[ANPPOM-L] The Geometry of Musical Chords by Dmitri Tymoczko

[Jos=?ISO-8859-1?B?6SA=?=Luiz Martinez]

Dear friends at Musikeion,


I've found this research of Dmitri Tymoczko quite interesting. Anyone would
like to try a semiotic interpretation?

Some more material at Dmitri Tymoczko's website:

http://music.princeton.edu/~dmitri/

Regards,
Martinez

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Science 7 July 2006:
Vol. 313. no. 5783, pp. 72 - 74
DOI: 10.1126/science.1126287

The Geometry of Musical Chords
Dmitri Tymoczko 

 A musical chord can be represented as a point in a geometrical space called
an orbifold. Line segments represent mappings from the notes of one chord to
those of another. Composers in a wide range of styles have exploited the
non-Euclidean geometry of these spaces, typically by using short line
segments between structurally similar chords. Such line segments exist only
when chords are nearly symmetrical under translation, reflection, or
permutation. Paradigmatically consonant and dissonant chords possess
different near-symmetries and suggest different musical uses.

Department of Music, Princeton University, Princeton, NJ 08544, USA, and
Radcliffe Institute for Advanced Study, 34 Concord Avenue, Cambridge, MA
02138, USA.


 E-mail: dmitri em princeton.edu