832766-stepwise continuity as a structural determinant in györgy ligeti's ten pieces for wind

7/28/2019 832766-Stepwise Continuity as a Structural Determinant in György Ligeti's Ten Pieces for Wind

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SThEWISEONTINUnIY SA

STRUCTURALEIIEMINANT

INGYORGYIGEI'i'S

TENPIECES ORWINDQUINiET*

CHARTLES.MORRISON

T HEERM "CENTRIC" is often used to characterizemusicwhich, althoughnot structuredaccording o the principlesof conventional,major-minor

tonality, snevertheless eard o be organizedaroundaparticular c (pitchclass)or pc complex.While some non-tonalpiecesmanifest ntricateand systematicdeterminantsofcentricity,otherpiecesarewithoutcomplicatedhierarchicalsys-

tems of relationships, elying,rather,on means of centricitywhich mayseemsimpleand basicby comparison. n suchcases, dentifying he structuralpointsandthe sourcesof motivationbetweensuchpointsis of criticalimportance.

In conventionallyonal musicwe maylook to the cadences orpointsof har-monicstability nddefinitionof key.And, althoughcadences onfirmstructural

*Anearlier ersion fthispaperwasread ttheSeventhAnnualMeeting ftheSocietyforMusicTheorynPhiladelphia,ctober,1984.



Ligeti's enPiecesorWindQuintet

points harmonically,we are often awareof tonal destinations before rrivalbecause of the systematicrelationsexplicitin directedharmonicprogressions

leading o those structuralunctures.'In centricmusic,cadencesalso function

structurally, ut eventsprior o suchpointsarenot necessarily directed" n thetraditional ense. In fact, it is often not easyto determinewhat the goals are

beforewe reach hem, and when we do reach hem we arecognizantof arrivalmorethroughconditionssuch asagogicaccent,dynamicexposure,andrhyth-mic caesura, han throughspecific unctionallydirectedprogressions. n these

instancest isonly after he locationand functionsof the piece'sstructuralpoints

are realized-a processwhich most often involvesexaminationof the musicalmaterial ut of itstemporalcontext-that we candeterminehow the structural

"pillars"areconnected. That is, once the piece is familiarand its structural

pointsknown, we cananticipatehose primarypoints(we "know wherewe are

going") within the context of that particularpiece-a condition I referto as"contextualanticipation,"and one which is otherwisemissing n light of theabsenceof traditionalonalprinciples.

Frequently, he materialinkingsuch structuralpoints,while not intrinsicallydirectedasto anapplicable ystemof relationsas n diatonictonality),consistsof

contextuallydirectedstepwisemotion. Thatis, whiletheearinevitably onnects

contiguous(andeven non-contiguous)pitchesand pcswhich are in a stepwiserelationship o one another,such connectionsareparticularlyignificant,andindeed most palpable, when the stepwise event (systematicallyarticulated

throughspecified riteria utlinedbelow)connectspointsotherwisearticulated,established, nd thuscontextually nticipated spointsof"centricorientation.In suchcases,stepwisecontinuitymaybe heardascontextuallydirected owardsa discerniblegoal, appreciablen lightof a known structuralramework,ratherthan

throughtendencies ntrinsic o the

progressiontself.

The presentstudywillfocus on contextuallydirectedstepwisecontinuity,asdescribedabove, as it functions in the expressionof pc centricity n GyorgyLigeti'sTenPiecesforWindQuintet 1968)-a workfeaturingmanydisparate nd

complex textureswhich, in and of themselves, impartgesturaland emotive

qualities. n the courseof thispaperwe willexamine ivepiecesfrom the Wind

Quintet, treating achas aseparate ontextualentity.2In thestudyof eachpiece,a firststep will be to establishthe identities of discerniblestructuralpoints,definedas sonoritiesclearlyarticulated t the beginning(i.e., structuraldepar-

ture points), pcs or pc complexesexpressed emphaticallyat or near the end(structuralrrivalpoints),and/or nteral cadencepointsdefinedbyfactors uchasrhythmiccaesura, ests,and othersurface ndicators f phrasecosure. These

junctureswill then be viewed as to centric,prolongational, r other functions,and as to the meansbywhichtheyareconnectedto determine fand how inter-

veninglinearprogressionsmaybe perceivedascontextuallydirected.It is important o stressat the outset that not allpitchandpc stepsuccessions

aresignificant;ather, nferredcontextuallydirected inearprogressionsmust, as

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PerspectivesfNewMusic

alluded o above,be comprisedof pitcheventswhicharesystematicallyxposedaccordingo stipulateddevicesand thus areperceptually erifiable.Forexample,

pitcheventscomprising tructural inearprogressionsmaybe emphasizedrela-

tive to others n closetemporalproximity hroughdynamicpunctuation,regis-tralexposure placinghemin apotentiallynferable utervoice),and/or imbralassociation. n other situations,systematicpatternsof pc unfoldingmaythem-

selvesbe consideredample or the inference f linear onnection.The criteriaor

assertionof primarypcs and pc complexesand for inferenceof directed inear

progressions are, however, specific to each context and will therefore be

explained n greaterdetailas eachpieceis studied.

Wewillbeginwith the fourthpiece,whichmaybe characterizedtexturally s

"soloistic,"an arrangementn which one instrument s heard o be morepro-nounced than its associates. n this piece it is the flute which is distinguishedfromthe othersthroughheightenedregistral, ynamic,andrhythmic xposure.One hearsmeasures -9 and 25-27 asimportant adences n the lowerregister,and measure19 as a cadencepoint in the higherregister.Otherbreak-offpointsin theupperregister-measures , 11,16,and 17-are somewhatexposedbecause

of abruptregister hiftsandare huspotentialelements n linear ontinuities n abroader cale.

