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DEBUSSY'S USE OF THE MOTIVE IN THEMATIC CONSTRUCTION
AS FOUND IN IMAGES I FOR PIANO
THESIS
Presented to the Graduate Council of the
North Texas State University in Partial
Fulfillment of the Requirements
For the Degree of
MASTER OF MUSIC
By
John F. Sheridan, B. M.
Denton, Texas
May, 1977
Im7
Sheridan, John F., Debussy's Use of the Motive in
Thematic Construction as Found in Images I for Piano.
Master of Music (Theory), May, 1977, 173 pp., 50 tables,
242 illustrations, 4 titles.
This study seeks to discover the extent and manner of
Debussy's use of the motive in thematic material. A total
of 40 melodic examples were analyzed in order to show their
relationship to a single motive, a three-note figure having
a step-leap relationship.
Using eighty-four series of examples, the study shows
the melodies analyzed to be 85% motive-derived. The study
concludes, therefore, that Images I is a remarkably econom-
ical work, using a single three-note motive as a unifying
and developmental basis.
-/ 4
TABLE OF CONTENTS
Page
LIST OF TABLES .......................
LIST OF ILLUSTRATIONS .. . ...
INTRODUCTION..... .........
Chapter
I. EVIDENCE o---e 0 0-...
Melodic FragmentationConjunct Simple Linear MelodyConjunct Compound Linear MelodyConjunct Complex Linear MelodyDisjunct Simple Linear MelodyDisjunct Compound Linear MelodyDisjunct Complex Linear Melody
iv
....viii
0 1
28
II. SUMMARY.-. -...
III. CONCLUSIONS - -
APPENDIX I.......-.-.-.....-
APPENDIX II
BIBLIOGRAPHY.......-.-...-..
134
146
148
150
. 0 . . . . 173
iii
LIST OF TABLES
Table Page
I. Statistics of Variant Usage as Found inMelodic Fragmentation Form 1.......... 32
IA. Summary of Primary Variant Usage by Group . . 33
IB. Total Summary of Variant Statistics asFound in Melodic Fragmentation Form 1 . 33
II. Variants Found in Melodic FragmentationForm 2................................38
IIA. Percentages of Variant Groups as Found inMelodic Fragmentation Couplings . . . . 40
IIB. Total Summary Percentages of Variants Foundin Couplings Used as Melodic Fragmen-tation Form 2........... ......... 40
III. Couplings Used as Melodic FragmentationForm 2................. . ........ 41
IV. Variants Found in CSLMF1 and CSLMF2According to Individual Use .......... 51
IVA. Percentages of Variant Use by Type as Foundin CSLMF1 and CSLMF2..................52
IVB. Percentages of Single and Coupling Usage ofVariants as Found in CSLMF1 and CSLMF2 . 52
V. Couplings Found in CSLMF1 and CSLMF2According to Individual Use . . .... 53
VA. Total Summary of Couplings Found in CSLMF1and CSLMF2......... ................. 54
VI. Variants Found in CCLM.--.............. 63
VIA. Percentage of Variant Use by Group as Foundin CCLM............................. 63
iv
Table
VII. Couplings Found in CCLM According toIndividual Use... . . . . . . . . .
VIIA. Total Summary of Couplings Found in CCLM
VIII. Variants Found in CCxLM According toIndividual Use . . . . . . . . . . . .
VIIIA. Percentage of Variant Use by Type as Foundin CCxLM . . . . . -.-.-. -. . . . . .
VIIIB. Percentage of Single and Coupling Usage ofVariants as Found in CCxLM . . . . . .
IX. Couplings Found in CCxLM According toIndividual Use .-...... . . . . .
IXA. Total Summary of Couplings Found in CCxLM
X. Variants Found in DSLM According toIndividual Use..-.-... . . . . . . . .
XA. Percentage of Variant Use by Group as Foundin DSLM . . . . . . . . . . . . ... .
XB. Percentage of Single and Coupling Usage ofVariants as Found in DSLM . . . . . .
XI. Couplings Found in DSLM According toIndividual Use.......... .. .
XIA. Total Summary of Couplings Found in DSLM
XII. Variants Found in DCLM According toIndividual Use........... ...
XIIA. Percentage of Variant Use by Group as Foundin DCLM . . - . . -.-.-. -. . . . . ..
XIII. Couplings Found in DCLM According toIndividual Use.......... .. .
XIIIA. Total Summary of Couplings Found in DCLM
XIV. Variants Found in DCxLM According toIndividual Use......... .. ..
V
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. 107
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Table
XIVA. Percentage of Variant Use by Group as Foundin DCxLM .-........-.-... .. ..
XIVB. Percentage of Single and Coupling Usage ofVariants as Found in DCxLM.. . . . . . .
XIVC. Percentage of Primary and SecondaryVariants Found in DCxLM --. . . . . .
XV. Couplings Found in DCxLM According toIndividual Use.-.... . . . . . . . .
XVA. Total Summary of Couplings Found in DCxLM
XVI. Primary Group I Variants According toIndividual Use .-........... .
XVII. Primary Group II Variants According toIndividual Use.-......-.-..... . .
XVIII. Primary Group III Variants According toIndividual Use.......-.-... .. ..
XIX. Primary Group IV Variants According toIndividual Use.-........... . .
XX. Primary Group V Variants According toIndividual Use.-........... . .
XXI. Secondary Variants According to IndividualUse . . - . - . . -. -. -. -. -. -. -. . . .
XXII. Collective Variant Usage and Percentage byGroup - . . - . - . -.-.-. -.-. -. . . .
XXIII. Variant Quantity and Usage by Group . . .
XXIIIA. Total Variant Quantity and Usage . . .-.-..
XXIV. Total Single and Coupling Usage of Variants
XXV. Couplings According to Individual Use . . . .
XXVI. Collective Coupling Usage According to Typeand Form.........-.-.-...... ....
XXVII. Collective Coupling Quantity and UsageAccording to Type and Form . . . . . . .
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LIST OF ILLUSTRATIONS
Figure Page
1. Reflets dans l'eau, Measures 1 and 2... . . ... 1
la. Motive as Found in Fig. 1 . . . . . . . . 1
2. Variant 2 (PGI) . . . . . . . . . . . . . . . 4
3. Variant 12 (PGII)............... 5
4. Variant 5 (PGIII)............... 5
5. Variant 11 (PGIV)........-.-.-..... 5
6. Variant 45 (PGV)........-.-.-.-.... . 6
7. Variant 1 (Secondary)....... ...... 6
8. Construction Diagram of a Four-note Coupling . 7
9. Construction Diagram of a Five-note Coupling . 8
10. CRTlFl Coupling . . . . . . . . . . . . . . . 8
11. CRTlF2 Coupling . . . . . . . . . . . . . . . 9
12. SRT2Fl Coupling . . . . . . . . . . . . . . . 9
13. SRT2F2 Coupling . . . . . . . . . . . . . . . 9
14. SRT2F3 Coupling.........-.-.-.-.-... 10
15. SRT2F4 Coupling.........-.-.-.-...-.-.-.. .0. 10
16. SRT2F5 Coupling......-.-.-..-.-....... 10
17. Remotely Related Coupling . . . . . . . . . . 11
18. Hommage a Rameau, Measure 25 . . . . . . . . . 11
18a. Melodic Extraction of Fig. 18 (MelodicFragmentation Form 1) . . . . . . . . . . 11
viii
Figure
24b
Page
18b. Variant Used as Melodic Fragmentation inFig. 18a . . . . . . . . . . . . . .
19. Reflets dans l'eau, Measure 10 -. . . .
19a. Melodic Extraction of Fig. 19 (MelodicFragmentation Form 2) - --.-. . ..
19b. Coupling and Variants Found in Fig. 19a .
20. Mouvement, Measures 162-166.-......
20a. Melodic Extraction of Fig. 20 (CSLMFl) .
20b. Coupling and Variants Found in Fig. 20a .
20c. Construction Diagram of Fig. 20a (CSLMFl)
21. Contour Graph of Melody Found in Fig. 20(CSLMFl) . . . . . . . . ... .....
22. Reflets dans l'eau, Measures 24-27 . .
22a. Melodic Extraction of Fig. 22.-... . .
22b. Couplings and Variants Found in Fig. 22a
22c. Construction Diagram of Fig. 22a (CSLMF2)
23. Mouvement, Measures 75-78.- ...-....
23a. Melodic Extraction of Fig. 23........ .
23b. Couplings and Variants Found in Fig. 23a
23c. Construction Diagram of Fig. 23a . . . .
24. Mouvement, Measures 67-73.-..... . .
24a. Melodic Extraction of Fig. 24 (CCxLM)
24b. Multivariant 1 as Found in Fig. 24a .
(i). Couplings and Variants Found inMultivariant 1...... .......
24c. Multivariant 2 as Found in Fig. 24a .
ix
11
12
12
12
13
. . 13
. . 13
. . 13
..14
..15
. . 15
..15
..16
..16
..16
..17
. . 17
18
19
19
19
20
Figure
24c(i)
24d.
25.
25a.
2 5b.
25c.
26.
26a.
2 6b.
26c.
27.
27a.
2 7b.
27b(i).
27c.
27c(i).
2 7d.
27d(i).
27e.
28.
28a.
28b.
29.
29a.
Couplings and Variants Found in Fig. 24a
Construction Diagram of Fig. 24a (CCxLM)
Reflets dans l'eau, measures 29-30 . . .
Melodic Extraction of Fig. 25 (DSLM) . .
Coupling and Variants Found in Fig. 25a
Construction Diagram of Fig. 25a (DSLM)
Reflets dans l'eau, Measure 14 *.. . .
Melodic Extraction of Fig. 26 (DCLM) . .
Couplings and Variants Found in Fig. 26a
Construction Diagram of Fig. 26a (DCLM),
Hommage a Rameau, Measures 17-24 . . . .
Melodic Extraction of Fig. 27 (DCxLM)
Multivariant 1 as Found in Fig. 27a
Coupling and Variants Found in Fig. 27b
Multivariant 2 as Found in Fig. 27a .
Coupling and Variants Found in Fig. 27c
Multivariant 3 as Found in Fig. 27a .
Couplings and Variants Found in Fig. 27d
Construction Diagram of Fig. 27a (DCxLM)
Reflets dans l'eau, Measures 1 and 2 .
Melodic Extraction of Fig. 28
Variants Found in Fig. 28a.-.......
Hommage a Rameau, Measure 25.-.....
Melodic Extraction of Fig. 29
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Figure
29b.
30.
30a.
30b.
30c.
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31a.
31b.
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32b.
33.
33a.
3 3b.
34.
34a.
34b.
35.
35a.
35b.
36.
36a.
37.
37a.
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Variant Found in Fig. 29a...-...
Mouvement, Measure 63..-...-...
Melodic Extraction of Fig. 30 -
Variants Found in Fig. 30a - -
Construction Diagram of Fig. 30a
Reflets dans l'eau, Measure 9 .-. -
Melodic Extraction of Fig. 31 .-.
Coupling and Variants Found in Fig.
Reflets dans l'eau, Measure 30
Melodic Extraction of Fig. 32 .-. -
Coupling and Variants Found in Fig.
Hommage a Rameau, Measure 24 .-. -
Melodic Extraction of Fig. 33 .-. -
Coupling and Variants Found in Fig.
Hommage a Rameau, Measures 53-54
Melodic Extraction of Fig. 34 .
Variants Found in Fig. 34a . -. .
Hommage i Rameau, Measure 67 .-. -
Melodic Extraction of Fig. 35 .-. -
Coupling and Variants Found in Fig.
Mouvement, Measures 162-166 . . . .
Melodic Extraction of Fig. 36 .-. -
Mouvement, Measures 167-170 . -. .
Melodic Extraction of Fig. 37 -
3 -
31a
3 -
32a
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3 3a
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35a
Figure Page
38. Mouvement, Measures 170-173.-.-.-.-.-.......42
38a. Melodic Extraction of Fig. 38........ . 43
39. The First Variant of Each of the ConjunctSimple Linear Melodies Form 1... . . 43
40. Couplings and Variants, CSLMF1 . . . . . . . 44
41. Contour Graph of CSLMF1 Found in Fig. 36a . 44
42. Contour Graph of CSLMFl Found in Fig. 37a . 45
43. Contour Graph of CSLMF1 Found in Fig. 38a . 45
44. Reflets dans l'eau, Measures 24-27 ..... 46
44a. Melodic Extraction of Fig. 44........ . 46
45. Reflets dans l'eau, Measures 50-53.. .... 47
45a. Melodic Extraction of Fig. 45 . . . . . . . . 47
46. Reflets dans l'eau, Measures 54-56 . .... 47
46a. Melodic Extraction of Fig. 46....... .. 48
47. First Coupling Found in Each of the CSLMF2Melodies, with Variants....... .. 48
48. Second Couplings Found in CSLMF2 Melodies,with Variants . . . . . . . . . . . . . 49
49. Contour Graph of CSLMF2 Found in Fig. 44a . 50
50. Contour Graph of CSLMF2 Found in Fig. 45a . 50
51. Contour Graph of CSLMF2 Found in Fig. 46a . 50
52. Reflets dans l'eau, Measure 10....... . 55
52a. Melodic Extraction of Fig. 52.-....... . 55
52b. Variant and Coupling Content of Fig. 52a 55
52c. Construction Diagram of Fig. 52a . . . . . . 56
53. Reflets dans l'eau, Measure 60....... . 56
xii
Figure
53a.
53b.
53c.
54.
54a.
5 4b.
54c.
55.
55a.
55b.
55c.
56.
56a.
5 6b.
56c.
57.
57a.
57b.
57b(i).
57c.
57c(i).
57d.
58.
Melodic Extraction of Fig. 53.-.....
Coupling and Variant Content of Fig. 53a
Construction Diagram of Fig. 53a . . . .
Hommage 3 Rameau, Measures 51-52 . . . .
Melodic Extraction of Fig. 54a
Coupling and Variant Content of Fig. 54a
Construction Diagram of Fig. 54a ... .
Hommaqe ! Rameau, Measure 71-.- . .
Melodic Extraction of Fig. 55.-.....
Couplings and Variants Found in Fig. 55a
Construction Diagram of Fig. 55a . .
Mouvement, measures 75-78.-.......
Melodic Extraction of Fig. 56.-.....
Coupling and Variant Content of Fig. 56a
Construction Diagram of Fig. 56a . -
Mouvement, Measures 67-73.-..... . .
Melodic Extraction of Fig. 57.-.....
Multivariant 1, Extracted from Fig. 57a
Couplings and Variants Found inMultivariant 1 (Fig. 57b) - .-.-..
Multivariant 2, Extracted from Fig. 57a
Couplings and Variants Extracted fromMultivariant 2 (Fig. 57c) -. . . .
Construction Diagram of Fig. 57a . -.-..
Mouvement, Measures 89-96 . . . . . . . .
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* . 71
Figure Page
58a. Melodic Extraction of Fig. 58 . . . . . . . . 71
58b. Multivariant 1, Extracted from Fig. 58a . . . 72
58b(i). Couplings and Variants Found in Multivar-iant 1 (Fig. 58b) ............ 72
58c. Multivariant 2, Extracted from Fig. 58a . . . 73
58c(i). Couplings and Variants Found in Multivar-iant 2 (Fig. 58c) ........ ... 73
58d. Construction Diagram of Fig. 58a.. ..... 74
59. Mouvement, Measures 97-103......... . 75
59a. Melodic Extraction of Fig. 59........ . 75
59b. Multivariant 1 Extracted from Fig. 59a . . . 75
59b(i). Couplings and Variants Found inMultivariant 1 (Fig. 59b).. . . . . . 76
59c. Multivariant 2 Extracted from Fig. 59a . . . 76
59c(i). Coupling and Variants Extracted fromMultivariant 2 (Fig. 59c)....... . 76
59d. Construction Diagram of Fig. 59a . . . . . . 77
60. Contour Graph of Melody Found in Fig. 57a . 78
61. Contour Graph of Melody Found in Fig. 58a . 78
62. Contour Graph of Melody Found in Fig. 59a . 79
63. Reflets dans l'eau, Measures 29-30...... .. 83
63a. Melodic Extraction of Fig. 63.-....... . 84
63b. Coupling and Variants Found in Fig. 63a . . . 84
63c. Construction Diagram of Fig. 63a . . . . . 84
64. Reflets dans l'eau, Measures 59-60.. .... 85
64a. Melodic Extraction of Fig. 64........ . 85
xiv
Figure
6 4b.
64c.
65.
65a.
65b.
65c.
66.
66a.
66b.
66c.
67.
68.
69.
70.
71.
71a.
71b.
71c.
72.
72a.
72b.
72c.
73.
73a.
64a .
6 5
65a
Coupling and Variants Found in Fig.
Construction Diagram of Fig. 64a
Reflets dans l'eau, Measures 65-66
Melodic Extraction of Fig. 65 ...
