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]

    ...............................

    (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]


Updates:

2002.09.23
2000.08.07


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