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.
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A prayer of the Pythagoreans shows the importance of the Tetractys (sometimes called the "Mystic Tetrad"), as the prayer was addressed to it.
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.
The Pythagorean oath also mentioned the Tetractys:
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 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.
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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.
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 third row of three positions represents three kinds of decisions an individual must make.
The fourth row of four positions represents the four Greek elements.
The tetractys occurs (generally coincidentally) in the following: