Musical Irrational Magnitude Error of Alain Danielou and Aurobindo: Thomas Váczy Hightower admits to 20 years of wrong information on his Musical Octave Pythagorean website

Yes thank you Thomas - the book The Fifth Hammer was written by a Comparative Literature Professor at Princeton - I gave the name as Professor Heller. Like you he is married so actually his last name is two names. haha.

With the exception of B#, or the ditonic comma,[10] ratio 531441/524288, Table 11.2 shows that the Chinese and Pythagorean progression of ratios are identical,

That website clarifies that what you erroneously call the Pythagorean Comma is actually the Ditonic Comma. http://www.chrysalis-foundation.org/China-s_Ch-in.htm  I was just letting you know I have contacted several people about this same error. I have been corresponding with Eduard in the U.K. who wrote a 2017 master's thesis on Pythagorean harmonics and he has the same math error you did. I did a 2000 master's thesis on this subject but I also had a math error in it - when I stated that the Tai Chi was based on logistic equations. The Daoist Chinese actually "added and subtracted" their fractions but not as geometric irrational magnitude. So then the Westerners say we can just convert it to multiplying and so get 9/4 but don't realize this was used by Philolaus to construct geometric magnitude! In other words doubling can be either squaring or multiplying, based on whether the square root is being calculated. So it is what I call the "bait and switch." That's what creates the mathematical error in the ratio.

Dear Professor Heller:

  the Pythagorean comma  = 531,441/524,288 in your book, p. 36 The Fifth Hammer

take care and happy soon Spring Equinox!

drew

Dear Drew Hempel,
I thank you for your interest in my work on the musical scale:  http://vaczy.dk/htm/scales2.htm. and since the dispute is about the Pythagorean musical scale I will quite from that chapter: 
<He discovered what later was called the Pythagorean comma, the discrepancy between 12 fifths and 7 octaves gives (3:2)^12 > (2:1)^7. Calculated through, it is: 129.74634 : 128 = 1.014. Or in cents: 23.5...
.....As far back as 2,500 years ago the Pythagorean figured out that it was impossible to derive a scale in which the intervals could fit precisely into an octave. The ancient Greeks explained this imperfection – the comma – as an example of the condition of mortal humans in an imperfect world. >

I do not agree of you general claim of being wrong on the Pythagorean comma. The second claim mentioned in my chapter  The spiral of fifths, I will agree of errors. I cannot understand those
I wrote this 20 years ago particularly close reading of a recommended book by Alain Daniélou, Music and the 
power of Sound, copyright 1943, revised 1995.  His chapter, The Cycle of Fifths page 39-43.
My calculations below I am unable to explain and simply wrong. As soon as I find time I will remover this. The sad thing is, that a lot of other formulation and points has to be rewritten. I had a that time got to much information and apparently unable to digest them properly. Thanks for you concern, sincerely Thomas Hightower 
I, C
II, G = 3/2
III, D = 9/8 = (3/2)2 * ½ (lower an octave)
IV, A+ ( a comma sharp) = 27/16 = (3/2)3 * ½ (lower an octave)
V, E+ (a comma sharp) = 81/64 = (3/2)4 * ¼ (lower 2 octaves).

So let's see what Alain Danielou used for his Cycle of Fifths?

 https://www.academia.edu/10981059/Music_And_The_Power_Of_Sound_-_Alain_Danielou

Somebody uploaded the book! Thanks.

In the mean time - let's review why the early Pythagorean Orthodox harmonics are the same as the Daoist Chinese harmonics!!

Henricus Glareanus (1547) says that the original Lyre of Hermes had three strings, corresponding the three original Seasons of ancient Greece (Summer, Spring, Winter, from high to low). He says that Orpheus added the fourth string, corresponding to Autumn, when that Season was adopted from the East. Most sources, however, attribute the Four-String Lyre to Hermes. (Godwin HS 198) Opsopaus

 In Empedocles' system, Zeus and Hera, who rule on Olympus, correspond to the opposed elements Air and Earth; Hades and Persephone, who rule in the Underworld, correspond to the opposed elements Fire and Water. Therefore Zeus and Hera represent the Marriage of Heaven and Earth (see part I on Earth for Hera as an Earth Goddess).

The second-century Neoplatonist Theon (Math. Chrem. Platon. Anag. II.xxxviii) gives a set of correspondences to the Tetractys, based on the properties of the first four numbers. For example, they are correspond to the Elements in order of decreasing subtlety: 1=Fire, 2=Air, 3=Water, 4=Earth.

 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.”

Professor Richard McKirahan reveals the secret:

The word translated epogdoic is not a musical term but a mathematical one. An epogdoic ratio is the ratio of 9 to 8. The occurrence of a mathematical term here is unexpected. It has been treated as an unimportant anomaly but in fact it is the key to the entire fragment....The word magnitude normally refers to physical size, but here it is given a new application, extending the notion of magnitude to include musical intervals.

 Or as Professor Borzacchini states:

These remarks raise the question of the difference between the ancient Pythagorean ‘musical’ perception as displayed in the Pythagorean idea of ‘linear number’ in Boethius [Philolaus] or in Nicomachus, and the modern ‘geometrical’ perception of the linear numerical magnitudes.

So sure enough Alain Danielou equates the three gunas with Sattva as the ....



Fascinating!! So Rajas is the Perfect Fifth 3/2 and 2/3 in both inversions of the I Ching!! Sattva is the Single Perfect Yang or Greater Yang resolved with the Octave - as 1-1 - and Tamas is the Greater Yin as what? The 3/4 of subharmonic octave as complementary opposite.

Sure enough Alain Danielou imposes the ERROR of Philolaus onto the Chinese tuning!! Hilarious

 So thanks to Thomas Váczy Hightower for pointing out how he got duped!!

Dear Thomas Váczy Hightower : Professor Patrick Moran does not use 9/8 tuning for his Chinese scale and also he does not "halve" the value of the frequency back into the scale. That is from Greek tuning (Western).

I, C
II, G = 3/2
III, D = 9/8 = (3/2)² * ½ (lower an octave)

 He claims Moran states this - but Moran does note state this at all! According to Moran the third note created as the Perfect Fourth of C as F - note D. So Hightower is secretly switching back to the lie of Philolaus as geometric magnitude.  The below ratio is from Philolaus using Geometric Mean as geometric magnitude of 9/8 divided into small magnitudes to create the semitone. It is NOT the Pythagorean comma.

It is higher than the fundamental by one comma, the Pythagorean comma (312 / 219 = 531,441/524,288,

Now compare his claim with a music professor!!

 results in the number 129.74632.
This ratio, 129.74632 : 128 is the Pythagorean comma. 12 perfect fifths do not equal up to 7 perfect octaves:

But as Váczy Hightower he does use, also, the early Orthodox Pythagorean comma, so he doesn't want to change his claim that the Pythagorean Comma is from the wrong geometric magnitude of Philolaus - he wants to keep BOTH. haha. But that is refusing to acknowledge the inherent complementary opposites of Yin and Yang as Tamas and Rajas - or 3/4 and 2/3 that can not be converted to symmetric geometric magnitude. Why? Because if 1 is C then 2 is C and 3 is G as 3/2 overtone while 3 is also F as 2/3 undertone. That is NOT allowed by the fake Pythagorean Comma that Alain Danielou also uses.

“To put the same thing in another way, we have just identified the frequency ratio 1.5 with the interval of a [perfect] fifth, although our table gave the value as 1.4983. The difference is only small – 1.13 parts in a thousand – but by the time we have taken the twelve steps needed to pass completely around the clock-face, it has been multiplied twelvefold into the difference of 13.6 parts in a thousand, which represents the aforesaid difference in pitch of almost a quarter of a semitone. When this is allowed for, the true clock-face is that shown in fig. 55; it extends to infinity in both directions and all simplicity has disappeared.” Sir James Jeans book Science and Music, (Dover Publications, 1968), p. 166

So thank you for exposing Alain Danielou as wrong! What the Chinese did was change the direction of the Perfect Fifths and Perfect Fourths for each octave! So they recognized that the root tonic is also the "phantom tonic" as it is called in music theory from the Perfect Fourth needing the octave changed by Philolaus in order to construct the geometric magnitude error that established science as a "deep pre-established disharmony" as math professor Luigi Borzacchini details.