Coupling and Variants Found in Fig.
Construction Diagram of Fig. 65a
Reflets dans l'eau, Measures 57-59
Melodic Extraction of Fig. 66 .-.
Couplings and Variants Found in Fig
Construction Diagram of Fig. 66a -
Contour Graph of DSLM Found in Fig.
Contour Graph of DSLM Found in Fig.
Contour Graph of DSLM Found in Fig.
Contour Graph of DSLM Found in Fig.
Hommage d Rameau, Measures 7-8
Melodic Extraction of Fig. 71 . . .
Variants Found in Fig. 71a . . . .
Construction Diagram of Fig. 71a
Hommage a Rameau, Measures 38-39
Melodic Extraction of Fig. 72 .
Coupling and Variants Found in Fig.
Construction Diagram of Fig. 72a
Hommage a Rameau, Measure 43 .
Melodic Extraction of Fig. 73 .-. -
72a . .
.
..
xv
64a
63a
64a
65a .
66a .
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Figure
7 3b.
73c.
74.
74a.
7 4b.
74c.
75.
75a.
75b.
75c.
76.
76a.
76b.
76c.
77.
77a.
7 7b.
77c.
78.
78a.
78b.
78c.
79.
79a.
Couplings and Variants Found in Fig.
Construction Diagram of Fig. 73a
Hommage a Rameau, Measure 48 . .
Melodic Extraction of Fig. 74 . . .
Couplings and Variants Found in Fig.
Construction Diagram of Fig. 74a
Mouvement, Measures 30-31
Melodic Extraction of Fig. 75 . . .
Variant Found in Fig. 75a
Construction Diagram of Fig. 75a
Mouvement, Measures 78-80 - - - - -
Melodic Extraction of Fig. 76 .
Coupling and Variants Found in Fig.7
Construction Diagram of Fig. 76a .
Reflets dans l'eau, Measure 14 .-. .
Melodic Extraction of Fig. 77 .
Couplings and Variants Found in Fig.
Construction Diagram of Fig. 77a . .
Hommage a Rameau, Measures 14-17 - -
Melodic Extraction of Fig. 78 .--.
Couplings and Variants Found in Fig.
Construction Diagram of Melody FoundFig. 78a . . - . . -.-.-.-. -.
in...... 106
Hommage a'Rameau, Measures 1-5-- - .
Melodic Extraction of Fig. 79 -- - .
109
110
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73a . . 93
93
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0 .94
74a . . . 94
. . . . . 95
95
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96
6a . . . 97
97
. 103
. 103
77a . . . 103
. .. ..... 104
-.. .. ... 104
.. ..... 105
78a ... 105
7
Figure
79b.
79b(i).
79c.
79c(i).
79d.
79d(i).
79e.
80.
80a.
80b.
80b(i).
80c.
80c(i).
80d.
80d(i).
80e.
1.
2.
3.
83a.
8 b.
83b(i).
8 c.
79a .
79a
79c
79a
Multivariant 1, Extracted from Fig.
Couplings and Variants Found inMultivariant 1 (Fig. 79b)
Multivariant 2, Extracted from Fig.
Couplings and Variants Found in Fig.
Multivariant 3, Extracted from Fig.
Couplings and Variants Found inMultivariant 3 (Fig. 79d)
Construction Diagram of Fig. 79a
Hommage a Rameau, Measures 10-13
Melodic Extraction of Fig. 80 -
Multivariant 1, Extracted from Fig.
Couplings and Variants Found in Fig. 80b
Multivariant 2, Extracted from Fig. 80a .
Couplings and Variants Found in Fig. 80c
Multivariant 3, Extracted from Fig. 80a .
Couplings and Variants Found in Fig. 80d
Construction Diagram of Fig. 80.-.-....
Contour Graph of Melody Found in Fig. 79a
Contour Graph of Melody Found in Fig. 80a
Hommage a Rameau, Measures 17-24 . . .
Melodic Extraction of Fig. 83... .....
Multivariant 1, Extracted from Fig. 83a .
Coupling and Variants Found in Fig. 83b .
Multivariant 2, Extracted from Fig. 83a .
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8 0
80a
Figure
83c(i)
83d.
83d(i).,
8 3e.
84.
84a.
84b.
84b (i) .
84c.
84c (i) .
84d.
84d(i).,
84e.
Coupling and Variants Found in Fig. 83c .
Multivariant 3, Extracted from Fig. 83a .
Couplings and Variants Found in Fig. 83d,
Construction Diagram of Fig. 83a . .
Hommage a Rameau, Measures 30-37 . .
Melodic Extraction of Fig. 84...... ..
Multivariant 1, Extracted from Fig. 84a .
Couplings and Variants Found in Fig. 84b
Multivariant 2, Extracted from Fig. 84a .
Coupling and Variants Found in Fig. 84c .
Multivariant 3, Extracted from Fig. 84a .
Couplings and Variants Found in Fig. 84d.
Construction Diagram of Fig. 84a . . .
xviii
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INTRODUCTION
Need for- the Study
The writing of this original research project was
initiated because of the virtual nonexistence of a theo-
retical bibliography concerning the music of Debussy.
There is a need for organized research into Debussy's com-
positional techniques. This study seeks to discover the
extent and manner in which Debussy uses ifotive to design
and unify his thematic material in Images I for piano,
which was completed in 1905.
The motive chosen for analysis occurs in measures 1
and 2 of Reflets dans l'eau, the first of the three pieces
in Images I.
Andantino nolto(f empo rubatll)
pp
Fig. 1--Reflets dans l'eau, measures 1 and 2
Fig. la--Motive as found in Fig. 1
1
2
E. Robert Schmitz refers to the three-note figure
shown in Figure la as "the theme. A perceptive comprehen-
sion of the right-hand patterns will reveal the mirroring
of that theme in diminution."1
Biographical Notes
Achille-Claude Debussy was born in Saint-Germain-en-
Laye, France, on August 22, 1862, and died in Paris on
March 25, 1918. In 1873, he entered the Paris Conserva-
toire and remained there for eleven years. During this
time, his studies included piano with Marmontel and theory
with Guiraud, Lavignac, Massenet and mile Durand. He was
also in Cesar Franck's class for a short time, though
Franck was displeased by his not modulating frequently
enough in improvisation.
In 1884, Debussy won the highest honor of the Conser-
vatoire, the Grand Prix de Rome, with the cantata, "L'Enfant
Prodigue". He left for Rome in 1885, but did not complete
the course of study, returning to Paris in 1887.
At this point, he settled down to a composer's career,
to which he confined himself for the remainder of his life.
In 1892, Debussy entered into maturity as a composer
by beginning work on a prelude, interlude and final para-
phrase inspired by Mallarme's eclogue, "L'Apres-midi d'un
E. Robert Schmitz, The Piano Works of Claude Debussy(New York, 1966), p. 102.
3
faune". After two years, however, only the prelude was
completed. He also began setting Maeterlinck's "Pelleas et
Melisande" to music, word for word. Completed in 1902, it
was premiered on April 30th at L'Opera-Comique and was an
overwhelming success.
Debussy died in 1918 after a long battle with cancer.
There are roughly three periods in Debussy's music:
the immature period to about 1890, then some twenty years
of mature work, followed by the decline of his final years.
Terms to be Used
All material and terminology will be presented in the
order of complexity, both in this glossary and in Chapter I.
Melodic extraction.--The removal of melodic material
from context for the purpose of analysis.
Interval.--The distance in pitch between two tones.2
Intervallic.--Pertaining to intervals.
Variant.---For the purpose of this study, a three-note
structure which is derived from the motive. Variant numbers
are assigned according to the order in which they appear in
Chapter I. Each of the following group examples is the
first of its kind to appear in Chapter I. Therefore, the
2 Willi Apel, "Interval," Harvard Dictionary of Music(Cambridge, 1969), p. 418.
4
variant numbers (2, 12, 5, 11, 45, etc.) are not in numeri-
cal order in this glossary.
Primary variant.--A three-note figure in which the
istep-leap" or "leap-step" relationship of the motive may
be seen. A step is the interval of a second. A leap is
any interval larger than a second. The leaps in the var-
iants may be altered without changing the basic character
of the motive, this being a practice of composers of all
schools.
The primary variant groups have been numbered accord-
ing to the first interval of all variants within the
particular group, beginning with the interval of a second.
Primary Group I (PGI) .--Primary variants beginning
with the interval of a second, followed by an interval
larger than a second.
Fig. 2--Variant 2 (PGI)
Primary Group II (PGII) .--Primary variants beginning
with the interval of a third, followed by a second.
5
Because the motive is composed of a third followed by a
second, PGII is the group that bears the closest resem-
blance to the motive. For the purpose of analysis, the
motive will be labeled as PGII.
Fig. 3--Variant 12 (PGII)
Primary Group 1II (PGIII).--Primary variants beginning
with the interval of a fourth, followed by the interval of
a second.
Fig. 4--Variant 5 (PGIII)
Primary Group IV (PGIV) .--Primary variants beginning
with the interval of a fifth, followed by the interval of
a second.
Fig. 5--Variant 11 (PGIV)
6
Primary Group V (PGV).--Primary variants beginning
with the interval of a sixth, followed by the interval of
a second.
Fig. 6--Variant 45 (PGV)
Secondary variant.--For the purpose of this study, a
three-note structure comprised of two leaps in opposite
directions. The "leap-step" relationship to the motive may
be seen by measuring each of the second and third notes of
the structure with the first note of the structure.
Fig. 7--Variant 1 (secondary)
Intervallic terminology.--For the purpose of this
study, the letters M, m, P, A and d will stand for the
adjectives Major, minor, Perfect, Augmented and diminished,
respectively. These letters will precede the digits 2, 3,
7
4, 5 and 6, which will stand for the intervals of a second,
third, fourth, fifth and sixth, respectively.
The adverbs "upward" and "downward" (abbreviated to
"up" and "dn") will follow the citing of an interval when
stating a variant formula; e.g. "m3up M2dn" means "the
interval of a minor third upward followed by the interval of
a Major second downward."
Construction diagram.--A figuration which illustrates
the structure of melodic material containing variants.
Coupling. -- For the purpose of this study, a four- or
five-note structure, resulting from the overlapping of two
variants.
Fig. 8--Construction diagram of a four-note coupling
The four-note coupling, shown in Figure 8, is formed
by joining the second and third notes of the first variant
with the first and second notes of the second.
8
Fig. 9--Construction diagram of a five-note coupling
The five-note coupling shown in Figure 9 is formed by
joining the third note of the first variant with the first
note of the second.
Closely related coupling Type 1 Form 1 (CRTlFl).--A
four-note coupling whose variants are primary, have identi-
cal intervallic content and each of which is the retrograde
inversion of the other.
CRTlFl Var. 10 Var. 11
Fig. 10--CRTlFl coupling
Closely related coupling Type 1 Form 2 (CRTlF2).--A
five-note coupling whose variants are primary, have identi-
cal intervallic content and each of which is either the
retrograde or the retrograde inversion of the other.
9
CRTlF2 Motive Var. 3
Fig. ll--CRTlF2 coupling
Semirelated coupling Type 2 Form 1 (SRT2Fl) .-- A four-
note coupling whose variants are primary and are "semi-"
retrograde inversions of each other due to intervallic
difference.
SRT2F1 Var. 9 Var. 12
Fig. 12--SRT2Fl coupling
Semirelated coupling Type 2 Form 2 (SRT2F2).--A four-
note coupling whose variants are primary.
SRT2F2 Var. 13 Var. 3
Fig. 13--SRT2F2 coupling
A As
iA
10
Semirelated coupling Type 2 Form 3 (SRT2F3) . --A four-
note coupling whose variants are primary and have semi-
identical intervallic content but whose directions differ.
SRT2F3 Var. 14 Var. 15
Fig. 14--SRT2F3 coupling
Semirelated cooling Type 2 Form 4 (SRT2F4) .-- A four-
note coupling whose variants are primary and of identical
intervallic content, but whose directions differ.
lin'
SRT2F4 Var. 16 Var. 19
Fig. 15--SRT2F4 coupling
Semirelated coupling Type 2 Form 5 (SRT2F5) .-- A f ive-
note coupling (Figure 9) whose variants may have any of the
relationships found in the SRT2F1, SRT2F2, SRT2F3 or SRT2F4
couplings.
SRT2F5 Motive Var. 18
Fig. 16--SRT2F5 coupling
IWqlw
I
I
11
Remotely related coupling (RR) .-- A four-note coupling
comprised of a primary and a secondary variant.
ff M
Var. 1 Var. 7RR (Sec.
Fig. 17--Remotely related coupling
Melodic fragmentation Form l.--For the purpose of this
study, the melodic statement of a single variant.
Fig. 18--Hommage a Rameau, measure 25
Fig. 18a--Melodic extraction of Fig. 18 (melodicfragmentation Form 1)
Var. 3
Fig. 18b--Variant used as melodic fragmentation in Fig. 18a
12
Melodic fragmentation Form 2.---The melodic statement of
a single coupling.
Lb
Fig. 19--Reflets dans l'eau, measure 10
Fig. 19a--Melodic extraction of Fig. 19 (melodicfragmentation Form 2)'.
RAI 1ACRTlFl Var. 10 Var. 11
Fig. 19b--Coupling and variants found in Fig. 19a
Linear melody.--Thematic material of length greater
than a coupling.
Conjunct simple linear melody Form 1 (CSLMFl) .-- Theme
comprised of a variant in juxtaposition with a coupling.
All examples found have identical construction diagrams.
13
-- ----------------------------------------
--. ... .- .- -.- .1. ------- ....
-0- .-- -
Fig..22b-Coupling n variansfren in6 Fg.126
Fig. 20a--Ceostrurct igramof Fig. 20a (CSLMFl)
Var. 164~
S _________________________________________
Fig. 2 20--Mouver nentvamasuresn 162 Fg.166
Fig. 20--Modic trction armof Fig. 20a (CSLMF)
14
Contour graph. -- An example which illustrates the shape
of a given melody. Contour graphs will be used to show the
similarities and differences in shape where the melodies of
a given melodic type (e.g. CSLMFl) have either identical or
semi-identical variant content and construction.
g#
e
d
a#
fR
e
Fig. 21--Contour graph of melody found in Fig. 20 (CSLMFl)
Conjunct simple linear melody Form 2 (CSLMF2) .-- A theme
comprised of two couplings in juxtaposition. All examples
found have identical construction diagrams.
15
17 - Ott,,
Fi ,__________ le urme su es 2-27--
m I I
Fig. 22a--Melodic extraction of Fig. 22
RR Var. 3 Var. 22
Fig. 22b--Couplings and variants found in Fig. 22a
I1 k riM60P
jMFV' w vv
SRT2F4 Var. 16 Var. 19
I I
I
16
Fig. 22c--Construction diagram of Fig. 22a (CSLMF2)
Conjunct compound linear melody (CCLM).--A theme com-
prised entirely of overlapped variants, which form couplings
within the theme. Each example will be accompanied by its
own construction diagram.
Fig. 23--Mouvement, measures 75-78
Fig. 23a--Melodic extraction of Fig. 23
17
CRT1F1 Var. 20 Var. 28
CRT1Fl Var. 28 Var. 20
CRTlFl Var. 20 Var. 28
Fig. 23b--Couplings and variants found in Fig. 23a
Var. 20 Var. 20 yar.16
Var. 28 Var. 28
ICRTlF1 CRT1F1 CRTlF1 SRT2F1
CCLM
Fig. 23c--Construction diagram of Fig. 23a
*alp
IL
SRT2Fl Var, 28 Var. 16
- A
18
Multivariant.--A group of notes found in a large melod-
ic form which may consist of single and/or overlapped
variants in juxtaposition with nonmotivic notes.
Conjunct complex linear melody (CCxLM) .-- A theme which
combines the juxtaposing procedure of CSLM and the overlap-
ping procedure of CCLM.
Toutes les i ots mrquies d signed Snores, ssn. dine ur!e reste tre-v /ger mnas sans sechereyse.
Vr '
VlP
------
Fig. 2 4--Mouvement, measures 67-73
r1 Id~. A*
I I - I
IL,
t'v '4F F '______ 1 T
Fig. 24a--Melodic extraction of Fig. 24 (CCxLM)
* I)ow
Fig. 24b--Multivariant 1 as found in Fig. 24a
CRTlF1 Var_20)Var 28
CRTlF1 Var. 28 Var
CRTlF1 Var. 20_Var. 28
SRT2F4 Var. 28 Var. 29
SRT2F4 Var. 29 Motive
Fig. 2 4b(i)--Couplings and variants found in Multivariant 1
19
j
ro-ol1 It As it jo
I I
I I I
I
I L,.oiI I
20
Fig. 2 4 c--Multivariant 2 as found in Fig. 24a
SRT2F4 Var. 29 Motive
SRT2F 4 Motivd Var. 18
Fig. 2 4 c (i) -- Couplings and variants found in Fig. 24a
Multivariant 1
Var. 28 Var. 28 MotiveVar. 20 Var. 20 Var. 29
Lii Li i Li
Multivariant 2
H] iMotive
Var. 29 Var. 18
LiiJJ
CRTlF1 CRTlF1 CRTlF1 SRT2F4 SRT2F4 SRT2F4 SRT2F5
IILJFig. 24d--Construction diagram of Fig. 24a (CCxLM)
'Ask
-4-- v - --- p- --- a &or
I-- I I
21
Disjunct simple linear melody (DSLM) .-- A theme in which
variants and/or couplings are found to be in juxtaposition
with one or more non-motivic notes.
