Composition and Context in Twelve-note Music of Anton Webern

Composition and Context in Twelve-Note Music of Anton Webern Author(s): Christopher F. Hasty Source: Music Analysis, Vol. 7, No. 3 (Oct., 1988), pp. 281-312 Published by: Blackwell Publishing Stable URL: http://www.jstor.org/stable/854084 Accessed: 25/11/2009 07:52 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=black. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected].

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CHRISTOPHERF. HASTY

AND CONTEXTIN TWELVE-NOTE COMPOSITION MUSICOF ANTONWEBERN

it would compositions, twelve-note ananalysisofanyofWebern's Inattempting seem appropriateto proceedby identifyingthe variousrow forms and that arisefrom their combination.The vast consideringthe relationships majorityof publishedanalyseshave employedthis strategy,and with Theseriesis strictlyfollowed,andthedisplayof row justification. considerable Webern,in formsoftenresultsin strikingtemporalandregistralsymmetries. importance of hismusic,clearlyattachesfundamental writingon thestructure thatrelateserialforms,andthecanonicprocedures to theseries,theoperations of rowforms.1On purelymethodological frequentlyusedin the deployment advantageto be gainedfrombasingan grounds,thereis also considerable for we can therebyaccount analysisof this music on serialorganization, Withoutanappealtothe foreverypitchclassof thecomposition. systematically serieswe wouldbe confronted,as we arein Webern'spre-serial,'free'atonal pitches music,with the morecomplexand less securetaskof interpreting detail. upona wealthof compositional to contextsthatarecontingent according wearefreed basisofmusicalstructure, therowastheautonomous Byregarding of contextual andthevagaries to a largeextentfromproblemsof segmentation which maybeseenasanover-simplification analysis.Andyetthissimplification of autonomy analyticmethodandthestructural callsintoquestionconventional therow. analyticmethodhavebeen of prevailing Althoughmanycrucialassumptions acceptedwithoutcriticismby theoristsconcernedwith the expansionand themore fortheanalysisofpitchrelations, procedures of systematic refinement generalquestionconcerningthe functionof the row and the relationof This haslongbeena subjectof controversy. andpre-composition composition of questionmaybestatedasfollows:Inwhatsenseis theroworthearrangement rowformsemployedin the compositionto be understoodas a basisfor the In orderto definetheproblemmoresharply,it maybe usefulto composition? mightbe Intheweakestsense,acomposition proposea rangeofinterpretations. toprovideanuninterpreted saidto bebasedontherowweretherowunderstood thatarenot according tocriteria bythecomposer fundofpitchclassesfashioned MUSIC ANALYSIS

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CHRISTOPHER F. HASTY

determined byserialprocedures, thuscreatinga musicalstructure whichis not contingent uponthepurported structural properties of therow.Inthestrongest sense,a composition mightbe saidto bebasedontherowif it weremaintained that the choiceand presentation of row formsfully determinethe musical structureas a whole.Now, it couldbe imaginedthatparticular compositions mightcorrespond to eitherof theseextremes,makingit impossible to drawany generalconclusionregardingthe functionof the row. However,it seems implausible thateitherof theseextremesituations couldconceivably obtain.A systematicdetermination of the sequenceof pitch classes,even if freely interpreted,can hardlyleave the musicalstructureof the composition untouched.On the otherhand, such a determination is open to limitless interpretations andmayonlyin a veryabstractand(asI shalllaterattemptto show)limitedsensebe saidto determine thestructure of themusicalwhole. Theassumption thatserialprocedures stronglydetermine musicalstructure is, I believe,implicitin mostanalyses of twelve-note compositions, particularly in analysesof Webern's music.Foranexplicitcontradiction of thisassumption we mayturnto an articlepublishedthirtyyearsagoin whichPeterStadlen (1958a),reflecting onWebern's Piano Vartations, presented a detailedcriticism of twelve-notemethod.Takinga positioncloselycorresponding to the weak senseof serialorganization sketchedabove,Stadlenargued(toquotea second articlewhichhe wroteshortlyafterwards to clarifyhis position)that 'serial manipulation - insofaras it is non-thematic - is meaningless andirrelevant. Sincetheeffectofserialactivityexistsmerelyinthecomposer's imagination, his compositionalfreedom is de facto restored'(1958b: 68). 'Far from overdetermining composition - the chargeusuallylevelledagainstthetwelvenotesystem-itdetermines it solittleastobecompletely irrelevant' (1958a:25). Stadlennevertheless grantsthat'alldodecaphonic worksareboundto containa numberofdecisionswhichthecomposer hastakennotonaestheticbutonserial grounds'(:27).Hethensuggeststhat'acertainindeterminacy ofpitchin atonal thinking'allowstheworka degreeof immunity'againstthe measureof serial irrelevancy it does,afterall,contain'(:27). Stadlen'sessayelicitedfromWalterPiston(1958),RobertoGerhard (1958) and RogerSessions(1958)a predictablyvehementdefenceof twelve-note technique.It shouldbenotedthatnoneofthesecomposers arguedfora 'strong' senseof serialdeterminacy. Sessions'positionis representative of theiropinion onthismatter: Once the initial choice has been made, the series will determinethe composer'svocabulary;but once the vocabularyhas been so determined, the largerquestionsof tonalorganizationremain.My own strongfeelingis that,whilethesequestionsmustcertainlybe answeredin termsnot aliento the natureof the series,it is not serialismas such thatcan everbe madeto accountfor them. I do not meanat all thatI am opposedin principleto the ideaof basingthestructureentirelyon the seriesitself,asWebernandothers havetriedto do. WhatI am sayingis that even in structuresso based,the 282

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COMPOSITION AND CONTEXT IN WEBERN'S TWELVE-NOTE MUSIC

acousticaleffect seems to me to derive in the last analysisnot from the of the seriesassuch,butfromtherelationshipsbetweennotes, manipulation as the composerhasby thesemeansset themup (:63).

of this to reviewin detailthe arguments Althoughit wouldbe rewarding debate,I shallheresimplypointout, as doesStadlenin his rebuttal,thathis criticsappearunwillingto addressthe centralquestionof the row'sprecise rather,to dismissthequestionasirrelevant preferring, significance, structural andSessions andlistener.ForGerhard ofbothcomposer to theproperconcerns is exclusivelythebusinessof thecomposer,whois in no way serialprocedure of thetheorist: boundby thenarrowperspective To me, as a composer,the questionof 'serialsignificance'is meaningless. Serialtechniqueis a composer'stechnique.It appearsthatcomposers,from Schoenbergto Stravinsky,havefoundserialtechniquepositivelyusefulin the processby whicha pieceof musicis made.If youarenota composeryour enquiryinto the 'significance'or 'audibilityof serialmanipulation'- from arise- is morethanpointless.... In the whichso manypseudo-problems artist'swork,reasonandpoeticimaginationmayby chancehavebeenmade to fuse, at some high temperature;why should you wish to undo the compound?(Gerhard1958:51)