 


 So now we come to the part of Thomas Váczy Hightower's website that I said I would return to when I posted yesterday. We can now reveal the error going on by Alain Danielou. The Chinese alchemical music tuning actually used the first root tonic as the Moon, not the Sun, and this is because the Moon is the yin qi energy that is then alchemically transformed into the Yuan qi via the solar yang qi, the Perfect Fifth.

 Theoretical interest in this division goes back to antiquity. Ching Fang (78–37 BC), a Chinese music theorist, observed that a series of 53 just fifths (${\displaystyle (3/2)^{53}}$) is very nearly equal to 31 octaves (${\displaystyle (2/1)^{31}}$). He calculated this difference with six-digit accuracy to be ${\displaystyle 177147/176776}$.^[2]

 I went into details about this in a previous blog post based on Professor Tito Tonitelli's book.

So certainly Danielou revealing this ancient alignment of the circle of fifths with the octave as also based on the sun and and lunar year difference is true but not quite at the level of simplicity that he explains and also he uses the WRONG "comma" based on the wrong harmonics of tuning - that the Chinese did not use, as I exposed via Professor Patrick Edwin Moran's website.

So Danielou was very very close in his analysis - and he actually worked with the Pondicherry Sri Aurobindo Ashram and he published with UNESCO - and the Actual Matrix Plan expose of Professor Oliver L. Reiser was ALSO published in the Ashram journal at Pondicherry - based on the "music logarithmic spiral" of Esther Watson. So Sri Aurobindo said he received Vivekananda's Shakti-Shiva soul while Aurobindo was in jail doing full lotus yoga and Vivekananda appeared to him when he died. Vivekananda said he knew when he was going to die but he also was a Freemason and so he promoted the "external path" of Freemasony. So the Divine Anarchy of Sri Aurobindo was actually based on Freemasonry - just as many of the original anarchists were also Freemasons. So Aurobindo got his math wrong as well since I know have three different sources triangulated the wrong Freemasonic logarithmic math to Aurobindo.




 So now Alain Danielou tries to represent the Spiral of Fifths based on male-female or yang-yin ratios but can you see his error? He just described based on the I Ching that the Perfect Fifth is actually Yang as Rajas - and now he is trying to claim it is both yang and yin such that the F+ is actually 3/4 as yin. But the truth of alchemy is actually to convert the yin of F+ back into F as the real yin-yang harmonics of the Single Perfect Yang. In other words if C is 1 then G is 3/2 and F as subharmonic is 2/3 and both are the Perfect Fifth in relation to the 1. But in the Western logarithmic tuning the F as subharmonic Perfect Fifth is converted to 4/3 by changing the root tonic, into the "phantom tonic" as Philolaus did.

So the Chinese used pitch pipes while Philolaus used a monochord. And so for the monochord from the lyre or lute (used in Babylonia and Egypt) - you can not have 4/3 wavelength of the original 1 root tonic so you have to use a double octave called the Greater Perfect System in order to hide this noncommutative truth. In other words for the real Orthodox Early Pythagoreans One is not a number since because of the infinite spiral of fifths there is eternal listening that turns the One into Light as Shiva - or the Counter-Fire or Hestia, or Zeus.

Hestia made an oath to Zeus that she would remain forever pure and undefiled,

That is the secret of the "three in one unit" as Ramana Maharshi calls it. So that the Sattva mind of light is used to go into Hestia and yet when light is turned around then time is zero but Light merges from individual ego into the spirit of the Universe as Shiva - and this spirit is able to Listen to Hestia, which breathes the light, to create new fire as the hearth of reality - the breathing is formless awareness that can not be seen but listened to as Nada - the OM of the Light of Shiva. This OM is the Shakti energy as reverse time or Kali energy from Kala.

So it originates as the Lunar one as the counter-earth in the relative void of the lower tan t'ien (the small intestines).  It then has to be built up in energy to access the Counter-Fire as the Hestia Absolute Void via the Shiva-Zeus-Hercules light of the heavens as the stars.

When the gods Apollon and Poseidon sought for her hand in marriage, Hestia refused and asked Zeus to let her remain an eternal virgin. He agreed and she took her place at his royal hearth.

