Notated and Heard Meter - Lester

7/28/2019 Notated and Heard Meter - Lester

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Notated and Heard MeterAuthor(s): Joel LesterSource: Perspectives of New Music, Vol. 24, No. 2 (Spring - Summer, 1986), pp. 116-128Published by: Perspectives of New MusicStable URL: http://www.jstor.org/stable/833216 .

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NOTAIED AND HEARD METERLLJOEL TIFS1 ER

HOSE OFUSwho attend to concertsof contemporarymusic with our eyesaswellasourears(foreven the most severelyabsolutemusicdoes, afterall,havea theatricalcomponent) havesurelypuzzled on occasionas we watchedthe conductor'sbaton performa wondrouslyintricatedance: what does thatmetriccommotion haveto do with the soundsemanating rom the ensemble?For while most tonal workseasily mparttheir metrichierarchyo us via con-tinuouslyregularpulseson severalevels,regular roupingof thesepulses,andfrequent mpulses reinforcing he notated meter, manya mid and late twen-tieth-century ompositiondoes not pretendto informus of itsmetricstructureif indeed it hasone in the senseof the metricstructure f a tonalcomposition.Iam not referringo those unfriendlyscoresthat refuseto specifydurationsoronly approximate hem, althoughsuch worksmaywell fall into this category.RatherI am thinkingmore seriouslyof scores I haveperformed,such as Bab-bitt's Compositionor FourInstruments1948) or Arie Da Capo(1974), which

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Notated and HeardMeter

specifywith considerableprecisionconventionalmeters and durations.For inthese scoresour currentwisdom andour knowledgeof the serialpermutationsbywhich the durationsarise ead us to assumethat the precisionof these dura-tions isquiteimportant o the structureof the piece.If, asI arguen thispaper,these durationsare not accuratelyperceptible n the absence of a traditionalmetrichierarchy, hen commonly-heldconceptionsof rhythmin this musicneed to be reassessedrom the bottom up.Performers reperhapsmost immediatelyawareof the disparitybetweenthe metricnotationsof such scores and theirsound, for they must learn themetricnotations n orderto playthe piece. I rememberquite vividly he scoresof hoursI spentin 1970 as a memberof the Da CapoChamberPlayers,earn-ing the violinpartandthen rehearsinghe ensembleof Babbitt'sCompositionforFour nstruments.Simply n order to playthe notes at the righttime, I had tolearn o hearmyown partas well as all the otherparts n the texture n a metricframework-the notated one. In effect,I had memorizedasilentclick-trackorthe piece-a click-trackagainstwhich the rhythms playedout theirjazzy syn-copationsandcrossrhythms. ndeed, "jazzy" seems the appropriateerm todescribehow I heard and playedthe rhythmsagainstthe silentmetricgrid. Imust haveratherthoroughly memorized that metricgrid, for if I listened tothe concerttapenot longafterperforminghe piece, I couldeasilyhear t auto-maticallyn the notated meter.But I can also rememberwell my surprisesome months laterwhen I lis-tened againto the tape. In the interim,I hadforgottenthe measure-by-meas-uremetric structureof the piece. And what had seemed to me in my daysoffamiliarity rhythmic-metric tructureof crystalline larityhad become thor-oughly opaque.Seeminglyerraticimpulsesdominatedthe soundscape.Did anaudience,anyaudience,hearonly this latterpieceand neverthe one that I hadstrivenso hardto perform?Now to be sure we allgo throughperiodswherewe get to know a pieceinconsiderabledetail followed by other periods lastingmonths, years,or evendecades,when we do not hearthatpiece. Forthe bulkof the tonalrepertoire,when we re-encounter he work we maywell havelost our detailedmemoryofit. But the experience, or me at least,has not meant that I findmyselfunableto orientmyselfin the work. Yet with the musicof Babbittandother twen-tieth-century cores I findthat experiencerecurringwith a frequency hat dis-turbs me.For that experienceraisesquestionsthat go to the heartof what we under-stand to be the rhythmic-metrictructureof this music.Does the piecethat Ihearone waywhileperformingt change tsverynaturewhen it crosses he pro-scenium?Does the piecethat I hearone waywhen I tape it changeits naturewhen passing hroughthe playback ystem?Are the metriccalculations f theperformeras unintelligibleand irrelevant o the listeneras some apiandancewould be in helpingus locate a particularwildflower in a meadow?Are therhythmic-serialomputationsof the theorist(orthe composeraswell) equally

