Definitions of tuning terms

© 1998 by Joseph L. Monzo

All definitions by Joe Monzo unless otherwise cited


quarter-tone


  • 1. Used in a general sense by many people to refer to microtonal intervals approximately half as large as the semitone, or thus measuring approximately 50 cents.

    There is less of a tendency to use it in this general sense today.

  • 2. Used as an exact measurement, it is calculated as the 24th root of 2, or 2(1/24), an irrational proportion with the approximate ratio of 1:1.029302236643, and an interval size of exactly 50 cents.

    It is the size of one degree, and thus the basic "step" size, in the 24-eq (or 24-ET) scale, also called the "quarter-tone scale" or system.

  • Several composers began composing in 24-ET early in the 20th century, including Charles Ives, Ivan Vyschnegradsky, and Alois Hába. Hába had several instruments specially built to be playable in this system.

    [from Joe Monzo, JustMusic: A New Harmony]

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    An interval of about 50 cents (¢), one half of a tempered semitone. [Chalmers here means specifically 12-tone equal temperament. -Monzo]

    Typical quarter tones in Just Intonation have ratios such as 36/35 or 33/34.

    [from John Chalmers, Divisions of the Tetrachord]


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