Brouillards" Author(S): Richard S

Pitch Organization in Debussy: Unordered Sets in "Brouillards" Author(s): Richard S. Parks Source: Music Theory Spectrum, Vol. 2 (Spring, 1980), pp. 119-134 Published by: University of California Press on behalf of the Society for Music Theory Stable URL: http://www.jstor.org/stable/746183 Accessed: 11/10/2008 17:23

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http://www.jstor.org Pitch Organizationin Debussy: Unordered Sets in "Brouillards"

by RichardS. Parks

This paperresults from a broadand ongoing investigationinto such as E. Robert Schmitz's essays on the piano pieces.4 All the naureof pitch organizationin the music of ClaudeDebussy.' share a common tendency to characterize Debussy's music It seeks primarilyto uncoverinformation about the relationships throughthe apparatusof harmonictheory5 so that, for example, between pitch resourcesand compositionalprocesses appliedto one finds reference to such things as "modal progressions," them in a single work by Debussy and, secondarily, to demon- "added-note" and "dominant-eleventh" chords, "parallel stratethat certain concepts of pitch-settheory may find advanta- chord-successions," and "unresolveddissonances." Elements geous applicationin his music. which do not fall within the confines of harmonictheory were A great many studies of Debussy's music appearto have had, describedand labeled in ways which sought to categorize them as their general objective, the intent of characterizingpitch as foreign to thattheory, but nonethelesswithin the purviewof a elements thought to be significant in ways which would (1) more general speculative theory which could embrace, as pos- permitcomparison with similar elements found throughouthis sibilities for pitch resources, elements found in the music of work, (2) identify fairly precisely, pitch and intervalliccharac- popular, folk, and non-Western cultures. "Pentatonic," teristicsof these elements which the analystsconsidered impor- "whole-tone" and "gypsy" scales have been cited as "exotic" tant, and(3) suggest connectionswith other, earliercomposers. infusions into Debussy's otherwisefamiliar vocabulary of pitch I refer to the work of authorssuch as Rene Lenormand2and resources. Br/iliou's essay on pentatonicismtypifies this ap- LaurenceDavid Berman,3as well as less theory-orientedworks proach.6

4E. RobertSchmitz, The Piano Worksof Claude Debussy (1950; reprinted., 'Researchfor this studywas assistedby a grantfrom Wayne StateUniversity. New York: Dover Publications, 1966). 2Ren6 A Lenormand, Study of Twentieth-CenturyHarmony, translatedby 5Theterm "harmonictheory" refershere to the corpusof treatises,texts, and HerbertAntcliffe (1915; reprinted., New York: Da Capo Press, 1976). Lenor- essays-in all its diversity-which purportsto deal primarilywith music from mand's so far as I the earliest monographis, know, attemptto examine compre- the so-called periodof commonpractice, by definingand seeking meaningin the and hensively systematicallythe aspect of harmonyin Debussy's music and to natureof chords and their contexts in that repertory. link features deemed innovative with the practices of his predecessors. 6ConstantinBrAiliou, "Pentatony in Debussy's Music," in Studia Memoriae 3LaurenceDavid "The Evolutionof Tonal Berman, Thinkingin the Music of Belae Bartok Sacra, 3d edition (London: Boosey and Hawkes, 1959). pp. Claude Debussy," 2 vols. (doctoral dissertation, Harvard, 1965). 351-98. 120 MusicTheory Spectrum

