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Page 224
hypaton. The terminology is very probably anachronistic, but the sense is that Lamprocles found a neater way of relating the Mixolydian to other modal scales.13 Later the development of larger kitharas and adjustable auloi made modal modulation during performance a more practical possibility, but this again involved fixing scales in definite positions relative to one another. However, practical requirements provided only part of the impetus. For the rest, it was a matter of delineating an intellectually satisfying system, in other words a neat and symmetrical one.
We get only glimpses of the course of these struggles. The earliest fragment of evidence is, I believe, to be gleaned from Alcman. In one of his Partheneia he invoked the Muse and then, finding in his own music the proof of her response, made his choir-girls exclaim 'the Muse cries forth, the clear-voiced Siren!' This Muse-Siren must represent the true, perfect sound that Alcman desired. Now, in another song his chorus more modestly says
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                  the Sirens' voice
is indeed more musical than ours,
for they are divine, and instead of (their) eleven
it is only ten girls that sing here.
Why should there be eleven Sirens? Presumably because there are just eleven true and perfect notes. According to an old Pythagorean saying, the octave which embodies the fundamental harmonic ratios (1:2, 2:3, 3:4) 'has the Sirens in it'; and in the cosmology of Plato's Republic the music of the spheres is made by eight Sirens, each responsible for a different note of the diatonic scale.14 Alcman, then, recognizes a divine system of eleven notes. If his music was pentatonic, the number might represent two whole octaves, for example A B c e f a b c' e' f' a'. If it was heptatonic, it might represent a combination of two disjunct tetrachords (= an octave) with one conjunct, or perhaps some other composite structure from which alternative scales could be abstracted.
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13 Aristox.(?) ap. ps.-Plut. De mus. 1136d. See JHS 101 (1981). 127.
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14 Alcm. PMG 30; 1. 96-9; Iambl. De vita Pythagorica 82; M. L. West, CQ 15 (1965), 200, 17 (1967), 11-14, JHS 101 (1981), 127. Nete, Mese, and Hypate are said to have been recognized as Muses at Delphi (Plut. Quaest. conv. 744c, cf. Censorinus fr. p. 90. 6 Jahn); and on an Argive dedication of about 300 BC (SEG 30. 382) they appear together with a fourth, Prata (dialect for Prota 'first'), who presumably corresponds to a local name for some other important note, e.g. Hyper-hypate.

 
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