|
|
|
|
|
|
|
extended beyond music to general cosmology. The health of the body or of the soul could be explained as dependent on proper 'attunement', on harmonic relationships ultimately reducible to numbers. The whole cosmos, the planetary and stellar spheres with their orderly revolutions, could be seen as a vast musical instrument with each component attuned according to the same scheme of ratios as obtains in our mortal music. Plato's harmony of the spheres is not some unimaginable, transcendental passacaglia or fugue, but the naked glory of the diatonic octave. |
|
|
|
|
|
|
|
|
Pythagorean theory was regularly projected back onto Pythagoras himself, and from the fourth century BC he is credited with having personally discovered the numerical basis of the concords. He is alleged to have heard them in hammer-blows coming from a smithy, and on investigation to have found that the weights of the hammers stood in the ratios 4:3, 3:2, and 2:1. He is then supposed to have reproduced the concords by putting equal strings under tension from a similarly graded set of weights. It has been pointed out ever since the seventeenth century that neither part of the story is in accord with the laws of physics.37 |
|
|
|
|
|
|
|
|
A more plausible account has the early Pythagorean Hippasus of Metapontum discovering or demonstrating the concords with bronze discs of equal diameter but different thicknesses: these really would give the required results. We may guess that Hippasus experimented with them not as a result of a brainwave coming out of the blue, but on the basis of knowledge built up by South Italian jingle-makers; for in that part of the world there was a tradition, going back to the eighth century, of metal tube and disc chimes.38 Hippasus' contemporary Lasus of Hermione, whom we have met earlier as a musicologist, is also mentioned as having studied the concord ratios, this time by striking vessels partly filled with liquid. This is again a scientifically dubious procedure, but there must have been some ground for naming Lasus in such a context. He is never called a Pythagorean. Perhaps he said something about harmonic ratios in his book.39 |
|
|
|
 |
|
|
|
|
37 Burkert, LS 375-7. |
|
|
|
|
|
|
|
|
38 See p. 126. One of the early Pythagorean dicta was that the sound made by striking bronze is the voice of a daimon residing in the metal (Arist. fr. 196; we are reminded of the Sirens' connection with musical notes, above, p. 224). Glaucus of Rhegium, c. 400 BC, cultivated the playing of tuned discs as an art, which seems to have been personal to him: Aristox. fr. 90; Burkert, LS 377. |
|
|
|
|
|
|
|
|
39 Theon Smyrn. p. 59.7ff. (corrupt text); see Burkert, LS 377f. |
|
|
|
|
|