The first most primitive way of making a computer write music is to have it come up with a random series of notes. This is essentially the same as drawing notes out of a hat and this kind of composition benefits little from the computer. Still, it can be fun to try, and it will give us something to build on. We can hope that with other techniques we can get something to sound more coherent.
Another thing we will take up at this point is something called a "stochastic process." This is a simple concept really. Randomness. The opposite is deterministic.
Traditional methods of composing are deterministic. The composer writes down the notes, and the performers perform them. Nothing is left to chance in terms of the notes played (interpretation is another matter). That's deterministic. The outcome can be predicted before the performance.
In a performance involving a stochastic process, the performance could be different every time. In Karlheinz Stockhausen's Klavierstücke XI, the performer is instructed to look at any of the segments of music strewn about the page and perform it at any tempo with any dynamic intensity. When (s)he reaches the end of the segment of music, (s)he is instructed to look at the dynamic markings printed there and use them to play the next segment of music his/her eye falls on. This is definately stochastic, since every time the piece is played, the listener should get a different rendition of it depending on where the performer looks. The outcome cannot be predicted ahead of time.
Random numbers are interesting little things from a mathematical point of view. Read some more about them and about how to generate pseudo-random numbers.
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Unfortunately, we could find nothing that wasn't too technical and/or required too much knowledge. There are no good intro books, and no web tutorials. Perhaps someone would like to write one?