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:
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]
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",