Fig. 25--Reflets dans l'eau, measures 29-30
Fig. 25a--Melodic extraction of Fig. 25 (DSLM)
SRT2F3 Var. 31 Var,.19
Fig. 25b--Coupling and variants found in Fig. 25a
22
Var. 31
Var. 19
Db
DSLM
Fig. 2 5c--Construction diagram of Fig. 25a (DSLM)
Disjunct compound linear melody (DCLM) .-- A theme con-
sisting of a scalewise passage from which variants and/or
couplings may be extracted.
Fig. 26--Reflets dans l'eau, measure 14
Fig. 26a--Melodic extraction of Fig. 26 (DCLM)
23
CRTlFl Var. 3 Mot ve
CRTlFlVar. 3 otive
Fig. 26b--Couplings and variants found in Fig. 26a
Var. 3 Var. 3
Motive LMotive
LTCRT1F1 CRTlFl
DC
Fig. 26c--Construction diagram of Fig. 26a (DCLM)
Dis junct complex linear 'Melody (DCxLM) . -- A theme in
which variants, couplings and/or multivariants are found
in juxtaposition with non-motivic material.
I~1,I
I P
_ _ - -
p074
IF - f - . --1- 1
Fig. 2 7 -- Homm'age 'a Rameau, measures 17-24
Fig. 27a--Melodic extraction of Fig' 27 (DCxLM)
24
rim gg 4191A-M Fw
oil
I I I I I- -
25
i 4 - - 1,a i 1% p Ion - I-1
_________I
Fig. 27b--Multivariant 1 as found in Fig. 27a
SRT2 2 Var. 44 Var. 4 5
Var. 44
Fig. 27b(i)--Coupling and variants found in Fig. 27b
Fig. 27c--Multivariant 2 as found in Fig. 27a
k
S RT 2F5
I A I
Var. 18
-.- 4 "-*
Var. 46
Fig. 27c(i)--Coupling and variants found in Fig. 27c
Fig. 27d--Multivariant 3 as found in Fig. 27a
r. -U., ., - .9 as - ---- :o - I .. -,
;FF
.11- -4ZL-- -A -W -W-AL-- -AW MF
A& _0 --- - IWF .
I
26
Ni I I
CRTlF1 Var. 2 Var 28
CRTlFl Var. 28'-Vr. 20
~CRT-1V~r. M 0 i tive
TCTTVF2 Mtv 1Vr20,
.. * A
TCRTlF1 Var 2 Var. 28
Fig. 27d(i)--Couplings and variants found in Fig. 27d
For the sake of space, the labeling of couplings in
Figure 27e has been abbreviated as follows: Cl for CRTlFl;
C2 for CRTlF2; S2 for SRT2F2; and S5 for SRT2F5. The motive
is designated by M, and variants are indicated by numbers
only.
44 44 18 20M'O20m20IT045 W466 2 8L MW28
G E G# F# G# A G# G#
G S2 E S5 G# F# G# A G# ClCl 92 C2 Cl G#
DCxLM
Fig. 27e--Construction diagram of Fig. 27a (DCxLM)
dp
l
27
Enharmonic.--"Tones that are actually one and the same
degree of the chromatic scale but are named and written
differently.',3
Statement.--For the purpose of this study, the term
"statement" will refer to the use of a variant or coupling.
There may be more than one statement found in a melodic
example.
3Apel, "Enharmonic. (2)," Harvard Dictionary, p. 293.
CHAPTER I
EVIDENCE
Melodic Fragmentation
Seven examples of melodic fragmentation Form 1 were
discovered. Figures 28, 28a and 28b represent the first
illustration of melodic fragmentation Form 1.
Andantino molto(Tempo rubato -- ~
Fig. 2 8--Reflets dans 1'eau, measures 1 and 2
Fig. 28a--Melodic extraction of Fig. 28
28
29
Var~l 4otiveVar.
Fig. 2 8 b--Variants found in Fig. 28a
Figure 28 represents the concurrent melodic frag-
mentation of two isolated variants which are stated
simultaneously with the motive. Variant 1, which is
secondary, appears in fragmentation a total of thirty-
one times: twelve times in measures 1-8, twelve times
in measures 36-43 and seven times in measures 71-78.
Variant 2, which is Primary Group I, is stated only
four times: twice in measures 1-8 and twice in measures
36-43. The motive is stated a total of six times in all
three passages.
Fig. 29 --Hommage a Rameau, measure 25
_T
Fig. 2 9 a--Melodic extraction of Fig. 29
30
Var. 3
Fig. 29b--Variant found in Fig. 29a
Figure 29 represents an example of an isolated variant
used as melodic fragmentation. The variant, known as Var-
iant 3, is shown in Figure 29b and is Primary Group I.
Fig. 30--Mouvement, measure 63
;I
Fig. 30a---Melodic extraction of Fig. 30
Var. 5 - u iFar. 4
Fig. 30b--Variants found in Fi . 30a
31
Fig. 30c--Construction diagram of Fig. 30a
Figure 30 is a further illustration of melodic frag-
mentation, involving the simultaneous statements of two
single variants which end on the same note. The var-
iants, shown in Figure 30b, are Variant 4, which is
Primary Group IV, and Variant 5, which is Primary
Group III. A diagram of construction is shown in
Figure 30c. These variants reappear in Measure 73.
Further examples of melodic fragmentation uti-
lizing single variants were found in the following
passages:
Reflets dans l'eau
(1) Meas. 12 (Variant 6 and Variant 7, onestatement each)
(2) Meas. 18-19 (Variant 8, two statements)
(3) Meas. 32-34 (Variant 9, three statements)
(4) Meas. 81-82, 85-86 (Motive, two statements)
The statistics of variant usage, as found in melodic
fragmentation Form 1, are represented in Table I.
32
TABLE I
STATISTICS OF VARIANT USAGE AS FOUNDIN MELODIC FRAGMENTATION FORM 1
Formula
m3dn M2dn*
P5up P4dn
M2dn M3dn.
M2dn m3dn-
d5up A2up
P4dn m2dn
P5dn M2up
P4dn M2dn
P4up m3dn
m2up m3dn
Type
PrimaryGroup II
Secondary
Primary
Group I
Primary
Group I
PrimaryGroup IV
Primary
Group III
Primary
Group IV
PrimaryGroup III
Secondary
Primary
Group I
Number of-Statements'
8
31
4
1
2
2
1
1
2
3
Percentageof Use
14.4
55.8
7.2
1.8
3.6
3.6
1.8
1.8
3.6
5.4
Table I shows the number of statements and percentage
of use of each of the isolated variants found as melodic
fragmentation. The variants are listed and numbered in
order of appearance and discussion. Further statistics
on the primary variants are shown in Table IA.
Variant
Motive
1
2
3
4
5
6
7
8
9
33
TABLE IA
SUMMARY OF PRIMARY VARIANT USAGE BY GROUP
Number of Percentage ofVariant Group Statements Statements
Primary Group I 8 36Primary Group II 8 36Primary Group III 3 13.5Primary Group IV 3 13.5
Table IA represents the summary statistics of primary
variants by group, as found in melodic fragmentation Form 1.
In arriving at these statistics, the primary variants were
considered within themselves. Statistics as compared with
secondary variants follow in Table IB.
TABLE IB
TOTAL SUMMARY OF VARIANT STATISTICS AS FOUNDIN MELODIC FRAGMENTATION FORM 1
Type Percentage
Primary . .-...-.-......-..-.. . . . . . . 39.6Secondary.............. ..... . . 59.4
Table IB shows the total summary statistics of primary
and secondary variants as found in melodic fragmentation
Form 1.
Five examples of melodic fragmentation Form 2 were
found. One CRTlFl coupling was found to be used as melodic
fragmentation Form 2 and is illustrated in Figures 31, 31a
and 31b.
34
Fig. 31--Reflets dans l'eau, measure 9
Fig. 31a--Melodic extraction of Fig. 31
CRTlFl _ Var. 10 Var
Fig. 31b--Coupling and variants found in Fig. 31a
As the variants shown in Figure 31b are retrograde
inversions of each other, the coupling in Figure 31b is
CRTlFl.
One SRT2Fl coupling was found to bp used as melodic
fragmentation Form 2 and is shown in Figures 32, 32a and
32b.
35
Fig. 32--Reflets dans l'eau, measure 30
Fig. 32a--Melodic extraction of Fig. 32
SRT2Fl Var. 9 Var. 12
Fig. 3 2b--Coupling and variants found in Fig. 32a
The variants of the above coupling are semi-identical.
While both Variant 9 and Variant 12 contain the interval of
a minor third, the major second of Variant 12 varies from
the minor second found in Variant 9. Each is a semi-
retrograde inversion of the other, forming an SRT2Fl
coupling. The coupling shown in Figure 32b is repeated
in Measure 31 of Reflets dans l'eau.
One SRT2F2 coupling was found to be used as melodic
fragmentation Form 2 and is shown in Figures 33, 33a and
33b.
36
Fig. 3 3--Hommage a Rameau, measure 24
Fig. 33a--Melodic extraction of Fig. 33
SRT2F2 Var-ar
Fig. 33b--Coupling and variants found in Fig. 33a
The variants shown in Figure 33b are primary, forming
an SRT2W2 coupling.
One SRT2F3 coupling was found to be used as melodic
fragmentation Form 2 and is shown in Figures 34, 34a and
34b.
Fig. 3 4 --Hommage a Rameau, measures 53-54
37
Fig. 34a--Melodic extraction of Fig. 34
A
Var. Var ,T
Fig. 34b--Variants found in Fig. 34a
As Variants 14 and 15 are semi-identical and differ
directionally, they form an SRT2F3 coupling.
One remotely related coupling was found to be used as
melodic fragmentation Form 1 and is illustrated in Figures
35, 35a and 35b.
Fig. 3 5 --Hommage a Rameau, measure 67
Fig. 35a-,-Melodic extraction of Fig. 35
38
Fig. 3 5b--Coupling and variants found in Fig. 35a
Figure 35b shows Variants 1 and 7 to be secondary and
primary respectively, forming a remotely related coupling.
Each of the variants discussed in the above examples
is shown in Table II.
TABLE II
VARIANTS FOUND IN MELODIC FRAGMENTATION FORM 2
-
Group m3 d T2F2-ariaH
0 M4J-H>-r
4~ )
7 ~ ~ ~ ~ ~ ~ ~ 0 Prmr 4d eoeyRMot
-PGrr 4-3Ird3dTFIvriz a) 4J-- 0H
Q)r~ (H H41Q)04 Ell :>1 0 (a0 )O 0 0DO4-
>0 Z-UP_____UzU zu
Secondary P5 up 7 Remotely Remote1P4 dn Related
3 Primary M2 dn 13 Semirelated Primary1Group I m3 dn T2F2 Variant
7 Primary P4 dn 1 Remotely Remote1Group III M2 dn Related
9 Primary m2 up 12 Semirelated Semi Retro 2Group I m3 dn T2Fl Inversion
39
TABLE II--Continued
4-)
4~ 44-)Cd 4 -)0 0 4 ('0
4-))U) 1::44-!W4J0 00 0O 0) (0
_______ 4-)>C) Hro (d r-q 4 -
PrimaryGroup I
PrimaryGroup IV
PrimaryGroup II
PrimaryGroup III
PrimaryGroup III
M2 dnP5 up
P5 upM2 dn
m3 dnM2 up
P4 upM2 dn
P4 dnm2 up
11
10
9
3
15
CRTlFi
CRTlFl
SemirelatedT2Fl
SemirelatedT2F2
SemirelatedT2F3
15 Primary m2 up 14 SemirelatedGroup I A4 up T2F3
RetroInversion
RetroInversion
Semi RetroInversion
PrimaryVariant
Semi-intervallic
Semi-intervallic
1
1
2
1
1
1
In Table II, each of the variants is listed in the
order of its discovery with its formula, the number of
its companion variants, the type of coupling they form,
the relationship to the companion variant and the number
of statements (both as couplings and as variants). Per-
centages of the variants used are listed in Table IIA.
10
11
12
13
14
40
TABLE IIA
PERCENTAGES OF VARIANT GROUPS AS FOUNDIN MELODIC FRAGMENTATION COUPLINGS
Type Quantity
Primary 4Group I
Primary 1Group II
Primary 3Group III
Primary 1Group IV
Secondary 1
% of Total'Quantity
40
10
30
10
10
Number ofNumber ofStatements
5
2
3
% of TotalStatements
41.5
16.7
25.0
8.3
Table IIA gives the variant percentages by group.
Each group is listed in numerical order. The number of
variants and variant statements within each group are
followed by their respective percentages. Total summary
percentages of the variants found in the couplings used
in melodic fragmentation Form 2 are shown in Table IIB.
TABLE IIB
TOTAL SUMMARY PERCENTAGES OF VARIANTS FOUND IN COUPLINGSUSED AS MELODIC FRAGMENTATION FORM 2
Type Percentage
Primary.............................................91.5Secondary .................. '.....-.-.-...-.......9.58.3
Table IIB gives the total summary of variants by
group. Coupling percentages are given in Table III.
41
TABLE III
COUPLINGS USED AS MELODIC FRAGMENTATION FORM 2
CouplingType
CRTlFI
SRT2Fl
SRT2F2
SRT2F3
Remotely Related
Number Timesof Type Used
1 2
Percentageof Number
20
20
20
20
20
Percentageof Use
16.6
33.3
16.6
16.6
16.6
Table III shows the couplings used as melodic fragmen-
tation. The couplings are listed by type. The number of
each type of coupling and times it is used are given, fol-
lowed by the couplings' respective percentages.
Conjunct Simple Linear Melody
Three examples of conjunct simple linear melody
Form 1 were discovered, and are shown in Figures 36a,
37a and 38a respectively.
6--------------------------------------
Fi . 6-M.vme tme s re 1 2-6
42
Fig. 36a--Melodic extraction of Fig. 36
P-
- - -------------------------------
t A
Fig. 37 --Mouvement, measures 167-170
L~~L
Fig. 37a--Melodic extraction of Fig. 37
-----
Fig. 38--Mouvement, measures 170-173
43
Fig. 3 8a--Melodic extraction of Fig. 38
The first three notes of each of the above three
melodies were found to be identical motivic variants
by reason of enharmonics, as shown in Figure 39.
V aTr-r.16 Var.Mouvement Mouvement MouvenentMs. 162 Ms. 167-8 Ms. 17
Fig. 39--The first variant of each of the conjunctsimple linear melodies Form 1.
As shown in Figure 39, each of the CSLMFl linear
melodies was found to begin with Variant 16.
Each of the variants in Figure 39 is in juxtaposition
with an SRT2F4 coupling. All three couplings are shown in
Figure 40 with their variant breakdowns.
44
SRT Var.-17 Var. 18Mouvement
- 4_
SRT2F4 Var, 17 Var. 18
MouvementMs. 171- 72
Fig. 40--Couplings and variants, CSLMF1
As shown in Figure 40, each of the couplings was found
to be identical to the other two in content. The contour of
all three melodies is shown on the graphs in Figures 41, 42
and 43.
G#
E
D
FF#
E
Fig. 41--Contour graph of CSLMF1 found in Fig. 36a
45
G
F
E
D
Bb
F#
E
Fig. 42--Contour graph of CSLMF1 found in Fig. 37a
D
Bb
Ab
E
C
B
Fig. 43--Contour graph of CSLMF1 found in Fig. 38a
46
The graphs in Figures 41, 42 and 43 show all three
conjunct simple linear melodies Form 1 to be identical
in contour as well as intervallic content.
Three examples of conjunct simple linear melody Form 2
were discovered, and are shown in Figures 44a, 45a and 46a
respectively.
Fi.-4--n - a a
Fig. 44--Reflets dans l'eau, measures 24-27
Fig. 44a--Melodic extraction of Fig. 44
47
1 -1
Fig. 45--Reflets dans 1eau measures 50-53
Fig. 45a--Melodic extraction of Fig. 45
Of Ioto
1 -s -
Fig. 46--Reflets dans 1'eau, measures 54-56
48
Fig. 46a--Melodic extraction of Fig. 46
All of the above melodies were found to be of identical
coupling content, as is shown in Figure 47.
