Ligeti Triads

ERIC DROTT

THE ROLE OF TRIADIC HARMONY IN LIGETI'S RECENT MUSIC I

A remarkable feature of Gyo È È rgy Ligeti's music dating from the late 1970s is the return of triads, seventh chords and other traditional tertian harmonies. In the 1960s, he received acclaim for works such as AtmospheÁ res and the Requiem, which stressed the textural and timbral shaping of clusters at the expense of harmony as it is traditionally understood. In contrast, his latest comp compos osit itio ions ns ma make ke freq freque uent nt use use of tria triadi dicc sono sonori riti ties es,, albe albeit it plac placed ed in unfamiliar contexts (one would be hard-pressed to describe his recent music as neo-tonal).1 The triad, previously scorned for its recollections of tonal practice, is now tolerated. Manifestations of this tendency can be seen in works such as Hungarian Rock, Passacaglia ungarese, the piano e Â Â tudes Arcen-ciel and Cordes aÁ vide, and the Horn Trio. Perhaps the clearest instance of his new approach to harmony occurs in the opening section of his fourth e Â Â tude, Fanfares (shown in Ex. 1). 2 The harmonies in phrase 1 of Fanfares are a result of the coincidence of the ostinato in the left hand and the more melodic dyads in the right hand. The ostinato (which runs throughout the entire piece) is composed of a diatonic tetrachord and its transposition by a tritone ± the first tetrachord begins on c (c, d, e, f), the second on f  (f , g, a, b). This simple bipartite structure conflicts with the asymmetric metre, which divides the bar into three uneven beat beatss of 3+ 3+2+ 2+3 3 quav quaver erss (the (these se unit unitss are are brou brough ghtt out out by acce accent ntss in the the ostinato), ostinato), accenting accenting the notes c, f and g g. The right hand's dyads coincide with these accented ostinato notes. From the perspective of set theory, the resultant simultaneities are trichords of set-class 3±11. Later, the addition of a fourth note to the texture expands the harmonic palette to include 4±27 tetrachords in phrase 3, 3±10 trichords in phrase 4 and 4±20 tetrachords in phrase 5. From the perspective of traditional harmonic practice, these chords are nothing other than a series of triads and seventh chords ± major triads in phrase 1, minor triads in phrase 2. In phrase 3, the addition of an extra note to various chords (placed a third below the root of the triads) introduces minor seventh chords. In phrase 4, diminished triads first appear. And in the final phrase in this section (phrase 5), major seventh chords enter. Although these verticals may be identified easily enough, it is more difficult to determine how they function in the present context. Reference to tonal

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Blackwell Publishing Ltd. 2003. Published by Blackwell Publishing, 9600 Garsington Road, Oxford OX4 2DQ, UK

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Ex. 1

Fanfares, bars 1±17

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Â tudes pour Piano. Premier livre. E ß

Schott Musik International GmbH & Co. KG, Mainz. Reproduced by kind permission.

practice is oblique at best. Fanfares engages with, as Mike Searby writes, `the voca vo cabu bula lary ry but but not not the the synta syntax x of tona tonall musi music' c'..3 What What is reta retain ined ed of this this `vocab `vocabula ulary' ry' is the the consti constitut tution ion of the harmon harmonies ies themse themselve lves. s. They They are all tertian sonorities; or, as the excerpt from Fanfares indicates, they are all chords built upon the foundation of the triad. This is evident in the expansion of the major triads of phrase 1 into minor seventh chords in phrase 3. In phrase 1, when when the the dyad dyadss are are situ situat ated ed abov abovee the the osti ostina nato to,, the the resu result ltin ing g tria triads ds are are exclusively major (C, F, D D, A, etc.); in phrase 2, when the dyads are below the ostinato, the resulting triads are exclusively minor (D, F, A, B B , etc.). In phrase 3, the dyads return to the upper register, and the chords are major once again ± at least until the entry of the C minor seventh chord in bar 23. The conc concep eptu tual al orig origin in of this this simu simult ltan anei eity ty is clea clear: r: the the C mino minorr seve sevent nth h is the the product of an E E major triad plus c. ß

Blackwell Publishing Ltd. 2003

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Ex. 1

Fanfares, bars 1±17

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Schott Musik International GmbH & Co. KG, Mainz. Reproduced by kind permission.

practice is oblique at best. Fanfares engages with, as Mike Searby writes, `the voca vo cabu bula lary ry but but not not the the synta syntax x of tona tonall musi music' c'..3 What What is reta retain ined ed of this this `vocab `vocabula ulary' ry' is the the consti constitut tution ion of the harmon harmonies ies themse themselve lves. s. They They are all tertian sonorities; or, as the excerpt from Fanfares indicates, they are all chords built upon the foundation of the triad. This is evident in the expansion of the major triads of phrase 1 into minor seventh chords in phrase 3. In phrase 1, when when the the dyad dyadss are are situ situat ated ed abov abovee the the osti ostina nato to,, the the resu result ltin ing g tria triads ds are are exclusively major (C, F, D D, A, etc.); in phrase 2, when the dyads are below the ostinato, the resulting triads are exclusively minor (D, F, A, B B , etc.). In phrase 3, the dyads return to the upper register, and the chords are major once again ± at least until the entry of the C minor seventh chord in bar 23. The conc concep eptu tual al orig origin in of this this simu simult ltan anei eity ty is clea clear: r: the the C mino minorr seve sevent nth h is the the product of an E E major triad plus c. ß



TRIADIC HARMONY IN LIGETI'S RECENT MUSIC

285

Further complicating the role of the triads and seventh chords in Fanfares is the consis consisten tentt strati stratific ficati ation on of the textur texturee into into two seemin seemingly gly indepe independe ndent nt laye layers rs.. The The cont contra rast st in char charac acte terr and and func functi tion on betw betwee een n the the two two part partss is apparent: the rigid and unvarying ostinato sets off the more fluid, apparently improv improvisa isator tory y succes successio sion n of dyads. dyads. The The simult simultane aneiti ities es produ produced ced from from the conjunction of these two parts are not pronounced; the fact that they only come into being by straddling two separate textural strands weakens their sense of cohesion. Nevertheless, there is a covert relationship established early in the piece between the two parts, which delimits the fund of harmonies available at any given moment. Since the dyads coincide with accented ostinato notes, and since the ostinato is (by definition) not subject to alteration, only a handful of harmonies is feasible. According to this constraint, the dyad falling on the downbeat of the notated bar in phrase 1 may harmonise with the c in the ostinato in three ways, forming a C major, an A A  major or an F major triad. In phrase 2, the same note in the ostinato yields a C minor, an A minor or an F minor minor triad. triad. Beyon Beyond d this, this, there there are no hardhard-an and-f d-fast ast rules rules that that deter determin minee whic which h part partic icul ular ar harm harmon ony y `sho `shoul uld' d' or `sho `shoul uld d not' not' be used used.. (The (The only only succession that Ligeti consistently avoids is direct repetition of a chord. Even though the ostinato's c and f can both be harmonised with an F major triad, there is no occasion when both notes are harmonised with the same chord consecutively.) This method of arranging the harmonies ensures not only that the music will avoid clear-cut tonal progressions, but also that the musical surface, taken as a whole, will be more or less chromatic. One way of accounting for the incongruity between diatonic harmonies and the overall chromatic pitch space they occupy ± not to mention the incongruity between the presence of triads (the quintessential markers of tonal music) and their resolutely non-tonal setting ± would be to place Ligeti's late music under the rubric of the postmodern. Certainly, these works represent a renunciation of the (late) modernist concern for stylistic consistency and purity, leaning instead towards a more inclusive musical language. Yet this way of understanding his recent music may turn out to be trivial, if postmodernism is taken as a periodising term; by this measure, everything written in the past twentyfive to thirty years is, in one way or another, postmodern. Furthermore, it is vita vitall not not to use use the the term term `pos `postm tmod oder ern' n' simp simply ly as shor shorth than and d for for musi musica call syncretism ± that is, it is vital not to efface what is distinctive about this restorative gesture.4 Saying that the use of triadic harmony is postmodern does not say much, given the breadth and vagueness of this term. To do Ligeti's harm harmon onic ic prac practi tice ce just justic ice, e, one one need needss to situ situat atee it more more prec precis isel ely. y. For, For, as Fred Freder eric ic Jame Jameso son n has has poin pointe ted d out, out, ther theree are are às às many many diff differ eren entt form formss of postmodernisms as there were high modernisms in place, since the former are . . . specific specific and local local reactio reactions ns against these models'.5 Jameson's observation suggests that the best way to approach Ligeti's `rediscovery' of triadic harmony Music Analysis, 22/iii (2003)

