Ask HN: Construct AI version of Beethoven?

Is it possible to construct an artificial intelligence composer AI Beethoven that constructs new music learnt from Beethoven previous works?

For example if you view Beethovens notes as tapes in a turing machine, feeds that into some kind of Hidden Markov model to get probabilities of following notes and possibly deep neural network or genetic algorithm blending good compositions? How would such an Artificial intelligence be constructed?