 So that refers to the difference between Fire and Water alchemically (Apollo and Poseidon) with Heaven as the Counter-Fire of Hestia and Zeus as the light of the stars as consciousness of Shiva. Jnana is Fire as formless awareness - or the secret Ether power of Light as Ramana Maharshi calls it. So you can not see the Self but you can logically infer it or listen to it. Dr. Peter Kingsley has noted the close parallels with early Christian views and the actual Logos of Pythagorean alchemy. Someone on youtube comments:

it's not that the spirit is 'carried' in the breath, but is the breath itself, since the word 'pneuma' means both breath and spirit. The idea came from the scientific materialist concept of the soul put forward by philosophers like Democritus, who thought that the soul was made up of atoms and came into the body through breathing. Hence 'inspire' to breath in/ have vitality and 'expire' to breath out/ die. This idea was later mixed up with other notions of the soul and that's where we get the 'pneuma hagion' in the new testament, which is usually translated 'holy spirit/ ghost' but could equally be rendered 'sacred breath'.

Ancient Lyre secret revealed

Fascinating but you are missing the alchemy secret that Peter Kingsley reveals. The Counter-Fire is the Void as Air that feeds the light because the 1 as the Light has to be put into the Void in the Earth. This means you focus or visualize your mind as fire spirit under the water element (3) into the Earth to create more Air as Aion kundalini energy or ionized neurohormones. Free details on my channel. thanks; the secret of the original Garden of Eden is alchemy!!

 "Dilmun is a land that is "pure", "clean", and "bright", a "land of the living" which knows neither sickness nor death. What is lacking, however, is the fresh water so essential to animal and plant life. The great Sumerian Water-God, Enki, therefore orders Utu, the Sun-God, to fill it with fresh water brought up from the earth. Dilmun is thus turned into a divine garden, green with fruit-laden fields and meadows."

Samuel.Kramer "The Sumerians", 1971 The University of Chicago Press

Furthermore Enki is known as the God of Wisdom, the "resourceful, skillful, handy and wise". He is the first God who is creating a World Order, a civilization, something that later on is copied by Osiris and Dionysos.

Put the Fire (Sun as spirit) Under the  Water to restore the Earth as new Steam (air) Qi Prana Aion energy. So the term "shenqi" as Yuan Qi actually means to put the Fire under the Water from the Golden Tripod of the Delphi and Cybele Phrygian worship of the Great Mother incubation meditation as the Snake Pythia Kundalini energy or Aion - to create Air as Qi or Prana  - the breathing of the Universe as eternal time as Kala or Kali that is reversed (negentropic force).

And so this means the truth of the Pythagrean Tetraktys is that the Perfect Fifth is inverted to change the Fire into the Earth (heart was originally Earth in Daoist alchemical elements due to this alchemical change). So that the Dragon of the heart builds up the qi energy (from the liver qi that is the force of the spirit of the heart) so that a lower tan t'ien alchemical Cauldron turns the hell of the Counter-Earth into the Counter-Fire of the Heavens.

Euripides, Bacchae 285 ff :
"He [Dionysos] was sewn up in Zeus' thigh . . . when Zeus snatched him out of the lighting-flame, and led the child as a god to Olympos, Hera wished to banish him from the sky, but Zeus, as a god, had a counter-contrivance. Having broken a part of the air (aitheros) which surrounds the earth, he gave this [i.e. a phantom baby] to Hera as a pledge protecting the real Dionysos from her hostility. But in time, mortals say that he was nourished in the thigh of Zeus, changing the word [from homeros ‘hostage’ to meros ‘thigh’] because a god he had served as a hostage for the goddess Hera, and composing the story."

And so Dionysos or Dionysus is actually this underworld transformation by the light of Zeus to change the Counter-Earth via the Qi energy of Hestia - into creating a Spirit-Qi body of Yuan Qi and Yuan Shen (this process detailed in the book Taoist Yoga: Alchemy and Immortality) and yet the whole time since Zeus as Spirit has to feed the Air of Hestia - the breathing of the Counter-Earth of Hades to transform Dionysus into a shen-qi double (and also to protect the real body of Dionysus as a human) - so too is alchemy starting with the Sublunar Air around Earth - the Counter-Earth actually just as yin qi, the immature level of the Yuan Qi as the nondual or "not-two" Shen-qi of alchemy - the three in one unity of Shiva and Shakti or Shen under the Moon (water) to turn Earth into Air as the Wind element of Mahayana Buddhism.

