Master Terrible's Sing-Along Quest

So I was working on an idea I had involving Dwarven work songs (I'm still researching the subject, I have no idea what Tolkein was thinking) when I had this random thought: A game in which, instead of dice, success or failure is determined by the players' ability to sing. Essentially a Tabletop Rhythm Game.

However, I'm not quite sure how to accomplish it. Certain things are easy enough; challenges may require the characters themselves to sing, such as infiltrating a mine and having to sing along with the workers to avoid detection or needing to learn a password in song, or there may be persuasion events that will go better if the player presents his case as a song. Other things are trickier, though. How would I handle combat? I can't exactly have the players get up and have a dance-off every time. Characters could have their own theme song, but what would be the advantage?

If anyone is willing to offer up rule ideas, I'd be grateful.

This sounds more like it should be brought up in Yack Fest.