Analysing Debussy: Tonality, Motivic Sets and the Referential Pitch-Class Specific Collection Author(s): Annie K. Yih Source: Music Analysis, Vol. 19, No. 2 (Jul., 2000), pp. 203-229 Published by: Wiley Stable URL: http://www.jstor.org/stable/854428 . Accessed: 16/07/2013 07:39
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This content downloaded from 143.107.252.213 on Tue, 16 Jul 2013 07:39:40 AM All use subject to JSTOR Terms and Conditions ANNIE K. YIH ANALYSINGDEBUSSY: TONALITY, MOTIVIC SETS AND THE REFERENTIALPITCH-CLASS SPECIFIC COLLECTION
It is well known that Debussy rebelled against conventions, that he wrote extensively about his desire to renew musical thought, and that he criticised the direction in which traditional training was leading the musical world. In a letter to Pierre Louys, Debussy wrote: 'tonic and dominant... [have] become empty shadows of use only to stupid children.'l His preference for linear over harmonic considerations is reflected in another letter (written in 1893, the same year he composed the String Quartet), in which he glorified Palestrina's treatment of voices '. . . crossing with each other to produce something which has never been repeated: harmonyformed out of melodies[emphasis added].'2 Most of his music, particularly that composed around the turn of the century, is characterisedby innovative sonorities (harmonies that are not deployed in a traditional 'tonal' way or that use 'non-functional' extended tertial chords). In the analysis of works that employ diatonicism but that are permeated with prominent 'experimental' sonorities that cannot easily be explained in functional-tonal terms, the issue of tonality is a complex one. In studying Debussy's music composed at the turn of the century, it is easy to assume that the mere presence of tonal elements endows it with unity and coherence. But by assuming tonal elements as basic and relegating other pitch elements to an ornamental role, the importance of prominent innovative sonorities and unconventional voice-leading can be overlooked, forcing them to fit an a priori tonal model. In other words, by positing a hierarchical relationship between diatonicism and chromaticism in this music, one may be blind to the possibility that the so-called 'experimental'features themselves may play a structuralrole. Coherence in Debussy's music, I shall argue, need not be explained exclusively in functional-tonal terms. Debussy's String Quartet ( 1893) is one such work that raises difficult questions for the analyst. Various approaches have been applied to music of this kind. The most common are: 1) modified Schenkerian paradigms and traditional Roman numeral style analysis;3 2) set-theoretic parsing of the harmonic vocabulary in terms of intervallic content;4 and 3) a non-integrative combination of the above.5 But Debussy's Quartet, I argue, does not fit into
Music Analysis, 19/ii (2000) 203 t) BlackwellPublishers Ltd. 2000. Publishedby BlackwellPublishers, 108 CowleyRoad, OxfordOX4 1JF, UK
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This content downloaded from 143.107.252.213 on Tue, 16 Jul 2013 07:39:40 AM All use subject to JSTOR Terms and Conditions 206 ANNIE K. YIH any of these paradigms.In this article) I propose an alternativeanalytical framework,one that is based on the concept of transformationsof motives containedin a referentialcollection of pitches. Beforepresenting my theory,however, I shall begin by examiningsome of the problemsinherent in each of the three approacheslisted above.Although Debussy's String Quartetexhibits some features- such as triadsand seventh chords- that can be explainedin termsof tonal function,and althoughit has key signatures defining diatonic pitch content, its tonal clarity is often challenged.Such is alreadythe casein the openingpassage of the Quartet(bars 1-33, Ex. 1). Fromthe preliminaryevidence of Ex. 1, it wouldseem possible to assume the predominanttonality to be G minor. The tonic triad on the downbeatsof all fourbars, the tonicpedal in bars34 andthe appearanceof V63 at bars 13-15 all suggestthe key of G minor.However, the linearpresentation of pitch materialsdoes not support such a clear reading. The consistent presenceof Abthroughout the passage,the diatonicmelody that suggestsEb in bars 17-21, the melodicemphasis of Ebmajor over G bass notes in bars22-5, and the harmonisationof the openingmelody in Eb (beginningin bar 26), all lead to the conclusionthat there may be two tonal centresat work:G, as the tonic of a minor-modecollection, though with a stronglyPhrygian inflection of scale-degree2, Ab;and Eb,as tonic of a diatonicmajor collection. Not only do alternationsbetween these two third-relatedtonal areas (albeit without a strong cadence on either tonic) create an ambiguous environment for a clear monotonalinterpretation, they also signifya polemicalharmonic interpretation of this openingmusic, that is, Ebas VI of G or G as III of Eb.6As the music progresses,it is furthercomplicated by non-tonalpitch elements(whole-tone, atonaland octatonic)that cannot be explainedin terms of traditionaltonal relationships.Furthermore, the key relationshipsacross the four movements arealso difficultto explainusing conventionaltonal theory. Using traditionalRoman numeral notation on a local level, one wouldhave to labelthe chordsas havingnumerous chromatic substitutions or alterednotes (forexample, in the secondchord of the first movement,the dominantseventh withlowered fifth, Ab,and a sub-tonicinstead of the leadingnote, Fuinstead of F:; in bars 12s25, a dominantpedal with a loweredthird, F¢, and lowered fifth,Ab, that occurs in the retransitionto the tonic;or, in bars 12942, wherea loweredsixth, Bb, appearswith a loweredfifth, Ab, over a dominantpedal). This is a ratherclumsy practice.One would also have to ignore the motivic significanceof severalinteresting, if unconventional,sonorities. If G is readas the tonalcentre for the 51rstmovement of the Quartet,then a modifiedSchenkerian analysis may be possible.Ex. 2 illustratessuch a tonal readingin which two occurrencesof a foregroundthird progressionmay be identifiedin the first movement.The last note of the first occurrence,1, becomesan innervoice as the beginningof the secondoccurrence of 3 overlaps
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Ex. 2 Debussy, String Quartet,first movement
f 11 1 6-z19 _ _ 620______
Gm: I ?V23, VIV V3; V7/ll ?11 V5; F: 11 Vl VIVI Vl V7/lll I Vl5
122 126 13S 143 161 175 ISI IS3 blus 118 120
as an upper voice at bar 138. The two third progressions, however, are only foreground events for they are not sufficiently supported by motivic and harmonic expansions to constitute an Urlinie.Although it seems on the surface that the first occurrence could be read as a prolongation of 3, or a 3-2 interruption, and thus as part of a 3-2-1 Urliniefor the movement (as are suggested by the use of beams in the graph), such a tonal reading is reductive to a fault, forcing the reading to fit a paradigm.7 The problems of a traditional tonal analysis are obvious in Ex. 2. The long stretches of music appearing in parentheses in the graph (bars 3F60,79-117 and 143-60), as well as other shorter passages, contain sonorities that can only be explained in modified tonal terms. Too much material of critical importance