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irrelevanto the listener? must confesssome chagrinatraisinghesequestions,since ornearly wo decadesnow I have beenlecturing o classes ndpreconcertaudiences(mostlyin connectionwith Da Capo ChamberPlayers oncerts)ontheeaseof perceivingherhythmic-metrictructure f this music. But I raise hequestionshere becausemy recent work on rhythmand meter in tonal musicleadsme to believethat the answers o thesequestionsmaywell requirea thor-ough rethinkingof the natureof meter andrhythm n muchtwentieth-centurymusic.

THE NATUREOFMETERI haveargued lsewhereabout the factors hatgiveriseto meter and to ourper-ceptionof meter.' That discussionpertainsdirectly o tonal music, but manypointsareextensible o nontonalmusicaswell. I willsummarize hat discussionhere,but without supportingargumentsoundin the citedsource,concentrat-ingon thosepointsrelevanto nontonalmusic.Meter is one form of accentuationn music. Accent is animpulsethatmarksoffapointof initiationn music. Accentuations rise rommanydifferentactorsand occur in a virtuallynfiniterangeof strengths.The impulsethat beginsanote createsan accent n relation o the sustainedportionof thatnote and thesustainedportionof theprecedingnote (orto thesilence hatprecedes henote).The beginningof a new pitchaftera repeatedpitchisaccentedn relation o therepetitions of the preceding pitch (pitch-changeccent).The impulse thatlaunchesarelativelyongerduration saccented n relation o the beginningof apreceding horterduration(thedurational ccent).The impulsethat articulatesthebeginningof amotive orpattern saccented n relation o the interiorof thatmotive(thepattern-beinningaccent)Thepointof achange nmelodiccontour saccented n relation o the melodic motion thatcontinues n one direction thecontourccent).The beginningof a textureof greaterdensity s accented thetex-turalaccent).The point of harmonicchangeis accented(the harmonic-changeaccent).And so forth.All of these typesof accent arecausedby an event occurring n the music.These typesof accent resonate n us as listenersby markingoff points in timedifferentiated rom those points that do not receive such impulses. Metricaccentsaresomewhatdifferent n nature,for metricaccentsnot only can butquite frequentlydo occur atpointsin time whereno accentualactor spresent.Once the meteris established,we perceivemetricaccentson silentdownbeatsand on beatsandbeat-subdivisionshat no eventarticulates.Formeteris apsy-chologicalphenomenon.It istheyardstickwherebywe locate he musical ventsof the piecein agridof time-points.Weperceivequitedifferently,orinstance,harmonicchangesthat anticipatea beat, that occuron a beat, and that occuraftera beat due to suspension.The gridof the metrichierarchy,n its role of

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yardstick,sakinto the frameof apainting-considerhow differentlywe wouldperceive he sameportraitwherein one framethe face is partlycoveredby theframe, n another rame he face s centered,and in a third frame he face soff-center.In tonalmusic,theaccentualprofileof the musiccreates ndcommonlyrein-forces he metrichierarchyormuch of the piece.Accentscausedbyavarietyoffactorsestablishpulses-regularlyecurring mpulses-on several evels. Accentson one levelgroupthe pulseson lower levels. The accents hat most convinc-ingly group pulsesto create he interactionof levelsthat is the metrichierarchyareharmonic-changeccents,durational ccents,and texturalaccents.Consider,forinstance,the veryopening of Mozart'sFortiethn Example1.The continuouseighthsin the violaestablishan eighth-notepulse. A quarter-note pulsethatgroupstheeighths npairsarises rom therepeatedpitch pattern-ing in the viola. The violinmelodyconfirms his quarter-noteevelby offeringquarternotes aswellas two-note slursgrouping he melodiceighths.Half-notepulsesgrouping he quartersn pairsarise rom theviolapatterning s well as themotivicrecurrencesn themelody.Thebassnotes on everydownbeatgroupthehalfnotes in pairs.Finally,a two-measurepulsearises rom the bass-notepat-terning,confirmedbythepaceof harmonicchangesaftermeasure4. All of theselevelsof pulsenestwithin one anotherasdepicted n Example2.

AllegromoltoVln. I, II

Via.

Vcl.Bass

1 R 2 J i k..^ / ''^ n J 3 J17 ^ r Srrr-r-^^dir.

P '' r '^r 1 0 Bf,bb?j r X J X - rp

EXAMPLE 1: MOZART, SYMPHONY NO. 40, MM. 1-9

t r tr:r-L r y r r,b , J I A X -r.

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2oo o

/ \ All evels recontinually resent uringr r thefirstphrases.I\

EXAMPLE 2

Becauseof the immediatepresenceof allthese nestedpulselevels,a listenerrapidlybuilds he frameof the metrichierarchyo that he or she canmeasureallthe musical ventsin relation o the multiple evelsof the metrichierarchy.Theopeningof Mozart'sFortiethprojectsarathercompletemetrichierarchy ecauseof the continuouspulseson so manylevels. In other tonalpassages, omelevelsmaybe presentby implicationonly. The quarter-noteevel at the openingofBeethoven'sFifth,forinstance, simpliedbythe quadruple roupingof eighthsbecausegroupingsof two arethe only possible evelthat can nest within four.But actualquarternotes in anydimensionbarelyoccurduringthe entirefirsttheme-groupof this work. And metricalambiguity,when it does arise n tonalmusic, virtuallyalwaysaffectsonly one or two levelsof the metrichierarchy,while the higheror lowerlevelsremainconstant.At all levelsof the metrichierarchy, ulsesdo not necessarilymarkoffequalunits in termsof clock time. Rather,pulsesmarkofffiunctionallyquivalntunitsof time. Werecognizeconstantpulsesevenwhen aperformer mploysrubato.In a ritardando r an accelerando,we do not hearfractionalportionsof a beatbeingadded to or subtracted rom the successivedurations,as in Example3b.Rather,we hearthe pulse itself slowing down so that successively onger orshorterdurations arefunctionallyequivalentto the precedingand followingpulses. In otherwords, we hear a ritardando s in Example3a, and not as inExample3b. In thissense,our notationalsystemdoes not insist thatdurationsbe equally ongwith a mechanicalprecision,but rather hatdurationsof some-whatdifferingengthsare heardasfunctionally quivalent ven whilewe recog-nize theirclock-timedifferences.

All this makesthe metricyardstick measuring ystemmarvelouslylexibleyet quite precise.Throughit we can appreciatehe metricpositionand hencepartof thestructuraltatusof anynote orevent inapiece,whileat thesametimebeingawareof evenminutealterations f the tempoin termsof clock ormetro-nomic time. While we aremeasuringmusicaleventswithin a metrichierarchy,we arecapableof marking ine distinctions hat areapparentlyarbeyond ournormalperceptualcapabilities.Psychological tudiessuggestthat for isolatedtones between .02 and 2 secondslong, tonesdifferingn length byless than10%

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areroutinelyheardasequivalent.2But whatever he valueof thisfinding or iso-lated tones, it is clearly rrelevant n a musicalsetting. Constant sixteenths,eighthsor quarters t J = 120areeasilydifferentiatedrom those valuesas themetronomechanges o J = 112or J = 128 (changesof lessthan 10%).We areawareof the changein pace, but sixteenthsremainsixteenths,eighthsremaineighths,andthe metricstatusof these valuesremains.J = 90 ritardado al - - - - - - - - - - = 60a)

P j J J J J J -JJ i r 11Ione two three one two three one two three one two threeb)

one two three one two three one two three one two three one two three

EXAMPLE 3

Indeed, the metrichierarchynvitesus to use it asayardstickwhile we listento andrespondto a tonalcomposition.As a phrasemoves toward ts cadence,for instance,we expectthat cadenceto arriveon a specificpoint in the metrichierarchy-onthe downbeatof aspecificmeasure.A cadencearriving sixteenthbefore ts notated downbeatwould not greatlyalterthe clock-timelengthof aphrase,but it would surelydisturbgreatlyour senseof arrival n that cadence.That we not onlycan butquiteeasilydo makesuchresponses o the musicdem-onstratesourability o calculatequite accuratelyargemultiplesof shortpulses;indeed, the levelsof pulsesthatare the metrichierarchyn effect do thismulti-plication or us.

