X-rated Bob wrote
Anybody know how I go about putting a tune that I composed in the public domain? I don't want to just make it freely available but also prevent anybody else claiming authorship and profiting thereby.
Having something in the public domain is not what you're after. A work is in the public domain after the copyright protection term for such a work has lapsed. Once something is in the public domain it's fair game for anyone.
X-rated Bob wrote
4) But I want to register it somehow so that nobody can claim authorship for the piece and thus profit by it
Technically there is no need to register anything to gain copyright protection, once the music is recorded or written down the work will be copyrighted. Included in that bundle of rights is what is called your Moral Rights, which include the right to be acknowledged as the author. It is then up to you to decide how you make use of such copyright. If you make the work available for non-commercial use you will still maintain the right to be acknowledged as the author.
You can't create music that's not copyrighted (a common misconception is that when people create open source software that software has no copyright. That is not correct, the people in whom the copyright vests chooses to license it in such a way that none of the proprietary restriction on use apply), so you will have to state the terms on which the work is made available.
You can either utilise it as an "all rights reserved" type work under a proprietary license or you can utilise something like a creative commons license allowing free non commercial use. If you chose to go the creative commons route you simply need to state that the work is made available subject the relevant creative commons license (non-commercial use, right of attribution reserved, etc). Creative commons even have little icons that you can use for the different licenses.
To prove that you’re the author of such a work you will have to prove that you created the work before they guy ripping of your piece of music did. The registered letter route is an option as you said, but anything that has a date objectively attached to it would work.
Tonedef wrote
What if said person ripped off your work, but changed a note or sequence here and there, thereby keeping the "intent" but thereby claiming it's 100% original? I guess it's situational and depends on the extent of the mods, but it's definitely a tricky one.
That's called an "adaptation" (as opposed to a straight up copy) and will amount to copyright infringement if the person making the adaptation is not authorised by the author to make such adaptation.