Such characterizationsare valid and useful as far as they go, an attempt to identify some of the sources of cohrence and and they may have been of vital importanceto musicianscloser economy from a perspectivenot so stronglyreferenced to earlier to Debussy's time, who were grapplingwith the novelty of his tonal music. One encounters certain sounds over and over in sound spectrum, trying to place it within their experiential Debussy's music, in many kinds of contexts, and so it seems musical world.7There is a limitationto this approachhowever, reasonableto adopt an approachwhich facilitatesidentification as it suggests an arbitrary quality about the composer's of, and distinctions between, similar and dissimilar sound- process-as thoughhe simply absorbedall these 'devices" and constructs. poured forth a confusion of harmonic and tonal distortions, While identificationof differences between dissimilar ele- contradictionsand exoticisms, which need only to be properly ments is not normallyproblematical, the question often arises identified and labeled to be understood.Such a view is incom- whether such elements also share common features (which patible with this author's perceptionof the composer's works might help to explainhow they contributeto a listener's sense of whom they impress, overall, as coherent, logical and highly coherence in a work, even as they manifest its diversity). One organized:as exhibiting economy and selectivity in their pitch may also wonder whether, and to what extent, elements which resources. Besides, they sound profoundlydifferent from the appear to be similarare in fact dissimilarwith regardto features repertoryof Debussy's antecessors, despite the fact that, taken which delimit sound-color.Pitch-set theory provides some use- out of context, a large proportionof the sound-elementsof his ful concepts and proceduresfor coping with these problems. pieces are familiar as constituentsof earlier music. It may be useful to state certainmethodological assumptions Not all analyticalstudies of Debussy's music are classifiable which influencethis author'sway of hearing.First, it is assumed with those described above. Studies by Herbert Eimert8and that economy of means is an importantconstituent in a work of Robert Moevs9 are less concerned with "devices" and tonal art;the less "things" a piece is "about," the moreeasily it may features, and reveal more aboutmotivic or what might be called be processed by the listener and the greater its coherence. cellular aspects of organization. Schnebel's study of "Brouil- Second, great works of musical art, while economical, often lards" reveals an interestin relationshipsbetween pitch organi- display a high degree of complexity in the utilizationof their zation, the acousticalcharacteristics of the piano, and timbre. 0 limited pitch resources. Thirdly, pitch organization-though it My study follows a less traditionalapproach and resultsfrom is not the only aspect of a composition nor, indeed, necessarily the most significant aspect-is more importantand may be emphasizedin analysis, even thoughit cannotbe separatedfrom 7The "message" of Lenormand's treatise is that Debussy's music was other but not thathis innovationsconsisted of the mannerand aspects. "new," altogethernew; This from a listener's of view rather extent to which his pitch resourceswere used, but thatthe resourcesthemselves study proceeds point may be traced to earlier practice. from that of the composer. Any speculation regarding 8HerbertEimert, "Debussy's 'Jeux,' "translated by Leo Black, Die Reihe, Debussy's motivations and intentions always originates from no. 5 (1961), 3-20. this perspective. 9Robert Moevs, "Intervallic Proceduresin Debussy: 'Serenade' from the Sonata for Cello and Piano, 1915," Perspectives of New Music, 8 (1969), 82-101. l?Dieter Schnebel, " 'Brouillards'--Tendencies in Debussy," Die Reihe, no. 6 (1964), 33-39. Pitch Organizationin Debussy 121

Some definitions and assumptionswhich obtainfor this anal- NormalOrder." 13 A set-formmay appearin eitherascending or ysis may be summarizedbriefly as follows. descending order, whichever arrangementmeets the criteriaof Octave equivalence is assumed throughout,so that the term Best Normal Order. Sets which carrythe same label but which "set" is used to mean "pitch-class set" and, in turn,pitch-class appearin opposite order (i.e. one ascending, one descending) set refers to a group of pitch classes. are inversionally equivalent. Integernotation, in which the twelve pitches of the tempered The selection process by which one decides what shall be chromatic scale are numberedin ascending order (with C=O, considered an analytical object is necessarily subjective. In C-sharp=1, . . . B=1 1) will be employed frequently. Intervals general, for this analysis, pitches have been groupedas entities will often (though not always) be reduced to six octave and on the basis of notationalcues, as well as heardcues. I have not inversionally equivalent classes, expressed in semitones. attemptedto examine every possible combination of pitches, Sets will be representedin the text and examples in two ways: nor even every "important" combination in the pages which parenthetically, either as pitch names expressed in integers follow. I have tried to cite those combinations which exhibit separatedby commas, or as interval-classarrays expressed in importantinterrelationships and combine togetherto affordone integers separatedby hyphens." (Thus a three-note set com- view of "what the piece is about." prised of the pitches D-E-G-sharp may be representedeither The piece which is to serve as a focus for this paper is as pitches [2,4,8] or as interval-arrays[2-4-6].) "Brouillards."14 All sets are unordered;that is, pitch-classorder is not considered to affect the identity of a set. 2. It is assumed that sets retaintheir identities underthe opera- tions of transpositionand inversion, and the various transposi- The piece begins with two brief gestures-each of an eighth- tionally and inversionallyequivalent permutations of a set will note's duration-which are immediatelyrepeated. Both consist be referredto as "set-forms." of seven notes: triads in the left hand articulated against Allen Forte's list of sets has been employed for the purposeof arabesque-likefour-note figures in the right. (Example 1 shows identifying and naming different collections.12 In examples bars 1-3 with all appropriatesets cited.) The second gestureis a displaying sets for reference, sets are arrangedin that adjacent transpositionof the first;both are forms of set 7-31. However, ordering within an octave which conforms to Forte's "Best the second is not a literal transpositionof the first in all its details. The firstleft-hand triad is a formof set 3 -11: the second of set 3-10. The first falling-figurein the righthand is a form of I Richard Chrisman, "Describing StructuralAspects of Pitch-Sets Using set 4-26: the second of set 4-27. In this way five pitch-class Successive Interval-Arrays,"Journal of Music Theory, 21 (1977), 1-28, sets of great importancefor the piece emerge (Example 2); describes a numberof useful applicationsfor interval arrays in analysis. quietly and with greatsubtlety, sets 3-11, 4-26, 3-10, 4-27, 12AllenForte, The Structureof Atonal Music (New Haven: Yale University Press, 1973), 179-81. I am indebtedto this source as a useful and convenient 13Forte,p. 4. reference for many conceptual and proceduralaspects of pitch-set theory in- 14ClaudeDebussy, "Brouillards," from Preludes,Book II (Paris;Durand et voked in this study. Cie., 1913), 1-6. 122 Music Theory Spectrum

