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Pythagorean cube – seven

cube seven points
cube seven points
cube seven points

Pythagorean teaching – From this comes the great occult axiom: “The center is the father of the directions, the dimensions, and the distances.”

This cube represents six points with man in the middle.

Seven Planetary Spheres

Ancient Greeks taught that souls come to the earth from, and return to the Milky Way via seven planetary spheres – those being Saturn, Jupiter, Mars the Sun, Venus, Mercury and the Moon. In the image above we see the stars and signs of the zodiac at the top, Saturn through Mercury down the back of the chair, the Moon in the sky and Earth in his hands.

The logic of this order doesn’t appear to make sense until you look at an image which shows the spheres mapped onto the seven points (including the center) of a hexagram. Note how the sun (symbolized by a point in a circle) is at the center of this diagram and how the planets are divided with the outer ones being ‘above’ the sun.

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Pythagorean Mathematics

Pythagoras… “The Pythagoreans indeed go farther than this, and honour even numbers and geometrical diagrams with the names and titles of the gods. Thus they call the equilateral triangle head-born Minerva and Tritogenia, because it may be equally divided by three perpendiculars drawn from each of the angles. So the unit they term Apollo, as to the number two they have affixed the name of strife and audaciousness, and to that of three, justice. For, as doing an injury is an extreme on the one side, and suffering one is an extreme on the on the one side, and suffering in the middle between them.

… Among many ancient nations the heptad is a sacred number. The Elohim of the Jews were supposedly seven in number. They were the Spirits of the Dawn, more commonly known as the Archangels controlling the planets. The seven Archangels, with the three spirits controlling the sun in its threefold aspect, constitute the 10, the sacred Pythagorean decad. The mysterious Pythagorean tetractys, or four rows of dots, increasing from 1 to 4, was symbolic of the stages of creation. The great Pythagorean truth that all things in Nature are regenerated through the decad, or 10, is subtly preserved in Freemasonry through these grips being effected by the uniting of 10 fingers, five on the hand of each person.

… The triad–3–is the first number actually odd (monad not always being considered a number). It is the first equilibrium of unities; therefore, Pythagoras said that Apollo gave oracles from a tripod, and advised offer of libation three times. The keywords to the qualities of the triad are friendship, peace, justice, prudence, piety, temperance, and virtue. The following deities partake of the principles of the triad: Saturn (ruler of time), Latona, Cornucopiæ, Ophion (the great serpent), Thetis, Hecate, Polyhymnia (a Muse), Pluto, Triton, President of the Sea, Tritogenia, Achelous, and the Faces, Furies, and Graces. This number is called wisdom, because men organize the present, foresee the future, and benefit by the experiences of the fast. It is cause of wisdom and understanding. The triad is the number of knowledge–music, geometry, and astronomy, and the science of the celestials and terrestrials. Pythagoras taught that the cube of this number had the power of the lunar circle.

 

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Tetraktys

Tetraktys

Tetraktys (Tetractys) of the Decad, The Monadic Values: There is no doubt that Sethian Gnostics applied the principles of this paradigm. ”Pythagorus  considered all things relative to numbers… How he conceived this process has never been satisfactorily explained.” (Bullfinch, pg. 289.) Perhaps this is the secret….

Pythagorus considered the monad as the source of all things. In the case of the tetraktys of the decad, the concepts of form and structure are related in mathematical values. These values work in harmony. They are not just a list, they are a set. The first and most obvious is numerical value is the digital sequence of one through ten. ‘Monad,’ 2. Decad, 3. Triad, 4. Tetrad, 5. Pentad, 6. Hexad, 7. Heptad, 8. Ogdoad, 9. Ennead, and 10. Decad.

 

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Pythagoras: Music and Space

Pythagoras

Pythagoras (6th century BC) observed that when the blacksmith struck his anvil, different notes were produced according to the weight of the hammer.

Number (in this case amount of weight) seemed to govern musical tone…

Cutting a sting in half creates the octave.

Image

He also discovered that if the length of the two strings are in relation to each other 2:3, the difference in pitch is called a fifth:

…and if the length of the strings are in relation to each other 3:4, then the difference is called a fourth.

Thus the musical notation of the Greeks, which we have inherited can be expressed mathematically as 1:2:3:4

All this above can be summarized in the following.

(Another consonance which the Greeks recognized was the octave plus a fifth, where 9:18 = 1:2, an octave, and 18:27 = 2:3, a fifth;)

This triangular figure of numbers in the shape of the Greek letter Lamda is the Tetrad of the Pythagorians. As was discussed by Plato in his dissertation on the Composition of the Soul; it is a set of numbers whose relationships with each other seemed to summarize all the inter-dependent harmonies within the universe of space and time.

Thus to have established the relationship between music and space/number fired the imagination of the Pythagorians and was taken up especially by the School of Plato and the subsequent Neo-Platonists. Pythagoras himself wrote nothing which has survived, and so it is the Platonists we have to thank for recording and developing what had hitherto been passed down through two hundred and fifty years of oral tradition.

Pythagoras taught that each of the seven planets produced by its orbit a particular note according to its distance from the still centre which was the Earth. The distance in each case was like the subdivisions of the string refered to above. This is what was called Musica Mundana, which is usually translated as Music of the Spheres. The sound produced is so exquisite and rarified that our ordinary ears are unable to hear it. It is the Cosmic Music which, according to Philo of Alexandria, Moses had heard when he recieved the Tablets on Mount Sinai, and which St Augustine believed men hear on the point of death, revealing to them the highest reality of the Cosmos. (Carlo Bertelli, Piero della Francesca, p. 60.)

This music is present everywhere and governs all temporal cycles, such as the seasons, biological cycles, and all the rhythms of nature. Together with its underlying mathematical laws of proportion it is the sound of the harmony of the created being of the universe, the harmony of what Plato called the “one visible living being, containing within itself all living beings of the same natural order”.

For the Pythagorians different musical modes have different effects on the person who hears them; Pythagoras once cured a youth of his drunkenness by prescribing a melody in the Hypophrygian mode in spondaic rhythm. Apparently the Phrygian mode would have had the opposite effect and would have overexcited him. At the healing centers of Asclepieion at Pergamum and Epidauros in Greece, patients underwent therapy accompanied by music.

The Roman statesman, philosopher and mathematician, Boethius (480-524 A.D.) explained that the soul and the body are subject to the same laws of proportion that govern music and the cosmos itself. We are happiest when we conform to these laws because “we love similarity, but hate and resent dissimilarity”. (De Institutione Musica, 1,1. from Umberto Eco, Art and Beauty in the Middle Ages. p. 31).