# Tetractys > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Tetractys > Markdown URL: https://mediated.wiki/source/Tetractys.md > Source: https://en.wikipedia.org/wiki/Tetractys > Source revision: 1342784781 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) {{Short description|Symbol of ten points laid in four rows}} thumb|200px| The tetractys The '''tetractys''' ({{langx|el|τετρακτύς}}), or '''tetrad''',{{citation|url= https://books.google.com/books?id=24vBaQDNy8UC|title=The Theosophical Glossary|page=302|publisher=Forgotten Books |isbn=9781440073915}} or the '''tetractys of the decad'''{{cite book|page=36|author=Eduard Zeller|author-link=Eduard Zeller|title=Outlines of the History of Greek Philosophy|edition=13}} is a [triangular figure](/source/triangular_number) 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](/source/triangular_number). As a [mystical](/source/mysticism) symbol, it was very important to the secret worship of [Pythagoreanism](/source/Pythagoreanism). There were four seasons, and the number was also associated with planetary motions and music.{{citation|url =https://books.google.com/books?id=DQpSA4CEnIwC| title = Pythagoras: pioneering mathematician and musical theorist of Ancient Greece| author = Dimitra Karamanides| publisher = The Rosen Publishing Group|year= 2005 |pages=65| isbn = 9781404205000}} ==Pythagorean symbol== # The first four numbers symbolize the ''[musica universalis](/source/musica_universalis)'' and the [Cosmos](/source/Cosmos) as: ## [Monad](/source/Monad_(philosophy)) – Unity ## [Dyad](/source/Dyad_(Greek_philosophy)) – Power – Limit/Unlimited (peras/[apeiron](/source/Apeiron_(cosmology))) ## Triad – Harmony ## Tetrad – Kosmos''The Pythagorean Sourcebook and Library'' by [Kenneth Sylvan Guthrie](/source/Kenneth_Sylvan_Guthrie) # The four rows add up to ten, which was unity of a higher order (The Dekad). # The Tetractys symbolizes the [four classical elements](/source/classical_element)—[air](/source/air), [fire](/source/fire), [water](/source/water), and [earth](/source/earth). # The Tetractys represented the organization of [space](/source/space): ## the first row represented zero [dimension](/source/dimension)s (a [point](/source/Point_(geometry))) ## the second row represented one dimension (a [line](/source/Line_(geometry)) of two points) ## the third row represented [two dimensions](/source/Cartesian_coordinate_system) (a [plane](/source/plane_(geometry)) defined by a [triangle](/source/triangle) of three points) ## the fourth row represented [three dimensions](/source/Three-dimensional_space_(mathematics)) (a [tetrahedron](/source/tetrahedron) defined by four points) A [prayer](/source/prayer) of the Pythagoreans shows the importance of the Tetractys (sometimes called the "Mystic Tetrad"), as the prayer was addressed to it. {{quote|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.Dantzig, Tobias ([1930], 2005) Number. The Language of Science. p. 42}} 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[Introduction to Arithmetic](/source/Introduction_to_Arithmetic) – [Nicomachus](/source/Nicomachus){{citation|url=https://books.google.com/books?id=q-1o3tUGcXMC&q=tetraktys+diatessaron&pg=PA66|title=The Musical Order of the World: Kepler, Hesse, Hindemith-Siglind Bruhn|isbn=9781576471173|last1=Bruhn|first1=Siglind|year=2005|publisher=Pendragon Press }}{{citation|url=https://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.04.0063:entry=musica-cn&highlight=pythagorean%2Cpythagoras|title=A Dictionary of Greek and Roman Antiquities(1890) – William Smith, LLD, William Wayte, G. E. Marindin, Ed.}} that the Pythagorean musical system was based on the Tetractys as the rows can be read as the ratios of [4:3](/source/diatessaron) (perfect fourth), 3:2 ([perfect fifth](/source/perfect_fifth)), [2:1](/source/Pythagorean_interval) (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](/source/unison) and the octave [2:1](/source/octave). Note that the [diapason](/source/diapason_(interval)), 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.{{citation|url=https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A2008.01.0386%3Asection%3D14|title=Plutarch, De animae procreatione in Timaeo – Goodwin, Ed. (lang.: English)}}{{citation|url=https://books.google.com/books?id=ehDG5mGUYAMC&q=tetraktys+diatessaron&pg=PA56|title=Sacred Architecture of London – Nigel Pennick|isbn=9781904658627|last1=Pennick|first1=Nigel|date=January 2012|publisher=Aeon Books }} {{quote|The Tetractys [also known as the decad] is an [equilateral triangle](/source/equilateral_triangle) formed from the sequence of the first ten numbers aligned in four rows. It is both a [mathematical](/source/mathematics) idea and a [metaphysical](/source/metaphysics) symbol that embraces within itself—in seedlike form—the principles of the natural world, the [harmony](/source/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.