Markov Chain Analysis of Musical Dice Games

TL;DR

This paper analyzes musical compositions using Markov chains, focusing on entropy, redundancy, and first passage times to understand tonal structure and composer differences, and introduces a Riemannian distance for musical dice games.

Contribution

It applies Markov chain analysis to a large dataset of musical pieces, introducing a geodesic distance based on Riemannian structure to compare musical dice games.

Findings

Entropy exceeds redundancy in tonal music.

First passage times reveal tonality and composer.

Riemannian distance measures differences in musical dice games.

Abstract

We have studied entropy, redundancy, complexity, and first passage times to notes for 804 pieces of 29 composers. The successful understanding of tonal music calls for an experienced listener, as entropy dominates over redundancy in musical messages. First passage times to notes resolve tonality and feature a composer. We also discuss the possible distances in space of musical dice games and introduced the geodesic distance based on the Riemann structure associated to the probability vectors (rows of the transition matrices).