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A Permutational Triadic Approach To Jazz Harmony And The Chord/Scale Relationship, John Bishop

LSU Doctoral Dissertations

This study provides an original triadic theory that combines existing jazz theory, in particular the chord/scale relationship, and mathematical permutation group theory to analyze repertoire, act as a pedagogical tool, and provide a system to create new music. Permutations are defined as group actions on sets, and the sets used here are the constituent consonant triads derived from certain scales. Group structures provide a model by which to understand the relationships held between the triadic set elements as defined by the generating functions. The findings are both descriptive and prescriptive, as triadic permutations offer new insights into existing repertoire. Further, …