Operations on MOSes: Difference between revisions

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This page describes common operations that can be performed on [[MOS scale|MOS scales]].

== Parent MOS ==

Given a MOS pattern xL ys, its '''parent''' is obtained by merging pairs of large and small steps together, creating a subset MOS. Mathematically, the parent MOS of zL ws is found by finding the values of z and w:

* Calculate z to be the smaller value of x and y, or min(x, y).

* Calculate w to be the absolute difference between x and y, or abs(x, y).

Examples:

* The parent of 5L 2s is 2L 3s.

* The parent of 2L 5s is 2L 3s.

* The parent of 5L 3s is 3L 2s.

== Sister MOS ==

Given a MOS pattern xL ys, its '''sister''' is obtained by reversing the roles of large and small steps, thus creating a yL xs pattern. It is called thus because a MOS pattern and its sister share the same ~~MOS as a subset~~ (for example, [[5L 2s]] and [[2L 5s]] both have [[2L 3s]] subsets), thus they share the same parent on the tree of MOS patterns (which corresponds to the [[scale tree]], via taking generator ranges).

Given a MOS pattern xL ys, its '''sister''' is obtained by reversing the roles of large and small steps, thus creating a yL xs pattern. It is called thus because a MOS pattern and its sister share the same parent (for example, [[5L 2s]] and [[2L 5s]] both have [[2L 3s]] subsets), thus they share the same parent on the tree of MOS patterns (which corresponds to the [[scale tree]], via taking generator ranges).

The ''sisterhood'' of xL ys is the set {xL ys, yL xs}. More generally, given a scale pattern a1X1 ... arXr with r step sizes X1 > ... > Xr, we call the set of patterns

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Examples:

* [[2L 5s~~]] is the~~ sister of [[5L ~~2s]] (~~and is ~~often~~ called the ~~anti-diatonic~~).

* The sister of 5L 2s is 2L 5s.

* ~~[[3L 5s]]~~ is the sister of [[5L 3s]].

* The sister of 5L 3s is 3L 5s.

== Daughter MOSes ==

Given a MOS pattern xL ys, its two possible '''daughters''' are obtained by splitting its large steps into two more smaller steps ''s'' and ''c'', where ''s'' is equal to the original small step and ''c'' (also called the ''chroma'') is the difference between a large step and small step. The daughters have two forms:

* (x+y)L xs, where splitting the original large step results in ''s'' being larger than ''c''. Here, ''s'' and ''c'' become the large and small steps, respectively.

* xL (x+y)s, where splitting the original large step results in ''c'' being larger than ''s''. Here, ''c'' and s become the large and small steps, respectively. This is also the sister of (x+y)L xs.

Examples:

* The daughters of 5L 2s are 7L 5s and 5L 7s.

* The daughters of 5L 3s are 8L 5s and 5L 8s.

== Neutralization ==

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+This page describes common operations that can be performed on [[MOS scale|MOS scales]].
+== Parent MOS ==
+Given a MOS pattern xL ys, its '''parent''' is obtained by merging pairs of large and small steps together, creating a subset MOS. Mathematically, the parent MOS of zL ws is found by finding the values of z and w:
+* Calculate z to be the smaller value of x and y, or min(x, y).
+* Calculate w to be the absolute difference between x and y, or abs(x, y).
+Examples:
+* The parent of 5L 2s is 2L 3s.
+* The parent of 2L 5s is 2L 3s.
+* The parent of 5L 3s is 3L 2s.
 == Sister MOS ==
-Given a MOS pattern xL ys, its '''sister''' is obtained by reversing the roles of large and small steps, thus creating a yL xs pattern. It is called thus because a MOS pattern and its sister share the same MOS as a subset (for example, [[5L 2s]] and [[2L 5s]] both have [[2L 3s]] subsets), thus they share the same parent on the tree of MOS patterns (which corresponds to the [[scale tree]], via taking generator ranges).
+Given a MOS pattern xL ys, its '''sister''' is obtained by reversing the roles of large and small steps, thus creating a yL xs pattern. It is called thus because a MOS pattern and its sister share the same parent (for example, [[5L 2s]] and [[2L 5s]] both have [[2L 3s]] subsets), thus they share the same parent on the tree of MOS patterns (which corresponds to the [[scale tree]], via taking generator ranges).
 The ''sisterhood'' of xL ys is the set {xL ys, yL xs}. More generally, given a scale pattern a<sub>1</sub>X<sub>1</sub> ... a<sub>r</sub>X<sub>r</sub> with r step sizes X<sub>1</sub> > ... > X<sub>r</sub>, we call the set of patterns
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 Examples:
-* [[2L 5s]] is the sister of [[5L 2s]] (and is often called the anti-diatonic).
+* The sister of 5L 2s is 2L 5s.
-* [[3L 5s]] is the sister of [[5L 3s]].
+* The sister of 5L 3s is 3L 5s.
+== Daughter MOSes ==
+Given a MOS pattern xL ys, its two possible '''daughters''' are obtained by splitting its large steps into two more smaller steps ''s'' and ''c'', where ''s'' is equal to the original small step and ''c'' (also called the ''chroma'') is the difference between a large step and small step. The daughters have two forms:
+* (x+y)L xs, where splitting the original large step results in ''s'' being larger than ''c''. Here, ''s'' and ''c'' become the large and small steps, respectively.
+* xL (x+y)s, where splitting the original large step results in ''c'' being larger than ''s''. Here, ''c'' and s become the large and small steps, respectively. This is also the sister of (x+y)L xs.
+Examples:
+* The daughters of 5L 2s are 7L 5s and 5L 7s.
+* The daughters of 5L 3s are 8L 5s and 5L 8s.
 == Neutralization ==