Emergence of Benford's Law in Music

TL;DR

This paper reveals that the distribution of note durations in classical music pieces from major composers follows Benford's Law, indicating a surprising mathematical pattern in musical timing data.

Contribution

It demonstrates for the first time that musical note durations in classical compositions exhibit Benford's Law across multiple composers.

Findings

Note durations follow Benford's Law distribution.

The logarithmic distribution applies to all digits, not just leading digits.

The pattern is consistent across different composers.

Abstract

We analyzed a large selection of classical musical pieces composed by Bach, Beethoven, Mozart, Schubert and Tchaikovsky, and found a surprising connection with mathematics. For each composer, we extracted the time intervals each note was played in each piece and found that the corresponding data sets are Benford distributed. Remarkably, the logarithmic distribution is present not only for the leading digits, but also for all digits.