III. THE PRINCIPLE OF VIBRATION. “Nothing rests; everything moves; everything vibrates.”–The Kybalion. This Principle embodies the truth that “everything is in motion”; “everything vibrates”; “nothing is at rest”; facts which Modern Science endorses, and which each new scientific discovery tends to verify. And yet this Hermetic Principle was enunciated thousands of years ago, by the Masters of Ancient Egypt. This Principle explains that the differences between different manifestations of Matter, Energy, Mind, and even Spirit, result largely from varying rates of Vibration. From THE ALL, which is Pure Spirit, down to the grossest form of Matter, all is in vibration–the higher the vibration, the higher the position in the scale. The vibration of Spirit is at such an infinite rate of intensity and rapidity that it is practically at rest–just as a rapidly moving wheel seems to be motionless. And at the other end of the scale, there are gross forms of matter whose vibrations are so low as to seem at rest. Between these poles, there are millions upon millions of varying degrees of vibration. From corpuscle and electron, atom and molecule, to worlds and universes, everything is in vibratory motion. This is also true on the planes of energy and force (which are but varying degrees of vibration); and also on the mental planes (whose states depend upon vibrations); and even on to the spiritual planes. An understanding of this Principle, with the appropriate formulas, enables Hermetic students to control their own mental vibrations as well as those of others. The Masters also apply this Principle to the conquering of Natural phenomena, in various ways. “He who understands the Principle of Vibration, has grasped the sceptre of power,” says one of the old writers. I

I've been looking into this a whole lot more and I wanted to share something that I found quite interesting. If you look at my feeble attempt at a wave pattern below. Imagine the solid line as a guitar string. The red waves above and below it are when it is strummed and this is the frequency at which it is vibrating. Seems low right? I know, believe me I looked for better images but had to settle for my own hastily created image.

Now there was a world renowned physicist named Louis de Broglie who theorized that electrons are in a wave pattern around the nucleus of the atom. The wave could only have a whole number of wavelengths thereby giving it a unique frequency. The more wavelengths the higher the frequency. A smaller amount of wavelengths would create a lower frequency but it is always a whole number of wavelengths around the nucleus.

Imagine the number of wave lengths being a fraction and not a whole number. You would get a skip or disturbance in the frequency and nature always follows the path of least resistance. The wave lengths would always be a whole number. Now imagine many different atoms vibrating at different frequencies and accepting one another or rejecting one another based on their frequencies but always following the path of least resistance.

Louis Victor Pierre Raymond duc de Broglie added to Bohr's model of the atom by reasoning that, since light could act like a particle, an electron could act like a wave. Since the energy E of a photon equals Planck's constant times the frequency f, or E=hf, de Broglie reasoned that the momentum p of an electron would equal Planck's constant divided by the wavelength l, or p=h/l. Using this and the reasoning that only a whole number of wavelengths (see picture) would be possible, de Broglie arrived at the same rule for electron orbits as had Bohr. In other words, a wavelength associated with an electron and derived from its momentum yields a standing-wave pattern identical to Bohr's allowed energy levels. As Einstein put it: "It may look crazy, but it really is sound!"

At a superficial level, scales consist of an ascending or descending sequence of tones where the initial and final tones are separated by an octave, which means the frequency of the final tone is twice that of the initial tone (the fundamental).

The probability that a random series of notes will produce a star-convex pattern is very small. Honingh and Bod try to explain this phenomenon by using the notion of consonance (harmony of sounds).

"GEOMETRY IS FROZEN MUSIC" Johann Wolfgang von Goethe

Geometric forms are considered to be the crystallizatons of the creative thoughts of God, and the human hand, in manipulating and constructing these forms, will learn to position itself (Sacred Geometry, 1982).

Music is to time what geometry is to space. Natural sound and music are a reflection of the Divine order. Just like we are often unconsciously affected by goodness or beauty, so we are also unconsciously moved by the interior nature of sound and its harmony. Just as you may not notice a film's soundtrack, yet it would lack intensity, context and richness without one.

The golden ratio is the mathematical proportion 1:1.618034...ad infinitum. Often called by its Greek name phi, it is also known as the Divine Proportion, the Golden Ratio, the Golden Section and the Golden Mean. It is indelibly inscribed in the heart of nature and man. Trace the thread of this "golden mean" from daisy to pyramid, from pine cone to Parthenon. Or from seashell to spiral nebulae as described above. The cosmos weaves its garments with perfect integrity, laced by the golden ratio. It is so omnipresent that many philosophers, artists, mathematicians, and scientists have considered it an essential component of beauty, perhaps integral to life itself. Plato considered it the key to the physics of cosmos.