Keeping n mind the firstcadencepoint in bars8-9 asa goalof motion, we

may perceive he flute and to some extent the clarinetand bassoon as contex-

tuallydirected owardthatpoint. The flutepart,forexample, s generally on-structedof successivewo-note oscillations, he upperand lower notes of which

maybe heardto defineindependent inearizations.Although the clarinetpart

opensin arelatively tepwise ashion,before ongit also takeson a bilinear truc-ture. Example1shows the flute and clarinetparts rom the scorewith the sug-gestedlinearizationsn the flute above the scoreandin the clarinetbelow.

Four details n Example1 arenoteworthy. First,the two streamsof linear

activity n the opening two barsof the flutemaybe conjoinedto forma largerprogression onnectingD5, the lowerpitch boundaryof the lowerstream,to

F#6, the arrivalpoint of the upperone.3 The linkingof these simultaneous in-earizationss achievedby the pivotalC6, the arrivalpoint of the lowerstreamanddeparturepointof the upperone, asindicatedbythe dotted beam.Second,theouterextremities f thislargeprogression,.e., D5 andF#6,maybe heard ocontinue to the two streamswhich

begin midwayn bar 2. The connectionin

eachcase saregistrallyisplaced emitone,D5 "ascending" o DM4n the lower

stream,and F06 descendingto F5 in the upper one.4 In the example, these

pitch-class tep connections areslurred.Third, while the flute partterminates

abruptlyat the end of bar6, the linearizations ffectedby its bilinear tructure

maybe heardto continue in the clarinetpart,as suggestedby the arrowfrombars6 to 7. The linearprogressiveendencies, nitiatedbythe flute andclarinet ttheonset of the piece,arebrought o aconvincing lose n measures to 8 bythe

160



Perspectivesof New Music

(a) Imm. 1 2 6 8

i= = =

-(cadential dyad)

?C9 R tI

-clarinet

(b) imm. 1 2 9 11 16-17 19

EXAMPLE 2: PIECE NO. 4, LARGE-SCALE STRUCTURE

The next contextuallyanticipated adencepoint is in measure19, where the

upper-voiceactivitysbrought o anabruptbut effectiveclose on the minorsev-

enth D6-C7 (clarinet ndfluterespectively).The dyadcomprisedofpcs D and

C, particularly hen expressedas a minorseventh,is now beginning o takeon

primary ignificance s the "central"pc complex.The piece up to measure19

revealsa prolongation f the D-C seventh from D5-C6 at the openingto D6-

C7 at bar19, with the D4-C4 majorsecondat the internal adence n bars8-9

functioningas an intermediatecomponentof the large-scale rotraction.Cog-

nizant of a new goal, we maystudyeventsleading o bar19forpatternsof con-textual ineardirectedness.

While thepitch-class tepsuccessionsD5 to D#4andF#6to F5, notedabove,

operatewithin the phrase-length rogressiono measure9, the changeof regis-terand, moreimportantly, he change n direction n measure2 haveimportantimplicationsat a broader evel of structure. There are two registral"planes"operating n thispiece, the upperone beingabandonedabruptlyby the shift inmeasure2. F#6 in that bar-i.e., the arrivalpoint of the top streamof linear

162




activity n the upper plane-links up registrallyo thatsamepitch in bar9, theopeningof the secondphrase.The essentialmotion in the latter akesoff fromthisreestablished igh pointand consistsof the progressionromF96to C07 inmeasures -11, to D7 in measures 6-17,and to Eb7 n bar19,the latterfalling oC7 at theendof theupperregistraltream,also n measure19. The arrival n D7in bar17 is accompanied y C6 in the clarinetwhile, as noted above, the flute'sfinalC7 occurswith D6 in the clarinet(thereby ffectinga voiceexchange).5 Thedetails of the large-scale rolongationof the D-C seventh, culminating n the

upperregister f measure19, aregivenin Example2b.

Concerningmeasures19-29, the finalphrase,all activity akesplacein thelowerregistral laneand the flute(thefeatured nstrument husfar n the piece)is now dynamicallyquivalent o the otherinstruments;hese measures reper-hapsbestunderstoodas a type of "coda." Rather hanreaffirminghe primacyof the pc complexcontainingC andD, the pieceends in a contextually"open-ended" fashionwith a C#4-D#4 dyad (asemitonehigherthan the close of thefirstphrase).The functionof thiscollection sunequivocal n lightof the open-ing of the next piece:C04and D04 encirleD4, the pitch centerof that piece,reiteratedn four-partunison in itsopeningbar.

The fifth piece, and its connection to the sixth, is the subjectof the next

example.As noted above, number5 beginswith an intensefour-partunisonreiteration f the pitchD4, afactorwhichimmediatelymbues hatpitchwith asense of primacy. n fact,no other eventis quiteso potent andit is not clear nthe preliminaryeadings f the piecehow sucha center smaintained nd where

(orevenif)pitchorpc closureoccurs.Wehaveapc centerstatedexplicitly tthe

beginningbut we appear o have no arrivalpoint (see the abruptclose of the

piecewith the indication"stop asthough tornoff'). The pc content of number

5 unfoldsaccording o fourdifferent welve-noteorderings,coincident,forthemost part, with the four main formalsections of the piece as delineatedbychanges n tempo and dynamics.In the firstand thirdsections, some pcs are

repeatedbeforealltwelvehavesounded, the twelfthpc signifying he endof thefirst ectionand, in thelattercase,the beginningof the fourth.6Thesecond andfourthsectionscontainno suchrepetitions; nce the twelvepcshavesoundedineachcase,the sectionis over.

