gaspard study of tonality
TRANSCRIPT
A STUDY OF TONALITY IN RAVEL'S "GASPARD DE LA NUIT"
A Thesis Presented in Partial Fulfillment of the Requirements
for the Degree Ma.ster of Arts
by
Charles Craymer Vedder, B. Se. in Ed. "
The Ohio State University
1951
Approved by:
ACKNOWLEDGMENTS
I am sincerely grateful to Dr. Norman F.
Phelps, Professor of Music, The Ohio State Uni
versity, for the very valuable assistance and
guidance which made possible the completion of
this thesis.
i
CHAPTER
I
II
III
IV
V
VI
TABLE OF CONTENTS
INTRODUCTION • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Statement of the Problem ••••••••••••••.••• The Choice of Music • • • • • • • • • • • • • • • • • • • • • • • Analytic Procedure •••••••••••.••••..••••.• Organization of Remainder of the Thesis •••
TERMINOLOGY • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Terminology for Vertical Structures •••••••
Triads • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Seventh Chords
Ninth Chords • • • • • • • • • • • • • • • • • • • • • • • • • • • Eleventh and Thirteenth Chords ••••••••• Additional Vertical Structures •••••••••
Terminology for Form •••••••••••••••••••••• Tables • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Figures ••••••••••••••••••••.•••••••••••
Terminology for Tonal Analysis •••••••••••• Basic Root ••••••••••••••••••••••••••••• Relief Chords • • • • • • • • • • • • • • • • • • • • • • • • • •
VERTICAL STRUCTURES • • • • • • • • • • • • • • • • • • • • • • • • • •
THE FORM •••••••••••••••• 0 ••••••••••••••••••••
Form of Form of Form of
. . . . . . . . . . . . . . . . . . . . . . . . . . . . Ondine Le Gibet Scarbo
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
TONAL ANALYSIS • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Ondine
Le Gibet Scarbo
• ••••••••••••••••••••••••••••••••• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
S1..U11lnary •••••••••••••••••••••••••••••••••••
CONCLUSIONS • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
1 1 2 2 2
4 4 4 6 8
10 1.4 16 16 16 17 17 18
19
28 28 33 36
44 44 53 60 82
84
BIBLIOGRAPh"Y ••••••••••••••••••••••••••••••••• 89
i1
LIST OF TABLES ---TABLE PAGE
I VERTICAL STRUCTURES IN ONDlNE ••••••••••••••••• 20
II VERTICAL STRUCTURES IN LE GIBET ••••••••••••••• 21
III VERTICAL STRUCTURES IN SCARBO ••••••••••••••••• 22
IV SUMMARY OF VERTICAL STRUCTURES IN "GASPARD DE LA NUIT" •••••••••••••••••••••••••••••••••••••• 24
V PERCENTILE OF DATA IN TABLE IV •••.•••.•••••••• 26
VI PERCENTILES BY VERTICAL STRUCTURE ••••••••••••• 27
VII THE FORM OF ONDlNE •••••••••••••••••••••••••••• 30
VIII THE FORM OF LE GlBET •••••••••••••••••••••••••• 34
IX THE FORM OF SCARBO •••••••••••••••••••••••••••• 37
iii
FIGURE
1
2
3
4
5
6
7
8
9
10
11
LIST OF FIGURES
FIGURATION FOR TRIADS •••••••••••••••••••••••
FIGURATION FOR SEVENTH CHORDS •••••••••••••••
FIGURATION FOR NINTIi CHORDS • • • • • • • • • • • • • • • • •
FIGURATION FOR ELEVENTH AND THIRTEENTH CHORDS
FIGURATION FOR ADDITIONAL VERTICAL STRUCTURES
FORM OF ONDlNE ••••••••••••••••••••••••••••••
FORM OF LE GIBET ••••••••••••••••••••••••••••
FORM OF SCARBO • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
TONAL ANALYSIS OF ONDlNE ••••••••••••••••••••
TonAL ANALYSIS OF LE GIBET ••••••••••••••••••
TONAL ANALYSIS OF SCARBO ••••••••••••••••••••
iv
5
7
9
13
15
32
35
40
51
59
80
CHAPTER I
INTRODUCTION
The significance of the work of Maurice Ravel and his
p.Lace in the musical firmament are no longer controversial,
yet aside from a few biographies and numerous articles in
periodicals and newspapers no attempt has been made to pre
sent a total picture of the kind of musica~ material he used
and his employment of this material.
Among the theorists, A. Eaglefield Hull, Ren6 Lenormand,
Horace Alden Miller, and others have quoted passages from the
works of Ravel to demonstrate various devices and F. H. Shera,
in his Debussy and Ravel, has given a brief analysis of a few
Ravel works. In view of the notab~e contributions that Rave~
has made to tile literature of music, particularly to the lit
erature for the piano, it is felt that a closer examination
of Lis works is both justified and desirable.
Statement of the problem. The problem for this thesis
was to determine what tonal system, if any, was emp~oyed by
Ravel in Gaspard de la Nuit. In order to determine this, it
was necessary to do an harmonic analysis and a formal analysis
of the music. A~so, it was found practicable to work out a
figuration that wouid show the exact structure of all chords,
including eleventh and thirteenth chords.
I
2
The choice of music. The piano suite, Gaspard de la
_N_u_i_t J consists of three pieces entitled On dine J Le .;;;;G..::i...;;.b...;;.e..;;;.t, and
Scarbo. In choosing this group of pieces for study, the in
vestigator was guided, in part, by the opinion of critics.
Alfred Cortot paid them tribute in saying, "These three poems
enrich the piano repertoire of our epoch with one of the most
extraordinary examples of instrumental ingenuity whicll the
industry of composers has ever produced."l Ravel's biographer,
Roland-Manuel, not only considered Gaspard de la Nuit as the
greatest of his piano works but declared that "In it, all his
qualities as a musician, and all the strength of his genius
are crystallizedo"2
Analytic procedure. The works studied were first ana
lyzed for their thematic content to determine the structural
divisions or form. Then the vertical structures or chords
were analyzed. Finally, tile relationship of the form and the
vertical structures was studied to determine what tonal system
was used.
Organization of remainder of the thesis. The next chap
ter is a presentation of terminology. It includes chord clas
sification, chord figuration, and the terms used in the tables
and diagrams of the form. There is also an explanation of the
new terms, nbasic r·oot tl and "relief chord, It which are used
IMadeleine Goss, Bolero, The Life of Maurice Ravel, p. 138. ----2Roland-Manuel, Maurice Ravel, p. 54.
3
in the tonal analysis.
The succeeding chapter, TIm VERTICAL STRUCTURES, contains
tables of the vertical structures showing the frequency of
their occurrence.
The form of each piece is shown by a table and a diagram
in Chapter IV.
In the following chapter, TONAL ANALYSIS, the tonal or
ganization of each piece is discussed and illustrated in de
tail.
The final chapter summarizes the findings of the thesis
and discusses their significance.
CHAPTER II
TERMINOLOGY
I. TERMINOLOGY FOR VERTICAL STRUCTURES
Triads. Triads are classified in the usual manner as
major, minor, diminished, and augmented. All chord roots
are shown by capital and lower case letters instead of the
customary Roman numerals. Capital letters are used to indi
cate the roots of major triads. Lower case letters indicate
minor triads while lower case letters with a small circle
indicate diminished triads. An augmented triad is shown by
a capital letter followed by a plus sign. A capital letter
followed by the sign -5 designates a triad with a major third
and a diminished fifth.
When a tone that agrees with the major scale of the root
of the triad is added to t he triad, it is shown by an Arabic
numeral in parenthesis following the letter for the triad.
If the added tone does not agree with the major scale of the
root of the triad, a plus sign placed before the numeral in
dicates that the added tone has been raised one half step;
a minus sign placed before the Arabic numeral indicates that
the added tone has been lowered one half step.
The figuration for triads is illustrated in FIGURE 1.
4
o = Major triad on 0
c = Minor triad on 0
CO • Diminished triad on 0
Of = Augmented triad on 0
o -5 = A triad consisting of a major third
and a diminished fifth
0(6)
0(f4)
0(-9)
:: A major triad with an added sixth
= A major triad wi th an added augmented
fourth
= A major triad with an added minor
ninth
FIGURE 1
FIGURATION FOR TRIaDS
5
6
Seventh chords. Seventh chords, other than diminished
sevenths, are classified according to four species, the fourth
species having four subdivisions. The figurations for the
various seventh chords as listed below are illustrated in
FIGURE 2.
1. First species seventh chord consisting of a major
triad and a minor seventh.
2. Second species seventh chord consisting of a minor
triad and a minor seventh.
3. Third species seventh chord consisting of a dimin
ished triad and a minor seventh.
4. Fourth species seventh chord consisting of a major
triad and a major seventh.
5. Fourth species seventh chord consisting of a minor
triad and a major seventh.
6. Fourth species seventh chord consisting of a dimin
ished triad and a major seventh.
7. Fourth species seventh chord consisting of an aug
mented triad and a major seventh.
8. Diminished seventh chord consisting of a diminished
triad and a diminished seventh.
1$
1$
1. 2. 3.
~L I tt II ~[ II
C7 (81) C7(S2) C7(83)
5.
.,1 C7 (S4m)
6. 7.
II Pfl II Ii II -e-
C7(840) crj (S4f)
FIGURE 2
FIGURATION FOR SEVENTH CHORDS
7
4.
t II
C7 (84)
8 • . ...A. ____
P~I -9-
If . 0
c07
8
Ninth chords. Ninth chords are classified according to
four species, each species having subdivisions. The figura-
tiona for the various ninth chords described in the following
list are illustrated in FIGURE 3.
1. First species ninth chord consisting of a major
triad, a minor seventh, and a major ninth.
2. First species ninth chord consisting of a major
triad, a minor seventh, and a minor ninth.