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is to read it through the lens of the specific, local modernisms to which it responds. And this in turn suggests that there is not a single exclusionary logic that explains the prohibition of triadic harmony during the ascendancy of atonal and serial music in the 1950s, but that there are a number of logics, which must be explored in their own particularity. To this end, I will begin by discussing two arguments against the use of the triad in modern music ± those posited by Pierre Boulez and Theodor Adorno ± before returning to Fanfares to see how it may counter such arguments.6 But two disclaimers are in order ± one terminological, the other historical. Firstly, I will use the term `triadic harmony' throughout this article to refer to the entire range of tertian sonorities that have their conceptual basis in the triad. In many cases, this usage reflects the actual processes at work in Ligeti's later music, where seventh and ninth chords are the products of adding notes onto a triadic substrate (such is the case in Fanfares). Furthermore, I will use this term in a deliberately loose manner, since the harmonies he employs are as much symbolic entities as they are generative or syntactic ones. His late works may allude to functional harmony, without invoking functions as such: they are empty referents. But although clear-cut tonal function may be lacking, these chords play upon (and against) an essential quality shared by triads and seventh chords ± their relative harmoniousness. As Boulez's and Adorno's comments on triadic harmony will demonstrate, the problem posed by triads (and, by extension, seventh chords) is not simply their potential to invoke tonal convention, but their ability to fuse individual pitches into a single, supervenient entity. It is the ease with which triads and seventh chords are able to `coalesce', to come together as single perceptual units relative to nontertian sonorities, that is at issue in Ligeti's later works ± an ease that is as much the product of the acculturated familiarity of these harmonies as of psychoacoustical factors. Secondly, it should be noted that Ligeti's belated response to the positions staked out by Boulez and Adorno is indirect in nature. His reaction to the modernist aesthetic typified by these two authors takes shape as a reaction to the modernist impulse found in his own works of the 1950s and 1960s. By subjecting his own compositional past to a form of self-reflexive critique, he is able not only to create a new compositional style, but also to sever his lingering association with Darmstadt. In an essay written in the 1980s, he muses on the àging' of modern music: `the modernism and the experimental avant-garde of the fifties and sixties, don't they seem to be passe Â, part of history, part of the academy as well?'7 He then qualifies this thinly veiled attack on what has become a safely canonical modernism by applying the same critique to his own former style. He recognises that if the avant-gardism of the 1950s and 1960s has become senescent, then his own music must be rejuvenated as well to avoid the same fate. Rather than repeating proven formulae, he declares himself in ß




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favour of à modernism of today': `For me, this signifies in the first place a distancing vis-a Á-vis the total chromaticism and the dense polyphonic tissues that had characterized my music at the end of the fifties and the beginning of the sixties.'8 Ligeti's attempt to transcend modernism can be read as an attempt to transcend his own prior domination by modernism's various taboos, and thereby to assert his independence as a composer. But to achieve this independence, he is compelled to distance himself in turn from what he considers to be the empty fashion of postmodernism (which he, like many German critics, tends to equate with neo-romanticism in music):9 We live in a period of artistic pluralism. While modernism and even the experimental avant-garde still exist, `post-modern' artistic movements are increasingly manifest. `Pre-modern' would, however, be a more accurate way of describing these movements, for the artists who take part in them are interested in restoring historic elements and forms: naturalism in painting, columns, cupolas and tympana in architecture, and, in music, the recovery of both tonality and rhythmic-melodic figures impregnated with expressionistic pathos. The syntax of the nineteenth century is present in all the arts. 10

This disdain for the postmodern ± the notion that it represents a callow restoration of the past ± explains in part Ligeti's desire to institute a `modernism of today' (even though his stark opposition of the modern and postmodern betrays a continuing loyalty to the sort of binary logic that postmodern thought allegedly replaces). It is my contention that Ligeti's use of the triad in his music dating from the late 1970s onwards exemplifies this desire, a desire to negotiate a position between what he sees as the totalising (and thus reductive) claims of modernism and postmodernism ± a position between a blind affirmation or an equally blind negation of convention. II

In his lectures on composition given at Darmstadt in 1960, Boulez accounted for the exclusion of triads in serialism over the course of an extended digression. The reason for avoiding such harmonies, he argued, has little to do with their stylistic or structural inconsistency within an atonal context. Rather, Boulez's primary justification for excluding the triad has to do with its potential to interfere with the perception of serial structures. He begins by describing the problem posed by octaves: . . . octaves create a weakening or hole in the succession of sound relationships by way of reinstating a principle of identity denied by the other sounds, so that they are at variance with the principle of structural organization in the world in which they appear; . . . octaves must be completely avoided, at the risk of structural nonsense.11


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In other words, he claims that the identity of pitch-class in octaves is so strong that it conflicts with the serial ordering in which the octaves are embedded. The relative salience of the octave sets it apart from the rest of the texture, which undermines the intended serial groupings. Thus, octaves create simple relationships that cut through the complex pitch structures of serial music. Boulez continues by including triads in his list of proscribed sonorities: . . . the same applies to common triads, not only when they appear in their own vertical dimension but also if they are the products of the superposition of several horizontal structures. As with octaves, they reinstate the principle of identity denied by all the other sounds . . .12

He gives an excerpt from Webern's String Quartet, Op. 28, to illustrate this point, without providing any commentary. Ex. 2 is a reproduction of this excerpt. Based on his discussion, it appears that his dissatisfaction with the passage stems from the two chords he marks (F major and D major), which ostensibly distract the listener from the work's motivic structure. The pertinent ìnformation' contained in this passage, for him, resides in its motivic structure; the triads are nothing but noise. Adorno's treatment of the triad charts similar territory, but in a more nuanced way. In his early writings, he is open to the idea that conventional musical language might still be employed in a critical fashion by ironising or subverting it. He does not exclude the residue of musical tradition a priori, but rather deems it to be of value so long as it is defamiliarised by the composer and thus turned into a vehicle for social and musical critique. Thus, in his essay, Òn the Social Situation of Music', he views the music of a composer such as Weill in a generally positive light.13 By the time Adorno had written Philosophy Ex. 2 Excerpt from Webern, String Quartet, Op. 28 (taken from Pierre Boulez, Boulez on Music Today, Ex. 10) [ 0 1 3 ] poc o rit.

arco

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pizz.

