The Ising model and random fields of scales

TL;DR

This paper introduces a simulated annealing model inspired by the Ising model to explore musical scales as random fields, enabling customizable analysis of scale configurations within the 12-tone equal temperament system.

Contribution

It develops a flexible thermodynamic model for musical scales using Gibbs measures, providing a novel computational tool for scale analysis.

Findings

Generates equilibrium scale configurations with adjustable properties

Provides an open access application for scale exploration

Models musical scales using concepts from statistical physics

Abstract

Random fields of scales result when the class of musical scales is thought as a set of sites, and a site can be in one of two possible states (or spins): On or Off. We present a flexible simulated annealing model that produces generic configurations arising from equilibrium states (or Gibbs measures) associated to hamiltonian energy functions defined in terms of musical interactions with parameters that can be manipulated to customize properties of the scales. The starting point is to think of the set of scales as the combinatorial class of integer compositions and the final result is an effective thermodynamic search engine implemented in an open access application for the 12-TET tuning system: Scaletor.