Metaphor Is There Alternative?

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The Metaphor of Musical Motion: Is There An AlternativeAuthor(s): Judy LochheadSource: Theory and Practice, Vol. 14/15 (1989/1990), pp. 83-103

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TheMetaphor fMusical Motion:Is ThereAnAlternative*Judyochhead

Almost hirtyearshavepassedsincePeterWestergaardrote: Theproblemfrhythmncontemporaryusic ies not n the difficultiesfextendingraditionalanalyticonceptsohandlencreasingomplexitynnewmusic, ut nthenadequacyoftraditionalnalyticonceptso handle nymusic/'1Muchhasbeenwrittenboutthe emporaltructuresfmusic inceWestergaard'srticle,ndmuch asbeengained.But ittle ttentionas been directed oward hekindsoftemporal oncepts hatunderlienalyticnd theoreticonstructs.incemusic s a "temporalrt/'2 emightwell consider henature ftemporal onceptionnthoughtboutmusic s a meanstowardlarifyingome f he roblemsssociated ith t.Difficultiesurroundingemporalityrenotunique omusic; satisfactoryayofconceivinghenature f ime as been problemince hebeginningsfphilosophy.Oneissue hasparticularelevance othoughtboutmusic: he oncept ftemporal*An earlier version of thispaper was given at the annual meetingof the Societyfor Music Theory,November9, 1985,Vancouver.Westergaard,"Some Problems nRhythmic heory nd Analysis/'PerspectivesfNewMusic,1/2 (1962);reprintedn Perspectivesn Contemporaryusic Theory,d. BenjaminBoretz and Edward T. Cone (NewYork:Norton,1972),226-37.2Music has been considered "temporal rt/' ya greatvariety f writers: hilosophers nd aestheticiansas well as musicians. For instance,Stravinskyn his PoeticsofMusic in theFormofSix Lessons trans.Arthur Knodel and Ingolf Dahl, New York, 1947, 29), writes that "...music is based on temporalsuccession and requiresalertness ofmemory.Consequentlymusic is a chronologicrt,as painting s aspatial rt."And from somewhat differenterspective, usanne K. Langerwrites n Feeling ndForm:"Music makes timeaudible, and its form nd continuityensible." New York:Charles Scribner's ons,1953),110.Recentlyome writers ave beenexploring patialfeatures f musical sound. For nstance, ee RobertMorgan "Musical Time/Musical Space," Criticalnquiry, /3 (1980), 527-38;Thomas Clifton,Music asHeard: A Study n AppliedPhenomenologyNew Haven: Yale UniversityPress, 1979); and JonathanBernard, InaudibleStructures, udible Music: Ligeti'sProblem, nd His Solution,"Musk Analysis, /3(1987),207-36 nd TheMusicofEdgardVarseNew Haven: Yale University ress,1987).These writers recareful opointout the nterpntrationftemporal nd spatial features.Whilerecognizing hevalidityand usefulness fexploring he patialmetaphor, have chosen to focus on temporality ere because thisis theessentialdimensionofmusicalphenomenaand because itposes so many conceptualdifficulties.

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The Metaphor of Musical Motion 85

with espectootherbjects.8he emporal etaphorssimilarlyelational;trequiresthe ssertionf first-orderime hatmoves r flowswith especto a second-ordertime.The musicalmetaphornvolves relativemotion etween ounds usually snotes,ntervals,rchords andtime,r imendtonal pace.Thevalidity f thetemporalmetaphor as vigorouslyebatedbya varietyfphilosophersnd scientistsnthe arly ears f his entury,ut hemusicalmetaphorhas beenemployeduiteuncritically.he ssuesarising rom hedebate lluminatesome f hedifficultiesurroundingusic's emporaltructure,owhichWestergaardalluded,ndsuggestomenew venues or houghtboutmusic.nparticular,willbeconcerned ith herelevance f the ssuesfor houghtboutcontemporaryusic.Changesnstructurehat haracterizewentieth-centuryusichaveposedsignificantproblemsor hosewhothinkbout hatmusic,nd theproblemf emporaltructureincontemporaryusic asbeen neof hemost erplexing.Thediscussion illproceeds follows: art summarizeshe entralssuesofthephilosophicalnd scientificebate; artI presentscritiquef hree ecentrticles nthe emporaltructuresftwentieth-centuryusic nlight fthese ssues;Part IIdraws ogetherhe woprior artswithgeneral emarks n the ignificancefthephilosophicalssues ormusicaloncepts.

IJ.M. E.McTaggartparked ebate bout emporal otionnanarticleppearingn1908 alled TheUnrealityfTime/'9 e demonstratedhat timesunreal" y rguingthat he woordinary aysofconceptualizingime re ogicallympossible. ne ofthese rdinaryonceptionsftimenvolves hemetaphorfmotion nd theotherexplicitlyenies t.Thesetwonotions ftime recommonlyeferredo as dynamicnd static ime.McTaggartalled hemheA-seriesndtheB-series.ynamicime,r theA-series,scharacterizedytensedanguage hat orrespondso the emporaleterminationsffuture,resent,ndpast.For xample,magine ou ive nMontanand that t sNewYear'sDay.On thisJanuaryay youreadabout nd lookatpicturesf theprevious

