Personally, I would have the blog on the same site as your (main) web site. Then I would create an internal link (meaning that it is a link from one page on your site to another page on your site), to the most appropriate "inner" page on your site.
Should I link the blog to OUTSIDE websites and/or blogs having to do with music, or pianos in particular?
Well, that gets a little tricky, but here goes:
In theory, you will dilute your page rank
by linking to other sites. In theory, any way.
On the other hand, you will increase your authority
by linking out to REALLY GOOD RESOURCES. If you see a page on someone else's site and you think, "Darn, I wish I had written that page," then I would link out to it.
If it is a good page, is relevant to your topic, and you think visitors to your site would appreciate / benefit from it, then it is a pretty good idea to link out to it.