ratio

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.

Euclid's definition: a mutual relation of two magnitudes of the same kind to one another in respect of quantity.

[from Partch 1974, Genesis of a Music, 2nd ed., Da Capo Press, New York, p. 73]

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rational

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.

[from John Chalmers, Divisions of the Tetrachord]

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