Moebius Beats: The Twisted Spaces of Sliding Window Audio Novelty Functions with Rhythmic Subdivisions

Abstract

functions (ANFs) representing songs with rhythmic subdivisions concentrate on the boundary of non-orientable surfaces such as the Moebius strip. This insight provides a radically different topological approach to classifying types of rhythm hierarchies. In particular, we use tools from topological data analysis (TDA) to detect subdivisions, and we use thresholds derived from TDA to build graphs at different scales. The Laplacian eigenvectors of these graphs contain information which can be used to estimate tempos of the subdivisions. We show a proof of concept example on an audio snippet from the MIREX tempo training dataset, and we hope in future work to find a place for this in other MIR pipelines.