Synchronisation and rhythm

Especially for generative music

2014-11-03 – 2019-10-23
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/taxonomise/disambiguate:

  • 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

Making rhythms

  • recurrent neural networks
  • hidden markov models

  • sync oscillator system

    • continuous Kuramoto, possibly on a graph with an interesting topology
    • or Strogatz/Perkel/Haken-style pulse-sync, possibly also on a graph
    • (Pikovsky and Rosenblum 2007)
    • Pulse coupled oscillators (Canavier and Achuthan 2007)
    • Deville’s Brownian calculus treatment suggests N!=4 and nearest neighbour networks
    • left-field idea: work using decaying harmonics through feedback - macroscopic karplus-strong.
    • any of these would be interesting with driving noise and arbitrary topologies. See also MIMO allpass.

Neurological/Psychological basis

Doelling:

“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.

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?

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.

Absil, P.-A, R Mahony, and R Sepulchre. 2008. Optimization Algorithms on Matrix Manifolds. Princeton, N.J.; Woodstock: Princeton University Press. http://public.eblib.com/choice/publicfullrecord.aspx?p=457711.

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. https://doi.org/10.1103/RevModPhys.77.137.

Adamo, Mike. 2010. The Breakbeat Bible: The Fundamentals of Breakbeat Drumming. Pap/Com edition. S.l.: Hudson Music.

Anderson, Christopher, and Arne Eigenfeldt. 2011. “A New Analytical Method for the Musical Study of Electronica.” In Proceedings of the Electroacoustic Music Studies Conference, Sforzando.

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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. https://doi.org/10.1109/CDC.2013.6760038.

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. https://doi.org/10.1093/imaiai/iat006.

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Canavier, Carmen, and Srisairam Achuthan. 2007. “Pulse Coupled Oscillators.” Scholarpedia 2 (4): 1331. https://doi.org/10.4249/scholarpedia.1331.

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———. 2001. Time in Indian Music: Rhythm, Metre, and Form in North Indian Rag Performance. Oxford Monographs on Music. Oxford University Press, USA.

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Collins, Nick. 2002. “Interactive Evolution of Breakbeat Cut Sequences.” In Proceedings of Cybersonica. London.

———. 2006. “BBCut2: Integrating Beat Tracking and on-the-Fly Event Analysis.” Journal of New Music Research 35 (1): 63–70. https://doi.org/10.1080/09298210600696600.

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———. 2009. “The Distance Geometry of Music.” In Computational Geometry, 42:429–54. https://doi.org/10.1016/j.comgeo.2008.04.005.

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–E6242. https://doi.org/10.1073/pnas.1508431112.

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———. 2001. “Synchronization and Rhythmic Processes in Physiology.” Nature 410 (6825): 277–84. https://doi.org/10.1038/35065745.

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. https://doi.org/10.1007/BF02154750.

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Hennig, Holger, Ragnar Fleischmann, and Theo Geisel. 2012. “Musical Rhythms: The Science of Being Slightly Off.” Physics Today 65 (7): 64–65. https://doi.org/10.1063/PT.3.1650.

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———. 2005. “The Euclidean Algorithm Generates Traditional Musical Rhythms.” In Proceedings of BRIDGES: Mathematical Connections in Art, Music and Science, 47–56. http://cgm.cs.mcgill.ca/~godfried/publications/banff.pdf.

———. 2010. “Generating ‘Good’ Musical Rhythms Algorithmically.” In Proceedings of the 8th International Conference on Arts and Humanities, Honolulu, Hawaii, 774–91. http://cgm.cs.mcgill.ca/~godfried/publications/Hawaii-Paper-Rhythm-Generation.pdf.

———. 2011. “The Rhythm That Conquered the World: What Makes a ‘Good’ Rhythm Good?” Percussive Notes 2: 52. http://cgm.cs.mcgill.ca/~godfried/publications/Percussive-Notes-Web.pdf.

———. 2013. The Geometry of Musical Rhythm: What Makes a "Good" Rhythm Good? 1 edition. Boca Raton, FL: Chapman and Hall/CRC.