Dissertation Index

Author: Jacobus, Enoch S. A.

Title: A New Geometric Model and Methodology for Understanding Parsimonious Seventh-Sonority Pitch-Class Space

Institution: University of Kentucky

Begun: May 2011

Completed: October 2012


Parsimonious voice leading is a term, first used by Richard Cohn, to describe non-diatonic motion among triads that will preserve as many common tones as possible, while limiting the distance traveled by the voice that does move to a tone or, better yet, a semitone. Some scholars have applied these principles to seventh chords, laying the groundwork for this study, which strives toward a reasonably comprehensive, usable model for musical analysis.

Rather than emphasizing mathematical proofs, as a number of approaches have done, this study relies on two- and three-dimensional geometric visualizations and spatial analogies to describe pitch-class and harmonic relationships. These geometric realizations are based on the organization of the neo-Riemannian Tonnetz, but they expand and apply the organizational principles of the Tonnetz to seventh sonorities. It allows for the descriptive “mapping” or prescriptive “navigation” of harmonic paths through a defined space.

The viability of the theoretical model is examined in analyses of passages from the repertoire of Frédéric Chopin. These passages exhibit a harmonic syntax that is often difficult to analyze as anything other than “tonally unstable” or “transitional.” This study seeks to analyze these passages in terms of what they are, rather than what they are not.

Keywords: Neo-Riemannian Theory, Seventh Chords, Parsimonious, Pitch-Class Space, Tonnetz, Chopin


I. Front Matter
A. Acknowledgements
B. List of Tables
C. List of Figures
D. List of Musical Examples
E. List of Files

II. Chapter 1: Scholarly Context
A. Introduction
B. Historical Perspective
C. Neo-Riemannian Theory
1. Abstraction
2. Exclusion
3. Speculation
4. Other
5. Conclusion

III. Chapter 2: Conceptual Dichotomies
A. Parsimony vs. Extravagance
B. Horizontality vs. Verticality
C. Extrapolation vs. Interaction
1. Extrapolation
2. Interaction

IV. Chapter 3: Theoretical Methodology
A. Introduction
B. Sonority Geometries
C. Sonority Networks in Two Dimensions
D. Sonority Networks in Three Dimensions

V. Chapter 4: Analytical Applications
A. Introduction
B. Chopin, Mazurka, Op. 7, No. 2
C. Chopin, Mazurka, Op. 68, No. 4
D. Chopin, Prelude, Op. 28, No. 4
E. Chopin, Prelude, Op. 28, No. 6
F. Chopin, Nocturne, Op. 27, No. 2
G. Wagner, Prelude to Act I, Tristan und Isolde

VI. Chapter 5: Conclusions and Further Research
A. Introduction
B. Examination of Non-Contiguous and Deeper-Level Structures
C. Exploration of Other Composers’ Approaches
D. Integration of Triadic Structures into the Lattice
E. Prescription for Composition and Improvisation
F. Summary

VII. Back Matter
A. Appendix
B. Bibliography
C. Vita


enochobus@gmail.com, 859.537.6660

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