The Music and Mathematics of Maximal Evenness in Graphs

TL;DR

This paper explores the concept of maximal evenness in graphs using physics-inspired potential energy, graph theory, and majorization, extending the idea into higher dimensions and connecting it to musical traditions and scales.

Contribution

It introduces a novel mathematical framework combining physics, graph theory, and musicology to analyze maximal evenness beyond traditional one-dimensional cases.

Findings

Extended maximal evenness to higher-dimensional graphs

Established connections between graph-theoretic concepts and musical scales

Linked mathematical models to Puerto Rican bomba music traditions

Abstract

We use the concept of electric potential energy from physics, the mathematical field of graph theory, and the notion of majorization to study maximal evenness in a broader mathematical context than what was previously possible, so that we can go beyond the well-known one-dimensional maximally even sets into higher dimensional and more geometrically complex territory. We investigate musical connections between certain generalizations of maximally even sets, one of the oldest Puerto Rican musical traditions of African origin called bomba, and with certain scales ranging from the familiar to the esoteric.