The Timaeus of Plato

c] TIMAIO2. 301
sometimes having no harmony in their movements owing to the
irregularity of the vibrations they produce in us, sometimes
being harmonious through regularity. For the slower sounds
overtake the motions of the first and swifter sounds, when
these are already beginning to die away and have become
assimilated to the motions which the slower on their arrival
impart to them : and on overtaking them they do not produce
discord by the intrusion of an alien movement, but adding the
commencement of a slower motion, which corresponds to that
of the swifter now that the latter is
beginning to cease, they
form one harmonious sensation by the blending of shrill and
deep. Thereby they afford pleasure to the foolish, but to the
wise joy, through the imitation of the divine harmony which is
given by mortal motions. And the flowing of all waters, the
fall of thunderbolts, and the wonderful attracting power of
are so nearly of the same pitch that the
lower reaches the ear before the higher
has had time to slacken at all. It is evident
from Plato's language that he conceived
the acuter sound both to travel
more swiftly through the air and to have
more rapid vibrations: he thus comes
very near the correct explanation of pitch,
but falls into the not unnatural error of
supposing that the more rapid vibration
causes a swifter progress through the air.
His theory of consonance is entirely unsatisfactory:
apart from any other objection,
the process he describes could only
produce unison, not concord. For he
cannot mean merely that the swifter vibrations
slackened clown so as to produce
a due numerical ratio to the slower, since
such a numerical ratio might have as well
existed at first. It is strange that Plato,
with his fondness for dt>a\oyia, should not
have based harmony of accords upon this.
It will be observed that the principle of
irfpiwffis is in no way concerned with the
present hypothesis.
9. i]8ovi]v (i^v rots apo