Having already shown that Plato neither for want
of skill nor for ignorance blamed all the other moods and
casts of composition, we now proceed to show that he
really was skilled in harmony. For in his discourse concerning the procreation of the soul, inserted into Timaeus,
he has made known his great knowledge in all the sciences,
and of music among the rest, in this manner: ‘After
this,’ saith he, ‘he filled up the double and treble intervals,
taking parts from thence, and adding them to the midst
between them, so that there were in every interval two middle terms.’
1 This proem was the effect of his experience
in music, as we shall presently make out. The means
from whence every mean is taken are three, arithmetical,
enharmonical, geometrical. Of these the first exceeds and
is exceeded in number, the second in proportion, the third
neither in number nor proportion. Plato therefore, desirous
to show the harmony of the four elements in the soul, and
harmonically also to explain the reason of that mutual concord arising from discording and jarring principles, undertakes to make out two middle terms of the soul in every
interval, according to harmonical proportion. Thus in a
musical octave there happen to be two middle distances,
whose proportion we shall explain. As for the octaves,
they keep a double proportion between their two extremes.
For example, let the double arithmetical proportion be 6
and 12, this being the interval between the ὑπάτη μέσων and
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the νήτη διεζευγμένων; 6 therefore and 12 being the two
extremes, the former note contains the number 6, and the
latter 12. To these are to be added the intermediate
numbers, to which the extremes must hold the proportion,
the one of one and a third, and the other of one and a
half. These are the numbers 8 and 9. For as 8 contains
one and a third of 6, so 9 contains one and a half of 6;
thus you have one extreme. The other is 12, containing 9
and a third part of 9, and 8 and half 8. These then being
the numbers between 6 and 12, and the interval of the
octave consisting of a diatessaron and diapente, it is plain
that the number 8 belongs to mese, and the number 9 to
paramese; which being so, it follows that hypate is to
mese as paramese to nete of the disjunct tetrachords; for it
is a fourth from the first term to the second of this proportion, and the same interval from the third term to the
fourth. The same proportion will be also found in the numbers. For as 6 is to 8, so is 8 to 12; and as 6 is to 9, so
is 8 to 12. For 8 is one and a third part of 6, and 12 of
9; while 9 is one and a half part of 6, and 12 of 8. What
has been said may suffice to show how great was Plato's
zeal and learning in the liberal sciences.
1 Plato, Timaeus, p. 36 A. See the whole passage in the treatise Of the Procreation of the Soul as discoursed in Timaeus, Chap. XXIX. (G.)
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