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Varese's 'Density 21.5': A Study in Semiological AnalysisAuthor(s): Jean-Jacques Nattiez and Anna BarrySource: Music Analysis, Vol. 1, No. 3 (Oct., 1982), pp. 243-340Published by: Blackwell PublishingStable URL: http://www.jstor.org/stable/854178Accessed: 21/05/2010 19:11

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JEAN-JACQUES ATTIEZ

VARESE'SDENSITY21.5': A STUDY INSEMIOLOGICALNALYSISTranslatedy AnnaBarry

CONTENTSIntroduction 244I - PART I (bs 1-23)1. The firstfive bars. 2482. Digressionon musicsemiologyand the informational pproach. 2553. The progressiono high G (b. 17). 2594. The zone of B (bs 18-23). 270II - PART II (bs 2X40)1. The percussive ection bs 2X28). 2722. Vertical allsand flights(bs 29-32). 2733. The flightsof 'Density'. 2764. Permutations f B, F# and A (bs 29-32). 2805. The end of PartII (bs 3g40). 282III - PART III (bs 41-61)1. Repriseof the opening bs 41-43). 2842. Permutations n B-D (bs 46-50). 2853. The last segment bs 51-61). 287IV - RECAPITULATION 289V- POIETICANALYSIS1. The poieticproblem. 3012. Melodicpoietics. 3033. Harmonicpoietics. 303VI - ESTHESICANALYSIS 319VII - COMPARISONOF ANALYSES 329(OMUSIC ANALYSIS1: 3, 1982 243

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JEAN-JACQUES ATTIEZ

INTRODUCTIONMusic analysis, as we understand t in the semiologicalperspectiveofattention o minutedetailandclarification, oesnot lenditselfwellto exhaus-tive presentation.In my book on music semiology(1975), I was able to give only a fewexamplesof my approach,and the smallnumberof semiologicallynspiredanalysespublished n periodicals s confined,for the most part, to partsofworks.l I am, therefore,particularlyrateful o JonathanDunsbyforhavingoffered o devotemanypagesofMusicAnalysiso thepublication,n English,of this analysisof 'Density21.5'. It firstappearedn a Frencheditionof 300copies n 1975,andis longsinceout of print.I havemadevariouschanges norderto correcterrors,to take into accountthe evolutionof my theoreticalideasin relation o a text now eightyearsold, andto clarifymy positiononsomeissues.The uncomfortableituationof analysis odaycan doubtlessbe explainedby the difficultyexperienced n drawingup and publishingwrittenmusicanalyses.Whenoneventures o reproach nalysesornotcoming o gripswiththedetailof a workandthemultipleconstituent ariableswhichgo to make tup, one is oftentold thatanalysisprofessors, n theirclasses,can 'go a longway' into a work. Couldmusic analysisbe an oralgenre, or even an oraltradition?2t must face the followingproblem:no analysis s trulyrigorousunlesswrittendown (Granger),an epistemological laboration f the adage'Verba olant,ssnptamanent', incethe record f the analysisenables t to bechecked:once it is writtendown, it is possibleto review, criticiseand gobeyondan analysis.Evenwitha veryelaborate ralanalysis, he listenerhasthe physicalproblemof being unableto retaineverything.If the teachermanages o give the impressionof havingpenetrated he work deeply, thelistenerwill be left with a positive'aura',but a cumulativeadvancement fknowledgecannotbe developedon the basisof impressions.The presentstudythereforeaimsto urgemusicologistsnterestedn analy-sis to takethe timeto record heirresearch ndoffersthe firstratherdetailedanalysisof an entireworkfroma semiologicalperspective.I am grateful oDavid Lidov for havingunderstood his: 'This long study is an importantcomplement o Fondements . . It givesa muchfullerpicturethanthe latterdoes of the scope and force of the author'smethods'(Lidov, 1977: 45).Writtenanalysisenablesus to takein allparameters, ot thatanoralanalysiscannotdo this, but it is extremelydifficultto masterthe combination f allparametersn the absenceof rules, tablesanddiagrams.Thisanalysiss alsothefirstto illustrateinksbetween heneutral evelandpoieticandesthesicdimensions, hough t in no wayclaims o offerexhaustivepoieticandesthesicanalyses.It is not proposed o givea newpresentation ftheperspectiveromwhichI amworking:3t shouldsufficeto rememberhata neutral evelis a descriptiveevelcontaining he mostexhaustivenventorypossibleof alltypesof configurationsonceivably ecognisablen a score.Thelevel is neutral because its object is to show neither the processes of

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VARESE'SDENSITY21.5: A STUDYIN SEMIOLOGICALNALYSIS

productionby whichthe workunfolds(poietics)nor theprocessesof percep-tion (esthesics) o whichit givesrise. In this senseit provisionallyeutralisesthe poietic and esthesic dimensionsof the piece. On the other hand, theneutral evelprovides heunitsin relation o whichpoieticandesthesicdata nSectionsV andVI will be examined.Yetanother ustification f thisneutral tatus s theuse, fromthebeginningto the endof the study,of theneutral evelas ananalyticaloolwhich s nevercalled into question, the partitioningof the work into units according oabstractparadigmatic xes, that is, axes which grouptogether denticalorequivalentunits from an explicitly stateslpoint of view. This technique sinspiredby methodssuggestedby Ruwet(1972:Ch. 4), a continuation f theteachingsof Jakobsonand Levi-Strauss,but it is not followedblindly:theproblems t presentsare discussedelsewhere Nattiez 1975:239-356). Thereaders referredo this sametext fora completepresentation f themethod-ologyusedin the neutraldescriptionof 'Density21.5'4.Theanalysisproceeds frombottomto top', thatis, fromthe smallestunitsto the largest, since Vareseworks with the differentiation f short units.Nevertheless, argersectionsappear n the piece. As theseare justifiedonlylateron, I shallbeginby giving,withoutcomment,a pictureof thehierarchicstructureof 'Density' n so faras it results fromthe completeanalysis, o thatthe readercan see how the minutiaewhich are to be examinedrelate tobroaderphenomena.Numbers n squarebracketsabovethe staverefer o the smallestunits.Barnumbersareunbracketed:

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JEAN-JACQUES NATTIEZ

Parts 1st partSectl ons ASequences I II

246 MUSICANALYSIS1: 3, 1982

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VARESE'S DENSITY 21.5': A STUDYIN SEMIOLOGICAL NALYSIS

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I- PART (bs1-23)1. ThefirstfivearsBeforegoinginto the workin detail,I shallillustratehe principles fsegmentationf themusical yntagm ccordingo thevarious aradigmaticaxes n ananalysis f theopening f 'Density':Ex.1I [1] A[2ad B[2b];; ; 2 $ aS j 2 $

3 , j | [4b], _3

rf , ' , '>= p 9 ] w 3X, F ] ^ 3 j

_

First,the left of the example:bs 4 and5 canbe seen,in fact,in twodifferentways AandB), showingtraightway hat heneutralevel s notrestrictedo onemanner f presentation,ut on the contrary isplayshediverse onfigurationsossible,houghwithout rofessiono unite hemall.Toavoid onfusion,henumbersn square racketsorrespondotheparti-tionedunits;a letterfollowing square-bracketedumberdesignatesheparticulararadigmaticlternativeherehereareseveral artitions. omannumerals esignate nitsregroupedt a higher evel;thesearediscussedbelow.5Asfaraspitch s concerned,hefirst hreenotes unit[1])arerepeatedttheendofb.3 ([3]).It is temptingo add othese heF#-G-F# ([5])of b.4.Theparadigmaticxisregroupsnitswhichareequivalentromagivenpointofview: hisdoesnotmean hat heyarehomogeneous.or[1],[3]and[5],IuseMolino'serm block, bloc].Theevaluationfaffinitywhichallowsustomake heseassociations,epends pona mixture f separateriteria:(1) Themelodicdentityf [1]and[3](F-E-F#)(2) Therhythmicimilarityf [1], [3]and[5]:Ex.2 [1XfUlJuJ ,2

t3]n l. '

[5g.r:' J S

JEAN-JACQUESATTIEZ


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VARESE'S DENSITY21.5': A STUDYIN SEMIOLOGICAL NALYSIS

Theparadigmatichythmicheme, hat s, thetrait ommonoa groupof units,consistshereof two shortvaluesplusone long.6(3) Butthis similaritys reinforcedy two other actors:(a) the two shortvalues orma kindof mordentlower n [1]and [3],uppern [5]);(b)the longvaluesare n everycasean F#.(4) Unit[5] beginsonthe samenotethatends[1]and [5].Allthis eadsus to 'neglect'hedifferenceetweenhetwosemiquavers[1]and [3]) and the two tripletsemiquavers[5]). The distrtbutionf theseelements ermits he connectionf theinitialF's andF# of the threeunits,althoughheyaredifferent.These woexamples f assimilation,o which anbeadded he engthf thefinalF's, illustratewhatmay be calledequivalencelasses.Within his classthere s a wholerange frelationships:ecauseheyarephysicallylose, t iseasier o assimilatehe semiquaverndtriplet emiquaverhan hecrotchet,and the compound aluequaver iedto dottedminim ied to triplet emi-quaver nder he samecategory,long',since he feelingof lengthby oppo-sition o thetwo shortvaluesdoes notpreventperception f the durationaldifferencesetween hethree progressivelyhorter)inalnotes.There sanother easonormaking paradigmaticssociationf Ex.1:froma widerdistributionalointof view,takinghe broaderontextntoaccount,[1], [3] and [5] initiate hree arger egments,, II andIII.7Thethreeremainingnits 2], [4] and[6]canbe organisedn twoways. nversionA of Ex.1, the criterions essentiallyhythmic:

Ex3[2ag zP X 4 S

3 1 3 & t

[4ad S J : S &3 3t I |[64 j

3 1 3 } 3fP

Despitedifferencesn detail, hisparadigmas hepatternong-short-long8sa commonheme.Thereare, however,wo anomalieso be considered:heinclusion f a semibreven [2a]and the two equalvalues triplet rotchets)whichend[6a].The semibreves all the more important ecause t forms partof aprocedure hich s especiallyommonn Varese:he constantengtheningfeachnewnote withinonemusical egment.9One phenomenonustifies heMUSIC ANALYSIS1: 3, 1982 249

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JEAN-JACQUESATTIEZparadigmaticsolation f the semibreve:he slur fromthe initialF to thesecondC of b. 2. Thedynamics-f-p alsogive heC conspicuousutonomy.Obviously,trictlypeaking necannot laimhe secondriplet rotchet f[6a]to be longer hanthe note immediatelyrecedingt, sincethey are ofidentical uration. hetotalparadigm,he blockwhich akesall parametersintoaccount,will n factneutralisehisanomaly ithregardo theshort-long-shortpatternhroughhe identicalinalpitchesof [4]and [6]:C#-G. Thismeans hat, in making he paradigm, nother ariablepitch dentity) shierarchicallyominantn relationo the rhythmicariable.Forthis reasonayoutB of Ex. 1 maybe morepertinent:hisparadigmsbased n theidentity f the finalnotesC#-G in all threeunits,not justtwo.Thusnew relationshipsegin o appear:heC# in particular,nitialonly n[2b]andcentraln [2b], 4b]and 6b],plays heroleofa pivotnote.Becausetalways recedesheG,which ndsnotonly hethreeunitswe aredealingwithherebut alsosegments , II and III, the F# of [2a]is not unconnected,paradigmatically,ith the F# of [1] and delays he arrival n G. Thesemelodic elationshipsreobviousn theparadigmn Ex. 4:

Ex.4['

< #2>-'J 3>[2S_Xss

1;gL \ semitone

k[3] [4a]

