History
Chinese mathematicians had been aware of the Pythagorean comma as early as 122 BC (its calculation is detailed in the Huainanzi), and circa 50 BC, Ching Fang discovered that if the cycle of perfect fifths were continued beyond 12 all the way to 53, the difference between this 53rd pitch and the starting pitch would be much smaller than the Pythagorean comma. This much smaller interval was later named Mercator's Comma (see: history of 53 equal temperament).
The first to mention the comma's proportion of 531441:524288 was Euclid, who takes as a basis the whole tone of Pythagorean tuning with the ratio of 9:8, the octave with the ratio of 2:1, and a number A = 262144. He concludes that raising this number by six whole tones yields a value G which is larger than that yielded by raising it by an octave (two times A). He gives G to be 531441. The necessary calculations read:
Calculation of G:
Calculation of the double of A:
Read more about this topic: Pythagorean Comma
Famous quotes containing the word history:
“At present cats have more purchasing power and influence than the poor of this planet. Accidents of geography and colonial history should no longer determine who gets the fish.”
—Derek Wall (b. 1965)
“The history of our era is the nauseating and repulsive history of the crucifixion of the procreative body for the glorification of the spirit.”
—D.H. (David Herbert)