The tetractys ( el, τετρακτύς), 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 A triangular number or triangle number counts objects arranged in an equilateral triangle In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triang ...
. As a
mystical Mysticism is popularly known as becoming one with God or the Absolute, but may refer to any kind of ecstasy Ecstasy may refer to: * Ecstasy (emotion), a trance or trance-like state in which a person transcends normal consciousness * Religious ...
symbol, it was very important to the secret worship of
Pythagoreanism Pythagoreanism originated in the 6th century BC, based on the teachings and beliefs held by Pythagoras Pythagoras of Samos, or simply ; in () was an ancient and the eponymous founder of . His political and religious teachings were wel ...
. 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 The ''musica universalis'' (literally universal music), also called music of the spheres or harmony of the spheres, is a philosophy, philosophical concept that regards proportions in the movements of celestial bodies – the Sun, Moon, and planets ...
'' and the
Cosmos The cosmos (, ) is another name for the Universe The universe ( la, universus) is all of space and time and their contents, including planets, stars, galaxy, galaxies, and all other forms of matter and energy. The Big Bang theory is the prev ...

as: ## (1) Unity (
Monad Monad may refer to: Philosophy * Monad (philosophy), a term meaning "unit" **Monism, the concept of "one essence" in the metaphysical and theological theory ** Monad (Gnosticism), the most primal aspect of God in Gnosticism * ''Great Monad'', an ...
) ## (2)
Dyad Dyad or dyade may refer to: * Dyad (biology), a pair of sister chromatids * Dyad (music), a set of two notes or pitches * Dyad (Greek philosophy), Greek philosophers' principle of "twoness" or "otherness" * Dyad (sociology), a group of two people ...
– Power – Limit/Unlimited (peras/
apeiron ''Apeiron'' (; ) is a Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is app ...
) ## (3) Harmony (Triad) ## (4) Kosmos (Tetrad). # The four rows add up to ten, which was unity of a higher order (The Dekad). # The Tetractys symbolizes the four classical elements
fire BBQ. Fire is the rapid oxidation of a material in the exothermic chemical process of combustion, releasing heat, light, and various reaction Product (chemistry), products. Fire is hot because the conversion of the weak double bond in molecula ...

air The atmosphere of Earth is the layer of gas Gas is one of the four fundamental states of matter In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (ph ...

water Water (chemical formula H2O) is an Inorganic compound, inorganic, transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known li ...

, and
earth Earth is the third planet from the Sun and the only astronomical object known to harbour and support life. 29.2% of Earth's surface is land consisting of continents and islands. The remaining 70.8% is Water distribution on Earth, covered wi ...

. # The Tetractys represented the organization of
space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameter A parameter (from the Ancient Greek language, Ancient Gre ...

: ## the first row represented zero
dimension In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...

s (a
point Point or points may refer to: Places * Point, Lewis Point ( gd, An Rubha), also known as the Eye Peninsula, is a peninsula some 11 km long in the Outer Hebrides (or Western Isles), Scotland. The majority of Point is connected to the rest of th ...
) ## the second row represented one dimension (a
line Line, lines, The Line, or LINE may refer to: Arts, entertainment, and media Films * ''Lines'' (film), a 2016 Greek film * ''The Line'' (2017 film) * ''The Line'' (2009 film) * ''The Line'', a 2009 independent film by Nancy Schwartzman Nan ...

of two points) ## the third row represented
two dimensions Two-dimensional space (also known as 2D space, 2-space, or bi-dimensional space) is a geometric setting in which two values (called parameter A parameter (), generally, is any characteristic that can help in defining or classifying a particu ...
(a plane defined by a
triangle A triangle is a polygon In geometry, a polygon () is a plane (mathematics), plane Shape, figure that is described by a finite number of straight line segments connected to form a closed ''polygonal chain'' (or ''polygonal circuit''). The ...

of three points) ## the fourth row represented three dimensions (a
defined by four points) A
prayer Prayer is an invocation An invocation (from the Latin verb ''invocare'' "to call on, invoke, to give") may take the form of: * Supplication, prayer Prayer is an invocation or act that seeks to activate a rapport with an object of w ...

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,
were required to swear a secret oath by the Tetractys. They then served as novices for a period of silence lasting five years. 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 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 In music theory Music theory is the study of the practices and possibilities of music Music is the of arranging s in time through the of melody, harmony, rhythm, and timbre. It is one of the aspects of all human societies. General ...
), 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
. 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.

Kabbalist symbol

There are some who believe that the tetractys and its mysteries influenced the early
Kabbalah Kabbalah ( he, קַבָּלָה, links=no ''Qabālā'', literally "reception, tradition" or "correspondence") is an esoteric Western esotericism, also known as esotericism, esoterism, and sometimes the Western mystery tradition, is a term ...

. A Hebrew tetractys has the letters of the
Tetragrammaton The Tetragrammaton (; ), or Tetragram, is the four-letter Hebrew Hebrew (, , or ) is a Northwest Semitic languages, Northwest Semitic language of the Afroasiatic languages, Afroasiatic language family. Historically, it is regarded as ...

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 Dion Fortune (born Violet Mary Firth, 6 December 1890 – 6 January 1946) was a British occultist The occult, in the broadest sense, is a category of supernatural The supernatural encompasses supposed phenomena or entities that a ...
writes: :The
point Point or points may refer to: Places * Point, Lewis Point ( gd, An Rubha), also known as the Eye Peninsula, is a peninsula some 11 km long in the Outer Hebrides (or Western Isles), Scotland. The majority of Point is connected to the rest of th ...
is assigned to Kether; :the
line Line, lines, The Line, or LINE may refer to: Arts, entertainment, and media Films * ''Lines'' (film), a 2016 Greek film * ''The Line'' (2017 film) * ''The Line'' (2009 film) * ''The Line'', a 2009 independent film by Nancy Schwartzman Nan ...

Chokmah ''Chokmâh'' ( ,חכמה ISO 259 or ''khok-maw) is the Biblical Hebrew word rendered as "wisdom" in English Bible versions (LXX ''sophia (wisdom), sophia'', Vulgate ').''Strong's Concordance'H2451 "from H2449 [חָכַם ''chakam'' "wise"]; wi ...
; :the two-dimensional plane to Binah (Kabbalah), Binah; :consequently the three-dimensional Solid geometry, solid naturally falls to Chesed. 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.

Tarot card reading arrangement

In a Divinatory, esoteric and occult tarot, 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 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 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 elements. * The Fire card is rightmost, representing dynamic creative force, ambitions, and personal will (philosophy), 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 reality, realities of day to day living.


The tetractys occurs (generally coincidentally) in the following: * the Eightfold Way (physics), 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, ten-ball pool * a Chinese checkers board * the Formation (association football)#4–3–2–1 (the "Christmas Tree" formation), "Christmas Tree" formation in association football

In poetry

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: :''Mantrum'' :''Your /'' :''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.''Search result for Tetractys

See also

*Pascal's triangle


Further reading

*von Franz, Marie-Louise. ''Number and Time: Reflections Leading Towards a Unification of Psychology and Physics''. Rider & Company, London, 1974. *Fideler, D. ed
The Pythagorean Sourcebook and Library
Phanes Press, 1987.
The Theoretic Arithmetic of the Pythagoreans – Thomas Taylor

External links

Examples of Tetractys poems
{{Ancient Greek philosophical concepts Tarotology Dot patterns Kabbalah Pythagorean symbols Poetic form Genres of poetry Greek mathematics Mathematical symbols