Pythagoras and the math of everything

Back in the Days, the measures of everything was One. In Antiquity, the four cardinal sciences or the Quadtivium-- Astronomy, Aritmethics, Geometry and Music, together with the Trivium-- Grammar, Logic, and Rhetoric, made up "the Seven Liberal Arts". Seeing everything as a whole, human body proportions was put in relation with the dynamics of sound and the dimentions of the Earth and the system of measurements in geometry and arithmetic.


This drawing shows a Monochord, a central instrument in Pythagorean music theory (the three top notes are placed incorrectly)

The ‘chamber tone’ in music for instance was (until Nazi-Germany standardised it to be A=440Hz) calculated to be A=432Hz based on Pythagoras’ calculations and tuning system. This tone is in perfect harmony with the Schumann resonance of 7.83Hz (“the hum of the Earth”). However, some dedicated the 432Hz frequency with C instead of A, but that’s mere semantics.


This table shows the ratios of Pythagorean music theory

In modern “tone-dynamics”, the distance between the (chromatic) notes of the (12-tone) do-re-mi scale is given by multiplying the given frequency by the twelfth root of 2. Thus an A# is defined as: 432Hz x 2^(1/12) ≈ 457.688. However, Pythagoras used a system of “perfect fifths” (quints) at a ratio of 2/3, which match the modern system, but only fairly: “the Pythagorean system would appear to be ideal because of the purity of the fifths, (but) other intervals, particularly the major third, are so badly out of tune that major chords [may be considered] a dissonance." [Benward & Saker (2003), Gunther, Leon (2011)].


This table shows the modern root ratios

As an example of how astronomy and music is linked in Pythagorean music theory, look at the ratios below, using some core numbers of classical astronomy (some might recognise some of these numbers from the Apocalypse of John and the Bible, which is not odd, these numbers reflect the science of those days):

144,000 : 333.3333 = 432 (classical chamber tone)
144,000 : 444.4444 = 324 (a quart below the chamber tone)
144,000 : 500 = 288 (a quint below chamber tone)
216,000 : 666.6666 = 324
252,000 : 777.7777 = 324
216,000 : 500 = 432

These are only a few examples, I could go on to show the whole scale and put the different frequencies in relation with conceptual core-figures of classical astronomy and geometry, but I'll let these few figures above speak for themselves.

I find this stuff extremely amazing and gives my every-day life a touch of the cosmos and the divine. The beauty of this is almost too perfect. No wonder they were more religious back then

reply to post by Utnapisjtim


Thank you, Pythagoras was one of the great minds that the human race has produced.

reply to post by Aleister


Indeed he was. Mostly known by the geometric theorem carrying his name, but he was far more than that. Below is a link to a great book I have on the subject:

Amazon link to "The Pythagorean Sourcebook" (ISBN 0-933999-51-8)

reply to post by Utnapisjtim

I find this stuff extremely amazing and gives my every-day life a touch of the cosmos and the divine. The beauty of this is almost too perfect. No wonder they were more religious back then

Oh me too, and what a beautifully illustrated, well understood thread.

It is my opinion that he was very "in tune" with the One and not so religious.

His mind went deep into the cosmos and for that reason he understood the meanings of not just music, but life.

MamaJ
reply to post by Utnapisjtim

 

I find this stuff extremely amazing and gives my every-day life a touch of the cosmos and the divine. The beauty of this is almost too perfect. No wonder they were more religious back then

Oh me too, and what a beautifully illustrated, well understood thread.

Thank you, I try to do my best

It is my opinion that he was very "in tune" with the One and not so religious.

Back then there were no real boundries between science and religion. Science was the Zion of Religion (pun intended).

His mind went deep into the cosmos and for that reason he understood the meanings of not just music, but life.

Indeed. They saw everything as One, "As above, so below" was the mantra.

Utnapisjtim

As an example of how astronomy and music is linked in Pythagorean music theory, look at the ratios below, using some core numbers of classical astronomy (some might recognise some of these numbers from the Apocalypse of John and the Bible, which is not odd, these numbers reflect the science of those days):

144,000 : 333.3333 = 432 (classical chamber tone)
144,000 : 444.4444 = 324 (a quart below the chamber tone)
144,000 : 500 = 288 (a quint below chamber tone)
216,000 : 666.6666 = 324
252,000 : 777.7777 = 324
216,000 : 500 = 432

These are only a few examples, I could go on to show the whole scale and put the different frequencies in relation with conceptual core-figures of classical astronomy and geometry, but I'll let these few figures above speak for themselves.

I find this stuff extremely amazing and gives my every-day life a touch of the cosmos and the divine. The beauty of this is almost too perfect. No wonder they were more religious back then

edit on 12-1-2014 by Utnapisjtim because: Typo: a missing A, how ironic

S&F Utnap -

Very informative threads you create, which I enjoy much, so I thank you
for dispensing your knowledge

The biblical number 144,000 seems to play into Pythogorean 3-4-5 method,
possibly a derivative of the Fibornacci sequence (the golden spiral) which
of course are calculated within the great pyramid of Giza.