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in the piece is left unaccountedfor by such an analysis. For central to Schenkeriantheory is the organicunity - on background,middleground and foregroundlevels - of similarand mutuallycorroborative melodic diminutions of the fundamentalline, which is itself foundedon membersof the tonic triad. Unity at the middlegroundlevel, in this case, would have to rely on relationshipsthat are not characteristicof tonal theory. In brief, these two overlappingthird progressionscan only be obtainedby modifyingSchenker's theoryin the followingways: 1) by ignoringthose passagesin parenthesis(in Ex. 2) that disrupta continuousharmonic progression (such passages make up almosthalf of the movement);and 2) by reducingmotivic characteristicsof distinctivenon-tonal sonoritiesto non-structuralentities. I shall return to variousset and motivicannotations of Ex. 2 in Part III below. Approachedfrom another perspective, one mightconsider Robert Morgan's concept of 'dissonantprolongation' for an explanationof the passages in parentheses,but they would have to be heard in the context of consonance- dissonancerelationships.8 In this study, I do not assumesuch a relationship; rather,I arguethat the harmonicrelationships depend on underlyingmotives, and that the music meandersthrough transformations of these motiveswithin referentialpitch collections. Confrontedwith a G-minorishsurface, supplemented with tetrachordaland pentachordalarrangements surrounding G, completewith Ab,A¢, F", F¢, Eb, E4, Bband BS in the openingsection of the first movement,one may speakof modal'inflections' within a G major,minor or Phrygianscale as the basicpitch material. By settling on the concept of monotonality, relegating modal inflections and non-tonal elements as expansionsof tonal harmonies,one assumestonal primacy and ignoresthe possibilityof otherunifying principles. To analysesuch materialsthroughout the Quartet,set theorywould seem to possessthe appropriatepower. Its advantageover othersystems lies in its self- referential nature for it need not be used to consider hierarchies of relationships(although such considerationsare, of course, possible). While set-theoreticoperations can reveala networkof interval-contentassociations, a strictlyset-theoretic analysis would not accountfor importanttonal features in the piece (as revealedabove), just as a strictly Schenkerianor functional harmonicanalysis would not account for the experimentalelements in the piece. Whatwould seem to be calledfor in Debussy'sQuartet, then, is an analytical approachthat is sensitiveto all aspectsof its soundingqualities. Part II of this articlewill introducetheoretical tools and conceptsfor the understandingof unity and diversity in the Quartet,and Part III makes use of these in a representativeanalysis of two passages previously identified in Ex. 2 as seeminglyinimical. The analysisoffers an alternativeway of hearingmotivic relationswithin a unifyingreferential context.
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II The Referential Pitch-Class SpecifwlcCollection (RPSC) Consideringthe pitch organisationof the first movementto be linear,and that the notion of third-relatedkeys (G and Eb) with modal inflectionsrenders a traditionaltonal reading too rigid, I proposea moreflexible theory that allows the coexistenceof variouspitch materials.My theoryunderstands Debussy's String Quartetto be foundedon a diatoniccollection of pitches and that the pitch constructsin this Quartetare regarded as referentialmotivic subsets with respectto this diatoniccollection. My analysisof the musicthen aimsto reveal how all pitch materialsare derivedfrom transformationsof motivescontained in this referentialpitch collection. This theory will not only consider the variousmaterials as unified, that is, that they are generatedfrom the same sourceand integratedby commonmotivic material,but will also accountfor the key relationshipsacross the movements,inexplicable through exclusive recourseto tonal principles. With two flats as the key signatureof the first movement,as well as the fact that it beginsand ends with a G-minortriad, I assumethe G-minorscale to be the basicpitch materialto whichall subsequenttransformational processes are applied and from which everything (harmonically and melodically) is generated.In the discussionthat follows, I shall refer to this scale as the ReferentialPitch-Class Specific Collection(abbreviated to RPSC).9Leading from this assumptionis a recognitionof G as the 'key note' of this scale. The 'key'of G is only identifiedby motivicassociation, however, for even though the membersof the scaleresemble those in a G-minorscale, they arenot always deployedaccording to tonal principles. This study identifiestwo local-leveltransformational processes to account for much of the pitch material:1) 'pc substitution',and 2) 'voice-leading transformation'.l°Both processeswill be applied to motivic subsets of the RPSC to explain their continuousdevelopment. The motivic focus of this articleoffers an appropriatetheoretic modelling of Debussy's preferencefor harmonies'formed out of melodies'(Lesure and Nichols 1987, p. 42). Pitch-classsubstitution is the processof substitutingone pitch for another in a harmonyor collection of pitches. Although this process is similar to Schoenberg'sconcept of 'transformation'- which he defines as the use of chromaticnotes to substitute for diatonic ones in order to expand tonal harmonies(Schoenberg 1969, pp. 4s50) - pc substitutionin this study is not restrictedto tonal formulations. Voice-leadingtransformation describes the transformationof one or more pitches in a harmony that has motivic significance,resulting in another harmony that is transpositionally-or inversionally-relatedto the original harmony.Take the D-F-Ab-C tetrachord,for example,in a context where
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This content downloaded from 143.107.252.213 on Tue, 16 Jul 2013 07:39:40 AM All use subject to JSTOR Terms and Conditions 210 ANNIE K. YIH monotonalityis not apparent.When D and C move to Eband B respectively, tetrachordEb-F-Ab-B is generated;as an unordered set, Eb-F-Ab-B is transpositionallyrelated to D-F-Ab-C. It is in this unorderedset relationthat the motivicsignificance of the relationshipbetween the two tetrachordsunder discussion is to be understood. Unlike harmonic transformation in Schoenberg'smusic, pc substitution and voice-leadingtransformation in Debussy's Quartet create new harmonic sonorities that are developed, emphasisedand projectedthrough repetition, sequence, chordal parallelism, and other transformationalprocesses. Consequently, emphases of non-tonal harmonies(including octatonic and whole-tone)and non-tonalvoice-leading subject the listener to differentpitch collectionsin relationto the diatonic RPSC. These generated harmonies cannot be described as functional substitutesfor tonal ones. Their omnipresenceis not only motivic but, more importantly,weakens the listener'sperception of tonal relationshipsin the traditionalsense. It is preciselythe prevalenceof these sets that underminesan exclusivelytonal reading. I extend the use of the term transformationto describe a voice-leading transformationbetween the two tetrachordsin termsof a voice-leadingset of four notes, B-C-D-Eb. These notes, which occur as linearevents, form what will be calleda voice-leadingtransformation tetrachord (abbreviated as VLT- tetrachord).As the music proceeds,this particularlinear set gainsprevalence; indeed, its particularvoice-leading pattern can be seen to be characteristicof Debussy'smusic in general.Though the conceptof transformationhere seems to resemble Lewin's 'INJection Function' - which describesan operation withina canonicalgroup or considerscanonical equivalence with respectto the total-intervalcontent of sets - my concept of VLT process focuses on the formationof a set that expressesthe linearvoice-leading motions in pitch space of pcs resultingfrom this process.1l The continuousdevelopment of motivic subsetsof the RPSC, understood throughthe two processes- pc substitutionand voice-leading transformation - and their resultantsets, will be exploredin the ensuinganalysis. In this way, the unity of the Quartetbecomes apparent.
