Steve Strogatz vs. Alain Connes, pt. 2: Music ratios are multiplicative noncommutative phase Yuan Qi

"Aside from their role as inverse functions, logarithms also describe many natural phenomena. For example, our perception of pitch is approximately logarithmic. When a musical pitch goes up by successive octaves, from one "do" to the next, that increase corresponds to successive doublings of the frequency of the associated sound waves. Yet although the waves oscillate twice as fast for every octave increase, we hear the doublings - which are multiplicative changes in frequency - as equal upward steps in pitch, meaning equal additive steps. It's freaky. Our minds fool us into believing that 1 is as far from 2 as 2 is from 4, and as 4 is from 8, and so on. We somehow sense frequency logarithmically." p. 134,
Math Professor Steve Strogatz, "infinite powers."
And now Fields Medal math professor Alain Connes stating the OPPOSITE:
"The only thing that matters when you have these sequences are the ratios, 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 [524288] is almost 3 to the power of 12 [531441]...... Musical shape has geometric dimension zero...There is a beautiful answer to that, which is the quantum sphere... .There is a quantum sphere with a geometric dimension of zero...I have made a keyboard [from the quantum sphere]....This would be a musical instrument that would never get out of tune....It's purely spectral....The spectrum of the Dirac Operator...space is not simply a manifold but multiplied by a noncommutative finite space......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..... the phase space of a microscopic system is actually a noncommutative space and that is what is behind the scenes all the time....A fascinating aspect of music...is that it allows one to develop further one's perception of the passing of time. ...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. [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!... .Algebra and Music...music is linked to time exactly as algebra is....So for me, there is an incredible collusion between music, perceived in this way, and algebra....I believe that this variability is more fundamental than the passing of time. And that it's behind the scene, meaning that the passing of time is a corollary of this..."
Fields Medal math professor Alain Connes (compilation of quotes)
Connes practices Chopin at home - with Chopin using complex harmonics that are very subtle. Here is what Professor Steve Strogatz emailed me in response to his first music pitch gaff:
"I didn't say more about music because I know so little about it!
Hope you enjoy the rest of the book."
So in fact logarithms originate from music theory and not the other way around! Math Professor Luigi Borzacchini:
"How did the Greeks discover incommensurability?" This is one of the most puzzling 'scripts' of the history of mathematics. The 'movie' usually shows a Pythagorean (Hippasus or Archytas for example) drawing a square with its diagonals (or a pentagon with its golden sections on sides and diagonals) (von Fritz 1944), or drawing dots in a square (Knorr 1975), or even making some computations (successive subtractions, ¢nqufa…resij) (Fowler 1987), and exclaiming: “But this is impossible! If I am not wrong, this means that geometrical, continuous magnitudes cannot be reduced to numbers, discrete entities! Pythagoras was wrong!”. Then a meeting of the sect takes place and all Pythagoreans swear to keep the secret of the 'scandal'. A Grundlagenkrisis for the ancient Pythagoreanism follows, for whose solution a brand new axiomatization will be necessary, which will lead to Eudoxus and Euclid.
This movie deserves great attention because its scenes are the background of our modern perception of the mathematical continuum, and, at the same time, these scenes are forced by this perception. To question the movie means also to discuss the most basic and undisputed premises of our current philosophical view of mathematics.
It is the aim of this paper to try to shed some light on the connection between the historical interpretation of the discovery of incommensurability and our idea of continuum: this is what I mean by a ‘cognitive’ approach."
Incommensurability, Music and Continuum: a cognitive approach. Arch. For History of Exact Sciences, 61 (2007)

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"This corresponds to the commutative property of addition of numbers. (a+b = b+a), and we may consider sentence
(2) to be a paradigm proof that this property applies to ratios." So here McKirahan is claiming the logarithmic additivity is what matters in music and NOT the pitch as absolute root tonic of the One - just as Strogatz is claiming it is the logarithmic OCTAVE that matters and NOT the multiplicative ratios as absolute pitch to the One that is Noncommutative phase - as Alain Connes claims.

