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Tetractys

The tetractys (Greek: τετρακτύς), or tetrad,[1] or the tetractys of the decad[2] 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. As a mystical symbol, it was very important to the secret worship of Pythagoreanism. There were four seasons, and the number was also associated with planetary motions and music.[3]
Pythagorean symbol
[edit]- The first four numbers symbolize the musica universalis and the Cosmos as:
- The four rows add up to ten, which was unity of a higher order (The Dekad).
- The Tetractys symbolizes the four classical elements—air, fire, water, and earth.
- 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)
A prayer of the Pythagoreans shows the importance of the Tetractys (sometimes called the "Mystic Tetrad"), as the prayer was addressed to it.
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[6][7][8] 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.[9][10]
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