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

To mention:

- correlograms
- periodograms
- “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 from them

## Making rhythms

- rhythms
- recurrent neural networks like http://arxiv.org/abs/1308.0850
- Renewal processes
- 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
- http://www.scholarpedia.org/article/Synchronization
- http://www.scholarpedia.org/article/Pulse_coupled_oscillators
- nice brownian calc treatment: http://www.math.uiuc.edu/~rdeville/research/nk.pdf 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.”

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

- Toussaint has all his clever-clogs papers online and there are some good ones in there, not to mention his video lectures. And since it’s devastatingly simple, there are many implementations:
- Blackdown on Offbeat 8ths and all that jazz
- Quasiperiodic Oscillation
- Kolmogorov-Arnold-Moser theory
- 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?

Nick Collins has done a whole lot of work here.

- 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, M. (2010). The Breakbeat Bible: The Fundamentals of Breakbeat Drumming (Pap/Com edition.). S.l.: Hudson Music.
- Collins, N. (2002). Interactive Evolution of Breakbeat Cut Sequences. In Proceedings of Cybersonica. London.
- Hockman, J. (2014). An ethnographic and technological study of breakbeats in hardcore, jungle and drum & bass. McGill University.
- cute parameterised breakbeats: Amen Pi
- minimal example breakbeat cut code for supercollider (not BBcut2 by nick collins, just something super simple)

## 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.

- How about self-similar models that include
*scaling*, as seen in financial and general fractal time series, instead of the pure translation ones that I see in music?

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