Grant Sanderson 3Blue1Brown covers up noncommutative phase Yuan Qi truth of music as Steve Strogatz

But he does NOT mention that this can ONLY be derived from noncommutative phase!! Oops.

When you play the Perfect Fourth as 4:3 you are neglecting to mention that the Lower Frequency was derived from Noncommutative Phase of doubling the 2/3 as the Undertone of the 1:1 fundamental frequency ratio. See Professor Richard McKirahan's translation of Philolaus for details - the first Greek use of irrational magnitude math was from Philolaus. So you say the ratio is 4:3 but as an Overtone harmonic that is NOT the lower note in the scale. It is the 4:3 as G to C and so would have to be a perfect fifth to the octave higher. See Alain Connes, Fields Medal math professor talk on quantum music of the sphere as cited by Math PRofessor Micho Durdevich for details - as I quote Durdevich:

"However, even in this case there is a highly non-commutative world of higher order collectivity algebras B(n). This can be used to capture the geometry of rotations, like those appearing in the classical Pythagorean octave versus perfect fifth considerations."

"the Pythagorean music school was rapidly able to calculate the tone fa-sol as the difference between the fifth do - sol and the fourth do - fa, and consequently as the ratio 3/2 : 4/3 = 9/8 [logarithm]....The Pythagorean tradition denied that it was possible to divide the tone into two equal parts (semitones [based on rational ratios])....Dividing the Pythagorean tone into two parts would mean admitting the existence of the proportional mean between 9 and 8, that is to say, 9 : [a] = [a] : 8, where 9:[a] and [a]:8 are the proportions of the required semitone....Clearly [a]= [square root of 9 x 8] and therefore [a] = (3 x 2) x [square root of 2]!"

Math Professor Tito M. Tonietti, University of Pisa, Italy and

"However, he [Archytas] noted that the product of the arithmetic mean and the harmonic mean is equal to the square of the geometric mean, so this gave a way of dividing the fifth of 3:2 into the product of 5:4 and 6:5."

A Truman State University review on Scriba, Christoph J. “Mathematics and music.” (Danish) and

"... the tyrant in the Republic as the tyrant's suffering is exactly 729 times that of a philosopher, using the metaphor of ... The ratio 729/512, three whole tones (8:9) above 512....“Since 9 actually reduces to a wholetone of 9/8, its cube will reduce to (9/8)³ = 729/512, a [FAKE] Pythagorean approximation to the square root. of two, a problem which fascinated Socrates in the marriage allegory.”

Ernest McClain, The Pythagorean Plato: Prelude to the Song Itself (Nicholas-Hays, 1978), p. 36

" no matter how high one goes in the harmonic series, a fundamental pitch will not produce a perfect fourth above the fundamental. ..Just as Slonimsky opined, the perfect fourth above the tonic is nowhere to be found. ... Thus the perfect fourth above the tonic enters the scene, not as part of a stable major scale, but as a tempter, a seducer, a built-in modulation away from the true tonic. The perfect fourth, and not the tritone, is the true “devil in music.” It’s no “subdominant.” It’s the phantom tonic."

By Kenneth LaFave
on October 17, 2007

"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."

Professor Fabio Bellissima,"Epimoric Ratios and Greek Musical Theory," in Language, Quantum, Music edited by Maria Luisa Dalla Chiara, Roberto Giuntini, Federico Laudisa, Springer Science & Business Media, Apr 17, 2013
See Alain Connes lecture on Music of the Quantum Sphere for more details.

"...a "universal scaling system," manifests itself in acoustic systems...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].... 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] ..."

Fields Medal math professor Alain Connes (compilation of quotes)

