Author: Kochavi, Jonathan, H.
Title: Contextually Defined Musical Transformations
Institution: SUNY Buffalo
Begun: September 1998
Completed: April 2002
Traditional approaches to musical analysis are object-oriented, whether those objects are harmonic triads, collections or orderings of pitch classes, rhythmic patterns, or other discrete sets of basic musical building blocks. As the focus of analytical models has gradually shifted from the object to the transformation over the past two decades, structural representations of musical progression have relied heavily on the standard twelve-tone operators, Tn and In. While powerful in their wide-ranging applicability, the operators’ abstraction limits their usefulness in situations where the transformational scheme is structurally linked to the objects that are being transformed. This study investigates a category of operators, called contextually defined transformations, that bridge the gap between analytical approaches that concentrate primarily on musical objects and those that are rooted in fully abstract mappings.
Two broad classes of contextual transformation are formally defined, mathematically investigated, and analytically applied. Contextually defined inversion operators generalize the standard In inversions with particular modes of transformation based both on the properties of the set class and the way that the elements of the set class are used in a composition. Special attention is paid to the neo-Riemannian operators, each of which is an example of a contextual inversion. The other category of contextual transformation explored here is the sequence succession operator, most often a contextual transposition, which is applied to diatonic sequences. Formal treatment of such operators leads to a general metric on tonal progressions based on degree of parsimony. Detailed analyses of Beethoven, Stravinsky, and Radiohead serve to demonstrate applications of contextual transformations.
Keywords: contextual, transformation, neo-Riemannian operator, diatonic sequence, mathematics, group theory, In Memoriam Dylan Thomas, Radiohead, Mass in C (Beethoven)
Chapter 1. Introduction
Chapter 2. Contextually Defined Inversion Operators
Chapter 3. Analytical Applications of Contextually Defined Inversions
Chapter 4. Parsimony and Contextuality of Diatonic Sequences
Chapter 5. Extended Analysis: Beethovenís Mass in C, Op. 86, Gloria
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