AN ANALYSIS OF TEXTURE
IN SELECTED PIANO ETUDES OF CHOPIN AND SCRIABIN
A Thesis
Presented in Partial Fulfillment o f the Requirements
f o r the Degree Master o f Arts
by
Daniel Dewitt Mickey 111, B.M.
The Ohio S t a t e University
1980
Approved by
School of Music
CONTENTS
..........................
..............................
LIST OF EXAMPLES
PREFACE
The
The
The
The
...................
................
...............
................
Purpose of the Study
Significance o f the Study
Etudes Selected f o r Analysis
Organizatlon o f the Study
Chapter
I.
11.
111.
IV.
.......
PROBLEMS IN THE ANALYSIS OF KUSICAL TEXTURE
Problems i n Defining Texture
. Problenis i n Determining Linear Independence
Specialized Problems i n Analyzing
Texture in Piano Music
.............
......
...............
BASIC TYPES OF MELODIC AND ACCOMPANIMENTAL
PRESENTATION
.....................
The Single Line . . . . . . . . . . . . . . . . . . . .
The Doubled Line . . . . . . . . . . . . . . . . . . .
Chordal Figuration . . . . . . . . . . . . . . . . . .
Arpeggiated Figuration . . . . . . . . . . . . . . . .
Alternating Figuration . . . . . . . . . . . . . . . .
Convol u ted Fi gura tion . . . . . . . . . . . . . . . . .
Summary . . . . . . . . . . . . . . . . . . . . . . . .
DENSITY . . . . . . . . . . . . . . . . . . . . . . . . .
Densi ty-number . . . . . . . . . . . . . . . . . . . .
Vertical Span . . . . . . . . . . . . . . . . . . . . .
Density-compression . . . . . . . . . . . . . . . . . . .
Spacing-distributisii . . . . . . . . . . . . . . . . .
Density i n the Etudes . . . . . . . . . . . . . . . . .
RANGE . . . . . . . . . . . . . . . . . . . . . . . . . .
.....................
Range-averages o f the Etudes . . . . . . . . . . . . .
Range-average
ii
Page
iv
vi
vi
vi i
vi i
ix
1
1
5
8
10
11
14
17
20
21
22
23
27
28
30
32
33
34
39
40
43
Chapter
Page
........................
APPENDIX: Determi n a t i o n o f Range-average . . . . . . . . . . . . . .
SELECT BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . .
V
.
CONCLUSIONS
iii
53
58
69
LIST OF EXAMPLES
Exampl e
.
1
.
3.
2
.
5.
6.
4
.
8.
9.
7
10
.
.
11
12
.
13 .
14
.
15 .
16
.
17 .
.
19 .
18
.
2 1.
22 .
20
23
.
24
.
Page
..
S c r i a b i n E t u d e Op . 8 No . 8. mm . 1-3. . . . . . . . . . . . . .
Chopin E t u d e Op . 10 No . 4. mm . 1-2 . . . . . . . . . . . . . .
S c r i a b i n E t u d e Op . 8 No . 2. mm . 1-2 . . . . . . . . . . . . .
S c r i a b i n Op . 8 No . 2. mm . 1-2. w i t h t h e melody n o t a t e d . . . .
Chopin E t u d e Op . 25 No . 6. mm . 27-28 . . . . . . . . . . . . .
S c r i a b i n E t u d e Op . 8 No . 10. mm . 58-60 . . . . . . . . . . . .
Chopin E t u d e Op . 25 No. 8. mm . 1-4 . . . . . . . . . . . . . .
S c r i a b i n E t u d e Op . 8 No . 7. mm . 1-2 . . . . . . . . . . . . .
S c r i a b i n E t u d e Op . 8 No. 8. mm . 1- 3 . . . . . . . . . . . . .
Chopin E t u d e Op . 25 No . 4. mm . 9-12 . . . . . . . . . . . . .
S c r i a b i n E t u d e Op . 8 No. 5. mm . 1-3 . . . . . . . . . . . . .
S c r i a b i n E t u d e Op . 8 No . 5. mm. 1-3. r e n o t a t e d . . . . . . . .
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 n d e p e n d e n c e
I
7
12
12
12
13
14
14
15
16
17
18
18
19
. . . . . . . . . . . . . . 20
Chopin E t u d e Op . 10 No. 12. mm . 10-13 . . . . . . . . . . . . 20
S c r i a b i n E t u d e Op . 8 No. 3. mm . 1- 4 . . . . . . . . . . . . . 2 1
R e d u c t i o n of Example 16 . . . . . . . . . . . . . . . . . . . 2 1
S c r i a b i n E t u d e Op . 8 No . 7. mm . 1- 2 . . . . . . . . . . . . . 22
Chopin E t u d e Op . 10 No . 9. mm . 1-3 . . . . . . . . . . . . . . 23
Chopin E t u d e Op . 25 No . 9. mm . 1-4 . . . . . . . . . . . . . . 25
Chopin E t u d e Op . 25 No . i 2 ;
. 1-2 . . . . . . . . . . . . . 25
Chopin E t u d e Op . 10 No . 2. f i n a l m e a s u r e . . . . . . . . . . . 28
S c r i a b s n E t u d e Op . 8 No . 12. mm . 1- 2 . . . . . . . . . . . . . 29
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
Chopin E t u d e Op . 25 No. 1. mm . 1-2
min
iv
Exampl e
25.
Page
Synopsis o f i n f l a t i o n and c o n t r a c t i o n o f t h e texture- space
as 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 r
components
..........................
V
30
PREFACE
The Purpose
o f the Study
This study examine; three basic characteristics of texture i n piano
music:
1) types o f melodic and accompanimental presentation, 2 ) density,
and 3 ) range.
I n selected compositions from the Chopin Etudes Opp. 10 and
25 and the Scriabin Etudes Op. 8 measurements o f 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 t h a t the texture of nineteenth century p i a n o
music, as exemplified by the etudes o f Chopin and Scriabin, i s lhrgely
dependent upon the types of f i g u r a t i o n used, and further, t h a t a l l o f the
figurations found i n these collections are derived from six basic types.
In t h i s context, the term "figuration" i s 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 l i n e 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 u s i n g the same type of
figuration share common textural traits t h a t can be measured according t o
viirious characteristics o f density and range, and these common t r a i t s are
-+
1. J , A. Westrup and F. L 1 . Harrison, "Figuration," The New Colle e
Encyclopedia clf Music, (New York: W . W . Norton, 1960
more strongly linked t o the type of figuration used t h a n t o the s t y l e of
the particular composer.
The Significance of the Study
Previous research dealing w i t h texture i s very limited, b o t h in
quantity and in scope.
Typically, studies t h a t do analyze texture are
concerned with orchestral or chamber music, placing t h e i r emphasis on
changes in instrumentation.
As a r e s u l t , the methodology and terminology
used in these multi-instrument analyses do not transfer well t o the investi g a t i o n of piano music texture.
Considering the importance of texture t o musical s t y l e , i t i s hard
t o understand the neglect t h a t texture, especially t h a t of the piano, re-
ceives i n theoretical writings.
Most writers limit t h e i r discussions t o
broad generalities and a few well-worn terms.
This study provides a s t a r t -
i n g p o i n t for f i l l i n g the v o i d by presenting clear definitions o f familiar
terms, introducing new terms, and presenting a systematic methodology f o r
deal i ng w i t h texture i n pi ano musi c.
The Etudes Selected f o r 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 c a l l y indigenous t o the piano,
and 2) each composition exhibits one dominant textural type.
The h i g h level
of performance technique demanded by concert etudes provides complex textures
t h a t are seldom found i n any other mediums.
Yet, the technical demands of
these works are n o t regarded as compromising t h e i r a r t i s t i c q u a l i t y or musical value, even t h o u g h t h e i r i n s p i r a t i o n stenis from pedagogy.
Etudes have
the further advantage of emphasizing one principal texture w i t h i n each
vii
piece individually, w1,ile providing a great variety of textures within the
coll ections.
Composers who wrote concert etudes include Chopin, Scriabi n , Rachmaninoff, Liszt, Mendelssohn, Schumann, and Debussy. Opp. 10 and 25 of
Chopin and Op. 8 of Scriabin were chosen for t h i s investigation because
t h e i r great similarity i n s t y l e and form afford a good basis f o r comparison.
The l a t e r etudes of Scriabin, Opp. 42 and 65, as well as the etudes by Rachmaninoff and Debussy, contain elements t h a t are post-Romantic, or even modern
A1 though the "Transcendental
in style, and are therefore less comparable.
Etudes" of Liszt are comparable i n s t y l e t o the works selected here, the
forms arid type o f 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.
I n 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 a l l binary
in form except for the l a s t variation which functions as a grand finale.
Mendelssohn's "Three Etudes" Op. io4 i s t o o small a collection to allow a
f a i r 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 t h e i r composition.
The similarities are apparently the result of intentional modeling.
Scriabin's o u t p u t i s usually divided i n t o three phases o f development, the
f i r s t of which has even been characterized as being "Chopinesque."* The
Etudes Op. 8 (1894) f a l l i n t h i s 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.
viii
Chopin'smusic and from the evident s i m i l a r i t i e s in the music (e.g., see
page 14 ) i t i s quite probable t h a t the Etudes Op. 8 were modeled on the
Chopin etudes.
The individual etudes examined in this study are l i s t e d i n the
following outline accarding t o s i x basic types of melodic and accompanimental presentation.
chapter two.
Each o f these basic types i s described i n detail i n
All of the Scriabin Etudes Op. 8 are examined.
The Chopin
etudes are selected from Opp. 10 and 25 on the basis of t h e i r similarity
of figuration t o the Scriabin etudes.
I.
Scri abi n
Etudes
Op./No.
Chopi n
Etudes
Op ./No.
Melodic presentation
A.
Single l i n e
818 8/11
10/2 10/4 10/6
2512 2517
B.
Doubled l i n e
816 8/9
8/ 10
2516 2518
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 l o l l 0
The Oraanization of the Study
As stated above, t h i s study is concerned w i t h three basic char-
a c t e r i s t i c s of texture i n piano music:
types of melodic and accompanimen-
t a l presentation, density, and range.
The logic f o r selecting these three
characteristics i s s e t forth i n chapter one.
The chapter begins w i t h a
general overview of texture by examining some o f the definitions of the
ix
term t h a t can be found in current l i t e r a t u r e .
I t continues with the estab-
lishment of the definition of texture t h a t i s 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 c l a s s i f i e s 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
g i v i n g precise definitions f o r each one.
The basic types of accompanimental
figuration discussed in chapter two are then compared according t o measurements 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 detail and then
is used t o contrast and compare the types of figuration and the styles o f
the composers.
Chapter five summarizes the methodology of the study and i t s results
and s e t s 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 both the study's
planning and i t s writing.
X
Chapter I
a
PROBLEMS IN THE ANALYSIS OF MUSICAL TEXTURE
One o f the most d i f f i c u l t problems i n analyzing texture i s defining
the term. The word can be defined i n a variety of ways. Three different
views of texture are examined below in order t o develop a workable definition.
The most problematic aspect of the definition involves considerations
of linear independence which, for the reasons explained in the l a s t two
sections of t h i s chapter, i s n o t examined in t h i s study.
Problems i n Definina Texture
According t o Wallace Berry, "Changes i n texture.
. .are
often among
the most readily perceptible and appreciable i n the experience o f music. II 3
If these changes are so apparent, then one would assume t h a t 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 i n d e t a i l . . Most references t o 'texture, even i n comprehensive analyses , are r e s t r i c t e d t o very
general observations that use descriptive words such as l i g h t , heavy, homophonic, and polyphonic.
Perhaps one reason f o r the small amount o f significant work i n t h i s
important area i s the lack of a clear understanding o f the concept Iltexture."
I t i s obvious t h a t analyses Snvolving a vague, nebulous concept will f a i l
t o produce meaningful results w i t h any precision or significance.
3.
In the
Wallace Berry, Structural Functions i n Music (Englewood C1 i f f s , New
Jersey: Prentice-Hall, 1976), 189.