Example3 illustrates he four twelve-note orderings, he firstand third ofwhich are ndicative f the

registrallypecificpitchesn the

piece;the second and

fourth, however, arepc representatives,ompressed nto one octaveto revealthe stepwisedispositionof theircontent.7 As can be seen from this mode of

representation, he first two orderingsunfold a wedge-like patternrevealingstepwisecontinuities n an ascendingand descendingdirectionconcurrently.The finaltwo orderings,on the otherhand,aredescending tepwisescalarpat-terns.Twotypesof stepwisecontinuityare husemployed n thispiece;thecon-

cept of directedness s it pertains o theseorderings,particularlyn connectionwith the earlyestablishedprimaryD4, however,hasyet to be explained.

163



164 PerspectivesfNewMusic

I(mm. 1-8)

II(mm. 8-9)

(mm. 9-12)

?k>J1 j>3r J i,

r io t 66 'i 9jM 11

'1

(mm. 12-13)

EXAMPLE 3: PIECE NO. 5, TWELVE-NOTE PATTERNS

OF PITCH-CLASS UNFOLDING

Asnotedearlier,hepitch D4-having been "encircled"bythe finalsonorityof the fourthpiece-is reiteratedn four-partunison in the openingmeasureof

thefifth,thusestablishingtsroleas the referentialpitch.The expandingwedge-

patternof pc unfoldingwhich followsrepresents motion awayfrom the D4

center.Although the final formalsection (asdefinedby tempo and dynamics)

beginswithEb3-the twelfth memberof the thirdpattern-the final welve-note

orderingactuallybeginswith thepcD (specifically 6); the descending tepwisepatternwhichfollowshasEb4as its finalpitch. Giventhe openingemphasisonD4 and the departure rom D6 in the fourth pc pattern, the final stepwisedescent sperhapsbestunderstoodas motion towardD4 (i.e., therertrally pe-ciJic itchcenterof the piece)-a goal not quiteattained.Althoughthe finalEb

completes the twelve-note aggregate,the piece remainscontextually open-ended as

regards c centricity,not unlikethe fourth

piece.And,as in the caseof

the latter,we mayonceagain ook to the nextpieceforpitch/pc"closure."

Havingbeen approached rom above in the finalorderingof the fifthpiece(allowingfor pc compression),the contextuallyanticipatedD is approachedfrombelow in the openingof the sixthpiece(where t occursas D5-an octave

higherthan the registrallypecificpitch centerof the previouspiece). The firstfour(unordered) itchesof number6 areA#4, B4, C5, andC#5(seeExample );thefifthpitch sD5 andis, appropriatelynough, the firstnote of the oboe-the



Ligeti'sTenPiecesforWindQuintet

featured nstrument n thesoloistic ixthpiece.D5, representing cclosurewithrespect o the fifthpiece, is thusemphasized hroughtimbral,articulative, nd

dynamicexposure.8

No. 5 No. 6

m. 13 mm. 1 2registrallyt I . b . 4-~ ~ ~ ~ ~ 1 .2 Jl, Il.~?1

speci icpitches I g. sO P, li' . eI

1

:I '^-(oboeI . entry)

L bJTJ KI |I-'-I

classes L j fIV

EXAMPLE 4: PITCH-CLASS CONNECTION BETWEEN PIECE NO. 5 AND PIECE NO. 6

Like the fifthpiece, the ninthopens with a unison reiterationollowedby a

wedge-likepatternof pc unfolding;here, however,the texture s one of a strict

three-voice anon. An overlap o the nextpieceplaysanimportant ole,againasin the fifthpiece, although n this instance t is not one of pc closureor delinea-tion of pc centricity.It is, rather,one of simpletwelve-notecompletionas the

canonunfoldsonly nine of the twelvepcs. The ascending tratumof number9unfolds the fourthEb-Ab(seeExample5a), a detail to which we will return nthe studyof the tenth piece. As indicated n Example5b, if the lower stratum

wereextended, the threemissingpcsoccur.These three,as well asthe originallowerstratumof the ninthpiece,arestatedat thebeginningofthe tenthpiece,asindicatedon the bottom systemof Example5b. In this sense, the tenth piececompletesa twelve-noteaggregatenitiated n the ninth piece although,assug-gestedabove, the overlapdoes not fulfilla closural unction in a pc centric ash-ion (as n the connectionof pieces5 and6).

The tenth piece of the Quintet has certainsimilarities o other piecesdis-cussedearliern this paper.Forexample, t resembles he fifthpiecein that its

pitchmaterials based o some extent on twelve-notepcunfolding n both linearand wedge-like patterns,although aggregate ompletion is less systematically

appliedhere than in the earlierpiece. Number 10 also has similarities o thefourthpiecein that it featuresone particularnstrument, he pitchdistributionof whichishighlydisjunctormultiregistral;ere t is the bassoonwhich ishigh-lightedin this fashion.One aspectof the angularbassoonpart,to which prin-cipalattentionwill befocussed n thisstudyof pc centricity nddirectedmotion,concerns the fact that pitches in the uppermost registerarearticulatedand

165




(a)

L No. 9

(b)

No. 10

e ended lower stratum:

L 4 4r. f M L i

mm. 1 2 / 3bassoon:

9: . I I^'r vlr;: ^

EXAMPLE5: WEDGE-PATTERNOF PC UNFOLDING IN NO. 9 AND TWELVE-NOTE

AGGREGATECOMPLETIONFROMNO. 9 TO NO. 10

exposedin such a wayas to be perceivedasconnected, therebyeffecting inear

stepwisecontinuityover alarger pan(i.e., on ahigher evelof structure).Before

we beginsuchastudyof pitchrelations,however,itwillbe helpful o establish

formalplanforthe piece.Two main sectionsmaybe discerned, eparated ythe extendedpauseof bar