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Thank you for sharing. The qigong master was part of a study at the University but he was supposed to do a "control" where he would see people but not heal them. The problem was that if he sees someone then when his mind detects the energy blockages the Emptiness is already healing the person! As physicist Olivier Costa de Beauregard emphasized, the paranormal is inherently precognitive. So also he had a study done by a Mayo Clinic medical doctor - Anne Vincent - on external qi healing of chronic pain. The study showed significant pain reduction on people who previously had no results from pain medication. But the skeptics complained that since the people WANTED to get healed therefore the study was a placebo effect. So Wilhelm Reich called this "Negative transference" - and Olivier Costa de Beauregard says the paranormal is constantly going on but is repressed by civilization. My argument is that the ecological crisis and social injustice is caused by the same reason that science is against the paranormal and this is explained by the noncommutative phase logic of music theory.
So what happened is that I studied music from age 5 and I took also music theory and studied from a former University music professor - taking private lessons in high school in orchestration, ear training, etc. And suddenly I had this realization that the Pythagorean natural number resonance was the secret harmony of the Universe due to the Perfect Fifth not being allowed as 2/3 but only as 3/2. This was a flash of an insight and so then I discovered Dr. John Beaulieu's book on "Biosonics" where he says that Yang is the Perfect Fifth as 3/2 and Yin is the Perfect Fourth as 4/3. So I realized that paranormal powers are from nonwestern meditation as orthodox Pythagorean philosophy. There is a meditation called the "small universe" meditation found in both China and India. The "three gunas" of India as the same as Daoism. I have a book on this called "Ancient Advanced Acoustic Alchemy" - it is free.
Stuart Hameroff - it turns out - got the SAME truth corroborated by an Indian scientist - dr. anirban bandyopadhyay with whom I corresponded. So as Hameroff says the truth is more like music as consciousness but most importantly it is "anharmonic" or Nonwestern music as the three gunas. So the Raja guna is 3/2 and the tamas is 4/3 and the octave is the Sattva as the Emptiness.
Anyway when I finished my Master's Degree to test out my music math hypothesis as alchemical meditation - I discovered yes this is real and I permanently transformed my psychophysiology - as an "enlightenment experience" in 2000. I opened up the third eye and achieved spiritual powers - I saw ghosts, had precognition and telepathy and did healing, etc.
So then I had to figure out how to transform this back into Western science so that I could explain it to people. I read one scholarly book a day and finally discovered Fields Medal math professor Alain Connes doing his youtube lectures on Quantum Music - he has several lectures on it. So he is the ONLY scientist who figured out the same secret - he calls it (2, 3, infinity). In other words because music is actually noncommutative phase then the future overlaps with the past as nonlocality reality of frequency-time energy. And so Connes says this is the basis for the unified field theory of relativistic quantum science but there has to be noncommutative calculus and a complete reversal of the symmetric based commutative algebraic geometry of the "Greek Miracle" so far. haha.
Of course Roger Penrose now admits that his Twistor model also relies on noncommutative quantum algebra but he says since he's a geometer then he doesn't really know how to do the noncommutative math. So I don't think Stuart Hameroff realizes this so much because it is NOT Platonic philosophy - as Penrose used to claim. haha. Actually - math Professor Luigi Borzacchini says there is a "cognitive bias" against the truth of the secret music origins of Western math. So that the "continuum" based on irrational numbers was actually from music theory that covered up the truth of noncommutative phase. Borzacchini calls this the "deep pre-established disharmony" as the "guiding evoltive principle" of science and he says the Platonic cover up of the music origins is "really astonishing" and "shocking." De Broglie did rediscover the truth with his "Law of Phase Harmony."

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In 1989 my first full time job was going door to door for Citizens for a Better Environment. In 1990 I lived in the wilderness in Alaska in a cabin for four months. In 1991 I became a worker for the University of Wisconsin-Madison Greens (and thus my FBI file began). 1992 I did a semester of School for Field Studies in Costa Rica - on conservation biology and "sustainable development" - 1993 I took environmental economics and finished a degree in 1994 with a focus on the "environmental option" of International Relations. 1996 I worked full time at Greenpeace and my boss said that his biggest concern was global warming.
By then I had been arrested a few times for protesting against nuclear waste storage in the Mississippi river on a native indigenous reservation - and against the Project ELF first strike nuclear submarine communication system. 1997 I was accepted to start a Master's Degree program that was self-designed focused on activism and I had co-founded the MN Free Burma Coalition. 1998 - got the University of Minnesota to divest $1.5 million from Total Oil for using slave labor and ecological destruction in Burma.
1999 was hired as an Op-Ed Minnesota Daily staff writer serving 50, 000 people as I worked as Resource Center of the Americas a nonprofit against the human rights abuse of US genocidal imperialism. 2000 got the University to join the Workers Rights Consortium as an independent nonprofit to boycott slave wage conditions for sports apparel.
Then I finished my Master's Degree by doing intensive nonwestern meditation through the African Studies department - whereby I discovered that Western consciousness is based on mass mind control. I discovered that ghosts are real as is spiritual healing. Also in 1998 I got arrested protesting against the clear cut of the last old growth forest in the Twin Cities - also the spiritual gathering for the "origin of creation" at the Mississippi and Minnesota river.
I had a dream of that protest - in 1995 - the dream was more real than being awake - of my Earth First! activist friends standing on the roof of a house with native indigenous activists - holding a banner to stop the destruction of the forest. In 1999 then I entered semi-retirement by working part time at Clean Water Action for ten years till 2009. During this time I rode an old 3 speed bicycle while I dumpster dived food - and did that year round for ten years while I read one scholarly book a day.
Then in 2009 I rode the old three speed bicycle out of the Twin Cities - and I took a pick axe and bow saw to the European Invasive buckthorn. I planted an acres of chestnut trees and berries - and grew a big vegetable garden using humanure compost. I worked at an organic fruit distribution warehouse and continued doing full lotus psychic pineal gland healing.
Yes I am definitely a troll - now I grow Shiitake mushroom in a swamp forest. In 1990 at Hampshire College for my first year music composition training I had composed a fugue for Moog synthesizer and Mayan flute whistle called "Troll Dance" - the music was on 4 trac but out of sync to the actual written fugue composition. My advisor was David Muesham as assistant to music professor Margo McKay Simmons.
Turns out David Muesham also got into yoga and physics - and now publishes on music meditation healing. The secret is "noncommutative phase" as relativistic quantum physics. I have free research on this - thanks for asking.

