One of the main differences between copyrights and patents is that in order to infringe on a copyright, you have to be willfully imitating it. Coincidentally creating an identical work is not copyright violation if you didn't know about it.
http://www.ladas.com/NII/CopyrightInfringement.html
'Copyright infringement is determined without regard to the intent or the state of mind of the infringer; "innocent" infringement is infringement nonetheless.'
As with patents though, I think the intent does play a role in determining damages.
Relevant quotes from wikipedia:
> "... two authors may own copyright on two substantially identical works, if it is determined that the duplication was coincidental, and neither was copied from the other."
> "Infringement requires... that the defendant copied the protected work... if two individuals both create a story that by pure coincidence is nearly identical, but each without knowledge of the other, there is no infringement since there is no copying."
So in the example the poster above gave, you can't just own the copyrights. You also have to get your work distributed widely enough to claim that the author was aware of your work, from which you can build a troll-ish infringement claim.
However, for copyright to apply, you actually have to copy something. If you coincidentally come up with the exact same song that someone else wrote already, but you never heard about the other person's song, you would not infringe copyright in the other person's song.
In contrast, patents infringement is "strict liability," meaning that you can infringe a patent without even knowing that the patent exists.
If there is an objection that the computer isn't considered a person, then form a corporation and copyright the songs to the corporation. The corporation is equally ignorant of any other music. Human judgment is only exercised by a second corporation that searches the first corporations extensive database to find popular melodies to license.
If your intent was to discover and then market tunes identical to popular copyrighted tunes, a court can view the totality of your system as 'copying' existing works. If your two corporations exist to obscure the real intent of the people behind them, a court can treat them as co-defendants.