1
2
minds of some authors, f o r example Ivor Keys and George Dyson, texture cons i s t s of a l l
'!"
characteristics of music combined
it1
a vague, holistic
manner.4 With t h i s kind of broad definition, there i s a temptation for
analyzers t o center t h e i r discussions on the area in which they are most
secure, i .e. , harmony-discussions having only occasional references t o the
other characteristics of music.
Such a definition i s inadNquate.
While
there are useful definitions o f a more specialiied nature, there i s , unfortunately, wide divergence of thought concerning the specifics of what tex
ture should e n t a i l .
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 definition
of texture.
Much l i k e woven fabric, music consists of horizontal
( "woof'l) and vertical ("warp") elements. The former are
the successive sounds forming melodies, the l a t t e r the
simul taneous sounds formi ng harmonies I t i s these el ements that maKe u p the texture.5
.
This i s too vague t o be a serviceable definition, b u t Apel does
elucidate his concept of texture by l i s t i n g the different characteristics
he would include for consideration:
homorhythmic, and 1 ight-heavy.
polyphonic-homophonic, polyrhythmic-
I n t h i s context, 1 ight-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: 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. I b i d .
.
3
Berry's Structural Functions i n Music contains one of the few i n -
depth discussions of texture t o be found.
t h a t are n o t defined precisely.
Berry carefully avoids terms
This practice results i n the use of
specialized terms t h a t , even t h o u g h they are very precise, make his writi n g s t y l e rather cryptic, as one can see in the followirig definition.
The texture of music consists of i t s sounding components;
i t i s conditioned i n part by the number of those components
sounding in simultaneity or concurrence, i t s qualities determined by the interactions, interrelations, and r e l a t i v e projections and subst nces of component lines or other component
sounding factors .7
The most notable feature o f Berry's statement i s his division of
texture i n t o quantitative and qual i t a t i v e characteristics.
t i v e characteristics include
l'.
. .the
The quanti t a -
number o f concurrent events [commonly
called thickness] as well as the degree o f 'compression' o f the events
within a given i n t e r v a l l i c space.Il8 He refers t o both thickness and compression as having measurable densities, b u t also s t a t e s t h a t these measurements do not r e f l e c t the subjective impressions o f dissonance and coloration
t h a t he asserts are v i t a l l y related t o density.
Berry's "qualitative"
characteristics include the relative independence and interdependence of
the horizantal components within the musical fabric as determined by direct i o n a l , intervallic, and rhythmic relationships.
In his G u i del ines for Sty1 e 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 a s specific
7. Berry, op. c i t . , 184.
8. Ibid.
characteristics of texture.
' 4
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' 1eavi ng the issue undecided as t o whether or not they are t o be viewed principally as characteri s t i c s of' texture. 9
For an analysis of texture t o be meaningful , one must clearly understand which of the many possibilities mentioned i n these definitions are t o
be considered characteristics of texture.
Because the validity of the
analytical r e s u l t s i s directly connected t o the precision of the definition,
a single c r i t e r i o n was adopted f o r deci ding which characteristics of texture
are appropriate f o r the study of these etudes.
I believe t h a t texture i n
the s t r i c t e s t sense should deal only w i t h characteristics t h a t are principally associated w i t h either vertical o r horizontal relationships.
This
criterion enables us t o define the concept of texture according t o three
basic characteristics:
1) 1 inear independence, 2 ) density, and 3) range.
Each of these characteristics involves either horizontal o r vertical factors of the texture.
"Linear independence" refers t o the relation-
ships between horizontal components.
The degree o f 1 inear independence
varies on a continuum from purely homophonic textures o r minimum independence , t 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 i t s e l f t o objective measurement.
For this
and other important reasons explained i n the next two sections of this
chapter, 1inear independence was deemed inappropriate as a characteristic
9. Jan LaRue, Guidelines for Style Analysis (New York:
1970) 3 23-34.
W.W.
Norton and Co.,
5
of texture i n this study.
In i t s place was substituted a classification
system based on types of melodic and accompanimental presentation.
The second characteristic, "density," refers t o the number of
components present a t any g i v e n moment and t h e i r arrangcment w i t h i n a
specific vertical span.
This concept involves the thickness, compression,
and spacing o f vertical components.
The t h f r d characteristic, "range,"
Each
refers t o the changes of pitch as the music progresses through time.
of these characteristics of texture i s explained i n further detail l a t e r
in the study.
The previously discussed criterion t h a t limits the definition of
texture enables us t o exclude the following factors since they are n o t
normally associated with either vertical or horizontal attributes:
instrumentatioii, dynamics, and articulation.
timbre,
Indeed, these additional fac-
tors do influence texture t o some degree, b u t , according t o the limited
definition presented above, they need n o t be considered i n a textural analysis.
Dissonance or, f o r t h a t matter, harmonic constructs, are primarily
vertical i n nature, b u t are commonly considered independent areas of investigation and have established systems f o r analysis.
need t o be subsumed under texture.
They therzfore do not
Siniilarly, rhythm i s primarily a hori-
zontal component, b u t one t h a t i s commonly considered an independent area
of investigation.
One cannot deny that components influence each other
e i t h e r directly o r indirectly.
However, for 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 t o examine components independently and selectively.
Problems i n Determining Linear Independence
Generally speaking, the horizontal components of texture r e s u l t from
the characteristics o f the individual lines and from the relationships t h a t
6
are formed between the lines,
I f each l i n e 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 classified as
"polyphonic."
Conversely, i f the principal melodic and rhythmic i n t e r e s t
centers i n one line, and the remaining parts are merely accompanimental and
function as one unit, then the components are not independent and the music
i s classified as "homophonic."
I t would be d i f f i c u l 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 independence 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 e a r l i e r withrn the range from extreme
independence of 1 i nes t o extreme interdependence of 1 i nes
.
Unfortunately, 1 inear independence does n o t easily lend i t s e l f t o
objective measurement, and t h i s i s probably the reason why Berry designates
1 inear indepecdence as a "qualitative" characteristic of texture." The
number o f variables and the complexity o f the relationships w i t h i n a texture make placement on the continuum a subjective judymerrt.
Berry presents
the following terms in an apparent attempt t o supply a systematic method
.
for descri b i rig 1 i near independence 11
10. Berry, op.cit.,
11. I b i d , 193-95.
185.
Ex. 1 Berry's terms for the description of linear independence
JJA-+&d
- __
1
homorhythmi c
.
I
4
*-
1
.
I
1
1
1
1
1
1
7
I
I
1
1
- - contradirectional
F
1
I
= hetero-
rhythmic
1j=&
contra-
This l i s t provides terminology for three relationships of three
different factors.
A t f i r s t glance, his array of terms seem t o provide a
systematic means for determi n i ng the degree of 1i near independence for any
work.
That i s the case, however, only for note-by-note comparisons between
two lines.
Any attempt t o label, for example, an eight-measure passage i n
four-part w r i t i n g would require a prohibitive number o f statements, or recourse t o descriptive general i t i e s t h a t destroy objectivity.
8
Speci a1 i zed Probl ems in Anal yzi ng
Texture i n Piano Music
Special analytical problems a r i s e when one deals with texture i n
piano music.
These problems can be attributed t o several factors inherent
in the medium i t s e l f .
F i r s t , the piano i s one of the few instrumental
mediums i n which a l l the voices o r parts are realized with the same timbre
( i .e., the same i f we disregard the subtle differences o f tone-color caused
by changes in register o r dynamics). This general lack of tone quality
differentiation makes i t d i f f i c u l t for a l i s t e n e r t o i s o l a t e individual ? a r t s
and, as a r e s u l t , allows the composer more freedom t o 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.
Second, the performer i s limited by the technical capabilities of
his hands.
Consequently coinposers write types of figuration t h a t are known
t o be practical and effective i n performance.
T h i s tradition i s always be-
i n g modified and extended, b u t regardless o f s t y l e changes there has existed
a standard core of performance s k i l l s that, can be expected of the pianist.
T h i r d , the piano, due t o i t s mechanism, has no capacity t o sustain
a tone a t a constant volume. This deficiency i s often compensated f o r
through use of repeated figures having constint and regular rhythmic impulses
that can e i t h e r simulate o r create the illusion o f a sustained sound.
The
inclusion of this type of textural f i l l i g r e e also f a c i l i t a t e s smoother, more
graduai changes i n dynamics since there are, a s a r e s u l t , many more intermediate 1evel s avai 1ab1 e between any two dynamic 1 evel s.
9
Fourth, and t h i s p o i n t i s important, most nineteenth- century piano
music, i n c l u d i n g t h e etudes under c o n s i d e r a t i o n here, f a l l s on t h e homophonic s i d e o f t h e l i n e a r independence continuum.
The reason f o r t h e
homophonic b i a s i n music o f t h e Romantic p e r i o d may be l i n k e d t o t h e s p e c i a l
a t t r i b u t e s o f t h e piano i t s e l f .
I n homophonic music, i t i s d i f f i c u l t enough
t o determine what t h e h o r i z o n t a l components are, l e t alone t o have t o attempt
t o q u a n t i f y t h e i r degree o f independence.
Because homophonic music i s n o t
as l i n e a r by d e f i n i t i o n , estimates o f l i n e a r independence seem l e s s i n f o r m a t i v e and a p p r o p r i a t e here than i n polyphonic works.
Because o f these f a c t s :
1) measurements o f 1i n e a r independence a r e i n a p p r o p r i a t e f o r
homophonic 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 Romantic
e r a piano music, and
3) methods f o r measuring l i n e a r independence a r e n o t p r e c i s e ,
even f o r polyphonic music,
the 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 study. T h i s f a c-
t o r should s t i l l be considered 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 e x t u r e ,
i n general, b u t f o r t h e purposes o f t h i s study and t h e p a r t i c u l a r body o f
music i t examines, i t i s n o t a p p r o p r i a t e .
I n i t s place, 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 system based on t h e types o f f i g u r a t i o n t h a t a r e used t o p r es e n t melodic and accompanimental components i n homophonic piano music.
classification
at all.
This
o f components i s n o t intended t o measure 1i n e a r independence
I t s o n l y purpose i s t o p r o v i d e a systematic s e t of d e s c r i p t i v e
terms w i t h which t o c a t e g o r i z e t h e broad v a r i e t y o f t e x t u r e s i n homophonic
piano music.
ation.
Chapter two e x p l a i n s t h i s system f o r c l a s s i f y i n g piano f i g u r -
Chapter I I
BASIC TYPES OF MELODIC AND
ACCOMPANI MENTAL PRESENTATION
Etudes are written specifically t o develop performers' competencies
by stressing particular performance s k i l l s .
As a r e s u l t , a principal text-
ural configuration t h a t involves one o f these s k i l l s i s used throughout
each of the Chopin and Scriabin etudes.
Consequently, classifying the etudes
according t o the s k i l l s involved also serves t o classify these textural configurations.
This method o f classification i s advantageous because a l l the
textural configurations i n the etudes can be related t o 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 t o this system.
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 easily distinguished because
they are delineated by separate components o f the figuration, most commonly,
the right hand playing the melody and the l e f t hand i n accompaniment.
Pri-
rrrarily, melody supplies horizontal content while accompaniment supplies
vertical 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
b o t h the melodic and accompanimental functions.
A t other times the accom-
paniment will include a f a i r l y independent l i n e t h a t supplies an additional,
t h i r d component.
B u t , i n general, melodic presentation and accompanimental
10
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 figurations of these two components can be classified into types according t o the
way they are presented.
In the works being considered, the melodic presenta-
tion can be divided into two types:
the single l i n e
doubled i n parallel intervals
Similarly, accompanimental presentation can be divided into four types:
1)
2)
3)
4)
chordal
arpeggiated
convoluted
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 i s t o be classified and show
the great variety t h a t exists w i t h i n the types.
In some cases these types
a r e divided into subcategories i n order t o provide f i n e r distinctions.
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 l i n e melody.
Examples o f this type can be grouped into two subcategories according t o
the performance d i f f i c u l t i e s of the pieces.
