Jane Piper Clendinning - The Pattern-meccanico Compositions of Gyorgy Ligeti

8/16/2019 Jane Piper Clendinning - The Pattern-meccanico Compositions of Gyorgy Ligeti

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The Pattern-Meccanico Compositions of György LigetiAuthor(s): Jane Piper ClendinningSource: Perspectives of New Music, Vol. 31, No. 1 (Winter, 1993), pp. 192-234Published by: Perspectives of New MusicStable URL: http://www.jstor.org/stable/833050Accessed: 16/01/2009 07:05

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THE PAIIEN-MECANICOCOMPOSIllONS FGYORGYGEI1

tLt

JANE PIPER CLENDINNING

INTRODUCTION TO THE MECCANICO COMPOSITIONS

G YORGYLIGETI HAS COMMENTED often on his interest in machineryand his expression of that interest in his music.1 He claims that the

clicking and ticking of the pieces he calls "meccanico" spring from afascination reaching back to his childhood. Ligeti uses the Italian term"meccanico" n a general way, referring to portions of any of his composi-tions that remind him of machinery gone awry, rather than to those usingany specific compositional techniques. In his interview with Peter Varnai,Ligeti recounts an episode from his childhood related to his interest in

mechanical sounds--


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Ligeti's attern-Meccanico ompositions

I was a child, I must have been about five, when I came on a volume of[Gyula] Krudy's short stories, which was a book quite unsuitable forchildren; someone gave it to me by mistake. It was in summer and Iremember being overcome by a strange melancholy, perhaps becauseof the heat, or was it my reading Krudy stories all alone in the loft?One of the stories was about the widow living in a house full of clocksticking away all the time. The meccanico-type music really originatesfrom reading that story as a five-year-old, on a hot summer afternoon.Afterwards, other everyday experiences came to be added to thememory of the house full of ticking clocks; images of buttons we pushand a machine would start working or not, as the case may be, liftsthat sometimes work and sometimes do not, or stop at the wrongfloor; the Chaplin film, Modern Times, one of the great movie experi-ences of my childhood. Recalcitrant machinery, unmanageable auto-mata have always fascinated me.2

Ligeti's interest in machines that do not quite work correctly is realized

musically in an experimental composition from 1962--Poeme Symphoniquefor one hundred metronomes. This piece - a "happening" with instructionsrather than a score-was never published.3 In 1981, at the request of hisfriend and former student Martin Bresnick, Ligeti described the perform-ance procedure for PoemeSymphonique. he following description is drawnfrom a transcription of Bresnick's notes:

The piece should last about 18 to 20 minutes. Ideally, there should be100 metronomes, but at least thirty are needed. All of the metronomesshould be wound down before the beginning of the piece. Ideally, thepiece should begin after intermission, with the people outside as thepiece begins. The metronomes should be wound with 360 and 180degree turns. Not too many should be set fast, but there should be atleast 16 to 20 slow ones in the first row. Perhaps, 20 to 30 should beslow. Perhaps one solo metronome should be set fast, but that wouldmake a new version.4

The metronomes tick mechanically at different speeds, each winding downin its own time until all of them have stopped. The rhythmic patternscreated by their interaction change continually and decrease in complexityas the metronomes stop one by one. Regarding the influence of this pieceon his later works, Ligeti remarks:

In 1962, immediately after Atmospheres nd Volumina, I composed awork for 100 metronomes; well, that was a kind of persiflage, anautomatic concerto for 100 pieces of apparatus.... Yet if you listen

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which is constructed from smallgroups

ofpitches rapidly repeated

inamechanical fashion with gradual changes of pitch content. The pitches of

the small groups are ordered, and, in the repetitions of the units, theirgeneral ordering does not change even if some of the pitches of the unit do.The durational values assigned to the notes of the melodies are brief-inevery case an eighth or less-which, combined with fast tempi, create arapid turnover of pitch in the melodic lines. The small units are repeatedquickly enough that the pitches almost fuse into a chord, creating a com-pound melody, complete with voice leading within each melodic lineconnecting adjacent harmonies.

The beginning of the eighth of the Ten Pieces for Wind Quintet illus-trates the distinctive compositional features of the pieces of this group (seeExample 1). This movement of the Ten Pieces begins with a dyad (D4-F4[3]) rapidly reiterated n the flute, clarinet, and bassoon.8 As the number ofpitches per voice expands from two to three by addition of one of thepitches filling in the span of three semitones [3], scalar units are estab-lished. In the first four measures the scalar patterns grow from four to five

pitchesin the three linear

strands,with

gradual changesof

pitchcontent.

Throughout, the units of repetition are partitioned by a skip from low tohigh or high to low in the scalar ine.

Although Ligeti included meter signatures and measures in the ensemblecompositions to allow coordination of the parts, he insists that the piecesbe performed without metrical accent.9 In the keyboard pieces, dotted linesmark the passage of every sixteen eighth notes to enable the performer tokeep his place in the score. Because there are no measures as such, locationsin these two composition will be indicated by the division number, with

divisions (abbreviated divs.) numbered consecutively from the beginningof the composition.

In each of the pattern-meccanico pieces, a substantial portion of thecomposition is built by pattern-repetition techniques, although not all ofthe compositions are exclusively constructed in this manner. In Continuumor Coulee, the meccanico activity lasts from the opening notes of thecomposition to the final ones, a span of approximately hree and a half tofour minutes.10 Two other compositions of this group, the eighth of theTen Pieces for Wind

Quintetand the fifth movement of the Second

StringQuartet,1 both movements of larger works, open with a pattern-meccanico section that is separated from the succeeding contrasting mate-rial by sustained tones.12 In several later compositions-Ramifications(1968-69), the second movement of Monument-Selbstportrait-Bewegung(1976), and the Drei Phantasien (1982)-Ligeti combines his pattern-meccanico concept with other compositional techniques, notably micro-canon and, in the case of the Drei Phantasien, noncontrapuntal writing.13

In this article, I will examine the construction of the pattern-meccanicocompositions and explore the small and large-scale tructures resulting from

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Perspectives fNew Music

For Rolf Bengtsson

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EXAMPLE 1: Ten Piecesfor Wind Quintet, MOVEMENT 8, MM. 1-5

the repetitive patterns. Although the compositions of the pattern-meccanico group share the basic features of construction described above,the details of implementation vary in the individual pieces and sections. Inexamining these compositions, I will comment on individual differences aswell as pervasive general characteristics f this group.

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MELODIC LINE CONSTRUCTION AND COMPOUND MELODY

The melodic lines that combine to form the pattern-meccanico texture aredifferentiated from each other by contrasting instrumental timbres in thesmall ensemble and vocal compositions and by parts for the left and righthands that function as separate strands in the keyboard works. Eachmelodic line can be divided into repeated small melodic fragments, orpatterns, which are partitioned by changes of range or direction14 and bythe repetition involved. For example, the patterns in the eighth of the TenPieces (shown in Example 1) are separated by a skip from high to low orlow to high between repetitions of distinct units.

The patterns in a melodic line may consist of segments that look andsound like fragments of "scales" or like arpeggiations of chords. I will referto segments which are built of successive skips of a [3] or larger in onedirection as arpeggiation segments (see Example 2). These patterns lookand sound like arpeggiations of chords and, in the pattern-meccanicocompositions, function as broken chords with stepwise voice leading con-

necting each arpeggiation pattern to the next. Through these stepwiseconnections, each melodic line can be thought of as several voice-leadingstrands of compound melody. However, the chordal structures created bythese arpeggiations usually do not correspond to traditional harmonies anddo not progress following traditional rules of harmonic function.

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? B. Schott's Sohne, Mainz, 1970. All rights reserved.Used by permission of European American Music DistributorsCorporation, sole U.S. and Canadian agent for B. Schott's Sohne.

EXAMPLE 2: ARPEGGIATION PATTERNS FROM Continuum, DIV. 127

The scalar units in Ligeti's melodies are made of three or more pitches,arranged in ascending or descending order, which are separated either by[l]s or [2]s (see Example 3). These units may or may not correspond tofragments of traditional scale forms (such as major, minor, modal, orwhole-tone scales).15 They do not consistently combine with adjacentpatterns to form larger scalar collections and do not imply traditional scale

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? B. Schott's S6hne, Mainz, 1970. All rights reserved. Used by permission of European American Music DistributorsCorporation, sole U.S. and Canadian agent for B. Schott's Sohne.

EXAMPLE 3: SCALAR PATTERNS FROM Continuum,DIV. 17, LEFT-HAND PART

hierarchies.16 Since there is no principal scale in these compositions, thescalar fragments cannot be treated as segments of or deviations from areferential scale. In the

pattern-meccanico compositions,scalar

patternsalso function as creators of compound melody, with stepwise linear connec-tions from each pattern to the next. The number of perceptible individualvoice-leading strands in the compound melody varies throughout thecourse of a pattern-meccanico section, usually being heard to increase asthe number of pitches in the pattern increases and to decrease as thenumber of pitches decreases. Typically, the uppermost and lowermoststrands sound continuous, with the additional strands splitting off betweenthem.

In addition to unidirectional scalar and arpeggiation segments, eithertype can be bidirectional or "circular" with both an ascent and descentincluded in each unit. The patterns in Continuum divisions 74-77 arerepresentative of the scalar circular type (right hand part division 74 shownin Example 4). Although circling patterns can be separated at any point,logical pattern divisions are at the highest or lowest pitch of the pattern(the turning points) or both. With either a high or low division, somepatterns have changes mid-pattern. However, once a change has been

established,it holds for both

ascendingand

descending partsof the

patternuntil another change occurs which supersedes it. The relative ambiguity ofthe pattern division makes the lines of this section seem more continuousthan those with obvious skips. In that the partitioning of patterns is simplyan analytical device to allow the pattern shifts to be studied more easily, Ihave divided the patterns where I hear the division.17 The patterns ofExample 4 I hear as circling units ascending then descending, yielding adivision at the lowest pitch. The circling arpeggiation patterns in measures13-18 of the fifth movement of the Second String Quartet have pitch shifts

so frequently that a top and bottom division is preferable the pitches of theviolin 1 part from the first half of measure 14 are shown in Example 5).18

? B. Schott's Sohne, Mainz, 1970. All rights reserved. Used by permission of European American Music DistributorsCorporation, sole U.S. and Canadian agent for B. Schott's Sohne.

EXAMPLE 4: SCALAR CIRCULAR PATTERNS FROM Continuum,DIV. 74, RIGHT-HAND PART


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7 7 7? B. Schott's S6hne, Mainz, 1971. All rights reserved.Used by permission of European American Music DistributorsCorporation, sole U.S. and Canadian agent for B. Schott's Sihne.

EXAMPLE 5: CIRCULAR ARPEGGIATION PATTERNS FROM MOVEMENT 5

OF THE SECOND STRING QUARTET, M. 14, FIRST VIOLIN PART

The changes of pitch in the internal voice leading of the melodic lines canbe described most easily by reducing the repeated patterns to their underly-ing harmonies. The changes in patterns are of several types: (1) theaddition or deletion of a pitch, (2) change in a pitch of the pattern, usuallyup or down by a [1], and (3) enharmonic respelling (which, of course,results in no change in the pitch content). The metamorphosis of pitchpatterns in the individual melodic lines of a composition can be illustratedin a pattern shift chart like that of Example 6 for the first section ofContinuum (divisions 1-56).19 In this chart, pitch shifts are indicated withan arrow, enharmonic respellings with a dashed arrow, and added ordeleted pitches by an angled bracket indicating the location in the patternof the addition or deletion.

L. H. R. H.

div. 1 112 div. 1 72

div. 15 A 1 div. 10 43

div. 17 5div. 18

div.A 58 1 div.20 4

L-L.14 -,

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EXAMPLE 6: PATTERN-SHIFT CHART, Continuum, SECTION 1

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div. 42 4 div.40 31

div 43 33 div. 45 97

div. 49 48 div.58 16

div. 56 49di5A A 49

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EXAMPLE 6 (CONT.)

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Continuum begins with a dyad from the middle range of the harpsichord(G4 Bb4 [3]) that is rapidly and evenly articulated with the hands playingalternate pitches of the dyad so that both pitches are always sounding. As athird pitch is added to the dyad in each hand part, the direction of scalarsegments is established (downward in the right hand; upward in the left).The initial pattern changes in this part of Continuum are note additions, asthe number of pitches in each hand grows to five. In the process of thesepattern shifts, the range expands from the G4 Bb4 of the beginning to spanthe F4 Cb5 [6] by division 18 (range graph, Example 7).20

The rapidly repeated patterns form a compound melody. The G4 andBb4 of the beginning are strongly emphasized by their reiteration inisolation for nine divisions and with F4 (forming a [2][3]) for five moremeasures prior to the introduction of other pitches. Stacks of [2][3] witheither interval on top and a stack of [2]s (whole steps) comprise theharmonic units that Ligeti calls the "typical Ligeti signals."21 These tri-chords appear in isolation at important structural points in Ligeti's music,such as the beginning and ending of sections, but are also the components

from which the fuller harmonic "stacks" within sections are built. We cansee this use of the Ligeti signals here-the next pitch that enters (Ab4)forms an additional Ligeti signal triad (F4 Ab4 Bb4 [3] [2]) overlapping thefirst. After such a strong emphasis on [2][3] and [3][2] triads in theintroduction of pitches, the chromatically filled [6] of the middle sectionscan reasonably be thought of as being built from additional overlapping[2]s and [3]s.