I -T RT2F4 Var. 16 Var. 19Reflets dansl'eau ms. 24-25
SRT2F4 Var. 16 Var19Reflets dansl'eau is. 50-51
SRT2F4Var. 20 VrReflets dansl-'eau ms-.54-55
Fig. 47--First coupling found in each of the CSLMF2melodies, with variants.
Figure 47 shows all three of the first couplings in
each of the CSLMFl examples to be SRT2F4 couplings. Each
of the first two couplings consists of Variants 16 and 19
respectively. The only difference between the third coup-
ling and the previous two is intervallic: the major third
of Variants 16 and 19 being replaced by the minor third in
49
Variants 20 and 21. The second couplings found in conjunct
simple linear melody Form 2 are shown collectively in Figure
48.
RR Var. 3 Var. 22Reflets dansi'eau ms. 25-27
RR Var. 23 Var. 24Reflets dansl'eauMsTST-52
RR Var. 3 Var. 22Reflets dansl'eau ms, 55-56
Fig. 48--Second couplings found in CSLMF2 melodies,with variants.
Figure 48 shows each of the second couplings as found
in CSLMF2 to be remotely related. The first and third coup-
lings were found to be identical (the final intervals of
major third and diminished fourth being enharmonic),. In
Variants 22 and 24, the intervallic relationship between
the first and third notes is an augmented prime (ebb to eb
and f to f# respectively), which is enharmonic with the in-
terval of a minor second. The second coupling of the three
differs from the other two in the following aspects: the
diminished fourth of Variant 23 opposed to the minor third
50
of Variant 3, and the diminished fourth and perfect fourthof Variant 24 opposed to the minor third and major third
(diminished fourth) of Variant 22. Contour graphs of the
CSLMF2 examples are shown in Figures 49, 50 and 51.
Ab
Gb
Fb
Ebl
Cb
Fig. 4 9 -- Contour graph of CSLMF2 found in Fig. 44a
B
A
GFF
C#~Fig. 50--Contour graph of CSLMF2 found in Fig. 45a
B
A
G#GF#
D#4
Fig. 51--Contour graph of CSLMF2 found in Fig. 46a
51
Figures 49, 50 and 51 show all three of the CSLMF2
examples to be of identical contour, although they .are only
similar intervallicly.
Each of the variants found in CSLMF1 and CSLMF2 is
shown in Table IV.
TABLE IV
VARIANTS FOUND IN CSLMFl AND CSLMF2ACCORDING TO INDIVIDUAL USE
Variant Type Number of Statements
3 Primary Group I 2
16 Primary Group I 5
17 Primary Group I 3
18 Primary Group I 3
19 Primary Group I 2
20 Primary Group I1
21 Primary Group II'1
22 Secondary 2
23 Primary Group 11
24 Secondary
Table IV lists each of the variants, as found in CSLM,
in numerical order with its categorization by group and
frequency of use. Percentages of use by group are shown in
Table IVA.
52
TABLE IVA
PERCENTAGES OF VARIANT USE BY TYPEAS FOUND IN CSLMF1 AND CSLMF2
Percentage Number of Percentage ofType Quantity of Quantity Statements Statements
Primary 5 50 12 57.12Group I
Primary 3 30 6 28.56Group II
Secondary 2 20 3 14.28
Table IVA shows each of the variant types, followed by
the quantity of different variants within that type, the
number of times each type is stated and respective percen-
tages. Further statistics are found in Table IVB.
TABLE IVB
PERCENTAGES OF SINGLE AND COUPLING USAGE OFVARIANTS AS FOUND IN CSLMFl AND CSLMF2
Usage Percentage
In couplings...................... 85.68Singly....................-.-... .. 14.28
Table IVB, which shows the collective percentages of
single and coupling usages, is based on the collective num-
ber of statements in Table IVA. Statistics concerning
couplings are found in Table V.
53
TABLE V
COUPLINGS FOUND IN CSLMF1 AND CSLMF2ACCORDING TO INDIVIDUAL USE
-I 'i-~1 1 4 i '-4
'H
0U
1
ca)4-)
4-)
a)Ici44:
MouvementMs. 163-64169-70, 171-72
4-)
Cd
U)ai)H4
>I,'Hq
4-)
0
En
4
rd 4-)
>zf- ___
17
18
PrimaryGroup II
PrimaryGroup I
M3 upM2 up
M2 upM3 dn
Inter-vallic
ai)
04
SRT2F4
IU)
U)
0
c)
3
0
crd
4-)
33.3
2 Reflets dans 1'eau 16 Primary M2 up Inter- SR 2 22.2Ms. 24-25, 50-51 Group I M3 up vallic T2F4
19 Primary M3 upGroup II M2 dn
3
4
5
Reflets dans l'eauMs. 54-55
Reflets dans l'eauMs. 25-27, 55-56
Reflets dans l'eauMs . 51-52
20
21
3
PrimaryGroup I
PrimaryGroup II
PrimaryGroup I
22 Secondary
23
24
PrimaryGroup I
Secondary
M2 up Inter- SRm3 up vallic T2F4
m3 upM2 dn
M2 dnm3 dn
m3 dnM3 up
M2 dnd4 dn
d4 dnP4 up
11 11.1
RemotefRR 121 22.2
Remote RR 1111.1
I
54
In Table V, each of the couplings is listed in the
order in which it was discussed. The places it occurs,
the numbers, types and formulas of the variants it con-
tains and the relationship between those variants are
given. In the final three columns, the coupling's type,
number of times it is used and percentage of times it is
used are given respectively. A summary of these statis-
tics is given in Table VA.
TABLE VA
TOTAL SUMMARY OF COUPLINGS FOUND IN CSLMFI AND CSLMF2
Coupling Percentage Number of Percentage ofType Quantity of Quantity Statements Statements
SRT2F4 3 60 6 66.6
RR 2 40 3 33.3
Table VA is a summary of coupling usage as found in
CSLMF1 and CSLMF2. With each type of coupling, its quan-
tity and collective number of statements are given with
respective percentages.
Conjunct Compound Linear Melody
Five examples of conjunct compound linear melody were
discovered. As all of the melodies were found to be of
varying construction, each will be followed by its own
diagram.
55
lp-
Fig. 52--Reflets dans 1'eau, measure 10
Fig. 52a--Melodic extraction of Fig. 52
-0-]
CRF Var. 10 Var 11
SRT2F2 Var. 11 Var, 25
1wW-WFAwIC TI "Fi Var. 25 TTVar,19
Fig. 52b--Variant and coupling content of Fig. 52a
56
Var. 10 V 1j Var. 25 ( 9
CRTlFl SRT2CRTlF1
Fig. 5 2 c--Construction diagram of Fig. 52a
As shown in Fig. 52c, each of the four variants
(top) combine to form three couplings (center) which in
turn combine to form a six-note melody (bottom).
Fig. 53--Reflets dans l'eau, measure 60
Fig. 53a--Melodic extraction of Fig. 53
57
CRTlFl Var. 26 Var. 18
CRTlFl Var. 18Vr.2
Fig. 53b--Coupling and variant content of Fig. 53a
Figure 53b shows the melody in Figure 53a to be com-
posed of two CRTlFl couplings. This same melody was found
in Reflets dans l'eau in the following passages: measure
62, measure 63, measure 79 and measure 80. A diagram of
construction is shown in Figure 53c.
Var. 26 Var. 18 Var. 26
CRTlFl CRTlFl
Fn
Fig. 53c--Construction diagram of Fig. 53a
58
ita TeoI01aa
Fig. 54--Hommage '%Rameau, measures 51-52
Fig. 54a--Melodic extraction of Fig. 54a
S RT2F Var. 14 Vr.15
S'T2F3 _Tar. 15 Var._27
Fig. 54b--Coupling and variant content of Fig. 54a
Figure 54b shows the melody in Figure 54a to be com-
posed of two couplings, both of which are SRT2F3 couplings.
A diagram of construction is shown in Figure 54c.
59
Var. 14 Var. 15 Var. 27
SRT2F3 SRT2F3
Fig. 5 4 c--Construction diagram of Fig. 54a
As shown in Figure 54c, each of the three variants
(top) combine to form two couplings (center) which in
turn combine to form a five-note melody (bottom).
F a u s
Fig. 55--Hommage a Rameau, measure 71
Fig. 55a--Melodic extraction of Fig. 55
60
SRT2F2 Var. 13 Var. 3
CRTlF1 <Var. 3 oti e
Fig. 5 5 b--Couplings and variants found in Fig. 55a
The melody shown in Figure 55a consists of two coup-
lings containing two variants each. The first coupling is
an SRT2F2 coupling and the second a CRTlF1 coupling. A
construction diagram is shown in Figure 55c.
Var. 13 Motive
SRT2F2 CRTlFl
'LIT1 qL
Fig. 5 5c--Construction diagram of Fig. 55a
As shown in Figure 55c, the three variants (top) com-
bine to form two couplings (center) which in turn form a
five-note melody.
61
Fig. 56--Mouvement, measures 75-78
Fig. 56a--Melodic extraction of Fig. 56
CRTlFl Var. 28Vr2
CRTVF1 Var. 20
SRT2Fl Var. 28 Var. 16
Fig. 56b--Coupling and variant content of Fig. 56a
62
The melody shown in Figure 56a consists of four coup-
lings made from five variants. The first three couplings
are CRTlF1 couplings, and the last is an SRT2Fl coupling.
A construction diagram is shown in Figure 56c.
VaF7 r Var. 21Var. 16Var. 28 Var. 28
LIP ILTLCRTlFl CRTlFl CRTlF1 SRT2F1
Fig. 5 6 c--Construction diagram of Fig. 56a
As shown in Figure 56c, the five variants (top) combine
to form four couplings (center) which in turn form a seven-
note melody.
Each of the variants found in CCLM is shown in Table
VI.
63
TABLE VI
VARIANTS FOUND IN CCLM
Primary
Primary
Primary
Primary
Primary
Primary
Primary
Primary
Primary
Primary
Primary
Primary
Primary
Primary
Primary
ype Number of Statements
Group II1
Group I1
Group I1
Group IV 1
Group III1
Group III1
Group I1
Group I1
Group I 5
Group II1
Group I 2
Group I1
Group II 10
Group III1
Group II 2
Table VI lists each of the variants in CCLM in numeri-
cal order with its categorization by group and frequency of
use. Percentages of use by group are given in Table VIA.
TABLE VIA
PERCENTAGE OF VARIANT USE BY GROUP AS FOUND IN CCLM
TypePrimary Group I
Primary Group II
Primary Group III
Primary Group IV
Number7
4
3
1
Percentageof Number
46. 2
26.4
19.8
6.6
Number of Percentage ofStatements Statements
12 40.0
14 46.7
3 10.0
1 3.3
Varian
Motive
3
10
11
13
14
15
16
18
19
20
25
26
27
28
t T5I
--- r- I
I.I
64
Table VIA shows each of the variant types, followed by
its quantity, number of statements and respective percen-
tages. In addition, all the variants are primary. Further
statistics concerning couplings are shown in Table VII.
TABLE VII
COUPLINGS FOUND IN CCLM ACCORDING TO INDIVIDUAL USE
0) ()U) 40)'aGru Igd F0a) 04 >4Js >1P rIna)rord E-1 4-4C) b) 0)4-j U) 0) 00) (d U)_) P -ird 4j 0 ) 4~
0'Hd-H '0 da) 0 q ) 00)
>1 Primry P5 pPs4on8 _ _ _ _ _p IV 2 _ _8n _
1 Reflets dans 10 Primary m2 dn ~Retro- CR~ 4.~76l'eau, Group I P5 up grade TlF2Ms. 10 Inver-
11 Primary P2 up sionsGroup IV M2 dn
2 Reflets dans 11 Primary P5 up Pri- SR 1 4.76l'eau, Group IV M2 dn mary T2F2Ms. 10 Var-
25 Primary M2 dn iants
Group I M3 up3 Reflets dans 25 Primary M2 dn Retro- CR 1 4.76l'eau, Group I M3 up grade TlFlMs. 10 Inver-
19 Primary M3 up sionsGroup II M2 dn4 Reflets dans 26 Primary M3 dn Retro- CR 5 23.80
l'Ieau, Group II M2 up grade TlFlins. 60 Inve r-
18 Primary M2 up sionsSGroup I M3 dn -
iseaums. 60
10
26
PrimaryGroup I
PrimaryGroup II
M2 upM3 dn
M3 dnM2 up
Retro-gradeInver-sions
CRTlFl
5 23.80-.j I
65
TABLE VII--Continued
=1 F - -__-__
0
6
7
ai)
ci)
a)
Hommage ARameaums. 51-52
HomageRameaums. 51-52
HommageRameaums. 71
H ommageRameaums. 71
Mouvementms. 75-77
Mouvementms. 75-76
Mouvementms. 76-77
I
z
14
15
15
27
13
3
3
Motive
20
28
28
20
28
16
U)
Primary
Group ITTPrimaryGroup I
Primary
Primary,Group III
PrimaryGroup III
PrimaryGroupI_PrimaryGroup I
PrimaryGroup IIPrimaryGroup II
PrimaryGroup IIPrimaryGroup II
PrimaryGroup I
Primary
-Group I
0
P4 dnm2 up
m2 upA4 upm2 upA4 up
A4 upM2 dnP4 upP4 up
M2 dnm3 dnM2 dnm3 dn
m3 dnM2 dnM2 upm3 up
m3 upM2 upm3 upM2 up
M2 upm3 upm3 upM2 up
M2 upM3 up
o-40wto
S '
El)~
0
a) r
04-)
4.76
r.'H
Seml-
inter-
vallic
semi-~~
inter-
vallic
Pri-
ma ryVar-
iants
Retro-
grade
Inver-
s ions
Retro-
grade
Inver-
s ions
Retro-
grade
Inve r-
sions
Semi'-retro-
gradeInver-sions
E00i)
04>H
H
04
SR
T2F3
SRT2F3
SRT2F2
CRTlFl
CRTlFl
CRTlFS
SRT2F1
4.76
.
11 4.76
12.S 4-7(;.A-
1 14.76
IiF
1 1 4.76
2 9.52
66
In Table VII, each of the couplings is listed in the
order in which it was discussed. With each coupling, the
places it occurs, variant numbers, types, formulas and
relationships are given. In the final three columns, the
couplings' types, numbers and percentages of times used
are given respectively. A summary of these statistics is
given in Table VIIA.
TABLE VIIA
TOTAL SUMMARY OF COUPLINGS FOUND IN CCLM
Coupling Percentage Number of Percentage ofType Quantity of Quantity Statements Statements
CRTlFl 7 58.31 16 76.16
SRT2Fl 1 8.33 1 4.76
SRT2F2 2 16.66 2 9.52
SRT2F3 2 16.66 2 9.52
Table VIIA is a summary of coupling usage as found in
CCLM. With each type of coupling, its quantity and collec-
tive number of statements are given with respective
percentages.
Conjunct Complex Linear Melody
Three examples of conjunct complex linear melody were
discovered. As the examples differed in construction, each
will be followed by its own diagram.
67
ppp---
u tes les notes marquee d signe...sonor, sany dre,le reste tris tger mains son& secheresse.
Fig.57--___ent measrs_7-7
Fig. 57--Mouvement, measures 67-73
Fig. 57a--Melodic extraction of Fig. 57
As shown in Figure 57, this theme is doubled in the
bass clef at the interval of a minor tenth.
I I I
68
II
Fig. 57b--Multivariant 1, extracted from Fig. 57a
CRTlIF1 Var. 20 Var. 28
CRTlFl Var. 28 Vat. 20
iw
CRTlFl Var. 20 Var. 28
SRT2F4 Var. 28 Var. 29
SRT2F4 Var. 29 Motive
Fig. 57b(i)--Couplings and variants found in multivar-iant 1 (Fig. 57b).
Figure 57b(i) shows Multivariant 1 (Figure 57b) con-
sists of five couplings made from six variants. The first
three couplings are CRTlFl couplings, and the last two are
SRT2F4 couplings.
69
A A
Fig. 57c--Multivariant 2, extracted from Fig. 57a
SRT2F4 Var. motive
SRT2F5 Motivd Var. 18
Fig. 57c(i)--Couplings and variants extracted fromMultivariant 2 (Fig. 57c).
As shown in Figure 57c(i), Multivariant 2 (Figure 57c)
consists of two couplings. The first is an SRT2F4 coupling
and the second an SRT2F5 coupling. A construction diagram
of Figure 57a is shown in Figure 57d.
70
Multivariant 1 Multivariant 2
Var. 28 Var. 28 Motive MotiveVar. 20 Var. 20 Var. 29 Var. 29 Var. 18
~LULU LULiw
CRTlF1 CRT1F1 CRTlFl SRT2F4 SRT2F4 SRT2F4 SRT2F5
Fig. 57d--Construction diagram of Fig. 57a
As shown in Figure 57d, Multivariant 1 consists of six
variants (top left). These six variants overlap to form
three CRTlFl couplings and two SRT2F4 couplings (center
left), which in turn overlap. Multivariant 2 consists of
three variants which overlap to form an SRT2F4 coupling and
an SRT2F5 coupling, which in turn overlap. Both multivar-
iants are juxtaposed, forming CCxLM Example 1 (bottom).
