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phrygian, Hypodorian, Dorian, Phrygian, Lydian, Mixolydian, and the intervals separating them, based on those of aulos-holes, were 3/4 tone, 3/4 tone, tone, 3/4 tone, 3/4 tone.27 There seems to have been general agreement on the sequence Dorian, Phrygian, Lydian, but only partial agreement about others. Several systems apparently lacked a Hypolydian, which, I have suggested, may have been Eratocles' invention. With Hypodorian and Hypophrygian, the principle was that they had conjunct tetrachords where Dorian and Phrygian had disjunct ones.28 |
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Aristoxenus criticizes all these schemes as lacking an overall rationale. What governs the number of the keys and the intervals at which they are arranged? His own system is founded on a set of axioms concerning the structure of scales, axioms held to reflect natural laws of melody. The main ones are: |
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1. All melodic scales are constructed of tetrachords, which are either conjunct or disjunct, and if disjunct separated by a tone. |
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2. The sequence of intervals within tetrachords follows the rules for the genus in question. |
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2. As a general corollary of (1) and (2), every note must either make the concord of a fourth with the fourth note along from it, or the concord of a fifth with the fifth note, or both. There are many particular corollaries, for example that a scale cannot contain more than two successive quarter-tones or semitones; it can have three successive tones only in the diatonic genus; and so on. |
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In working.out his system of keys Aristoxenus was not primarily concerned with the placement of modal scales interpreted as octave species: there are only seven species, but he made thirteen keys. He appears not to have spoken of the species under their Eratoclean modal names at all, but allowed the concept of mode to be sub-merged in that of key. What he was more concerned about was to provide for and account for every kind of modulation. |
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Modulation, he determined, presupposed a note, interval, or tetrachord common to two keys. The most harmonious modulations (and actually the most usual) were those which exploited the one |
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27Harm. 2. 37; see Barker, GMW ii. 154 n. 33. This last system (apparently alluded to also by Heraclid. Pont. fr. 163 ap. Ath. 625a) implies aulos scales in which the diatonic tetrachord had the form 3/4 + 3/4 + 1 tone; cf. pp. 97-100. The Mixolydian species is here B  d e  g a b, the Lydian  , the Phrygian d-d', and so on, with  and  throughout for c and f. |
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28 Cf. p. 183. |
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