Research ArticlePHYSICS

The structure of musical harmony as an ordered phase of sound: A statistical mechanics approach to music theory

See allHide authors and affiliations

Science Advances  17 May 2019:
Vol. 5, no. 5, eaav8490
DOI: 10.1126/sciadv.aav8490

Abstract

Music, while allowing nearly unlimited creative expression, almost always conforms to a set of rigid rules at a fundamental level. The description and study of these rules, and the ordered structures that arise from them, is the basis of the field of music theory. Here, I present a theoretical formalism that aims to explain why basic ordered patterns emerge in music, using the same statistical mechanics framework that describes emergent order across phase transitions in physical systems. I first apply the mean field approximation to demonstrate that phase transitions occur in this model from disordered sound to discrete sets of pitches, including the 12-fold octave division used in Western music. Beyond the mean field model, I use numerical simulation to uncover emergent structures of musical harmony. These results provide a new lens through which to view the fundamental structures of music and to discover new musical ideas to explore.

This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.

View Full Text