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What did the shapes mean to Pythagoras, and what influence did his interpretations have on later esoteric philosophy? I am more curious about the 2D shapes rather than the platonic solids, but I do not know if their is a way to address this question with out talking about both.

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The School of Pythagoras reduced everything to number, color and sound (or generally speaking...vibration) which came from the schools of ancient Egypt.  The numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 (and also significant 11, 12, etc) all had fundamental meanings that are correlated to the related 2D shapes *and thus 3D).  This is not talking about numerology but instead fundamental vibratory correspondence.   There are many sites which give good descriptions and philosophically why they were significant to Pythagoras. (i.e. http://jwilson.coe.uga.edu/EMAT6680Fa06/Hobgood/Pythagoras.html)  -Leo

Thanks Leo!

To expand on this, a word must be said on Geometry. The 2D shapes you are speaking of can be found as a basis for the creation of 3D objects (the square transforms into the cube), in particular what we call the "Platonic Solids". These objects are Sacred. If you study the object known as "the Flower of Life" you will begin to understand Pythagoras. The Flower of Life is nothing more than dots and circles, yet by drawing lines and connecting the dots, symmetry and geometry begin to appear.

As Leo had stated, all things can be broken down to the simplest expression that we call vibration. Vibration gives rise to form and form is governed by Geometry. To make it simple, a bowl of still water has a perfectly reflective surface. If you drop a single droplet of water into that bowl the surface will dramatically change. The energy of the drop enters the still water and disturbs it - vibration - and causes the water to assume the form of that vibration - a wave - until the energy is absorbed into the water and becomes still once again. The wave generated from the drop is originated from that point and diffused outward in a perfect circle. If you were to measure the individual peaks and valleys within the wave you would physically see the resonant frequency of that wave and it's magnitude. This happens with every exchange of energy in the universe from atoms to galaxies.

The importance of the Platonic solids has to do with a concept we call harmonic resonance or fractals. If you had a tuning fork and produced a sound with the same frequency as the tuning fork, the fork would vibrate as soon as those specific sound waves reached it. Going further, if you had a crystal glass that resonated on the same harmonic as that fork (example: fork 100 Hz  and glass 10000Hz) the glass would vibrate with the fork.

This is paramount to understand. When we speak of the Schumann frequencies, which are the resonant frequencies of the planet in the upper atmosphere, we are also speaking of brain waves because they share the same "shape". Musical instruments, particularly pianos are keyed to specific frequencies and we give them names - A sharp, B flat etc) Pythagoras described the specific frequency "shape" for very special frequencies. We call these frequencies the Solfeggio. These frequencies resonate in harmony on the atomic scale all the way up into the cosmos, both above and below the extremes of our electromagnetic spectrum. Consider our entire spectrum like a single C key on the Cosmic piano. By vibrating one of these solfeggio frequencies the resonance causes vibration on the atomic scale all the way up the influencing planetary harmonics. Very powerful tones. Their usage and functions are not common knowledge, but the shapes we see everywhere.

Thanks Michael. This is the first time I have heard of the Solfeggio frequencies. Sounds interesting. I remember seeing a demonstration of the effect that various frequencies had on sand. The sand was sitting unconstrained on what looked like a thin piece of rubber stretched over a speaker box of some sort. In the video it appeared that the frequencies were making the sand form into patterns. The higher the frequency used, the more complicated the pattern that the sand would make. It would be interesting to see what type of patterns the Solfeggio frequencies would create. Also, you have any specific thoughts on the Metatron's Cube?

Metatron's Cube is THE template for the solfege as well as the Platonic solids. Also to incorporate into this is the Law of 9. Combine this knowledge with the Fibonacci sequence and Phi and the famous 3 4 5 triangle. The numbers 432 and 144 are very powerful.

I'm not familiar with the Law of 9. Do you know where I could find out more about it? I'm guessing that 432 and 144 are powerful because they add up to 9? 

Brad you are talking about cymatics. Metatron's Cube can be held in suspension using cymatics and the ancient solfege or Pythagorean intervals if played as a whole scale chord. Otherwise each note will resonate to the corresponding geometry found in metatron's cube.

That really makes me want to try it. :)

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