Example 1

Modere

3-1 1 (7.4.0) 1 /3(.6.4.33 ,0 ( 2.5) 7-31 (7.6.4.3.1.0. 10)

Example 2

10. 3-11 (7,4.0) - 3-10 ( 11.2.5) I_~~ 17-31~~- (7,6,4.3, 0) U r -I bo-, I bo&V I - _I 1 ? 6. _ VY o0 -- - ;,, l-^ X h I'H' 'v Bo bo k.. - , uW-)-1 - 0 bL-r 1.1.3L6~4-264-26 (10.,1.3,6)( 4-27 (8.10. 1.4)

and 7-31 are exposed and affirmed in the repetition which subsidiary pitch resources which appear throughout the piece follows. may later be seen to arise, to some extent, from procedures The second and third measures contrast with the first, at the which occur in these measures and to extend these procedures same time revealing clues about the subsequent utilization of the into their own domains. five sets and certain properties each possesses. Even the many Pitch Organizationin Debussy 123

Measure 2 quickens the tempo of the left-hand chords, pre- Example3 senting three transpositionsof set 3-11 (in its inversionally equivalent majorand minor triadforms), against a single pitch 2 3 (D-flat) in the righthand. The coincidence of the D-flat with the A 7-35 (11.0.24.5,7.9) 7-35 AC third (3-11) chord yields anotherform of set 4-27, while the . IA.- 1 same pitchjoined to the fourthchord produces a new set (4-19). The thirdbar contains two forms of 3 - 11 andone of 3 - 10 in the left-hand while the hand in succes- chords, right superimposes, Copyright1913 Durandet Cie. Used by Permissionof the Publisher,Theodore sion, forms of 4-26, 4-27 and 4-26 again, the whole joining Presser Company. Sole RepresentativeU.S.A. in features identical or similar to those of measure 1 (the last seven notes form a new set, 7-32). Several processes may be observed in these three measures of eight pitch classes alternatingwhole and half-steps within an with respect to the use of the five "primary" sets-as well as to octave). The small sets projectthis featureonly weakly, due to the use of the other'non-primary" sets. First, the small primary theirtonal connotationsas noted above. Because they are more sets arejoined in differentways to producethe largeprimary set, likely to be closely associated with these tonal constructs, they 7-31. Second, the same small sets are joined in ways which requiresome element of supportto rendertheir connection with synthesize new sets-for example, set 7-32 grows out of the octatonicism inferableto the listener. Only set 7-31 is unam- union of 3 - 11 and4-26 in bar3 (thirdeighth). These processes biguously octatonic, lacking but a single pitch of forming that recurrepeatedly, resulting in a great varietyof materialsrelated superset. In this piece, as we shall see, it is the synthesis of the to the primarysets. A thirdprocess appearslater, in which the smaller sets into the large one which either emphasizes or large primaryset is partitionedinto new subsets. This may be suppressestheir octatonic property. This can be heardin the first thought of as a kind of "opposite" to the second process threemeasures, where the predominanceof set 7 - 31 in measure described above. While it does not occur explicitly in the first 1 and through the first two eighths of measure 3 projects the three bars, it might be consideredimplicit in measure3, where octatonic coloring, while its absence in measure 2 results in a the three triads of the left hand form the same seven-note quite different sound-color.15 collection as those of bar2 (set 7-35 [11,0,2,4,5,7,9]; Example 3). 