The Living Thing / Notebooks : Synchronisation

In the deserts of Sudan
And the gardens of Japan
From Milan to Yucatan
Every woman, every man

Hit me with your rhythm stick
Hit me, hit me
Je t’adore, ich liebe dich
Hit me, hit me, hit me
Hit me with your rhythm stick
Hit me slowly, hit me quick
Hit me, hit me, hit me

— Ian Dury & The Blockheads - Hit Me With Your Rhythm Stick

Note on rhythm, the understanding and making, amnd detecting of it.

To mention:

Making rhythms

Neurological/Psychological basis


“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.”

Not surprisingly, the study found that musicians have more potent oscillatory mechanisms than do non-musicians—but this discovery’s importance goes beyond the value of musical instruction.

“What this shows is we can be trained, in effect, to make more efficient use of our auditory-detection systems,” observes study co-author David Poeppel, a professor in NYU’s Department of Psychology and Center for Neural Science and director of the Max Planck Institute for Empirical Aesthetics in Frankfurt. “Musicians, through their experience, are simply better at this type of processing.”

Previous research has shown that brain rhythms very precisely synchronize with speech, enabling us to parse continuous streams of speech—in other words, how we can isolate syllables, words, and phrases from speech, which is not, when we hear it, marked by spaces or punctuation.

However, it has not been clear what role such cortical brain rhythms, or oscillations, play in processing other types of natural and complex sounds, such as music.

To address these questions, the NYU researchers conducted three experiments using magnetoencephalography (MEG), which allows measurements of the tiny magnetic fields generated by brain activity. The study’s subjects were asked to detect short pitch distortions in 13-second clips of classical piano music (by Bach, Beethoven, Brahms) that varied in tempo—from half a note to eight notes per second. The study’s authors divided the subjects into musicians (those with at least six years of musical training and who were currently practicing music) and non-musicians (those with two or fewer years of musical training and who were no longer involved in it).

For music that is faster than one note per second, both musicians and non-musicians showed cortical oscillations that synchronized with the note rate of the clips—in other words, these oscillations were effectively employed by everyone to process the sounds they heard, although musicians’ brains synchronized more to the musical rhythms. Only musicians, however, showed oscillations that synchronized with unusually slow clips.

This difference, the researchers say, may suggest that non-musicians are unable to process the music as a continuous melody rather than as individual notes. Moreover, musicians much more accurately detected pitch distortions—as evidenced by corresponding cortical oscillations. 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.

Haken: I found this paper fascinating, although the fact they spun several whole books out of it afterwards seemed to me to be gilding the lily.

To read

Breakbeat cuts

Slicing up your percussion line into mad junglist syncopations is a whole world of its own. Asides from selling a lot of vinyl, it has attracted significant academic interest.

Think of group theory angle, like a Rubik’s cube. Is it a pure group theoretic problem? Or are there additional constraints on a breakbeat cut such that it is still considered rhythmic?

Nick Collins has done a whole lot of work here.

Periodicity Analysis

I’m coming at this from a musical angle; The correlation at different scales can be weird and wonderful and I wonder if some algorithm from the world of Nonlinear Time Series Wizardry could help.

This overlaps with a lot of things, but my core question is best summarised:

Can I use machine learning to identify what about breakbeat cuts makes them rhythmically interesting? What range of repetition between infinite sameness and total chaos is musically attractive?

More generally, identifying cycles and periodicity is itself interesting, so I’ll collect some notes to that purely abstract end here too.


