Definitions of tuning terms

© 1998 by Joseph L. Monzo

All definitions by Joe Monzo unless otherwise cited


just intonation


    a system of tuning based on notes whose frequencies have small-integer rational relationships.

    The scales produced are almost always unequally-spaced, and usually exhibit various types of symmetry.

    When unqualified, "just intonation" generally means a 5-limit tuning, as described in my paper. Systems with a higher limit are frequently called extended just intonation.

    A cycle of 3/2s ["5ths"], or of any other just ratio, will never return exactly to the frequency of the origin.

    [from Joe Monzo, JustMusic: A New Harmony]

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

    Any tuning system which exclusively employs intervals defined by ratios of integers may be called Just Intonation, though some authors restrict it to systems whose intervals are derived from the first six overtones, 1, 2, 3, 4, 5, and 6. Such systems are often termed "Five Limit" or "Senary" systems after Zarlino's "senario" (Partch, 1949, 1974, 1979). The most common example of such a system is the tuning of the Major Mode as 1/1 9/8 5/4 4/3 3/2 5/3 15/8 and 2/1.

    Just Intonation is contrasted to Equal Temperament and Unequal Temperaments such as Meantone which combine rational with irrational intervals.

    [from John Chalmers, Divisions of the Tetrachord]


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