Peanut Gallery Independent Praise of Drew Hempel's research

The disgustingly typical common dismissal of yours of Drew's worth is telling. Can't handle anything too far beyond your comfort zone so you don't at all engage, as Drew would say, with his information. Much of which is simply discerning the fundamental structure linking revered traditional scriptures and cuttingedge science and it's explication in human life on Earth.
Then of course you project by claiming he is not engaging well... you're right, but you are still denying your hypocrisy, as you are too scared to admit that the reason you say you don't appreciate any of his writing is probably not because it is all false but because it is occult to your limited mind.
You can't argue with the facts and are too dumb to handle his points so you resort to smear tactics.
Who cares if some nut spams the net. It is only disruptive to the weak of mind. Fact is Drew has an "original" conclusion that deserves global discussion and you censor it like a welltrained shill, which I assume you are not.

Drew's idea. 2:3 is Yang, 3:4 is Yin... ie 666 is Yang. But he might repeat it like the example below, at which 99% of readers will throw their hands up in incomprehension and only folk like me, a stubborn OneTruthLover, bother to really get what he is saying. To say his is crazy is stupidly missing the point, plus to which he seems saner than most of the zombies who pretend humanity. He may a mixed up lake but at least he is not a puddle of puke.
Brace yourselves,
"I've posted that in fact musicologist Ernest McClain had already gleaned this from Plato -- see his Pythagorean Plato -- and that in fact while 5/4 was the Greek Miracle as the cube root of two leading to amplitude as classical mathematics for 3 dimensional form

the Tai Chi Perfect 5th-4th as 2:3 and 3:4 Yang and Yin (my discovery) is the QUANTUM secret of 2-dimensional energy intensity from frequency, not classical amplitude."

Needless to say he condenses much meaning in few words so you gotta read more his of his spiel to get it. His earliest piece on the greek Miracle is best.
Cloud Tiger, a Tai Chi practitioner in the UK, 2009

Hempel, proficient in a wide sprectrum of intellectual pursuits including math and music --- and far from being deluded in any sense of the word as brought forth in the above quote by Hui Neng --- is also an eastern spiritual renaissance master as well. Just as much too, in the aforementioned areas and others far afield, as a search of his name will show, or did before he just simply disappeared into cyber space or infinity, he was one of the most prolific contributors on the net. His writings and books lean heavily toward a variety of eastern spiritual aspects, with a strong personal emphasis on qigong and meditation executed almost exclusively through the use of the full lotus position.

Additionally, even though Drew has resurfaced and available for interaction to all comers, I have however, NOT changed any of the above content of the original page because in my opinion it still remains highly relevant, showing all kinds of insight into who and where Hempel comes from, from any number of angles. Good to hear you are back. The internet wasn't the same without you.

The Wanderling, advaita meditation online site page on Drew Hempel

First we have to address the root of this possible problem.

the main root of all of this is the conceptual axiom that the parts of a system should be symmetrical if it desires to be in HARMONY. This in math is called COMMUTATIVE RING, or AxB=BxA.

From this principle (the commutative ring) we created a body of rules and paradigms in science, and even in religion, that separates our perception from nature itself (our game of denying being part of it) For example, as someone on this forum talked about maxwell´s quaternions in here. To work with an asymmetrical principle (most of things in nature) with our math that has as a main basic principle the commutative ring we first need to CHANGE what we gonna study, I mean, our science takes the information in nature which is assymétrical and DIVERGENT and converts it to an symmetrical and CONVERGENTE group of data to work with.
This is, as a principle, exactly what we did with the musical scales, as drew demonstrated.

In ancient music we got the asymmetrical intervals and, mainly since old non-pre-socratic Greece, we develop the obsession and the desire to “correct” it´s ugliness (natural asymmetry), so we transformed ancient music into symmetrical intervals. Buy by doing so we generate a comma, an extra group of data that can´t be used and should be discarded and watched over to avoid its return, because if this comma returns to the scale, it will create a hell of a mess to the fragile artificial symmetry we applied to it. So, conceptualy, the kind of technology we create, it prefers to change nature into artificial symmetry instead of flowing with it.

So it´s a matter of the right tool for the right job. And our Math has no asymmetrical tool for the job. IT´s all about the commutative ring, so even when working with asymmetrical systems (like nature) it has to convert it into symmetrical to process it. IT´s simple, drew is saying that western math and music take what is divergent (spiraling out) by nature and converge it before giving any kind of result. It´s a fact. Check, I don´t know, Wikipedia?, to get informations about the commutative ring and the non-commutative ring.

Now, I´m not 100% with drew on the consequences of “raping” nature with symmetry. I do know drew for the last 10yrs. Or so. I´m very good at math and good enough in music. I´m so-so in physics, i´ve studied electrical engineer for two yrs before change my mind and go to journalism school and drop it too to work as a photographer and illustrator and now as a computer graphics animator and advertising film director. So I have some background to understand a great chunk of drew hypothesis.

We try to solve all with symmetry, as the case with the music intervals, therefore, as in the case of music intervals, we create commas in science and all the range of activities that rely on science.

So this is the radical part of this use of musical model to explain things: if we try to understand nature (that is asymmetrical and divergent) with concepts and tools that are symmetrical and convergent) we gonna create dissonances in return and enter in a cycle of solving a dissonance with more symmetry to generate even more dissonance in the next octave ´till we # everything up! (we are already doing so! Our tech gives us marvelous stuff at the same time it acidify the oceans ending up #ing up with animals that depends on ultrasound for communication to reproduction. Our tech gives us marvelous tools as computer hi-res screens, but in return any cycle above 30hz is with time stressful to the human cells, etc, etc.)

non-commutative is so alien to our understand of thing that, as an example, if you go to Mr. Wolfram Math repository site you gonna find only ONE EMPTY page about it!!non-commutative is so alien to our understand of thing that, as an example, if you go to Mr. Wolfram Math repository site you gonna find only ONE EMPTY page about it!!

Now let´s go to the possible solutions for this.

1.full-lotus as a solution. Drew said full-lotus can transform the excess of electrochemical information in the lower body into electromagnectic information in the upper body. Some angry scientific trolls started to make fun of it.

for the materialistic people the thing is in the physiology.

siting in full-lotus will put a great chunk of pressure into your SACRUM! The sacrum is empty and pressure there will start to create small levels of ultra sound that will TRANSDUCE the energy from electrochemical into electromagnetic (remember, SOUND is PRESSURE WAVES, and it´s been prove that ultrasound can transduce energy from one state to other… use uncle google, he is your friend!! )… so this is one of the main reasons why full-lotus is a great tool.

It took me one year of daily chikung to sit in full-lotus with ease, before my one year of spring forest qigong I could barely sit in freestyle (like an north American indian) for more than a couple of minutes without felling a hell of pain in my back and legs!

After i´ve learned to sit in full-lotus, it´s a #ing bliss, full-lotus and half-lotus all day long. I even cut the legs from all my tables in my studio so I can sit in full-lotus and half-lotus anternated all day!!

So it´s one solution, but it´s a personal one.

2. Music create patterns in our brain.
It´s known that music create patterns in our brain. So if we just listen to music made with symmetrical and proportional intervals, some kind of patterns will form… with non-western music (mostly live, since hard to find speakers in home and computers that can produce ultrasound! ) so with non-western music we can generate other kind of patterns, since the intervals are asymmetrical. Drew have posted links to papers demonstrated, among otherthings, how ultrasound can stimulate the brain, the center of the brain, so on.

Also, Pineal Gland is a place made for sonoluminescence production. See? Pineal gland has fluid and cavitation in it! So with ultrasound stimulus in it we can ionize it a lot, we can produce tons of melatonie, and also we can generate little bubbles of light! By my personal experience, seeing light while practicing small universe (the oldest meditation that exist, it´s part of spring forest chikung and also is a “secret” inside the kriya yoga school) is relaxing, insightful and healing.
So, changing the king of music we listen to is a way of changing the patterns in our brain and so maybe it will reflect in the patterns we create in the world too.

3.creating a science where natural resonance ratios are important.
Well, this third item i´ll say nothing, since it´s what i´m working for the past 5 yrs. But a simple example of using natural resonance (non-comutative) musical ratios in technology is The Sonic Bloom, it´s a kit with audio from birds generating the fifth and forth in a repeated way so the intensity will affect the plants cells to expand more, taking more nutrients. It´s amazing. I use it to feed my home grown food (i´m a raw vegetarian) as my wife garden.

And this is just the tip of the iceberg…

Now those open minded, the daily practice of small universe from spring forest qigong, or the listening of music without symmetrical intervals, or the use of tech like the sonic bloom are just a few of the examples of the changes we can make personally or collectively to a better and more harmonious world.
And those so full of the “right” paradigm, well, you can keep projecting your anger on drew, it´s funny to read your assumptions about my crazy druid friend!

KALLISTI and have a nice day and a lovely life!
Guto Novo.
Correspondent for 15 years in Brazil

Seriously drew is next level, beyond even Dobbs, Ebert, Heidegger, Mcluhan etc.
Another UK practitioner-philosopher
"The universe and I came into being together; I and everything therein are One."

"If then all things are One, what room is there for speech? On the other hand, since I can say the word 'one' how can speech not exist? If it does exist, we have One and speech -- two; and two and one -- three(14) from which point onwards even the best mathematicians will fail to reach (the ultimate); how much more then should ordinary people fail?">"

- Chuang Tzu, 300 BCE

"Sound is the bridge between God and the soul" SHRI DHYANYOGI

a “universal scaling system”, ... this discrete scaling manifests itself in acoustic systems, as is well known in western classical music, where the two scalings correspond, respectively, to passing to the octave (frequency ratio of 2) and transposition (the perfect fifth is the frequency ratio 3/2), with the approximate value log(3)/ log(2) ∼ 19/12 responsible for the difference between the “circulating temperament” of the Well Tempered
Clavier and the “equal temperament” of XIX century music. 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,∞}. -
Math professor (field medals) Alain Connes on quantum music as noncommutative time-frequency origin of reality from infinite spiral of perfect fifths!
Our brain is an incredible ....receives moments of space of the photons we receive and manufactures a mental picture. Which is geometric. But what I am telling you is that I think ...that the fundamental thing is spectral [frequency]....And somehow in order to think we have to do an enormous Fourier Transform...on geometry. By talking about the "music of shapes" is really a fourier transform of shape and the fact that we have to do it in reverse. Alain Connes, 2012

Stanford Quantum physicist Eddie Oshins:
This representation only works for the (more fundamental) 1/2-integral representations (i.e. spinors/turns/quaternions) but also lets one build the vector and tensor representations. The converse does not hold....this property of "noncommutivity" in itself might be valuable in some way.
My claim, and original idea, has been that this is circumnavigating a T'ai Chi (Yin/Yang) symbol! More recently (Oshins, 1993b) I have suggested that this proximate technique can be used to realize Wing Chun kung-fu's "bong sau/tan sau" movement out of the Kauffman/Oshins "quaternionic arm" discussed and referenced below in end note 5.
I believe that this may be a way to get mind to code the relative relationship of part of oneself with respect to the rest of oneself (self-referential motion) and can explain the concepts of being "centered"/"one"/"integrated"/"extended"/"whole" etc. which one strives for in meditation.
Oshins, E. (1993). A Test for Classical Psychospinors. (pdf) In Abdullah, F. (Ed.) Conservation and Invariance. Cambridge, UK: Alternative Natural Philosophy Association, London England.

Manfred Euler's 2013 description of acoustic STM - Scanning Tunnelling Microscopy builds on his previous connections between the quantum acoustic realms.
Near-field imaging with sound waves compelling demonstrates the inadequacy of pictorial realism and promotes more abstract views of the reality displayed.
A comparison of sound and matter waves clarifies that these [noncommutative] limitations exist in principle.
2016: de Broglie clocks as synchronization: a tangible model of how mass emerges.
matter waves are locally in phase with the particle clocks (de Broglie's Law of Phase Harmony).

The clock runs forever so it's self-sustaining (consciousness-energy). It resonates with the quantum vacuum. The harmonic beats create dynamic energy.

So then you have a "phase particle" that can be faster than the speed of light - superluminal - and a "mass particle" that is slower than the speed of light as the "group wave" of the "phase wave." The beats of the phase wave then are "in resonance" with the quantum vacuum - and so create mass from the massless field, explaining the Higgs mechanism.

"Universal coherence" - a "mind boggling outlook."

Coherence as consciousness.
"Ghost Tones"
Manfred Euler is a Professor Emeritus of Physics at the University of Kiel.

It's actually a Klein Bottle so you can't see the 5th dimension.

The red is a logarithmic singularity - but that is just classical physics.

So the foundation of reality is quantum - which is noncommutative phase as the 5th dimension.

So light as a photon is a point but as a wave it is nonlocal - but this means it is in 2 places at the same time - as the 5th dimension that is noncommutative.

People think that doesn't make sense - how can it be in two places at the same time? Actually basic music theory explains this.

So for example the Perfect Fifth is C to F as subharmonic 2/3 while the Perfect Fifth is C to G overtone harmonic as 3/2.

So C = 2 while F=3=G at the same time. That is noncommutative phase. It is also called "Fourier Uncertainty" or "time-frequency uncertainty" - and that is the true foundation of reality.

So for example de Broglie - studying relativity - realized Einstein had a problem - as energy goes to the speed of light then time as wavelength slows down, gets bigger. That means as frequency goes higher then time also gets bigger. That violates a fundamental property since Pythagoras that frequency is inverse to time as wavelength (from music theory).

So de Broglie realized since quantum physics is real there has to be a phase wave that is faster than the speed of light. So you have a mass wave that is the "group phase" - and then you have a particle phase that is called the "internal clock" or a 2nd clock that is the phase wave of the particle - also called the "pilot wave" - and this comes back from the future.

So there is a Harvard physicist who works with Stephen Hawking - and this Harvard Physicist says that the future already exists and reality is a holograph. So the 4D universe is actually a projection of this 5th dimension of noncommutative phase that is time-like.

This is how precognition is real.

Thursday, May 11, 2017

My last blog "saved" by ancient knowledge?

It appears that someone had the temerity to actually save a few of my blog posts - on his Tumblr

The same person also created an "ancient knowledge" harmonics site

Or maybe they're just recommending that site. seems to say they author all of these site.

And their Ancient Knowledge youtube vid series

I'm talking about the person who posted/created the Ancient Knowledge video - 6 parts or 7 1/2 hrs long.   the first part is on sound as consciousness.

Right so out of gratitude - I repost my Do-Ohm Up the Yin-Yang! book:

The Devil’s Interval and the Pre-established Disharmony of Western Science:
The Secrets of Inner Sound Alchemy Spiritual Paranormal Energy Explained by Music Theory

Drew Hempel, M.A.

This article (e-book/blogbook) is LONG with about 25 years of research summarized into it. If I had to sum it up into one phrase it would be this seemingly silly one - this innocent question that started it all for me:
So we can just ignore that it is C to F as the Perfect Fifth in one direction while it's C to G as the perfect Fifth in the other direction?

First off - new to me - some "traditional" Bushmen music of the original humans. Even this Mbira playing is more modern, from Bantu influence. Still a nice example of what this article is promoting. Listen to it as you read on! Sounds strange to you? haha. Just wait for its secrets to be revealed.

Warning: This article is not just about music theory and Taoism but rather it is exposing a lie at the foundation of Western mathematics. 432 cultists also will be debunked in this article. Finally do not "speed read" this article (the format of this article is not linear - if something is not clear just keep reading, explanations will follow and you can circle back - like a spiral). If you are a 432 cultist and you do not engage with the content of this article but instead just rehash 432 lies and I point this out - please do not blame the victim. I am a victim if I post this link and instead of the reader engaging with my content they just ignore it and spew forth 432 lies. If I point out the lies in response - again do not get upset at me since I was not the first one to ignore the content of this article. haha. That is my warning to 432 cultists.

For example one of the 432 cultists states: 
 Capturing F#:
The most obvious source is to begin with that which we have agreed to call the pitch, or tone, of F#. I use the tuning scale where C = 1 cycle per second, or 1Hertz. The numbers on this scale are slightly flatter than the scale using C=l.03 (A = 440). On the tuning chart where C=1, all F#s fall in octaves on the following hertz numbers (rounded off):
1.4, 2.8, 5.6, 11.25, 22.5, 45, 90, 180, 360, 720, 1440 etc.

The issue I am talking about is not based on choosing a certain letter for a certain number - that is numerology. You can make a certain number line up with a certain letter - it doesn't mean anything. The secret of Taoism is exactly against this "one to one correspondence" between number and letter which is gematria as symmetric numerology. So 2:3 is C to F while 3:2 is C to G. Same "C" as 1 hertz but the C to F is an undertone as yin and the C to G is overtone as yang. To use geometric angles for frequency already assumes a symmetric one to one correspondence based on a contained infinity. Listening as meditation is not geometry and it is not a contained infinity. The Tao can not be "captured." The Perfect Fifth/Perfect Fourth as the Tai Chi symbol: source,

Instead go to the links given for 432 given below. For example a 432 and Sacred Geometry video from sent to me by a 432 cultist, in the first 25 seconds shows images of irrational magnitude geometry symbols next to Egyptian architecture. The Egyptians, as I detail in this article, did not use irrational magnitude geometry! Stop the 432 lies. It's repeatedly claimed that Egyptian ancient instruments "unearthed" have 432 hertz but no evidence is provided. In this article I give the evidence of "unearthed" Egyptian instruments and they don't have 432 Hertz! Another 432 lie is that neanderthal flutes used 432 hertz! I searched all the academic articles I could find on the subject covering six different ancient bone flute discoveries between 40,000 BCE and 6,000 BCE. Nothing - no mention of 432 hertz. Again stop the 432 lies.

So not only is the 432 geometry video promoting just another equal-tempered tuning irrational magnitude scale (i.e. F# as 720 - as close to the irrational magnitude tuning as possible) but it's all based on the size of the so-called "sacred" geometry. Sure the angles stay the same but the sound of an object is obviously based on the size - a bigger triangle or square and you get a lower sound - which is, guess what, not the same frequency! Anyone who doesn't have enough common sense to notice this is a cult follower, plain and simple. So the idea of basing frequency on angles which stay the same no matter the size of the object is not accurate at all - it's a lie. Fourier analysis has proven that any geometric form can be created from the basic sine waves but that the Fourier Uncertainty Principle, the time-frequency uncertainty principle, demonstrates an underlying infinite non-local formlessness to this process of time-frequency energy creation out of the low rational harmonic numbers. O.K. consider, in contrast, astronomy professor Gerald Hawkin's "fifth theorem" of Euclid that he claims to have discovered.
See blog for images
The F# as the Devil's Interval, the tritone, as the geometric mean and most dissonant neutralization of the scale

In fact Gerald Hawkin's claims are from the original continued proportion analysis at the origin of Western mathematics as explained here - for sacred geometry sound analysis, the ratios of geometric areas, not the angles of the areas. So, for example, Hawkins analyzed a triangle circumscribing and inscribing circles or a square circumscribing and inscribing circles or a hexagon circumscribing and inscribing circles. He always found that the ratios were simple numbers like 2:1 or 4:3 - the Pythagorean harmonic ratios. Those ratios stay the same, no matter what the size of the object is as long as the relative size of the circumscribing and inscribing objects also change in the same relative proportion. These ratios are nothing new at all but geometric length is not the same as arithmetic distance - something this article will discuss in greater detail. Remember we listen to sound - sound is not dependent on a visual geometry! The West is very much a visual-oriented culture measuring time as a spatial distance (speed)! But in reality frequency is based on listening and time is not limited to spatial distance as wavelength.

The mysticism of 432 actually is from originally using a 60-based number system from Sumeria and Babylon with Egypt also using this - all for a Solar based calendar - tied to Vedic Brahmin philosophy as well. Mathematician Abraham Seidenberg in a series of "origins of ritual geometry" articles in Archive for History of Exact Sciences explains that the Pythagorean theorem was approximated as far back as 3000 BC in Brahmin India, and the Pythagorean Perfect Fifths music scale was documented in the 2nd millennium BCE based on the Sumerian musical terms of some of the cuneiform texts. Professor John Curtis Franklin, email communication, April 12, 2011. Penn museum cuneiform music article: here Seidenberg notes that the Pythagorean triangles in Egypt had the base of the triangle equaling Isis, and the height as Osiris, and the hypotenuse as the complementary opposite resonance between Set and Horus. These ancient empires used Solar Dynasty ritual priests practicing sacred geometry ritual sacrifice from music harmonic ratios as Gods and Goddesses contacted and transmitted through mantras or srutis.

This ritual sacrifice process started in 10,000 BCE through what archaeologists call "the symbolic revolution" as an attempt to use male-based rectlinear geometry to contain the wild, untamed infinity of Mother Nature. By 1200 BCE iron-based technology in India had become more valuable than the silver-based lunar female goddess energy. The chariots for warfare, spreading iron-based farming, were designed by an approximation of the Pythagorean Theorem to "square" the circle and then even circular female-oriented houses were destroyed and circular ritual sacrifice altars had to be made the same area as the squares. Seidenberg's articles in Folklore Volume 94 issue #2, 1983; Vol. 80, 1969 and Vol. 70, 1959, are in collaboration with Lord Raglan, as a promotion of this mass ritual sacrifice as the spread of rectilinear architecture, called the separation of heaven and earth based on the separation of a man, through ritual sacrifice, heaven being the alchemical head and earth being the lower body of the man. In contrast real orthodox Pythagorean harmonics are based on the harmony of heaven and earth. Juzhong Zhang, Xinghua Xiao, and Yun Kuen Lee, “The early development of music. An analysis of the Jiahu bone flutes,” Antiquity Journal, July, 2005 documents a Pythagorean 12 tone scale in China from the sixth millennium BCE.
 The yogic goal of bodily and spiritual balance is consonant with the Indo-European notion of ‘measure’ which surfaces as a cardinal attribute of the cognate ‘medical’..., and which is the essence of ‘meditation.’ In Greece we find ideas of harmony applied extensively to the body, often (but not exclusively) in Pythagoreanizing sources as a concomitant to the belief that the mind or soul is simply the ‘attunement’ of the body – the Harmony which supervenes on its
harmonized components….
 John Curtis Franklin, “Harmony in Greek and Indo-Iranian Cosmology,” The Journal of Indo-European
, Volume 30, No. 1 and 2., 2002, p. 13.

