William A. Sethares (born April 19, 1955) is an American music theorist and professor of electrical engineering at the University of Wisconsin.
(For instance, Pythagoras made observations relating to this, and the ancient Chinese Guqin contains a dotted scale representing the harmonic series.)
The source of these ratios, in the pattern of vibrations known as the harmonic series, was exposed by Joseph Sauveur the early 18th century and even more clearly by Helmholtz in the 1860s.
Where microtonal music was previously either dissonant (due to being played with harmonic timbres to which it was not "related"), or restricted to the narrow range of harmonically related tunings (to retain sensory consonance), Sethares's mathematical and musical work showed how musicians might explore microtonality without sacrificing sensory consonance.
As one reviewer of the second edition[5] of this book wrote, "Physics had built a prison round music, and Sethares set it free.