Most modern readers would dismiss this as the typical Platonic idea that any sort of art needs to have a message. Music should "correct any discord" inside us and bring harmony into our souls. Composers of the last 500 years have certainly used music more as a means of portraying reality rather than delivering a sermon or giving us inner peace. That way, Stravinsky's Rite of Spring can be a "beautiful" piece insofar as it represents well the reality that he's trying to portray, much like a painting of a battle can be beautiful, though its subject is grotesque.
This is definitely in conflict, it seems, with Plato's view of how music should function. What's fascinating here is that Schoenberg's theory of atonality seems to be a reversion to this way of thinking about music.
Recall that Schoenberg's central idea is that all notes in the overtone series are equally comprehensible. Labeling certain notes as "dissonant" or "consonant" in a tonal center is, therefore, pure social conditioning, favoring certain notes on the overtone series simply because they occur earlier. With this in mind, Schoenberg is essentially advocating the atonal system because it is a more proper representation of how harmony naturally ought to occur. He's not trying to destroy harmony, from his perspective, but simply to broaden its scope. (Cf. why he favored the term "pantonal" over "atonal".)
Return to the Plato. Timaeus is advocating didactic music, its efficacy resulting from "the sound of the voice and the sense of hearing". It's the way nature naturally gives us a sense of harmony. If (and it's a big if) Schoenberg is right that our notion of good harmony is social conditioning, then, really, he's advocating composing music for exactly the same reason Plato is. He wants it to be natural. Atonality is more natural to the way harmony works. It is truly "bringing the soul into harmony and agreement with itself".