The fractal dimension of music: Melodic contours and time series of pitch

TL;DR

This study compares fractal dimensions of melodic contours in classical and folk music, finding that detrended fluctuation analysis is more reliable than box counting for analyzing short musical time series.

Contribution

It demonstrates the effectiveness of detrended fluctuation analysis over box counting in assessing the fractal properties of musical melodies.

Findings

Folk music tends to have lower fractal dimensions than classical music.

Detrended fluctuation analysis is preferable for short time series.

Box counting shows significant biases near dimensions close to two.

Abstract

We analyze the fractal dimension of melodic contours and pitch time series of classical music and folk music tunes. The fractal dimensions obtained from box counting and detrended fluctuation analysis show significant differences. They are ascribed to the low accuracy of box counting for dimensions close to two as well as to a possible bias because the pitches in the time series are connected by lines to obtain the melodic contour used in the box counting analysis. We observe a tendency that folk music exhibits lower fractal dimensions than classical music, but further studies are needed in order to assess cutoff effects in the comparatively short folk music tunes. We conclude that detrended fluctuation analysis is the preferable method for fractal analysis of music, and this verifies previous studies of analysis of short time series.