Le marteau sans maître and the Logic of Late Capitalism



Roger W.H. Savage


Pierre Boulez's Le marteau sans maître is a modernist musical landmark that prefigures a postmodernist world. (1) Following his experiments with total control, Boulez, in Le marteau, rejects the automatistic compositional systems spawned by a fetish for rigid serial procedures. As an exercise in Cartesian doubt, this fetish engenders the moribund aesthetic from which Boulez's struggles to free Le marteau sans maître. The advance that Le marteau represents over the high serialist world it leaves behind manifests the work's central paradox: through folding an element of indeterminacy into its generative construction, Le marteau sans maître surpasses modern music's reduction to quasi-mathematical systems by simulating a return to a principle of expression more familiar to Schoenberg's freely atonal works.

By mastering the paradox of a musical world that envelops the sense of irrationality engendered by the exercise of indiscriminate serial control, Le marteau captures the logic of late capitalism within its high modernist style. In his book Postmodernism; or, the Logic of Late Capitalism, Frederick Jameson characterizes postmodernism "as an attempt to think the present historically in an age that has forgotten how to think historically in the first place." This forgetfulness is critical to the experience of the postmodern world, where the logic governing processes of production and distribution constitutes a system that eclipses its global hold. According to Jameson, "postmodern consciousness, may . . . amount to not much more than theorizing its own condition of possibility, which consists primarily in the sheer enumeration of changes and modifications." (2) Reduced to clocking these variations, postmodern consciousness justifies the simulacra of choices and possibilities engendered by a system that charts them in advance. Despite postmodernist hostilities toward totalizing systems, this justificatory stance conceals from itself how the systemic production of differences occludes their constitutive global order.

Le marteau's prefiguration of the logic of late capitalism inheres in its rejection of a totalizing serialist program. Through breaking with the reductivist ethos of total serial control, Le marteau exploits total serialism's incipient irrationality by simulating Schoenberg's profoundly dissonant world. Schoenberg's renunciation of tonality echoes in Le marteau's ethereal sound-universe. Their resonances reveal conflicting historical dispositions. Poised at the precipice of a modernist confidence in rational strictures, Le marteau attests to a precarious condition in which reason and discord are in danger of surrendering their meaning and force.


The Dissonance's Emancipation

Le marteau 's distance from Schoenberg's world at first obscures a deeper affinity between Boulez's reformed serialist practices and Schoenberg's expressionistic style. In drawing distinctions between Le marteau and Pierrot lunaire, a work with which Le marteau has sometimes been compared, Boulez comments that Le marteau sans maître follows a period of experimentation with serial procedures. Composed at a time when "strict serialism was being abandoned in the hope of discovering more general and more flexible laws governing sound phenomena," (3) Le marteau escapes the sterility of reductivist serial operations. Conversely, Schoenberg composed Pierrot lunaire in 1912, before he discovered his twelve-tone method. From Boulez 's vantage-point, Schoenberg's compositional power "vanished from that part of his work that he considered most worthy to survive" (4) - namely, his twelve-tone works. Rather, for Boulez, Schoenberg's power is manifest most forcibly in works that, at first, seemed to Boulez the most ephemeral of Schoenberg's oeuvre.

The distinction Boulez draws between Le marteau sans maître and Pierrot lunaire - that is, that "one was written before and the other after a period of more radical research" (5) - defines Schoenberg's discovery as a critical watershed. For him, as for Schoenberg, Schoenberg's invention of a compositional practice based on the twelve-tones was comparable in its organizational power to that of the tonal principle it supplanted. The distinction Boulez draws between Pierrot lunaire's coquettish flirting with "bad taste," and the purity of René Char's poetic language in Le marteau sans maître, masks the critical difference between Pierrot's aesthetic ambiguity and Le marteau's stylistic rigor. (6) The works that, for Boulez, attest to Schoenberg's compositional power manifest the perplexing condition evinced by this ambiguity: prior to Schoenberg's discovery of the twelve-tone method, Pierrot lunaire and Erwartung, together with his other freely atonal works, break with tonality without replacing it with a comparable organizing principle. Consequently, this break is a defining moment for the experimentation in 12-tone and serial techniques that precedes Le marteau's stylistic reformation.

