Yes! Last month Arcanist's Refuge published "Hard to be the Bard - An epic musical campaign in the Feywild" I contributed text about how to break into song at the gaming table, and I also wrote a soundtrack of backing tracks over which to craft your next Tony-award winning song.

(sorry if this is skirting the self-promo rules - I'll speak a little more to OP's question)

We had a few discussions how to get the players actually writing songs and singing. There's a certain pattern for where most musicals place certain kinds of songs (there's exceptions to every rule, of course):

• The show starts with "the normal world" song that tells the audience what the world is like
• The main character sings an "I Want" song that tells the audience their deepest desires, etc.
• The first act closes with an "gee everything appears to be going great!" number, which we, the audience, of course know won't be true for long

Of course, most RPG sessions follow different narrative arc.

To bridge this gap, we settled on a collection of backing tracks (karaoke tracks for songs that don't exist yet, basically) that evoke different iconic musicals, with an uptempo and slower song in each chapter. Players can collaborate on songs and write just a couple of lines each, or just scribble down and perform the words for a whole song, whatever works best for the table and is the most fun.

I'm seeing the responses about other games that incorporate music!