Why pray, is the number nine the most perfect? Because it is the square of the first odd number, and unevenly odd since it is divided into three triads, of which again each is divided into three units.
But not only the virtue of numbers but a natural way of counting he showed, as in the catalogue of ships he made (I. ii. 509):—
With these came fifty ships; and in each
Were sixscore youths, Boeotia's noblest flow'r.
And again (I. xvi. 170):—
They were fifty men.
Whence it is possible to compute that as all the ships were near 1200, and each had 100 men, the whole number is 12 myriads—120,000.
Again speaking. of the Trojans (I. viii. 563):—
A thousand fires burnt brightly; and round each
Sat fifty warriors in the ruddy glare.
He enables one to compute that without counting allies they were 50,000 men.
Now music being closest to the soul, since it is a harmony produced by different elements, by melodies, and by rhythms, intensifies what is relaxed and relaxes the intense. The Pythagoreans have clearly proved this, and before them Homer. For he gives praise to music, in the case of the Sirens, to which he adds the following (O. xii. 188)