The proximity of Le marteau sans maître's post-hyperrational aesthetic with Schoenberg's expressionistic one conceals a decisive difference between them. Boulez highlights this difference by distinguishing between the periods of research that he identifies with Schoenberg's twelve-tone works and his high serialist ventures. Schoenberg's break with tradition emancipates the dissonance from the normative requirement of its resolution; Boulez's reformulation of high serialist practices revalues his previous attempt to make a clean sweep of traditional precepts.

Schoenberg frees dissonance from requiring its resolution by renouncing tonal closure. By refusing to force his music into "the Procrustean bed of tonality," (7) he contests the sense of reason manifest by the principles of tonal coherence. Traditionally, the final cadence justifies the necessity of a course of musical progress that unifies individual moments within the totality they comprise. Consequently, tonal closure establishes the work's or movement's coherence and identity as the goal that confirms the logic of a work's progression. Expressive uses of dissonance during the late nineteenth and early twentieth centuries weaken the closing cadence's legitimacy by loosening tonality's hold. Confronted with the loss of the traditional closing's compositional pertinence, Schoenberg resolves the dilemma of the cadence's faltering legitimacy by emancipating dissonance.

Freeing dissonance from its required resolution paradoxically intensifies its discordance by arresting the drive toward resolution. The aporia that Carl Dahlhaus identifies - namely, that the dissonance's isolation proves to be the reverse of its emancipation - highlights the temporally dynamic nature of dissonance. (8) Schoenberg lays bare the musical phenomenon of closure by shattering the tonal order. By suspending dissonance's resolution, he exposes how closure and resolution are temporally and dialectically dependent upon overcoming discord. Schoenberg's proclamation of a state of emergency, which Dahlhaus suggests contradicted a prevailing confidence in progress by affirming the tendency to view approaching historical events as an impending disaster, acquires its force through giving a figure to the dissonance's aporetic emancipation. (9) This proclamation announces the crisis to which Schoenberg's freely atonal works give voice: by exposing the emancipated dissonance's uncertain futurity, Schoenberg's subversion of tonal order expresses a failing confidence in humanity's ability to master its own destiny. (10)

Emancipating dissonance engenders the perplexing unity of a work that paradoxically coheres only in a temporally fragmented way. The "deep ambivalence about the value of order and logic in composition," (11) which Joseph Auner argues accompanies Schoenberg's reliance on intuition in composing works such as Erwartung, underscores the aporias produced by Schoenberg's renunciation of tonality. The courage Schoenberg praises in looking the puzzle of a work's irreducible disharmony "in the eye" without timidly asking about the 'solution'" (12) eschews the "notion of a higher order standing behind apparent disharmony." (13) By laying discord bare, Schoenberg articulates the experience of a crisis that militates against the modernist pretense to master history and time. (14)

The twelve-tone method's retrospective justification for the dissonance's emancipation subsequently reduces Schoenberg's radical break with tonality to the narrative logic he negates. Ironically, by subordinating his renunciation of tonality to the twelve-tone method's discovery, Schoenberg and his commentators ratify the "grand" narrative subverted by Schoenberg's rejection of tonal closure. Retrospective justifications of Schoenberg's initiative legitimate the twelve-tone method's continuity with tonal conventions that Schoenberg's emancipation of dissonance leaves behind. The comparison that Schoenberg draws between the twelve-tone method's centralizing power and tonality's gravitational force eclipses the rupture between them. (15) Despite his assault on tradition, the "grand" narrative he and his commentators invoke subsumes the critical impulse that, in his expressionistic works, turns against the master narrative of reason's role within a modernist concept of history's ineluctable advance. As a measure of the retreat from this crisis, the twelve-tone method's historical and aesthetic justification eclipses the aporetic condition to which the dissonance's emancipation attests.