Thereis an assumptionrunningthroughall theseessaysthattheoryand technique.The be limitedto theplaneof twelve-tone analysiswillnecessarily of blameforthedisparity,feltby allparties, disputecentreson anassignment betweenthe musicalresultand what is takento be the technique.From theoryproduces pointofview,thepositionofthecritic,compositional Stadlen's heis engagedin as 'insofar who, composer, of the the part on self-mystification is' (1958a:26). he thinks what he producing not is the series, manipulating Takinga morepositiveview of the composer'sknowledgeand intuition, Gerhardand Sessionsinsist that analytictheory,being restrictedto the of techniqueand the datumof the series,can neverhopeto rationalization approachthe creativefreedomof the composer.It is not permittedto music makes actually ofwhatthecomposer theorythatit mayaspiretoadetermination of theseries: [Stadlen]is reducedto weighingsuch 'evidence'as he hasbeenableto gain from analysisof twelve-notemusic againstthe 'letter'of the rules, as he readsand understandsthem. In otherwords,his approachis boundto be one-sidedlytheoreticaland speculative.I should like to assurehim that betweentheoryandpracticethereis hereanintervalwhichmereanalyzingevenif it werebetterinformedandmoreaccuratethanhis - cannotpossibly hopeto bridge.Analyticalmindandcreativeimaginationevidentlyworkon differentwavelengths.The vital informationaboutthe potentialitiesof the serial technique is not availableexcept on the wave-lengthof creative MUSIC ANALYSIS

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CHRISTOPHER F. HASTY

experience.(Gerhard1958:54) Musicaltheory,whichis by natureabstract,andmusic,by natureconcrete, areincommensurable, and neithercan be validated,or the reverse,by the other.(Sessions1958:58)

Attemptingto drawsomeconclusionfromwhatseemeda ratherfruitless exchange,GeorgePerle(1959)raisedanissuecrucialto suchcontroversies inan essayappropriately entitled'TheoryandPracticeinTwelve-Tone Music'.Perle perceived thattheopportunity foraproductive debatehadbeenmissedbecause of a failureto groundthe disputein a closeandunbiasedanalysisof musical works.He concludedthatthequestionof 'therelationbetweenthesetandthe effective(audible)featuresof the music"based"uponit' is a questionthat cannotsimplybedismissed,andthatanadequate answermustproceedfroman analysisof themusicmoresophisticated thanthecustomary tracingof rows: If thereis a meaningfulconnexionbetweenthe assumedserialbasisof the workandthe apparentlynon-serialelementsthatonedoes 'detectandfollow in audition,'then this impliesthe existenceof certainassumptionsthatare not statedamongthe givenpostulatesof set-structure.In this . . . caseit is the responsibilityof the analyst to attempt to describe these unstated assumptionsand theirrelationto the given postulates.Anythingless than this is an irrelevantactivityon his own part(:60).

In the threedecadesthat separateus fromthe Stadlendebate,analytic techniqueshavecertainlybecomemoresophisticated, butlittlelighthasbeen shedontheproblematic relationoftheseriestothecomposition 'based'uponit. Indeed,amongtheoriststheproblemhasbeenlargelyignored.Sinceanalytic methodhasfollowedcompositional theoryin concentrating attentionon the structural properties of sets,it is notsurprising thatanalystshavefoundtwelvenote theorysufficientfor the descriptionof musicalstructure.2And yet numerousstatements fromcomposers of twelve-note music,likethosequoted above,pointto a realmof musicalcreationthatcannotbe rationalized by the abstractions of currenttwelve-note theory.Certainly analysiscanneverexhaust theimrneasurable richnessofitsobject.Butevenif 'analytic mind'and'creative imagination' occupyseparateplanes,our attemptsat mediationdemandan opennessto musicalfeatures'thatonedoes"detectandfollowin audition"'whetheror not thesefeaturesconformto ourpresentunderstanding of serial procedures.In the hopeof facilitatingsucha mediation,I shallpresentan approach to Webern's musicthatavoidsthea przort of structural determination bytheseries.I seekananalyticmethodthatbeginsfroma positionof neutrality regardingthe structuralfunctionof the series,a pointoutsidetwelve-note theorythatcouldallowus to testassumptions of conventional analysisandto discoverthe extentto whichWebern'spre-compositional orderingof pitch classesdetermines musicalstructure. Thisundertaking willnecessarily involve 284

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COMPOSITION AND CONTEXT IN WEBERN'S TWELVE-NOTE MUSIC

of pitchrelationsaffordedby twelve-note a reassessment of theinterpretation theory. therelationof pitchesorpitchclassesis detached Underserialinterpretation orabstracted fromotherdomainssuchasduration,accent,pulse,contourand timbre.Thisabstraction leadsustoaskhowtheseotherfeaturesofthemusicare organizedandhow they mightbe relatedto the pitch-classstructure.If an analysisof rowformshasrevealedthe pitchstructureof the work,we might Suchan eachindividually. thenturnourattentionto otherdomains,analysing in manyrespectsto the positiontakenmany analyticapproachcorresponds Thedifficultywiththisapproach yearsagobyproponents of totalserialisation. a changein one independent; is that musicaldomainsare not structurally domainwill not leavethe structureof the othersuntouched.If the various related,howcanwe go about featuresof themusicalobjectareso inextricably pointfromwhichwecanorder analysing thewhole?Is theresomeArchimedian In conventional analytictheory,pitchorpitch thewholeof musicalstructure? relationsperse classhasservedas thisprivilegeddomain.Andyet pitch-class Meticulously offerus little insightinto the totalityof musicalorganization. canrarelybe crafteddetailsof duration,accent,contourandinstrumentation andwhentheyaretreatedbyanalysts,they rationalized by theserialstructure, aregenerallyrelegatedto the 'musicalsurface'- a surfacecuriouslydetached In viewof the frequentlackof connectionin fromthe serial'background'.3 of rowformsandthe articulations Webern'smusicbetweenthe deployment of alldomains,sucha surfacewouldseemto function createdbytheinteraction of thework. to concealthetruestructure Arguingfora differentpointofview,I shallpresentwhatI hopemayproveto anydomain tothismusic.Ratherthanregarding beamoreproductive approach asprivileged, wemayinsteadfocusourattentionontheresultof theinteraction or of all domains,thatis, on the moregeneralissueof musicalarticulation therelations of rhythminthebroadest senseof theterm.Fromthisperspective, according tothefunctionstheserelations pitchesordurations canbeinterpreted as perform in thecreationofmusicalgestureandform.Aswillbecomeapparent In of formandstructural functionis problematic. we proceed,thedescription exchangingthe simplicityof serialstructurefor an analysisof contextual structuralformations,we are confrontedwith far greatercomplexityand of Webern's ambiguity.In returnwe mayhopeto gaina betterunderstanding profoundlyricism,a qualitytoooftenignoredin analysis. the I wishtomakeit clearfromtheoutsetthatthequestionsI raiseconcerning usefulness oftwelve-note theoryfortheanalysisofmusichavenobearingonthe theory.A centralthesisof this valueof twelve-notetheoryas compositional hasbeenhindered of thetwelve-note literature essayis thatourunderstanding and analytictheory.I shalladdressthese by a confusionof compositional of portionsof twoworks:theopening questionsthrougha detailedexamination phraseoftheQuartet, Op.22(1930),andthefirstsectionoftheOp.30Varzations for Orchestra (1940).The Quartetwill providethe basisfor a discussionof generalmethodological issues. With Op.30, I shall proposea larger-scale MUSIC ANALYSIS

