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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. . . . . . . . . . . . .
i i
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Chapter Page
V . CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . 53 APPENDIX: Determi n a t i o n o f Range-average . . . . . . . . . . . . . . 58SELECT BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . 69
iii
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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
i v
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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
v i i
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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.
v i i i
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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
i x
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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.
1
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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,"
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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.
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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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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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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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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.
EXAMPLE 19 Chopin Etude Op. 10 No. 9, mm. 1-3.
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
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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.
EXAMPLE 21 Chopin Etude Op. 25 No. 12, mm. 1-2.
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.
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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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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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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
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F IGURE I Key-numbers o f t h e Piano Keyboard
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FIGURE 2 Range-averages o f the Chopin Etudes
I
I I
I I I i
y7sJ - 8 - J
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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