12(please efer o thescore).Thea-section onsistsof two phrases, achofwhichcomprises disjunct egment(i.e., measures to 5 in thefirstphraseand6 to 7 in

the second)followedby a conjunctsegment.The b-section s more continuous

than the openingbut mayalsobe divided nto two phrases.The first s entirelydisjunct,the second comprisedof a disjunctsegmentfollowed by a conjunct

segmentwhich concludes he piece.The two disjunctphrases,althoughnot sep-aratedby a conjunctsegmentas in the a-section,are neverthelessseparatedbywhatI have termeda "phrasedivider." This is simplya briefdisjunct ragmentin measure14 which, like the conjunctsegmentsin the a-section,occurs at a

much lowerdynamic evel than the disjunct egmentswhich frame t. The twomain sectionsarealsodifferentiateddynamically.Forexample, n the a-section,the disjunctsegmentsarefrtissimo while the compressedportionsarepiano.In

the b-section, the disjunctsegmentsarefrtissimo (fi) while the phrasedivider

and finalconjunctsegmentarepianissimo,ivingthe b-sectiona widerdynamic

range.Regardingpc centricity,as in the pieces examined thus far, we must first

166




establishthe most structuralpoint(s) in the piece. Upon hearingnumber10(evenfor the first ime), one is surelycompelledto hearthe D5 of bar15 astheultimate arrivalpoint; it is the only time in the piece that all five instrumentssound at once, with four of the fiveinstrumentssoundingthe emphaticD5. Ifwe take his note as the pitchcenter,we mayexamine he piecefromthe start osee if the primacyof that pitch (orpc) is established arlier nd, if so, how the

variousoccurrences reconnected. If there are no suchintermediate tructuralarrivals n D, it remains o establishhow the eventsleading o bar15 relate o

and arecontextuallydirected towardthe importantculminationpoint in that

measure.In highlydisjunct extures,such as the bassoonpart n thispiece, pitches n

the registral xtremitiesare most readilyperceivedas they delineate the spacewithin which allactivityoccurs.And, in this piecewe will be most sensitive o

pitches n the register losest to the anticipated oal, D5. With this in mind, we

mayperceive he bassoon'sEb4 n measure3 asan importantpitch event. Not

only is it accentedagogically elative o the pitcheswhich precedeit, but it isstressedthroughalackof registral reparation;.e., there areno pitchesprior oEb4whichliein a

(registrallypecific) tepwiserelationshipo it. While this isalso

the casewith B2 in measure1andA3 in measure3, the registersn whichthose

pitchesoccurareimmediately upersededby higherones. The registernitiated

by Eb4, however, is not relinquished n this manner;rather,it remains the

uppermostone in which pitches, although non-contiguous,mayneverthelessbe heardasconnected,effectingapredominantly tepwisecontinuity oward he

goal, D5. (The fasttempo of the piece is an important actor n the perceivedconnection of pitches which are not temporallyadjacent.)The pitch eventsreferred o are F#4in bar 3 andG4, F4, and Ab4in bar5, Ab4beingthe high

point of the firstphraseand the culminationpoint of the ascending uccessionthus far n the piece(seeExample6).The ascending ourth, Ebto Ab,in the firstphrasemaybe perceivedas con-

textuallydirected o the D5 of bar15;in this sense it is not merelya successionbut rather "progression. 9Itsprogressive uality s a resultof itsmovingcloserto the inferredgoalin both temporaldistance i.e., horizontally),andintervallicdistance i.e., vertically).As a resultof the inferreddirectedness f the openingascending ourth, we remainawareof the sudden breakingoff of that registerafter he Abof bar5 andmay expect,withinthe contextof thispiece,aresump-

tion of the upper-voice inearprogressionat some laterpoint. That Ab4is thefirstpitch in the uppermost register n the second phrase(measure7), again

unprepared egistrallyi.e., within the secondphrase) s, I feel, not entirely or-tuitous. The progressionnitiated n the opening phrase s thus resumed n thesecondphraseandcarried ne semitonehigherto A4 in bar 7 (the latterbeingpunctuatedby pitches n threeother instruments!).Example6 shows the total

pitch content of the first two phrases(the a-section)expressed n pitch-classterms for illustration f the stepwiseandwedge-likepatternsof unfolding;the

167




temporalorderings

maintained,apartrom those with a

/\which

indi-cates he two havebeen reversed o facilitatenference fcontinued"ascending"or "descending" motion. The top staff of the exampleincludesonly those

pitches in the upper-voiceprogressionand are here notated in their properregister.

(first phrase)

mm. 1

(a)

(b)

(c)

(second phrase)

mm. 6 7 7-11 (15)

I

(bCK9: :% #j7(registral preparation for continuation

of upper-voice structural progression)

EXAMPLE 6: PIECE NO.10,

MM. 1-11(a-SECTION),

SHOWING UPPER-VOICE

STRUCTURALPROGRESSIONAND PATTERNSOF PITCH-CLASSUNFOLDING

WhiletheA4 of bar7 isnot thehigh pointof the secondphrase-the ensuingrapid lourishextendsup to E5-in a "structural" ense it is the highest.The

primary ventsthus far n the pieceoccur in the uppermostregisterof the dis-

junctsectionsmarkedirtrnimo.The conjunct ectionof thefirstphrase,atpiano,servesonly to return o the openingregister. n the secondphrase, he conjunct

section, also atpiano,againoccursafterthe high point of the progressionhasbeenarticulated ndthusservesasimilarly on-structural ole.It mightbe heardas a type of "postcadential xtension" (the previousarrival n A4 being per-ceived as a "half-cadence"), ervingmerelyto "prepare"us registrallyor the

anticipatedcontinuation of the structuralascent in the second section of the

piece(seeExample6c). Thattheconjunctsegment n measures -11 snot one ofstructural import seems substantiated by the fact that the E5 of bar 11is

168

5-6 . (15)



Ligeti'sTenPiecesfor WindQuintet

approachedn ahighlytentativemanner(note the diminuendoopianissimo,hedecreasingevel of rhythmicactivity,and the esitandondication n the score).