III Bars 1-33 I beginwith the identificationand discussionof the principalmotives and their inherentproperties in the firstmovement of the Quartet,followed by examples of the mannerin which they are expandedthrough the two processesat the surface level. As a generalprinciple, it is assumedthat such motives may alreadyhave undergone transformations and are thus not pitch-specificsubsets
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ANALYSINGDEBUSSY 211 Ex. 3 Melodic and harmonic motives (first bars. 1 movement, bars 1-33) 2 Xey' set 3 m-3 (4-26) m-1 (3-7) ^ t . m-1
m- 1 (3-7) i:bb 0 2 m-2\b -* ,>m-2;! m-2 (3-2) m-2 m-4 + r + h 1 (4 27) (4-10) h-1 (4-27) h-2 Gm: I (4-25) V3> III vs; I ofthe RPSC. (This is not the dissimilarto examplesof tonic.) tonal music that begin in Ex. 3 (bars1-3) shows fourprincipal motives: two formation.In this and the eachin linearand vertical are ensuingexamples, the two labelledas m-l and m-2, and linear(melodic) motives h-2.Of the two vertical all these motives,only one (harmonic)motives, h-l and pitch-class formof m-l in the upper specificsubset of the RPSC; part(G-F-D) is a pc-specific the otherscontain pitches membersof the RPSC (Aband that are not inflectionsif a Ft) but could be heard tonal readingwere assumed. as modal importantis that What makesthese four their boundarypitches form motives minor'key' triad pc-specificmembers of the (G-Bb-D), which appearsas the G- movement. first and last chord of the Theidentification of the two linear motives First,they both appearin depends on several to the outerparts; second, factors. eachother; third, their they appearin counterpoint and significanceis emphasisedby reappearancein the same immediaterepetition thesemotives will instrumentalparts. Other factors becomeapparent as this study identifying processesthat require further continues,for they involve Thefirst explanation. linear motive, m-l, is a outliningG and pitch-class specific D; it is playedby violin 1 trichord (G-F-D) emphasisedby its in bar 1. The immediatereappearance, significanceof m-l is inretrograde and playedby the same transposedup a minorthird: instrumentbut F-Ab-Bb.Motive m-2, which MusicAnalysis, 19/ii (2000) g Blackwell Publishers Ltd. 2000
This content downloaded from 143.107.252.213 on Tue, 16 Jul 2013 07:39:40 AM All use subject to JSTOR Terms and Conditions 212 ANNIE K. YIH consistsof speciE1cpcs G-Ab-Bb,outlines G and Bb;it is playedby the cello in counterpointto m-l in bar 1. Like m-l, m-2 also recursimmediately in the same instrumentbut is inverted,transposed and reordered:Ab-F-G. Set-theoreticlabels are useful at this pointto representthe motives'inherent propertiesand are pertinentto the descriptionof motivicrelationships. Using Forte'snomenclature, m-l and m-2 are identified(on Ex. 3) as set-classes3-7 and 3-2, respectively.12The relationshipof the secondto the first appearance of m-l can thus be expressedas T3(3-7);and, the relationshipof the secondto the first appearanceof m-2 can be expressedas T1I(3-2). Motives in Ex. 3 show a distinctionamong (close-to-surface) structural levels. Such a hearingis intuitively correct, given the prominenceof these motives in the melodic figuration.Beams in Ex. 3 drawattention to motivicrepetitions in the opening phrase. Althoughmost of the motivic materialoccurs at or close to the surface,a relativelydeeper level of motivicactivity may also be perceived.Consider the expansionof m-l. A new dimensionmay be addedto the beginningnotes of groupedsurface events of m-l, thus generatinga tetrachord,labelled m-3 in Ex. 3. Motive m-3 (G-F-D-Bb, representedas set-classF26) is a pc-specific subsetof the RPSC. This motive constitutesthe threenotes of m-l (G-F-D) and a fourthnote, Bb,which followsD of m-l at a leap of a sixth, endingthe first fragmentof the opening phrase on the downbeatof bar 3. The same tetrachordalso constitutesthe first and third triads(G-Bb-D and Bb-D-F, or tonic and mediantof G) in bar 1. Becausetetrachord F26 is a subset of the pentatonic5-35, emphasis of its pentatonicsonorous quality weakens the listener'sperception of the key of G. Whilem- 1 is expandedin the violin 1 part,m-2 is expandedin the cellopart. If repetitions of smaller motives are grouped into larger units, another dimension may be added to motive m-2, generatinga second tetrachord (superset)motive, F-G-Ab-Bb, which is featuredin the bassline andis labelled as m-4 in Ex. 3. Like m-3, this tetrachordis generatedfrom the union of two interlocking inversionally-relatedtrichords, 3-2: G-Ab-Bb (m-2), pc set [7,8,10], and Ab-FF, pc set [5,7,8], expressedas T3I of m-2 [7,8,10]. This unorderedlinear tetrachord,S10, is characterisedby its symmetricalBIP: [2][1][2].13The significanceof this BIP lies in its having the characteristic propertyof an octatonicset. Whilethe significanceof m-3 lies in its beinga pc- specifictetrachord of the RPSC, the secondtetrachord, m-4, is a linearmotive; the prominenceof both tetrachordsemerges as the music proceeds. All pitchesof the four melodicmotives of the outer-mostaudible parts spell D-F-G-Ab-Bb. These notes form pentachord5-25, which reappearsas an importantsounding body laterin the Quartet.The pentachord5-25 is a subset of both the diatonicand the octatoniccollections: the emergenceof octad8-28 in the Quartethelps makeclear the significanceof this pentachord.
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As harmonicprogression in this music does not projectunity exclusivelyin tonalterms, prevalence of motivicmanifestations in the verticaldimension may aptlysubstitute for unifyingtonal principles. In additionto the two trichordand two tetrachordmotives (labelled in Ex. 3), two verticalsonorities are labelled h-l andh-2. The first,which consists of specificpcs D-F-Ab-C, is emphasisedby a downbow on the secondbeat of bar 1. It harmonisesF of m-1 and Abof m-2, whereF andAb are perceived as passingnotes of theirrespective melodic motives expandingmembers of the G-minorkey triad.Like the melodicmotives, these harmonies'sonorous properties also havemotivic significance. The motivic significanceof h-l lies in its being the progenitorthrough pc substitutionsand/or voice-leadingtransformations of other non-pc-specific subsetsof the RPSC. A casein point occursthrough pc substitutionof Ft for F where motive h-2 (D-Ft-Ab-C) is generatedby transformationfrom h-l on the last beatof bar2 (indicatedby a curvingarrow at the bottomof Ex. 3). The second motive h-2, arrangedin its prime form, is identified as F25 (the French-sixth chord). Pc set 4-25 is a symmetricaltetrachord with BIP: [2][4][2]. Although one could regard Ab as substitute for A and hence a dominant-seventhchord, one wouldthen be ignoringthe music'scharacteristic whole-tonequality. Transformationsof harmoniesthrough pc substitution,pc-adjacency voice- leading and voice-leading transformationare a common practice in late nineteenth-centurymusic. In relationto the diatonicRPSC, both motivesh-l (D-F-Ab-C, henceforthidentified as tetrachordS27) and h-2 (D-Ft-Ab-C, identifiedas 4-25) can be explainedas sets generatedby pc-substitutionfrom a pitch-specificsubset of the RPSC, D-F-A-C (tetrachord4-26), with Abof D- F-Ab-C substitutingfor A of S26; and F25 is generatedfrom D-F-A-C by substitutingF: andAb for F andA respectively.Although D-F-A-C (arranged in its prime form, A-C-D-F) is not harmonicallyexploited here, another transposition(T7) of tetrachordS26 has been featuredas melodicmotive m-3 in the opening thematicunit, D-F-G-Bb. This transposedset is also a pc- specificsubset of the RPSC. The pc-specific motive m-3, tetrachord S26, when arranged as an unordered set (D-F-G-Bb), is characterised by its symmetrical BIP: [3][2][3];its internalintervallic configuration can be describedas a union of two interlockinginversionally-related trichords, pc-set 3-7 (two forms of motivem-l): G-F-D (m-l), pc set [2,5,7], and F-G-Bb, pc set [5,7,10],where the relationshipof the latter to the former is ToI of [2,5,7]. It can also be described as two inversionally-relatedsubsets: the 'key' set G-Bb-D that occursas the first verticalchord and Bb-D-F that occurs as the third. Aside frombeing a subsetof 5-25 (mentionedabove), m-3 (set 3-7) is also a subsetof the pentatonic 5-35 (F-G-Bb-C-D), another prevalent harmony in the Quartet.
