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 …

This paper studies the “integration” problem of nineteenth-century harmony—the question
whether the novel chromatic chord transitions in this time are a radical break from or a …

This article develops the notion of modal spelled pitch class by combining Julian Hook's
theory of spelled heptachords and Steven Rings's heard scale degree. Modal spelled pitch …

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 analytical methods in mathematical music theory, we determine the structure of
the subgroup J of GL(3,Z_12) generated by the three voicing reflections. We determine the …

This contribution responds to a growing interest in the application of Discrete Fourier
Transform (DFT) to the study of pitch class sets and pitch class profiles. Theoretical …

This article describes an approximate set theory modeling intuitions shared by musicians
such as Cowell, Schoenberg, Messiaen, and Persichetti. The author considers five …

This article examines the musical sequence as a nexus of melodic, linear, and harmonic
processes commonly found in tonal music from the seventeenth to the early twentieth …

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 …

Schubert's song Ganymed has attracted a great deal of interest from analysts on account of
its progressive tonal plan, which is often seen as a challenge to Schenkerian theories of …