RE: Markov analysis

The Illiac Suite for string quartet by Lejaren Hiller and L. Isaacson
was composed I think with a Markov model. Named after the Illiac
computer of the 50's that ran the program. This work is on a Wergo CD.
I've read an article about it many years ago, but don't remember the
reference alas.
A Markov model is a stochastic model of some system. Each event (note,
phrase, interval, symbol in a message, some occurrence or whatever)
has a fixed probability that may depend on earlier events. In a
so-called first order Markov model the probabilities depend on only
the last previous event. In a second order model they may depend on
the previous two events, etc. A zero order model is also possible.
If one generates music with a Markov model then the probabilities may
be calculated from one or more existing pieces. The idea is then to
get music that is similar, yet different. If a first order model is
taken then it doesn't sound similar at all, just random. If the model
order is too high however, then whole phrases will come out alike the
original.
So it is a rather simplistic way of generating music and with the high
degree of randomness, one could argue it is still noise, the Markov
model merely colours it. A zero order Markov model produces white
noise.

A reference from Piet van Oostrum's electronic music bibliography:
( http://www.cs.ruu.nl/pub/MIDI/DOC/bibliography.html )

Machine Models of Music, From Minsky to Mozart, edited by Stephan
Schwanauer and David Levitt

Cambridge: MIT Press, 1993
ISBN 0-262-19319-1 $45

Machine Models of Music brings together representative models ranging
from Mozart's "Musical Dice Game" to a classical article by Marvin
Minksy and current research to illustrate the rich impact that
artificial intelligence has had on the understanding and composition
of traditional music and to demonstrate the ways in which music can
push the boundaries of traditional AI research.

The authors include prominent figures in linguistics (Johan Sundberg,
Ray Jackendoff), computer science and AI (Fred Brooks, Marvin Minsky,
Terry Winograd, Herbert Simon, Peter Neumann), music theory (Allen
Forte), composition (Fred Lerdahl, Charles Ames), psychoacoustics
(Christopher Longuet-Higgins, Jamshed Bharucha), and the odd middle
ground of "computer music" (James Moorer, Hiller and Isaacson).

Manuel Op de Coul coul@ezh.nl

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