The pantheon of songwriters who created the Great American Songbook, the canon of the most important and influential popular songs from the 1920s through the 1950s when hits tended to come from the worlds of Broadway and Hollywood, has been pretty much carved in granite. George Gershwin, Cole Porter, Irving Berlin and Richard Rodgers are on American music’s Mount Rushmore while Jerome Kern and Harold Arlen are perhaps the prime candidates for a fifth spot.

But “Ain’t Misbehavin’,” playing at Beach Haven’s Surflight Theatre through Sept.