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yeah only I discovered this from my own music training while I was in high school. So as I already explained to you if the Perfect Fourth is LISTENED to - as "above" the root tonic then since it is NOT a natural overtone of the root tonic therefore the Perfect Fourth is the new root tonic. I realized this from my own training in PLAYING music. This is why for the equal-tempered tuning that you are praising - the octave is the Geometric Mean Squared while the Perfect Fourth has to be 4/3 as the Harmonic Mean and the Perfect Fifth has to be 3/2 as the Arithmetic Mean so that the multiplication of the Perfect Fifth and Perfect Fourth can be converted into logarithms within the SAME scale. And this then covers up the noncommutative phase truth of the Perfect Fourth as necessarily derived from the lower octave that is actually a Perfect Fifth in the opposite direction.
Again Dr. Oscar Abdounur:
The Emergence of the Idea of Irrationality In Renaissance Theoretical Music Contexts
"For instance, if one begins with F an octave lower – instead of c –, which corresponds to the ratio 3:4 decompounded by 1:2, that is, 3:2, then after compounding it with a fifth, generated by 2:3, it will result in 1:1, that is c, from which the process initiated. and the continuation of the process will happen as in the previously mentioned scale."
So that explains again that the Perfect Fourth as 4/3 is derived from the Perfect Fifth as noncommutative phase in the opposite direction.
The Emergence of the Idea of Irrationality In Renaissance Theoretical Music Contexts
OScar JOãO abDOuNur

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​ @Topher The11th yeah only I discovered this from my own music training while I was in high school. So as I already explained to you if the Perfect Fourth is LISTENED to - as "above" the root tonic then since it is NOT a natural overtone of the root tonic therefore the Perfect Fourth is the new root tonic. I realized this from my own training in PLAYING music. This is why for the equal-tempered tuning that you are praising - the octave is the Geometric Mean Squared while the Perfect Fourth has to be 4/3 as the Harmonic Mean and the Perfect Fifth has to be 3/2 as the Arithmetic Mean so that the multiplication of the Perfect Fifth and Perfect Fourth can be converted into logarithms within the SAME scale. And this then covers up the noncommutative phase truth of the Perfect Fourth as necessarily derived from the lower octave that is actually a Perfect Fifth in the opposite direction.
Again Dr. Oscar Abdounur:
The Emergence of the Idea of Irrationality In Renaissance Theoretical Music Contexts
"For instance, if one begins with F an octave lower – instead of c –, which corresponds to the ratio 3:4 decompounded by 1:2, that is, 3:2, then after compounding it with a fifth, generated by 2:3, it will result in 1:1, that is c, from which the process initiated. and the continuation of the process will happen as in the previously mentioned scale."
So that explains again that the Perfect Fourth as 4/3 is derived from the Perfect Fifth as noncommutative phase in the opposite direction.
The Emergence of the Idea of Irrationality In Renaissance Theoretical Music Contexts
OScar JOãO abDOuNur
and so
“Any who doubt that the musical ratios are all of greater inequality, i.e., that the antecedent or first term in each is greater than the consequent or second term, should consult Archytas DK 47 B 2. This Fragment requires that the ratios be of this form if the assertions about the three means [arithmetic, harmonic and geometric] are to be true. Accordingly, the ratios assigned to the octave, fifth, fourth and minor sixth, must be 2:1, 3:2, 4:3 and 8:5, and not 1:2, 2:3, 3:4 and 5:8, respectively, as Mosshammer and others would have them.”

