Author: Foley, Gretchen
Title: Pitch and Interval Structures in George Perle's Theory of Twelve-Tone Tonality
Institution: University of Western Ontario
Begun: September 1997
Completed: January 1999
George Perle, American composer and theorist, has authored an innovative theory called _Twelve-Tone Tonality_ (1977; 2nd ed. 1996), an atonal compositional system based on the conjunction of interval cycles and inversional symmetry. This dissertation explicates Perle's theory in a reorganized, more accessible format, providing detailed analyses of two etudes from Perle's Six Etudes for Piano (1973-76). The analyses differentiate between the abstract dimension of the twelve-tone tonal constructs and their concrete realization at the musical surface, and show both local and long- range structure. The analyses extend beyond Perle's own dissemination of the theory by utilizing the tools of pitch-class set theory as well.
The study explores the fundamental entities of Perle's theory, the cyclic sets, outside the context of twelve-tone tonality, from which emerge close associations of set classes identified as "imbricated cyclic set families." These families share a number of structural properties, including inversional symmetry, transpositional combination, and equivalence in other modular universes. The study also introduces an original similarity relation, the RSYM relation, to reflect the symmetrical nature of the intervallic similarity between pairs of set classes in the ICS families.
Through the presentation of the tenets of twelve-tone tonality, the theoretical exploration of the cyclic sets, and the analysis of selected works, the dissertation aims to show the depth and potential of the theory, both within and outside its own context.
Keywords: atonality, axis of symmetry, interval cycles, inversional symmetry, modular equivalence, George Perle, pitch-class set theory, similarity relations, transpositional combination, twelve-tone tonality
Chapter 1: Introduction
Chapter 2: The Theory of Twelve-Tone Tonality
Chapter 3: Structural Properties of Cyclic Sets
Chapter 4: Analysis of Etude No.1 and Etude No.4 from Six Etudes for Piano by George Perle
Chapter 5: Conclusions
Dr. Gretchen Foley
School of Music, Station 16
Eastern New Mexico University
Portales, NM 88130
Tel: 505-562-2271 or 505-562-2377