03 [5,0 3

[6] , 3 }zJ w1


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VARESE'SDENSITY21.5': A STUDYIN SEMIOLOGICALNALYSIS

It is no exaggerationven o calltheF# a kindof leading oteto Gwhosesyntagmaticosition nddurationmaket a 'polar ote'.In so faras thistableopensaseparatearadigmaticxis oreachnewnote, ts configurationanbecalledoblique,stablishedetweenines1 and3 bythe addition f G, onesemitone boveF#.(Thisdetailwill assume certainmportanceateron.)Thefinalnotesof[1],[3]and 6]haveprogressivelyhorterhythmicaluesandthesame s truehere(semibreve,rotchet,riplet rotchet).Theinitialnotesof [2b],[4b] and[6b],however, ecomeprogressivelyonger triplet:dottedquaver,quaveriedto crotchet nddottedcrotchetiedto crotchetrespectively).LayoutB shouldnot supersedeayoutA. Justas it isperfectlyegitimateoemphasiseherepetitionf C#-Gwhich oncludesegments, II andIII,wemustalso ake ntoaccounthe caesuraetweenG ofb.2 andallthatprecedesit because f the slur.Wehave, herefore,o takeaccount f a contradictionbetween he two paradigmatichoices.The neutral evel shows,by itspositioningneachparametricrame uccessively,hat hemelodic,hen herhythmicrganisationothhave heirown ogic; hiscanbeseenonlywhenthe othervariablesreprovisionallyeutralised.y putting ogether ll theinformationabulated,heworkingsf a principle hich ppearsobe charac-teristic f thispiecel s revealed:heprinciplef deception.Thewholeof thisopening assagewillnowbere-examinedith heaccenton thesyntagmaticrogression:neunit[1] of threenoteswitha chromaticrise(F-F#Sendson a longF#;thearrival n Gis delayed y a second roupof threenotes(C#-F#-C#) which s connectedo whatprecedest by aslur.A restfollows.Theinitialunitreappears, itha slightly horterinalnote,but this timegoes directly o G which, n [4], frameshe C#;herethough,withthe samerhythmicype(long-short-long),t is theC# whichframeshe F# ([2]).In the samebreath,he motive rom 1] returnsn theformof [5] describedbove,here ollowed either y C# norG,but byan E([6])whichprecedeshefinalC#-Gmarked iminuendo.hese hreenotes,atdistributionallyquivalentoints,outline diminishedifthchordC#-E-G,suggested ythe C#-Gfromb.2 onwards,ndcompletedy theE of b.5 inexlremis).hismeansof delayingheG in b.2, withan intermediarynit ofthreenotes,representshe principle f deception.The privileged istribu-tionalposition f C#-G n[2],[4]and 6]strengthenshe istener'smpressionofhavingbeendupedn [2].Naturally,helistener oesnotconsciouslynddiscursivelyerceive he workexactlyaccordingo the processdescribedhere,buta detailed escriptionf theneutralevelcansubsequentlyeusedtodescribe phenomenonhichsfunctionallyertinentromanesthesic ointof view;whenwe speakof deception,weare,afterall, describingneffectuponsomeone.Attentionmustbe drawno a feature f themethodusedup to thispoint:theresearch rocess onsistsof isolating nitsaccordingo criteria f para-digmatic ssociation. uta different ointof viewhasnowbeenadoptedthat of syntagmaticuccession.Havingbegunwith a relatively bstract

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descriptionf unitsregroupednabsentia to useSaussure'sxpressiontheyarethenprojected ntotherealaxiswhere hey inkup.Notethatthedescription f thesyntagmaticrogressionuggestedboveuses nformationndsegmentationstablishedroma paradigmaticointofview.Somemusicanalysesavealreadysedparadigmaticresentation,1lutinintroducingomusicologyheconcepts fsyntagmndparadigm,tructurallinguistics ndsemiologyfferathematisationfthisdistinction. systematicsearchortheparadigmsf relatedunitseffectsregroupingsndclassifica-tions, thusadvancingowards typologicalnowledge f worksandtheirconstituentlements; he thematisationf the paradigmaticrinciplewillrequireus to identifya category f upward-surgingigures 'flights': ee,belowof II-2);the thematisationf syntagmaticrganisationringsus tostudy heirdistribution.n previouslyublished nalyses,12eemphasisedparadigmaticecompositionfworksbecausehisaspectwasnotconsideredsystematicallyn classicalmusicology. n the presentstudy,we wish toconcentraten syntagmaticrogression,ut otakeasa basis he nfonnationyielded y heparadigmaticiewpoint. heorder fdiscovery ndofexpositiondoesnotnecessarilyoincide:n thisparagraphe havestressedhemethodused(projectionf theresultsof paradigmaticecompositionntothesyn-tagmaticxis); romnowonweshall ollowmorecloselyheorder n whichthe unitsappear. t is simplya matterof rememberinghatparadigmaticsenabledhem o beidentified.Theparadigmaticndsyntagmaticescriptionfthenumberednitsnthescore f 'Density' oesnotcompleteheanalysis.n note7three easonsweregiven orregroupinghefirstsixunits nto argeregments,abelled , II andIII.Onemightaskwhy,both nitially ndthroughouthisstudy, hesmallunitsappearobeused oestablishhelarger nes,whilstonehearing f thepiecepermitsmmediatedentificationf thelargestections.This extcouldhavebegunbyjustifying,nbroad erms,hedivision fthepiece ntothreeparts, hedivision fPart intotwosections-A andB, thedivision f A intothreesegments-I, II andIII,thedivision f I intotwounits-[1] and[2],etc. Buttheprocedurefrombottom o top' s preferredbecausehehierarchicallyoremportantnitsarenot dentifiedccordingothecriterian use forclassical ndromanticmusic: epetition f themes,oflongphrases ndof periods.Varese laysonsubtle hythmicifferentiationsandavoidsstrictmelodicrepetitions;t is thesedistinctionswithwhichascrupulousnalysishould eal irst.AsLidov ightlyays, Varese as eftallthe a priorimplicationalelations f musicalonalitybehind.The uniquesystemof thework s its onlysystem.Instead f the tensionbetween tyle(abstract)ndexampleconcrete),hework akes tslife and tsenergyromthe complexity ndambiguity f its internally eveloped ssociationsndcontrasts.The taxonomy endersheseexplicit' Lidov1977:4445). Anemphasisedote, a generalmelodic onfiguration,rhythmic r intervalliccontrast etween wopassageswilldefinea largesection.Thisis why it iseasier o understandhe largeunitswhenoneknowsfromwhichsmallerphenomenaheyareconstructed.


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At the end of this studythe divergencesn decision-makingmongmusicologistsegardingormal rganisationillbe examined, utwhat, nfact,is a form?To speak, or example, f theformABA s to recognisecertain aradigmaticamiliarityetweenwosegments,eparatedya thirdwhichs consideredo constitute separatearadigm.n analysis,hepara-digmatic recedeshesyntagmatic.f ABA s inflected sABA', t is becausetheparadigmaticinksbetweenA andA ' areconsideredo be looser hanthosebetweenA andA. In classic ormal nalysisheuseof two identicalsymbols asnever ignifiedtrictdentity f AandA, butratherheneutralis-ationof differencesonsideredo benegligible.n aworkike'Density',heidentificationfparts rsections reaterhan hesmallunits s possible, venobvious,butonlystartingromasmallnumber f variables hicharehierar-chically ominantn relationoothers. f formal nalysesf 'Density' ifferfromoneresearchero anotherseeSectionVII), his s becausehedominantvariablesrenotnecessarilyhesame or everyone:ere, heforms not theresult fcommon racticemongomposersnthecourse f a givenperiod fmusical istory,but is theconsequencef a relative ndmobile onvergenceof paradigmaticquivalenceriteriabetweensections,for listenersandanalysts like.Thesedivergencesreneitherdramaticorregrettable,ro-vided hatwe areconsciousf thereasons ehind hem.Theregroupingf the firstsixunits ntothreesegmentswasjustified ythreecriteriaseenote7). Othervariablesxplainwhythese hree egmentseachhavea certain utonomy, ut alsoa family esemblancehichdisting-uishes hem romwhat ollowsandenables s to look,to beginwith,at thefirstsixbarsalone:(1) Segment presents -E-F#-C#-G insuccession.egmentsI andIIIusethe samenotes,butin a different rder.(2) There s a certain nalogyn thedistributionf intervalsn the threesegments:

I [1] ld 2a 5a[2] 5a 5d 6a (2d)II [3] ld 2a la[4] 6d 6a (ld)III [5] la ld 2d[6] 3d 6a (6d)

Thenumeralsesignatehenumber f semitonesontainednthe interval(nodistinctions madebetween naugmentedecond nda minor hird):andd mean ascending'nd'descending';racketedntervalsmark joins'betweenegments.The nterval etweenG andF in b.3 iseffectivelyeutral-ised by the rest, but the joiningntervalbetween 4] and[5] has greaterweight, ince he slurcovershewholeofsegmentsIand II.Thecriterionfa resthasnotbeenusedto identify 4] and[5].A problemuchas thatofjoiningntervalshowsclearlyhowtheweight f eachvariable epends nmanydifferentactorswhich,themselves,hangeaccordingo particularMUSICANALYSIS1: 3, 1982 253

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JEAN-JACQUES ATTIEZ

contexts.Nevertheless,constant canbedrawn rom heexaminationf theseintervallicyntagms:very egment eginswitha semitone ndendswithatritone, n accordanceitha seriesof continuousugmentation:I 1 2 5 6II 1 2 1 6 6III 1 1 1 2 3 6

(3) Thestudyof intervallicirections iscloses notheryntagmaticrin-ciple:I 1X,/(\) 2/\/ (X)

II 3\ /(/) 4N/(

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2.Digressionnmusicemiologynd henformationalpproach'3The analysisof the openingof 'Density'suggestsseveralconclusions

concerninghe epistemologicaltatusof the neutralevel. WhenRuwetimagineda machineoridentifyinglementarynits' 1972:112),he pro-videdametaphor hich vokesheexplicit haracterfthemethod roposed,butwhichcouldbe said o imply,rather angerously,hat heseproceduresareof analgorithmicharacter;hefact hatanalysisanbegin fromhetop',andrequires onstant ig-zaggingetweensmall'and'largeunits',showsquitewellthatexplicits not synonymous ithalgorithmicrmechanical.Theanalysis f the firstfivebarscombinedwosteps: hefirstgesture,intuitiventhat t implies confusedollectionf criteria,onsists fdefiningwhatMolino allsblocks. t soonappearshat nnoneof themare hecriteriaof paradigmaticssociation omogeneous.A studyof the 'partitionings'(decoupages),o longercarried ut by block,but parametery parameter(pitches,henrhythms,henintervalstc.) shows hatno singleparameterdominatesheconstitutionf theblocks,whichare heresultofa conflux fvariables hoseweight hangesn eachnewcontext.As acomparison,onsidernapproachf the nformationalype.At first, twouldnecessarilytartatthebottom ndproceed oteby note.Ascanwouldidentifyall identical nits,taking henotestwo, thenthree,thenfourat atime,andsoon.Atthe evelof pitch, hemachineooks irst oralltheF- E'sinthepieceand inds hem nb.3.Then,after canninghesixty-one arsofthework, t startsagainwithE-F: which t finds n bs 3 and54 etc. Theprocedureor unitscomprisinghreenotes s simplerincewecanstate hefollowingule: f unitA (twonotes)s followed yunitB (twonotes)and helastnoteof A is the firstnoteof B, A + B constitutes three-note nit,providedhatthesamesuccessionf notes s foundelsewhere. hus,thereappearo be twenty-onehree-notenits n 'Density',orexample -E-Ft,bs 1-3,G-Ct-G, bs 4 and5-6. Eventhen,in the lattercaseit shouldberecognibedhat hemachine oesnot takerests ntoaccountince heunitofbs5-6 contains tripletquaverest.Inthisway,wecangoup tothelongestunitin the piece.It containsninenotes:B-Ft-A-F#-B-A-B-F:-A (bs32-33,repeatedn b.34).Thisoperations repeatedntheotherdimensionsf thepiece: ntervals,rhythm,dynamics,modesof attack,andslurs.Note thatthe graphic epresentationf unitsdefinedn thiswayis notdifferent romthe systemof paradigmaticotationproposedby Ruwet,thoughhetablesarenecessarilyiderandshorter.Thetableofunits ormedby notestakentwo by two comprises,yntagmatically,ne hundred ndthirty-sixnitsofwhich ifty-one rerepeated. he ntervalnventoryegins:


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JEAN-JACQUES A1TIEZ(1= semitone, = descending,= ascending)ld 2a 5d 5a5d 6a 2dld 2a la6ald lald 2d 3d6a 6d6a2a la 3d 3a3d 3a

2a lald lald laetc.This tableclearly howsa patternof unitsof 2, 3, etc. intervals:orexample,d-2a (bs 1 and3), 2a-la (bs6 and8)Such'accounting'annotbe calledanalysis,but is rathera 'physical'inventory.Givenhatnotallpossibleorms ftransformatonre oreseeable,as soonas relationshipsreestablishedetweenunitsthatarenot strictlyidenticalwe enterthe realmsof analysis,but it mustbe recognizedhatcultural ndtheoretical nowledge, prioris ndaural mpressionsffectuc beclslons.Thedifferenceetween ninventoryndactual nalysiss that t doesnotappearobepossibleodeducehe atterrom he um fthe nformationrovidedbytheormer.nfact,partitioningarriedutnotebynoteandparameteryparameteroespresentproblems:l4(1) Acertain umberfvariablessreduced,rom hestart,othestatus f

hapax,hat s, theyarenotattachableo othervariables,emainingsolatedandunusablen theinventory.Rhythmicalues reacase n point:withtheexceptionfinitialnotesof 'phrases',haracterisedytwosemiquaversbs1,3,9, 15,21,41,43),therearevery ewstrict epetitionsnthepiece.Fromhethirdnoteof thepiece,thevaluesof theF: in bs 1-2 and heF: of bs 3- 4mustbemade quivalentnorderoobtain n nterestingesult-a departurefromhedata.Thealgorithmicrocedureends oomuchweight othenoteas the minimalpertinentunit. As Molinowrites, t 'is an "amalgam"fheterogeneousharacterisations:t indicatesneabsolute itch,virtualnter-vals,degreesandfunction,andvirtualdurationswhichcould,potentially,carryhythms.Thisis whyanisolated otecouldnever onstitute unit: tsmostmportantropertiesintervals,egrees nd unctions,hythms)emainvirtual ntilat leasta secondnoteis joined o it' (1975:55).Theexampleshows learlyhowphenomenaertinentoranalysis represent tthe'top'256 MUSICANALYSIS1: 3, 1982

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VARESE'SDENSITY21.5: A STUDY IN SEMIOLOGICALNALYSIS

but not at the 'bottom': he equivalencewhichthe proceduredemonstratesbetweenphysicallydifferentvalues s one suchcase, and t is hard o see how acomputercould automaticallystablishan equivalencewhich depends on ajudgementf similarity ranscending oncreteresemblances nddifferences.(2) Even amongrepeatedunits, the inventoryrevealsphysically denticalphenomenawhichdo not have the samesignificance.For example: he unitG-F of b.3 wouldbe pickedup by the machinebecauseof its occurrence nb.43 (G-Et: wemust allowenharmonic otes to be coded n identical ashionwhich is justifiablen this music). The same is true of the unitG-F# whichappearswice n b.4 andreappearsn bs42 and 43. In viewof the rests n boththese examples, and also of the distancebetween and diversityof theircontexts,these'repetitions' o notappearo be of any use. Transpositions atypicalcase. The inventorydealingonlywithpitch willpick up therepetitionof F-E-F: in bs l and 3, but will establishno relationbetween hisand theE-D:-F from b. 15.The intervalnventory,on the otherhand, willpick outld- 2a in bs 1, 3 and 15, butwithoutbeing ableto show,since pitchdoes notcome into it, thatthe ld-2a of b. 15 is a transposition f the othertwo. Thentherhythmic lementmust beadded: he unitstaken rombs 1, 3 and15 havein commonwith thefirst threenotes of b.9 therhythm wosemiquavers lus along. The intervallic unit is not identical: Db-C-Db = ld- la, but theconnectionof the units throughthe intermediary f the rhythmgives la apresumed quivalencewith 2a.We see, then, thattheinterestf arecurrencesnotindependent f its context: t dependson its insertionnto a block,hat is,a more or less homogeneous roupconstructedby the analyston the basis ofone orseveralcriteria,dominantndconvergent, hat do notconstituteall thecriteriawhich couldhave beenbrought nto theanalysis.Until wehave proofthat the criteriaareunsuitable, heyjustify he analytical hoices; his is whythey must be renderedexplicit. For this reason, Molinocalls them quasi-crzterza.(3) Finally, thenote by noteinventorydoes notpermit heidentification fphenomenawhichnormalmusicalcompetencesolatesatonce. We see in theparadigmaticablesthat [4] introducesa G wherebefore herewas a Ct, andlaterweshallhaveanE. Theimportance ivento thesenotespresupposes hatallprecedingmaterial i.e. therhythmic igure,and theanalogiesbetween 1],[3] and [5])andwhat follows(Ct-G) has beenanalysed.Does thismeanthatinventories f material reuseless?GillesNaud(1979)hasproposeda methodwhich, on a single table, 'reports'recurrences,parameterby parameter,variableby variable,togetherith nformationdrawnfrom the completedanalysis.There is, therefore,no limit to the numberof possiblecolumns.l5Therefollows anexampleof what canbe obtainedwith thismethod,appliedto the beginningof the piece:


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JEAN-JACQUES ATTIEZ

x= semiquavery- triplet quaverz- crotchet

Idonot ntend oundertakelaboriousnventoryfunits:t ispossible,n aspecifictudy,to takeshortcuts. Froma methodologicalointof view,however,hecomparisonuggestedyNaud owhichwecanreferor imitedverificationocusesourattentionnthreepoints:(1) It tellsus, by comparisonf physicaldataandanalyticalecisions,258 MUSICNALYSIS1: 3, 1982

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which variablesare strategicMolino'sterm). For example, the unit G-Fwhichjoinsthe firsttwo segmentsof Ex. 1, doesnot havethe samevalueastheF-E or theE-F# of theopening.G-F assumes hestatusofa joiningunit.All thejoiningunitsof thepiecemightbe studied orcertain ommon raits-an interval,perhaps,whichis characteristicn relation o all the otherinter-vals of the work. These comparisons hould permit the identificationofcontextsndsituationshichgive certainvariablesmoreweighthanothers.(2) Secondly,Naud's inventorytable is an aide-memoire,n instrumentwhich confrontsus with phenomena hat the 'fromthe top' procedureofparadigmaticnalysismight leaveout. Once it is discovered hat F-E-F#,withits characteristichythm, s animportantthematic' lementof thepiece,the intervaltablecan be scannedto see if ld-2a is found elsewhere.Thissuccessionappearsn bs 10-11, in the trillof b.20 andin b.39, andmakes tpossible o showhowthesetwo characteristicntervals orma developmentalthread,andat whatprivilegedpoints(before he returnof the real'theme'atbs 15, 21 and41).(3) Finally,the tablein columnsshowsup, on one page, conflictingseg-mentations,he identificationf whichwouldotherwise equire omparisonfparadigmaticables,often spreadover severalpages. Here, a conflictarisesbetweenthe melodicsegmentationwhichisolatesC#-G and the slurwhichisolatesG. Thepartitioninginallyadopteddoesnotexclude heother,since thasbeen shownthatit couldbe pertinent romanotherpointof view.3. TheprogressionohighG (b. 17)Concerning he first five bars in toto.What, in fact, is the beginningof'Density'?Looking aheadas far as b. 17, we can call it a melody whichremains aithfulto romanticgestures,characterised y a crescendo.he cres-cendos, of course,dynamic thefofb.3 andb.8, thettofb.9, thetftofb.11,the crescendof bs 13-14 and 16-17), but existsalsoin a moremetaphoricalsense: the progressionof rhythmsand intervals,and the melodic ascentwhich, at b.5, has only just takenoff. A 'romantic'ascent, then, but onewhichconstantly rustrates xpectations onditionedby tonaldynamics: hesamephenomenons foundin b.8, asin b.2, thenbetweenbs 8 and9, andinb.16.The functionof sectionA (bs 1-5) is to introduce,afterthe motivewhichwinds aroundF#, the tritoneC$G three times. Momentum s generatedC#-G reappearsn b.6 andthe upsurgeof themelodyendsonlyin b. 17withthe high G. For this new section, B, Ex. 5 shows the organization f themelodicprogressionbs S8):


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- J b*

JEAN-JACQUESATTIEZ

Ex.5 ^ [63 , 3 j

3p sud iho v ton e

Here,6] sreintroducedsamemorandum.nthesameway hatC$-Gof[7]is aetake f [6], [8]containsheG-Bbtaken rom 7].If inb.8 therewerenotclearslurovertheBbandC whichdivides hem rom heprecedingnotes,nemight ay hatVareseepeatsG-Bboncemorebefore oinguptoC.utthisis a newdeception:heprogression#-G-A-Bb of [7],pickedoutytheslur,theprecedingestandthebreath-markfter helongBb,isrepeatedutonly n respecto pitch,asG-Bb-C-Db:Ex.6

ButheBb sisolatedrom heGbytheslurwhich onnectsttoC,and heC,

subjectedodistinctiveynamicmphasis,s separatedromDbbydurationdelayingtsarrival,ndbyabreathwhicharrestshemomentum:hemove-mentC#-G/ C#-G-A-Bb delaysG-Bb/ G-Bb-C-Db. Therewillnotbeperfectymmetry.Themelodic nalysismustbecompletedya rhythmicescription. singthe ypology resentedbove,weobtain:[7][8][9]

bc or eal

Notethatc ore for[8]indicates hatthequaverofb.8 maybeconsideredohaveadurationperceptively qual o thatof theprecedingripletcrotchets. n


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VARESE'S DENSITY21.5': A STUDYIN SEMIOLOGICALNALYSIS

any case, [8] is framedby two units whoserhythm s characterisedyprolongation.t is already pparenthat the rhythmic onfigurationsreorganised ifferentlyrom hoseof sectionA. In b.6, something uitenewbegins.Theparadigmaticrofile f Ex. 4 wasoblique nlybecauseGwasadded ntherightof theF: axis.Thisprofiles primarilyerticalandater n Ex. 8 itsobliqueharacters moremarked). romb.9 tob. 11. t returnsovertical:is theonlynoteoutsidehe playof permutationsetweenDb andC whichsspread ver wobars:Ex.7 melody rhythm

k a r E] _ f3 t11]7 fi r 5 6rmfubsoo mfubito

H ,\, E2] Ht semitonc

S t f t3 ' 3: tf r

[10]mustbe paradigmaticallyssociatedith 1],[3]and 5]: t borrowsheirrhythmicype a2 (two semiquaverslus a dottedminim,as against wosemiquaverslus a triple-dotted inimn [1])andtakes he formof a lowerratherhanan uppermordent s in [1].In so faras [10]doesnotcontain heintervallicuccessiond-2a whichwouldallow he introductionf Ft, onesemitone igherhanF, the ntervallicatternd-la allowst, in contrast,ostayput. Thus,[10]and ts prolongations[11]and [12])constitute tran-sitionbefore 13] which ntroducesD, underlinedy a crescendond tripleforte,accordingo a rhythmica2)and ntervallicld---la) onfigurationre-ciselyas in [1]. Thepattern short-short-long'hus definesan equivalenceclass,just ikethe developmentalrocedure hichconsists f upwardemi-tonalprogression. b appearshusto be a kindof preparationor the D inb.ll. In a sense,theplay of permutationsn twonotescontributeso theprinciple f deception:t delays he appearancef a predictablevent, theascento D.16MUSICANALYSIS1: 3, 1982 261

