Synchronisation and rhythm

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

• Archimedean rhythms. Toussaint has all his papers online](http://cgm.cs.mcgill.ca/~godfried/rhythm-and-mathematics.html) and there are some good ones in there, not to mention his videolectures. And since it’s devastatingly simple, there are many implementations:

  • Wouter Hisschemöller (java source https://github.com/WouterHisschemoller/Euclidean-Pattern-Generator)
  • reason
  • M4L by phil archer
  • M4L by beniii

• Blackdown on Offbeat 8ths and all that jazz

• Quasiperiodic Oscillation

• Kolmogorov-Arnold-Moser theory

• Weird connection, to my mind: Terry Tao, The Poisson-Dirichlet process, and large prime factors of a random number.

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?

• The “Amen Break”: The Most Famous 6-Second Drum Loop & How It Spawned a Sampling Revolution
• The-breaks is a collaborative archive of who-sampled-whom, which is not always breakbeat cuts, but often enough dammit.
• (Adamo 2010)
• (N. Collins 2002)
• (Hockman 2014)
• cute parameterised breakbeats: Amen Pi
• minimal example breakbeat cut code for supercollider (not the famous BBcut2 by Nick Collins, but simpler)

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.

References