Synchrony between things, especially organisms

Entrainment, synchronisation, dancing together

When complicated things sync to each other. For application to music, see rhythm.

Mathematical basis of synchronisation

TODO: abstract models without much biological support.

Neurological basis of synchronisation

Excited to read the new one by Jonathan Cannon A Bayesian perspective on entrainment with behavioral supportr.


“We’ve isolated the rhythms in the brain that match rhythms in music,” explains Keith Doelling, an NYU Ph.D. student and the study’s lead author. “Specifically, our findings show that the presence of these rhythms enhances our perception of music and of pitch changes.” […] Brain rhythms, they add, therefore appear to play a role in parsing and grouping sound streams into ‘chunks’ that are then analyzed as speech or music.

Or how about a dynamical systems approach? Famously, (Haken, Kelso, and Bunz 1985) does this: I found this paper fascinating, although the fact they spun several books out of it afterwards seemed to me to be gilding the lily.

Interpersonal synchronisation

Much to wonder about. For now, see the review in Basso, Satyal, and Rugh (2021) of stuff like (Basso, Satyal, and Rugh 2021; Kinreich et al. 2017; Toppi et al. 2016; Valencia and Froese 2020).

we synthesize findings from anthropology, sociology, psychology, dance pedagogy, and neuroscience to propose The Synchronicity Hypothesis of Dance, which states that humans dance to enhance both intra- and inter-brain synchrony

Brains Might Sync As People Interact — and That Could Upend Consciousness Research

People synchronize in various ways when we interact with one another. We subconsciously match our footsteps when we walk. During conversations, we mirror each other’s postures and gestures.

To that end, studies have shown that people synchronize heart rates and breathing when watching emotional films together. The same happens when romantic partners share a bed. Some scientists think we do this to build trust and perceive people as similar to ourselves, which encourages us to behave compassionately.

Surprisingly, people synchronize their neural rhythms, too. Researchers like Tom Froese, a cognitive scientist from the Okinawa Institute of Science and Technology in Japan, think that these findings could upend our current models of consciousness.

Pretty much everything up-ends our current models of conscious though, apparently, so…


  • correlograms
  • “vector strength” and event-based doohickeys versus continuous-signal systems
  • Kuramoto oscillators
  • Circle map
  • phase locked loops
  • “Entrainment” (Is that phase locking from the analysis rather than design perspective?)
  • The attraction of Pythagorean rhythms
  • machine listening for it
  • Lucky People Center International
  • Autocorrelation structures and simulating point processes from them


