Author: Danby, Judd
Title: Array and Superarray Structure and Projection in Milton Babbitt's recent Orchestral Music
Institution: University of Illinois at Urbana-Champaign
Begun: March 1995
Completed: November 1997
This paper investigates Milton Babbitt's generalized aggregate practice in Ars Combinatoria (1981), the Concerto for Piano and Orchestra (1985), and Transfigured Notes (1986), alternating between analysis of the fundamental properties of generalized aggregate arrays and superarrays and examination of the manner in which Babbitt composes from those basic materials, often revealing underlying stylistics assumptions which are separable from any systematically definable aspects of his basic structures.
Chapter 1 begins with a brief discussion of Schoenberg's influence upon Babbitt's aggregate practice, followed by an overview of basic twelve-tone terminology and concepts, with emphasis on all-partition hyperaggregate arrays and superarrays.
Chapter 2 examines interrelated properties of the common set-class, the all-partition hyperaggregate array-classes, and the superarrays of the three works, with a focus on variance and invariance within array-forms under inversion/transposition.
Chapter 3 demonstrates the ways in which Babbitt projects his structures onto the musical surface through orchestration, register, dynamics, and surface rhythm, pausing midway to consider a listener's experience of these pieces in relation to the manner in which they are constructed.
Chapter 4 shifts primary focus to the musical surfaces of the works, examining how they are wrought from the underlying building blocks. Particular attention is paid to the manner in which aggregates are composed out, points of structural minimalism which draw the listener's attention, and the underlying structural rhythm of the three works.
Chapter 5 briefly summarizes Babbitt's practice, separating his chosen materials and stylistic assumptions from the fundamental properties and broad structural potentialities of generalized aggregate arrays, and offers other possibilities and points of departure for generalized aggregate composition which can be adapted to suit a variety of musical needs and tastes in shaping a musical work.
Keywords: Generalized aggregates, array, superarray, hyperaggregate array, Babbitt, all-partition array, structural rhythm
Chapter 1: Introduction
Chapter 2: A Comparative Anatomy
Chapter 3: Array and Superarray Projection
Chapter 4: The Musical Surface
Chapter 5: Reflections and Points of Departure
Appendix: Setform Matrices and Complete All-Partition Arrays
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