Have to share a coincidence you probably didn't see coming! My friend & neighbor, Billy, loves old musicals, so I sent him your clip. He immediately dropped me a note that it was from "Broadway Rhythm 1944", a show in which his uncle had a role! I just copied it (the movie) for him about a month ago on TCM, and we'll all be watching it one movie night upcoming... Now you tell me...what were the odds?!
Live music is so great :)