3. The small sets-3 - 11, 4-26, 3 - 10, 4-27-are all common sounds in tonal music. Harmony characterizesthem, respec- The materials of the first three measures recur in diverse tively, as the majortriad (or its inversionalequivalent, the minor contexts throughout the piece, and an account of events is triad),the minor-minorseventh chord, the diminishedtriad, and facilitated by providing some sort of "formal plan" for the the major-minorseventh chord (or its inversionalequivalent, the diminished-minorseventh chord). The seven-note primaryset (7 - 3 1) is not a familiarcombination in the harmonic vocabulary 15Inaddition to the small primarysets cited in bar2, new sets 4-19 and 7-35 of tonal music. also appear-the latterperhaps less conspicuousthan the former. Neither4-19 All five sets are subsets of the "octatonic" scale (composed nor 7-35 are subsets of the octatonic scale. 124 MusicTheory Spectrum work. The piece can be characterizedas conformingto a kind of It must also be noted that the distinctions between transitional rondo scheme (ABACA), where each adjacent pair of lettered and thematic sections attenuate towards the ends of the piece. sections is separated by a "transitional" or "coda" section. The A sections feature a return to the material of the first three Such a formal plan is diagrammed in Figure 1. The plan arises bars, either in whole or in part. In the first such return, measure from a "conventional" perception of the piece as consisting of 24 (last four eighths) corresponds to measure 1, bar 25 to bar 2, elements-passages-which could be termed "thematic" in a and bar 26 to bar 3. Bars 27-28 correspond to bar 4, but the general sense and elements which, by comparison, may be alterations are significant. (Bars 27-28 will be examined in heard as fulfilling connective, change-effecting or concluding detail shortly.) The third and last A section is only a shadow of roles-labeled "transitional" or "coda." the original. Bars 43-44 (last two eighths) employ material of The exact points of subdivision have been reached with diffi- bars 1-2, but in truncated form -only one statement of the culty in some instances. However, the divisions posited here corresponding earlier bars' material sounds each time. Bars permit a productive examination of the piece and minor changes 45-46 reiterate the two transpositions of set 7-31 of bar 43. would not significantly alter the results of this analysis. (The pedal C which is articulated in bars 43-46 is a significant The chief criterion for designation of divisions has been the tonal addition to this return of A material, but as tonal consider- pronounced changes in thematic material and rhythmic charac- ations are not in the sphere of set relations, upon which this ter which occur intermittently. Sections labeled with letters are analysis focuses, it will not be dealt with. It is but one of many easy to distinguish "thematically." The "transitional" and tonal cues which point to C as "centric" for this piece.) "coda" passages pose difficulties for they tend to mix familiar The transitional passages which separate each pair of sections with new material. They are distinguished from the "thematic" contain some appearances of A material and in this manner sections which adjoin them by the assertion of their different affirm the primary sets in toto, as first exposed in the piece. rhythmic character; they are less obviously regular-more Examples may be found in bars 5-6 of the first transition (the complex in their greater range of durational values - than are the last two eighths of each bar), and in bars 20 and 21 of the second lettered sections. At the same time, they evince a simpler and transition (last two eighths of each bar). The material of the third lighter texture, usually consisting of only one rhythmic "voice" transition (29-31) is "new," though not entirely bereft of at a time. primary sets. However, they emerge in new environments here,

Figure 1. A formal plan for "Brouillards"

BARS: 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

A tran- B tran- A tran- C tran- A coda sition sition sition sition #1| #2 #3 #4 Pitch Organizationin Debussy 125

Example 4

3-11 (1,10,6)

Copyright1913 Durandet Cie. Used by Permissionof the Publisher,Theodore Presser Company. Sole RepresentativeU.S.A. representedonly by forms of the triadic set 3-11 (Example4; contexts: the first and second transitionsand the coda do so as the [1,10,6] form in the rapid-note left-hand figure of bars well. The third and fourth transitionsemploy different pitch 29-30 is perhapsunlikely to be discernedas a separateentity, materials,though traces of the originalresources in the form of embedded as it is in set 4-18). set 3-11 do appear. However, the B and C sections are alto- The fourth transition(38-42) contains no conspicuous dis- gether different in their relationshipto our primarysets. positions of primarysets, though one form of 3-11 (8,4,1) is The B section (bars 9-17 in the formal plan) emerges from outlinedby the skips in bar 39 (Example5; see also bar 19 of the the last two measuresof the first transition,out of the union of second transition for a similar outlining). This is somewhat 3-11 with 4-26, in the gesture which appears on the third reinforcedby the shape of the line itself, in which the stepwise eighth of bar7 (formingnew set 7 - 21), recursin bar8, andthen motion may "direct" the ear from the initial C-sharpto E, and persists throughthe next five measuresas an ostinato(Example towards G-sharpfrom G (Example 6). 7). This set (7 -21), bornof a new synthesisof the small primary The "coda" following the last A section contains the three- sets, contrastssharply (in its intervalliccontent) with set 7-31, note primary sets (3-10 and 3-11) in the left hand in bars so that the B section is distinguishedfrom the A section by a 48-52, without the four-note overlay of measures 1-2. marked change in sound color (though not in sound density, In summary,not only do the A sections employ the primary since seven-note combinationsremain the norm for each ges- sets exposed in bars 1 -3 in similarand thus readilyrecognizable ture). These particularseven-note sets differ considerably in 126 Music Theory Spectrum

Example 5

8. bassa ------j

Example 6

3-I 1

a , Ln ir' i v:--^- A - r (iI,I i

-11 ( , 4, I) Pitch Organizationin Debussy 127

Example 7

7-21 (:I32111,10,7,6)) 1-26)((I( ) ) I 7-21 7-21 7 8 / 10~- -6

[] 6 etc.

L- ( X/ * / / lfI j I__H' i

3-I1 (2,1 1,7)

intervallic content; as Figure 2 shows, they share no common Figure2. Intervalvectors for sets 7-31 and7-21 entries for any interval class across their vectors. while to the The "melody" of the top staff, adhering pitch 7-31 as well [336333] contentof the ostinato, articulatestwo new combinations 7-21 [424641] as anotherform of a familiarone (Example8). The threepitches of bars 10-11 -the lone F-sharpplus the C-sharpdecorated by the grace note D- yields set 3-4. The next barrearticulates the F-sharpon beat one but this time it is decoratedby G, forming set 4-8 with the lower figure of beat two. The continuationof staves), as the second half of a new melodic shape (the first half the lower line on the top staff of bar 13 unfolds set 3-11 as forms set 3-5) and again, similarly, in the fourthtransition, in (1,10,6)--a transpositionalready cited in connection with the bars 39 and 41 (Example 10). third transition(see Example 4), which follows this section. In this way, the first transitionintroduces a new set (4-8), Set 4-8 was articulatedearlier, in bars 5 and 6 (first two which recurs in the B section's "theme," containing set 3-4 eighths), in a different transposition (Example 9). Set 3-4 embeddedwithin (articulatedin bar 11). The latterwill provide recurs later, in the second transition (bars 19 and 23, lower a basis for materialin transitions2, 3, 4 and in the coda; thus a 128 MusicTheory Spectrum

Example 8

13 3-11 (1,10,6) 14 15

Copyright1913 Durandet Cie. Used by Permissionof the Publisher,Theodore connection between contrasting "transitional" and "thematic" Presser Company. Sole RepresentativeU.S.A. material is established in the B section. The third transition (bars 29-31) is quite different in character from the others. As cited in Example 4, it includes sets 3- 1, 3-5 and 4-18 in the rapid notes which open bars 29 and 30. Each of the last eighths of those measures combine two forms of set 3-11 in an ornamental figure which sums to set 6-30-in a total of two transpositions (Example 11; compare to Example Example 9 4). Thereafter, in bar 32, an ostinato begins which includes five notes: a form of set 5-19 (Example 12). With the exception of 3-11 these sets all lie outside the matrix of primary sets. 4-8 (7.8.01) 5 The C section itself issues from the ostinato of bar 32, to n I which it adds, in bars 33-34, a melodic shape of two bars' :/ b/ \ L t^ duration, moving in eighth-notes (for the most part) in the left /'2 N hand These effect a in the -A - '~I1 (Example 13). moving eighths change ostinato of bar 32 (based upon set 5-19), in that one note, D, is not always present; it is often replaced by one of three other pitches. The four notes which are consistently present (9,8,6,3) Copyright1913 Durandet Cie. Used by Permissionof the Publisher,Theodore form a combination labeled 4-13. Taken together, the moving Presser Company. Sole RepresentativeU.S.A. eighths also form set 4-13, but in a permutation inversionally Pitch Organizationin Debussy 129