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of Modern Music, however, his position had become more rigid. Here he treats

the triad as particularly susceptible to ideological distortion, arguing that the sense of accord intrinsic to this sonority, while tempting, presents a specious image of reconciliation to listeners. In a thoroughly antagonistic society, one that not only promotes but also feeds upon alienation and social fragmentation, such an audible token of social harmony becomes false. Furthermore, the absorption of discrete notes into a single, fused harmony suggests that the sense of accord manifest by the triad is grounded in a regressive form of domination. This latter point hinges upon his striking phenomenological reading of the sonority: The more dissonant a chord, the more sounds contained . . . the more `polyphonic' is this chord . . . The predominance of dissonance seems to destroy rational, `logical' relationships. Dissonance is nevertheless still more rational than consonance, insofar as it articulates with great clarity the relationship of the sounds occurring within [the chord] no matter how complex ± instead of achieving a dubious unity through the destruction of those partial moments . . . through `homogeneous' sound.14

Like Boulez, Adorno notes that the triad possesses a force of attraction, but he goes further in claiming that the cohesion of the triad effectively effaces its constituent pitches. The audible unity of the triad is purchased at the expense of the individual note. Hence, the image of social harmony that the triad projects is reactionary in character, a throwback to a historical situation where the unity of the social organism was vouchsafed by a transparent form of domination (feudalism). Instead of a progressive surpassing of alienation, then, the triad is emblematic for Adorno of a wholly regressive subordination of the individual with respect to the totality; instead of confronting the social antagonisms inherent in a class-based society, the embrace of the triad by modern composers would disguise these contradictions at the aesthetic level. In contrast, Adorno sees dissonant sonorities as symbolically resisting such a regressive form of domination, since they do not absorb discrete notes into a single, unified sonority. Not only is the dissonant sonority valorised for its intrinsic `polyphony'15 ± i.e. its refusal to subvert the impulses of the individual notes in favour of a single, global impulse ± but also because it better reflects the social fragmentation and alienation endemic in advanced capitalism, and in this regard is considered to be more honest to the structure and experience of modernity.16 Let us return now to Fanfares, to evaluate it in relation to Boulez's and Adorno's arguments. What is striking about this and other eÂ tudes is their adamant emphasis on the horizontal, rather than the vertical, dimension. Despite the presence of triadic harmony, whose intrinsic tendency is to fuse these two polyphonic layers together into a single consonant sonority, the Music Analysis, 22/iii (2003)

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Ex. 3

Stratification in the opening of Fanfares (bars 1±7)

(3

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1986 Schott Musik International GmbH & Co. KG, Mainz. Reproduced by kind permission.

layers manage to maintain a strong degree of independence from one another. The source of this independence lies in the conflicting rhythmic organisation of the two layers (as Ex. 3 shows). Whereas the ostinato is three `beats' long (the `beats' being uneven groups of two and three quavers), the dyads' phrases are five `beats' long, keeping the two parts out of alignment. As a result, the dyads' rhythmic patterning is irregular, constantly changing with respect to the ostinato. The dyads' first melodic unit has the rhythm 3+2+3+3+2; the second has the rhythm 3+3+2+3+3; and the third has the rhythm 2+3+3+2+3. It is only with the fourth melodic unit that the rhythmic patterning of the dyads begins to repeat, completing the cycle. The two parts lack a sense of coordination at the level of the phrase, a fact that is compounded by the repetitions of the ostinato. The lack of variation in the ostinato reinforces the sense that the two parts proceed along separate tracks, diminishing the salience of any vertical formed by the coincidence of the two layers. Although the parts do come into alignment once every five bars, the asynchronous phrase structure of the parts denies a sense of textural coherence. In this respect, Fanfares is representative of Ligeti's later works, in that the simplicity of its harmonies stands in contrast to the complexity of its rhythm. Indeed, this excerpt shows how the use of triads intersects with another preoccupation of his recent work, namely the exploration of rhythmic and metric dissonance. The two tendencies seem to go hand in hand: harmonic consonance offsets rhythmic/metric dissonance and vice versa. It is hardly a coincidence that Ligeti's restoration of the triad in the late 1970s occurs at roughly the same time as his first attempts to synthesise the dual influences of ß




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Conlon Nancarrow's Studies for Player Piano and the polyrhythmic intricacies of sub-Saharan music.17 The result of this conjunction is that metric and harmonic dimensions are placed in conflict with one another. The two dimensions pull in opposite directions: the consonant harmonies tend to unify the texture, while the multiplicity of rhythmic patterns stratifies it. This conflict ± between horizontal and vertical dimensions ± is hardly new to Western music; it is simply that Ligeti's works exacerbate a feature present in all polyphonic music. Both his later music and more traditional contrapuntal genres play off the perceptual difficulties involved in focusing one's attention on multiple simultaneous structures. As the theorist James Wright and the psychologist Albert Bregman have asserted, auditory processes possess the Gestalt principle of `belongingness', which consists in `the tendency for a particular piece of sensory evidence to be allocated to one or another perceived object, but not to both at once'.18 The consequence of this principle is that it sets simultaneously unfolding dimensions at odds with one another, so that our ability to perceive coherence in one dimension curtails our ability to perceive coherence in the other. That is to say, it is easy to hear a note as part of a line or as part of a chord, but it is difficult to hear a note as part of both at the same time. This sheds light on Adorno's criticism of the triad: because of its acoustical consonance and cultural familiarity, it always threatens to outweigh the polyphonic impulse of the individual notes. Wright and Bregman assert that if the factors favoring the sequential grouping of the components are stronger, the fusion of simultaneous elements may be inhibited. Similarly, if the factors favoring simultaneous fusion dominate, the components may be restricted from grouping sequentially with other components that resemble them. 19

Bearing this in mind, it is easy to see how Ligeti's organisation of rhythm and harmony at the opening of Fanfares addresses the listener's inability to attend fully to both line and chord at the same time. Both present the listener with structured perceptual objects. The rhythmic and textural independence of the parts is conducive to stratification, whereas the sheer familiarity of the triad is conducive to cohesion. Since it is difficult to concentrate on both structures at the same time, listeners will tend to focus on one more than the other: one plane is foregrounded, and the other is `heard' (if not `listened to' as such). And since the factors favouring auditory streaming more often than not outweigh those favouring vertical cohesion in his recent works, it is more likely that listeners will direct their attention towards the horizontal dimension. The consonance of the triad is present, but it is relegated to a secondary position in the perceptual field. Even if Ligeti's music from the late 1970s onwards manipulates some of the same characteristics that guide conventional polyphony, it is nonetheless clear Music Analysis, 22/iii (2003)

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that his music uses them for an entirely different purpose. Wright and Bregman, whose article addresses the rules of traditional counterpoint, note that the conflict between horizontal and vertical structures is often used as a means of lessening the phenomenal impact of dissonance. For instance, the stepwise preparation and resolution of dissonances in strict counterpoint affords enough cohesion in the horizontal dimension that the discord present in the vertical dimension tends to be weakened. From this perspective, the continuity provided by something as simple as a passing-note helps to soften the impact of non-harmonic notes by deflecting attention away from whatever vertical sonorities they may incidentally form with other voices.20 In most polyphonic compositions, this principle is extended to the formal level, so that the relative independence of the lines within phrases is redeemed by the fact that they come together in stable, fused sonorities at points of syntactic import, such as cadences. These points of harmonic cohesion thus take on rhetorical significance, in that they affirm the centripetal, unifying force of the triad over the centrifugal force of the line. But, as the excerpt from Fanfares indicates, Ligeti turns the same attribute of conventional polyphony on its head. Here, the factors that favour horizontal integration do not serve as a means of suppressing dissonance, but work instead as a means of suppressing one's perception of the consonant sonorities themselves. From this perspective, his use of triads can be seen as a compromise between a modernism that proscribes conventional harmonies and a tradition that demands their presence. By situating the triad in a context that is designed to fragment texture into seemingly unrelated layers, he is able to undercut the triad's function as a means of unifying the texture into a whole. III

Rhythmic and metric conflict is perhaps the most effective way of splitting musical texture into discrete horizontal layers. But it is not the only way. Three additional strategies undermine the fusion of vertical sonorities in Ligeti's recent music, dividing the texture by means of harmonic collection, melodic process or the use of repetitive figures. In this section, I shall discuss excerpts from three works (the tenth piano e Âtude, Der Zauberlehrling; the Alla marcia movement from the Horn Trio; and the second piano e Â tude, Cordes aÁ vide) in order to illustrate these additional strategies.