3. Second species ninth chord consisting of a minor
triad, a minor seventh, and a major ninth.
4. Second species ninth chord consisting of a minor
triad, a minor seventh, and a minor ninth.
5. Third species ninth chord consisting of a dimin
ished triad, a miner seventh, and a major ninth.
6. Third species ninth chord consisting of a dimin-
ished triad, a minor seventh, and a minor nin th.
7. Fourth species ninth chord consisting of a major
triad, a major seventh, and a major ninth.
8. Fourth species ninth chord consisting of a minor
triad, a major seventh, and a major ninth.
9. Fourth species ninth chord consisting of a dimin-
ished triad, a major seventh, and a major ninth.
10. }i'ourth species ninth chord consisting of an aug
mented triad, a ma jor seventh, and a maj or ninth.
11. Fourth species ninth chord consisting of a major
triad, a major seventh, and a minor ninth.
9
1. 2. 3. 4. 5.
C9 (83)
6. 7. 8. 9. 10.
1* ttl II I ~ i II i II it[ II ~
C-9 {S3) C9 {S4) C9 {S4m) C9(S4 0 ) C9(34f)
1I. 12. 13. 14.
I; I II ~l II 3 II . q ; C-9(84) C-9(54m) 0-9 (54 0 ) C- 9(S4f)
FIGURE 3
FIGURATIOn FOR NINTH CHORDS
12. Fourth species ninth chord consisting of minor
triad, a major seventh, and a minor ninth.
13. Fourth species ninth chord consistlng of a dimin
ished triad, a major seventh, and a minor ninth.
14. Fourth species ninth chord consisting of an aug
mented triad, a major seventh, and a minor ninth.
Eleventh and thirteenth chords. The writer of this
10
thesis is aware of the differences of opinion which exist among
theorists regarding the existence of eleventh and thirteenth
chords. That little is known of these chords in our American
system of teaching is pointed out by Horace Aiden Miller.
"The English and the l"rench are the ones who make use of
analyticai processes that recognize these chords, the former
sometimes to an exaggerated degree." l
In the present analysis, all dissonances, except pedal
points, that are ieft unresoived until the sounding of the
next chord are considered chord members or tones added to the
chord. "W'hen our musical perception becomes so habi tua ted
to a certain resolution that we no longer require it, but
preferably desire the immediate moving forward to another chord,
thus eliminating the unnecessary step, then the first chord
becomes a definite entity, and a new harmony is born. u2
If the eleventh or thir·teenth above the root appears as
lHorace Alden Miller, New Harmonic Devices, p. 58.
2I!?..±.2. , :w. 59, 60.
11
a harmonic tone with a seventh or ninth chord, the structure
is called an eleventh or thirteenth chord, but if the eleventh
or thirteenth appears with a triad without the seventh, the
structure is called a triad with an added fourth or an added
sixth. Likewise, when the interval of a second or a ninth
above the root appears with a triad Witilout the seventh, the
structure is called a triad with an added second or added
ninth.
In the figuration for eleventh and thirteenth chords,
the lower four or five tones of the chord are indicated as
a species of seventh or ninth chords, whichever the case may
be. Then the numbersll or 13 or both are placed in paren
thesis following this indication. Nhen the interval of the
eleventh is perfect and the thirteenth is major, the figures
11 and 13 are used. The plus sign is placed before the figure
when the tone is a half step higher and the minus sign is used
when the tone is a half step lower. FIGURE 4 shows the figura
tion for the eleventh and thirteenth chords that are listed
below.
1. An eleventh chord consisting of a first species
seventh chord and a perfect eleventh.
2. An eleventh chord consisting of a first species
ninth chord and a perfect eleventh.
3. An eleventh chord consisting of a first species
seventh chord and an augmented eleventh.
4. An eleventh chord conSisting of a first species
ninth chord and an augmented eleventh.
5. A thirteenth chord consisting of a first speciea
aeventh chord and a major thirteenth.
S. A thirteenth chord cODai.ting of a first epeciea
ninth chord and a major thirteenth.
12
? A thirteenth chord consisting of a fourth species
ninth chord, a perfect eleventh, and a major thirteenth.
S. A thirteenth chord consisting of a first species
seventh chord, an augmented eleventh, and a major thirteenth.
9. A thirteenth chord consiating of a third species
aeventh chord, a perfect eleventh, and a minor thirteenth •.
10. A thirteenth chord consisting of a fourth species
ninth chord and an augmented thirteenth.
13
1. 2. 3. 4. • I; pi
--e-II i II !i II ~ II
0'7(81)(11) 0 9 (81)(11) 0'7(81)(1'11) 09 (81)(1-11)
5. 6. 7. 8.
1$ -4- -4-
I ~ tt II pi II II II -e-
07
(81)(13) 0 9 (81)(13) 0 9 (84)(11,13) 07 (81) (,"11,13)
9. 10.
1$ ~i II Ji II
07 (83)(11,-13) 0 9 (84 0 ) (f13)
FIGURE 4
FIGURATION FOR ELEVENTH AND THIRTEENTH OHORD8
14
Additional vertical structures. The few remaining ehord
structures which have not been described and for which no fig
uration has been given are listed below and illustrated in
FIGURE 5.
1. A first species seventh chord whose fifth has been
raised a half step.
2. A first speoies ninth chord whose fifth has been raised
a half step.
3. A first species seventh chord whose fifth has been
lowered a half step.
4. A first species ninth chord whose fifth has been
lowered a half step.
5. A first species seventh chord which contains a minor
third in addition to its major third.
6. A first species minor ninth chord which contains a
minor third in addition to its major third.
7. An eleventh chord consisting of a first species
seventh chord with major and minor third present and an aug
mented eleventh.
8. A thirteenth chord conSisting of a first species
seventh ohord with major and minor third, both a perfect and
a diminished fifth, and a thirteenth.
1.
1$
5.
I{~
2. 3.
191 II IPS II p~i II -B- -e- -e-
C7f5(Sl) 09f5(31) C7-5(31)
6.
ii II rr II
C7 (Sl) (1\13) C-9 (Sl)(M3 )
8.
I~
FIGURE 5
FIGURATION FOR ADDITIONAL
VERTICAL STRUCTURES
15
4.
ppl II -fT-
09-5(Sl)
7.
p Ji II
C 7 ( Sl ) (M3 ) (I'll)
II
16
II. TERMINOLOGY FOR FORM
Tables. In Chapter IV, THE FORM, four-column tables are
used. In the first column, labeled "Portion," the various di
visions or parts of the piece such as ttsubjectlt and "transi
tionU are indicated. ~he second column, "Source of and/or
treatment of material," denotes the phrase or section of the
piece from which the material is derived and/or the treatment
of the material used. The third column shows the number of
measures in each phrase, section, or motive. The location of
each division of the form is shown by measure numbers in the
fourth column.
Figures. In FIGURES 6, 7, and 8, the form of each piece
is diagrammed. Each dash represents a measure and the Arabic
nunJ-erals above the dashes are the measure n1lr.1bers of the -beginning of each phrase or section. The dashes are grouped
to show the division of the music into phrases, sections, and
motives. Each group of dashes is labeled with such terms as
t'Introduction, tf ttSub jec t," etc. All information in parenthe ses
indicates the source of the material and/or the treatment of
the material used or developed in that particular phrase or
section.
1'1
III. TERMINOLOGY FOR TONAL ANALYSIS
In the chapter where the tonal analysis of Gaspard de
1a .!il!.ll is discussed two new terms, "basic root" and "relief
chord," are used.
In the phrases and sections where the chord relation
ships did not indicate a key it was discovered that one chord
or various c.J:lords built on the same root were most used. This
I'oot seemed to be the center of hS.rmonic activity while chords
built on other roots provided harmonic variety. To describe
this harmonic technique these two new terms were adopted.
Basic root. The basic root is the most frequently oc
curring chord root or the root which occupies the major portion
of the time value in a phrase or section. Any type of chord
from a triad to a thirteenth chord may be constructed on the
basic root and any number of these chords may occur in a
phrase or section. These chords are built in thirds and the
lower tone of the lowest third in the chord is the basic root.
The basic root usually starts or ends a phrase or does both but
this is not always the case. Frequently, the basic root is
used as a pedal point for the entire phrase or for most of the
phrase. Transitions or phrases that are transitional in char
acter may have two or more basic roots.
The basic root analysis is not used in phrases or sections
where the establishment of key by conventional chord relation
ships is obvious.
18
Relief chords. All chords constructed on roots other than
the basic root are called relief chords. Their function is
to provide harmonic variety or to lead into the next phrase.
A relief chord which is the final chord in a phrase may be
prolonged to extend the phrase without its becoming a basic
root. The basic root and the roots of the relief chords may
have any interval relationship.
CHAPTER III
THE VERTICAL STRUCTURES
In this chapter tables are used to show the exact
number of each kind of vertical structure found in Gaspard
de la Nuit. There is a table for eacll piece and a table
which summarizes the vertical structures in the entire work.
The two additional tables are percentile evaluations of the
harmonic material. The first is a conversion of TABLE IV in
to percentages. The second is a percentage tabulation of the
individual harmonic classifications.
All chord structures have been analyzed as being built
in thirds and the lower tone of the lowest third in the chord
is the root.
