I was wondering if it would be appropriate to share say an mp3 of improvisation or some composition on a pdf or if this is not that kind of site?
No, the main problem with that sort of post is that it couldn't meet our question requirements... This is, after all, a Question and Answer site, not a discussion forum or music sharing site.
Various folks share music (their own or favourite pieces) in chat, which may serve your needs.
As Doktor Mayhem says, posting your work as part of a general 'what do you think of this? comments please!' request on the main site doesn't really work here if there's no specific question about music being asked.
However, I do think it would be great if we could share more music, and for now I think it's fine do to so in the main chat room. I'm not sure how many comments you'll get (the chat room is pretty quiet), but the more people we have sharing music in there, the noisier it will be...