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JEAN-JACQUES ATTIEZ

A studyof therhythmic aradigmEx. 7 right) howshow Varesentro-duces omevarietynto a melodic equencewhichcouldhavebeenmonoto-nous. [10], distinctive ecauseof its long finalnote,its crescendond thesemiquaverestwhich eparatest fromwhat ollows,belongso therhythmictypea2as we noted; 11]takes he lasttwonotesof [10],justas[9] did with[8]; typea1 (short-long)einforceshe parallelismetweenhe Db's of [10]and 11],a2being imply nextensioneftof a1 ora1a transformationf a2byelision f the nitialnote); 12],themelodicnversionf [10],belongso typeb (triplet uaver lusquaver lusquaver iedto tripletquaver);13]beginswith hesame wonotesas[10]andhas he same hythmicype a2),butendson D. The crescendohichbeginson Db and ends ff contributeso theemphasisf thisunit.Theres bias n the segmentationf [11]and 12].Theyare eparatedeither y breathingorslur.The ollowingmightbeproposed:

Ex8[11] 012]1 F

3b;3 3 z3v tr- r

Thefirstunitofthisexamplewouldbecome hemelodicnversionf [10]andthe secondwouldborrowts first wonotes.The lengthof Db in [11]makesthis segmentationifficulto accept, speciallyince ts repetitionnd engthin-[10] ive t decisivemportance.heneutralnalysis, owever,mustadmitthe configurationf Ex. 8 if onlyto foreseecertainperformers'hoiceofphrasing.Thefollowingable Ex.9) forbs 11and12 s bothmelodic ndrhythmic.It ismelodicnshowinghetreatmentf G#-D:G# n the ower ctaven [15]thenD in the loweroctave n [16]followedby an expansiono the rightofA-D#, semitonesespectivelyboveG#-D; intheupper ctave,A, BbandEtoo willbe a semitone bove he notesof [16].Rhythmically,efindtypesaandb: moreprecisely, 1 n [14] and[15], prolongedy b in [16]and [17].The rhythmicmomentumollows hatof the melodicprogression.

In [14] theD was writtenn brackets.t wouldbe possible o imaginepartitioningasednot onthe paradigmaticeadingG:-D but onD-GS, asshownby the right-handaradigm. am reluctanto see it in this way, notbecausehe D mightbelong o twounits weshall ee nb. 36 that his s nota


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VARESE'SDENSITY21.5: A STUDYIN SEMIOLOGICALNALYSISEx .9

P r 5 r >sE5] 3 , 3S a ist s. . stL

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organisationf things.Whats appropriateo theneutralevel s tomakeaninventoryfallanalyticalossibilitiesndI shall how,asfaraspossible,hepoieticoresthesicpertinencef someof these.[17]wasconstructedrom 16],using hefamiliarroceduref raising yonesemitone.UnlikeEx.9, theintervalsrenot dentical,ven houghbothunitsdoendwithatritone,but nbothcases herhythmormsacontinuousprogressiontypeb:triplet emiquaver,ripletquaver, uaver, ottedquaverontheonehand,andquaver, uaver, ottedquaver,emibreventheother)andthesuccessionf directionss thesame \ / / ).Concerningheroleof semitonesnd mportanceftritones:sforsectionA, it is interestingolookatintervallicehaviouretween nits 7]and[17].First,weshallgroup heseunits ntolargeregments:

B I [71 6a 2a la (3d)II [8] 3a 3d (3a)[9] 2a (la)III [10] la la (ld)[11] la (ld)[12] la ld (la)[13] ld 2a (6a)IV [14] 6d (6d)[1S] 6a (6a)[16] Sd + 6a 6a (6a)l7V[17] 12d l+a 3a (12d)Unlike ectionAsegmentsandIIofBshowatendencyodiminution:21 3 3 2. Then nthe'permutation'one segmentII)Vareseworks nlywithsemitones.The toneending[13] is a step towards egment V whichisdominated y tritones fouroccurrenceseforeG of [16], then afteradescendingeapof a compound erfectourth hree ritoneseadingo A of[17]).Comparing13]withpreviousntervallicequences,we canseehow

Varesearieshepaths rom hesemitoneo thetritone:A I: 1 2 S 6II: 1 2 1 6III: 1 2 3 6B [13]: 1 2 6 (the nversionf 6 2 1in [7The ritones a characteristicnterval:t splits hetemperedcale ntotwoequal arts nd snotwithout nalogyothesemitone,whichdivideshescaleintowelve qualparts.8 Thiscontributesothetautnessfthepiece.Aswecansee, the intervals redistributedn privilegedones: he tritones ndsegments, IIandIIIof A, anddominateection VofB, after hesemitonezone.SegmentV combines hesetwo features:he initialA of [17] is asemitoneboveGS,a tritone boveD: ; theinterval etweenA andBbis a264 MUSICANALYSIS1: 3, 1982

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semitoneandthe lastinterval Bb-E) a tritone.(There s oneintervalmissingfromthe first thirteenbarsand almostentirelyabsentfromthe rest of thepiece,themajor hird.19Thisis probablybecauset is aparticularlyonsonantinterval,and'Density21.5' is articulated y seconds,tritonesandsevenths.)In [17] (segmentV) there are intervalsnot heardbefore:a descendingoctave, a compoundsemitone which is followed once again by a tritoneending.Withthecompoundourthof [16]thesearethelargestntervals f thisopeningpassageand they widen the ambit(starting rom the semitone) nwhichthe melodiccurvecan flower.But the progression,n evidencesince[7], is notover.In b. 15,we findthemelodico-rhythmicigureof theopening:[4] is transposedup a seventh(inversionby semitone),butremindersof theopeningarenotconfined o [18]. [19]takes henotesof [18] na gesturewhichis not withoutanalogy o the passage rom[1] to [2]: E-D#-F / D#-F here,andF-E / F# / C#-F# before.[20]and[21]contain hesamenotesre-orderedas the firstfew bars:E-F-F#-G.Finally,as regardsntervals, 18]to [21]showthe sametendencynotedforsegmentA and between[10] and [16], that is, the continuousbroadening,afterthe celebrationof tritones n [4] to [17], in tones, semitonesandtheircompoundrevisions,whichdoesnot passthrough he intermediaryntervals3, 5 and6:

[18] 1 2 2[19] 2 2[20] 1 2 1+ (1)[21] 1++SectionB endson the samenote as sectionA, afterwhichthe riseto highGbegan b. 7). The intervalof [21]is a doublecompound emitonebetweenF#andG, the twopredominant otesof [1]and[2]. It wouldbeanexaggerationto speakof acoda,butthecomposers roundingoffandsummingup, andnotonlythroughallusions o theveryopeningof the piece.Hereis theparadigmof bs 15-16:Ex11 i0180 S 4nf f mff w f3- , 3 'm d F 3 1 ) 1 t L# w- ## Wu

(I)74/-

g bs 6 i z o fI rm U f T

*g--mf>Eto 3 f*g

Ex.14b

EH-ef cL"-'

-^

fP w - _,ff9c -

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Thenewnotes romeachunitactuallyormanascendingtep-wise rogres-sion n relationo thosepreceding:Ex.15;> o .. bo w bo zqoWo^s o ct,,)#O o

Canwe speakof tonalityhere?A scale,firstminor G,A, Bb, C, D) thenchromaticDt, E, F, F,t, G)unfolds,butnoteveryaddednoteis felt asbeingnthekeyofG:onthecontrary,tevery ransientoint hetonalitysuncertainince henotesnaunitorsegmentean owardspolarnotewhichis differentach imeandwhich, tself, eans owardsnother otethatwillpredominateubsequently.ach ransientointof these irstseventeenarsdelineatesmoment which stablishestself naprecise mbit nd sexceededonlybysuccessiveonesorsemitones:Ex.16

[1g-t2 [2,@' o bo t.. o I

[1] [6] [72o | U bot80 t9]O bo l s[lo]-[120 [13]

01 ]-E ] E0 [1 ]n bt -o I to I I[18]-[20] t2og202603

Ir27g

p wubito


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VARESE'S DENSITY21.5: A STUDY IN SEMIOLOGICAL NALYSIS

It should lsobe noted hat,whereasn [12]-[13] here s a slow rillendingsemitonehigher D), in [24] there s a rapid rill whichfollows he sameintervallic attern descendingemitone, scendingone),the pattern f [1]which he phrasing f bs 19-20(another se of deception)s not supposedohide. [24] s a kindof responseo [22]-[23]: hese astdescend hromaticallytowardsG: withfournotes B-A-B-G:); [24]climbsup to D in inversion(B-Ct-B:-D): only B: alters he symmetry.But this note is important,heraldinghe B$t f [28]. [24],whoseanalogyo [1] hasbeenmentioned,s asortof transitiono [25]whichclearlyborrowsts rhythm or thatof [10]).SectionC is thus attached o sectionA by two procedures:n [22] by therhythm f [2], in [25] by the rhythm f [1], and in [24] by the intervallicpatternof [1]. [26] plays on the A already ntroducedwhich occupies,distributionally,he placeof B and akes herhythm f [2]and 22].[27]usesonly hefirst wonotesof [26].Since 25]we havenot efttheambitA-B, justas [22]-[23]establishhemselves etweenG: andB. [28]willplay,an octavehigher,on the C: andB: introduced y [24]. The appoggiaturas a sortofinversion f the owermordent f [22]and 25],and ectionC endsa semitoneabove he polarB: a transitions assured.This section s divisiblentotwo 'moments',achof whichmay n turnbedivided nto two:

C Ia [22] 23Ib [24]IIa [25] 26 27IIb [28]Ia-Ib and IIa-IIb are n fact symmetrical:a andIIa showa tendencyodescentor to stasisand both are followedby an abrupt hangeof register.Theyarecharacterisedy tonesandsemitones[22]:1 1; [23]:2 2 3; [25]:1 12; [26]:1 1 2; [27]:1). The twosegments ndby leapsof a tone,displaced panoctave, n the sameway hat herisesof [17]and 21]close egments and

VI of B.Mostmusicologists21gree hatb. 23 is theendof thefirstpartof thepiece.Actually,romb. 24 onwardsVarese sescompletely ifferent ompositionalprocedures.We see sectionC moreas a transition etweenwhatprecedes ndwhat ollows:becausen b.17 the climax n the highG completed progres-sion nstigated t the beginning; ecause ectionC is the privilegedoneof anote whichwe had not heard;becausehe alternationall/rise-stagnation/risedoesnotshowa clearpicture s n thefirst wosections the mportantotesof the foursegmentsirstoutline he chordB-G:-D, then hegroupB-At-B: whichstays uspended ut is identicalo the intervallic attern f [1].

