Analysis of Texture in Piano Etudes of Chopin and Scriabin PDF
Analysis of Texture in Piano Etudes of Chopin and Scriabin PDF
Analysis of Texture in Piano Etudes of Chopin and Scriabin PDF
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.
Approved by
School of Music
CONTENTS
..........................
..............................
LIST OF EXAMPLES
PREFACE
The
The
The
The
...................
................
...............
................
Chapter
I.
11.
111.
IV.
.......
.............
......
...............
.....................
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
.
3.
.
5.
6.
.
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 . . . . . . . .
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
..........................
30
PREFACE
The Purpose
o f the Study
and 3 ) range.
25 and the Scriabin Etudes Op. 8 measurements o f density and range are
-+
used in these multi-instrument analyses do not transfer well t o the investi g a t i o n of piano music texture.
The h i g h level
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
and often based on variation technique while the Chopin and Scriabin etudes
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.
2.
The Chopin
I.
Scri abi n
Etudes
Op./No.
Chopi n
Etudes
Op ./No.
Melodic presentation
A.
Single l i n e
818 8/11
B.
Doubled l i n e
816 8/9
8/ 10
2516 2518
25110
A.
Chordal figuration
8/ 5
10/11 2514
B.
Arpeggiated figuration
812 8/4
C.
A1 ternating figuration
811 8/3
10/ 10
D.
Convoluted figuration
817 8/12
1019 l o l l 0
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.
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-
Chapter I
a
. .are
often among
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
minds of some authors, f o r example Ivor Keys and George Dyson, texture cons i s t s of a l l
'!"
it1
a vague, holistic
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 .
polyphonic-homophonic, polyrhythmic-
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 -
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.
l'.
. .the
The quanti t a -
Berry's "qualitative"
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.
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.
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
Each of these characteristics involves either horizontal o r vertical factors of the texture.
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.
For this
and other important reasons explained i n the next two sections of this
W.W.
timbre,
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.
e i t h e r directly o r indirectly.
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."
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
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
185.
JJA-+&d
- __
1
homorhythmi c
*-
1
.
I
I
1
1
- - contradirectional
F
= hetero-
rhythmic
1j=&
contra-
different factors.
systematic means for determi n i ng the degree of 1i near independence for any
work.
two lines.
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.
in the medium i t s e l f .
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
The
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
t o q u a n t i f y t h e i r degree o f independence.
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
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
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
Chapter I I
BASIC TYPES OF MELODIC AND
ACCOMPANI MENTAL PRESENTATION
As a r e s u l t , a principal text-
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
Pri-
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.
11
presentation can be considered independently, w i t h each note of a particular
chordal
arpeggiated
convoluted
a1 ternating
12
Nr.8
The
I;
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
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.
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 ,
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-
No. 10 r e s p e c t i v e l y .
t o a l a r g e extent.
EXAMPLE 7
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
The funcit
Chopin Op. 25
i n b o t h hands.
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 .
16
EXAMPLE 9
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.
o f the right hand i s not linked t o the melody a t any certain interval, nor
I t s pitch i s
Here
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
then this added part can be said t o serve primarily i n a melodic role; i t s
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:
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
T h i s melodic inde-
Nr. 8
18
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:
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.
Large leaps
19
separate staves.
EXAMPLE 13 Scriabin Etude Op. 8 No. 5, mm. 1-3 renotated.
PO
'Y-
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.
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.
21
eb
-d-
contour.
A1 ternating Figuration
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
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.
ing pattern o f chord tones which has a linear contour t h a t changes direction
often.
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.)
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
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
---
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.
---
25/ 1
2.
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.
F i r s t , these etudes
(J=iiz.)
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
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.
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.
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
Since these
27
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
the
As a r e s u l t , t h e d e n s i t y -
I'
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 .
23.
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
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.
To under-
Example 25
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
'I)
"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.
vert*ical s p a n s
h ij i
be used.
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 .
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
were spread out over a vertical span o f five octaves, then the density-cornpression would be much lower.
12
Density-compression
31
12 = 2.71
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.
33
domain t h a n i t i s o f texture.
..
I f an arrangement o f notes i s
Again however, t h i s
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.
34
The results of such
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 .
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
.-
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
---
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
4.75
4.71
36
With respect t o the measurements i n Table I , one should note that
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.
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
This type
of the others.
44, which are a b o u t twice the magnitude of the other arpeggiated 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
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-
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
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
The
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.
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 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
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
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 .
With
T h i s f i n d i n g suggest;
t h a t t h e two com-
tcj
I n etudes,
challenge t h e performer.
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.
These
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
Consider
An a l t e r n a t i v e approach would be t o
". . . d i f f e r s
Accord-
from range
low p i t c h . " 2 0
Unfortun-
or low."
~~~~~~
839.
39
40
tessitura?"
No m a t t e r
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-
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.
l t has t h e advantage
This operation
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.
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
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.
nurnber of samples.
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:
'
17 = 4 1 semitones
42
FIGURE I
43
notation.
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
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.
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
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
45
FIGURE 2
=I
U
y7sJ
II
-8-J
Table I 1 1
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
.@
47
FIGURE 3 .
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.
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.
S c r i a b i n ' s use o f
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
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
of
Etude
L
1
1
Legs t o Studies
Doubl ed L I nes
Arpeggi ated
F1 gura t i ons
13.3
17,O
15.0
Hands
Rlqht
hand
LQft
ha ntl
Left
hand
1ow
Type
hand
1ow
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
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
This r e s t r i c t i o n
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
This characteristic
The combined
T h i s i s e3pec-
Aver-
52
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
iis
I t i s precise
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-
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 measurements o f
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 -
The d i f f e r e n c e s between t h e s t y l e s of
One d i f f e r e n c e
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 s i g n i f i c a n t
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.
tend t o limit the span of the l e f t hand--perhaps the constant motion of the
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.
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
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.
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-
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 -
Such
An i n t e r e s t -
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
Although t h e d e t a i l s
A S o c i a l H i s t o r y (New York:
Simon
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
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
Right- hand
Hiqh
--Low
Measure
L e f t -hand
H i qh
nurrihe rs
Low
-
61
1-2
14
50
34
34
3-4
20
46
46
63
35
27
25
5-6
7 -8
14
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
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
49
29
72
69
68
68
70
73
68
68
68
68
66
51.2
40.8
69.2
14.8
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
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
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
-
I1 iq h t hand
High
&-
5
3
56
56
36
27
72
77
49
22
61
12
56
41
77
7
12
51
75
59
31
31
52
33
72
62
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
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
47
40
14
17
45
41
57
40
17
60
40
22
57
45
60
40
60
56
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
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
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
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
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
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
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
52
42
62
10-12
12
46
29-35
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
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
Left- hand
High
Low
Right- hand
High
&
Measure
numbers
Left- hand
Low
High
1-6
21
41
21
74
7-12
13-18
25
78
58
25
13
13
56
35
59
56-63
64-71
72-79
80-87
i5
1-7
42
28
8-15
45
28
74
78
16-23
24-31
45
28
45
32-39
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
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
43
47
78
20.2
49.5
44.0
74.8
7884
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:
New York:
S t . Martin's
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.
Frankfort:
C. F. Peters,
LaRue, Jan.
New York:
Dennis
1970.
New York:
Harmony; S t r u c t u r e and S t y l e .
New York:
McGraw-Hill Co.,