Tetractys
The []tetractys, or tetrad, or the tetractys of the decad 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 Pythagoreanism. There were four seasons, and the number was also associated with planetary motions and music.
Pythagorean symbol
- The first four numbers symbolize the musica universalis and the Cosmos as:
- # Monad – Unity
- # Dyad – Power – Limit/Unlimited
- # Triad – Harmony
- # Tetrad – Kosmos
- The four rows add up to ten, which was unity of a higher order.
- The Tetractys symbolizes the four classical elements—air, fire, water, and earth.
- The Tetractys represented the organization of space:
- # the first row represented zero dimensions
- # the second row represented one dimension
- # the third row represented two dimensions
- # the fourth row represented three dimensions
The Pythagorean oath also mentioned the Tetractys:
It is said that the Pythagorean musical system was based on the Tetractys as the rows can be read as the ratios of 4:3, 3:2, 2:1, forming the basic intervals of the Pythagorean scales. That is, Pythagorean scales are generated from combining pure fourths, pure fifths, and the simple ratios of the unison 1:1 and the octave 2:1. Note that the diapason, 2:1, and the diapason plus diapente, 3:1, are consonant intervals according to the tetractys of the decad, but that the diapason plus diatessaron, 8:3, is not.
Kabbalist symbol
In the work by anthropologist Raphael Patai entitled The Hebrew Goddess, the author argues that the tetractys and its mysteries influenced the early Kabbalah. A Hebrew tetractys has the letters of the Tetragrammaton 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. The occultist Dion Fortune writes:The relationship between geometrical shapes and the first four Sephirot is analogous to the geometrical correlations in Tetraktys, shown above under #Pythagorean symbol, and unveils the relevance of the Tree of Life with the Tetraktys.
Occurrence
The tetractys occurs in the following:- the baryon decuplet
- an archbishop's coat of arms
- the arrangement of bowling pins in ten-pin bowling
- the arrangement of billiard balls in ten-ball pool
- a Chinese checkers board
- the "Christmas Tree" formation in association football
In poetry
The tetractys was created by Ray Stebbing, who said the following about his newly created form: