An analytical approach to non-isochronous meter: Variable beat length in groove-oriented jazz
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Despite the vast majority of the Western Canon being constructed of beats of uniform duration, some beats have definitively different lengths. Building on the works of Fred Lerdahl, Justin London, and Christopher Hasty, this thesis attempts to analyze groove-oriented jazz examples which exhibit variable beat length. The first portion of the thesis focuses upon describing different formations which exhibit variable beat length. These descriptions allow an analyst to compare any metric formation to a prototypical formation, which only contains beats of a single duration. Since all formations are compared to a single prototype, one can transitively use the findings to compare any two metric formations to one another. The second portion focuses on mathematical formalization of the first part. This allows an analyst to abstractly compare any meters within a space which contains every metric formation.