Whereas he a-section scomprisedof two clearly rticulatedphrases, he firstof whichcontributes he openingfourthof the upper-voiceprogression ndthesecondextending t byasemitone,the b-section s lessclearlydividedinternally.As noted above, itstexture s morecontinuous,facilitating steadydriveto theultimatearrivalpoint, D5 of bar15. As regardshe fundamentalprogressionothatpoint, the sectionopenswithAb4andcontinues o encircleA4 (thehighestpointof the progression eached n the openingsection), the latteroccurringn

measures13 and 15. Upon reaching he second A4 (measure 5), an immediateascent eads o the goal.These two encirclements,he finalapproach o D5, andthe patternsof pc unfoldingare llustratedn Example7.10The unfoldingofpcsin the b-section s, as indicated n the example, esssystematicallyrganized ncontinuous linearpatterns han the a-section. It is paradoxical,however, thatthe pc stepwise ragmentshat areapparent redirecteddownward(asopposedto the upper-voice tructural scent).

mm. 13 14

upper-voice progression:

(a)

PC

(b). ?1 -

unfoldin 1 -

* = encirclements of A

(final structualmm. 14 15 ascent) 16-21

r/O~~~~~~~~~~~~~(-

(a)L

(b) [

I_7 r 74.

I:m7, nt -iq19~~~~~~~; Ft . ,4-, *',1o

vi registrally specific conjunct segments:(c) s

(recalls register of opening) f-- '

EXAMPLE7: PIECE NO. 10, MM. 13-END (b-SECTION), SHOWING UPPER-VOICE

STRUCTURALPROGRESSIONAND PATTERNSOF PITCH-CLASSUNFOLDING

In the initialreadings f the piecewe perceived he D5 in bar15 asthe moststructural ventin the pieceand thuscharacterizedt asthe pitch center.And,on closerinspectionwe observed how a large-scaletepwiseprogression pansthe aandb-sectionsof the pieceto arriveatthatpoint. On amorefundamental

169




level,the

progressionmaybe heardas two

overlappingritonesas indicated n

Example8a. The pointof overlap nvolves he semitoneAb4-A4, articulatednthesecondphraseof the a-sectionas the extensionof the initialascending ourth,andin the b-sectionas the connection between the opening pitchto the begin-ningof the finalascent n bar15. At a stillmorebackgroundevel, the progres-sionspansamajor eventhEb4-D5. In pc terms,the overallprogressionmaybe

thought of as a chromaticneighbour motion to D, the minor second beinginvertedand filled n asa majorseventh(seeExample8b). It is interesting hatthe representation f an underlying econd as a surface eventhis the primary

techniqueused throughout the pieceat the most foreground evel: where theunfoldingofpcs occurs n astepwise ashion which sfrequent), t isexpressed tthe surface sadisjunct uccessionof sevenths.

mm. 3 5/7 (7)13 15 (15)

/l)a-section: I I

(a)

(b)

b-section: I

large-scaleprogression: j _

-A ,- ,^^^L I I-

EXAMPLE 8: PIECENO. 10, LARGE-SCALESTRUCTURE

Only the status of the finalconjunctsegmentof the piece remainsunspec-ified.Given the emphaticarrival n D5 in bar15-the structural adenceof the

piece-this finalportion sperhapsbestunderstoodas apostcadential xtension,not unlike hat whichoccurredatthe end of thea-section although hefunctionof this finalsegmentis not one of registral reparation).The two mainformalsections of the piecearethus balanced,eachconcludingwith a non-structural,

registrally ompressed egmentata low dynamic evel.The function of the finalCO s somewhatambiguous: t could be a finalexpressionof the pc C whichoccurred n the upper-voiceprogression,not in its "proper"place(betweenBand D), but simultaneouslywith the finalD5. Or, perhaps t serves o balancethe piece registrally: ust as the extension at the end of the a-section fore-shadowedthe register f the structuralgoal, the finalextensionrecalls he regis-terof the openingof the piece.

170




The balanceof thispaper

will be devoted to a detailedanalysis

of the first

piece, one which featuresan "ensemble"texture(asdistinctfrom the soloistictexturedefinedearlier).Thatis, the overall extureatanygiventime is the com-

positeof al instrumentalparts,the shifts n these homogeneoustexturesoften

markingnew formal ections.In the firstpiece,forinstance, he scorerevealsheextremeindependenceof parts nteractingn a rhythmically omplexmannerwhichcharacterizeshe openingsection,measures -16,and thegreaternterde-

pendence or subgroupingof parts,generally essactive in nature, which dis-

tinguishes he finalsection.

Asregardstructuralpoints,the openingfifteenmeasuresgiveus littleto holdon to, asthe sonoritiesare n aconstantstateof flux.The emphaticunisonC inbars16-19, while indeed compelling,grows into a more complexand intense

sonority.The latter sultimately upersededbythe final oftand almostpeacefuldyad.The perceived ffect s one of resolution nto the latter(please efer o the

score).Wemayassume he primacyof the finalC5-D5 dyadas both the central

pc complexandthe ultimatearrivalpointandproceedto substantiatehischar-acterizationwith astudyof the events whichprecede t.

In the first welvebarsof theopeningsection,each nstrumentalpartconsists

of asuccessionof linearpitch pairs eparatedby rests(pleaserefer o the score).Taking he altoflutein measures2-4 as an example,the initialpitchof the first

pair,B3, beginsatpianssimoand isgraduallyncreaseddynamically.At or nearthe mezzoforte eakof the crescendo,03, the secondpitchof the pair, s articu-latedand isaccompanied yadiminuendo acktopianissimo.At thispointabriefrestoccursand the pattern s repeated.Although the peaksof dynamic nten-sification nd corresponding itch change n the fiveinstrumentsoccur in rela-

tivelycloseproximity,asforexample n measures3 to 4, theynevertheless o so

independentlyof one another.Thisresults n a

highlyfluctuantharmonic abric

and complex polyphonictexture;it is in consideration f this texturalarrange-ment thatextended inearcontinuitieswill be revealed.

