Some mathematical and computational relations between timbre and color

TL;DR

This paper explores the structural similarities between timbre and color using category theory, proposing a computational framework to modulate and relate these sensory phenomena through mathematical models.

Contribution

It introduces a novel categorical approach to relate timbre and color, bridging physics, perception, and computation with a focus on structural similarities.

Findings

Proposes a categorical model linking timbre and color

Suggests a framework for modulating sensory variations

Highlights structural parallels between auditory and visual phenomena

Abstract

In physics, timbre is a complex phenomenon, like color. Musical timbres are given by the superposition of sinusoidal signals, corresponding to longitudinal acoustic waves. Colors are produced by the superposition of transverse electromagnetic waves in the domain of visible light. Regarding human perception, specific timbre variations provoke effects similar to color variations, for example, a rising tension or a relaxation effect. We aim to create a computational framework to modulate timbres and colors. To this end, we consider categorical groupoids, where colors (timbres) are objects and color variations (timbre variations) are morphisms, and functors between them, which are induced by continuous maps. We also sketch some gestural variations of this scheme. Thus, we try to soften the differences and focus on the similarity of structures.