71
s a 7 s A e
f 7-- f---;(u
_p ;.4t n e07 N6r
m u en
-06 -o,
~IT_K ____
Fig. 58--Mouvement, measures 89-96
Fig. 58a--Melodic extraction of Fig. 58
i ON-AV
72
Fig. 58b--Multivariant 1, extracted from Fig. 58a
arl
S RT2F4Var. 29 Motive
Fig. 58b(i)--Couplings and variants found in Multivar-iant 1 (Fig. 58b).
Figure 58b(i) shows that Multivariant 1 (Figure 58b)
consists of a single variant in juxtaposition with two over-
lapped couplings which are made from three variants. Both
couplings are SRT2F4 couplings.
73
Fig. 58c--Multivariant 2, extracted from Fig. 58a
1i~~
SRT2F4 Var. 29 Motive
SRT2F5 Motive Var. 18
Cflr.Fl Var.18
Fig. 5 8c(i)--Couplings and variants found in Multivar-iant 2 (Fig. 58c).
Figure 58c(i) shows that Multivariant 2 (Figure 58c)
contains three couplings, consisting of four variants. The
couplings are an SRT2F4 coupling, and SRT2F5 coupling and
a CRTlFl coupling, respectively. A construction diagram
is shown in Figure 58d.
74
Multivariant 1 Multivariant 2Var. 16 Var. 29 F1Var. 29 V Var. 18KV]
Var. 28 LMotive Motive .IJVar. 26
Var. 16 SRT2F4 SRT2F4 SRT2F4 SRT2F5 CRTlFl
Fig. 58d--Construction diagram of Fig. 58a
As shown in Figure 58d, Multivariant 1 is composed of
four variants (top left), which form the configuration of
one variant in juxtaposition with two overlapped SRT2F4
couplings (center left) . Multivariant 2 consists of four
variants (top right), which overlap to form three couplings,
which in turn overlap (center right). Both multivariants
are juxtaposed to form the second example of CCxLM
(bottom).
75
I1 A
Fig. 59--Mouvement, measures 97-103
HL41
Fig. 59a--Melodic extraction of Fig. 59
Fig. 5 9b--Multivariant 1 extracted from Fig. 59a
Uzir
TV
71
II'
SRT2F4 Var. 17
SRT2F4 Var. 18 ar. 30
Fig. 5 9b(i)--Couplings and variants foundiant 1 (Fig. 59b).
in Multivar-
As shown in Figure 59b(i) , Multivariant 1 (Figure 59b)
consists of a single variant in juxtaposition with two over-
lapped couplings which aremade from three variants. Both
couplings are SRT2F4 couplings.
Fig. 59c--Multivariant 2 extracted from Fig. 59a
SRT2F5 Var. 9 Motive
Fig. 5 9 c (i)--Coupling and variants extracted fromMultivariant 2 (Fig. 59c).
76
Var. 1R
9E PF
MP IfI,.
Var. 2 0
+
77
As shown in Figure 59c(i), Multivariant 2 (Figure 59c)
consists of an SRT2F5 coupling.
A construction diagram of Figure 59a is shown in
Figure 59d.
MultivariLant _tt-ariant 2Var. 17 Var. 30 Motive
Var. 20 Var. 18 Var. 9
SRT2F4 SRT2F4 SRT2F5
Var. 18
Fig. 59d--Construction diagram of Fig. 59a
As shown in Figure 59d, Multivariant 1 is composed of
four variants (top left) which form the configuration of one
variant in juxtaposition with two overlapped SRT2F4 coup-
lings (center left). Multivariant 2 consists of two
variants (top right) which overlap to form one SRT2F5
coupling (center right). Both multivariants are juxtaposed
to form the third and final example of CCxLM (bottom).
78
Although the above melodies differ slightly from each
other in variant makeup and construction, they are similar
in contour, as shown in the contour graphs found in
Figures 60, 61 and 62.
9
e
d
b
i
Fig. 60--Contour graph of melody found in Fig. 57a
e
d
b
a
Fig. 61--Contour graph of melody found in Fig. 58a
79
e
Fig. 62--Contour graph of melody found in Fig. 59a
As shown in Figures 60, 61 and 62, all three of the
CCxLM examples are of similar contour, although they differ
slightly in intervallic content.
Each of the variants found in CCxLM is shown in
Table VIII.
TABLE VIII
VARIANTS FOUND IN CCxLM ACCORDING TO INDIVIDUAL USE
Variant Type Number of Statements
Motive Primary Group II 5
9 Primary Group I 1
16 Primary Group 1 1
17 Primary Group II1
18 Primary Group I 3
20 Primary Group I 326 Primary Group III
28 Primary Group II 329 Primary Group I 430 Primary Group II1
4i
80
Table VIII lists each of the variants found in CCxLM,
in numerical order with its categorization by group and
frequency of use. Percentages of use by group are shown
in Table VIIIA.
TABLE VIIIA
PERCENTAGE OF VARIANT USE BY TYPE AS FOUND IN CCxLM
Percentage Number of Percentage ofType Quantity of Quantity Statements Statements
Primary 5 50 12 5.220Group I
Primary 5 50 11 4.785Group II
Table VIIIA shows each of the variant types, followed
by the quantity of different variants within that type, the
number of times each type is stated and respective percen-
tages. Further statistics are found in Table VIIIB.
TABLE VIIIB
PERCENTAGE OF SINGLE AND COUPLING USAGEOF VARIANTS AS FOUND IN CCxLM
Usage Percentage
Singly. ...........-.-...-.-.-........ 8.7In couplings. .................-.-. ..... 91.3
81
Table VIIIB, which shows the collective percentages of
single and coupling usages, is based on the collective num-
ber of statements in Table VIIIA. Statistics concerning
couplings are found in Table IX.
COUPLINGS FOUND
TABLE IX
IN CCxLM ACCORDING TO INDIVIDUAL USE
U))
4u metriar M0 -
4-) 4-) (U4 ) 0ci
68-7:i0 I nvHr-
ci)rd( 054- _ U
0Ur)(00 ( 0 ) Orq
2 Movement 20 Primary M3 up Retro- CR 2 13.3ms. 67-69 Group ICm up grade TlFl
68-70Inver-28 Primary m2 up sions
Group II M3 up
o0 Primryd2 0 sins ~ Hci-
3 Mouvement 28 Primary m3 up Inter- SR 2 13.33ms. 68-69 Group II M2 up vallic T2F490-91
29 Primary M2 upGroup I m3 dn
_--I-Ins 869Gop I 2 p al i T2F
Movementms. 60-7071-7291-92
29
Motive
PrimaryGroup I
PrimaryGroup II
M2m3
m3M2
updn
dndn
Inter- SRvallic T2F4
4 26.664
82
TABLE IX--Continued
UU)
04 0
Q) H
_P >11 oe
Cl)0 0r_4U)4-3 r-1) OU)Q
> > P4
5 kMouvement Moti ve Primary m3 dn Semi- SR 2 13. 33ps. 71-73 Group II M2 d inter- T2FU
93-95 vallic
18 Primary M2 up
Group I M3 dn
6 Mouvem 18 Primary M2 up Retro- CR 1 6 66ms. 94-6 Group I M3 dn grade 0TlF
Inver-
26 Primary M3 dn sions
Group III M2 up
7 Movement 17 Primary M3 up Inter- SR 2 6.66ms. 98-99 Group II M2 up vallic T2F4
18 Primary M2 upGroup I M3 dn
8 Movement 18 Primary M2 up Inter- SR 1 6.66Ms. 99- Group I M3 dn vallic T2F4100
30 Primary M3 dnGroup II M2 dn
9 Movement 9 Primary m2 dn Semi- SR 1 6.66Ms. 101- Group I m3 dn inter- T2F5103 vallic
Motive Primary m3 dnGroup II M2 dn
8 Mouvemen 18 rmr 2u ne- SR 1 .6
In Table IX, each of the couplings is listed in the
order in which it was discussed. With each coupling, the
places it occurs, variant numbers, types, formulas and
83
relationships are given. In the final three columns, the
couplings' types, numbers and percentages of times used
are given respectively. A statements of these statistics is
given in Table IXA.
TABLE IXA
TOTAL SUMMARY OF COUPLINGS FOUND IN CCxLM
Coupling Percentage Number of Percentage ofType Quantity of Quantity Statements Statements
CRTlFl 3 33.3 4 26.66SRT2F4 4 44.4 8 53.33
SRT2F5 2 22.2 3 20.00
Table IXA is a summary of coupling usage as found in
CCxLM. With each type of coupling, its quantity and col-
lective number of statements are given with respective
percentages.
Disjunct Simple Linear Melody
Ten examples of disjunct simple linear melody were
discovered.
FE-
Fig. 63--Reflets dans l'eau, measures 29-30
84
L~J
Fig. 63a--Melodic extraction of Fig. 63
- RT2F3
Fig. 63b--Coupling and
Var. 31 Var. 19
variants found in Fig. 63a
Figure 63a is an illustration of disjunct simple linear
melody. The SRT2F3 coupling is shown in Figure 63b with its
variants. It appears in juxtaposition with the nonmotivic
Db. A construction diagram is shown in Figure 63c.
Var. 31Var. 19
Fig. 63c--Construction diagram of Fig. 63a
As shown in Figure 63c, the two variants (top) overlap
to form an SRT2F3 coupling and juxtapose with the nonmotivic
Db (bottom).
--- It L I
L Av DJUZ --IRV r. --
I I i
I
i F3
85
Fig. 64--Reflets dans l'eau, measures 59-60
Fig. 64a--Melodic extraction of Fig. 64
SRT2F4 Vr 20 Var, 21
Fig. 64b--Coupling and variants found in Fig. 64a
The melody in Figure 64 is composed of an SRT2F4 coup-
ling in juxtaposition with two nonmotivic notes. The theme
is repeated in Reflets dans l'eau, measures 61-62. A
construction diagram is shown in Figure 64c.
Var. 20
Var. 21C Cb
SRT2F4CCb
Fig. 64c--Construction diagram of Fig. 64a
I
86
As shown in Figure 64c, the variants (top) overlap to
form an SRT2F4 coupling and juxtapose with the nonmotivic
c and c-flat (bottom).
Fig. 65--Reflets dans 1'eau, measures 65-66
Fig. 65a--Melodic extraction of Fig. 65
SRT2F4 Var. 32 Var. 33
Fig. 65b--Coupling and variants found in Fig. 65a
The melody found in Figure 65a is identical in con-
struction to the theme found in Figure 64a. A construction
diagram is shown in Figure 65c.
87
Var. 32
Var. 33D# C#
SRT2F4 D# C#
Fig. 65c--Construction diagram of Fig. 65a
As shown in Figure 65c, Variants 32 and 33 overlap to
form an SRT2F4 coupling which is juxtaposed with the non-
motivic D3 and C-sharp.
Fig. 66--Reflets dans l eau, measures 57-59
31 F3 '7
Fig. 66a--Melodic extraction of Fig. 66
RA B
88
SRT2F4 Var. 20 Var. 21
SRT2F2 Var. 6
Fig. 66b--Couplings and variants found in Fig. 64a
Figure 66a consists of couplings and a multivariant
which are joined by a nonmotivic note (c'). A construc-
tion diagram is shown in Figure 66.
Var. 20 Var 3 4 1ar.3Var. 21 Var. 6
C
SRT2F4 C CRTlF1 SRT2F2
LIT'J, LLFig. 6 6 c--Construction diagram of Fig. 66a
89
As shown in Figure 66a, the first two variants (top
left) overlap to form an SRT2F4 coupling (center left).
The multivariant (top right) forms two couplings, a CRTlFl
coupling and an SRT2F2 coupling, respectively (center
right). The melody is formed by juxtaposing the SRT2F4
coupling with the nonmotivic c' which is, in turn, juxta-
posed with the multivariant (bottom).
The contours of the themes shown in Figures 63 through
66 are shown in Figures 67 through 70.
C
Fig. 67--Contour graph of DSLM found in Fig. 63a
Eb
DbCCbBb
Fig. 68--Contour graph of DSLM found in Fig. 64a
Fig. 69--Contour graph of DSLM found in Fig. 65a
90
Eb
IDI
C
G
F
Bb
Fig. 70--Contour graph of DSLM found in Fig. 66a
As shown in Figures 67 through 70, the melodies found
in Figures 63a through 66a are of similar contour. Figure
70 shows the first half of the melody found in Figure 66a
to be of a contour similar to those of the three preceding
examples.
Fig. 7 1--Hommage a Rameau, measures 7-8
Fig. 71a--Melodic extraction of Fig. 71
91
Var. 34 Var. 34 Va
Fig. 71b--Variants found in Fig. 71a
The melody shown in Figure 71a contains three variants,
the first two of which are juxtaposed. The second variant
is juxtaposed with three nonmotivic notes (b, c-sharp,
d-sharp), which in turn are juxtaposed with the third var-
iant. The third variant is juxtaposed with one nonmotivic
note (d-sharp2). A construction diagram is shown in Figure
71c.
Var. 34 Var. 34 Var. 36
D# G# B C# D# D# D#
Fig. 71c--Construction diagram of Fig. 71a
Fig. 7 2--Hommage a Rameau, measures 38-39
Fig. 72a--Melodic extraction of! Fig. 72
92
RR Var. 1 --- r---
Fig. 7 2b--Coupling and variants found in Fig. 72a
Figure 72a illustrates a theme in which a nonmotivic
note is juxtaposed with a remotely related coupling. This
theme reappears in Hommage a-Rameau in measures 40-41, 41,
41-42, 47, 66-67, 69, 70, 72 and 74. A construction dia-
gram is shown in Figure 72c.
Var. 1
Var. 7
F#
RR
Fig. 7 2 c--Construction diagram of Fig. 72a
Fig. 73--Hommage a Rameau,. measure 43
Fig. 73a--Melodic extraction of Fig. 73
93
RR Var. 1 Var. 7
CRTl'l Va_ 7 Var. 37
Fig. 73b--Couplings and variants found in Fig. 73a
Figure 73a illustrates a theme in which a nonmotivic
note is juxtaposed with a remotely related coupling which is
overlapped with a CRTlFl coupling. This theme appears again
in measures 44, 45 and 46 of Hommage a Rameau. A construc-
tion diagram is shown in Figure 73c.
Var. 1 Var. 37
Var. 7
A
A RR CRTlFl
Fig. 73c--Construction diagram of Fig. 73a
94
~;AE~ir
Fig. 74 --Hommage .Rameau, measure 48
Fig. 74a--Melodic extraction of Fig. 74
Ivar 38 Var. 39
Var. 39 Var. 40
Fig. 74b--Couplings and variants found in Fig. 74a
Figure 74a illustrates a theme in which a nonmotivic
note is juxtaposed with a remotely related coupling which
is overlapped with a CRTlFl coupling. The variants in the
0 K-- -_ _ _ _ _I.RR
-- I
95
CRTlFl coupling are retrograde inversions of one another by
reason of enharmonics. Both the augmented fourth in Variant
44 and the diminished fifth in Variant 45 are tritones.
This theme appears again in Hommage a Rameau, measures
49 and 50. A construction diagram is shown in Figure 74c.
Var. 38 Var. 40
Var. 39 W iB
Ll FB RR CRTlFl
Fig. 74c--Construction diagram of Fig. 74a
Fig. 75--Mouvement, measures 30-31
Fig. 75a--Melodic extraction of Fig. 75
96
Var. 37
Fig. 75b--Variant found in Fig. 75a
Figure 75 contains an example of a disjunct simple
theme in which a nonmotivic scale passage appears in jux-
taposition with a Primary Group I variant. This theme
recurs in Mouvement, measures 32-33, 38-39, 40-41, 140-
141, 142-143, 148-149 and 150-151. A construction diagram
is shown in Figure 75c.
ar. 37
G F E
Fig. 75c--Construction diagram of Fig. 75a
KpFig. 76--Mouvement, measures 78-80
Fig. 76a--Melodic extraction of Fig. 76
97
CRTlFl a.2
Fig. 7 6 b--Coupling and variants found in Fig. 76a
Figure 76a illustrates a nonmotivic scalewise passage
in juxtaposition with a CRTlFl coupling. - A construction
diagram is shown in Figure 76c.
Var. 20
J J, J Var. 28G# F# E D#
Fig. 7 6 c--Construction diagram of Fig. 76a
As shown in Figure 76c, the two primary variants (top
right) overlap to form a CRTlFl coupling which is juxta-
posed with the nonmotivic scalewise passage (bottom).