The vertical onorities n the section underdiscussion-that is, those effected

byeachindependentpitchchange-span the range rom D3 to C4. The highestpitchesof successive erticalities,egardlessf instrument,maybe heardascon-

nected,resultingn aderivedtop voice. The secondhighestpitchesmaybesimi-

larly onnectedto formasecondvoice,andso on. The five-voice inear tructurewhichresults s illustrated n system(b)of Example9. The horizontalanddiag-

onallinesand arrows race he various nstrumentalpartsas theirpitcheschangeposition n successive erticalities.ALegendof symbolsused isgivenasthe first

pageof Example9.)

171




LEGEND

I.S.W.U.N. = incompletesemitone/whole-toneupperneighbour

I.S.W.L.N. = incompletesemitone/whole-tone owerneighbour

u.n. = upper neighbour

l.n. = lowerneighbour

e.p. = embellishingpattern

[forsystem(b)specifically]:

(a) (b)

-same instrument;sameposition in verticality;with parallel lash, as in (b),

pitchesseparated ya rest

(c) (d) (e)

9 W \ 7- t 9- b

9:

-same instrument; hangeof position nverticality;withparallellash,as in (d),pitchesseparated y arest

_-in (e), no pitchchange,but positionchange n verticality

[forsystem(c)specifically]:

- - = correspondso (a)and(c)above

yi f = correspondso (b)and (d)above

r^[ | = secondpitchin a differentnstrument;secondpitchoverlaps he first

EXAMPLE 9: PIECE NO. 1, OUTER-VOICE PROTRACTION, FIVE-VOICE

STRUCTURE, AND LATERAL VOICE-CROSSING PROGRESSIONS




ii

(b)five-voice tructure:mm.2 3 4 5 6 7

I I I I I I I I I I I I I I I II I II I I I I I I I I I

(c)lateral oice-crossing rogressions:10* 11

EXAMPLE (CONT.)

T T f f '4Pr \ -VI:t 7 v'

r f

r- Jognm_

r

173

Wl

W

I

I




7,. I~~ ~~~~~~.. .. !

I m11 12 13

mf

',i? i (e.h.). _,_/ .....-~... .J. -/,~.c.)

2Ti'- -y ff

mfhrn.

mf

mf

~fA A A +\f(bsn.)

I'*^~~~~~~~~~ ~mf

b '~~~~~~~I,~~N

-" b'

/ - ^ '̂'---'-"-'-̂ 'EXAMPLE9 (CONT.)

175




[seesystem (a)i

below]

13 14 15 16 (b-section) 17

.... I I I

20 21 22

.--,1

9: II

I lT. ^g.o ?Io,E.. o E" A*-'.D1

(bsn )l H- : |

|t-7_

",* * , "' "',*

.,n,- -.,-., i

9: ' i II

-section b-secti on

_ 141Ip.t. .n.

p.t. I.n.

EXAMPLE (CONT.)




As levels andii ofsystem(a)indicate,

D3 and C4 areestablished ndmain-tainedin the outer voices as pitch boundariesof this section through simple

neighbourmotion; lowerneighboursonly, in the caseof C4, andupperneigh-boursonly, in the caseofD3. D3 and C4 thus definethe texturalspace ofmeas-ures 1-14) within which all linearactivityoccurs, particularlywhen the twoextremities ccuradjacento eachother as n measures , 9, and 11.Thesewillbereferredo asprimary ccurrenceswhile instances fC4 occurring lonearecon-sideredsecondary.The outer voices in particular reexamplesof one type ofextended inearcontinuityandmaybe consideredhierarchically oreimportant

thanthe threederived nnervoices ortwo reasons: he outervoicesare hemostreadilyperceived,and in this case the two pitches protractedn these voices-

apart rom definingtexturalspace n the a-section-have specialsignificancenthe overallpitchstructureof the piece. Concerning he latter,even at thisearlystagewe can infer a pitch-class orrelation etween the openingminorseventhdefinedbythese outerpitchboundariesand the major-second yadwhichcon-cludes the piece. To establish he meansby which we aredirected rom one tothe other, however,requiresurtherinquiry.

Therelatively arrowambitusof the fivevoices ngeneralandthe outer voices

in particular, esults n a somewhatstaticviewof this section, savefor the briefinstancesof directedmotion offeredby the dynamicallyluctuantpitch pairs.More extended examplesof directedmotion may be discernedby invokinga

procedure term "lateral oicecrossing."The resulting inearcontinuitiesaddanotherdimensionto the protraction fD3 and C4-a dimensionwhichwillbeshown to bemore"dynamic" han theouter-voicemaintenanceustdescribed.

Lateralvoice-crossingevents arestepwiselinearizationswhich traverse heaforementioned five-voice structure, thereby connecting the two pitchextremities in a crosswise fashion as indicated on

system (c)of

Example9.