One group uses slow tempos and
requires a very lc-yato s t y l e , often w i t h the accompanimental chords o r lines
written f o r the same hand, compounding the difficulty of obtaining smooth
legato connections.
Etudes of this type, which are called "legato studies,"
have confi g u r a t i ons simi 1a r t o Example 2.
12
EXAMPLE 2 Scriabin Etude Op. 8 No. 8, mm. 1-3
Lcnto (Tempr) rubatoj
Nr.8
Etudes belonging t o a second group, having a d i s t i n c t 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 i n Example 3 has a figuration typical o f many of these p eces.
I;
A l t h o u g h velocity studies are one of the most common types i n the
etude genre, Scriabin d i d n o t include any o f these i n his etudes.
Perhaps
Scriabin was leary of this type because o f the numerous pieces written for
sheer technical d i s p l a y since C h o p i n .
One characteristic o f melodic presentation t h a t might be overlooked
w i t h o u t careful analysis i s the use of polyphonic melody as i n the case of
Example 4.
13
In polyphonic melody, one "voice"--at l e a s t i t i s notated as one
voice--presents two or more related melodic ideas. Thus, what 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 t h i s relationship apparent.
Notice the simp1 i c i t y of the step-pro-
gression t h a t under1 ies t h i s 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 a t some given
level of structure, i t must s t i l l be considered a single- line type of
melodic presentation since i t i s perceived as one l i n e a t the most immediate, surface level.
This i s also a practical consideration because o f
the large degree of textural variation that can exist between structural
levels--each level can have a different "texture." To be rigorous,
"texture" should only refer t o the actual surface o f the music.
After a l l ,
12. Felix Salzer and Carl Schachter, Counterpoint i n Composition; The
Study of Voice Leading (New York: McGraw-Hill , 1 9 6 9 ) , 153-160.
14
we use t h e phrase "rought t e x t u r e ' ' t o d e s c r i b e an o b j e c t whose surfaces a r e
rough w i t h o u t making any i n f e r e n c e s as t o i t s i n t e r n a l composition.
An ex-
ample l a t e r i n t h e chapter a l s o i l l u s t r a t e s t h e n e c e s s i t 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 L i n e
The second b a s i c t y p e o f melodic p r e s e n t a t i o n c o n s i 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 .
Chopin and S c r i a b i n each wrote an
etude w i t h t h e r i g h t - h a n d p a r t doubled i n thirds- - Op. 26 No. 6 and Op. 8
No. 10 r e s p e c t i v e l y .
t o a l a r g e extent.
I n b o t h o f these t h e melodic l i n e s move c h r o m a t i c a l l y
There i s a l s o a marked s i m i l a r i t y between t h e motives
used i n t h e m i d d l e s e c t i o n s o f these t e r r a r y forms, as seen i n Examples 6
and 7.
The resemblance o f these motives s t r o n g l y suggests t h a t S c r i a b i n
m i g h t have consciously imStated t h e Chopin Etudes, a t l e a s t i n t h i s case.
EXAMPLE 6
Chopin Etude Op. 25 No. 6, m i . 27-28.
EXAMPLE 7
S c r i a b i n Etude Op. 8 No. 10, mm. 53-60.
15
Each composer a l s o wrote etudes w i t h t h e r i g h t - h a n d p a r t doubled
*in s i x t h s .
EXAMPLE 8
Example 8 shows t h e opening o f t h e one by Chopin.
Chopin Etude Op. 25 No. 8, mm. 1-4.
,
Not o n l y does t h e r i g h t hand present t h e melody i n s i x t h s i n t h i s
example, b u t t h e l e f t hand a l s o c o n s i s t s o f s i x t h s q u i t e o f t e n .
t i o n o f t h e 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.,
provides a harmocic scheme.
The funcit
But a t times t h e l e f t hand p a r t becomes melodic,
as i n t h e second h a l f o f measure f o u r i n Example 8.
Melodies doubled a t t h e octave abound i n piano l i t e r a t u r e , making
t h i s d i f f i c u l t f i g u r a t i o n an obvious s u b j e c t f o r etudes.
Chopin Op. 25
No. 10 and S c r i a b i n Op. 8 No. 9 each g i v e t h e p i a n i s t p r a c t i c e w i t h octaves
i n b o t h hands.
A v a r i a t i o n o f t h i s scheme occurs when one o r more notes
a r e f i l l e d between t h e octaves.
i s a case i n p o i n t .
The r i g h t hand o f S c r i a b i n ’ s Op. 8 No. 7
16
EXAMPLE 9
Scriabin Etude Op. 8 No. 7, mm. 1-2.
The question i s whether or not the added middle p a r t ' s role i s t o
reinforce the melodic function o r the accompanimental function.
J u s t be-
cause these notes are played in the same r e g i s t e r as the melody does not
necessarily mean t h a t t h e i r function i s likewise melodic.
Tt,e middle note
o f the right hand i s not linked t o the melody a t any certain interval, nor
does i t always move i n the same direction as the melody.
I t s pitch i s
determined by the harmony and the d o u b l i n g s of the accompaniment. B u t ,
the rhythm and r e g i s t e r of t h i s l i n e obviously 'reinforce the melody.
Here
i s an instance where Berry Is termi no1 ogy f o r 1 i near independence is useful
.
He would classify this l i n e as "homorhythmic-heterodirectional-contrain'erv a l l i c , " which provides a concise description, b u t does not c l a r i f y the
original problem of determining function.
Since the types of figuration are determined by the technical demands 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.
performance, belongs w i t h the melody.
The added p a r t , in terms of
This decision rests on the 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 articulation, rhythm, and register.
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 l i n e and the doubled line.
The former i s divided into legato
17
s t u d i e s and v e l o c i t y s t u d i e s .
The l a t t e r i s d i v i d e d i n t o t h r e e types:
doubled t h i r d s , doubled s i x t h s , and doubled octaves.
One shoJld bear i n
mind t h a t these l i m i t e d c a t e g o r i e s a r e a p p r o p r i a t e o n l y f o r t h i s body o f
music.
Doubled 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 found i n these etudes be-
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 period.
may be found i n works i n d i f f e r e n t s t y l e s .
However, o t h e r doublings
13
Chordal F i g u r a t i o n
The most elementary accompaniment s t y l e i s t h e simple chordal f i g u r a t i o n , such as t h e one found i r . S c r i a b i n ' s Op. 8 Nos. 8 and 11.
I n each
of these etudes t h e chords a r e p r e s e n t i n both t h e r i s k t - and l e f t - h a n d p a r t s ,
an arrangement t h a t r e q u i r e s t h e r i g h t hand t o p l a y t h e melody and a p a r t o f
t h e accompanifient a t t h e same time.
i ' h i s procedure can r e s u l t i n pieces
t h a t sound d e c e p t i v e l y easy s i n c e t h e l i s t et n e r hears o n l y a melody supported
by chords, 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 simultaneously
c o n t r a s t i n g dynamics, a r t i c u l a t i o n s , and/or rhythms w i t h one hand.
One should n o t e t h a t t h e accompaniment i n Op. 8 No. 8 can be d i v i d e d
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 separate
r e g i s t e r , has some melodic c h a r a c t e r i s t i c s o f i t s own.
T h i s melodic inde-
pendence r e s u l t s i n a t e x t u r e made up o f t h r e e separate s t r a t a as shown i n
Example 10
EXAMPLE 10 S c r i a b i n Etude Op. 8 No. 8 mm. 1-3.
Lento (Tempo rubato)
Nr. 8
13. For example, see t h e l a s t s e t o f etudes by S c r i a b i n , Op. 65 Nos. 1,2,
and 3.
18
In i t s simplest conformation, homophonic music consists o f two
strata--one melodic and the other accompanimental
.
Yet, as l a t e r examples
will show, the number of s t r a t a can vary greatly, from just one t o four o r
more.
The Chopin etude in Example 11 i s arranged i n three s t r a t a as was
Example 10, b u t with one major difference:
the chordal stratum i n the
middl e requires two hands t o perform.
Example 11 Chopin Etude Op. 25 No. 4 , mn. 9-12.
As before, the r i g h t hand has both melody and chords, and now the
l e f t hand has the bass l i n e and chords also. The l e f t hand must skip a
sizable distance i n order t o play both parts.
The major technical d i f f i c u l t y
of t h i s piece i s the accurate extecution o f these large leaps.
occur i n b o t h hands o f the following example.
EXAMPLE 12 Scriabin Etude Op. 8 No. 5, mm 1-3.
Large leaps
19
Here i t i s possible t o consider the texture i n four different
components : a me1 ody i t s chordal accompaniment, a counter-me1 ody or "echo 'I
and i t s accompaniment.
Example 13 shows the different s t r a t a 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 s t r a t a .
The constant leaping from one register t o another causes the l i s t e n e r t o
separate the events into discrete groups.
The e f f e c t i s similar t o the
polyphoriic melody discussed e a r l i e r a l t h o u g h i n this case the effect i s so
easily perceived t h a t i t i s apparent on the surface level while the
PO
'Y-
phoni c me1 ody requires some abstraction on the p a r t of the l i s t e n e r .
Because the large change i n register can i n e f f e c t add another stratum t o
the texture, types o f chordal figuration must be further divided i n t o two
subcategories--one simp1 e and one w i t h large leaps.
20
Arpegyiated Figurations
The second type of accompaniment i s the arpeggiated figuration,
which i s a chordal unit presented in a simple linear fashion, either ascendi 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 a l l the notes
can be reached without lifting the hand or turning t h e thumb under the fingers.
The left-hand part o f Chopin's Op. 25 No. 1, the "harp" etude, i s 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 position even t h o u g h the figure covers a large span.
EXAMPLE 14 Chopin Etude Op. 25 No. 1, mrn, 1-2.
The second subcategory of arpeggiated figuration i s shown in the
following example from the "revolutionary" etude.
21
In this example the five o r 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 i t s linear
contour.
A1 ternating Figuration
The t h i r d type of accompaniniental figuration i s similar t o a tremolo
effect.
I t consists of an alternation between two notes or groups of notes.
The t h i r d etude o f Scriabin's Op. 8 uses t h i s figuration in both hands.
EXAMPLE 16 Scriabin Etude Op. 8 No. 3, mm. 1-4.
I f Example 16 contains accompanimental figures in both hands, then
where i s the melody? By l i n k i n g every other note of the figuration into
1ines and el i m i n a t i n g octave doubl ings , the texture changes radically, reveal i n g the familiar texture o f a four-voice choral e.
EXAMPLE 17 Reduction o f Example 16
22
Consi dered from the viewpoint o f "layer analysis," Example 17
presents the 1 eve1 directly beneath the actual foreground. A t t h i s level
the melody and the linear nature of the remaining voices become clear.
It
appears t h a t the melody actually exists on a more remote level t h a n the
accompanimental figuration.
S t r i c t l y speaking, there i s no melody a t the
surface level due t o the alternation.
B u t since the actual texture, < . e . ,
the texture a t the most foreground level, i s generated by linear motion,
one can easily extract the linear motion of the underlying level.
This
example can, a t l e a s t a t the foreground level, consist of only accompanimental f i gura t i on.
Convoluted Figuration
The fourth type of accompanimental presentation i s designated here
as the "convoluted" figuration.
This type consists of any regularly repeat-
ing pattern o f chord tones which has a linear contour t h a t changes direction
often.
The convoluted figuration can be considered a broken chord whose
tones are sounded i n an irregular order, i . e . , i t produces a contour t h a t
cannot be described as ascending o r descending, b u t has a specific organization t h a t controls the contour. The Alberti bass of the Classical era
provides a simple example of this type.
Scriabin uses the convoluted f i g u r -
ation i n his etude i n Bb minor, shown in Example 18.
EXAMPLE 18 Scriabin Etude Op. 8. No. 7, mm. 1-2.
Presto tenebroso, agitato
Nr. 7
23
The f i g u r e i n t h e l e f t - h a n d p a r t repeats every s i x t h eighth- note,
i n a p a t t e r n t h a t can be g e n e r a l l y described as l e a p i n g down-up-down-downup-down w i t h t h e upward leaps l a n d i n g on t h e beat.