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theresultsof thatdiscussion. analysis,incorporating of tworowforms.Inthe Theopeningof Op.22,shownasEx. 1, is composed example,uncirclednumeralsindicatethe pitchesof the row labelledP1; inversion indicatethepitchesof Ill. Ill is a preciseregistral encirclednumerals Eachpairofinversionally trichordally. ofP1,andbothrowformsaresegmented differences, yet,becauseofrhythmic inimitation; is presented relatedtrichords foreachrowformthe thetworowformsdonotformacanon.Figure1tabulates of qualities:upperversuslowervoiceandduxversuscomes. Within opposition Ex. 1 pJ'+_Itte

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of thesequalitative eachrowform,trichordsexhaustthe fourcombinations distsciions. This patterngreatlyobscuresthe two rowformsas percepiible If we wishto identifytwovoicesin thispassage,Ex. 2 presentsa constituents. Upperandlowervoicesmix trichordsfrom morecompellingsegmentation. bothrowformsandtogethersuggesta bipartitedivisionof the phrase.The groupingsanda pointof divisionis markedby a repetitionof instrumental a differentsetclass, ofduxandcomes. Eachof thefourunitsconstitutes reversal set foundas a onlyone of which(setclass5-1)is equivalentto an unordered linearsegmentof the row.4Since these four units are the most obvious moreclearlyaudiblethanthetwolinesthat ofthephrase- certainly consiituents arebrokenby the variablerhythmandchangesof timbre- I shallbeginby the rhythmicfactorsthatconnector segregatetheseunits.The considering thesimplebipariitedivisionandmakethe shownin Ex. 3 contradict groupings of Ex. 2 mightsuggest.As passagemorefluidthantheratherstaticsymmetry this a crotchetpulse.Unit2 annihilates Ex.3 indicates,thefirstunitestablishes a quaverpulse, strongbeatandestablishing pulse:beginliingon a perceptually of unit1, thepitchEb. No afterthelastconstituent it entersfivesemiquavers 286

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COMPOSITION AND CONTEXT IN WEBERN'S TWELVE-NOTE MUSIC

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MUSIC ANALYSIS

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COMPOSITION AND CONTEXT IN WEBERN'S TWELVE-NOTE MUSIC

regardedas primarystructural unitsof the composition, aninvestigation into theirconstitutionand theirrelationto one anothercommendsitself as an obviousanalyticapproach. Beforeembarking onsuchananalysis,I shallreturn to the pre-compositional realm,whichsuppliesthe constituentelementsof phrases. IntrueBauhaus spirit,Weberndevisesalimitednumberofmodulesbasedon a few elementary distinctions.The row shownin Ex. 10 containsonly two intervalclassesformedby adjacentpitchclasses:intervalclasses1 and3. The tetrachordal segmentation oftherowyieldstwosetclasses:twoformsof setclass 4-3,relatedasorderedcollections bytheoperation of retrograde inversion; and one formof 4-17,a retrograde inversionof itself.Excludingretrogrades, two rowformsareemployed producing sixdistincttetrachordal collections, labelled A, B, C, D, E andF in Ex. 10.AlthoughI believethereis reasontoquestionthe Ex. 10 4-3

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autonomy of rowformson perceptual grounds,thesesixtetrachords canoften be heardasrelatively clearconstituents of thecomposition. Detachedfromthe row,theycanbe regarded asbeinggenerated by a seriesof binaryoppositions, shownin Fig. 2. Similarly, binarismpervadestheconstruction of tetrachordal modulesin the domainsof rhythmandcontour.Two alternating tempiare employed: ;>)= 160and;>)= 112.Therearetwobasic,asymmetrical patternsof relativeduration: long-long-short-long andlong-short-long-long. Twogeneral metricalpatternsaredistinguished: a syncopated figureanda dottedfigure, associated withset classes4-3 and4-17respectively (seeEx. 8, tetrachords A1 andB1).The vocabulary of contoursis givenin Fig. 3. Fromthe elementary distinction down-upandup-down,Webernconstructs fourcontourpatterns.8 It is interestingto notethatin orderto differentiate the fourrelatedcontour forms- prime,retrograde, inverseandretrograde inverse- Webernemploys the minimumnumberof pitchesand the minimumnumberof changesin direction: fourpitchesandonechangeof direction.Throughthecombination MUSIC ANALYSIS

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Fig. 2 2 successiveintervals: intervalclasses 1 and 3

