Savage Serenade was written by Herman Hupfeld who also wrote As Time Goes By (1931). I think Savage was written in 1930 (don’t have my reference material in front of me) for a show called The Little Follies.
I am thinking of a different Hupfeld song. I will check back in here after the Red Sox finish beating the Yankees.
Hupfeld also wrote When Yuba Plays the Rhumba on the Tuba (Down in Cuba) (1931), which contains some topical references to the world of 1931--unemployed New Yorkers selling apples, prohibition, Betty Boop cartoons, and the smash hit song El Manisero (The Peanut Vendor). "Yuba" also got a reference in the 1932 hit song Crazy People.