Author: Schultz, Rob
Title: A Diachronic-Transformational Theory of Musical Contour Relations
Institution: University of Washington
Begun: June 2006
Completed: June 2009
Although the relatively recent proliferation of research into musical contour theory has indeed yielded a plethora of vital analytical and methodological insights, a crucial phenomenological problem remains to be fully addressed: its implicit reliance upon a synchronous analytical perspective whereby a contour’s constituent elements, though ordered in time, are in fact interpreted as fully and simultaneously present entities. The musical processes that these contours describe, however, obviously do not present themselves in this manner—their constituent elements occur in direct succession, not simultaneously. Such contours, therefore, cannot be regarded as truly autonomous musical objects; rather, they represent but a single link—albeit the crucial, culminating link—in a cumulative transformational chain of contours that unfolds diachronically. The contour <1023>, for instance, begins as the singleton <0>, and evolves successively into <10> (its first two elements) and <102> (its first three elements) before coming to exist as such.
This dissertation develops a system of contour relations that is fully contingent upon this implicit process. Chapter One introduces and develops the basic principles involved in such an approach, which is centered around the construction of a universal contour tree diagram that provides the foundation for relating contours based on the similarity of their diachronic-transformational histories. Chapter Two provides a more comprehensive account of the contour transformational process by incorporating C-Pitch Adjacency Subsets (C-PAS) into the system. This necessitates the development of contour relationship “networks” and the subsequent organization of them into their own hierarchy of relationship types. In Chapter Three, these principles are applied to the multi-level structural space generated by Robert Morris’s (1993) Contour-Reduction Algorithm, which not only extends their utility beyond the strictly foreground level, but also reveals some striking new principles and systems of relations. Chapter Four demonstrates the efficacy and novelty of the diachronic-transformational approach through the analysis of musical excerpts from works by Beethoven, Berg, Webern, Messiaen, and Holland-Dozier-Holland. Finally, Chapter Five offers some concluding remarks and explores the potential for future research using this methodology.
Keywords: Contour, Transformation, Phenomenology, Hierarchy, Similarity Relations
Chapter One: Basic Tenets of the Diachronic-Transformational Approach
Chapter Two: C-Pitch Adjacency Subsets and their Impact on the Diachronic-Transformational System
Chapter Three: Incorporating Structural Hierarchy into the Diachronic-Transformational System: The Contour-Reduction Algorithm
Chapter Four: Analytical Applications
Chapter Five: Conclusion and Avenues for Further Research
Department of Music and Dance
University of Massachusetts
Amherst, MA, 01003