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| == Naming scheme == | | == Naming scheme == |
| Since numbers tend to be dry, Graham Breed has proposed a [[MOS Naming Scheme|naming scheme for MOS scales]]. See the [[Catalog of MOS]] for a listing of MOS in the more usual Ls scheme. See also the [[pergen]]s page. | | Since numbers tend to be dry, Graham Breed has proposed a [[MOS Naming Scheme|naming scheme for MOS scales]]. See the [[Catalog of MOS]] for a listing of MOS in the more usual Ls scheme. See also the [[pergen]]s page. |
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| == Neutralization operation ==
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| '''Neutralization''' is the operation of taking a MOS pattern and creating a new MOS pattern with the same number of notes, but with some of the steps replaced with what would be "neutral seconds" according to the original MOS pattern.
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| The input to the operation of neutralization is really (MOS pattern, generator range), not just (MOS pattern). MOS pattern alone implies a generator range, but the range is the widest possible generator range that generates the pattern. For example, 4\7 to 3\5 for 5L 2S.
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| When you neutralize a MOS pattern xL yS, you turn whatever step the MOS pattern has less of (let's say that's y, the same thing will work for x if x < y), and replace the y of that step size and y of the other step size into a neutral MOSsecond (i.e. half of Ls). The remaining scale steps (which are all L or all S, depending on whether x > y or x < y) are kept the same. (Note: The input to this operation is not a temperament; different moses of the same temperament can have different neutralizations that suggest different temperaments.) Finally, the resulting scale steps are arranged in a MOS pattern. The resulting pattern is (x-y)L 2yS if x >= y, and 2xL (y-x)S if x <= y.
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| If x = y the resulting scale will just be (x+y)-edo = 2x-edo. For example 5L 5s becomes 10edo.
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| When a scale is neutralized there would be restrictions on the resulting generator size and step sizes; i.e. a neutralized scale would be more than just the MOS pattern itself. For example, a 3L 4s with generator > 3\10 could not result from neutralizing 5L 2s, because the fifth would get too big for a 5L 2s MOS if the generator is > 3\10.
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| Examples:
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| * Neutralizing 5L 2s (gen between 4\7 and 3\5) results in 3L 4s, with generator between 2\7 and 3\10.
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| * Neutralizing 5L 3s (gen between 3\8 and 3\5) results in 2L 6s with period 1\2 (!) and generator between 1\8 and 1\10 (sinaic to flat neutral 2nd).
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| * Neutralizing 2L 5s (gen between 6\11 and 4\7) results in 4L 3s with generator 3\11 to 2\7.
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| == Variations == | | == Variations == |
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| * [[Muddle]]s are subsets of MOS parent scales with the general shape of a smaller (and possibly unrelated) MOS scale. | | * [[Muddle]]s 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 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]] |
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| == As applied to rhythms == | | == As applied to rhythms == |