Complexity, time and music

TL;DR

This paper explores the application of algorithmic and dynamical complexity measures to musical time series, revealing insights into the intrinsic nature of musical evolution and complexity over history.

Contribution

It introduces a novel approach to quantify musical complexity using dynamical systems theory and entropy, linking musical evolution to intrinsic fractional properties.

Findings

No systematic increase in complexity over musical history

Dynamical measures reveal intrinsic fractional properties of music

Complexity measures do not correlate straightforwardly with historical evolution

Abstract

The concept of complexity as considered in terms of its algorithmic definition proposed by G.J. Chaitin and A.N. Kolmogorov is revisited for the dynamical complexity of music. When music pieces are cast in the form of time series of pitch variations, concepts of dynamical systems theory can be used to define new quantities such as the {\em dimensionality} as a measure of the {\em global temporal dynamics} of a music piece, and the Shanon {\em entropy} as an evaluation of its {\em local dynamics}. When these quantities are computed explicitly for sequences sampled in the music literature from the 18th to the 20th century, no indication is found of a systematic increase in complexity paralleling historically the evolution of classical western music, but the analysis suggests that the fractional nature of art might have an intrinsic value of more general significance.