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Encyclopedia of Microtonal Music Theory

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A mutual relation of two magnitudes of the same kind to one another in respect of quantity.

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[Harry Partch 1974, Genesis of a Music, 2nd ed., p 73]

A relationship, or interval, expressing the vibrations per second, or cycles, of the two tones concerned, generally in the lowest possible [integer] terms;...simultaneously a representative of a tone and an implicit relationship to a "keynote" -- or unity.

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[John Chalmers, Divisions of the Tetrachord]

Pertaining to ratios, such as 4/3 or 7/6.

Rational intervals are musical intervals between tones whose frequencies may be defined by ratios of whole numbers.

Irrational or tempered intervals are defined by irrational numbers.

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