MUSIC ANALYSIS1: 3, 1982 271

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JEAN-JACQUES ATTIEZ

II PART I (bs24-40)Part I comprisesectionA (bs 24-28)whichs characterisedypercussive

useoftheflutekeys,sectionB(bs29-32),sectionC (bs32-36)andsectionD(bs36-40).The thirdpart III)beginswitha returno themotif rom 1].1. Thepercussiveectionbs24-28)

Thesegmentationfthissectionsobvious ecause f thenumerousests:Ex.19

[29], 3 ,

[3] + + X.[312 + [3i

#S 77S7'?, p Pt3i3 + +

[34] + +

nn [3i + 3 + '

03i +,b:

Varese wells irstonE-Ct. Can 29]be drawnrom heE-C: of [6]? tistemptingonotethatbs2X28arecast n theambitCt-(E)-D whichs thatof the openingof the piece(bs 1-11)untilthe introductiony a playoftritonesb. 12)of a newmodeof progression.n [31],Varesenverts heE-Ct. Thislastnote,prolonged y the D of [32],becomeshepivotnote([33] [34]) ollowedbyD ([35] [37]).ThepassagendsonanEb,heardhere or thefirsttime,andstandsaboveD asa compoundminor econd.This wholesection s, then, autonomous. he firstunit ([29])moveswithouta break o the last ([37])by a playof successive dditions ndsuppressions.ncontrasto thefirst wenty-threears,accentednddotted


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VARESE'SDENSITY21.5: A STUDYIN SEMIOLOGICALNALYSISnotesareusedsystematically.heregularhythmype s predominantndappearsivetimes.Therestsare onger ndmore requenthan nprecedingsections. n PartI, sub-sections andB areseparatedy a rest:there s atripletcrotchet est between 6] and [7], [19]and [20];semiquaverestbetween10]and[11];quaver estbetween23]and[24],[24]and[25].Adottedcrotchet estdivides 17]and[18],before he returnof the initialmotive,andPartI endsona minimrest.InPart , these ongrestsenjoyaprivilegedistributionalosition:heyprecedehereturn fthe nitialmotive([3]and[18]in thetwoversions losest o [1] rhythm hort-short-long;descendingemitone, scendingone).In thiswe find:a minimrestbetween29]and[30]and(approximately)between32]and 33],adotted rotchetestbetween33],[34],[35]and 36](tothenearestriplet emiquaver),crotchetestbetween30]and 31],[31]and 32],[35]and 36],[37]and 38],andaquaverestbetween36]and 37]:longrestspredominate.Finally,his s theonlymoment fthepiecewhereVarese ses hepercus-siveeffectof thefingers ntheflutekeys.Becausehiswasanewuseof theinstrument,hesefive barshaveattractedmostcomment ndsufficed oinscribehepiece n musichistory:t is really ince henthatcertain urelytechnical ropertiesf instrumentsavebeenusedto musicalnds.2. Verticalfallsndflightsbs29-32)Withthe tempochange n b. 29 and the descendingeapswhichthecomposersessystematicallyorthefirst imehere, omethingifferentgainbegins:

Ex.20t38,

[39]29

_[40Xt $+


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--43 A; J4T'lQl[432 t br^t

Ex.21bs 1-2

Ws' O tsZ t (# " ) O[42] [43ai

o ("-) ^ O bo

JEAN-JACQUESATTIEZ

[43> [43in ;-/st t420 3 9

These eapsare n factsimilaro thoseof [16](G#-D#), [17](A-A)and[20]F#-E#),butthisfigurescombinedor hefirst imewith hecharacter-istichythmicypea2 rom 1](short-short-long).hedifferenceetweenhelongF#'sof [38]and[40] s onlya semiquaver,ndthisallowsus to groupthemn anequivalencelass.In [38]to [40],we arestruckby the playof minorandmajor econds,simple,ompound r invertedG-F#, F#-E#, E#-G (at the join),G-F#,F#-G,G-F#. Throughhissystematicreservationfsmallntervals, aresemakes specialuseof clashes f seconds.[42]and[43a]present patterneminiscentf thefirstbarsof thework:

Here, he ntervallicequences identical:nascendingone,adescendingperfectourth,anascendingiminishedifth.Thecombinationf intervallicdirectionswiththeircontinuous roadeningmakeseachnewnote,on theascendingrdescendinglopes,higher rlowerhan heprecedingne.Thisprinciplefmotivicdevelopments found lsewhere,ven f the ntervalsrenotidentical.nEx.22thetwo nstancesromEx. 18arereinsertedoshowthelinkbetweenhesefourfragments hichreliesuponthealternationfdirectionsnd heplayof simpleorcompoundemitones,ven houghhereis nointervaldentity:


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EX.22 4b 12 S,} (o) - ZXn to ) StZ

bs 16-17.s go

(} $0-----,

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JEAN-JACQUES ATTIEZ

withprogressivehythmicypes: ypeafrom 38] o [42]and ypeb in [43].3. TheflightsfDensityI shallnowbreak way, xceptionally,rom heprincipleollowedrom hebeginning f thisanalysis ydepariingrom he inear nfolding f thepiece.[43] s compared ithanalogoushenomenalreadyncounteredr tocome.I havegiven hem he genericname flight':

Ex.24bS 12-13

Theyarenot all of one type: herearebreathsn bs 13and 16 withslursstraight fterwardsn bs 13, 31, 58. Butonecouldsay thattheyarticulatethree ypesof 'crescendo':non-metaphoricalrescendo< fff), augmentationof rhythmicalues bs 12-13:quaver,dottedcrotchet, henquaver,dottedcrotchet, emibreve; . 16:crotchet, rotchet, emibreve;s 31-32: semi-quaver,dottedquaver,crotchet,dottedcrotchet,dotted crotchet;b.44:quaver,dottedcrotchet,dottedminim;bs 5W61: ripletcrotchet,ripletcrotchet,crotchet, hen quaver,crotchet)dotted crotchetand crotchet,minim, emibreve),ndfinallyanunrelentingise n pitch towards in b.13,G n b.21, A in b. 32, C: inb. 44, B in b. 60).These lights redifElcultodescriberomamelodic ointof view: nthefivesegmentshere s afeeling ffunctionalimilarity,uthow s thisto be made xplicit? here s noobviousregularityntheintervaleries.22 ll thatcanbeobserveds a certain refer-ence or taut' nddissonantntervals, ut f we lookat thewholepiece, hereis nothingpecial n that.


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t O b . R2, .R2, ' | { _! bo .* 7, R

_

b- bo{b o \. tone \ \ \t+22 R

ts' ' . '0 jR2'R R2 _ '80 #s'. q

(R signifies ctavedisplacementndR2 double-octaveisplacement)But the flightsdo not haveonly paradigmaticnalogies. yntagmatically,theyhaveacharacteristicistribution.irst,andmostobviously,heyendanimportantectionin b. 13, segmentB = IV of Part ; in b. 17, Part ; in b.32, sectionB of PartII; in b. 45, sectionA of Part II; in b. 60, the entirepiece).Equally,wesee that he positioningf theechappeesanbe studiednrelationo anothermelodic ypealready ncountered permutations.here

b. 1 6

followsa list of the two typesconcerned:

VARESE'SDENSITY21.5: A STUDY IN SEMIOLOGICAL NALYSIS

Theconstructionalrinciple f theflightsmustbesought lsewhere,n theroleplayedbysemitonesn the appearancef newnotes:Ex.25

bS t2-13 bs 31-32

Flights

[17][21][43]

[63][82] [83]

Permutations[10][14][18][25][44][54][59][64][71][79]

- [13]- [16]- [20]- [27]- [51]- [56]- [62]_ [70]_ [74]- [81]


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JEAN-JACQUES ATTIEZ

Infourcases utoffive([17], 21],[63], 82]-[83])heflights reprecededyapermutation:nthree asesoutof five([7],[43],[63]) excepthatsince helastechappeendsthepiece t is literallyhreecasesoutof four theyarefollowedby a permutationthus,two'flights' reframedby permutations,[17]and 63]).Evidently,ermutationsonstituteneaspect f thecontext fflights, ustasflights onstituteneaspect f thecontext fpermutations:hisis an importantmelocticyntagmaticlement f 'Density'.Finally) lightshavea thirddistributionalharacteristic,n the left thistime: n fourcasesoutof five,one of thetwounitscontains descendingcompoundnterval:(1) beforeheflightof [17],descendingompoundourth t thebeginning

of [16];(2) beforeheflightof [21],descendingompoundemitonettheendof[20];(3) beforeheflightof [43],descendingompoundemitonettheendof[41];(4) beforeheflightof [82]and[83],descendingompoundmajorecondat thebeginningf [81].Returningoramomentothecontent f theflights,we recallhat hefirsttwo ([17]and[21])containan ascendingompoundemitonen one-andtwo-octaveisplacementespectively,ndwearetemptedo seeif intervalsgreaterhanan octavehavesomeprivilegedelationshipo flights.Everyinstance fdescendingompoundntervalsot noneofthetwounitspreced-ing anechappees a join([24]-[25]: ompoundminor hird; 28]-[29]:com-pound ugmentedourth;32]-[33] nd 33]-[34]:ompoundemitone;69]-[70]:major hirdwith doubleoctavedisplacement;74]-[75]:compoundminor ixth).Withascendingompoundntervalsutside heflights,sevencasesoutof tenarealsoover oins [27] [28], [38]-[39],80]-[81]:compoundmajorecond;36]-[37], 39]-[40], 63]-[64]:ompoundemitone;70]-[71]:compounderfect ourth). 24]and[77]contain compoundmajor econdand [33]hasa compoundemitone.The inventorywillbe affectedby thefollowing bservations:

(1) Every nstance f a compoundemitone, scending nddescending,from 33]to [37], s found n a section f Part Iwherebecause f therests t isdifficultogivetheproposedartitioningf unitsanabsolutevalue.Should31]and 32] b.25)constituteneortwounits,and 35],[36]and[37](b. 28)one,two orthreeunits?Wemighthesitate. t isthereforenteresting, hetherrnotjoinsare nvolved,o examineheimportancef compoundemitonesn sectionB.(2) The same ypeofproblemsposedby thejoin 27]-[28], ince 28] s to[27]astheC::-B: trill n b. 20wasto the preceding . Moreover,heintervals thesame.Thisassimilations allthemoreappropriatenthat[24]and [27]-[28]arenot withoutanalogyo the flights: eapto a

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Beforea Tritone [17]flight Semitone [20]Semitone [41]Major econd [81]Withina Semitone [17]flight Semitone ndouble-octavedisplacement [21]In an Tone [20]assimilated Tone [27]- [28]flight Tone [77]PartII, Semitone [33] Semitone [32]- [33]SectionA Semitone [36]- [37] Semitone [33]- [34]


muchhighernote, crescendo,ontextof permutation.t will laterbeshownhatunit[77]couldhavebeenconsiderednechappeeere tnot'afflicted'with a diminuendo.f, therefore,assimilatedlights' eemsappropriate,t is interestingo note that[24], [27]-[28]and [77]allcontain compoundmajorecond.Allother ases- except hedebat-able exampleof [36]-[37] romsectionA of Part II - areclearlypositioned t joins([38]-[39],[39]-[40],[63]-[64],[70]-[71],[80]-[81])(3) Once woof thesixdescendingntervalsavebeen ocatedn sectionA,theother our [24]-[25], 28]-[29], 69]-[70], 74]-[75]) reclearly t

a

olns.

