Old film - romance between classical and jazz musicians

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Quite a while ago I saw a movie on AMC. It was probably made in the 40s, but possibly the 30s or 50s. It was about a woman who either studied or played classical music. She fell in love with a jazz musician. I remember one scene where she tries to focus on classical music but keeps hearing the strains of a song - "Do you love me, do you love me?" sung by the jazz musician. Does this sound familiar to anyone?



Good grief, I think you're right. How did I miss THAT when searching IMDB? I even Googled the phrase "Do you love me."

Thanks :-)