19
20
TABLE I
VERTICAL STRUCTURES IN ONDINE
Structure Number of Occurrences
Major triad Major triad (6) Major triad (-6) Minor triad Minor triad (2) Minor triad (6) Minor triad (4,6)
Seventh chord (51) Seventh chord (53) Seventh chord (S3)(M3) Diminished seventh chord
Ninth chord (51) Ninth chord -9(51) Ninth chord (32) Ninth chord -9(S2) Ninth chord (S3)
Eleventh chord consisting of: Ninth chord (31)(11) Ninth chord -9(31){fll) Ninth chord (33)(11)
Thirteenth chord consisting of: Seventh chord (31)(13) Seventh chord (S4)(13) Ninth chord (Sl)(13) Ninth chord (Sl)(-13) Ninth chord -9{Sl}(13)
Polychordal structures consisting of: Diminished triad and major triad with roots one half step apart
DiminIshed triad and major triad with roots a whole step apart
Diminished seventh chord and major triad with roots a major third apart
Ninth chord -9(Sl) and major trIad with roots a minor third apart
Total
13 1 1 5 6 2 3
S 9 2 1
27 5 5 2 2
3 1 3
3 3 4 2 3
6
1
6
1
128
21
TABLE II
VERTICAL STRUCTURES IN LE GIBET
structure
Major triad Ma jar triad (9) Minor triad Minor triad (4) Minor triad (9) Diminished triad
Seventh chord (81) Seventh chord (Sl) (~) Seventh chord (S3)
Ninth chord (Sl) Ninth chord -9(81) Ninth chord (82) Ninth chord (S3)
Eleventh chord consisting of: Ninth chord (Sl)(~ll) Ninth chord -9(Sl)(11)
Thirteenth chord consisting of: Seventh chord (81)(13) Seventh chord (81)(-13) Ninth chord -9(81)(M3)(fll,13)
Total
Number of Occurrences
6 10
6 5
10 2
4 2 5
17 3 3 3
1 6
8 2 1
94
22
TABLE III
VERTICAL STRUCTURES IN SCARBO
Structure
Major triad Major triad -5 Major triad (2) Major triad (6) Major triad (~6) Major triad (9) Maj or triad (-9) Major triad (f4, -6) Major triad (6, 9) Major triad (6, -9) Minor triad Minor triad (f4, 6) Augmented triad (f4) Augmented triad (f6) Diminished trl ad
Seventh chord (81) Seventh chord -5(Sl) Seventh chord (Sl)(~:5) Seventh chord (82) Seventh chord (S3) Seventh chord (S4) Seventh chord (S4m) Diminished seventh chord
Ninth chord (Sl) Ninth chord -9(~1) Ninth chord -9-5(Sl) Ninth chord -9(Sl)(M3) Ninth chord -9-5(Sl)(M3) Ninth chord (S2) Ninth chord (S3)
Eleventh chord consisting of: Seventh chord (Sl)(fl1) Seventh chord (Sl)(M3)(fll) Seventh chord (S2)(fll) Seventh chord (53)(11) Seventh chord (S4)(fl1) Ninth chord (Sl)(11) Ninth chord (Sl)(r11)
Thirteenth chord consisting of: Seventh chord (Sl)(13)
Number of Occurrences
52 8 1
46 6 1 1 1 1 1
27 11
1 9 1
31 1 :5 2
17 2 2 1
19 11
2 4 1 2 5
20 4 8 1 4 1 2
11
23
TABLE III (CONTINUED)
Structure
Thirteenth chord consisting of: (Cont.) Seventh chord (Sl)(M3)(13) Seventh chord (Sl)(~ll, 13) Seventh chord (Sl)(~3)(f5)(13) Ninth chord (~1)(13) Ninth chord - (Sl)(13) Ninth chord -9(Sl)(M3)(13) Ninth chord -~(Sl)(f11, 13) Ninth chord - (S4){13)
Total
Number of Occurrences
5 3 2 2 7 1 4 1
346
TABLE IV
SUMMARY OF VERTICAL STRUCTURES IN GASPARD DE LA NUIT
24
Structure Number of Occurrences
Major triad Major triad -5 Major triad (2) Major triad (6) Major triad (f6) Major triad (-6) Major triad (9) Major triad (-9) Major triad (f4, -6) Major triad (6, 9) Major triad (6, -9) Minor triad Minor triad (2) Minor triad (4) Minor triad (6) Minor triad (9) Minor triad (4, 6) Minor triad Cf4, 6) Augmented triad (f4) Augmented triad (f6) Diminished triad
Seventh chord (Sl) Seventh chord -5(Sl) Seventh chord (Sl)(~3) Seventh chord (52) Seventh chord (83) Seventh chord (S3)(M3) Seventh chord (S4) Seventh chord (S4m) Diminished seventh chord
Ninth chord (Sl) Ninth chord -9(Sl) Ninth chord -9-5(Sl) Ninth chord -9(Sl)(M3) Ninth chord -g-5(Sl)(~3) Ninth chord (S2) Ninth chord -9(S2) Ninth chord (33)
Eleventh chord consisting of: Seventh chord (Sl)(fll)
71 8 1
47 6 1
11 1 1 1 1
38 6 5 2
10 3
11 1 9 3
43 1 5 2
31 2 2 2 2
63 19
2 4 1
10 2
10
20
25
TABLE IV (CONTINUED)
Struoture
Eleventh chord consisting of: (Cont.) Seventh chord (Sl){M3){f11) Seventh chord (S2){f11) Seventh chord (S3){11) Seventh chord (S4){f11) Ninth chord (Sl){ll) Ninth chord (SI)(f11) Ninth chord -9{Sl){11) Ninth chord -9(Sl){f11) Ninth chord (S3)(11)
Thirteenth chord consisting of: Seventh chord (Sl)(13) Seventh chord (Sl)(-13) Seventh chord (Sl)(~3)(13) Seventh chord (Sl)("ll, 13) Seventh chord (Sl )(~3)( P5) (13) Seventh chord (34)(13) Ninth chord (Sl){13) Ninth chord (Sl)(-13) Ninth chord -9(31)(13) Ninth chord -9(Sl)(M3)(13) Ninth chord -9(Sl)(,,11, 13) Ninth chord -9(Sl) (!!3) (f11, 13) Ninth chord -9(S4)(13)
Po1ychorda1 structures consisting of: Diminished triad and major triad with roots one half step apart
Diminished triad and major triad with roots a whole step apart
Diminished seventh chord and major triad with roots a major third apart
Ninth chord -9(Sl) and major triad with roots a minor third apart
Total
Number of Occurrences
4 8 1 4 4 3 6 1 3
22 2 5 3 2 3 6 2
10 1 4 1 1
6
1
6
1
568
26
TABLE V
PERCENTILES OF DATA IN TABLE IV
structure Ntunber Percentage
Triads 237 41.7
Seventh chords 90 15.9
Ninth chords III 19.5
Eleventh chords 54 9.5
Thirteenth chords 62 10.9
Polychordel structures 14 2.5
Total 568 100.0
TABLE VI
PERCENTILES BY VERTICAL STRUCTURE
A. TRIADS
Structure
Triads without added tones Triads with added major sixth Triads with other added tones
Total
Number
120 49 68
237
B. SEVENTH CHORDS
Structure
First species seventh chords Third species seventh chords All other seventh chords
Total
Number
49 33
8
90
C. NINTH CHORDS
:::>tructure
First species ninth chords All other ninth chords
Total
Number
89 22
III
D. ELEVENTH AND THIRTEENTH CHORDS
Structure
Augmented eleventh chords All other eleventh chords Thirteenth chords
Total
Number
40 14 62
116
27
Percentage
50.6 20.7 28.7
100.0
Percentage
54.4 36.7 8.9
100.0
Percentage
80.2 19.8
100.0
Percentage
34.5 12.1 53.4
100.0
CHAPTER IV
THE FORM
This chapter is a presentation of the formal analysis of
Gaspard de la Nuit. The form of each piece is shown first by
h table and then by a diagram. The arrangement and terminology
of the tables and diagrams has been explained in Chapter III.
However, it should be mentioned that in counting measures in
phrases and sections the first full measure has been counted
as measure one. An exception to this procedure occurs at tne
beginning of Ondine where the half measure of the introduction
is counted as measure one.
Due to the almost complete absence of conventional har-
monic cadences the formal structure has been determined prin-
cipally from the melodic line of the pieces.
The form of Ondine. The Sonata-Allegro form has been
employed in Ondine.
The exposition begins with a two-measure introduction.
The first subject which follOWS consists of a series of closely
related phrases approximating a ternary design. A transition
leads to Subject II. The second subject consists of two simi-
lar phrases, the melodic material of which has been borrowed
from the first subject.
In the development, both subjects are used at various
pitch levels with varied harmonizations and accompaniments.
A new two-measure melodic idea is introduced in this section.
28
29
The subjects appear in reverse order in the recapitula
tion. In addition to being somewhat curtailed, the subjects
are melodically and harmonically modified. Ondine closes with
a short cadenza followed by three measures of an arpeggiated
C-sharp major triad.
The details of the formal analysis of Ondine are shown
in TABLE VII and FIGURE 6.
Portion
:EXPOSITIUN Introduction Subjeot Ia Subjeot Ib Subjeot 10 Transition Introduotion Subjeot IIa Subjeot lIb
DEVELOPMENT Section 1 Section 2
Section 3
Seotion 4 Section 5 Section 6
(Retransi tion)
RECAPITULATION Subjeot IIa Transition Subject Ia Subjeot Ib
TABLE VII
THE FORM OF ONDINE
Souroe of, and/or treatment of materials
like Ia like 18
like IIa
Subjeot 18 Motive Z (new) Subjeot Ia Motive Z Subjeot IIa Motive Z Motive Z Motive Z
varied
varied varied
Number of measures in phrases, seotions, or motives
2 6 6 8 8 2 5 5
3 2 3 2 5 3 2 4
6 8 4 4
Measure numbers
1 - 2 3 - 8 9 -14 15-22 23-30 31-32 33-37 38-42
43-45 46-47 48-50 51-52 53-57 58-60 61-62 63-66
67-72 73-80 81-84 85-88 ~
Portion
RECAPITULATION (Cont.) Cadenza Closing chord
TABLE VII (CONTINUED)
Source of. and/or treatment of materials
Subject Ic
Number of measures in phrases, sections, or motives
1 :3
Measure numbers
89 90-92
CA .....
