Mystical systems
Tetractys
Direct answer
Tetractys: The tetractys is a triangle of ten dots in four rows of one, two, three and four, revered by the Pythagoreans as the figure of the number ten.
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At a glance
- Also called
- tetraktys, ten dots triangle
- Found in
- Mystical Systems
- Related
- Pythagorean Numerology, Monochord, Sacred Geometry, Quadrivium
The tetractys is a triangle of ten dots in four rows of one, two, three and four, revered by the Pythagoreans as the figure of the number ten.
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What does the tetractys represent?
The tetractys is ten points arranged in a triangle: one in the top row, then two, three and four. Its name comes from the Greek for four. The Pythagoreans held it sacred because the first four numbers add to ten, their perfect number, and because the rows give the ratios of the musical concords: two to one for the octave, three to two for the fifth and four to three for the fourth.
Ancient writers also read the rows as the point, the line, the surface and the solid. Later traditions added much. Some Renaissance and modern occult writers set the four letters of the Hebrew divine name on it, or matched it to the ten sefirot. Those readings are theirs, and are not found among the early Pythagoreans.
On the tree of the hidden arts: Sacred geometry.
What sets Tetractys apart
It is a number shown as a shape, which is how the early Pythagoreans thought of all numbers: pebbles laid out in triangles, squares and oblongs. Ten is the fourth triangular number, and the figure can be read at once as a count, as a picture and as a scale. No other emblem of an ancient school is at the same time its creed, its oath and a working diagram of its chief discovery, the ratios of the concords.
- Dots: ten, in rows of one, two, three and four
- Name: from the Greek tetra, four
- Musical ratios: 2 to 1 the octave, 3 to 2 the fifth, 4 to 3 the fourth
- Spatial reading: point, line, surface and solid
- Oath: quoted by Sextus Empiricus and Iamblichus
- Kinds listed: eleven, by Theon of Smyrna, second century CE
Often mistaken for something else: The Kabbalistic Tree of Life also has ten points, but it comes from medieval Jewish sources and has no historical link with the Pythagorean figure.
The story behind Tetractys
Pythagoras left no writings, so the tetractys is known from later reports. The oath of his followers, sworn by the one who handed down the tetractys, is quoted by writers of the first centuries CE such as Sextus Empiricus and Iamblichus. Theon of Smyrna, in the second century CE, listed eleven kinds of tetractys. Christian cabalists of the Renaissance joined it to the Hebrew name of God.
Why Tetractys matters
Tetractys shows in one small figure how the Pythagoreans joined counting, geometry and music, which is the root of all later number lore.
How to read Tetractys
Readers lay it out with coins to see the ratios in its rows; historians cite it as the emblem of the Pythagorean school.
Tetractys in practice: an example
The ten pins of a bowling lane are set out as a tetractys: four at the back, then three, two and one.
Where readings of Tetractys go wrong
The Hebrew letters and cabalistic meanings often printed on it are later additions and not Pythagorean.
Sources and editorial method
This entry summarizes the tradition in the Almanac's own words; where no source is listed, it is an editorial summary rather than a primary text, and symbolic readings are named as the tradition's, not as fact.
- Source
- The Great Almanac Dictionary
- Category
- Mystical Systems
- Aliases
- tetraktys, pythagorean tetractys, tetractys of the decad, ten dots triangle
- Last updated
- 2026-09-26
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Common questions
What does the tetractys represent?
To the Pythagoreans it stood for the number ten as the sum of one, two, three and four, and for the order of the world, since its rows hold the ratios of the musical concords.
Why did the Pythagoreans swear by the tetractys?
Their oath named the teacher who had handed it down. They took it as the key to number, and number as the key to everything, so it was the most solemn thing they had to swear by.
Is the tetractys connected to the Kabbalah?
Only by later writers. Renaissance Christian cabalists placed the four Hebrew letters of the divine name on its rows. Nothing of the kind is found in the ancient Pythagorean sources.
