Definitions of tuning terms

© 1998 by Joseph L. Monzo

All definitions by Joe Monzo unless otherwise cited


12-EQ


    My abbreviation for the usual and familiar 12-tone equal-tempered scale, the standard scale tuning used on keyboard, fretted string, and woodwind and brass instruments.

    It is calculated by taking the twelfth root of each successive power of 2, from 0 to 11, with higher or lower "octaves" of these 12 notes assumed to be, and tuned as, equivalents. The 12th root of 2 can also be written as 2(1/12), the next degree, the 12th root of 22, as 2(2/12), etc., which is the way I normally write it on this website.

    Any number to the 0th power equals 1, so the starting note of the scale, or 2(0/12), has the ratio 1:1.

    Exponents which have numerators which are multiples of 12 form "octaves", as in the following:

    2(12/12)=21=the ratio 2:1=the "octave",
    2(24/12)=22=the ratio 4:1=2 "octaves",
    2(36/12)=23=the ratio 8:1=3 "octaves",

    These proportions, the origin and its octaves, are obviously all powers of 2. All other divisions in this scale are proportions known as irrational numbers.

    As a result, this scale was never tuned with absolute precision, with the exception of the "octaves" of the starting-note, until just a few decades ago, with the introduction of electronic and digital instruments and tuners.

    It is frequently abbreviated as 12-ET or 12tET by others.

    [from Joe Monzo, JustMusic: A New Harmony]


  • For many more diagrams and explanations of historical tunings, see my book.

  • If you don't understand my theory or the terms I've used, start here.



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