This p a r t i c u l a r pattern
has an ambiguous harmonic rhythm which S c r i a b i n emphasizes through t h e beami n g o f t h e eighth- notes and t h e phrasing marks o f t h e l e f t hand.
The har-
monies change every two beats, w i t h each new harmony beginning two e i g h t h notes b e f o r e t h e f i r s t and t h i r d beat of t h e measure, r e s u l t i n g i n a harmonic rhythm t h a t i s o u t o f phase, o r d i s p l a c e d i n r e s p e c t t o t h e rhythmic
i m p l i c a t i o n s o f t h e meter.
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 convoluted
f i g u r a t i o n used by Chopin.
EXAMPLE 19 Chopin Etude Op. 10 No. 9, mm. 1-3.
Allcgro, :nolto agitato
:to.)
Contained w i t h i n t h e upper p a r t of t h e accompanimental f i g u r e i s
a countermelody.
accompaniment.
Once again, t h e r e i s a melodic l i n e nested w i t h i n t h e
This results i n a texture consisting o f three strata l i k e
those i n e a r l i e r examples, except t h a t i n t h i s case, t h e harmonic support
i s below t h e t w o melodic l i n e s i n s t e a d o f between them.
Summary
An o u t l i n e i s presented here t o summarize t h e types o f f i g u r a t i o n
discussed i n t h i s chapter.
F o l l o w i n g each t y p e a r e l i s t e d t h e etudes t h a t
make use o f t h a t t e x t u r e as a p r i n c i p a l component o f t h e piece.
24
Scriabi n
Etudes
1.
Op./No.
Chopin
Etudes
Op ./No.
Melodic p r e s e n t a t i o n
A. S i n g l e l i n e
B.
11.
1.
Legato study
8/8 8/11
10/6 25/7
2.
V e l o c i t y study
---
10/2 10/4 25/2
Doubled l i n e
1.
Doubled i n octaves
8/9
25/10
2.
Doubled i n t h i r d s
8/ 10
25/6
3.
Doubled i n s i x t h s
816
2518
Accompanirnental p r e s e n t a t i o n
A.
B.
C.
Chordal f i g u r a t i o n
1.
Simple
---
10/11
2.
Large l e q p s
815
25/4
Arpeggiated f i g u r a t i o n
1.
One hand- position
---
25/ 1
2.
More than one
hand-posi t I on
8/2 8/4
10/8 10/12
8/1 813
10/10
8/7 8/12
10/9 l o l l 0
A1 t e r n a t i n g f i g u r a t i o n
D. Convoluted f i g u r a t i o n
25
Nine of the twenty-four Chopin etudes are not included here i n any
o f the above categories.
This i s done for two reasons:
F i r s t , these etudes
contain textures which are combinations o r 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.
EXAMPLE 20 Chopin Etude Op. 25 No. 9 , mm. 1-4.
Assai allegro
(J=iiz.)
Op. 25 No. 1 2 uses a variation o f 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 t h fingers, which
means the hands can transverse the keyboard w i t h o u t ever t u r n i n g the thumb
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 different technical s k i l l .
Example 21 t o Example 15.
EXAMPLE 21 Chopin Etude Op. 25 No. 12, mm. 1-2.
Compare
For
f
26
These combinations o r special v a r i a t i o n s o f t h e f i g u r a t i o n types
i n t h e n i n e remaining etudes could be i n c l u d e d i n t h e category system by
c r e a t i n g new designations.
But t h i s i s n o t d e s i r a b l e because o f t h e second
reason f o r excluding these etudes:
p a r t s i n t h e etudes o f S c r i a b i n .
they have no d i r e c t l y comparable counterThe puwose o f t h i s chapter i s t o p r o v i d e
l a b e l s f o r the t e x t u r e s common t o the two composers i n order t o make meani n g f u l comparisons.
Although one could s p e c i f y more and more types, t h i s
procedure would n o t b e n e f i t t h e present study since i t would d i m i n i s h t h e
bases f o r t h e comparison o f t e x t u r e .
Chapter I I I
DENSITY
As i t i s presented i n chapter one, the investigation of texture i n
piano music texture involves three major categories: melodic and accompanimental presentation, density, and range.
The second o f these, density,
concerns the number o f components sounding a t one time and the rel?,tive
spacing of these components. This chapter examines the Chopin and Scriabin
etudes with respect t o t h e i r textural density.
I t begins w i t h a detailed
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 etudes
and follows w i t h a comparison of the types o f accompanimental presentation
and t h e i r use by each composer.
Discussions of textural density often contain descriptions such as
lightlheavy or thin/thick w i t h o u t 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.
I n addition, these terms are
ambiguous because they can r e f e r 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 lines.
Since these
terms can connote so many different t h i n g s , the adoption o f a more precise
vocabulary is essential.
I n his Structural Functions in Musics Berry pro-
vides some terms t h a t are more precise in t h e i r description of textural
components. Those re1 evant t o density incl ude "densi ty-number ,'I "texturespace," and "density-compression .
14. Berry op. c i t . , 209, 249.
27
The following discussion examines
28
these and two new terms, " v e r t i c a l span" and " s p a c i n g- d i s t r i b u t i o n . ' '
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 concept o f texture- space due t o t h e
l a t t e r ' s i n a p p r o p r i a t e n e s s f o r t h i s study.
Density-number
Density-number r e f e r s t o t h e number o f p i t c h e s 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 chord.
Chopin Etude Op. 10 No. 2, f i n a l meas.
EXAMPLE 22
m
Obviously, t h e density-number i n pclyphonic music i s e q u i v a l e n t t o
t h e number o f v o i c e s i n t h e t e x t u r e ( p r o v i d e d t h e r e a r e no systematic doublings)
.
However, i n Example 22 which i s homophonic, most o f t h e h o r i z o n t a l
p a r t s a r e l e s s c l e a r l y d e f i n e d and t e n d t o merge i n t o v e r t i c a l formations.
The l a c k of h o r i z o n t a l d e f i n i t i o n causes t h e v e r t i c a l u n i t s , i.e.,
the
chorda: s t r u c t u r e s t o t a k e on mors prominence -ni t h e musical s t r u c t u r e .
When density- number no longer r e f e r s t o t h e number o f voices, i t must r e f e r
t o t h e number o f p i t c h e s i n each chordal s t r u c t u r e .
As a r e s u l t , t h e d e n s i t y -
number i n homophonic music does n o t always correspond e x a c t l y t o t h e number
o f " parts.
I'
A c c w d i n g t o Berry, densi ty-number r e f e r s t o t h e number o f p i t c h e s
w i t h i n a v e r t i c a l u n i t which, i n r e s p e c t t o homophonic music: o f t h e n i n e t e e n t h century, can be d e f i n e d as a p a r t i c u l a r chordal u n i t .
With t h i s i n
29
mind, one can see t h a t the notated duration of pitches m i g h t not overlap
a t any point, and y e t they can function harmonically as part of the same
chordal u n i t .
Consider the left-hand part of the Scriabin etude i n Example
23.
EXAMPLE 23 Scriabin Etude Op. 8 No. 12, mm. 1-2.
All of the pitches i n the left- hand part express tonic harmony.
When the
horizontal motion o f the accompanimental figuration i n t h i s passage i s reduced t o long notes, a s shown i n Example 24, the chordal u n i t can be seen
t o have a density-number of seven.
EXAMPLE 24
Figuration reduction G f the left-hand p a r t of Example 23.
a
71
Notating the pitches of an accompaniment a s a block chord makes i t
e a s i e r not only t o observe the density-number, b u t a l s o the other measurements 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 vertical structure.
30
Vertical Span
"Vertical span" i s a measurement of density which i s proposed t o
replace Berry's term "texture-space" as an a1 ternative more appropriate t o
t h i s study.
Both refer t o the same characteristic o f texture.
To under-
stand the reasoning for t h i s substitution requires examining both ideas.
Berry defines texture-space as
.
. .the f i e l d enclosed by "lines" tracing the ?itch
successions of outer components in addition t o the
two vertical, or diagonal , "1 ines" 1 inking components
a t " l e f t - r i h t " extremeties a t some 1wel of given
structure. 18
In other words, texture-space i s the f i e l d delineated by the outermost parts.
I t i s a two-dimensional shape t h a t points o u t how gradually
o r suddenly the relative changes i n 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 o f the texture-space
as expressed i n contradirectional relation o f outer components.
15. Berry op. c i t . , 249.
16. Berry op. c i t . , 254.
31
The concept of texture-space i s most useful i n dealing w i t h "textural 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' t h i s study, however, i s n o t placed on the progression of texture,
!)ut rather on measuring textural density on an absolute scale, in order t o
faci 1 i t a t e comparisons between pieces . I 7 An absol Ute scale permits measurements independent o f any arbitrary reference p o i n t .
For example, "thick"
chords require a reference chord t h a t i s thinner (or "nornial
'I)
for the term
"thick" t o have meaning. The same chord m i g h t seem t o be "thin" when ccmpared t o a different reference chord.
Nevertheless, a chord with a dersity-
number of seven retains t h a t density-number no matter what the coinparison
might be.
Because i n Berry's scheme, texture-space has a referential nature
that i s qualitative rather t h a n quantitative, and i t s emphasis i s direzted
toward textural progression, this concept will not be useful, as such, i n
this study.
Instead the quantitative correlate o f texture-space, i .e.,
vert*ical s p a n s
h ij i
be used.
The term vertical span i s proposed as a description of the expanse
of each vertical u n i t measured individually.
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 way
analog information i s convarted t o d i g i t a l information.
17. For an analysis o f textural progression, see Calvin E. Holden, The
Organization of Texture i n Selected Piano Compositions o f C1 a u d r Debussy. Dissertation, University of Pittsburgh, 1973.
32
Dens i ty -Compression
Density-compression i s Berry's term f o r the number of pitches w i t h In Example 24 above, there are seven pitches
in a particular vertical span.
w i t h i n the span o f two octaves and a f i f t h .
I f the same number of pitches
were spread out over a vertical span o f five octaves, then the density-cornpression would be much lower.
I f the vertical-span were reduced t o one
Stated precisely, density-compression
octave, then i t would be much higher.
i s the r a t i o o f density-number t o vertical span.
In order to make a l l measurements o f density-compression easy t o
compare, a l l the r a t i o s in t h i s study are converted t o a number o f pitches
Numerical l y , the densi ty-compression equal s the density
per one octave span.
number divided by the vertical span measured in semitones multiplied by
twel ve semi tones per octave:
Density-compression = Density-number
Vertical span
x
12
For instance, in Example 24 there are seven pitches w i t h i n a vertical span
o f 31 semitones.
Density-compression
=
31
x
12 = 2.71
When measuring density-compression one should realize t h a t the r a t i o
of pitches per octave span does n o t necessarily represent the subjective
impression o f density.
This impression i s affected by the degree o f disson-
ance involved i n the vertical structure, as well as by the register 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
t e r t i a n relationships, even though the l a t t e r i s compressed into a smaller
vertical span.
B u t dissonance i s more properly an aspect o f the harmonic
33
domain t h a n i t i s o f texture.
I n addition, the subjective impression of
dissonance i s d i f f i c u l t t o quantify. Therefore,
..
. i t i s a convenience t o regard the evaluation of dissonance
as a d i s t i n c t parameter.
., considering density [density-coinpression] as the simple r a t i o of number t o space.18
.
The same reasoning j u s t i f i e s excluding evaluations of register from
the determination o f density-compression.
I f an arrangement o f notes i s
transposed down i n t o a lower register, i t will sound more dense t h a n i t
originally did.
This effect i s probably due t o the overtones being shifted
i n t o a range t o which our ears are more sensitive.
Again however, t h i s
effect can not be quantified i n t o the measurement o f densi ty-compression.
Spacing-di stribution
Berry does not provide a term t o designate the vertical arrangement
of the spacing,
This component of texture i s , nonetheless, an important
factor in the analysis of textural density.
For instance, the figuration
shown e a r l i e r in Example 23 spans two octaves and a f i f t h , has a density-
number o f 7 , and a density-compression o f 2.71 pitches per octave.