8The uestionfhowmetaphoricaleaningrises s complexndbeyond he copeof this aper.Byassertinghat hemeaningftemporal otion erives rompatialmotion imply ot hat heres noreal ense nwhich emporal otion,n a broadermeaning,xists utonly hat here re nosubstantialentities hichhangepatialocationseealsonote 6below).MarionGuckexplores owmetaphormayfunctionor nalysis n "Musical magesas MusicalThoughts:heContributionfMetaphoroAnalysis/'nTheorynly,/5 June981), 9-42.9J.M. E.McTaggart,TheUnrealityfTime/'Mind, 7 1908), 57-74.Volume 14/15 (1989/9O)



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yearthathasoccurred,ou watch the footballgames that reoccurringow, nd youmakeplans to turnover a new leafduringtheyearthatwill occur. Underlying histensed anguage s a notion fchange.For nstance,n thatJanuary ay nMontana, neventyouexpect ooccur saythefirst asteofa summer omato changesfrom einga pleasantexpectation,obeinga flavorfulxperiencenJuly,obeinga fondmemoryinNovember. t is thisconceptofchangethat ncorporateshemetaphor ftemporalmotion.10Static time, the B-series, is characterized by non-tensed language such asbefore/after nd earlier than/later than. Temporal designations such as thesedetermineermanent rder elations. or nstance,fan eventXatrYls earlier han neventY atT2,thenXis always arlier hanY.Or in other erms,he first ay of 1989 salwaysearlier han he astdayof1989.Descriptionsftime ccording o theA-or B-series ccountfor ne kind oftemporalstructure:herelation etween uccessive ventsna temporal eriesor, notherwords,orderrelations. omprehensive onsiderations f time n philosophical nd scientificliterature eal withstructures f order nd ofduration r extension. he questionoftemporalextension s a separate but not unrelatedissue; it will not,however,beconsidered ere.Both thedynamicand staticformulations f timeare conceptually vailable inordinaryanguage and,as we will see later, othoccur nmusic theoreticnd analyticlanguage).It is justas commonforus to refer o dynamicprocessessuchas growth,decay,evolution, nd development s to staticrelations uch as before after,arlierthan/ ater than. n ordinary sage thetwo concepts re equally viable.McTaggart,however,pointed out a contradiction n these two conceptionswhich led to hisassessment f time'sunreality.McTaggart's rgumenthas twoparts.The first ollowsfrom heassumptionthattimenvolveshange. incethe orderof events s permanentn theB-series,McTaggartmaintains hat tatic imecannot ccommodate hange.Consequently,hemeaningofthe earlierthan/laterthandesignationsof theB-seriesdepends upon thefuture-present-past elationsof theA-series. n otherwords, themeaning oftheB-seriesdepends on the temporaldeterminationsof theA-series.The second part of theargument emonstrateshattheA-series s contradictory.veryevent n an A-serieshas, simultaneously,ll threemutually ncompatibletemporaldeterminations; orMcTaggart,t s contradictoryosaythat n event hat s present ow,willhave been n10Thedirection f this motion tself hanges accordingto usage. Ifwe say that an eventchanges frombeingfuture, obeing present, obeingpast,there s a motionfrom uture owardthepast. But fwe saythat n object becomes something for nstance, n apple becomes rotten then there s a motionfromthepasttowardthefuture.Theory and Practice



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thefuture,nd willbe inthepast.Thecontradictions notresolved ythe ssertionthat he vent as these emporaleterminationssuccessively."his ssertionequiresthentroductionf second-orderime eries. hemomentsf his econd-ordererieswouldalsohave, imultaneously,he hree emporaleterminations,equiringgainthe ssertionfa third-ordereries,nd so the rgumentoes nan infiniteegress.Since heA-seriesemainsontradictorynd since heB-seriesepends n theA,timeis unreal.Thisproofncited roponentsfboth heA-and B-series odevelop rgumentscounteringcTaggart'thesis. he ssues hatwere entralo thedebate etween headvocates f heA- ndB-seriesrose ithersresponsesoMcTaggart'sroofrto thecompetingheory.11ssuespertinento themusical onsiderationselow representedas "arguments."our rgumentshat haracterizeheB-theoryrepresented irst,followedyfourhat haracterizeheA-theory.Argumentsf theB-theory

