# centitone, iring

[Joe Monzo, Tonalsoft Encyclopedia of Microtonal Music Theory]

A unit of interval measurement proposed in 1898 by Widogast Iring, and again in 1932 under the name "centitone" by Joseph Yasser.

A centitone or iring is the logarithmic division of the 12-tone equal temperament (12-edo) semitone into 50 equal parts. It is calculated as the 600th root of 2, expressed mathematically as 600√2, or 2(1/600), with a ratio of approximately 1:1.001155913. It is an irrational number. The formula for calculating the centitone or iring value of any ratio is: cents = log10r * [600 / log102] or cents = log2r * 600 , where r is the ratio.

A centitone or iring is:

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### centitones / irings calculator

Ratio may be entered as fraction or floating-point decimal number.
(value must be greater than 1)

For EDOs (equal-temperaments), type: "a/b" (without quotes)
where "a" = EDO degree and "b" = EDO cardinality.
(value must be less than 1)

Enter ratio: = centitones (irings)

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