Author: Santa, Matthew S.
Title: Studies in Post-Tonal Diatonicism: A Mod7 Perspective
Institution: City University of New York
Begun: February 1998
Completed: May 1999
There is a substantial body of music written in the 20th century in which the notes of a diatonic scale predominate, but which often lacks one or more of the other basic requirements necessary to be considered tonal: 1) a centricity around a single tone p erceived as tonic; 2) a harmonic organization based on triads and seventh chords; 3) a
hierarchical organization of functional harmonies; and 4) a contrapuntal substructure based on the laws of species counterpoint. Such music, by the likes of Barber, Copland, Prokofiev, and Stravinsky, has always posed a problem for music theorists, since neither traditional tonal analysis nor pc-set analysis yields satisfying analytic results. This dissertation argues that the problems inherent in analyzing post-tonal diatonic music can be solved by a careful application of set theory modulo 7, in interaction with the more familiar mod12 set theory. The first chapter outlines a system of mod7 set theory designed specifically for the analysis of post-tonal diatonic music . Chapter 2 then utilizes that system to analyze a range of post-tonal diatonic works in order to demonstrate the system's validity, its flexibility, and its explanatory power. Chapter 3 rigorously examines chordal tone centers in post-tonal diatonic music, an aspect of centricity that has thus far only been discussed in the vaguest of terms. Chapter 4 deals with structural levels in post-tonal diatonic music, presenting an approach that considers both the salience of individual pitches, and their place in the work's formal and motivic structure, in determining their structural weight. The final chapter explores how diatonic partitionings of the octave interact with pentatonic, whole-tone, octatonic, and chromatic partitionings in much
music of the 20th c entury, and addresses the analytic problems posed by such interactions.
Keywords: post-tonal, mod7, centricity, diatonic, set theory, Prokofiev, Stravinsky, Bartok, Copland, Barber
Chapter 1: Set Theory, Mod7
Chapter 2: Motivic Analysis, Mod7
Chapter 3: Chordal Tone Centers
Chapter 4: Structural Levels
Chapter 5: Beyond Mod7: Relating Diatonic and Nondiatonic Materials
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