But this
information does n o t show how the notes are distributed w i t h i n the vertical
space. The pitches could be evenly spaced, o r several pitches could be concentrated a t one extreme.
The term spacing-distribution i s proposed for t h i s
component of textural density.
I t may be defined as a description of the
pattern o f pitch distribution w i t h i n a particular vertical unit.
Spacing-distribution is a component of density that may be more
usefully characterized i n general than as an absolute quantification. To
specify the distribution of p-itches within a vertical span precisely would
18.
Berry, op. c i t . , 209-10.
require a complete l i s t i n g of the intervals present.
34
The results of such
a procedure would be more cumbersome t o cope with than the original n o t a t i o n
of the niusic t h a t was t o be described.
benefit t o any analysis.
Obviously t h i s would have l i t t l e
The more sensible option i s t o generalize the
character of the arrangement by pointing out certain distinctive featdres.
For example, the spacing-distribution o f Example 24 seen e a r l i e r could be
characterized as a symmetrical arrangement with open spacing a t the extremes
and concentrated i n the center.
To summarize, a particular vertical arrangement, a t some given level
has three quantitative parameters:
,
1) densi ty-number--the number of pl tches
present i n a vertical structure, 2 ) vertical span--the expanse or space the
vertical structure occupies, and 3) density-compression-- the number of p i t ches per octave span.
I n a d d i t i o n , there i s one "descriptive" parameter,
spacing- distribution, which concerns the pitch distribution pattern within
the vertical span.
Density i n the Etudes
Because the vertical structures i n the etudes are typically presented
i n the accompaniment and not i n the melody, though harmonies m i g h t be implied
by linear motion, the r e s t o f t h i s chapter examines those etudes i n which
the principal textural components have accompanimental functions. A representative 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-
a c t e r i s t i c s o f density readily apparent.
The measurements bken from these
reductions are compiled in Table I for the comparison o f various accompanimental figuration types and o f the averages for each composer.
Tab1 e I .
DENSITY IN ACCOMPANIMENTAL FIGURATION
Vertical
Span
DensityCompression
8/ 7
8/12
4
5
5
7
19
19
24
36
2.53
3.16
2.50
2.34
closed
closed
closed
closed
Average
5.25
24.50
2.63
--
DensityNumber
Etude
Op/No.
Spacing
Distribution
Convoluted Figurations
10/9
10/ 10
at
at
in
-in
top
top
Riddle
middle
.-
Arpeggi ated Figurations
10/8
10/ 12
8/ 2
8/4
12
5
5
3
44
24
28
21
3.27
2.50
2.14
1.71
closed
open a t bottom
closed in middle
open evenly
Average
4.34.
24.34
2.12
---
Figurations w i ' t h Large Leaps
25/4
8/ 5
5
5
31
31
1.94
1.94
closed a t t o p
open in middle
Average
5 .OO
3 1 .O
1.94
---
A1 ternating Figurations
8/ 1
8/ 3
4
4
24
19
2 .oo
2.53
open a t bottom
open evenly
Average
4 .OO
21.50
2.27
---
23.25
26.14
2.53
2.16
closed a t t o p
open a t t o p
Averages f o r Each Composer
Chopi n
ScriaOin
*
4.75
4.71
Etude 10/8 i s n o t averaged ( see below, pages 36-37)
36
With respect t o the measurements i n Table I , one should note that
the density-compression averages can be determined by two a1 ternative
methods which give slightly different results.
In the f i r s t method, which
i s the one used i n this study, the result i s obtained by averaging the
various measurements of density-compression of the individual etudes withi n 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 f i r s t method 5s used here because i t i s 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 t h a t the etudes with convoluted figurations have the
highest densi ty-numbers and the highest densi ty-compressions.
This type
has the second largest vertical spans, b u t i t should be noted t h a t there
i s only a difference of three semitones between three of the four types.
The etudes w i t h arpeggiated figurations include one, Chopin's
Op. 10 No. 8, whose vertical structures are radically different from any
of the others.
This etude has a density-number o f 12 and vertical span of
44, which are a b o u t twice the magnitude of the other arpeggiated etudes.
I t s density-compression i s also higher than that of the other etudes.
The
reason for this wide discrepancy i s t h a t the arpeggios of the etude occur
i n the r i g h t - h a n d p a r t and the melody i s i n the left-hand part.
This
reversal of roles places the arpeggios i n a drastically different register
of the piano.
The different tonal qualities and f a s t e r decay times o f
this register make the validity of any comparison of density questionable.
Another important factor i s the prominence of the arpeggios and the relative insignificance of the melody i n the l e f t hand.
Normally melody i s a
37
foreground event w i t h accompaniment b e i n g background. l9
The accompani-
mental f i g u r a t i o n s u p p l i e s more c o n t e n t t o t h e composition than does t h e
melody and t h e r e f o r e i s n o t l i m i t e d t o t h e s u b s e r v i a n t r o l e o f background.
Because of these s u b s t a n t i a l d i f f e r e n c e s Etude Op. 10 No. 8 i s n o t computed
i n t h e averages f o r i t s t y p e o r f o r Chopin's o v e r a l l averages o f d e n s i t y .
The etude cannot be e n t i r e l y d e l e t e d from t h e study, however, on, t h e b a s i s
o f t h e above reasons.
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 p e g g i a t e d
accompaniments w i t h r e s p e c t t o b a s i c types o f p r e s e n t a t i o n arld w i t h r e s p e c t
t o range.
The remaining t h r e e etudes w i t h arpeggiated f i g u r a t i o n s have an
average density- number o f 4.34.
The v e r t i c a l span, as mentioned above, i s
v e r y s i m i l a r t o t h e convoluted type.
The density-comprescion l i s t e d f o r
t h e a r p e g g i a t e d t y p e r e v e a l s t h a t Chopin p r e f e r s arpeggios w i t h r e 1 z t i v e l y
c l o s e spacing w h i l e S c r i a b i n p r e f e r s a more open spacilig.
The accompaniments w i t h l a r g e leaps a r e t h e onl,: t y p e o f f i q u r a t i o n s
t h a t have a s u b s t a n t i a l l y d i f f e r e n t average measure of v e r t i c a l span.
This
r a d i c a l l y h i g h e r average must be expected s i n c e t h e c o n s t a n t l e a p i n g o f t h e
hands w i l l n e c e s s a r i l y i n c r e 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 produce lower density- compression because
t h e same number of p i t c h e s a r e b e i n g spread over a l a r g e r space.
It i s
i n t e r e s t i n g t h a t a1 though 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 generates t e x t u r e s
w i t h more s t r a t a , i t has, a t t h e same time, lower density- numbers and dens i ty- compressions.
Perhaps t h e c o m p l e x i t y o f numerous t e x t u r a l s t r a t a com-
pensates for reduced d e n s i t i e s .
19. Foreground and background h e r e do n o t r e f e r t o l e v e l s o f s t r u c t u r e ,
b u t t o t h e r e l a t i v e degrees o f i n t e r e s t and content- - perhaps t h e y
should be c a l l e d l e v e l s r f perceptual immediacy.
38
The t y p e o f f i g u r a t i o n found l e a s t o f t e n i n these etudes i s t h e
a1 t e r n a t i n g type.
The averages of t h e densi ty-numbers and t h e v e r t i c a l spans
suggest a reason f o r i t s i n 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 r e s t r i c t i v e type, having both t h e lowest density-number and t h e smalle s t v e r t i c a l span.
I t appears t h a t t h e c o n s t r a i n t s o f t h e f i g u r a t i o n do
n o t p e r m i t as much t e x t u r a l complexity as do t h e o t h e r types.
D i f f e r e n c e s between t h e two composers' use o f t e x t u r a l d e n s i t y
o v e r a l l a r e very minimal.
One c h a r a c t e l - i s t i c d i f f e r e n c e i s t h e i r p r e f e r -
ences of s p a c i n g - d i s t r i b u t i o n .
I n the top portion o f the figurations,
Chopin's spacing i s r e l a t i v e l y c l c m w h i l e S c r i a b i n ' s i s more open.
With
r e g a r d t o t h e d i f f e r e n c e s between the composers, the o v e r a l l averages f o r
o t h e r f a c t o r s a r e s l i g h t when compared t o t h e amount o f v a r i a t i o n observed
between t h e types of f i g u r a t i o n .
T h i s f i n d i n g suggest;
t h a t t h e two com-
posers 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 type i n approximately
t h e same manner, o r perhaps, were guided by t h e same c c m s t r a i n t s .
composers s t r i v e for t e x t u r a l complexity i n o r d e r
tcj
I n etudes,
challenge t h e performer.
I t i s p o s s i b l e t h a t each type o f f i g u r a t i o n has 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 w i t h o u t compromising t h e musical q u a l i t y o f t h e
works.
These l i m i t s , whether t e c h n i c a l o r s t y l i s t i c , c o u l d account f o r t h e
marked s i m i l a r i t i e s .
Chapter I V
RANGE
Range, l i k e o t h e r a t t r i b u t e s o f t e x t u r e , s u f f e r s from a l a c k o f
Moreover, no p r e c i s e o r o b j e c t i v e data have been p v s e n t e d ,
investigation.
n o r has an adequate terminology 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 probably due t o t h e apparent s i m p l i c i t y o f t h e concept.
Range is commonly d e f i n e d as t h e extreme expanse encompassed from the lowe s t t o t h e h i g h e s t p i t c h w i t h i n a composition.
determined by t h e two extreme p i t c h e s .
I n o t h e r words, range i s
Such a d e f i n i t i o n i s inadequate
because t h e amount o f i n f o r m a t i o n i t provides i s very l i m i t e d .
Consider
t h e f a c t t h a t a piano p i e c e o f o n l y f i f t y measures may c o n t a i n over a
thousand notes.
A sample o f two o f these notes cannot be expected t o r e -
veal much about t h e p i e c e as a whole.
An a l t e r n a t i v e approach would be t o
conceive o f range i n a manner s i m i l a r t o t h e concept o f t e s s i t u r a .
i n g t o t h e Harvard D i c t i o n a r y o f Music, t e s s i a t u r a
". . . d i f f e r s
Accord-
from range
i n t h a t i t does n o t take i n t o account a few i s o l a t e d notes of e x t r a o r d i n a r i l y h i g h or
low p i t c h . " 2 0
Thus one could say t h a t t e s s i t u r a concerns
t h e p i t c h range used most o f t e n , i n c o n t r a s t t o t h e extreme range.
Unfortun-
a t e l y t h e r e i s no c l e a r c u t way t o determine which p i t c h e s should be e l i m i nated because they a r e " e x t r a o r d i n a r i l y h i g h
or low."
For instance, how
many times should a p i t c h appear i n a p i e c e t o be considered " w i t h i n t h e
~~~
20. Apel, op. c i t . ,
~~~~~~
839.
39
~
~
40
tessitura?"
Should t e s s i t u r a be based o n l y on the number o f times each
p i t c h appears, o r should d u r a t i o n values a l s o be considered?
No m a t t e r
what t h e answer, t h i s type o f concept r e q u i r e s examining every n o t e o f t h e
music and a p p l y i n g s t a t i s t i c ? l procedures t o o b t a i n a meaningful r e s u l t .
Such an approach would be too i n v o l v e d t o be j u s t i f i e d , even i f an accepta b l e d e f i n i t i o n o f " e x t r a o r d i n a r y" c o u l d be found.
Range-average
A procedure t h a t would seem t o o f f e r a reasonable compromise between
examining o n l y two notes and examining every note, i n v o l v e s t h e use o f a
sampling process.
By d i v i d i n g a composition i n t o a c o n v e n i e n t l y l a r g e num-
ber o f segments, t h e extreme h i g h and low p i t c h e s i n each segment can serve
as r e p r e s e n t a t i v e samples o f t h e whole.
t o p r o d w e a "range-average."
These samples can then be averaged
T h i s averaging process m i t i g a t e s t h e e f f e c t
of e x t r a o r d i n a r y p i t c h e s w i t h o u t having t o d e f i n e c r i t e r i a w i t h which t o
i d e n t i f y them.
