Clifton Callender

composition, music theory, mathematics

This is a three-way collaboration with Ian Quinn and Dmitri Tymoczko that, in the process of developing a very general geometric model of voice leading, recasts much of contemporary music theory in terms of a continuous, geometrical approach that contrasts with the discrete, combinatorial approach dominant in the field. The key is to form mathematical quotient spaces where points correspond to classes of chords and paths between points correespond to classes of voice leadings. There’s also lots of cool pictures, so have a look!

Callender, Clifton, Ian Quinn, and Dmitri Tymoczko. Generalized Voice-Leading Spaces. Science 18 April 2008: Vol. 320 no. 5874. Detailed supplemental material.