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 such as IcVSIM and ANGLE, and gives a sample of how these continuous spaces can be used to investigate the structural properties underlying the Z-relation (see joint work with Rachel Hall, below).

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!

This is an analysis that focuses on the voice-leading and harmonic constraints underlying many of the chord progressions in Ligeti's fifth Piano Etude, which the composers describes as "almost a jazz piece." Ligeti's harmonic approach in this etude seems less systmatic than many of his other works, but extending Neo-Riemannian approaches to efficient motions between tertian harmonies of indefinite size reveals the basic principles at work.

Empirical research with my FSU colleague Nancy Rogers that answers some of the questions I pose in the paper below on voice-leading distance.