3. The Platonic Modes were a subject of interest to the early musical writers, and were discussed by Aristoxenus himself (Plut. _de Mus._ c. 17). If Aristoxenus had had access to such an account as we have in Aristides, we must have found some trace of it, either in the extant _Harmonics_ or in the quotations of Plutarch and other compilers. 4. Of the four scales which extend to the compass of an octave, only one, viz. the Dorian, conforms to the rules which are said by Aristoxenus to have prevailed in early Greek music. The Phrygian divides the Fourth _a-d_ into four intervals instead of three, by the sequence _a b b* c d_. As has been observed, it is neither the Enharmonic Phrygian species (_c e e* f a b b* c_), nor the Diatonic _d-d_, but a mixture of the two. Similarly the Mixo-lydian divides the Fourth _b_-_e_ into four intervals (_b b* c d e_), by introducing the purely Diatonic note _d_. The Lydian is certainly the Lydian Enharmonic species of the pseudo-Euclid; but we can hardly suppose that it existed in practical music. Aristoxenus lays it down emphatically that a quarter-tone is always followed by another: and we cannot imagine a scale in which the highest and lowest notes are in no harmonic relation to the rest. 5. Two of the scales are incomplete, viz. the Ionian, which has six notes and the compass of a Seventh, and the Syntono-lydian, which consists of five notes, with the compass of a Minor Sixth. We naturally look for parallels among the defective scales noticed in the _Problems_ and in Plutarch's dialogues. But we find little that even illustrates the modes of Aristides. The scales noticed in the _Problems_ (xix. 7, 32, 47) are hepta-chord, and generally of the compass of an octave. In one passage of Plutarch (_De Mus._ c. 11) there is a description--quoted from Aristoxenus--of an older kind of Enharmonic, in which the semitones had not yet been divided into quarter-tones. In another chapter (c. 19) he speaks of the omission of the Tritê and also of the Nêtê as characteristic of a form of music called the [Greek: spondeiakos tropos]. It may be said that in the Ionian and Syntono-lydian of Aristides the Enharmonic Tritê (_b*_) and the Nêtê (_e_) are wanting. But the Paramesê (_b_) is also wanting in both these modes. And the Ionian is open to the observation already made with regard to the Phrygian, viz. that the two highest notes (_c d_) involve a mixture of Diatonic with Enharmonic scale. We may add that Plutarch (who evidently wrote with Aristoxenus before him) gives no hint that the omission of these notes was characteristic of any particular modes.