Firstrgument:heB-series an accommodatehange. his rgumentests n thedistinctionetweenemporalecomingndtemporalhange,nimportantistinctionsinceMcTaggartefineshanges a fundamentaleatureftime.B-theoristsontendthatMcTaggartonfusedecoming ith hange. hey how hat ecomingeflectshetemporalelationf nobservero series f vents ndthat ecomings not ntrinsicto theevents hemselves.n theB-serieshange s defined ydifferenttates fanobject t differentimes. hangemaybe demonstrated hen tmaybe stated, orinstance,hat tan earlierime he pple sripe nd ata later imehe pple s rotten.Secondrgument:heconceptf tatic ime estmodels imenthe bjective orld.UnderlyingheB-theorisfsositions the ssumptionhat ime s an existentnthe11A limitedbibliography bout the debate over theA-and B-series s givenbelow. For a morecompletelist ofreferences ee RichardGale, ThePhilosophyfTime London:Macmillan,1968),503-06.WorksbyB-theorists nclude: BertrandRussell, Introduction oMathematical hilosophyLondon: George Allen &Unwin, 1919) and An Inquiry ntoMeaning& Truth New York:Norton, 1940); Nelson Goodman, TheStructurefAppearanceCambridge,Mass.: HarvardUniversity ress,1951);W. V. Quine, "Mr.Strawsonon Logical Theory/'Mind 62 (1953);A. J.Ayer,The ProblemfKnowledgeLondon:Macmillan, 1956);andJ.J.C. Smart,Philosophynd Scientific ealism London: Routledge & Kegan Paul, 1963). Works byA-theorists: C. D. Broad, ScientifichoughtLondon: Kegan Paul, Trench,Trubner,1923); P. Marhenke,"McTaggarf AnalysisofTime/'TheProblemfTime,University fCaliforniaPublications n Philosophy18 (1935);W. S. Sellars,"Time and the WorldOrder/'Minnesota tudies n thePhilosophyfScience II, H.Feigl,G. Maxwell, and M. Scriven, ds., (Minneapolis:University f Minnesota Press,1962);M. Capek,'The Inclusion ofBecoming n thePhysicalWorld,"TheConcepts fSpaceandTime,M. Capek ed., BostonStudies n the hilosophyfScience,XXII Dordrecht:D. Reidel, 1976); and J.N. Findlay,"An ExaminationofTenses,"ContemporaryritishhilosophyII,H. D. Lewis,ed. (London:GeorgeAllen & Unwin,1956).

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physical orld nd that conceptftime hatmodels his bjectivexistentsprior oany theroncepts.he hirdrgumentestsnthis ssumption.Third rgument: emporalbecoming s mind-dependent.The change thatcharacterizesfutureventwhen t becomes resentr when tbecomes astexistsonly nrelation o an observer;n otherwords,becoming ependson the "nowawareness" f an observer. -theoristslaim hatwhile ome eventsnthenaturalworldmaybe describeds a uni-directional,symmetric,nd transitiveeries, heygiveno evidencef emporalecomingpart romhe rientationf n observer.12Fourthrgument:emporal esignationsn terms fthe B-series re prior odesignationsn terms f theA-series. B-theorists ontend hat the statement"Schoenbergied nthepast"means Schoenbergiedat a time hat s earlier hananotherime."Argumentsf theA-theory

Firstrgument:he tensed eterminationsffuture,resent,ast, ndtherelatednotion fbecoming,restructuresf theobjective orld.A-theoristsrgue hatwehave certain nowledgeffuture,resent,ndpastevents,nd of thebecomingfevents. hey ssert hat xperienceeveals heobjectivetructuresf theworld, ndfurther,hat he ime fan observers notdistinguishablerom hat f theobjectiveworld. hedeterminationf nobject reventspast, resent,rfuturey n observerinvolves cognitivect, nd"if he ognitivectsof nobserverre ntrinsicallyitherpastorpresent,hen he bjects fthese cts,which recontemporaneousith hem,must ikewisee ntrinsicallyitherast rpresent."13ince ime f he bjective orld12The emporalproperties funi-directionality,symmetry,nd transitivityharacterize he "classical"conceptof time.Withrespect o the uccessionA B C D thesepropertiesmaybe formulated s follows:

A is followedbyB,BbyC,and C byD Uni-DirectionalityIfA is beforeB,thenBis notbeforeA. AsymmetryIfA is beforeB,and B isbeforeC, thenA is beforeC. Transitivity

The reader nterestedn furthernvestigation ftemporalproperties nd conceptsmayfind hefollowingbooks useful:P. C. W. Davies, Spaceand Time n theModernUniverseNew York:CambridgeUniversityPress, 1977), and Bas. C. van Fraassen,An Introductiono thePhilosophyfTime nd Space (New York:RandomHouse, 1970).13P. Marhenke,//McTaggart/snalysis of Time/' Universityf California ublicationsn Philosophy, 8(1934), Berkeley:University fCaliforniaPress,1935),162.Theory and Practice



