To my uneducated ears this sounds like some kind of off kilter "My Favorite Things" deviation, but it is most likely some variation on some other Olde English traditional tune. Nonetheless, the composers both come from jazz and big band backgrounds, so it's not hard to imagine that their take on 19th century music might be a little warped or different! Tony Crombie was a drummer, pianist & bandleader, & Bill LeSage was a pianist for The Johnny Dankworth Seven & a bandleader himself. Not much horror in their credits but they did compose music for a few cool titles like "Pussycat Paradise", "Striptease Murder" & "The Spider's Web."
In this scene from Poe's famous story, "The Tell-Tale Heart", Edgar Marsh seems to have a bit of an inferiority complex, among other apparent problems, including not being able to deal with the opposite sex!
But let's give Edgar a little credit here, it's just not really that hard to imagine why he wouldn't want to Buy Her Another Drink!
Edgar's a vicious killer and a jealous librarian, I think we have a problem!
This is the guy with the haunting heart!
Wow, what a hangover, good thing I didn't drink anything!!!