How can discrete pitches and chords emerge from the continuum of sound? Using a
quantum cognition model of tonal music, we prove that the associated Schrödinger equation …

Abstract Filtered Point-Symmetry is a tool for manipulating iterated maximally even sets over
time. The dissertation explores how this tool affects our conception of musical networks and …

This paper deals with the algebraic structure of the sequence of harmonics when combined
with equal temperaments. Fractals and the golden ratio appear surprisingly on the way. The …

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 …

We develop formalism for generating pure-tone systems that best approximate the
modulation/transposition properties of equal-tempered scales. We define six measurements …

The aim of this article is to describe mathematically different tuning systems, to study their
mathematical properties, and to propose a construction allowing their comparison. In order …

The famous results of Carey and Clampitt [N. Carey and D. Clampitt, Aspects of well-formed
scales, Music Theory Spectr. 11 (1989), pp. 187–206] focus on scales generated by one …

Having participants listen and react to musical stimuli is one of music cognition's
foundational methods. Whereas most researchers have used stimuli adapted from existing …

This work investigates whether there are harmonic sets which are universally prioritized
when fitting the chromatic just scale with equal-tempered tunings. We design a method to …

Abstract scales are formalized as a cyclic group of classes of projection functions related to
iterations of the scale generator. Their representatives in the frequency domain are used to …