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Ex. 4 First movement, bars 19s205 Ex.4
Violins and Viola in 8ves doubling with cello [119tWS2 rrrrUnJ;Elzn;;;;;;;;lJ;J;nxJnlUnxJ;;;;;;lns;
[198;Wprr::nrrrr:lrrrrrr::::rrlffttrrCft¢::l:¢: Jl
Thus far, of the four tetrachord motives identified, the property of symmetry is contained in three: 4-26, 4-25 and 4-10. We shall see below that the prevalent use of symmetricaland inversionally-relatedsets undermines an exclusively tonal analysis. Having identified the principal motives in bars 1-3 and their inherent properties, the last part of this article will discuss how these motives are integratedand expanded at the surface level through the two processes of pc substitutionand voice-leading transformation.Compared with those generated from motives m-l and m-2, other symmetrical and inversionally-related sets occur less conspicuously. The diatonic pitches of the four melodic motives (ignoringAb and F: for the time being) spell the pentatonic 5-35, G-Bb-C-D-F. Unordered,5-35 is a symmetrical set, a pitch-specific subset of the RPSC, and has an ambiguous tonal property. Like other pitch-specific subsets of the RPSC, this pentachord appears in different dimensions throughout the Quartet.One prominent instance occurs at the conclusion (codetta) of the first movement in a running passage, with specific pitch-classes of this pentachordin unisons and octaves. (See Ex. 4, first movement, bars 194-205.) Symmetrical and inversionally-related sets, much favoured by Debussy in theQuartet, also occur in conjunction with expansions of the melodic and harmonicmotives in multi-dimensional ways. (Exs. 5a and b present graphic analysesof bars 1-13.) Beginning in bar 1 in Ex. 5a, G4 of m-l (G-F-D) is expandedin violin 1 by registral transfer to G5 in bar 5. As G5 descends to F5 onthe second beat of the same bar, F5 is expanded from that point by registral transferto F4 in bar 8, ending on D4 on the fourth beat of the same bar. The rhythmicand melodic emphases of F5 to F4 yield a non-functional fully- diminished-seventhchord, which can be identified as an octatonic tetrachord 4-28,B-D-F-Ab. As shown in the example, 4-28 appears in linear as well as vertical configurations. The expansion of m-l is echoed in the cello part by the melodic expansion of T3I of [7,8,10], G-Ab-F (pc set [5,7,8], shown as slurred notesin the example). The note G2 from the opening unit is connected to Ab2 onbeat four of bar 5 through a circle of perfect fifths that begins on the downbeatof bar 5. Ab2 in the cello is then connected up to F3 (on the fourth beatof bar 8) as a member of an arpeggiation of tetrachord 4-28 (Ab2-B2-D3- F3).The motion from G2 in bar 1 to Ab2 at the end of bar 5, which then
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ANALYSINGDEBUSSY Ex. 5a First 215 movement, bars 1-13
bars. 1 5 6 8 m-l (3-7) / I
l 6-27 6-z49 8-28 Ex.5b
bars. 1 5 6 8 10 13 '4;7 ;X.- / ,< X .
(Gm h-l (4-27) V9) 5cEx.
bars.8 9 10 1211 13
4-28 4-27 4-27 h-l 4-27 T2(I(4-27)) h-l
continuesto F3 in bar 10, yields a AsmovesG2 in a large-scale reordered circle of descending motive m-2 (G-Ab-F). involvedin this perfect fifths to Ab2 motion yield a in bars 58, the notes whichalsois a diatonic hexachord 6-32 symmetrical set. (G-C-F-Bb-Eb-Ab), Music Analysis,19/ii (2000) t Blackwell Publishers Ltd. 2000
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216 ANNIE K. YIH
Fig. 1 Transformationsof motive h-l (D-F-Ab-C)
bars 5-8 bar 8 bar 13
3
Ab Ab Ab Ab > A ]
F F F F > F: J
S27 (h-1) F28 S27 S27 F27 5-31 5-31 1 11 1 6-27 6-z49
l l 8-28
In bars 5-8, 8-12 and 12-13 (Ex. 5c), the harmonic motive h-1 undergoes three transformations, generating octatonic elements, and culminating in the octatonic octad 8-28 (D-Eb-F-F"-Ab-A-B-C).14 (See Fig. 1 for a summary of the voice-leading transformationsof motive h-1, F27.) As B substitutes for C as a lower neighbour note in bars 6-8, an octatonic tetrachord F28 is generated. Then, in bars 10-12, two notes, Eb and B, oscillate with their neighbour notes D and C of motive h-1, respectively. These four notes draw attention to their pairing as two voice-leading dyads (B to C and D to Eb), forming a VLT-tetrachord F3, B-C-D-Eb. (Tetrachord F3 has the octatonic characteristicof a BIP [1][2][1].) D and C of h-1 (s27) move through voice- leading transformationto Eb and B, respectively, resulting in another S27 (F- Ab-B-Eb). This new form of h-1 (F-Ab-B-Eb) is related to h-1 (D-F-Ab-C) at T3. Eb and B and the four notes of motive h-1 spell another octatonic hexachord 6-27. (B-C-D-Eb-F-Ab is one of only six classes of octatonic hexachords contained in the octatonic octad 8-28.) Fu and A appear in bar 13, voice-leading transformations of F and Ab respectively. This transformation changes D-F-Ab-C (h-1) into D-F"-A-C, an inverted form of h-1 at T2, which can be expressed as T2I of [2,5,8,0]. The two notes F and Ab have been rendered significant through voice exchange in bars 8-12, and the change of F and Ab to Fu and A makes them stand out as two pairs of related dyads. Together, the four linear notes spell another octatonic VLT-tetrachord S3, F- F"-A"-A. With Fu and A added to the four notes of motive h-1, they spell the octatonic hexachord 6-Z49 (another one of only six octatonic hexachords).
