Hemiolic metric space in Afro-diasporic popular musics

Pitch spaces such as the circle of fifths model change through time in a composition, recording, or improvisation. Metric spaces theorized over the past twenty years do the same for changes (notated or not) in meter. Trajectories in either space and their potentially reinforcing or conflicting relationships contribute to deeper interpretations of musical form. None of the metric spaces proposed to date is well suited to Afro-diasporic popular musics, which characteristically tend to pose regularly uneven metric foregrounds against rigid and recursively even metric backgrounds. This article introduces a new metric space specifically applicable to such repertoires. The article opens with a brief review of existing metric spaces. Part 1 is an exploratory metric analysis of Afro-Brazilian guitarist Baden Powell’s 1967 recording of “Canto de Xangô,” which motivates the theoretical developments of part 2. Part 3 is a short analysis of his 1963 recording of “Sorongaio” that demonstrates both how hemiolic metric space can newly be analyzed in pure-duple environments and how this metric space can be isomorphic with pitch space.