Alan C. Bowen, "The Minor Sixth (8:5) in Early Greek Harmonic Science, " The American Journal of Philology, 1978.
Geometric mean = alogon as irrational number.

9/8 cubed = square root of two = Devil’s Interval tritone

5/4 = cube root of two

3/2 squared = 9/4 halved into octave as 9/8.

3/2 x 4/3 = 2 (geometric mean squared).

log(3:2×4:3)=log(2:1)

log(3:2)+log(4:3)=log(2:1)

Math professor Luigi Borzacchini called this cover-up by Plato and Archytas, “shocking” and “really astonishing” and the new alogon-based math created a “deep preestablished disharmony” that guides the evolution of Western science.

Simon Stevin in the 16th C. Renaissance rediscovered Archytas 5/4, cube root of 2 secret, as the foundation for logarithmic equal-tempered tuning. 1605, referring to his French work on arithmetic (1585, this ed. Vol. II B) where he had shown that the requirement of twelve equal ratios leading from 2 to 1 involves the twelfth root of 2. (unpublished until the 20th C.).

The

secret of the sect music equation

for the compounding proportions of the sidelengths is this:

A:X::X:Y::Y:2A = 1:5/4::5/4:8/5::8/5:2.

Euler gave Mendelssohn Mose the idea of using the ancient Delian combining problem of doubling the cube from Archytas to question and solve the equal temperament tuning.

A surviving fragment of the work of Archytas of Tarentum (ca. 350 BC) states, “There are three means in music: one is the arithmetic, the second is the geometric, and the third is the subcontrary, which they call harmonic” [7]. The term subcontrary may refer to the fact that a tone based on this mean reverses the order of the two fundamental musical intervals in a scale. It is believed that Archytas or one of his contemporaries gave the name “harmonic” to the subcontrary mean because….[see the book, "Infinite Series"].

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"However, even in this case there is a highly non-commutative world of higher order collectivity algebras B(n). This can be used to capture the geometry of rotations, like those appearing in the classical Pythagorean octave versus perfect fifth considerations." Music of Quantum Circles October 2017 In book: The Musical-Mathematical Mind (pp.99-110) Professor Micho Đurđevich Institute of Mathematics, UNAM, Mexico

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I read a military document that was published around 2004 I think - basically stating in terms of Nature versus Humans versus Machines - the machines will win out. I published an expose called the "Actual Matrix Plan" - about a think tank study that corroborated my Master's Thesis - so for example we know now that "truth" of reality is now being determined by the strongest negative emotions as machine algorithms and so the Matrix is literally feeding off the human emotional and brain energy to create reality.
So now we rely on supercomputers using chaos math iterations to determine our supposed correct policy science (like abrupt global warming). But the supercomputers can not model Nature - as ecology is too complex - and so the science will always be behind the ever accelerating ecological crisis. We have maybe around five years left because the arctic is about to go ice free for the first time in three million years.
A good book on this is "The Religion of Technology" by former MIT History professor David F. Noble. Essentially it's Platonic symmetric mathematics from the wrong music theory - I'm currently reading Math professor Steve STrogatz's book, "infinite powers" on the calculus as a promotion of Platonic philosophy - and Strogatz gets the music theory wrong. Fields Medal math professor Alain Connes is the only person I've found who promotes the truth of the music math as noncommutative phase.
Eddie Oshins worked at Stanford Linear Accelerator Center on what he called "quantum psychology" and he also taught Neigong as Wing Chun internal martial arts - and Oshins realized that noncommutative phase was the secret of Neigong alchemy meditation. So this is also based on negentropy as Olivier Costa de Beauregard realized. Civilization actually promotes Entropy against the Negentropy of Nature despite science claiming the opposite - hence our abrupt global warming crisis. The Emptiness is the same as noncommutative phase - as Sir Roger Penrose recognizes and thus he calls it the "Measurement Problem" with consciousness defined by the Godel Incompleteness Theorem.
So yes the technology will "mimic" enlightenment but with the opposite trajectory - through the destruction of ecology - whereas our original enlightenment training was in promotion of ecological harmony. So science relies on left brain dominance and right hand dominant technology while ecology is based on left-handed amino acids and right-brain dominant ecological consciousness. So the left brain is proven to lie about reality - and the Big Lie is now the Matrix taking over. I agree with you - even H.W.L. Poonja, the top student of Ramana Maharshi, stated that the pollution now is too bad for a yogi to really achieve supreme complete enlightenment - aka the immortal "yang shen" golden body. As he pointed out - yes there's still a few meditation masters hiding out in the mountains - as in China also - yet they can not change what I call the "trajectory of tantric technology."
What I did was sit in full lotus in public in Minneapolis and so I then sent out energy out of the pineal gland - as a higher frequency healing - and I took in lower frequency energy blockages and transformed them through my heart. I did this to promote revolution in Minneapolis because the healing energy is based on the right side vagus nerve as inherent female orgasmic bliss energy. I used up my own body's energy by doing this but I have no regrets. Through meditation then I can reconnect to the Emptiness that is impersonal - if I need to.
But I was just doing psychic healing as I had fallen out of enlightenment from the spiritual healing. I was only in the Spiritual healing level for a few weeks but I received very strong "negative transference." Essentially I was doing Exorcisms of the evil - for example the liver blockages from alcoholism that causes people to be violent, etc.
Yes modern civilization is based on evil - from just our diet of salt, sugar, alcohol....but the original sin is male ejaculation addiction due to lack of spiritual training. Our original human culture - the San Bushmen - requires ALL males to do the spiritual healing training and thus the culture is controlled by the females and there is no war and it is peaceful as the book, "The Harmless People" by Dr. Elizabeth Marshall Thomas reveals. The truth of our Original Human Culture has been covered up and lied about by even most scientists just as most scientists do not know about noncommutative phase.