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andon withinthetetrachord Thisarrangement hasan effecton segmentation set class4-3 Weretetrachordal segmentalassociations betweentetrachords. displayed in theformof Ex. 1lb, theseunitswouldbreakupintotwodyads.As alsohelpsto obscurethe Exs. 1lc and1ld illustrate,the registralasymmetry A and D (andlikewisebetween pitch-classinvariantsbetweentetrachords withinthe thematic tetrachords C andF). Webernalsopreventsarticulation tetrachords by employingregistralinterval11ratherthan13. Theinterval13 expandedmotionby semitone,creatingthe aural canfunctionas a registrally Thiseffectcanbeclearlyheardin impression of a stepwiselineardisplacement. Ex. 11e,whereDb is displacedby C. By minimisinginternalsegmentation, and the two Webernstrengthensthe relativeautonomyof the tetrachords tetrachordal set classes.From these few examplesit shouldbe clearthat of pitchclasses.Like Webern's constructivism extendsfarbeyondtheordering butratherfunction thechoiceof rows,suchdecisionsdonotgeneratestructure possibilities. Whatis madeofthesepossibilities to narrowthefseldof structural is thequestionI shallnextaddress. Phrase1 is givenin Ex. 12.TheencircledlettersA-Flabelthesixtetrachord mark identifyparticular instances.Asterisks collections andnumericsubscripts ordering ofthe registral thoseinstancesthatdonotconformto thepredominant appearin phrase1, whereI have tetrachords 4-3 and4-17.All six tetrachords in the phrase markedfiveconstituentunits.The mostextremediscontinuity as separates thefirsttwounitsandfunctionsinparttoisolatethefirsttetrachord a mottoforthe piece.Unit2 is quitedisruptiveand,as we shallsee, playsa B1 Inunit2, tetrachords generative rolein theformof theentirefirstvariation. and D1 are inextricablybound together.Groupingand rhythmare very I shalldiscussoneof ambiguous hereandadmitmanypossibleinterpretations. MUSIC ANALYSIS

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thesepossibilities.Belowthe repeatedpitchesB andD, one canheara line movingin successivesemiquavers: Bb, EW,GS, C,".The most prominent intervalexposedhereis intervalclass5- BS-ESandGS-CX. Intervalclass5 does notappearamonganyof thepitchesofunits1or3. However,thecontourofthis line- up-up-down - is thecontourof unit3. Thehighpointsof theselines- GS in unit2 andGin unit3- forma strongconnection bysemitone.TheC#ending unit2 mayalsobelinkedto unit3, if wecanheara repetition in thelineC,"-F-E of a registralsegmentation of unit 1, A-Db-C.This possibilityis illustrated beneaththeexample.WhatI wishto showbytheseobservations is thatunit2 is notconnected to unit1butis connected tounit3. Unit1is, ofcourse,similarto unit3:botharerepresentatives ofsetclass4-3,andeachis relatedtotheotherby the operationof retrograde inversion.But, althoughsuch transformational operationscan for somepurposesbe usefulabstractions, they oftenhavea 300

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COMPOSITION AND CONTEXT IN WEBERN'S TWELVE-NOTE MUSIC

matterswhencomplicated bycontour,rhythmand dubiousstatusinperceptual to sayin whatperceptual sensethelowBbof unit1 context.Thusit is diff1cult corresponds to thehighGin unit3. Maywenothear,rather,a correspondence l

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minorthird firstthreeof unit3, F-E-G?Oragain,havingheardtheascending betweenthef1rstandlastpitchesofunit1,A-C,willwethenheartheconnection inversionorasanotherrisingminorthird? in unit3, F-Ab,asa retrograde relationsaside,unit3, althoughobviouslya The complexities of intervallic intensified: it is a fifthhigher,forte rather variation of unit1, is by comparison thanpiano, twiceas fastas unit 1, andplayedby tromboneratherthanthe tothe Thisintensification is afittingresponse comparatively diffusecontrabass. highlyenergeticunit 2. In fact unit 2 seemsto providean impetusfor the development of the phraseby introducinga breach,whichis progressively unit1from healed.Incontrast tothechangesofpulseandthefermatiseparating quaver unit2 andunit2 fromunit3, units3, 4 and5 areunitedbya continuous theline pulse.Unit3 is connectedto unit4 by thewholetoneG-A,continuing ofC1.F1andE1, F1is atransposed retrograde begunonGbinunit2. Tetrachord whilerepresentatives ofdifferentsetclasses,havethesamecontour.Units4 and E2. 5 aremostobviouslyjoinedby therhythmicelisionof E1andits retrograde unitwereit notfor Infact,therewouldbe noreasonto identifyE2asa separate to units 1 and 3. E2mediatesopposing its specialfunctionalrelationships qualitiesA1andC1to closethephrase.Thoughofadifferentsetclass,E2sounds pattern.The verysimilarto C1,havingthesamecontour,registerandduration moststrikingdifferences betweenA1andC1weredynamics(Apiano; Cforte), speed (C moves twice as fast as A) and timbre(tromboneopposedto a contrabass). E2returnsto a dynamicofpiano; it createsa ritardbyintroducing duplegrouping;and,playedby triplegroupingof quaversintothe prevailing and bassclarinet,E2excellentlymediatesthetimbraloppositionof contrabass trombone.Also,E2returnsto themiddleC, sustainedby fermatain A1,andat minorthirdES-Canswerstheascending theendof thephrasethedescending thirdA-Cin unit1. of unit2, Unit4, withwhichE2is elided,is in manyrespectsa simplification this gestureinto the phrase.Unit 4 containstwo functioningto incorporate by registerandhavingthe samecontour imitativecomponents differentiated and rhythmicpattern.Imitationmighthavebeen heardin unit 2 had the componentsnot beenso tangled.The two figuresB1and D1 havethe same rhythmicpattern,delayedby a semiquaver,and are relatedin contourby retrograde inversion. Phrase2, given as Ex. 13, beginswith tetrachordD. This is the first in register). of D (D1in phrase1wasaberrant registrally canonical appearance to A1,whichopenedphrase1 in Exceptforregister,D2is stronglyanalogous contrabass. Althoughthethreeelidedunitsof phrase2 resemblethefirstthree thetotalcontour),thetwophrasesarein unitsof phrase1 in gesture(inverting MUSIC ANALYSIS

