This article introduces a type of harmonic geometry, Fourier phase space, and uses it to
advance the understanding of Schubert's tonal language and comment upon current topics …

The discrete Fourier transform on pitch-class sets, proposed by David Lewin and advanced
by Ian Quinn, may provide a new lease on life for Allen Forte's idea of a general theory of …

This article investigates the use of octatonic chord progressions at deeper structural levels in
the music of Maurice Ravel. Octatonic chord progressions are successions of triads and …

This article introduces uniform patterns, voice-leading patterns that are purely regular when
represented with generic intervals. Generic intervals are continuous-valued intervals that are …

Filtered Point-Symmetry (FiPS) is a tool for modeling relationships between iterated
maximally even sets. Common musical relationships can be studied by using FiPS to model …

In this paper, we examine relationships between signature transformations, Filtered Point-
Symmetry (FiPS), and voice-leading spaces, with a strong emphasis on the role of scalar …

This article introduces basics of a theory of generated tone systems. It is built on an explicit
conceptualization of the notion of comma and yields illuminative insights into diverse areas …

We extend the theory of maximally even sets to determine the evenness of partitions of the
chromatic universe U c. Interactions measure the average evenness of colour sets …

Journal of Mathematics and Music's recent special issue 7 (2) reveals substantial common
ground between mathematical theories of harmony advanced by Tymoczko, Hook, Plotkin …

Motivated by the music-theoretical work of Richard Cohn and David Clampitt on late-
nineteenth century harmony, we mathematically prove that the PL-group of a hexatonic cycle …