The Devil's Interval refers to irrational magnitude geometry. When in the 17th Century Francis Bacon studied the secrets of the octave he declared: "The Cause is Dark." This article is not just about some "reference frequency" as so-called sophisticates like to claim - you know people who memorized a bunch of things by rote and so think they are very intelligent. Since the 17th Century with the origins of modern science, "The most concordant simultaneous tones are ones that coincide most regularly and frequently,..." IDEAS OF ORDER IN SEVENTEENTH-CENTURY MUSIC WRITING 2012 m.a. thesis link This came to be known as the “the coincidence theory of consonance” thereby disowning the Pythagorean Tetrad of 1:2:3:4 based on the philosophy of numbers. Modern music theorists still rely on this 17th C. idea to be "sophisticated." David Hykes "Harmonic World" music is based on the same principles this article elaborates on - the rational number harmonics as sound healing

or more harmonic overtone music here

Yeah that's right - I want you to be listening to sacred overtone music while you read this article.

The content of this article covers a lot of different territory so don't just glance at it and think you know what it's about. Prepare to learn something new in this article - not some whimsical "sound byte" by people using Audacity or other tone generator software but who know nothing of real music theory. I have advanced music training from being enrolled in college and university music composition degrees and trained in classical piano performance for 12 years, advanced music theory, ear training, orchestration, playing all different music genres in classical, jazz, rock, punk, country, folk, blues, reggae, bands, choirs, etc. I also performed a classical piano concert, memorizing the Bach Italian Concerto, Brahms, a Mozart sonata, avante garde John Cage and my own original compositions.

1) Taoism teaches that yin is 4/3 (C to F) as the Perfect Fourth and yang is 3/2 (C to G) as the Perfect Fifth. So also does real Pythagorean harmonics - not the fake pythagorean harmonics that are taught in the West. See image of the Perfect Fifth/Fourth as Tai Chi symbol. Why is this image so important? It demonstrates that "before frequency" which is a symmetric commutative measurement, the rational integers of the Tetrad-Tai Chi are non-commutative and asymmetric, thereby creating nonlinear feedback as infinite energy. Physicist Charles Madden in his Fractals in Music: Introductory Mathematics for Musical Analysis (1999, reprint 2007) points out that the Tai Chi symbol is not a fractal. Because of the yin-yang (Perfect Fourth/Fifth) resonance it is asymmetric and therefore not a logistic or irrational logarithmic equation. Click on the image to enlarge it.
See blog for images

2) Those perfect fourth/perfect fifth intervals are found in all human cultures and used for trance healing. See Bushmen trance dance video and, as this link gives, 84 music examples you can listen to from all over the world! How does this work? Clearly we are talking about the most unifying basic principle of humanity. The Bushmen are the original human culture and their music trance healing is from before 70,000 BCE! Genetically humans are from a bottleneck of just a few thousand homo sapiens - we are more alike than chimps are to each other or bonobos are to each other. After 70,000 BCE biologically modern humans spread around the world to become the thousands of human cultures using this secret of shamanic alchemy energy healing. For example the oldest philosophy in India is based on the "three gunas" for trance yoga healing alchemy and the "three gunas" (sattva, rajas and tamas) are the same as the yin-yang-Emptiness resonance dynamics from the Tai-Chi-Tetrad. an interview on music therapy in India
Nada Centre for Music Therapy, Chennai ( indicates that all types of music - including Indian ragas - which have to be necessarily pleasant can be categorized into three groups on the basis of their qualities : sattva, rajas and tamas. here
These intervals, as proven by quantum chaos science (ignored by the skeptics), using low rational integers, create the strongest nonlinear feedback as a driving resonance. I will explain this in detail documented by science as the "Devil's Staircase."

Notice that the Bushmen men trance dancing are moving in the Tai-Chi symbol! This video documents the origins of qigong and yoga and trance dance healing as N/um, a boiling energy that is stored in the belly and rises up the spine as electromagnetic force, turning into light spirit energy via the third eye pineal gland. More on this process in the article.
3) The reason the Perfect Fourth and Perfect Fifth work as healing energy is because they create the infinite spiral of fifths which means infinite energy in both directions.  An excellent music theory article on the infinite fifths This is not the same as an infinite spiral of thirds or sevenths, etc. The Perfect Fourth is not made from the harmonic overtones since the fundamental tone as the denominator does not allow a 4/3 fraction. In other words the harmonics as ratios are the rational numbers so 1 is the fundamental tone, 2/1 is the octave and 3/2 is the Perfect Fifth but 4/3 does not use 1 or 2 as the denominator - the denominator has to be either the fundamental tone or the same note doubled as the fundamental tone. This is the heart of the matter - what exactly is the fundamental tone? Again I am not referring to a "reference frequency." A composer wrote a music theory article titled, "The Phantom Tonic," and in an attempt to analyze this conundrum states: "Not a fourth above, but a fifth below: the phantom tonic." here Tonic meaning the fundamental tone.

Listening is actually an infinite process of energy creation due to this paradox of the Tetrad-Tai Chi Perfect Fifth and Perfect Fourth. So the Perfect Fourth is made from the undertone, making it a complementary opposite harmonic, C to F as 2/3x, a Perfect Fifth in the opposite time. The energy is infinite because the overtones and undertones, as asymmetric complementary opposites, naturally pull towards the octaves since they are close harmonics as the Pythaogorean Tetrad 1:2:3:4 which is also the Tai Chi symbol. See infinite spiral of fifths images. 

4) Because it's an infinite spiral the sound resonates into ultrasound and infrasound which then ionizes chemicals as electrochemical energy. This study shows music instruments do go into ultrasound from the 40th harmonic on up to the 108th harmonic. But again that is not the issue as much as the Perfect Fourth/Fifth document a nonlinear feedback that is strongest - so that the higher harmonics being more dissonant, thereby create stronger undertone beats and the process reinforces itself. This is proven in science as the quantum Law of Phase Harmony discovered by Louis de Broglie. I will go into detail about this more below. 
It was in 1925 that French scientist Louis Victor Pierre Raymond duc de Broglie discovered that the electron was actually a wave of vibration. These waves properly follow the same property and characteristics of vibration as the vibrating string of a musical instrument, the waves being complete with overtones. (We are familiar with the presence of overtones on the vibrating string from the experiments of Pythagoras and his monochord – a single-stringed instrument he built to display how musical scales were produced by the natural overtone series). 
An atom such as uranium has more that 90 electrons, each capable of its own harmonies, and all this can be recorded by a spectroscope. From this, one can conclude that all matter is made of waves. Therefore, we, and the world we live in, are vibrations…

When the electrochemical life force energy is ionized it creates electromagnetic energy as force called chi or qi energy. When this process continues it creates light as higher frequency electromagnetic energy. The light energy also enables superliminal signals - precognition and astral travel holographically. It is coherent light as biophoton laser light.

5) This ancient universal secret was rediscovered in quantum physics as the time-frequency uncertainty principle. For 1 hertz value the time-frequency uncertainty is an error of 2 hertz. When the complementary opposites of the Tetrad as the Tai Chi symbol are examined - using hertz analysis - the same 2 hertz difference is found. I do this analysis in the article. image of scale used for analysis. This means that the order of multiplication as time-frequency or frequency-time changes the value of the tone: 2/3 is C to G in one direction as overtone or C to F in the other direction as a subharmonic or undertone. It is a non-commutative operation just as is the quantum time-frequency infinite energy process, as the article explains. This secret violates the logarithmic commutative basis for Western math and so the "x" has to be used to cover up this secret complementary opposite value of time-frequency as the shamanic healing energy of the Tetrad-Tai-Chi symbol. The 2/3x has to be converted to a 4/3 value to hide the undertone complementary opposite dynamic - by doing so, the fundamental tone has been shifted. I will discuss this in the analysis of the final section. Click on the image to enlarge it.
See blog for images

6) This cover-up shows that our modern concept of frequency and amplitude is wrong because they do not use time-frequency uncertainty. In quantum biology time-frequency uncertainty means that over 70 octaves of mind-body energy are coherent and coordinated spontaneously as superliminal signals - non-local faster-than light information considered to be consciousness as God or the Emptiness or just the spacetime continuum, the foundation of reality. This is called the "rainbow worm" by Dr. Mae-Wan Ho, a Taoist quantum biologist who agrees that this quantum coherence explains not only the energy in the body but it's ability to create paranormal spiritual powers. The heart is the co-ordinating location but again it is quantum chaos in science - a higher dimensional location beyond the physical - that is holographic as coherent biophoton spirit energy - creating a spontaneous OHM sound as the Tetrad-Tai Chi energy, sound into light or sonofusion from sonoluminescence. The Use of Sound Healing with Patients Undergoing Cancer Treatment Mitchell L. Gaynor MD youtube talk

7) This training creates a permanent mind-body transformation and it used to be the norm for males to do this training to open up the third eye so that the light energy is transmitted as healing energy, but the training is through this inner sound listening process creating sonoluminescence - sound into light.  This is called "turning the light around" in the Taoist training - with our eyes open the spirit biophoton energy leaves our body. By emptying out the left-brain conceptual mind through trance music then the right brain activates the lower body energy that is ionized, creating a laser resonance of nonlinear feedback. This creates the lower body center as the Taoist "lower tan tien" behind the belly - the boiling "N/um" energy of the original human Bushmen culture where all males trained to do this to create the real love heart-pineal gland connection. The real secret of sound is that it is used to create light energy but this has been lost in modern Western times ever since the origins of Western civilization. The loss of this training is why modern human culture is based on warfare and violence.

8) The reason this secret remains lost is because it challenges the very foundation of Western thinking - the square root of two mathematics that everyone learns in 10th grade high school. The square root of two actually originated by covering up the real Pythagorean shamanic harmonics of the Tetrad-Tai Chi symbol. That was promoted by Plato - this cover-up.

Part One: The bizarre rejection of qigong by materialistic “skeptic” scientists

I have been engaging the skeptics online about qigong, a type of paranormal training considered to be fake by the skeptics. The reasoning of the skeptics is very interesting. One skeptic, an undergraduate student with an atheist website, recently responded to me in regards to a qigong master:

“I don’t say that the ‘tricks’ performed by Master Zhou are absolutely as I described them. Rather, like a proper skeptic, I claim that there are alternative explanations for the tricks he is performing without resorting to claims that he’s performing real magic and using supernatural powers. We have a natural explanation which is infinitely more parsimonious an answer then using a magic force that no scientist has ever been able to measure, despite its claimed reality and power. You are guilty of committing the fallacy known as an argument from ignorance. You are claiming that, because we may not have any rational explanation for trick X or trick Y, then it is somehow reasonable to usher in chi as a not only possible, but plausible alternative.” Colin Wright, “An American Atheist,”

This response is actually quite bizarre because it states that since there is ostensibly a more efficient explanation that is rational therefore the use of “irrational” chi is not only unneeded but an example of ignorance. On the contrary, the claim of the qigong master should be taken seriously and a tradition of energy training going back 5,000 years (twice as long as Western civilization) should first be explored at length, without it first being dismissed as ignorance. I know qigong energy is real since to finish my master’s degree at the University of Minnesota I did the qigong “inner alchemy” training as self-directed research and as part of the African Studies Department.  For example Dr. Ann Vincent led a “gold standard” randomized controlled study  of qigong master “external qi” healing and she called the results “especially impressive.”

I know the skeptics dismiss this as simply the Mayo Clinic doctor (at a top medical research hospital) somehow falling prey to the placebo effect but this relies on a strange interpretation of the results. The healings were very effective but then as the longer time went by with no more qigong healings, the results were not as significant. This is then interpreted by the skeptics to mean the effects were just psychological, wearing off as time went by. On the contrary – the qigong worked for the four treatments given over four weeks. That’s why when it was discontinued at four weeks the results diminished so at eight weeks no significant difference was noted. In no way did the clients claim to be permanently healed but only that the qigong effectively relieved their chronic pain while for at least three years previously no Western medicine could achieve that result. The skeptics then state that because the people wanted to get healed this made the qigong effective, as if the people did not want to get healed when they took Western medicine! Haha.

Also there have been many testimonials of people healed by qigong of serious conditions that in no way could be just psychological. For example Esther Trejo was on an oxygen tank 24 hours constantly for several years and after 8 weeks of qigong healing by a qigong master she was able to go off the oxygen tank. She was also a Mayo Clinic patient and the Mayo Clinic would have had to give her a lung transplant due to her rare disease but she did not want to take someone’s lungs. The qigong worked so well she didn’t even have scar tissue and this testimonial was covered by Gary Rebstock, a reporter for the local television news. Gary interviewed several others who experienced miracle qigong healings: Gary Rebstock also recorded video testimonial of a man healed of a club foot by a qigong master! Others have been healed by qigong of serious epilepsy – again a Mayo Clinic epilepsy patient who had been on 40 different meds at the same time but still no results. He was healed by qigong and he lives in my home town – I met his mom. He is now attending a college focusing on Asian traditional meditation and medicine. These have been verified by the doctors but the materialistic skeptics reject these results since they are not part of a “double blind” study. This type of rejection borders on, as I stated, the bizarre. But now I will demonstrate just how deep this rejection of qigong is based in Western science – the rejection of qigong goes to the very foundation of Western science.

Part Two: Plato’s Lambda was a promotion of the Devil’s Interval music covering up real paranormal qigong training

What was my connection to studying qigong as part of the African Studies Department? My premise of investigation was non-dualist philosophy that challenged the claims of Plato and Aristotle’s inherent hierarchy of natural law, dismissing other cultures as barbarian, subhuman and savage. I will now make a proposal – maybe a metaphor, but nevertheless hopefully a “sound byte” to summarize this research. Plato popularized the Devil’s Interval, through what’s called “Plato’s Lambda,” as the foundation of the Greek Miracle for what later became Western science.

See blog for images.

 Image of Plato’s Lambda which describes three dimensional space from squaring.  Plato closed off the infinite power of sound by “squaring” it into a closed circle. In the West we are taught this image of the “circle of fifths” but in actuality music as energy is an infinite spiral of fifths.

My proposal: Cultures that did not practice the Devil’s Interval, based on the Greek Miracle of irrational magnitude, were then dismissed as savage, barbaric, subhuman, to be made into slaves, etc. Music theorist Jamie James points out that not only, as is well known, did Plato have a disdain for music and its uncontrollable social power, but he was hostile “towards mousike (which it ought to be born in mind, meant any human activity governed by the Muses).” James cites researcher Cornford, who remarks how in Timaeus Plato defines the concept of the World Soul by the Pythagorean ratios but he stops at the end of the fifth octave overtone, where the overshooting comma of Pythagoras occurs – the difference between six whole tones and the octave.  This is because Plato was relying on his Lambda to “contain” the comma of Pythagoras created by the difference between the natural perfect fifths and the octaves – 3 does not go into 2 evenly.  According to Cornford Plato's choice of the Pythagorean Limited over the Unlimited (the prime dialectic of Pythagoras) was a reflection of Plato's perception of a closed system reality.  James, Harmony of the Spheres, pp. 46-47, citing E.M. Cornford, Plato's Cosmology (London: Routledge, K. Paul, 1937).

"The introduction of novel fashions in music is a thing to beware of as endangering the whole fabric of society, whose most important conventions are unsettled by any revolutions in that quarter."    --Plato, The Republic     (c.428 B.C.-c.347 B.C.)

The key “sound byte” with 432 hertz is “militarization of music” from a standardized, logarithmic tuning. Other than that 432 hertz is based on FAKE Pythagorean teachings that are actually from Plato - not Pythagoras! O.K. so let's focus first on debunking the online 432 Hertz cult. It's really just people who can use some programs to modulate tuning without really understanding basic music theory. haha. It's ironic since using high tech gadgetry then becomes an excuse to embrace some supposed ancient past of 432 purity which is total b.s.  Let's consider first the 432 evidence:

1) I've read lots of "first hand accounts" about aliens but that doesn't mean I believe them. haha. 432 Hertz "first hand accounts" are folklore - it doesn't mean anything. I could give you a first hand account now about the Goblin in my bedroom.

2) Any musician knows Bob Marley used 440 when he played live because he played with other instruments like horns that are pre-tuned to that standard.  O.K.please read this basic music tuning information about Bob Marley which proves he did not use 432 hertz despite the "first hand accounts":

In many pieces of Bob Marley instruments like a Fender Rhodes (an instrument that was build for 440Hz and has no microtonal capabilities) or an original Hammond Organ is used (some sources say a change in the power frequency could effect the pitch because the motor is speed locked to it, but this I can't say for sure). On some of his albums and at some live performances a horn section participates. In particular when a saxophone is used (conical wind instrument), there will be intonation issues if Concert Pitch 432Hz is used instead of the Concert Pitch the instrument was build for (440Hz for most brands). 

3) I've read all the 440 Hertz information  but why are the brainwashed culties ignoring the early 440 use in the 1800s? A hundred years before the Rockefellers and Nazis? haha. The fact that 440 was used a hundred years before the Rockefellers and Nazis debunks that "conspiracy."

4) Native Indians did not use FREQUENCY because frequency ITSELF is a "divide and average" concept from Western culture.  Frequency was created by Mersenne in the 1600s.

5) So these "ancient" flutes - where's the proof? Again 432 as a tone note is not the same as a modern scale that uses 432.  So all that 432 music on youtube is based on modern logarithmic scales which means all you have to do is change the key and there is absolutely no 432 hertz in the music. haha.

Those are five basic reasons why 432 hertz is a silly cult easily debunked. With 440 tuning the Hertz is derived from a logarithmic transduction of ultrasound piezoelectric tuning back down, by doubling of frequency with the last doubling given as 440 Hertz for the “A” note to tune all the instruments together. Since logarithmic is usually based on powers of ten then 440 Hertz is used. This 440 hertz instead of 432 hertz was the final logarithmic mathematical step that closed off “open tuning” which means the string instruments and vocal singing naturally resonating to the Perfect Fifth and Perfect Fourth overtone harmonics, not logarithmic square root numbers but just rational integer harmonics.  It’s not any one specific frequency at issue but rather the system of frequencies used as a mathematical philosophy! As one website posts: “This is an important point to make – and one many 432ruthers do not seem to understand – everything moves along with the frequency relationships. It’s like moving a Rembrandt painting a fraction of an inch down a wall and claiming an improvement. All the notes have moved, but the frequency relationships between them are identical (Table 2).”  Another “debunking” of 432 website agrees that the frequency is a “natural resonance” frequency but it is based on the arbitrary “one second” time measurement:  “An octave is the frequency and wavelength ratio 1:2. 256 Hz is an octave of the time unit one second: There are eight doublings of frequency – and correspondingly eight halvings of the wavelength – in the 'interval' from 1 Hz to 256 Hz: 1-2-4-8-16-32-64-128-256. You reach concert pitch A4 = 432 Hz by moving three perfect fifths (ratio 2:3), up from 256 Hz and one octave down. In numbers : 432 Hz = 256 Hz x (3/2)3:2 (= 256 x 27 /16). In other words, already quite fishy, how to get from the time unit of one second to the frequency value 432 Hz.”

A great logarithmic spiral shell image for the octaves on that site. People experience music as a logarithmic or doubling multiplication process but that is not the same as a closed materialistic system that contains sound by amplitude, which is the case with the Western irrational magnitude measurements. We are taught that humans can only hear sound to a certain range of frequencies but it is known that young people who have undamaged ears can hear ultrasound, for example. More importantly when sound becomes ultrasound or infrasound then it ionizes electrochemical energy, creating blissful heat. Even more so the ultrasound creates “acoustic cavitation” which turns sound into light energy by bending spacetime as a vacuum! How does that work? The surface area of the sound wave collapses at a faster rate than the volume of the air that supports the wave so that the “group velocity” of the sound is travelling at a faster rate than the materialistic medium that is supporting it (air or water or even a black hole). I will give further details of course but consider that even outer space has acoustic vibrations as gravity wave “ripples”
When string instruments play they naturally tune themselves to the "open" or natural resonance of the 2/3 and 3/4 frequencies - the Perfect Fifth and Fourths of the infinite harmonic number series. It is the infinite harmonic series that gives music its power and the infinite harmonic series is from natural numbers – simple yet very powerful.  The reason this is true, in science, is called “time-frequency uncertainty” and more on that below. So that is why the violin, without frets, was called “the Devil's Instrument” because these open natural frequencies more easily induce trance.

The main song of this “Devil's instrument” was the tarantella trance.
“...the historic Dance of the Tarantula, a healing trance dance for women from the Greek rites of the “Baccantes.” Women involved in these rites, called Tarantate, danced the “Pizzica Tarantata” (“the bite of the spider tarantula,” also called “the bite of love”). A bite of love supposedly drove them to dance in a wild frenzy in order to free themselves of repressed sexual desires. The dominant music was percussion, with large tambourines playing non-stop to a 12/8 beat, with loud accents. By spinning and stomping their feet, participants symbolically expelled the ‘poison’ of the mythical bite of the tarantula from their bodies.” This is very similar to African trance healing music found in many forms and often “underground” from the patriarchal monotheistic religions like the Zar trance music for women of Islamic African societies. “For centuries women in Africa and the Middle East have used Zar music to cure pain in times of stress or illness.”