These overlapping [2]s and [3]s commonly form a third harmonic unit,[1][2] or [2][1], which Ligeti also uses as an independent harmony.22Although Ligeti does not list this combination as a "Ligeti signal" it ispervasive in his compositions from this time period. The consistentappearance of [1][2] or [2][1] and a stack of [2]s (which Ligeti listed as a"signal") as harmonic entities in these pieces raises an interesting questionin regard to the "scalar" patterns-could these also be considered "arpeg-giations" in Ligeti's harmonic system? In that the "scalar" patterns areconnected by stepwise voice leading in the compound melody, the "scalar"patterns are also treated as "arpeggiations" of Ligeti's harmonies.

SMALL-SCALE PATTERN NTERACTION

In each of the pattern-meccanico sections, the individual melodic linesenter simultaneously and continue without pause to the end of the section.No line is to predominate-all must be independent, yet balanced involume and articulation.23 As the lines are combined, the individualchanges of pitch as illustrated in the pitch shift charts are not always

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audible, but the complicated interrelationships of the lines and their pat-terns contribute directly to the sound of the pattern-meccanico composi-tions. In addition to forming harmonies as discussed above in reference tothe opening of Continuum, the interaction of the patterns of the individualmelodic strands also creates rhythmic activity. This rhythmic activity is ofseveral types, ranging from the readily audible pulsing rhythmic patternsmade by entrances and exits of pitches through the process of pitch shifts tothe subtle rhythmic shadings of pattern beginning accents.

Although the durations in Continuum are limited to rapid eighth notesthere is a sense of rhythmic diversity stemming from the interaction of thepatterns. Of the pattern changes, some draw the listener's attention morethan others. In the first section, the registral expansion of the opening isfollowed by eighteen divisions of relative stasis as far as registral filling isconcerned, which is enlivened by an interchange nvolving the lowest pitchin each hand (F4 and F a 4). The entrances and exits of the F4 and F 4 arereadily audible, set off by the lack of change in the other pitches of thepatterns. The reiterations of F4 (added in the right hand part in division

10) are clearly audible, sounding far enough apart to cause a perception ofa pulse, until an F4 is also added in the left hand (in division 17), causingthe pitch to sound frequently enough to fade into the background. Ligeticomments on this rhythmic pulse--

Here what you perceive as rhythm is not rhythm coming from thesuccession of notes your fingers play. The actual rhythm of the piece isa pulsation that emerges from the distribution of the notes, from thefrequency of their repetitions.... the accelerando of the rhythm istherefore the result of an increased frequency of a note, it is realizedthrough a modified note distribution.24

These audible pulses, which can accelerate or decelerate according to thefrequency of the appearance of a pitch, create rhythmic patterns in theabsence of durational diversity. Although internal pitch changes contributeto the sense of pacing in these pieces, in general, pattern shifts affecting theouter voice-leading strands, and therefore, the outer boundaries of the

range spanned, are the most readily audible.In performing a line, players naturally tend to accent the perceivedbeginning of patterns slightly in order to keep their place. When theseparate melodic strands are combined, these accents emphasize the inter-action of patterns in the individual strands of the texture. When patternbeginnings coincide, a stronger accent occurs; when the pattern beginningsare offset, the slight accents mark the shifting of the patterns in relationshipto one another, making audible rhythmic patterns as a result of the com-bination of the individual lines. Ligeti comments on the interaction:

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"... what attracts me is the idea of superimposing everal evels,severaldifferent time-grids moving at different speeds, and so very subtly achiev-ing rhythmical eviations."25

The pattern-interaction raph for the first section of Continuum sshown in Example 8. In this graph, he eighth note is the durational nitfor each division on the x-axis and each of the hands has been assigned ahorizontal strip. The entry of the first note of each pattern s shaded. Asnoted previously, he number of pitches per pattern n the first part ofContinuum grows from two to five. Beginning n division 28 with the finaldisappearance f the F4, pitches are removed gradually, evealing [2][1](Ft 4 G$ 4 A4) as pitches are subtracted ntil only a dyad (F$ 4 and Gt 4)remains. The addition, and later subtraction, of pitches in the hands isoffset, causing a shifting of pattern beginnings between the two hands.

RH i

LH 1 2 3 4 5

6 7 8 9 10

12 13 14 15

16 17 18 19 20

21 22 23 24 25

26 27 28 29 30

31 32 33 34 35

36 37 38 39 40

41 42 43 44 45

46 47 48 49 50

51 52 53 54 55

EXAMPLE 8: PATTERN-INTERACTION GRAPH, Continuum, SECTION 1

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When the patterns both consist of only two pitches, as they do in theopening and closing divisions of this section, the beginnings of the patternsare unclear-the patterns are simply an oscillation of two equal pitches-and are less likely to be accented, making pattern beginning alignments lessnoticeable than when the patterns are longer. In contrast, the accentscreated by the pattern beginning alignments of the five-note patterns indivisions 16-24 are quite audible. In general, the longer the pattern, themore noticeable are consecutive pattern beginning alignments. When thepattern beginnings are aligned for more than two or three patterns andhave three or more pitches in each pattern (as they do in divisions 20-30and divisions 43-45), the performer is particularly ikely to emphasize thepattern beginnings, causing more of an accent than occasional patternalignments or aligned dyads. Between these points of alignment, thepatterns shift in relationship to one another, with pattern beginningscoinciding to create an accent only after several repetitions of patterns ofdifferent lengths. The net effect of these small accents created by pattern-beginning alignments over the course of the section is that of deceleration

(the accents become farther apart) as the number of pitches in the patternsincreases, and of acceleration (the accents become closer together) as thepattern lengths decrease, which parallels the expansion/contraction ofrange.

SECTIONAL HAPING

The sectionalshaping

in each of thepattern-meccanico movements,

likethat of the opening of Continuum just considered, is created by a complexinteraction of factors, with the use of range or pitch-space as the primaryagent in creating both sectional coherence and divisions between sections.In each of the compositions, range is not solely responsible for the audiblesectional structure-shaping in pitch-space is supported and reinforced byLigeti's harmonic practice and by changes in the perceived pacing.

Ligeti's harmonic practice as illustrated in these compositions (and themicrocanonic group26 from the same time period) is quite interesting. The

adjacent harmonies do not connect progressionally-there is no establishedprogressional hierarchy, nor a sense of tension/resolution driving one har-monic "stack" o the next. The basic process is additive-pitches are addedto those already sounding to increase the range spanned or to increase theinternal filling of an already established span. These added pitches typicallyform harmonic building blocks similar in intervallic structure to thosealready sounding by combining with pre-existing pitches to make addi-tional components with the same design. There are two methods by whichLigeti completes this harmonic process: either the additive

procedureis

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reversed by removing pitches to close range or thin the texture (oftenrevealing harmonic components that were hidden within) or the process ofexpansion of range or filling of a span may be carried to an extreme, thencut off abruptly. These harmonic processes, through the compound melodyof the repeated patterns, create the two typical registral shapings for thepattern-meccanico compositions: an expansion/contraction (of which theopening section of Continuum is typical) and an expansion which is brokenoff at its widest point (used in the second, third, and fourth sections ofContinuum). The harmonic

processis not

purelyadditive in that some

pitches (and the harmonic components they form) are continued as a partof the texture while others fade out as new ones are added. Ligeti comparesthis harmonic process to crystal formation in a supersaturated solution;27 Idescribe it as kaleidoscopic metamorphosis.

