos: A Social History (New York: Simon and Schuster, 1954), 494-96, 564-65. of this study, the concepts and terminology are conceived on a larger scale. It is hoped that others will find these ideas fruitful in a great variety of situations. APPEND1 X

Deterrni na t Ion of Range-averages Scriabin Etude Op. 8, No. 1 Scriabin Etude Op. 8, No. 2

Measure Left-hand Riq ht- hand Measure Left-hand Risht -hand numbers -Low High Low- High n uti1 b e r s -Low -H i& -Low" High 1-5 16 46 36 57 1-2 22 40 41 58 6-10 17 46 36 58 3-4 22 48 42 60 11-15 16 49 36 63 5-6 22 48 41 58 16-20 9 48 33 62 7-8 15 48 37 53 21-25 16 55 40 65 9-10 6 47 34 56 26-30 22 46 38 58 11-12 4 50 37 59 31-35 20 41 40 57 13- 14 6 43 35 61 36-40 16 52 36 64 15-16 6 42 32 52 4?.-45 17 49 40 65 17-18 5 48 41 58 46-52 17 65 33 ai 19- 20 10 51 37 63 Averages 16.6 49.7 36.8 63.0 21-22 10 51 41 63 23-24 10 53 38 54 25-26 10 29 38 50 Averages 11.4 46.6 38 .O 57.3 APPEND1 X

DetermJnaLion of Range-,averages Scriabin Etude Op. 8, No. 3 Scriabin Etude Op. 8, No. 4 Measure Left-hand Right-hand Measure Left- hand Ri ah t-hand numbers -Low High --Low Hiqh --nurrihe rs -Low Hiqh -Low" Hbk 1-11 22 48 34 61 1-2 14 46 38 62 12-22 17 50 34 5 3-4 20 46 39 60 23-33 3 63 27 78 5-6 14 44 38 57 34-44 3 35 25 51 7 -8 15 43 34 55 45-55 8 46 35 61 9-10 24 46 40 56 56-66 13 37 34 51 11-12 26 48 43 58 67-77 13 39 33 56 13-14 29 52 48 65 78-88 22 48 34 61 15-16 17 46 39 60 89-99 18 50 38 65 17-18 14 46 38 62 100- 110 3 63 32 78 19-20 21 46 39 60 111-122 3 42 22 63 21-22 15 44 39 60 23-24 10 75 Averages 11.4 47.4 31.6 62.7 51 31 Averages 18.3 46.5 38.8 60.8 APPEND1 X Determination of Range-averages Scriabin Etude Op. 8, No. 5 Scriabin Etude Op. 8, No. 6 Measure Left-hand R ig ht - hand Measure Lef t-tiand Riqht-hand numbers -Low Hi& 5- High nutribers -Low High low" tii 1-6 15 53 36 68 1-5 18 49 42 68 7-12 10 55 32 70 6- 10 15 56 48 73 13-18 15 51 36 63 11-15 13 51 42 72 19-24 18 56 36 68 16-20 22 53 41 69 25-30 10 51 36 65 21-25 22 53 45 68 31-36 15 51 36 65 26-30 15 53 37 68 37-42 12 55 34 70 31-35 13 49 34 70 13-48 10 51 32 67 36-40 15 49 42 73 49-54 13 51 34 65 4 1-45 20 53 42 68 55-58 20 63 36 80 46-50 13 53 38 68 51-55 13 Averages 13.8 53.7 34.8 68.1 48 44 68 56-60 13 49 46 68 6 1-65 1 49 29 66

Averages 14.8 51.2 40.8 69.2

m 0 APPEND1 X

Detcmina tion of Range-ave%*ages

Scriabin Etude Op, 8, No. 7 Scriabln Etude Op, 8, No, 8 Measure Left-hand R1gh t- hand Mcasure Left-hand Right-hand numbers LOW cHir& Low Hi& InI -1-1in)be r s Low ttiqh Low High - _y - -- .I- 1-7 14 50 38 62 1-6 17 41 38 58 8- 14 16 43 36 57 7- 12 12 41 33 62 15-21 14 50 33 62 13-18 10 50 35 60 22-28 13 33 29 53 19-24 30 57 48 62 29-35 11 33 29 53 25-30 32 53 48 61 36 -4 2 10 30 28 53 31-36 17 55 38 60 43-49 9 37 33 57 37-42 17 4 I. 40 62 50-56 14 50 38 62 43-48 13 37 36 58

