The Tetractys, also known as the decad, 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 followers of the secret worship of the Pythagoreans. A triangular number is a number that can be arranged in the shape of an equilateral triangle. ... Mysticism (ancient Greek mysticon = secret) is meditation, prayer, or theology focused on the direct experience of union with divinity, God, or Ultimate Reality, or the belief that such experience is a genuine and important source of knowledge. ... The Pythagoreans were an Hellenic organization of astronomers, musicians, mathematicians, and philosophers; who believed that all things are, essentially, numeric. ...

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Pythagorean symbol

1. The Tetractys symbolized the four elements - earth, air, fire, and water.
2. The first four numbers also symbolized the harmony of the spheres and the Cosmos
3. The first four numbers added up to ten, which was unity of a higher order
4. The Tetractys represented the organization of space:
   1. the first row represented zero-dimensions (a point)
   2. the second row represented one-dimension (a line of two points)
   3. the third row represented two-dimensions (a plane defined by a triangle of three points)
   4. the fourth row represented three-dimensions (a triangular pyramid defined by four points)

A prayer of the Pythagoreans shows the importance of the Tetractys (sometimes called the "Mystic Tetrad"), as the prayer was addressed to it. Several ancient Classical Element ideas exist. ... For other uses of the word, see cosmos (disambiguation) The cosmos is the universe, especially when thought of as an orderly or harmonious system. ... Dimension (from Latin measured out) is, in essence, the number of degrees of freedom available for movement in a space. ... Prayer is an effort to communicate with a God, or to some deity or deities, either to offer praise to the deity, to make a request of the deity, or simply to express ones thoughts and emotions to the deity. ...

"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 musical, geometric and arithmetic ratios of which the harmony of the universe so composed. The first quartenary is 1,2,3,4. There are 11 total quartenaries. And the perfect world which results from these quaternaries is geometrically, harmonically and arithmetically arranged" Music is an art, entertainment, or other human activity which involves organized sound, though definitions may vary. ... Geometry (from the Greek words Ge = earth and metro = measure) is the branch of mathematics first introduced by Theaetetus dealing with spatial relationships. ... Arithmetic or arithmetics (from the Greek word αριθμός = number) in common usage is a branch of (or the forerunner of) mathematics which records elementary properties of certain operations on numerals, though in usage by professional mathematicians, it often is treated as synonym for number theory. ...

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, 3:2, 2:1, forming the basic intervals of the Pythagorean scales. Pythagorean scales are based on pure fifths (in a 3:2 relation), and pure fourths (in a 4:3 relation) which form a stable optimally blending intervals. The ratios of 1:1 and 2:1 generate stable purely blending intervals. See diatessaron (interval) for the musical term. ... In harmony, diapente is the ratio 3:2 (sesquialterum) between a pair of frequencies or, equivalently, the ratio 2:3 between a pair of wavelengths. ... The word diapason is used in a number of musical contexts. ... In music, a unison is an interval, the ratio of 1:1 or 0 halfsteps and zero cents. ...

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 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."

— Attributed to Iamblichus For alternate meanings, such as the musical instrument, see triangle (disambiguation). ... Mathematics, often abbreviated maths in Commonwealth English and math in American English, is the study of abstraction. ... Metaphysics (Greek words meta = after/beyond and physics = nature) is a branch of philosophy, and related to the natural sciences, like physics, psychology and the biology of the brain; and also to mysticism, religion, and other spiritual subjects. ... This article is about musical harmony. ... Pythagoras (582 BC – 496 BC, Greek: Πυθαγόρας) was an Ionian mathematician and philosopher, known best for formulating the Pythagorean theorem. ... Two historical persons go by the name Iamblichus (Greek: Ιάμβλιχος) A Greek novelist; see Iamblichus (novelist) A neoplatonist philosopher; see Iamblichus (philosopher) This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ...

Kabbalist symbol

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 left to right. 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 tree of life Kabbalah (קבלה Reception, Standard Hebrew Qabbala, Tiberian Hebrew Qabbālāh; also written variously as Cabala, Cabalah, Cabbala, Cabbalah, Kabala, Kabalah, Kabbala, Qabala, Qabalah) is a religious philosophical system claiming an insight into divine nature. ... The Tetragrammaton in Phoenician (1100 BC to 300 CE), Aramaic (10th Century BC to 0) and modern Hebrew scripts. ... The Tree-of-Life is a fictional plant (the ancestor of yams, with similar appearance and taste) in Larry Nivens Known Space universe, for which all Hominids have an in-built genetic craving. ...

Tarot card reading arrangement

In a Tarot reading, the various positions of the tetractys provide a representation for forecasting future events. Tarot (Tar-oh) is a system of symbolical images. ...

The first row of a single position represents the Premise of the reading, forming a foundation for understanding all the other cards. The term card has many different meanings. ...

The second row of two positions respresents 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.
• 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.