Der Zauberlehrling

Beginning in bar 66 of Der Zauberlehrling, Ligeti uses the harmonic differentiation of voices to undercut the impact of triadic harmony. Throughout this ß



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passage, the chromatic aggregate is divided into two discrete collections (as seen in Ex. 4). The right hand plays melodies based on the white-note diatonic scale, and the left hand plays melodies based on the black-note pentatonic scale. This partitioning of the chromatic, reminiscent of Barto Âk, has been a mainstay throughout Ligeti's career, serving to dilute the neutrality of total chromaticism by distributing it into distinct collections (see, for instance, bars 13±22 of AtmospheÁres (1961), where he partitions the aggregate in this way in order to lend colour to an otherwise harmonically neutral cluster). This procedure allows him to have it both ways, as it were, reconciling the ostensible modernity of chromaticism with the ostensible conventionality of diatonicism. The situation is complicated in this passage by the presence of triads. Each hand presents descending scalar fragments, their entrances staggered with respect to one another, and these overlapping lines are arranged so that a triad is formed at the beginning of each fragment, where a new line intersects with the end of a line in the other hand. As in Fanfares, the perception of the triads is weakened by the segregation of the layers on the horizontal dimension. In Der Zauberlehrling, however, it is the staggering of the lines and, more importantly, their organisation according to two discrete harmonic spaces that disrupts the ability of the vertical sonorities to bridge these spaces. The Alla Marcia from the Horn Trio

In both Fanfares and the passage from Der Zauberlehrling discussed above, rhythm plays a vital role in stratifying the horizontal dimension. In the middle section (bars 31±103) of the Alla marcia, the third movement of the Horn Trio,21 such rhythmic differentiation of the layers is altogether lacking (the opening bars of this section are shown in Ex. 5). Rhythmically, this section consists of a virtually unbroken succession of crotchets; texturally, it is homophonic, set in two voices for the most part, breaking into a thicker texture only towards the end of the section. There is a reason for this general lack of rhythmic and textural variation. As it turns out, two different ordered arrangements of the chromatic aggregate form the harmonic framework for the section. The rhythmic and textural uniformity ensures that each of these orderings is presented as a fixed succession of six dyads. The first of these orderings of the aggregate (Ex. 6a) recalls the distorted `horn-call' motif that opens the first movement of the work, transposing the motif down a major third. Similarly, the second of these orderings (Ex. 6b) anticipates the opening of the final movement, transposing the first three dyads of the Finale down a minor second. The two orderings thus serve as connective tissue, linking the opening and closing movements of the work. But the two orderings also serve to parse the section into even, fourbar groups: two statements of ordering A are followed by two statements of ß




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Ex. 5 Horn Trio, third movement (Alla marcia), opening bars of the middle section Più mosso, ohne Akzente, sehr gleichmäßig und fließend / without accents, very evenly and fluid . = 76 (ganze Takte / whole bars) 31 32 33 con sord., legato, espressivo con delicatezza

34

35

36

37

Vn ( poco) con sord.

(simile)

sempre poco in relievo

Horn in F ( poco) dolce, espressivo con tenerezza espressivo con delicatezza

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sempre legatissimo

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(simile) 8 simile

ß


ordering B, which are followed by two further statements of A, and so forth. Irregular slurring and frequent changes in timbre prevents this section from becoming monotonous. The phrasing contradicts the articulation of the underlying harmonic structure. Towards the end of the section, another factor contributes to the obscuring of the underlying pitch structure ± the `filling-out' of the texture with triads and other harmonies. Extraneous pitches begin to appear during the latter half of the section, supplementing those that comprise the two ordered aggregates. The first of the extraneous pitches appears at the end of bar 57, with the C  in the horn. The addition of this pitch realises the latent harmonic potential of the Music Analysis, 22/iii (2003)

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ERIC DROTT

Ex. 6a Ordering A of the aggregate, middle section of the Alla marcia

Ex. 6b Ordering B of the aggregate, middle section of the Alla marcia Ordering B:

3

6

8

4

6

3

Opening dyads of Horn Trio, IV:

3

6

8

dyad with which it coincides (E±G) by forming a C minor triad. Other structurally `superfluous' pitches surface over the next twenty bars or so, although it is only around bar 79 that the accretion of pitches begins in earnest. From here until the end of the section in bar 103, more and more notes accumulate around the series of dyads that make up the alternating orderings of the aggregate, forming at first triads, then seventh chords and then ninth chords. Ex. 7 is a harmonic reduction of bars 79±97. The remainder of the passage (bars 99±103) continues the accumulation of pitches, burying all traces of triadic harmony beneath the welter of notes. Diatonic clusters, followed by chromatic clusters, gradually take the place of the triads and seventh chords. In the Alla marcia, the horizontal and vertical dimensions still compete with one another, albeit in a manner that is altogether different from the conflict encountered in Fanfares and Der Zauberlehrling. On the one hand, the vertical dimension is more cohesive than in works such as Fanfares, insofar as the extra pitches not only harmonise with the fixed succession of dyads, but also fail to stray rhythmically from the other part. Neither rhythm nor register slice up pitch space into discrete, horizontal layers. There is nothing in the setting, in the arrangement of the parts, that works against the audibility of the resulting chords. On the other hand, there is a more subtle force that serves to distinguish the component pitches of each harmony from one another, a force that runs counter to the cohesion of the vertical dimension. It is not the way that the chords are presented that leads to their fragmentation, but the harmonies themselves ± the pitches that comprise them ± that deny their simple ß




297

Ex. 7 Harmonic reduction, Alla marcia, bars 79±97 A

ordering: 79

A

E 7

D 7

AM7

[0146] B M/m

f

E 7

D 7

d

A 7

g

g

[0347]

B

B

83

B

G7

E

B 7

[026]

F

[025]

A

f

E

B

[016]

am 7

(+g)

gm7

DM7(+g)

A

87

A 7

g

7

c 7

am7(+g )

cm7

f m7

A M7

B

G7

c m7(+g)

[0246]

c (+d )

f

B

91

f 7

G7

EM7

B 7

g

7

FM7

g m7

cm9

A9

am7

A 95

‘F9’

‘G9’

c m7

[0127]

gm7(+c )

AM7

‘E 9’

[012468t]

[014579]

Note: All accidentals affect the note that immediately follows. The notation reflects (roughly) the score of the Trio in spacing and in spelling of chords. For the purposes of identifying chords, the analysis assumes enharmonic equivalence where necessary (i.e., A–D –E–A in bar 79 is identified as an A major seventh chord, despite the unusual spelling).

cohesion. The distinction between structural and non-structural pitches, between the notes that make up the chromatic framework of the section and the notes that decorate this framework, is enough to subvert the chordal texture. Indeed, the sheer repetitiveness of the two aggregates works against the fusion of the chords, since this not only establishes but also reinforces the two orderings in the listener's ear.23 A makeshift hierarchy is set up within the Music Analysis, 22/iii (2003)

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298

Ex. 8

ERIC DROTT

Cordes aÁ vide, bars 1±16 Andantino con moto, molto tenero

= 120

dolce, espr. sempre legatiss.

Piano m.g.

(con ped.)

3

3

3

3

3

3

sempre

sempre

3

3

3

3

3

espr.

3

3

3

espr.

Horn Trio. ß


ß




299

horizontal dimension between the invariant dyads that form the core of the section and the mutable notes that accompany them. It is this hierarchy ± a hierarchy that is not a product of a pre-existent musical syntax, but simply the product of repetition ± that derogates vertical sonorities, fixing them in a secondary position. Á vide Cordes a

Like the middle section of the Alla marcia, the opening bars of Ligeti's second piano e Âtude, Cordes aÁ vide,24 are homophonic (see Ex. 8).25 Up to bar 11, both hands play even streams of quavers, although differences in phrase length, slurring and accentuation add a degree of rhythmic tension to the passage. (Following bar 11, the piece introduces increasingly complicated polymetric relationships between the two voices.) But unlike the middle section of the Alla marcia, Cordes aÁ vide does not differentiate the horizontal layers by means of a quasi-hierarchical distinction between structural and non-structural pitches. Rather, stratification arises in this work out of melodic directedness: the pattern of descending perfect fifths that gives this piece its title (open strings) recurs with such regularity that it stresses the linear dimension over the harmonic. This strong horizontal impulse disguises the intervallic and harmonic relationships created by the counterpoint of the two voices ± namely the series of imbricated seventh chords that are a by-product of the ubiquitous melodic fifths. Ex. 9 labels the seventh chords present in bars 1±4. Like the remainder of the section, this four-bar excerpt is rife with such intimated harmonies, which overlap to such a degree that multiple harmonic interpretations are possible. The left hand's line, in particular, is more predictable than the looser material presented in the right hand. Its phrases present a sequence of seven quavers, all of which consist of a series of descending fifths, with the final quaver serving as a link to the following phrase. There is, in addition, a regular pattern that guides the large-scale trajectory of the left hand's groups. The accented notes that initiate each phrase form an ascending line (as seen in Ex. 10). At first, each

