He leaves out music theory!
Let's make this easy! In standard music theory you rely on logarithms and exponentials.
So you SQUARE the Perfect Fifth as 3/2 x 3/2 and then you HALF it back into the "same" octave to get 9/8 as the major 2nd music interval.
(3/2 x 3/2) x 1/2=9/8
NOW let's consider the Daoist way of the same 9/8 result from a noncommutative process.
You take 3/2 x 3/4. Why? (yin x yang=Emptiness as non-local noncommutative nondualism!)
Because actually the frequency in this case is inverse to the wavelength so it is 2/3 as wavelength x 4/3 as wavelength (of the 2/3). So you get ... 8/9 as wavelength as 9/8 as frequency or 3/2 x 3/4.
Chinese philosophy Professor Patrick Edwin Moran
The Chinese rule is very simple: Take 2/3 of the length of the open string, and put down a fret there. Then take 4/3 of that second length and put down a fret there. The third step is to take 2/3 of the last length, then 4/3, and so forth. Let's see how that works.
The Chinese system is based on the mathematical method of working back and forth by taking 3/2 of a base frequency, 3/4 of the frequency so produced, and so forthSo why is the Chinese music theory noncommutative while the Western music theory is not?
For the Western music theory when you square 3/2 (as a Contained Symmetric Geometric Space) to 9/4 and then HALF it - you are "halving" from the 3 octave - the fifth of the G octave. So the root tonic was changed by changing the direction of the octave! This is why the Overtone Series does NOT allow the Perfect Fourth harmonic while for the Harmonic Series the "direction" of infinity is reversed (since the Harmonic Series diverges otherwise and the geometric can then not be "contained."
In order to determine the frequency of the G key in the second octave, we need just apply rule 1 to g' (which would give us the key g" with a frequency of 3).
So this math pdf ADMITS to changing the root tonic (c' to c") of the octave to g' to g" but then "pretending" it did not happen by then "halving" back into the same original root key of C octave - so that the 3/2 was now geometric mean squared - and NOT based on the original octave root tonic as a noncommutative phase truth of reality F=3=G at the same time!
By "adding" the Perfect Fifth as geometric mean squared then the goal is to "contain" infinity of noncommutative time-frequency through symmetric irrational magnitude math as geometry. This is the bait and switch - by squaring it first then you hide the noncommutative conversion of the octave. https://www.whitman.edu/Documents/Academics/Mathematics/bartha.pdf
This is why you can just multiply 3/2 x 3/4 for the same result because the direction of the octave as 4 is being reversed. So D to G is a Perfect Fourth as 3/4 of 2/3 (yin of yang noncommutative time-frequency) instead of 9/4 (as symmetric geometric magnitude, the D to C).
So in the Chinese music theory it is C and then G as 2/3 wavelength and 3/2 frequency and then 3/4 of G as the wavelength to get 4/3 frequency as D (the major 2nd to C). So you are never LYING about the root tonic as C - but rather revealing the truth as noncommutative phase of 4 to the 1 via the 3 (so that the octave has now changed to 3 as G instead of the 1:2:4 as C.
The Chinese and Pythagorean gamuts use the following ratios: 1/1 same
2187/2048 vs. 256/243
9/8 same
1968/1638 vs. 32/27
81/64 same
1771/1331 vs. 4/3
729/512 same
3/2 same
6561/4096 vs. 128/81
27/16 same
5905/3277 vs. 16/9
243/128 same
Yes but HOW they are achieved - that simple number of 9/8 - is very different!!
So this is why the typical Western Liar of the Lyre definition of the Pythagorean Comma just "collapses" the octave as geometric mean squared definition (not the truth of Noncommutative phase as 2, 3, infinity). So instead of 3/2 to the 12th - you get 3 to the 12th and 2 to the 19th (instead of to the 7th). Wiki on Pythagorean Comma:
It is equal to the frequency ratio (1.5)12⁄27
Reduced by using COMMUTATIVE geometric mean square math to:
The idea being that 3/2 does not matter on its own when we KNOW for a fact that 2/3 is ALSO the Perfect Fifth as C to F subharmonic - NOT just 3/2 frequency. And so F=3=G at the same time as the NEW octave that is noncommutative to the 1:2:4 original octave doubling/halving process.
So when Thomas Noll states the "fifth" is more elementary pdf he really is just repeating Archtyas' argument of the Perfect Fifth as defined as "Geometric Mean Squared" - NOT as inverse frequency/wavelength noncommutative phase logic (the truth of reality).
So then Peter Pesic tells us - Music and the Making of Modern Science google book
This then implied that without adding any new information (or hammers) that between the interval of the fourth and fifth emerges the ratio of 8:9, later called a tone or whole step because it is the step between these two intervals which according to Nichomachus "was in itself discordant, but was essential to filling out the greater of these intervals."p. 11
Boethius rejected the fifth hammer while Nichomachus accepted it - because 9/8 is the "vanishing mediator" that covers up the noncommutative phase truth of reality! Yin-yang-Void or the "three gunas" of India - the Tetraktys or Tetrad of Orthodox Pythagorean philosophy....
Boethius tells us that "the fifth hammer, which was discordant with all, was rejected."p. 11
Why the discrepancy? Boethius UNDERSTOOD that 9/8 was being USED as the "bait and switch" to create geometric mean squared - and he rejected it as not truly Pythagorean.
So on page 17 Peter Pesic admits that using 9/8 relies on the Geometric Mean Squared - and that is why it was rejected! But Peter Pesic (considering himself a highly sophisticated mathematical music analyst NEGLECTS to mention that 9/8 also is being used to cover up the NOncommutative Phase truth of 2/3 and 3/4 - what the Daoists and Orthodox Pythagoreans (and the three gunas of India) EMBRACE!!
And if you don't know about it - then you don't know what you're missing!
On this basis it seems plausible that the fifth hammer that Pythagoras discarded as "dissonant with them all" was irrational with respect to them....But, as the Greeks already realized, a perfectly equal division of a tone (as of an octave) would require the use of an irrational magnitude as will become of crucial importance in chapter 4.p. 17, Peter Pesic - Professor at St. John's College is supposed to be "fancy" at sophisticated math music but he covers up the Ancient Advanced Acoustic Alchemy truth!
Noll, T. (2007). Musical intervals and special linear transformations. Journal of Mathematics and Music, 1(2), 121–137. doi:10.1080/17459730701375026"The non-commutative interval group considers intervals as pathways rather than sums....we inspect also the free non-commutative group F = <P, Q> of ‘pythagorean pathways’, which is generated by two letters P and Q representing octave P8 and fifth P5, respectively."
url to share this paper:
http://sci-hub.tw/10.1080/17459730701375026
On the other hand, the ancient Pythagorean musical scale, naturally leads to a simple quantum circle. We explore different musical scales, their mathematical generalizations and formalizations, and their possible quantum-geometric foundations. In this conceptual framework, we outline a diagramatical-categorical formulation for a quantum theory of symmetry, and further explore interesting musical and geometrical interconnections.The Musical-Mathematical Mind: Patterns and Transformations edited by Gabriel Pareyon, Silvia Pina-Romero, Octavio A. Agustín-Aquino, Emilio Lluis-Puebla, chapter Music of the Quantum Circle by math professor Micho Durdevich
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.
Durdevich M: Algebro-Geometric Constructions of Subquantum Theories, Doctoral Thesis, Faculty of Physics, University of Belgrade, Serbia [in Serbian :)] (1993)
http://www.math.unam.mx/~micho/subq.html
No comments:
Post a Comment