Jazz line and augmented scale theory : Using intervallic sets to unite three and four tonic systems

Despite the prevalent use of intervallic cells as source material among modern jazz composers, little research has been published on bridging the divide between the atonal approach of set theory and the more tonal harmonic tendencies of classic jazz. Modern jazz language thrives on diverse harmonic and melodic elements, but jazz lines that deviate from given harmonies still tend to be generalized as being "outside the changes" – an unfortunate description that fails to specify the logic behind complex lines. While tonal hierarchy is typically framed in terms of major and minor tonalities, tonal hierarchy can also be derived through a reexamination of the pitch intervals that comprise the augmented scale. My theoretical research has included extensive study of three-tonic systems (e.g. Coltrane changes), four-tonic systems (tri-tone substitutions, etc.), and historical compositional practices ranging from ancient Greek systems through 20th century techniques. This study concludes that the augmented scale unifies three- and four-tonic systems while also establishing tonal hierarchy in music incorporating elements of set theory. This paper is part of a larger study on augmented scale theory and serves as an introduction to my research on this topic. My intent in researching augmented scale theory is to help the jazz composer and improviser reach creative freedom while approaching Coltrane changes and other challenging chord progressions, to assist in reconciling tonal and atonal structures, and to contribute to future research on jazz and set theory.