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_ **W (E)(4-3)

manyrespectshighlydissimilar. Bycomparison phrase2 is quitechaotic.Pulse is lostandconstituents arenot clearlyarticulated; otherthanD2,tetrachords breakdownthroughfragmentation and elision.The pointof disintegration ironicallytakesplaceat the midpointof pre-compositional symmetry.I shall offera few commentsaboutthis particular disorder.In a newtexture,D2is accompanied byF2,whichis registrally anomalous andsplitbetweentwoquite dissimilar instruments - harpandcontrabass. Likeunit2 inphrase1, D2andF2 stronglyprojectintervalsforeignto the rulingtetrachordsonorities,here intervalclasses5 and6. F3initiatesanewirregularity: notonlyis registerfurther distorted,but a new contouris introduced- up-down-up.This patternis continued intoB2.Becauseof thispattern,therhythmandtherepeated pitches, it is possibleto heara tetrachord beginningon F in the bass:F repeated-FX repeated asGS-ES-D (up-down-up). Thesepitchesformaninstanceof setclass 4-3 but, as it were, an accidentalor false versionof the set, otherwise representedas one of the collectionsA, D, C or F. The functionof this connection is todetachfromtetrachord B2thefinalpitch,B. Webern's phrasing supportsthishearing;noticethe dotoverD andthesforsando markingon B. The newformof 4-3, markedZ belowthe example,is usedonlyoncein this variation. Thesimultaneity E3is alsoananomaly.SincethehighB continues its crescendo pastthischord,itsfailuretopunctuate theendingofthephraseleaves thismusicquiteurgentlyopen.Thereis onetetrachord of thesixmissingfrom thisseciion:tetrachord A. Phrase3, shownin Ex. 14a,beginswithareturnoftetrachord A, nowintuba. Asin phrase2, themottoorthemeis accompanied, in thiscaseby a versionof tetrachord D splitbetweenharpandviola.D3revivesthe newcontourof the 302

MUSIC ANALYSIS

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COMPOSITION AND CONTEXT IN WEBERN'S TWELVE-NOTE MUSIC

Ex. 14

I

i

I_

X

cs u)

I C ._

dZ

I >

.-

51

-

I

X

l

l

I

.

iD il

-N

+

t

m) - @

I

R

1

¢

-

)X; 10

MUSIC ANALYSIS

7:3, 1988

303

.

w

CHRISTOPHER F. HASTY

previousphraseand continuesthe intervallicpatternof tetrachordZ: up one semitone, down three, up eleven. Between the two tetrachordsthere is no instanceof intervalclass6, andthe oneinstanceof intervalclass5 ishidden. The accompanyingD3 now emergesin unit 2 as a prefigurationof the thematic statementD4, which in turn is accompaniedby a verticalizationof A (A3), addingthe remainingbrassto the tuba. Unit 3 revivesa developmentbegunin phrase1, by presentinga cleartwo-voiceimitation.Rhythmandtheinversional of tetrachordsB andE combineto producea greatvariety pitch-classsymmexcry of imitativeconnections.Thus B3and E4can be relatedby transposition,with the firstandlastintervalsinverted,by retrogradeinversion,orby theretrograde of threeconsecutiveintervals.In Fig. 4 thisfigureis comparedto the twoearlier attemptsat imitationin phrase1. Strict(albeitcomplex)imitationis now made possible by the use of the same set class, 4-17. Particularlystrikingare the timbralreferencesto phrase 1. B1 and B3 (oboe), E2 and E4 (bass clarinet) representthe only cases in this variationin which the same tetrachordal collectionis performedby the sameinstrument,a featurefurtherdistinguished by the fact that solo oboe and solo bass clarinetare not used elsewherein this variation.Note also that these four tetrachordsappearin the samerhythm,a set class4-17(afigure'mistakenly'takenup in dottedfigurewhichcharacterizes phrase1 by D1in imitationof B1,andabrogatedby E1in imitationof F1).This rhythmicfeaturemakesit possibleto hearin unit 3 of phrase3 a referenceto the last segmentof the open phrase2 (B2-E3).Sinceunit 2 of phrase3 is alsoquite clearlyrelatedto the lastsegmentof phrase2 (and,in a differentway,to the first segmentof phrase2), to my earthiscommonlineagehelpsto connectunits2 and 3 in phrase3. Fig. 4 Imitative units: Phrase 3

Phrase 1 Unit 4 & 5

Unit 2 4 17 Bl-Oboe 4-3

*Dl-Vla.

4-3

Fl-Vl.

(unit5)

4-1 7 El-Vcl.+E2-B.Cl.

Unit 3 | 4 17 B3-Oboe 4-1 7 E4-B.Cl.

The aboveobservationspointto newcomplexitiesinvolvedin ourattemptsto interpretphrase3. If, as I believeto be the case, phrase3 functionsto closethe first variationas a whole, it does this by reconcilingor synthesizingprevious musical developments. I suggested earlier, in connection with intervallic cancoexistas latentpossibilitiesto be relations,thata varietyof interpretations 304

MUSIC ANALYSIS

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COMPOSITION

AND CONTEXT

IN WEBERN'S

TWELVE-NOTE

MUSIC

realizedas largercontextsunfold.Thishypothesisof structural formation,or therelationof partto whole,canbebroadened to covercomplexeventssuchas phraseconstituent (unit),phraseorphrasegroup.Chronologically latereventsif theyareto coherewithearliereventsandthusavoidtheappearance of 'one damnedthing afteranother'- will carryan increasingly heavycontextual burden.Thereseemto be limitson howmuchmusiccanbe successfully held together,and I believethat the sevenvariationsof Op.30, althoughoften elegantlyelided,represent suchlimits.I shallnowconsidersomeof thewaysin whichphrase3 interprets,and is interpreted by, phrases1 and 2, firstby indicating individual correspondences andthenbyspeculating onthesynthesis of thesectionasa whole. Thefirsttwounitsof phrase3, thoughpresenting differentsets,canbeheard as a compressionand simplification of phrase2 (units 1 and 3), omitting references to thedisruptive middlesegment.Similarities betweenthesepairsof unitscaneasilybe ascertained by the reader.(Differences willbe considered later,in connection withotherstructures.) Althoughthereturnto tetrachord A atthebeginningof phrase3 is anobviousinvocation of phrase1, units2, 3 and 4 of phrase3 alsorevivephrase1 throughtheirsimilarity to thefirstthreeunits of thatphrase.Theconnection of phrase3, unit3 andphrase1, unit2 hasbeen discussedabove (and indicatedschematically in Fig. 4). The remaining correspondences are very strong:in virtuallyall respects- allowingthe inversionof durationpatternanddynamics- in phrase1, A1(unit1) is to C1 (unit3) what,in phrase3, D4(unit2) is to F4(unit4). Likeunits1 and3 of phrase1, thecorresponding units2 and4 of phrase3 presentsetsof the same class(set class6-1), displayedin the sameregistralordering,and similarly excludethe intervalof the tritone.Note, however,thattimbraloppositionin phrase1 (contrabasses piano,trombone forte)is nota featureofphrase3, which combinesstringsandbrass(tuttiviolinsandbrassforte,soloviolinandmuted brasspiano).The differences herearealsosignificant.Unit3 in phrase3 is a clarification of thecorresponding unitin phrase1 andis nowincorporated into thethree-unit group,in partby register.As opposedto phrase1, D4andF4in phrase3 appearin thehighestregister- theregisterof phrase2 (D2andB2).D4 andF4arealsodistinguished fromtheircounterparts in phrase1(A1andC1)by the accompaniment of lower punctuatingchords (A3 and C3), again a development initiatedin phrase2. Thethree-unit groupthatopensphrase1 emergesasa centralgestureof the variation.9 Theschema- monophonic statement piano,disruptive polyphonic outburstforte, intensifiedmonophonicstatementforte- can be heard(with registersinverted)in the threeelidedunitsof phrase2. Althoughphrase2 repeatsthisgesture,phrase2 doesnothingtoclarifyorcontinuethestructure of phrase1. The juxtaposition of phrase2 to the relativelyclosedphrase1 is a rupturein theform.Phrase3 in manywayshealsthisruptureandat thesame timejoinsthethreeunitsintoa continuous line,invertingtheinitialgestureof opening (crescendo,accelerando)into a gesture of repose (diminuendo, ritardando). (Thislasteffectmayaccountfortheanomalous dynamic levelofD4, MUSIC ANALYSIS