Example 10

(I12.7)- ) , . ) :-. 3-4 (1,5,()) 18 - 22 I -> ;w ; r i(^T- w--i^y j)- 0i^

Copyright1913 Durandet Cie. Used by Permissionof the Publisher,Theodore equivalent to that of the ostinato (11,0,2,5). The interaction of Presser Company. Sole RepresentativeU.S.A. the ostinato form of 4-13 with the melodic form yields various five-note combinations-including, of course, set 5-19 when the variable pitch is D. (Figure 3 depicts these relationships by Example 11 representing the ostinato form of set 4-13 as a large rectangle intersecting a series of small rectangles which represent each F pitch of 4-13 in its melodic form.) It is the intersection of these A29 k G pitches with the ostinato which produces the range of five-note I sets cited on 13. (The and assume the IM/|-,^ tWrpm^i^-0'- - II Example example figure I listener retaining the two sixteenths of the left hand [6,9] articu- 6.1 lated on each quarter.) If bars 33-34 are viewed as a phrase, each half-phrase Copyright 1913 Durandet Cie. Used by Permissionof the Publisher,Theodore (antecedent bar 33 and consequent bar 34) yields a different Presser Company. Sole RepresentativeU.S.A. permutation of set 7-31. (The four forms of set 7-31 are cited to the right of bars 33-37 of Example 13.) Bars 36-37 trans- pose the material of bars 33-34 (where t=5) and so also the sets found there. Though the large set, 7-31, is quite conspicuous, Example 12 very few small primary sets occur (3-11, 3-10 and 4-26 all appear-they are cited in Example 13, bars 32-34, and are located in 32 , easily corresponding bars 36-37-but they seem far 9 k II less prominent than the "new" four and five-note sets). Ive 11 Taken as a unit, the sum of all of the entire two bars of

Example 13

,Section C ------8 ------, Un peu relenu 31 _ - - .d A 33 t A '32 ._ -. ._-. _-, t- 8-8-^-^ / -'&.--s I 7-31 -gstii7 PP y J j- 310(112 (2.3,5.6.8.9.1 I)

J __S ~- _ 1 1 jPP~~~~~~' tS~~ / 3-11 (9,6,2)

5-19 (9,8,6,3,2) 5-19 (9.8,6,3.2) 5-10(9.8,6.5.3) 5-19 (9,8.6.3,2) 5-25(11.9.8.6.3)

3------, ( ?------, A A* 35 ^^. (^L . t,

7-31 (3,2,0,11.9.8,6)

j Sv .______------

5-19 5-19 (7,6,4, 1.0)

- 37 -, ^ 4- Z- , h0 ^--- V LJvf7t Fr_ r Ff

I -31 7-31 bLr.J^Mb F : . >(8,7,5, < pupp (7,8,10,11,1,2,4) :' 4,2, I\ 11) I I ij ^ J J~ bJ J j IH 5-19 5-25 5-31 51 5-105-19(2,1,11,7,6)(2,1,11,1,8)2,1,11,7,6) 5-19 5-25 (4,2,1,11,8) (5-25) (2,1,11,8,5)

Figure3. Diagramof bars33-34 showinginteraction of inversionally equivalent4-13 set forms

BARS r-33 I 134 I 4-13: (9,8,6,3) 8 ...... _._ - 6 ------_ ___------

P171_p...... 1 . 1 i 1 4-13: (11,0,2,5) 2 5 2 11 2 11 0 J --

(Examples 4 and 11) and those of this C section (Example 13) comparisonof the five-note set in the right handwith the earlier can be seen in the fact that all are subsets of the octatonic scale. measures indicates that these five notes most nearly resemble Most of them (primarysets 3-11, 3-10 and 4-26 excepted) the four-notecombination sounded against the (7,4,0) form of sound octatonic due to the presence of tritones and minor sec- set 3-11 in bar 1 (first eighth); here in bar 4, the five notes onds (often in multiples) and alternatingwhole and half steps consist of thatset 4-26 with the additionof A-flat. If the latteris between adjacent tones, more characteristicof this collection removed, for purposesof comparison, and the seven-note resi- than of the major and minor scales. In a sense, the transition due identified, the resultantset is 7-21--in exactly the trans- preparesthe way for an increaseof octatonic sound color which position used for the B section ostinatoof bars9-14! (Example reaches its fullest expression in the C section. 14 shows the 7-21 residue to the right; compare with 7-21 4. shown in Example 7). And indeed, a close connection may be heard between the sound color of bar 4 and the B section's Returningto bar4 of the first A section, one may observe that ostinato. In a sense, the materialof bar4, emergingfrom thatof while it resembles the precedingmeasures in its articulationof a bars 1-3, actually anticipates, in a subtle way, the ostinato of triadin the left hand (set 3-11, this time as [2,11,7]), the right the B section. handnow contains five pitches insteadof the usual four (Exam- Bars 27-28 of the second A section resemblebar 4, with the ple 14). Together,both handsprovide a total of eight pitches (set bipartiteset 8-20 appearingon the first half of each measure, 8-20)-but this reveals little about any possible connection but the third and fourth eighths are different here. They too between bar4 and those which precede and follow. However, a consist of eight notes (providingtwo transpositionsof set 8-27 132 MusicTheory Spectrum