EXPOSITION
Subject Ia Ic (like Ia) Transi t10n Introduction 1 3 ____ _
Ib (like Ia) 9 ------
15 ______ _ 23 ______ _
Subject IIa lIb (like IIa) 38
Introduct ion 31_ 33 ___ _ - - - --
DEVELOPMENT
Sect. 1 (Sub ject Ia) 43 __
Sect. 2 Motive Z (new) 46_
sect. 6
(Sub ject Ia) 48 - --
Sect. 4 Motive Z .28_ -
Sect. 5 Motive Z 61
Retransltion (Motive Z)
- - §.3 __ _
RECAPITULATION
Sect. 3 Motive Z ,21_
(Sub jact IIa) 53 ___ _
Subject IIa (var1ed) Transition Subject Ia (varied) £.7 ____ _
Subject Ib (varied) 85 - - --
73 ______ _ 81 __ _
Cadenza (Subject Ie) 89
FIGURE 6
FORM OF ONDlNE
Closing chord 90 __
~ l'O
33
The ~ ££ ~ Gibet. A ternary design has been employed
in Le Gibet.
The introduction consists of a repeated octave which is
used as a pedal point throughout the entire piece.
Part A and part B each consist of a series of five phrases.
The first phrase of part B is a transposition of the first
three measures of the final phrase of part A. These two parts
are further related by a descending melodic whole step which
occurs at the end of phrases band c of part A and in phrases
f, g, and h of part B.
The return of part A of Le Gibet which corresponds to the
recapitulation of Ondine has been given a similar treatment.
The original melodic matel'ial appears in reverse order as in
Ondine. Only three of the original five phrases return and
these are separated by interludes. The repeated octave which
has been used throughout the piece is all that appears in the
two closing measures of Le Gibet.
A detailed formal analysis of Le Gibet is given in TABLE
VIII and FIGURE 7 which follow.
Port1on
PART A ---- Introduction
Phrase a Phrase b Phrase a Phrase c Phrase d
PART B - Phrase d
Phrase e Phrase t Phrase g Phrase h
RETURN OF PART A Pbrase1 -Interlude Phrase c Interlude Phrase a Codetta
TABLE VIII
THE FORM OF LE GIBET
Source of, and/or treatment of materials
like phrase b like phr ase a
transposed
like phrase e
like phrase d phrase e
phrase e
Introduction
Number of measures in phrases, sections, or motives
2 3 2 2 2 5
3 3 5 4 3
5 2 2 4 3 2
Measure numbers
1 - 2 3 - 5 6 - 7 8 - 9 10-11 12-16
17-19 20-22 23-27 28-31 32-34
35-39 40-41 42-43 44-47 48-50 51-52
(,:! ~
~~=--"'-~~7""-
PART A
Introduction 1
PART B
Phrase a 3 - --
b 6
a 8_
c (like b) 10 - -
d (like a) 12 ___ _
d (transposed) 17
e f (like e) g h 20_ _ 23 ___ _ ~8_ _ _ 32 __
RETURN OF PART A
Phrase i (like d) 35 - - ---
Interlude (phrase e) 40
a Codetta (introduction) 48_ 51
FIGURE 7
FORM OF LE GIBET
c 42
Interlude (phrase e) 44 __ _
CA C1I
36
The form of Scarbo. The Sana ta-Allegr·o design has again
been used in Scarbo.
The exposition begins with a long introduction. Subject
I and Subject II each consist of a series of phrases, some of
which are repeated. There. is no transition between the subjects.
In the development, the first subject has been utilized
to a greater extent than the second subject. In sections nine
and ten a new theme has been introduced and alternated with
material from both subjects. This new theme has been developed
from the tllree-tone motive of the introduction.
The recapitulation begins with a modified version of the
introduction. The subjects which appear in their regular order
are curtailed. The recapitulation has the character of another
development section due to the varied treatment given the two
subjects.
The coda uses material from both subjects.
The details of the formal structure of Scarbo are shown
in TABLE IX and FIGURE 8 which follow.
Portion
EXPOSITION Introduction Subject Ia Interlude Subject Ib Interlude Subject Ib Transition Subject Ic Subject Id Subject Ia Subject IIa Subject IIa Subject lIb Subject IIc Subject lId Subject lIe Sub j ect lIt" Subject IIg Subject lIt" Subject IIg Subject Ilh Subject IIi Transition
TABLE IX
THE FORM OF SCARBO
Source of, and/or treatment of materials
repetition
varied Subject Ib repetition like Ic varied
curtailed
l1ke lIb like lIb like lIb like IIa 11ke lIt" transposed transposed
l1ke lIb. Subject IIh
Number of measures in phrases, sections, or motives
7, 7, 17 5
14 7, 7
8 7
6, 9 4, 4
7 11 12 10 8 5 8 4 6 5 6 5 4 4
16
Measure numbers
1 -3l. 32-36 37-50 51-64 65-72 73-79 80-94 95-102
103-109 1.10-.120 12.1-J.32 133-.142 143-150 15.1-.155 156-163 164-.167 168-173 174-178 179-184 185-.189 190-.193 194-197 198-2.13
(A ..;f
TABLE IX (CONTINUED)
Portion Source of, and/or Number of measures Measure treatment of materials in phrases, secti~ns, numbers
or motives ---DEVELOPMENT
Section 1 Subject Ib 7, 14 214-234 Section 2 Subject Ib 6, 15 235-255 Section 3 Subjeot Ic 4, 4 256-263 Section 4 Subject Ic 4 264-267 Section 5 Subject Ib 4, 4 268-275 Section 6 Subject IIf and Ic 1, 4, 8 276-288 Section 7 Subject lIt and Ic 2, 4, 8 289-3U2 Section 8 Subject lIt and Ic 2, 9 303-313 Section 9 Xa (new theme) 4 314-317
Subject Ic 3 318-32U Xb (new theme) 3 321-323 Subjeot lIt 1 324
Sect10n 10 Xa 4 325-3S8 Subject Ib 2 329-330 Xb 4 331-334 Subject Ic 3 335-337
Xa and Subject Ic 7 338-344 Section 11 Subject Ic 4, 4, 13 345-365 Section 12 Subject lIt 16 366-381 Section 13 Subject Ia 13 382-394
RECAPITULATION Introduction 7, 7, 13, 8 395-429 Subject Ib Augmentation 7 430-436 Interlude 4 437-440 Subject Ib Augmentation 7 441-447 Transition 6, 6, 8, 9 448-476 ()I
Subject IIa varied 7, 8 477-491 m
Portion
RECAPITULATION {CONT.} Subject IIa Subject lId Subject lIt Subject IIg Subject lIt Subject IIg Subject IIh Transition
CODA Section 1 Sect10n 2 Section 3 Section 4 Section 5 Section 6 Section 7
TABLE IX {CONTINUED J
Source of, and/or treatment of materials
transposed varied varied varied transposed transposed repet1tion Subject IIh
Subject lIt Subject IIf Subject Ia Subject lIt Subject Ib Subject IIf Introduction
Number of measures in phrases, sectIons, or motives
10, 9 10
6 5 6 5
4, 4 5, 7
5, 5 7 4 8
10 14 12
Measure numbers
492-510 511-520 521-526 52'7-531 532-537 538-542 543-550 551-562
563-572 573-579 580-583 584-591 592-601 602-615 616-627
C.4 (0
EXPOSITION
Introduction 1 8 15 ------- ------- -----------------
Subject Ia Interlude Ib Ib (repetition) 32 ___ _ 37 51 ------------- ------ ....
58 _____ _
Interlude Ib (varied) Transition (Ib) 65 ______ _ 73 _____ _ 80_ _ _ _ _ 86 _______ _
Ic 99 - - --
Id (like Ic) 103 ____ _
Subject IIa 121 ------------
Ia (varied) 110 -----------IIa (curtailed) 133 _______ _
lIb ,143 _____ _
Ic 95 - - --
IIc (like lIb) 151 -- ---
lId (like lIb) 156
lIe (like lIb) 164 __
lIt (like IIa) IIg (like lIt) lIt (transposed) --------
IIg (transposed) 18£ - - -
IIh 190 - - --
IS.§. ___ _ 17.1 __ _ 179 ___ _
IIi (like IIh) 1,91 --
FIGURE 8
FORM OF SCARBO
Transition (IIh) 198 ----------------
tIIoa
___ ~~ __ ~._~" .... _",,~"e, "
DEVELOPMENT
Section 1 (Ib) 214 _ _ _ _ _ 221 ___________ _
Section 2 (Ib) 235 _ _ _ _ 241 ____________ _
Section 3 (Ie) 256 _ _ 260 _ _
Section 5 (Ib) Section 6 (IIf and Ie) 268 272 ---- ---- :E,76 277 _ _ 281 _____ _
Section 7 (IIf and Ie) 289 g91 _ _ 295 _____ _
Section 8 (IIf and 10) 303 302, _ _ _ _ _ __
Section 9 Xa (new theme) 314 -- --
Section 10 Xa (Ib) ,225 _ _ 329
Section 11 (Ie)
(10) ~18 _
Xb 331 __
345 349 353
Xb 321 _
(Ie) 335 - --
(lIt) 324
(Xa and Ie) 338 -------
---- ---- -------------
FIGURE 8 (CONTINUED)
Section 4 (Ie) 264 __
... .....
