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 [Greek:(olo)phypomai], and again on the words [Greek: en brotois], viz. the notes _a# a* a_ (if the genus is the Enharmonic). The same notes occur in reversed order on [Greek: akatou] and [Greek: (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 [Symbols: flat], 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[1]. 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). [Footnote 1: Dr. Crusius, however, detects a [Symbols: phi]; (the sign for _g_) over the first syllable of [Greek: kateklusen] and the second syllable of [Greek: pontou]. There is little trace of them in his facsimile.] § 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 ([Greek: 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 ([Greek: tetrachordikai diaireseis]) which the most ancient musicians used for the [Greek: 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_