Riemann Zeta Function disproves Western Music tuning while Noncommutative Phase proves the Riemann Zeta Function!

 
 

 The Zeta function is a very important function in mathematics. While it was not created by Riemann, it is named after him because he was able to prove an important relationship between its zeros and the distribution of the prime numbers. His result is critical to the proof of the prime number theorem.

But what makes the analyticity work for the mathematical object makes the music that might come out of it inherently out of tune.

https://pbelmans.ncag.info/blog/2012/01/09/the-flaw-in-all-western-music-is-related-to-the-riemann-zeta-function/

 The important part: The linear independence over the rationals of the logarithms says that these cannot be equal, so the only possible pole is located at $s=1$. In layman terms: if there was another pole we would see $2^m=3^n$ but as the left-hand side is even and the right-hand side is odd this equality is impossible for integral exponents.

So sums up a mathematician - "inherently" meaning by Western music tuning standards of course (pick your snazzy "hip" youtube music theory channel with lots of followers, i.e. Adam Neely, etc.)

 Let me
admit it : i was probably wrong in this post to
advise against downloading A walk in the noncommutative
garden by Alain Connes and Matilde Marcolli. After all, it seems
that Alain&Matilde are on the verge of proving the biggest open
problem in mathematics, the Riemann
hypothesis using noncommutative geometry.

So funny how the first mathematician admits the Riemann Zeta Function disproves Western music tuning and yet does NOT admit that true music tuning is via noncommutative phase! http://math.louisville.edu/~mathclub/docs/mhawthorn.pdf

Then we have Connes et. al. claiming to PROVE the Riemann Zeta Function using noncommutative phase logic and then Connes lectures on how real music truth is from Noncommutative phase logic. haha. http://empslocal.ex.ac.uk/people/staff/mrwatkin/isoc/zetatuning.htm

From: gwsmith@gwi.net (Gene Ward Smith)
Newsgroups: sci.math
Subject: Re: number theoretic (or statistical?) basis of music theory and harmony
Date: 8 May 1998 16:59:27 GMT

Kjinnovatn wrote:
Here's a little puzzler that I've been wondering about: If you investigate the number-theoretic basis of music theory, it all hinges on the fact that certain simple fractional powers of 2 "accidentally" happen to be very close to simple fractions. I noticed a quarter century ago (but never published) that this Diophantine approximation problem is closely connected to the Riemann Zeta function, in that good values correspond to high values along lines whose real part is fixed. This relationship extends into the critical strip, and along the line Re(z) = 1/2, which allows some amusing formulas to come into play. One can distinguish different microtonal systems by the argument of zeta, and adjust them by slightly stretching or shrinking the octave to the nearest Gram point, with an eye to slight improvements of the approximations involved on average, in some sense of average. You may now double your fun by bringing in group theory, and noting that a microtonal system is also closely related to homomorphisms from finitely generated subgroups of the group of positive rational numbers under multiplication to the free group of rank one. The kernels of these homomorphims determine the relations between such systems - a system with 81/80 in the kernel behaves very differently in terms of harmonic theory than one without 81/80 in the kernel.

How come scientists can piece the logic together? Because of the Western "cognitive bias" (math professor Luigi Borzacchini) against the TRUTH of nonwestern music tuning as natural complementary opposites. Westerners have been brainwashed by schooling at a young age - the Pythagorean Theorem, etc.

oops!

Connes on Entropy, Noncommutative phase logic and Riemann Zeta Function - lecture

  The size of a step in octaves is 1/x, and hence the size of the octave in the zeta peak value tuning for Nedo is N/x; if x is slightly larger than N as here with N=12, the size of the zeta tuned octave will be slightly less than a pure octave. Similarly, when the peak occurs with x less than N, we have stretched octaves.

 https://en.xen.wiki/w/The_Riemann_Zeta_Function_and_Tuning#Relationship_to_Harmonic_Entropy
and
Connes lecture on noncommutative phase music theory math as the unified field theory