The Emancipated Dissonance's Simulacrum

Boulez's radicalization of Schoenberg's discovery, that relating the twelve-tones only to each other restores a sense of logic, seals this eclipse by consecrating this master narrative's legitimacy. The urge that motivates Boulez to "reduce the articulations of the [musical] discourse . . . to pure serial functions" (16) in Structures 1a ratifies the twelve-tone method's legitimacy by denouncing Schoenberg's failure to realize the import of his discovery. By condemning Schoenberg's "profound misunderstanding of serial functions as such, as engendered . . . by the actual serial principle," (17) Boulez accedes to the master narrative shattered by Schoenberg's abandonment of tonal closure. His radicalization of the twelve-tone method establishes a new order in which a hierarchy of global functions replaces the emancipated dissonance's vehemence with its own systems of generative processes.

Structures 1a represents one of Boulez's attempts to "make a clean sweep of one's heritage . . . to see how it might be possible to reconstitute a way of writing that begins with something which eliminates personal invention." (18) This experiment notwithstanding, the compositional automatism Boulez achieves through the serial coordination of pitches, durations, dynamics and modes of attack produces an excess of order that engenders the work's disorder. An obsession for matrices [magic squares] in Structures 1a leads to the pointless transplantation of the pitch series which, György Ligeti remarks, arbitrarily reorders series of durations. (19) By supplanting Schoenberg's lack of concern with the "logical connection between serial forms as such and derived structure," (20) Boulez seeks to eradicate all vestiges of any "pre-existent, non-serial rhetoric." (21) The incipient irrationality engendered by this attempt manifests the contingencies of particular structural configurations. Derived from a system of serial co-ordinations whose numerical values correspond to pitches, durations, dynamics and modes of attack, these configurations are a function of this serial universe's self-sustaining, generative processes.

Boulez's denunciation of the fetish of numerically coordinated serial structures in Le marteau sans maître folds the insipient irrationality of Structures 1a into its aesthetic practice. Through reacting violently against the "sterile cul-de-sac" (22) of an order intended to guarantee the composer's infallibility by virtue of its conceptual integrity, Boulez reforms his compositional ideal by expanding the serialist universe. By introducing an element of local indeterminacy, he institutes a more labile serial rhetoric, which is itself a function of a systemic derivation of structural differences that simulate the tensions and ambiguities haunting Schoenberg's expressionistic works.

In Le marteau sans maître, Boulez subsumes the rational excesses of Structures 1a within Le marteau's reformed serial rhetoric through the systemic creation of structurally differentiated configurations. His use of the technique of pitch multiplication in the opening movement, avant l'artisanat furieux, evinces his rejection of a quasi-mathematical rigor. By incorporating structural differences within its generative process, pitch multiplication produces arrays of intervallic complexes that are only irregularly reducible to the original series from which they are derived. Multiplication here consists in augmenting the intervallic content of a subgroup drawn from a series with that of another by adding the latter to the former. (23) Dividing a series into asymmetrical groups (grouping a series into subgroups of 2, 4, 2, 1 and 3 pitches respectively, for example) systematically deforms the serial uniformity that is also the source of Structure 1a's conceptual sterility. On Lev Koblyakov's analysis, the exchanges between flute, vibraphone, guitar and viola in the movement's opening measures derive from the multiplication of serial complexes. (24) In Le marteau sans maître, systemic deformation is the obverse of the systemic integration that, for Boulez, constitutes the serialist universe's founding principle.

Le marteau's advance beyond Boulez's experimentation with total serialism in Structures 1a depends upon this systemic production of serially differentiated complexes to institute instances of local indiscipline within a serially disciplined style. Stephen Heinemann regards the complex multiplication that he describes Boulez deploying in Le marteau sans maître and Oubli signal lapidé (composed, according to Lev Koblyakov, two years earlier than Le marteau sans maître and subsequently withdrawn) as "an elegant, logical extension of the serialist tradition that provides the composer with a great deal of flexibility at the local level." (25) Yet, the logical connection between derived pitch complexes and the generative series that he identifies in his analysis evinces how the serial operation that generates these complexes also differentiates between them. By circumscribing differences that licence the work's local indiscipline, these operations engender an aura of expressive excess. Through capitalizing on this aura, Le marteau's aesthetic masters the paradox of discipline and indiscipline by folding them together.

