The tetractys (Greek, Modern (1453-);: τετρακτύς), or tetrad, or the tetractys of the decad[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 Pythagoreanism. There were four seasons, and the number was also associated with planetary motions and music.
A prayer of the Pythagoreans shows the importance of the Tetractys (sometimes called the "Mystic Tetrad"), as the prayer was addressed to it.
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.
It is said[3] 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.
In the work by anthropologist Raphael Patai entitled The Hebrew Goddess, the author argues that the tetractys and its mysteries influenced the early Kabbalah.[4] 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 point is assigned to Kether;
the two-dimensional plane to Binah;
consequently the three-dimensional solid naturally falls to Chesed.[5]
The relationship between geometrical shapes and the first four Sephirot is analogous to the geometrical correlations in Tetraktys, shown above under
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. A sample tetractys would look like this:
MantrumYour /
fury /
confuses /
us all greatly. /
Volatile, big-bodied tots are selfish. //
The tetractys was created by Ray Stebbing, who said the following about his newly created form:
"The tetractys could be Britain's answer to the haiku. Its challenge is to express a complete thought, profound or comic, witty or wise, within the narrow compass of twenty syllables.[6]