User:Ganaram inukshuk/MOS scale: Difference between revisions

An alternate definition of a multi-period MOS scale is a MOS scale in which the quantities of large and small steps are ''not'' coprime.

A moment-of-symmetry scale of ''x'' large steps and ''y'' small steps, where ''x'' and ''y'' are whole numbers, is denoted using the [[scale signature]] ''x''L ''y''s. In cases where one does not wish to distinguish between step sizes, the notation ''x''A ''y''B can be used instead, which can either refer to ''x''L ''y''s or ''y''L ''x''s.

By default, the [[Equave|equivalence interval]], or equave, of a MOS scale is assumed to be the [[octave]]. In discussions regarding MOS scales with [[non-octave]] equivalence intervals, the equivalence interval can be enclosed in angle brackets of either < > (less-than and greater-than symbols) or {{Angbr|&nbsp;}} (Unicode symbols U+27E8 and U+27E9). Whereas "5L 2s", for example, refers to an octave-equivalent pattern of 5 large and 2 small steps, 5L 2s{{Angbr|3/1}} refers to the same pattern but with 3/1 as the equivalence interval. To avoid conflicts with HTML tags, the use of Unicode symbols is advised over the former.

Although the most unambiguous way to refer to a MOS scale is by its scale signature, several naming schemes have been created that assign unique names to them. For a discussions on such names, see [[MOS naming]].

== Properties ==

<original stuff below here>

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: [http://anaphoria.com/mos.PDF ''Moments of Symmetry'']. There is also an introduction by Kraig Grady here: [http://anaphoria.com/wilsonintroMOS.html ''Introduction to Erv Wilson's Moments of Symmetry''].

As for using MOS scales in practice for making music, the period and equivalence interval are often taken to be the octave, but an additional parameter is required for defining a scale: the ''step ratio'', which is the ratio of the small step (usually denoted ''s'') to the large step (usually denoted ''L''). This is usually written as ''L''/''s'', however, using ''s''/''L'' has the advantage of avoiding division by zero in the trivial case where ''s'' = 0. Different step ratios can produce very varied sounding scales (and very varied corresponding potential temperament interpretations) for a given MOS pattern and period, so it's useful to consider a spectrum of simple step ratios for tunings. The [[TAMNAMS #Step ratio spectrum|TAMNAMS]] system has names for both specific ratios and ranges of ratios.

===Basic properties===

*Every MOS scale has two ''child MOS'' scales. The two children of the MOS scale ''a''L ''b''s are (''a'' + ''b'')L as (generated by generators of soft-of-basic ''a''L''b''s) and ''a''L (''a'' + ''b'')s (generated by generators of hard-of-basic ''a''L''b''s).

*Every MOS scale (with a specified [[equave]] ''E''), excluding ''a''L ''a''s⟨''E''⟩, has a ''parent MOS''. If ''a'' > ''b'', the parent of ''a''L ''b''s is min(''a'', ''b'')L|''a'' &minus; ''b''|s; if ''a'' < ''b'', the parent of ''a''L ''b''s is |''a'' &minus; ''b''|L min(''a'', ''b'')s.

See:

*[[Mathematics of MOS]], a more formal definition and a discussion of the mathematical properties.

*[[MOS Cradle]] is a technique of embedding MOS-like structures inside MOS scales and may or may not produce subsets of MOS scales.

*[[Operations on MOSes]]

{{Main| MOS rhythm }}

*[[Diamond-mos notation]], a microtonal notation system focussed on MOS scales

*[[Metallic MOS]], an article focusing on MOS scales based on metallic means, such as [[phi]]

*[[Gallery of MOS patterns]]<!-- sort order in category: this page shows above A -->