Here's some food for thought:
Positive concepts are lodged at the harmonious third, fourth, sixth, eight and ninth "notes", which were considered to be most harmonious with the 12th; while negative concepts are found at the more dissonant fifth, seventh, 10th and 11th.Given a 12-note chromatic scale, which was more than likely NOT generally used for the music of Plato's time, the third degree of the scale would be a whole step from the root, the fourth degree, would be a minor third away from the root, the sixth degree would be a perfect fourth from the root, the eighth degree would be a perfect fifth, and so on. It doesn't make any musical sense to me.
If the degrees of the 12-note chromatic scale have particular qualities when they sound by themselves, then Plato would have to have had absolute pitch mixed with a kind of synesthesia. What respectable synesthete would divide notes simply between pleasant and dissonant. If that were true Plato would probably have written a lot more specifically about music. I believe that when he discussed modes he was commenting on the linear harmonic nature of a set of pitches going from "tonic" to "tonic" on instruments that did not have the ability to alter themselves chromatically (the lyre vs. the pedal harp, for example).