Pianist and woman in second story apartment

This movie has two main characters – a guy who plays piano and a woman. The guy’s piano is in a second story apartment by a window overlooking the street. The woman in the movie comes to his place often, and they have heated discussions about something. I don’t remember if he was teaching her piano, or if he was just a pianist. I just remember her sitting by him while he plays on his grand piano. I also recall that, at the end of the movie, the woman leaves and he goes into a club and joins a (jazz?) band that a friend had been wanting him to join. Joining the band is his second choice (only made because the woman wasn’t going to be part of his life).