Thanks a lot You really know your stuff. However, why is it that Yin and Yang on page 39 are defined as the 2/3 undertone and 3/2 overtone, yet on page 44, Yin suddenly becomes a 4/3 interval?
Wow you really cut to the chase! Impressive. pdf book on "rhetorical traditions in Neidan for female alchemists" 2007 Ph.D. thesis, pdf link
So there are three levels of analysis - the original is 1) "complementary opposites" and then 2) "divide and average" and the final is the Greek Miracle - (leading to modern science). Richard Bertschinger - part 1 - speaks on his Secret of Everlasting Life book youtube
So the Chinese attempted a 60 or - 53 note scale based on the "divide and average" math - in which case 4/3 is the Perfect Fourth as yin and 3/2 is the Perfect fifth as yang.
So the three in one harmony - means that the Octave is 2/1 or 1/2 - with the above alternation of Perfect Fifth and Perfect Fourth. The "Divide and Average" math means this "converges" to the octave but never gets there. Richard Bertschinger: 3 in 1 secret of everlasting life neidan alchemy youtube
So the closest approximation to lining up the octave and the Perfect fifth/Perfect Fourth is the 53 note scale.
Sounds crazy right - 53 notes IN ONE OCTAVE. haha.
But at first this is theoretical - right - actually Alain Danielou made a keyboard with 53 notes.
The Indian scale of 22 notes - or around there is also originally based on this Octave-Perfect Fifth/Fourth.
So in those systems - as Stephen Hawking points out - the geometry is "sacred" and therefore a transcendent infinity - while the arithmetic continues infinitely.
So in that system - each number is "male" and "female."
For example Kepler was against the "closed" equation of the golden ratio but Kepler was in favor of the Fibonacci Series whereby each number is "male" and "female" based on Pythagorean principles that "converge" as number - but NEVER actually complete the convergence.
So this is called the "infinite spiral of fifths" - and in music theory it is empirically true - in other words it's not just "theory" - it is the actual harmonic series.
So that was the dominant "divide and average" math - from Egypt to Babylonia to India to China - Bronze Age math, let's call it.
But the first system - the "three in one unity" as the "three gunas" or Pythagorean harmonics - it's called Orthodox - it just uses the Octave-Perfect Fifth-Perfect Fourth.
In other words - no 9/8 even. For example Gurdjieff taught the Law of Three but then he also expanded it to 5/4 and 8/5 and 9/8, etc. and so this caused Westerners to just assume he was still using a "divide and average" math which then easily just turns into Western symmetric math as the Greek Miracle, etc.
O.K. so as I said - Orthodox Pythagorean - no 9/8 even (which is from 3/2 squared and then doubled back to the same octave so 9/4 is 9/8).
Instead - the "3 in 1" unity is based on noncommutative phase - which means that the Perfect Fourth as yin - is alchemically transmuted into the 3/2 subharmonic as the Perfect Fifth. Richard Bertschinger - on the Great Oneness as the 3 Jewels - youtube Taoist alchemy neidan
So in other words geometrically - as I state - F=3=G - at the same time. Two places at the same time - which is to say you can't see it travel instantaneously - as time = 3 - an instant in two places - but you can listen to it as the 4th dimension of space or the 5th dimension as time.
O.K. so in alchemy the goal is to convert the yin energy into yang.
So the question you asked - is - like I said - it cuts to the Chase.
Remember reality is holographic - so you just entered into a black hole of my brain. haha. I was just thinking about this.
So noncommutative phase actually means that everything is happening at the same time - from the perspective of light.
So when we "turn the light around" this means time goes to zero - but at the same time there is Yuan Qi - that is yang qi as the Perfect Fifth that harmonizes all apparent movement in 4D spacetime - from the 5th dimension.
I go into this more in detail on my blog - with various posts and articles.
So I could elaborate - but basically - the Perfect Fourth as yin - is a different geometry and so it's still a complementary opposite - but it has a different math value - whereas when the yin qi is turned to yang qi, this actually creates a reverse time nonlocal harmonization from the future.
This is called the Law of Phase Harmony by de Broglie - I devised an equation that connects the Taoist alchemy training to his physics based on Pythagorean analysis of Einstein and quantum entanglement.
So I hope you see what I'm getting at.
As the qigong master I studied from states: The simplest is the most powerful.
There is a qigong lineage that "sells" on this site - or they used to - but they use the time "The Single Yang" - and that is the same concept. The Great Oneness: Secret of Everlasting Life" - Richard Bertschinger - youtube
I ran across it again recently - in an academic paper on Taoist alchemy in religious rituals - that the goal is to turn all the energy into Heaven Yang energy.
So this is considered the Yang Shen golden body - but in reality it is an infinite process from the Emptiness that is a "3 in 1" unity as eternal motion.
In the Dao De Jing it says: “When there is no desire, it is possible to see the mystery.” If one observes inside, then the upper, middle and lower are also observed and can link together. The classic says: if you attain one thing, all things will be accomplished. Once Yuan Jing, Yuan Qi and Yuan Shen meet, Dan Gong (Elixir Achievement) is achieved. Then in the dark mysterious pass, the aperture of Xuan Pin, and the origin of yin and yang, the Shenqi resides. Secrets of the Single YangIt is kind of like the paradox - if something moves so fast then you don't see it move at all. When light is turned around and time goes to zero - there is still a hidden momentum to light due to this noncommutative phase - and this is also the Tai Chi.
