Thanks for the reminder on this interesting topic, Michael. I'll certainly look into implementing this technique in ImproSculpt too, as soon as time permits. Maybe the easiest and most effective way would be to use the csound API to access the CsoundAC methods from the Python host (?), more efficient than re-implementing the same in Python. Regarding this, how "fully ported to all platforms" is CsoundAC now, is it distributed in all binary builds ? best Oeyvind 2008/4/18, Michael Gogins : > Actually, on closer examination, it looks like geometry.pdf contains both the Science paper (or a version or draft of it) and the online supporting materials, labeled as such. > > When I first got interested in algorithmic composition around 1984, I had this basic idea of a chord as a point in an N-dimension Euclidean space myself. Unfortunately, I had neither the mathematical background, nor the music-theory background, to develop this idea, so for me it died stillborn. > > Therefore, for me, this paper represents a welcome and graspable entry into mathematical music theory. From it and ealier papers I've been able to learn quite a bit about math and also about music theory. > > I think Tymoczko is pretty level-headed and empirically minded, doesn't try to push things too far, is more interested in fundamentals than in elaborations (unlike some of his colleagues), and tries hard to make himself understandable (also unlike some of his colleagues, and this is not so easy, believe me). Most importantly, think the ideas in the paper are at an appropriate level of abstraction and fit the data reasonably well. > > The various equivalence classes/orbifolds, group generators, fundamental domains, and so on in this paper and related papers provide the first instances of music theory that I have been able to more or less directly translate into code for algorithmic composition with useful results. > > Tymoczko himself has written some Java software to illustrate these ideas, which you can download from his Web site. I recommend trying it out -- it should make what is an orbifold etc. much easier to see. > > I suspect Tymoczko is playing with this stuff for algorithmic composition himself. I don't what the other authors might be up to. > > Drew Krause, by the way, a composer friend of mine here in New York, has been working with related ideas (chords as points moving in the Tonnetz, etc.) in Lisp code for algorithmic composition then rendered with Csound. > > Regards, > Mike > > -----Original Message----- > >From: Michael Gogins > >Sent: Apr 18, 2008 1:31 PM > >To: csound@lists.bath.ac.uk > >Subject: [Csnd] Re: Re: [Cs-dev] Geometrical music theory > > > >I believe the link you provide below is to the article they originally wrote. It looks like the Science editors then chopped it in two, a short Science article written in incomprehensible jargon and the rest which is now the "online supporting materials." > > > >So I think your link points to a more readable paper covering the same ground. > > > >It also is possible that there are errors in the linked paper that have been corrected in the Science materials. > > > >Thanks for the question, > > > >Mike > > > >-----Original Message----- > >>From: Steven Yi > >>Sent: Apr 18, 2008 11:23 AM > >>To: csound@lists.bath.ac.uk > >>Subject: [Csnd] Re: [Cs-dev] Geometrical music theory > >> > >>Hi Michael, > >> > >>I think I found the article here: > >> > >>www.music.princeton.edu/~dmitri/geometry.pdf > >> > >>Could you confirm if this is the same article as that found in Science? > >> > >>Thanks! > >>steven > >> > >>On Fri, Apr 18, 2008 at 6:08 AM, Michael Gogins wrote: > >>> I bring to your attention the following publication by Clifton Callender, Ian Quinn, Dmitri Tymoczko, "Generalized Voice-Leading Spaces", 18 April 2008, Science 320, 346 (2008). > >>> > >>> This article and supporting online material summarizes the last several years of work by these scholars on geometrical music theory, which involves representing voice-leading spaces as orbifolds, chords as points in such spaces, and so on. > >>> > >>> I mention this here because the CsoundAC Python extension module (written by me) for algorithmic composition with Csound uses some of these ideas for score generation, voice-leading, and score transformation. I am confident that the geometrical representation of musical entities will continue to bear new fruit in algorithmic composition for some time to come. > >>> > >>> Anyone interested in the algorithmic composition (or analysis) of pitch related materials should find this paper a very useful summary of this important and innovative approach to mathematical music theory. > >>> > >>> Regards, > >>> Mike > >>> > >>> > >>> > >>> ------------------------------------------------------------------------- > >>> This SF.net email is sponsored by the 2008 JavaOne(SM) Conference > >>> Don't miss this year's exciting event. 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