Le marteau's polemical relation with the serial discourse's reduction to its "zero degree" (26) depends upon its mastery of this paradox. By rationalizing the incipient irrationality of hyper-rational constructs, the stylistic practice of Le marteau sans maître transforms the process where all possibilities are determined into one that differentiates between coordinated components. The kaleidoscopic character of serially generated structures gives rise to a glassy, ethereal quality, which Steven Winick suggests transmutes "the irrational chaos of our age into music." (27) In the work's sixth movement, bourreaux de solitude, for example, networks of circulating pitches, durations and dynamics/modes of attack obfuscates their overall coordination. The fluidity of a matrix in which each permutation produces a new coordination of these parameters obscures the systemic operations that produce the differences they engender. Continually shifting an additive series of durations and a series of dynamics/modes of attack against a chromatic scale produces twelve systemically differentiated alignments. Consequently, these individuated permutations are a function of their global coordination within the matrix that governs their differences. (28)

Le marteau's aura of inspired unpredictability is a function of the paradox it masters. By simulating the explosive world of Schoenberg's freely discordant music, Le marteau sans maître abandons the rigorously contrived world of Structures 1a for the disciplinary order of more expansive techniques. Separated from Schoenberg's expressionistic world by an experiment in radical control, Le marteau recaptures the animate, ephemeral quality of the dissonance's aporetic emancipation.

The recapture of a principle of expression in this post-experimental work eclipses its stylistic raison d'être. By singling out Le marteau sans maître as a striking example of the rejection of "post-Webernian pointillism," Theodor W. Adorno abrogates his own critique of modernist music. For him, Le marteau stands as a "critique of the ideology of [initiating] any absolutely new beginning," (29) such as Boulez attempted in Structures 1a. From Adorno's vantage point, Le marteau's renunciation of the tendency to completely rationalize the compositional process recovers the horizon of Schoenberg's expressionistic impulse. By assimilating Le marteau's auratic quality to the sensuous allure of Pierrot lunaire's "crystalline unity of imaginary essence and a totality of dissonance," which he argues draws "modern art into a no-man's-land that is the plenipotentiary of a livable world," (30) Adorno obscures the difference between them. For him, modern music contradicts its own idea by reproducing the rational strictures that he identifies with a wholly administered society. The cost to this music, for the construction of a transparent nexus of meaning, is its "own aesthetic substance and coherence." (31) Le marteau sans maître advances this cost through its regulation of local indeterminacies; through its simulation of the dissonance's aporetic emancipation, its stylistic logic extends beyond the hyper-serialist organization that Adorno identifies with instrumental reason's calculative ethos.

Replacing hyper-rational constructs with global operations that regulate local indeterminacies effectively inverts the transparency of the nexus of relations governed by each. The opacity of Le marteau sans maître's serial complexes conceals the global determinations of local indeterminacies. Uniquely individuated figures are a function of the system of derivations that coordinate them. Consequently, the differences between individuated figures, which in Schoenberg's atonal works evince the principle of "developing variation," create the semblance of disjuncture, rupture and discord. Transposed from the paradigmatic onto the syntagmatic plane, super- and juxtaposed serial complexes mimic the perplexing condition engendered by Schoenberg's renunciation of tonality.

Le marteau 's aura of furious calm, which David Gable attributes to Boulez's characteristic inversion of tradition, bears out the paradox that this work masters. (32) The order that encompasses the furious exchanges on the syntagmatic plane engenders a feeling of the sublime. This feeling springs from the apparent discord between serially derived fragments and the work's temporal configuration as a whole. Yet, by engendering this discord, the order that escapes representation replaces the real condition for the sublime with its own simulacrum. According to Kant, the feeling of the sublime is the "feeling of displeasure that arises from the imagination's inadequacy" to provide an adequate representation for an object. However, this feeling "is at the same time also a pleasure, aroused by the fact that this very judgment, namely, that even the greatest power of sensibility is inadequate, is [itself] in harmony with rational ideas." (33) Consequently, the pleasure that reason takes in its own idea elevates the imagination beyond the abyss in which it "is afraid to lose itself." (34) Le marteau's inversion of the condition for this feeling marks its reversal of the twelve-tone method's radicalization: by mastering the paradox of expressive excesses engendered by the system that disciplines them, Le marteau sans maître - the "hammer without a master" - advances the ideal of serial rhetoric by simulating its aesthetic return.

The sense of sublime violence that envelops Le marteau's kaleidoscopic fragments attests to the atmosphere of desolation that surrounds its destruction of dissonance and discord. By replacing the emancipated dissonance's vehemence with differentially derived serial complexes, Le marteau usurps the temporal force unleashed by Schoenberg's refusal to resolve dissonances and discords. Interstices and disjunctions that simulate this force on the syntagmatic plane are only the obverse of differentially derived complexes. Hence, the illusion of their temporal vehemence is a function of the same operation that engenders an aura of furious calm. René Char's text in bourreaux de solitude pointedly announces the "thought" that Le marteau expresses: "Le pas s'est éloigné le marcheur s'est tu / Sur le cadran de l'Imitation/ Le Balancier lance sa charge de granit réflexe" (The footstep has receded the walker is silent/ On the dial of Imitation/ The Pendulum sets in motion its load of reflex granite). (35) The hammer that measures the dead intervals of its own movement, Le marteau sans maître presages the passage from the crisis manifest by Schoenberg's subversion of tonal order, to a condition in which the failing confidence in our ability to master our destiny gives way to historical forgetfulness.


Le marteau sans maître and the Logic of Late Capitalism

The occultation of the crisis manifest by Schoenberg's renunciation of tonality draws Le marteau's expression of its rarefied world onto this historical ground. By exploding the principle of unity inherent to tonal schemata, Schoenberg's emancipation of dissonance lays bare the crisis of a mode of historical thinking that presumes to grasp history in its totality. Schoenberg's negation of tonality, which he effects by renouncing tonal closure, anticipates more recent suspicion of "grand" historical narratives by contesting their presumption of an ideal temporal synthesis. By supplanting the perfect mediation projected by the principle of tonal closure, his figuration of unresolved discords radically negates tonal closure's justificatory schema.

Expressionistic works such as Erwartung and Pierrot lunaire therefore voice a crisis whose force extends beyond the tonal tradition's explosive rupture. By challenging tonality's justification as the principle of a work's temporal coherence - a challenge that evinces the fin de siècle's failing confidence in its political and social institutions - these works articulate an experience that Hans-Georg Gadamer suggests strangely unifies the twentieth century, following the First World War. (36) According to Gadamer, Europe's optimism regarding "progress and bourgeois cultural idealism could not survive" the First World War's technological slaughter. After the First World War, Europe's shattered self-consciousness lapsed deeper into doubt. This lapse, which the neo-Kantian era's "great romancers, Nietzsche's extreme radicalism, and . . . ideology critique and psychoanalysis" (37) disseminated, is symptomatic of the modernist crisis. Schoenberg evinces this crisis by abandoning an ideal temporal coherence rooted in the principle of tonal closure. Consequently, the crisis he unleashes bears out the historical experience prefigured by his freely atonal works.

Le marteau sans maître's relation to this experience highlights the difference between its post-hyper-serialist aesthetic and that of Schoenberg's expressionistic compositions. By mastering the paradox of the hammer that beats out forms without the guiding hand of a master, Le marteau evinces an artful discipline that conceals its global determinations behind the semblance of local differences. Through supplanting automatistic serial procedures, its techniques resemble the art of discipline that Michel Foucault argues "individualizes bodies by a location that does not give them a fixed position, but distributes them and circulates them in a network of relations." (38) According to Foucault, discipline "may be identified neither with an institution nor with an apparatus; it is a type of power, a modality for its exercise, comprising a whole set of instruments, techniques, procedures, [and] levels of application." (39) In short, by fabricating differences delimited and controlled by centralizing forces, discipline proves itself to be a technology of power.