Seot1on 12 (lIt) Seotion 13 (Ia) 366 _ _ _ _ _ _ _ _ _ ____ _ 382 __________ _
RECAPITULATION
Introduotion 395 402 409 421 ------- ------- ------------- ----------
Subjeot Ib (augmentation) 430 ____ _
Transl tlon Seotion 1 448 ------
Seotion 2 454 ___ _
Subject IIa (varied) 477 484
Interlude 437 - - --
Seotion :3 460
Subjeot Ib (augmentation) 441 -------
Seotion 4
-------- 468 ____ . __ _
IIa (transposed) 492 502 ------ -------- ---------- ---------
lId (varied) 511 -------- ..... -
IIg (transposed) 538 __ _
I III
IIi' (varied) 521_ - - -
543 __ I III .§.47 __
IIg (varied) 527 - - - --
lIt (transposed) 532 ------
Transition (IIh) 551 _ _ _ .§.56 _ _ __ _
FIGURE 8 (CONTINUED) .. to
CODA
Sect10n 1 (IIr) 563 _ _ _ 56~ __ _
Seotion 5 (Ib) 592 _______ _
Sect10n 2 (lIt) 573 ____ _
Seotion 6 (IIr)
Section 3 (Ia) 580 __
Section 4 (lIt) 58! _____ _
Section 7 (Introduction) 616
FIGURE 8 (CONTINUED)
... ~
CHAPTER V
TONAL ANALYSIS
The present chapter contains a complete tonal analysis
of Gaspard de la l!Bll showing how keys and basic roots have
been determined. The analysis has been done and is presented
phrase-wise and section-wise. In each illustration the names
of the chords are shown below the staff while the chord roots
and their duration appear in notation on the staff.
In addition, the basic roots and keys which have been
determined by the phrase-wise and section-wise analysis are
shown by a graph which follows the discussion of the tonal
analysis of each piece.
I ONDINE
EXPOSITION
Introduction (meas. 1-2).
l~ <~Q
'Cf'
The key of C sharp is indicated by these two measures
of a trilled C sharp major triad.
Subject Is (meas. 3-8).
Cfct (Sl)
I J. Af'(S1)
44
J. I J
45
Subject Ib (meas. 9-14).
Di9(S2) B'(Sl) Dw'\S2) :B"(S1) if 1'(") i~
Subject Ic (meas. 15-22).
C'''(Sl)
Ii r II r: J.
The entire first subject is in the key of C sharp major.
The return of the melody and harmony of Ia in the first two
measures of Ic together with the sUbdominant-tonic progression
from measures fourteen to fifteen maintain the tonality of C
sharp despite the fact that the tonic chord is a first species
nin th chord.
Transition (meas. 23-30).
I©:~ ~f ~. I;. J Itt E: 11;\ 116 ; ;
D,"(S1}(11) Bt7 (S3) El'(Sl) A~'(S3) ] 'l(S1) 'B-' (61)(13)
This transition is in the key of G sharp. The tonic
chord of the first measure and the dominant eleventh chord of
the next three measures seem to justify this analysis. The
46
remaining chords starting in measure five are III, VI, II,
and III.
Introduction (meas. 3~-32).
IfJFt'6l C· n71f1 ~ Gt-
Subject IIa (meas. 33-37).
Q
G4f'l(S1)(-13)
SUbject lIb (meas. 38-42).
19:f;1~if Zl Ig r· Ire e It e .g Ii J I I \ 1 f G #'1 (Sl)(-13) FfQ(Sl) FJ-~(S2) Fit"' (Sl) F1-"l(Sl) D~
The entire second subject inc~uding its introduction is
in the key of G sharp. The dominant chord in phrase a is a
third species seventh cl10rd rather than the usual first species
type. Phrase b ends with a dominant triad.
DEVELOPMENT
Section 1 (Ia) (meas. 43-45).
8
The basic root is D sharp whi~e the first species ninth
chord on A is the relief chord.
47
Section g (Motive Z and Ia) (meas. 46-50).
f?~ijq9qqqij I b. I; d·ltt J. be .z b· I z. d
C7lS1) GI17 (51) C C"(Sl)- bP"(Sl} C9 (S1)
The basic root is C. The relief chord is the first species
seventh chord on G flat.
Section 3 (Motive Z and IIa) (meas. 51-57).
Q. I I; d.14d. ; I )1 A7(Sl} E!>'l(Sl)
Throughout this entire section, except in tile last measure,
the tone A is used as a pedal point. The basic root for this
section is A. All other chords are relief chords.
Section 4 (Motive Z) (meas. 58-60).
I o
The basic root is C sharp while the relief chord is a
first species seventh chord on G.
Section ~ (Motive Z) (meas. 6l-62).
:B~"(S1) E'1(S1) B "~(Sl)
The basic root is B flat. The relief chord is the first
48
species ninth chord on E.
Section ~ (Retransition) (Motive Z) (meas. 63-66). ~~-------- ~--~-- -
In this section there are four basic roots, each one oc
cupying a measure. The melodic figure of the first measure
recurs sequentially in each of the following measures.
RECAPITULATION
Subject IIa (varied) (meas. 67-72).
L·
The key is B minor. This is one of the few places in
Gaspard de l! Nuit where a first species dominant chord pro-
gresses to a tonic chord.
Transition (meas. 73-80).
19:ij~ijqq # );>14'0 glri# r 11r' E7 Er . t=' ~ ~~~ .y (j C{b) Ftlb) F."'(SIt)(ll) 4. (It,") c: t .. ,,,}
19:f(i$ r ,J j I ~~ri I J. q ~ .
Ff7 (Slf.)(13) a. (It-It.) Gf7(S1) F*7(S"'}(~3) D~~ (S 1)
49
The first four melody tones of the original transition
which occur after Subject Ic are used with the C major chord
in measures one and two of this transition. In the third
measure this same melody commences again, but then continues
as in the original transition.
The basic root is C for the first two measures but shifts
to F sharp for the remainder of the transition.
Subject I! (varied) (meas. 81-84).
The basic root is G sharp.
Subject 12 (varied) (meas. 85-88).
The melody of this phrase which is quoted above is un
harmonized. All the tones except G sharp are in the D melodic
minor scale. This phrase can be interpreted in D minor or as
having a basic root D. In the present analysis the key of D
minor has been chosen.
50
Cadenza (Io) (meas. 89).
C/Eb-'\(Sl) :Bj(o ,}(O'lo ~tO CAo7o :BYio
\9." [ ~i e : ~ f ,~ This polyohordal oadenza begins and ends with ohords
built on E flat and D sharp with their roots in the bass.
This fact coupled with the relative duration of these chords
makes D sharp the basic root.
Closing chord (meas. 90-92).
a~ ,
The basic root for these three measures is C sharp.
The graph showing the basic roots and keys for Ondine
follows.
B~
A
G#
G
Ft
F
E
Eb
D
C#
C
B B p
A
1 Measures
2i
Le<sen d ~ --= Keys -- !; basIc r oots
t ,
-
!
r
I I 51 58
FIGURE 9
TONAL ANALY SIS OF ON DINE
I I
.....
l..-
I..-I
-
61 ~3 6 5 , ",.,. hb
P, ch t'latr'eS
, I BII
A
G:
G
n F
E
- D:#-or E\)
- D
C ~
c B Bp
A
, I 7 '73 75 81 85 89 90 9:<"
. . .
.
52
In view of the preoeding anal~sis the following state
ments can be made:
1. Ondine begins in the ke~ of C aharp and ends with
a basio root C aharp.
2. In the exposition, the first subjeot is in the key
of C sharp while the second subjeot is in G sharp, the dominant
ke~.
3. In the reoapitulation, subjeot IIa, whieb appears first,
is in the key of B. Subject Ia has a basio root G .harp and
subject Ib is in the key of D minor.
4. Keys have been established in phrases and .ections
totaling fifty-tive measures while basio roots have been u.ed
in thirt~-.even measures. Of the total ninety-two measures
these figures represent 59.8 per cent and 40.2 per cent respec
tively.
5. All twelve tones except F and G have been used as
basic roots and/or as key oenters.
S. Tones outside the sca!e of C sharp major have been
used as key centers anq{or basic roots in only eighteen measures.
This is 19.6 per cent ot the total number of measures in the
pieoe.
7. The tonic tone, C sharp, and the dominant, G sharp,
have been used as basio roots and key centers in phrases and
sections tota!ing twenty-nine measures and twenty-tive measures
respectively. Taken together, these figures represent 59.8
per oent of the total measures in Ondine.
53
II LE GIBET
PART A
Introduction (meas. 1-2).
I*~~&i i ¥jl,,?j3:jJ ~ "S:;:~~':,,;;::~'/ "!"'",',, '
This repeated B flat which constitutes the introduction
continues throughout the entire piece as a pedal point.
Phrase ~ (meas. 3-5).
I ;
As shown above, the chords of this phrase are built in
fifths and parallel the melody which is in the top voice.
These chords which conform to the natural minor scale of E
flat establish the key of E flat minor.
Phrase b (meas. 6-7).
A diminished triad on B flat is the only chord used in
this phrase. The tone B flat is the basic root for the phrase.
Phrase ~ (meas. 8.9).
12:~~tb8f!lJ~ i--' ..tp(q) C ~(q) D~~) ..Q.~(t.l)
Only the second and third measures of phrase a recur
here. The key, of course, is E flat minor.
Phrase c (like b) (meas. 10-11).
54
A third species seventh chord on B flat is the only chord
used in this phrase. The basic root is B flat.
Phrase d (like a) (meas. 12-16).
19:~p) , I 1 "l ,;- I; i ~I £ C;' • r. ,. Ir~Q
-e- . {b(*) B~ -CJ(Sl)(11) BbQ(S1) ~Wj.)
This phrase which closes with two measures of chords
built in fifths and fourths, as shown above, is in the key
of E flat minor.
PART ~
Phrase d (transposed) (meas. 17-19).
r E' P -'t (S1)(11)
The tone E flat which is used as a pedal point throughout
this phrase is the basic root.
55
Phrase e (meas. 20-22).
Fp'(Sl)
The basic root for this phrase is F flat since it 1s the
most used root and the eenter of harmonic activity.
