Would it be possible to make a statistical model of a jazz solo and use it to create new ones?  Take a standard, and let’s focus on the saxaphone, say.  Go to the solo and estimate a Markov transition kernel which tells you the probability distribution over the next tone conditional on the previous tone.  In particular you want the joint probability distribution over the following note (or just the interval) and the note’s value (eighth, quarter, etc.)  Feed it tons and tons of recordings of sax solos for the same tune (that’s why you want a standard.)

Once you have estimated your kernel, simulate it.  Will it be music?  How much of an improvement do you get if the state variable is the last two notes instead of just one?  If your state variable is the last n notes, at what n are improvements no longer noticeable?

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