The notes employed, according to the interpretation given above, give the scale g-a-a*-a♯-d-e-e*. If the genus is Chromatic, as M. Ruelle is disposed to think, they are g-a-a♯-b-d-e-f. When these scales are compared with the Perfect System we find that they do not entirely agree with it. Whether the genus is Enharmonic or Chromatic the notes from a to e* (or f) answer to those of the Perfect System (of the same genus) from Hypatê Mesôn to Tritê Diezeugmenôn. But in either case the lowest note (g) finds no place in the System, since it can only be the Diatonic Lichanos Hypatôn. It is possible, however, that the scale belongs to the period when the original octave had been extended by the addition of a tone below the Hypatê—the note, in fact, which we have already met with under the name of Hyper-hypatê ([p. 39]). Thus the complete scale may have consisted of the disjunct tetrachords a-d and e-a, with the tone g-a. It may be observed here that although the scale in question does not fit into the Perfect System, it conforms to the general rules laid down by Aristoxenus for the melodious succession of intervals. It is unnecessary therefore to suppose (as Dr. Wessely and M. Ruelle do) that the scale exhibits a mixture of different genera.
It must be vain to attempt to discover the tonality of a short fragment which has neither beginning nor end. The only group of notes which has the character of a cadence is that on the word (olo)phypomai, and again on the words en brotois, viz. the notes a♯ a* a (if the genus is the Enharmonic). The same notes occur in reversed order on akatou and (kat)eklusen. This seems to bear out the common view of the Enharmonic as produced by the introduction of an 'accidental' or passing note. It will be seen, in fact, that the Enharmonic notes (a* and e*) only occur before or after the 'standing' notes (a and e).
Relying on the fact that the lowest note is g, Dr. Wessely and M. Ruelle pronounce the mode to be the Phrygian (g-g in the key with one ♭, or d-d in the natural key). I have already put forward a different explanation of this g, and will only add here that it occurs twice in the fragment, both times on a short syllable [42]. The important notes, so far as the evidence goes, are a, which twice comes at the end of a verse (with a pause in the sense), and e, which once has that position. If a is the key-note, the mode—in the modern sense—is Dorian (the e-species). If e is the key-note, it is Mixo-lydian (the b-species).
§ 33. Modes of Aristides Quintilianus.
The most direct testimony in support of the view that the ancient Modes were differentiated by the succession of their intervals has still to be considered. It is the account given by Aristides Quintilianus (p. 21 Meib.) of the six Modes (harmoniai) of Plato's Republic. After describing the genera and their varieties the 'colours,' he goes on to say that there were other divisions of the tetrachord (tetrachordikai diaireseis) which the most ancient musicians used for the harmoniai, and that these were sometimes greater in compass than the octave, sometimes less. He then gives the intervals of the scale for each of the six Modes mentioned by Plato, and adds the scales in the ancient notation. They are of the Enharmonic genus, and may be represented by modern notes as follows:—
| Mixo-lydian | b-b*-c-d-e-e*-f-b |
| Syntono-lydian | e-e*-f-a-c |
| Phrygian | d-e-e*-f-a-b-b*-c-d |
| Dorian | d-e-e*-f-a-b-b*-c-e |
| Lydian | e*-f-a-b-b*-c-e-e* |
| Ionian | e-e*-f-a-c-d |
Comparing these scales with the Species of the Octave, we find a certain amount of correspondence. As has been already noticed ([p. 22]), the names Syntono-lydian and Lydian answer to the ordinary Lydian and Hypo-lydian respectively. Accordingly the Lydian of Aristides agrees with the Hypo-lydian species as given in the pseudo-Euclidean Introductio. The Dorian of Aristides is the Dorian species of the Introductio, but with an additional note, a tone below the Hypatê.
The Phrygian of Aristides is not the Enharmonic Phrygian species; but it is derived from the diatonic Phrygian octave d-e-f-g-a-b-c-d by inserting the enharmonic notes e* and b*, and omitting the diatonic g. By a similar process the Mixo-lydian of Aristides may be derived from the diatonic octave b-b, except that a as well as g is omitted, and on the other hand d is retained. If the scale of the Syntono-lydian is completed by the lower c (as analogy would require), it will answer similarly to the Lydian species (c-c).