Initially, I couldn't find the credit for Oscar Levant as the composer of "Carnival". But it's in the "soundtrack" section.
Oscar Levant was a concert pianist, friend of George Gershwin and a pretty good character actor. He was also a real character, as revealed on the Jack Paar show when I was a kid. He just about personified the term raconteur. I remember him talking about writing for movies, and he may have been talking about this movie.
He actually played himself in the movie "Rhapsody in Blue", with Robert Alda as George Gershwin.