METER IN THE MUSIC OF BABBITT

Turning rom the tonalrepertoireo more recentmusic,let us now studytheaccentual-metricprofileof the opening passage rom Babbitt'sCompositionorFour nstrments(1948).Example4 presents he beginningof the clarinet olothatopensthe piece.In relation o almostanytonalpassage, hispassageprojectsapaucityof pulselevels. Shorterrhythmicvaluesdo not occur n extendedseries;as aresult,thesepulsesare establishedonly intermittently.At the rhythmic evels that wouldgroup these short pulses, those causes of metric accentuationthat are mostpowerful n tonal music areeitherabsentor areso irregularn their occurrences

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that they fail to layout the next higherlevel of regularityhatwould itselfbeorganizedby stillhigherregularitieso create he metrichierarchy.Harmonic-changeaccents are irrelevant o this music, as arepattern-beginningaccents.Durational ccentsarethe onlystrongaccentual actorsatworkhere,alongwithother weakeraccentuations uch as contouraccents, exturalaccents,andpitch-changeaccents.P JI II1 4 3 21 4 3

it. i.,,.2 1 4 3 2 14 3 2r 199-rin M

? 1949 MerionMusic Inc.Used by permissionof the publisher

EXAMPLE4: BABBITT,Compositionor Four nstruments,OPENING

Thus, even if there weregreater egularity f pulsesat several evels n thesepassages,anyperceived ense of meter would be relativelyweak andsubjecttobeingeasilyupset by conflictingaccentuations.But the rhythmicserializationthatgivesrise to the rhythmicvalues n this and other passagesprecludes uchregularity.The result s the absenceof ametrichierarchyn the sensethatsuchahierarchys projected by almostall tonal music. Impulsesoccur, markingofftime-points.But without sufficientregularityn anyset of impulses,therearetoo few cueswhich resonatewithina listener o enablehim or her to establishametricgrid.Thissituationhasramificationsor theperceptionof suchmusic.Thesense nwhich eventsgainsome of their structuralmeaningby occurringat particularpointsin the metrichierarchy,he measurement f durations,andthe senseoftempoitselfalldiffer rom theircounterpartsn tonalmusic.Without the perceptualmetricgridsynchronizedwith the soundingmusic,the sense in which someeventsanticipatehe beat,aresuspendedpastthebeat,or arriveon the beat is irrelevant ere. The variousimpulsesareallaudible,ofcourse,as are theirmanifoldcombinations.But without a gridof pulses,with-out thepowerfuleffectsof the arrival f anexpectedeventon apredictableime-pointorof the syncopatedplacementof strongaccentuations ff the beat,there

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is a sense in which the impulses are not moored to a larger system ofmeasurement.This rhythmicsenseis akin to aspectsof the pitchstructuringn this piece.The variouspermutations, ranspositions,and inversionsof the combinatorialtrichords hatgiveriseto the derivedsets, the concentration n averyfew har-monic intervalswithin each sectionof the Composition,he agregates formed

throughout by the combinatorial et segmentsin each of the four structuralvoices-all these areaudibleand form the substanceof pitch relations.But alltheserelationshipsxist without the yardstick f the gravitationalullof a tonicnote or sonority.The relationshipsloatin relation o eachother. Similarly, llthe rhythmicstructurings elateto one another,but not to the yardstick f ametrichierarchy.But there s a difference etweenhavingpitchrelationshipsunctioningwith-out a central onic andhavingrhythmic elationshipsunctioningwithout amet-richierarchy.Pitchesare discreteandidentifiablentities. Linearand harmonicintervalsmaintain heiridentitywhetheror not a tonic ispresent.And a givenpitchremains hatpitchwhen it recurs.But in the absenceof the yardstick f ametrichierarchy,we maynot be perceivingdurationsn the same manneras weperceive hem in musicwith a metrichierarchy.This leadsto the second ramification f nonmetricrhythmicstructure-themanner in which durationsareperceived.As discussedabove, in music thatprojectsametrichierarchywe measurelengthsof notesin termsof pulsesattheirmetric evel,not in termsof durationmeasuredbyclock time. I can conceiveofno model thatmight explainhow the mind couldmeasuredurationswith anydegreeof accuracy nd relate he lengthsof these durations ne to anotherwith-out apulseas a common denominatorof two ormore durations. n the absenceof a metrichierarchy,manyof the durationsof the piece,no matterhow metro-nomically heyareperformed,maynot be perceptiblen the mannerimpliedbytheirnotated duration.Reviewthe opening clarinetsolo of the Compositionor FourInstrumentsnExample . The durations rise rom a1,4, 3, 2 proportion,asdepictedover thescore n Example4. Butin order o perceive,say,the Dbin measure2 as half hedurationof the Ebin measure1, a listenerwould have to be maintaining six-teenth-note pulse throughout measures1 and 2. The lone opening B hardlyestablishes sixteenthpulse.And though alistenermust be aware hat after heensuingEb,the C and Db are eachshorter han theirprecedingnote, withoutdeciding(in advanceand apartfrom the impulsesin the music) to use a six-teenth-notepulse, he orshe would have no wayto measureexactlyhow muchshorterthese notes are. The sixteenth is the common denominatorof the Eb(foursixteenthslong)andthe C (threesixteenthslong).Or considerthe openingthreemeasuresof the Arieda Capo n Example5.The measure-longpulseis clear n measures1-2. But how could a listenereverknow to subdivide hatmeasure-long ulseinto twelfths(eighth riplets) o that

