Yes, you do have to pay to use copyrighted music on your web site.
I get variations on this question all the time. People have heard the term "fair use," and that word "fair" sounds really promising. They get to thinking that whatever they want to do is probably "fair use."
Alas, as Inigo says to Vizzini in The Princess Bride: "you keep using that word. I do not think it means what you think it means."
"Fair use" is an extremely specific legal doctrine applying only to a handful of situations. "We're just some guys and we want to play some music on our site" is not one of those situations.
For more information, see the United States Copyright Office fair use page.
Even if you do follow the fair use rules— which probably don't cover what you want to do anyway— there is still a possibility that you will be sued and be forced to prove your use was legitimate in court.
Frankly speaking, the music industry just isn't very friendly. Especially with regard to the Internet.
My advice? Work with an unsigned band. You probably personally know at least six people who are in unsigned garage bands and would give their left arm to have their music heard by the visitors to your web site... Or by anyone at all! Believe me, the toughest part of being an independent musician is getting heard.
Or see my article how do I get the rights to play copyrighted music on my Internet radio station? for complete details on how to legally play copyrighted music on your site.
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