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
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
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.
Neurological basis of rhythm
See Synchronisation.
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.
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
BBcut2by 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
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.
Cannon, Jonathan. 2021. “Expectancy-Based Rhythmic Entrainment as Continuous Bayesian Inference.” PLOS Computational Biology 17 (6): e1009025.
Clayton, Martin. 2001. Time in Indian Music: Rhythm, Metre, and Form in North Indian Rag Performance. Oxford Monographs on Music. Oxford University Press, USA.
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.
Demaine, Erik D., Francisco Gomez-Martin, Henk Meijer, David Rappaport, Perouz Taslakian, Godfried T. Toussaint, Terry Winograd, and David R. Wood. 2005. “The Distance Geometry of Deep Rhythms and Scales.” In CCCG, 163–66.
———. 2009. “The Distance Geometry of Music.” In Computational Geometry, 42:429–54.
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): E6233–42.
Ellis, D.P.W., C.V. Cotton, and M.I. Mandel. 2008. “Cross-Correlation of Beat-Synchronous Representations for Music Similarity.” In IEEE International Conference on Acoustics, Speech and Signal Processing, 2008. ICASSP 2008, 57–60.
Foote, Jonathan. 1999. “Visualizing Music and Audio Using Self-Similarity.” In Proceedings of the Seventh ACM International Conference on Multimedia (Part 1), 77–80. MULTIMEDIA ’99. New York, NY, USA: ACM.
Glass, Leon. 1991. “Cardiac Arrhythmias and Circle Maps−A Classical Problem.” Chaos: An Interdisciplinary Journal of Nonlinear Science 1 (1): 13–19.
———. 2001. “Synchronization and Rhythmic Processes in Physiology.” Nature 410 (6825): 277–84.
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.
Haken, Hermann, J A Scott Kelso, and Bunz. 1985. “A Theoretical Model of Phase Transitions in Human Hand Movements.” Biological Cybernetics 51 (5): 347–56.
Hennig, Holger, Ragnar Fleischmann, Anneke Fredebohm, York Hagmayer, Jan Nagler, Annette Witt, Fabian J Theis, and Theo Geisel. 2011. “The Nature and Perception of Fluctuations in Human Musical Rhythms.” PLoS ONE 6 (10): –26457.
Hennig, Holger, Ragnar Fleischmann, and Theo Geisel. 2012. “Musical Rhythms: The Science of Being Slightly Off.” Physics Today 65 (7): 64–65.
Hockman, Jason. 2014. “An Ethnographic and Technological Study of Breakbeats in Hardcore, Jungle and Drum & Bass.” PhD Thesis, McGill University Libraries.
Lattner, Stefan, and Maarten Grachten. 2019. “High-Level Control of Drum Track Generation Using Learned Patterns of Rhythmic Interaction.” In IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA 2019).
Parncutt, Richard. 1994. “A Perceptual Model of Pulse Salience and Metrical Accent in Musical Rhythms.” Music Perception: An Interdisciplinary Journal 11 (4): 409–64.
Pikovsky, Arkady, and Michael Rosenblum. 2007. “Synchronization.” Scholarpedia 2 (12): 1459.
Pikovsky, Arkady, Michael Rosenblum, and Jürgen Kurths. 2003. Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge University Press.
Robertson, A. N., and M. D. Plumbley. 2006. “Real-Time Interactive Musical Systems: An Overview.” Proc. Of the Digital Music Research Network, Goldsmiths University, London, 65–68.
Robertson, Andrew N. 2011. “A Bayesian Approach to Drum Tracking.” In.
Robertson, Andrew, and Mark Plumbley. 2007. “B-Keeper: A Beat-Tracker for Live Performance.” In Proceedings of the 7th International Conference on New Interfaces for Musical Expression, 234–37. NIME ’07. New York, NY, USA: ACM.
Robertson, Andrew, and Mark D. Plumbley. 2013. “Synchronizing Sequencing Software to a Live Drummer.” Computer Music Journal 37 (2): 46–60.
Robertson, Andrew, Adam M. Stark, and Mark D. Plumbley. 2011. “Real-Time Visual Beat Tracking Using a Comb Filter Matrix.” In Proceedings of the International Computer Music Conference 2011.
Robertson, Andrew, Adam Stark, and Matthew EP Davies. 2013. “Percussive Beat Tracking Using Real-Time Median Filtering.” In Proceedings of European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases.
Temperley, David. 2000. “Meter and Grouping in African Music: A View from Music Theory.” Ethnomusicology 44 (1): 65–96.
Toussaint, Godfried. 2005. “Mathematical Features for Recognizing Preference in Sub-Saharan African Traditional Rhythm Timelines.” In Pattern Recognition and Data Mining, edited by Sameer Singh, Maneesha Singh, Chid Apte, and Petra Perner, 3686:18–27. Berlin, Heidelberg: Springer Berlin Heidelberg.
Toussaint, Godfried T. 2004. “A Comparison of Rhythmic Similarity Measures.” In ISMIR.
———. 2005. “The Euclidean Algorithm Generates Traditional Musical Rhythms.” In Proceedings of BRIDGES: Mathematical Connections in Art, Music and Science, 47–56.
———. 2010. “Generating ‘Good’ Musical Rhythms Algorithmically.” In Proceedings of the 8th International Conference on Arts and Humanities, Honolulu, Hawaii, 774–91.
———. 2011. “The Rhythm That Conquered the World: What Makes a ‘Good’ Rhythm Good?” Percussive Notes 2: 52.
———. 2013. The Geometry of Musical Rhythm: What Makes a “Good” Rhythm Good? 1 edition. Boca Raton, FL: Chapman and Hall/CRC.
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