Complexity Measures of Music

TL;DR

This paper introduces a technique analyzing music volume to detect crucial events, linking musical complexity to brain dynamics, and compares multifractality in computer versus human performances to better understand musicality.

Contribution

It extends previous work by confirming the role of crucial events in music through volume analysis and explores multifractality as a measure of musicality beyond crucial events.

Findings

Crucial events in music have a complexity index mu ~ 2.

Music performances exhibit different multifractal spectra, with human performances being broader.

Multifractality may better measure musicality than crucial events alone.

Abstract

We present a technique to search for the presence of crucial events in music, based on the analysis of the music volume. Earlier work on this issue was based on the assumption that crucial events correspond to the change of music notes, with the interesting result that the complexity index of the crucial events is mu ~ 2, which is the same inverse power-law index of the dynamics of the brain. The search technique analyzes music volume and confirms the results of the earlier work, thereby contributing to the explanation as to why the brain is sensitive to music, through the phenomenon of complexity matching. Complexity matching has recently been interpreted as the transfer of multifractality from one complex network to another. For this reason we also examine the mulifractality of music, with the observation that the multifractal spectrum of a computer performance is significantly narrower than the multifractal spectrum of a human performance of the same musical score. We conjecture that although crucial events are demonstrably important for information transmission, they alone are not suficient to define musicality, which is more adequately measured by the multifractality spectrum.