composition, music theory, mathematics
Recent work by Ian Quinn investigates the harmonic quality of pitch-class sets through the use of the discrete Fourier transform. This paper uses the continuous Fourier transform to extend Quinn’s work to continuous pitch and pitch-class sets, demonstrate distance measures in continuous Fourier spaces that correlate strongly with existing interval-based similarity measures, and gives a sample of how these continuous spaces can be used to investigate the structural properties underlying the Z-relation (the latter based on joint work with Rachel Hall).
Continuous harmonic spaces, Journal of Music Theory 51.2, 2007 (published in 2009). Winner of the David Kraehenbuehl Prize.