Now we come to one of nature's greatest mysteries, the creation of matter by sound. "And God SAID, let there be light." "In the beginning was the WORD, ... and the Word was God."

In the ancient Hindu Vedas: "In the beginning was Brahman with whom was the Word. And the Word was Brahman."

It is the mantra, the creation vibration. It is the ancient sound by which we live; it has always been there. The Om symbol is a sacred syllable representing Brahman, the impersonal Absolute - omnipotent, omnipresent, and the source of all manifest existence. Brahman, in itself, is incomprehensible; so a symbol becomes mandatory to help us realize the Unknowable. Om, therefore, represents both the unmanifest (nirguna) and manifest (saguna) aspects of God. That is why it is called Pranava, to mean that it pervades life and runs through our prana or breath. Aum is said to be the essence of all mantras, the highest of all matras or divine word (shabda), brahman (ultimate reality) itself. Aum is said to be the essence of the Vedas. By sound and form, AUM symbolizes the infinite Brahman (ultimate reality) and the entire universe.

Dr. Aline Honingh and Prof. Rens Bod from the ILLC did this for nearly 1,000 scales from all over the world, from Japan to Indonesia and from China to Greece. To their surprise, they discovered that all traditional scales produced star-convex patterns.

OM - The divine sound - Vibration of the universe - this upload demonstrates proper chanting of this Holy sound OM

The universe therefore consists of glorious trembling tones, of a wonderful vibration. Pythagoras called it the music of the spheres.

Proof that, for any five lattice points in convex position, another lattice point is on or inside the inner pentagon of the five-point star they form.

Geometric forms are considered to be the crystallizatons of the creative thoughts of God, and the human hand, in manipulating and constructing these forms, will learn to position itself (Sacred Geometry, 1982).

"GEOMETRY IS FROZEN MUSIC" Johann Wolfgang von Goethe

So it would seem we reach that point where the real mystery of the pentagram is sound conjuring up a pattern, of sound or as you say crystallized. The Pentagram surrounded by a circle believed to be able to conjure up the devil or demons. The devil actually being what you could or might create with the sound that sustains and defines the pattern a infinite number of possibilities, of worlds within worlds within worlds. How odd isn’t it that our pentagon is the center of a war department violently shaping the world! The coincidences are so striking that the odds of them not being inter-ralated are miniscule to none. So we identify a key construct to the ordering of the universe.

In this paper the property of (star-) convexity is used to describe and explain the goodness of musical items. We noted that several musical items are (star-) convex but that this process is not reversible: convex sets do not per se make good chords/scales/etc. Convexity is used to describe "underlying" features in music but no "surface" features such as rhythm and melody. This suggests that (star-) convexity may serve as a condition for the "goodness" or musical items. With this, we could hypothesize that people listening to a piece of music strive to perceive convex structures.

HARMONY is a state recognized by great philosophers as the immediate prerequisite of beauty. A compound is termed beautiful only when its parts are in harmonious combination. The world is called beautiful and its Creator is designated the Good because good perforce must act in conformity with its own nature; and good acting according to its own nature is harmony, because the good which it accomplishes is harmonious with the good which it is. Beauty, therefore, is harmony manifesting its own intrinsic nature in the world of form. (The Pythagorean Theory of Music and Color)

How odd isn’t it that our pentagon is the center of a war department violently shaping the world! The coincidences are so striking that the odds of them not being inter-ralated are miniscule to none. So we identify a key construct to the ordering of the universe.

It is not generally known, but the standard Western system of musical pitch (i.e. note frequency), in part, approximates to the same frequency pattern as our solar system (i.e. as taught by Theosophy). This should come as no surprise since the universe can be thought of as an enormous cluster of interwoven vibrating (or oscillating) energy waves. Indeed, it could be said that the vibrations that compose our universe (and everything in it) represent the reverberating sound of the Voice of God.

the frequencies of the natural notes of our musical system (i.e. as represented by the white keys of a piano keyboard) can be re-calculated so that they fit neatly into a framework that is based on multiples of the number 49. And this can be done without varying the notes significantly from their original values in the standard system.

Hans Kayser was a German art and music theorist and founder of modern harmonic research in the 20th century.

The acoustic-musical laws in a more comprehensive, more universal overall context, focusing on a possible relationship of these laws to the planets and spheres to make, was a beginning with Pythagoras of Samos in ancient and medieval popular exercise (see harmony of the spheres ), which in modern times, although lost its appeal but did not disappear entirely.

Since 1920, Kayser was working on the reformulation of the Pythagorean thought and tried the findings of Johannes Kepler (Harmonic mundi) and Albert Thimus of a harmonic order of the world on the basis of metaphysical speculation to revive.