The aura that emanates from the exercise of this technology in Le marteau marks this work's distance from the crisis announced by Schoenberg's emancipation of the dissonance. Its atmosphere of controlled violence, which springs from differential operations that give rise to a semblance of discord, eclipses the crisis that Schoenberg unleashes. By operating within the sheen of these supremely ordered operations, Le marteau's simulation of the experience to which this crisis attests is the work's ultimate paradox. As a polemical rejoinder to hyper-rational serial strictures, Le marteau sans maître metes out its distance from Schoenberg's atonal world through surpassing the twelve-tone method's radicalization.

Le marteau's controlled violence prefigures the logic of late capitalism by folding the crisis engendered by the emancipated dissonance's negation of tonal closure into its compositional style. The "inverted millenarianism," (40) which, Frederic Jameson suggests, replaces the utopian or dystopic premonitions with the sense of the end of the modernist project, presupposes a radical break with the idea of historical progress. By deriving its existence from the "waning or extinction of the hundred-year-old modernist movement," (41) postmodernism eschews the crisis portended by humanity's failing confidence in its capacity to master history; modernist art's aesthetic or ideological repudiation announces the end of this crisis by inverting its apocalyptic millenarianism. (42)

Le marteau prefigures this end in mastering the paradox of disciplined indiscipline. Its significance as a modernist work notwithstanding, its stylistic logic resembles the "systemic modification of capitalism" (43) that Jameson identifies with postmodernism. By transforming processes of production and distribution into a global network, this modification institutes a system of regional differences. Jameson astutely argues that, despite postmodernist hostilities to the concept of totalization, a "system that constitutively produces differences remains a system." (44) Through its global expansion, capitalism's dispersive and atomistic logic conceals its totalizing function within a system of socio-economic and geo-political differences. The impossibility of mapping the totality of relations within a system of circulating differences evinces an ethos that resonates with Le marteau sans maître's aura of disciplined violence. By mastering its paradox, the "hammer without a master"sounds out the ethos of a world whose forgetfulness of the crisis manifest in Schoenberg's atonal works becomes its own historical condition.




Le marteau sans maître's distance from Schoenberg's expressionistic world anticipates the destiny of the crisis to which Schoenberg's renunciation of tonality bears witness. By abandoning tonality, his emancipation of dissonance radically negates the sense of temporal coherence and unity rooted in the principle of tonal closure. Despite the twelve-tone method's retrospective justification of the dissonance's emancipation, this historic event shatters the "grand" historical narrative of which it is a part. Schoenberg's rejection of the principle of tonal closure exposes the crisis at the heart of the modernist project by giving voice to the crisis of a utopian horizon that recedes more quickly than it can be approached.

Le marteau's distance from Schoenberg's expressionistic world is prescient of a condition in which historical forgetfulness replaces the thought of this crisis. Its riposte to the incipient rationality of hyper-rational constructs anticipates this condition's inverted millennialism by folding an incipient irrationality into its aesthetic rationale. Schoenberg's negation of tradition expresses the lapse into doubt that haunts the modernist confidence in progress; Le marteau's rejoinder to the twelve-tone method's radicalization exploits the excesses that spring from Boulez's attempt to expunge all vestiges of tradition. The aura that emanates from Le marteau's artful discipline consequently transfixes its raison d'être in the labyrinthine coordination of kaleidoscopic figures.

Le marteau's occultation of the experience, to which Schoenberg's renunciation of tonal closure attests, presages a condition that Jameson identifies with postmodern consciousness. By emanating from the transposition of kaleidoscopically generated figures onto the syntagmatic plane, Le marteau 's prescient aura prefigures the fate of an age that may have forgotten how to think historically. Poised between Schoenberg's engagement with the modernist experience and a failure of historical thought, Le marteau sans maître's auratic world presents the challenge of renewing our historical substance.


June 2005 Los Angeles, California

1. An earlier version of this paper was presented at the Ninth Conference of the International Society for the Study of European Ideas, University of Navarro, Pamplona, Spain, 2004.

2. Frederic Jameson, Postmodernism: or, the Cultural Logic of Late Capitalism (Durham: Duke University Press, 1991), p. ix.

