When the Beat Goes Off
Holger Hennig -- holgerh@physics.harvard.edu
Dept. of Physics
Harvard University
Cambridge, MA 02138
Ragnar Fleischmann -- ragnar.fleischmann@ds.mpg.de
Theo Geisel -- geisel@ds.mpg.de
Max Planck Institute for Dynamics and Self-Organization
Göttingen, Germany
Popular Version of paper 4aMUa1
Presented Thursday morning, October 25, 2012
164th ASA Meeting, Kansas City, Missouri
Note: The following text is adapted from the report “When the beat goes off” by Taylor Beck published in the Harvard Gazette (July 19, 2012), http://news.harvard.edu/gazette/story/2012/07/when-the-beat-goes-off/
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Have 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, where purely random fluctuations (called white noise) are added to the rhythms, by which the regularity of musical rhythms can be randomized to some extent. But what exactly is the nature of these deviations in human musical rhythms?
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Deviations in human drumming. The two plots shown here were obtained as the Ghanaian drummer on the right played a hand drum while listening to regular metronome beats. (a) In this two-second time slice, green lines indicate metronome beats and red lines, determined from the absolute extremum of the audio signal of each beat, indicate the striking of the drum. (b) Over a period of 1030 beats, deviations from regular metronome beats (dn) exhibit long-range correlations. The five deviations from panel a are marked with red squares. They illustrate how the drummer switches from playing ahead of the metronome at beat number 284 to playing almost simultaneously with the metronome at beat number 288."Photo: Courtesy of Agbenyega Attiogbe-Redlich, www.hippocritz-school.com." |
Rhythm pulses inside the brain of a Ghanaian drummer, sitting in a physics laboratory in Göttingen, Germany. His hands caress the skin of a bongo drum, guided by the metronome’s tick through his headphones. He plays for five minutes, filling the sterile lab environment with staccato sounds. Though the drummer is a professional, like all humans, his rhythm is imperfect. Each time his hand hits the drum, his beat falls ahead or behind the metronome typically by 10 to 20 milliseconds. That’s less than the time it takes for a dragonfly to flap its wings, but you can tell the difference in the music. On average, he anticipates the beat, and plays ahead of it, 16 milliseconds ahead. Are these deviations random, or correlated in a way that can be expressed by a mathematical law?
A feature of panel b that immediately catches the eye is the existence of trends in the time series. For example, the deviations corresponding to beats 200–280 average to −29 ms, distinctly greater in magnitude than the mean deviation. For quite some time, the drummer played well ahead of the metronome. In contrast, about half a minute (90 beats) earlier, the drummer tended to play slightly behind the metronome clicks. Clearly, the deviations are not purely random. If a given beat is sounded ahead of the metronome, subsequent beats are also likely to be played early. We studied the play of both professional musicians and laypeople, including pop and rock songs. Analyzing the drummers’ playing statistically, we found that the deviations are correlated across long timescales [1,2]: tens of seconds to minutes. A given beat depended not just on the timing of the previous beat, but also on beats that occurred minutes before: the time series exhibit so-called long-range correlations (LRCs). It is as if the human brain has an enduring memory for those deviations.
The trends in the time series in panel b are correlated: Patterns of fluctuations are likely to be repeated. This property is found for short and long patterns — hence on different timescales. The pattern can be seen as a fractal — a self-similar structure. Fractal patterns are the recurring shapes seen in snowflakes, the leaves of a fern, and even the coastline of Britain. If you zoom into a fractal, you see something that looks similar to the whole thing again. Deviations in human musical rhythms, like snowflakes and coastlines, are fractals.
The discovery that human deviations in musical rhythm follow a pattern could influence how audio engineers "humanize" computer-generated music. We found that rhythm deviations follow this pattern whether the rhythm is played by hand, foot, or vocals - suggesting it is intrinsic to musical sense. Different versions of a pop song were produced: "humanized" using either the usual "random-error" method (which consists of white noise), or a new "long-range-correlated-error" method where the timing of the beats contains LRCs. Most listeners preferred the LRC version to the random-error version, suggesting that people prefer music that deviates from perfection in a natural way: a balance of predictability and surprise. (White noise can be considered pure surprise). Apparently, the memory inherent in LRCs is just right to sustain that balance.
So these deviations in rhythm patterns seem to be intrinsic, and preferred. But how do they relate to the beat of our brains? There are different clocks in the brain, clocks on different timescales, such as circadian clocks on a 24-hour timescale. However, for the millisecond regime it is widely unknown which neuronal network allows the human to be so precise. Long-range correlations discovered here in musical rhythm have also been found in the fluctuation of auditory nerve firing in cats, in human brainwaves, and in heart rate.
To err is human. But isn't that part of the complexity and beauty of human activity? Yes - even more if the human happens to be a really good drummer.
References:
[1] H. Hennig et al, "The nature and perception of human musical rhythms", PLoS ONE 6, e26457 (2011)
[2] H. Hennig, R. Fleischmann, T. Geisel, "The science of being slightly off", Physics Today, 65, 64-65 (2012)
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