In this scale, as has been pointed out (p. 71), the notes which are at the distance of an octave from each other are always expressed by two _successive_ letters of the alphabet. Thus we find-- [Greek: b - g] is the octave _e - e_, the Dorian species. [Greek: d - e] " " _c - c_, the Lydian species. [Greek: [digamma] - z]" " _g - g_, the Hypo-phrygian species. [Greek: ê - th] " " _a - a_, the Hypo-dorian species. Westphal adopts the theory of Boeckh (as to which see p. 11) that the Hypo-phrygian and Hypo-dorian species answered to the ancient Ionian and Aeolian modes. On this assumption he argues that the order of the pairs of letters representing the species agrees with the order of the Modes in the historical development of Greek music. For the priority of Dorian, Ionian, and Aeolian he appeals to the authority of Heraclides Ponticus, quoted above (p. 9). The Lydian, he supposes, was interposed in the second place on account of its importance in education,--recognised, as we have seen, by Aristotle in the _Politics_ (viii. 7 _ad fin._). Hence he regards the notation as confirming his theory of the nature and history of the Modes. The weakness of this reasoning is manifold. Granting that the Hypo-dorian and Hypo-phrygian answer to the old Aeolian and Ionian respectively, we have to ask what is the nature of the priority which Heraclides Ponticus claims for his three modes, and what is the value of his testimony. What he says is, in substance, that these are the only kinds of music that are truly Hellenic, and worthy of the name of modes ([Greek: harmoniai]). It can hardly be thought that this is a criticism likely to have weighed with the inventor of the notation. But if it did, why did he give an equally prominent place to Lydian, one of the modes which Heraclides condemned? In fact, the introduction of Lydian goes far to show that the coincidence--such as it is--with the views of Heraclides is mere accident. Apart, however, from these difficulties, there are at least two considerations which seem fatal to Westphal's theory: 1. The notation, so far as the original two octaves are concerned, must have been devised and worked out at some one time. No part of these two octaves can have been completed before the rest. Hence the order in which the letters are taken for the several notes has no historical importance.