I would like to do research on automatic music composition. At the lowest level , I would like to start from discrete frequency levels as states. Here I would like to know the mathematical tools I can use for this? I have heard of markov chains and chaos theory etc used in this purpose. But one professor recently told that graph theory will be helpful in automated music composition. Is it so? Can someone recommend me the books required for starting such a research.
There is an open source on the similar project you may be interested: http://sourceforge.net/projects/amc/ The program generated chords and bass lines from .wav or .midi input.
The book "Algorithmic Composition" by Gerhard Nierhaus provides a very readable overview of approaches to automatic music composition.
(It may be cheaper on other book selling web sites)