The registral shapings are often accompanied by change in the amount ofharmonic tension present in the music. For example, in the first section ofContinuum, the expansion and registral filling is accompanied by anincrease in harmonic tension. As a result of the harmonic process, the

number of perceptually dissonant harmonic intervals between the voice-leading strands of the compound melody increases toward the middle ofthe section-moving toward the chromatic filling of the span-departingfrom and returning to the contextually stable Ligeti signal harmonies at thebeginning and end. As range closes and the texture thins anticipating theclose of the section, tension gradually is dissipated rather than "resolving"in a traditional manner. In many of the sections which feature a registralexpansion that is broken off, the harmonic tension increases over the courseof the section and is not dissipated at the section's end.

An additional aspect of formal shaping in the pattern-meccanico com-positions is the perceived variation in the pacing, or the speed at which themusic seems to move forward. This feature of the music is effected byseveral surface elements that have already been mentioned: the frequency atwhich pitches are articulated n the individual melodic lines (determined bythe duration of individual pitches of a pattern), the pattern interaction(accent alignment as a marker of progress), and the rate at which thepatterns shift in the different voices (rate of change in the pitch content of

melodic strands). The balance among these elements differs from section tosection, with some predominating in one section, and others in othersections. The rate of pattern shifts and the interaction of pattern-shiftplacement in different melodic strands are illustrated in a pattern-change-rate graph.

Relatively active and static sections of pitch change coordinate withregistral shaping as the primary section-creating features in Coulee (seepattern-change-rate graph, Example 9). In this graph, the units on thex-axis represent one division of the music. A square is shaded on the y-axis

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Ligeti's attern-Meccanico ompositions 207

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for each pattern shift in that durational unit for each voice. Since there is noaudible change of pitch, pattern shifts involving only enharmonic respell-ings are not indicated. The gradual growth of pattern-change activity in thefirst sixty-five divisions, the static portions in divisions 65-88 and 92-118,and the fast-paced changes of the concluding measures are easily identifia-ble on the pattern-change-rate graph. This graph, in combination with therange graph for Coulee (Example 10), clearly illustrates the sectional divi-sions at divisions 65 and 118. Throughout the composition, changes in

pattern lengthare allocated to the two hand

partsto make

pattern begin-nings align as little as possible. Since the pattern beginnings coincide rarelyand irregularly, the contribution of the lengthening and shortening ofpatterns is limited to a subtle slowing of pacing as the pattern lengthincreases and quickening as the length decreases. However, rapid multiplepattern changes like those of the end of Coulee are particularly noticeable tothe listener.

At this point, we will examine the third section of Continuum (divisions89-125),28 which illustrates the second registral shaping typical of the

pattern-meccanico compositions-an expansion ending at its widest point.The third section is divided into three subsections based on pacing and useof range. Registral space in the first subsection, divisions 89-105, isrelatively thinly filled (range graph, Example 7) with a slow rate of pitchchange (pattern-change-rate graph, Example 11). After the held D4 of theleft hand becomes a rapidly reiterated dyad with the addition of A3 indivision 92, the patterns in both hands gradually expand to three, then fourpitches. As in the first section, the addition of pitches filling in the dyadsestablishes direction and creates a

registral skipthat divides the melodic

strand into recognizable units of repetition. Each pitch that is added formsLigeti signal trichords with those that are still sounding (see harmonicdetail, Example 12). The pattern beginnings in this subsection are inten-tionally aligned whenever they have the same number of pitches (twopitches, divisions 92-96; three pitches, divisions 99-101; and four pitches,from division 103), creating a series of evenly spaced pulses, but they shiftin relationship to each other when the number of pitches is different(pattern-interaction graph, Example 13).

Following the relatively inert first subsection, a dramatic expansion ofrange (from a span of F3 FW [13] to a span of Ft 2 Gb5 [36]) begins,enabled by a change in pacing from slow to very fast. In division 105,patterns begin to be repeated only two to three times before a pattern shift(pattern-change-rate graph, Example 11). The acceleration n pacing is notcreated by a change in pattern length, a decrease in the duration of notes, oran increase n tempo - all of which remain constant- but by the more rapidturnover of pitch content in the patterns as represented in the pattern-change rate. The pacing gradually speeds up to only one statement of most

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210 Perspectives fNew Music

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1C 4

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EXAMPLE 12: HARMONIC DETAIL, Continuum, DIVS. 96-103

RH

LH 89 90 91 92 93

* wmm"mmm"mm'"mmmm 'p ff In m- ,W- ,94 95 96 97 98

99 100 101 102 103

108104 105 106 107

109 110 111 112 113

114 116 117 118115

119 120 121 122 123

124 125

EXAMPLE 13: PATTERN-INTERACTION GRAPH, Continuum, SECTION 3

B,


22/44


patterns by division 111, then to two or three changes per pattern shiftafter division 115. As is usual in the pattern-meccanico compositions, thepatterns shifts are predominantly by [1], allowing the expansion of range tobe smooth and even, though rapid. The level of internal activity is aug-mented in division 111 by the addition of a fifth pitch to the right-handpatterns, which causes the pattern beginnings not to be aligned for the firsttime since division 103 (pattern-interaction graph, Example 13). Althougha fifth pitch is added to the left hand part in division 113, the patternsremain out of phase to the end of the third section. The expansion of range,the increase in the number of pattern changes, and the nonalignment ofpattern beginnings combine to create a strong sense of motion and activityin the middle subsection, which contrasts sharply with the subsectionspreceding and following it.

The range-graph detail for this subsection, Example 14, illustrates thestepwise pattern shifts and the resulting harmonies. Most of the pitches inthis section interact with the others sounding in temporal and registralproximity to form continually changing stacks of [2]s and [3]s, but the

harmonic impression of this subsection is that of the opening of range, withthe individual harmonies subservient to the overall motion. As the registrallimits of section three are reached, the middle segment of range emptieswhile the extremes become chromatically filled. The chromatic filling here,like that in the first section of Continuum, generates an increase in theharmonic tension. For the first time in the piece, the hands move intoseparate sections of the range and are no longer overlapping.