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Ex. 6 Fourth movement, bars 15-24
bars 15-l6 17-l8 19-20 2l-22 23-24
j 7 D t4; it1b§ 1Z1l44 f : F
:) p1,7 II"SiS s;f > 7h17F"|k"W4^>5t+- ttlit44J; ht1#? r 5-ha tt - 4-28 4-28 4-28 4-28 5-31 5-31
8-28 (stemmed notes)
When we consider all eight notes together, they spell the octatonic octad 8-28, B-C-D-Eb-F-F-Ab-A. While it is possible to read the passage as a connection of the G-minor tonic triad in bar 1 to an inverted dominant chord on the downbeat of bar 13, as Richard Parks (1989, p. 10ff) has done, such a tonal reading neglects the motivic significance of h- 1 in supporting the melodic motives and their transformationsin bars 2-12. The voice-leading transformationsof h-1, S27, are summarised in Fig. 1, revealing: 1) the two occurrences of the VLT- tetrachord 4-3 (B-C-D-Eb and F-F"-Ab-A) between two pairs of transformationally-relatedtetrachords (s27); 2) the derivation of two of only six classes of octatonic hexachords (6-27 and 6-Z49); and 3) the generation of the octatonic octad 8-28. The emerging importance of these eight pitches, which first appeared as the pitch-class specific octad in bars 8-13 of the first movement, can be found in bars 15-24 of the fourth movement, where they are featured as two F28s (Ex. 6). Other octatonic sets appear at higher structural levels in the music. Two pairs of inversionally-related octatonic pentachords (5-28 and 5-31) are contained in the two hexachords, 6-Z49 and 6-27 respectively, in bars 1-13 of the first movement. The two pairs of inversionally-related pentachords, 5-28 and 5-31 and their inverse, and their symmetrical BIPs are illustrated in Figs. 2a and b respectively. (Their significance, however, will not be observed until after bar 34, in the first passage that appears in parentheses in Ex. 2.) While the above discussion has focused on Debussy's preference for sym- metricaloctatonic elements, the following discussion will reveal the integrationof voice-leading-relateddiatonic and octatonic pitch elements. Pertinent to fore- ground events, several pairs of inversionally-related diatonic chords in the Quartetare of particularmotivic interest to Debussy. Among the more prominent diatonic chords, we find three common traits: 1) that most of the referential pitch-specific subsets have symmetrical properties; 2) that the relationship between these subsets is usually inversional at a transposed level; and 3) that larger sets usually contain interlocking inversionally-relatedsubsets. Because these pairs of diatonic chords are contained in the RPSC (representedas septad 7-35), an examinationof 7-35's content and its inherent properties may prove
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Fig. 2a Fig. 2b bars 1-3 bar 13 bars 8-12 C C C C > B B l 3 D D D D D > Eb
Ab Abb > A F3 ' ' F , Ft Ft F F F
S27 S1125 T2I(t27) S27 F28 S27 l 11 1 5-28 T2(5-28) 5-31 T3(5-3t)
6-z49 6-27
T2I(5-28) /
5-28 1 l B C D F Ab = 5-31 C D F F: Abl A C D D Eb F Ab B = T3(5-31) I 11 IL 11 11 IL I I I ILLI 11 1 BIP: 2 3 1 3 1 3 2 BIP: 1 2 3 3 useful. Fig. 3 demonstrates referential pitch-specific subsets contained in the RPSC and their interrelationships.One of 7-35's most characteristicdiatonic properties is its six occurrences of perfect fifths: its interval-class vector reads [254361].15 Two of many examples of each of these diatonic subsets in the Quartet are given in Exs. 7a-b and 8a-b (reductive analyses of bars 17-27 and 27-33, respectively). As has been discussed in reference to Ex. 5, the six pitches, which are presented in a circle of fifths, G-C-F-Bb-Eb-Ab, in the cello part in bars F5, spell hexachord 6-32. Although Ab of this 6-32 is not a pitch-specific member of the RPSC, the boundary pitches, G-Ab, are pitch-specific members of m-2, trichord 3-2. The internal structure of 6-32 also has motivic significance. 6-32 contains two interlocking inversionally- and trans- positionally-equivalent pentatonic pentachords, 5-35: Eb-F-G-Bb-C and C- Bb-Ab-F-Eb. The first pentachord appears in its pitch-specific form, as a subset of the RPSC; the notes are expanded by melodic figurations at the surface level and appear as 'out-of-order' fifths, Bb-G-C-F-Eb. Pentachord
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ANALYSINGDEBUSSY 219
Fig. 3
7-35:G A Bb C D Eb F G 3-7\ 3-7 3X7 Bass line of bars S5: 5-35: F IC Ebl | Fl G |
Bassline of 3-7 3-7 3-7 bars 1l \ / 183-194: 5-35:4 | Bb IC I | D F|
Bass line of bars 5-35:1Bb G C S F Eb 5-35:s Eb Db Gb l Cb Ab 21-28: 3-7 1 1 3-7 1 l 3-7 3-7
Ex. 7a First movement, bars 17-27
bars. 17 21 22 23 24 26 27 1+v0,.,+..,? ; t;
5-25 5-34 5-34 5-6 EN: V I- V- - - (1) III VI II (V) I - VII-I omitted omitted
EN: V ) I
Ex. 7b
bars. 17 21 22 23 24 26
I J j ; C ;t SIP: 3-5-5-2 b C 3 C 5 5 2
5-35
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ANNIE K. YIH 220
Ex.8a First movement, bars 27-33 33 30 31 32 bars 27 29 28 __ _ _ - _ _ >, A iN L _,#,,= A 1 1o D ^ 4-10 $8wR e r Y , sb 19 X >
) V- -I Gm: VI (
Ex.8b
30 32 bars. 27
v ,5-35 SIP:2-5-5-3 2 1 .E I .S l R I
V I) ( Gm:VI partconnecting the appearsas an expandedbass line in the cello Bb-G-C-F-Eb 26. (The notes are the Eb-majortriad on the downbeatof bar Ebtheme to notes in the cello part Ex. 7b.) As shown in Ex. 7a, these five beamedin of m-l, F to G, in the the connectionof two of the specificpitches support 27 (Ex. 8b) is expandedto bar 30 violinpart. Then, the Eb-majortriad in bar pentachord5-35, which appearsin a transposed bythe occurrenceof another The form in the cello part, Eb-Db-Gb-Cb-Ab. and again 'out-of-order' of two of the of the second pentachordsupports the connection occurrence 1 part (Ex. 8a).l6 specificpitches of m-2, Ab to G, in the violin for the motivic interrelationshipsof structurally I have thus far accounted accountof this in bars 1-33. Althoughan exclusivelytonal importantpitches unifyingaccount of all possible,the motivicapproach provides a more passageis non-tonal)in this music. the pitch materials(diatonic, octatonic, whole-tone,
Bars 34 60 passage in which tonal functions are Bars 3s60 constitute the first extended materials are present, they are not not discernible. While diatonic pitch
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ANALYSINGDEBUSSY 221
Ex. 9 First movement, bars 3s60
bars. 34 36 39 43 47 4S n>2 (S2) m-2 (3a2) _ _ _ _
0o9 ;J WrJc.-'>'; ii;>>hrJr;r r Fr >>t§rWr et1s?a=1l ¢4r
4-27 4-27 4>27 4>2? 4>27 427 4>27 6-z23 6-30
bars.49 S0 51 S3 55 S6 S7 S8 S9 60 4-10 410 427 i$7 = ;02 pse1-| 2 ; fv _
