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smallest possible intervals. So a notation invented by them might be expected to reflect this approach, for example by dividing each semitone into two steps and each tone into four. The principle of the notation we are examining is fundamentally different. |
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Its inventor took the notes of the diatonic scale across the span of two octaves or just over (a'-A, or G?) and designated them by letters, whose apparently chaotic order16 must reflect a sequence of technical names or mnemonic syllables that lies beyond our ken.17 The system of triads, in which the symbol rotated through ninety degrees to the left denoted the first sharp and the symbol reversed the second sharp,18 was surely designed to deal with the enharmonic/chromatic pyknon, with which it is intimately bound up in the fully developed notation. It characterizes the movable notes as modifications of the standing note below them. Sachs and Gombosi argued that this reflected techniques of obtaining all three notes of the pyknon from the same lyre-string; but their position has been subjected to damaging attack. It is much more likely that what lies behind the triadic notation is the production of the three notes by closing or partly opening the same hole of the aulos.19 In the diatonic genus the lower movable note would still be produced in this way, by half-stopping, but not the upper one; and in the notation the first sharp is used for the lower note in diatonic, just as in enharmonic and chromatic.20 |
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There was no need for sharps on any note above e', since e'-a' was the highest tetrachord in the two-octave scale. This must be connected with the fact that the three positions of 46 N are used not to provide f' with sharps but to notate the top three notes f' g' a'. We |
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16 We cannot be sure of all their identities, but in the article cited I suggest that they were, from 46 downwards, nu, beta. gamma, pi, kappa, omikron, vau, upsilon, tau, lambda, epsilon, heta. rho. sigma. Westphal's interpretation, according to which notes an octave apart are regularly designated by adjacent letters (cf. Monro, op. cit. 71), depends on some untenable identifications. |
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17 Cf. NG xiii. 336, s.v. Notation: 'There further exist non-alphabetical letter notations: that is, notations in which an item in the musical order is specified by reference to the position of the letter not in an alphabet but in some other order. Such letters are abbreviations of syllables or words . . . . An Indian example is quoted, in which notes are designated by Sanskrit letters that stand for names of the degrees of the scale. |
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18 The triad 10-12  does not, as transmitted, fit this formula, but erhaps originally it was  . Some distortion has occurred in the triad 37-39. |
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19 See pp. 66, 95, 235 n. 42; H. Husmann (as above, n. 12). |
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20 This use of the same symbol for the lower movable in all genera is often connected with Archytas' scheme of harmonic ratios, where, contrary to all later reckonings, the lowest interval of the tetrachord is of equal size in each genus (p. 168). |
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