On the basis of these observations nd distinctions,a table of thedistributionf compoundntervalsn the piececanbeformulated:Ascendingntervals Descendingntervals

Joins Semitone [39]- [40][63] [64][38]- [39][80]- [81][70]- [71]

Minor hirdTritoneAugmented ifthMajor ixth[24]- [25][69]- [70][28]- [29][74] [75]

TonePerfectFourth


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JEAN-JACQUES ATTIEZ

Itwas 43]whichmotivatedhisdigression.tisthethirdofthefiveflightsand, naway, t is central.Thefirst lightendsonahighE, thesecond n ahighG(b. 17),thehighestnoteuptothatpoint.Gthendisappearsorelevenbars,andreappearsshighGinb. 29. It is usurpedn b. 31byA. Thelastflightconcludeshepieceon a highB, theprivilegedotefromsectionC ofPart , absentrom hefirst wosections fPart I.G, AandBmaintainheirprivileged elationshipn termsof immediateontext,of registerandofdistribution.hethird ection fPart Iis infact,apermutationonewheretheintermediary# insertstselfbetweenB andA.4. Permutationsf B, F# andA (bs32-36)

A doesnot play a rolecomparableo thatof G. Here t closessegment[44]-[45]witha longnote,butin [51] t is B thatcloses hesecond egmentwith hesamevalue adottedminim).ThezoneofAis, infact, ntermediary:therestof thepiecepreparesheclimax f theworkonhighB.Afterabriefpassagenaslowerempo crotchet 60,bs29-32) he nitialtempo eturnsn [44].TheB-F#-A adopts,nthesame egister,he ast wonotesof the flight,fillingthemout, and,as GillesNaudpointsout, therhythm f thebeginningf [44] s related o thatof [43]:[43]= semiquaver,ottedquaver, rotchet,[44]= triplet emiquaver,ripletdottedquaver,riplet rotchet

In [44]there s a tripletand n [43] heG#is a crotchet, utthearticulationpointof eachnote s, in bothcases,proportionallyomparablen relationothe preceding ne. Thus, this opening ectionborrowsts rhythmic ndmelodic omponentsrom heprecedingchappee,nd hewholeofsectionCwillbe cast n theambitof its lasttwonotes.Butconsiderhedevelopmentfrom 44]:Ex.26

s . ,

gr j

s . . . n

8 - n

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VARESE'SDENSITY21.5: A STUDY IN SEMIOLOGICAL NALYSIS

This paradigms melodic,butthe only rational artitioning usttake ntoaccount he slurwhich inksthelastB of b. 32 to b. 33:Ex.27[440 i4

& . . 1

t460 3 9 g 3& . ,_#t T;

[48S8 - 1

3 3This s certainlyheonlyplace nthepiecewhere segmentsrepeated. hereis, of course,a transformationelision f the A) atthe end of [47], but [48],whichprolongst, adoptsmelodicallyhe last two notesof [44] and [46].Hence he A from 47] in Ex.27 iS in brackets: arese annot ccept strictrepetition. hesimilarityetween45] and 46] iS SOgreat hat,accordingothe principle f deception,t arrests he momentumovvards the secondslurendson theFt. How,then, s the subsequent usic o beanalysed? heproblems identicalo thatencounteredn bs 10-13. Rhythmicransforma-tionswill nowbe shown n relationo the melodicnvariant:

E>c.28X [ Q ] t

E i O------ n

L.ME[502 8 - - - - - - - - nr#S

3 3; 6025 ] ,< ,

3ar^: G 7 ' S S ' '_ B


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JEAN-JACQUES ATTIEZ

It is in extremishat[51] reintroduceshe B. Note that,melodically,51]adopts hedescendinguccessionA-F#-B whichconcludes . 32, but asalwaysheunitwhich reateshisequivalencesimaginary,ecause ftheslurwhich eparates44]from 45].23Rhythmicallynd intervallically,his section s distinguishedrom theprecedingndensuing ections y theabsence fsemitones,he argenumberof minorhirds,perfect ifthsandminor evenths, ndby typesa1,b ande:I [44] a1 a1 7a 3a 3d (7d)[45] b lOa lOd 7a 3a (lOa)II [46] a1 a1 7a 3a 3d (7d)[47] b lOa lOd 7a (3a)

III [48]a1 3d (3a)[49] e 3d (3a)[50] e 3d (3a)[51] b 3d 7dThe breathbetween 45] and [46], like the repeatof the sameunits in[46]-[47],ustifieshe demarcationf segments andII. Segment II,up tothe falling ifth(F#-B), is dominated y minor hirds.Therhythmicypes,then, havea characteristicistribution:1 is alwaysat the beginning f asection,b at the endande in anintermediateosition.5. Theendof PartII (bs36-40)SectionC hasdeveloped nthe same hreenotes:C, a semitonebove heprecedingB, seemsto be an intruder.Armedwith a triple orte, t is theculminationf thecrescendoegunat the end of b. 35, butbecause f unit[53], t willbe linkedo E. ThisC caneasilybe accepted smarkingheendofsectionCandthe beginning f sectionD:

Ex.29X ''7^t'lr.

[5! t9i

?

055] , 3 t >y

P SU6fb fp


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, Lt , 7L572---I br

[56 SPv r 2^"3 '2 'fPInthesameway,it doesnotmatterwhether heEbof [53]is theendof [53]orthe beginningof [54]. We attach t to [53] since the diminuendoakesit aprolongationf C andof thefirstEb. Incontrast, hetton D isolates 54]withits ownslur.The mostimportanthingis thatthe restof theparadigmhowshow [54]-[58] is constructed n relationto Eb, D and Db by a play ofpermutationswhich can be read from the table above. Rhythmicallyanddynamically,55]-[58] s characterisedy thesameprocedure:24hefinalnoteof thefourunitsis always hortened;t is eitherpiano ndstaccato[55], [57],[58])orof a shorterwrittenduration [56])andfollowsanaccentedforte ote.In the sectiontakenas a whole, the distributionof rhythmic ypesis ratherscattered: l threetimes, b once, c twice, e once, and [56]whichis the onlyexampleof b inverted.25There are, therefore,roughlyas manyshort-longtypes as long-short.The intervallicdistribution,combinedwith the zonesamongwhich the differentnotes are divided(C-Eb / D-Eb / Eb-Db-B)delineates hreesegments n this section,wherethe semitonealternateswithmajorsixths, wherethe semitoneclasheswith the tone and wherethe finalintervals a descendingdiminishedourth.Thewhole s, however,dominatedby a tendencyto descent, felt from [51] of the previoussection. The firstsegmentendson Eb, the secondon D (a semitone ower)andthe thirdon Bthe lowestnote of sectionD: the B dominated ectionC but had not beenheardagain.PartII canbe describedas fullof contrasts ndhesitations.SectionA: twopermutation ones (E-Ct-D and Ct-D-G:). SectionB: threerapidfalls,then flight to high A. SectionC: permutation one (B-F:-A). SectionD:descent o B withpermutationoneon Db-D-Eb. WhilePartI wascharacte-risedby the rise to high G, PartII, with its varieduse of rhythmic ypes,dynamicsandmelodicdirections,seemsto be intermediaryndthis is partlydue to the largenumberof 'permutationones'. Evidently, hreesegmentaltypes will have three functionsin this piece: the permutations stagnant,delaying heappearancef a newnotewhich s generally semitonehigher;oroblique paradigmsallow the piece to progress;or rapid flights lead to aclimax.Between hem,thesetypessetupa dialectic: hepermutation ctsasabrakeondevelopment in relation o theobliqueparadigms ndtheflights tfavoursa periodof restrather hanmomentsof tension.Vareserestores,on


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JEAN-JACQUES ATTIEZ

anotherevel,what hetonal ystemsno longer ble o offer,byalternationfdistinctunctionalypes.III PART II (bs41-61)1. Reprisef theopeningbs4143)Fromb.41there s areprise.Theinitial empo eturnscrotchet 72) while[59] s anexact ransposition,semitone bove 1],of the first hreenotesofthe piece,whichpermits direct rrival n Gwithouthe'suspensions'f [2].This is probablywhyit is repeatedwith durationalhortening f the G)withoutntermediaryevelopmentn unit [60]:Ex.30

01 ]

4 F , _ J _ , >m fS W

- w

1 06$ i Lg b^t?t-i2xJ : 2sJ q;t I [

g t$s t(F"_, r 1 [62] 3

- to v b. v j 4

r - - e

p26i 3

p[610 3 31e1 2P=r y26i 3

Thisparadigmssimple: henotesn unit 61]arepermuted,hen heorderat the headof the paradigmeturnsn[62].It is interestingotrace he originof the D andthe Ab of [62]:Ex.31

[2] 3[lg


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[62] s anexactmelodicranspositionf themelodicontourn thefirst wounitsofthepiece.Therhythmsf [59] o [62]arenot denticalo theopening.However,n [S9]and [60],typea2of [1]occurs.Interestingly,efore he flightof [63], already nalysed,he intervallicsyntagm ears omeanalogyosectionA ofPart , in the progressiverowthof the same ntervals,rom hesemitone o the tritone:A I [S9] a2 ld 2a (ld)II [60] a2 ld 2a (2d)[61] a2 la la (ld)[62] b ld 2a Sd 6a (la)

Thisintervallicrogression,ogetherwith the tendencyo risewhich sinitiatedt theendof unit[62]with he ntroductionf anAb(notyet heard),is reinforcedy progressivehythmicypes,a2andb: it is easy o see,here,howb is an expansionf a2Theanalysis asbegun,n respect f theflightsn Ex.24,on theD of [62].Butthe slurandcrescendolearlysolate 63].ThecaesuraetweenAb andAis anotherdeception'n the risebeginningwithD.2.PermutationsnB-D (bs4S50)

Afterthe flight,Varesereturns o his predilectionor playingon twoalternatingotes: hisrecallshe wayDbandCareexploitedn bs9 and10.TheB andD at issuearepositioned,espectively,semitonebovehenotesof the flight Bb- Ct). The D, moreover,s broughtn byCt, acompoundsemitone bovet. This time,the D appearso predominate:Ex.32

[6 8 - - - - - - n, 3 ,

t) , 3L68-.---------------------,

3 3t6 6] ; 3 - - - - - - - - - - - - - - - - '

f t 'Y ,


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JEAN-JACQUES ATTIEZ

26703 'f S f

[ , s ,

06! - ,

This s doubtless ecause f rhythmicypesa andb which onfer longvalueon the finalD's:Ex.33

5 r r, ;3 3

r 6 5 ] r ( a 2 ,3 3 3

0660 : : r r (a23 >s3

067] : r 5 (a13 3

0680 r r S[69] C b)

Less mportanthanG andB, D neverthelesslaysa decisive ole n certainintermediaryoments:tcloses heplayaround in b. 21;wefind t againna privileged aradigmaticositionn bs 25, 26 and28; t willreturn efore hefinalflight as the uppernote of the permutationsf bs 5S58. It owes itsparticularmportanceothe registraleapafterC# of [63]whichmakes t thehighestnoteof the piece.


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VARESE'SDENSITY1.5: A STUDY N SEMIOLOGICALNALYSISThiswhole ection falternating'sandD'sendsonalittlemelodicigurewhichs theinversionf theinitialF-E-F# andoutlines finaldescent:

Ex.34s t to ne

,2X {w O #.

3st toneI j r 11-11 _ _ _ 5 . #

B P f P

[70] s treated s anappendixosectionBforseveraleasons:irst,becausetheopeningfffis heendof thecrescendorom 69]; econd,becausehere s abreathonlyin the middleof the bar;finallybecausehe characterf thesectionbeginningwith [71] s quitedifferent.3. Thelastsegment(bsSI-61)

Thisdoesnot mean,as in previousases, hat hereareno linksbetweenthisfinal phrase'ndwhatprecedest. BetweenCandF# of[71]wehave hesamedescendingritoneas betweenD and Ab of b. 50 in double-octavedisplacement.ut,aboveall,[71]bears omerelationo thewidedescendingintervalsn rapid hythm f [38],[39]and[40],and,toa lesser xtent, 53]:Ex.35,7

t539 > '_ [54]r - ff

070 s

[72]v.

