Jazz harmony: pitch-class set genera, transformation, and practical music - Richards, William (My University, 2012)
Contemporary jazz musicians draw from a rich and varied collection of techniques and strategies used towards the realization of harmonic succession, voicing and voice-leading, and linear improvisation. While musicians recognize the distinctiveness of various jazz chord-scales and harmonies, they also talk about “source scales” and chord families, and describe processes that apply to the manipulation of chord progressions including chord and chord-scale substitution, interpolation, and reduction. Aligned to jazz theoretic discourse, this paper presents a model of set-class space in which scales and chords typical of the jazz language coalesce into pc-set genera and form inter-generic relations through transformation. The model suggests a holistic, theoretical definition of jazz harmony and offers musicians a way of thinking about relations among scales and harmonies in terms of a transformational system that resides in transformational space, which in turn can be employed systematically and imaginatively towards the creation and interpretation of jazz music.
Presented on June 1, 2012 at The Canadian University Music Society Conference held at Wilfrid Laurier University, Faculty of Music in Waterloo, Ontario.
Keywords: jazz harmony; jazz theory; chord-scales; source scales; transformation; near-equivalency; pc-set genera; transformational system; pc-set theory; set-class space; transformational space; diatonic; lydian b7