So because the left hand is odd and the right hand is even therefore the equation is noncommutative. Put more simply, since 2 does not go into 3 then the multiplies of 2 and 3 also remain asymmetric in their value. The reason they are asymmetric is because of the octave value changing in relation to the 3.
"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 then it was recently claimed to me that if there is a Hertz harmonic relation between two frequencies then that same harmonic pitch does not hold for other Hertz values. This covers up that the INVERSION has to occur to the octave in order to achieve the Hertz values. So we can see the above crucial difference is the SAME difference I have pointed out for the Pythagorean Comma in Sir James Jeans calculation versus the typical logarithmic assumption. The above logarithmic assumption already assumes that the Octave Pitch can simply be reduced to one value!
So Alain Connes, et. al., present the tritone pitch ratio as the basis for noncommutative phase logic.
Whereas the FIRST logarithmic equation does NOT make that assumption and so maintains a 3/2 fraction for the Perfect Fifth (pdf link) (since based on noncommutative phase the 3/2 is a different frequency pitch than 2/3 in relation to the root tonic or octave).
https://www.whitman.edu/Documents/Academics/Mathematics/bartha.pdf
So by explaining that the Perfect Fourth as 4/3 is allowed by using the INVERSE of "rule two" - this is what I call the "Bait and Switch" - which is NOT mentioned is that going DOWN a Perfect Fifth is a different PITCH to the root tonic as the Perfect Fourth and so it can not be simply "doubled." In other words a Perfect Fifth is NOT a Perfect Fourth - our ear hears the different in relation to the root tonic due to the difference in frequency overtones and undertones. So that means a different "octave" has to be used.
So in this cause the "rule 1" is now applied to G instead of C so that G is the new octave. In the way Philolaus set it up by flipping his Lyre around then F is the new octave instead of C. So it's 0 to 8 for 3/4 as 6/8. So either way the root tonic has to be changed which then changes the pitches of the Fifths to the octaves, in order to achieve the 9/8 as irrational magnitude for geometric magnitude pitch (not frequency/time pitch).
http://elixirfield.blogspot.com/2019/11/reviewing-secret-noncommutative.html
https://elixirfield.blogspot.com/2019/05/a-chaos-scientist-freaks-out-about-what.html
So then as I quote Connes - he REVERSES the order of the 2 and 3 values for 3/2 or 2/3.
Connes:
the ear is only sensitive to the ratio, not to the additivity...multiplication by 2 of the frequency and transposition, normally the simplest way is multiplication by 3...2 to the power of 19 is almost 3 to the power of 12....time emerges from noncommutativity....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 qn for the real number q=2 to the 12th∼3 to the 19th. 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.
So my academia upload gives more details.
https://www.academia.edu/41186978/Two_Three_infinity_How_music_is_the_formal_language_of_the_unified_field_theory_The_Noncommutative_Nondualist_and_Nonlocal_Positive_Pressure_Zero_Mass_math_music_model_of_Fields_Medal_math_professor_Alain_Connes
2 to the power of 19 [524288] is almost 3 to the power of 12 [531441]...
So when I had "cut and paste" from his blog then the math graphics got lost.
for the real number .
time emerges from noncommutativity....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 q (to the n) for the real number q=2 to the 1/12th∼3 to the 1/19th.[the 19th root of 3 = 1.05953 and 12th root of 2=1.05946] 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....This means it is a zero dimensional object! But it has a positive volume!
So when we invert the geometric symbols we are also inverting the fractions so that it's 2 to the 19th divided by 3 to the 12th OR 2 to the 1/12th divided by 3 to the 1/19th."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."
By the way - this is the SAME argument I made to the math teachers authoring their book on the Pythagorean Theorem - that you can not just invert a geometric symbol without realizing that it is noncommutative: Hidden Harmonies: The Lives and Times of the Pythagorean Theorem - by Ellen Kaplan, Robert Kaplan.
So in this talk he [Sir Roger Penrose] demonstrates why mathematical induction logic is limited. I had sent a letter making this same claim to the Kaplans married couple that crank out "popular" math books. haha. [my blog post in August 2017]
https://ecoechoinvasives.blogspot.com/2017/12/hypatia-reincarnated-finally-good.html
It’s tangent is CA/BC = m/1 = m. Therefore, the slope is the tangent of the angle of slope. And so we can see what just happened - the Y value got reduced, as a function of time, to a limit of zero as a pure geometric magnitude "point" of no dimension! Aka "m."
as long as it is a "fixed point" (in time).
And that my friends is the bait and switch. There is no "fixed point in time." There is eternal motion. The only way we can experience a true "fixed point" is if there is no space at all - when light is turned around back on to itself - but this creates reverse time energy as noncommutative phase - the superluminal pilot wave from the future!
I challenged the Kaplans about the very same problem of assuming a commutative value of a geometric point with a one to one conversion to number. In other words is infinity a symmetric inversion to zero? No. So you can have 3/1 = the same OCTAVE by using "G" = C for creating irrational geometric magnitude for 9/4 (from D to C from the G octave value of 6 to 1 or 9/6 for D to G). But as music theorists point out you can NOT have 4/3 as the Perfect Fourth because 3 can not be in the denominator as the octave multiple of the 1 in geometry!
In other words the C octave to G harmonic used for the 9/4 (D to C) ratio is by claiming the WRONG harmonic resonance value of 3 for the 1 to infinity. So instead of a 3/1 value it is a 9/6 value with the 6 as a harmonic of the 3 (G to G' new octave). Then the 9 is the "bait and switch" to 9/4 and halved back into the same octave of the C as 9/8 for irrational geometric magnitude - thereby covering up the noncommutative phase truth of reality.
So then when Connes states in regards to music theory - that it is Noncommutative - this is what he is referring to!!
"It is precisely the irrationality of log(3)/ log(2) which is responsible for the noncommutative [complementary opposites as yin/yang] nature of the quotient corresponding to the three places {2, 3,∞}. The formula is in sub-space...."
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