Definitions of tuning terms

© 1998 by Joseph L. Monzo

All definitions by Joe Monzo unless otherwise cited

generator

    1.

    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


    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]

Updated: 2001.6.28

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