Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
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Fluctuations in human musical rhythms

The nature and perception of fluctuations in human musical rhythms


handsHave you ever wondered why music generated by computers and rhythm machines sometimes sounds unnatural? One reason for this is the absence of small inaccuracies that are part of every human activity. Professional audio software therefore offers a so-called humanizing technique, by which the regularity of musical rhythms can be randomized to some extent.

But what exactly is the nature of the inaccuracy in human musical rhythms? Studying this question for the first time, we found that the temporal rhythmic fluctuations exhibit scale-free long-range correlations, i.e., a small rhythmic fluctuation at some point in time does not only influence fluctuations shortly thereafter, but even after tens of seconds. While this characterization is relevant for neurophysiological mechanisms of timing, it also leads to a novel concept for humanizing musical sequences. Comparing with conventionally humanized versions listeners showed a high preference for long-range correlated humanized music over uncorrelated humanized music. (Photo: Courtesy of Agbenyega Attiogbe-Redlich,


Reports on this work

Harvard Gazette (cached PDF version)

Physics Today

Spektrum der Wissenschaft (in German)

Press release by the Max Planck Society

Report by Deutschlandfunk (in German)



Online survey

We held an online survey, where participants were able to listen to both exact recordings of music by J.S. Bach and to versions of these songs that were humanized using the different techniques.


Examples of humanized audio samples

The diference between the humanizing approaches can be understood by listening to the following two musical excerpts, which are available below in different humanized versions (1/f humanizing and conventional white noise humanizing):

J.S. Bach, Invention no.1 in C major, BWV 772

Bach Invention1


J.S. Bach, Prelude no. 2 in C minor (Well-tempered Clavier Vol. II, BWV 871)

bach Prelude 2



Audio samples of humanized music can be found in the audio gallery.

Media coverage

Science Editor's Choice, "Perfecting the not quite perfect", 334, 1183 (2011)
Nature Physics news & views, "Perfecting imperfection", 7, 930 (2011)
Nature Research Highlight, "Doctoring the beats", 479, 153 (2011)


Contact:  Holger Hennig 

Members working within this Project:

 Theo Geisel 
 Ragnar Fleischmann 

Former Members:

 Jan Nagler 
 Annette Witt 
 Holger Hennig 

Selected Publications:

H. Hennig, R. Fleischmann, A. Fredebohm, Y. Hagmayer, J. Nagler, A. Witt, F. Theis, and T. Geisel (2011).
The nature and perception of fluctuations in human musical rhythms
PLoS One 6(10):e26457.