Musical rhythms

Perfecting imperfection

When György Ligeti composed Continuum for harpsichord in 1968, he played masterly with the limitations of human sound perception. Humans can only separate 18 or so individual sounds per second; when notes arrive in quicker succession, we perceive them as one continuous sound. The harpsichord can be played at a pace very close to — although not quite at — that limit, but the instrument's mechanics produce additional sounds that tip the sequence over the threshold. The result then is a truly overwhelming listening experience.

Ligeti's creation of 'musical continua' highlights one aspect of human music perception. Holger Hennig and colleagues have explored another, and demonstrate how rhythmic imperfections influence our listening experience (PLoS ONE 6, e26457; 2011).

Hennig et al. asked volunteers, both musicians and non-musicians, to produce rhythmic patterns ranging in complexity, guided by a metronome. They were given various means of sound generation — drumming, singing and tapping with a hand on a drumhead. Those performers who were able to follow the metronome for an extended period of time tended to produce comparable patterns of temporal deviations from the perfect interbeat intervals. Most interestingly, these deviations — typically of the order of ten milliseconds — displayed long-range correlations. Fluctuations at one point of the rhythmic sequence could influence the behaviour several tens of seconds later. (Such long-range correlations were, however, absent when volunteers were not able to stay in time with the metronome.)

Does this tendency to introduce imperfections with long-range correlations also have a bearing on how we perceive music? It's a question that's particularly relevant for computer-generated music. Perfectly timed beats output by a computer do sound artificial, and professional software often sports 'humanizing' features. According to Hennig et al., these tools are based on the addition of white-noise fluctuations — that is, the extent of temporal deviation from the ideal is uncorrelated between successive tones. As an alternative approach, the authors instead introduced correlated 1/f noise. When they played the two versions of humanized electronic music to members of local choirs, on average listeners preferred, to a statistically significant degree, the new 1/f-noise version to its white-noise counterpart.

But listen for yourself: audio samples are available on the authors' website (http://www.nld.ds.mpg.de/humanized_audio), as well as a link to a survey, through which the researchers hope to gather further data on just what musical imperfection should sound like.

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Trabesinger, A. Perfecting imperfection. Nature Phys 7, 930 (2011). https://doi.org/10.1038/nphys2169

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