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Music and fractals

What is a fractal?

Loosely speaking, a fractal pattern is distinctly recognizable no matter how much you zoom in or out, a property known as self-similarity. For example, if you show a pattern to a person looking through a microscope and to an astronaut looking down from orbit with a telescope, and they describe the same thing, then that pattern is self-similar. Fractal patterns show up both in mathematics and nature, from the intricate contours of the Mandelbrot set to the mesmerizing florets of the broccoli-like vegetable romanesco. Scientists recently noticed that when people make musical rhythms, the resultant pattern of sound has a fractal nature.

Some physicists have found fractals in the drum pattern for the ’80s recording “I Keep Forgettin'” by Michael McDonald. The drums were laid down by Jeff Porcaro.

The study isolated and studied Porcaro’s use of the hi-hat, paying close attention to note values and dynamics.

Science News said:

Both the intervals between sixteenth notes and their volumes wavered throughout the piece. Moreover, those variations were similar on time scales ranging from a few seconds to the length of the entire song (3 minutes and 39 seconds), showing that the pattern formed fractals, the researchers reported on 3 June in PLOS ONE. “It seems that the timekeeper in the brain not only produces fractal timing,” Hennig says, “but likely also fractal intensity or, in this case, loudness.”

The loudness and spacing of the hi-hats were independent of each other, suggesting Porcaro was controlling them separately.

I’m pretty sure one would be able to identify fractals in many pieces of music, whether they were created consciously or not. In any case, check out the full article here.

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