The r e s u l t i n g "range-average" i s a c t u a l l y a compromise be-
tween t h e ideas o f "extreme range" and " t e s s i t u r a . "
l t has t h e advantage
o f being more r e p r e s e n t a t i v e than t h e extreme range w h i l e n o t r e q u i r i n g an
*
o v e r l y in v o l ved process f o r i t s determi n a t i o n .
The f o l l o w i n g procedure was used t o determine t h e range-averages.
Each etude was d i v i d e d i n t o from t e n t o t h i r t e e n segments o f approximately
equal l e n g t h .
The h i g h e s t and lowest p i t c h e s o f b o t h t h e l e f t - and r i g h t -
hand p a r t s were recorded separately f o r each segment.
The p i t c h e s were then
converted t o numerical values u s i n g t h e standard key-numbers found on pianos
(subcontra A i s key number 1, f i v e - l i n e C i s key number 88).
f a c i l i t a t e s t h e computation o f averages.
This operation
Although t h e piano has no i n t e r -
v a l s s m a l l e r t h a n a semitone, t h e averages were i n d i c a t e d w i t h i n a t e n t h
o f a semitone, due t o t h e p r e c i s i o n o f t h e computation.
With t e n o r more
41
samples, t e n t h s o f a semitone i n t h e average have been regarded as s i g n i f i cant figures.
T h i s convention a l s o reminds t h e reader t h a t t h e range-
averages a r e based on several p i t c h e s and do n o t r e p r e s e n t an a c t u a l n o t e
of t h e composition.
The s i z e o f t h e i n t e r v a l between t h e low and h i g h
averages measured i n semitones was a l s o computed.
This interval i s re-
f e r r e d t o as t h e "range-span. I'
For a simple example o f t h e procedure, imagine a p i e c e o f music
d i v i d e d i n t o two s e c t i o n s o f equal l e n g t h .
s e c t i o n a r e C and e 2
g
#2
.
.
The extreme p i t c h e s o f t h e f i r s t
The extreme p i t c h e s a f t h e second s e c t i o n a r e D and
To f i n d t h e range- average y these p i t c h e s a r e f i r s t converted t o num-
bers u s i n g t h e key-numbers l i s t e d i n f i g u r e I :
9''
= 60.
C = 16, e2 = 56, D = 18,
The l o w p i t c h e s a r e added t o g e t h e r 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 t h e h i g h pitch-.s.
The averages can t h e n be converted back i n t o conventional n o t a t i o n :
2
17 = C#, 58 = f#
.
The span i s determined by t h e i n t e r v a l between t h e lows
and t h e highs.
F i r s t s e c t i o n : C t o e2 = 56 - 16 = 40 semitones
Second s e c t i o n : D t o g#2 = 60 - 18 = 42 semitones
40 42 = 41 semitones
2
Average:
'
I n d e r i v i n g t h e average-span, a s h o r t c u t method, which gives t h e
same r e s u l t s i s t o s i m p l y f i n d t h e d i f f e r e n c e between t h e low and h i g h numb e r s o f t h e range- average.
58
-
17 = 4 1 semitones
42
FIGURE I
Key-numbers o f t h e Piano Keyboard
43
Range-averages of the Etudes
The measure numbers and sample pitches for the individual segments
of each etude are l i s t e d i n the tables of the Appendix. The range-averages
and span-averages given i n the tables o f the Appendix are summarized here
i n Tables 11, 111, and IV.
These tables are accompanied by Figures 2 , 3,
and 4, which represent the pitches of the respective tables i n conventional
notation.
The reader i s cautioned a t t h i s p o i n t t o remember t h a t the
columns labeled "low" and " high" contain numbers representing pitch or keynumber, whi 1e the col umns 1abel ed "span" represent interval s measured i n
semi tones.
By comparing tables I1 and 111, one can observe t h a t the leh-hand
low note averages of the Chopin etudes vary from GG t o E , and average together t o give C, while Scriabin's left-hand notes vary from EE t o D and
average owt t o AA.
Thus one can see t h a t Scriabin's low notes tend t o be
Comparing right-hand h i g h notes
reveals t h a t the Chopin etudes vary from c2 t o c4 a n d average out t o eb 3 ,
a b o u t a minor t h i r d lower, t h a n Chopin's.
while the Scriabin etudes vary from .;.* t o g'3
and average out t o c3.
Thus
one can see t h a t Scriabin's h i s h notes tend t o be about a minor t h i r d lower
t h a n Chopin's.
Also observe that the low averages for both composers are
much more consistent than the h i g h averages, which vary over larger spans.
The left-hand h i g h s and the r i g h t - h a n d lows vary over a span of
slightly more than an octave, and average together a t approximately the
same pitches for b o t h composers, i .e.
w i t h i n two semitones of each other.
There i s an overlap o f the r i g h t - and left-hand ranges o f a perfect f i f t h
for Chopin and a minor seventh for Scriabin.
I t i s interesting t h a t b o t h
composers' overlaps center on the pitch eb 1 and t h a t the true center of the
piano keyboard f a l l s between e 1 and f 1 .
T a b l e I1
CHOPIN ETUDE RANGE-AVERAGES
Etude
Left
hand
1ow
-
Left
hand
high
left
hand
25/ 10
16.8
45.4
2516
15.5
2518
R i gh t
hand
7 ow
Right
hand
high
Right
hand
span
Hands
combined
span
28.7
37.7
67.4
29.7
50.6
50.2
34.7
41.4
74.4
33 .O
58.9
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
OP/ No
span
_
I
_
.b
P
45
FIGURE 2
Range-averages o f the Chopin Etudes
=I
U
I
I
y7sJ
I
II
i
-8-J
Table I 1 1
SCRIABI rJ ETUDE RANGE-AVERAGES
Etude
Op/No
Average
Left
hand
Left
hand
h!llh
s p a n
32.6
71.6
39 .O
63.7
43.5
40.4
69.5
29.1
57.4
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
13.5
48.9
35.5
36.7
63.8
27.1
50.3
2E!.!!
53.7
45.8
12.1
55.6
14.8
1ow
.7.9
Right
hand
Hands
comb incd
Right
hd nd
spJn.
Riqht
hand
1ow
___
Left
had
high
.@
P
m
47
FIGURE 3 .
Range-averages o f the S c r i a b i n Etudes
48
The most s i g n f f i c a n t d i f f e r e n c e between t h e two composers can be
seen i n t h e average l e f t - h a n d spans.
S c r i a b i n ' s l e f t - h a n d p a r t s tend t o
90 b o t h h i g h e r and lower than Chopin's, and a c t u a l l y span a range an augmented f o u r t h l a r g e r than Chopin's.
The most s t r i k i n g s i m i l a r i t y can be
found i n t h e combined span- - there i s o n l y two- tenths o f a semitone d i f f e r ence between t h e two composers i n t h i s r e s p e c t ,
Recause t h e number o f keys on the piano had n o t y e t been standardi z e d when Chopin was w r i t i n g , one might ask whether a d i f f e r e n c e i n t h e
s i z e o f t h e keyboard c o u l d account f o r some o f t h e d i f f e r e n c e s i n rangeaverages.
To answer t h i s question, one needs o n l y t o examine the "extreme
ranges" o f the etudes.
Chopin must have expected t h a t h i s music would be
performed on an Instrument ranging a t l e a s t from CCC t o f 4 (key numbers
4 t o 81) s i n c e he wrote these p i t c h e s r e p e a t e d l y even i n t h e e a r l i e s t
4
etudes. S c r i a b i n wrote o n l y p i t c h e s from AAA t o e ( 1 t o 80) i n Op. 8
even though the 88-note keyboard was a l r e a d y standard.
S c r i a b i n ' s use o f
the lowest t h r e e keys i s too i n f r e q u e n t t o account f o r h i s range-averages
being lower than Chopin's.
I n t h e twelve etudes o f Op. 8, S c r i a b i n uses
key 1 once, key 2 once, and key 3 l e s s than 10 times.
Because range- aver-
ages a r e based on several p i t c h samples from each etude, they a r e n o t
s i g n i f i c a n t l y a1 t e r e d by such i n f r e q u e n t occurrences. The problem of t h e additional
because:
upper range a v a i l a b l e t o S c r i a b i n , b u t n o t t o Chopin, i s i m m a t e r i a l
1) S c r i a b i n never uses t h i s range i n ttiese etudes, and 2) t h e
h i g h e r range-averages a r e found i n t h e Chopin etudes.
Table I V and F i g u r e 4 compare and c o n t r a s t t h e etudes according t o
t h e types o f p r e s e n t a t i o n developed i n chapter two.
The most obvious r e -
s u l t of t h i s comparison i n v o l v e s t h e l e g a t o type o f s i n g l e l i n e f i g u r a t i o n .
I t s use of h i g h notes i n t h e r i g h t - h a n d p a r t i s much more r e s t r i c t e d t h a n
Table I V
RANGE-AVERAGES FOR TIIE FIGURA’TION TYPES
Right
hand
span.
comb1ned
y an
56.4
19.1
39.3
39,2
70.2
31 .O
56.2
35.5
36.7
65.5
28,9
52,3
46.4
31.2
39b1
67.7
28.6
52.6
48.9
32.8
37.5
C6.8
29.4
50.8
49.3
32.3
38.7
65.9
27.2
48.9
47.7
32.8
37 69
65.3
27.4
50.4
Ll!f t
hand
N I !]h 1;
-
hhh
span
17.2
42.7
25.5
37
14 .O
50.6
36.6
48.5
Convoluted Flguratlons
15.1
A1 terna t l ng F i gura t ions
16.1
of
Etude
L
1
1
Legs t o Studies
Doubl ed L I nes
Arpeggi ated
F1 gura t i ons
13.3
Figurations w i t h Large Leaps
17,O
Average o f All Etudes
15.0
Hands
Rlqht
hand
LQft
ha ntl
Left
hand
1ow
Type
hand
1ow
a
0
4
50
FIGURE 4,
Range-averages f o r t h e F i g u r a t i o n Types
Legato
studies
Doubled
1inc
Arpeggiated
figurations
*El
Convol u t e d
F i gura t ion
A1 t e r n a t ing
Figuret i o n
b
e
- 1
I
Average of All Etudes
h
Figuration with
Large Leaps
a.
-1
51
those o f t h e o t h e r types,
The average h i g h p i t c h o f t h e l e g a t o s i n g l e
l i n e etudes i s almost an octave lower than t h e o t h e r s .
This r e s t r i c t i o n
r e s u l t s i n a much s m a l l e r r i g h t - h a n d span also, sirice t h e r i g h t- h a n d l o w
average i s approximately t h e same.
The l e f t - h a n d highs a r e a l s o more re-
s t r i c t e d i n t h i s type, being approximately an augmented f o u r t h lower than
most o f t h e types.
accordingly.
Likewise, t h e span o f t h e l e f t hand i s r e s t r i c t e d
The lower boundary of t h e range-averages f o r t h e l e g a t o
s i n g l e l i n e etudes a r e t y p i c a l o f t h e o t h e r types a s w e l l .
I n fact, the
low ranges of a l l t h e types do n o t v a r y more than two o r t h r e e semitones,
suggesting t h a t t h e lower range o f each hand i s r e l a t i v e l y s e t w h i l e t h e
upper range f l u c t u a t e s .
The etudes w i t h the melody doubled i n p a r a l l e l i n t e r v a l s have i n
b o t h hands t h e wides spans o f t h e v a r i o u s types.
This characteristic
concerns t h e average highs s i n c e t h e lows t e n d n o t t o vary.
The combined
span i s d l s o w i d e r than the o t h e r types, exceeding them by about a p e r f e c t
fourth.
J u s t because t h e spans o f t h e i n d i v i d u a l hands may b o t h be w i d e r
than those o f another type, i t does n o t n e c e s s a r i l y f o l l o w t h a t t h e span
of t h e two hands combined w i l l a l s o be wider.
Even though S c r i a b i n uses
l a r g e r l e f t - h a n d spans and almost t h e same r i g h t - h a n d spans o f Chopin, i t
i s s t i l l t h e case t h a t t h e two composers use combined spans t h a t a r e almost
identical.
