Τετρακτύς) is a triangular figure
consisting of ten points arranged in four rows: one, two, three,
and four points in each row. As a mystical
symbol, it was very important to the secret worship of the Pythagoreans
- The Tetractys symbolized the four
elements — earth, air,
fire, and water.
- The first four numbers also symbolized the harmony of the spheres and the
- The four rows added up to ten, which
was unity of a higher order (in decimal).
- The Tetractys represented the organization of space:
- the first row represented zero-dimensions (a point)
- the second row represented one-dimension (a line of two points)
- the third row represented two-dimensions
(a plane defined by a triangle of three points)
- the fourth row represented three-dimensions (a tetrahedron defined by four points)
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".
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:
- "By that pure, holy, four lettered name on
- 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
ratios of which the harmony of
the universe so 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
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.
- "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."
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.
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. 
Below is only a single variation for
The first row of a single position represents the Premise of the
reading, forming a foundation for understanding all the other
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
- 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.
In literature and popular culture
- von Franz, Marie-Louise. Number and Time: Reflections
Leading Towards a Unification of Psychology and Physics. Rider
& Company, London, 1974. ISBN 0-09-121020-8