GLOSSARY OF SELECT PYTHAGOREAN TERMS

Analogia -- Literally, "through proportion." Hence, continued geometrical proportion or ratio. See logos.

Apeiron -- Boundless; Unlimited; Infinite; Indefinite. One of the Pythagorean first principles in the Table of Opposites. See peras and Indefinite Dyad.

Harmonia -- A "joint" or "fitting together;" hence, the musical scale comprised within the octave. Also, music per se; philosophically, the principle of Union, opposite Strife. Also, a Pythagorean name of the number Three, because a third element must be introduced to mediate between or join together two separate principles or numerical values.

Indefinite Dyad -- Plato's term for the Pythagorean principle of Apeiron, as contrasted with the One, the principle of Limit.

Kosmos -- "Order." Also, "ornament." First applied to the universe by Pythagoras, hence cosmos means world-order. Also, a Pythagorean name of the numbers Six and Ten.

Logos -- Usually translated "Word" or "Reason." In the mathematical and Pythagorean sense, the same as the Latin ratio, i.e. "proportion;" hence also, a principle of mediation. Can also mean "principle;" the plural logoi can be translated as "principles," "reasons" or "causes," or (mathematical) "ratios."

Mean or median -- The middle term in a mathematical proportion which links two extreme terms together in harmonia. The three most important are the Arithmetic, Harmonic, and Geometric means, which underlie the structure of the musical scale in Pythagorean tuning. In the following equations, the two extremes are A and C, and the mean term is B.

Arithmetic Mean: B = (A +C) / 2
Harmonic Mean: B = 2AC / A + C
Geometric Mean: B = √A x C

Monochord (kanon) -- A one-stringed musical instrument with a movable bridge used for dividing the string at any length. The monochord is used to demonstrate the harmonic overtone series and the principles on which the musical scale is based.

Peras -- The principle of Limit or Boundary. The opposite of Apeiron, the Unlimited.

Symphonia -- Literally, "sounding together." "Harmony," agreement or concord. The term applies to the perfect intervals or consonance of the octave, fifth, and fourth, par excellence. This is the modern meaning of the word "harmony," but not the ancient one.

Tetraktys -- (from tetras, four). "Fourness." Also, the first four numbers, especially when arranged in an equilateral triangle, the sum of which is the number Ten. Hence also, the Decad.

The Tetraktys symbolizes the perfection of Number and the elements which comprise it. The Tetraktys also contains the symphonic ratios which make possible the musical scale, i.e., 1:2, the octave; 2:3, the perfect fifth; and 3:4, the perfect fourth.

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