I would love to see a real-time bebop improvisation generator in the style of Charlie Parker, Sonny Rollins, Bill Evans, et. al. - bebop is definitely a musical (jazz) language that I bet would be well suited to RNNs.
It feels like it would be an achievable goal, given the right kind of training material.
Maybe hiring a session pianist for a few days to harmonise a bunch of key/tempo normalised jazz standards on a midi keyboard, so that the harmonisations and melody input are separate, labeled data?