So the three in one unity - it is both the change of relative reality in 4D spacetime but it is also from the perspective of light as Yuan Shen - nonmovement that has "doing" in it - I am quoting "Foundations of Internal Alchemy."
Let me know if you think I am just b.s.ing - but another secret is that Pythagorean philosophy states that "One is not a number" - this is a secret of the Yang Shen again - when time goes to zero based on the light as the individual spirit consciousness then it merges into universal consciousness which has so much light that the whole 4D universe of spacetime disappears and yet there is still "formless awareness" or the Yuan Qi as the Emptiness that still creates 4D spacetime eternally.
So by resonating with our source of reality - then we can see the future, have levitation, physical transformations, and change the past - but it is not "us" doing it - it is this impersonal transformation process that is an eternal listening.
So it is stated that Kali is both the destruction and creation of the Universe but Kali is also from Kala as time.
The same is true of Chronos and Kronos.
So geometry as space collapses into pure listening as time-frequency - the Emptiness is time as formless awareness while the frequency is the spirit as light. This is the "3 in 1 unity" that is the simplest and yet most powerful - and it's also called the "point of origination" - just as in physics - light collapses to an infinite photon in space yet at the same time light is entangled nonlocally as infinite awareness that can not be seen and also creates energy as new mass.
Another way to say this is what I call the I-One-Eye - and I made that term up ten years ago. But then I discovered that Louis Kauffman, the math professor, was making the same claim - and still is as we corresponded recently - that the number one is actually the I-thought as light - that is noncommutative in time and therefore as noncommutative time, as an imaginary number series that changes phase, as complementary opposites - it then spins out reality.
The only thing is that because he's a mathematician he still has to convert that to "symmetric" math of modern Western mathematics. He worked with Eddie Oshins who I cite - since I wrote that pdf - Oshins discovered the same secret I realized about noncommutative phase - and he taught Wing chun but he was a real quantum physicist at Stanford but he also was a quantum psychologist.
So you can read his work - I blogged on him - for more secrets - he calls it self-similar movement or quaternion movement.
So we can say that - yin jing turns to yang jing which is yin qi that turns to yang qi which is yin shen that turns to yang shen which is yuan jing which creates yuan qi from yuan shen.
So the final stage when you go into the Emptiness for real - there is a unification of the 3 into the 1 - and this is why the yin disappears. The yin shen has to be transformed into yang shen and this is done by transforming the yin qi into yuan qi.
In the end the Yang Shen - golden body - vaporizes into the Yuan Qi because it is not the individual spirit that is really doing the training. Another way to say this is "No One is listening" or "the cosmic mother will never be unveiled."
So your question actually has no answer - it is an infinite listening process since the 2 and 3 never collapse symmetrically since they are noncommutative or complementary opposites. In this sense the 4 is like the infinite that can not be expressed with any mental concept or symbol - and yet the 4 at the same time is the expansion into the material realm of yin - so that the original origins get forgotten about.
So it's not that the Perfect Fourth as 4/3 does not exist - it just means that is how the energy expands and contracts into itself. So some music alchemists - create the Lamdomba - which, as I said is this attempt to "contain" the infinite through divide and average numbers - but starting with Plato they made the bold leap of just embracing the discontinuity.
Math professor Luigi Borzacchini states that the concealment of Orthodox Pythagorean philosophy, to make the Greek Miracle, is "really astonishing" and "shocking" and is a "deep pre-established disharmony" that "guides the evolutive principle of science." I have corresponded with him about this. Borzacchini states that for the Pythagorean orthodox philosophy - there is no separation between discrete number and the continuous.
So real Pythagorean philosophy was based on 5 years of silence before Pythagoras could even be met in person - and even then it was through some concealment - and his name literally means "snake master" - and so whether he ever existed, who knows. But the training is real and yet most of us would instead want to expand the numbers - to try to figure out how to line up the octave with the Perfect Fifth (and it's complementary opposite).
So we can state that the Perfect Fourth is from the perspective of what's called Fourier Uncertainty or time-frequency uncertainty - you fundamentally can not measure infinite time and frequency, at the same time - and so you fundamentally can not HAVE the Perfect Fifth in two places at the same time - when you ASSUME that you need an external math continuum or geometric "line" as physical space to measure time.
Is that starting to make sense? Pythagoras taught that all is Number and Harmony - but instead his true teaching got warped into "all is geometry."
So if you really study the conundrum of say irrational geometry - the truth is actually that space itself "collapses" into time that can not be seen and that this is a mind-body transformation training. But since humans left the forest - vision is our main perception instead of listening - and so it is very difficult for us to believe that there is this infinite 5th dimension that is "time-lie" as instantaneous signalling or communication, the foundation of reality.
thanks - if you read all of this - I am impressed - as I had to hope I could "sell" you on something. haha.