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no matter how high one goes in the harmonic series, a fundamental pitch will not produce a perfect fourth above the fundamental. ..Just as Slonimsky opined, the perfect fourth above the tonic is nowhere to be found. ... Thus the perfect fourth above the tonic enters the scene, not as part of a stable major scale, but as a tempter, a seducer, a built-in modulation away from the true tonic. The perfect fourth, and not the tritone, is the true “devil in music.” It’s no “subdominant.” It’s the phantom tonic."
IV: The Phantom Tonic
By Kenneth LaFave
on October 17, 2007

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" .. Pythagorean tuning were first considered by musical theorists [445, 7] in order to answer the need of a new musical language provided by polyphony. anachronistically speaking, this means that, supposing both these both cycles meet, there would be m and n integers such that (2:3)n = (1:2)m, that is, 3n = 2m+n, which is impossible, since the left term is odd and the right is even. "

- Dr. Oscar Abdounor

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Colloquium 7: Philolaus on Number. (2012). Proceedings of the Boston Area Colloquium of Ancient Philosophy, 27(1), 211–239 Professor Richard McKirahan: "Can we do something similar
with Philolaus’s other claim that 3:2 + 4:3 = 2:1? We might think that this
would amount to the claim that 12:8 + 12:9 = 12:6, but this is not an obvious
result, since it is not immediately clear how to perform the addition. But
think what the addition involves. We begin by taking the length corresponding
to the ratio 3:2, namely the length 12 to 8. In other words, we start at 12
and take 2/3 of its length. Then we add a length corresponding to the ratio
4:3, but this time we are starting not at 12 but at 8 and we want to take 3/4
of that. 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 and the length 8 to 6, we get
the length 12 to 6, which corresponds to the ratio 2:1. This is the correct
result and further, it turns out that these procedures are correct and generalizable."
So again the root tonic is CHANGED from 0 to 12 as the root tonic or "C" to then 0 to 8 as the NEW root tonic so that 2/3 as the new "one" or root tonic now creates 4/3 as 8/6. But then the ORDER is REVERSED for the Logarithm so that instead of 0 to 8 it is not 12 to 6 as "geometric magnitude" so that 4/3 is 8/6 PLUS 12/8 as 3/2 to equal 2 as the logarithmic math.

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@valar It's called "primordial time" by Math professor Lou Kauffman. Time doesn't exist as Spacetime causation that is linear but time exists as noncommutative frequency-time. So there is time as the future and past overlapping as precognition that is paranormal. I just finished relativistic quantum physicist. Dr. Olivier Costa de Beauregard's book "Time: A physical magnitude." So the Wiki page on Costa de Beauregard makes no mention of the paranormal since Wiki thinks the paranormal is "woo woo" when in fact the CIA had classified the mention of the paranormal by Costa de Beauregard - it was underlined by the CIA. Most of Costa de Beauregard's published papers argue the paranormal is inherently the truth of reality as relativistic quantum negentropy. This is very funny that mainstream science is not advanced enough to know the paranormal is real.

