Tetractys
Encyclopedia
The tetractys or tetrad, 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.
A prayer
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, 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:
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 music
al, geometric
and arithmetic
ratios of which the harmony of the universe is 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 arithmetically arranged.
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.
Quote:
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.
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 third row of three positions represents three kinds of decisions an individual must make.
The fourth row of four positions represents the four Greek elements.
Triangular number
A triangular number or triangle number numbers the objects that can form an equilateral triangle, as in the diagram on the right. The nth triangle number is the number of dots in a triangle with n dots on a side; it is the sum of the n natural numbers from 1 to n...
consisting of ten points arranged in four rows: one, two, three, and four points in each row. As a mystical
Mysticism
Mysticism is the knowledge of, and especially the personal experience of, states of consciousness, i.e. levels of being, beyond normal human perception, including experience and even communion with a supreme being.-Classical origins:...
symbol, it was very important to the secret worship of the Pythagoreans.
Pythagorean symbol
- The Tetractys symbolized the four elementsClassical elementMany philosophies and worldviews have a set of classical elements believed to reflect the simplest essential parts and principles of which anything consists or upon which the constitution and fundamental powers of anything are based. Most frequently, classical elements refer to ancient beliefs...
— earthEarthEarth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
, air, fireFireFire is the rapid oxidation of a material in the chemical process of combustion, releasing heat, light, and various reaction products. Slower oxidative processes like rusting or digestion are not included by this definition....
, and waterWaterWater is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...
. - The first four numbers also symbolized the harmony of the spheres and the CosmosCosmosIn the general sense, a cosmos is an orderly or harmonious system. It originates from the Greek term κόσμος , meaning "order" or "ornament" and is antithetical to the concept of chaos. Today, the word is generally used as a synonym of the word Universe . The word cosmos originates from the same root...
. - The four rows added up to ten10 (number)10 is an even natural number following 9 and preceding 11.-In mathematics:Ten is a composite number, its proper divisors being , and...
, which was unity of a higher order (in decimalDecimalThe decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....
). - The Tetractys represented the organization of spaceSpaceSpace is the boundless, three-dimensional extent in which objects and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum...
:- the first row represented zero-dimensionDimensionIn physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...
s (a pointPoint (geometry)In geometry, topology and related branches of mathematics a spatial point is a primitive notion upon which other concepts may be defined. In geometry, points are zero-dimensional; i.e., they do not have volume, area, length, or any other higher-dimensional analogue. In branches of mathematics...
) - the second row represented one-dimension (a lineLine (geometry)The notion of line or straight line was introduced by the ancient mathematicians to represent straight objects with negligible width and depth. Lines are an idealization of such objects...
of two points) - the third row represented two-dimensions (a plane defined by a triangleTriangleA triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....
of three points) - the fourth row represented three-dimensionsThree-dimensional spaceThree-dimensional space is a geometric 3-parameters model of the physical universe in which we live. These three dimensions are commonly called length, width, and depth , although any three directions can be chosen, provided that they do not lie in the same plane.In physics and mathematics, a...
(a tetrahedronTetrahedronIn geometry, a tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids...
defined by four points)
- the first row represented zero-dimension
A prayer
Prayer
Prayer is a form of religious practice that seeks to activate a volitional rapport to a deity through deliberate practice. Prayer may be either individual or communal and take place in public or in private. It may involve the use of words or song. When language is used, prayer may take the form of...
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 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."
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 music
Music
Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...
al, geometric
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
and arithmetic
Arithmetic
Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of combining numbers...
ratios of which the harmony of the universe is 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 arithmetically arranged.
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
Diatessaron
The Diatessaron is the most prominent Gospel harmony created by Tatian, an early Christian apologist and ascetic. The term "diatessaron" is from Middle English by way of Latin, diatessarōn , and ultimately Greek, διὰ τεσσάρων The Diatessaron (c 160 - 175) is the most prominent Gospel harmony...
