6. It is impossible to decide the question of the modes of Aristides without some reference to another statement of the same author. In the chapter which treats of Intervals (pp. 13-15 Meib.) he gives the ancient division of two octaves, the first into dieses or quarter-tones, the second into semitones. The former of these ([Greek: hê para tois archaiois kata dieseis harmonia]) is as follows: [1] 2 3 4 5 6 7 8 9 10 11 12 [Symbols: -o < 6 1-1 9 L J A V E 3] [Symbols: o- > 9 n 6 J r- v 0 3 E] 13 14 15 16 17 18 19 20 21 22 23 24 [Symbols: 3.. N 1-1 3 E , '- cc > < Y Y] [Symbols: r a..1-1 E 3 A ,'- 33 < Y] After every allowance has been made for the probability that these signs or some of them have reached us in a corrupt form, it is impossible to reduce them to the ordinary notation, as Meibomius sought to do. The scholar who first published them as they stand in the MSS. (F. L. Perne, see Bellermann, _Tonleitern_, p. 62) regarded them as a relic of a much older system of notation. This is in accordance with the language of Aristides, and indeed is the only view consistent with a belief in their genuineness. They are too like the ordinary notation to be quite independent, and cannot have been put forward as an improvement upon it. Are they, then, earlier? Bellermann has called our attention to a peculiarity which seems fatal to any such claim. They consist, like the ordinary signs, of two sets, one written above the other, and in every instance one of the pair is simply a reversed or inverted form of the other. With the ordinary signs this is not generally the case, since the two sets, the vocal and instrumental notes, are originally independent. But it is the case with the three lowest notes, viz. those which were added to the series at a later time. When these additional signs were invented the vocal and instrumental notes had come to be employed together. The inventor therefore devised a pair of signs in each case, and not unnaturally made them correspond in form. In the scale given by Aristides this correspondence runs through the whole series, which must therefore be of later date. But if this is so, the characters can hardly represent a genuine system of notation. In other words, Aristides must have been imposed upon by a species of forgery. 7. Does the fragment of the _Orestes_ tell for or against the Modes described by Aristides?