Operations on MOSes: Difference between revisions

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== Neutralization ==

Given a MOS pattern ''x''L ''y''s, '''neutralization''' is the process in which pairs of large and small steps are each replaced with two neutral mossteps, whose size is defined as n = (L+s) / 2, with respect to the original ~~mos~~.

Given a MOS pattern ''x''L ''y''s, '''neutralization''' is the process in which pairs of large and small steps are each replaced with two neutral mossteps, whose size is defined as n = (L+s) / 2, with respect to the original scale.

{| class="wikitable"

|+Example with 5L 2s neutralized to 3L 4s

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* Neutral step becomes the small step as it's smaller than the original large step.

|}

The neutralized MOS has a quantity of neutral mossteps that is twice that of min(''x'', ''y''), and a quantity of remaining large or small steps that is abs(''x''-''y''). This scale has the same number of steps as the original, but with different sizes of L and s ~~compared to~~ the original.

The neutralized MOS has a quantity of neutral mossteps that is twice that of min(''x'', ''y''), and a quantity of remaining large or small steps that is abs(''x''-''y''). This scale has the same number of steps as the original, but with one step size that is different from the original. Since the size of a neutral step is, by definition, between the sizes of a large and small step (as it's the average of the two step sizes), whether the neutral step becomes the new large or small steps solely depends on the number of large or small steps in the original scale:

Since the size of a neutral step is, by definition, between the sizes of a large and small step (as it's the average of the two step sizes), whether the neutral step becomes the new large or small steps solely depends on the number of large or small steps in the original scale:

* If there are more large steps than small steps in the original scale (that is, if in ''x''L ''y''s, x > y), then the neutral step becomes the small step and the original large step becomes the new scale's large step. The neutralized scale is ''(x-y)''L 2''y''s.

* If there are more small steps than large steps in the original scale (that is, if in ''x''L ''y''s, x < y), then the neutral step becomes the large step and the original small step becomes the new scale's small step. The neutralized scale is 2''x''L ''(y''-''x)''s.

* If there are more large steps than small steps (that is, if in ''x''L ''y''s, x > y), then the neutral step becomes the small step and the original large step becomes the new scale's large step.

* If the number of large and small steps is the same in the original scale, the the neutralized scale is an equal division of the octave with ''x''+''y'' divisions. In other words, the large and small steps are [[equalized]].

* If there are more small steps than large steps (that is, if in ''x''L ''y''s, y ~~< x~~), then the neutral step becomes the large step and the original small step becomes the new scale's small step.

* If the number of large and small steps is the same, the the neutralized scale is an equal division of the octave with ''x''+''y'' divisions. In other words, the large and small steps are [[equalized]].

Examples:

@@ Line 40: / Line 40: @@
 == Neutralization ==
-Given a MOS pattern ''x''L ''y''s, '''neutralization''' is the process in which pairs of large and small steps are each replaced with two neutral mossteps, whose size is defined as n = (L+s) / 2, with respect to the original mos.
+Given a MOS pattern ''x''L ''y''s, '''neutralization''' is the process in which pairs of large and small steps are each replaced with two neutral mossteps, whose size is defined as n = (L+s) / 2, with respect to the original scale.
 {| class="wikitable"
 |+Example with 5L 2s neutralized to 3L 4s
@@ Line 63: / Line 63: @@
 * Neutral step becomes the small step as it's smaller than the original large step.
 |}
-The neutralized MOS has a quantity of neutral mossteps that is twice that of min(''x'', ''y''), and a quantity of remaining large or small steps that is abs(''x''-''y''). This scale has the same number of steps as the original, but with different sizes of L and s compared to the original.
+The neutralized MOS has a quantity of neutral mossteps that is twice that of min(''x'', ''y''), and a quantity of remaining large or small steps that is abs(''x''-''y''). This scale has the same number of steps as the original, but with one step size that is different from the original. Since the size of a neutral step is, by definition, between the sizes of a large and small step (as it's the average of the two step sizes), whether the neutral step becomes the new large or small steps solely depends on the number of large or small steps in the original scale:
-Since the size of a neutral step is, by definition, between the sizes of a large and small step (as it's the average of the two step sizes), whether the neutral step becomes the new large or small steps solely depends on the number of large or small steps in the original scale:
+* If there are more large steps than small steps in the original scale (that is, if in ''x''L ''y''s, x > y), then the neutral step becomes the small step and the original large step becomes the new scale's large step. The neutralized scale is ''(x-y)''L 2''y''s.
+* If there are more small steps than large steps in the original scale (that is, if in ''x''L ''y''s, x < y), then the neutral step becomes the large step and the original small step becomes the new scale's small step. The neutralized scale is 2''x''L ''(y''-''x)''s.
-* If there are more large steps than small steps (that is, if in ''x''L ''y''s, x > y), then the neutral step becomes the small step and the original large step becomes the new scale's large step.
+* If the number of large and small steps is the same in the original scale, the the neutralized scale is an equal division of the octave with ''x''+''y'' divisions. In other words, the large and small steps are [[equalized]].
-* If there are more small steps than large steps (that is, if in ''x''L ''y''s, y < x), then the neutral step becomes the large step and the original small step becomes the new scale's small step.
-* If the number of large and small steps is the same, the the neutralized scale is an equal division of the octave with ''x''+''y'' divisions. In other words, the large and small steps are [[equalized]].
 Examples: