Now Plato's view on mathematical things was that the human mind is in itself thoroughly informed on species or figures, and axioms and conclusions about things. However, when it seems to learn, it is merely being reminded by sensible diagrams of those things which it knows on its own account. He conveys that with singular ingenuity in the Dialogues by introducing a slave who when questioned by his master makes all the replies as desired.
Kepler book iv chapter i page 297
The discovery of true and secret Harmony is only possible if the Soul already contains knowledge of all things. Harmony in no way can come from outside the soul. If that were the case, knowledge would not be possible, and the mind would be as Aristotle puts it, as a blank slate.
Here is a fragment of Plato's Meno dialogue where he outlines the Doctrine of Recollection through the introduction of a Slave Boy.