Modeling synchronization in human musical rhythms using Impulse Pattern Formulation (IPF)

When musicians perform in an ensemble, synchronizing to a mutual pace is the foundation of their musical interaction. Clock generators, e.g., metronomes, or drum machines, might assist such synchronization, but these means, in general, will also distort this natural, self-organized, inter-human synchronization process. In this work, the synchronization of musicians to an external rhythm is modeled using the Impulse Pattern Formulation (IPF), an analytical modeling approach for synergetic systems motivated by research on musical instruments. Nonlinear coupling of system components is described as the interaction of individually propagating and exponentially damped impulse trains. The derived model is systematically examined by analyzing its behavior when coupled to numerical designed and carefully controlled rhythmical beat sequences. The results are evaluated by comparison in the light of other publications on tapping. Finally, the IPF model can be applied to analyze the personal rhythmical signature of specific musicians or to replace drum machines and click tracks with more musical and creative solutions.

[1]  R. Parncutt.  A Perceptual Model of Pulse Salience and Metrical Accent in Musical Rhythms , 1994 .

[2]  Rolf Bader,et al.  Nonlinearities and Synchronization in Musical Acoustics and Music Psychology , 2013 .

[3]  Alan Edelman,et al.  Julia: A Fresh Approach to Numerical Computing , 2014, SIAM Rev..

[4]  L. V. Noorden,et al.  Resonance in the Perception of Musical Pulse , 1999 .

[5]  J. Argyris,et al.  An Exploration of Dynamical Systems and Chaos: Completely Revised and Enlarged Second Edition , 2015 .

[6]  R. Church,et al.  Preferred rates of repetitive tapping and categorical time production , 1994, Perception & psychophysics.

[7]  Theo Geisel,et al.  The Nature and Perception of Fluctuations in Human Musical Rhythms , 2011, PloS one.

[8]  Viktor Müller,et al.  Intra- and Inter-Brain Synchronization during Musical Improvisation on the Guitar , 2013, PloS one.

[9]  Peter E. Keller,et al.  Adaptation to tempo changes in sensorimotor synchronization: Effects of intention, attention, and awareness , 2004, The Quarterly journal of experimental psychology. A, Human experimental psychology.

[10]  D. Gilden.  Cognitive emissions of 1/f noise. , 2001, Psychological review.

[11]  Holger Hennig,et al.  Synchronization in human musical rhythms and mutually interacting complex systems , 2014, Proceedings of the National Academy of Sciences.

[12]  B H Repp,et al.  Processes underlying adaptation to tempo changes in sensorimotor synchronization. , 2001, Human movement science.

[13]  B. Repp.  Sensorimotor synchronization: A review of the tapping literature , 2005, Psychonomic bulletin & review.

[14]  E. Schöll,et al.  Noisy Dynamical Systems with Time Delay: Some Basic Analytical Perturbation Schemes with Applications , 2016 .

[15]  G. V. van Orden,et al.  Self-organization of cognitive performance. , 2003, Journal of experimental psychology. General.

[16]  Norimasa Yamada,et al.  Nature of variability in rhythmical movement , 1995 .

[17]  H. Haken,et al.  A theoretical model of phase transitions in human hand movements , 2004, Biological Cybernetics.

[18]  John A. Michon,et al.  Timing in temporal tracking , 1967 .

[19]  S. Schwerman,et al.  The Physics of Musical Instruments , 1991 .

[20]  Theo Geisel,et al.  Musical rhythms: The science of being slightly off , 2012 .

[21]  T. Geisel,et al.  Correlated microtiming deviations in jazz and rock music , 2017, PloS one.

[22]  W. Kinzel,et al.  On the Interplay of Noise and Delay in Coupled Oscillators , 2016 .

[23]  B. Repp.  Diversity and commonality in music performance: an analysis of timing microstructure in Schumann's "Träumerei". , 1992, The Journal of the Acoustical Society of America.

[24]  Robert Mores,et al.  The impulse pattern formulation (IPF) as a model of musical instruments-Investigation of stability and limits. , 2019, Chaos.

[25]  S Handel,et al.  The meter of syncopated auditory polyrhythms , 1981, Perception & psychophysics.

[26]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[27]  Viola Priesemann,et al.  Microtiming Deviations and Swing Feel in Jazz , 2019, Scientific Reports.

[28]  A. Kristofferson,et al.  Response delays and the timing of discrete motor responses , 1973 .

[29]  Michael J. Richardson,et al.  Complexity matching effects in bimanual and interpersonal syncopated finger tapping , 2016, Neuroscience Letters.

[30]  Michael H. Thaut,et al.  Multiple synchronization strategies in rhythmic sensorimotor tasks: phase vs period correction , 1998, Biological Cybernetics.

[31]  Karsten Ahnert,et al.  Synchronization of sound sources. , 2009, Physical review letters.

[32]  Andreas Daffertshofer,et al.  A model for phase transitions in human hand movements during multifrequency tapping , 1996 .

[33]  L. H. Shaffer,et al.  Performances of Chopin, Bach, and Bartok: Studies in motor programming , 1984, Cognitive Psychology.

[34]  R. Mores,et al.  Influence of the supporting table on initial transients of the fretted zither: An impulse pattern formulation model , 2021, 180th Meeting of the Acoustical Society of America.