Musical theories of Pythagoras, 1492. Men playing musical instruments and making sounds. At top left, an anvil is struck with hammers. Top right: Pythagoras playing the musical scale on bells and on water-glasses. He has made a sort of xylophone using glasses filled with ever smaller amounts of water. Bottom left: Pythagoras' discovery of the dependence of the musical intervals on certain arithemtical ratios of lengths of strings at the same tension. Bottom right: Pythagoras and Philolaus experimenting with musical pipes. Illustration from Theorica musicae (Theory of music) by Franchino Gaffurio.