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that listenercould understand he duration romthe downbeat of measure3 tothe cello Abas 5/2 of that measurepulse?For without havingdecidedto sub-divide the measure nto twelfths, that J-3 ,composite-rhythmdurationthatopensmeasure3 issimplyanunequaldivisionof the measurepulse.Thefollow-ingsubdivision f themeasure- 3,- between the celloAband the clarinetC-may be half the opening durationof the measure n clock time. But withouthavingheard hatopeningdurationasa singlepulsewith asubpulseof half theduration,I canimagineno wayalistenercould measure hatrelationship.J=90 :Flute , - b

Clarinelt1^j , ji d acon V _sord.#^ R

Violin ' '

con sord.Violoncello X "J' 8 2

EXAMPLE 5: BABBITT, Arie daCapo,OPENING

It mattersnot that asensitiveperformancefAriedaCapomightdelineate5/2of a measure nmeasure1byaprecisecutoffof the clarinetnotes. The issuehereis whetherthere saconceivablemodel thatexplainshow themindcancalculatea5/udivisionof apulsewithouthavingmadethedecision o subdivide he meas-ure-pulse nto twelfths.In the sensethata listenermightjust as well decide todivide the measure-pulse nto elevenths or thirteenths, or not to divide themeasure-pulset allpendingsomecue from themusic,the decision o divide hemeasure-pulsento twelfths swholly arbitrary. herefore,n the absenceofmet-ricpulses,I believethat it is a fallacy o treatperceiveddurationsaccording otheirnotations. Forwithout that arbitrary ecision to subdivide the notatedmeasures n twelfths(tripleteighths)and then consider ive twelfthsas a unit tobedivided nhalf,how couldany istener verperceive he2:1relationship f thefirst two durations n measure3? I understand hat at the openingof AriedaCapo ifferentmetricstructures rise hatoperate ndependentlyof one another.And the measure-pulsehat is establishedby the downbeats of measures1-3mayexist on a differentstructuralplane from that that arisesby the 2:1 rela-tionshipamong the firsttwo composite-rhythmdurations n measure3. Butthat does not altermy questionconcerninghow a listenermight everlearntohearsuch asimplerelationship s the 2:1 in measure3 in the absenceof ametrichierarchyhatallows hatlistener o measure hoseunitsasunits.

