another mathematician Simon Willerton ignores noncommutative phase of music theory as the Liar of the Lyre! Classic expose

 

 So we have that claim https://golem.ph.utexas.edu/category/2010/02/a_look_at_the_mathematical_ori.html

And this claim:

 

 So by assuming a SYMMETRIC squaring of the half-tone thereby the noncommutative Subharmonic of 2/3 as C to F (that is doubled to 4/3) can be ignored!!

The "pretty close" turns out to be a quarter tone over the spread of the 12 notes of the scale as Sir James Jeans points out - and the disharmony continues in both directions as infinity - or the "deep pre-established disharmony" (math professor Borzacchini).

So we know from Professor Richard Mckirahan that Philolaus FLIPPED the Lyre around. So what does the mathematician do? 

 

 He says it's like going DOWN from E to B or from A to E but he neglects to mention that while the numeric ratios of the "two outer strings" maybe a 4/3 as a Perfect Fourth in the first case going Down to E from B is actually a Perfect Fifth - NOT a Perfect Fourth as 4/3. Oops.

This is another example of what I call the "Bait and Switch" as the Liar of the Lyre at the origin of Western science. Borzacchini calls it a cognitive bias against music.

Simon Willerton

http://www.simonwillerton.staff.shef.ac.uk

I am a pure mathematician interested in various aspects of geometry, topology, category theory, metric spaces and quantum algebra.

 

Dear Professor Willerton: Your music theory blog post says you are "going down" on the Lyre and then you are "getting ahead" of yourself. Professor Richard McKirahan did a translation of Philolaus showing that indeed Philolaus flipped the Lyre around to achieve the Pythagorean tuning you refer to based on 4/3 (and thus introducing the concept of geometric magnitude as the secret music origin of Western math - see math professor Luigi Borzacchini on incommensurability as a deep pre-established disharmony.

https://golem.ph.utexas.edu/category/2010/02/a_look_at_the_mathematical_ori.html

He says it's like going DOWN from E to B or from A to E but he neglects to mention that while the numeric ratios of the "two outer strings" maybe a 4/3 as a Perfect Fourth in the first case going Down to E from B is actually a Perfect Fifth - NOT a Perfect Fourth as 4/3. Oops.

This seems a simplistic error unless we consider Connes, etc.

On the other hand, the ancient Pythagorean musical scale, naturally leads to a simple quantum circle.

By taking the inverses L to 1/1 + L and 1/infinity=0, we can identify M = {0, 1, 1/2, 1/3,...}. The geometrical picture is that we have a circular object, unifying infinitely circular 'oscillating modes.' The limiting oscillating mode is the classical mode....All other modes are purely quantum 'virtual modes,' so we can not distinguish separate fibers over the classical points labeling these modes. The entire structure is a unified and irreducible quantum circle....

The oscillating modes base space M...will be quantum (noncommutativity of the algebra V).

There is something profoundly quantum in all music.
https://books.google.com/books?id=Xf06DwAAQBAJ&pg=PA104&lpg=PA104&dq=homological+algebra+noncommutative+music&source=bl&ots=KYiXMI021b&sig=ACfU3U3RuUDPAJliQHGMPmZz6QCBEZQF5w&hl=en&sa=X&ved=2ahUKEwipkZOm6uroAhVWXM0KHW3iAzcQ6AEwE3oECAwQNA#v=onepage&q=homological%20algebra%20noncommutative%20music&f=true

and
http://www.math.unam.mx/~micho/subq.html

Physics Beyond the Limits of Uncertainty Relations

by Micho Durdevich