The static third subsection, divisions 119-25, although providing apoint of repose after the rapid motion of the second subsection, does not

effect a release of the harmonic tension accumulated n the previous subsec-tion. The patterns in both hands are segments of the chromatic scale (CX5to Gb5 and F 2 to Bb2) symmetrical around C4. There is no change ofpattern in this subsection, and consequently, no variation in registral fillingor pattern interaction. The level of tension continues to build through thethird subsection, not because of harmonic processes (there are no changesof harmonies), but because the anticipated resolution of the tension accu-mulated in the second subsection is withheld.

With itsrelatively

staticopening, extremely

activemidsection,

and com-pletely static ending, the third section has more internal contrast than dothe other sections of Continuum. Although changes in pacing like those ofthis section often contribute to sectional divisions, here the discontinuitiesare overridden by the continuity of the patterns, both in their continuousrepetition and in the smoothness of the pattern changes, and in the steadyincrease in tension throughout the section. In comparison to the strongdiscontinuities that separate the third section from those that precede andfollow it, the changes in pacing within the third section merely mark

internal divisions of the section, rather than dividing at the sectional level.

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C7 i i

I I I

* right hand

E left handC6 I

C5

C4

C3

C2

C1105 110 115

EXAMPLE 14: RANGE-GRAPH DETAIL, Continuum, SECTION 3

120

COMBINATIONS OF SECTIONS INTO PIECES

Ligeti's pattern-meccanico compositions are constructed either entirelyusing this technique (as in Continuum and Coulee) or by a combination ofseveral techniques (as in the fifth movement of the Second String Quartetand the eighth movement of the Ten Pieces for Wind Quintet). I willillustrate the former by considering the combination of pattern-meccanicosections in Continuum and comment on the latter in regard to the move-ment from the Ten Pieces for Wind Quintet. The five sections of Con-

tinuum illustrate the shaping of sections by various combinations of use of

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range with pattern shifts, the pacing of pattern change, and the interactionof pattern beginnings (see range graph, Example 7). The sectional shapingof the first and last sections (divisions 1-56 and 143-205, respectively) isthat of intensification (registral expansion, acceleration of the pattern-change rate, and an increase in the length of the patterns) followed by acontraction (both in register spanned and in the pattern length) accom-panied by a deceleration in the pattern change rate. In the second, third,and fourth sections (divisions 50-88, 89-125, and 126-143, respectively),the

registral patternis that of an

expansion,with the section

separatedfrom

the one that follows by a discontinuity at the height of the expansion. InContinuum, the discontinuities are created by a combination of timbralchanges (dividing the third section from the fourth and the fourth from thefifth), abrupt changes in registral filling (dividing sections two from threeand three from four), and by marked changes in active register (dividing thethird section from the fourth and the fourth from the fifth).

The overall gesture of the first four sections is a registral expansionaccompanied an intensification of forward motion and harmonic tension.

After these sections, the compositional problem arises of what to do next-how to bring to a halt a composition which has built up substantial forwardmomentum. Ligeti solves this problem by bringing back the sectionalshaping of the opening section but adapts it to form a closing gesture bymoving the expansion/contraction to the extreme high register. The regis-tral discontinuity and the sudden shift from a wide span to a narrow onebetween the fourth and fifth sections breaks off the registral expansion,increasing tension, and acceleration of the previous sections at its apex,preparing for the close. As the registral span contracts for the last time inthe piece and a dyad (Fb7 Eb7) is reached in each hand part, a new patternis formed-one of sound and silence-as one tone of the dyad in each handis replaced with a rest. The incorporation of rests in these patterns allowsthe texture to continue to thin without simultaneously reducing the num-ber of active pitches. In division 193 the range contracts to a unison (theonly unison in the composition), which yields to silence in division 205.

In his plan for the Ten Pieces for Wind Quintet, Ligeti designed each ofthe even-numbered movements to be a "mini-concerto" for one of the five

instruments, in which the traditional characterization of that instrumentwould be explored in a soloistic setting. The eighth movement, for example,is intended to exploit the traditional sustained cantabile character of thehorn and its timbral possibilities.29 The role of the lengthy pattern-meccanico passage at the beginning of the eighth movement is to providean introduction for the horn solo.

The initial measures of the eighth of the Ten Pieces for Wind Quintet aresimilar to the first section of Continuum in the use of range, the type ofpattern shifts, and in the harmonies created by the filling and expansion

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from the initial [3] in the first few measures. However, the rate of patternchange is much more rapid than the keyboard compositions, with four ormore pattern changes per measure (four quarter notes) as compared to lessthan one change per division (pattern-change-rate graph, Example 15).30Because of the faster rate of pattern change, the length of time anyindividual harmony sounds is fleeting, necessitating a finer resolution forthe range graph (time unit of a quarter note) to show the harmonic detail(range graph, Example 16).

As the contraction ofrange begins

in measure 8, the instrumentalpartsbegin to share various patterns as if in canon (pattern-shift chart, Example

17).31 Each pattern is represented both ascending and descending and withsome patterns spelled enharmonically. The number of repetitions of apattern in a melodic line varies, as do the durations assigned the pitches ofthe pattern. The contraction of range continues through the canonic pre-sentation of patterns in measures 9-12. The sectional shaping throughmeasure 12 would seem to prepare a section break, but there is no abruptchange of pattern type or texture common in sectional divisions. Instead of

a section break, the shaping prepares another important event-theentrance of the horn for the first time in the movement. The horn enterssoftly, as if sounding far away, hen swells into the first soloistic melodic lineof the movement. As the horn becomes louder, the rate of pattern change inthe other instruments accelerates, with single statements of patterns replac-ing the previous repetitions. The increase in the rate of pattern change iscombined with a lengthening of durations assigned to the pitches inmeasures 14-15, creating the impression of slowing rather than ofacceleration-it is as if the horn melody rises up from the midst of thefrantic machine-like activity and subdues it.

The section ends with relatively low-pitched trills in the clarinet andhorn beginning in measure 16, which die away into the beginning of thesubsequent section. Compared to the rest of the movement, the openingsection is relatively stable-the motion is continuous, without changes intempo, and the variation in dynamics is limited to a diminuendo inapproach to the sectional close. In contrast, the remaining twenty-fivemeasures of the movement are marked by dramatic changes in the character

of the musical material accompanied by a variety of tempi and dynamiclevels.

PATTERN-MECCANICO IN LATER COMPOSITIONS

The pattern-meccanico techniques developed in compositions from the1960s reappear in combination with other procedures in several subse-quent pieces. In Ramifications 1968-69) for string orchestra or twelve solo

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E luteI clarinetfl bassoon ~ ~

m

1 5 10

EXAMPLE 15: PATTERN CHANGE RATE, Ten Pieces,MOVEMEN

CS

C4

1

EXAMPLE 16:

5 10

RANGE GRAPH, Ten Pieces,MOVEMENT 8,

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Flute Clarinet Bassoonm.l

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EXAMPLE 17: PATTERN-SHIFT CHART, Ten Pieces, MOVEMENT 8, MM. 1-15

217

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28/44


Flute

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EXAMPLE 17 (CONT.)

