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Geometrical music theory

Tue, 2008-04-29 13:55 — Mark Dow

Science 18 April 2008 Vol 320, Issue 5874 has a wonderful article about the geometry of music, how  "many musical terms can be understood as expressing symmetries of n-dimensional space, where each dimension represents a voice in the score. Identifying—gluing together—points related by these symmetries produces exotic mathematical spaces (orbifolds) that subsume a large number of geometric models previously proposed."

Demonstration of how discrete dynamical systems can be identified with topologies, in particular trefoils on the 3-half-twist Mobius band like these illustrations of mine.

"Geometrical music theory suggests new directions for research in traditional music
theoretical topics, such as chord and voice leading similarity, and new tools for teaching and conceptualizing music, and will perhaps inspire composers. Moreover, one can envision practical applications of geometrical music theory, such as in the design of music visualization tools, interactive musical toys, or even new musical instruments."

Musical orbifolds on mobius trefoil

Comments

Mon, 2008-05-05 19:53 — PSR

Bach

is very geometrical. I particularly recommend finding Bach performances on a solo instrument violin cello are ok -im not a fan of harpsichord- lute, piano and the GUITAR are good for Bach (both are oddly non-baroque era instruments). Solo instrument arrangements allow clarity of each note in combination with minimal harmony which lets you really see/hear the intricate structure best. Its the dissonances [interference patterns] in chord choices and polyphony ie parallel melodies that result in harmonies of which the fugue is the pinnacle that make Bach so unique and humbling. When playing, and to a lesser extent, listening to his stuff I semi-visualize things similar to the images above. Mozart is too flowery, Beethoven too expansive, Bach.

"single notes form a trefoil knot that is the boundary of a thrice-twisted mobius strip"...the trick will be to make this sound cool.

Mark yes if you are ever contemplating the 4th dimension music helps. A central geometrical axiom of western music is the circle of 4ths/5ths. It has a really beautiful simple basis in the overtone series in which I see a close parallel to your aperiodic subunit construction work. 

Thanks again for another good post. 


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