Because he outer-voiceprotractiondescribedaboveestablishesD3 and C4 as

extremities, hesepitches maybe perceivedascontextuallyanticipated oalsofthe lateralvoice-crossingvents. In this sense the lateralprogressions recontex-

tuallydirectedwithin the a-section.The actualpitch connectionswhich effecttheseextended inear ventsmayoccur nasingle nstrumentorfrom one instru-ment to another.When asingle nstrument s involved,the two pitchesmaybeconnected in a legatoashion or they may be separatedby a brief rest. (Theseconnectionsaredifferentiatedgraphically ccording o the Legend given at the

beginningof Example9.) When the connectioninvolvestwo instruments hetwo pitchesof the connectionoverlapnd in most cases he new pitchincreases

dynamicallywhile the firstpitch of the connection decreases;a "transferof

energy,"so to speak,occursfromone instrument o the otheras aresultof the

overlap.Asindicatedon system(c)of Example9, eachoccurrence fD3 maybe heard

as thearrivalpoint (orgoal)of aninferred ateralvoice-crossing rogressionromC4 and, in turn, as the departurepoint for an ascending ateralprogression o

177




C4. Eachof the occurrences fC4 maybe heardas the arrivalpointof aninferredlateralprogression, xceptin measure8. Also, those occurrences f C4 adjacentto articulations f D3-referred to earlier sprimary ointsof arrival-doserve ointroduce ateral ontinuities o D3 as does the secondaryoccurrence n bar5.The secondaryC4 of measure8-i.e., the only one notapproachedby a lateral

progression-appropriatelyails o initiate uchanevent.These inferred lateralvoice-crossingprogressions, then, are examplesof

extendedstepwisecontinuitieswhich aretruly dynamic n theirexposureandmaintenance f thepitchboundariesD3 andC4-dynamic in the sense thatthey

involve contextuallydirectedstepwise connections acrosshe five-voicefabricthereby inkingone pitchboundary o the other. In thissense,the lateral vents

complement he more staticouter-voiceprotraction escribed arlierwhereeach

pitch boundarywasmaintainedindependentlyf theotherthroughsimpleneigh-bourmotion.

However, while theseinferred ateral vents have been characterized s con-

textuallydirected, t wasasserted arlierhat they occuronly in the firsttwelvemeasuresof the openingsection. The situation, n fact,changesafterbar12, ascan be seenfrom the score:specifically,he pitch-pair egmentationof the indi-

vidual instruments is abandonedand each instrumentalpart becomes more

complexrhythmically.While the instrumentscontinuethroughone finalcres-cendo o mezzoort and back, the individual ines containfrom seven to nine

pitches instead of the two which comprisedthe earlierpitch pairs.In short,rhythmic ntensification enders achinstrumentalpartmoreapparent s a per-ceivedcontinuity.

The pitch boundariesD3 and C4 are, however, maintainedthrough thesemeasuresandC4 in particulars articulated t the dynamicpeaksof the Englishhorn and bassoon

in measures13 and 14. Followingthis, rhythmic ntensifica-tion continuesbut the density s reduced o threeinstrumentsoperatingwithinthe reducedrange rom D3 to F3. This reduction n part-density nd textural

space saccompaniedbyasteadypianissimoevelandthuscompriseswhatmightbeheardasabrieftransitionntothe b-section.It issignificanthat theabsenceofthe upperboundaryC4 in the two-bartransition s in partoffset by the con-tinueddynamicexposureof thatpitchin the two precedingmeasures.

Eachof the two modes of pitch maintenance n the a-sectionimpliescon-tinuation in a differentway. For example, the neighbour-note protraction

revealsa relatively taticmaintenanceof the two pitch extremes; ndeed, thelonger hesepitchboundaries emain ntact,the moreapenetration f the spaceso clearlydefinedbythem seemsinevitable.Also, asmentioned,the lowerpitchis protractedby its upper neighbour only, and the upper pitch by its lower

neighbour only; again, the "opposite" neighbour in each case might be

expected. As regardsateralvoice crossings,the verynatureof theircrosswise

traversal,onnectingD3 to C4 andC4 to D3, suggests he possibilityof octave

completion n eachcase.

178




As we shallsee,

each of the aforementionedmplications

s realized n the b-

section,but becausepitchescomprisinghe latteroccuraboveC4, as ndicatedat

the end of system (b) in Example9, linearcontinuity over the entire pieceinvolvesconsiderationof pitch-class tepwise motion-i.e., stepwise connec-

tions betweencomponents n registrally isplacedpositions.In lightof thiscon-

dition, the unisonC5 atfortissimo, hich opens the finalsection in such adra-

maticway, is multi-functional n achieving arge-scaleinearcontinuity. For

example,as indicatedat the end of system (a)on Example9, it may be inter-

pretedas apitch-classowerneighbour o D3, the lowerpitchboundaryofthe a-

section,the latter ransferredup two octaves n the finaldyad;and as apitch-classupper neighbourto C4, the upper pitch boundaryof the a-section,the latter

transferredup one octavein the finaldyad.These arethe so-called"opposite"

neighboursreferred o earlier,and reflect,over a broaderspan, the relativelystatic (but now registrallydisplaced) neighbour motion around the pitchextremities f the a-section.In addition,C5 maybe heardas apitch-class ass-ing-tonewith respect o the lateralvoice-crossing ventsof the a-sectionas indi-catedatthe end of system(c)of Example9: e.g., D3 to C4, throughC05to D5of the finaldyad, and C4 to D3 through Db5 to C5 of the finaldyad. These

connectionsrepresentmoredynamicanddirectedlarge-scaleontinuities onsis-tent with the lateral ventsthemselves. Theendresult feitherinterpretations theinveion andregisterhiftoftheprotrcted itchextremitiesfthea-section. he pri-macyof the collectioncomprisedof pcs C and D is thus substantiated.1Theaffiliation f the closingdyadwith the openingis further einforcedbyits returnto theoriginalempoanddynamics,andtheaccompanyingquasiecondicationnthe score.

Beforeleaving his discussionof the firstpiece,one additionalaspectof linear

continuitys worth

noting.It concernsconnection to the third

piece,a

piecewhich iscloselyrelatedtexturally,dynamically, ndproportionally.12s system(b)in Example10shows, the penultimate onorityof the firstpiececontracts othe finaldyadand thatdyad, in turn, maybe heardto expandto the openingsonorityof the thirdpiece. Notice that the two expandedsonoritieshaveB4,C05,and D#5in common. In addition o this, the fifth,E3 to B3, whichframesthe openingsonorityof the firstpiece, is linearized n the formof an ascendingtrillat the end of the thirdpiece.The registral rch ormedby the juxtapositionof these two pieces s indicatedon the bottom systemof Example10.

