[P3] Poster: Day 3

[P3-15] Statistical analysis of small-integer ratios in bioacoustics and music

*Yannick Jadoul¹, Tommaso Tufarelli, Chloé Coissac¹, Marco Gamba², Andrea Ravignani^1,3,4 (1. Department of Human Neurosciences, Sapienza University of Rome, Rome (Italy), 2. Department of Life Sciences and Systems Biology, University of Turin, Turin (Italy), 3. Center for Music in the Brain, Department of Clinical Medicine, Aarhus University, Aarhus (Denmark), 4. Research Center of Neuroscience “CRiN-Daniel Bovet”, Sapienza University of Rome, Rome (Italy))

Keywords:

categorical rhythm,vocalization,timing,meter,statistical assumptions

Rhythmic structure is ubiquitous in human culture as well as in nature, but is hard to capture in all its complexity. One common pattern in human music are temporal intervals whose relative durations can be expressed as small-integer ratios. For example, the durations of a quarter note and an eight note are related in a 2:1 ratio (Roeske et al., 2020). Recent work has found that the small-integer ratio categories do not just occur in most human musical cultures, but also in a broad range of animal species’ vocalizations or behavioral displays. However, biological systems are noisy, and empirically measured intervals rarely form an exact small-integer ratio, and so, statistical methods are necessary to objectively assess whether an observed behavioral intervals approximately conform to a specific integer ratio. We explain a commonly-used approach for assessing the presence of inter ratio categories in temporal sequences, and then mathematically assess whether this leading integer ratio analysis method in behavioral research makes valid statistical and biological assumptions. In particular, we (1) make the temporal properties of empirical ratios explicit, both in general and for the typical use in the literature; (2) show how the choice of ratio formula affects the probability distribution of rhythm ratios and ensuing statistical results; (3) provide guidance on how to carefully consider the assumptions and null hypotheses of the statistical analysis; (4) present a comprehensive methodology to statistically test integer ratios for any null hypothesis of choice. Our observations have implications for both past and future research in music cognition and animal behavior: They suggest how to interpret past findings and provide tools to choose the correct null hypotheses in future empirical work.