Well, yes, but you'd already dismissed "ABC and other notation", which I took as covering MIDIs.
If you mean tunes as opposed to songs, I guess the question's been answered: (a) historically the Digital Tradition was originally about songs (especially lyrics) (b) there are good other tune sites, and the ones for musicians deal in ABC which is ideal and the equivalent of song lyrics as text.
My first reply assumed you meant something like MP3. There, apart from the bandwidth problem, you're talking about actual recordings so there are going to be copyright issues, except where the users upload recordings of their own performances. That's pretty well covered by sites like MySpace, anyway.
One possibility for Mudcat would be a place where people post links to their own web sites with their uploaded MP3's on. That way Mudcats' bandwidth wouldn't be compromised and we could point each other at tunes.