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Have you ever wondered why music generated by computers and drum machines sometimes sounds unnatural? One reason is the absence of small imperfections that are part of every human activity. Whatever your favorite music recording may be, rhythmic deviations accompany every single beat. The offsets are typically small, perhaps 10–20 ms. That’s less than the time it takes for a dragonfly to flap its wings, but you can tell the difference in the music.
Audio engineers have known about the phenomenon for a long time. They will even add slight random deviations to a computer-generated musical piece to give it a more human feel, a procedure sometimes called humanizing. But the precise nature of the deviations made by humans playing complex rhythms has only recently been explored. Are the variations completely random from one beat to another, or are they correlated in a way that can be expressed by a mathematical law? To seek an answer, we turned to time series analysis, a technique widely used in chaos theory.
