Symbolic Dynamics of Music from Europe and Japan

TL;DR

This paper applies symbolic dynamics and block-entropy analysis to compare the complexity of Japanese and Western European musical texts, revealing insights into their underlying structural constraints and non-randomness.

Contribution

It introduces a method to quantify musical complexity through block-entropy scaling laws, comparing distinct musical traditions using symbolic dynamics.

Findings

Japanese and European music show different entropy scaling behaviors.

Complexity correlates with the degree of non-randomness in musical texts.

Constraints in musical structures can be quantitatively assessed.

Abstract

After a brief introduction to the theory underlying block-entropy, and its relation to the dynamics of complex systems as well as certain information theory aspects, we study musical texts coming from two distinct musical traditions (Japanese and Western European) encoded via symbolic dynamics. We quantify their information content or also known as the degree of "non-randomness" which essentially defines the complexity of the text. We analyse the departure of "total randomness" to the constrains underlying the dynamics of the symbol generating process. Following Shannon on his attribution to these constraints as the emergence of complexity, we observe that it can be accurately assessed by the texts' block-entropy versus block-length scaling laws.