Book 14
7
Thus these thinkers are like the ancient Homeric scholars, who see minor similarities but overlook important ones.
7
Some say that there are many correspondences of this kind; e.g., the middle notesi.e., the μέση(fourth) and παραμέση(fifth), whose ratios can be expressed as 8 : 6, 9 : 6. of the octave are respectively 8 and 9, and the epic hexameter has seventeen syllables, which equals the sum of these two; and the line scans in the first half with nine syllables, and in the second with eight.i.e., a dactylic hexameter whose sixth foot is always a spondee or trochee has nine syllables in the first three feet and eight in the last three. For τὸ δεξιόν meaning the first part of a metrical system see Bassett,Journal of Classical Philology 11.458-460.
8
And they point out that the interval from α to ω in the alphabet is equal to that from the lowest note of a flute to the highest, whose number is equal to that of the whole system of the universe.Alexander suggests that the number 24 may have been made up of the 12 signs of the zodiac, the 8 spheres (fixed stars, five planets, sun and moon) and 4 elements. We must realize that no one would find any difficulty either in discovering or in stating such correspondences as these in the realm of eternal things, since they occur even among perishable things.
9
As for the celebrated characteristics of number, and their contraries, and in general the mathematical properties, in the sense that some describe them and make them out to be causes of the natural world, it would seem that if we examine them along these lines, they disappear; for not one of them is a cause in any of the senses which we distinguished with until respect to the first Principles.Cf. Aristot. Met. 1.3.1, Aristot. Met. 5.1, 2.