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doesnotdifferromhe ime f xperience,ecomingnd the ensed eterminationsffuture,resent,ndpast reobjectivetructuresf ime.Secondrgument:n mportantntologicalifferencexists etween ast nd futureevents,ndthis ifferences inked othe bjectivityf now" wareness. sproof,heA-theoristsemonstratehat hefour-dimensionalepresentationfspaceand timegives vidence f theontologicalifferencef thepastand future.hey rgue hat,accordingorelativityheory,o eventnthe ausalpastof ny ingle onceivablyealobserveranever e containednthe ausalpastof ny theronceivablyeal bserver.Inotherwords, asteventsnthephysicalworlddifferrom uturevents,nd the"now" f ubjectivewarenesss thatmomenthateparateshe utureromhe ast.Thirdrgument:-theoristsrgue hat emporaleterminationsf theB-seriesredependentntemporaleterminationsftheA-series.hey howthat he tatement"Schoenberg'sirth s earlier han choenberg'seath"means hat fSchoenberg'sdeaths nthe resent,choenberg'sirthsinthe ast.Further,-theoristslaim hatthe ranslationf tensed tatementnto nuntensed neresultsna lossofmeaning.For nstance,he tatementSchoenberg'seathn1951 s later han isbirthn1874"doesnot ell sthat choenbergs dead.Fourthrgument:cTaggart'claim hat heA-seriess contradictorynvolvesconfusionetween -andB-relations.orMcTaggart,heB-seriesntails ermanentrelations f orderbetween ermanentvents.TheA-series ntails mpermanentrelationsetweenermanentvents. -theoristsrgue hatMcTaggartonceives f heA-seriess a sort f chorus-line"f vents crosswhich he spotlightf he resent"moves, iving ach event tsmomentaryresentness.uch conceptiononfuses hedefiningeaturesfA- ndB-time. ccordingotheA-theorists,heA-seriesnvolveschange ftime, hat s, t nvolves hechangingfevents, ot usta changentherelationsetweenvents.14An nvestigationfthephilosophicalssumptionshat nderliergumentsor heA-and B-seriesheds ome ight n thedifferencesetween he wonotions ftime.1514The -theoristssed this easoningocounterhe rgumenthat heB-seriesan ccommodatehange.Theargumentf theB-theoristsests n thedistinctionetween n event nd an object:n event oesnotchange n the B-series utan objectmayexist n differenttates t differentimes.A-theoristsdemonstrate hat hange s not mpliedbystatementsracing hehistory f an object bysuchstatementss the pple s ripe b onetime nd rottentanother.hey rgue hat heripe tate ftheappleatthe arlier ime ever hanges,nd thus t s an eventn theB-series.ince hese repermanentstates f he bject,heB-seriesannotccommodatehange.15A uestionhat arallels hedebate verdynamicnd static ime oncernshe oleofmetaphorntheconstitutionfmeaning. roponentsf a literalisticheoryfmetaphorwouldmake thefollowingclaims:1)motionnspacehas a significancepecificallyinked othat ontext,nd 2)the ransferf hatsignificancerom ne context oanother,n a metaphor,esultsna loss ofmeaning. roponentsf aconstitutiveheory ouldclaim hatmetaphoricalanguage onstitutesnique meanings,nfact, y

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While thequestions bout time hat haracterizehedebate arisefrom nalyticphilosophynthe wentieth-century,he wo ides eflectifferentoncerns ithin hisphilosophicalradition.rgumentsor heB-series re based onthe ssumptionsfPhilosophicalealism. -theoristsssume hatanguageandescriben ndependentlyexistingndobjectiveeality. istorically,uch notion frealityas beendefinedyexistencendexistence as been ssociated ith niversaisnd the ranscendanceftime,notherwords,with ermanence.hepermanencef order elationsntheB-series ives ime realityhat asproved ifficultodefine therwise.ntheA-series,nopart f ime anbe said to 'exist7':he ast snomore,he utures notyet,nd thepresents constantlyecominghepast.Thus,withno existingrpermanentarts,dynamicimes not "real" tructuref heworld.Argumentsor heA-seriesome utofphilosophieshat evelop romxperienceandordinarysesof anguage. -theoristsrgue romhe ositionhat ealitynvolvesa reciprocalelation etween heworld nd the anguage-user.hey ontend hatlanguageeflectshis elationnd thus eveals he ealityf heworld.Thedebate ver tatic nddynamicime eneratedommentaryemonstratinghevalidityot nly fone onceptionver notherut lso ofboth o ong s theyrenotconfused.One writer, .N. Findlay, laims that statements bout the worldcharacterizedybothA-and B-relationsremeaningfulut that henon-tensedstatementsf heB-seriesrepreferableince heyre lways rue rfalse.16e showsthatMcTaggart'saradox esultsrom combinationfthe wokinds frelations:osaythat single vent s simultaneouslyast,present,nd futures to ascribe hepermanentelationsf heB-seriesotheA-series.17TheargumentsfferedyA-andB-theoristsbove re formulatedosupporthepriorityf oneconceptionvertheother.t s notmypurpose oadvocate itherpositionspreferable;ather,t s touse the ssues risingromhe ebate s a basisfora critiqueftheoriesboutmusic's emporaltructure.hecritique illbe concernednot nlywithwhat onceptionorconceptions)f ime peratena theoreticalontextapplying conceptrom ome pecificontexto a differentontext.nthe nstancefmotionhat sourconcernere, he pplicationf concepthat erives rom visual nd tactileonfrontationithpaceto the ess comprehensible omainoftimeconstitutes otonlya newmeaningbut,further,terminologyhere one xisted.16J.N.indlay,Time:A Treatment/'ustralianournalfPhilosophy,9 1941);reprintednGale,ThePhilosophyfTime, 43-62.17Phenomenologistsould pproach hedistinctionetween ynamicndstatic ime uitedifferently.MartinHeidegger haracterizesime s a fundamentalrameworkfexperience a temporalpreadthat ncompassesuture,resent,ndpast.Thistemporalrameworks prior o andmakespossibleotheronceptionsf ime. he tatic nddynamiconceptionsre wo uchpossibilities.Theory and Practice



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butalso with he arger hilosophical ssumptionshatunderlie heconception.Further,sing philosophicalasisfor hecritiquellows for n interdisciplinarycomparisonetweenemporalonceptshat rovides broaderase for nderstandingthe roblemfmusic's emporaltructures.II

PartIpresentsritiquesf rticlesythreeuthors: llen orte,hristopherasty,andDavid Lewin.18 acharticle ffers theorybouttemporaltructureased onexamples rawnfrom hetwentieth-centuryepertory.havechosen o focusontheoriesboutmusic romhepresententuryreciselyecausemuch fthismusicchallengeshe pplicabilityfwell-establishedemporal onceptsboutmusic ndbringso head he eneralroblemf ormalizinghe emporaltructuresfmusic.Allen orte aseshismodel f emporaltructuren thepremisehat durationsthemostmportantspect f hythm"90-91). hispremiseeems oputForte'sheoryoutside heboundaries fthis ritiqueince hedebate ver tatic nddynamicimeconcernsheorder tructuresnotthedurationalor metric)tructuresoftime. hetwo tructuresrenot oclearlyeparable,owever,nd the rder elationsmplicitnForte'sheoryeservettentionere.

