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Aristoxenus added an eighth at the top to complete the octave, (g') Hypermixolydian. Then he filled in the semitone gaps by declaring that each of the names except Hypodorian, Dorian, and Hyper-mixolydian stood for two keys, a higher and a lower one a semitone apart. If this sounds odd, let us reflect that it is not so very different from what we do when we speak of A flat and A natural, or F natural and F sharp. Aristoxenus' reason for doubling names in this way was not that he could not think of any extra ones. It was that the 'flat' or 'sharp' keys did not correspond to any new octave species. The Dorian ('C') key brought the Dorian E species onto the screen, as it were. The Phrygian ('D') key brought the Phrygian D species. But an intermediate  key could only produce the E species a semitone higher or the D species a semitone lower; there is no  species between them. |
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Aristoxenus' system was close to the one generally accepted in later Antiquity. The final step was taken sometime before Varro, we do not know by whom. It was a reform of the nomenclature, with the addition of two further keys for the sake of symmetry. In Aristoxenus' scheme the Hypo- names, Hypodorian, Hypophrygian, Hypolydian, had come to stand for the keys a fourth below Dorian, Phrygian, and Lydian respectively.31 In the new system the old names Ionian and Aeolian were brought in and arbitrarily attached to the 'flat' keys between Dorian and Phrygian ( ) and Phrygian and Lydian ( ); the prefix Hypo- was generalized so that it applied to all five in the same way; and the prefix Hyper-, which Aristoxenus had casually introduced in baptizing his Hypermixolydian, was likewise compounded with the names of the five central keys to denote the keys a fourth higher, Hypermixolydian being accordingly renamed Hyperphrygian. The two new keys, Hyperlydian and Hyperaeolian, were invented to fill out this scheme. They were really superfluous, because they duplicated existing keys an octave lower. Table 8.2 sets out Aristoxenus' thirteen-key and the reformed fifteen-key system.32 |
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31 It had not always been so, cf. pp. 228f, above. |
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32 The main sources are Cleon. p. 203.5ff. and Aristid. Quint. p. 20.5ff., where Aristoxenus' keys are listed and glossed with their current equivalents. Cf. also Varro fr. 282 p. 304 Funaioli; Heliodorus ap. schol. Dion. Thrax (Grammatici Graeci, i. 3) |
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(Footnote continued on next page) |
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