Rhythmic Analysis in Animal Communication, Speech, and Music: The Normalized Pairwise Variability Index Is a Summary Statistic of Rhythm Ratios

Rhythm is fundamental in many physical and biological systems. Rhythm is relevant to a broad range of phenomena across different fields, including animal bioacoustics, speech sciences, and music cognition. As a result, the interest in developing consistent quantitative measures for cross-disciplinary rhythmic analysis is growing. Two quantitative measures that can be directly applied to any temporal structure are the normalized pairwise variability index (nPVI) and rhythm ratios (rk). The nPVI summarizes the overall isochrony of a sequence, i.e., how regularly spaced a sequence’s events are, as a single value. Meanwhile, rk quantifies ratios between a sequence’s adjacent intervals and is often used for identifying rhythmic categories. Here, we show that these two rhythmic measures are fundamentally connected: the nPVI is a summary static of the rk values of a temporal sequence. This result offers a deeper understanding of how these measures are applied. It also opens the door for creating novel, custom measures to quantify rhythmic patterns based on a sequence’s rk distribution and compare rhythmic patterns across different domains. The explicit connection between nPVI and rk is one further step towards a common quantitative toolkit for rhythm research across disciplines.