Transposition and time-warp invariant algorithm for detecting repeated patterns in polyphonic music

Abstract

Finding repetitions in music is a fundamental music information retrieval problem that has several scientific and engineering applications. A popular algorithm for the problem is SIA, the structure induction algorithm developed by Meredith et. al. [10]. SIA is transposition invariant, allows gaps between the notes, and can process both monophonic and polyphonic music. However, the algorithm does not allow any distortion in the time dimension.In this paper, we introduce a new algorithm that has all SIA's capabilities, but also respects time-warp invariance. Such invariance is highly needed, for instance, when there are rhythmic variations in the music, or the input data stems from a live performance. Like SIA, our algorithm works in O(n 2 log n) time, where n denotes the number of notes, and can efficiently process inputs of thousands of notes using current computers.

A model of large-scale thematic structure

“…Computational identification of themes in music is a task of some difficulty. Methods for repetition detection in general for symbolic music have been produced for an array of purposes within the field of Music Information Retrieval, and with varying degrees of success (a summary of this body of research is given in Janssen et al, 2014, as well as the more recent work of Ren et al (2017); Melkonian et al, 2019;Laaksonen & Lemström, 2019). These methods seek to identify repeated material by searching for matching subsequences -with either exact or inexact matches -within the string of a given musical representation, or using 'geometric' approaches where melodies are considered as shapes in a multi-dimensional feature space (classification and summary given in Janssen et al, 2014).…”