# Rhythm

Especially for generative music

November 3, 2014 — October 23, 2019

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, and 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
- much of this overlaps with the mathematical a neural foundations of synchrony

## 1 Making rhythms

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.

## 2 Neurological basis of rhythm

See Synchronisation.

## 3 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:

Blackdown on Offbeat 8ths and all that jazz

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

## 4 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)
- (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)

## 5 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.

## 6 References

*The Breakbeat Bible: The Fundamentals of Breakbeat Drumming*.

*Proceedings of the Electroacoustic Music Studies Conference, Sforzando*.

*PLOS Computational Biology*.

*Time in Indian Music: Rhythm, Metre, and Form in North Indian Rag Performance*. Oxford Monographs on Music.

*Proceedings of Cybersonica*.

*Journal of New Music Research*.

*CCCG*.

*Computational Geometry*.

*Proceedings of the National Academy of Sciences*.

*IEEE International Conference on Acoustics, Speech and Signal Processing, 2008. ICASSP 2008*.

*Proceedings of the Seventh ACM International Conference on Multimedia (Part 1)*. MULTIMEDIA ’99.

*Chaos: An Interdisciplinary Journal of Nonlinear Science*.

*Nature*.

*Journal of Mathematical Biology*.

*Biological Cybernetics*.

*PLoS ONE*.

*Physics Today*.

*IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA 2019)*.

*Music Perception: An Interdisciplinary Journal*.

*Scholarpedia*.

*Synchronization: A Universal Concept in Nonlinear Sciences*.

*Proc. Of the Digital Music Research Network, Goldsmiths University, London*.

*Proceedings of the 7th International Conference on New Interfaces for Musical Expression*. NIME ’07.

*Computer Music Journal*.

*Proceedings of European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases*.

*Proceedings of the International Computer Music Conference 2011*.

*Ethnomusicology*.

*ISMIR*.

*Pattern Recognition and Data Mining*.

*Proceedings of BRIDGES: Mathematical Connections in Art, Music and Science*.

*Proceedings of the 8th International Conference on Arts and Humanities, Honolulu, Hawaii*.

*Percussive Notes*.

*The Geometry of Musical Rhythm: What Makes a “Good” Rhythm Good?*