I think absolutely anybody can write 12 tone music, and an algorithm could easily be made for that, but the only people who actually listen to 12 tone music are geeks and professional classical musicians.
Tintinnabulation (google Arvo Pärt) is also a possibility. Pärt's music usually follows a strict pattern, very predictable. However, the thing that makes his music incredible is the way he breaks the pattern, sometimes in such a way that one note at the beginning effects all subsequent notes.
(My organ prof did a a lot of research on this)
There are lots of rules in music that exist because anything different sounds strange or bad to us, simply because it's not something we are used to. (example: parallel fifths in voice leading was actually banned by the Vatican for a time because it "came from the devil". Parallel fifths will still get you docked on Music Theory exams, as I discovered from personal experience.)
Lots of people who don't even know these rules instinctively follow them because if they weren't followed, the music wouldn't sound good.
Even if a program were made that can follow all the established rules of music theory, the computer won't be able to determine when it's necessary to break these rules for the sake of making the music sound better.
That's also why only certain people are composers. Being able to listen and determine what sounds good and knowing how to make it better is difficult!
Okay I'll stop... although I didn't even mention counterpoint, form, or film scoring!
Edit: My point: Anybody can make music, but only certain people will be able to make music that sounds great.