4-27 4-27 27 4-27 4-27 subjected to functional tonal treatment and the harmonies appear to be derived from other means of organisation. The discussion below of Ex. 9 (bars 34-60) supports my contention that the harmonic language of the work is principally that of motivic expansion. In bars 34-5, the beginning and ending harmonies of the first phrase segment, C-Eb-Gb-Bb and Eb-Ab-C-Gb (melodically and rhythmically emphasised in Ex. 9), support a transposed inverted form of motive m-2 (Eb5-Gb5-F5) in the violin 1 part. While the two harmonies combine to spell the dominant-ninth chord of Db, what follows is not the expected Db triad but a Gb-seventh chord with an added C that cancels any implication of Cb as the tonic, as has been suggested by the Gb-seventh chord. These harmonies make no sense as tonal configurations but can be explained in terms of harmonic and melodic motives that have been presented at the beginning of the piece, and now resurface in new manifestations. Explained in the light of set-theoretic relationships, the first two harmonies in bars 34-5 (C-Eb-Gb-Bb and Eb-Ab- C-Gb) are two forms of 4-27 that are inversionally equivalent at T6, and the next seventh chord in bars 36-8, Gb-Bb-Db-Fb, is also a 4-27, inversionally equivalent to the first seventh chord C-Eb-Gb-Bb at T4. (Fig. 4 summarises their properties.) Debussy's preference for inversionally-relatedchords, rather than a more traditional tonal harmonic conception, is clearly at the root of this passage. Because these harmonies occur in a linear and sweeping fashion such that not one single harmony is emphasised, the listener can perceive a union of these three inversionally-relatedtetrachords. They form a collection of pitches
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Fig. 4
Bars 34 35 36-38 Gb Gb Gb Bb > Ab > Bb Eb Eb > Fb ' 4-3 C C > Db
S27 T6I(4-27) T4I(s27)
6-27 that belongs to the Db-major scale (septad 7-35); and in bars 36-8, where F is changed to Fb, a combination of the parallel major and minor scales of Db is suggested. What follows in bars 39-47 is a passage that might be explained as related to bars 34-5 in terms of modified modal theory; such an explanation, however, would suggest that a new system of musical thought is suddenly being used. The resulting combination of different analytical perspectives would constitute a kind of material disunity that is not musically apparent in this piece. I believe that this passage may be explained as an expansion of melodic and harmonic materials already presented in the first section of the movement. First, in bar 39, there are two tetrachords (F-Ab-D-Bb and Ab-Cb-F-Db), which are transposed and inverted forms of motive h-1, pc set [0,2,5,8], 4-27; they are expressed as TloI of [0,2,5,8] and T1I of [0,2,5,8] or h-1, respectively. When these two tetrachords are combined, the result is the octatonic hexachord, 6-27 (D-Db-Cb-Bb-Ab-F), which is inversionally equivalent to the prominent hexachord 6-27 (B-C-D-Eb-F-Ab) at T1 in bars 8-12 (refer to Ex. 5a). Second, in bars 39-47 at the end of the arpeggiation of tetrachord 4-27, F-Ab-D-Bb or TloI of [0,2,5,8], another 4-27 is generated through voice-leading transformation.Bb and F of the F-Ab-D-Bb tetrachord move to B and E, respectively, generating E-Ab-B-D. This latter 4-27 is related to the former at T6. The combination of these two tetrachords generates another octatonic hexachord, 6-30 (Ab-Bb-B-D-Eb-F). (This hexachord is the third of six possible hexachords in the octatonic octad.) Third, a motivic voice-leading event associates tetrachord 4-25 (motive h-2) with its immediate successor, tetrachord 4-27 (motive h-1), in bars 36, 48 and 50. (The pairings of 4-25 and F27 sets are marked by horizontal brackets in Ex. 9 and their voice-leading is shown in letter names in Fig. 5.) In bar 36, a voice-leading event involves the upper adjacencynote C of Gb-Bb-C-Fb (tetrachord4-25) moving to Bb of Gb-
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Bb-Db-Fb (tetrachord 4-27). Although C in bar 36 moves melodically to Bb, these two tetrachords in bar 36 are related by voice-leading transformation where Db substitutes for C. Fig. 5 demonstrates in letter names the three occurrences of pc substitution between the three pairs of 4-25 and 4-27, in bars 36, 48 and 50. The enharmonic relationship of the second and third pairings of the transformationsin bars 48 and 50 further emphasise the harmonic significance of the two tetrachords (motives h-l and h-2). In bar 48, the substitution of Bb for Bb of E-Ab-Bb-D (4-25) generates tetrachord4-27 (E-Ab-B-D). The notes of tetrachord F25 in bar 48 are then enharmonically respelled as E-G"-A"-D in bar 50. A: of this latter 4-25 also moves by pc substitution to B of tetrachord 4-27. The union of any one of the three pairs of tetrachordsF25 and 4-27 yields an octatonic pentachord 5-28. (The generation of pentachord 5-28 from the union of tetrachords 4425 and 4-27 was earlier illustrated in Fig. 2a.) As already discussed, Fig. 2a shows the transformation of pitch-specific motive h-1 (D-F-Ab-C), tetrachord 4-27 in bar 1, through tetrachord 4-25 (D-F"-Ab-C) in bar 3, to its inverted form D-Ft-A-C at T2 in bar 13. The transformationby icl of the inverted form of h-1 into the whole-tone sonority tetrachord 4-25 would not have been significant had their relationship not been emphasised by their reappearance in bars 36, 48 and 50. Such recurrences weaken the seemingly 'dominant-seventh' sonority of tetrachord D-F"-A-C or T2I of h-1 (D-F-Ab-C), emphasising the union of any one of the three pairs of tetrachords 4-25 and 4-27 as one sonority. It is not difficult to hear the specific pitches of the two transposed forms of tetrachord 4-25 (Gb-Bb-C-Fb in bar 36 and E-Ab-Bb-D in bar 48, which is then enharmonically emphasised as E-G"-A"-D) form a whole-tone hexachord, Gb-Ab-Bb-C-D-E (6-35). 6-35 is found in several sections of the piece (such as in bars 97-100 of the first movement and bars 157-9 of the second movement.) The prevalence of whole-tone harmonies also cancels the seemingly 'dominant-seventh' function of tetrachord D-F"-A-C. Fig. 2a illustrates two interlocking inversionally-relatedpentachords, which generatethe octatonichexachord SZ49; they are expressedas 5-28 and In(5-28). As summarisedin Fig. 5, the three occurrencesof the pairing of tetrachordsF25 and S27 in bars 36, 48 and 50 belong to the inversion at a transpositionlevel of 5-28 type. Tetrachords S25 and S27, not paired in immediate succession in bars 1-13, now do so and can be paired to create an inverted form of 5-28 at a transposition level in bars 36, 48 and 50, and in other significant parts of the Quartet. Finally, the use of harmonic motive h- 1 (tetrachord4-27) in association with melodic motives m-1 (trichord 3-7) and m-2 (trichord 3-2) in bars 48-58 presents another significant dimension of motivic unity. (The melodic
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224 ANNIE K. YIH Fig. 5
bar 36 bar 48 bar 50 Fb Fb D D D D
