Here is some simple monophonic output from a second order Markov chain in MaxMSP. Using Debussy and Scriabin as source material.

Read the full tutorial here:

http://www.algorithmiccomposer.com/2010/05/algorithmic-composition-markov-chains.html

new-aesthetic:

Algorithmic Composition: Computational Thinking in Music | July 2011 | Communications of the ACM (via namebound)

This patch uses one subpatch to generate all the material and another that functions as a ‘conductor’ changing the note density, dynamics, pitch ranges, number of voices etc as the composition progresses.

See a full tutorial for Max and PureData at http://www.algorithmiccomposer.com/2011/09/tone-rows-puredata-and-max.html

Tone row etude using OpenMusic algorithmic composition software.
The first patch plays through the tone row with random octave distribution and random transposition of each row. Rhythm trees generate the rhythms. Three instances of the first patch are played with increasing note density.
The second patch plays through the tone row harmonically, with one to five notes sounds at a time. This patch is repeated with higher rhythmic density, finally the melodic tone row patch is played.

For full details of the algorithmic composition patch see http://www.algorithmiccomposer.com/2011/09/open-music-tone-rows-and-maquette.html

A simple algorithmic composition that randomly chooses a MIDI program number, note length and scale note for each of the 16 MIDI channels and then fades each note in and back out over the course of the note.

Read the full tutorial for MaxMSP and pd here

http://www.algorithmiccomposer.com/2010/05/algorithmic-composition-with-timbres.html

Algorithmic Composition, a second order Markov chain in PureData.

See the full explanation and tutorial here:

http://www.algorithmiccomposer.com/2011/06/second-order-markov-chains-in-puredata.html