3. Pierre Boulez, Orientations, trans. Martin Cooper (Cambridge, Mass.: Harvard University Press, 1986) p. 330.

4. Boulez, Orientations, p. 330

5. Boulez, Orientations, p. 330.

6. See Boulez, Orientations, p. 343. Where "Pierrot, following Hartelben's text, is full of stylistic and aesthetic ambiguities - 'coquetry flirting with bad taste', as Schaeffner calls it - . . . the purity of René Char's language [in Le marteau sans maître] forbade anything of that sort." According to Boulez, this obliged him "to discover a style 'as such' free of any oblique references."

7. Arnold Schoenberg, Style and Idea, trans. Leo Black (Berkeley: University of California Press, 1975), p. 86.

8. Carl Dahlhaus, Schoenberg and the New Music, trans. Derrick Puffett and Alfred Clayton (Cambridge: Cambridge University Press, 1987), p. 77.

9. Dahlhaus, Schoenberg and the New Music, p. 88.

10. See my "Dissonant Conjunctions: Schönberg, Adorno, and Bloch," Telos 127 (Spring 2004).

11. Joseph Auner, "'Heart and Brain in Music': The Genesis of Schoenberg's Die glückliche Hand," Constructive Dissonance, ed. Juliane Brand and Christopher Hailey (Berkeley: University of California Press, 1997), p. 118.

12. Arnold Schoenberg, Letter to Kandinsky, 19 August 1912, Schoenberg/Kandinsky Letters, pp. 54 - 55. Cited by Auner, "Heart and Brain in Music," p. 118.

13. Auner, "Heart and Brain in Music," p. 118.

14. See Paul Ricoeur, Time and Narrative vol. 3, trans. Kathleen Blamey and David Pellauer (Chicago: University of Chicago Press 1988), pp. 207 ff.

15. Schoenberg, Style and Idea, p. 86.

16. Pierre Boulez, Stocktakings from an Apprenticeship, trans. Stephen Walsh (Oxford: Clarendon Press, 1991), p. 175.

17. Boulez, Stocktakings, p. 213.

18. Boulez, Conversations with Celestin Deliège, English trans. (London: Ernst Eulenburg Ltd., 1976), p. 56.

19. György Ligeti, "Pierre Boulez," Die Reihe 4 (1975), p. 39.

20. Pierre Boulez, Stocktakings, p. 212.

21. Boulez, Stocktakings, p. 213.

22. Pierre Boulez, Conversations with Célestin Deliège, , p. 64; see Pierre Boulez, Boulez on Music Today, trans. Susan Bradshaw and Richard R. Bennett (London: Faber & Faber, Ltd., 1971), p. 106.

23. For example, if a "harmonic" subgroup F-E is multiplied by itself, this minor 7th would be doubled. The resulting "harmonic" complex consists of two minor 7th intervals placed one above the other (F-E-D). Similarly, "multiplying" a second subgroup B-D-A -B by the first F-E produces the "harmonic" structure B-D-A-B-C-C#-A-B. Given a series of five "harmonic" domains, this additive transpositional technique generates twenty-five such structures (five subgroups "multiplied" in all possible combinations), ten of which appear twice.

24. See Lev Koblyakov, Pierre Boulez: A World of Harmony (New York: Harwood Academic Publishers, 1991), pp. 3 ff. The exchanges in the opening measures are based on two sequences of serially generated complexes: one produces a progression of exchanges between the flute (E-A#-D#-E-F (ossia D-G#-D#-E-F); G-A-B) and vibraphone (B-B-D; E-F-A-A-F#; C); the other produces a progression of exchanges between the guitar (F#-G#; C#-F-E; E) and viola (A-G-B; D-F-F#-A7). On Kobylakov's analysis, transpositions of series "create, so to speak, a higher system of pitch interrelation of domains" (p. 5). The "harmonic" complexes in the first cycle of Le marteau sans maître (movements I, avant l'artisanat furieux, III, l'artisanat furieux and VII, après l'artisanat furieux) are generated from derived transpositions of five different series. See also Boulez, Orientations, p. 137.