Bb Bb Ab Ab G: G: Gb Gb E E E E T :T T T T T 4-25 4-27 4-25 4-27 4-25 4-27 l l l l l l TnI of 5-28 TnI of 5-28 TnI of 5-28 occurrences integrated with h- 1 are explicated in reduction in Ex. 9). Tetrachord4-10, which was discussedearlier as generatedby combiningthe inversionally-relatedm-2 (trichord3-2) in the cello partin bars now 1-3 (Ex. 3), is featuredin the violin 1 and cello partsin bars48-58. In bars cellopart 48-53, the featuresmotive m-1, E3-A2-G3 (trichord3-7); as G3 is toG4 in transferred bar55, it is precededby Fj4, generatingtetrachord 4-10, Then,F"4 is E-F"-G-A. expandedin bars56-9 by two interlockingtrichords, 3-2 m-2),Fj4-A4-G4 (motive and G4-E4-F:4; the union of these two trichordsyields anotherform of tetrachord4-10, E-F"G-A. In bars 56-9, tetrachord4-10 (E-F"-G-A) in the cello tetrachord supportsanother 4-10 (A-B-C-D) in the violin 1 part.The lattertetrachord alsogenerated 4-10 is by the union of two interlockingtrichords, 3-2 (motive B5-D6-C6and m-2), C6-A5-B5. Integratedwith these linear tetrachordsin the verticaldimension, as shown in Ex. 9, are a series of transformationsof the harmonicmotive h-1, tetrachord4-27. Although limitationsof space prohibit analysis of the remainderof the Quartet,the materialsaccounted for in the sectionsabove are foreground representativeof processescontained throughout the Quartet.Before I conclude, shallshow briefly I that motivicassociations can also accountfor the large-scale designof key relationshipsacross the four movements. Even though much of the Quartetdoes not concernitself with tonalharmonic traditional usage,the parallelmajor and minor key signaturesof G andDb areused throughout.The key signatureof the first minor, movementsuggests G that of the secondsuggests G major.The third movement notesof the begins with Db-majorscale (supported by the key signatureof five flats), shiftto the with a C"-minorscale in the middlesection before returning to the notes ofthe Db-majorscale in the finalsection. (The changefrom first Db-majorto minor appearsin bars 3s8 of the first movement.)The notes of dominatethe Db major openingof the fourthmovement, before a shift to the notes of the G-minorscale takes place in bars31-124. Afterfurther melodic expansions in
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This content downloaded from 143.107.252.213 on Tue, 16 Jul 2013 07:39:40 AM All use subject to JSTOR Terms and Conditions ANALYSINGDEBUSSY 225 severalpassages in the middlepart of the fourthmovement, the Quartetends with a traditionalcadential progression in the key of G major. Using tonaltheory, one wouldnot be able to accountfor the choiceof these particularkeys or providelinks betweenthe motiviclanguage of the piece and these nominal key centres. The way to an integratedpicture lies in that collectionof pitches derivedfrom the combinedpitches of the G-majorand -minor, and Db-majorand -minor, triads, that is, those triads that form the referentialsonorities of the four movementsof the Quartet.The collectionof pitches obtained from these four triads is: G-Ab-Bb-B-Db-D-Fb-F, the octatonicoctad 8-28.17
Conclusion The generationof octatonic,whole-tone and non-tonalpitch elementsfrom the diatonicRPSC and its motivicsubsets through pc substitutionand voice-leading transformationoffers an alternativetheory for explainingthe relationshipsand integrationof variouspitch materialsin Debussy'sQuartet. Detailed discussion of two representativesections suggests that the use of a combinedlinear and set analyticalapproach reveals the motivicunity of the variouspitch materials more convincinglythan does any othersingle analytical method. In brief, four observationscan be made.First, by understandingtetrachord S27 as a motivic-harmonicentity, and by perceivingthat its transformed equivalentsare generatedthrough voice-leading transformation at the surface level, one can appreciatethe unifying function of the motive. Second, as expansionsof the harmonicmotive h-l are integratedwith the two melodic motives m-l and m-2 (which are containedin the octatonicoctad 8-28), the two seeminglytonal (bars 1-33) and non-tonal (bars 3s60) sections in the Quartet'sfirst movementcan thus be explainedas motivicallyunified. Third, with harmonicmotive h-1 functioningto supportthe expansionof the two melodic motives (m-l and m-2), one can appreciatethe motivic unity of octatonicand whole-toneharmonies that are generatedby pc substitutionand voice-leadingtransformation of subsets of the diatonic RPSC. Finally, an understandingof the correspondencebetween the interactionof motives and the large-scaleoctatonic structure suggests the particularkey scheme of the larger four-movementstructure and provides the means of access to an integratedunderstanding of this music.
NOTES 1. Debussy's search for a harmonic language and ways of creating coherence beyond those circumscribed by traditional practice can be revealed through letters and articles he wrote before and during the time he composed his Quartet. Debussy
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wrote the letter to Pierre Louys after he returned from attending the Universal Exhibition in 1889 (Lesure 1980, pp.70-73; Lesure & Nichols 1987, pp.76-7). In 1893, Debussy proclaimed the importance of linear over vertical approaches (Lesure & Nichols 1987, pp.40442). 2. This is recorded in Lesure & Nichols 1987, pp. 4(}42. In another context, he denouncedthe Paris Conservatoirefor its 'altogetherfaulty' teachingof harmonyas chords independentof linear considerations(Vallas 1929, p.26). Later, in 1902, he preferredBach's 'free play of sounds whose curves, parallelor contrary,produced the wondrous efflorescence of arabesque',to more harmonicallyconceived music (Ibid., pp.26-7). For a discussion of Debussy's use of the term arabesquemusicale see Eigeldinger 1988-9, pp. 514. Eigeldinger points out Debussy's awarenessof the aesthetics, both poetic and symbolic, of the term during 189(}91. 3. Among the earliest applications of Schenkerian concepts to post-tonal music are Katz (1945) and Salzer (1952). See also, more recently, Matthew Brown (1993, pp. 1274 2). While it is possible to apply to Debussy's early works Brown's systematic redefinition of the boundaries of Schenker's theory by identifying four techniques that move away from nineteenth-century formal models, I shall present an alternative theory for Debussy's music. 4. An early application of set theory to post-tonal experimentalmusic may be found in Allen Forte's article on Liszt's music (Forte 1987, pp. 209-28). Richard S. Parks (1989) identifies non-tonal pitch materials in Debussy's later works in a most revealing way. In two other articles, Forte uses set theoretic paradigms to reveal motivic organisation in one of Debussy's later pieces (Forte 1989, pp. l(} 16) and attempts to cover the use of octatonic elements in a wide range of Debussy's music (Forte 1991, pp. 125-69). 5. The earliest use of an approach that combines tonal and set theoretic paradigms appears in Forte's article on Schoenberg's music (Forte 1978, pp. 133-76). Forte uses Schenkerian methods to reveal advanced chromatic tonal material, and unordered pitch-class sets to disclose atonal material in the music. Michael L. Friedmann, in his article on one of Debussy's later works (Friedmann 1982, pp. 22-35), uses a combined but non-integrative approach to reveal the non-tonal materials within the underlying tonal structure. Howard Cinnamon, in his article on Schoenberg (Cinnamon 1993, pp. 127- 70), also uses a similar approach. 6. For a discussion of tonal ambiguity created by third relationships, see Stein 1985. 7. Schenker understood an 'organic' structure as occurring when motives can be seen to generate the musical events on all three levels (foreground, middleground and background)of a work. We can perceive organic unity when the fundamental line and the bass arpeggiationare 'composed out' through melodic and rhythmic figurations. Such tonal unity is not apparent here. Forte (1988, pp. 31548) cautions that 'the uncritical application of Schenkerianparadigms to certain kinds of music has often led to poor results ... and has obscured important issues that require confrontation'. 8. See Morgan 1976. The concept of consonance-dissonance relationship and the
