From: goldstrn@thinf2.tuwien.ac.at (Martin Goldstern)
Newsgroups: sci.math.research
Subject: Re: mathematically defined musical patterns?
Date: 9 Mar 1998 11:14:45 GMT

Steve Lefevre (slefevre@freenet.columbus.oh.us) wrote:

:   I'm wondering if anyone's done any work with mathematics in music.
: Specifically, I was recently thinking that you could take a certain genre
: of music, or a certain composers' works, and mathematically define the
: reoccuring patterns within the music.
For example, the paper 
   Tichy, Robert F.; Winkler, Reinhard
   Bemerkungen ueber Pseudozufallszahlen und deren Anwendung zur
   Komposition von Walzern. (Remarks on pseudo-random numbers and their
   application to composing waltzes). (German)
   [J] Sitzungsber., Abt. II, Oesterr. Akad. Wiss., Math.-Naturwiss. Kl.
   200, No.1-10, 53-64 (1991). [ISSN 0723-9319]
   (Zentralblatt 751.11039)
mentions that such a proposal has already been made by Mozart.  I assume
that the bibliography contains some relevant references. 

Also, Hofstadter's "Goedel-Escher-Bach" (Zentralblatt 457.03001)
draws (superficial?) connections between certain patterns 
- in particular, "self-reference" -- in Goedel's theorems,
Escher's paintings, and Bach's music. 

Martin.Goldstern@tuwien.ac.at
==============================================================================

From: Chris Hillman <hillman@math.washington.edu>
Newsgroups: sci.math.research
Subject: Re: mathematically defined musical patterns?
Date: Mon, 9 Mar 1998 04:11:30 -0800

On 9 Mar 1998, Steve Lefevre wrote:

>   I'm wondering if anyone's done any work with mathematics in music.
> Specifically, I was recently thinking that you could take a certain genre
> of music, or a certain composers' works, and mathematically define the
> reoccuring patterns within the music. For instance, taking Bach's work,
> and defining the probability and percentage of instances in which a
> certain note or chord follows another note or chord. Sort of setting up
> `boundaries', in which any music that falls within those boundaries could
> be said to be Bach-like. 
>   Can anyone point me in the right direction?

There is a figure in Eigen & Schuster, Laws of the Game, comparing (as I
recall) the intervals between immediately succeeding notes in Bach &
Beethoven.  In theory, musical scores should be susceptible to the same
sort of statistical textual analysis which has been used to sort out (for
instance) who wrote which parts of the Federalist papers or the Bible or
other multiauthor works.  See the paper by Aaron Wyner on my page

  http://www.math.washington.edu/~hillman/Entropy/infcode.html

You might try posting your question in rec.music.classical since several
mathematically minded musicians and musical mathematicians frequently post
in that ng.

Chris Hillman