Example 14

4 7-21 (,2,, I1 I

this time), partitioned into forms of set 3-11 ([7,3,0] and and thatform, combinedwith the left hand's 3-11, producesan [2,5,9]) and five-note sets. The first of the latterconsists of the alien set, 7-Z37 (6,5,3,2,0,10,9). Nonetheless, one may con- same notes which occur on beat one of each bar (10,8,6,3,1), templatethe passages of bars4 and 27-28 vis-a-vis theirsubtle the second, of (0,10,8,6,3). If the reasoningof bar4 is pursued differences and their occurrences in only two of the three A here, one may again reject the A-flat from the first set-for sections. Could it be thatwe experiencea hint of preparationfor purposesof comparison-and discover thatthe seven-note resi- the B section's shift in predominantseven-note set material, due forms set 7-31 in its original transposition throughbar 4's supersetof set 7-21 which, having to fulfill a ([7,6,4,3,1,0,10], Example 15; compare to Example 1). different kind of anticipatoryrole in bars 27-28, undergoes a A similarprocess appliedto the last eighth of bar27 produces subtle change (into 7-21's superset followed by 7-31's less felicitous results. The five notes in the right hand do not superset) and, being unnecessaryin the concluding A section, closely resemble any four-note primary set form of bar 1; does not appearthere at all? a instead, they resemble (but are not identical to) transposition 5. of the precedingeighth of bar 27. However, if all five notes are viewed as candidatesfor exclusion, one in particular-B-flat- Several architectonicprocesses may be perceivedin "Brouil- leaves a primary set form (4-27 as [8,6,3,0]) which in turn lards" througha set interpretationof the piece. First of all, a combines with the left-hand's 3-11 form to produce another connectionexists between the formalplan and the primarysets transpositionof set 7-31 (9,8,6,5,3,2,0). Since set 7-31 is to cited in that materialfirst presentedin the piece recurs subse- be ascendent, one could extend to the C section, by analogy to quently in similarforms, therebydefining the A sections in the bar 4, the suggestion of anticipation, of that set's impending rondo scheme. The contrastingsections-B and C-draw upon importance.Such an inference is speculative-especially since the sets too, but find different applications for them. The B thereis anotherpitch (A-flat) in the right-hand'slast eighth (bar section employs the small sets, 3-11 and 4-26, butjoins them 27) whose rejection would yield a form of primaryset 4-27, in a manner which forms a contrasting seven-note superset, Pitch Organization in Debussy 133

Example 15

, 7. 6,4, I ?..I.. ,~I"--, , A "(9116~~->'_b . - *^L7-3 .0) A bs^kb,, . * (.6 I1 -10,0)1 A ~Xkblel"_ L. - , * L i _ ....,,/- "- - i .... , .i-o

