Alain Connes point out real music is noncommutative. I quote: a “universal scaling system”, ... this discrete scaling manifests itself in acoustic systems, as is well known in western classical music, where the two scalings correspond, respectively, to passing to the octave (frequency ratio of 2) and transposition (the perfect fifth is the frequency ratio 3/2), with the approximate value log(3)/ log(2) ∼ 19/12 responsible for the difference between the “circulating temperament” of the Well Tempered Clavier and the “equal temperament” of XIX century music. It is precisely the irrationality of log(3)/ log(2) which is responsible for the noncommutative [complementary opposites as yin/yang] nature of the quotient corresponding to the three places {2, 3,∞}. -The first natural thing that you would try to get, to get this space would be a sphere, so you can compute the spectrum of the sphere, it is an object of dimension two. So this would never work. You think you are in bad shape because all the shapes we know ...but this is ignoring the noncommutative work. This is ignoring quantum groups. There is a beautiful answer to that, which is the quantum sphere. Musical shape has geometric dimension zero....We could classify finite space...it's related to mathematics and related to the fact that there is behind the scene, when I talk about the Dirac Operator, there is a square root, and this square root, when you take a square root there is an ambiguity. And the ambiguity that is there is coming from the spin structure. Math professor (Fields medal) Alain Connes on quantum music as noncommutative time-frequency origin of reality from infinite spiral of perfect fifths! Our brain is an incredible ....perceives things in momentum space of the photons we receive and manufactures a mental picture. Which is geometric. But what I am telling you is that I think ...that the fundamental thing is spectral [frequency]....And somehow in order to think we have to do an enormous Fourier Transform...on geometry. By talking about the "music of shapes" is really a fourier transform of shape and the fact that we have to do it in reverse. Alain Connes, 2012
Alain Connes point out real music is noncommutative. I quote: a “universal scaling system”, ... this discrete scaling manifests itself in acoustic systems, as is well known in western classical music, where the two scalings correspond, respectively, to passing to the octave (frequency ratio of 2) and transposition (the perfect fifth is the frequency ratio 3/2), with the approximate value log(3)/ log(2) ∼ 19/12 responsible for the difference between the “circulating temperament” of the Well Tempered
Clavier and the “equal temperament” of XIX century music. It is precisely the irrationality of log(3)/ log(2) which is responsible for the noncommutative [complementary opposites as yin/yang] nature of the quotient corresponding to the three places {2, 3,∞}. -The first natural thing that you would try to get, to get this space would be a sphere, so you can compute the spectrum of the sphere, it is an object of dimension two. So this would never work. You think you are in bad shape because all the shapes we know ...but this is ignoring the noncommutative work. This is ignoring quantum groups. There is a beautiful answer to that, which is the quantum sphere. Musical shape has geometric dimension zero....We could classify finite space...it's related to mathematics and related to the fact that there is behind the scene, when I talk about the Dirac Operator, there is a square root, and this square root, when you take a square root there is an ambiguity. And the ambiguity that is there is coming from the spin structure.
Math professor (Fields medal) Alain Connes on quantum music as noncommutative time-frequency origin of reality from infinite spiral of perfect fifths!
Our brain is an incredible ....perceives things in momentum space of the photons we receive and manufactures a mental picture. Which is geometric. But what I am telling you is that I think ...that the fundamental thing is spectral [frequency]....And somehow in order to think we have to do an enormous Fourier Transform...on geometry. By talking about the "music of shapes" is really a fourier transform of shape and the fact that we have to do it in reverse.
Alain Connes, 2012