Quantifying Regularity in Music Structure Analysis

This article describes objective measures of segment regularity for use in evaluating musical structure annotations. The core idea derives from identifying simple ratio relationships between segment durations (e.g., 2:1 or 3:4), and can be implemented in both musical time (beats) or absolute time (seconds). Extensions are proposed to further quantify regularity within labeled segment groups, across hierarchical levels, and evaluate balance or uniformity of segment durations. We demonstrate the efficacy of the proposed methods with an empirical study of several standard datasets for music structure analysis. Our findings indicate: 1) under reasonable assumptions of tempo stability, regularity can be reliably measured in absolute time, 2) most existing datasets exhibit regularity, 3) regularity interacts meaningfully segment labelling, 4) regularity and balance are distinct concepts, and 5) multi-level segmentations exhibit cross-level regularity.