The l e f t - h a n d span o f t h e convollited t y p e o f f i g u r a t i o n i s s l i g h t l y
s m a l l e r t h a n t h e doubled- line t y p e o r t h e arpeggiated type.
T h i s i s e3pec-
i a l l y t r u e i f we d i s a l l o w S c r i a b i n ' s Op 8 No. 12, which appears t o have an
e x c e p t i o n a l l y l a r g e span compared t o t h e o t h e r etudes o f i t s type.
Aver-
aging o n l y t h e remaining t h r e e etudes produces a span o f 27.8 semitones,
which i s s m a l l e r t h a n a l l t h e types except f o r t h e l e g a t o s i n g l e l i n e etudes.
52
The range- avenges o f t h e types of f i g u r a t i o n w i t h a l t e r n a t i o n and
l a r g e leaps reveal n o t h i n g s i g n i f i c a n t l y d i f f e r e n t from what appears t o be
normal f o r t h e etudes i n general.
T h e i r averages correspond very c l o s e l y
t o t h e range-averages o f a l l t h e etudes taken together as a group.
The arpeggiated f i g u r a t i o n s use the lowest ranges o f a l l t h e types
i n both the r i g h t and l e f t hands.
However, t h e d i f f e r e n c e between any of
t h e types i n respect t o t h e average lows i s marginal.
The average-spans
o f t h e i n d i v i d u a l hands i n t h i s type a r e a l s o wider than most types, p a r t i c u l a r l y f o r t h e l e f t hand, which i s o n l y exceeded by one o t h e r type, L e . ,
t h e doubled 1ine type.
Chapter V
CONCLUS IONS
The most problematic aspect o f 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 t o characteristics t h a t
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 p i a n o music, an analysis of
1 inear independence was inappropriate.
I n i t s place was substituted a
system which categorizes f i g u r a t i o n i n t o basic types according t o the
function i t perfoms (melodic or accompanimental) and t o the performance
technique i t requires t o be realized.
The proposed definition of texture can be evaluated i n two ways-according t o i t s precision and i t s usefulness in practice.
i n t h a t i t relegates characteristics such
iis
I t i s precise
instrumentation and dynamics
t o separate areas of investigation, thus reducing the number of variables
t h a t can complicate the investigation.
The usefulness of the definition
can be supported by the many quantitative measurements t h a t are shown
t o be available i n this study for the objective analysis o f s t y l e and
structure i n homophonic piano music.
The system proposed for classifying melodic and accompanimental
presentation can be evaluated from several p o i n t s of view.
new terminology for the description of piano figuration.
53
I t provides
I t provides a
54
procedure f o r c l a s s i f y i n g complex f i g u r a t i o n i n terms o f extension, v a r i
a t i o n , and combination o f s i x b a s i c types o f f i g u r a t i o n .
-
From t h e stand-
p o i n t o f compositional s t y l e , chapter two p o i n t s o u t t h e c l o s e r e l a t i o n s h i p
between t h e piano music o f Chopin and S c r i a b i n t h a t r e s u l t s from t h e use o f
similar figurations.
One f a c e t o f t h e f i g u r a t i o n c l a s s i f i c a t i o n system
t h a t m i g h t n o t be apparent i s i t s f l e x i b i l i t y .
The system i s open-ended-
t h e c a t e g o r i e s can be d i v i d e d o r combined i n a number o f ways t o p r o v i d e
t h e degree o f d i s c r i m i n a t i o n a p p r o p r i a t e f o r a p a r t i c u l a r body o f music.
The examination o f t e x t u r a l d e n s i t y provides support f o r t h e d e c i s i o n
t o c l a s s i f y t h e v a r i o u s f i g u r a t i o n s i n t o b a s i c types.
The measurements o f
d e n s i t y reveal t h a t c e r t a i n types have p a r t i c u l a r a s s o c i a t e d c h a r a c t e r i s t i c s .
F o r *instance, t h e convoluted t y p e o f accompaniment has t h e h i g h e s t d e n s i t y numbers and density- compressions.
l a r g e s t v e r t i c a l spans.
F i g u r a t i o n s w i t h l a r g e leaps have t h e
A1 t e r n a t i n g f i g u r a t i o n s have t h e sitiallest d e n s i t y -
numbers and s m a l l e s t v e r t i c a l spans.
The d i f f e r e n c e s between t h e s t y l e s of
Chopin and S c r i a b i n w i t h regard to d e n s i t y were minimal.
One d i f f e r e n c e
t h a t was observed was t h e c h a r a c t e r i s t i c s p a c i n g - d i s t r i b u t i o n used by each
composer.
The Chopin etudes e x h i b i t closed spacing a t t h e t o p o f t h e v e r t i -
c a l u n i t s w h i l e t h e S c r i a b i n etudes have open spacing a t t h e t o p and c l o s e d
spacing i n t h e m i d d l e o f t h e v e r t i c a l u n i t s .
D i f f e r e n c e s between Chopin's and S c r i a b i n ' s use o f range a r e a l s o
minute.
There a r e more s i m i l a r i t i e s than d i f f e r e n c e s .
Moreover, t h e o n l y
a p p a r e n t l y s i g n i f i c a n t d i f f e r e n c e s a r e Chopin's use o f s l i g h t l y h i g h e r
p i t c h e s and S c r i a b i n ' s use o f wider l e f t - h a n d spans.
These f i n d i n g s add
more support t o t h e assumption s t a t e d i n t h e Preface t h a t t h e two composers
w r o t e i n a very s i m i l a r s t y l e w i t h r e s p e c t t o t e x t u r e .
More s i g n i f i c a n t
f i n d i n g s were observed between types of f i g u r a t i o n t h a n between t h e composers I
55
styles. This f a c t j u s t i f i e s the attention given the distinction i n
chapter two concerning basic types of figuration.
In general i t can be ob-
served that the low range-averages of b o t h hands tend to remain constant i n
a l l the basic types while the upper range-averages vary.
I t would seem logi-
cal t o assume t h a t increases i n range would occur equally i n both directions,
b u t the evidence suggests t h a t t h i s i s not the case.
Etudes t h a t have a predominance o f parallel doublings contain higher
Etudes w i t h convoluted figurations
pitches and wider spans t h a n the others,
tend t o limit the span of the l e f t hand--perhaps the constant motion of the
part precludes larger intervals due t o technical 1 imitations, or perhaps the
large s k i p s would tend t o polarize the accompaniment i n t o separate bass and
middle register parts t h a t can no longer function as an entity.
Legato
single l i n e etudes have much more limited ranges t h a n other types and do not
venture into the upper registers nearly as much.
Perhaps the legato effect
i s hampered by the piano's inabiiity t o sustain volume in the higher registers.
Some care must be taken i n drawing conclusions based on these results.
Several factors should be kept i n mind.
First, the methods used for averaging
ranges i s arbitrary in certain respects, since the number and the size of the
units sampled varies somewhat. Second, the results, s t r i c t l y speaking, apply
only t o these two collections o f etudes and do not necessarily r e f l e c t upon
other genres, other composers, o r piano texture i n general.
However, the
etudes were, i n part, selected as being representative of the complex, i d i o matic texture of nineteenth century concert pieces.
these etudes was separated by s i x t y years.
Third, the composition of
A l t h o u g h the piano of Chopin's
time was f a i r l y advanced technically, certain developments i n the construction
and design of the piano m i g h t have been responsible for some of the differences
between composers.
The changes t h a t occurred d u r i n g t h i s time include:
56
c a s t i n g t h e i r o n frame i n one s o l i d p i e c e i n s t e a d o f u s i n g composite frames
o f t h r e e o r more separate pieces, i n c r e a s i n g t h e s t r i n g t e n s i o n (now p o s s i b l e
due t o t h e s t r o n g e r frames and improved piano w i r e ) from a t o t a l o f 10.9 t o n s
t o about 30 tons, o v e r s t r i n g i n g and f a n n i n g o u t t h e bass s t r i n g s , and r e l o c a t i o n o f t h e sounding board bridge.*'
Changes o f t h i s k i n d c o u l d poss-
i l b y account f o r S c r i a b i n ' s use o f lower r e g i s t e r s , s i n c e these improvements
changed t h e q u a l i t y o f t h e bass notes.
The q u e s t i o n s r a i s e d i n t h i s d i s c u s s i o n about t h e conclusions suggest
many p o s s i b i l i t i e s f o r f u r t h e r i n v e s t i g a t i o n u s i n g t h e concepts and methodology presented i n t h i s study.
For example, t h e r e l a t i o n s h i p s between types
o f f i g u r a t i o n and d e n s i t y and range found here Frcbab1.y extend t o genres
o t h e r than etudes.
A s t u d y s i m i l a r t o t h i s one c o u l d be designed t o i n v e s t i -
gate s h o r t " c h a r a c t e r pieces" 1 i k e those found i n Schumann's "Carnaval , ' I
s i n c e they, l i k e t h e etudes, a r e each s t r u c t u r e d around one p r i n c i p a l t y p e
o f figuration.
A l a r g e r s t u d y c o u l d examine t h e homophonic piano m u s k o f
several composers , t h e r e b y invol v i ng a g r e a t e r v a r i e t y of s t y 1 es , and coul d
h i g h l i g h t t h e t e x t u r a l d i f f e r e n c e s of v a r i o u s composers and/or s t y l e s .
Such
a s t u d y m i g h t p r o v i d e useful i n f o r m a t i o n concerning s t y l e i d e n t i f i c a t i o n and
t h e p a r t i c u l a r c h a r a c t e r i s t i c s o f music by i n d i v i d u a l composers.
An i n t e r e s t -
i n g s t u d y a l o n g a d i f f e r e n t l i n e o f thought c o u l d examine t h e i n t e r n a l , formal
s t r u c t u r e o f l a r g e r works such as t h e Beethoven sonatas u s i n g these methods
o f analysis.
One c o u l d a l s o i n v e s t i g a t e t h e p r o g r e s s i o n o f t e x t u r e throughout
a work t o determine what types o f p a t t e r n s a r e present.
Although t h e d e t a i l s
o f methodology presented h e r e a r e t a i l o r e d t o meet t h e p a r t i c u l a r requirements
21. A r t h u r Loesser. Men, Women and Pianos:
and Schuster, 1954), 494-96, 564-65.
A S o c i a l H i s t o r y (New York:
Simon
o f t h i s study, t h e concepts and t e r m i n o l o g y a r e conceived on a l a r g e r s c a l e .
I t i s hoped t h a t o t h e r s w i l l f i n d these ideas f r u i t f u l i n a g r e a t v a r i e t y o f
situations.
