Do you know that you’re telling a joke?
There is some funny music where “you” know you’re telling a joke. That is, the character you portray during the song is consciously being funny. Think Tom Lehrer.
Other funny music gets funnier the more your character doesn’t show that they get the joke. I think “Weird” Al Yankovic often commits in that way to his humor – his performance is deadly serious, even as the song itself is hilarious, and the seriousness makes the song that much funnier.
(The same is true for stand up comedians, of course – maybe the difference between Robin Williams and Steven Wright.)
I love to program funny songs for choirs (there needs to be more of funny choral repertoire!). But when you do, it’s an important and too often undiscussed question: “When I sing this song, do I know I’m funny?”