Actually in contrast to the 432 Hertz, “militarization of music” started much earlier with Plato promoting the Dorian mode (modern happy music is now in the Ionian mode). Actually it is more the rhythm (slowed down frequency) which really controls the music and so syn (sin) copation or off-beat rhythm is the key to trance: Syncopation or a slow rhythm. Reggae is great music therapy because of the focus on slower and deeper rhythm - reggae heals actually because of the 60 beats per minute Mozart Effect which is from slow baroque music that induces strong alpha brain waves (15 hertz) as serotonin trance. For example it is proven by science that the purring of cats heals the body of people! The emphasis is on the low frequencies which naturally increase the amplitude, as any boom box testifies the power of the bass in dub music.  Elizabeth von Muggenthaler, (2006) “The Felid Purr: A Biomechanical Healing Mechanism,” Proceedings from the 12th International Low Frequency Noise and Vibration Conference, p. 189-208. “Vibrational stimulation between 50-150 Hz has been found to relieve suffering in 82% of persons suffering from acute and chronic pain (Lundeberg, 1983).” A science project found that Cows produce 1000 pounds more milk to classical music because of the slow relaxing beat compared to modern music

I used to play in a roots reggae band myself and then, from my classical piano training, I memorized the Bach Italian Concerto with my favorite part being the second movement, a slow baroque movement. I never knew why I liked it so much until soon after I took part in a paid medical experiment study to earn some college money. The nurse had to give me an EEG and I never had one before - she exclaimed: "You have very strong alpha waves!" I didn't realize what this meant but I did know people thought I was stoned a lot although I never smoked, I was just in a very happy trance all the time. Then I remembered my piano teacher being very impressed at how fast I memorized Bach music. Now I knew why - it was the "Mozart Effect" from my favorite slow second movement - the increased alpha waves had increased my visual memorization skills. My piano teacher even recommended I attend an elite chamber music camp with other classically trained musicians - my roommate at the camp was a violist and music composer who got a perfect SAT score with a full ride music scholarship to Harvard. We even composed music together one day and he went on to teach at Columbia University in NYC, etc. Meanwhile I pursued my trance discovery to the deeper Pythagorean-Taoist qigong connection!

I did immerse myself in music which, I learned, as a listening trance increases the dopamine (the tingling eargasm) and even at deeper levels (the slow rhythm) the serotonin and (7 beats per minute) the oxytocin heart-love levels. So for drumming the rhythm as trance music has been shown to be usually 7 beats per second, thereby synchronizing and amplifying the heart energy which has a much stronger - 1000 times stronger magnetic field - than the brain. So this is also created by bouncing the legs or "shaking" that happens when the ball of foot is rested with the knees bent - the vibrations are 7 beats per second as Dr. Bradford Keeney emphasizes. So when this process is combined with opening up the heart energy - the lower body energy is sublimated up the spine and then down the front of the body to the heart. So it is more than just listening but the learning of an instrument or dancing to music - the synchronization - has been proven to increase the auditory part of the brain more significantly but also music increases the integration of the brain. here and here - increased corpus callosum from intense music study before age 7

Obviously we can’t “escape” Western music but it was discovered when Western music was played to a tribe in Africa that had never been exposed to it that people intuitively know the emotional power of music. So that the “program” effects of music - whether a melody is happy (major), sad (minor), or scary (tritone focus), is actually universal.  But music has continued to rely on the basic tunings from natural consonance simple ratios. Dr. Sandy Trehub has even documented that babies naturally like consonant music while Dr. Kathleen Wermke found infants cry out in simple music ratios regularly and it's not just from exposure to music but due to auditory design.” Elena Mannes, producer, The Music Instinct: Science and Song, PBS Documentary, June 2009.  Dr. Thomas Fritz tested Western consonant tuning on the Mafa tribe in northern Cameroon – a tribe completely unexposed to Western music. The tribe correctly identified the emotions for happy, sad, and scary music. Dr. Fritz states: “The emotional expression of the music is inherent in the music itself. And it is not solely decodable through cultural imprinting.” 

“When looking at the acoustic representations of the consonant harmonic intervals there is a clear pattern of peaks and the autocorrelation is perfectly periodic. The period of the autocorrelation corresponds to the fundamental of bass of the interval. Yet with the dissonant intervals, there was no true periodicity. Instead the acoustic spikes occurred inconsistently.” 

see blog for images.

The stronger brain waves more synchronized from the Perfect Fifth intervals. 

From: Dimensions of Music, Neurolinguistics, Rice University.
“Here, we explore the theory of synchronization properties of ensembles of coupled neural oscillators to demonstrate why simple frequency ratios may have achieved a special status and why they are important for auditory perception. The analysis shows that the mode-locked states ordering give precisely the standard ordering of consonance as often listed in Western music theory. Our results thus indicate the importance of neural synchrony in musical perception.”

This power of music and emotions is encoded in the natural harmonic overtones and undertones. In my first year of college I studied the power of the Fibonacci math series in music and I did a research report on it. I included some of this in my 2000 University of Minnesota master’s thesis on music theory. The deeper reason of music healing is from the “paradox of the poles”:  As Rothstein describes, “These two consonant tones (fifth and fundamental) have strongly dissonant overtones...[and] are the poles of tonal musical drama.” Edward Rothstein, Emblems of Mind: The Inner Life of Music and Mathematics, p. 28. Or to put Rothstein into perspective:  “Generally, overtones which are close in frequency produce dissonance, unless, they happen to be exactly the same. This is why two notes exactly a Perfect Fifth apart sound consonant, while if one note is slightly out of tune, the pair sounds very dissonant. For example, if you play the note at 660 Hz just 10 Hz too high, at 670 Hz, the second harmonic will be at 1340 Hz. This will beat with the harmonic at 1320 Hz in the first note with a frequency of 20 Hz, and this will sound very unpleasant! So, consonance and dissonance are really determined by the frequencies of the overtones of the two notes.”  Interference in Time: Beats

It is this paradox of the poles that defines the description of thesis and antithesis in the dialectics of music theory.  Erno Lendvai states, “The tritones' overtones act as subdominants [fourths] and as dominants [fifths] at the same time. These two positions neutralize and again, the tritone's relationship to the tonic [fundamental] is found, the two are acoustically interchangeable.” Lendvai, Bela Bartok, p. 24. Jeans provides the following on the topic: “In the case of wider intervals such as C and F# [the tritone] there are no beats to be heard, either pleasant or unpleasant, but Helmholtz asserted that C and F# sound badly together because certain of their harmonics (e.g. g' and f'#) make unpleasant beats.” Jeans, Science and Music, p. 157. The Perfect Fifth and Perfect Fourth are taught as the “circle of fifths” in Western music theory but in reality they are the infinite spiral of fifths.  “A true (just) perfect 5th contains no beating, because it is a true 3:2 ratio. An equal tempered perfect 5th contains beats but they are not that ‘rough’ sounding, because the beating is slower than with, say, an equal tempered major 3rd, which sounds very rough and out of tune.” Online comment citing Harry Partch, "Genesis of a Music"

So by having “no beats” the Tetrad-Tai Chi tap into the infinite spiral of energy where there is no fundamental note but rather an infinite listening process. When we get into time-frequency uncertainty this will be clarified.
People mistakenly claim Plato promoted music as the secret harmony of the soul but this is not true! “Having discarded music and gymnastics, Socrates proposes considering the science of “number and calculation” (522 C6-7)…. The link between the correct use of mathematics and the capacity of this discipline to lead to an extrasensible dimension recalls the link between the correct use of the science of harmony (of music in general) and the potential of this art to establish a contact with the soul and supersensible harmony.” Francesco Pelosi, Plato on Music, Soul and Body (Cambridge University Press, 2010), p. 118. Plato actually promoted a new type of mathematics based on irrational magnitude – the Greek Miracle – but the “secret” of Plato which made him so mysterious is that he got this new type of math from music theory, from the Devil’s Interval itself. What is the Devil’s Interval? Here’s how it’s explained from music mathematics:

“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. pdf link here

see blog for images

So that link shows an image of how the Perfect Fifth as 3/2 and the Perfect Fourth as 4/3 are squared geometrically to create 9/8. As you can see the 3/2 and 4/3 as complementary opposites, just like the Tai-Chi symbol but with the creation of 9/8 then an attempt is made to “contain” the otherwise infinite resonance of the Perfect Fourth and Perfect Fifth or 1-4-5 music intervals. “Since 9 actually reduces to a wholetone of 9/8, its cube will reduce to (9/8)³ = 729/512, a 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 Again this was not really a “Pythagorean” approximation, as I will document below – but it was the cover-up by Plato of real Pythagorean teachings. In fact as sound healer John Beaulieau of Biosonics, Inc. discovered the sacrum of the body, origin of the word sacred, creates a Perfect Fifth interval ratio as the key healing ratio: “For example, the distance between your extended toe to the top of your sacrum relative to the distance from the top of your sacrum to the top of your head is also 3::2.” The Perfect Fifth ratio. So when we open up the sacrum of the lower back, what sound healer alchemist Gurdjieff called the “Kundabuffer,” then the life force energy is able to harmonize again with our third eye – the harmonization of heaven (third eye) with earth (sacrum). When the lower back is “closed” off then people are subconsciously controlled by the Kundabuffer.

Economics Professor Michael Hudson concurs about the Devil’s Interval: “The worst problem in tuning occurs in the interval of three whole tones, e.g., between C and F#/Gb in the “natural” untempered methods of tuning. If the ratio of the octave is 2:1, then the ratio of C to F# represents the square root of two — an irrational number. (Burkert [1972:441] notes that the harmonic mean discovered in the context of Pythagorean music theory has a major use precisely in approximating the square root.)” Michael Hudson’s essay, “Music as an Analogy for Economic Order in Classical Antiquity” in Jürgen Backhaus (ed.), Karl Bücher. Theory, History, Anthropology, Non-Market Economies (Marburg:Metropolis Verlag, 2000): pp. 113-35 citing Burkert, Walter (1972), Lore and Science in Ancient Pythagoreanism (Harvard University Press, 1972). So this philosophy of reality not only was the basis for the Greek Miracle creating western science but also the elite control of the technology – justified still by the logarithmic fake Pythagorean cover-up. “The necessity of tempering pure intervals, defined by the ratio of integers, is one of the great themes of Plato’s Republic. In his allegorical form, “citizens” modeled on the tones of the scale must not demand “exactly what they are owed” but must keep in mind “what is best for the city.” Ernest McClain, The Myth of Invariance: The origins of the Gods, Mathematics and Music, from the Rg Veda to Plato (Nicholas-Hays, 1976), p. 11. 

Economics Professor Hudson clarifies McClain’s promotion of Plato’s fake Pythagorean cover-up: “Pythagoras became the patron saint of the most anti-democratic clubs. They used the principles of musical harmony as a patina of pseudo-science to give intellectual legitimacy to a movement whose worldly consequences were anything but harmonious. The Pythagorean clubs became a network of civic cults rising above the local sphere to which most clubs related. There seems to have been some connection with the Delphi temple (the name Pythagoras means “voice of Pythia,” the snake-goddess of Delphi and its oracle). They have been likened to the Free Masons, in that they served as a kind of Council of Foreign Relations or New World Order…. Archytas [the collaborator of Plato] developed the musical scale into a political metaphor for the scales of justice. What gave music this imagery of social balance and just proportion was the ability of its mathematics of harmonic (“geometric”) proportions to serve as an analogy for how inequities of wealth and status rendered truly superior men equal in proportion to their virtue — which tended to reflect their wealth. By this circular logic the wealthy were enabled to rationalize their hereditary dominance over the rest of the population.”

Let's take a closer look at this secret Archytas music philosophy of Plato:

I quoted Plato on Music, Body and Soul - what was the context of that quote? here
[522a] that we seek.” “No.” “Is it, then, music, so far as we have already described it?1” “Nay, that,” he said, “was the counterpart of gymnastics, if you remember. It educated the guardians through habits, imparting by the melody a certain harmony of spirit that is not science,2 and by the rhythm measure and grace, and also qualities akin to these in the words of tales that are fables and those that are more nearly true. But it included no study that tended to any such good as
1 The ordinary study of music may cultivate and refine feeling. Only the mathematics of music would develop the power of abstract thought.
And so what again was Plato's mathematics of music? Quoting Mark Faller's Plato's Harmonic Democracy [sic]
 Timaeus tells us that the Demiurge needs to bond tangible
earth with visible fire. To do so, we are told we will need a third to draw them together. Of the
nature of this bond, Timaeus relates: "And of all bonds the best is that which makes itself and the terms it connects a unity in the fullest sense: and it is of the nature of a continued geometrical proportion to affect this most perfectly." The geometrical mean is most perfect in that it both
conserves the "form" of the relationship, the ratio, as well as provides a universal
interchangeability between the means and extremes.... The movement which the
Timaeus was meant to breath into the inanimate animals of the Republic is a kind of natural growth within this released expansion.

More details here in this critique of Kennedy's music Plato analysis:
Kennedy says is related to Plato’s “so-called ‘quarternotes’ mentioned in the Republic at 531a4” (p. 18, n. 68). Kennedy sees significant divisions occurring at every quarter of each of his twelve “notes,”16 but relating this to Plato is problematic. The term referenced as “quarternotes” is actually pyknomata17 (dense or compressed things), which in the context of the
10 discussion may be considered to be equivalent to an enharmonic diesis (approximately the quarter of a 8:9 tone, hence often referred to as a “quartertone” in English)....

Moreover, Plato specifically refers in the cited passage to such intervals by saying that some believe “that that is the smallest interval, by which measurement is to be made, while others take issue with them, saying that the notes sounded are already the same.”18 In other words, the pyknomata are intervals so small that people argue whether the two notes are the same or not....

Plato himself gives one important example of a musically significant number in the
much-discussed “Myth of Er” of the Republic. Here, Plato famously writes about a group of eight sirens standing on the rim of the circles of the Spindle of Necessity, each singing a note of constant pitch, “and the eight notes together make up a single scale [mian harmonian].” (Rep., 10.617b)....

The early Pythagorean Archytas, for example, suggested a
diatonic division of the diatessaron into a whole tone (8:9),.... we can say with
some confidence that the music theorists in Plato’s circle—above all Archytas, also of Tarentum—were very much the kind of rationalist Pythagoreans.... Continuing with the Timaeus construction, Plato notes that his two series result only in intervals with the Pythagorean ratios 2:3, 3:4, and 8:9 (the whole tone).... If Plato were using a hidden Pythagorean musical scale within his dialogues, it would have to use similar principles as the Timaeus scale, which is a rational extension of Greek music theory and Pythagorean principles to create
a system whose large span could represent the cosmos.
 Mckay, John Z., and Alexander Rehding. 2011. “The Structure of
Plato’s Dialogues and Greek Music Theory: A Response to J. B.
Kennedy.” Apeiron 44, no. 4.

Youtube interview with ancient language/music academic Jay Kennedy on cracking Plato's secret Pythagorean code

Your claims promise to revolutionize the history of the birth of Western thought. How is that so?
JK: These findings do open up many new lines of research which promise to revise our understanding of ancient Greek philosophy, science, literature, politics, and music theory.
 a revised and comprehensive discussion of the musicological background to  the musical `scales’ embedded in the dialogues, showing that the same scale used by Plato was discussed by Theon of Smyrna and that the use of `quarternotes’ equally-spaced between the major notes had precedents in the fourth century (following Andrew Barker’s The Science of Harmonics in Ancient Greece)

And so Ernest McClain who also cracked this music code of Plato says what about this equal-spaced (irrational magnitude) scale:
 Plato saw the necessity of temperament for systems meant to function in harmony, be  they musical scales, planetary orbits, or communities of just men.
 from McClain's book: the Pythagorean Plato.

"Magnitudes have all the characteristics Plato attributes to Apeiron."
p. 394

Socratic, Platonic and Aristotelian Studies: Essays in Honor of Gerasimos Santas 2011
And so then you have Proclus directly stating if there were no Apeiron there would be no irrational magnitudes.  From this googlebook review link

citing Vassliis Karasmanis, "Continunity and Irrationality in Ancient Greek Philosophy and Mathematics."
In other words Apeiron as formless awareness Emptiness was redefined by Plato – as a lie – as a contained materialistic infinity. We all learn the square root of two Pythagorean Theorem in 10th grade high school geometry but rarely do we learn it actually originated from music theory. An overview of music theory from a physics perspective is here with images of the piano keyboard: the real issue here is: what was the original use of this Pythagorean music theory? When Plato promoted the Devil’s Interval through his Lambda he was covering up the real teachings of Pythagoras. The Pre-Socratic philosophers, the real origin of Western civilization, did practice a type of shamanic training with the same foundation as qigong – a philosophy called the musical Logos, part of the tradition of Apollo. Peter Kingsley, a Ph.D. philosopher, had his thesis on Pythagorean philosophy published by Oxford University Press in 1997, Ancient Philosophy, Mystery and Magic. In that book Kingsley says:
“By the time of Plato and Aristotle, the doors of understanding were closed.... Argument [became] more important than appreciation, reinterpretation, an easy substitute for understanding.... [The devolution] destroyed the mythical dialectic.” p. 108, 

Kingsley continued his research with more popular-focus books like In the Dark Places of Wisdom, and Reality. Kingsley’s first academic work was largely dismissed by the Academy because Kingsley took the Pythagorean philosophers, (aghast), at their word. Kingsley did not dismiss their views as arguments “from ignorance” as would have the materialistic skeptics. Kingsley actually investigated the Pythagorean claims of magical training. In Kingsley’s last book he traces the Pre-Socratic origins of this shamanic meditation back to Asia.

I have been asked by many online to further elucidate the Pythagorean music theory explanation for paranormal energy training and these questions and critiques have been the perfect criticism necessary to hone and clarify my thinking. In the West we think of sound as defined by a vibrating substance – a string or reed or tube, etc. But sound also, more fundamentally, is a process of listening and it is this process that enables discovery of the secret infinite power at the source of sound – the ancient alchemical energy called nada (sound yoga) by the Indian yogis – the subject of “psychic music” analysis by paranormal investigator D. Scott Rogo. He noted that when people have near death experiences the music they hear is usually vocal singing or stringed instruments. But Rogo did not understand this secret of why. The reason is the voice and “open” tuned instruments rely on the natural harmonics which are infinite as frequency – they don’t rely on the Western attempt to contain sound as a geometric physical logarithmic measurement. So I am talking about music by humans – even before instruments were used – music as the secret of alchemical paranormal energy training relying on the 1-4-5 music intervals.

I have quoted the M.I.T. book on how the “scandal of the irrational” is from the “sound of square roots” and  how 9/8 is the major second music interval, cubed as the tritone, the Devil’s Interval.  Plato’s Lamba models this 9/8 ratio but it was created from the Perfect Fifth of the natural harmonics by listening to how sound divides itself through overtones and undertones, rationally. So the first tone as 1 is an infinite creation process whereby sound actually, via frequency, transduces into other forms of energy: heat, ultrasound, electromagnetic energy and even spacetime travel. I will go into how Western science can explain this alchemical transformation of sound energy but my point is this secret was discovered experientially by the original human culture – the Bushmen, from at least 70,000 years ago, and it was passed on as the secret shamanic traditions of healing energy for humanity – qigong in China, yoga in India and trance dance shamanism found in the thousands of indigenous tribal cultures worldwide.  So the Perfect Fifth is 3/2 as part of the Pythagorean Tetrad – you square it to get 9/8 and cube 9/8 to get the tritone, the Devil’s Interval aka "the unutterable" or "diabulus in musica." People have created numerous New Age music healing “systems” (i.e. the Rosicrucian octaves from sound into light) but they all still rely on this 9/8 assumption which is from squaring the Perfect Fifth as an attempt to contain it in a symmetric geometric materialistic measurement. These systems are not the real secret behind “the unutterable” which challenges our very concept of time and space.

Part Three: What is really meant by the infinite energy as sound energy?

While the Pythagorean philosopher Peter Kingsley gives the context for a musical shamanic tradition, he does not give the specifics of the music theory – what in the Pythagorean alchemical tradition is known as the Tetrad or Logos, the 1:2:3:4 music ratios, the equivalent of nada for the Indian yogis – also called Spanda under tantric philosophy.  The music theory has consistently been misunderstood in the West – why? Because it is so simple yet very powerful and very radical. This is why there are so many New Age proposals of different healing frequencies, etc. but they all still rely on a logarithmic “Greek Miracle” materialistic model that creates the Devil’s Interval as a geometric irrational magnitude. For example the Westerner Alain Danielou created a 53 note music instrument which he argued was the closest to the Perfect Fifth natural ratio harmonics and this was part of his work for UNESCO studying Indian yogic tantra. But Danielou was still projecting a Western materialistic idea of sound as a visual wavelength measurement instead of sound as a magical listening process for internal mind-body transformation.  Googlebook review of Music: A Mathematical Offering by David Benson, page 225 on the 53 note scale:

 And so this issue of infinite frequency is noted but then cast aside by Western trained physicists and mathematicians: “There does not exist a finite number of positive integral of true fifths to an integer value of octaves as the Fundamental Theorem of Arithmetic states that there is no positive integral power of 3/2 as an integral power of 2.[3] Presenting an infinitely long series, a physically impracticable scale can be found by extending the scale beyond the Pythagorean limits of seven tones. One must address the fundamental effect that this would have on any musical instruments as an infinitely long scale could be ‘infinitely difficult’ to document for the benefit of musicians, let alone offering any practical solutions to instrument development.” Again it is assumed that sound must be measured by a physical vibration as a scale on geometry instead of sound as a listening process of energy transformation or alchemical transduction.