Phrase f (like e) (meas. 23-27).
\
The tone E is the basic root for the first measure and
a half of ttlis phrase. The measure and a half of relief
chords which follow lead to the basic root, C sharp, of the
last two measures.
A",S1)
56
Only the pedal point, B flat, is sounded with the melody
in tLe first measure and a half of this phrase. The melody
tones, all of which are diatonic in d minor, supported by the
dominant seventh chord in the second measure of the phrase,
establish the d minor tonality. Despite their chromatic
structure, the roots of the remaining chords are in the d
harmonic minor scale.
Phrase h (meas. 32-34).
Although the dominant harmony is not used in this phrase,
the g minor tonality is indicated by the tonic triad of the
first measure and the entire melodic pattern which is derived
from the natural minor scale of G. The chords of the last t'NO
measures are built on the submediant of the G minor scale.
RETURN OF ~!
Phrase 1 (like d) (meas. 35-39).
J G'1(S3)
l~' ~ ~l ,~ )::? It a l ~~#* I
Cct(S3) t C'(S3} f Ap C"{S3)
The tone C which is used as a pedal point throughout this
phrase is the basic root. All chords built on other pitches
57
are relief chords.
Interlude (phrase e) (meas. 40-41).
The basic root is G flat.
Phrase c (meas. 42-43).
The basic root is G flat.
Interlude (phrase e) (meas. 44-47).
I !h\\& njn~- • ·· .. ·"?:"Ifi·t. Gb'J {Sl} ~b" ... b(4-) Ab'lt1,)(+1.1)
One and one-half beats of the final melody tone of phrase
c have been elided and this interlude begins at that point.
Despite this fact, the basic root, G flat, continues for the •
full time of the phrase plus one measure (measure 44). Hence,
G flat is the basic root for the anacrusis and first full
measure of this interlude.
The last three measures of the interlude are felt to be
in the key of E flat since the chords are built on the principal
scale steps of that key.
58
Phrase a (meas. 48-50).
E •. ... 0 I .; 1-......
Eb"(S2.)
This final phrase of Le Gibet, an almost exact recurrence
of the initial phrase of the piece, is in E flat minor. All
the chords conform to the natural minor scale of E flat.
Codetta (mess. 51-52) • . -~~ .... -------------
~ Gibet close~ with this repeated B flat which has been
used throughout the entire piece as a pedal point.
The graph showing the basic roots and keys for Le Gibet
follows.
I •
a.sures
~ I I
l-
8 10 12
le~end :
-- = keys
17
--- = basIC roots
I I U, 2..8 32
F IGURE 10
T ON AL A NALYSI S OF LE G IBE T
I I I . 35 4 D
I 52.
t> ltch na mes
Bb
A
A~
G
G\:7
F
E or Fb
Ell
D
etc
60
In view of the preceding analysis, the following state-
ments can be made:
1. Le Gibet begins and ends in the key of E flat minor.
2. Part A begins and ends in the key of E flat minor.
3. The final phrase in the return of part A is in the key
of E flat minor.
4. Keys have been established in phrases and sections
totaling twenty-seven measures while basic roots have been used
in phrases and sections totaling twenty-five measures. Of the
total fifty-two measures, these figures represent 51.9 per cent
and 48.1 per cent respectively.
5. In phrs.ses and sections totaling only eighteen meas-
ures have tones outside the natural minor scale of E flat been
used as key centers and/or basic roots. This is 34.6 per cent
of the total number' of measures in the piece.
6. The tonic tone, E flat, and the dominant, B flat, have
been used as basic roots and key centers in phrases and sections
totaling twenty-three measures and four measures respectively.
Taken together these figures represent 51.9 per cent of the
total measures in Le Gibet.
III SCARBO
EXPOSITION
Introduction (meas. 1-31).
1':%; l'I 'l ~:r!r -I Z~ -7 7. ;.< -
crt E{+~)
61
19',11. 'L 1'2 r,
cr#
17.12121 I'; 12./- -Et+6)
The three-tone motive of the first measure consists of
the leading tone, tonic, and dominant tones of the key of G
sharp. The augmented sixth chord of the next five measures is
sounded over a dominant pedal point, D sharp. The entire intro
duction consists of these factors which well establish the key
of G sharp.
Subject Ia (meas. 32-36).
\
19:ti~t .\. \ ), I r' \) .
This phrase is in the key of G sharp. The D sharp major
triad is the dominant chord and provides the resolution for
the final augmented sixth chord of the introduction. The phrase
ends with 8. subdominant chord.
Interlude (meas. 37-50).
v~r\*ft .t. G
Ct(b,9)
./ } .
The basic root is C sharp.
Subject Ib (meas. 51-64).
:B-5
62
I ]. :11 E"(Sl)(13) B-S
The basic root is B while the seventh chord on E is the
relief chord. The bass tone for the entire phrase is B.
Interlude (meas. 65-72).
;: /. I r' G-1I'7(S3)
The basic root is G sharp.
Subject Ib (varied) (meas. 73-79).
I '( I II. I z I [ I 1. I i I 13-5
The basic root is B while the seventh chord on E is the
relief chord. The bass tone for the entire phrase is B.
Transi tion (Ib) (meas. 80-94).
~:\\ r l~ ~'Ir If
I !r' I r- I {
63
The basic root is E since the chords built on that tone
dominate this transition. All chords built on other tones are
relief chords.
Subject Ic (meas. 95-102).
l:r*1\ ). t);*Wt~·j 1: :i l)J
The basic root is D sharp.
Subject Id (like Ic) (meas. 103-109).
I'J\\ it I)· 1 ~ 1 ~ 121 Z 1 Z 1- I ]j
The basic root is D sharp.
Subject 180 (varied) (meas. 110-120).
I ), I ,.. i \
T. \ ,.
C. :Dt"7(S3)(11) Dt
The first subject is brought to a close with this recur-
rence of phrase a. The basic root is D sharp for the entire
phrase.
-7 I 11. I P. I 7·
64
Ie 1 7
The basic root is A sharp. All chords built on other tones
are relief chords.
Subject IIa (curtailed) (meas. 133-142).
., I
• • , I Z :B7(Sl)(t23)(.,.11) At7(Sl)(tl3)(! 5)(13)
19~\\ '2 :; To
p. ( .' ~"'.···h . pxp U". >' J ;i'~' :.~'
I k j '1 ::B7(Sl)(t23)(+11) A1I'1(Sl)(tl3)(13) . A'7(SlXt!3) Gt:7(S1)\1j3;{13)
Again, the basic root is A sharp and all chords built
on other tones are relief chords.
Subject lIb (meas. 143-150). - -" - "'--
I Y. I z I 19:iJ(i4 0 I Z I z w fi If ~It
~""(s1) :B(o)
The key is B major. This is another rare instance of
a dominant chord resolving to a tonic triad and confirming a
key.
65
Subject IIc (like lIb) (meas. 151-155).
G! '1 (S1) Fil(51)(~3)(13) Ff"(S1) 13\b) C;"($1)(13)
As in Subject lIb the key is B major.
Subject lId (like lIb) (meas. 156-163).
19liJ', r 1 t 1 r l!f k r I r I r' 111 IJ ~ J 1111 r-epeated. tOl1es A ~-'1(Sl)(-t11)(l3) C "(53) Dp (l::I)
This phrase which is like phrase b of the second subject
is in the key of D flat major. A dominant thirteenth chord
followed by a leading tone seventh chord which r e sol ves to a
tonic triad confirms the key.
Subject lIe Jlike lIb) (meas. 164-167).
I ;t: ~p 9} ~ i p, I j' I r' Itt t1 , )1) l¥ I
Ap -'(51)(1-11)(13) C7(S3) DlP(h) D~+(+'f')
This phrase which closes with another authentic cadence
is in the key of D flat major.
Subject IIf (like IIa) (meas. 168-173).
:B~7 (52.)(+11)
The basic root for this phrase is B flat.
66
Subject IIg (like IIf) (meas. 174-178).
).
The tone B flat is the basic root.
Subject IIf (transposed) (meas. 179-184).
El17(S2)(+11}
The basic root is E flat.
Subject 1lg (transposed) (meas. 185-189) •
? . , f' El:J'T(S2.)(+l1) E ,,7(S"')(+11)
The basic root is E flat.
Subject 11h (meas. 190-193).
Dt <f(S3J
TIle basic root is D sharp while the thirteenth chord on
B is the relief chord.
Subject !Ii (like IIh) (meas. 194-197).
:8-9 (51)
67
The basic root is D sharp while the chord built on B is
the relief chord.
Transition (IIh) (meas. 198-213).
fO:8i·i• § C· V- I '1. 7;-
• l z- I ·2 I· I, (. t·
a. a. (+If.) b) G-i-'\ (S 1) F~(+4-)b)
The tone A is the basic root for five measures. ~le relief
chord on G sharp of the 'sixth measure is followed by ten meas-
ures where the basic root is F sharp.
DEVELOPMENT
Section 1 (Ib) (meas. 214-234).
F#-s
F*-S If'(Sl)(B) :B'7(Sl) ".B'(S1)(B)
I ~i'P:: I ~ I ~. I Z I ,:;- ;'; I Z I " 1tj£~ .L It r. ?
The basic root for tilis section is F sharp. The last
seven measures of this section are a prolongation of the re-
lief chord on B.
68
Section 2 (Ib) (meas. 235-255). . ,
• I J. ). I 9. I
C.,-5 Ct:-5
I :t ¥it t I .~. I r ' I . ('
1 Z I 9. I 7. I V. I '7. I ~. I This section is a transposition of section 1. The basic
root is C sharp while the relief chords are built on F sharp.
Section ~ (Ie) (meas. 256-263).
( 9:',;\ t
(. I r' I r' I ij r ;t :11
G#: .1L G .. ~(S1.) F c~
The basic root is G sharp. The remaining chords are the
relief chords.
Section! (Ic) (meas. 264-267).
19}!jq~ ~ v· L' (. • J r,
. F1F-~(S1) F1f F#= -'" (S1)
The basic root is F sharp for this section.
Sec tion.§ (Ib) (meas. 268-275).
W§ II\. I P. I Y. I P. I ? I i. I 7. I 9. I -:8'1 (S 4-)
69
The basic root for this section is B.
Section 6 (IIf and Ic) (meas. 276-288) •
rp:h q r' r' I b r' , , .,' . I r : JI r' G 7 (S1H+ll)(13) Go R..~ 'B'1(S3) E
W II r I ,.I. I r i I r IV. I ~ I ~ 1 ...t.~ "B'I(S3) E Co G
The basic root is G. All chords built on other pitches
are the relief chords.
Section 7 (IIf and Ic) (meas. 289-302).
I r' IQ ;\, I r' , ;;\ ,tl r' I • E "(Sl){ +11)(1 '3) E c. G-.'1(S1) c. Q.. E
,.\. t , c' I .J r. .7 r·
.7 r·
c C-tr A7(S2.) E
This section is a transposition of Section 6. The basic
root is E while the chords built on other pitches are the
relief chords.
Section 8 (IIf and Ic) (meas. 303-313).
. ' . I p ). I ) .
70
The key of E flat minor is clearly established in this
section. Al though. not nota ted as such, the ninth chords on
C flat are augmented sixth chords which resolve to dominant
harmony in each instance. The final chord of the section is
a tonic triad preceded by a dominant seventh chord ...
Section Q (new theme, Ic, IIf) (meas. 314-324).
19:111 C· I -z r· I r· I ~. "L I •
t Att07" F1t-l"/~) F1t(-~) -t- .g. ( + ij.), )
This section is in the key of B minor. Dominant harmony
is used in all but the last two measures where the tonic triad
occurs.
Section 10 (new theme, Ib, Ic) (meas. 325-344).
19: it J. . } r ./ r· --\. , .7
1 • y-
-8-- D-q (.S1)(1-3)
.} n L, hlli r , J r' I y~ • i
Tit
G '1 ./ 2 .. il· I .). I . / 74>
:at> "(5 1)(1~) lh'(S1)
This section is in the key of G minor. The new tileme
of Section 9 is used here but, this time, is extended. The
key of E flat is suggested by the first species seventh chord
71
of the last three measures but is not confirmed.
Section 11 (Ic) (meas. 345-365).
f91!b~b ~\. I q r I III. I & .\. I .~. I q C· I ;'. ])'1 (S3) E'(51) D'1(S3) D,"1 (S1) D'I(S3) E'(51.) :D"lS3)
!)p'l(S1) D'1(S3) :OJ) F~ d.,0 :n~ Fb "D'{S3)
I ~~r 12 p & .1 ,.ttJj" t 6 c· I ~! I :!. ':'7 ,. I ';7 c.
F~ D'(S3)
The tone D is the basic root for this section. The
chords constructed on other pitches are relief chords.
Section 12 (lIt) (meaa. 366-381).
9---- p-- "-I'Jg9q if I v' I J b~ I.E r I r
C A~+{ ... ") C Gbl"}. C Ap+{+(,)
C Gj,(") C AH(+") C Ap+(+C.} C A~+(~) C Ap+( ... ,,}
19: \1 r· I g ) ,~ pl. 2. 1 »" r, I Sz. •
Ab+(+") C Ab+(+") C
The basic root for Section 12 is c. Section 13 (Ia) (meas. 382-394).
72
w p;1 . I ~3 I 2. I ;. I Z. I ~. ·1
J3bCJ (S2.)
The basic root for this section is B flat. Although a
trill from C to D flat is used for the first seven measures,
tl ... 6 C sounds as a no:nharmonic tone resolving to B f la t when
tL.e ninth chord on B flat occurs.
RECA PITULA'l'I ON
Introduction (meas. 395-429).
't~ E( .... ")
I ~r ~ it I z I z I .). I 7. I -E t+")
~ E(+ID)
[:rVitl' ;6 I 2·1;t· I V. I 7. I ) I 7. I >. I 9. I Y. I Dl7(Sl)
The key of the introduction is, again, G sharp. The
same harmonic factors that were used in the introduction of
the exposition appear here.
'73
Subject Ib (augmentation) (meas. 430-436).
-9-' Ct -'I (Sl)(tj3)(13)
The key of G sharp continues in this phrase with dominant
harmony in the first three measures. A submediant thirteenth
chord is employed in the last three mes_sures.
Interlude (meas. 437-440).
), . ·7 ? .
-7 7.
E9{Sl) (;'(S3)
When used in the exposition this passage was truly an
interlude. Here, however, it is transitional in character
with two basic roots. The first two measures have the tone
E for basic root while G is the basic root for the third and
fourth measures.
Subject Ib (augmentation) (meas. 441-44'7).
I;tfif I I .. z I -2 I .;L t ). I 9- ?: I I 7. Z. Q.
. -:....
F~-"(Sl)(13) E-9(S1J(13) E-'(S1)
The basic root for this phrase is F sharp. The last
three mea.sures are a prolongation of the relief chord, the
root of which is E.
• I
~ . ,
74
~i t I
:BP{b) A(,,) BHb) l)tlt) C(b) Dpl") D{") E~(") D(") DHb) C(b) :B(")
b p! I.t b. ~ 1:J-+- \J..IIL ~-+- .... S ..... q1.. ~...L. 19:~ is 9 t t r I :t 1-' C I I I J I
Bb(") A<'-) BL{b) B(~) C(b) D~(") C(") B(") C(") Cl(b) :Dt") n .... (") The tone B flat is the basic root of this section. The
B flat major triad is the point of departure and return for
this series of chords moving by half steps.
Transition, Section 2 (meas. 454-459).
I~:~J-t .. ~, ~. -; < L =t U: r' flo\.
C-jj:~(Sl) J),f'I(Sl) Ct«t(S1) DfF7(Sl)
19:§\~ d:2£12 j\, ,) . J. C#"(S1) IHr7(Sl) Ci-'tlS1)
The tone C sharp which acts as a pedal point for this
section is the basic root.
Transition, Section 3 (meas. 460-467).
The basic root B is the bass tone for this entire secti0c
except the last two measures.
'75
Transi ti on, Sec ti on 4 (meas. 468-4'76).
). G1f~(Sl)(11)
G1t'l(S1)(+1l) A"(Sl)(+ll) E"(Sl){+11) G .. "{S1)(;t-11) A'(Sl){+l1J
The basic root is G sharp.
Subject IIa (varied) (meas. 4'7'7-510).
Ftf"(S1)(t!3) F 1'=
D#7(S3)
Ft-'(S3) Ft9(Sl}
The tone F sharp which is used as a pedal point through
out Subject IIa is the basic root.
Subject lId (varied) (meas. 511-520). 0-
• 7 r. ,7 z.
76
Ap(",)
The key is A flat major. Twice during Subject lId the
dominant harmony is followed by a tonic six-four while the dom
inant of the key, E flat, is in the bass throughout.
Subject IIf (varied) (meas. 521-526).
F"(S2)(+11)
The basic root is F.
Subject IIg (varied) (meas. 527-531).
F"(S2,) (+11) F7(S*")(+11)
The basic root is F.
Subject IIf (transposed) (meas. 532-537).
The basic root is B flat.
Subject 1lg (transposed) (meas. 538-54~.
I :}l/&~ ). ry Ii
-"1. ? .,t ) .
-t{t-lf)b) :Bb7(S:t)( +11) Bp7{S'I-)t+H)
77
The basic root is B flat.
Subject IIh (meas. 543-550).
The basic root is A sharp.
Transition, Section 1 (IIh) (meas. 551-555).
[g'.!?!; ~ j' I § ,#' •
I ·7 r- I ~r- I ./ I·
et. ""( +*jlo) Q..
The basic root is A.
Transition, Section 2 (IIh) (meas. 556-562).
In this section, each measure has a basic root. The three
tone melodic figure of the first measure is used sequentially
in each succeeding measure. The basj,c root shifts with each
recurrence of the melodic figure. As shown above, the seven
basic roots are A, G sharp, F sharp, F, E flat, D, and C.
Section 1 (IIf) (meas. 563-572).
;. :11
13 G+(+to) 13 :B'1(S1)t+l1.)
78
The basic root is B.
Section 2 (IIf) (meas. 573-579).
-E Flt'7 -S(Sl) E E
The basic root is E.
Section ~ (Ia) (meas. 580-583).
, , •• ). .7 I •
C~q(S2) C4t'1 (51)
The basic root is C sharp.
Section! (IIf) (meas. 584-591).
The basic root is G sharp.
Section 5 (Ib) (meas. 592-601).
I ; I i I ;: I 7. I Y. I ? I V. I ?: IE' .
The basic root is F sha.rp.
Section 6 (IIf) (meas. 602-615).
, 7. I r'
79
~- -.""----~~--~-~---~- .. -.--~ .. --- ----- ,-'------.----------
19:!b~ j. I Y. I z! ;;, I p~ !~ ! ;;I. B
The single bass tone B in the last measure of this section
provides the resolution for the thirteen measures of dominant
ninth chord. Bence, the section is in the key of B.
Section 7 (Introduction) (meas. 616-627) • .
I f)~tf§~ g J I y: I y. I.\. I 9. I z I jl. B :B{q)
19~b!'# . ·z I ~. t J. I ~ .,
II .1. I. . • I
]3' "B" (S Lt- "")
This final section of the coda continues the key of B
major. established in section 6.
The graph showing the basic roots and keys for Scarbo
follows.
