Dissertation Index

Author: Kelley, Robert T.

Title: Modulo-Seven Transformations in Post-Functional Music

Institution: Florida State University

Begun: March 2004

Completed: April 2005


Many musical compositions from the end of the nineteenth century and the beginning of the twentieth century retain some elements of functional tonality but abandon others. Most analytical methods are designed to address either tonal music or atonal music, but no single method completely illuminates this body of extended-tonal music. While both tonal and post-tonal theory have been extended in various ways to address this music, the use of tonal theory for analysis of this repertoire has not been completely formalized. The main obstacle for prolongational views of extended tonality is finding sufficient conditions for establishing that certain harmonies are structural in the absence of traditional harmonic function. In this regard, acoustical measures of stability, motivic connections, and chord equivalence all may form a part in determining the structural harmonies. Prolongational analyses of music may be represented by Schenkerian notation or transformational networks based on Lewin's Generalized Musical Intervals and Transformations (1987). This study explores a number of specific graphing techniques, including the diatonic lattice (Jones 2002), the just- intonation Tonnetz, and mod-12/mod-7 prolongational networks. After using group theory to explore the relationship of diatonic scale theory and tuning theory to transformational and prolongational analysis, excerpts from Wolf, Wagner, and Ravel are analyzed using mod-7 transformations. In giving support for prolongational analyses of chromatic and neo-tonal music, this study provides a case for tonality-based approaches to post-functional harmony.

Keywords: Transformation Theory, Diatonic Scale Theory, Schenkerian Analysis, Nineteenth-Century Chromaticism, Extended Tonality, Richard Wagner, Hugo Wolf, Maurice Ravel


I. Chromatic Harmony, Diatonic Scale Theory, and Post-Tonal Prolongation
1. Introduction
2. Recent Theories of Chromatic Music
3. Diatonic Theory
4. Prolongation in Post-Tonal Music
II. Just Intonation as Diatonic Interpretation
1. Tuning in 5-Limit Just Intonation
2. Diatonic Spelling based on 5-Limit Just Intonation
3. Homomorphisms Among Scale Systems and Tuning Systems
4. Generalizing Diatonic Structures into 5-Limit Just Intonation
III. Spatial Graphs and Transformational Networks
1. The Just-Intonation Tonnetz
2. Just-Intonation and Mod-12/Mod-7 Transformational Networks
3. Prolongational Transformational Networks
IV. Methodologies for Determining Chordal Salience in Post-Functional Music
1. Finding Chord Roots
2. Finding Structural Chords
3. Impediments to Prolongation
V. Analytical Examples
1. Enharmonic Progressions in Wolf's "Und steht Ihr früh"
2. Directional Tonality in Wolf's "Der Mond"
3. Post-Functional Progressions in Wagner's Tristan und Isolde
4. Non-Tertian Progressions in Ravel's Valses Nobles et Sentimentales
5. Post-Functional Non-Tertian Progressions in Ravel's Gaspard de la Nuit
VI. Conclusions
1. The Use of Diatonic Theory for Extended Tonal Music
2. The Place of this Work within the Field of Music Theory


Department of Music
Lander University
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320 Stanley Avenue
Greenwood, SC 29649-2099
Office: 864-388-8774
Fax: 864-388-8144

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