Thetetractys (Greek:τετρακτύς), ortetrad,[1] or thetetractys of the decad[2] is atriangular 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 fourthtriangular number. As amystical symbol, it was very important to the secret worship ofPythagoreanism. There were four seasons, and the number was also associated with planetary motions and music.[3]
Aprayer 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.[5]
The Pythagorean oath also mentioned the Tetractys:
It is said[6][7][8] that the Pythagorean musical system was based on the Tetractys as the rows can be read as the ratios of4:3 (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 unison1:1 and the octave2:1. Note that thediapason, 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.[9][10]
The Tetractys [also known as the decad] is anequilateral triangle formed from the sequence of the first ten numbers aligned in four rows. It is both amathematical idea and ametaphysical symbol that embraces within itself—in seedlike form—the principles of the natural world, theharmony 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.
In the work by anthropologistRaphael Patai entitledThe Hebrew Goddess, the author argues that the tetractys and its mysteries influenced the earlyKabbalah.[11] A Hebrew tetractys has the letters of theTetragrammaton inscribed on the ten positions of the tetractys, from right to left. It has been argued that theKabbalistic 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 occultistDion Fortune writes:
The relationship between geometrical shapes and the first fourSephirot 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.
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The tetractys occurs (generally coincidentally) in the following:
In English-language poetry, a tetractys is a syllable-counting form with five lines. The first line has one syllable, the second has two syllables, the third line has three syllables, the fourth line has four syllables, and the fifth line has ten syllables.[13] A sample tetractys would look like this:
The tetractys was created byRay Stebbing, who said the following about his newly created form: