|
|
I welcome
feedback about this webpage:
 |
Definitions of tuning terms
© 1998 by Joseph L. Monzo
All definitions by Joe Monzo unless otherwise cited
generator
Refers to an interval whose distance is repeated
over and over again until it closes or nearly closes
a cycle.
The "cycle of 5ths" illustrates one example,
in which reference is made to a large number of different scales
or tuning systems
built from a generator whose size is approximately that
of a "perfect 5th", typically anywhere from about 680
to 720 cents. All
meantone tunings fall
into this category, as well as a number of other tunings.
Pythagorean tuning is probably
the oldest and longest-lasting example of this cycle.
Outside of
microtonal music-theory,
this particular cycle (of "5ths") ordinarily designates the cycle
arising from the
12-EDO tuning system, in which
case the generator is an "5th" with an
interval of 700 cents.
Alternatively, the 12-EDO
tuning can also be viewed as having a generator the size of a
"4th" of
500 cents (the "cycle of 4ths"), or as a
semitone of 100 cents (the
chromatic
scale).
In all of these cases, assuming
"octave"-equivalence, the
12th instance of the generator returns exactly to the
pitch-class
of the original note, thus closing the cycle to
12 pitches, an example of finity.
In April 2001, an investigation by Dave Keenan of the properties
of scales built from various generators resulted in the rediscovery
of the
MIRACLE
scale, from which Paul Erlich derived the
"Blackjack" scale.
See MIRACLE
and decimal notation,
and my
55-EDO webpage,
for examples of how scales are built with a generator.
See also MOS
1.
2.
In periodicity-block theory,
there are small intervals called
unison-vectors, a select few
of which are able to generate a kernel, which
in JI is the periodicity-block
enclosing a finite set of ratios
on the lattice.
[from Joe Monzo, JustMusic: A New Harmony]
|
(to download a zip file of the entire Dictionary, click here) |
|
|
I welcome
feedback about this webpage:
|