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,