APPEND1 X
Deterrni na t Ion o f Range-averages
S c r i a b i n Etude Op. 8, No. 1
Measure
numbers
Left- hand
Low
High
-
1-5
6-10
11-15
16-20
21-25
26-30
31-35
36-40
4?.-45
46-52
16
17
16
9
16
22
20
16
17
17
16.6
Averages
46
46
49
48
55
46
41
52
49
65
49.7
S c r i a b i n Etude Op. 8, No. 2
R i q h t -hand
High
Low-
36
36
36
33
40
38
40
36
40
33
36.8
57
58
63
62
65
58
57
64
65
ai
63.0
Measure
n uti1be rs
Left-hand
Low
H i&
-
1-2
3-4
5-6
7-8
9-10
11-12
13- 14
15-16
17-18
19-20
21-22
23-24
25-26
22
22
22
15
6
4
6
6
5
10
10
10
10
Averages
11.4
40
R i sht-hand
High
Low"
58
29
41
42
41
37
34
37
35
32
41
37
41
38
38
60
58
53
56
59
61
52
58
63
63
54
50
46.6
38.O
57.3
48
48
48
47
50
43
42
48
51
51
53
APPEND1 X
DetermJnaLion o f Range-,averages
S c r i a b i n Etude Op. 8, No. 3
Measure
numbers
Left- hand
High
Low
-
1-11
12-22
23-33
34-44
45-55
56-66
67-77
78-88
22
48
17
3
3
89-99
100- 110
111-122
Averages
S c r i a b i n Etude Op. 8, No. 4
Right- hand
Hiqh
--Low
Measure
L e f t -hand
H i qh
nurrihe rs
Low
-
61
1-2
14
50
34
34
5
3-4
20
46
46
63
35
27
25
5-6
7 -8
14
8
46
35
78
51
61
13
37
34
13
22
39
48
18
3
3
11.4
Ri ah t- hand
Low"
Hbk
38
62
44
39
38
60
57
15
43
34
55
9-10
24
51
11-12
26
46
48
40
43
56
58
33
34
56
61
13-14
15-16
29
17
52
48
65
46
39
60
50
63
42
38
65
17-18
46
78
19-20
22
63
21-22
47.4
31.6
62.7
23-24
51
38
39
39
31
62
32
14
21
15
10
60
75
Averages
18.3
46.5
38.8
60.8
46
44
60
APPEND1 X
Determination o f Range-averages
S c r i a b i n Etude Op. 8, No. 6
S c r i a b i n Etude Op. 8, No. 5
Measure
numbers
Low
-
1-6
15
7-12
10
13-18
15
18
Left- hand
Hi&
31-36
10
15
37-42
12
13-48
10
49-54
55-58
13
20
53
55
51
56
51
51
55
51
51
63
Averages
13.8
53.7
19-24
25-30
-
R ig ht hand
5- High
36
68
70
63
68
65
65
70
67
65
80
34.8
68.1
36
32
36
36
36
36
34
32
34
Measure
nutribers
1-5
6- 10
11-15
16-20
21-25
26-30
31-35
36-40
4 1-45
46-50
51-55
56-60
6 1-65
Averages
L e f t-tiand
High
Low
-
Riqht-hand
low"
t i i
18
15
49
56
42
48
68
73
13
22
51
42
53
22
53
41
45
15
53
37
13
15
49
34
49
42
20
53
42
13
13
13
53
38
48
44
49
46
1
49
29
72
69
68
68
70
73
68
68
68
68
66
51.2
40.8
69.2
14.8
m
0
APPEND1 X
D e t c m i n a t i o n o f Range-ave%*ages
S c r i a b i n Etude Op, 8,
Measure
numbers
Left- hand
H i &r
LOW
c
1-7
8- 14
14
50
16
15-21
22-28
29-35
36 -4 2
43-49
50-56
57-63
64-70
71-77
11
10
9
14
16
14
2
Averages
12.1
S c r i a b l n Etude Op, 8, No, 8
No. 7
R 1 gh t- hand
H i&
Low
_y
-
Right- hand
High
Mcasure
nI in)be r s
Left- hand
Low
ttiqh
17
41
38
58
12
41
33
35
48
62
60
53
55
48
61
38
4 I.
40
36
60
62
I1
1
62
43
38
36
57
1-6
7- 12
14
50
33
62
13-18
10
50
13
33
33
30
37
50
45
29
53
53
19-24
25-30
57
53
50
33
41.3
Low
.
I
-
33
57
31-36
37-42
38
62
43-48
30
32
17
17
13
36
57
49-54
12
37
JJ
58
37
55-60
16
36
40
54
29
62
50
Averages
17.6
44.8
39.1
59 * 5
33.3
57.1
29
28
37
C)-
62
58
APPEND1X
Determination o f Rsngc-averages
S c r i a b i n Etude Op. 8, No. 9
Measure
numbers
1-10
11-20
21-30
31.-40
41-50
51-60
61-70
7 1-80
81-90
91-100
101-103
Averages
Left- hand
High
Low
-
S c r i a b i n Etude Op. 8, No. 10
-
I1 iq h t hand
High
&-
5
3
56
56
36
27
72
77
8
49
22
61
12
56
41
77
7
12
51
75
59
31
31
7
52
33
72
62
8
53
36
76
7
6
56
35
77
55
30
79
12
48
31
60
7.9
53.7
32.6
71.6
Measure
nurn b e r s
7
1-10
11-20
21-30
31-40
41-50
51-60
61-70
7 1-80
81-9G
91-100
101-110
111-122
Averages
Left- hand
Hiqh
Low
L _
Rictht-hand
Low"
High
1
.
-
17
17
60
40
52
40
12
60
41
9
47
40
14
17
45
41
57
40
17
60
40
22
57
45
5
60
40
5
60
56
5
42
67
29
33
74
68
74
64
57
69
74
73
68
74
62
77
55.6
40.4
69.5
5
12.1
m
N
APPENDIX
D e t e r m i n a t i o n o f Range-averages
S c r i a b i n Etude Op. 8, No. 12
S c r i a b i n Etuqe Op. 8, No. 11
Measure
Left- hand
High
Right- hand
High
Low-
Measure
n urnbe r s
nurnbe rs-
Low
-
1-5
26
46
37
57
1-5-
6-10
19
46
32
6-10
11-15
46
32
16-20
12
12
57
53
47
33
63
21-25
21
50
37
57
26-30
14
50
14
46
58
55
26-30
31-35
38
32
36-40
19
48
33
36-40
4 1-45
46- 50
19
46
38
57
55
41-45
14
33
33
45
46-50
51-54
14
50
57
69
Averages
16.7
46.2
36.5
56.9
L e f t -hand
High
Low
-
Right- hand
mHigh
19
7
51
38
67
55
38
70
55
39
46
41
43
39
42
34
51
38
5 1.
39
48
45
46
38
51-55
7
10
13
3
7
7
6
7
7
62
26
70
72
70
61
65
70
70
67
79
Averages
8.5
50.0
37.7
69.2
11-15
16-20
21-25
31-35
m
w
APPEND1 X
D e t e r m i n a t i o n o f Range-averages
Chopin Etude Op. 25, No. 6
Chopin Etude Op. 25, No. 4
Right- hand
High
Right- hand
Low
High
-
Measure
numbers
Left- hand
Low
High
-
45
44
68
47
68
45
53
75
46
19
12
50
20
1-6
7-12
48
80
13-18
20
45
44
64
13-18
10
63
38
80
19-24
24
45
40
61
19-24
48.
50
75
25-30
19
45
43
60
25-30
18
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
45
40
68
41
35
36
80
18
17
12
51
49-54
43-48
49-54
55-60
61-65
16
25
46
38
40
61
12
41
54
12
36
33
28
79
40
55-60
61-64
40
Averages
20.1
44.8
42.6
63.6
Averages
15.5
50.2
41.4
74.4
Measure
numbers
Left- hand
Low
High
-
1-6
20
7-12
Low-
72
m
F
APPENDIX
D e t e r m i n a t i o n o f Range-averages
Chopin Etude Op. 25, No. 7
Measure
numbers
Low
1-7
17
44
40
8- 14
15
44
15-21
25
22-28
Left- hand
Chopin Etude Op. 25, No. 8
Right- hand
Low
High
-
Measure
Left- hand
High
Right- hand
High
numbers
-
Low
56
1-3
12
48
45
67
36
56
4-6
17
50
45
67
44
39
60
7-9
21
53
74
9
52
42
62
10-12
12
46
29-35
7
43
43
60
13-15
24
36
36-42
43-49
15
43
40
61
16-18
24
36
17
44
39
56
19-21
17
57
50-56
44
36
56
22-24
57-63
10
21
48
36
56
25-27
17
12
50
55
64-69
17
29
31
48
17
53
Averages
15.3
43.5
38.2
57.1
28-30
31-33
10
36
34 36
17
46
46
40
40
44
45
45
46
41
33
38
Averages
16.7
47.2
42.3
-HiCJtl-
-
Low
-
64
58
76
74
69
70
67
64
77
68.9
APPENDIX
Determination o f Range-averages
Chopin Etude Op. 25, No. 10
Measure
numbers
1-10
11-20
21-30
31-40
41-50
51-60
61-70
71-80
81-90
91-100
101-110
111-118
Averages
L e f t - hand
High
Low
9
21
8
17
22
20
22
20
22
17
14
10
16.8
Chopin Etude Op.10, No. 6
Right-hand
High
Low
-
39
53
60
46
47
43
47
43
47
35
39
46
38
41
63
75
78
67
67
61
67
61
67
65
63
75
45.4
37.7
67.4
33
43
a4
36
37
38
38
38
38
38
Measure
numbers
1-5
L e f t - hand
High
Low
27
24
24
14
10
6-10
11-15
16-20
21-25
26-30
31-35
36-40
41-45
46-50
51-53
27
24
19
Averages
19.o
12
15
13
41
41
38
37
29
36
35
26
41
41
Right-hand
Low
High
_
I
_
33
43
35
35
33
34
36
36
33
43
34
31
50
51
56
58
48
55
53
43
36.2
52.2
52.2
55
50
55
APPEND1 X
Determi n a t i o n o f Range-averages
Chopin Etude Op. 10, No 9
Chopin Etude Op. 10, No 8
Measure
numbers
Left- hand
High
Low
Right- hand
High
&
Measure
numbers
Left- hand
Low
High
7
1-6
21
41
21
74
7-12
13-18
25
78
58
25
13
13
56
35
59
56-63
9
64-71
8
72-79
80-87
i5
1-7
8
42
28
8-15
9
45
28
74
78
16-23
24-31
8
45
28
6
45
32-39
5
40-47
48-55
Right- hand
High
64
41
40
40
60
19
41
40
64
19-24
12
36
36
58
76
25-30
50
31-36
37-42
50
48
41
73
76
11
28
21
48
40
77
77
64
61
28
74
43-48
21
41
28
29
47
74
81
49-54
55-60
21
21
46
41
33
45
45
62
78
61-67
21
65
40
45
43
44
72
72
77
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
41
APPEND1 X
Determi n a t i o n o f Range-averages
Chopin Etude Op. 10, No. 10
Measure
numbers
Low
1-7
8- 14
24
19
15-21
20
22-28
Left- hand
High
Chopin Etude Op. 10, No. 12
Right- hand
High
Measure
numbers
49
50
47
43
43
70
72
1-7
8-14
39
76
45
70
44
41
44
72
36-42
17
24
25
50
50
43-49
19
59
50-56
19
57-63
64-70
19
24
71-77
Averages
29-35
Low
-
Left- hand
High
Low
-
Right- hand
High
Low
-
60
43
28
28
74
78
15-21
11
16
11
43
28
74
14
10
9
47
47
75
22-28
29-35
36-42
48
25
25
35
78
76
73
43
80
43-49
11
60
50
76
59
48
48
43
77
74
50-56
57-63
12
28
28
74
54
81
64-70
42
29
74
81
12
50
43
11
14
43
43
36
76
71-77
9
43
47
78
20.2
49.5
44.0
74.8
7884
4
60
33
81
48.3
32 .O
76.4
Averages
11.o
69
SELECT BIBLIOGRAPHY
Apel, W i l l i . "Texture", Harvard Dictionary o f Music, 2nd e d . rev. and enl.
Cambridge, Massachusetts: Bel knap Press, l F 6 T
S t r u c t u r a l Functions i n Music.
Prenti ce-Hal 1 , 1976.
Berry, Wallace.
Jersey:
Englewosd Cliffs, New
Bowers, Fathion. The New S c r i a b i n ; Enigma and Answers.
Press, 1973.
.
New York:
S t . Martin's
S c r i a b i n ; A Biography of the Kuss-ian Composer 1871-1915, 2 v o l s .
1969.
Tokyo: Kodansha I n t e r n a t i o n a l
Chopin, F r e d e r i c .
n.d.
EtGden, ed. by Herrnann S c h o l t z .
Frankfort:
C. F. Peters,
Dyson, George. "The Texture of Modern Music," Music and Letters IV ( 1 9 2 3 ) ,
Nos. 2 , 3, and 4.
Ganz, Peter F e l i x . "The Development o f the Etude for Piano f o r t e . "
D i s s e r t a t i o n , Northwestern U n i v e r s i t y , 1960.
Garvelmann, Donald. S c r i a b i n : Complete Piano Music, booklet for the record
album o f the same t i t l e , perf. by Michael P o n t i . SVBX 5462, 5463, and
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