179




Nc. 1 No. 3

mm. 1-14 15-16 16-22 22-24 1-9 9-12 12-end

I - _"k%S'jIt

- *(1 senza \

(a) I diminuendc

(b)

v O r'.---(m,,)

r ',

9 AfjP4]& --

'I: ?)] ,,L . i,.L'

e ,. : r-\(c)

:IX

EXAMPLE10: ELEMENTSOF CONNECTION BETWEEN

THE FIRSTAND THIRD PIECES

In the foregoing tudywe have examinedavarietyof ways n which the cen-

tricityof a particular c or pc complexis established,approached n a contex-

tuallydirectedmanner,andprolonged.The waysin which variousexpressionsof stepwisemotion-in a singleoctaveor spreadover several-effectthe afore-

mentioned directedapproaches nd prolongationshave been of primarycon-cern.It wasdetermined hatstepwiseconnections n bilinear nstrumentalparts(numbers and10),andtwelve-notepatternsof pitch-class nfolding number5

and to some extent10)effecteddirected inearcontinuities owardsestablished

structuralgoals. Overlapping f pieceswas found to provide welve-noteaggre-

gatecompletion n one instance numbers9-10) andpc closure n others(num-bers4-5 and5-6). In the openingsection of the firstpiece,outer-voiceprotrac-tion and lateral voice crossing were found to be of significance in the

establishment ndprolongationof the primarypc complex,while the finalsec-

tion was seento relyon stepwiseconnectionsacross everalregistersorthelarge-scaleprolongation f that collectionacross he entirepiece.

180




NOTES

1. It ispreciselyhroughthe "predictability" f suchfunctionalharmonicpro-gressions n nineteenth-centurymusic that a particular eyarea s inferablewithout explicit tatementof the tonic.

2. During the course of this paperseveralreferencesaremade to the score

(Mainz:B. Schott'sS6hne, 1969), whichshouldbe availableo the reader.

3. Registrally pecificpitches will be designated accordingto the followingoctavedistribution:

8

0 ^ __

8

Cl C2 C3 C4 C5 C6 C7

4. Whenever the terms ascendingor descendingareenclosed in quotationmarks t denotes pc motion in which the directionofregistral eparations

opposite to that of the pc motion. Forexample,in the "ascending"stepsuccessionD5 to D#4, D5 ascends o D#4 in pc termsbut descends o D#4in registralerms.

5. Bymeasure 7the flutepart akeson asingle-line tructurehusallowing heclarinet o contribute o thecadence ntervalsmeasures 7and19).A similar

patternmaybe noted atthe end of the firstphrasewhere the bilinear truc-ture of the clarinetpartcontracts n a wedge-like ashion,allowing he bas-soon to contribute he second streamof activityand,ultimately, hesecond

pitchof the cadence inthe lowerregistral lane).

6. Thatis, the thirdsectioncontainsonly elevenpcs;the formal tructureandtwelve-notepc patternsoverlapat thispoint.

7. While thesemaybe moreproblematic sstepwiseevents, theirpc stepwisestructureneverthelessremains

significantwithin the context of

Ligeti'smusicallanguage.

8. Thatis, the oboe's timbre s muchmorepenetrating hanthatof the otherinstruments,the oboe parthasarticulativenstructionsdifferent rom itsassociates refer o the score),and itspitchesareattackedsfpascompared o

sfppn the otherinstruments. t is alsosignificanthatD5, articulated t the

beginningof thesixthpiece,not onlyprovidespc closure orthe fifthpiece,but alsorepresentshe pc centerof the sixth asthe latterendson D3 in theclarinet.

181




9. This fourth progression, Eb-Ab,is the same span as the upper line ofthe wedge-patternof pc unfolding in the ninth piece, discussedabove.

While number9 occurs in the highestpartof the instrument'srange,the

upper-voice progression n number10, initiatedby the aforementioned

fourth progression,occurs n a like fashion n the uppermostregionof the

bassoon'srange.

10. The C05 of bar 13 is indicated n parentheses ecause t is not articulated s

emphatically s the others n thisregister ratherhanbeingarticulatedwith

a >, it occursundera slur).C05is, however,functionally ignificant s the"leading-tone" o D5; itsappearance eremaybe said o offsetthe factthat

C5 does not appear mmediatelypriorto D5 in bar 15 but, rather, n the

hornwiththe bassoon'sD5. In termsof pc successions,however,both thelower andupperleading-toneso D (i.e., C andEb)areheardimmediately

prior o D5 in the bassoon(seeExample7b).

11. Here, the collectionofpcs C and D is primary egardlessf the interval n

which the pcsareexpressed.Recall hat in number4 the complex ofpcs C

andD wasalsocentralbutdifferentiation asmade between theforegroundexpression f the dyadas a seventh(primary) nda second(secondary).

12. That is, both numbers 1 and 3 are "ensemble" pieces ranging from

pianissimoo mezzoorte. As regardsproportion, both the first and third

piecesareformallypartitioned ccordingo thegoldensection. Number 1 isone hundred beats long, the golden section of which is sixty-two; the

emphaticCOn octavesentersduringbeat63. Number 3 is sixty-fourbeats

long, the octave-doubled hemeenteringon beat39-the goldensectionof

sixty-four.On a larger cale,the firstand thirdpieces,taken asan uninter-

rupted continuity, are themselves in a golden-section relationship:the

twenty-fivemeasure irstpiece is the golden section of the total forty-onebarsof both pieces.

182

832766-stepwise continuity as a structural determinant in györgy ligeti's ten pieces for wind

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