Tuesday, August 20, 2019

Soundless Harmony and Noncommutative Phase as ancient alchemy: Revisiting Fabio Bellissima on the secret music origins of Western math




So this is precisely the same argument I made - well I didn't rely on Euclid but modern analysis of Euclid - for a math paper that math professor Joe Mazur asked me to submit for publication. It's original form is online somewhere - I found it a few years ago on some forum. My Archytas analysis - when I had a dream of an equation and I sent it to Borzacchini, another music-math professor who has recently retired. I wonder if Bellissima references Borzacchini! Also I wonder if Bellissima is willing to acknowledge the noncommutative phase truth origin of music theory math logic!!

Let's take a look at a few of his papers on this topic.

https://sci-hub.tw/10.1080/17498430.2015.1044697

This first one is the Euclid analysis above. I can't wait to dig in!

Propositions VIII.4–5 of Euclid's Elements and the compounding of ratios on the monochord

ArticleinBSHM Bulletin Journal of the British Society for the History of Mathematics 30(3):1-17 · August 2015



So what I like about his analysis so far is he is getting into the nitty-gritty of the cognitive style involved in the mathematical logic. Most math papers just whizz through the logic as if they're a computer doing calculations. Bellissima is willing to slow down to analyze just what type of thinking is going on!! As Borzacchini points out - this "willful ignorance" about the music origins of math is due to a "cognitive bias."

So next Bellissima emphasizes that in Music the "interval" or pitch (he does not use that term yet) is PERCEIVED (that implies pitch) to be the same if the RATIO is the same (not the "difference"). So here he is explicating the geometric connection to music.

And then we get to the zinger:



Ok - fascinating stuff if you want to truly dissect Euclid, which he does.

So I had this precognitive thought yesterday - I was thinking how the concept of what I've been researching and conveying - the REASON that Westerners can not delve into this easily - is because we automatically associate music theory with sound, as a materialistic tuning device. Rather Pythagorean theory is the origin of sound from harmonic numbers - not sound itself. It is rather listening to the origin of sound. Listening does not require sound but it is STILL based on harmonics. And this is what becomes meditation. Or as Bellissima cites this concept:

Soundless Harmony.



Ok so Bellissima is emphasizing that the fact that Euclid did not associate compounding ratios with multiplication and that the same is true in music theory, therefore corroborates the music origins of the compounding ratios as theorems.

So then Bellissima goes into a detailed discussion of Zarlino's use of Euclid....

And wraps up with this:




So he is then HINTING at noncommutative phase logic - through his analysis of Zarlino. This is quite fasincating.



So by concatenation he also means "the Interval Question" (which is based on the order of the numbers)....in which case you can get the same result from multiplication as with compounding but the multiplication implies a reversal of order that is commutative - something that MISSES the noncommutative process or "mediation" - the means being different - as Zarlino had emphasized.

OK Now onto Bellissima's next paper!

It's on "mode" - I'm not sure I'm going to include this as it does not seem focused on the issue at hand... What's after this?

Logarithmic anamorphosis of Pythagorean intervals

ArticleinBollettino di Storia delle Scienze Matematiche 31(2) · December 2011
right - an earlier version. We'll see what we can find. No link to read it.

same with the other one.... So it's just an early summary of Zarlino.


Dear Professor Bellissima: Thank you for your wonderful analysis on the music origins of Western math. I did not notice you citing math professor Luigi Borzacchini? Math professor Luigi Borzacchini: 
"Boethius’ text that I am going to analyze shows that the early musical theory of incommensurability was somehow known, even though it had been overcome by a sudden rupture." 
 (see below). It's readable also online. Also Professor Richard McKirahan: 
 "The word translated epogdoic is not a musical term but a mathematical one. An epogdoic ratio is the ratio of 9 to 8. The occurrence of a mathematical term here is unexpected. It has been treated as an unimportant anomaly but in fact it is the key to the entire fragment [Philolaus]....The word magnitude normally refers to physical size, but here it is given a new application, extending the notion of magnitude to include musical intervals." 

Again, Professor Borzacchini states:
 " These remarks raise the question of the difference between the ancient Pythagorean ‘musical’ perception as displayed in the Pythagorean idea of ‘linear number’ in Boethius [Philolaus] or in Nicomachus, and the modern ‘geometrical’ perception of the linear numerical magnitudes." 
So then in my own mathematical analysis: http://elixirfield.blogspot.com/2018/06/why-hertz-hurtz-as-ditonic-comma-lie.html scroll way down - I then quote you from 1999:
This musical property is the counterpart of the principle mathematical characteristic of the Pythagorean diatonic, very Pythagorean indeed, constituted by the fact that each interval of the scale is expressed by the ratios of type 2 to the m divided by 3 to the n OR 3 to the m divided by 2 to the n.
So my question for you is - do you realize the importance of this empirical truth of "noncommutative phase" being covered up? Fields medal math professor Alain Connes has rediscovered this noncommutative phase truth of music theory logic as the foundation for his new unified field "relativistic quantum" science!  https://www.youtube.com/watch?v=bIziuv-WLMM
I quote him on my blog - for further details. I also have a book "Ancient Advanced Acoustic Alchemy" - linked as a free read - detailing how his noncommutative phase secret of music theory was the key for meditation training as the core of our ancient Orthodox Pythagorean philosophy (also the three gunas of India and yin-yang-Emptiness of Daoism, going back to the San Bushmen original human culture).
thanks and I look forward to your response.
I did correspond with math Professor Borzacchini, starting in 2001 or so. He is now retired.

drew hempel

Incommensurability, Music and Continuum: A Cognitive Approach

ArticleinArchive for History of Exact Sciences 61(3):273-302 · May 2007 with 45 Reads



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