C)- 57-63 16 45 36 57 49-54 12 37 JJ 58 64-70 14 50 37 62 55-60 16 36 40 54 71-77 2 33 50 29 Averages 17.6 44.8 39.1 59 *5 Averages 12.1 41.3 33.3 57.1 APPEND1 X Determination of Rsngc-averages Scriabin Etude Op. 8, No. 9 Scriabin Etude Op. 8, No. 10 Measure Left-hand I1 iq h t - hand Measure Left-hand Rictht-hand

numbers Low High &- High -7n urn ber s Low Hiqh 1.-Low" High - L_ 1- 10 5 56 36 72 1-10 17 60 40 74 11-20 3 56 27 77 11- 20 17 52 40 68 21-30 8 49 22 61 21-30 12 60 41 74 31.-40 12 56 41 77 31-40 9 47 40 64 41-50 7 51 31 75 41-50 14 45 41 57 51-60 12 59 31 72 51-60 17 57 40 69 61-70 7 52 33 62 61-70 17 60 40 74 7 1-80 8 53 36 76 7 1-80 22 57 45 73 81-90 7 56 35 77 81-9G 5 60 40 68 91-100 6 55 30 79 91-100 5 60 56 74 101-103 12 48 31 60 101-110 5 42 29 62 111-122 5 67 33 77 Averages 7.9 53.7 32.6 71.6 Averages 12.1 55.6 40.4 69.5

m N APPENDIX

Determination of Range-averages

Scriabin Etuqe Op. 8, No. 11 Scriabin Etude Op. 8, No. 12 Measure Left-hand Right-hand Measure Left- hand Right-hand nurn be r s- -Low High -Low- High n urn be rs -Low High m- High 1-5 26 46 37 57 1-5- 19 51 38 67 6-10 19 46 32 57 6-10 7 55 38 70 11-15 12 46 32 53 11-15 7 55 39 70 16-20 12 47 33 63 16-20 10 46 41 72 21-25 21 50 37 57 21-25 13 43 39 70 26-30 14 50 38 58 26-30 3 42 34 61 31-35 14 46 32 55 31-35 7 51 38 65 36-40 19 48 33 57 36-40 7 5 1. 39 70 4 1-45 19 46 38 55 41-45 6 48 45 70 46- 50 14 33 33 45 46-50 7 46 38 67 51-54 14 50 57 69 51-55 7 62 26 79

Averages 16.7 46.2 36.5 56.9 Averages 8.5 50.0 37.7 69.2

m w APPEND1 X

Determination of Range-averages

Chopin Etude Op. 25, No. 4 Chopin Etude Op. 25, No. 6

Measure Left-hand Right-hand Measure Left-hand Right-hand numbers -Low High -Low High numbers -Low High -Low- High 1-6 20 45 44 68 1-6 19 45 50 75 7-12 20 46 47 68 7-12 12 53 48 80 13-18 20 45 44 64 13-18 10 63 38 80 19-24 24 45 40 61 19-24 18 48. 50 75 25-30 19 45 43 60 25-30 21 51 45 81 31-36 19 47 43 64 31-36 19 65 41 77 37-42 20 45 44 68 37-42 19 55 51 79 43-48 20 46 44 64 43-48 17 51 35 80 49-54 18 45 40 68 49-54 12 41 36 72 55-60 16 46 40 61 55-60 12 41 33 79 61-65 25 38 40 54 61-64 12 36 28 40 Averages 20.1 44.8 42.6 63.6 Averages 15.5 50.2 41.4 74.4

m F APPENDIX Determination of Range-averages Chopin Etude Op. 25, No. 7 Chopin Etude Op. 25, No. 8 Measure Left-hand Right-hand Measure Left-hand Right-hand numbers -Low -HiCJtl- -Low High --numbers -Low High -Low High 1-7 17 44 40 56 1-3 12 48 45 67 8- 14 15 44 36 56 4-6 17 50 45 67 15-21 25 44 39 60 7-9 21 53 46 74 22-28 9 52 42 62 10-12 12 46 40 64 29-35 7 43 43 60 13-15 24 36 40 58 36-42 15 43 40 61 16-18 24 36 44 76 43-49 17 44 39 56 19-21 17 57 45 74 50-56 10 44 36 56 22-24 17 50 45 69 57-63 21 48 36 56 25-27 12 55 46 70 64-69 17 29 31 48 28-30 17 53 41 67 31-33 Averages 15.3 43.5 38.2 57.1 10 36 33 64 34 - 36 17 46 38 77 Averages 16.7 47.2 42.3 68.9 APPENDIX Determination of Range-averages

