310
PLATO
(/3) Music.
In music Plato had the advantage of the researches of
Archytas and the Pythagorean school into the numerical
relations of tones. In the Timaeus we find an elaborate
filling up of intervals by the interposition of arithmetic and
harmonic means 1 ; Plato is also clear that higher and lower
pitch are due to the more or less rapid motion of the air. 2
In like manner the different notes in the ‘ harmony of the
spheres poetically turned into Sirens sitting on each of the
eight whorls of the Spindle and each uttering a single sound,
a single musical note, correspond to the different speeds of
the eight circles, that of the fixed stars and those of the sun,
the moon, and the five planets respectively. 3
(y) Astronomy.
This brings us to Plato’s astronomy. His views are stated
in their most complete and final form in the Timaeus, though
account has to be taken of other dialogues, the Phaedo, the
Republic,, and the Laws. He based himself upon the early
Pythagorean system (that of Pythagoras, as distinct from
that of his successors, who were the first to abandon the
geocentric system and made the earth, with the sun, the
moon and the other planets, revolve in circles about the ‘ cen
tral fire ’) ; while of course he would take account of the
results of the more and more exact observations made up
to his own time. According to Plato, the universe has the
most perfect of all shapes, that of a sphere. In the centre
of this sphere rests the earth, immovable and kept there by
the equilibrium of symmetry as it were (‘ for a thing in
equilibrium in the middle of any uniform substance will not
have cause to incline more or less in any direction ’ 4 ). The
axis of the sphere of the universe passes through the centre of
the earth, which is also spherical, and the sphere revolves
uniformly about the axis in the direction from east to west.
The fixed stars are therefore carried round in small circles
of the sphere. The sun, the moon and the five planets are
also carried round in the motion of the outer sphere, but they
have independent circular movements of their own in addition.
1 Timaeus, 35 c-36 B. 2 lb. 67 b.
3 Republic, 617 E. 4 Phaedo, 109 A,