User:Ganaram inukshuk/MOS scale: Difference between revisions
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=== Erv Wilson's original definition === | === Erv Wilson's original definition === | ||
Erv Wilson | Erv Wilson first described the concept in 1975 in ''Moments of Symmetry''. A moment-of-symmetry scale consists of: | ||
* A generator and an [[equivalence interval]], called the period, which is usually the [[octave]]. | * A generator and an [[equivalence interval]], called the period, which is usually the [[octave]]. | ||
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== Notation and naming== | == Notation and naming== | ||
{{See also|MOS naming}} | {{See also|MOS naming}} | ||
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. | 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. Other notations may use different symbols for ''x''L ''y''s, such as ''a''L ''b''s, but these notations are identical. | ||
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| }} (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. | 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| }} (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. | ||
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=== Step ratio === | === Step ratio === | ||
{{Main | {{Main|Step ratio}}{{See also|TAMNAMS#Step ratio spectrum}} | ||
When it comes to musical applications, the ''step ratio'', the ratio between the size of the scale's large and small step, can have a profound effect on how the overall scale sounds. The step ratio is usually denoted as L:s, to disambiguate it from [[Ratios|frequency ratios]], though the notation s:L is sometimes used to avoid division-by-zero. | When it comes to musical applications, the ''step ratio'', the ratio between the size of the scale's large and small step, can have a profound effect on how the overall scale sounds. The step ratio is usually denoted as L:s, to disambiguate it from [[Ratios|frequency ratios]], though the notation s:L is sometimes used to avoid division-by-zero. | ||
===Relationship between MOS scales=== | ===Relationship between MOS scales=== | ||
{{Main|Operations on MOSes}}{{See also|Recursive structure of MOS scales}}{{See also|MOS scale family tree}} | |||
=== | === Advanced properties === | ||