7:3, 1988

305

s

'

w

'

(D)(A)

l

l

Vl.solo

>

+

CHRISTOPHER F. HASTY

shownin Ex. 15below.)Attheriskof pressingtheanalogybeyondtherealmof the audiblyverifiable,I suggestthat the threephrasesreenactthis initial phrase3 wouldnotonlyrepeatthegesture gesture.Underthisinterpretation, revealthe whole. This conclusionmay be mademore but simultaneously sets. of 'themaiic' plausibleby a consideration set classes4-3 and 4-17 appearto have somewhat The two tetrachordal by B andE, seems differentfunctions(seenote9). Setclass4-17,represented (Thisis, of of a two-voicecounterpoint. untangling involvedin a progressive sinceE2alsofunctionsto close course,somethingof an oversimplification, phrase1, andB2togetherwithE3funciionsto openphrase2 andto provokea of Ofthefourrepresentaiives reaciionwhichwillleadto thesecondvariation.) A andD, whichareplaced is giventotetrachords setclass4-3,clearprominence in oppositionin phrases1 and2 andunitedin phrase3. A summaryof this B andD, tetrachords is givenin Fig.5. Inphrase1,unit2, comprising structure too,thatD hereis theonlyregistrally (Remember, evenanarchic. is disruptive, in the phrase.)The phrasecloses,but withoutfully anomaloustetrachord thisfigure;thatis, elementsof closureinvolveunits1, 3, 4 and5. absorbing of unit2 of phrase1. It is highly Phrase2 maybe construedas an outgrowth of D, andit is abandoned exceptfortheiniiialthemaiicstatement disorganized by way of a somewhatambiguousstatementof B. Phrase3 organizesthe disparateelementsof phrase2 andunitesthemaiicstatementsof A and D. ofA andD. Intllehighlyrestricted thesefourstatements Example15compares A andD in phrases1 and2 are,except worldWebernhascreated,tetrachords for dynamics,maximallydissimilar.Withphrase3, the totalconfiguration marks Noiicethattheonlyexpression similarity. bringsA andD intomaximum aregivento D in phrase2 andA in phrase3. to appearin thisvariation Fig. S Var.I

Var.II

r---

Phrase 3 Phrase 1 Phrase 2 Ob.Vla. V1. W.W. A +D B A [B-D] D

t |

l

(F)

|

Cb.

306

Vl.solo

Tb.

VI.tutti|

C

A

D

Vl.solo Vl.II(consord.) B C

MUSIC ANALYSIS

7:3, 1988

j

P

pP

11).

solo

P

i,:;

''

;

WP

,!jf

e

COMPOSITION AND CONTEXT IN WEBERN'S TWELVE-NOTE MUSIC

Ex. 15 -Contour,-Tempo,-Interval

Succession, + Dynamic, -Duratifn

-Pitch,

Pattern.

Phrase 3

Phrase 2

Phrase 1

I })= 112

J8= 112

J8= 160

t

I.es5op°#r.

g

2)= 160

e

@ sehr zart

^

tr

#

8

,i,

w Cb.tutti

Vl.tutti

r

t

^

hr

+ Contour, + Tempo, + Interval Succession, + Dynamic, + Texture (accompanied)

+ Contour, + Tempo, + Interval Succession, - Dynamic* A'-A2:+ Pitch, + Duration Pattern (LLSL) D2 _ D3:+ Pitch, + Duration Pattern (LSLL) *D4of Phrase 3 and B2of Phrase 2: + Contour + Duration of Pattern + Dynamic + Texture

effectedby phrase3, theimmediate consolidation In spiteof theremarkable weakerthanthatproduced senseofclosureattheendofphrase3 is considerably bythelastunitofphrase1. Example14aindicatestheelisionofthetwosections throughunit 4. The ascendingpatternof minorthirdsshownbeneaththe and to thesenseof continuity in unit3, seemsto contribute example,beginning this see that we Ex. 14b, thus to participatein the elision. Consulting deviceis closelyrelatedto oneof themeansby whichclosurewas transitional in achieved phrase1. (In contrastto phrase1 of Op.22,the registralaxisof symmetry,herethe pitchEb, is obscuredas a focalpitch.)As wasintimated earlier. wasinitiatedconsiderably intothesecondvariation above,thetransition Webernhasgradually transformation, andmasterful In anentirelyunexpected at the end of phrase2, a failed simultaneity turnedthe ratherunpromising figurefor the secondvariation.The punctuation,into the accompaniment we have articulations connectionof thesethreeunitsmatchesthe structural labelled5-3inEx. above.Itneedbenotedhereonlythatthesonorities observed and similarin sound,bothintervallically 14a,belowunits2 and4, arestrikingly andthushelpto directus intothenewsection. timbrally, MUSIC ANALYSIS