Statistics on the use of variants in disjunct simple
lineal melody are shown in Table X4
98
TABLE X
VARIANTS FOUND IN DSLM ACCORDING TO INDIVIDUAL USE
Variant Type Number of Statements
1 Secondary 14
6 Primary Group IV 1
7 Primary Group III 14
19 Primary Group II 1
20 Primary Group I 4
21 Primary Group II 3
28 Primary Group II1
31 Primary Group 1 1
32 Primary Group I1
33 Primary Group II 1
34 Primary Group I 3
35 Primary Group I 1
36 Primary Group I 1
37 Primary Group I 12
38 Secondary 3
39 Primary Group III 3
40 Primary Group I 3
Table X lists each of the variants in DSLM in numer-
ical order with its categorization by group and frequency
of use. Percentages of use by group are given in Table XA.
99
TABLE XA
PERCENTAGE OF VARIANT USE BY GROUP AS FOUND IN DSLM
Percentage Number of Percentage ofType Number of Number Statements Statements
Primary 8 47.04 26 38.74Group I
Primary 4 23.52 6 8.94Group II
Primary 2 11.76 17 25.33Group III
Primary 1 5.88 1 1.49Group IV
Secondary 2 11.76 17 25.33
Table XA shows each of the variant types, followed by
its quantity, number of statements and respective percen-
tages. Further statistics concerning couplings are shown
in Table XB.
TABLE XB
PERCENTAGE OF SINGLE AND COUPLING USAGEOF VARIANTS AS FOUND IN DSLM
Usage Percentage
In couplings...... . . . . . . . . . . . . . . . 16.39Singly.. ...-.-.. . . . . . . . . . . . . . . . . 83.44
Table XB, which shows the collective percentage of
single and coupling usage, is based on the collective
number of statements in Table XA.
Further coupling statistics are shown in Table XI.
100
TABLE XI
COUPLINGS FOUND IN DSLM ACCORDING TO INDIVIDUAL USE
Cl)(2) 4-4lo L0a) Q4>-
'ea4 GrorIi-rICdE-' LP a~C) t;)-3 U atlli0 rdUE
4-s.4)59-6-)0,
Cl) P -PCd -0,q I-JH Cl)Cd(d d4J H (DU)ca)U
-H4-H -H(d Q Q a) C 1
61-6 21Pri4ry 3 u
1 Reflets dans 31 Primary m2 up Semi- SR 1 3.1251'eau, Group I M3 up inter- T2F3ms. 29-30 va66ic
19 Primary M3 upGroup II M2 dn
2 Reflets dans 20 Primary M2 up Inter- SR 3 9.375l'eau, Group I m3 up vallic T2F4ms. 59-60,61-62 21 Primary m3 up
Group II M2 dn
3 Reflets dans 32 Primary m2 up Inter- SR 1 3.1251'eau, Group I m3 up vallic T2F4ins. 65-66
33 Primary m3 upGroup II m2 dn
4 Reflets dans 34 Primary M2 up Retro- CR 1 3.1251'eau, Group I P5 dn grade TiFiins. 58 Inver-
6 Primary P5 dn sionsGroup IV
Reflets dans1'eau,ms. 58-59
6
35
PrimaryGroup IV
PrimaryGroup I
P5 dnM2 up
M2 upM6 dn
Pri-
maryVar-iants
SRT2F2
1 3.1255
101
TABLE XI--Continued
CiU)Q)) En) O)4-1
a) 040(1) 10H
4amauE-s38r-Pa)4rdd - 41E-,44-2-,a) 4a)
7 ma 7 Priar d Otr0 C )d 412n39 H 41-H0 -Hvr
H8l,44)(39)PrimryHA4a)
o~ Md C 0 Mda 0 ::j H a) -H
6 Hommage 1 Secondary P5 up Remote RR 14 43.750Rameau, ms.38-9 P4 dn40-1,41,41-2,4344,45,46,47,66- 7 Primary P4 dn67,69,70,72r74 Group II M2 dn
7 Hommagen 27 Primary P4 dn Retro- CR 4 12.500Rameau, is. 38- Group III M2 dn grade TlFi39,40-41,41, Inver-41-42,47,66- 37 Primary M2 dn sions67,69,70,72,74 Group I P4 dn
8 Hommage a 38 Secondary A5 up Remote RR 3 9.375Rameau, ins. A4 dn48, 49, 50
39 Primary A4 dnGroup III m2 dn
9 Hornmage a 39 Primary jA4 dn Retro- CR, 3 9.375Rameau, ins. Group ITT m2 dn grade TiFi48, 49, 50
40 Primary m2 dnGroup I P5 dn
10 Mouvement, 20 Primary M2 up Retro- CR 1 3.125ins. 79-80 Group I m3 up grade TiFi
Inver-28 Primary m3 up sions
Group II M2 up
102
In Table XI, each of the couplings is listed in the
order in which it was discussed. With each coupling, the
places it occurs, variant numbers, types, formulas and
relationships are given. In the final'three columns, the
couplings' types, numbers and percentages of times used
are given respectively. A summary of these statistics is
given in Table XIA.
TABLE XIA
TOTAL SUMMARY OF COUPLINGS FOUND IN DSLM
Percentage Number of Percentage ofType Quantity of Quantity Statements Statements
CRTlFl 4 40.0 9 28.125
SRT2F2 1 10.0 1 3.125
SRT2F3 1 10.0 1 3.125
SRT2F4 2 20.0 4 12.500
RR 2 20.0 17 53.125
Table XIA is a summary of coupling usage as found in
DSLM. With each type of coupling, its quantity and collec-
tive number of statements are given with respective
percentages.
103
Disjunct Compound Linear Melody
Two examples of disjunct coupound linear melody were
found.
Fig. 77--Reflets dans l'eau, measure 14
Fig. 77a--Melodic extraction of Fig. 77
CRTlF1 Var. 3 Mot v
CRTl Fl Var. -3-- motive
Fig. 77b--Couplings and variants found in Fig. 77a
Two CRTlFl couplings, shown in Figure 77b, were found
in the melody shown in Figure 77a. A construction diagram
is shown in Figure 77c.
104
Var. 3 Var. 3
Motive Motive
CRTlFl CRTlF1
Fig. 77c--Construction diagram of Fig. 77a
As shown in Figure 77c, the variants (top) overlap,
forming two CRTlFl couplings (center). The couplings are
superimposed (bottom), forming the scalewise melody in
Figure 77a.
Fig. 78--Hommage a Rameau, measures 14-17
S 133
I4gI U
S
Fig. 78a--Melodic extraction of Fig. 78
e ~g w F Tf alr.1 -
SRT2F5 Motive Var, 8
CRTlF2 Var. 18 Var. 19
CRTlFl Va r. 3 Motive
SRT2F5 Motive Var,8
I-s F im-se i 1. IF . U l .mi m. a mf W, W mi ligmo-U"ei. .m -in i
CRTlF2 Var. 18 Var. 19
F ig. 78b--Couplings and variants found in Fig. 78a
105
, 9 - - 1, - -
471
I I,- .1.
I I I
j
-
ri4-)
Co
E t
Erd
co rd>
gr-'): 10
106
CN
Cl)
LI)
p
00
r4
"H
0c
0
0
Ei
0)(H
J
0
0Cl
00
Figure 78c illustrates the nine variants (top) which
form the couplings (middle) contained in the second example
of DCLM (bottom). The nonmotivic notes are interspersed.
Statistics on variants found in DCLM are shown in
Table XII.
107
TABLE XII
VARIANTS FOUND IN DCLM ACCORDING TO INDIVIDUAL USE
Variant Type Number of Statements
Motive Primary Group II 5
3 Primary Group I 4
18 Primary Group I 2
19 Primary Group II 2
Table XII illustrates the individual use of variants in
DCLM. Further variant statistics are shown in Table XIIA.
TABLE XIIA
PERCENTAGE OF VARIANT USE BY GROUP AS FOUND IN DCLM
Percentage Number of Percentage ofType Number of Number Statements Statements
Primary 2 50 6 46.14Group I
Primary 2 50 7 53.83Group
II
All variants used in DCLM are primary variants used in
couplings.
Statistics on couplings found in DCLM are shown in
Table XIII.
108
TABLE XIII
COUPLINGS FOUND IN DCLM ACCORDING TO INDIVIDUAL USE
H PmPae aancerfd z ) ) oa
ms. 1-7 G0uWIIM2 d
Ramau GruZI 2d vali T2F5 Oic
Wms.-14-017Dr-4 Z44 ) rd)U) ) 0
-H4-H-H rd 0-1 .Qca) Oc0)ci) $ 4 A4-4 -o Cd C(d 0 Mdca) 0 V- i
1 Reflects dans 3 Primary M2 dn Retro- CR 4 50l'eau, ins. 14 Group I m3 dn grade TIFiHommage a Inver-Rameau, Motive Primary m3 dn sionsins. 14-17 Group II M2 dn
2 Hommage a Motive Primary m3 dn Inter- SR 2 25Rameau, Group II M2 dn vallic T2F5ms. 14-17
18 Primary M2 upGroup I M3 dn
3 Hommage a 18 Primary M2 up Retro- CR 2 25Rameau, Group I M3 dn grade T1F2ins. 14-17
19 Primary M3 upGroup II M2 dn
In Table XIII, each of the couplings is listed in the
order in which it was discussed. With each coupling, the
places it occurs, variant numbers, types, formulas and
relationships are given. In the final three columns, the
couplings' types, numbers and percentages of times used
are given respectively. A summary of these statistics is
given in Table XIIIA.
109
TABLE XIIIA
TOTAL SUMMARY OF COUPLINGS FOUND IN DCLM
Percentage Number of Percentage ofType Quantity of Quantity Statements Statements
CRTlF1 1 33.3 4 50
SRT2F5 1 33.3 2 25
CRTlF2 1 33. 3 2 25
Table XIIIA is a summary of coupling usage as found in
DCLM. With each type of coupling, its quantity and collec-
tive number of statements are given with respective
percentages.
Disjunct Complex Linear Melody
Four examples of disjunct complex linear melody were
found.
Lent et graVe(dan ie stye., d'ul Sarabnande rmais sans rigueur. -
pp 'x j~.i detdoucment soutenu
Fig. 79--Hommage aRameau, measures 1-5
110
3
3
I I t 3
Fig. 79a--Melodic extraction of Fig. 79
Fig. 79b--Multivariant 1, extracted from Fig. 79a
SRT2F2 Var. 13 Var. 3
CRTIF1 Var. 3 Motive
CRTlF2 Motive Var. 20
CRTlF1 Var. 20 Var. 28
CRTlFi Var. 28 Var. 20
SRT2F3 Var. 20 Var. 33
CR lFl Var. 33 Va r. 41
Fig. 79b(i)--Couplings and variants found in Multivar-iant 1 (Fig. 79b).
I . ii
Imele mslte l As ltsspsiesr- - - --
11 11 III -liggil i-II Mmmm.I 1 mga IIJ II III 1 II | 111 .L ---.- -1 -Jr ----- - - -11 i - I 1-' UI I -I I tini.g lim pgpi pg|,
3
-000
111
TI T #JE4
Fig. 79c--Multivariant 2, extracted from Fig. 7 9a
SRT2Fl Var.I 9 Var.2
SRT2Fl Var. 12 Var "8
Fig. 7 9 c(i)--Couplings and variants found in Fig. 79c
Fig. 79d--Multivariant 3, extracted from Fig. 79a
CRT1F1 Var. 42 Var. 9 SRT2Pl Var. 9 Vr 12
SRT2Fl Var. 12 Var. 18SRT2F5 Var. 18 Motive
CRTF_1 Motive _ Va r. 3 _ C RT I F I Var. otiv
Fig. 7 9d(i)--Couplings and variants found in Multivar-iant 3 (Fig. 79d).
1 di I 1 1 - - - - -til illMit il li 11 1 1
112
The above melody (repeated in Hommage a Rameau, mea-
sures 26-30 and 57-61) contains fifteen couplings made up
of eighteen primary variants. A construction diagram is
shown in Figure 79e.
10 0
EC
E3r-c3
-4
Eg ro
~E
E CEr.-
113
For the sake of space, the labeling of variants and
couplings in Figure 790 is abbreviated. The motive is la-
beled M, and each variant by its number only. A closely
related Type 1 coupling is indicated by C followed by a
number which indicates its form. A semirelated Type 1
coupling is indicated by S followed by a number which in-
dicates its form.
Fig. -- ~~~s s -1
Fig. 80--Hommage & Rameau, measures 10-13
3 -K
3 3 3
Fig. 80a--Melodic extraction of Fig. 80
+--7711 016 1 IT IW
114
Fig. 80b--Multivariant 1, extracted from Fig. 80a
SRT2F2 Var. 33 Va 3
CRTlpl lar. 3 Notive
T Motive Var 20
CRTIFI Var. 20 Var. 28
CRT1F1 Var. 28 Var. 20
4F
SRT2F4 Var. 20 Var. 21
SRT2F!. Var.'21 Var. 25
SRT2 F5 Var 25 Var. 33
CR Var. 33 Var41
Fig. 80b(i)--Couplings and variants found in Fig. 80b
Fig. 80c--Multivariant 2, extracted from Fig. 80a
115
SRT2FT2 Var. 9 Var. 12
SRT2F T Var 12 Mar va
Fig. 80c(i)--Couplings and variants found in Fig. 80c
Fig. 80d--Multivariant 3., extracted from Fig. ra
CRTIFh Var. 42 Va. 9
S RT2FI Var. 9 Var. 12
SRT2Fl Var. 12 Var. I
SRT2F5 Var. 18 Motive
M2tive V 43
Fig. 80d (i) -- Couplings and variants found in Fig. 80d
The above melody consists of sixteen couplings made up
of nineteen primary variants. A construction diagram is
shown in Figure 80e.
116
13rM ,M 28Mi~ n1 L3~W- U O 4 2J3M5 DTlM
A# D# F#A#
42 r1 2 M M m9L L1 8 U 4 3
S2 Cl C2 Cl ClS4 Sl S5 ClA#Sl Sl8D# F# A#
Cl Sl Sl S5 S4
Fig. 80e--Construction diagram of Fig. 80
Because of the largeness of the above diagram, Figure
80e has been divided into three principal sections. The
first and second multivariants are shown on the top line,
divided into single variants; and the third multivariant is
similarly shown on the second line. The coupling divisions
are shown in the same manner on the third and fourth lines.
The bottom line of the diagram shows the complete construc-
tion of the theme.
The melodies shown in Figures 79a and 80a are similar
in contour, coupling/variant content and construction. The
second multivariants of both themes are identical, and the
coupling/variant content and construction of the first and
117
third multivariants of both themes vary only slightly. (See
Figures 79e and 79e.) Similarities and differences in con-
tour of the melodies are shown in Figures 81 and 82.
C#w
BAW
G#
ED#
-a --s re4 $/B
F#
B
G#
F#
ED#
C #
Fig. 81--Contour graph of melody found in Fig. 79a
118
C
A
Gf
,F* -
B
F#
D #
Ct
B
A#
F#
Fig. 82--Contour graph of melody found in Fig. 80a
Each of the above graphs is divided into three phrases.
Each phrase contains a multivariant and the nonmotivic note
which follows it, where applicable.
119
iJ s
1 1o
F. 8--omag Rpeumesues172
- . .. - ...
7.... C 7
Fig* 83 Hommage a Rameau, measures 17-24
-T- A- .1--it ----
I14
0--APT-T -L--,A It -_ TI="-
Fig. 83a--Melodic extraction of Fig. 83
- ~ ~ ~ ~ J ER 2 ~I -tH-- 4
ILL
w
120
I-F
Fig. 83b--Multivariant 1, extracted from Fig. 83a
frV
SRT2F2 Var. 44- Var.-45
Var. 44
Fig. 83b(i)--Coupling and variants found in Fig. 83b
Fig. 83c--Multivariant 2, extracted from Fig. 8 3a
SRT2F FVar.Var.46
Fig. 83c(i)--Coupling and variants found in Fig. 83c
Fig. 83d--Multivariant 3, extracted from Fig. 83a
r 10, i i - - d 0
IL - --. a
7114 w jpw w
i
121
CRTlF1 Var. Z20 -Var. 28
CRT1F1 Var. 28 Var. 20
~~~~T~lF Var 20 Motive
Motive Var. 20
C I~lVr.2 Var. 28.
Fig. 83d(i)--Couplings and variants found in Fig. 83d
The melody in Figure 83a contains a single variant,
which is primary, and seven couplings consisting of ten
primary variants. A construction diagram is shown in
Figure 83e.
