Genie, the song was written in waltz time. Also on youtube is Dolores del Rio, original soundtrack. A Much better rendition.

She had a rather heavy accent, thus didn't survive the transition to talking films, except in this classic film, and the great musical, "Flying Down to Rio" (Rio by the sea-o) where she played a Brazilian. She continued in films, but mostly in Mexican productions.

Ramona Del Rio

?"I need you, my own" - she sings this instead of "I made you my own." I think it is better.