7:3, 1988

307

f

Pc¢

-

P

CHRISTOPHER F. HASTY

idea.In structural presentsa uniqueandhighlyimaginative Eachvariation the secondvariation,whereeach pitch of a tetrachordformsa different setclasscanreplacecontourandregister withtheaccompaniment, pentachord transposed as an orderingdevice.In this secondvariation,the continuously would rowsegmentsis notstatic,astheserialstructure patternof overlapping inaclimaxinphrase6. culminating intensified, suggest,butbecomesgradually to thecompletion of a phrasecorrespond Again,nowheredoesthearticulation doesnotcontinuethestructural of a rowform.Althoughthe secondvariation in thefirstsection,it doesdevelopandclarifythe wehaveexamined formations - themiddleof phrase2 in thefirstvariation thatwasleastassimilated material linearpattern(bs27ofanewcomposite (Ex.13).InEx. 16,thefirstoccurrence phrase2 of thefirst to compared of A andD) is 31, followingthe restatement twoRIvariation second the in variation.As in phrase2 of thefirstvariation, The 6-Z13. class set form to overlapped relatedformsof set class4-3 are variation first the in 2 phrase by introduced contour(up-down-up) anomalous featureof the secondvariation.It is interestingto becomesa characteristic of the row are observehow in the secondvariationthe threetetrachords in the embedded is structure this Although hexachord. collapsedintoa single by constituted is 13 6-Z of instances these of none 10), Ex. (see centralhexachord row. the of a form of 4-9 ordernumbers Ex. 16 RI

Rl

/\

4-3

4-3

l

l

s (g,f

S

4-17

6 1

6-Z13

l Plo: 9

4-3

10

12 2

11 P7: 1

G

l

C9#uU 6-Z13

1

3 Rs,:4

2

4 5

fi 7

Var.1, phrase2

I

t

e f |-

-

l

D

-

4

Var.2, phrase 2 (bs 27-31 )

4-3

X°

Is: I 3

/\-

;

I

Z

FS

I

I

_e

1- rSl:j lt

t#t(7)

4

djfc

(see also phrases 4, 6 and 8)

308

N

} Ct,'N MUSIC ANALYSIS

7:3, 1988

COMPOSITION AND CONTEXT IN WEBERN'S TWELVE-NOTE MUSIC

Theaboveanalysisreturnsus- withgreaterinsight,I hope- to questionsof periodI have the formationof the three-phrase Certainly serialdeterminacy. similarto thatascribedto the a taskof unification outlinedaboveaccomplishes retrogradesymmetryof SystemI (Ex. 8), even thoughthe meansdiffer ofthelastthreeunitsofphrase3 tothefirstthree radically. Thecorrespondence oftherowformsRIs(phrase in thecorrespondence unitsof phrase1is mirrored 3) andPs(phrase1),althoughmanyof thefeatureswenotedabovecanbe seen in On the otherhand,the coincidence relationship. to subvertthe retrograde relatedrow forms,P1o(perhapsa more phrase3 of two transpositionally germanelabelhere than RIs)and Ps, is crucialto manyof the contextual structurespresentedby our analysis.Also conformingto that analysisand inversionalsymmetryof SystemI are the two the retrograde contradicting (D4, (C2,B2,A2)andIs (F1,E2,D2)-RIg Ps (A1,B1,C1)-R9 pitchretrogrades, mighthavebeenmademorepalpablehadthe E4,F4).The pitchretrogrades duration patternsalsobeenreversed,ashappens,forexample,intheretrograde These row by E2 (long-short-long-long). of E1 (long-long-short-long) althoughcuttingacrossphraseboundaries,nevertheless correspondences, A1andA2withD2andD4, andin several associatethe thematictetrachords analysis.Onemayarguethata otherwaysconformto resultsof ourcontextual precedes,andthusformsthebasisof, later of therowstructure determination of To arguein this way,however,is to confusethe chronology refinements. withthecreationof themusicalwhole,for,asI havetriedto show composition above, the row structureitself becomes determinedonly throughthe contained in theseries.Thisdialectic of a fewof thepossibilities composing-out (1958):If, 'in leadsusto askagainwithGerhard anddetermining of determined may. . . havebeenmadeto fuse theartist'swork,reasonandpoeticimagination whyshould[we]wishto undothecompound?' at somehightemperature, I have concentratedon the contextualat the expense of the 'prein in partbecauseI wantto redresswhatI viewasanimbalance compositional' relations music,andinpartbecauseI regardcontextual theanalysisofWebern's such as thosetracedaboveas a fusionof planand execution,blurringthe In conclusion,I suggestthatan distinctionof 'reasonandpoeticimagination'. fromcontextoffersuslittleinsightintothe ofrowformsabstracted examination formof Webern'smusicand obscuresmanyof the analyticand aesthetic bothinplanand resources, questionsposedbythismusic.Webern'sstructural in execution,extendfarbeyondthe orderingof pitchclassesto encompassa varietyof mutuallyconditionedmusicaldomains.We may concurwith ... Sessions'sjudgment(1958)that'thelargerquestionof tonalorganization must certainlybe answeredin termsnot aliento the natureof the series', providedwe alsograntthatit is thenatureof the seriesto be opento limitless Fromthis perspective,the dispositionof rowformsisolated interpretation. fromthe totalityof musicaldomainsmaybe seenas a largelyundetermined and,as such,canbe reifiedonlyat thecostof possibilities matrixof structural music. of twelve-note severelylimitingourunderstanding

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CHRISTOPHER F. HASTY

NOTES 1. For a detailedandhighlyilluminatingexaminationof Webern'sunderstandingof the natureof the row, see BarbaraZuber(1984).In this essayZuberundertakesa close analysisof Webern'swritingsin the contextof his readingof Goetheand Plato. 2. Thereare,of course,somenotableexceptions.Adornofrequentlycriticisedin very generalterms the tendencyto reify twelve-notetechnique.Among analystsof Webern'smusicJonathanKramerand ArnoldWhittallhavecalledinto question the structuralhegemonyof the series by drawingattentionto the disparityin Webern'scanonicwritingbetweenthe intervallicstructureof the rowandthatof the resultingsimultaneities(Kramer1971;Whittall1987). 3. WhileWebern'smusicis rarelytreatedwith such sophistication,therearemany recentanalyticstudiesof Schoenberg'stwelve-notemusicthattakeinto accounta varietyof complexserialprocedures,coordinatingthesewith domainsotherthan pitch (see, for example,Peles 1983-4and Samet1985). However,I submitthat these studies too are limited by the technology of compositional(or precompositional)theoryin thatnon-pitchcriteriafor segmentationareinvokedonly to the extentthey can be used to confirmthe purportedserialprocedures.These samecriteriaused withoutprejudicewouldreveala host of non-prescribedpitch relations.Suchselectivityexcludesmanyimmediatelyaudiblestructuresandoften of dubiousperceptualstatus. resultsin interpretations 4. Set-classnumbersfollowthe classificationfoundin AllenForte(1973),pp.l79-81 (Appendix1). areindicatedby BrianFennelly(1966)in his analysis 5. Manyofthese contradictions of thismovement.Fennellywritesthat'incomparisonto [movement]I, anelegant, carefullywroughtprecisionorganism,[movement]II is unrestrained.Insteadof preservingthe cleanformaldivisionsandanalogiesofthe substructure[i.e. series], thereis intentionalblurringof the substructuralorganizationin the realizationof the superstructure'(:315). While Fennellyshows a sensitivityto contextrarely found among commentatorson Webern's twelve-note music, I believe he in the first overestimatesthe congruenceof 'substructure'and 'superstructure' movement.For example,in the secondsectionof movementI (bs 6-15), Fennelly identifies two phrases on the basis of row completion.However, an analysis undertakenalongthe linesI haveproposedabovewill revealthreephrasesformed by theinteractionof alldomains.LestI riskoverstatingmyposition,I shouldpoint out thatthereareinstances,althoughtheyarerelativelyrarein Webern'smusic,in whichfeaturesof rowstructurecontributemoresignificantlyto musicalform.See, for example,JohnRahn'ssensitiveanalysisof the theme(bs 1-11)of the second movement of the Symphony, Op.21 (1980:4-17). Rahn discusses (:11-12) problemsinvolved in an attempt to generalizesome of the discoveriesof his analysis. 6. ForWebern'scommentson the formof thispiece, givingthe designation'Thema' to the first section, see his letter to HildegardJone, 13 August 1941 (Webern 1959:17). 310

