I've been doing galois theory all week, and while I now have a shadow of understanding how it works, it's completely boring so I'll relate this amusing anecdote instead:

I listen to midi files a lot, almost as much as MP3s. they are much smaller, they take no CPU time, you can get lots of them without violating copyright law, and if you have a good sound card they can be good background music while coding. there's a nearly limitless supply of classical, nursery rhymes, and nintendo music, which is pretty good, but to make it even better I've cooked up a markov chain generator which can process midi thru abcmidi and crap out new stuff. it really only works well with music that has repetitive structure, but that's OK because most classical, nursery rhymes and video game music does.

so tonight, we're listening to some otaku's disassembly of the final fantasy 3 cave music fed through the trusty markov script, and lo and behold, we hear the unmistakable dramatic strainings of the final fantasy 6 opera sequence, before you fight ultros. "oh my hero!" we listen to the source material, and it's nowhere to be found. it must be in a different key, hidden in the bass line or something. we never would have guessed.

so now you know. the corndogs who write the music for these games reuse the same themes between games. perhaps they too use a markov chain generator to make new soundtracks from old. nothing but your average "sneaking around in caves" music, and there's a beautiful opera hidden in it.