The Abelian axioms—A framework for analyzing interaction and improvisation in a jazz group

In this study, we asked four professional jazz musicians to rehearse, record, and analyze their performances. The musicians used five short pieces, composed for the study using techniques informed by pitch-class theory and inspired by discrete mathematics, as a departing point for group improvisations. The improvisations were transcribed, and the transcriptions and recordings were used during interviews to stimulate the participants’ recollections of their intentions and experiences while improvising. Analyses of the transcriptions and interviews provided insights into how experienced improvisers interact, make decisions, and share responsibility during an improvisation. We show how the participants altered and reused compositional elements, such as intervals and motifs, and how they interacted when phrasing in similar and different ways. The contributions made by this study include the development of a framework for analyzing improvisation, the description of a simplified transcription process, and the production of a recording to accompany this article.