Absil, P.-A, R Mahony, and R Sepulchre. 2008. Optimization algorithms on matrix manifolds. Princeton, N.J.; Woodstock: Princeton University Press.
Acebrón, Juan A., L. L. Bonilla, Conrad J. Pérez Vicente, Félix Ritort, and Renato Spigler. 2005. “The Kuramoto Model: A Simple Paradigm for Synchronization Phenomena.” Reviews of Modern Physics 77 (1): 137–85.
Basso, Julia C., Medha K. Satyal, and Rachel Rugh. 2021. “Dance on the Brain: Enhancing Intra- and Inter-Brain Synchrony.” Frontiers in Human Neuroscience 14: 586.
Boumal, Nicolas. 2013. “On Intrinsic Cramér-Rao Bounds for Riemannian Submanifolds and Quotient Manifolds.” IEEE Transactions on Signal Processing 61 (7): 1809–21.
Boumal, Nicolas, Amit Singer, and P.-A Absil. 2013. “Robust Estimation of Rotations from Relative Measurements by Maximum Likelihood.” In 52nd IEEE Conference on Decision and Control, 1156–61. Firenze: IEEE.
Boumal, Nicolas, Amit Singer, P.-A. Absil, and Vincent D. Blondel. 2014. “Cramér-Rao Bounds for Synchronization of Rotations.” Information and Inference 3 (1): 1–39.
Buhusi, Catalin V., and Warren H. Meck. 2005. “What Makes Us Tick? Functional and Neural Mechanisms of Interval Timing.” Nature Reviews Neuroscience 6 (10): 755–65.
Canavier, Carmen, and Srisairam Achuthan. 2007. “Pulse Coupled Oscillators.” Scholarpedia 2 (4): 1331.
Cannon, Jonathan. 2021. “Expectancy-Based Rhythmic Entrainment as Continuous Bayesian Inference.” PLOS Computational Biology 17 (6): e1009025.
Carter, G.Clifford. 1987. “Coherence and Time Delay Estimation.” Proceedings of the IEEE 75 (2): 236–55.
Clayton, Martin. 1997. “Metre and Tal in North Indian Music.”
———. 2001. Time in Indian Music: Rhythm, Metre, and Form in North Indian Rag Performance. Oxford Monographs on Music. Oxford University Press, USA.
Collins, J. J., and I. N. Stewart. 1992. “Symmetry-Breaking Bifurcation: A Possible Mechanism for 2:1 Frequency-Locking in Animal Locomotion.” Journal of Mathematical Biology 30 (8): 827–38.
Demaine, Erik D., Francisco Gomez-Martin, Henk Meijer, David Rappaport, Perouz Taslakian, Godfried T. Toussaint, Terry Winograd, and David R. Wood. 2005. “The Distance Geometry of Deep Rhythms and Scales.” In CCCG, 163–66.
———. 2009. “The Distance Geometry of Music.” In Computational Geometry, 42:429–54.
Doelling, Keith B., and David Poeppel. 2015. “Cortical Entrainment to Music and Its Modulation by Expertise.” Proceedings of the National Academy of Sciences 112 (45): E6233–42.
Ellis, D.P.W., C.V. Cotton, and M.I. Mandel. 2008. “Cross-Correlation of Beat-Synchronous Representations for Music Similarity.” In IEEE International Conference on Acoustics, Speech and Signal Processing, 2008. ICASSP 2008, 57–60.
Elman, Jeffrey L. 1990. “Finding Structure in Time.” Cognitive Science 14: 179–211.
Feldman, David P, and James P Crutchfield. 2004. “Synchronizing to Periodicity: The Transient Information and Synchronization Time of Periodic Sequences.” Advances in Complex Systems 7 (03): 329–55.
Fischer, Ingo, Raúl Vicente, Javier M Buldú, Michael Peil, Claudio R Mirasso, M C Torrent, and Jordi García-Ojalvo. 2006. “Zero-Lag Long-Range Synchronization via Dynamical Relaying.”
Fokker, A D. 1968. Unison Vectors and Periodicity Blocks in the Three-Dimensional (3-5-7) Harmonic Lattice of Notes. Koninkl. Nederl. Akademie van Wetenschappen.
Freidlin, Mark I., and Alexander D. Wentzell. 1993. “Diffusion Processes on Graphs and the Averaging Principle.” The Annals of Probability 21 (4): 2215–45.
Freidlin, Mark, and Matthias Weber. 1998. “Random Perturbations of Nonlinear Oscillators.” The Annals of Probability 26 (3): 925–67.
Glass, Leon. 1991. “Cardiac Arrhythmias and Circle Maps−A Classical Problem.” Chaos: An Interdisciplinary Journal of Nonlinear Science 1 (1): 13–19.
———. 2001. “Synchronization and Rhythmic Processes in Physiology.” Nature 410 (6825): 277–84.
Guevara, Michael R., and Leon Glass. 1982. “Phase Locking, Period Doubling Bifurcations and Chaos in a Mathematical Model of a Periodically Driven Oscillator: A Theory for the Entrainment of Biological Oscillators and the Generation of Cardiac Dysrhythmias.” Journal of Mathematical Biology 14 (1): 1–23.
Haken, Hermann, J A Scott Kelso, and Bunz. 1985. “A Theoretical Model of Phase Transitions in Human Hand Movements.” Biological Cybernetics 51 (5): 347–56.
Hennig, Holger, Ragnar Fleischmann, Anneke Fredebohm, York Hagmayer, Jan Nagler, Annette Witt, Fabian J Theis, and Theo Geisel. 2011. “The Nature and Perception of Fluctuations in Human Musical Rhythms.” PLoS ONE 6 (10): –26457.
Hennig, Holger, Ragnar Fleischmann, and Theo Geisel. 2012. “Musical Rhythms: The Science of Being Slightly Off.” Physics Today 65 (7): 64–65.
Ichinomiya, Takashi. 2004. “Frequency Synchronization in a Random Oscillator Network.” Physical Review E 70 (2): 026116.
Keith, W. L., and R. H. Rand. 1984. “1∶1 and 2∶1 Phase Entrainment in a System of Two Coupled Limit Cycle Oscillators.” Journal of Mathematical Biology 20 (2): 133–52.
Kinreich, Sivan, Amir Djalovski, Lior Kraus, Yoram Louzoun, and Ruth Feldman. 2017. “Brain-to-Brain Synchrony During Naturalistic Social Interactions.” Scientific Reports 7 (1): 17060.
Mateo, David, Nikolaj Horsevad, Vahid Hassani, Mohammadreza Chamanbaz, and Roland Bouffanais. 2019. “Optimal Network Topology for Responsive Collective Behavior.” Science Advances 5 (4).
Mirollo, R., and S. Strogatz. 1990. “Synchronization of Pulse-Coupled Biological Oscillators.” SIAM Journal on Applied Mathematics 50 (6): 1645–62.
Mirollo, R., and S. H. Strogatz. 2007. “The Spectrum of the Partially Locked State for the Kuramoto Model.” Journal of Nonlinear Science 17 (4): 309–47.
Moreno, Y., and A. F. Pacheco. 2004. “Synchronization of Kuramoto Oscillators in Scale-Free Networks.” EPL (Europhysics Letters) 68 (4): 603.
Parncutt, Richard. 1994. “A Perceptual Model of Pulse Salience and Metrical Accent in Musical Rhythms.” Music Perception: An Interdisciplinary Journal 11 (4): 409–64.
Pikovsky, Arkady, and Michael Rosenblum. 2007. “Synchronization.” Scholarpedia 2 (12): 1459.
Pikovsky, Arkady, Michael Rosenblum, and Jürgen Kurths. 2003. Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge University Press.
Schöner, Gregor. 2002. “Timing, Clocks, and Dynamical Systems.” Brain and Cognition 48 (1): 31–51.
Semjen, Andras, Dirk Vorberg, and Hans-Henning Schulze. 1998. “Getting Synchronized with the Metronome: Comparisons Between Phase and Period Correction.” Psychological Research 61 (1): 44–55.
Strogatz, Steven H. 2000. “From Kuramoto to Crawford: Exploring the Onset of Synchronization in Populations of Coupled Oscillators.” Physica D: Nonlinear Phenomena 143: 1–20.
———. 2004. Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life. Hyperion.
Toppi, Jlenia, Gianluca Borghini, Manuela Petti, Eric J. He, Vittorio De Giusti, Bin He, Laura Astolfi, and Fabio Babiloni. 2016. “Investigating Cooperative Behavior in Ecological Settings: An EEG Hyperscanning Study.” PLOS ONE 11 (4): e0154236.
Toussaint, Godfried T. 2004. “A Comparison of Rhythmic Similarity Measures.” In ISMIR.
———. 2013. The Geometry of Musical Rhythm: What Makes a “Good” Rhythm Good? 1 edition. Boca Raton, FL: Chapman and Hall/CRC.
Valencia, Ana Lucía, and Tom Froese. 2020. “What Binds Us? Inter-Brain Neural Synchronization and Its Implications for Theories of Human Consciousness.” Neuroscience of Consciousness 2020 (1).

No comments yet. Why not leave one?

GitHub-flavored Markdown & a sane subset of HTML is supported.