MUSIC ANALYSIS

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COMPOSITION AND CONTEXT IN WEBERN'S TWELVE-NOTE MUSIC

7. Elsewhere(Hasty 1984)I have discussedthe generalissue of phrasestructurein post-tonalmusicin greaterdetail. 8. Althoughcontourpatternin Fig. 3 is regardedsimplyas a sequenceof directions, it is possibleto representcontourmorespecificallyas a registralorderingby taking into account the registralposition of each pitch vis-a-visthe remainingthree pitches. Michael Friedmann(1985) has proposedsuch a representationin his conceptof 'contourclass'. From this perspective,the registralanomaliesof all thosetetrachordsthatpresentnormativedirectionalcontourscanbe accountedfor throughthe operationsof retrograde,inversionandretrogradeinversion.Thus D1 canbe regardedas a registralinversionof D in Ex. 10, F2as a retrogradeof F, and A3(see Ex. 14a)as a retrogradeinversionof A. 9. Webern(1960:68)writesto WilliReich, 3 May 1941: Everythingthattakesplacein this piecerestson the two ideaspresentedin the firstandsecondbars(contrabassandoboe)!Butthiscanbereducedeven further,forthe secondfigure(oboe)is itselfalreadya retrograde:the second two tonesarethe retrogradeof the firsttwo, but in rhythmicaugmentation. The first figure (contrabass)returnsonce againin the trombone,but in diminution!Andthe motiveandintervalsreturnin retrograde.Thatis how I haveconstructedmyrow- presentedby thesethreegroupsof fourtones. But the unfoldingof motivesalso participatesin the retrograde,though employing augmentationand diminution! [Here Webern may also be referringto the retrograde(inversional)relationshipof the twohexachords, a retrogradenot entirelycoordinatedwith durationalvalues.]These two typesof variationleadalmostexclusivelyto the actualideasof the variation, that is, a variationof motives proceeds, by and large, only within this framework.Andyet throughallkindsof shiftsin thecentreof gravitywithin the two figures, somethingnew in metre, character,etc. is continually emerging.- Justcomparethe firstrepetitionof the firstfigurewithits first form (tromboneand contrabass,respectively)!And so it goes throughout the entirepiece:in the first twelvetones, and hencein the row, the entire contentof the pieceis germinallypresent!In prototype!!!- And,in bs 1and 2, bothtempi(observethe metronomemarkings!)of the pieceas well!!! [my translation] REFERENCES Fennelly,Brian,1966:' StructureandProcessin Webern'sOpus22', Tournal ofMusic Theory,Vol. 10, pp.300-28. Forte,Allen,1973:TheStructure ofAtonalMusic(NewHaven:YaleUniversityPress). Friedmann,Michael, 1985: 'A Methodologyfor the Discussion of Contour:Its Applicationto Schoenberg'sMusic',ZournalofMusic Theory,Vol.29, pp.223-47. Gerhard,Roberto,1958:'AproposMr Stadlen',TheScore,No. 23, pp.50-7. Hasty,ChristopherF., 1984:'PhraseFormationin Post-TonalMusic',TournalofMusic MUSIC ANALYSIS

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CHRISTOPHER F. HASTY

Theory,Vol. 28, pp.167-89. Kramer, Jonathan, 1971: 'The Row as Structural Background and Audible Foreground:The First Movementof Webern'sFirst Cantata',3rournal of Music Theory,Vol. 15, pp.l58-81. Peles, Stephen,1983-4:'Interpretation of Sets in MultipleDimensions:Notes on the SecondMovementof ArnoldSchoenberg'sStringQuartetNo. 3', Perspectives of New Music,Vol. 22, Nos 1 and2, pp.303-52. Perle, George, 1959: 'Theory and Practice in Twelve-Tone Music (Stadlen Reconsidered)',TheScore,No. 25, pp. 58-64. Piston,Walter,1958:'MoreViewson Serialism',TheScore,No. 23, pp. 46-9. Rahn,John, 1980:BasicAtonalTheory(New York:Longman). Samet,SidneyBruce, 1985:'HearingAggregates'(Diss., PrincetonUniversity). Sessions,Roger, 1958:'To the Editor',TheScore,No. 23, pp.58-64. Smalley,Roger, 1975:'Webern'sSketches(II)', Tempo,No. 113,pp.29-40. Stadlen,Peter, 1958a:'SerialismReconsidered',TheScore,No. 22, pp. 12-27. -1958b: "'No RealCasualties"?',TheScore,No. 24, pp.65-8. Webern,Anton, 1959:BriefeanHildegard3rone und3rosef Humplik(Vienna:Universal). -1960: WegezurneuenMusik,ed. WilliReich(Vienna:Universal). Whittall, Arnold, 1987: 'Webernand Multiple Meaning',MusicAnalysis,Vol. 6, pp.333-53. Zuber, Barbara, 1984: 'Reihe, Gesetz, Urpflanze, Nomos', Musik-Konzepte Sonderband: AntonWebern II (Munich:EditionText + Kritik),pp.304-36.

312

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