Fortemodels emporaltructureytranslatingurationsasdefinedy score)ntonumericalalues.This ranslationakes omparisonfdurationaluantitiesimplerand allows one todetermineroportionalelations etween urations.n Forte'swords, his ranslationpresentisihythmictructuren theclearest ossibleway,detached romrdinaryotation,ith tsbiastoward raditionalnterpretation"91).Examplea cites hefirstixbarsofthefifth ovementromWebern's agatellesorString uartet, p. 9. Exampleb showsForte's proportionalraph" f those ars,whichhave nnotated.InExampleb thenumbersssociated ith ither olidhorizontalines rbrokendiagonalinesrepresenthe alues f he urationalnits hat anbedeterminedromthe core. durationalnitnForte'smodel anreferoeitherf wodifferentinds ftemporalxtension:hat callnoteurationndresultanturation.heprecisextentfeither indofdurational nit s figured etween hebeginningattack) nd end18Allenorte,Aspects fRhythmnWebern's tonalMusic/'MusicTheorypectrum,(1980), 0-109;Christopherasty, RhythmnPost-TonalMusic:Preliminaryuestions fDuration ndMotion/'JournalfMusicTheory,5/2 (Fall 1981),183-216; nd David Lewin,"Some InvestigationsntoForegroundhythmicndMetric atterning,"usicTheory:pecial opics,d.Richmond rowneNewYork:AcademicPress,1981),101-36.Mycritiques re notcomprehensive;hey ddressonlythoseaspects f he hreerticleshat repertinento considerationfunderlyingemporaloncepts.

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Example la: Webern,ixBagatellesor tringuartet,p.9,V, ars1-6uerst angsam (J^= ca.40)l 'LJJLlL ' ' VJLJJF^rr an Sieg amSttgtmitDampftrZ^= il " - ,4 - ,4 y K = i = ^ uh J

/w- = = - ^^ ^^^^ iw>==- -Copyright924byUniversal ditionA.G.,Wien.Copyrightenewed; llRights eserved; sedby permissionfEuropeanAmerican usic;Distributorsorporation,ole U.S. and Canadian gent or niversal dition

Example lb: Forte's Proportional raph"ofWebern, p. 9, V,bars1-6[Author'snnotationsnbold]Palindrome1 : 2 6 6 18 6 6i 24 2 : 3 48 4 j i 5 j j j1 2 ' i2 12 12 | i : 3o :(12:24) [i2]^**r; ^ . : 1 i K &t i2 12 .-# ri2^w.^ [12] 36 ' J : 30 ; ; N 18 t

24 ^ / [6] 36 24| I12 : 182 : 3(release) ofa note,but a durationalunit s notnecessarilyequivalentto theactualsounding engthof a note.In Forte'sterms, durationalunit "is determined y thefollowing airofnodes [i.e., or urpurposes,dotson theproportionalraph]: ttack oattack, ttack orelease, eleasetoattack,nd releaseto release " (94)

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(the 1"of he roportion)annot esaidto "exist" ntil he ndofbar1,until fterhefirst nitof12has already ccurred. he model deals withformed, otforming,structures.Further,hemodel oesnot ddress he hangingtatus f structure.or nstance,it does notdealwith he hange romnincompleteoa completedtructurever hetime fbar1 throughhedownbeat fbar2.WhileB-theoristslaim hat heB-seriescan ccommodatehange,he ituations somewhat ore omplicatednForte'smodelsince t nvolves urationalroportions.hemodel omparesurationalventswhichsometimesre nd sometimesrenotdiscrete.tdoesnot ollow he hangesver imeof a single bject. hus eventhoughhedurationalvents equire ime omanifestthemselves,hemodels not oncernedith he ctual unrolling"f he uration.Forte'smodel learlyests pon ssumptionsf heB-series.t describesormedrpermanenttructuresharacteristicf hat eries. urationsave nobjectivexistenceandcomparativeelationsetween hem re fixed. he modelpositsnotstructureswhichmanifesthemselvesver ime ut definiteebof omparativeelations.Hast/sarticlepecificallyddressesmotion s an aspect fmusic ndlinks ttoduration.hefirstart fhiswork onsiders otionnd durationromphilosophical

perspective,nd the econd art resentstemporal odel or ost-tonal usic asedon the deasof he irstart.Thephilosophicaliscussionests n the ssumptionhatmotions a structureftemporalhenomena185).Hasty ites hework fthephilosopherrrolHarris oclarifyhe dea that emporalontinuityndchangere t the oot fmusical urationandmotion.20arris oints ut that emporaluccessionntheonehandrequiresnotion fchange r mpermanenceetween vents nd,on theother, continuitybindingventsogether.urationtselfs inconceivableithoutnotion f ontinuitybetween iverse ventsnsuccession. arris's ommentsescribehedualnature ftemporalelationsndarereminiscentf he istinctionsharacterizinghe ebate verdynamicnd staticime.21Hastydevelops concept fmusicalmotion romhisdualnature ftemporalrelations.e stateshat etweenhe uccessiveventsf musical resentationheresa qualitativeelation.f,betweenwoormore vents, unity btains ymeans facontinuityetween hem,hen hequalitativeelationmaybe describeds musical20SeeErrolE. Harris, Timeand Eternity/' eview fMetaphysics,9 (1976),464-82.21Boththe static and dynamic formulationsof timerequire some notion of change and continuity.Philosophicaltreatmentsf timehave always pointedout thisduality,but in eitherformulation,ne ofthesetwofeatures s emphasized.Theory and Practice