8-27 (8,7,6,4,3, 1,0,1)-7 ,,,,,)) (I

V V Q^Q^K W^?~~~~~~4

Copyright1913 Durandet Cie. Used by Permissionof the Publisher,Theodore Presser Company. Sole RepresentativeU.S.A. preceding transition, which are saturatedwith octatonic sets. The rest of the time-that is, in the A sections and transitions and coda--it depends upon the presenceof set 7-31 and on the 7-21. The C section eschews the small primarysets in favor of proportionof non-octatonicnew sets presented. For instance, the large one (7-31) which is partitionedinto new four and the fourthtransition exhibits a paucity of octatonic sets, relying five-note combinations. The transitionalsections utilize mate- instead upon non-octatonic(and non-primary)sets 3-5, 3-4, rial directlyborrowed from the A sections, and they also initiate 4-9, and 6-5. important"new" materials (though these are seen to harbor connections with the "old," in the B section). In a mannerof 6. speaking, the new materialof the transitionsmay be thoughtof as having been "spun-off" the original material, asserting its Were it necessaryto characterize"Brouillards" in a word, I independencein those passages. would propose "dichotomous." The piece strikesme as ambig- The aspectof octatonicismis also tied to the formalplan. The uous in severalrespects: in its fluctuationbetween octatonicand potential for octatonicism exists in all the primarysets, but at non-octatonicpassages (is it octatonic or not?), its use of pri- times it is entirely thwarted, as in the case of the B section. mary sets in the B and C sections (does 7-31 result from the Elsewhere it is strongly exploited, as in the C section and union of the small sets or do the latterresult from the partitioning 134 MusicTheory Spectrum of the large set?), the formal plan itself in its dual aspects of The process of discovering such combinationsand their sub- rondo scheme with transitionsand coda versus alternationof sequent dispositions is facilitated-aurally as well as passages of contrastingrhythmic character and texture-a view visually-by approachingthe music from the perspective of in which the "transitions" assume a stature of importance pitch-set relations. One sees and hears connections between comparableto the letteredsections (this view supportedby their apparentlydiverse elements which one might otherwiseignore. relatively equal lengths in the work). Finally, there is, in the One may also become aware of distinctive features among appearanceof the score, a sense of dichotomy in the way the otherwise similar elements which might escape notice. composer is constantlyjuxtaposing and superimposingflats or Moreover, some advantages derive from the absence, in sharps against naturals-diatonic C-naturalin the left hand in set-theory, of notions such as "tension" and "resolution," of bars 1-4 against flats in the right hand; C-natural(dominant "motion" and "repose" as parametersdefining propertiesof triad)for bars 9-17 in the left hand against sharpsin the right. pitch combinations.The emphasis on intrinsicand quantifiable There is a suggestion of indecision or lack of resolutionin this propertiesin set theoryis especially compatiblewith pieces like dimension which persists to the very end, where the last sound "Brouillards," where quantitative changes occur from one heard is the leading-tone triad (not the "tonic" C-major), temporalpoint to another,but wherecoherence does not depend against the still-floating A-flat in the right. This quality of uponthe resolutionof "conflicts" traditionallyconsidered to be ambiguityor "lack of focus" alludes to the title of the piece- implicit in certain pitch combinationsor contexts. "Fogs"-by the presentationof resources and manipulative One is not constrained from observing other aspects of proceduresat the beginning of the piece which point in two or Debussy's music, including that of tonality. On the contrary, more directionsat once, all of which are then affirmedlater in identificationof set relationshipsoften seems to support,albeit the piece. The conflict between contrastingcharacteristics is not from a different perspective, conclusions one may draw from resolved in the conclusion-the listeneris left projectingthem in other modes of pitch analysis.16 his mind's ear-yet it is remarkablehow interdependentall Other pieces examined by this author exhibit pronounced elements of the piece are, including (and contributingto) this differences in both pitch resourcesand process, suggesting that aspect of dichotomy. whateverinsight is gained into the natureof Debussy's compo- To a ratherlarge extent, Debussy's music (of which "Brouil- sitional process throughthe apparatusof pitch-set theory does lars" may be consideredtypical) reveals, in its pitch resources, not include the revelationof a system or formulafor producing combinationswhich exhibit characteristicslying beyond tradi- pieces. Althoughcertain shared characteristics can be observed tional notions of harmony,voice-leading, and a referentialtone in his music-"favorite" sets, idiosyncraticways of using sets and sonority(tonic). On the one hand, he seems to have fastened in some mattersof detail-each piece is its own master. upon some pitch combinationswhich would arise only coinci- dentally in music traditionallytonal and which would require stringent restraints in terms of voice leading and harmonic 16Although"Brouillards" provides a less congenial example than certain other in this for this reasonexhaustive have not on the other, he seems to have viewed these and pieces regard-and compilations procedures; been includedhere-a casual survey of set forms vis-a-vis invariancepoints to a more "conventional" combinations, in isolation and in their high correlationbetween the white-notematerial (of bars 1- 17, 20-21, 24-28, interrelationships,in ways which transcendor thwarttheir tra- 42-46, 49-52 left hand) and the scale of C major (i.e. set 7-35, ditional tonal implications. [11,0,2,4,5,7,9]).