Ex. 9

Harmonic progression, Cordes aÁ vide, bars 1±4 B M7 E –B

F M7 e m7

bm7

A M7 gm7

cm

dm7

E M7 C M7 (no 3rd)

b 7

C 7


em7

DM7 [027]

d7

E 7

ß

A M7 E M7 f m7

EM7


300

ERIC DROTT

Ex. 10 Left hand's ascent, Cordes aÁ vide, bars 1±13 1

2

3

4

5

6

7

8

9

10

12

13

group begins a semitone above the previous one; later, when the line deviates from the stepwise motion, there is still some attempt to fill in the gaps. The motion from c2 in bar 4 to d 2 in bar 5 is followed by a compensatory downward motion to d2 in bar 6, before the ascent resumes its course. Likewise, the groups skip over f 2 at first, proceeding from e2 in bar 7 to f 2 and then g2 in bar 8, before `correcting' the mistake by touching upon f 2 in bar 9. The only truly radical break in this gradual ascent comes at the very end of the passage, with the skip from f 2 in bar 9 to b 2 in bar 10, a skip that effectively marks the close of the e Âtude's opening section.

In contrast, the right hand represents the melodically free voice during this section, presenting the perfect fifth as a mobile motivic cell. Listening to the piece, there is little to suggest a logic guiding the choice and juxtaposition of these fragments; there are sudden shifts in registers, motifs break off without warning and the transposition of motifs seems arbitrary. Analysis suggests, however, that harmonic concerns play a role in determining the path followed by the right hand's motifs. A case in point is the repetition of the opening motif in bar 2, which is broken off prematurely. Ex. 11a compares the first statement of this motif with its repetition in bars 2 and 3. At the beginning of bar 3, the music unexpectedly leaps up to c3 instead of returning to a2, as occurs in the Ex. 11a 1

2

Ex. 11b 2

parallel octaves

ß




301

initial statement of this motif in bar 1. Had the motif continued as before, the series of seventh chords would have been disrupted, as Ex. 11b demonstrates; indeed, the result would have been parallel octaves between right and left hands. Similar harmonic considerations guide the right hand's motion elsewhere during the first eleven bars, with sudden breaks in the melodic line acting to preserve the succession of seventh chords formed between the two voices. But even if latent harmonic concerns are a motivating factor in the organisation of the right hand's motifs, the texture ensures that these harmonies occupy a secondary position in the listener's perceptual field. By rendering the two lines so distinct, so independent of one another, Ligeti relegates the harmonies to the phenomenal background, concealing the influence that harmonic considerations exercise on the right hand's line. 26 Instead of determining the course of the lines, the vertical relationships sound more like the inadvertent result of the coincidence of the lines.

*

In all of these works ± Fanfares, Der Zauberlehrling, the Alla marcia and Cordes aÁ vide ± horizontal and vertical dimensions are set at odds with one another. But in each, Ligeti effects this opposition differently ± through conflicts in rhythm and phrase structure in Fanfares, through the differentiation of harmonic collections in Der Zauberlehrling, through ostinati in the Alla marcia and through melodic process in Cordes aÁ vide. As a result, each of the works responds in its own way to the arguments of Boulez and Adorno. For Boulez, the triad is problematic because of its tendency to interfere with other structures. In Fanfares and other such works, however, the extreme polyphonic stratification reverses the situation. It is now the horizontal forces that interfere with the perception of the triad. For Adorno, on the other hand, it is the tendency of the triad to obscure the particular that casts doubts on its aesthetic and ideological legitimacy. Clearly, the textural stratification encountered in these works forestalls the triad's ability to conjoin the various pitches into a homogeneous unit. Yet in order to accomplish this feat ± in order to dissolve the force binding simultaneous notes together ± it is necessary to strengthen the force binding successive notes together. It is the use of regular metres, predictable ostinati and contrasting harmonic collections that ensures that the cohesive force of the lines is commensurate with that of the harmonies. In Ligeti's works, individual notes may escape from the domination of the triad that Adorno so abhorred, but only by being absorbed into horizontal structures instead. Music Analysis, 22/iii (2003)

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302

ERIC DROTT

IV

The interdiction on the triad in Adorno's and Boulez's writings can be traced back to Schoenberg. Yet in his writings on the subject, Schoenberg voices fewer objections to the consonance of the triad than either Boulez or Adorno (which is not to say that the avoidance of consonance had no role to play in his aesthetic considerations). Nor was his objection to the use of the triad predicated on ideological grounds (at least not explicitly). Writing in 1926, early on in his deployment of the twelve-note technique, Schoenberg was sensitive to the residues of tonal practice that triads possessed. Thus, his argument against the presence of triads in post-tonal music rests as much on the syntactical implications these harmonies would have as on their purely sonorous or perceptual qualities. The triad, according to Schoenberg, was more than a euphonous collection of notes; it was a token of the tonal system as a whole, with all of its syntactical norms and expectations. To incorporate a single triad into an otherwise non-tonal context was to run the risk of deforming this context, as the triad brought into play an entire system of musical relationships. For this reason, he claimed that My formal sense (and I am immodest enough to hand over to this the exclusive rights of distribution when I compose) tells me that to introduce even a single tonal triad would lead to consequences, and would demand space which is not available within my form. A tonal triad makes claims on what follows, and retrospectively, on all that has gone before. 27

Schoenberg's comments could be reformulated as follows: listeners steeped in tonal music cannot help but hear triads as expressing tonal functions. Composers who indulged in placing such structurally unsupported harmonies in their works were guilty of misleading the listener, making promises they could not keep. One way of avoiding the problem outlined by Schoenberg would be to expunge any trace of triadic harmony from post-tonal music. Yet Schoenberg himself did not feel that such harmonies ought to be restricted solely to strictly tonal compositions (a fact that is borne out in a number of his later works, such as The Ode to Napoleon): èven standing where I do at the present time, I believe that to use the consonant chords, too, is not out of the question, as soon as someone has found a technical means of either satisfying or paralyzing their formal claims'.28 He allows the possibility of including triads and other familiar tertian chords in non-tonal contexts only if the historical and conventional associations that these chords carry with them can be neutralised ± that is, if the internal organisation of a work could somehow defuse their residual tonal functions. In some respects, his fears seem over-inflated. One may doubt whether the presence of a triad in a twelve-note work, say, could singlehandedly overturn its internal structure and institute a quasi-tonal hierarchy. ß




303

His fears may be accounted for in part by his perception of the historical situation at the time he made these comments; at an early stage in the establishment of the twelve-note technique as an alternative to tonality, he justifiably saw the continuing sway of convention as a tremendous threat. Besides, his fears seem more plausible when reformulated along more moderate lines. He is surely correct to claim that triads and seventh chords are not neutral entities, but are charged with associations that are difficult, if not impossible, to avoid. Indeed, it is hard to imagine a method that would be capable of severing totally the connection that listeners make between such harmonies and tonal practice. It is more likely that some residue of their tonal use will linger on for most listeners, even if such harmonies are arranged in a manner that consistently disappoints habitual expectations. A single triad may not be able to transform a twelve-note piece into a tonal one all by itself, but it may influence how one hears its immediate musical context. Schoenberg's comments are suggestive of the interpretation of triads and seventh chords in Ligeti's later works. By deflecting attention away from these chords, Ligeti effectively weakens their `formal claims'. If such harmonies are themselves subordinated perceptually, then whatever residual tonal impulse they possess will be subordinated as well. Yet even if these impulses are marginalised, this does not mean that they disappear altogether. Rather, their impact on the perceived surface of these works is indirect. Just as the triads and sevenths, taken by themselves, are `heard' without being `listened to', so too are the successions they form. Progressions that conform to the listener's expectations ± be they the ingrained expectations of tonal syntax or those raised by the immanent constraints of the work ± will give the music a semblance of coherence; those that fail to do so will give a semblance of unpredictability. Once again, Fanfares will serve as the point of departure. An argument could be made that the triads used in the opening phrase (F major, B major, C major, A major, etc.), in addition to the trichord outlined by the accented notes in the ostinato (C, F and G, which are enharmonically equivalent to an F minor triad), project F as some sort of centric pitch. But the chord-to-chord succession resists a straightforward tonal interpretation. Likewise, the presence of harmonies that fall outside the putative tonal centre of F (such as the E major triads in bars 3 and 7) are hard to reconcile with a tonal reading. From this perspective ± the perspective of inculcated tonal expectations ± the succession of resultant harmonies is unpredictable. Although listeners may not attend to this succession as the most salient dimension of the musical fabric, it will nonetheless colour their perception of the piece. At the same time, the predictability of the ostinato works against this implicit sense of harmonic unpredictability. The work may exploit one's expectations vis-a Á-vis tonality, but it manages to satisfy other expectations at the same time. Despite the Music Analysis, 22/iii (2003)

ß


304

ERIC DROTT

relative flexibility in the choice of harmonies (each accented ostinato pitch can be harmonised with one of three triads), the simple fact that the dyads must harmonise with C, F or G, depending on metric position, limits the fund of chords available at any moment, as well as in the phrase as a whole (in the first phrase, the harmonic vocabulary is limited to C, F, A, D, B and E triads).29 Lacking a conventional syntax, the music offers up an ersatz one. The result is a succession that is both predictable and unpredictable at the same time: the chords are predictable to the extent that they invariably harmonise with the accented notes of the ostinato, unpredictable to the extent that the progressions resulting from this constraint escape the residual demands of tonal syntax. The same ambiguous situation holds in many of the other works discussed in this article. There is an interplay between the linear impulse, which typically guides the harmonic motion and provides it with its immanent logic, and the inability of the resulting succession to fulfil whatever tonal implications the triads might suggest. Consider Cordes aÁ vide. In the opening section (Ex. 8), the relative regularity of the descending fifths in the left hand maps out a restricted set of possible sonorities. The intervallic consistency and predictability of the horizontal dimension compensates for the absent tonal syntax. Each sonority created out of the falling fifths pattern in both hands will sound `justified' as a consequence. This offers Ligeti the opportunity to play the expectations created by the internal structure of the work off the residual tonal implications of the underlying harmonies. For instance, following the d3 that begins bar 4, the right hand's line breaks off, its next phrase beginning some two octaves lower, on c 1 (see Ex. 12). This disruption in the right hand's line coincides with the low point of the left hand's line, marking the moment as particularly salient. The harmonies that ensue gain relative prominence as a result: in particular, the A major seventh harmony formed by the parallel tenths between the hands comes to the fore. Yet the registral break that occurs at this moment is mitigated by the way it is prepared: the dyads immediately preceding the leap down to the c1 spell out an E dominant seventh. It is unlikely that listeners will directly perceive this harmony; it is more likely that this gesture will indirectly Ex. 12

d7

ß

Quasi-cadential progression, Cordes aÁ vide, bars 3±4

E 7

A M7 E M7




305

influence how the salient musical features are understood. Elsewhere in Ligeti's late works the disjunction between the presence of tertian harmony and the absence of tonal syntax gives the music a sense of consistent unpredictability. Here, the momentary coincidence of intrinsic expectations (the falling fifths) and extrinsic ones work to smooth over the palpable disjunction in the melodic line. This passage is vital for understanding the dialogue established between Ligeti's triadic pieces and the tonal system to which they implicitly refer. Chords and (as is the case in this passage) brief progressions associated with common-practice tonality are not assumed; they are generated by the systems set up by Ligeti. For the most part, this means that the demands of tonal syntax are partially negated. But the result of this denial of expectations is not so much a feeling of frustration as one of defamiliarisation. The vocabulary stays the same, along with occasional fragments of a familiar syntax; it is simply that the harmonic substructure is arranged according to an alien logic, one that sounds sensible in its own right, but that is strange nonetheless. V

By way of conclusion, I should like to discuss a passage in Ligeti's sixth piano e Âtude, Automne aÁ Varsovie, which epitomises the dichotomy between triadic harmony and linear stratification that I have sketched thus far. Of the first set of e Âtudes, the sixth is by far the most complex, unfolding in some passages as many as four distinct metric layers at the same time. Yet the most striking moment in the piece comes approximately halfway through, when the proliferating lines come to a momentary halt. At first there is a brief interlude that presents the theme ± the `lamento' motif that recurs in many of Ligeti's recent works ± in parallel tritones, at the registral extremes of the piano. Following this interlude, the music returns to the simple melody plus accompaniment texture of its opening, with the left hand performing the lamento motif while the right hand picks up the tritone as an accompanimental motif (shown in Ex. 13). This simplicity is short-lived, however. Almost immediately, in bar 63, the middle voice begins to move in contrary motion to the descending lamento theme, creating melodic wedges (as shown in Ex. 14). As the passage continues, the twovoice polyphony in the left hand is filled out: notes begin to accumulate around the dyads, providing harmonic support. The lower voice introduces a third note to the lamento line in bar 68, which is eventually joined by a fourth note in bar 72. The addition of these notes transforms the line from a succession of dyads into a series of descending seventh chords.

In this passage, the way that the seventh chords are formed provides their sequence with a semblance of logic. By gradually adding notes to the lamento


ß


306

Ex. 13

ERIC DROTT

Automne aÁ Varsovie, bars 58±79

8

58

8b

8

62

con ped. 8b 8

64

8

66

8

68

dim.

Horn Trio. ß


ß




307

8

70

8 sim.

72

crescendo poco a poco

8

74

(cresc.)

8

76

sotto

(cresc.)

8 cresc. poco a

poco

78


ß


308

Ex. 14

ERIC DROTT

Melodic wedges, Automne aÁ Varsovie, bars 62±7

62

theme, the succession of chords takes advantage of the predictability of this theme. As in Fanfares and Cordes aÁ vide, whatever logic the series of chords has derives from the force of the lines that comprise it. But before long, the fragmentation that had been temporarily held at bay begins once again. In bar 73, the top voice in the left hand's incomplete D minor seventh chord splits off to form a new pulse stream. Whereas the left hand's succession of chords had adhered to a pulse made up of seven semiquavers, the new line beginning with the C presents a pulse made up of multiples of four semiquavers (the pulse is notated by crotchets and semibreves on the score). The same phenomenon occurs in bar 77. Here, the lowest note splits off, forming a pulse stream whose basic unit consists of multiples of five semiquavers. This process of fragmentation distils in a single gesture the primary characteristics of triadic harmony in Ligeti's recent music. As with the other works discussed thus far, in Automne aÁ Varsovie triadic harmony ceases to serve as an emblem of cohesion, but instead becomes radically unstable, incapable of being held together. But unlike the other works, here the stratification of parts is dramatised. The chords unravel before us, under pressure from the centrifugal force of the polyphonic layers. The ability of triadic harmony to unify the musical texture, to bridge the space separating different polyphonic threads, dissolves. Harmonies are built up only to splinter into independent lines. If, for Schoenberg, the problem with using triadic harmony in post-tonal music was the danger of awakening inappropriate expectations in the listener, then the solution to this problem posited by Ligeti's recent works is to use the strong linear impulse to overwhelm such expectations. If, for Boulez and Adorno, the problem with triads lay in their tendency to cut across the musical work, interfering with the `proper' perception of its intrinsic, autonomous pitch structure, then Ligeti's response is to explore the possibility of reversing this tendency, so as to cut across the triad itself. Yet the restoration of the triad in the works discussed above, a compositional manoeuvre that opposes the modernist desire to escape or obliterate convention, is hardly an absolute rejection of modernism. Instead of simply affirming the tradition that gave rise to triadic harmony, Ligeti's music reaches a similar end by pursuing an entirely different route: it strives to negate the modernist tradition of negation. 30 In ß




309

other words, his desire for a `modernism of today' can be understood as applying the critical, exclusionary aesthetic of modernism to modernism itself (although this way of transcending the modernist aesthetic may approach a postmodernist ethos too much for Ligeti's liking).31 His use of the triad does not simply depart from the serial goal of creating a self-contained musical structure, free from the weight of tradition. Rather, what is truly distinctive in his deployment of the triad in Fanfares, Cordes aÁ vide, Automne aÁ Varsovie and other such works is that it challenges the cohesive function of triads, even in the process of restoring them.

NOTES

1.

This return of the triad may be understood as an extension of the `restoration of interval' described by Jonathan Bernard in `Ligeti's Restoration of Interval and Its Significance for His Later Works', Music Theory Spectrum , 21/i (1999), pp. 1±31.

2.

In the examples, I identify major and minor triads with upper and lower case letters (e.g. C and c for C major and c minor triads), respectively; 7 by itself designates dominant sevenths (e.g. B7); M7 designates major seventh chords; and m7 designates minor seventh chords. On occasion, a harmonic designation will be given to incomplete `chords', so that a 3±8 trichord may represent, for instance, an incomplete dominant seventh. Even though this expands the range of possible tertian sonorities considerably ± to the point where it may seem that the term ceases to serve as a useful distinction ± it is almost always the case that such incomplete chords will be situated in a series of unambiguous triads and sevenths. In other words, context makes it quite clear whether a 3±4 actually represents an incomplete major seventh chord, or whether it is just a 3±4.

3.

Mike Searby, `Ligeti's ``Third Way'': ``Non-Atonal'' Elements in the Horn Trio', Tempo, 216 (2001), p. 17. Along similar lines, Richard Steinitz remarks that the use of triadic harmonies in a non-tonal fashion `generate[s] a less definable ``supertonality'' (Ligeti has called it ``consonant tonality'')'. See Richard Steinitz, Gyo È rgy Ligeti: Music of the Imagination (London: Faber and Faber, 2003), p. 291.

4.

For discussions of Ligeti's relationship to postmodern aesthetics, see Searby, `Ligeti the Postmodernist?', Tempo, 199 (1997), 9±14; Be Âatrice RamautChevassus, Musique et postmoderniteÂ (Paris: Presses Universitaires de France, 1998), pp. 90±95; and John Cuciurean, À Theory of Pitch, Rhythm and Intertextual Allusion for the Late Music of Gyo Èrgy Ligeti' (PhD diss., SUNY Buffalo, 2000), pp. 139±82 (esp. pp. 180±82). There has been a strong inclination among writers on Ligeti's music, however, to dispute the `postmodernity' of his late style: see, for instance, Searby, `Ligeti the Postmodernist?'; Hermann Danuser, `Zur Kritik der musikalischen Postmoderne', in Das Projekt Moderne und die Postmoderne, ed. Wilfried Gruhn (Regensburg: Gustav Bosse Verlag, 1989), pp. 69±83; Constantin Floros, Gyo È rgy Ligeti: Jenseits Avantgarde und Postmoderne (Vienna: Lafite Verlag, 1996), pp. 229±31; and Steinitz, Gyo È rgy


ß


310

ERIC DROTT

Ligeti , pp. 328±9. Attempts to distance Ligeti from the term `postmodern' may be a result, in large part, of his own expressions of disdain for its aesthetic (see n . 9).

5.

Frederic Jameson, `Postmodernism and Consumer Society', in Hal Foster (ed.), The Anti-Aesthetic (Port Townsend, WA: Bay Press, 1983), p. 112.

6.

A more comprehensive survey of Ligeti's harmonic language would account for the intermittent appearance of triads and seventh chords in his music of the late 1960s and early 1970s. These harmonies, after being more or less suppressed in the music he wrote immediately following his departure from Hungary in 1956, gradually reappear in the later 1960s (following the Requiem), and usually adopt one of two different guises. Firstly, these chords may occur as individual links within a longer process of gradual harmonic transformation. The chords that emerge in this case are evanescent entities; furthermore, they are typically masked by other, concurrent sonorities. For instance, beginning in bar 110 of Melodien, the cello unfolds a D  minor chord, at the same time as the viola unfolds a C major chord and the second violin a G major chord. As a result of their overlap, none of these chords is audible as such. These harmonies have a purely notational existence. (Other instances of the same general approach occur in Melodien, bars 88±91, first and second violins; CouleÂe, p. 11, fourth system; and Ramifications, bars 81ff.) Secondly, triads and seventh chords occasionally crystallise in the form of the oft-cited `Ligeti signal' ± the diatonic sonorities that emerge when the massed chromatic clusters so characteristic of his music of the 1960s disperse. Usually, such Ligeti signals consist of some combination of major seconds and minor thirds (such as [024], [025] or [036]). Occasionally, however, a triad or seventh will emerge. An interesting case in point can be seen in bar 30 of Ramifications, where a B seventh chord results from the combination of a B±F  dyad (played by the second group of strings) and a D±A dyad (played by the first group of strings). Notationally, this appears to be a B minor seventh chord. Yet because the first string group is tuned a quarter-tone higher than the second, the resulting chord lies somewhat awkwardly between a B minor seventh and a B major seventh. The aim, it would seem, is to defamiliarise the chord. Other, similar `cameo' appearances by triads or seventh chords can be found in bar 90 of Lux Aeterna (the D minor chord in the basses) or bars 87±91 of Continuum (which features successive B major and minor triads).

7.

`. . . le modernisme et l'avant-garde expe Â rimentale des anne Âes cinquante ou encore des anne Âes soixante, n'appartiennent-ils pas aussi au passe Â , a Á l'histoire, a Á l'`àcade Âmie''?' (Ligeti, `Ma position comme compositeur aujourd'hui', Contrechamps, 12/13 (1990), p. 8).

8.

`. . . je me declare pour un modernisme d'aujourd'hui. Pour ma part, cela signifie en premier lieu une prise de distance vis-a Á-vis du chromatisme total et des denses tissus micropolyphoniques qui caracte Ârisaient ma musique vers la fin des anne Âes cinquante et au de Âbut des anne Âes soixante' (ibid.).

9.

Largely absent in the early reception of postmodernism by German-language music critics is an appreciation for what Hal Foster has termed the `postmodernism of resistance'. Rather, in German writings on contemporary music a suspicion is more frequently encountered that what passes for postmodernism is aesthetically (if not ideologically) regressive. This has much to do with the

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equation of postmodernism with neo-romanticism ± problematic from an American perspective, but comprehensible from a German one, given the prominence of composers such as Wolfgang Rihm, Hans-Ju È rgen von Bose and Wolfgang von Schweinitz during the 1970s and 1980s. Helga de la Motte-Haber, for instance, has noted that, in Germany, `The term ``postmodernism'' spread like wildfire and throughout the early 1980s was more or less universally defined as a neo-conservatism which seemed to characterize the Neo-Romantic language of a new generation of composers' (`Postmodernism in Music: Retrospection as Reassessment', Contemporary Music Review, 12/i (1995), p. 77). The general scepticism towards postmodernism in German critical circles may also be a result of the profound influence of Frankfurt School thinkers such as Adorno and Ju È rgen Habermas. Adorno's defence of modern music, and Habermas's repudiation of certain strands of postmodern thought as the work of `young conservatives', serve to fuel whatever suspicions German-language writers on contemporary music might bear towards the idea of the postmodern. See Habermas, `Modernity: an Incomplete Project', in Foster (ed.), The AntiAesthetic, pp. 12±15. 10.