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motion. t is theformation fa unity,whatHastycallsa structure,hat s the basis ofmusical motion. In his words: "What is required formotion to take place is theformationf structurer whole between ramongevents" 191).Hast/s discussionofthephilosophicalbasis of musical motionclearlyrests on adynamicconcept of time that feeds his interest n developing a temporalmodelapplicableto the structuresfpost-tonalmusic. He positsthe"mind-dependence" fmotion, ontending hat it s not the materialworld tself ut our mode ofcognitionwhich reates emporal elations"191).His definition fmotion ythe "formation fstructure"ests n a uni-directionalemporal eries, he tensed eriesofdynamic ime.While born of the continuityof a structure,musical motion depends on theimpermanenceftemporal elations s defined ya dynamic eries.The model oftemporal tructure astypresents n Part I of his articleproceedsfrom is definitionf musicalmotion.To illustrate ismodel,Hastyconsiders he first12bars ofWebern'sOp. 27PianoVariations,hirdmovement.22 hepresent iscussionwillfocuson bars1-2only;Example2a cites hesebars.Hastybeginswith he ssertionthat the "continuous event of bars 1and 2 [is] a unit,"what he also refers o as a"structuralomponent" 197). The discussion of this unitdemonstratests structuralcoherenceby showingvariousways in which the differentlementsof the unit areassociated. Hasty calls such associations segmentations,nd conceives of themasdifferentnterpretations,ifferentaysinwhich "groupofnotesmaybe heard" 197).WhileHasty dentifies our egmentationsf theunit nbars1-2,Example2b citesonlythefirst.InSegmentation/1 shown nExample2b) thefirst nd last notes reunitedbyanequivalentduration nd are called elementA; by the same criterion,he second andthird otesare united nd called element . These two elements re themselves nitedas a "higher-leveltructure"y nterval lasssimilarity:oth re nstances f c 1.Otherfactors ssociating ElementsA and B are contour a retrograde or inversional)relation and pattern ofmetrical accent- again a retrograde relation (weak,strong/strong,eak).Hasty identifies notherunifying actor f the first egmentation:nterval-classassociation.nSegmentation/1, he ccontent fthefour ossiblethree-noteubsets sshown n brackets.These ic formations,hebracketed c numbers, re the basis ofaunifyingssociation.Hastywrites hat nElementA there s "a motion rom...[l, ,5] to[1, 3,4] while n B thisorder s reversed" 199).Thisretrogradeelation etween he cassociations nitesA andBas a structure.In his philosophicaldiscussion,Hastyassertsthatmusical motion nd continuityresultfrom heformation f structures. uch a theoretical oncernrestsfirmly n a^Hastyalsoconsiders ars -5 romtefanWolpe's ormor iano1959).

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Example 2a: Webern, ariationsorPiano,Op. 27,MovementII,bars1-2.Hasty'analysisfUnit .RuhigfliessendJ=ca. 80

fli i-Unitl 2 nr1 P f

in - I pf1- *?fi

Copyright937byUniversal dition. opyrightenewed;AllRights eserved; sed bypermissionfEuropeanAmerican usic;Distributorsorporation,ole U.S.and Canadian gent or niversal dition

Example 2b: Hasty7"Segmentation/1/'Webern,p.27,MovementII,bars -2

j[ y^ ^^^^T^S; >v + contourretrograde)r ' bow + orderf c associationretrograde)[1,4,5] '*y [1 3,4] + patternfmetricalccentretrograde;(i.e.,A weak, trong^-^^ B strong,eak)

[1,3,4] V^Xl^S]A B i+ durationo ) + duration4 )-durationA/B

dynamiconcept f time.Whilehis ntentions toprovide n understandingfthedynamicelations e conceives musicalmotion,isdemonstrationsfsuchmotionsometimesear racesf taticelations.or nstance,asty's ssessmenthatheresamotionromhe cassociation1, ,5] to that f 1,3,4] doesnot ccount or hefactthat he pecificcassociationsfEl? rerealized ne-by-onethey comento eing")while he cassociationsfD occur allatonce."Thestructurembuingmotion eremaybe said to "clickntoplace"or, s Hasty uggestednearlier omments, ayTheory and Practice