(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
Unison
In music, the word unison can be applied in more than one way. In general terms, it may refer to two notes sounding the same pitch, often but not always at the same time; or to the same musical voice being sounded by several voices or instruments together, either at the same pitch or at a distance...
and the octave 2:1
Octave
In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...
. 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.
Quote:
- "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 mathematicalMathematicsMathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
idea and a metaphysicalMetaphysicsMetaphysics is a branch of philosophy concerned with explaining the fundamental nature of being and the world, although the term is not easily defined. Traditionally, metaphysics attempts to answer two basic questions in the broadest possible terms:...
symbol that embraces within itself—in seedlike form—the principles of the natural world, the harmonyHarmonyIn music, harmony is the use of simultaneous pitches , or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic...
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 — PythagorasPythagorasPythagoras of Samos was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him...
."
Kabbalist symbol
Yahweh
Yahweh is the name of God in the Bible, the God of Abraham, Isaac, Jacob, Jews and Christians.The word Yahweh is a modern scholarly convention for the Hebrew , transcribed into Roman letters as YHWH and known as the Tetragrammaton, for which the original pronunciation is unknown...
(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
Tree of life (Kabbalah)
The Tree of Life, or Etz haChayim in Hebrew, is a mystical symbol used in the Kabbalah of esoteric Judaism to describe the path to God and the manner in which he created the world ex nihilo...
, 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. http://www.cs.utk.edu/~Mclennan/BA/PT/D-tet.html 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 willWill (philosophy)Will, in philosophical discussions, consonant with a common English usage, refers to a property of the mind, and an attribute of acts intentionally performed. Actions made according to a person's will are called "willing" or "voluntary" and sometimes pejoratively "willful"...
. - The Air card is to the right middle, representing the mind, thoughtThought"Thought" generally refers to any mental or intellectual activity involving an individual's subjective consciousness. It can refer either to the act of thinking or the resulting ideas or arrangements of ideas. Similar concepts include cognition, sentience, consciousness, and imagination...
s, and strategies toward goals. - The Water card is to the left middle, representing the emotionEmotionEmotion is a complex psychophysiological experience of an individual's state of mind as interacting with biochemical and environmental influences. In humans, emotion fundamentally involves "physiological arousal, expressive behaviors, and conscious experience." Emotion is associated with mood,...
s, feelings, and whims. - The Earth card is leftmost, representing physical realitiesRealityIn philosophy, reality is the state of things as they actually exist, rather than as they may appear or might be imagined. In a wider definition, reality includes everything that is and has been, whether or not it is observable or comprehensible...
of day to day living.
Other symbols
- An archbishopArchbishopAn archbishop is a bishop of higher rank, but not of higher sacramental order above that of the three orders of deacon, priest , and bishop...
's coat of armsCoat of armsA coat of arms is a unique heraldic design on a shield or escutcheon or on a surcoat or tabard used to cover and protect armour and to identify the wearer. Thus the term is often stated as "coat-armour", because it was anciently displayed on the front of a coat of cloth...
shows two tetractys designs. - The tetractys is the fourth triangular numberTriangular numberA triangular number or triangle number numbers the objects that can form an equilateral triangle, as in the diagram on the right. The nth triangle number is the number of dots in a triangle with n dots on a side; it is the sum of the n natural numbers from 1 to n...
's geometrical representation. - Coincidentally, the pins in ten-pin bowlingTen-pin bowlingTen-pin bowling is a competitive sport in which a player rolls a bowling ball down a wooden or synthetic lane with the objective of scoring points by knocking down as many pins as possible.-Summary:The lane is bordered along its length by semicylindrical channels Ten-pin bowling (commonly just...
are ordered in the tetractys pattern. - Chinese checkersChinese checkersChinese checkers is a board game that can be played by two, three, four, or six people, playing individually or with partners...
In literature and popular culture
- Tetraktys is the name of a Pythagorean cult in the mystery novel The Night Villa by Carol Goodman.