A#or B b
A
GJ or AI,
G
F#
F
E
D ~ or E ~
D
Clor D ~
C
"B Ato ... Bb
A Gil:
1 Me-as ures
I 37
I I ~
! I
"
-
I 51 65 13 eo 95 12.1
I
14- 3 15 b
Le~end :
- - - = keys
1Ela
--- = basIc roots
-
179 1 ~
I I
I
~
-
-
1-8 % 0 lfb8 tt77 511 511 532 tt5tt
r--
.. ,
1 ~
'--
1
.. .
551 563 573 580 592, 602-557 S8't
Pit c h na.mes
~orBb
A
G'orAb
G
Ft
F
E D#o,.Eb
D
C~orDp
C
B
At,,~Bb
A
G~
81
In view of the preceding analysis the following state
ments can be made:'
1. Scarbo begins in the key of G sharp minor and ends
in the key of B major.
2. In the exposi tion, the introduction and. the initial
phrase of the first subject are in the key of G sharp minor.
Various basic roots and keys are used in the remainder of the
first subject and throughout the second sUbject.
3. In the recapitulation, the introduction and Subject
Ib which follow are in the key of G sharp minor. Various basic
roots and keys are used in the remainder of the first subject
and throughout the second subject.
4. The last two sections of the coda are in the key of
B major.
5. Keys have been established in phrases and sections
totaling 181 measures while basic roots have been used in
phrases and sections totaling 446 measures. Of the total
627 measures these figures represent 28.9 per cent and 71.1
per cent respectively.
6. All twelve tones have been used as basic roots and/or
as key centers.
7. In only ninety-eight measures or 15.6 per cent of
the total measures have tones outside the scale of B major
been used as key centers and/or basic roots.
8. The tonic, G sharp, and the dominant, D sharp, of
the key of G sharp minor have been used as basic roots and
82
key centers in phrases and sections totaling 122 measures and
57 measures respectively. Taken togetber, these figures rep
resent 28.5 per cent of the total measures in Scarbo.
9. The tonic, B, and the dominant, F sharp, of the key
of B major have been used as basic roots and key centers in
phrases and sections totaling ninety-seven measures and ei~lty
seven measures respectively. Taken together, these figures
represent 29.3 per cent of the total measures in Scarbo.
Summary. The following observations can be made of the
complete work, Gaspard de la Nuit:
1. Keys have been established in phrases and sections
totaling 263 measures while basic roots have been used in
phrases and sections totaling 508 measures. Of the total 771
measures, these figures represent 34.1 per cent and 65.9 per
cent.
2. Ondine begins in the key of C sharp and closes with
a basic root, C sharp. This indicates a tonal center of C
sharp for the entire piece.
3. Le Gibet begins and ends in the key of E flat minor
which indicates a tonal center, E flat, for tne entire piece.
4. Scarbo begins in G sharp minor and ends in B major.
As shown in items 8 and 9 on page 81 the tonic and the domi
nant of each key are used with almost equal frequency. How
ever, since the last sections of the coda firmly establish the
key of B major, the listener would likely choose B as the tone
center. In the present analysis it will be considered as such.
83
5. In each piece the tones of the scale represented by
the tonal center of the whole piece are used as basic roots
and temporary key centers more frequently than tones outside
the scale.
CHAPTER VI
CONCLUSIONS
Gaspard ~ la ~ is preponderantly harmonic music.
Except for the relationship of the melodic line and the bass
line there is an almost complete absence of contrapuntal devices
in the work. Its characteristic sound and its tonal implica-
tiona depend not only upon the function of the vertical struc
tures but upon the kinds of vertical structures used and the
frequency of their occurrence.
As shown in TABLE V on page 26, Ravel was partial to
vertical structures larger than triads since 58.3 per oent of
his harmonic material is in that category. In addition, ap
proximately fifty per cent of the triads have added tones
(TABLE VI on page 27). Of the added tones, the added major
sixth is the most frequent.
According to TABLE V, the order of preference for chords
larger than triads is ninth chords, seventh chords, thirteenth
chords, and eleventh chords. Among the seventh and ninth chords
Ravel favored first and third species seventh chords and first
species ninth chords (TABLE VI on page 27). This information
contradicts Roland-Manuel insofar as Gaspard de la Nuit is
concerned, when he states,
From this [what seems to be a projection of the melody into the harmonic plan] arises the marked preference in his harmony for the chords known as secondary sevenths and ninths, which are naturallY formed
84
85
on modal tonics of D and E.l
These chords which are classified as second species seventh
and ninth chords in the present analysis are very infrequent.
In fact, Ravel used only two second species seventh chords
and only ten second species ninth chords in this entire work.
As indicated in TABLE VI on page 27, the chord of the
augmented eleventh is much more frequent than the other types
of eleventh chords. This chord, based on the principle of
natural resonance has been described as "characteristic of
Ravel's harmonic idiom."2 Thirteenth chords are slightly more
frequent than eleventh chords. Taken together, e~venth and
thirteenth chords constitute approximately twenty per cent
of the vertical structures used.
Among the most infrequent of all vertical structures are
diminished triads, diminished seventh chords, and augmented
triads. Of the t en augmented triads employed, all have added
tones. Other infrequent structures include second and fourth
species seventh and ninth chords.
Ravel's preference for classical form is exemplified in
Gaspard de la Nuit by his use of Sonata-Allegro form in Ondine
and Scarbo and the ternary design of Le Gibet. However, with
in these structural designs he has maintained complete freedom
and flexibility.
lRoland-Manuel, Maurice Ravel, p. 115.
2Gilbert Chase, "Maurice Ravel," The International Cyclopedia of Music and Musicians, Third Edition, p. 1502.
86
The subjects are not written in part forms or in phrase
forms such as periods and double periods. Rather, they con
sist of a series of phrases, some of which recur and some of
which are repeated. The phrases of the first subject of
Scarbo are interspersed with interludes and a transition.
In Ondine a transition is used between the first and second
subjects while in Scarbo there is none.
The development sections of Ondin~ and Scarbo consist
mainly of the reiteration of complete phrases from the ex
posi tion with varied harmoniza ti ons and varied accompaniment
figures. Occasionally, some of the original melodic intervals
and original rhythms are modified. New thematic material has
been introduced in the development sections of both Ondine and
Scarbo.
A noteworthy feature of the recapitulation of Ondine
and the return of part A in Le Gibet is the reversal of the
order of melodic material when it is restated in these sections.
In all three pieces the subject material is curtailed in
the recapitulation or in the return of part A.
The varied treatment of the subjects coupled with their
curtailment in the recapitulations of Ondine and Scarbo lend
these sections the character of another development.
Scarbo is the only piece which is concluded with a coda.
Gaspard de la Nuit adds nothing new to formal principles
and devices already in existance.
The common thought in all definitions of tonality has
87
been that a relationship of musical materials to a tone center
is involved. Since the establishment of our tonal system,
composers have continuously extended the boundaries of tonality.
Numerous twentieth century composers have set up their own
arbi trary systems of tonal relationship, contending that the
feeling of tonal unity and tonal r ela tionship can be achieved
by other means than the traditional dominant-tonic formula.
As revealed in the present analysis, Ravel did not evolve
a new system of tonal relationship but extended the boundaries
of the old with the so-called basic root technique.
According to the summary of Chapter V on page 82, each
piece in Gaspard de la ~ has an established tone center by
virtue of the manner in which it began and ended. In this,
Ravel has used a traditional concept.
It is within these two extremities that a new principle
of tonal extension, the basic root technique, has been employed.
Its significance is demonstrated by the frequency of its use.
Basic roots occur in phrases and sections which constitute
65.9 IE r cent of the total measures in Gaspard de la Nuit
(Summary, Chapter V).
As explained on page 17, the basic root is the most fre
quently occuring chord root or the root which occupies the
major portion of the time value in a phrase or section. All
chords constructed on roots other than the basic root are called
relief chords. The basic root and the roots of the relief
chords may have any interval relationship. Since the basic
root analysis is not used in phrases or secti ons where the
88
eatablisI:..tIllent of key by conventiona.l chord re la tionsh.ips is
obvious, it follows that the basic root, the relief chords, and
the type of vertical structures used must not have a relation
ship which will establish a key.
No particular plan seems to have been followed in the in
terval relationships of basic roots or of basic roots and the
temporary key centers of phrases. Tonal unity is B.chieved
simply by using the tone s of the scale represented by tr.le tonal
center of the whole piece as basic roots and temporary key
centers more £requently than tones outside that scale. As
mentioned in the summary of Chapter V on page 82, this is the
case in each piece.
The basic root technique is not needed in the analysis
of e very Ravel work. It was employed in Gaspard de la ID!ll
only after it was found the. t conventional analytic techniq'l,les
failed to satisfactorily explain the tonal relationships.
89
BIBLIOGRAPHY
Chase, Gilbert. "Maurice Ravel," The International Cyclopedia of Music ~ Musicians, Third edition, 1500-1504.
Goetschius, Percy. The Larger Forms of Musical Composition. New York: J. Schirmer, Inc., 1915.
Goss, Madeleine. Bolero, The Life of Maurice Ravel. New York: Henry Holt and CompanY;-1940. --
Hull, Arthur Eaglefield. Modern Harmony. London: Augener Ltd. [no d.].
" Lenormand, Rene. ! StudX of Modern Harmony. London: J. Wil-liams Ltd.[n. d.].
Miller, Horace Alden. New Harmonic Devices. Boston: Oliver Ditson Co., 1930.
Piston, Walter. Harmony. New York: W. "N. Norton and Company, Inc., 1941.
Ravel, Maurice. Gaspard de la Nuit. Paris: A. Durand & Fils, 1909.
Roland-Manuel. Maurice Ravel. London: Dennis Dobson Ltd., 1947.
Shera, F. H. Debussy and Ravel (Dr. Arthur Somervell, Editor, Musical Pilgrim.) London: Humphrey Milford, 1927.