Rhythm as an ordered phase of sound: how musical meter emerges in a statistical mechanical model

TL;DR

This paper presents a statistical physics-inspired model of musical rhythm and meter, revealing phase transitions from disorder to order that align with Bach's compositions, offering insights and generative methods.

Contribution

It introduces a novel model combining psychological preferences and physics concepts to explain and generate musical rhythms and meters.

Findings

Model exhibits phase transitions from disordered to ordered rhythms.

Predicted rhythmic characteristics match Bach's compositions.

Provides a new framework for studying and generating musical rhythms.

Abstract

We develop a model of musical rhythm and meter based on optimizing the trade-off between human psychological preferences for perceiving repeated patterns in time with a desire for variety and complexity. By mapping these competing preferences onto analogous quantities in statistical physics, we define an effective free energy which is minimized in the grand canonical ensemble. Using a mean field approximation, we observe phase transitions in the model from disordered events in time to orderings that closely reproduce those seen in music. We then compare the range of rhythmic characteristics predicted by the model to a dataset drawn from compositions by Johann Sebastian Bach, finding generally good quantitative agreement. The results provide a new lens through which to study musical rhythm, and a method for generatively producing rhythms.