218

Clarinet

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29/44


string players, Ligeti achieves a new level of synthesis of pattern-meccanicoand microcanon. The canonic treatment of the patterns in this compositionresembles that of the small ensemble pieces discussed previously in that thenumber of repetitions of a pattern before a pattern shift and the briefdurations assigned the pitches vary from instrument to instrument, thoughthe sections of pattern-canon are more extensive, encompassing most of theeight-and-a-half minutes of this piece. The influence of microcanon isstrongly felt in the staggered entrances and the use of four to eight parts(occasionally more) in the canon. The treatment of pattern shifts, patterninteraction, and pacing in Ramifications s similar to the earlier composi-tions, therefore those features will not be considered in detail here. Oneaspect of the composition, however, does complicate both analysis andperformance-the division of the string orchestra into two groups tuned aquarter tone apart (Group I at A=453 Hz; Group II at the usual A=440Hz).32 The registral progression in each group as notated can be repre-sented easily enough (see range graphs for the first 33 measures in Example18),33 but the special circumstances of performance cause problems in

representing graphically the actual composite sound of the two groups.First of all, the canonic patterns of Group I are sometimes notated asemitone lower than those of Group II (causing Group I to sound around aquarter tone lower than Group II), but other times are notated the same(making Group I sound a quarter tone higher than Group II). The twogroups alternate in this fashion throughout the composition, making aregistral shaping Ligeti describes as follows:

... in one skein, individual parts that are twisted together move indivergent directions so that the strands of the voices gradually becomedisentangled. The total form is made up of the alternation of ramifica-tion and unification of the parts and of the rents or bunching togetherof the net-formation that ensues from this.34

In addition to the changing relationship between the groups, a secondfactor makes graphic representation of pitch problematic: the composerexpects skilled orchestral players to find it difficult to play consistently "out

of tune" for the duration of a piece this length, causing the intonation tofluctuate constantly as each player struggles to avoid equalizing the tuning.Problems with this last aspect of Ligeti's design for the composition havemade him disappointed with the realizations of this work-either theinstrumentalists have been unable to avoid equalization of the tuning, orthey have maintained it too accurately, without enough fluctuation.35

The second movement of the composition for two pianos, Monument-Selbstortait-Bewegung 1976), also features a combination of Ligeti's "tradi-tional" pattern-meccanico techniques with new ideas. The complete title

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220 Perspectives fNew Music

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of this movement, "Selbstportrait mit Reich und Riley (und Chopin istauch dabei)" [Self-Portrait with Reich and Riley (with Chopin in thebackground)] alludes to the connections between Ligeti's pattern-meccanico compositions and the minimalist compositions of Steve Reichand Terry Riley. Although Ligeti states that he was unaware of the music ofthe two Americans until his first visit to the United States in 1972,36 hispattern-meccanico compositions and their minimalist techniques devel-oped concurrently in the 1960s, sharing the characteristic ncessant repeti-tion of small melodic units, gradual change of pitch content, and phaseshifts created by changes in the repeated units. However, Ligeti's pattern-meccanico compositions and American minimalism differ in several signifi-cant ways, including their cultural roots and the composer's intentions,which are reflected in the degree of control the composer wishes to retainover the resulting performance.

In each of the early pattern-meccanico compositions, every detail of theperformance-including the number of times a pattern is to be repeated, thealignment of the pattern-meccanico strands, and the relative duration of

the pitches-is specified in the score. In typical minimalist pattern-repetition or phase compositions the pitch and rhythm of the pattern andthe pattern ordering are specified, but the number of repetitions and thealignment depend on the performers' realization of the score instructions.The minimalist composer intends for the performers o listen to the activityof the others and react based on what they are doing, making the perform-ance a group interpretation of "the piece." Ligeti incorporates some ofthese elements of performer choice in "Selbstportrait." As in Continuumand Coulee, the patterns are to be played as fast as possible, but evenly,without accents. The alignment between the parts is somewhat variable,dependent on the skill of the performers, with the performers nstructed insome parts of the movement not to be concerned with precise coordinationof the parts. The number of repetitions indicated in each part is likewiseflexible, with one to eight repetitions to be counted exactly, eight to twelveto be accurate o within one either way, twelve to eighteen repetitions to beaccurate to within two of the indicated count, and eighteen repetitions ormore to be "approximate." At some points, the pianist is instructed to

disregard the repetition count and listen for a specific event in the otherpart prior to moving to the next pattern.

Throughout much of this composition Ligeti uses a special pianistic/rhythmic technique: in each piano part the left hand is assigned a chord,which the pianist is to depress silently and hold down until instructed tochange it; meanwhile, the right hand repeats small groups of pitches, somecoinciding with the depressed keys of the left hand part, others not. Thepitches already depressed by the left hand do not sound, making rests withthe duration the pitches would have had.37 The combination of nonsound-ing and sounding notes in the patterns creates an alternation of pitches and

222


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34/44


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most common in earlier pattern-meccanico compositions (the expansion/contraction or the expansion ending at the widest point). Rather, theyshare characteristics with the registrally static portions of sections in Con-tinuum (beginning and ending of the third section) and Coule (middle ofthe second section).

The flexibility afforded the performers in "Selbstportrait" means thatthe composer releases his control over the precise alignment and interactionof patterns and the exact durations of some of the activities, but it is afreedom within limits. If the performers follow the instructions carefully,playing as fast as possible, counting the repetitions as instructed, andentering on the cues given by the other pianist, each performance hould besimilar. The pattern combinations, the sequence of events, and thereforethe harmonies, are completely under the control of the composer.

In a recent set of songs, the Drei Phantasien nach Friedrich Hilderlin from1982, Ligeti uses a variety of short microcanons, pattern-meccanico, andvarious combinations of the two with short contrasting chordal and freecontrapuntal passages to form the musical texture. Phrases and subphrases

of the text are set individually, highlighting the images of the poems.Compared to the compositions considered previously in which a singletechnique predominates for many measures, these songs are artfulpatchworks-a combination of little bits of this and that. The microcanon ofmeasures 29-49 of the first song shows pattern-meccanico nfluence in thatthe canon melody has repetitions of "partial patterns,"41 but only meas-ures 12-21 of the third song are constructed with traditional pattern-meccanico techniques. In these measures, the word "purpurne" (purple) sset in pattern-meccanico in sixteen parts, each of which has its owncompound melodic line and pattern shifts. The stepwise pattern shiftsresult in a motion from the opening pitches through a chromatically-filledportion, ending in repeated pitches forming a harmony made of overlap-ping Ligeti signal [2]s and[3]s-Eb3 F3 G3 A3 B3 C4 doubled at the octave tomake [2] [2] [2] [2] [1] [3] [2] [2] [2] [2] [1] (range graph, Example 21). Theregistral shaping is paralleled by changes in perceived pacing brought aboutprimarily by variation in pitch durations, which alter the number of pitchentrances in a time span (the number of entrances per temporal unit is

illustrated in Example 22). Pacing increases through shorter durations ofpitches as the registral space fills and slows through longer durational valuesas the harmonies created by the pattern-meccanico become static towardthe end of the passage.

