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
>>
>>
>>
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