Just as Kingsley reveals a great cover-up about Pythagorean philosophers, so too has the specifics of the music theory been kept hidden. Westerners must radically unlearn many assumptions that start to be presented as solid truths in early education. For example the Pythagorean Theorem did not come from Pythagoras but the Pythagorean Theorem did have its origins in music theory. I corresponded with math professor Luigi Borzacchini who wondered if this music origin of the Greek Miracle was the “secret of the sect?” His research paper eventually got published: “Incommensurability, music and continuum: a cognitive approach.” (English). Arch. Hist. Exact Sci. 61, No. 3, 273-302 (2007).

What's Borzacchini mean by incommensurability and music theory? I devote a whole section to his analysis below but first this - his airing of the topic on a professional math forum in 1999: here Jul 12, 1999 5:39 AM
I think that probably it is wrong to look for the 'first' proof of the incommensurability, even because the numerical 'fact' of some incommensurable results (for example side and diagonal of the square) was already known to the Babylonians, whereas a rigorous proof required instead
the introduction of the "absurd" proof in an earlier visual and constructive mathematics, so that the theorem had to be proved together with the establishment of its method of proof.
However it is of great relevance the hypothesis of a 'musical' background for the discovery. And actually a 'negative' proposition, asserting the incommensurability in musical and arithmetic terms, can be found in the prop.3 of the "Sectio Canonis", ascribed to Euclid (Appendix).
The same proposition can be found in Boethius' "De Institutione Musica" iii,11 (DK 47 A19), ascribed to Archytas: "No mean proportional number can ever be found between two numbers in a ratio superparticularis". 'Ratio superparticularis' is the 'epimorion diasteema (logos)', i.e. the ratio n+1:n or mn+m:nm, for n,m integers (Appendix).
So it sounds very abstract but with incommensurability we are talking about the infinite and paradoxes at the foundation of Western civilization – paradoxes that the materialistic skeptics would like to ignore but the real thinkers of the West admit remain very real. Borzacchini describes these unsolved paradoxes:
 “(iii) after Dedekind, Cantor, Hilbert, Zermelo, Goedel, Cohen we know that the Aristotelean and Euclidean continuum admits numerable models, that we can not give to its modern versions a first order categorical axiomatization, that the geometrical continuum can not be proved coincident with the numerical one, that it can not be empirically verified, that the place of the numerical continuum in the transfinite hierarchy is one of the greatest so far open questions, that it is linked to the most disputed axiom of set theory, etc.” Luigi Borzacchini, “Music and Incommensurability,” Historia-Matematica, August 18, 1999.

Now most people are probably not going to follow all the insides of mathematical logic and its secret musical problems but math is the language of science – and Borzacchini states the foundation of science, due to these paradoxes, is a “pre-established disharmony.” Again the secret is the role of music theory at the origins of the Greek Miracle, the discovery or invention of the Pythagorean Theorem based on incommensurability. To quote Borzacchini again: “Hence Arithmetic is the source of that preestablished harmony between reality and language that we can not not believe after almost four centuries of astonishing achievements, but we must even say that, neither tendentially, syntactic representation can thoroughly mirror reality, become someway iconic. And this because it is marked in its basic principles with a preestablished disharmony, that is even its hidden evolutive principle.”

Borzacchini also has a paper published: [2001]  “Light as a Metaphor of Science: a pre-established disharmony.” Semiotica, 2001, 136, November 200, pp. 151-171. His term, “pre-established disharmony” is evidently a spin on Leibniz' claim of a pre-established harmony to Western science.

For those of you who still don't believe Borzacchini is talking about the arithmetic connection to music - here is his description of his book in Italian: Plato's Computer.
This idea of syntactic representation was the basis of the parallel genesis of Greek philosophy and mathematics, but ever since this beginning it was clear that, inside this relationship between those two worlds, there was a deep ‘preestablished disharmony’: words and things were not alike, neither in their being nor in their becoming, some words (being, not, true, equality) did not represent any ‘thing’, a part of a word did not represent a part of the represented thing, language represented diachronically a synchronical reality. This disharmony grounded many formal paradoxes that endure up to the present time, first and foremost ‘the liar’ [3rd and 4th chapters]. ... Beyond language, music also played a role in the development of Greek mathematics (even the discovery of incommensurability probably had its beginning in the musical problem of the tone dichotomy), an involvement that lasted until the 17th century: afterward, mathematically there will only be ‘sound’, and musical harmony will become something belonging only to the irrational realm of ‘beauty’ [11th chapter].
Now for those of you still in denial, hopelessly following your Platonic Cult of Western Civilization - here is Borzacchini again - he is clearly not equating Western math with the "pre-established harmony" he mentions as arithmetic (so don't cling to his use of that phrase as if it equally balances out the deep preestablished disharmony.
The syntactic paradigm [pre-established deep disharmony] was the result of the Platonic and Aristotelian foundation, and developed its 'strong' form at the beginning of the XX century science.

In this framework modern science achieved its greatest breakthroughs: quantum mechanics, formal logic and computer science. All of them, however, can not avoid the occurrences of the never ending paradox connected to the syntactic paradigm. Below the surface of the antinomical form, we can maybe reveal the deep 'preestablished disharmony' of the link between human knowledge and reality.
So what’s another way of stating this fundamental difference between arithmetic and geometry vis a vis music theory? Einstein famously stated if a person does the same thing over and over expecting different results it’s the definition of insanity. But people mainly know the “pop” version of Einstein without noting the irony of Einstein being profoundly influenced by the top mathematician Henri Poincare who used the term “relativity” before Einstein. Poincare also created the original chaos mathematics. Number theory tells us a very different yet fundamental way of thinking about chaos math – if we do a simple thing over and over (e.g. meditation), the result, contrary to Einstein’s claim, is radically different and not insane. Why? Because that simple thing uses rational numbers as non-linear resonance. 

Here’s how a number theory book explains it. Number theory in science and communication: with applications in cryptography, physics, digital information, computing, and self-similarity by Manfred Schroeder (Springer, 2009). Schroeder states how amazing it is that the differences between rational and irrational numbers actually determine the creation of chaos – that chaos is simply the irrational number extending the digits unpredictably and never repeating.  “In fact, the deterministic chaos, which dominates many a physical discussion these days, is ultimately understandable in these simple terms: the evolution of a complex number, in the final analysis, is akin to the left-shifting of digits of a real irrational number. No matter how precisely the initial conditions are known, temporal evolution will sooner or later bring the originally unknowable, far-right digits (representing the exact initial conditions) into the neighborhood of the ‘decimal’ point, where they will dominate the system’s behavior, which will then seem chaotic.”(p. 402) Meanwhile Schroeder states that resonance using rational, low Pythagorean integers is too powerful and causes matter to disintegrate through nonlinear feedback.

So again the "irrational" number are actually - empirically - an infinite spiral of energy that can not be precisely predicted by science. Here's how Charles Madden describes it in his Fractal Music book as quoted in The Two - Part and Three - Part Inventions of Bach: A Mathematical Analysis Honors Project By Jennifer Shafer 2010
As this process is repeated, the values found for π on each iteration “swing positively and
negatively from side to side in a smaller and tighter trajectory, and could be said to spiral in on
the limit. The center of this convergence (the circle itself) is the attractor.”
So the "squaring" already assumes, incorrectly, a symmetric geometric measurement in order to "contain" the infinity but as this article shows, the empirical reality of number as harmonics is that the geometry is asymmetric as infinite time. The source of reality as consciousness is number as holographic harmonics - a formless, non-material one-dimension that creates all the other dimensions of spacetime.

Has this process of energy-matter from natural numbers been tested physically? Yes: “Mogens Jensen,Tomas Bohr and I, working at the University of Copenhagen, recently investigated phase locking in great detail. We found that at the transition to chaos the motion is always locked: As one changes the frequency of either oscillator – for example, by changing the length of a pendulum or the frequency of a driving force – the ratio between the two frequencies locks onto every single rational value…. If one subjects a pendulum to a fixed driving frequency and plots the actual frequency of the pendulum against the natural frequency or length of the pendulum, one obtains a curve consisting of an infinity of steps.”  Chapter on the “Devil’s Staircase” as this is called – from the Devil’s Interval. scribd link here for A book on nonlinear physics. 

O.k. my emphasis in the quote – rational numbers, infinite chaos and too powerful for Western science: We can model and discover the Devil’s Staircase but it is not as a technological reproduction or in other words, too bad for the skeptics: a double blind experiment is impossible. Why? The results are unpredictable yet the phenomenon is real. The “Devil's Staircase” pattern has previously accounted for the frequency of natural phenomenon, such as earthquakes and avalanches and arrhythmia heart beats and even punctuated equilibrium in evolution – an unpredictable big step after a number of small gradual changes. But if the “natural frequency” of a machine is discovered then it will cause the machine to break down. Of course this “Devil’s Staircase” assumes a logistic, symmetric equation still – it’s not based on non-commutative quantum time-frequency. 

1) Devil's Interval is the Tritone. 2) The Harmonic Series diverges so it's the "invention of the Devil." 3) The Devil's Staircase is the nonlinear quantum chaos harmonic oscillator of the Perfect Fifth and Octave. That's the Simple Answer – a triangulation of evidence for the Perfect Fifth/Perfect Fourth as the secret to alchemy.

O.K. so without being mired down in these paradoxes of Western science, called “self-organized criticality,” which get ignored by the skeptics, we need to address qigong on its own terms and we can do so via the Pythagorean Logos music theory, which, ironically, was the secret origin of Western science. When we look at the origins of Western science the real experts agree with Borzacchini that music was involved – only they don’t understand how. To quote David Fowler, author of The Mathematics of Plato’s Academy (Oxford University Press) “...the manipulations of music theory seem to depend fundamentally on the operation of compounding, an operation which seems to pose some serious problems for mathematicians. My purely speculative that music theory might plausibly give some help with this problem.” Fowler though wanted to dismiss this music connection and as Borzacchini points out – the Western science created a “disharmony” by changing the Pythagorean Logos to create the irrational magnitude as the Greek Miracle.

So if the Pythagorean Logos did come from Asia originally, as Peter Kingsley documented, then what was the music theory connection in Asia for the qigong training? The Yellow Emperor, Huang Ti, in 2700 BCE, told Ling Lun to create the “infinite spiral of fifths” music tuning based on the Perfect Fourth music interval as yin and the Perfect Fifth musical interval as yang, according to the 240 BCE book, Lü-shih ch’un-ch’iu (The Spring and Autumn of Lü Pu-Wei). Empirically the frequencies are infinite.  “Before the idea of frequency existed, however, the same relation was expressed simply in terms of length, the length of a resonating agent multiplied by 2/3 being equivalent to the frequency multiplied by 3/2. The length of a zither string, then, multiplied by 2/3 gives a note which when struck is a perfect fifth higher than its fundamental. This is the first step (or ) in a process which evolves an unending spiral of notes. The length of the resonating agent which sounds the perfect fifth is then multiplied by 4/3, the resulting note being a fourth below the perfect fifth . . .” Joseph Needham, Science and Civilization in China, Volume 4, Part I, pp. 172–173. So once again we are questioning the very concept of frequency! Here’s details on how a Chinese traditional instrument would be tuned using the Pythagorean spiral of fifths:

As arising from the Diapason or Tai Ch'i of the Wu Chi (the void), sound healer John Bealieau comments, "the fourth and fifth work together as yin and yang...The fifth and the fourth are the basis for the 1-4-5 chordal progressions found throughout music of all cultures." Bealieau, Music and Sound in the Healing Arts, p. 47 In Taoism this “infinite spiral of fifths” is practiced as 12 notes applied to the body-mind for alchemical transformation. It’s called the “small universe” or microcosmic orbit meditation. You can read an introduction to this – with this book link here: and the real traditional explanation of the 12 “notes” or nodes of the infinite scale is explained in this crucial book Taoist Yoga: Alchemy and Immortality here in full free read: 

There we have it folks – a non-Western music theory explanation of internal alchemy training. Is it “ignorance”? No – it’s very real. What did the ancient Chinese know – what was their secret? Let’s quote a Western physicist: “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 (my emphasis). See image archived here of the infinite spiral of fifths

There you have it again folks: empirical infinity. Now in music theory this is, as I mentioned with the Chinese, called the “infinite spiral of fifths.” It’s considered in the West to be music theory as simply numerology – something not important and only requiring a “compromise” or “adjustment” so that a rational system of measurement can be devised (i.e. irrational magnitude system). “We are thus faced with the fact that there is no end to this process we have initiated: transposition up a fifth and transposition down a fifth take us on infinite journeys, ever generating new notes, even if some of these... are tantalizingly close. The journey can be thought of as traversing a spiral... for each 30º step clockwise we spiral outwards and transpose up a fifth, while for each 30º step anti-clockwise we spiral inwards and down a fifth. Adjacent points on the same ray of the spiral differ by the Pythagorean comma.”

-Neil Bibby, Tuning & Temperament: Closing the Spiral,” chapter one of Music and mathematics : from Pythagoras to fractals by John Fauvel,. Oxford ; New York : Oxford University Press, 2003
In other words the Westerners need to “contain” infinity to feel like we are in control – and hence the creation of incommensurables aka irrational magnitudes. This issue is quaintly explained and brushed away as the “scandal of the irrational” as if the well-intentioned yet naïve Pythagoreans had stumbled upon some deeper truth they could not handle. As Peter Gorman says, “The dyad [or Diapason, the octave and its overtones] was a symbol of infinity, hence Pythagoras must have known about its irrational [sic] properties.” Peter Gorman, Pythagoras: A Life (London: Routledge and Kegan Paul, 1979), p. 137. The Void for Pythagoreans was the principle of differentiation, “in Pythagorean arithmetic, the principle of differentiation is the first even number, the dyad….” Dominic O'Meara, Pythagoras Revived, (Oxford University Press, reprinted 1990), pp. 67-68. The Westerners have it turned around – the real secret power of infinity was covered-up and replaced by a “compromise” since the real alchemical inner training could no longer be accepted. 

So then we get “sophisticated” explanations of how naïve listeners, stooped in Pythagorean shamanic ignorance, needed to slowly adjust, over centuries, to the tritone, the Devil’s Interval, which, as we’ve shown, is actually the origin of the square root of two mathematics. See Peter Pesic: Isis. 2010 Sep;101(3):501-30. “Hearing the irrational: music and the development of the modern concept of number.” O.K. again the focus here is to unlearn all this Western science training and to take the ancient Chinese at face value – the infinite numbers as the yin and yang of Taoist inner alchemy qigong training. Just like the Taoists, Pythagoreans taught that numbers, like yin and yang, were female and male. So the number one was male but actually not a “number” since it represented the first form of infinity. The number two was female but was the form as matter yet resonated with and from the female formless origin of the number one – the female formless called Apeiron by the Pythagorean philosophers. Sounds too woo-woo? Again consider physicist James Jeans – the “infinite spiral of fifths” is empirically real – it is infinite frequency as number. It is energy that considered too chaotic by Western science, creating the “Devil’s Staircase” – an unpredictable infinite resonance in Nature.

Part Four: The elaborate cover-up of Pythagorean Qigong training, now as the Greek Miracle of Science

So what happened in the West? The infinite number from music theory taught by the Pythagoreans was changed – yang is 2/3 and yin is three fourths – from the Pythagorean Logos of 1:2:3:4, the Tetrad.  The Orthodox Pythagoreans only used the Tetrad but you won’t learn this by studying Pythagorean philosophy since it has been kept secret.  To quote an expert: “Orthodox Pythagorean theory recognizes five consonances: fourth, fifth, octave, twelfth, and double octave; and these are represented by the multiple and superparticular ratios [n + 1 : n] from the tetrad. The number 8 obviously does not belong to the tetrad.” André Barbera, "The Consonant Eleventh and the Expansion of the Musical Tetractys: A Study of Ancient Pythagoreanism," Journal of Music Theory, 1984. Like I said, the Pythagorean Theorem did not come from Pythagoras! No 8 means no 9/8 which means no 9/8 cubed as the square root of two, no Devil’s Interval and no “scandal of the irrational.”

So where did these irrational numbers come from? Philolaus never became an Orthodox Pythagorean and instead he broke the vow of secrecy by trying to write down the teachings which were then used by Archytas, a military engineer, and his collaborator Plato. See J.B. Kennedy’s paper, “Plato’s Forms, Pythagorean Mathematics, and Stichometry,” Apeiron: A Journal for Ancient Philosophy and Science, 2010, pdf link: “Greek theorists like Plato’s correspondent Archytas constructed measures of relative musical harmony.” Carl A. Huffman, Archytas of Tartenum: Pythagorean, Philosopher and Mathematician King (Cambridge University Press, 2005). Huffman argues that Plato and Archytas were host-friends and competitive colleagues – with Archytas stressing the practical side of Pythagorean harmonics while Plato emphasized the pure philosophy of Pythagorean Number. Both Plato and Archytas were relying on Philolaus and therefore were not “orthodox” Pythagoreans. 

  So ... “it is interesting that Philolaus uses no other term for the tone than the mathematical ratio 9/8.” Philolaus of Croton: Pythagorean and Presocratic: A Commentary on the Fragments and Testimonia with Interpretive Essays by Carl A. Huffman Cambridge University Press, Jul 22, 1993, p. 163. It is interesting isn’t it? Because there had not yet been a conversion by Archytas to the symmetric, irrational magnitude of the Pythagorean ratios. Hence Philolaus would not have used any other term for 9/8 while Archytas created the new “geometric mean” term for the square root of two.  Here’s a graph image explaining the means used by Archytas: 
See blog for images

We find further confirmation that this use of 9:8 from the orthodox Pythagorean Tetrad 1:2:3:4 is an innovation of Archytas and his possible pupil Eudoxus in “Pythagorean Mathematics and Music,” by Richard L. Crocker, The Journal of Aesthetics and Art Criticism, 1963. Crocker notes that R. P. Winnington-Ingram's, “Aristoxenos and the Intervals of Greek Music,” (1932) as an article “admits that the pre-Platonic theorists used the tone 8:9 to construct a scale, but for some reason is reluctant to attribute this construction to the Pythagoreans.” Yep, “some reason” – unknown, until now: “Apart from the interval sizes, which were disputable, Archytas overturns the otherwise canonical relationship between the enharmonic and the two other genre.” P. 196, Stefan Hagel, Ancient Greek Music: A New Technical History (Cambridge University Press, 2009). 

"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!"

Math professor Luigi Borzacchini has done the best work in exposing this ancient "secret of the sect" as he questions the founders of the Greek Miracle of what became western science. 
"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 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." 

So, in other words, music proved you can "not" physically construct an infinity while geometry created a way around the conundrum - the first proof, due to the truth of alchemical training, had to remain a secret! Borzacchini confirms this secret: "Many authors (Szabo, Knorr, Burkert) have discussed Boethius’ text, and all of them have recognized a musical phase in the discovery of incommensurability." You can't talk about something that is not real (a physical demonstration of the infinite). The only real truth is non-physical consciousness and so it must be taught in silence - the real Pythagoreans practiced nine years of silence as inner sound yoga training! As Borzacchini explains, "a purely negative result (speaking about 'something which is not') had to fall under the blows of the negative judgment paradox. Such paradox forbade speaking about what is not, and played a crucial role from Parmenides to the Sophists and Plato, widespread between the end of the V and the beginning of the IV century in Athens, as witnessed in Plato’s Sophista (Plato 1964)." 

So then Borzacchini states that irrational magnitude as incommensurability was something of a revolution: " rose instead from the basic cultural and political questions of the (not only Pythagorean) ancient Greek culture, where music and the relationship between musical modes and state/society played a role that is difficult to understand nowadays, and were essential ingredients of both society and the time of Archytas and Plato a sharp rupture occurred that fostered a shift from musical to geometrical incommensurability, so that we can find nothing about the geometric approach in the extant Pythagorean fragments as well as nothing about the musical approach in Plato or Aristotle." In other words we are talking about a serious cover-up and what exactly was the previous role of the Pythagorean harmonic music ratios? Indeed it was just like the qigong training or yoga training or trance shamanic music healing training of the original human culture. Borzacchini notes that this Greek Miracle discovery indeed was an extension of a longer tradition: "From a comparative historical point of view, it is worth remembering Iamblichus’claim that the musical proportions were introduced by Pythagoras but originated in Babylon. According to Needham (1954, IV, 177), even the Chinese musical theory concerning pitches had the same origin, even if in China they were organized not as a “scale”, but as a “court” and a “spiral of fifths”." Borzacchini states that what enabled this continued to evolve into the Greek Miracle as a rupture - was the natural experience of the geometric continuum as a materialistic infinite process of division. And finally Borzacchini exposes this continuum, the basis for the "pre-established disharmony" as a formal idea of Western science: "If the continuum has never got empirical evidence or logical naturality, if it stems from complex processes of cognitive development and if it does not appear outside western civilization, we can suppose that also its evolution in Greek mathematics had to be quite complex." Of course readers will have to find access to an academic database to read Borzacchini's paper in full - which is a stunning expose of mathematical-music philosophy. I've had the pleasure of corresponding with him a few times - I had a dream of an equation of the musical origins of math which I scribbled and sent to him back in 2001. He responded that my math was good but that there's no historical proof for it.