W 45W JWU 4 6 J JJJ 2 8 WUMW8G E G#F#G#AG# G#
GS2 E S5 G# F# G# A-G# Cl Cl C2 C2 C1G#
WJLLLJJLiP" JMIFig. 83e--Construction diagram of Fig. 83a
122
oamncer u pai!Id u OU 1N
4-®r- -w -
pp
Fig.o 84--Hommage a Rameau, measures 3 - 3 7
\j it/
Old
Fig. 84a--Melodic extraction of Fig. 84
Fig. 84b--Multivariant 1, extracted from Fig. 84a
123
eSRT2F3, Var. 14 Var. 15
SRT2F3 Var. 15 Var. 27
SRT2F2 Var. 27 Va r. 10
CRTlFl Var. 10 Var. 11
Fig. 84b(i)--Couplings and variants found in Fig. 84b
i
Fig. 84c--Multivariant 2, extracted from Fig. 84a
* i oA6 11 40
SlRT 2F4 Var. 20 Var. 21
Fig. 84c(i)--Coupling and variants found in Fig. 84c
Fig. 84d--Multivariant 3, extracted from Fig. 84a
A AL -4 .- --- . - - I - -I- I --= rdr- *-," IF = W a
Ar.
I
tJH
11 Cr5II>
Cd
H
4ti
*1N
CNE-4)
17
>1
H
C")
HE-
~ii
IM
q:1
co
124
ri%~'t -)
0
%BL&l,40r-- a)
>
4-30
Cd
H
H
j1 TV~
--U'*F
A'4 r.I CdI>
rd
00
'H
I
'H
04-
EH
.H
I ( .
PnA
mv-
Cdl
fii4-) H'
PrHH-
LO,
ii
-44P4
I I
I I
4-
'00
-4
I
CN
E-4
125
The melody in Figure 84a contains sixteen couplings
consisting of eighteen primary variants and one secondary
variant.
A diagram of the melody's construction is shown in
Figure 84e.
E
< r-4 C
E0
- Ii
33 L
EHE
4-)
CT:j 14= 0Ww
E0
126
Statistics on variants found in DCxLM are shown in
Table XIV.
TABLE XIV
VARIANTS FOUND IN DCxLM ACCORDING TO INDIVIDUAL USE
Variant Type Number of Statements
Motive Primary Group II 143 Primary Group I 99 Primary Group I 8
10 Primary Group I111 Primary Group IV 112 Primary Group II 813 Primary Group III 414 Primary Group III 215 Primary Group I 216 Primary Group I118 Primary Group I 920 Primary Group I 1221 Primary Group II 225 Primary Group I127 Primary Group III 228 Primary Group II 633 Primary Group II 441 Primary Group I 442 Primary Group II 443 Primary Group I144 Primary Group III 245 Primary Group I146 Primary Group II147 Secondary 148 Primary Group I149 Primary Group V 150 Primary Group I1
Table XIV lists each of the variants in DCxLM in numer-
ical order with its categorization by group and frequency of
use. Percentages of use by group are given in Table XIVA.
127
TABLE XIVA
PERCENTAGE OF VARIANT USE BY GROUP AS FOUND IN DCxLM
Percentage Number of Percentage ofType Quantity of Quantity Statements Statements
Primary 13 48.1 51 49.47Group I
Primary 7 25.9 39 37.83Group II
Primary 4 14.8 10 9.70Group III
Primary 1 3.7 1 .97Group IV
Primary 1 3.7 1 .97Group V
Secondary 1 3.7 1 0.97
Table XIVA shows each of the variant types, followed
by its quantity, number of statements and respective per-
centages. Further statistics concerning variants are
shown in Table XIVB.
TABLE XIVB
PERCENTAGE OF SINGLE AND COUPLING USAGEOF VARIANTS AS FOUND IN DCxLM
Usage Percentage
In couplings.. ....... . . . . . . . . . . . . . 98.94Singly....................... .. 0.97
Table XIVB is based on the collective number of state-
ments in Table XIV. Table XIVC follows.
128
TABLE XIVC
PERCENTAGE OF PRIMARY AND SECONDARYVARIANTS FOUND IN DCxLM
Type Percentage
Primary. ....... ........ 98.94Secondary............. ........ ......0.97
Table XIVC is based on the collective number of state-
ments found in Table XIVA. Coupling statistics are shown
in Table XV.
TABLE XV
COUPLINGS FOUND IN DCxLM ACCORDING TO INDIVIDUAL USE
H) ri 4i 0)W9 04)04-) > E4 rc$ a) roM z t4-40) ty0) a
4-) 0toyO 0Oto Cfat(En 4-) 4J-P4J 0-I0JO D 4J )
0Hr1 0H -H r.H__ 0) Cd d :jd 4-) H )to a)tEn
, , H26,r aH-) 00)0: ) PP ::$ r. P r:o rd Cd 0 Cd0) 0 H a) H
>U r U Z H PHomma-ge 13 Primary P4 upiPri- SRA T4,444
Rameau, ins. Group III M2 dn mary T2F21, 10, 26, Var-51 3 Primary M2 dn iants
Group I m3 dn2 Hommage a 3 Primary M2 dn Retro- CR 9 9.999
Rameau, Ms. Group I m3 dn grade TlFl1,10,26,57, Inver-4-5,29-30 , Motive Primary m3 dn sions60-1,36-7,37 1_ Group II M2 dnL__ ________I_--_I
Hommage aRameau, ms1, 10, 26,51, 22-23
MotiveI
20
PrimaryGroup II
PrimaryGroup I
m3 dn Retro- CRM2 dn grades TlF2
M2 upm3 up
5 15.5553
129
TABLE XV- -Continued
Rameu, s. GoupI m3u4.rad 4TlF
5 ( H::1ge >1 Pi4ryP3 urRtraCR) 555
cr 4- z P4-4 0 U) ar-4 U) t)yc) 0 (n M U
wci)-) 4) 00 04J
I- 2,10 -1,0Ive r6-27,5a - 200riary M2 p son
57>21ru I m3 cur6 omag Z2 PrHr M2 p m- R 3. 333
U) OJ -) O4 ) (U0 rd 0
7 Homma-ge i 3H0Primary M3 up Retro- CR 4 4.444
Rame'au, ms . Group II m2 dn grade, TlFl12 -11 7, Inver -
8 7 5128 Primary m2dn sins
58, 22, 23Gro up II M3up
4 Hommage 2 Primary m2 up Retro- CR 6 6.666Rameau, ms. Group I m3 up grade T2Fl1-2, 10-11, Inver-26-27, 51- 28 Primary m3 up sions-58, 22 Group II M2 up
5 Hommage 28 Primary m3 up Seir- SR 5 5.5553Rameau, ms. Group II M2 up raer- T2Fi1-2, 12-, gae26-2, 56- 20 Primary M2 up inr
57, 22 Group I m3 up sins
86rHommage 20 Primary m2 up Semi- SR 3 3.333Rame'au, ins. Group I m3 up intr- T2F331-2, 262,gvadei56,28,33,12 Primary m3 dnup er
_________5___Group II M2 dnp ____ _______
9 Hornmage A3:3 Primary m3 up Retr- CR 4 4.444Rameau, ins. Group II M2 dnprer-TiFi2,1 1 127,Invde57 4, 9f 18 Primary M2 dnpinse
58, 59__ Group I M2 up sio ns___
Hommage aRameau, ms.4, 13, 29,60
42
9
PrimaryGroup II
PrimaryGroup I
m3 dnm2 up
m2 upm3 dn
Retro-gradeInver-sions
CRTlFl
4 4.44410
130
TABLE XV--Continued
U)
a a,0G u 3 a0
Gr>1p IIr2)dnCdz P 4-4L(1) UO0)
4aJau n.Mrop0I 20n rae w~
U)4 64j -er4-J04D
3 riar M0d s0n
HGrp Id H3)dnU)04H4 riH -H rd 0 ) 0a)
::0) 4 -i 4 -4r-4 0 _oa Cdd 0 rd a) 0 a- )-_H
11 Hommage 18 Primary M2 up Inter- SR 4 4.444Rameau, is. Group I M3 dn vallic T2F54113, 29,60 Motive Primary m3 dn
Group II M2 dn12 Hommage 2Motive Primary m3 dn Retro- CR 3 3.333
Rameau, ms. Group II M2 dn grade T2Fl41 29, 60 Inver-
3 Primary M2 dn sonsGroup I m3 dn
13 Hommage A 20 Primary M2 up Inter- SR 2 1.111Rameau, is. Group I m3 up vallic T2F410-11, 33-34 21 Primary m3 up
Group II M2 dn sins14 Hommage a 21 Primary m3 up Inter- SR 1 1.111
Rameau, is. Group II M2 dn vallic T2F110-11
25 Primary M2 dnGroup I M3 up
15Hominage a 25 Primary M2 dn Semi- SR 1 11111Rameau, ins. Group I M3 up retro- T2F511 grade
33 Primary m3 up Inver-Group II m2 dn sions
16 Hommage A Motive Primary m3 dn Inter- SR 1 111Rameau, ins, Group II M2 dn vallicIT2F413
43 Primary M2 dn____ ____ ___ ___ Group I m3 UPI_ _ _ _ _ _ _ _
Hommage ARameau, is.17-18
44
45
PrimaryGroup III
PrimaryGroup I'
P4 upM2 up
M2 upA5 dn
Pri-mnaryVaniants
SRT2F2
1 1.111171
131
TABLE XV--Continued
a a .o itr T2a)0) W 0
M E-46LOri-ary)MM a)
-P r.rty) En d E4-14- 4 0 r. ) O 0
H H gHiaryq2Ptr- CR 1H- 0)rd Cdrd4J r-1 (1HE E
HHtvrd Prmar)y 3a)o0dVd 0 a) 0_ _ _ _ _ _ _ _ _ _ _ U ZE 24
18 Hommage A 18 Primary M2 up Semi- SR 1 1.111Rameau, ms. Group I M3 dn inter- T2F519-20 vallic
46 Primary M3 upGroup II m2 up
19 Hommage a20 Primary M2 up Retro- CR 1 1.111Rameau, Ms. Group I m3 up grades T2F222
Motive Primary m3 dnGroup II M2 dn
20 Hommage 14 Primary P4 dn Semi- SR 2 2.222Rameau, ms. Group III m2 up inter- T2F331, 35 valic
15 Primary M2 upGroup I A4 up"
21 Hommage A 15 Primary m2 up Semr- SR 2 2.222Rameau, ms. Group I A4 up inter- T2F331-32, 35 vallic
27 Primary A4 upGroup III M2 dn
22Hommagea 27 Primary A4 up-Pri- SR 1Rameau, ins. Group III M2 dn mary T2F231-32 Var-
10 Primary M.2 dn iants- Group I _P5 up ___
23 Hommage a 10 Primary M2 dn Retro- CR 1111Rameau, ins. Group I P5 up grade TiFi32-33 Inver-
11 Primary P5 up sions__________ ______Group IV,- M2 dn,___ __ ___
IioLmage aRameau, ms.34-35
lb
47
PrimaryGroup I
Secondary
M2 upM3 up
M3 upP4 dn
Remote RR 13 1.1114~ "
132
TABLE XV--Continued
Co
343
4 riar 4dn0
4Gr-iII 2)up,s I En T2F2 DM OZU)
3 - V-ar-- M 4jO0 5 4-)- Hrr 24-Hdn-Hnt
27 Hommag e''a4 SecriaryM3 u2pdRet- C RR .RameaU,_Ms.Gr4Iu g
34-3514 Primary P4 dn
Group III m2 up26 Hommage 27 Primary A4 up Pri- SR 1 1.111
Rameau, ms. Group III M2 dn mary T2F235-36 Var-
48 Primary M2 dn iantsGroup I m6 up
27 Hommage a M48t Primary M2 dn Retro- CR 1 1.111Rameau, ms. Group I m6 up grade TlFl36-37 Inver-
49 Primary m6 up sionsGroup V M2 dn
28 Homage a o49 Primary m6 up Pri- SR 1 1.111Rameau, ms. Group V M2 dn mary T2F236-37 Var-
3 Primary M2 dn iantsGroup I m3 dn
29 Homage tMotive Primary m3 dn Retro- CR 1 1.111RamIneau, is. Group II M2 dn grade TlF237 Inver-
3 Primary M2 dn sions________ ___ Group I m3 dn
30 Hommage a Motiv7e Primary m3 dn Pri- SR 1 1.111Rameau, ins. Group II M2 dn mary T2F237-38 Var-
50 Primary M2 dn iantsGroup I IP5 dn _____
In Table XV, each of the couplings is listed in the
order in which it was discussed. With each coupling, the
places it occurs, variant numbers,, types, formulas and
133
relationships are given. In the final three columns, the
couplings' types, numbers and percentages of times used
are given respectively. A summary of these statistics is
given in Table XVA.
TABLE XVA
TOTAL SUMMARY OF COUPLINGS FOUND IN DCxLM
Percentage Number of Percentage ofType Quantity of Quantity Statements Statements
CRTlFl 8 26.6 33 39.237
CRT2F2 3 10.0 7 8.323
SRT2Fl 3 10.0 17 20.213
SRT2F2 6 20.0 9 10.701
SRT2F3 3 10.0 7 8.323
SRT2F4 2 6.6 3 3.567
SRT2F5 3 10.0 6 7.134
RR 2 6.6 2 2.378
Table XVA is a summary of coupling usage as found in
DCxLM. With each type of coupling, its quantity and collec-
tive number of statements are given with respective
percentages.
CHAPTER II
SUMMARY
The motive and fifty variants which were discovered
were found to be used three hundred twenty-four times. (See
Tables XVI through XXI.)
TABLE XVI
PRIMARY GROUP I VARIANTS ACCORDING TO INDIVIDUAL USE
2 d ,d H)4H *H N H (0)0r4
3o M0dnrdd 1 21 r%44 9 W
9 tmHp mOdn 3 2 0 0 H 14
0d a) (Uo 0 W 1dO cc0 U U ) U U 0
2 M2dnp43dn 4 0 0 0 0 0 0 0 0 43 M2dnm3dn 1 1 0 2 1 0 0 4 9 189 m2up m3dn 3 2 0 0 0 1 0 0 8 14
10 M2dnP5up 0 1 0 0 1 0 0 0 1 315 m2upA4up 0 1 0 0 1 0 0 0 2 416 M2upM3up 0 0 3 2 1 1 0 0 1 818 M2up M3dn 0 0 3 0 5 3 0 2 9 2220 M2up m3up 0 0 0 1 2 3 4 0 12 2223 M2dnd4dn 0 0 0 1 1 0 0 0 0 225 M2dnM3up 0 0 0 0 0 0 0 0 1 129 M2up m3dn 0 0 0 0 0 4 0 0 0 431 m2upM3up 0 0 0 0 0 0 1 0 0 132 m2upm3up 0 0 0 0 0 0 1 0 0 134 M2upP5dn 0 0 0 0 0 0 3 0 0 335 M2upM6dn 0 0 0 0 0 0 1 0 0 136 M2upP5up 0 0 0 0 0 0 1 0 0 137 M2dnP4dn 0 0 0 0 0 0 12 0 0 1240 m2dn P5dn 0 0 0 0 0 0 3 0 0 341 m2dn m3up 0 0 0 0 0 0 0 0 4 443 M2dn m3up 0 0 0 0 0 0 0 0 1 145 M2up A5dn 0 0 0 0 0 0 0 0 1 148 M2dn m6up 0 0 0 0 0 0 0 0 1 150 M2dn P5dn 0 0 0 .0 10010 0 10 1 1
134
135
TABLE XVII
PRIMARY GROUP II VARIANTS ACCORDING TO INDIVIDUAL USE
H. H- ,qa)r .HH " Ha)> rO rO aHra 4 4
0Hb) 4 - 0 ) H i4 -1 z X,1 Z,0d a)p0 a) CdO W6 0 UW U) u U U)U0
M m3dn M2dn 8 0 0 0 1 5 0 5 14 33
12 m3dn M2up 0 2 0 0 0 0 0 0 8 1017 M3up M2up 0 0 3 0 0 1 0 0 0 419 M3up M2dn 0 0 0 2 1 0 1 2 0 621 m3up M2dn 0 0 0 1 0 0 3 0 2 626 M3dn M2up 0 0 0 0 10 1 0 0 0 11
28 m3up M2up 0 0 0 0 2 3 1 0 6 1230 M3dn M2dn 0 0 0 0 0 1 0 0 0 133 m3up m2dn 0 0 0 0 0 0 1 0 4 542 m3dn m2up 0 0 0 0 0 0 0 0 4 446 M3up m2up 0 0 0 0 0 0 0 0 1 1
TABLE XVIII
PRIMARY GROUP III VARIANTS ACCORDING TO INDIVIDUAL USE
-p4
)ZH -H Q) H -HaJN H CNICd .0o o d 0 rZ r J " , zZ H
5 P4dnn2dn 2 0 00 0 WOO 0 27 P4dn(M2dn 1 1 0 0 0 0 14 0 0 16
13 P4dnM2dn 0 1 0 0 1 0 0 0 4 614 P4dn m2up 0 1 0 0 1 0 0 0 2 427 A4up M2dn 0 0 0 0 1 0 0 0 2 339 A4dn m2dn 0 0 0 0 0 0 3 0 0 344 P4dn M2up 0 0 0 0 0 0 0 0 2 2
136
TABLE XIX
PRIMARY GROUP IV VARIANTS ACCORDING TO INDIVIDUAL USE
o o 0 o M 0 PC
H M *H r:; H t *H) V,
-1 d 4J 4 (d 4J 4 0 4 1.4 XN 4 , I 40d 0 4 ()C0 $W4 d 0 uCl) C)u u toU u 0__r1444 J44 r1'4 4J N U U U u Q 04 d5up A2up 2 0 0 0 0 0 0 0 0 26 P5dn M2up 1 0 0 0 0 0 1 0 0 2
11 P5up M2dn 0 1 0 0 1 0 0 0 1 3
TABLE XX
PRIMARY GROUP V VARIANTS ACCORDING TO INDIVIDUAL USE
H, N:j roJQ r 0 o H
-a 0 W C-0 (V4Cd0 UaC o0ou u w U.U0> P-14-PF 4 ri -P-)P14 u U U, u C-) :1C:)q
49 m6up M2dn 0 0 0 0 0 0 0 0 1 1
TABLE XXI
SECONDARY VARIANTS ACCORDING TO INDIVIDUAL USE
H (~H -H (DrN H N
-o - I-J Hro d 40 F-N - 1 2 N :2:N -0 tp -H o tn r re o i i -q (Cd 0 (d 0 ()p ) r U U C U U 0
1 P5up P4dn 31 1 010 0 0 14 0 0 468 P4up m3dn 2 0 0 0 0 0 0 0 0 2
22 m3dn M3up 0 0 0 2 0 0 0 0 0 224 d4dn P4up 0 0 0 1 0 0 0 0 0 138 A5up A4dn 0 0 0 0 0 0 3 0 0 347 M3up P4dn 0 0 0 0 0 0 0 0 1 1
137
In Tables XVI through XXI, the use of each variant is
represented according to each form of melodic fragmentation
and linear melody. In the final column, the total number
of statements of each variant is shown.