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98 LOCHHEAD

problem as thatistenerseard he ulses s a metrichenomenon.oth he xpectedametricesponsendthe eported etricesponsereshownnExample a. Lewin'stheoryddresseshe uestionfwhyisteners ight espondnsuch metric ay. hefollowingresentationfLewin's heory illfocus nthe ownbeatccurringith hefifthulse, r notherwords, hedownbeatccurringfterhe econd ar ineofthe"metricesponse"n Example a. Lewinarguesthat hisfifthulsehas a uniqueprominence.Lewin epresentshe ttackoints f he ulses na timeine nd abels ach ttackpointaccording o elapsed units oftime;the unitsare reckoned ccording oBamberger'sriginalxperiment.his ime-pointeriess shownnExample b.Thedownbeat fpresentoncerns annotatedt time-point4 n theexample. ewin'sdiscussion roceeds hroughour hronologicaltages fthe istening rocess hatcorrespondothe ime-points,5, 9,and 14.Eachstagerepresentsmoment hencertainurationalnits reperceived.Thefirsttageof the istening rocessoccurs t time-point,atwhich imedurationalnit f2haselapsed. he econd tage ccursttime-point.At this tageLewin laims hat listenererceives durationf3unitsthat urationetweenime

Example 3a: Tworesponses o a seriesof dentical ulses separatedbydurationsf1,2,3,4,and5units f imeAmetric I I I I hResponse m * s j(rit.) MUMetric 4 I I I IResponse 4 J J J J

Example 3b: Lewin's Tune-pointeries" f he uccessiveulsesMetricownbeat

1.1..1...I , , , it = 0 2 5 9 14

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points and5) and a duration f5 unitsthat uration etween ime oints and5).Further,e daims hat he uration of tage s retained.For ach tage f he isteningrocess,ewin onstructstablendicatingerceivedand retainedurations.xample c shows he able or tage .Theuppermostowofthetable ndicatesdurationalunits that re possible in this nstance.The rowunderneathabulates henumberf those urationalnits erceivednd retainedtStage .At his tage, equals ,therereentriesf under he urationsf ,3, nd 5.Whatkind f nformationhemodelyields t the downbeat" ftime-point4 scrucial or ewin's heory.his s Stage4 ofthe isteningrocess,nd its durationaltable s shownnExampled.Thedurationalntriesf tage areuniquewith especttopriortages ecause wodurations,and9,havebeen experienced"wicewhilenodurationwas experiencedmorethanoncein Stages1-3. Lewin attaches pecialsignificanceo the act hat hedurationalntriestStage areunique s such.He callsthisnumerical act he"peaking" t this tage nd correlateshispeakingwith heperceptionf downbeatttime-point4.Lewin akes he heoryutof he aboratorynd uses tto considermetrictructureinthe ixth ieceofSchoenberg'sp. 19miniatures.he score fbars1-6 s givennExample a andis annotatedo showtime-points.ewin s interestednwhether ismodelofdurationaleaking onfirmshenotated ownbeatfthepiano's eft-handchordnbar5; this s the nlynotated ownbeat f thefirst bars.Example b s anannotated ersionfLewin'sdurationalable or ars1-6.The column n thefar eft

Example 3c: Stage ofLewin'sisteningrocessd= 234579 12 14numberf d 110 10 0 0 0experiencedat t= 5

Example 3d: Stage ofLewin'sisteningrocessd= 234579 12 14numberofd 1112 12 11experiencedat t= 14

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shows time-pointsthat correspond to attacks in the score, and the uppermost,horizontal ow showspossibledurations or his xcerpt.In Example4b I have underlined herowof duration ntries or ime-point7,thetime-point orresponding o the notated downbeat of bar 5. I have also circlefourentriesn thisrow;theseentries re Lewin's numerical eakingvalues.Time-point7,unique with tsfourpeaking entries, earswhat Lewin calls a "maximalfunctionalictus" 112), nd thedurational eaking ttime-point7confirmshenotateddownbeatofbar 5.Lewin's model restson a dynamicconceptoftime. t formulates notion ofuni-directionalhangebyshowing hetransformationfperceived nd retaineddurationsover thechronological tagesof a listening rocess.While theconcept f motion s notexplicitlyncorporated,t underliesLewin's model. The durationaltransformations,which are charted n the durationtables,formulate he "becoming"ofa structuralevent,n thiscase an ictusor downbeat.And,thechronological tagesofthe isteningprocess tand na tensed pastand present) elation o oneanother.The model posits a listener and a listening process taking into account theapperception ftemporal nits.The approachdoes not tackle heproblems f istenercompetence nd individualdifferencesetween isteners.Nor does it considerwhatkinds of durationaldiscriminations re perceptuallypossible. For instance, n thediscussion fthemetrical esponse ntheBamberger equenceofdurations, ewindoesnotconsiderwhy listener erceives durational nitof2ratherhan durational nitof1at time-point; sincea singleunit has been heard, t seemslikelythat listenerwould interprettas a duration f1and successiveunitswould be reckoned ccordingto it as a standard.25 he listenern Lewin'smodel is not a real or ideal listener utrather function ftemporal hange.26Lewin's model does notpositthepermanent elations fstatic ime; tallows formultiple emporal esignations fa singleevent.For nstance, durational ventmaybe perceived, etained t Stage1,retained t Stage2, and so on.27 n terms ftheA-theorists,ewin'smodel ncorporates changing f events.^One mightposit a sophisticated ognitiveprocess thatwould compare a succession ofdurationsandarriveat a largestcommon unit.Lewin does not make such an argumenthere but ratherprovides forsuch a processtheoretically.26As a side issue here, t s interestingonote thatLewin's model of timeresemblesHusserl's model as itis articulated n ThePhenomenologyf nternalTime-Consciousness,rans.JamesChurchill Bloomington:Indiana University ress,1964),especially48-52. For an analysis of Husserl's ideas on temporality,eeIzchakMiller,Husserl, erception,ndTemporal warenessCambridge,Mass.: MIT Press,1984).27Inthe article"Phenomenology,Music Theory, nd Modes of Perception/'Music Perception, (1986),327-392,Lewinemploysa similarmodel inwhichthe nterpretationsfeventschangeovertimewiththeadditionof newperceptual nformation.Theory and Practice