O.K. there has been an accusation to me that Borzacchini is not referring to music theory when he says a pre-established deep disharmony exists as the origin and evolutive principle of Western science. Here is another quote from Borzacchini to established that phrase directly connected to music theory:

The simplest form of this dis-harmonic core is probably also today the ancient ''negative judgement paradox'': <given that an affirmative statement corresponds to a fact in the world, something that is, we have that a negative statement corresponds to something which is not, but a statement about what is not, is about nothing and hence is impossible >. Here we find out the ancient irreducibility between being and not being, which cuts off any full matching between reality and language, between being and sign. And this disharmony has been the great source that has produced in the last more than two thousand years the evolution of the syntactic paradigm and the whole western civilisation cultural framework.
From the conclusion of Borzacchini's essay on Being and Sign

So what has to be clear is that the continuation of the Babylonian algebraic analysis (harmonic mean x arithmetic mean = geometric mean squared) was combined with a Brahmin insight into the void as a materialist ritual sacrifice - sunyata as "negative infinity" which Aristotle was against. In other words by inventing irrational magnitude the arithmetic ratios had to be with a value greater than one so that a theoretical abstract fiction of a physical geometric infinite magnitude could be created - first zero, then square root of two, then cube root of two and so on, into higher dimensions of technocracy as the evolution of pre-established disharmony. This Greek Miracle was only established by using the Attic phonetic alphabet (originating from Indo-European roots) to create a commutative, symmetric geometric algebra of irrational magnitude - a "positive" embrace of a theoretical "contained" infinite that did not empirically exist. That is why the Perfect Fifth as 2/3x could not be allowed! It had to be covered-up, hidden with a "bait and switch" method since the Perfect Fifth as 2/3x is C to F while the Perfect Fifth as 3/2x is C to G - thereby violating the commutative myth of geometry using reversal time as a spatial wavelength. 

The origin of time can not be seen but we can listen to it as consciousness, the source of the thoughts in our mind, as the source of the I-thought. This is why in India consciousness was the goddess Kali that through creation and destruction created time as a spiral which enables precognition of the future. Ancient Greeks knew time as Kronos - the God as Saturn which created Chronos as Time? How because Jupiter as the God of space (Apollo) protects Earth from comets. But what happens? As Kepler discovered the harmonic resonance of Saturn and Jupiter, through the Pythagorean low overtones, has great power. "Mars, for example, covered a perfect fifth, from C to G, the ratio 3:2, while Saturn sounded out perfect third. All the planets could produce glorious they intoned their way around the orbits, until each planet produced its own song." (Thomas Levenson, Measure for Measure: A Musical History of Science, 1994, p. 112).  Quantum chaos resonance has rediscovered this secret! So unpredictable in detail but with great accuracy, the orbits of Saturn and Jupiter, in the future, will resonate from being in the same plane, thereby resonating an asteroid to get thrown out of orbit, with Jupiter no longer protecting  Earth, and the asteroid or comet destroying all 3-D bifocal life on Earth. Life will still exist on earth but the illusion of three-dimensional space as the "contained" geometric infinity will be destroyed and consciousness as holographic infinite time as an eternal present will be restored.  “Chaotic Heavens: Can mysterious wobbles in Jupiter and Saturn’s orbits spell doom for life on Earth?” of the Feb. 28th, 2004 issue of the magazine New Scientist that the ratio of 2:5 causes asteroids and comets to destroy all life on Earth. pdf link
What is really going on here? We are talking about the difference between arithmetic as pure number and then Western math as dependent on geometric measurement. Westerners are taught, very early on, that if something can’t be measured systematically using math then it is not real but this philosophy of the skeptics covers up the real paradoxes between arithmetic and geometry – the “pre-established disharmony.” The skeptics may admit that measurement can never be perfectly exact but it is the best possible system. But, what the skeptics need to realize is that while the math of irrationals is precise it is not accurate! Again when it comes to infinity we have just shown that real music theory of the Perfect Fifths and Perfect Fourths, the ratios of 2/3 and 3/4, can’t be contained and this is the secret of yin and yang energy for internal alchemy. Now also consider that Perfect Fifth and Perfect Fourth music intervals are found in all human cultures – not just the Chinese Taoists or Pythagorean philosophies.

The birth of the blues: how physics underlies music J M Gibson Argonne National Laboratory, 9700 Cass Avenue, Argonne IL 60439, USA  I watched this talk on realplayer and Gibson emphasizes that blues music has its power by bending or trying to subvert the Western equal-tempered logarithmic tuning – the “crushed” notes of the flat third and flat seventh are closer to the rational number overtone ratios – 4:5. This link has a physicist explaining how a different fundamental string frequency is chosen and then the overtones are taken for the perfect fifth and major third and from that process the scale is created – the same intervals but different frequencies since a different starting pitch is used. But what is left out is that this process for natural overtones is actually infinite and so in reality there is no original starting wavelength or time with its inverse frequency – not as a “zero” materialistic geometrically contained infinity. 

The early Near East or Levant civilizations used a “divide and average” math which approximated the convergence of the irrational square root of two but the arithmetic was still infinite while the geometry was sacred and not a “contained” infinity.

The infinite spiral of fifths as pure number energy of sound are lied about - "contained" - into an octave measurement. This error of math creates what's called the "comma of Pythagoras" - the inherent difference between 12 notes created from fifths and their closest octave tuning - 7 doubling of the octave. This "comma" can never be resolved - infinitely - since 2 and 3 do not go into each other evenly with no remainder. So, for example, the Chinese created a 60 note scale in an attempt to "converge" this inherent difference - but it is not the same as equal-tempered tuning, because the philosophy of the "infinite spiral of fifths" accepts the infinite energy creation from yin-yang dynamics.

So then 5/4, the major third, was used as “just tuning,” as an extension of the Pythagorean Tetrad since 5/4 is from 9/8, the major second, doubled. As musicologist Ernest McClain explains in his analysis: “Differences between the two systems (Spiral Fifths for the Arabs and Just Tuning for the Jews) are always a comma….that “cross over” from the “Pythagorean comma”.... This crossover over near-coincidence [is] acceptable today in Equal-Temperament theory – is no greater than the error in the first pair (A vs G, Plato’s harmonic and arithmetic means shared by both systems).” Ernest G. McClain, “Children of Abraham,” 2007. The equal-tempered logarithmic scale is considered the “materialist” scale subset of the larger tonal scales, the 72 srutis, created by the infinite spiral of fifths used in traditional Indian music tuning. listen to traditional Raga dipak here  “The idea is that the tritone is surrounded on the tone circle by the fourth (4/3) on its right and the fifth (3/2) on its left, two inverse tones. We can then repeat this by finding the average of this new value and its symmetrically placed inverse, and continue this procedure. The following algorithm shows how this succeeds in deriving the Vedic approximation.” Jay Kappraff, “Ancient Harmonic Law,” Bridges, New Jersey Institute of Technology, 2007.

One comment by a musician online to my research explained it this way: “In western 12tet [12-tone equal-tempered scale] there is no difference in terms of frequency between the diminished fifth and augmented fourth intervals (both 600 cents, exactly half an octave). But in other western and Asian tuning systems the augmented fourth and diminished fifth have different ratios, and they exist as separate intervals in the harmonic series.” So this is not to say that the tritone does not exist within the natural rational number harmonic series, but rather the Western equal-tempered tuning attempts to “contain” the tritone through the concept of incommensurability. Instead of non-Western sacred geometry being commensurable and the “divide and average” arithmetic infinitely harmonizing, the Western arithmetic gets squared so that it “converges” to an incommensurable contained infinite geometry as irrational magnitude. Award-winning math teacher J.J. Asher, in his article, “The Myth of the Irrational Numbers,” pdf link here describes the problem as this: “Irrationals are becoming numbers but they will never, for all of eternity, be numbers. Think about this: (sq rt) 2 = 1.4142135... and the integers continue on forever approaching some value but never ever reaching it. Since (sq rt) 2 will never be a number because it is in continual motion moving towards some number, it is a non-number. Since it is a non-number, it cannot be located on the number line. I conclude then that only rational numbers have a location on the line and hence only rational numbers are real numbers.”

So for example Kepler was against the “closed” solution for the Golden Ratio triangle instead embracing the infinite Fibonacci numbers as “male” and “female” harmonic ratios.  The Golden Ratio sound is demonstrated by the Shofar horn but as sacred geometry – not a “contained” irrational magnitude. So for the Golden Ratio of A:B::B:A-B the algebraic result is A(A-B) equals 2, 3, 10, 24, 65, 168 while B squared equals 1, 4, 9, 25, 64, 169 creating the male-female (complementary opposite) convergence. (“Kepler’s Celestial Music,” in Studies in Musical Science in the Late Renaissance, 1975, Warburg Institute, Oxford University). The Golden Ratio is originally “A:B as B:A + B” but that's not the contained materialistic infinity of gematria (promoted by the incorrect Pythagorean gematria of Leonard Horowitz and the Solfeggio early Western scale - see this debunking of the fake Pythagorean Leonard Horowitz Solfeggio scale for exposing why it is incorrect). Kepler realized that the replacement of “A + B” with “C=A-B” used to solve the Golden Ratio for the quadratic equation, as a “contained” infinity, is wrong. When A(A-B) exceeds B Squared the number is Masculine and where it falls short it is Feminine. For Kepler, the method of exhaustion, derived from “Plato’s Theory of Numbers,” (for the square root of two, the ratio of the triangle diagonal to the side as an infinite fraction series converging on the irrational, by alternately greater and less ratios) exposes the inherent Pythagorean complementary opposites of evolution – the male and female principles. (“Plato's Theory of Number,” by Ivor Bulmer-Thomas, The Classical Quarterly, 1983). 

In music theory the Golden Ratio represents the first attempt to “contain” the infinity as geometry for the Greek Miracle when Archytas “doubled the cube” using geometry. The music ratio compound numbers using complementary opposites reveal the secret solution: the major third, 5/4, from 9/8 doubled, is the complementary opposite of 8/5, the minor sixth, of the Fibonacci series.  5/4 then approximated the cube root of two based on the secret conversion of the music ratio compound numbers. Stuart Isacoff, Temperament: How Music Became a Battleground for the Great Minds of Western Civilization (2003). “The frequency ratio represented by four semitones, for example the interval from C to the E above it, is called a major third. This represents a frequency ratio of ... cube root of 2:1, or roughly 1.25992:1. The just major third is defined to be the frequency ratio of 5:4 or 1.25:1.” P. 292 pdf link Mathematics of Music:  

Archytas could apply his geometric mean: the continued proportion of Hippocrates can also be cubed so that A is 1 and 2A is 8 and the volume proportion for doubling the cube is 1:2::2:4::4:8. Since the cube root of this equation means that X equals 5/4, the major third music interval as the cube root of two, then the cube root of four, as Y, gives the harmonic ratio of 8:5, the complementary opposite of 5/4 (the music interval the major third, 5/4, is inverted as the minor sixth, 8:5). The secret of the sect music equation for the compounding proportions of the side lengths is this: A:X::X:Y::Y:2A = 1:5/4::5/4:8/5::8/5:2. We find this same Archytas compound ratio approach for precise calculation of “doubling of the cube” to construct catapults in 350 BCE. Stanford Encyclopedia of Philosophy. “In other words when music theory paved the road toward the discovery of incommensurability the idea of geometric magnitude was too clumsy to develop and even to understand such discovery, and it was exactly the possibility of the geometric drawing of a not-existent music interval to foster the development of the Aristotelean continuity.” Luigi Borzacchini, “Music and Incommensurability,” Historia-Matematica, August 18, 1999. So these geometric proofs actually rely on the music ratios as harmonic string lengths. Thankfully the promoters of Platonic technocracy, the Lyndon LaRouchites, provide ample evidence of this: and for a detailed explanation of Archytas’ geometric conversion of music ratios see this article:

And in contrast to the technocrat "contained" geometric infinity LaRouchites, math professor Luigi Borzacchini gives a much more nuanced analysis of the transistion from the Orthodox Pythagorean music analysis to the materialistic infinity of Platonic geometry: here Borzacchini's later published version of this analysis is behind paywall except by going to your local college or university with database access or hard print journal access. As Borzacchini states, debunking the LaRouchites:
Anyway I stress that such a flaw was not a limit inherent in the
musical-arithmetical approach, because a rigorous proof could be built with
the techniques of the VIII book of the Elements, and without reference to
geometric similarity
....The first is that incommensurability was not the result of simply technical philosophical or mathematical problems, but rose instead from the basic
anthropological and political questions of the (not only Pythagorean, but
tout court) ancient Greek culture, where music and the relationship between
musical modes and state played a role that today for us is difficult to
understand, in any case were the essential ingredients of both society and
culture.The second is that there was between Archytas' and Plato's schools a sharp rupture causing a shift from musical to geometrical incommensurability, so
that we can find nothing about the geometric approach in the extant
Pythagorean fragments, nothing about the musical in Plato or Aristotle.
Why does no one think this is important? Because in the West we define sound by what we measure visually when in fact originally we listen to sound. When we listen then the resonance is due to the push-pull of the 1-4-5 music intervals, the basis for the blues, which then also became the basis for rock and jazz. Why do they “push and pull”? Because the Perfect Fifth as the 3 does not evenly divide into the octave as 2. It’s that simple – yet that radical. The Greek Miracle covered this up by creating the square root of two as the tritone, the Devil’s Interval. In the West we are taught to think hearing 1-4-5 over and over is boring and simplistic but that is because we hear it from the constraints of the equal-tempered tuning logarithmic system. In reality the 1-4-5 is infinite just as 2/3 was sacred for the Egyptians and just as the Cantor Set only uses 1 and 2/3 and yet it is considered infinite, but as math professor Borzacchini points out this has created unsolved paradoxes. 

We want to think that the octaves are doubling in frequency but empirically this is not true – even though Western math and science has constructed this logarithmic geometric lie. In reality the “infinite spiral of fifths” shows us that the value of the octave changes because geometrically the pitch value changes depending on the direction of the measurement – it is truly non-commutative!  Image of the Infinite Spiral of Fifths:
See blog for images

It is very possible that there is secret military technology based on this sonofusion infinite energy alchemical reality. Dr. Andrija Puharich was a CIA mind control scientist who constructed a device creating ultrasound resonance to split water. The inventor Stan Meyer relied on John Keely’s principles to do this, as Dale Pond reported: “Dale Pond is reported to have recommended this water sonofusion propulsion to Stan Meyers who attended a John Keely natural resonance energy conference. Keely relied on ultrasound standing wave resonance – 42,800 CPS (Hertz) -- for his water dissociation plasma propulsion.” “Verification of Frequency to produce Etheric Force from Water,”, 12/20/97. Sonofusion aka cold fusion continues to be investigated with increasing claims of success and even supposed production for industrial energy use in the works. John Keely, just like Victor Schauberger who claimed to have created sonofusion water propulsion of aircraft for the Nazis and the U.S. military – both of them only used rational numbers for their math, no logarithmic irrational numbers. 

Theo Paijmans in his biography of John Keely, argued that the evidence shows that John Astor, the richest man in the U.S. at the time, who funded Keely’s secret sound free energy inventions, then absconded Keely’s results back to the Skull and Bones secret society that Astor was a member of. The problem or the secret of these types of technologies is that they are really quantum energy which means they are dependent on the consciousness of the person interacting with the external devices. There really is no “free” energy it’s just that some energy natural resonates from the infinite source of reality. Dale Pond in his John Keely lecture video actually lists the expansion of 2 and 3 infinitely and so this is exactly what I am talking about -- the "infinite spiral of fifths." Then Dale Pond says how it's the female energy as “negative attraction” by implosion or acoustic cavitation – again this is the same as what I've been saying, what the Pythagoreans called Apeiron. Dale Pond also states that the consciousness of the individual is tied to the energy – that it is mental energy when the energy is at the highest level of density and frequency and intensity. 

Arthur Young, inventor of the Bell Helicopter (tied in with the Puharich-C.I.A. Stargate Conspiracy) realized this key secret of alchemical energy:  “The cube roots of one are the points that divide the circle in three equal parts…But all these roots can be expressed in terms of square roots.” (his book Mathematics, Physics and Reality.) Young argued that this procedure, using Gauss’ i-1 grid, proved that time is inherently asymmetrical and, as Dr. Heinz Pagel points out in his book Perfect Symmetry (p. 358) if space is highly curved then particles are created out of nothing. The first use of this math was in the Egyptian Pyramids, as described in Napier’s book The Story of i: An Imaginary Tale. The real “pyramid power” is like the full lotus yoga position, the highest secret of French Freemasonry, as professor Hugh B. Urban revealed.   Professor Hugh B. Urban, “Elitism and esotericism: Strategies of secrecy and power in South Indian Tantra and French Freemasonry,” Numen-International Review for the History of Religions 44 (1): 1-38, 1997). The All Seeing Eye of the Pythagorean Tetrad can’t be visualized since “one” is not a number – that is the secret of the Nine of the Stargate Conspiracy, the ancient Ennead that controls the world. The Klein Bottle demonstrates this principle – it is the fourth dimension in three dimensions just as real pyramid power or the full lotus yoga position – the Klein Bottle inherently can’t be visualized. This is the real meaning of “Order out of Chaos” as the Golden Ratio is sacred to the Freemasons – the attempt to contain the continued fraction of 1 plus 1 divided by 1, infinitely. In other words, the slowest converging irrational number is actually the inverse, the most “stable” example of what in reality is a rational number chaotic resonance free energy process, most powerfully expressed by the Pythagorean Tetrad or Taoist Tai-Chi symbol.
Peter Kingsley notes, "In terms not only of formal and structural analogies but also of historical contacts, there can be no separating the Thracian Orpheus [of Pythagorean equivalence] from central-Asiatic shamanic tradition." This connection with Taoism is also made explicit by the motif of the Pythagorean master Empedocles who, "dies a miraculous death by vanishing into thin air but who leaves a tell-tale item.... A more classic Taoist concept is that of achieving the divine state either by fashioning a spirit-body...thoughtfully leaving a pile of discarded garments...."
Ancient Philosophy, Mystery and Magic, Oxford Ph.D. thesis, 1995, p. 236.

Part Five: Re-embracing the ancient Chinese secrets of qigong healing energy

Wouldn’t it make sense that if internal alchemy training is the real basis of paranormal phenomenon then it should be explained by something that is found in all human cultures? If something is physiologically true to humans, albeit rarely discovered in modern times, would it at least be apparent in all human cultures? Yes and indeed it is – the Perfect fifth and Perfect Fourth music intervals are found in all human cultures and the original human culture, the Bushmen of Africa, practiced a music shamanism as central to their culture. This music inner alchemy training, called Tshoma, is ignored even in the “psychedelic” counterculture – even though it is the focus of the original human culture for 90% of human history – from before even human language! Anthropologist Elizabeth Marshall Thomas, author of The Harmless People, lived among the Bushmen for several years and she states: “There are things about the antiquity of the Bushmen’s culture that we didn't know. A musicologist found very important music which was used at a woman's first menarche called ‘elan music’ (honoring the fat-rich antelope). This ‘elan music’ was also present in other language groups of other Bushmen language groups and also the noun-less speakers who are not exactly Bushmen but they're related. This means that way back before these groups diverged, somebody invented or composed (this) music and then they took it with them.” Interview with Elizabeth Marshall Thomas, Paula Gordon Show (Peterborough, New Hampshire, July 19, 2008). We’re talking at least 70,000 years ago!

Again the Bushmen trance dancing healing music in action. This original culture still survives as Dr. Bradford Keeney has documented in his several books on the master healers of the Bushmen.

Biologically the music-based shamanic inner alchemy paranormal training was the focus of 90% of human history and yet it remains largely unknown to modern society. As musicologist Dr. Victor Grauer documents in his blogbook, Sounding the Depths, the shamanic trance music relying on the 1-4-5 music intervals as male and female alchemical principles was spread around the world as trance dance paranormal spiritual music. We in the West may not think of it as music but more as chanting, mantras yet the secret is much more sublime.  “For a long time western rationalists smiled at the notion that the sound of a single word [a vowel mantra], a single syllable should have a formative, shaping, creative power....” Noel Berendt, The World Is Sound: Nada Brahma: Music and the Landscape of Consciousness, p. 44. Dr. Grauer has documented this universal connection with the tuned scales based on this original Perfect Fifth/Fourth harmonics. Listen to this examples of the shamanic trance music worldwide based on the 1-4-5 music intervals. 

Chapter 18 of Dr. Grauer’s blogbook: “Closely related types of instrumental hocket, similar to that of the pipe, flute, whistle, horn and percussion ensembles of Africa, have also been found in roughly the same regions, among indigenous peoples of New Guinea, the Solomon Islands, Indonesia (Flores, Bali, Java, among others), the Philippines, Vietnam, and certain other enclaves in Southeast Asia, and China. We find somewhat similar practices, both instrumental and vocal, in certain villages in Russia and other parts of Europe, both East and West, and also the Andes and other regions of Central and South America. In some cases we hear vocal instrumental interactions of a very similar type.... While the Chinese myth places the Yellow Emperor and the Yellow Bell well back into a vaguely defined “olden times,” when China itself was being established as a state, according to my version of the myth tuned pipes originated at a much earlier time, before modern humans voyaged out of Africa -- and well before that, to the time before humans learned to speak to one another. And despite all the many tens of thousands of years from that primeval time to this, we still find ensembles of pipes and panpipes, still cut from lengths of cane, still tuned, in a great many cases (though not all), more or less according to the system described in the story of the Yellow Bell, based on the simple whole number ratios, 2/3 and 4/3. Remarkably, we still find, all over the world, musical traditions, both instrumental and vocal, based, more or less, on those exact same ratios.1 And just as the Yellow Bell became the foundation of so much that was central to Chinese civilization, so did the ratios long ago established in the “law of pipes” become the foundation of so much of importance in other civilizations, as, for example, in the pioneering mathematics and physics of the ancient Greeks, where the exact same ratios were ‘discovered’ by Pythagoras.”

These songs sound too primitive to be really powerful but they are accompanied by trance dancing which is like Tai-Chi practice. 

The females sing all night long which transmits their N/um energy or jing (life force energy) into the males. By trance dancing the males take in the female energy but ionize it using their spirit light energy of the heart-mind and third eye – the !Kia trance state. So then this is sent back to the females as higher frequency light healing energy – spirit or quantum coherent light energy – that heals the females, it’s called “yin spirit” energy in Taoism. Kenyan Ritual Witchcraft Music gives this secret of their tribal drumming healing music as “eating the females.” But as understood in tantra – the life force energy is lower frequency so it takes a lot of jing energy to create qi energy (electromagnetic force) and then a lot of qi energy to create shen energy (the coherent laser light spirit energy). So for a male to send out shen spirit energy he is using up more energy than he receives when taking in the life force jing energy from the singing or sounds of the females. 

Nevertheless that is the open process of energy conversion that was the key to peaceful and happy healthy living for the original human culture. Dr. Bradford Keeney calls the healing energy an “impersonal eroticism” because it’s based on the males training to open up their sacrums – to ionize the energy up the spines as “boiling heat” and so the males during puberty go through Tshoma – a month of trance dance fasting away from the females. This enables the males to fully open their third eyes so they can then recharge their energy directly through the shen laser higher frequency – called the Shakti tantra energy from Indian yoga.  “Hearing the sounds may drive the visionary experiences. Songs become called 'lines' or 'ropes' that take you somewhere.” Dr. Bradford Keeney on the Bushmen trance dance healing.

The Modernity of Witchcraft: Politics and the Occult in Postcolonial Africa by Peter Geschiere and Janet Roitman (University of Virginia Press, 1997) also gives these secrets taught as qigong in China.  “A good example is the notion of djambe among the Maka of eastern Cameroon….To them the djambe is a force – or even a being – that lives in the belly of a person. It permits its proprietor to transform himself or herself into a spirit or animal and to do all sorts of other exceptional things. This force can be used to kill, and according to my spokemen, often is. One could therefore translate djambe as 'witchcraft.' But the same djambe, like the evu of the neighboring Beti, can also be used in a more positive sense: for instance to heal or to affirm one’s prestige.” The Modernity of Witchcraft: Politics and the Occult in Postcolonial Africa by Peter Geschiere and Janet Roitman (University of Virginia Press, 1997), p. 13
So the energy is stored in the behind the belly called the “lower tan tien” in the qigong training.  When this energy opens up as a "kundalini" experience it is after the lower tan tien is filled with "yin qi" energy and it converts to "yang qi" via the heart-pineal gland holographic resonance. This is experienced as a OHM sound which, as the qigong master states, OHM is the origin sound for any sound we perceive. OHM is just the Tai Chi-Tetrad in resonance as the infinite Perfect Fifth/Fourth harmonics. The sound of OHM emanating spontaneously from the heart is the contact with the impersonal universal soul energy. The sound of OHM indicates the harmonization or resonance of life force energy into qi or prana - electromagnetic energy from out of the 2nd chakra or the lower tan tien, behind the belly.

This Tai-Chi practice is again is the harmonization of heaven and earth while modern society using logarithmic math is a Freemasonic mass sacrifice ritual called the “separation of heaven and earth.” My free book Alchemy of Rainbow Heart Music gives the details. A pdf link: here.  Dr. Bradford Keeney in his several books on the Bushmen miracle healing emphasizes how the secret to activating the energy in the belly as boiling heat N/um is the shaking of the body at 7 beats per second for the deeper Theta R.E.M. trance state. So that activates the dreaming light spirit energy of the third eye to create the lower tan tien or N’um energy center behind the belly – it is the ionization of the life force energy. This is also called "tummo" by the Tibetans - the jing energy of qigong internal alchemy training that creates the "lower tan tien" behind the belly. here Here you can see this phenomenon is well documented by top science research. Wim Hof, a Westerner, has also trained in tummo and then he has made himself fully available for numerous repeatable science tests by numerous scientists.  I blogged in great detail on Wim Hof. here

Instead of getting caught up in the materialistic concept of a sound-scale we need to understand and embrace the empirical truth of the infinite energy of the Perfect Fifth and Perfect Fourth ratios. It took Simon Stevin in the 15th century to carry on the work of Archytas – to once again argue that 5/4 was the cube root of two and the tritone was the square root of two.  Stevin’s acknowledged the alternative as unfathomable – infinity stared back at him as unacceptable for his mind: 

“One further comment by Stevin in L'Arithmetique is worth recording. He noted that, as we stated above, Euclid's Proposition X.2 says that two magnitudes are incommensurable if the Euclidean algorithm does not terminate. Stevin writes about this pointing out what today we would say was the difference between an algorithm and a procedure (or semi-algorithm): Although this theorem is valid, nevertheless we cannot recognise by such experience the incommensurability of two given magnitudes. ... even though it were possible for us to subtract by due process several hundred thousand times the smaller magnitude from the larger and continue that for several thousands of years, nevertheless if the two given numbers were incommensurable one would labour eternally, always ignorant of what could still happen in the end. This manner of cognition is therefore not legitimate, but rather an impossible position .... J J O'Connor and E F Robertson, “The real numbers: Pythagoras to Stevin,” MacTutor History of Mathematics, 2005.

The reality according to the Bushmen is that everything is based on male and female principles and this is expressed through the Perfect Fourth and Perfect Fifth music intervals, as infinite alchemical energy so that it is not linear time - but entering into a holographic non-local dimension that has precognition through superliminal spirit communication. This secret was passed on throughout shamanic cultures and formalized by the Taoists: “Between heaven and earth, they say, there is perfect harmony. Now, 3 is the emblem of heaven, 2 is the symbol of earth. If two sounds are in the proportion of 3 to 2 [the perfect fifth interval], they will harmonise perfectly as heaven and earth. All the tubes were cut on the same principle, … The lüs [notes] were divided into two classes, the yang lüs and the yin lüs… Everything in Nature belongs to one of these two grand categories, from whose combinations and reciprocal action results all that exists or takes place in the universe.” J.A. Van Aalst, Chinese Music (Shanghai: Chinese Imperial Customs Service, 1933), p. 8. 

The Taoists understood that sound, from the complementary opposite yang and yin resonance, was transduced into higher and lower frequencies of energy – which they called “chi” or qi energy.  Chinese, not being a phonetic language, did not have the "one to one" correspondence between number and symbol mainained for the commutative logic as the Greek Miracle - the syntactic paradigm of "pre-established deep disharmony" as Borzacchini discusses the Chinese in his online essay. 

John S. Major explains, contrary to claims the Chinese created an equal-tempered scale, about the traditional Chinese spiral of fifths music: “The ratios given here will yield an untempered chromatic scale regardless of what note is chosen as the fundamental.” The Chinese concept of music as radically different than the West: “This is not simply a case of assigning pitchpipes to the 24 nodes as a system of correspondence; rather the qi [energy] of the nodes themselves were believed to resonate these tones. With the arrival of each seasonal node, in other words, the appropriate pitchpipe was supposed to spontaneously emit its note.” John S. Major, “Celestial Cycles and Mathematical Harmonies in the Huainanzi,” Extreme-Orient, Extreme-Occident, 1994. See also Erica Brindley, Music, Cosmology and the Politics of Harmony in Early China, (SUNY Press, 2012).

So now the modern world listens to mainly “equal-tempered” logarithmic Westernized music without realizing it is also the foundation for Western science as well – incommensurability, irrational magnitude and the symmetric logic that has continued to expand into higher dimensions of math and applied technology. I exposed this as the Actual Matrix Plan - that I discovered soon after my masters thesis - and the Actual Matrix Plan completely corroborated my masters thesis in 2000. 

The principle of reality defined by male and female number ratios has been lost – although the inner alchemy paranormal philosopher Gurdjieff tried to bring it back but Westerners did not understand, again, due to the long tradition of Western symmetric-based logic. If reality is not limited to only that which can be systematically measured then how can we “contain” infinity? As Gurdjieff explained the secret of the Logos is logically inferred from the I-thought by a process of internal listening. There is no need for irrational belief – just listen to the source of the I-thought as logical inference. Science still debates, “what is the meaning of consciousness?” And for each of us the “I-thought” goes away while in deep dreamless sleep. By listening to the source of our I-thought something is discovered beyond any assumptions of solipsism: An energy from higher and lower frequencies as sound transforms and transduces itself through resonance. This is called "turning the light around" which means by closing the eyes and listening or staring in a trance, repeating an internal mantra (focusing the left brain as "immutable thought"), the electromagnetic brain waves are resonated into the frequency of spirit light through transducing the piezoelectric pineal gland.

O.K. so physiologically – psycho-physiologically – quantum biology trumps physics. Logic as listening even trumps biology. There can’t be a technology to “measure” or systematically reproduce the logic of human listening.  On the quantum level we are taking photons (light) and phonons (sound). In this science experiment sound traveled faster than light but only as a “group wave” – not as a communication signal. (A new experiment finally proved in 2015 that only one photon is also an entangled nonduality wave of faster-than-light communication and so it's not a result of a group wave statistical measurement but it's actual physical entanglement - faster than speed of light - see below). But again this is not listening

Science is trying but readers should consider that this process of listening was actually the secret origin for Western science itself – only science cheated and “compromised” – tried to “contain” the infinity to create standardized symmetric mathematics. Again this secret music origin of Western science is covered-up! Even the square root of two is a geometric measurement that is based on a “pre-established disharmony.” This pre-established disharmony is the secret “evolutive principle” of Western science, so as the logarithmic dimensions of math expand, so too does the inherent destruction of Western science, with its also unjust logarithmic proportions. 

I could “explain” the time-frequency uncertainty principle but again the focus of this article, despite the displaced inaccuracies of Western science, is the original human physiological goal of the inner alchemy paranormal training. The book that actually gives the details of this training, called Taoist Yoga: Alchemy and Immortality, was considered by the original author, Zhao Bichen, to be an “ancient Chinese science.” What is the focus of that book? An internal alchemy practice called the “small universe” or “small heavenly cycle” or “microcosmic orbit” that uses 12 notes or nodes along the outside of the body-mind – that’s right: 12 notes as in the 12 notes of the music scale created by the “infinite spiral of fifths” of Pythagorean music theory. What if the 12 notes learned in Western music theory as the “circle of fifths” were not really a circle? Did we not just learn in this article that empirically, in actuality, the yang or 3/2 ratio as the Perfect Fifth, 1.5, is really not a circle, but is really infinite? Yes this was confirmed by Sir James Jeans.

If this training was easy then there would be a lot of qigong masters out there. In actuality the Orthodox Pythagoreans required nine years of silence for the real Logos training! That’s right – internal listening for nine years! As the Taoists teach, the right and left hands are yang qi and yin (yuan shen) and the upper body is yang and the lower body is yin and so by aligning these parts then a harmonic energy circuit is created. So for example by putting the tongue against the roof of the mouth this connects the front (yin) and back (yang) energy channels. A person has to practice this yin-yang philosophy to find out if it is true. By the way a hadith of Islam states Mohammed knew the left hand was lunar and the right hand was solar and he learned this in the context of training in the alchemical blacksmith knowledge, newly spread by Islam to the Arabs.

Part Six: Quantum Physics now reaffirms the ancient nonwestern science of qigong healing

What if, instead of “arguing from ignorance” like the skeptics claim, we rather took Pythagoras and the Taoists at their word? What if frequencies really were empirically infinite? As they really are. In fact this truth was rediscovered by physicists when the quantum realm was first explored – called the Fourier Uncertainty Principle or the Time-Frequency Uncertainty Principle. It is before, empirically, and therefore more important than the better known Heisenberg Uncertainty Principle. “Human hearing beats the Fourier uncertainty principle” Feb 04, 2013 by Lisa Zyga link here  
The researchers think that this superior human listening ability is partly due to the spiral structure and nonlinearities in the cochlea

Read more at:
 The researchers think that this superior human listening ability is partly due to the spiral structure and nonlinearities in the cochlea.
The researchers think that this superior human listening ability is partly due to the spiral structure and nonlinearities in the cochlea. Previously, scientists have proven that linear systems cannot exceed the time-frequency uncertainty limit. Although most nonlinear systems do not perform any better, any system that exceeds the uncertainty limit must be nonlinear.

Read more at:
The researchers think that this superior human listening ability is partly due to the spiral structure and nonlinearities in the cochlea. Previously, scientists have proven that linear systems cannot exceed the time-frequency uncertainty limit. Although most nonlinear systems do not perform any better, any system that exceeds the uncertainty limit must be nonlinear.

Read more at:
The researchers think that this superior human listening ability is partly due to the spiral structure and nonlinearities in the cochlea. Previously, scientists have proven that linear systems cannot exceed the time-frequency uncertainty limit. Although most nonlinear systems do not perform any better, any system that exceeds the uncertainty limit must be nonlinear.

Read more at:
Another way to think of this is time is the period as wavelength space and it's inversion is the frequency but because of the quantum time-frequency uncertainty principle the shorter the time is the more spread out the frequency. So if you want to see if time accelerates then the frequency is spread out and conversely if the frequency goes to zero then the time spreads out to infinity -- which is also the point De Broglie is making about quantum relativity. O.K. so what happens is that we're talking about the source of sound as consciousness but on a physical level this means that a quantum singularity is achieved that then reverses time to create a mini-black hole with positrons (antimatter) instead of electrons. Dr. Sean Carroll on quantum field theory
“But the quantum field theory philosophy says that there is not even a particle. What you start with is a field – something that looks waving, something that fills all of space, like the electromagnetic field or the gravitational field – then you apply the rules of quantum mechanics to that, and miraculously what comes out when we look at it are particles.
Dr. Carroll corrects the high school physics teachers - these fields of energy exist without needing particles! There does not need to be a materialist source for these energy fields and the fields guide reality. 
Researchers demonstrate quantum entanglement, prove Einstein wrong
What Einstein termed "spooky action at a distance" has been successfully demonstrated for the first time.
 A single photon (particle of light), for example, can be split into two particles that are still connected -- that connection is called entanglement. The single particle's wave function spreads over large distances, but the particle itself is never detected in more than once place -- when measured, the wave function collapses.... The team split a single photon between two laboratories and tested whether the choice of measurement in one caused a change in the local quantum state in the other laboratory.

So the issue of subtracting frequencies under the condition of time-frequency uncertainty means that the logarithmic expansion of time causes an increase in frequency or vice versa -- this was described again with the higher harmonics resonating into ultrasound. The higher frequency has more energy intensity because of the quantum time-frequency uncertainty -- and this creates the relativistic nonlinear feedback with the ELF waves from the subharmonic beats -- as was pointed out by CIA mind control scientist Dr. Andrija Puharich as well.  “Schwinger points out that even though the Maxwell equations call for a symmetry between electric charge and magnetic charge, the cold fact is that no magnetic counterpart to the electric charge is known....the proton now has a frame of reference which (depending on its energy) may have a wave length which is equal to the radius of the solar system....the 1 KHz signal, the acoustic phonon displacement....will set up a magnetic will be picked up by the hydrogen proton....the higher the magnetic field the higher the frequency of precession.”

So the resonance of a sound based on the natural overtone series enables the harmonics to go into ultrasound which then produces a quantum nonlinear beating -- as higher harmonics have closer resonance overtones themselves -- so from the get go it's a nonlinear overtone resonance process that then feedbacks into the subharmonics which are then amplified this the same feedback process as a quantum relative resonance.

So subharmonics resonate the proton wavelength as jing energy (tummo heat, N/om or kundalini) -- what I was calling the ultrasound ionization of electrochemicals -- so the subharmonics of the ultrasound harmonics as ELF waves actually cause the ionization but this goes into a singularity as a mini-blackhole.

So the wavelength as time expands then relativistically as the subharmonic low frequency starts to go to zero -- the amplitude of the wavelength as time phase (before it's converted to amplitude classical) then spreads out to a cosmic distance -- as Puharich points out the ELF proton quantum relativistic wavelength as such a low frequency is half of the solar system.  This is the double time of phase that is de Broglie's Law of Phase Harmony.

So there's the Pythagorean cosmic "sound of the planets" natural resonance.

By time reversal there is "destructive" and "constructive" interference of the amplitude through phase reversal -- and so that is the resonance as acceleration of frequency with slowing down of time with it's reversal. So the time flows backwards at half the speed due to the quantum relativistic bending of spacetime.

Again the frequency is the quantum energy while the phase is the spatial time and the amplitude is from the resonance of the interference pattern -- the measuring of the amplitude is "uncertain" - the more the frequency is measured, the less the time is measured and vice versa.

O.K. so Puharich says there is a "beat" subharmonic due to the frequency difference between the proton and electron. Their beat subharmonic is 657 hertz but is lowered to 600 hertz. He then states that due to the Tetrahedron structure of water there is a phonon pumping -- sound -- just like a laser. Sonofusion -- like sound into light like a biophoton laser. He cites Fritz Popp on this and Puharich calls it Phonon Hydron.  So again this is from the subharmonic of the precession (backwards time) of the proton from the electron frequency orbiting the proton.  Not subtracted but divided into the proton precession. So it's a division ratio.

O.K. so Puharich says there's proton-proton resonance between hydrogen atoms at the ELF frequency of 8 hertz. So then he gives the reverse time phase velocity difference between the precession of the proton and the electron orbit as 1/.125 which creates harmonics that increases the amplitude of the water electrolysis. (citing Puharich’s book ELF-Magnetic Model of Mind and Matter pdf link: here it is.

O.K. Puharich calls this Phonon Hydron -- which means that the subharmonic of the proton precession and the electron orbit around the proton is acoustic energy as sound -- 100 hertz range and that the hydrogen proton coupling is in the ELF range of 8 hertz -- but that this creates sonofusion as a singularity. It splits water into hydrogen free energy and it also creates "biological weak transmutations" via Kervan equations -- which means that the protons change, not just the electrons, and so there is alchemical transmutation of elements from weak ELF waves (the trance dance 7 beats per second vibrating of the legs also in Tai Chi horse stance with thighs parallel to ground, the theta brain wave REM vision state of heart spirit energy).

So the highest sound we hear in our ears resonates into ultrasound in our brains and the subharmonics of the ultrasound turn into ELF waves which then ionize our electrochemicals as alchemy. This process is nonlinear feedback that reverses spacetime - creating precognition and astral spirit travel through coherent biophotons. Our spirit stores holographic information in our etheric electrochemical emotional yin qi (yang jing) energy of the organs. Our spirit has its future encoded in our deep emotional energy of the heart - the deep love desire - is our future fate of our spirit, the connection of the astral to the etheric. Whereas the soul is the impersonal infinite light that is eternal as light on its own experiences no time.
However, since the electron spin generates an observable magnetic
moment, we should conclude that electron zitter [phase] generates an observable electric
dipole field fluctuating with the zitter frequency. Evidently the classical coupling of
the electron source to its field must be modified so the energy in the dipole field is not
radiated away. That aside, the consequences of such a field can be investigated.
Evidently it would have implications across all of quantum mechanics, including
electron diffraction, tunneling, Lamb shift, vacuum fluctuations, van der Waals and
Casimir forces. Of course, what works for electrons is likely to be relevant to models
of all fermions. David Hestenes, "Hunting for Snarks in Quantum Mechanics"

So actually this phase as the double or internal clock of the electron has now been verified - first theorized by de Broglie when he discovered the paradox of Einstein relativity violating the Law of Pythagoras (frequency as inversely proportional to time as wavelength). O.K. so phase has been verified by David Hestenes and this remains largely unknown since the double internal clock model of de Broglie was ignored by physicists. This new experimential verification explains many anomalies in science - including the Bose-Einstein superconductivity that is sometimes considered a metaphor for spiritual consciousness. But the key concept again is the mass is actually frequency and by resonance, which happens easier at colder temperatures, then, ironically, the frequency resonance energy increases. Hence the irony of alchemy. Sonofusion. In other words the unknown origin of "magnetic moment" is actually from this left-hand asymmetry of the internal clock or time energy - creating spontaneous free energy and this knowledge can be used for resonance alchemy.

As I explained in previous articles – from a Western perspective we can say the sound, focused internally, resonates into the ultrasound and infrasound and this creates a piezoelectric transduction from the ultrasound frequencies. A good example of this is called “frisson” in music theory – it is when people get the chills or “skin orgasm” from listening to music. 
Musical chills: Why music gives us the thrills - sciencedaily This is from the upper harmonics having more beats which then creates a stronger subharmonic resonance. It’s a nonlinear feedback between higher and lower frequencies with lower frequencies having significant stronger amplitude. 

So actually this is why the tritone as Devil's Interval is used for the diminished seventh chord (two tritones a minor third apart, e.g. B-F, D-A) as an enharmonic chord substitute of the perfect fifth. detailed here as the tritone substitution term in jazz. As this article gives the music theory - the "paradox of the poles" so that the overtones and undertones are complementary opposites. Sure enough a composer blogging using the phrase "the frisson on a Neopolitan chord" and Neopolitan refers to the flat sixth chord as the enharmonic of a seventh chord. It's the enharmonic substitution as tritones that creates the frisson. frisson isn't limited to frequency pitch changes in music - an excellent analysis here. This process creates a neurohormone increase of dopamine from sound, “frisson,” – the sound has transduced or resonated as electrochemical energy. This process is combined with the yin-yang body-mind exercises. Frission is inner ear activation of the vagus nerve connection to the pineal gland.

Now that explanation of “ultrasound” assumes a Western logarithmic measurement. For example the online expose of 440 Hertz introduced as the new standard A note tuning by the military-industrial-petrochemical-banks scheming to create World War II. 

