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The Geometry of Consonance: Music and Mathematics 

Santa Fe Institute
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Dmitri Tymoczko
August 27, 2009
Elementary concepts of music theory can be translated into the language of contemporary geometry. Musical chords live in interesting geometrical spaces called "orbifolds" spaces that contain unusual twists and strange "singularities" analogous to the black holes of General Relativity. Tymoczko provides an accessible, multimedia introduction to this new way of thinking about music, in which the audience can both listen to and watch pieces of music as they move along cones, Mobius strips, and other geometric objects. He will conclude by explaining how Chopin's famously mysterious E minor prelude traces an intriguing path along a necklace of four-dimensional cubes.

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17 июн 2024

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Комментарии : 7   
@danielwoodwardcomposer2040
@danielwoodwardcomposer2040 8 лет назад
Music is Art. Sound is science.
@leerodgers3005
@leerodgers3005 9 лет назад
This is very helpful being able to see his presentation (as fuzzy as this is). It's probably worth getting Tymoczko's book especially since hypercube algorithms are already well-known programming chores, and a minor remapping would make for a workable tonal tesseract or 4-D tonal mobius.
@roderik1990
@roderik1990 6 лет назад
I believe that space is closer to the surface of a klein bottle, than that of a mobius strip. (at roughly the 1 hour mark) Because two mirrored mobius strips glued together on their edge form a klein bottle.
@kermitfrog593
@kermitfrog593 3 года назад
Blown away by the ease with which you are able to distill these complex concepts. Bravo.
@ac12484
@ac12484 6 лет назад
Great lecture. Btw, major fifth *does* divide the octave in half, but because of the log scale and equal temperament division, it appears above half... So although many ideas sound beautiful in this lecture, not all reasoning is 100% mathematical... Especially the argument about the good chords dividing the octave “nearly but not precisely evenly” - which is an artefact of the equal temperament scale. I’m gonna try to rework these circles in log frequency space. P.S. Oh, no, he explained that problem with piano keyboard in the first answer to the audience question ;)
@zacdagypsy
@zacdagypsy 8 лет назад
Music is a personal experience.
@siquod
@siquod 6 лет назад
"It's not a rotation!" * rotates the circle around y-axis *
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