An analysis and comentary about Rene Leibowitz's Treatise on 12 tone composition (includes pictures)
Series, Form and Function: Comments on the Analytical Legacy of Ren Leibowitz and Aspects of Tonal Form in the Twelve-Tone Music of Schoenberg and Webern 1 John MacKayAlthough the most important of Rene Leibowitzs writings on the series and thematic process, his "Treatise on Twelve-Tone Composition," remains unpublished, important indications of his analytical perspectives are to be be found in his discussion of the Webern Concerto op. 24 in Que'est-ce que c'est que la musique de douze sons? of 1948. 2 The present study will review portions of both of these writings and advance observations on tonal linearity and centering which, although extraneous to Leibowitz's analytical outlook, are clearly functional within the context of his structural and serial parsings. In many pieces a clear sense of tonal form and "argumentation" can be observed in much the manner that Schoenberg described in his Theory of Harmony,3 and his article "Problems in Modern Harmony"4 (1934) and this will be pursued at greater length in concluding analyses of the Minuet of the Suite op.25 for piano solo and the Klavierstcke op. 33b. Qu'est-ce que c'est que la Musique de Douze Sons? and Classical Phrase Structure
The discussion of the structural function of the series in Qu'est-ce que c'est que la musique de douze sons? is embroidered with issues of esthetics, orchestration, twelve-tone technique and classicism. It is here that Leibowitz first juxtaposes thematic statements of Webern and Beethoven (the first movement theme of the Sonata op.2, #1 was also used by Webern in his The Path to the New Music 5) illustrating their respective "sentence" structures (see Example 1a) and making observations on Webern's micro-serialism (i.e. the intervallic retrograde, inversion and retrograde inversion of the three-note cellular motives of the series) throughout the thematic and motivic design.
The model/response relationship of the Schoenbergian sentence is shown to articulate the functions of tonic/dominant in the Beethoven and prime form and retrograde serial structures, as well as the orchestrational contrast of the concertino and solo timbres in the Webem. The reductions of both thematic structures involve rhythmic intensifications leading to cadences on the dominant in Beethoven and an unfolding of the retrograde form in Webern which, as in the "response,u may indeed be his serial substitute for the dominant. Leibowitz observes therefore, that what Beethoven accomplishes in his preparation and cadence via a dynamic climax, ritardando and melodic descent onto the dominant, Webern's does in a similar dynamic intensification and a diminuendo, deceleration and increase in harmonic density. Leibowitz's notion of the second theme in the Webern (he does not pursue any further parallelism with the Beethoven theme) is somewhat problematic in Qu'est-ce que c'est que la musique de douze sons? since it does not correspond to the rhetoric of the tempo changes. Instead of admitting a transitional link to a new structure in measures 11 to 12 (see Example 1 b) Leibowitz sees the shift to more subdued dynamics and to the serial superpositions of these measures as the immediately distinguishing factors of the second theme. A developmental extension of the theme is seen in measures 13-22, and a third section consisting of a more cumulative elaboration is proposed in mm. 22-23 prior to the brief concluding phrase (mm. 24-25) which closes out the opening "A" section of the A-B-A sonata design of the movement.
Leibowitz's hyper-segmentation of these passages overlooks, however, a more contrapuntally complex model and repetition in measures 13-14 and 15-16 with distinctive recurrences of upper register G#s of m. 14 and 16 and mid-register E flats in measures l 3 and 17. As in a sentence form, these provide a stable point of departure for the ensuing development of overlapping trichords of the following measures. Leibowitz does however make the important observation of the climactic resolution in m. 23 to a single sequential series which concludes the expository alternation between the successive serial dispositions of the primary theme and the harmonic relaxation into the superimposed series of the secondary ideas and in the structures which follow in the central section of the movement in measures 26-45.