"The B.B.C. tuning-note is derived from an oscillator controlled by a piezo-electric crystal that vibrates with a frequency of one million Hz. This is reduced to a frequency of 1,000 Hz by electronic dividers; it is then multiplied eleven times and divided by twenty-five, so producing the required frequency of 440 Hz. As 439 Hz is a prime number a frequency of 439 Hz could not be broadcast by such means as this."
Musical Cult Control: The Rockefeller Foundation's War On Consciousness Through The Imposition Of A=440HZ Standard Tuning MedicalVeritas by
Leonard G. Horowitz, DMD, MA, MPH, DNM(hon.). 

So the “one million Hz” is the ultrasound – and this is translated back into sound – but the opposite process occurs in the body-mind. Horowitz notes that the tuning for A used now then creates the “Devil’s Interval” when compared to the tuning for A that he advocates. What needs to be realized is that the ancients didn’t conform to specific frequencies but rather it is the Devil’s Interval itself that is the problem since the whole concept of “frequency” assumes a logarithmic measurement that creates the Devil’s Interval as the tritone or square root of two. Horowitz does not question these logarithmic measurements but in fact science is now based on quantum physics as the foundation of knowledge – not on classical, logarithmic-based math. 

Quantum physics uses non-commutative math, not the symmetric commutative property of logarithms. So this non-commutative math is the rediscovered truth of the ancients – the order that is used to measure the time or wavelength versus frequency changes the pitch that is perceived or the value of the energy. For example the Egyptians did not use the frequency 444 or 432 nor did the Egyptians use the Golden Ratio (contrary to the New Age propaganda) -  for no 440 and for Dr. Corrina Rossi’s book on how Egypt did not use the Golden Ratio.

Yet the Egyptians did use a diatonic scale based on the same Pythagorean philosophy – Pythagoras studied in Egypt for 23 years. More importantly the ratio 2/3 was sacred for the Egyptians just as it was for the Chinese as yang energy.  Why? Because of this infinite transmutation of sound into light energy. Classical physics assumes energy is measured by amplitude wavelength while quantum physics measures energy by frequency and the time used is infinite – it is not contained by a geometric wavelength. So the original human culture, the Bushmen, did not even use any music instruments and yet the result of their music is alchemical healing energy which got passed down as the secret paranormal training of the Taoists of China, the Yogis of Asia, and the Pythagoreans of ancient Greece.

Another level of music healing is called the “Mozart Effect” which is from the slow baroque movements of 60 beats per minute – this resonates the brain to a slow level more in synch with the heart, so that the serotonin levels are increased along with increased alpha brain waves (15 beats per second). A trance rhythm of seven beats per second which resonates with the deeper slower and stronger theta brain waves of R.E.M. visionary dreaming. It’s visionary since the person is listening in a trance but not asleep. The delta “dreamless” slow wave sleep state has been shown to enhance memory learning so if a melody is played to a person while in that dreamless sleep state their subconscious then learns the melody better to be remembered when awake.

There are “external” examples of this sound as energy transformation phenomenon as I have discussed before – sonoluminescence. Philip Callahan provides an experiment of such sound transduction: “Lighting up the atmosphere with sound is a phenomenon I have been easily able to accomplish since 1969.... A snapped rubber band gives off an ELF radio wave in the 100- to 200-Hz region.... By stimulating a mixture of ethanol and ammonia, or sex scents, with an ELF wave, I can create photon harmonics throughout the infrared, and even visible, regions of the spectrum. The electric sound field vibrates the molecules.... Those harmonic waves travel up and down the photon electromagnetic spectrum the same way harmonics do from a plucked banjo string. In one direction, the harmonics move to higher frequencies along the infrared region and even move into the visible region. When such waves hit solid objects like cells or insect antenna, they scatter out other waves of electromagnetic energy that are actually coherent (marching together) and amplified. Pictured is a Fourier transform spectrum (original recordings for historical purposes) of just such waves. The experiment shows cabbage looper sex scent modulated by ELF (60-120 Hz) lab visible light and blown out at five mph wind speed across two model round towers.” Philip S. Callahan, Insect Molecular Bio-Electronics (College Park, MD: Entomological Society of America, 1967) and Philip S. Callahan, Paramagnetism: Rediscovering nature's secret force of growth (Metairie, LA: Acres, USA, 1995)

Sound therapist Jonathan Goldman remarks, "We can actually feel different parts of our body vibrate with sound. For those who have had no experience working with the subtle body [vital energy or chi], this physical resonance makes it easier for them to accept the possibility of resonating subtle energy as well...." Jonathan Goldman. Healing Sounds: The Power of Harmonics. (Boston, MA: Element, 1996), p. 116. Goldman has extensively explained the healing effects of harmonic overtone mantra practices. He reports that when escorted to a normally off-limits chamber of a Mayan pyramid and asked to produce a mantra, his voice caused the secret room to become full of light called sonoluminescence.

The process of energy transduction as infinite frequency is holistic and this is what is really difficult for people to wrap their heads around the secret. There is no start or end to this energy but it is alive as consciousness – we exist within it. So, for example, quantum physicist Louis de Broglie discovered a paradox in Einstein’s Theory of Reality – as light energy is in a vacuum it is speeding up in frequency (a smaller wavelength) but then time slows down (a bigger wavelength) which means this violates the fundamental Law of Pythagoras! De Broglie called this discovery the Law of Phase Harmony
 “de Broglie Wave Mechanics - In 1923, while still a graduate student at the University of Paris, Louis de Broglie published a brief note in the journal Comptes rendus containing an idea that was to revolutionize our understanding of the physical world at the most fundamental level. He had been troubled by a curious "contradiction" arising from Einstein's special theory of relativity. First, he assumed that there is always associated with a particle of mass m a periodic internal phenomenon of frequency f. For a particle at rest, he equated the rest mass energy mc² to the energy of the quantum of the electromagnetic field hf. That is, mc² = hf where h is Planck's constant and c is the speed of light. De Broglie noted that relativity theory predicts that, when such a particle is set in motion, its total relativistic energy will increase, tending to infinity as the speed of light is approached. Likewise, the period of the internal phenomenon assumed to be associated with the particle will also increase (due to time dilation). Since period and frequency are inversely related, a period increase is equivalent to a decrease of frequency and, hence, of the energy given by the quantum relation hf. It was this apparent incompatibility between the tendency of the relativistic energy to increase and the quantum energy to decrease that troubled de Broglie. The manner in which de Broglie resolved this apparent contradiction is the subject of the famous 1923 Comptes rendus note [Comptes rendus de l'Académie des Sciences, vol. 177, pp. 507-510 (1923)].”

Wavelength as time is reciprocal to frequency. So if frequency gets higher as larger then wavelength should get smaller but the opposite happens for light energy in a vacuum. In Einstein’s relativity wavelength gets longer (time slows down) when frequency gets bigger (light energy) and they are not reciprocal. But again this “Law of Pythagoras” is a cover-up of the secret real Pythagorean inner alchemy training.  So with real inner alchemy we are talking about before Hertz – before symmetric math. So De Broglie realized that there has to be two time measurements – one of phase before it is turned into a symmetric amplitude or wavelength measurement. So the phase time is superluminal – faster than the speed of light. Sure enough science has confirmed this reality: Quantum "spooky action at a distance" travels at least 10,000 times faster than light By Brian Dodson March 10, 2013

Of course mainstream physicists say this does not violate Einstein’s relativity because no signal or no real communication can be done faster than the speed of light – it’s only “after” the symmetric measurements are done – only after the phase is converted back into time as wavelength. But what if this experiment is done “without” the technology? De Broglie did consider this as possible through consciousness!  

“If, within [the old Louis de Broglie-Bohm hidden variable model (with pilot wave or quantum potential)], it proves possible to take explicitly into account the (undeniable!) fact that Wigners friend is conscious, it is conceivable that the basic idea underlying this solution can be extended, outside the model, to the general theory....To sum up, within this conception it is considered that even microsystems can be endowed with “internal states of consciousness” (or “protoconsciousness”, whatever this may be) that are elements of a basic, not publicly accessible, reality, rather than of empirical reality.” Bernard d’Espagnat, “A tentative new approach to the Schroedinger cat problem,”

Science has shown that humans emit biophotons and that ultrasound resonates the quantum microtubules creating quantum photon energy.  “It turns out that the microtubules have residences in the kilohertz to megahertz range and I think the ultrasound is stimulating these microtubules and having an effect on consciousness.” Alex Tsakiris, 133. Dr. Stuart Hameroff, “On Quantum Consciousness and Moving Singularity Goal Posts,” Skeptiko Podcast, April 11, 2011. Good vibrations: Mediating mood through brain ultrasound July 18, 2013 So then the biophotons of consciousness are resonated – by listening to the source of the I-thought – and this process creates increased electromagnetic energy. I went into this process more in my previous article, “The Secret Science of Spiritual Healing.”

The Buddhists taught this method of meditation as “sound-current” a translation of Quanyin, the female form of Buddha in China but also known as the “inner ear method” of Buddhist meditation. By listening to the source of sound it resonates up into ultrasound and a high pitch hearing is heard: 
"Monitoring neural vascular function with Doppler ultrasonic imaging provides unexpected support for the brain ultrasound demodulation theory. When the imaging beam was focused at the center of the brain, patients reported hearing a high audio sound, much like tinnitus. When the ultrasonic beam was directed at the ear, the sound disappeared. Setting the brain into resonance resulted in a clear high-pitch, audible sensation consistent with brain resonance in the 11- and 16-kHz range....Because ultrasound produces high audio stimulation by virtue of brain resonance, the direct use of high audio stimulation is more economical in power requirements and still stimulates the brain at resonance.”  

Dr. Martin L. Lenhardt, “Ultrasonic Hearing in Humans: Applications for Tinnitus Treatment,” International Tinnitus Journal, Vol. 9, No. 2, 2003, p. 3 and p. 6. Dr. Mae-Wan Ho reports, “Any mechanical deformations of the protein-bound water network will automatically result in electrical disturbances and conversely, electrical disturbances will result in mechanical effects….detecting ultrasound emissions from mechanoelastic vibrations caused by electrical pulses applied to the tissues. Proton jump-conduction is a form of semi-conduction in condensed matter, and is much faster than conduction of electrical signals by the nerves. Thus the 'ground substance' of the entire body may provide a much better intercommunication system than the nervous system.” From “The Acupuncture System and The Liquid Crystalline Collagen Fibres of the Connective Tissues: Liquid Crystalline Meridians” American Journal of Complementary Medicine (in press, 2000). Since collagen is the most common protein in the body, as a piezoelectric force, with mechanical pressure, it creates the liquid crystal water as proton alchemy sonofusion energy.

Ajahn Sumedho, a bhikkhu of the Theravada school of Buddhism, from his book The Sound of Silence, describes this inner activation of ultrasound to create electromagnetic paranormal energy:
 “As you calm down, you can experience the sound of silence in the mind. You hear it as a kind of high frequency sound, a ringing sound that's always there. It is just normally never noticed. Now when you begin to hear that sound of silence, it's a sign of emptiness - of silence of the mind. It's something you can always turn to. As you concentrate on it and turn to it, it can make you quite peaceful and blissful. Meditating on that, you have a way of letting the conditions of the mind cease without suppressing them with another condition. Otherwise you just end up putting one condition over another.”

In the Taoist qigong alchemy training this high pitch sound is considered activation of the kidney energy (again it activates the vagus nerve for the gut brain ionization of serotonin as kundalini N/om heat - the quantum subharmonics of ELF waves) and a strong low voice means strong kidney energy. The biosonics healer Dr. John Bealieau has done research documenting the role of the vagus nerve from the yin-yang harmonics of the Perfect Fifth/Fourth - so the inner ear activates the vagus nerve which connects down to the lower body organs, including the reproductive organs. Science calls this the HPA axis - Hypothalamus-Pineal-Adrenal axis.

So then neurohormones like dopamine and serotonin get turned into neurotransmitters but by ionizing the vagus nerve through innersound alchemy of overtone and undertone harmonics this enables the lower body serotonin which are in huge amounts to bypass the blood-brain barrier, via the vagus nerve ionization. The pineal gland is bypassed by the vagus nerve directly - bypasses around the blood-brain barrier. This ionization is activated by the pineal gland inner ear connection - the inner ear of humans used to be the jaw bone of our tree shrew primate ancestors. When primates lived in the forest with trees then hearing is the dominant perception, not vision since three-dimensional depth is lacking in a thick forest. This increase of brain serotonin and dopamine from the vagus nerve activation is called the "inner smile" in Taoism since again the inner ear connects to the third eye as the pineal gland.

Don G. Campbell, B.M.E.D.,
Director of the Institute for Music, Health, and Education in Boulder, Colorado, states,
“The vagus nerve and the emotional responses to the limbic system (specific areas of the brain responsible for emotion and motivation) are the link between the ear, the brain, and the autonomic nervous system that may account for the effectiveness of Music Therapy in treating physical and emotional disorders.” 

Those are just the beginning of the practice - called building up the jing energy in Taoist qigong training. Read the book Taoist Yoga: Alchemy and Immortality for the details. The left side vagus nerve is the reptilian vagus nerve that connects to the right side of the heart, the source of Yuan Qi. Link on my blog sidebar. So the "throat singing" of the Tibetan monks is from vagus nerve activation - hear it here.
It is interesting to note that Tibetan monks do not practice their vocalization. They improve the
control of the ventricular folds through meditation! Meditation is a conscious
mental process that induces a set of integrated physiologic changes termed the
relaxation response. The elastic property of the ventricular folds may be affected
by meditation through autonomic functions. They become so relaxed that they
vibrate with complete closures at half the frequency of the true vocal folds....It is my hypothesis that overtone singing focuses the mind automatically on the weak pitch of the prominent nth harmonic. from Kargyraa and meditation by Chen-Gia Tsai here

Suffice it to say that the real qigong masters are way beyond the understandings of science because again quantum biology can only document these quantum entanglements in life without being able to reproduce the technology. Real qigong masters really do experience superluminal signals – information from the future – precognition – and also real qigong masters really do create coherent quantum biophotons as spirit energy which then leaves the body and holographically the spirit energy travels into the past or future or the spirit energy travels across space to heal people or see things at a distance. I have posted over a dozen different qigong masters demonstrating telekinesis abilities in videos – compiled the videos to one place on my blog. Qigong Master Telekinesis aka psychokinesis videos - a compilation: Skeptics debunked!

Finally real qigong masters can transform matter, again by increasing the intensity of the light energy or biophotons, so that a physical transformation, via proton transduction, takes place. Here is how one Taoist quantum biologist explains the science of what she calls “quantum jazz:”

“New evidence indicates that hydrogen is quantum delocalized between neighbouring water molecules, predisposing water to proton conduction, especially in confined nanospaces; water nanotubes aligned by collagen fibres [the most common protein in the body] fulfill all the criteria for proton superconduction, making them excellent candidates for the meridians of traditional Chinese medicine, as first proposed 15 years ago.” Liquid Crystalline Superconducting Meridians by Dr. Mae-Wan Ho, 06/02/2013

A quantum physicist gives an excellent music theory explanation of infinity from the time-frequency uncertainty principle: 
“When Δν is 0.1Hz, Δt should be more than 1 /(4π *0.1) sec which is about 0.80 sec. Middle C of the equal temperament is calculated approximately as 261.6256 Hz. If you want to determine C with this precision 0.0001Hz, you need Δt of 800 sec, or 13 min 20 sec. If you want to get the exact Middle C, you need an infinite time and a continuous wave of C. In other words, theoretically we cannot get the perfect fifth tone with a frequency f ( that is ν ) from a root tone with a frequency f0 by calculating f = f0 × 3/2.” 
Uncertainty Principle for Temperament by Iori Fujita,  

So that uncertainty of time and frequency with the two as reciprocal actually does affect real music tuning – empirically. Again this proves the “infinite spiral of fifths” is the empirical truth.
But for non-Western Pythagorean Tai-Chi Qigong Logos we do not assume a Hertz symmetric measurement of time as wavelength. Why is this? Because such an assumption already relies on symmetric irrational magnitude for number while the Perfect Fifth “sacred” inner alchemy music is just pure number as ratio. So what is the empirical error of Western tuning based on this non-commutative truth rediscovered by quantum physics? Physicist Iori Fujita tells us:  
“But even Δt is 1.000 sec, the bandwidth remains about 2 Hz.” 

Now I came to this same conclusion doing my own calculations when people online demanded that I explain my reasoning for the secret music theory origin of inner alchemy training. I can show my analysis below.

Part Seven: The Music Theory Explanation of Inner Sound Alchemy Qigong Paranormal Energy

So again we are unlearning the very foundations of Western science itself – from the secret music theory origins. I have referred to math professors Borzacchini and David Fowler for this claim but now another source: 
“Your will recall that Pythagoras noticed that the note emitted by a plucked string rose by an interval of a fifth if the string was reduced to 2/3 of its length. He also noted that the interval of a fourth was obtained by reducing the string to 3/4 of its length. The difference between a fourth and a fifth is a tone, whose ratio (8/9) is obtained by dividing 2/3 by 3/4. That is probably the earliest manifestation of a logarithmic law.”  

In perfect harmony by John Webb Again that is assuming symmetric math – notice what is missing? The geometry of the math is based on symbols as time wavelength. In other words C is 1 and G is 3 as an overtone harmonic but F is 3 as a subharmonic. 2/3 is C to F as subharmonic and 3/2 is C to G as overtone.

Let me give you another example of the cover-up: 
“When we add intervals [logarithmic law], what we’re actually doing is multiplying ratios.  So P5 + P4 = 3/2 * 4/3 = 2/1 = P8. When we subtract intervals we’re dividing ratios, which is multiplying by the reciprocal, so P5 – P4 = 3/2 * 3/4 = 9/8 = M2.  And P8 – P5 = 2/1 * 2/3 = 4/3 = P4.  Since multiplication of ratios is commutative, then addition of intervals is also commutative.” 

What is missing? The symbols of the geometry as wavelength! So even though the reciprocal of the ratio is allowed - it's geometric value is assumed to be the same - despite 2/3 (the fifth that gets turned into its reciprocal) is C to F while its reciprocal as 3/2 is C to G - a complementary opposite geometric value (like yin and yang).

The commutative symmetric math is geometry requiring the symbols for the wavelengths. Here we get the math as number frequency ratios and the music intervals but not the geometry symbols of the music notes (C, F, G, etc.). By skipping one part of the equation it is very easy to cover-up the real truth of infinite alchemical energy. I’m not saying these people are doing it consciously – a “bait and switch conspiracy” – only that this issue is so basic and so radical that it is not even noticed.

Taoist qigong master Michael Winn agrees with me about the secret music origins of inner alchemy paranormal training: 
“But the fifth is a given of the Chinese pentatonic scale (possibly symbolized by five dots in the center) and is omnipresent in Daoist cosmology as the first female (2) and first male (3) number, as cited previously in verse 42 of the Daodejing.” Michael Winn on the 6 Taoist healing sounds and the sounds of the emotions of the organs.

The commutative principle means that it would be the same geometric symbols with the inversion of the ratio but this does not hold for real natural resonance principles of music.  The commutative principle is the foundation for Western philosophy and mathematics as detailed in professor Ian Stewart's book, Why Beauty is Truth:  The History of Symmetry. In contrast to Stewart’s book physicist Frank Close’s book Lucifer’s Legacy focuses on the paradoxes from this secret asymmetry lurking in science: Lucifer's Legacy The Meaning of Asymmetry By FRANK CLOSE Oxford University Press 
“The deeper one looks, the more asymmetry becomes apparent and seemingly necessary for anything `useful' to have emerged.”
That's why in the neglected origins of music theory the value of “x” is not given for 2/3x as F to C = G to C as 3/2x. Please refer to Figure 2 in this link of the “Doe a Deer” Solfeggio scale showing 2/3x as F to C By equals I mean they are both the Perfect Fifth as a continued proportion frequency ratio F/C::G/C.  But obviously they are not equal - that is the "bait and switch" - it's assumed they are commutative so that the "ratios" can have reciprocals - but 2/3 is C to F as a subharmonic while 3/2 is C to G as a harmonic. Anyone who knows the experience of playing music knows that those are not equals as reciprocals - there is an inherent drive of complementary opposites by the 1-4-5 music intervals which is the basis for Blues music and the 1-4-5 music intervals are found in ALL human cultures on Earth (except Western culture which turned them into logarithmic tuning). It's the same “C” but one ratio is as wavelength and the other is as frequency based on the Law of Pythagoras using complementary opposites – not based on the logarithmic “containment” of infinity through geometry. The term “frequency ratio” then is what Slavoj Zizek calls a “vanishing mediator.” In other words the inverse is non-commutative geometrically and so the logarithmic value of using the reciprocal changes the geometric value. This is what was rediscovered about time and frequency for the quantum physics - the order of multiplication changes the value of the music harmonics as Taoist-Pythagorean complementary opposites. 

But what is the big lie at the foundation of Western science?! To quote the above again:

we’re dividing ratios, which is multiplying by the reciprocal...Since multiplication of ratios is commutative
WRONG. The Law of Pythagoras is sacred to science yet it is non-commutative geometrically as time when the subharmonics are considered.  Western science assumes time is a symmetric geometric wavelength Hertz. Plato said "time is the image of eternity" and Plato defined infinity (Apeiron) as irrational geometric magnitude. You can't "see" time - you listen to time as infinity. This same non-commutative secret of time and frequency aka Fourier Uncertainty was rediscovered in the quantum relativity physicist Louis de Broglie’s Law of Phase Harmony. Phase in quantum physics is non-commutative but it has to be converted to commutative symmetric math for a physical amplitude measurement even in quantum physics.

