H. Riemann noncommutative de Broglie undertone Pythagorean relativistic quantum beat music Yuan Qi

"However, even in this case there is a highly non-commutative world of higher order collectivity algebras B(n). This can be used to capture the geometry of rotations, like those appearing in the classical Pythagorean octave versus perfect fifth considerations."
Music of Quantum Circles
October 2017
DOI:10.1007/978-3-319-47337-6_11
In book: The Musical-Mathematical Mind (pp.99-110)
Professor Micho Đurđevich
Institute of Mathematics, UNAM, Mexico citing Alain Connes:
"a non-commutative algebra naturally engenders a one-parameter group of automorphisms that makes it evolve, that makes it rotate in such a way that the passage from xy to yx corresponds to what evolution yields for the purely imaginary value t = sqrt(-1) of the parameter t of the evolution group. We must ... introduce evolution only after choosing a state in the algebra, but the evolution obtained is modified only by inner automorphisms and these are in a certain sense invisible. Here, I believe, is the key link that Hamilton sought between time and algebra. ..."
In the book "Triangle of Thoughts" (American Mathematical Society, 2001) Alain Connes, Andre Lichnerowicz, and Marcel Paul Schutzenberger discuss the interrelationships among Mathematics, Physics, and Philosophy.
The truth of Noncommutative Phase gets covered over in the discussion of Overtones and Undertones versus Harmonics and Subharmonics.

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Alain Connes: "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. 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. This is a function that the brain does amazingly well, because we think geometrically....The quantum observables do no commute; the phase space of a microscopic system is actually a noncommutative space and that is what is behind the scenes all the time. They way I understand it is that some physical laws are so robust, is that if I understand it correctly, there is a marvelous mathematical structure that is underneath the law, not a value of a number, but a mathematical structure." Fields Medal math professor Alain Connes (compilation of quotes)

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Sorry the sound was turned off on the phone - see the links for further details. thanks

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"the phase space of a microscopic system is actually a noncommutative space" - So you just proved that you don't even have basic reading skills! Congratulations. Hilarious. And no - not everyone who studies quantum mechanics knows this because most people rely on the Schrodinger wave equation - not the Heisenberg matrices. Olivier Costa de Beauregard points out that irony about quantum mechanics - people think they understand it because the math is fairly simply compared to relativity yet the concepts and true understanding of quantum mechanics is too difficult for most. As Professor Jean Bricmont points out - even Stephen Hawking did not properly understand Bell's inequality test of EPR. haha. And I just quoted Fields Medal math professor Alain Connes stating that mathematicians do not realize that noncommutative phase logic is the foundation of reality - just as you proved yourself by insisting that noncommutative geometry was a subset of commutative geometry. As Connes emphasizes - quantum mechanics has disproven this.
"What we consider the here and now, this world, it is actually just the material level that is comprehensible. The beyond is an infinite reality that is much bigger. Which this world is rooted in. In this way, our lives in this plane of existence are encompassed, surrounded, by the afterworld already. When planning I imagine that I have written my existence in this world on a sort of hard drive on the tangible (the brain), that I have also transferred this data onto the spiritual quantum field, then I could say that when I die, I do not lose this information, this consciousness. The body dies but the spiritual quantum field continues. In this way, I am immortal."

Prof. Dr. Hans-Peter Dürr, former head of the Max Planck Institute for Physics in Munich

"That is the reason why when people are doing quantum physics, if you only use quantum mechanics, they do not see the difference. Only if you go into relativistic theory, you have not only one, but an infinite number of them, disappearing as matter and occurring at interactions. So we are in a way mislead by Schroedinger who said, "Why do we need the Matrix mechanics of Heisenberg, when with only the algebra I make the Schrodinger equation that is in space and time. And that is the way, to my mind, the reason why we are on the wrong track. If the biologists try to get an understanding of biology is a complicated [interrupted] of the old physics. They make it so complicated...if you have dead matter and glue it together....it will never get alive."