Welcome to Robert Kelley's dissertation webpage. My dissertation may be downloaded as a PDF (3.62 MB). To receive a CD or hard copy by mail, please . Some papers that show parts of my research include: Charting Enharmonicism on the Just-Intonation Tonnetz, In the Dark Shadow: Enharmonic Equivalence as Dramatic Subtext in Two Wolf Lieder, Reconciling Tonal Conflicts: Mod-7 Transformations in Chromatic Music, Evaluating Prolongation in Extended Tonality, and A Mathematical Model of Tonal Function. If you are interested in my work or have any comments or suggestions, feel free to email me at <>. The Music Theory Online Dissertation Listing of Modulo-Seven Transformations in Post-Functional Music

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• Abstract
• Supervisory Committee
• Project History
• Table of Contents

Abstract

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.

Dissertation Committee

• Michael Buchler, committee chair / dissertation advisor
• Jane Piper Clendinning
• Evan Jones
• Charles E. Brewer, outside committee member

Project History

• September 2003: Committee established
• October 27, 2003: Written Preliminary Examination submitted to committee
• November 18, 2003: Passed Oral Preliminary Examination
• December 13, 2003: Submitted prospectus draft to committee for review
• February 7, 2004: Presentation of paper on mod-7 transformations at FSU Theory Forum
• March 5, 2004: Prospectus approved by committee.
• March 26-27, 2004: Presentation of paper on mod-7 transformations at the second annual meeting of Music Theory Mid-Atlantic.
• April 1, 2004: MODVLO7 (v1.0 beta) is now available for diatonic prolongational analysis. This software package will be released alongside the electronic version of my dissertation.
• August 5, 2004: Draft of chapter 2 is complete.
• August 13, 2004: First draft of chapter 3 is complete.
• September 7, 2004: Posted new revised versions of Charting Enharmonicism on the Just-Intonation Tonnetz and Reconciling Tonal Conflicts: Mod-7 Transformations in Chromatic Music online.
• November 4, 2004: First draft of chapter 4 is complete.
• January 15, 2005: Presentation of Evaluating Prolongation in Extended Tonality at FSU Theory Forum
• February 1, 2005: First draft of dissertation submitted to committee.
• March 22, 2005: Passed defense
• April 2, 2005: Presentation of Evaluating Prolongation in Extended Tonality at the third annual meeting of Music Theory Mid-Atlantic.
• April 5, 2005: Dissertation available online (PDF, 3.62 MB).
• May 11, 2005: ISO image of dissertation CD including supplemental materials available online (100 MB). To receive a CD or hard copy by mail, please .
• August 9, 2005: New version of dissertation posted online. (Please update your files!) Errata corrected in text, and incorrect recordings of musical examples replaced in CD distribution.
• March 5, 2006: More errata corrected (including a crucial typographical error in the function zeta_t). Please update your files!
• August 5, 2006: Corrected a conceptual error in the function zeta_t and one proof, expanded the layout of several proofs for ease of reading and understanding, and corrected a few more minor errata.
• May 25, 2007: Corrected a few minor errata and updated external links in bibliography.

Chapter Outline

1. 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
2. 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
3. Spatial Graphs and Transformational Networks
   1. The Just-Intonation Tonnetz
   2. Just-Intonation and Mod-12/Mod-7 Transformational Networks
   3. Prolongational Transformational Networks
4. Methodologies for Determining Chordal Salience in Post-Functional Music
   1. Finding Chord Roots
   2. Finding Structural Chords
   3. Impediments to Prolongation
5. 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
6. Conclusions
   1. The Use of Diatonic Theory for Extended Tonal Music
   2. The Place of this Work within the Field of Music Theory

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