In other words Light is eternal, as Aristotle points out, since without light, then time does not exist and yet with light you can turn time around to zero which then accesses reverse time energy of Hestia! This creates a new "one" as a physical transformation of matter via the physical transformation of spacetime of Hestia (as the Emptiness breathing) which bends the light - since all matter is actually made of light bent around due to relativistic mass.

After his descent to Hades' underworld to retrieve his lost love Eurydice, Orpheus became a priest of Dionysus, suffering the same death as the god.

Hi Eduard: I discovered a website that had the same math error but he did not want to his admit his mistake. So thank you for having both the humility and courage to admit that the real Pythagorean Comma is from the Perfect Fifth as subharmonic and overtone harmonic at the same time! I go into the Orphic alchemical details in my latest blog post that exposes how Alain Danielou's book misled Thomas Váczy Hightower. 

Musical Irrational Magnitude Error of Alain Danielou and Aurobindo: Thomas Váczy Hightower admits to 20 years of wrong information on his Musical Octave Pythagorean website

http://ecoechoinvasives.blogspot.com/2018/03/musical-irrational-magnitude-error-of.html

Thanks again!

drew

isdisasystemMarch 7, 2018 at 12:06 PM

Wonder if that's what struck Brian Jones instinctively when he went out of his way in the late 60's to go record the pan pipes of Jajouqua in Morocco ?

VoidisyinyangMarch 7, 2018 at 3:15 PM
Thanks for sharing! Yes as you bring back my memories of visiting the most traditional Berber village in Morocco and experiencing a trance music wedding procession. haha. The culture does not allow unmarried females and males to talk to each other so - also one of the authors I cite - Wim - von - he did an intensive anthropological experiential training in shamanic ecstatic trance music in a Berber village in Tunisia. And we know the Sufis of Morocco do 40 day fasts just like Jesus and Mohammed - and did Pythagoras do a 40 day fast like Chunyi Lin? There's something about 40 – The 40 days of Pythagoras, Greek .


..https://theijtema.com/2013/03/30/40-days-of-pythagoras/

Mar 30, 2013 - So you will have to go on a 40-day fast, continuously breathing in a certain manner, with a certain awareness on certain points.” (Note that he had the knowledge but not the experience – Blog author). There was no other way, so Pythagoras had to pass through this training. After 40 days of fasting and .."

Indeed. Actually that black smith story was a 27 day fast in a cave worshipping Zeus and Zeus is tied to what instrument? 


"Pan Flute - Ancient History Encyclopedia
https://www.ancient.eu/Panpipes/

Jun 17, 2012 - The pan flute or panpipes (syrinx) was a musical wind instrument first used by the ancient Greeks. Most commonly played by shepherds, ... Fleeing his attentions, Syrinx pleaded with Zeus to save her and just when Pan captured her, Zeus turned the Nymph into reeds. Enraged, Pan smashed the reeds into .."


Bingo.
So the Cosmic Mother is from trying to unify the 360 Solar calendar with the Moon - with the extra 5 days to align with the lunar calendar meaning alchemically that only when the Moon energy is filled up first then the Cosmic Mother is returned to (Nirvikalpa Samadhi).

(365.2425 (solar) + 354.3829 (lunar))/2 = 719.6254/2 = 359.8127 days, rounding to 360....Ancient Egyptians used this solar-based calendar for civil purpose and a lunar calendar for religious purposes....He plaid a board game with Khonsu the god of the moon. Khonsu lost and in turn gave some of his moon light to Djehuty. He had enough moon light after Khonsu lost so many times to make 5 extra days. Since these 5 extra days where not a part of the normal year Nut was allowed to be with her husband and give birth.


MDC: nwt
Gardiner: Nut
Budge: Nut, Nu-t
Transliteration: Nut
Coptic: Nout ⲛⲟⲩⲧ?
Hebrew: Nut, Nuth נות
Greek: Nout Νουτ, Nevet Νεβέτ, Neout Νέουτ
Demotic:
Arabic: Not نوت
English: Nut
Kemetic: Nut
Alt: Nuit
Pronounced: Nüt
Meaning: She of the sky