Your statement where I have highlited, I would enjoy seeing that
completed works if ever you have the time to complete that task!?!

Again...enjoying your threads - be well

HumAnnunaki
S&F Utnap -

Very informative threads you create, which I enjoy much, so I thank you
for dispensing your knowledge

Thank you, I'm flattered. Honestly

The biblical number 144,000 seems to play into Pythogorean 3-4-5 method,
possibly a derivative of the Fibornacci sequence (the golden spiral) which
of course are calculated within the great pyramid of Giza.

I have found a direct relationship between Pi and Phi. The golden ratio of the radius of a circle equals 1/10th of it's circumference. Ten horns of the Dragon anyone?

Your statement where I have highlited, I would enjoy seeing that
completed works if ever you have the time to complete that task!?!

Again...enjoying your threads - be well

Thanks again. Maybe I'll provide more numbers later in the thread. I'll keep it in mind.

Utnapisjtim

I have found a direct relationship between Pi and Phi. The golden ratio of the radius of a circle equals 1/10th of it's circumference. Ten horns of the Dragon anyone?

Maybe I'll provide more numbers later in the thread.

Yes, I agree with your Pi/Earth circumference theory

The great pyramid of Giza is a Pi monument showing the earth's dimensions
also correlated in the bible defined by Pythagorean principle.

Interesting to note is that -

Pi multiplied by itself [or squared] (2)+1= the same to the 13th place,
which consequently is the ONLY number doing so!

Thirteen (13) is the half-way mark number in earth's (our solar system) 25,920 year preccession,
which some say is calculated by Giza's link to Orion.
Be well.

reply to post by Utnapisjtim


A couple of vids if I may. The first is a 1959 Walt Disney summary of P's career, with attention on the pentagram. Until the last couple of hundred years or so (I really don't know how long, pulling that out of my magick Christmas hat) the pentagram was not considered evil, but a beautiful mathematical symbol and discovery. Walt Disney knew this, and knew his stuff, and honors it while at the same time he educated the American nation of the late 1950s here:




The second I haven't watched, but it feels good. It's a long one, and I'll watch it later myself. Found it on another thread on P (I can't spell his name if you paid me), and at some point maybe we can put up a post on this thread to the few other good threads on The Great Man's (as good as spelling it) work:



The Wikipedia page to the first video, a portion of the movie/television program "Donald in Mathmagic Land":

en.wikipedia.org...

reply to post by Aleister


Loved the Donald video! Go Disney! It sums up some of the beauty and simplicity of nature's math principles. The golden section/ratio/number/spiral/rectangle &c is found all over the Cosmos, or as Pythagoras possibly would have said it (in Hermetical echo): As above, thus below…

Thanks for posting. I'll look through the other video when I have some more time later tonight.

Thought I'd give you a heads-up on the Shumann resonance.

In the normal mode descriptions of Schumann resonances, the fundamental mode is a standing wave in the Earth–ionosphere cavity with a wavelength equal to the circumference of the Earth. This lowest-frequency (and highest-intensity) mode of the Schumann resonance occurs at a frequency of approximately 7.83 Hz, but this frequency can vary slightly from a variety of factors...

Source: en.wikipedia.org...

Never actually done the math myself, but I have a predisposition that the Schumann resonance is the base of the Pythagorean music scale. If I could make a program that would batch calculation (modulation) down from A = 432 Hz following the do-re-mi system to find out if my suspicion is justified and what note 7.83 Hz would be had we been able to hear it. If that rings true, this could be another clue as to whether the ancient Greeks knew the circumference of Earth, since the Shumann resonance has a wavelength equal to the length of the equatorial parallel.

They say birds adjust their singing to be in harmony with the Schumann resonance. Not sure I buy in on that, but it's plausible I suppose.

Edit: Ah, Bollocks! I just did the whole math crunching frequencies for the notes down octaves from 432 Hz using both Pythagorean and modern tuning, and then the connection was lost and I had to reset the router.

Anyway, in short: The results showed that the Schumann resonance lies somewhere between a second and a third above above the fifth octave below 432 Hz in both cases, thus no direct interrelation from my lay-man's point of view. There may however be certain dynamics involved that I am unaware of, and my math may be completely wrong, but atleast, nothing much to see.

