An exercise in formalizing jazz leadsheet structures

Abstract

To analyze traditional jazz music in a way that attends to its idiom and performance practices, I develop two formalizations of jazz leadsheets, while also considering the relationship between sound and algebraic theory it initiates. First, I represent leadsheets as digraphs of chordal movement and articulate a digraph category. Second, I represent leadsheets as strings of chords and develop quotient semigroups on these strings using equivalence relations based on jazz performance practice. I produce a metric for leadsheets from these quotients. Then I apply the two formalizations to a set of twenty jazz standards and consider how the results compare with a listener's experience. I also include two original leadsheets composed to test the formalizations. Though they are grounded in jazz conventions, I conclude these formalizations often do not agree with a listener's perception; I consider what this implies about their construction and the general project of music algebra.