It was Pythagoras who discovered that the 5th and the octave of a note could be produced on the same string by stopping at 2â„3 and ½ of its length respectively. Harmony therefore depends on a numerical proportion. It was this discovery, according to Hankel, which led Pythagoras to his philosophy of number. It is probable at least that the name proportion was due to it, sinceIamblichus says that this proportion was called originally and that Archytas and Hippasus first called it . Nicomachus gives another reason for the name, viz. that a cube being of 3 equal dimensions, was the pattern : and having 12 edges, 8 corners, 6 faces, it gave its name to harmonic proportion, since:
James Gow (scholar)