The Pythagorean tetractys (what mathematicians would call the "fourth triangular number") has been shown to be the "Rosetta stone" that deciphers fundamental information about the universe embodied in the sacred geometries of religions. To study this pioneering discovery, visit www.smphillips.8m.com. You will encounter for the first time the sublime, mathematical nature of the Pythagorean cosmos (in fact ALL levels of reality!).

micpsi
The Pythagorean tetractys (what mathematicians would call the "fourth triangular number") has been shown to be the "Rosetta stone" that deciphers fundamental information about the universe embodied in the sacred geometries of religions. To study this pioneering discovery, visit www.smphillips.8m.com. You will encounter for the first time the sublime, mathematical nature of the Pythagorean cosmos (in fact ALL levels of reality!).

Or you can add the info to this thread (or make your own) about the tetractys.

Here is the Wikipedia page on tetractys, and the first section after the intro is about Pythagoras and I suppose people who worshipped his discoveries. If people worshipped my discoveries they could bake me bread, and I could pick which one of them had to be silent for three years:

en.wikipedia.org...

A prayer of the Pythagoreans shows the importance of the Tetractys (sometimes called the "Mystic Tetrad"), as the prayer was addressed to it.

"Bless us, divine number, thou who generated gods and men! O holy, holy Tetractys, thou that containest the root and source of the eternally flowing creation! For the divine number begins with the profound, pure unity until it comes to the holy four; then it begets the mother of all, the all-comprising, all-bounding, the first-born, the never-swerving, the never-tiring holy ten, the keyholder of all".

As a portion of the secret religion, initiates were required to swear a secret oath by the Tetractys. They then served as novices for a period of silence lasting three years.

micpsi
The Pythagorean tetractys (what mathematicians would call the "fourth triangular number") has been shown to be the "Rosetta stone" that deciphers fundamental information about the universe embodied in the sacred geometries of religions. To study this pioneering discovery, visit www.smphillips.8m.com. You will encounter for the first time the sublime, mathematical nature of the Pythagorean cosmos (in fact ALL levels of reality!).

Not directly related, but still it is, did some anatomic measurements of myself and deviced a personal cubit-metre of the virtual kind and measured my arm's length to be aproximately 3/2 of my cubit. What I found out was truely amazing. Think that you hold this cubit at arm's length and hold it straight in front of you.

Made a sketch in Illustrator based on the two measures:


Now if my calculations are correct, the ends of the cubit metre on arm's length equal 2/3rds the distance between you and the object you want to measure. So if you know the distance to somewhere, you can calculate approximate dimentions given all measures are given in your cubit.

Went a little further and calculated the angle of the two dotted lines in the picture, and plotting in values for adjecent and oposite and got just below 36,9°, slighly more than the babylonian standard of 36 degrees or 1/10th of the circle on arm's length, then again, perhaps I am supposed to stretch my arm to the side? I'll check it out later.

reply to post by Utnapisjtim


Tried another aproach to check if the Schumann resonance of 7.83 Hz relates to the Pythagorean tuning. By simply double up from 7.83 and see if something happens.

Octaves:
7.83 x 2 = 15.66
15.66 x 2 = 31.32
31.32 x 2 = 62.64
62.64 x 2 = 125.28
125.28 x 2 = 250.56
250.56 x 2 = 501.12

Perfect fifths:
7.83 x 1.5 = 11.745
15.66 x 1.5 = 23.49
31.32 x 1.5 = 46.98
62.64 x 1.5 = 93.96
125.28 x 1.5 = 187.92
250.56 x 1.5 = 375.18
501.12 x 1.5 = 751.68

Anyone seeing something of significance here? These are all frequencies in Hz supposed to be in perfect harmony with the Schumann resonance. This was a complete waste of time it seems.

From my own works of study, these are my private findings.
(always in search of higher education)

Enjoy!


Math constitutes Geometry with the two combined to read astronomy.
Interesting is that [2.1] is the measurement for astronomical units,
(correction may need citing)



Be well all

micpsi
The Pythagorean tetractys (what mathematicians would call the "fourth triangular number") has been shown to be the "Rosetta stone" that deciphers fundamental information about the universe embodied in the sacred geometries of religions. To study this pioneering discovery, visit www.smphillips.8m.com. You will encounter for the first time the sublime, mathematical nature of the Pythagorean cosmos (in fact ALL levels of reality!).

The Tetraktys is important in Pythagorean music theory, in that it includes the three main symphonic ratios in the Pythagorean music scale: Octaves: 1/2, Perfect fifths: 2/3 and Perfect fouths: 3/4 -- From the top down see two and two rows as fractions.

HumAnnunaki

Interesting is that [2.1] is the measurement for astronomical units

The 1:2 triangle imposed in the gallery is the base of constructing the golden ratio, and defining the golden number phi:



Below you can see how you divide the baseline of a 1:2 right triangle according to the golden ratio :



The hypothenus measures √5 as given by the Pythagoras theorem

Pythagoras

Quotations by Pythagoras


Number rules the universe.
-Quoted in D MacHale, Comic Sections (Dublin 1993)

Number is the ruler of forms and ideas, and the cause of gods and demons.
-Iamblichus, c. 245 – c. 325

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