So there is a "bait and switch" – the frequency has to be greater than value one or else the algebraic equation harmonic mean times arithmetic mean does not equal the geometric mean squared.  4/3 (Perfect Fourth) x 3/2 (Perfect Fifth) = Square root of 2 (tritone) squared (octave).   Notice that the subharmonic is less than value one - the value 2/3x but it is now hidden or covered-up for the logarithmic equation as the Greek Miracle.  2/3x has to be "doubled" so that it is no longer less than value one. 9/8 was from 3 squared / 2 squared or 9/4 then halved into 9/8, the major second interval. This is the secret formula using the tetrad compound ratio 6:8:9:12 from Babylonian mathematics that enabled the Greek Miracle of science.

So 2/3x as F to C is the subharmonic not the wavelength of C to G as 3/2 frequency. 2/3x subharmonic is then doubled (assuming this symmetric reciprocal inversion) - even though 3/2 is the frequency as the inverse of wavelength – 2/3x is not the frequency as the inverse of wavelength because it has to be doubled as 4/3x as C to F, the Perfect Fourth. We have just violated the “Law of Pythagoras” just as does light signals in Einstein’s relativity using the quantum Law of Phase Harmony. Again 2/3x is the subharmonic. So if you use the same C – the 2/3x as F to C and the same C is 3/2x as C to G. 2/3 is F to C is Perfect Fifth and 3/2 is C to G is Perfect Fifth. You can't just use the commutative reciprocal of the ratio since C to F is a different time value as phase subharmonic - instead of the assumed commutative wavelength time value.

Let's return back to an article I linked in the "summary" above: 

The perfect fourth, and not the tritone, is the true “devil in music.” It’s no “subdominant.” It’s the phantom tonic.

Non-commutative. See the “bait and switch” – I added in the geometric symbols and suddenly the equation is non-commutative while Western science has to be commutative. So 2/3x as F to C can not be allowed since it exposes the non-commutative truth or the yin-yang dynamics, the complementary opposites of real internal alchemy energy! The empirical truth of Western symmetric logic using the phonetic “attic” alphabet requires a cover-up with the ratios as only greater than one. To quote an expert: 
“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. (my emphasis).

The music interval pitch is, when we listen, perceived as complementary opposites but this is hidden and covered up to create symmetric commutative mathematics. Technically in Western music and sound physics this is called “frequency shifting” as explained here: But again this analysis puts the empirical truth of “frequency shifting” within an assumed classical physics framework when in reality the opposite is true! Frequency shifting is the empirical truth of sound itself – there is no fundamental tone as a physical wavelength but this is only discovered by listening to the source of sound from within ourselves.

So the Perfect Fourth is not a harmonic in the overtone series but the Perfect Fifth is the third harmonic with the octave as C – so it's C to G as the perfect Fifth or 3/2. So then the frequency is the inverse of the wavelength so that the frequency is 3/2 and the wavelength is 2/3. But with the Perfect Fourth this does not work because it is the complementary opposite of the Perfect Fifth – so again it is non-commutative. 

O.K. so then you take the subharmonic of the Perfect Fifth so that the harmonic is 3 and so the subharmonic is 1/3 – going the reverse direction of the octave. So this means it goes in the reverse time direction. So then the secret is that there are undertone subharmonics that increase in amplitude at the same time there are overtone harmonics of the perfect fifth – but since they are non-commutative then there is an inherent resonance or push-pull that drives the resonance, an inherent yin-yang dynamic. It's a nonlinear feedback resonance. That is the secret of inner alchemy energy.

Frequency and wavelength both assume symmetric irrational logarithmic values. I'm talking about music theory of inversion or complementary opposites. So A to C = C to A.  6/5 is A to C and C to A is 5/6. That is the commutative value just as with 2/3x = 3/2x. (notice I used "x" and not the geometric symbols - because that is the cover up). Same geometric symbols inverted with same frequency ratios. But the reality of music is that it is non-commutative or complementary opposite harmonics. So we have either the number ratios or the music intervals (Perfect Fifth) or the geometric symbols - but not all three at the same time because of the bait and switch. O.K. now let's add the music intervals: Again 6/5 is A to C and C to A is 5/6 but 6/5 is the minor third and 5:6 is the major sixth. So they are not the same perceived pitch music interval and so their numerical inversion is non-commutative – the number does not line up with the geometric symbol when the music perception is considered. So to achieve the commutative value then 5/6 has to be doubled to 5/3 so it has a value greater than one, just as 2/3x the subharmonic had to be doubled to 4/3 as frequency. So if we left out the music interval perception it appears to be commutative but when we include the music perception with the frequency math and the geometric symbols we discover it is non-commutative.

O.K. I'm talking about very radical thinking - meaning these "bait and switch" commutative explanations for music theory convert ratios like 8:9 into fractions as 9/8 via a geometric means irrational magnitude - again the value has to be greater than one - even though the description is of a vibrating string that has a fraction less than one - "an interval of a fifth if the string was reduced to 2/3 of its length." So that means the length value starts at zero to one if the fraction is less than one but we have to realize that in this case zero does not exist because the 2/3x is actually a subharmonic! 2/3 the length of what? Of an infinite string - that's what. As Daniel Bournelli's competitor for the harmonics of the vibrating string in the 18th century, D’Alembert relied on Rameau who did believe in infinite overtones from the one vibrating string – although both D’Alembert and Rameau realized there was no actual physical vibrating string to this philosophy – instead it was pure mathematics. 
“As soon as the corps sonore vibrates, it divides itself into aliquot [integer] parts and produces as a consequence different sounds. Can we know at present what is the principle of this division? It is one of those first causes the understanding of which is above our faculties, and for which the true philosophes today search.” 

Thomas Street Christensen, Rameau and musical thought in the Enlightenment (Cambridge University Press, 2004), p. 167. 
“In fact, the known physical fields – electric, magnetic, gravitational, nuclear and so on – are all modeled, in mathematical physics, by the same abstract field, known to mathematics as the d’Alembertian wave equation.” 

Ralph Abraham, “The New Sacred Math,” World Futures, 62: 6-16, 2006. Jean D’Alembert emphasized music theory as the secret model for reality. Christensen, Thomas. “Music Theory as Scientific Propaganda: The Case of D'Alembert's Élémens[sic] De Musique.” Journal of the History of Ideas, Vol. 50, No. 3 (Jul.–Sep., 1989): 409-427.

That is why the subharmonic as 2/3 is C to F while the harmonic as overtone is C to G as 3/2. There is a difference between listening to sound as harmonics and trying to convert sound to a geometric wavelength. The process of internal listening is a process of yin-yang alchemical energy.  As math professor Borzacchini states: 
" Plato and Aristotle the reference of incommensurability becomes exclusively geometrical. The “secret of the sect”? So well kept by Archytas on the geometrical side and betrayed on the musical side," Historia Matematica listserve [HM] Music and Incommensurability, Luigi Borzacchini, Mon, 12 Jul 1999.

The Law of Pythagoras is the origin of Number and harmony (frequency as harmonics) and the Law of Pythagoras is based on complementary opposites – not symmetric logarithms and irrational numbers. The Harmonic Series diverges – that's the origin of the title of the math book The Number Devil.  Remember that the tritone is the “Devil’s Interval” and the tritone is created by converting the complementary opposite number ratios into the symmetric irrational square root of two. So that is the cover-up – the real devil is not the divergent number ratios but the irrational number or geometric “containment” of infinity.

“Divergent series [real Pythagorean harmonics] are the invention of the devil.” —  mathematician Niels Abel

O.K. so the tritone creates the square root of two measurement (see above for M.I.T. analysis). But everyone "knows" the square root of two is correct right? I mean everyone learns this "truth" by 10th grade of high school. Or maybe not? Sure enough the real mathematicians know that the square root of two is logically a lie.  Check out professors Sayward and Hugly:
“A popular view is that the great discovery of Pythagoras was that there are irrational numbers, e.g., the positive square root of two. Against this it is argued that mathematics and geometry, together with their applications, do not show that there are irrational numbers or compel assent to that proposition.” 

 Philip Hugly & Charles Sayward Philosophy 74 (2):169-176 (1999).  (my emphasis).

Of course the “square root of two” exists right? Unless you are honest about incommensurability as a real mathematician is – then infinity stares you down. But that's just some obscure philosophy journal right? Nope.  

The myth of irrational numbers, January 2008, by James J. Asher, Prize-winning math instructor.

What is missing between the logical error of geometry and arithmetic? Besides the fact that the “point” of long division arithmetic length is converted to a geometric side for area, something else: Complementary opposite music harmonics or the Pythagorean Tetrad, the Tai-Chi symbol. I knew this when I took "enriched geometry" in 10th grade and that's why I didn't continue further into logarithmic mathematics - I knew I was being presented with a lie, candy-coated as the truth. I could see the gap in the logic. Why? Because I knew the secret music theory of Pythagoras intuitively from the complementary opposites of the Perfect Fourth and Fifth intervals, from playing music. Then I took quantum physics as my very first physics course and our instructor stated this should always be the case since quantum physics is the foundation of physics. But instead everyone learns classical physics so they get the foundation of science wrong!

The idea of a frequency being “the answer” in no way questions the symmetric “divide and average” math to create frequencies – what I'm saying is that the “divide and average” math is wrong – not one frequency versus another. So the Western system of “divide and average” math is wrong (the source of vast ecological destruction and social injustice) and the true meaning of the Pythagorean Tetrad is the same as the Tai-Chi in Taoism or OHM in the three gunas of India (the oldest African-sourced philosophy of India) – a resonance of complementary opposites. The West is awash in “secret” New Age harmonic frequency systems but they all, including the infamous 432 Hertz cult, rely on “divide and average” mathematics that assume a logarithmic convergence.

I am asked online – is an octave a doubling of Hertz or not? I have pointed out that this is precisely the “bait and switch” issue that was covered up:  Instead of an inversion of the frequency and wavelength (as non-commutative subharmonic) there has to be a doubling of the fraction first to hide the non-commutative relation of the Perfect Fifth and Perfect Fourth. Music is in time not space – any musician knows that the G to C interval is a Perfect Fourth – not a Perfect Fifth.  So the 200/300 Hertz interval is 66 Hertz while the 300/200 hertz interval is 150 hertz. So that 66 Hertz is F to 100 Hertz as C – a Perfect Fifth subharmonic. 150 Hertz is the Perfect Fifth as C to G. The same C and so it's non-commutative (2/3 as F to C and 3/2 as C to G).

Now the question is repeated: Is there a doubling of octaves or not with frequency? O.K. so for Hertz again on the Harmonic Series – it is 3/2 since the “root” frequency is 100 Hertz and it is the “root” frequency that is doubled as the octave; So then G to C as 4/3 can’t be used as the Perfect Fourth; It is inconsistent with the “root” frequency as 1 or 100 hertz. The 3 is not the “double” of 1 or 2. In other words in the same scale if G to C is 4/3 then why is G to C as 4/3 in the harmonic series not allowed for defining the Perfect Fourth?  So instead the subharmonic of 1 as the Harmonic Series or 100 Hertz is used as 2/3x or C to F in the opposite direction – a longer wavelength. So we can just ignore that it is C to F as the Perfect Fifth in one direction while it's C to G as the perfect Fifth in the other direction?

I have been asked if this meant that the subharmonic was a subset of 3/2x and I answered yes. Harmonics are perceived as pitch intervals and not just Hertz frequency. So it’s been stated then that using “F” as the new root frequency for doubling the octave you still get – close to, but not quite the doubling of the octave of 100 hertz as C. Let’s check the Hertz: 132 plus 66 = 198 Hertz. Yep it's almost the same as 200 Hertz. It’s two Hertz off – exactly the same difference as the error of time-frequency uncertainty with the truth of the “infinite spiral of fifths.” I’ll repeat from above, Physicist Iori Fujita: “But even Δt is 1.000 sec, the bandwidth remains about 2 Hz.”

There’s another way to explain this Fourier of time-frequency uncertainty principle that clarifies things. “If the frequency difference is one hertz (one vibration per second), then you hear an interference beat every second.... But you probably found that, when the frequencies differed by 3 Hz, you needed (very roughly) about a third of a second. When they differed by 1 Hz, you needed more time. So, roughly speaking, if the frequencies differ by Δf, then you need a time of 1/Δf to notice.” 

So notice how the "measurement" of quantum time-frequency uncertainty is now based on listening and the time it takes to hear the difference! A difference of 2 hertz (the bandwidth) takes 1 second to hear. As I said - this is because of the non-commutative or complementary opposite resonance of yin and yang or 2/3 and 3/2 as the Perfect Fourth and Perfect Fifth. The esoteric meaning of this listening to time is the heart-beat is the origin of the "second" measurement - but the heart beat is syncopated (the order of the beat changes its value). When the heart beat speeds up which means, as per quantum time-frequency uncertainty, it takes longer to hear the difference because the bandwidth is smaller - time is experienced as slowing down because your heart-mind is processing information (beating) at a faster rate and so you perceive reality as smaller intervals and so time appears to move slower. In actuality this is because the kidney energy (again the vagus nerve connection to the brain) floods the brain with adrenaline and dopamine which over-stimulates the neurons recording memory. For old people if they don't get new experiences then it seems like time doesn't exist since the slower hertz or frequency of doing the same thing all the time means much less time is needed to perceive the differences and so time is experienced as going very fast (or not existing at all) - no memories are being recorded.This is detailed here: John Brockman, “Parallel Memories: Putting Emotions Back Into The Brain, A Talk With Joseph LeDoux,” The Third Culture, 2/17/1997

The ability to “create” frequency is dependent on how long of time you get to do so and so frequency is really not measured by a contained geometric wavelength as is the case for amplitude. In other words the higher your energy frequency resonates with its vacuum light source (a spacetime white-black hole) then less time is experienced subjectively as the subharmonic interference beat. So then the intense high frequency resonance as laser energy (from the ultrasound sonofusion) resonates subharmonics as the proton water alchemy of hydrogen bonds - creating the loud OHM sound from the heart as the deep vagus nerve activation of the Yuan Qi energy creating Yuan Shen energy.  As inner sound alchemy meditation then the OHM sound creates the Perfect Fifth/Fourth/Octave resonance of a finer tuning in higher and lower frequencies. This is the secret meaning of the "zero" beats as the absolute void that I discuss in my masters thesis of 2000, Epicenters of Justice: Music theory, radical ecology and sound-current nondualism. Physicist Charles Madden wanted me to explain that meaning to him and it took me 14 years to now finally be able to do it! haha. The "zero" beats is actually from this inherent non-commutative process of resonance that is eternal time-frequency subharmonic-overtones. my old masters thesis had not made this distinction yet, stating incorrectly that logistic equations were equal with the tai chi symbol Madden pointed out in his Fractal Music book that the Tai Chi symbol is not a fractal since a fractal relies on the commutative logistic equations. That was the key insight I needed to continue this research of the secret Pythagorean alchemy connection to Taoist training. See googlebooks link on Madden explaining Yin-yang symbol is not a fractal
So Western science has waved off this difference as inconsequential but the issue is that doubling the octave is directly tied to doubling the Perfect Fourth in comparison to the “root” frequency and also halving the Perfect Fifth in relation to the “root” frequency – using the double octave as 9/4 to get 9/8. 9/8 is then cubed as the Devil's Interval – the tritone as the square root of two. This creates the pre-established disharmony that covers up the truly rational inner alchemy paranormal spiritual energy.

Now how do we relate this back to the quantum time-frequency uncertainty principle? Dr. Mae-Wan Ho explains: 
“The quantum coherent organism is not just a theoretical concept; it needs more than simply applying conventional quantum theory to organisms. The conventional quantum mechanics needed to be stretched, and that’s what I did in my book. The analogy is a multi-mode laser that is pumped up to be coherent in many frequencies, a whole range of frequencies. The wide range of frequencies in an organism is just fantastic. In my book, I say that it’s like 70 doublings of the octave." 
"I use the analogy of ‘quantum jazz’ to express the quantum coherence of the organism. It goes through a fantastic range of space and time scales, from the tiniest atom or subatomic particle to the whole organism and beyond. Organisms communicate with other organisms, and are attuned to natural rhythms, so they have circadian rhythms, annual rhythms, and so on. At the other extreme, you have very fast reactions that take place in femtoseconds. And all these rhythms are coordinated, there is evidence for that.” (my emphasis). 

So this is through quantum coherence as non-local communication as consciousness and yet also as time-frequency uncertainty resonance.

So the science can see the evidence but it can’t use it as technology, the math in real time is based on time-frequency uncertainty using quantum entanglement, superluminal signals. Logically we can infer consciousness from this process, quantum jazz, found through the Taoist yin-yang principles of non-commutative natural resonance. This is science the skeptics want to ignore – P.Z. Myers dismissed quantum biology when I mentioned it on his materialist blog back in 2006. Now quantum biology has made the cover-story of Scientific American: V. Vedral, “Living In a Quantum World,” SciAm, June, 2011. 

 As Vlatko Vedral states: 
“In the modern point of view, the world looks classical because the complex interactions that an object has with its surroundings conspire to conceal quantum effects from our view.”

What does this mean fundamentally? When we start listening the non-dual truth, proven by quantum coherence that is superluminal, is that the “music” is listening to us as consciousness – call it God, the Emptiness, the spacetime continuum, or “the pilot wave” as de Broglie called it. This is infinite energy creation due to the inherent complementary opposites of reality – we exist within this process as a part of it and we can choose to resonate with it, thereby creating more harmonized energy that goes through the full spectrum of frequencies to find where energy is best needed. 

This is already proven for plants - Unusual quantum effect discovered in earliest stages of photosynthesis Because the moment when the quantum effect occurs is so short-lived -- less than a trillionth of a second -- scientists will have a hard time ascertaining biological and physical rationales for their existence in the first place. ‘It makes us wonder if they are really just there by accident, or if they are telling us something subtle and unique about these materials,’ Tiede said. ‘Whatever the case, we're getting at the fundamentals of the first step of energy conversion in photosynthesis.’

It’s also in birds - "Nature has, for whatever reason, been able to protect quantum coherence better than we can do with molecules that have been specially designed," says team member Simon Benjamin of the Centre for Quantum Technologies in Singapore. So the natural resonance harmonics continue to be discovered and affirmed – despite the skeptics ignoring the science due to their materialistic dogma.

For humans, it's just a matter of practicing this philosophy. I urge people to study the book "Taoist Yoga: Alchemy and Immortality" which uses the 12 notes of the infinite spiral of fifths as the means to creating energy that in reality is based on this same time-frequency uncertainty principle rediscovered in quantum physics. Enjoy. So science has the Devil's Staircase which means that the low rational integers resonate as nonlinear harmonics so the higher you go into overtones the stronger the amplitude of the undertone beats are. The driving resonance is strongest when the low natural harmonics are used.

So it's not one "frequency" - and in fact Hertz relies on a symmetric commutative definition of time as wavelength (amplitude) but rather because of time-frequency uncertainty then reality is non-commutative and the energy as consciousness is non-local. So we exist within sound as consciousness - no "one" is listening but rather the consciousness is listening to us. We discover this by a deep process of listening - there is no start or end to listening. In fact hearing is the final perception that is maintained at death so it is used to test unconscious people in comas to see if they should have the plug pulled or not.

So my article gives the evidence that the perfect fourth/fifth harmonics has the strongest brain resonance and also that ultrasound naturally resonates the skull cavity while the ELF subharmonics create sonofusion. So put that together and you have the Tai-Chi Tetrad as the best way to resonate the mind-body for alchemical healing.

But yeah the qigong master has said that these external technologies like rife machines or magnets, etc. can help and heal but overtime can create problems - because again the secret is not any one frequency but rather this eternal number resonance since 2 does not go into 3 and 1 is not really a number just as there is no source to the I-thought. We can logically infer the time-frequency uncertainty as non-local consciousness since when frequency is zero then time as phase (subharmonics) is infinite and vice versa but that process of listening never ends. So that is how zero-point energy works - because it is asymmetric or non-commutative number then it spontaneously creates energy as form.

I have some updates to the above research. Enjoy - May 2015
It's too bad Goodman in his fascinating book "Sonic Warfare" misspells Evens' name as Evans (I corrected it below):
Aden Evens applies the concept of the surd to sound signal processing and defines it as “a discontinuity that represents the specificity, the unique moment of the original signal —.. .[ ensuring] that no wholly accurate recreation is possible, that no analysis can
do justice to the original signal” (p. 229). Such glitches force engineering to deal constructively
with the problem, for example, the local intervention of the Lanczos sigma as
a response to the Gibbs phenomenon. Aden Evans, “The Surd,” in Virtual Mathematics:
The Logic of Difference
, ed. S. Duff y (Manchester, U.K.: Clinamen Press, 2004).

 Evens notes that the “superiority” of the analog stems not from a
limitation of the digital substitution, its difference from an actual object, but
crucially — and this is the crux of their differential ontology — it is “rather a productive
difference, a not- yet- determined, an ontological fuzziness inherent to
actuality itself. Difference as productive cannot be digitalized.” The processual
nature of the actual, and its generation of singularity, must exceed its capture.
In other words, the actual for Evans exceeds the sum of its digitized parts. This
is not merely a phenomenological point. Elsewhere, Evans develops a parallel
argument using intuitionist mathematics in relation to the concept of the differential
(specifically the surd) from calculus and what Deleuze termed the
process of differentiation.

This is great to see the postmodernist analysis agree with me about the "surd" (irrational magnitude) and sound - only the postmodernists are missing the key secret of complementary opposites which I provide. I did send this link to Evens though so maybe he'll respond! Check out Goodman's Sonic Warfare book - pdf link - fascinating read!
playing both the higher (inaudible) and lower (audible) bands together enhanced neuronal activity in the alpha frequency range
Citing the Japanese research on Gamelan that I cite in my research elsewhere.  Inaudible High-Frequency Sounds Affect Brain Activity: Hypersonic Effect Alpha wave being key for serotonin Tummo energy and the Mozart Effect.

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