The Ising model and random fields of scales
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.
Cite
@article{arxiv.2507.00071,
title = {The Ising model and random fields of scales},
author = {Ricardo Gómez Aíza},
journal= {arXiv preprint arXiv:2507.00071},
year = {2025}
}
Comments
41 pages, 23 figures, additional material at https://github.com/gomiza/scaletor