Minor element of correction. For the vast majority of musical content, there is no such thing as copyright free. Copyright is the legal protectable ownership of a piece of music by the creator of that music or the group they have sold those rights to. All music is copyrighted, with notable exceptions around the 90-100 years old and older mark as that is commonly when copyrights expire.
There are 3 basic types of license that all music falls under.
Standard licensed music requires a royalty based fee for use. Royalties are a period or volume centric fee (cost per times played, or per people listening).
Royalty Free is music that is licensed on a single fee basis, meaning that you pay a one time fee and can use the music afterwards in multiple areas without paying royalties.
Open license is something like the Creative Commons which is a license that allows you to use the content, without a monetary cost, but it comes with other restrictions preventing you from reselling the music, etc.
What you're looking for is an open license. Google Creative Commons and you will find plenty of it. Incomptech is a good source, but far from the only one out there.
This lesson in copyright law is brought to you by the letter T.
