# MOS scale

## Contents

# Definition

An **MOS** or **Moment Of Symmetry** is a scale in which every interval except for the period comes in two sizes. The term "MOS," and the method of scale construction it entails, were invented by Erv Wilson in 1975. His original paper is archived on Anaphoria.com here: Moments of Symmetry. There is also an introduction by Kraig Grady here: Introduction to Erv Wilson's Moments of Symmetry.

Sometimes, scales are defined with respect to a period and an additional "equivalence interval," considered to be the interval at which pitch classes repeat. MOS's in which the equivalence interval is a multiple of the period, and in which there is more than one period per equivalence interval, are sometimes called **Multi-MOS's**. MOS's in which the equivalence interval is equal to the period are sometimes called **Strict MOS'**s. MOS's in which the equivalence interval and period are simply disjunct, with no rational relationship between them, are simply MOS and have no additional distinguishing label.

With a few notable exceptions, Wilson generally focused his attention on MOS with period equal to the equivalence interval. Hence, some people prefer to use the term distributionally even scale, with acronym DE, for the more general class of scales which are MOS with respect to other intervals. MOS/DE scales are also sometimes known as *well-formed scales*, the term used in the 1989 paper by Norman Carey and David Clampitt. A great deal of interesting work has been done on scales in academic circles extending these ideas. The idea of MOS also includes secondary or bi-level MOS scales which are actually the inspiration of Wilsons' concept. They are in a sense the MOS of MOS patterns. This is used to explain the pentatonics used in traditional Japanese music, where the 5 tone cycles are derived from a 7 tone MOS, which are not found in the concept of DE.

## Mathematics

See:

- Mathematics of MOS, a more formal definition and a discussion of the mathematical properties.
- Generator ranges of MOS, organized by number of scale steps and quantity of L/s steps.
- MOS Diagrams, visualizations of the MOS process.

# Names for MOS

Since numbers tend to be dry, Graham Breed has proposed a naming scheme for MOS scales. See the Catalog of MOS for a listing of MOS in the more usual Ls scheme. See also the pergens page.

# Variations on MOS Scales

- MODMOS Scales are derived from chromatic alterations of one or more tones of an MOS scale, typically by the interval of L-s, the "chroma".
- Muddles are subsets of MOS parent scales with the general shape of a smaller (and possibly unrelated) MOS scale.
- MOS Cradle is a technique of embedding MOS-like structures inside MOS scales and may or may not produce subsets of MOS scales.

# MOS As Applied To Rhythms

David Canright was the first to suggest Fibonacci Rhythms in 1/1. This led to Kraig Grady to be the first to apply MOS patterns to rhythms. Two papers on the subject can be found here:

- A Rhythmic Application of the Horagrams from Xenharmonikon 16
- More on Horogram Rhythms.

MOS structures and thinking can be applied to the design of rhythms as well. See MOS Rhythm Tutorial