Volume 8, Number 3, October 2002
Copyright © 2002 Society for Music Theory
Hook, Julian L. "Uniform Triadic Transformations." Indiana University, May 2002.
AUTHOR: Hook, Julian L.
TITLE: Uniform Triadic Transformations
INSTITUTION: Indiana University
BEGUN: February, 2000
COMPLETED: May, 2002
ABSTRACT: A simple algebraic framework is proposed for studying triadic transformations. Included are the neo-Riemannian transformations P, L, and R, and other transformations recently studied by Lewin, Cohn, Hyer, and others. Hyer’s group of 144 transformations is extended to a group of 288, in which composition of transformations may be defined in a simpler and more unified fashion. Each of these "uniform triadic transformations" (UTTs) is represented in componentwise fashion by an ordered triple consisting of a sign (indicating whether the transformation preserves or reverses mode) and two integers mod 12 (indicating the intervals through which the roots of major and minor triads are transposed). This formalism simultaneously generalizes and simplifies much recent work in triadic transformations, and provides some clarification of the relationship between those transformations that behave in characteristically "Riemannian" ways (such as P, L, and R) and others that do not (such as ! th! e "dominant" and "mediant" transformations)--a relationship that some have found confusing or disturbing. The algebraic structure of the UTT group is studied in some detail, with emphasis on the Riemannian subgroup and other simply transitive subgroups and on the many intersections with other recent studies in transformational theory. The interaction of UTTs with inversion operators is examined. The methods presented are applicable not only to consonant triads but in many other settings as well, including set classes other than triads, equal-tempered systems other than that with 12 notes, certain diatonic structures, and some serial relationships. A variety of examples demonstrate some of the analytical potential of the theory.
KEYWORDS: algebra, group theory, transformations, neo-Riemannian, Lewin, Cohn, Hyer
1. Triads and UTTs
2. Riemannian UTTs
3. Simply Transitive Groups of UTTs
4. The Structure of the UTT Group
5. UTTs and Inversion Operators
6. Beyond Triads
7. Analytical Applications I: Twelve-Tone Examples
8. Analytical Applications II: Triadic Examples
Appendix: Glossary of Algebraic Terms
School of Music
Penn State University
University Park, PA 16802
Bribitzer-Stull, Matthew P. "Thematic Development and Dramatic Association in Wagner's Der Ring des Nibelungen." Eastman School of Music, July 2001.
AUTHOR: Bribitzer-Stull, Matthew, P.
TITLE: Thematic Development and Dramatic Association in Wagner's Der Ring des Nibelungen
INSTITUTION: Eastman School of Music
BEGUN: January, 1999
COMPLETED: July, 2001
ABSTRACT: The associative power of music has fascinated musicians throughout history. Among other things, it has prompted considerable interest in associative themes (or Leitmotive). The locus classicus of associative thematic technique is, of course, Wagner's Der Ring des Nibelungen; as such it has often served as a focus for analysis. The danger of such analysis, however, lies in the lure of oversimplification; unraveling the meanings of associative themes entails coming to grips with a warp and weft as tangled as that woven by the Norns themselves.
The typical approach towards identifying and naming themes has been entity-centered--a one-dimensional mapping between music and meaning. This study widens the scope of these earlier investigations by adopting a transformative view. Such a view allows for the richness of accumulative meaning in which the methods of thematic developments themselves function as a hermeneutic for reflecting upon the drama. Four discrete categories of transformations are defined and illustrated by this thesis. First, Thematic Mutation allows for qualification of the original meaning of a theme when its musical materials have been modified. Second, Thematic Transformation provides for the construction of dramatic relationships between musically-related, but distinct, themes. Third, Contextual Reinterpretation investigates the manner in which thematic association can be affected by context alone. Fourth, Thematic Metamorphosis, embraces a larger view of motive within Wagner's music.
Of these categories, the final one demands the most elaboration. It comprises a study of associative themes, motivic parallelism, and the deep Schenkerian levels in order to claim that thematic association is not solely a foreground phenomenon. In so doing, an investigation is made into the intersection between Schenkerian, Baileyan, and functional views of tonality in Wagner's music dramas. This inquiry into the unique interaction between tonality, drama, and Wagner's motivic method of composition serves as a springboard from which to launch hypotheses about formal organization in Der Ring.
KEYWORDS: Wagner, leitmotif, theme, association, Ring cycle.
1.The Beast at the Center of the Labyrinth:
Wagner Analysis and the Associative Theme
1.1. What is an Associative Theme?
1.1.1. Motive, Theme, Phrase, and Melody
1.1.2. Theme and Musical Association
1.2. The Prototype Model
1.2.1. The Associative Theme in
Wagner's Other Operas
1.2.2. A Three-fold View of Thematic Identity
2. Thematic Mutation
2.1. Change of Mode
2.2. Harmonic Corruption
2.3. Thematic Truncation
2.4. Thematic Fragmentation
2.5. Change of Texture
3. Thematic Evolution
4. Contextual Reinterpretation
4.1. Associative Transposition
4.2. Thematic Complexes
4.3. Thematic Irony
5. Thematic Metamorphosis
5.1. The Theoretic Cooperative
5.1.1 Schenker Theory
5.1.2 Bailey's Theories
5.1.3 Function Theory
2.2. Tonality, Theme, and Form: The Musical Triumvirate
5.2.1 Tonality and Theme
5.2.2 Theme and Form
5.2.3 Tonality and Form
2.3. Synthetic Analysis
5.3.1 Previous Approaches
5.3.2 Some Notes on the Graphs
5.3.4 Analytic Observations on Das Rheingold
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School of Music
University of Minnesota
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