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CONCLUSION

In this article, I have presented an approach to the study of the shaping andstructure of Gy6rgy Ligeti's pattern-meccanico compositions. The factorsthat create the audible shape in these compositions involve a complexinteraction of various elements at several "levels" of structure. The graph-ing techniques demonstrated in this study allow the contribution of variousdetails to the overall structure to be examined in isolation and in conjunc-tion with each other-leading to a fuller understanding of Ligeti's intrigu-ing pattern-repetition compositions.

C6

C5

C4

C3

C212 15 20

EXAMPLE 21: RANGE GRAPH, Drei Phantasien, SONG 3, MM. 12-21

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45

40

35

30

25

20

15

10

5

12 15 20

EXAMPLE 22: ENTRANCE GRAPH, Drei Phantasien, SONG 3, MM. 12-21

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NOTES

1. This article is drawn from my dissertation "Contrapuntal Techniquesin the Music of Gyorgy Ligeti" (Yale University, 1989) and is anexpansion of a paper given at the 1991 South Central Regional TheoryConference. I wish to express my thanks to my dissertation advisorJonathan Bernard and to my colleague James Mathes for their carefulreading and insightful comments on earlier versions of this article.

2. Peter Varnai, Beszegetesek igeti Gyorggel Budapest: Zenemiikiad6 Val-lalat, 1979). This interview of Ligeti by Peter Varnai s translated fromthe Hungarian as "Ligeti-Peter Varnai" by Gabor J. Schabert in Ligetiin Conversation London: Ernst Eulenberg, 1983), 17.

3. Ligeti's published descriptions of this piece are either vague or differ indetails. See Pierre Michel, "Entretiens avec Gyorgy Ligeti," in GyiorgyLigeti: Compositeur d'aujourd'hui (Paris: Minerve, 1985), 155 and

158-159.4. My thanks to Martin Bresnick for sharing his notes and recollections of

this conversation with me.

5. Josef Hausler, "Zwei Interviews mit Gy6rgy Ligeti", in GyorgyLigeti:eine Monographie, dited by Ove Nordwall (Mainz: B. Schott's Sohne,1971), translated from the German by Sarah E. Soulsby as "Ligeti-Josef Hausler" in Ligeti in Conversation London: Ernst Eulenberg,1983), 108.

6. Varnai, 39-40; See also comments in Ursula Sturzbecher, "Gy6rgyLigeti," in Werkstattgespr&che mit Komponisten (Cologne: Gerig,1971), 38.

7. Varnai, 22-23.

8. I will refer to vertical intervals (and to stacked vertical intervals) byintegers in square brackets, each of which indicates the number ofsemitones of an interval (for example, [6] for a tritone; [3][2] for aminor third below a minor second) with the intervals in stacks listedfrom lowest to highest, following the practice of Jonathan Bernard inTheMusic ofEdgard Varese New Haven: Yale University Press, 1987).Since registral spans are important in Ligeti's music, pitch intervalswill be used throughout rather than pitch-class intervals or intervalclasses. I will use the nomenclature of the Acoustical Society of Amer-ica throughout for labeling of pitches [middle C = C4].

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9. This treatment of metrical notation is typical for Ligeti's compositionsfrom this time period. He remarks in his interview with Peter Varnai(pages 13-14):

Of course, I went on using bar lines and conventional musicalnotation in most of my compositions: in the actual music, how-ever, bar-lines had no other function for me than as points ofreference, to keep the four string players of a quartet from driftingaway from one another. My music is a continuous flow, unbrokenby bars ...

Ligeti conveys his intentions to the performers in the performanceinstructions at the beginning of the score to Lontano and many of theother compositions from the late 1960s.

10. On initial inspection, Coulee appears to be a remake of Continuum fororgan rather than harpsichord. However, the methods of sound pro-duction in the harpsichord and organ cause a reversal of the "problem"posed by the instrument: in Continuum, Ligeti attempts to make aninstrument known for its extremely rapid decay of tones sound contin-uous; in Coule, he attempts to make an instrument associated withsustained tones sound discontinuous.

11. Although the third movement of the Second String Quartet is oftenassociated with the compositions of the pattern-meccanico group, ithas not been included in this study because it differs significantly fromthe other compositions of this group at each level of structure: thesmall units of repetition or patterns consist of only one pitch and donot undergo the same type of change as the multi-pitch patterns of thepattern-meccanico compositions, making the shaping of the movementdiffer from those typical of the pattern-meccanico compositions. Thismovement discussed in detail in Jonathan W Bernard, "Voice Leadingas a Spatial Function in the Music of Ligeti," in Some Perspectives nMusic since 1960, edited by Graham Hair (forthcoming).

12. Compared to others of Ligeti's compositions, the pattern-meccanicopieces have received little attention in the theoretical literature to date.Articles dealing with the Second String Quartet and the Ten Pieces forWind Quintet by Kaufmann, Lichtenfeld, and Morrison and a surveyarticle by Frisius in which some of the pieces are mentioned do nottreat the pattern-meccanico movements in detail. (Rudolf Frisius,"Tonal oder postseriell?," Musik und Bildung 7, no. 10 (1975), 490-501; Harald Kaufmann, "Ligetis Zweites Streichquartett,"Melos 7, no.

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5 (1970), 181-186; and Monika Lichtenfeld, "Zehn Stickefuiir Blser-quintett von Gyorgy Ligeti," Melos 39, no. 6 (1972); and Charles D.Morrison, "Stepwise Continuity as a Structural Determinant inGyorgy Ligeti's Ten Piecesfor Wind Quintet," Perspectives fNew Music24, no. 1 (Fall-Winter 1985), 158-82.) The lone exception is ananalytical article by Uve Urban on Continuum-Uve Urban, "SerielleTechnik und barocker Geist in Ligetis Cembalo-Stuck Continuum,"Musik und Bildung 5 (1973), 63-70.

13. These compositions also have received little attention in the analyticalliterature, and what has been written is either very brief or focussed ona specific aspect of the composition. A short article providing anoverview of Ramifications by Orazio Mula and the brief analyticalcomments on the second movement of Monument-Selbstportrait-Bewegung which are a part of Reinhard Febels rather substantial articleon the entire composition fall into the first category (Orazio Mula,"Ramifications," in Ligeti, edited by Enzo Restagno (Torino: E.D.T.Editions, 1985), 168-72; and Reinhard Febel, "Gyorgy Ligeti:Monument-Selbstportrait-Bewegung (3 Stiicke fur 2 Klaviere),"ZeitschriftfiirMusiktheorie , no. 1 (1978), 35-51 and 9, no. 2 (1978),4-13). Monika Lichtenfeld's comments on the texts selected for theDrei Phantasien fall into the second (Monika Lichtenfeld, "Da LeGrand Macabre con un saggio sulle Holderlin-Phantasien," rans. LuisaMennuti and Riccardo Morello, in Ligeti, edited by Enzo Restagno(Torino: E.D.T. Editions, 1985), 47-57).

