→ What Are Your Rights as a Composer
These rights are known as "intellectual property rights" and are granted by federal law (with more than 160 countries having treaties honoring each country's copyright laws, see our FAQ #9).
These are "ownership" rights that usually attach to the actual songwriters
of the original work, both of the music and the lyrics. Among these rights is the exclusive right to basically do whatever you want with the music and songs you write (while no one else can, without your permission or without paying royalties).
If the song has just a single songwriter, figuring out who holds the copyright is pretty simple. But problems can arise when there are multiple composers. If there is no agreement available among multiple composers, the law will generally assume that everyone has an equal interest as joint owners of the copyright. So if you DON'T want it to be that way, make sure you have a separate written agreement which specifies what percentage each songwriter has contributed, or how to otherwise split up the copyright ownership for purposes of future royalties, sale of publishing rights, etc.
We've written a short article on this subject here