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[1093a] [1]

If all things must share in number, it must follow that many things are the same; i.e., that the same number belongs both to this thing and to something else. Is number, then, a cause; i.e., is it because of number that the object exists? Or is this not conclusive? E.g., there is a certain number of the sun's motions, and again of the moon's,1 and indeed of the life and maturity of every animate thing. What reason, then, is there why some of these numbers should not be squares and others cubes, some equal and others double?There is no reason; all things must fall within this range of numbers if, as was assumed, all things share in number, and different things may fall under the same number. Hence if certain things happened to have the same number, on the Pythagorean view they would be the same as one another, because they would have the same form of number; e.g., sun and moon would be the same.2 But why are these numbers causes? There are seven vowels,3 seven strings to the scale,4 seven Pleiads; most animals (though not all5) lose their teeth in the seventh year; and there were seven heroes who attacked Thebes. Is it, then, because the number 7 is such as it is that there were seven heroes, or that the Pleiads consist of seven stars? Surely there were seven heroes because of the seven gates, or for some other reason, and the Pleiads are seven because we count them so; just as we count the Bear as 12, whereas others count more stars in both. [20] Indeed, they assert also that Ξ, Ψ and Ζ are concords,6 and that because there are three concords, there are three double consonants. They ignore the fact that there might be thousands of double consonants—because there might be one symbol for ΓΡ. But if they say that each of these letters is double any of the others, whereas no other is,7 and that the reason is that there are three regions8 of the mouth, and that one consonant is combined with ς in each region, it is for this reason that there are only three double consonants, and not because there are three concords—because there are really more than three; but there cannot be more than three double consonants.

Thus these thinkers are like the ancient Homeric scholars, who see minor similarities but overlook important ones.

Some say that there are many correspondences of this kind; e.g., the middle notes9 of the octave are respectively 8 and 9, and the epic hexameter has seventeen syllables, which equals the sum of these two;

1 5 in each case, according to Aristotle; cf. Aristot. Met. 12.7.9, 11.

2 Cf. previous note.

3 In the Greek alphabet.

4 In the old heptachord; cf. note on Aristot. Met. 5.11.4.

5 Cf. Aristot. Hist. An. 576a 6.

6 According to Alexander ζ was connected with the fourth, ξ with the fifth, and ψ with the octave.

7 θ, φ, and χ are aspirated, not double, consonants.

8 Palate, lips, and teeth.

9 i.e., the μέση(fourth) and παραμέση(fifth), whose ratios can be expressed as 8 : 6, 9 : 6.

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