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rhythms.That the rhythmicnotation does not accurately epresentthe per-ceivedrhythmic tructuressmore a reflection n thesystemof notationwe haveinherited han on the music.Theperformer, iventhewaywe have beentrained o countdurations,musthave some metricframe n orderto learn o playthe durations ntendedby thecomposer.But whereas n tonal musicthe metric rameusedbythe performersgenerallyhe metricframere-createdn the mindof the listener o perceive hemusic,in works ikeBabbitt'sCompositionorFour nstrumntsandArie da Capothis isnot the case.I defyany istenerwho hasneverseen the scoreof eitherpieceto re-create he barring f eitherone afterasmanyhearings she or she wishes.MiltonBabbitthimselfhas informedme in the contextof readings rrehearsalsof the Compositionforour nstrumentshat the metricnotationsarefor the con-venienceof the performer. ndeed, in those sectionsof the piecefeaturing lter-nationsbetweenJ = 120 and J = 80, Babbittwould havepreferred notationthathadnot yet beenused in 1948,namelyusing 3jas thedenominatorof themetersignatureorthe J = 80 sectionsso thatthe entirepiececouldbe notatedatJ = 120(Vat 120= 3J,at80).OlivierMessiaen,whose musicsurelycontrastsgreatlywith that of Babbitt,discussesa similarnotationaldilemmaconcerningmetric notation in his Tech-niques fMyMusicalLangutge4 written n the samedecadeasBabbitt'sComposi-tionforFour nstruments.Messiaen ound that when he composed passageswiththe added-value urations o characteristicf hismusic,he couldnotateandbarthem ashe pleasedonlyso longasallparts n the ensemblewere in rhythmicorensemble unison. As soon as other conflictingpartsenteredthe score, such anotationhad to be abandoned n favorof anarbitrarymetricnotation so thatallpartscouldbe coordinatedn performance.SeeExample6, whichpresents heunison openingof the sixth movement fromMessiaen'sQuatuorpourafin dutemps ndan earlierappearance f the same tune in an ensembletexture n thefourthmovement.Themetricallyreenotationof thesixthmovement isfineforensembleperformance.But the violinistand cellistmust also learn he tune instrict2/4 in orderto staywith the clarinetistn movement 4. Imagine rying operform he passage rom movement 4 wereit notated as in Example7. Nev-ertheless,t ismyexperiencehatthemelodyis heardbylisteners hesameway nmovements 4 and 6-that is, the listenerprobablyhears he fourth-movementpassage sin Example7.

In conclusion,I believethatrhythmicnotationsof the Babbittcompositionsand of manyothertwentieth-centuryworkscannotreliablybe consideredaccu-raterepresentationsf the perceivedmetricstructureof thismusic,andcannotnecessarily e consideredaccuraterepresentationsf the perceiveddurationsofindividual ones. Attemptsto explainor analyze he rhythmic-metrictructureof this or muchotherposttonalmusicon the basisof thesenotations nsteadofon the basisof the perceptionof these valuesmayverywell be a misdirectedstudy. I am not surethatI cancontributeat this time to an approach o these

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issues that does not relyon assumingsuch a one-to-one relationshipbetweennotatedsymbol and perceivedduration.But I am convinced that until we astheoristscan createa model thatsolves thisproblem,we willhave failed o sys-tematically ddresstemporalaspectsof this music n amanner hat accordswithourhearingof the music.

Decide, vigoureux, granitique, un peu vif (.h176 env.)1 ? ^Iq 6r-r?b lJ 1r I Iif

SIXTH MOVEMENT

von(doublcd thrcee Poctaves lower

h', , \1\ IClar J J ipp ? 1942 DurandS.A.

FOURTH MOVEMENT Used by permissionof the publisher.Theodore PresserCompanySole RepresentativeU.S.A. and Canada

EXAMPLE 6: MESSIAEN, Quatuorpourafindutemps

r I U J fv tF I e bi2 i17 _ 1

^P< LJ |l6 Ld J |4 TTJ li JIJ ;7- l4? 1942 Durand S.A.Used by permissionof the publisher.Theodore PresserCompanySole RepresentativeU.S.A. and Canada

EXAMPLE 7

sf4 66r b bh L11 r t Zj -

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128 PerspectivesfNewMusic

NOTES

1. TheRhythmsof TonalMusic (Carbondale:Southern Illinois UniversityPress,1986).2. SeeC. D. Creelman,"Human Discrimination f AuditoryDuration,"inJournal ftheAcoustical ocietyofAmerica34 (1962): 582-93, and LeonardDoob, PatterningfTime New Haven: YaleUniversityPress,1971).3. DavidLewin,"SomeInvestigationsntoForegroundRhythmicand MetricPatterning," n Music Theory:pecialTopics,d. RichmondBrowne (NewYork:AcademicPress,1981), pp. 101-37. The problemwas firstproposedbyJeanneBamberger.4. The TechniquesfMy MusicalLanguage, rans. John Satterfield(Paris:AlphonseLeduc, 1944), chapter7 (pp. 28-30).

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Notated and Heard Meter - Lester

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