Pythagoras

Further, he observed that if you take two strings in the same degree of tension, and then divide one of them exactly in half, when they are plucked the pitch of the shorter string is exactly one octave higher than the longer: 
Again, number (in this case "amount of space") seemed to govern musical tone. Or does musical tone govern number?


Thus the musical notation of the Greeks, which we have inherited can be expressed mathematically as 1:2:3:4

(Another consonance which the Greeks recognized was the octave plus a fifth, where 9:18 = 1:2, an octave, and 18:27 = 2:3, a fifth;)