Leibowitz similarly divides the central section into "phases": an initial phase (mm. 26 - 35) which has certain thematic qualities in its presentation and immediate varied repetition of the motivic cell followed by reductive shorter phrases (involving new grace-note figures) and a temporary cadence. A second phase (not shown) then appears to develop features of the first and second themes of the exposition to a registral and rhythmic climax in anticipation of the sixteenth-note figures of the return of the opening theme. The discussion of these measures relates more to orchestration - the role of the piano in the ensemble texture - and to the series, focusing pedagogically on the use of "pivot" tones between successive rows in Webern's serial technique. The central section however, also contributes certain features of tonal reference. The melodic trichords of Leibowitz's second theme in ms. 12 and 13 (Ab-C-B natural overlapping with E-Eb-G) are recalled in the opening thematic fragments of measures 26 and 27, and the cadential dyad Eb-E natural in the trumpet at the end of the exposition and at the end of the central section in the trombone.
Leibowitz comments on the condensations in the "reprise" (or recapitulation) of significant components of the exposition, particularly the elision of the "repetition" and in the abbreviated versions of the reductions and cadence in the first theme. Although the second theme is only slightly abbreviated, Leibowitz makes much out of the climactic extension which is expanded by the intercalation of measures 57 and 58 in the clarinet and oboe - recalling the grace-note figures of the central episode and providing a midregister preparation for the climax in quarter-note triplets and for the concluding, although still abbreviated, fortissimo statement of the first theme.
Leibowitz's structural insights can be pursued further in the resolution of the movement where the closing thematic iterations of the series (ms. 63-68) echo the presentation of the beginning of the recapitulation in ms. 45-49, saturating this.particular trichordal partitioning 6 of the series. In contrast, the final cadence in measure 69 reasserts the trichordal partitioning of the model and repetition of the very opening presentation of the first theme of the movement. This reflects further structural oppositions since the trichordal partitioning of the beginning of the secondary and central themes is also that of the model, repetition and reductions of the closing thematic statement, (ms. 63-68), and in the very opening theme itself the initial partitioning gives way to that of the secondary ideas at the beginning of the reductions (compare mm. 6-7 and 11-13 in the concertino.) The role of the cadential and pivotal E-Eb dyad is further echoed in measure 62 as the climactic development of the secondary theme unravels in anticipation of the final recapitulation of the opening thematic structure of the movement. Leibowitz's discussions of the second and third movements of the Concerto op. 24 pursue the same sensitive treatments of formal structure, orchestration and serial disposition with which he began in the first movement and later continued in his Introduction a la Musique de Douze Tons. In these writings however, he does not pursue the same detailed attention to thematic structure and function in the disposition of the series. An opportunity in the Concerto is missed particularly in the second movement where, as observed by later analysts 7 , a very clear and elaborate period structure exists (see Example 2.)8 The symmetrical motivic structure of the antecedent plays with emphases on Eb, often in association with G natural (i.e. the motivic correspondence of measures land 5 and the cadential G-Eb of ms. 11 and. 12.) While the consequent moves away from these emphases, there is a clear return to the centering of a midregister Eb and accompanying G natural at the end of the central section (ms. 51-58, not shown) and at the close of the movement (ms. 74-75). Eb is similarly the goal of the interlocking descending thirds which begin in measure 65 D-Bb (ms.64-65), B-G (m.66-67), F#-D (ms. 69-70), Eb -13 in measure 72 before the final G-Eb in measures 74-75. "A Treatise on Twelve-Tone Composition"
Leibowitz's "Treatise on Twelve-Tone Composition" was compiled as a teaching manual for his students in the early 1950's.9 It offers step-by-step pedagogical orientations in the use of the series in relation to Schoenbergian concepts of classical thematic structure, development, and formal process. In the first part of the treatise, he differentiates between "closed structures," the typical structures of prinicpal themes, "intermediary (i.e. transitional) structures" and "secondary" structures or the typical structures of secondary themes. He provides a wealth of examples from late Webern (Symphony op.21, Concerto op.24, Variations op.27, and Kantata op.29) and from Schoenberg's music of the 1930's and 1940's (Klavierstcke op. 33 a and b, the Fantasy for violin and piano, the Concerto for piano and orchestra, the Fourth String Quartet, Accompaniment to a Cinematographic Scene op.34, Chamber Concerto op.43 and Survivor from Warsaw .46.) A second portion of the treatise concerns the typical form of "re-expositional" structures (developments and recapitulations) as well as what he terms "autonomous structures" (introductions, episodes and cadenzas, codas, stretti and terminal cadential seqments) and a third part discusses "various thematic structures" (the "scherzo," slow movement and finale themes) "canons, fugatos