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IHIn a famouspassage fromBookXI of theConfessions,ugustine aments, What,then,s time? know well enoughwhat t s,provided hatnobody sksme;but f amasked what t s and try oexplain, am baffled."28uchan observation ervesus well:We know full well what rhythm nd musical motion are, but our attemptstocomprehendhemna formal ense,while notunsuccessful,ften esultnparadoxicalquestions bouttheverynature fthese emporaltructures.Some oftheenigmassurrounding emporality lowfrom he visual bias of ourlanguage and hence our conceptualmodels. Language equips us better o describephenomena visually rather than aurally apprehended.29 Sounds, like time,areephemeral nd cannotbe said to exist angiblyike a book or clarinet. ur inabilityomake time nd sounds"stand till" o that heymaybe "grasped"conceptually,o thatwe may "see" what theyare all about, may be correlatedwith a less developeddescriptiveanguageand conceptual rameworkpplicabletotemporal nd soundingphenomena.The discourseof theories boutmusic's temporal tructure orks within imilarconstraints flanguage, constraints hat bear on theproblemofmusic's temporalstructuren musictheorynd analysis.Forexample, he theoreticaluestionofwhatconstitutes musicalwhole (a groupor segment) nd theanalytical eterminationfsucha wholearetemporalssuesrelated o theproblem f how temporal nitytselfspossible.The problem risesfrom woways ofconceptualizingimethatunderlie hedistinctionsetween tatic nd dynamic ime.So on one hand,time s conceived s asuccession f discrete owsor momentsnwhichdistinct ifferencesfbeforend afterobtain.On the otherhand,time s conceived s constant low nwhich thecontinuousdistinctionsfpast,present,nd future btain.These twoviews mustbe reconcilednorder o formulateheconcept fa temporalwhole orunity; hat s, distinctmomentsof uccessionmustbe unified ycontinuous low.The problem of temporal grouping and segmentation engages both theserequirements.hebasis for ontinuitynd an articulationf theeventsconstitutingtemporalunitrequireboth a theoretical nd an analytical determination.Thesedeterminations,hilenotsimplymade and resting n issuesofcriteria,reessentiallytemporal,ngaging uestions forder, uration, nityamongothers).28St.Augustine,Confessions,ookXI,trans.R. S. Pine-CoffinNew York,1977),264.29ThephilosopherDon Ihde discusses thisbias in Listeningnd Voice:A PhenomenologyfSound Athens,Ohio,1976), ee Chapter1,"In PraiseofSound/' 3-16.

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The distinction etweenstatic and dynamic time that has been our focus heretouches on only a part of the larger topic of temporality, ut it raises issues ofsignificanceormusic. The title fthisessay,whileostensiblysking falternatives othemetaphor f musicalmotionexist, sks another uestion:What are thetemporalconceptsunderlying hought boutmusic and how do theybear on theoretical ndanalytical roblems oncerning emporal tructure?The discussion above showed a static model underlyingForte's theory.Thestructurese formulates re tunelessly rue and notmind-dependent. asty's theoryaddresses hequestionofmusicalmotiondirectly,ut his structuresear traces f staticrelations, nd Lewin's theory ormulates tructureccordingto dynamicprinciples.Mere dentificationfthetypeof modelunderlying theorys notthegoal here,butrather meansbywhichto comprehendwhatthat heory an and cannot ssert boutmusicalphenomena.Difficulties urroundingeach model are various and oftenraise ontologicalquestionsaboutmusic itself nd our observations f it. For instance, bout theoriesbased on static ime, ne might sk ifstructure an exist partfrom tsapprehensionand whether listener s implicitn thetheorytself.One would also have to inquireafter he role of the score n determinations f structure:pecifically,oes the visualinformationof the score provide a satisfactoryrepresentationof the soundingphenomena,or does visuallyapprehended nformationorrespond o thatwhich saurally pprehended?Abouttheories ased on dynamic ime,one might sk whethermotion s said tooccur n the transformationf a singleevent ormusical object,or is it a qualityofrelation etweendifferentvents?Questionsabout the score arise here too: is motionattributable o theeye scanningthepage in analysisor performance? ow does itsvisual informationorrespond o thesounding experience fthe istener?Questionsabout theroleand capabilities fthe istenerrisefordynamic ime:Can listenersmakethe kinds of temporal discriminationsproposed by the theory?How does oneinvestigatestructures hateither mplicitlyor explicitly nvolve a listener?Thesequestions ften order n largerphilosophicalssues butthey refundamental oanytheoreticalranalyticalpproach, nd as suchthey eserve ttention.It has been mypurpose herenot to endorse any particularmode of temporalconceptionbut to clarify heassumptionsunderlying heories bout thetemporalstructure f music. Such a clarificationllows us to better nderstandwhat a theorymay or may not achieve and thus to fosterprogress toward a more satisfactoryunderstandingfmusic'stemporal tructure.

Volume 14/15 (1989/9O)

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