Definitions of tuning terms

© 1998 by Joseph L. Monzo

All definitions by Joe Monzo unless otherwise cited


moment of symmetry, MOS


    A term coined by Erv Wilson in 1975. The process of producing a scale of melodic integrity by the superposition of a single interval (generator). Those points where there are only 2 different size intervals are called moments of symmetry. This cycle has the property that any occurrence of an interval will always be subtended by the same number of steps.

    When a harmonic system is used instead of a single interval and all the melodic gaps are filled the scale is referred to as a constant structure.

    It has been found useful to utilize deeper levels within the MOS. The best example of this Bifocal MOS are the pentatonics taken from the Diatonic. Here from a Parent MOS (Diatonic) another smaller MOS (Pentatonics) set can be found which, although it will not have the property of every interval being subtended by the same number of steps, the generator interval (fourth or fifth) will be.

    [from Kraig Grady]


(to download a zip file of the entire Dictionary, click here)

  • 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
  • I welcome feedback about this webpage:
    corrections, improvements, good links.
    Let me know if you don't understand something.


    return to the Microtonal Dictionary index
    return to my home page
    return to the Sonic Arts home page