The collective number of statements is shown by group
in Table XXII.
COLLECTIVE VARIANT
TABLE XXII
USAGE AND PERCENTAGE BY GROUP
0 0 33 .04o
riay1 2.15P-) . 3008
l::rlH -qr- q aHW(NHr-4 (N ~I0 0 tyCD-
Cdrd P )ro-u C u cT u u x______ 44CU U C)P.-ZC 0
Primary 8 5 6 6 12 12 26 6 51 132 40,656Group I
Primary 8 2 3 3 14 11 6 7 39 93 28.644Group II
Primary 3 3 0 0 3 0 17 0 10 36 11.088Group III
Primary 3 1. 0 0 1 0 1 0 1 3 2.156Group IV
Primary 0 0 0 0 0 0 0 0 1 1 .308Group V
Secondary 33 1 0 13 101 0 17 0 1 55 16.940
In Table XXII,
is shown according
the collective use of each variant group
to each form of melodic fragmentation and
linear melody. The total number of statements of each group
is shown, and percentages of the total are in the final
138
column. Further statistics with regard to variants are
shown in Table XXIII.
TABLE XXIII
VARIANT QUANTITY AND USAGE BY GROUP
Variant Quantity Percentage Total PercentageType of Type of Type Statements of Total
Primary 23 45.08 132 40.656Group I
Primary 11 21.56 93 28.644Group II
Primary 7 13.72 36 11.088Group III
Primary 3 5.88 3 2.156Group IV
Primary 1 1.96 1 .308Group V
Secondary 6 11.76 55 16.940
Table XXIII shows the collective quantity and usage of
each variant group with respective percentages.
TABLE XXIIIA
TOTAL VARIANT QUANTITY AND USAGE
Variant Quantity Percentage Total PercentageType of Type of Type Statements of Total
Primary 45 88.20 269 82.852Secondary 6 11.76 55 16.940
Table XXIIIA illustrates the total quantity and usage
of variants with respective percentages.
139
TABLE XXIV
TOTAL SINGLE AND COUPLING USAGE OF VARIANTS
Usage Quantity Percentage
Singly 72 22.176
In couplings 252 77.616
In the course of research, a total of fifty-three coup-
lings which were used a total of one hundred seventy-five
times were discovered.
Individual use of each coupling is shown in Table
XV.
TABLE XXV
COUPLINGS ACCORDING TO INDIVIDUAL USE
0
4 3
4-)
o >4 rd P 0 U) U U>U) U UU OD__ I AU U U ~ __ _
10
11
912
133
1415
17
2
1
1
1
u
0
0
0
0
u
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
1
8
4
2
0
3
10
6
4
15
2
3
4
5
C., A
TlFl
SRT2Fl
SRT2F2
SRT2F3
RR
I
140
TABLE XXV--Continued
4-JJ
$:i Q)(N H CNHrd o HW
H) H0O 4 _qo a) W 0" (U) U U U /) UE-4H>_ _ _ _ . au I u IU U _ _ __1
1 V7 1 11% 1 1 0%U
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
SR IT2F4
SRT2F4
SRT2F4
RR
RR
SRT2F2
CRTlFi
CRTlFl
CRTlFl
SRT2F3
CRTlFl
CRTlFl
CRTlFi
SRT2F1
SRT2F4
SRT2F4
I17
18
1619
2021
322
2324
1125
2519
2618
1826
1527
3Motive
2028
2820
2816
2829
29Motive
U
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
U
0
0
0
0
1
1
5
5
1
1
2
1
1
0
0
1
0
0
0
0
0
0
0
I
0
0
2
1
0
2
4
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
9
6
5
0
0
0
4
2
6
2
1
1
1
5
6
3
14
11
7
1
2
4
141
TABLE XXV--Continued
0
-P(d
44JI~i -Hj ) CN H (N
Hrd H04 H OOi 0C
04 4 M1 X4 1 X 4-o0C >1 m a) l) U l)0 U 0
U E-q p U U U__ _
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
SRT2F5
SRT2F4
SRT2F5
SRT2F3
SRT2F4
CRTlFI
SRT2F2
CRTlFi
RR
CRTlFl
CRTlF2
CRTlF2
SRT2F3
CRTlFI
SRT2FI
CRTlFl
Motive18
1830
9Motive
3119
3233
346
635
737
3839
3940
1819
Motive20
2033
3341
1218
429
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
4
3
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
'0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
3
4
8
4
4
1
1
1
1
1
1
4
3
3
2
5
3
4
8
4
142
TABLE XXV--Contitued
0
o Hri H CNH r14 FXH
o0 W OH.cr U U ciu,U ___ ~ I4 U U U U _ __
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
SRT2F5
CRTlF1
SRT2F1
SRT2F5
SRT2F4
SRT2F4
SRT2F5
CRTlF2
SRT2F2
RR
RR
SRT2F2
CRTlFI
SRT2F2
CRTlF2
SRT2F2-
18Motive
Motive3
2125
2533
Motive43
4445
1846
20Motive
2710
1647
4714
2748
4849
493
Motive3
Motive50
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
3
1
1
1
I
1
1
1
1
1
1
1
1
1
1
143
In Table XXV, the use of each coupling is shown accord-
ing to each form of melodic fragmentation and linear melody.
In the final column, the total use of each coupling is
given.
The collective number of coupling statements is shown
in Table XXVI according to type and form.
TABLE XXVI
COLLECTIVE COUPLING USAGE ACCORDING TO TYPE AND FORM
0
SR2F 4 2>1 -P 017 2
4.) () r_
rq -H a) CN
0RT2F 7 J 0 0:24 (d 8 -1
$T3 4 U) 0 2 U 1 U 7 0-P
CRTlFl 14 1 0. 0 16 4 9 4 33 67
CRT1F2 4 0 0 0 0 0 0 2 7 9
SRT2FI 4 2 0 0 1 0 0 0 17 20
SRT2F2 7 1 0 0 2 0 1 0 8 12
SRT2F3 4 1 0 0 2 0 1 0 7 11
SRT2F4 9 0 3 3 0 8 4 0 4 22
SRT2F5 5 0 0 0 0 3 0 2 6 11
RR 6 1 0 3 0 0 17 0 2 23
In the final column of the above table,
totals of each type of coupling are
tics are shown in Table XXVII.
the statement
given. Further statis-
144
TABLE XXVII
COLLECTIVE COUPLING QUANTITY AND USAGEACCORDING TO TYPE AND FORM
Percentage of Number of Percentage ofType Quantity Total Quantity Statements Total Statements
CRTlFl 14 26.404 67 38.19
CRTlF2 4 7.544 9 5.13
SRT2Fl 4 7.544 20 11.40
SRT2F2 7 13.202 12 6.84
SRT2F3 4 7.544 11 6.27
SRT2F4 9 16.974 22 12.54
SRT2F5 5 9.430 11 6.27
RR 6 11.316 23 13.11
Table XXVII illustrates the collective quantity and
usage of each coupling type, with respective percentages.
Further statistics are shown in Table XXVIIA.
TABLE XXVIIA
TOTAL COUPLING QUANTITY AND USAGE BY GENERAL TYPE
Percentage Percentageof Total Number of of Total
Type Quantity Quantity Statements Statements
Closely 18 34.148 76 43.32Related
Semirelated 29 54.494 76 43.32
Remotely 6 11.316 23 13.11Related
145
Table XXVIIA represents total coupling quantity and
usage by general type, with respective percentages.
A total of twelve examples of melodic fragmentation
were discovered: seven examples of melodic fragmentation
Form 1 and five examples of melodic fragmentation Form 2.
A total of thirty examples of linear melody were dis-
covered: three examples of CSLMFl, three examples of
CSLMF2, five examples of CCLM, three examples of CCxLM,
ten examples of DSLM, two examples of DCLM and four exam-
ples of DCxLM.
The following fifteen examples of linear melody were
of similar contour within their own types and were thus
graphically comparable: all three examples of CSTMFl, all
three examples of CSLMF2, all three examples of CCxLM, four
examples of DSLM and two examples of DCxLM.
CHAPTER III
CONCLUSIONS
From the foregoing evidence, the following conclusions
have been drawn.
The material analyzed in this study was found to be
85% motive-derived. In Images I for piano, Debussy has
fashioned a remarkably economical work, using a single
motive as the primary source of development throughout the
series of pieces.
Of the total number of statements of the motive, two-
thirds were found to be used in an overlapped context,
while one-third of the statements were single. The predom-
inant use of overlapped statements of the motive reinforces
the maintenance of thematic unity. (See Table XVII,
p. 135.)
Unity has also been maintained by the predominance of
variants used in an overlapped context as opposed to isolat-
ed statements, and by the predominant overlapping and/or
juxtaposition of like variants throughout Images I. (See
Tables XIV and XXVIIA.)
Unification of thematic material is also insured by
the frequent repetition of many of the variants, both in
146
147
single and overlapped context. (See Tables XVI through XXI
and Table XXV.)
A strong interrelationship of the themes results from
the predominant use of the "leap-step" and "step-leap"
variety of variants which most closely resemble the motive.
The "leap-leap" variants are restricted to single statements
and, in overlapped context, to the shorter melodies. "Leap-
leap" variants in overlapped context are frequently stated
in enharmonic values.
While the larger melodies are confined to individual
pieces, the shorter forms were found to be interspersed
through all three pieces.
Melodies of identical and similar contour are varied
in the following ways: (1) slight changes in variant con-
tent which appear in melodies of similar contour, (2) the
addition of variants to an existing melody and (3) restate-
ment of melodies of identical contour and variant content
in enharmonic notation.
It is concluded, finally, that the three pieces of
Images I were conceived and designed by Debussy to be per-
formed as one, rather than separately, and that the motive,
as first stated in Reflets dans l'eau, is the unifying
force of the three pieces and the basis of Debussy's devel-
opmental process of the thematic material of Images I.
APPENDIX I
VARIANTS FOUND IN RESEARCH
Number Type Formula
Primary Group
Secondary
Primary Group
Primary Group
Primary Group
Primary Group
Primary Group
Primary Group
Secondary
Primary Group
Primary Group
Primary Group
Primary Group
Primary Group
Primary Group
Primary Group
Primary Group
Primary Group
Primary Group
Primary Group
Primary Group
Primary Group
Secondary
Primary Group
Secondary
Primary Group
III
IV
II
IV
III
IV
III
II
II
IV
II
III
III
I
I
II
I
II
I
II
Motive
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
m3dn
P5up
M2 dn
M2dn
d5up
P4dn
P5dn
P4dn
P4ur
m2up
M2dn
P5up
m3dn
P4up
P4dn
m2up
M2up
M3up
M2up
M3up
M2up
m3up
m3dn
M2dn
d4dn
M2dn
M2dn
P4dn
M3dn
m3dn
A2up
m2dn
M2up
M2 dn
m3dn
m3dn
P5up
M2dn
M2up
M2dn
m2up
A4 up
M3up
M2up
M3dn
M2 dn
m3up
M2dn
M3 up
d4dn
P4 up
M3up
148
I
149
APPENDIX I--Continued
Number Type Formula
Primary Group
Primary Group
Primary Group
Primary Group
Primary Group
Primary Group
Primary Group
Primary Group
Primary Group
Primary Group
Primary Group
Primary Group
Secondary
Primary Group
Primary Group
Primary Group
Primary Group
Primary Group
Primary Group
Primary Group
Primary Group
Secondary
Primary Group
Primary Group
Primary Group
II
III
II
I
II
I
I
II
I
I
I
I
III
I
I
II
I
III
I
II
I
V
I
M3dn
A4up
m3up
M2up
M3dn
m2up
m2up
m3up
M2up
M2up
M2up
M2dn
A5up
A4dn
m2dn
m2dn
m3dn
M2dn
P4up
M2up
M3up
M3up
M2dn
m6up
M2 dn
M2up
M2 dn
M2 up
m3dn
M2dn
M3up
m3up
m2dn
P5dn
M6dn
P5up
P4dn
A4 dn
m2dn
P5dn
m3up
m2up
m3 up
M2up
A5dn
m2up
P4dn
m6 up
M2dn
P5dn
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50v I
APPENDIX II
Reflets dans l'eau.
Andantino molto(Tempo rubato)
P14 A 0 _p___ -- ___PI.ANO
p PP
- pp-
- - - -
-~ p - ~ pp~p
Hi
r zPubished in the U.SA. by
Cop yrgi by A.DbradIi as, 1905 , , Pari,4 Pa a d a Imadaletp.
150 th 1mr--cr rompaN
150
156
1. 14
IF ---
-~ ---- 1
pp Pp
Lentse et 1as ta v s -wlo -t
44 A-
-~ - * ~ 22-- - A-
-- - - -- ------ - --
-t --- -- .----
.... ...
157
8
Hommage Rameau
Lent et grave(dans le style d'une Sartbmnde mals sans rigueur.)
pp express 7f ct douvement soutenu
- -
N U - - p. I i -- -
? I ?j.1
lip-i
--- - -- -- ---
~2EV V
D.- F. 615 (')
PIANO
Tm thn d 'e'euliaa rl
rjpvrizht by A.Durad% nfil.,1905.
-
159
Commencer an peu u d csous du mouv
pppp
TvT
au MoatOv
p _ - - ~ - ~ - p
En anmant
creso
* $_
cre - --
D- F. 6615 (2)
161
12
p- p pp
pp p-
4tt
A A' 4 - A
r- -4fi- -
pp -- p-
Unp upius pn
-pp
_ _ u PPP
I d -
-- D. F.66115 (2)
162
13
Movement
AalM6i (avec un.e legirefti. fantasque als prte'se)
IA YO _ } _. S S
PIANO
pp li tt .n a ~u
7Fr7-"w
~- - ~- ----------
Jill ~ 4
CopyrighL by A. DurAnd & FA 1905. D,.& F. 6 6 15 (3 )
166
17
47.
PP
tjt
Tluie Iis noes marquee dii sine.... sonores sons dorede/e rente ter tiger mois sns siherressr.
_ _ _ -- _ W
V------
77 _7- ___
- %3EV L
un per en dehor
D. & F. 66 1 r,(2
167
K e4 agot
pp
In gm.n..t. nt-- s i r.anspr eser
177
4Zj At
L __ R_ _ _-__4-L
f2-~
p/
) ~-&-~
74 .
=
I'1
172
at -0_ ;_ _ _A, -OR_-
IV
- ~ - * -~~
- -
-------- ----- - ----------
8(
--------------
-O. - A. A'd&Fi~ 6~ ~
Ch. A, Dorittid % o i . P68L5 (a)
BIBLIOGRAPHY
Books
Schmitz, E. Robert, The Piano Works of Claude Debussy, NewYork, Dover Publications, Inc.,J1966.
Dictionary Articles
Apel, Willi, "Enharmonic. (2) , " Harvard Dictionary of Music,Cambridge, The Belknap Press of Harvard UniversityPress, 1969.
"Interval," Harvard Dictionary of Music,Cambridge, The Belknap Press of Harvard~UniversityPress, 1969.
Musical Compositions
Debussy, Claude, Images I, Bryn Mawr, Elkan-Vogel, Inc.,1905
173