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Professor Richard McKirahan:

"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. "

"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."

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Yes the square root of 2 was originally from music theory as 9/8 cubed (approximated). So this is from Archytas (not Orthodox Pythagorean music philosophy). "the Pythagorean music school was rapidly able to calculate the tone fa-sol as the difference between the fifth do - sol and the fourth do - fa, and consequently as the ratio 3/2 : 4/3 = 9/8 [logarithm]....The Pythagorean tradition denied that it was possible to divide the tone into two equal parts (semitones [based on rational ratios])....Dividing the Pythagorean tone into two parts would mean admitting the existence of the proportional mean between 9 and 8, that is to say, 9 : [a] = [a] : 8, where 9:[a] and [a]:8 are the proportions of the required semitone....Clearly [a]= [square root of 9 x 8] and therefore [a] = (3 x 2) x [square root of 2]!"
Math Professor Tito M. Tonietti, University of Pisa, Italy
and
"However, he [Archytas] noted that the product of the arithmetic mean and the harmonic mean is equal to the square of the geometric mean, so this gave a way of dividing the fifth of 3:2 into the product of 5:4 and 6:5."

A Truman State University review on Scriba, Christoph J. “Mathematics and music.” (Danish)
and
"The 'demusicalization' of the theory of proportions by Plato is shocking." (Borzacchini, p. 281 of his academic article on the topic, "Incommensurability, Music and Continuum: A Cognitive Approach").... "...this 'removal' seems really astonishing!"

Then Math Professor Luigi Borzacchini pulls out his trump card: "However, I think I can prove that in the Platonic Academy there was a trace of this earlier approach, with a tight connection between music, numerical means and similarity, and without any reference to geometric figures, such as square or pentagon." Borzacchini, again, is revealing a cover-up: "Why these silences? And why this sudden and radical change?" (hiding the secret musical origins of western science!). "Why this sharp change? I think the first reason was that the musical proof was only negative, whereas the geometrical approach allowed the effective construction of incommensurable magnitudes."
and
“The sound of square roots
Take two strings, one sounding an octave higher than the other, so that their lengths are in the ratio 2:1. Then find the geometric ratio (also called the mean proportional) between these strings, the length x at which 2:x is the same proportion as x:1. This means that 2:x = x:1; cross-multiplying this gives x squared =2. Thus, the “ratio” needed is √2:1 ≈ 1.414, in modern decimals. This is close to the dissonant interval called the tritone, which later was called the “devil in music, ” namely the interval composed of three equal whole steps each of ratio 9:8. The tritone is thus 9:8 × 9:8 × 9:8 = 729:512 ≈ 1.424.” from “Scandal of the Irrational” M.I.T. Press.
and
"... the tyrant in the Republic as the tyrant's suffering is exactly 729 times that of a philosopher, using the metaphor of ... The ratio 729/512, three whole tones (8:9) above 512....“Since 9 actually reduces to a wholetone of 9/8, its cube will reduce to (9/8)³ = 729/512, a [FAKE] Pythagorean approximation to the square root. of two, a problem which fascinated Socrates in the marriage allegory.” Ernest McClain, The Pythagorean Plato: Prelude to the Song Itself (Nicholas-Hays, 1978), p. 36

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Voidisyinyang Voidisyinyang
1 year ago
read up on Sir Roger Penrose - the acceleration of space is FEEDING the big bang at the origin of the Universe. Time is asymmetric. Or Dr. Jack Sarfatti goes into this. So we live in a holograph but the 5th dimension CREATES spacetime. So the future already exists and precognition is real.

[voidisyinyangvoidisyinyang]

"Ma [Perfect Fourth], although consonant to Sa (root tonic), is alien to the overtone series and is not evoked in the sound of Sa. On the other hand, Sa is evoked in the sound of Ma, since Sa is a fifth above Ma and is its second overtone.

For this reason it can be argued that the tendency to view Ma [the Perfect Fourth] as the ground-note has a 'natural' basis. The same cannot be said for Pa as Sa is not part of its overtone series.

