## Definitions of tuning terms © 1998 by Joseph L. Monzo All definitions by Joe Monzo unless otherwise cited

cents, ¢

An interval measurement invented by Alexander Ellis and appearing in his appendix to his translation of Helmhotz's On the Sensations of Tone [1875].

A cent is the logarithmic division of the 12edo Semitone into 100 equal parts. It is calculated as the 1200th root of 2, or 2(1/1200), with a ratio of approximately 1:1.0005777895. It is an irrational number.

The formula for calculating the cents-value of any ratio is:

cents = log10(ratio) * [1200 / log10(2)]

Cents are almost universally used as a small logarithmic measurement to compare interval sizes; I prefer Semitones, but still use cents often, especially in these Dictionary definitions.

[from Joe Monzo, JustMusic: A New Harmony]

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(abbreviation: ¢) A measure of musical interval width invented by A. J. Ellis. There are 100¢ to the 12-tone equally tempered semitone and 1200 cents to the octave. Cents are equivalent to 1200 times the base 2 logarithm of the frequency ratio.

[from John Chalmers, Divisions of the Tetrachord]