The Pythagorean discovery that the pitch of a note depends on the length of the string which produces it, and that concordant intervals in the scale are produced by simple numerical ratios (2 : 1 octave, 3 : 2 fifth, 4 : 3 fourth, etc.), was epoch-making: it was the first successful reduction of quality to quantity, the first step towards the mathematization of human experience – and therefore the beginning of Science.
