Famous “Amen Break”, champion drum loop sampled by everyone, has a long history.
You can catch most of it in this short MixMag documentary released in 2019:
What I want to focus on today is article from 2008 “The Amen Break and the Golden Ratio” by Michael S. Schneider, mathematician.
“Human bodies and created sounds, like flowers, crystals and galaxies, can never exactly equal any ideal mathematical template. But the major wave peaks of the Amen Break, and many of its smaller ones, seem reasonably close to being an expression of the fractal nature of the wonderful Golden Ratio. I wonder what it would sound like if it was more precisely proportioned to the ideal, but I also know that slight differences are what make it human and alive.”
Article has since been refuted, for example by Sean Barrett in 2012 “The Amen Break Does Not Involve The Golden Ratio”.
But I would argue that what Michael Schneider saw in Amen Break drum loop still stands in principle, and can be applied to any musical or rhythmical construction:
“A whole line may be divided in such a way that the length of the whole relates to its large part in the same way that the large part relates to the small part. In other words, the same relationship appears on different scales, comprehending a mathematically balanced whole.”