Chopin Etude Op. 25, No. 10 Chopin Etude Op.10, No. 6 Measure Left-hand Right-hand Measure Left-hand Right-hand numbers -Low High Low High numbers High Low High - -Low _I_ 1-10 9 39 33 63 1- 5 27 41 43 55 11-20 21 53 43 75 6-10 24 41 35 50 21-30 8 60 a4 78 11-15 24 38 35 55 31-40 17 46 36 67 16-20 14 37 33 50 41-50 22 47 37 67 21-25 10 29 34 51 51-60 20 43 38 61 26-30 12 36 36 56 61-70 22 47 38 67 31-35 15 35 36 58 71-80 20 43 38 61 36-40 13 26 33 48 81-90 22 47 38 67 41-45 27 41 43 55 91 - 100 17 35 38 65 46-50 24 41 34 53 101-110 14 39 38 63 51-53 19 33 31 43 111-1 18 10 46 41 75 Averages 19 .o 36.2 52.2 52.2 Averages 16.8 45.4 37.7 67.4 APPEND1 X

Determi nation of Range-averages

Chopin Etude Op. 10, No 8 Chopin Etude Op. 10, No 9

Measure Left-hand Right-hand Measure Left-hand Right-hand numbers numbers Low High High -Low High & High 7 1-7 8 42 28 74 1-6 21 41 40 64 8-15 9 45 28 78 7-12 21 41 40 60 16-23 8 45 28 74 13-18 19 41 40 64 24-31 6 45 25 78 19-24 12 36 36 58 32-39 5 58 25 76 25-30 11 50 41 77 40-47 13 56 35 73 31-36 28 48 48 77 48-55 13 59 50 76 37-42 21 41 40 64 56-63 9 61 28 74 43-48 21 41 40 72 64-71 8 45 28 74 49-54 21 46 45 72 72-79 i5 45 29 81 55-60 21 41 43 77 80-87 33 62 47 78 61-67 21 65 44 81 88-95 21 69 33 81 Averages 19.7 44.6 41.5 69.6 Averages 12.3 52.7 32.0 76.4 APPEND1 X Determi nation of Range-averages

Chopin Etude Op. 10, No. 10 Chopin Etude Op. 10, No. 12

Measure Left-hand Right-hand Measure Left-hand Right-hand numbers -Low High -Low High numbers -Low High -Low High 1-7 24 49 43 70 1-7 11 60 28 74 8- 14 19 50 43 72 8-14 16 43 28 78 15-21 20 47 39 76 15-21 11 43 28 74 22-28 17 45 41 70 22-28 14 47 25 78 29-35 24 44 44 72 29-35 10 47 25 76 36-42 25 50 50 75 36-42 9 48 35 73 43-49 19 59 43 80 43-49 11 60 50 76 50-56 19 59 48 77 50-56 12 43 28 74 57-63 19 48 43 74 57-63 11 43 28 74 64-70 24 50 54 81 64-70 14 42 29 81 71-77 12 43 36 76 71-77 9 43 47 78 7884 Averages 20.2 49.5 44.0 74.8 4 60 33 81 Averages 11 .o 48.3 32 .O 76.4 69 SELECT BIBLIOGRAPHY

Apel, Willi. "Texture", Harvard Dictionary of Music, 2nd ed. rev. and enl. Cambridge, Massachusetts: Bel knap Press, lF6T Berry, Wallace. Structural Functions in Music. Englewosd Cliffs, New Jersey: Prenti ce-Hal 1 , 1976. Bowers, Fathion. The New Scriabin; Enigma and Answers. New York: St. Martin's Press, 1973. . Scriabin; A Biography of the Kuss-ian Composer 1871-1915, 2 vols. Tokyo: Kodansha International 1969. Chopin, Frederic. EtGden, ed. by Herrnann Scholtz. Frankfort: C. F. Peters, n.d. Dyson, George. "The Texture of Modern Music," Music and Letters IV (1923), Nos. 2, 3, and 4. Ganz, Peter Felix. "The Development of the Etude for Piano forte." Dissertation, Northwestern University, 1960. Garvelmann, Donald. Scriabin: Complete Piano Music, booklet for the record album of the same title, perf. by Michael Ponti. SVBX 5462, 5463, and 5474 (1974). Holden, Calvin E. "The Organization of Texture in Selected Piano Compositions of Claude Debussy. I' Dissertation, University of Pittsburgh, 1973. Keys, Ivor. The Texture of Music; From Purcell to Brahms.- Londun: Dennis Dobson, 1961. LaRue, Jan. Guidelines for Style Analysis. New York: W. W. Norton and Co., 1970. Loesser, Arthur. Men, Women and Pianos; A Social History. New York: Simon and Schuster, 1954. Nordgren, Quentin R. "A Measure of Textural Patterns and Strengths," Journal of Music Theory IV/1 (April 1960), 19-31. Ratner, Leonard G. Harmony; Structure and Style. New York: McGraw-Hill Co., 1962. Salzer, Felix and Carl Schachter. Counterpoint in Composition; The Study of Voice Leading. New York: McGraw-Hill , 1969. Skrjabin, Alexander. Etiden, Band I of Ausgewihlte Klavierwerke, ed. by Gunter ?hilipp. Frankfort: C. F. Peters, 1965.