Tetractys

The tetractys (greek τετρακτύς), or tetrad,^[1] is a triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row, which is the geometrical representation of the fourth triangular number. As a mystical symbol, it was very important to the secret worship of the Pythagoreans.

Pythagorean symbol

The Tetractys symbolized the four elements — earth, air, fire, and water.
The first four numbers also symbolized the harmony of the spheres and the Cosmos.^{[citation needed]}
The four rows added up to ten, which was unity of a higher order (in decimal).
The Tetractys represented the organization of space:
1. the first row represented zero-dimensions (a point)
2. the second row represented one-dimension (a line of two points)
3. the third row represented two-dimensions (a plane defined by a triangle of three points)
4. the fourth row represented three-dimensions (a tetrahedron defined by four points)

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".^[2]

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.^{[citation needed]}

The Pythagorean oath also mentioned the Tetractys:

"By that pure, holy, four lettered name on high,

nature's eternal fountain and supply,

the parent of all souls that living be,

by him, with faith find oath, I swear to thee."

The Pythagorean Sourcebook claimed that there were 2 quaternaries of numbers, one which is made by addition, the other by multiplication, and these quaternaries encompass the musical, geometric and arithmetic ratios of which the harmony of the universe is composed. The first quaternary is 1,2,3,4. There are 11 total quaternaries. And the perfect world which results from these quaternaries is geometrically, harmonically and arithmetically arranged.

It is said^{[citation needed]} that the Pythagorean musical system was based on the Tetractys as the rows can be read as the ratios of 4:3 (perfect fourth), 3:2 (perfect fifth), 2:1 (octave), forming the basic intervals of the Pythagorean scales. That is, Pythagorean scales are generated from combining pure fourths (in a 4:3 relation), pure fifths (in a 3:2 relation), and the simple ratios of the unison 1:1 and the octave 2:1. Note that the diapason, 2:1 (octave), and the diapason plus diapente, 3:1 (compound fifth or perfect twelfth), are consonant intervals according to the tetractys of the decad, but that the diapason plus diatessaron, 8:3 (compound fourth or perfect eleventh), is not.

Quote:

"The Tetractys [also known as the decad] is an equilateral triangle formed from the sequence of the first ten numbers aligned in four rows. It is both a mathematical idea and a metaphysical symbol that embraces within itself—in seedlike form—the principles of the natural world, the harmony of the cosmos, the ascent to the divine, and the mysteries of the divine realm. So revered was this ancient symbol that it inspired ancient philosophers to swear by the name of the one who brought this gift to humanity — Pythagoras."

Kabbalist symbol

Symbol by early 17th-century Christian mystic Jakob Böhme, including a tetractys of flaming Hebrew letters of the Tetragrammaton.

A tetractys of the letters of the Tetragrammaton adds up to 72 by gematria.

There are some who believe that the tetractys and its mysteries influenced the early kabbalists. A Hebrew Tetractys in a similar way has the letters of the Tetragrammaton (the four lettered name of God in Hebrew scripture) inscribed on the ten positions of the tetractys, from right to left. It has been argued that the Kabbalistic Tree of Life, with its ten spheres of emanation, is in some way connected to the tetractys, but its form is not that of a triangle.^{[citation needed]}

Tarot card reading arrangement

In a Tarot reading, the various positions of the tetractys provide a representation for forecasting future events by signifying according to various occult disciplines, such as Alchemy. [1] Below is only a single variation for interpretation.

The first row of a single position represents the Premise of the reading, forming a foundation for understanding all the other cards.

The second row of two positions represents the cosmos and the individual and their relationship.

The Light Card to the right represents the influence of the cosmos leading the individual to an action.
The Dark Card to the left represents the reaction of the cosmos to the actions of the individual.

The third row of three positions represents three kinds of decisions an individual must make.

The Creator Card is rightmost, representing new decisions and directions that may be made.
The Sustainer Card is in the middle, representing decisions to keep balance, and things that should not change.
The Destroyer Card is leftmost, representing old decisions and directions that should not be continued.

The fourth row of four positions represents the four Greek elements.

The Fire card is rightmost, representing dynamic creative force, ambitions, and personal will.
The Air card is to the right middle, representing the mind, thoughts, and strategies toward goals.
The Water card is to the left middle, representing the emotions, feelings, and whims.
The Earth card is leftmost, representing physical realities of day to day living.

Occurrence

Roman Catholic archbishop's coat of arms

The tetractys occurs (generally coincidentally) in the following:

the baryon decuplet
an archbishop's coat of arms
the arrangement of pins in ten-pin bowling
a chinese checkers board

References

^ The Theosophical Glossary, p. 302
^ Danzig, Thomas ([1930], 2005) Number. The Language of Science. p.42