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JEAN-JACQUES ATTIEZ

tW*-*s s [SS WS

t 1 >, (_) 077 J R[d P w

3br F:crcsc. rnolto[29I'/ fE >

-ff4; F[802

3 > I t82]e, te

Even hough 71]beginswitha C and 38]withaG, thefall o F#- E# on apracticallydenticalhythm nd hedemisemiquavermake omparisonith[38] egitimate. hisparadigmaticable hows herhythmicransformationsin relationo melodicdata,but the implicitunitswhichemerge annotberetainedecauseheslurshave he upperhand.Numbers 74]and[75]marktheboundariesfmore ealunits.Ex. 35 thusbrings wocontradictoryevelsofsegmentationogether. t willbenoticed hat 72]and 53]are mmediatelyfollowed ya unitofthesame hythmicype [73]and 54]),e, whichalsohasthe samenumber f notes.From 75]onwards,he composers sliding o another aradigmaticxis.Ex. 35demonstrateshat hisentire oncludingegmentfromb. 51)formswhole,since we progressowards he final highB by successivehanges.These changesareof a particularlyharacteristicature:n [75], E# (F)becomesE, asemitone elow.The C onthe leftof theparadigmecomesC#(a semitone igher). 76]marks he firstattempt t melodic light: or themomentwestayon G,asemitone bovehenewF#, itselfatoneaboveE. In[77],as in bs 5 and6, Varese dopts wopreceding otesandrises o A26 acompoundoneabove he G).[78] ntroduces Bb,thepitch-class semitoneaboveA of [77]. In [79], D, a seventh inversionf thesecond) romE, isadded. 80]and 81]playon C,E, D, [82] akes heBbof [78]whichhus illsinthe nterval -D of [79].There ollowshe final light,whose onstruction


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on playsoftonesandsemitones,s shown n Ex.24, togetherwith heway nwhich t endsonB.This endings thusa resume of all thatprecedes:hefallsof bs 51and52,theplayof permutations,he progressionn G thenA andB andthe finalflightareall proceduresncounteredreviously. hetendencyo returnoeventsromhefirst woparts,whichwenoted or hetwoprecedingections,is confirmedere:afterhavingecalled hatgoesbefore,Varese ndertakesriseto thelast climatic ointwhichGandA prepare.

IV RECAPITULATIONThe tableon thefollowing agesattemptso givea globalpicture f thepiece by assembling,n synopticorm, the essential lementswhichhaveunderpinnedhisanalysis.Onthe eft,segmentationtfour evels:partsPartI etc.),sections,egmentsndunits.Then hethreeprincipleata: hythmictypes,intervallicequences ndmelodicpattern.On the right, a generalcharacterisationf the syntagmsn units:zonesof permutation,f progres-sion,of flightandof descent.27This tablecould, n addition, avecarriedtherdescriptiveariables:orexample, lursanddynamics, oth of whichare essentialo the piece.Buttheyaroseaboveall, in the preceding ages, o delineateheunitsso thatI

considert unnecessaryo includehemhere.


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o

PartISegmentation Rhythmic ypes Intervallic equences Melodic Pat

A I [1][2]II [3][4]III [s]

ld 2a (Sa)Sa Sd 6a (2d)ld 2a (la)6d 6a (ld)la ld (2d)3d 6a (6d)

a2da2da2"d"

B [6]I [7]II [8][9]III [10][11][12][13]IV [14][15][16]V [17]

bc or eala2alba2alalbb

6a 2a la (3d)3a 3d (3a)2a (la)ld la (ld)la (ld)la ld (la)ld 2a (6a)6d (6d)6a (6a)Sd + 6a 6a (6a)12d l+a (l+d)

C$G/A-BbG - Bb/CDb -C/DG#- D

/A- D:A-Bb - E

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ation Rhythmic ypes Intervallic equences MelodicpaVI [18] a2 ld 2a (2d) E - D# - F[19] c 2a (2d)[20] al al l+d (la) /[21] la++ (8d)+

Ia [22] d ld la (O) B-A#[23] d 2d 2a 3d (3a) /[b [24] d 2a+ ld 2a (3+d) B+C# B#Ia [25] a2 ld la (2d) B-A#[26] d la la (2d)[273 al la (2a ) /B

I [29] e 3d (3a) E - C#[30] e 3d 0 (O)

Segment

c :

Part IIA

to semiquaver[33] e l+a (l+d) C#-D-G#

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[43]

Melodicpaegmentation Rhythmic ypes Intervallic equences

/EbG-F$E:

IG-G$E-Bb-G$B

ld 12d ld (2+a)ld 12d (l+a)ld 12d ld (O)lOd lla la l+d(la)la la (Sa)6a lOa3a lOa lOd)

B I [38][39][40]II [41][42]

a3a2a3a2a2b

KFFAI [44][45]II [46][47]III [48][49][50][51]

7a 3a 3d (7d)lOa lOd 7a 3a (lOa)7a3a3d(7d)lOa lOd 7a (3a)3d (3a)3d (3a)3d (3a)3d7d(1a)

al albal albaleeb

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t: - 7A= ;

Ct-v CC

r r t r CC:v v ,/ m m

Ct Ct Ce Y Ctr t Ct r Ct

ce ce ct D D

u)

- r N 'e cC:> < E-vt C -ooN tQ - Lo N= r t 'e t 'e r t

ou) =Q u)

+. - =

= - o

$ ce D X ce = t) t

N m t V S X= - , m m m m mn I . . .

-v s} -vm o s} mt 'e 'e 't

D ce ce ce

v)

293

'e

. -t # n m

v*ct

bt

- - -

ct

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Segmentation Rhythmictypes Intervallic equences Melodicpa[68] al[69] bIII [70] e

A I [71][72][73][74][75]IIa [76][77][78]IIb [79][80][81][82][83]

6d ld (7a)6d (ld)7a 6d (la)7a (8+d)2d ld 3a 3d (3a)2d la (3d)3a 2+a (lld)6d 6a (lOd)4a lOa (lOd)4d (2+a)2+d 4a (6a)4a 4a 7a (2a)2a 2a 6a

SF$E:

/EE-F$G I/BCE-DBb-D-F$CD$EtB

a3alecc + da2bdbalebb

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VARESE'S DENSITY21.5: A STUDY IN SEMIOLOGICALNALYSIS

The 'melodic pattern'column summarizesa phenomenonwhich has beendiscussed constantlyhere the progressionof the piece by a successionofzones of privilegednotes whichare overshotby new addednotes. This givesthe followingoverallpicture:Ex.36,part one

[1 ]-L63g '>P

[70

t82-t9] , b.Ed-[120bo .,

L10,.,E40-05]

o

01 ,o

[170

[180-[19]0 >, o

[ ] 21]o >[2i-S2@ " g o

L2- [280 " t

MUSIC ANALYSIS : 3 , 1982 295

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JEAN-JACQUES ATTIEZE>c.36, part two

[29]-032] [33]_[370

X 4 14 #-$ o I o b l

[44]-05 1]

[52]-[53] 0540-[570 058]- b Xo 1x^ o | b*.

Ex.36,part three0590-2620 ,, bn"-vo ' g bsw 4vw264]-0690 [700

40 1S4nW[ ]eLL [7SS [76, L7d 9]8t] i2]-g83] #E"+Z_The progressiono highG in b. 17 is followed y a zoneof hesitation hichalsobelongs o B (bs 18-23).Part I, dividedntofour moments',omprises:playaroundE, C#, D, thenC#, D, G#; successivealls hena climax n A;playaroundB, F#, A; playaroundC, Eb, D, Db. Part II contains: eprise,permutationsn B;D anda finalphrase.Four syntagmaticamiliesmay be extracted rom the melodicpattern:permutation,rogression,light,descent.Usinga horizontaline ( ) forpermutation,nobliqueine / ) forprogression,narrowedbliqueine / )for flights,and a descending blique ine ( \ ) for descent,we obtain hefollowing eneral icture f the piece:

PartI _/_/ /t /\/_/PartII _/_/\//_Part II _// / /

MUSIC ANALYSIS1: 3, 198296

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VARESE'S DENSITY21.5': A STUDY IN SEMIOLOGICAL NALYSIS

Thisplanshowsclearly he tendencies f eachpart:Part -ascent,Part I -hesitation, artIII ascent-descent-ascent.Throughouthe analysis, he sections nd segments avebeen different-iatedmostoftenby contrast:A of PartI groups ogether hythmicypesa2and d, whereas II of B in the samepart s characterisedy successions fsemitones.During he courseof the analysis ominantariables ave beenemphasised oment y xnoment. he completeableenables n assemblyobe madeof all the componentsf the musicalmaterial ndconsequentlyoreplace ominant ariables y thosewhicharenot dominant.Thiskindof tablealsomakes t possible o verifywhether r not there s acorrelationetween wo phenomena. y definition,he foursegmentalypesontherightarecorrelated ith hemelodic atterns nd ntervallicequences.Do they correspondo the rhythmic ypes?A hypothesiss that regulartypeswill correspondo stagnant onesof permutation,hat typesa, b, c(augmentation)illcorrespondo zonesof progression,tc. Thepartitioningof the four unctionalypes s nowprojectedntothe rhythmicypes notingthat heydo not necessarilyorrespondo segments ndsections):Permutation Progression Flight Descenta2d a2d a2d b c or e ala2al b a2al al b ba2c al al al ddda2d al a2e e ale e e a3a2a3a2a2 bal al b al al ba e e b al be al al c ca2a2a2 b bb a2a2al al b ea3al e c c da2b db al e b bTryas we might,no particularorrelationanbe discerned etween hythmicand functionalypes. This negative esult s still progress: nless herearegaps in our inventory f variables whichcould alwaysbe filled in byanotheresearcher it shows hat he mpressionf stagnationrprogressionis due onlyto modalities f the melodic ine.The value of the procedureollowed s, in any case, obvious:withoutrelying n the complete able,particularlyookingat functionsn termsof


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JEAN-JACQUES ATTIEZvariables,t couldhavebeenstated hatrhythmicypeb wasabsolutelycharacteristicftheflight bfive imes,asopposedoa1andd1once),whichstrue n away,butb is found ixtimes n thepermutationsndfour imes nthe progressions here t is as frequent s a2. It is impossibleo claim,therefore,hatb istherhythmicariable hich orrespondsotheflight inceit is foundelsewhere,n combinationithothervariables. hesame s truefore, mostly ited npermutationones except necaseofdescent)wherewefindalltheother ariablesoo. Avariablesnotpertinentnrelationoagivenfunction,28n anyabsoluteense,and,except n thecaseof b, theredonotappearo be anycorrelationstrongenough o extract endencies f anyinterest.Here,theflight s, in fact,a special,distributionallyrivilegedase(fiveoccurences)n theprogression:f welookatthekindsofunits nwhichb isfound,wecanstate hat ntwelve asesoutofseventeen,heseunitsendwithoneorseveralscendingntervalsinseven asesoutoftwelve,allthe ntervalsascend). t appearso be possibleo establish, nanot)zerevel,correlationsbetweenwoormoreparticularariablesnteredn thetable.Theres norecipe orfindingnterestingombinations:heanalysisunc-tionsonthebasisof hypotheses hichcanbeneither onfirmedorrefutedunless taxonomicescriptionsavailable hichsasresponsiblendexhaus-tive aspossible.Thisis doneby 'churning'hedata, hat s, projectinghecharacteristicsf onedatumontoanother,tartingwiththose ntuitivelyeltto be the mostpromising.29t wasshown,for example, hatflightshadparticularnternal nddistributionalharacteristicssection I/3).Studyofthe tablereveals hat,withinone segment, here aremanypermutationsfollowedmmediatelyya progression.heseare:

PartI B III [10]-[12]/[13]IV [14]-[15]/[16]VI [16]-[20]/[21]Part II A I [59]-[61]/[62]C IIa [79]-[81]/]82]-[83]Withthe exception f [25]-[27]/[28], heseparadigmshowaninterestingrhythmicnalogy:


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r C- 5, | / s 3Beforehenotewhich reatesheprogression,tthebottom ftheparadigm,there s rhythmic ccelerationhrough he use of the tripletafterbinaryrhythmsndan ncreasenthenumberfnotesnthe astunit exceptnthefirst ase).Thesameprocedure illhavebeennotedn [44]-[45],buttheretdoesnotlead oaprogression.t is rareoroneprocedureobeencounteredin100% f cases:musical tyle s nota system.Letus lookatthepermutationsntwonotes:

Db- C [10]-[13]B - A: [25]-[28] semitoneE - C: [29]-[31]F: [49]-[511 minor hirdJ | - JD - B

MUSICNALYSIS1: 3, 1982 299

[64]-[69]

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JEAN-JACQUES ATTIEZ

The ntervalliconstants in itselfremarkable.t becomes venmore emark-ablewhen t is noticed hat the firsttwo followpassageswhichcontainnointervals reaterhana minor hird.As for heother hreepermutations,heyappear ftersegmentswhere he perfect ifth is present,one of the rarestintervalsn the piece, oundonly n [51],[73]-[74] nd 82].It is therefore oexaggerationo postulate correlationetween ermutationsn two notes,the nterval f a minor hirdanda contextn which he perfect ifthappears.Still more little correlations ould probablybe found in this piece.Moreover,he globalperspectivef ourneutral nalysisn musical emiologyis, we know,stylistic: hismeans hat f otherworksby Varese reanalysed,it shouldbe possible o pick out fromour tablecorrelationsr phenomenawhose identifications not permittedby 'Density'alone. Returning o'Density' n the basisof a wider ield of workswouldbe thatmuchmoreefficient, iven hatwe wouldalready avedrawn p a prettydetailednven-toryof variables. he neutralevel, t mustbe stressed,s onlya 'moment' fanalysis.A few general bservationsn the methodologysedhere:(1) It is possible o partitionparameter y parameter, ut the globalsegmentationserformed n the syntagmatichainare the resultofintuition bout heconvergencef different ariablest a givenmomentandthe hierarchicominancef someof these.The collation f infor-mation, parameter y parameter, ariableby variable, hows theconstitutionf theglobal egment.Thisglobal egment anbe deducedfromthe sum of the individual egmentations,ut only to describetexture.There s, therefore, o logical r necessaryrder ccordingowhichan analysis houldbe conducted nd presented: ere, as else-where,the orderof reasoning oes not coincidewith the orderofdiscovery.(2) One particular onsequence f this principle s manifest n theconstruction f equivalence lasses:when the assimilationhe of

rhythms f [1], [3] and [5] was proposed, n spite of theirphysicaldifferences,t wasnotonlybecausehesedifferences ereminimal, utbecause, nanotherevel,melodicdentity F-E-F#) induced nassem-bly of theserhythmic nits.It is impossibleo say, therefore,hat herhythmic nalysis s purelyrhythmic:n fact) otherparametersretaken nto account.The resultof all this is a mixture.(3) I have poken everalimesofprojectzon.hishasa double ole.First, tpermits he evaluationf the roleof onevariablen relationo another,as in the previous ase. But it also has an heurtsticalue: t enablesinterestingorrelationso be discovered etween ariablesf differenttypes.Consequently,here s no limit o thenumber f projectionst ispossible o performromone variable ntoanother:his is essentiallywhy analysiss endless,and even f one hopes o put one'sfingeronsomecharacteristicorrelations,here s still the convictionhatother


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equallyvalidrelationshipsmay haveescapedourattention.Thereare,therefore,no rigorousrules for determiningwhich projectionswillproveviable.We canprocedeonly by trialanderror.(4) Thus, correlations re establishedbetweendisparate haracterisationsof different ypes and levels:one exampleof this is the distribution fflights. This is identified, on the left, by a descendingcompoundinterval,amoreconcretedatum hanrhythmicypes n general,or thantype b which, positionedat the end of a segmentandwith its play ofsemitones n the pitch structure,characterisests content.(5) A great deal of intuitionenters into the research,but althoughtheobjectiveof taxonomicclarification s confirmation, t may equallyresult n invalidation.Thiswas thecase, in the research hase,forrests:it wasassumed hatthey couldbeentered n different lassesaccordingto the typeof segmenttheydelineated.A studyof the taxonomicdatareveals hatthe onlyinteresting onstants the unusualpresenceof restsin the 'percussive' ectionof PartII one of its characteristics.

V POIETICANALYSISSeveral imes, hereandelsewhere, herehas beenoccasion o recallthe factthatneutralanalysiss anessentialbut intermediarytage n the semiologicalapproacho musicalworks.In thisandthe ensuingsection he intention s toshowhow the dataof neutralanalysisrelateto thoseof poieticandesthesicanalysis.1. The oieticroblemThere are two ways in which the phenomenacataloguedby the neutralanalysiscan be consideredpoieticallypertinent.To the extentthatanalysisdeals with the score, it is directedat the only traceeft by the composer.Thereforeit is possible to considerthat recurrent raits demonstrate hepreferences f the composer orcertaincompositional rocedures;heyenjoythe presumptionf poietic pertinence. This presumptionis confirmedparticularlyf otherworksby thesamecomposer ontain hesetraits don'twesay'he likesto do this, he likes to do that'?),orif ourhistoricalknowledgeoftheevolutionof musical anguage stablisheshat,on thebasisof theheritagereceivedandexperiencedby Varesewhenhe began o compose,he decided oorienthis compositional ractice n this or thatdirection.30This poieticproceduremay be qualifiedas inductive:

poietics; neutralevelBut it is justas feasible o startwith an externalpoieticelement-a sketch,aroughdraft,a commentary-andproject t ontothe work,eitherto directthe


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JEAN-JACQUES ATTIEZ

analysisccordingly,r to reorganisehe neutralevel,constructedndepen-dentlyof the external atum:; work

poietic ata > orneutralevel

In the first, inductiveperspective,whichtraits dentified y the neutralanalysis avea poieticpresumption?(a) Theprinciple fdeception: have hownhow t governedevelopmen-tal procedures, t the sametimefrustratinghe expectationsf theWesternistener.Thus,theprocedures escribedtandoutfrom hewiderangeof habitshandeddownby the dynamics f the romanticmusicalphrase,whoseprinciplesf progressionndelevationVaresepreserves utconstantlyontradicts.(b) Theprinciplef maximal ifferentiation:n theneutralevelrhythmicequivalencelasseswereconstructedtypesa to e), but it must berememberedhatVareses carefulowritevalueswhichareas distinct

aspossibleromone another.Oneof his favouriteroceduresonsistsofmultiplyinghe number f dots rom hebasisof agivenvalue as nIntegrales).Slurs, ripletquavers rsemiquaversntroduceubtledif-ferentiationsrombinaryvalues.Equivalenceroupings ave, there-fore,a presumptionf esthesicpertinenceboveall in oneparticularcase.Thisdoesnotmean hat hedifferenceetween crotchetied o asemiquaverndacrotchetiedto atriplet emiquavers imperceptible,but it cannotbe perceived n the same evel. The discernmentf arhythmicrogressiontypesa andb) and hediscernmentf aminimaldifference etween wo valuesarenotincompatible. etailed xperi-mentswould n any casebe requiredo establishhethreshold elowwhich wounitsareconfused ndabovewhich heyaredistinguishedfromoneanother.(c) Thepoeitic ounterparto thealternationension/relaxation,hat s, themethods hosenby Varese o create hisesthesic ffect:playof semi-tones,dissonantntervals,rescendi,heconfigurationf flightson theonehand,andthe permutationsf stagnantonesonthe other.But in the secondperspective,here s acomment yVarese n'Density',

published,without eferenceo its source,by HildaJolivet, ivenhere n itsentirety:Despitethe monodiccharacter f 'Density 21.5', the rigidityof its struc-ture is definedovertlyby the harmonic chemecarefullydescribed n the


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unfoldingof the melody. 'Density21.5' is basedon two short melodicideas, the first, modal andin binaryrhythm,which beginsandends thepiece, and the second, atonal and in ternaryrhythm, which lendselasticity o the shortdevelopmentseparatingeiterations f the first dea(Jolivet 1973: 110).I shalluse this externalpoieticdocumentn a preciseperspective:ftermakirlgnappraisal,tscontentswillbeapplied o theconfigurationsf theneutral nalysisn order o reorganiset. Theobjectives obviouslyo com-pare hetwopictures f thework husobtained ndto define hestatusofneutral nalysisn relationo thiskindof poieticanalysis.2. Melodic oietics

We begin by examininghe secondpart of this text whichdealswithmelodicdeas.Thequalificationsmodal' nd atonal' illbesetaside ince, fthe twoideascorresponds I believe o [1]and [2], it is notclear hatthesecond houldbe moreatonalhan hefirst,or thefirstmoremodalhan hesecond.Onecouldobserve oundphilologicalrinciplesnd turnto othertextsbyVarese,n anattempto shed ighton themeaningf thesewords.ButVaresewasno theoretician,ndnothingn hiswritings1983)helpsus tounderstand hathemeans,here,by'modal'.Withregardo'atonality',hesetwoquotationsan be set offagainstachother:[Incontemporarymusic],whetherwe deny its presenceor not, we senseatonality.There s no need to havea tonic, with its thirdand fifth, in orderto establisha tonality 1934).My language s naturallyatonal,althoughcertainthemes, certainnotesrepeated n the manner of tonics, constituteaxes aroundwhich soundmassesappear o agglomerate. n this way, musicaldevelopment rows,little by little, throughthe repetitionof certainelementswhich are pre-sentedn ach time, in a differentaspect,andinterest ncreaseshrough heoppositionof planesand the movementof perspectives. f themes reap-pear,they have a different unction n a new medium:dynamics 1930).All of this asttextcouldbe applied o 'Density 1.5',but t doesnothelptopinpointhemeaning f 'atonal' s opposedo 'modal': nthebasisof thesetwoquotationshepiececouldbe qualifiedtonal'ustasmuchas 'atonal'.Thebinary/ternaryppositionsmoreelling. have hereforelayed longandconstructedparadigmaticablewhere xesofequivalenceredefined ytherhythmicharacterf units, binary rternaryEx. 38below).The firstaxis hereforeontains1] and tstransformations.otice hat 5] hashad obeplacedn the second xisbecausetsrhythms ternary.71]and[72]have

beenplaced n the firstaxisbecause f theiranalogousistributionalositionandparadigmaticinkwith 1]throughhe ntermediary38].Thesecond xiscontains ll theunitswithatleastone'irregular'alue.Thereforethirdaxismust be opened,one not mentioned y Varese,whichgroups ogether llunits hatareneitherareturno thefirst dea',nor nternaryhythm,hat s,MUSICANALYSIS1: 3, 1982 303

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those hat ollowa ternarynitandprecedehereturn f anotherernarynitorof the first idea'.Whatmaybe concludedromthis example?First, it mustinciteus toapproach oietic nformation itha measure f caution:his informationdefines fieldof equivalence hich s notsystematicallyrecise.31We havealreadyad odiscardhedesignationsatonal'nd modal'.Vareseays hatthefirstdeaendshepiece:nfact, t lastappearsn strict epetitiontb.42ofa sixty-one arwork.Moreover, e talksof 'shortdevelopments'etweenreiterationsf twomelodicdeas,butthesecond aradigmsby far hefullest(forty-fivenitsasopposedotwelveor he irst). fthehypothesissadoptedthat hefirstbasicmelodicdeacorrespondsott

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