14. Many of the features analysts typically cite as partitioners of melodiclines - rests, durations markedly onger or shorter than those precedingor following, and variations in articulation, for example--are absent orsuppressed in these compositions. In the absence of diversity of artic-ulation, with a limited range of fleeting durations, and with rangerestricted in individual lines, the simple act of changing direction orskipping in the opposite direction is magnified in importance as apartitioning feature. In some cases, "traditional" transmitters of dis-continuity, such as rests, are less notable as partitioning factors in these

pieces as changes of direction--for example, the occasional rests in themelodic lines of the pattern-meccanico section of the eighth of the TenPieces are so brief as to not sound as discontinuous as the changes indirection in the line.

15. Of course, what a pattern looks ike does not always correspond withwhat it sounds ike However, performers of these pieces are likely to seeand hear the similarity of these figures to familiar melodic gestures andbring out the "scalar" r "arpeggiative" nature of the patterns.

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16. In tonal contexts, the term "scale" refers to a collection of pitchesarranged n ascending or descending order with the distance from onepitch to the next usually a [1] or [2]. Traditional scales imply morethan collection content, however. They also indicate a hierarchicalrelationship between the members of the scale based on theirplacement.

17. These flowing, continuous melodic lines could certainly be dividedinto patterns differently without altering the basic observations regard-

ing pattern shift types and placement.18. I also think that performers play arpeggiation patterns differently,

emphasizing the ascending or descending sweep of the line rather thanthe "rolling undulations" of the scalar patterns.

19. Continuum divides into five sections: divs. 1-56, 50-88, 89-125,126-43, and 143-205. The exact location of the sectional divisionbetween the first and second sections is unclear, n that the dyad whichends the first section continues uninterrupted into the second. On theinitial hearing of this composition, the listener is likely to perceive thesectional division at the point where an additional pitch is added to thecontinuing dyad (division 56). On subsequent hearings, as the eventsof this portion of the composition become familiar, the dyad can beheard as attached to either the first section (with the section division atdivision 56), to the second section (with the section division at division50) or to both as a bridge (elision of sections divisions 50-56). I preferthe latter solution. Urban, in his analysis of Continuum, divides the

sections at division 52.20. Range graphs ike this one illustrate changes in pitch content over time.

The units of the y-axis of the graph each represent a semitone of thechromatic scale. The Acoustical Society of America pitch designationsfor C's (pitch-class 0) are indicated on the left side of the graph. Guidelines are provided between pitch classes 0 and 1 and between 6 and 7.The divisions on the x-axis of the graph represent a durational unit(here the division) as indicated in the labeling of the graph, with guide

lines at regular ntervals. All pitches sounding within a durational unitare shaded, illustrating the pitch content to the resolution of thedurational unit.

Many scholars, including Uve Urban, Pozzi Escot, and JonathanBernard, have found this type of graph useful for examination ofregistral/temporal relationships in Ligeti's compositions. See Urban,"Serielle Technik"; Pozzi Escot, "Charm'd Magic Casements," inContiguous ines: Issues nd Ideas n the Music of the 60's and 70's, editedby Thomas DeLio (Lanham: University Press of America, 1985), 31-

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56; Jonathan W. Bernard, "Inaudible Structures, Audible Music:Ligeti's Problem and his Solution," Music Analysis 6, no. 3 (October1987), 207-36; and Bernard, "Voice Leading."

21. Virnai, 27-32 and Michel, 167. Ligeti, like many of his contempo-raries, avoids harmonic intervals that imply major or minor triads.However, he remarks that he felt the need for "interval signals [that]were neither tonal nor atonal yet somehow ... afforded the possibilityof operating with alternate tension and resolution" (Varnai, 27). He

indicates his "preference for two-pole, empty tritones, octaves, majorseconds or indeed two major seconds on top of one another" andstates that "... another "typical Ligeti signal" is a fourth made up ofa minor third and a major second or the other way round" (Varnai,29).

22. The relationship between a trichord and a second trichord formedfrom the interlocked intervals of the first is discussed in detail inBernard, Varese, 4ff. He refers to the second trichord in this relation-

ship as the first-order derivative of the initial trichord, created by aninfolding of the initial trichord, and proves that each trichord has onlyone interlocked, or infolded orm. To my knowledge, the other tri-chordal relationships described by Bernard are not systematicallyemployed in Ligeti's music.

23. The necessity for the independence and equality of strands is empha-sized in the performance nstructions and dynamic markings or each ofthe compositions, and in the recommended registrations for the

harpsichord and organ works.24. Varnai, 61.

25. Hausler, 108.

26. By microcanon, I refer to those of Ligeti's micropolyphonic composi-tions in which a melodic line is set against itself in strict canon in manyvoices at short time intervals to form the musical texture. Lux aeterna(1966) and Lontano (1967) are typical of Ligeti's microcanonic com-

positions from the 1960s. Later compositions in which he employedmicrocanonic techniques are the Drei Phantasien (1982) and MagyarEtiidk (1983).

27. Varnai, 15-16.

28. Urban indicates the beginning of the third section at 86 and the end atdivision 119. My sectional divisions are based in large measure ondiscontinuities, which I hear as "dividing off" sections; Urban seemsto base sectional divisions on "points of arrival" with the "arrival"attached to the section that follows.

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39. The range graph for the first section of this movement shows theapproximate span between pitch additions or deletions and the pitchesinvolved in any particular point but does not represent the exacttemporal distances between those events. In this example (and thenext) the relative durations of events have been approximated bymultiplying the number of notes (sounding and nonsounding) in eachpattern by the number of pattern repetitions and allocating one unit onthe graph to each twenty notes before the next pattern shift, alwaysrounding down to the nearest twenty (I selected twenty notes as thetemporal unit to provide sufficient resolution without making thegraph unwieldy and difficult to read). The vertical grid lines on thegraph represent the locations of both pattern shifts and rehearsaldivisions (each pattern shift is assigned a rehearsal division in thescore).

40. In this graph, the time units were determined as in the range graph forthis section. The number of sounding and nonsounding notes in eachpattern are indicated between the vertical guide lines for that rehearsalnumber, showing the pattern length and the balance between sound-ing and non-sounding notes.

41. These canon melodies incorporate immediate repetitions of smallgroups of pitches within the line and pattern shifts following pattern-meccanico practice, but not all pitch groups are repeated, there is not aconsistent pattern length, and partitioning of units is often unclear.

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Jane Piper Clendinning - The Pattern-meccanico Compositions of Gyorgy Ligeti

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