Abdallah, S. A., Ekeus, H., Foster, P., Robertson, A., & Plumbley, M. D.(2012) Cognitive music modelling: An information dynamics approach. In 2012 3rd International Workshop on Cognitive Information Processing (CIP) (pp. 1–8). DOI.
Acebrón, J. A., Bonilla, L. L., Pérez Vicente, C. J., Ritort, F., & Spigler, R. (2005) The Kuramoto model: A simple paradigm for synchronization phenomena. Reviews of Modern Physics, 77(1), 137–185. DOI.
Berlinkov, M. V.(2013) On the probability of being synchronizable. arXiv:1304.5774 [Cs, Math].
Buhusi, C. V., & Meck, W. H.(2005) What makes us tick? Functional and neural mechanisms of interval timing. Nature Reviews Neuroscience, 6(10), 755–765. DOI.
Cagnacci, A., Soldani, R., Laughlin, G. A., & Yen, S. S.(1996) Modification of circadian body temperature rhythm during the luteal menstrual phase: role of melatonin. Journal of Applied Physiology, 80(1), 25–29.
Canavier, C., & Achuthan, S. (2007) Pulse coupled oscillators. Scholarpedia, 2(4), 1331. DOI.
Carter, G. C.(1987) Coherence and time delay estimation. Proceedings of the IEEE, 75(2), 236–255. DOI.
Clayton, M. (1997) Metre and Tal in North Indian Music.
Clayton, M. (2001) Time in Indian Music: Rhythm, Metre, and Form in North Indian Rag Performance with Audio CD (Oxford Monographs on Music). . Oxford University Press, USA
Collins, J. J., & Stewart, I. N.(1992) Symmetry-breaking bifurcation: A possible mechanism for 2:1 frequency-locking in animal locomotion. Journal of Mathematical Biology, 30(8), 827–838. DOI.
Demaine, E. D., Gomez-Martin, F., Meijer, H., Rappaport, D., Taslakian, P., Toussaint, G. T., … Wood, D. R.(2005) The Distance Geometry of Deep Rhythms and Scales. In CCCG (pp. 163–166).
Demaine, E. D., Gomez-Martin, F., Meijer, H., Rappaport, D., Taslakian, P., Toussaint, G. T., … Wood, D. R.(2009) The distance geometry of music. In Computational Geometry (Vol. 42, pp. 429–454). DOI.
Desain, P., & Honing, H. (2001) Modeling the Effect of Meter in Rhythmic Categorization: Preliminary Results. Journal of Music Perception and Cognition, 7, 145–156.
DeVille, L. (2012) Transitions amongst synchronous solutions in the stochastic Kuramoto model. Nonlinearity, 25(5), 1473. DOI.
Doelling, K. B., & Poeppel, D. (2015) Cortical entrainment to music and its modulation by expertise. Proceedings of the National Academy of Sciences, 112(45), E6233–E6242. DOI.
Dorrian, H., Borresen, J., & Amos, M. (2013) Community Structure and Multi-Modal Oscillations in Complex Networks. PLoS ONE, 8(10), e75569. DOI.
Duan, Q., Park, J. H., & Wu, Z.-G. (2014) Exponential state estimator design for discrete-time neural networks with discrete and distributed time-varying delays. Complexity, 20(1), 38–48. DOI.
Ellis, D. P. W., Cotton, C. V., & Mandel, M. I.(2008) Cross-correlation of beat-synchronous representations for music similarity. In IEEE International Conference on Acoustics, Speech and Signal Processing, 2008. ICASSP 2008 (pp. 57–60). DOI.
Elman, J. L.(1990) Finding structure in time. Cognitive Science, 14, 179–211. DOI.
Engbert, R., Krampe, R. T., Kurths, J., & Kliegl, R. (2002) Synchronizing Movements with the Metronome: Nonlinear Error Correction and Unstable Periodic Orbits. Brain and Cognition, 48, 107–116.
Engbert, R., Scheffczyk, C., Krampe, R. T., Rosenblum, M., Kurths, J., & Kliegl, R. (1997) Tempo-induced transitions in polyrhythmic hand movements. Physical Review E, 56, 5823–5833. DOI.