The thesis can be expressed in the following way: If two drones either a fourth or fifth apart are sounded, one of these will 'naturally' sound like the primary drone. It is not always the lower of the two which will sound primary, but the one which initiates the overtone series to which the other note (or one of its octaves) belongs. By amplifying a prominent overtone the secondary drone lends support to the primary and intensifies its 'primary' character."
The Rāgs of North Indian Music: Their Structure and Evolution
Front Cover
Nazir Ali Jairazbhoy
Popular Prakashan, 1995

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So there is a difference between 2/3 of the 1 when the "one" is a sound that is listened to and not a physical vibration of a string. So this is why Western music tries to claim that undertones don't exist because you need a 3/2 wavelength in order to have a 2/3 frequency and the 3/2 wavelength is longer than a 1:1 fundamental frequency ratio. So you understand that 4:3 can NOT be an overtone because the denominator is not the same pitch of the root tonic as the one (or "C"). So that is the difference between the Harmonic Series (that assumes a closed geometric ratio) in contrast to the overtone series. For example in traditional Indian raga music if there are two notes played and it is a 4:3 as Perfect Fourth higher then it is well known that the Perfect Fourth is HEARD as the root tonic!! So this is also why in traditional Chinese music the octave is not used to try to "contain" the scale as a symmetric doubling - even though the octave was obviously known. Instead of constructing the scale as multiplying 3/2 to try to line up with the octave (as is done in the Pythagorean scale creating the Pythagorean Comma) the traditional Chinese scale takes 2/3 of the 1 and then 4/3 of the 2/3 for the Perfect Fourth.

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@Topher The11th Maybe Sir James Jeans will help clarify the math for you: 1.05946309436 So that is the value of the 12th root of 2 for equal-tempered tuning. So then you take that to the 7th as 7 half steps from the tonic and you get = 1.49830707688 And so that appears to be close enough to 1.5 for 3/2 as the Pythagorean-Daoist harmonics. But as Sir James Jeans points out - this "error" multiples. So 2 to the 7th is 128 and 3 to the 12th is 531441 And so the assumption is that the logarithms can be added so you get 2 to the 19th=524288 And so the Pythagorean Comma is 531441/524288=1.01364326477 Whereas if you take 3/2 to the 12th instead of assuming that the octave can be divided out of the 3 though "halving" - then you get 129.746337891/128=1.013671875

Sir James Jeans:

"To put the same thing in another way, we have just identified the frequency ratio 1.5 with the interval of a [perfect] fifth, although our table gave the value as 1.4983. The difference is only small – 1.13 parts in a thousand – but by the time we have taken the twelve steps needed to pass completely around the clock-face, it has been multiplied twelvefold into the difference of 13.6 parts in a thousand, which represents the aforesaid difference in pitch of almost a quarter of a semitone. When this is allowed for, the true clock-face is that shown in fig. 55; it extends to infinity in both directions and all simplicity has disappeared.”

Sir James Jeans book Science and Music, (Dover Publications, 1968), p. 166

So Sir James Jeans is DIVIDING 1.5 by 1.4983 to get 1.001335 which is 1.33 parts in a thousand in contrast to 1.0136 being 13.6 parts in a thousand. But this is assuming that 2/3 is also NOT the Perfect Fifth. In other words the Ditonic Comma assumes you can not just multiply but also "halve" the Perfect Fifth back into the octave - thereby "losing" or hiding this multiplying factor!!

OK now we can return back to Dr. Oscar Abdounor:

The chromatic Pythagorean scale is:
The notes F and c found in the table presented before, 131072:177147 = 0, 73990527641 and 262144:531441 = 0, 49327018427, respectively are slightly different from 3:4 and 1:2, which are those of the Pythagorean scale. as mentioned before, a do (c) was considered the initial note, so this result means that the fourth and the octave obtained by the aforementioned process are not
exactly the same obtained in the discovery with the monochord, attributed to Pythagoras, of the numerical ratios corresponding to the main intervals of the musical scale. One can put it down to the fact that the aforementioned cycles of the octaves and of fifths don’t meet, as it will be shown later and that the best approximation for this meeting occurs with 7 octaves and 12 fifths. So it is plausible that the ratios determined by the fourth and by the octave in the Pythagorean scale result from the experiment of the monochord, namely, from the musical perception that such ratios produce these intervals, they were the perfect consonances in the context of Greek music and which were capable of being produced by ratios composed by small numbers, being easier to relate to the intervals using only the ear....

