Here's a relevant excerpt from research I did on college into this. FWIW, my research was specifically into genetic algorithms and generating similar musical styles as the input music. It didn't perform particularly well but had some surprises.
From my research, a Markov model could potentially be viable for this demo in particular. However, it wouldn't be viable for longer generation of music where you're trying to produce an actual song. The biggest problem being that it doesn't have the concept of melody in it.
--- research after here ---
A Markov model utilized by Herfort and Rehberger [17] uses the immediate previous note in order to determine the next note against a set of probabilities. This is a fairly simple algorithm as the set of rules is not large, but it is extremely short-sighted by nature. This “first order” Markov chain is not capable of determining a probability based on a large sequence of pitches. To counteract this, “N-order” Markov chain models can be determined to look more deeply into the past, but the complexity of the rule set increases exponentially with added depth. Further, every aspect of music that is to be modeled would require its own Markov model. For instance, there would need to be a model for pitch, duration, etc. This leads to a potentially huge Markov model rule set where all chains are independent of each other. Thus, Markov chains are good at composing musical melodies on the micro level (such as a measure) but fail to produce quality music at the macro level.
[17] Rehberger, Leopold. “Composing music using AI algorithms.” GRIN Publishing GmbH. 2004. " rel="nofollow">http://www.grin.com/en/e-book/108991/composing-music-using-a....
Source: https://github.com/sb8244/GeneticMusicComposition