- Samuel BeckettSamuel BeckettSamuel Barclay Beckett was an Irish avant-garde novelist, playwright, theatre director, and poet. He wrote both in English and French. His work offers a bleak, tragicomic outlook on human nature, often coupled with black comedy and gallows humour.Beckett is widely regarded as among the most...
's novel MurphyMurphy (novel)Murphy, first published in 1938, is a novel as well as the third work of prose fiction by the Irish author and dramatist Samuel Beckett. The book was Beckett's second published prose work after the short-story collection More Pricks than Kicks and his unpublished first novel Dream of Fair to...
has a mention to the tetrakyt in its opening pages. - The Tetraktys is also the name of an underground psychedelic folk band based in CalgaryCalgaryCalgary is a city in the Province of Alberta, Canada. It is located in the south of the province, in an area of foothills and prairie, approximately east of the front ranges of the Canadian Rockies...
. - The Tetraktys is mentioned in the novel The Oxford MurdersThe Oxford Murders (novel)The Oxford Murders is a novel by the Argentine author Guillermo Martínez, first published in 2003. There is a 2005 translation by Sonia Soto....
, by Guillermo MartínezGuillermo MartínezGuillermo Martínez is an Argentine novelist and short story writer.Martínez was born in Bahía Blanca, Argentina. He gained a PhD in mathematical logic at the University of Buenos Aires....
. The novel was turned into a filmThe Oxford Murders (film)The Oxford Murders is a 2008 film directed by Álex de la Iglesia. This thriller film is adapted from the novel of the same name by the Argentine mathematician and writer Guillermo Martínez. The film stars Elijah Wood, John Hurt and the Spanish actress Leonor Watling.-Plot:It is 1993...
. - The 2009 novel Tetraktys, by RSA senior scientist Ari Juels, pits a classicist turned computer scientist against an ancient Pythagorean cult.
- True Worshipers of the Ineffable Tetractys, or T.W.I.T., is the name of a secret organization in Thomas PynchonThomas PynchonThomas Ruggles Pynchon, Jr. is an American novelist. For his most praised novel, Gravity's Rainbow, Pynchon received the National Book Award, and is regularly cited as a contender for the Nobel Prize in Literature...
's novel Against the DayAgainst the DayAgainst the Day is a novel by Thomas Pynchon. The narrative takes place between the 1893 Chicago World's Fair and the time immediately following World War I and features more than a hundred characters spread across the United States, Europe, Mexico, Central Asia, and "one or two places not strictly...
. - The Tetraktys is a central plot element in the video game, 'Assassin's Creed: Brotherhood'. 2010
- Tetraktys is the name of an album released in 2010 by the electronic musician Laskfar Vortok on the NaboaMusic label.
See also
- Monad
- DyadDyad (symbol)The Dyad is a title used by the Pythagoreans for the number two, representing the principle of "twoness" or "otherness".Numenius said that Pythagoras gave the name of Monad to God, and the name of Dyad to matter...
- TriadTriad (symbol)The Triad is a Pythagorean title for the number three. According to Priya Hemenway they considered it the most beautiful number, as it is the only number to equal the sum of all the terms below it, and the only number whose sum with those below equals the product of them and itself.-See also:*...
- TetradTetrad (symbol)The tetrad or number four is the first number formed by the addition and multiplication of equals. To the Pythagoreans, this symbol and number represented justice as it is the first number that is divisible every way into equal parts.-See also:*Monad*Dyad...
- DecadDecadPythagorus regarded the number 10, or "decad" as being a perfect number, which was often represented by the tetractys, which embraced the whole nature of number....
- PentadPentadThe pentad was a Pythagorean term for the quantity of five.-See also:*Related greek numerical terms**Monad **Dyad **Triad **Tetrad **Decad *Other...
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. The Pythagorean Sourcebook and Library. Phanes Press, 1987.