Revisiting the Noncommutative Music of the Quantum Sphere

The Music of Quantum Spheres - Fields Institute for Research in ...

https://www.fields.utoronto.ca/programs/scientific/14-15/.../KhalKhaliIntroSlides.pdf

Project Outline. ▻ Spectral Geometry: can one hear the shape of a drum? ▻ What is a noncommutative space and how to measure its shape? ... It is a mathematical theorem that fundamental frequencies of any object/shape ... the 'algebra of functions' on a mysterious, magical, noncommutative space! But there is no magic.

 



 

 
 

What about the relation with music? One finds quickly that music is best based on the scale (spectrum) which consists of all positive integer powers ${\displaystyle q^n}$ for the real number ${\displaystyle q=2^{\frac{1}{12}}\sim 3^{\frac{1}{19}}}$. Due to the exponential growth of this spectrum, it cannot correspond to a familiar shape but to an object of dimension less than any strictly positive number. As explained in the talk, there is a beautiful space which has the correct spectrum: the quantum sphere http://noncommutativegeometry.blogspot.com/2012/10/the-music-of-spheres.html

https://www.thedaobums.com/topic/47438-frequency-split-from-is-non-duality-actually-a-fundamental-truth-or-just-another-philosophy%C2%A0/

So I did a "thread" at thedaobums reviewing this noncommutative phase music research.

Too bad no one can understand this stuff. haha. Except for a few of you out there - thanks for encouraging my research.