What constitutes a musical pattern?

Abstract

There is a plethora of computational systems designed for alagorithmic discovery of musical patterns, ranging from geometrical methods to machine learning based approaches. These algorithms often disagree on what constitutes a pattern, mainly due to the lack of a broadly accepted definition of musical patterns. On the other side of the spectrum, human-annotated musical patterns also often do not reach a consensus, partly due to the subjectivity of each individual expert, but also due to the elusive definition of a musical pattern in general. In this work, we propose a framework of music-theoretic transformations, through which one can easily define predicates which dictate when two musical patterns belong to a particular equivalence class. We exploit simple notions from category theory to assemble transformations compositionally, allowing us to define complex transformations from simple and well-understood ones. Additionally, we provide a prototype implementation of our theoretical framework as an embedded domain-specific language in Haskell and conduct a meta-analysis on several algorithms submitted to a pattern extraction task of the the Music Information Retrieval Evaluation eXchange (MIREX) over the previous years.