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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