... Pythagorean tuning were first considered by musical theorists [445, 7] in order to answer the need of a new musical language provided by polyphony. anachronistically speaking, this means that, supposing both these both cycles meet, there would be m and n integers such that (2:3)n = (1:2)m, that is, 3n = 2m+n, which is impossible, since the left term is odd and the right is even. "
and this:
"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."
Professor Fabio Bellissima, "Epimoric Ratios and Greek Musical Theory, " in Language, Quantum, Music edited by Maria Luisa Dalla Chiara, Roberto Giuntini, Federico Laudisa, Springer Science & Business Media, Apr 17, 2013
and this by Fields Medal math professor Alain Connes:
"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 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 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 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 root∼3 to the 19th root [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)

So notice that for the exponential function it is 2 to the 19th and 3 to the 12th but for the logarithmic function it is the 12th root of 2 and the 19th root of 3. This is the noncommutative phase secret of music theory that ONLY Fields Medal Math professor Alain Connes emphasizes - you can see his several lectures on youtube on the Music of the quantum sphere for further details.

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"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."
Professor Fabio Bellissima, "Epimoric Ratios and Greek Musical Theory, " in Language, Quantum, Music edited by Maria Luisa Dalla Chiara, Roberto Giuntini, Federico Laudisa, Springer Science & Business Media, Apr 17, 2013
So that also explains the noncommutative phase of music.
So then as Fields Medal Math Professor Alain Connes explains:
See Alain Connes lecture on Music of the Quantum Sphere for more details.
"Nature is quantum. Nature is very quantum. ..Why should Nature require some noncommutativity for the algebra? This is very strange. For most people noncommutativity is a nuisance. You see because all of algebraic geometry is done with commutative variables.... And this answer is coming from quantum way you can hear the music of shapes...which would be its scale in the musical sense; this shape will have a certain number of notes, these notes will be given by the frequency and form the basic scale, at which the geometric object is vibrating....]. And the only thing you need to know...is the relative position of the algebra...a "universal scaling system, " manifests itself in acoustic systems....There is something even simpler which is what happens with a single string. ... They are isospectral [frequency with the same area], even though they are geometrically different [not isomorphic]....when you take the square root of these numbers, they are the same [frequency] spectrum but they don't have the same chords. There are three types of notes which are different....What do I mean by possible chords? ..Our notion of point will emerge, a correlation of different frequencies...The space will be given by the scale. The music of the space will be done by the various chords. It's not enough to give the scale. You also have to give which chords are possible....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 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 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 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)

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Voidisyinyang Voidisyinyang
What is pretty hilarious is that physics got Negentropy and Entropy turned around. As Gee McFearSun emphasizes, "civilization is a Heat Engine" - whereas physics tries to claim that the infrared radiation from Earth is "entropy." Oops - that completely ignores that the solar energy is quantum nonlocal with photosynthesis - as quantum biology proves. Mother Nature is taking revenge.

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check out the nonlinear positive feedbacks of abrupt global warming as documented by conversation biology professor Dr. Guy McPherson. So also go to the "arctic news" blogspot for Dr. Maria Carmen Solana posts and Professor Andrew Glickson. Also check out Dr. Jim Massa science talk channel - an oceanographer. Also go to the "arctic sea ice" forum and check out Dr. Jim Hunt's blog "The great white con" - also check out former Cambridge physics PRofessor Peter Wadhams - who went to the arctic 50 times. Also search "biological annihilation" into googlescholar. Fact is that currently on Earth we are experiencing the fastest increase in CO2 and methane emissions - and this is an amplifying feedback. Life shuts down from lack of photosynthesis after 104 degrees Fahrenheit. I realize you think Technology is a Religion that can Save Us - for example NASA promoting "synthetic ecology" in outerspace. That is precisely our problem - that people worship technology due to being brainwashed by the wrong logarithmic/exponential math from Platonic philosophy. So we think "the calculus" has been so successful but in fact it's turned around. Civilization is a Heat Engine as Entropy while Nature as ecology is Negentropy - study quantum biology. A good book on this is "Life on the Edge" by professor JohnJoe McFadden. thanks

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You say "tune" but that's not the same as "listen." So to "tune" the F as 2/3 of the C as the root tonic pitch - even if it is an octave higher still does not change the listening pitch relative to the root tonic. So again if your root tonic pitch is established as the one then the F is listened to if heard as the Perfect Fourth to the One as a NEW root tonic because the "F" is not a natural overtone as 4/3 to the root tonic. This is why going UP a Perfect Fourth to the octave C is actually a Perfect Fifth BELOW the octave just as C to G is 3/2 and therefore to claim a Perfect Fourth "below" the octave would still be the G if the C is to remain the root tonic. That is based on listening with the "C" as the same root tonic.