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This content downloaded from 143.107.252.213 on Tue, 16 Jul 2013 07:39:40 AM All use subject to JSTOR Terms and Conditions ANALYSINGDEBUSSY 227 definition of prolongation and its application to post-tonal and atonal music in the late nineteenth and early twentieth centuries have also been discussed by many theorists - among them, Parks (1989), Salzer (1952), Straus (1987) and Wilson (1984). 9. The concept of a referential pitch-class specific collection in this article is conceived as a pitch-specific diatonic scale and not as a diatonic subset of the 12- note chromatic universe, as discussed in John Clough's and Jack Douthett's article (1991). By making this distinction, I assign the pitch-specific diatonic scale a fundamental structural role. The complementary pitches, which complete the 12-note chromatic universe, are generated through the transformationsof subsets that comprise the RPSC. 10. I thank Allen Forte for suggesting the term for the second process. 11. One particularly important publication is David Lewin's GeneralizedMusical Intervalsand Transformations(1987). See chapter 6 for the discussion of INJection Function and chapter 5 for related issues. 12. Set names facilitate the identification of sets that are associated by related properties, for example, properties such as equivalent successive ic patterns or total interval content. Because symmetrical sets are sometimes interlocked to form larger sets, inversionally-related sets will always be identified explicitly: In(3-7) thus designates the inversion of set 3-7. 13. Forte's BIP refers to the total interval-class pattern of a pc set in its prime form. The use of SIP (Successive Interval-Class Pattern) in Exs. 7b and 8b is derived from Forte's BIP, which, in the former case, refers to the ordered interval-class successions that occur as the pitches of a pc set unfold in time in the music. See Forte (1979, p. 63ff). 14. See Pieter van den Toorn (1983, pp. 50-51). According to van den Toorn, the notes belong to the octatonic octad, 8-28, Collection II. 15. The figure also explicates the structures and sub-structures of those inversionally-related chords contained in the RPSC, a characteristic diatonic septad. The configurations of larger subsets derived from each sub-structural level are based on the interlocking of transformationally-relatedsubsets of the diatonic septad 7-35. 7-35 contains a pair of interlocking transformationally- related hexachords, 6-32 (Bb-C-D-Eb-F-G and D-C-Bb-A-G-F, where both hexachords are inversionally equivalent at a transposition level); each of the two 6-32s contains a pair of interlocking pentatonic pentachords, 5-35, where both pentachords are also inversionally equivalent at a transposition level; and, each 5- 35 contains a pair of interlocking trichords, 3-7, that are inversionally equivalent. 16. Incidentally, the SIP of the first 5-35 and that of the second are in retrograde relationship. The first pentachord reads [3][5] [5] [2] and the second [2][5] [5] [3] . 17. See Forte 1991 and van den Toorn 1983, pp. 50-51; according to van den Toorn, the notes belong to the octatonic octad, 8-28, Collection I.
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REFERENCES Brown, Matthew, 1993: 'Tonality and Form in Debussy's Preludea l'Apres-midi d'unfaune', Music TheorySpectrum, 15/ii, pp. 12742. Cinnamon,Howard, 1993: 'Tonal Elementsand Unfolding NontriadicHarmonies in the Second of Schoenberg's Drei Klavierstucke,op. 11', Theory and Practice, 18, pp. 127-70. Clough, John and Douthett, Jack, 1991: 'MaximallyEven Sets', 3tournalof Music Theory,35/iii, pp. 93-173. Eigeldinger, Jean-Jacques, 1988-9: 'Debussy et l'idee d'arabesque musicale', CahiersDebussy, 12-13, pp. 5-14. Fontainas, Andre, 1928: 'Mes souvenirs du symbolisme', in Essais critiques,10 (Paris:La Nouvelle Revue Critique),pp. 92-3. Forte, Allen, 1973: The Structureof Atonal Music (New Haven: Yale University Press). , 1978: 'Schoenberg'sCreative Evolution: The Path to Atonality', Musical Quarterly,641ii, pp. 133-76. , 1987; 'Liszt's ExperimentalMusic and Music of the Early Twentieth Century', 19th-CenturyMusic, 101iii,pp. 209-28; republishedin Music at the Turnof the Century:A 19th-CenturyReader, ed. Joseph Kerman (Berkeley: University of CaliforniaPress, 1990). , 1988: 'New Approachesto the Linear Analysis of Music', ffournalof the AmericanMusicological Society, 411ii, pp. 315-48. , 1989: 'Motivic and Linear Design in Debussy's La Terrassedes audiences du clair de lune', Analysemusicale, 16, pp. 10-16. , 1991: 'Debussy and the Octatonic',Music Analysis, 101iii,pp. 125-69. Friedmann,Michael L., 1982: 'ApproachingDebussy's Ondine',Cahiers Debussy, 6, pp. 22-35. Katz, Adele T., 1945: Challengeto Musical Tradition:A NezvConcept of Tonality, Chapter7 (New York: Knopf). Kostka, Stefan, 1990: Materialsand Techniquesof Tzventieth-CenturyMusic (New York: Prentice-Hall). Lesure, Francois (ed.), 1980: Claude Debussy: Lettres 1884-1918 (Paris: Hermann). Lesure, Francois and Nichols, Roger (eds. & trans.), 1987: Debussy Letters (Cambridge,MA: HarvardUniversity Press). Lewin, David, 1987: GeneralizedMusical Intervals and Transformations(New Haven: Yale University Press). Morgan,Robert, 1976: 'Dissonant Prolongation:Theoretical and Compositional Precedents',3tournal of Music Theory,20, pp. 49-91. Parks, Richard S., 1989: The Music of Claude Debussy (New Haven: Yale University Press).
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Salzer, Felix, 1952: StructuralHearing: Tonal Coherencein Music, 2 vols. (New York: CharlesBoni). Schoenberg, Arnold, 1969: StructuralFunctions of Harmony,ed. Leonard Stein (New York:Norton). Stein, Deborah, 1985: Hugo Wolfs Liederand Extensionsof Tonality(Ann Arbor: UMI ResearchPress). Straus, Joseph N., 1987: 'The Problem of Prolongationin Post-Tonal Music', 3tournalof Music Theory,31li, pp. 1-21. Vallas, Leon, 1929: The Theories of Claude Debussy, trans. Maire O'Brien (London: Oxford University Press). van den Toorn, Pieter, 1983: The Music of Igor Stravinsky (New Haven: Yale University Press). Wilson, Paul, 1984: 'Concepts of Prolongation and Bartok's Opus 20', Music TheorySpectrum, 6, pp. 79-89.
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