source file: mills2.txt Date: Wed, 26 Jun 1996 08:54:11 -0700 Subject: RE: Markov analysis From: COUL@ezh.nl (Manuel Op de Coul) 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 Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 26 Jun 1996 18:52 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id JAA10365; Wed, 26 Jun 1996 09:52:47 -0700 Date: Wed, 26 Jun 1996 09:52:47 -0700 Message-Id: <9606261652.AA06880@arthaud.saclay.cea.fr> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu