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Volume 8
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Article

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

by
Yannick Jadoul
1,*,†,
Francesca D’Orazio
1,*,†,
Vesta Eleuteri
2,
Jelle van der Werff
1,
Tommaso Tufarelli
3,
Marco Gamba
4,
Teresa Raimondi
1,‡ and
Andrea Ravignani
1,5,6,‡
1
Department of Human Neurosciences, Sapienza University of Rome, 00185 Rome, Italy
2
Department of Behavioral and Cognitive Biology, University of Vienna, 1030 Vienna, Austria
3
Independent Researcher, Beeston NG9, UK
4
Department of Life Sciences and Systems Biology, University of Turin, 10124 Turin, Italy
5
Center for Music in the Brain, Department of Clinical Medicine, Aarhus University & The Royal Academy of Music Aarhus/Aalborg, 8000 Aarhus, Denmark
6
Research Center of Neuroscience "CRiN-Daniel Bovet", Sapienza University of Rome, 00185 Rome, Italy
*
Authors to whom correspondence should be addressed.
†
Co-first authors.
‡
Co-last authors.
Vibration 2025, 8(2), 12; https://doi.org/10.3390/vibration8020012
Submission received: 27 November 2024 / Revised: 10 March 2025 / Accepted: 15 March 2025 / Published: 24 March 2025
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Abstract

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.
Keywords: nPVI; rhythmic measures; bioacoustics; vocalization; timing; temporal sequences nPVI; rhythmic measures; bioacoustics; vocalization; timing; temporal sequences

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MDPI and ACS Style

Jadoul, Y.; D’Orazio, F.; Eleuteri, V.; van der Werff, J.; Tufarelli, T.; Gamba, M.; Raimondi, T.; Ravignani, A. Rhythmic Analysis in Animal Communication, Speech, and Music: The Normalized Pairwise Variability Index Is a Summary Statistic of Rhythm Ratios. Vibration 2025, 8, 12. https://doi.org/10.3390/vibration8020012

AMA Style

Jadoul Y, D’Orazio F, Eleuteri V, van der Werff J, Tufarelli T, Gamba M, Raimondi T, Ravignani A. Rhythmic Analysis in Animal Communication, Speech, and Music: The Normalized Pairwise Variability Index Is a Summary Statistic of Rhythm Ratios. Vibration. 2025; 8(2):12. https://doi.org/10.3390/vibration8020012

Chicago/Turabian Style

Jadoul, Yannick, Francesca D’Orazio, Vesta Eleuteri, Jelle van der Werff, Tommaso Tufarelli, Marco Gamba, Teresa Raimondi, and Andrea Ravignani. 2025. "Rhythmic Analysis in Animal Communication, Speech, and Music: The Normalized Pairwise Variability Index Is a Summary Statistic of Rhythm Ratios" Vibration 8, no. 2: 12. https://doi.org/10.3390/vibration8020012

APA Style

Jadoul, Y., D’Orazio, F., Eleuteri, V., van der Werff, J., Tufarelli, T., Gamba, M., Raimondi, T., & Ravignani, A. (2025). Rhythmic Analysis in Animal Communication, Speech, and Music: The Normalized Pairwise Variability Index Is a Summary Statistic of Rhythm Ratios. Vibration, 8(2), 12. https://doi.org/10.3390/vibration8020012

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