'Disharmony' is a Greek word with Latin prefix meaning 'absence of harmony' or 'bad harmony'. So why not 'dysharmony', as 'dysfunction' or 'dyspepsia'?
Dis is a Latin prefix, whereas Dys is a greek one. Much of English stems from Latin, so it certainly makes sense for Dis to be the more common prefix, though you are correct that Dys as a prefix has a similar meaning to Dis.
Dys is often used in a scientific context (where Greek gets a fair amount of use in addition to Latin) for terms like Dysgraphia and Dyslexia. Dys tends to be used more to mean "bad, improper" rather than "the opposite of," as you'll note from my examples; Dysgraphia is not the opposite of writing, but rather means that one's writing is impaired.