25. Stephen Heinemann, "Pitch-Class Set Multiplication in Theory and Practice," Music Theory Spectrum 20: 1 (Spring 1998), p. 93.

26. Pierre Boulez and Pierre-Michel Menger, "From the Domain Musical to IRCAM: Pierre Boulez in Conversation with Pierre-Michel Menger," Perspectives of New Music 28: 1 (Winter 1990), p. 6; see Pierre Boulez, Conversations with Célestin Deliège, p. 55.

27. Steven Winick, "Symmetry and Pitch-Duration Associations in Boulez's Le marteau sans maître," Perspectives of New Music 24: 2 (1986), p. 281.

28. See Winick, "Symmetry and Pitch-Duration Associations in Boulez's Le Marteau sans maître"; Wayne C. Wentzel, "Dynamic and Attack Associations in Boulez's Le marteau sans maître,' Perspectives of New Music 29: 1 (Winter 1991). Wentzel's and Winick's analyses show how pitch-duration associations and those of dynamic and attack in bourreaux de solitude comprise a more fluid system than that of Structures 1a's precompositional matrices. See also Ulrich Siegele, Zwei Kommentare zum «Marteau sans maître» von Pierre Boulez (Neuhausen Stuttgart: Hänsler Verlag, 1979), pp. 54 ff.; Lev Koblyakov, Pierre Boulez: A World of Harmony, pp. 35 ff.

29. Theodor W. Adorno, Aesthetic Theory, trans. Robert Hullot-Kentor (Minneapolis: University of Minnesota Press, 1997), p. 216.

30. Adorno, Aesthetic Theory, p. 40; see Theodor W. Adorno, Philosophy of Modern Music, trans. Anne G. Mitchell and Wesley V. Blomster (New York: Seabury Press, 1973), pp. 85 ff.

31. Theodor W. Adorno, "The Aging of the New Music," Telos 21 (1988), p. 97.

32. David Gable, "Boulez's Two Cultures: The Post-War European Synthesis and Tradition," Journal of the American Musicological Society 43: 3 (1990), p. 437.

33. Immanuel Kant, Critique of Judgment, trans. Werner S. Pluhar (Indianapolis: Hackett Publishing Co., 1987), pp. 114 - 115. Kant describes the sublime as "an object (of nature) the presentation of which determines the mind to think of nature's inability to attain to an exhibition of ideas" (p. 127). Hence "if something arouses in us, merely in apprehension and without any reasoning on our part, a feeling of the sublime, then it may indeed appear, in its form, contrapurposive for our power of judgment, incommensurate with our power of exhibition, and as it were violent to our imagination, and yet we judge it all the more sublime for that" (p. 99).

34. Kant, Critique of Judgment, p. 115.

35. Translation in Peter F. Stacey, Boulez and the Modern Concept (University of Nebraska Press, 1987), p. 55.

36. For a discussion of the fin de siècle's failing confidence, see Carl. E. Schorske, Fin-de-Siècle Vienna: Politics and Culture (New York: Alfred A. Knopf, 1980).

37. Hans-Georg Gadamer, Praise of Theory: Speeches and Essays, trans. Chris Dawson (New Haven: Yale University Press, 1998), p. 27.

38. Michel Foucault, Discipline and Punish, trans. Alan Sheridan (New York: Vintage Books, 1979), p. 146.

39. Foucault, Discipline and Punish, p. 215.

40. Jameson, Postmodernism, p. 1.

41. Jameson, Postmodernism, p. 1.

42. See Ricoeur, Time and Narrative vol. 3. For Ricoeur, this crisis is an event in thinking about history that measures itself against the past's, present's and future's speculative unity in an eternal present. According-ly, this event awakens historical consciousness to the hermeneutical condition of understandings and initiatives that take shape between the past and the future.

43. Jameson, Postmodernism, p. xii.

44. Jameson, Postmodernism, p. 343; see p. 333. See also Jean-François Lyotard, The Postmodern Condition: A Report on Knowledge, trans. Geoff Bennington and Brian Massumi (Minneapolis: University of Minnesota Press, 1984).