The Kolmogorov Complexity of Irish traditional dance music
Michael McGettrick, Paul McGettrick
TL;DR
The study estimates the Kolmogorov complexity of Irish traditional dance melodies by applying Lempel-Ziv compression to sequences of ABC notation letters that encode notes with uniform length. By comparing two LZ variants (LZ78 and LZ77) on a sample of reels and jigs, it quantifies tune repetitiveness via compression ratios and then normalizes for sequence length to compare intrinsic complexity across tune types. The results show reels are marginally less complex than jigs after adjustment, and demonstrate that more repetitive tunes yield stronger compression, offering a potential learning aid for selecting tunes by difficulty. The work highlights a quantitative information-theoretic framework for analyzing music and suggests directions for applying the approach to other tune families and harmonic contexts.
Abstract
We estimate the Kolmogorov complexity of melodies in Irish traditional dance music using Lempel-Ziv compression. The "tunes" of the music are presented in so-called "ABC notation" as simply a sequence of letters from an alphabet: We have no rhythmic variation, with all notes being of equal length. Our estimation of algorithmic complexity can be used to distinguish "simple" or "easy" tunes (with more repetition) from "difficult" ones (with less repetition) which should prove useful for students learning tunes. We further present a comparison of two tune categories (reels and jigs) in terms of their complexity.