}} ==Kabbalist symbol== [[Image:Boehme-heart.jpg|thumb|right|Symbol by early 17th-century Christian mystic [Jakob Böhme](/source/Jakob_B%C3%B6hme), including a tetractys of flaming Hebrew letters of the Tetragrammaton.]] [[Image:Tetragrammaton-Tetractys.png|thumb|A tetractys of the letters of the Tetragrammaton adds up to 72 by [gematria](/source/gematria).]] In the work by anthropologist [Raphael Patai](/source/Raphael_Patai) entitled ''[The Hebrew Goddess](/source/The_Hebrew_Goddess)'', the author argues that the tetractys and its mysteries influenced the early [Kabbalah](/source/Kabbalah).{{Cite book|last=Patai|first=Raphael|url=https://archive.org/details/hebrewgoddess0000pata|title=The Hebrew Goddess|date=1967|publisher=Wayne State University Press |isbn=0-8143-2271-9|url-access=registration}} - Chapter V - The Kabbalistic Tetrad A Hebrew tetractys has the letters of the [Tetragrammaton](/source/Tetragrammaton) inscribed on the ten positions of the tetractys, from right to left. It has been argued that the [Kabbalistic Tree of Life](/source/Tree_of_life_(Kabbalah)), 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](/source/Dion_Fortune) writes: :The [point](/source/Point_(geometry)) is assigned to [Kether](/source/Keter); :the [line](/source/Line_(geometry)) to [Chokmah](/source/Chokmah); :the two-dimensional [plane](/source/plane_(geometry)) to [Binah](/source/Binah_(Kabbalah)); :consequently the three-dimensional [solid](/source/Solid_geometry) naturally falls to [Chesed](/source/Chesed).The Mystical Qabalah, Dion Fortune, Chapter XVIII, 25 The relationship between geometrical shapes and the first four [Sephirot](/source/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. ==Occurrence== [[File:Women_Bowling_(2870338513).jpg|thumb|[Ten-pin bowling](/source/Ten-pin_bowling) pins in a tetractys]] [[Image:Template-Metropolitan Archbishop.svg|thumb|100px|right|[Coat of arms](/source/Coat_of_arms) of an [archbishop](/source/archbishop) of the [Catholic Church](/source/Catholic_Church)]] The tetractys occurs (generally coincidentally) in the following: * the [baryon decuplet](/source/Eightfold_Way_(physics)) * an [archbishop](/source/archbishop)'s [coat of arms](/source/coat_of_arms) * the arrangement of [bowling pins](/source/bowling_pins) in [ten-pin bowling](/source/ten-pin_bowling) * the arrangement of [billiard ball](/source/billiard_ball)s in [ten-ball pool](/source/Ten-ball) * a [Chinese checkers](/source/Chinese_checkers) board * the ["Christmas Tree" formation](/source/Formation_(association_football)) in [association football](/source/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.{{citation|url= http://www.volecentral.co.uk/vf/englishsyllable.htm#Tetractys|title=English Syllable Counters}} 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](/source/Ray_Stebbing), who said the following about his newly created form: :''"The tetractys could be Britain's answer to the [haiku](/source/haiku). Its challenge is to express a complete thought, profound or comic, witty or wise, within the narrow compass of twenty syllables.''{{Cite web|url=http://bensonofjohn.co.uk/poetry/formssearch.php?searchbox=Tetractys|title=Ben Johnson - Poetry Forms - Tetractys|website=bensonofjohn.co.uk}} == See also== *[Pascal's triangle](/source/Pascal's_triangle) ==References== {{Reflist}} ==Further reading== *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}} *Fideler, D. ed. [http://www.american-buddha.com/cult.pythagsourcebook.htm The Pythagorean Sourcebook and Library] {{Webarchive|url=https://web.archive.org/web/20150509045621/http://www.american-buddha.com/cult.pythagsourcebook.htm |date=2015-05-09 }}. Phanes Press, 1987. *[https://books.google.com/books?id=5j0tQCKwpnMC&q=tetraktys+diatessaron The Theoretic Arithmetic of the Pythagoreans – Thomas Taylor] ==External links== *[http://tetractys-ichthys.blogspot.co.uk Examples of Tetractys poems] * ''Min Chen''. [https://news.artnet.com/art-world/5-occult-symbols-decoded-2704827 Unlocking the Occult: 5 Mystical Symbols and Their Secret Histories] // Artnet News — Oct. 30, 2025 {{Ancient Greek philosophical concepts}} Category:Dot patterns Category:Genres of poetry Category:Ancient Greek mathematics Category:History of mathematics Category:History of poetry Category:Kabbalah Category:Mathematical symbols Category:Poetic forms Category:Pythagorean symbols Category:Tarot Category:Concepts in ancient Greek metaphysics --- Adapted from the Wikipedia article [Tetractys](https://en.wikipedia.org/wiki/Tetractys) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Tetractys?action=history)). 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