Ermentrout, G., & Rinzel, J. (1996) Reflected Waves in an Inhomogeneous Excitable Medium. SIAM Journal on Applied Mathematics, 56(4), 1107–1128. DOI.
Feldman, D. P., & Crutchfield, J. P.(2004) Synchronizing to Periodicity: the Transient Information and Synchronization Time of Periodic Sequences. Advances in Complex Systems, 7(3), 329–355. DOI.
Fischer, I., Vicente, R., Buldú, J. M., Peil, M., Mirasso, C. R., Torrent, M. C., & García-Ojalvo, J. (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, M. I., & Wentzell, A. D.(1993) Diffusion Processes on Graphs and the Averaging Principle. The Annals of Probability, 21(4), 2215–2245. DOI.
Freidlin, M., & Weber, M. (1998) Random perturbations of nonlinear oscillators. The Annals of Probability, 26(3), 925–967. DOI.
Freidlin, M., & Weber, M. (1999) A remark on random perturbations of the nonlinear pendulum. The Annals of Applied Probability, 9(3), 611–628. DOI.
Glass, L. (1991) Cardiac arrhythmias and circle maps−A classical problem. Chaos: An Interdisciplinary Journal of Nonlinear Science, 1(1), 13–19. DOI.
Glass, L. (2001) Synchronization and rhythmic processes in physiology. Nature, 410(6825), 277–284. DOI.
Glazier, J. A., & Libchaber, A. (1988) Quasi-periodicity and dynamical systems: An experimentalist’s view. IEEE Transactions on Circuits and Systems, 35(7), 790–809. DOI.
Guevara, M. R., & Glass, L. (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. DOI.
Haken, H., Kelso, J. A. S., & Bunz. (1985) A theoretical model of phase transitions in human hand movements. Biological Cybernetics, 51(5), 347–356. DOI.
Harrison, M. T., Amarasingham, A., & Kass, R. E.(2013) Statistical Identification of Synchronous Spiking. In P. M. DiLorenzo & J. D. Victor (Eds.), Spike Timing: Mechanisms and Function. CRC Press
Hennig, H., Fleischmann, R., Fredebohm, A., Hagmayer, Y., Nagler, J., Witt, A., … Geisel, T. (2011) The Nature and Perception of Fluctuations in Human Musical Rhythms. PLoS ONE, 6(10), 26457. DOI.
Hennig, H., Fleischmann, R., & Geisel, T. (2012) Musical rhythms: The science of being slightly off. Physics Today, 65(7), 64–65. DOI.
Hockman, J. (2014) An ethnographic and technological study of breakbeats in hardcore, jungle and drum & bass. . McGill University
Ichinomiya, T. (2004) Frequency synchronization in a random oscillator network. Physical Review E, 70(2), 26116. DOI.
James, R. G., Mahoney, J. R., Ellison, C. J., & Crutchfield, J. P.(2010) Many Roads to Synchrony: Natural Time Scales and Their Algorithms. Arxiv.
Keener, J. P., & Glass, L. (1984) Global bifurcations of a periodically forced nonlinear oscillator. Journal of Mathematical Biology, 21(2), 175–190. DOI.
Keith, W. L., & Rand, R. H.(1984) 1∶1 and 2∶1 phase entrainment in a system of two coupled limit cycle oscillators. Journal of Mathematical Biology, 20(2), 133–152. DOI.
Lambert, A. (2012) A Stigmergic Model for Oscillator Synchronisation and its Application in Music Systems. (Vol. 18, pp. 247–252). Presented at the ICMC2012
Larsson, M. (2013) Self-generated sounds of locomotion and ventilation and the evolution of human rhythmic abilities. Animal Cognition, 17(1), 1–14. DOI.
Li, C., Chen, L., & Aihara, K. (2007) Stochastic synchronization of genetic oscillator networks. BMC Systems Biology, 1(1), 6. DOI.
McClintock, M. K.(1984) Estrous synchrony: Modulation of ovarian cycle length by female pheromones. Physiology & Behavior, 32(5), 701–705. DOI.
Mirollo, R., & Strogatz, S. (1990) Synchronization of Pulse-Coupled Biological Oscillators. SIAM Journal on Applied Mathematics, 50(6), 1645–1662. DOI.