`Nous vivons dans une pe Âriode artistique pluraliste. Alors que le modernisme et me Ãme l'avant-garde expe Ârimentale existent encore, des mouvements artistiques ``post-modernes'' se manifestent de plus en plus. ``Pre Â-modernes'' serait toutefois un mot plus juste pour designer ces mouvements, car les artistes qui en font partie s'inte Âressent a Á la restauration d'e Âlements et de formes historiques: le naturalisme en peinture, les colonnes, coupoles et tympanons en architecture et, dans la musique, une tonalite Â retrouve Âe ainsi que des figures rythmiques-me Âlodiques impre Âgne Âes de pathos expressionniste. La syntaxe du XIXe sie Ácle est pre Âsente dans tous les arts' (Ligeti, `Ma position', p. 8). Elsewhere, he has said that `My taste runs counter to the neo-movements. I hate neo-Expressionism and I can't stand the neo-Mahlerite and neo-Bergian affectations, just as I can't stand postmodern architecture' (Tunde Szitha, À Conversation with Gyo È rgy Ligeti', Hungarian Music Quarterly, 3/i (1992), p. 17). See also his comments on postmodernism in `Wohin orientiert sich die Musik? Gyo È rgy Ligeti im Gespra Èch È sterreichische Musikzeitschrift, 49/i (1994), pp. 7±8. mit Constantin Floros', O

11.

Pierre Boulez, Boulez on Music Today, trans. Susan Bradshaw and Richard Rodney Bennett (London: Faber and Faber, 1971), p. 46.

12.

Ibid., p. 48.

13.

Theodor Adorno, Òn the Social Situation of Music', in Essays on Music, selected with introduction, commentary and notes by Richard Leppert, trans. Susan H. Gillespie (Berkeley: University of California Press, 2002), pp. 391±436. Observe that the only thing separating Weill's `surrealistic' music from Stravinsky's neoclassicism in Adorno's opinion is its conscious connection of aesthetic alienation to social alienation. Hence, already at this early stage of his work on the sociology of music, Adorno detects a risk in the appropriation of convention for critical ends: Ìt is beyond question that Weill's music is today the only music of genuine social-polemic impact, which it will remain as long as it resides at the height of its negativity; furthermore, this music has recognized itself as such and has taken its


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ERIC DROTT

position accordingly. Its problem is the impossibility of remaining at this height . . . The further course of events reveals another danger in ambiguity: illusion blends into false positivity, destruction into communal art within the realm of the status quo, and behind this mocking primitivity, conjured forth by its bitterness, comes into view the naõ Ève-credulous primitivism of a reaching-back . . .' (pp. 410± 11). At this point, he exempts Weill from this potential backsliding (he notes that ìt is hardly to be expected that he will fall victim to the dangers of the undangerous'), but such comments set the stage for the later hardening of his position vis-a Á-vis attempts to integrate tonal means into modern music. 14.

Theodor Adorno, Philosophy of Modern Music, trans. Anne G. Mitchell and Wesley Blomster (New York: Seabury Press, 1973), p. 59.

15.

Elsewhere, Adorno opposes the stability of triadic harmony to the instability of atonal harmony ± harmony that has become latently polyphonic: `With the increasingly dissonant character of harmony, the tension in individual sonorities also increased. No sonority was self-contained, like the old consonance, the ``resolution''. Every sonority seemed to be laden with energy, to point beyond itself, and every one of the distinct individual notes contained within it required an independent ``melodic'' continuation of its own, instead of there being a succession of one synthesized overall sonority after another' (`Function of Counterpoint', in Sound Figures, trans. Rodney Livingstone (Stanford, CA: Stanford University Press, 1999), p. 127).

16.

By the time of his Aesthetic Theory (ed. Gretel Adorno and Rolf Tiedemann, trans. Robert Hullot-Kentor (Minneapolis: University of Minnesota Press, 1997)), Adorno's position had evolved further. What is remarkable in this later work is his attempt to rescue harmony from its prior stigmatisation. This is a twofold process. Firstly, he generalises harmony by resurrecting the classical aesthetic idea that harmony, broadly construed, concerns the balance between part and whole: ìnspiration, if it is to count, must gel; that tacitly presupposes an element of organization and coherence, at least as a vanishing point' (p. 157). Secondly, he maintains that modern art, despite the appearance of disorder and incoherence, still possesses a faint link with this broader conception of harmony, insofar as such art stands in a relationship of determinate negation with respect to the classical notion of harmony. Even if there is no immanent unity in a given work, this unity persists insofar as the active denial of harmony depends upon a memory or trace of some antecedent notion of harmony: `What speaks for the survival of the concept of harmony as an element is that artworks that remonstrate against the mathematical ideal of harmony and the requirement of symmetrical relations, striving rather for absolute asymmetry, fail to slough off all symmetry. In terms of its artistic value, asymmetry is only to be comprehended in its relation to symmetry' (p. 158). What proves problematic, then, is the specific form that harmony takes in the triad, since the chord presents an imbalance in the relationship of part to whole. It is not harmony that is to be discarded, but a particular manifestation of harmony: `The mistake of traditional aesthetics is that it exalts the relationship of the whole to the parts to one of entire wholeness, to totality, and hoists it in triumph over the heterogeneous as a banner of illusory positivity' (p. 157). The spectre of this mistake haunts the broader notion of

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aesthetic harmony as well, to the extent that the attempt to coordinate the various parts of a work risks lapsing into a form of domination: `With regard to its elements, such aesthetic harmony is negative and stands in a dissonant relation to them: they undergo something similar to what individual tones once underwent in the pure consonance of a triad' (p. 157). What is intriguing here is Adorno's claim that the aims of the whole do not accord with the aims of the elements, which introduces a point of conceptual dissonance to the otherwise perceptual consonance of the triad. 17.

Â tudes for Piano', Sonus, 9/i (1988), pp. 3±7; See Ligeti's comments in Òn My E È ber Conlon Nancarrow', ``Èine unglaublich direkte Emotionalita È t'': U MusikTexte, 73/74 (1998), pp. 61±4; and in his interview with Denys Bouliane, `Stilisierte Emotion: Gyo È rgy Ligeti im Gespra Èch', MusikTexte , 28/29 (1989), pp. 52±62.

18.

James K. Wright and Albert S. Bregman, Àuditory Stream Segregation and the Control of Dissonance in Polyphonic Music', Contemporary Music Review, 2 (1987), p. 70.

19.

Ibid., p. 72.

20.

The preceding discussion is drawn from Wright and Bregman (ibid., p. 74).

21.

A brief discussion of this section can be found in Ulrich Dibelius, `Ligetis Horn Trio', Melos, 46/i (1984), pp. 54±5.

22.

Ligeti's fascination with just intonation and alternative tuning systems ± incipient in works like the Horn Trio and the Piano Concerto ± has assumed a more prominent position in his musical output during the 1990s, in works such as the Violin Concerto and the Hamburg Concerto. This fascination may be traced back to a number of sources, including Harry Partch (whose music Ligeti encountered during his sojourn in California in the early 1970s); the late works of Claude Vivier; the music of sub-Saharan African and Balinese gamelan music (the latter explicitly cited in the eighth e Âtude, Fem); and, most recently, the music of the French Spectralists (hence the title of the fifth movement of the Hamburg Concerto ± `Spectra').

23.

In fact, this passage can be seen as manifesting what Wright and Bregman describe as the `principle of repetition' in auditory streaming: `. . . the obstinate repetition of the same melodic unit, from which the `òstinato'' derives its name, clearly contributes to the perceptual segregation of simultaneous tones in polyphony.' They continue by asserting that the òstinato seems to have the effect of capturing each tone into a larger linear structure, the repetitive sequence of tones. The sequence itself seems to act as a unit, whose repetitions group sequentially with one another, rather than with simultaneous tones' (Àuditory Stream Segregation', p. 80).

24.

In its original published form, the e Âtude was entitled Cordes vides. However, Ligeti changed the title in the so-called `final' edition of the e Âtudes to Cordes aÁ vide. The change in title may have something to do with the latter's richer potential for wordplay. No longer does the title simply refer to òpen strings', but


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Ligeti Triads

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