Ever wonder what music produced by a Markov chain might sound like? Yeah, me too! ...and... wonder no more! So I went to where the piano is and grabbed the more regular, simple score I could find. As it turns out it was Mozart's Twinkle Twinkle variations (Zwolf Variationen uber "Ah, vous dirai-je, Maman" KV 265). Because it is written in C major and the notes are mostly regularly spaced this was great! I used the first variation (more notes) to produce a transition probability matrix. Perhaps an important thing to note (pun intended) is that the range is from B to E (about an octave and a half). The little song produced is about 30 measures and has no real tune to it, although in some parts it does resemble the original melody. Also, I added three non-random notes at the end to make it end gracefully.
Of course, arranging it a bit it can sound marginally better; here's how I've done it, adding accompaniment and instruments, using Garageband's licks and prefabricated transitions (to save time). Enjoy!
(I hope Mozart is not writhing in his grave!)