Mirollo, R., & Strogatz, S. H.(2007) The Spectrum of the Partially Locked State for the Kuramoto Model. Journal of Nonlinear Science, 17(4), 309–347. DOI.
Moreno, Y., & Pacheco, A. F.(2004) Synchronization of Kuramoto oscillators in scale-free networks. EPL (Europhysics Letters), 68(4), 603. DOI.
Paluš, M., Komárek, V., Hrnčí vr, Z. vek, & vSt verbová, K. (2001) Synchronization as adjustment of information rates: Detection from bivariate time series. Phys. Rev. E, 63(4), 46211. DOI.
Perkel, D. H., Schulman, J. H., Bullock, T. H., Moore, G. P., & Segundo, J. P.(1964) Pacemaker Neurons: Effects of Regularly Spaced Synaptic Input. Science, 145(3627), 61–63. DOI.
Pikovsky, A., & Rosenblum, M. (2007) Synchronization. Scholarpedia, 2(12), 1459. DOI.
Pikovsky, A., Rosenblum, M., & Kurths, J. (2003) Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge Nonlinear Science Series). . Cambridge University Press
Robertson, A. N.(2011) A Bayesian approach to drum tracking.
Robertson, A. N., & Plumbley, M. D.(2006) Real-time Interactive Musical Systems: An Overview. Proc. of the Digital Music Research Network, Goldsmiths University, London, 65–68.
Robertson, A., & Plumbley, M. (2007) B-Keeper: A Beat-tracker for Live Performance. In Proceedings of the 7th International Conference on New Interfaces for Musical Expression (pp. 234–237). New York, NY, USA: ACM DOI.
Robertson, A., & Plumbley, M. D.(2013) Synchronizing Sequencing Software to a Live Drummer. Computer Music Journal, 37(2), 46–60. DOI.
Robertson, A., Stark, A., & Davies, M. E.(n.d.) Percussive Beat tracking using real-time median filtering.
Robertson, A., Stark, A. M., & Plumbley, M. D.(n.d.) Real-Time Visual Beat Tracking Using a Comb Filter Matrix.
Schöner, G. (2002) Timing, Clocks, and Dynamical Systems. Brain and Cognition, 48(1), 31–51. DOI.
Strogatz, S. H.(2000) From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Physica D: Nonlinear Phenomena, 143, 1–20. DOI.
Strogatz, S. H.(2004) Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life. . Hyperion
Temperley, D. (2000) Meter and Grouping in African Music: A View from Music Theory. Ethnomusicology, 44(1), 65–96. DOI.
Toussaint, G. (2005a) Mathematical Features for Recognizing Preference in Sub-saharan African Traditional Rhythm Timelines. In S. Singh, M. Singh, C. Apte, & P. Perner (Eds.), Pattern Recognition and Data Mining (Vol. 3686, pp. 18–27). Berlin, Heidelberg: Springer Berlin Heidelberg
Toussaint, G. T.(2004) A Comparison of Rhythmic Similarity Measures. In ISMIR.
Toussaint, G. T.(2005b) The Euclidean algorithm generates traditional musical rhythms. In Proceedings of BRIDGES: Mathematical Connections in Art, Music and Science (pp. 47–56).
Toussaint, G. T.(2010) Generating “good” musical rhythms algorithmically. In Proceedings of the 8th International Conference on Arts and Humanities, Honolulu, Hawaii (pp. 774–791).
Toussaint, G. T.(2011) The rhythm that conquered the world: What makes a “good” rhythm good?. Percussive Notes, 2, 52.
Toussaint, G. T.(2013) The Geometry of Musical Rhythm: What Makes a “Good” Rhythm Good?. (1 edition.). Boca Raton, FL: Chapman and Hall/CRC
Wilmer, A., de Lussanet, M., & Lappe, M. (2012) Time-Delayed Mutual Information of the Phase as a Measure of Functional Connectivity. PLoS ONE, 7(9), 44633. DOI.
Yang, X.-S. (2010) Firefly Algorithms for Multimodal Optimization. arXiv:1003.1466 [Math].