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"(2) For from string 1 to string 4 is a grasp, from string 4 to string 7 is an interval
of the high-pitched strings, from string 7 to string 5 is a grasp, and from
PHILOLAUS ON NUMBER
RICHARD MCKIRAHAN
So Philolaus had to FLIP the Lyre around to create the "liar of the lyre" - the right and left hands thus also flipped
"The second thing to notice is that “interval of the high-pitched strings” no longer applies only to the interval of the four highest-
pitched strings; it also applies to the interval of the five lowest-pitched strings!"

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"Step twelve uses 2/3 and provides about 527.1 hertz. Note that the true octave is at 520 hertz. Using this system would never permit derivation of the true octave. But the method used here continually divides frequencies by two (or multiplies string lengths by two) to make a gamut all the notes of which fall within one octave, so it is clear that the early Chinese had a clear idea of how to define and use the octave. The values derived in this twelfth step are not used in normal musical practice. "

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"So instead of taking 12:9, which is 3/4 of 12, we take 8:6, which is 3/4 of 8. And so by adding the length 12 to 8 [as geometric magnitude not wavelength!!] with the length 8 to 6, [as geometric magnitude, not wavelength!!] we get the length 12 to 6, which corresponds to the ratio 2:1."
and
"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."
Professor Richard McKirahan

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"since (1, 5) = (7, 4) and since (4, 1) = (5, 7)." Only they are NOT the same since C to G does NOT equal c' to F and since F to C does not equal G to c'. They are different pitches to the one. Richard McKirahan tells us to "ignore absolute pitch." But nonwestern music tuning is based on absolute pitch! So that there is never a perfect fourth overtone to the root tonic.

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"Just as (1, 5) = (5, 1), 25 so (1, 5) + (5, 7) = (5, 7) + (1, 5); they are both equal to O, another instance of commutativity." OK so this claim by Philolaus and McKirahan would be the SAME as Strogatz claiming that the melody opening of Star Wars followed by "Here Comes the Bride" is the SAME as flipping them around so that "Here Comes the Bride" is followed by the "Star Wars" opening melody ratio. But obviously it's NOT the same melody if you flip them around because the pitch is different relative to the ONE root tonic.

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"ascending via one interval (a fourth above the bottom note), and descending via another (a fifth above the bottom note)." So here Professor Richard McKirahan practices the "bait and switch" of Philolaus - because he says "via another" instead of via the OCTAVE descending and thus "descending an octave beginning at the bottom note" means that Philolaus has FLIPPED his Lyre around!! So that the octave is now the bottom note but NOT the root tonic (meaning the "bottom" is not the lowest frequency or longest string). So in other words he is ASCENDING his actual playing of the instrument as the "grasp" but because he flipped the lyre around he is now descending the frequency. "In the first case we go up a fourth and then a fifth, in the second we go up a fifth and then a fourth; it makes no difference which way we go, the result is the same." So here McKirahan (and Philolaus) are claiming that the "result" is that the octave is a geometric magnitude that no longer maintains the same root tonic relation of the PITCH. So that (1, 4) = (7, 5) = S (Grasp) when in fact 1 to 4 is C to F and 7 to 5 is c' octave to G (NOT F). So they are NOT equal as pitch to the root tonic. (4, 7) = (5, 1) = H (upper hand). Again they are NOT equal because 4 to 7 is F to c' octave while 5 to 1 is G to C. Both are a Perfect Fifth but the pitch is different relative to the root tonic. So Philolaus and McKirahan are saying IGNORE the natural overtone series of the root tonic based on listening to the ONE and instead just focus on the geometric tuning of the materialistic strings.

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OF A NON-COMMUTATIVE VERSION
OF THE PHASE DOUBLING We prove that the
quantum dynamical entropy equals the classical value log 2

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Hilarious - Adam Neely just posted a "devil's tritone" debunking vid - he repeats the Platonic 9/8 cubed math to create the tritone as the square root of two. But he has NO conception of noncommutative phase yet! So I posted a bunch of noncommutative phase music theory quotes. And he just deletes them. Maybe slowly they'll sink in? I doubt it. Hilarious.