Operations on MOSes: Difference between revisions

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== Sisterization ==

'''Sisterization''' is the operation of taking a MOS pattern xL ys and reversing the roles of large and small steps, thus creating a yL xs pattern, called the ''sister'' of xL ys. ~~Inverted~~ MOS patterns are often denoted with the prefix ''anti-''.

'''Sisterization''' is the operation of taking a MOS pattern xL ys and reversing the roles of large and small steps, thus creating a yL xs pattern, called the ''sister'' of xL ys. It is called thus because they share the same MOS as a subset (for example, [[5L 2s]] and [[2L 5s]] both have [[2L 3s]] subsets), which is the parent on the tree of MOS patterns (closely related to the Stern-Brocot tree). A sister of a MOS pattern are often denoted with the prefix ''anti-''.

If xL ys has a generator range between a\x and b\(x+y) (it always holds that a < b), then its ~~inversion~~ yL xs has a generator range between b\(x+y) and (b-a)\y.

If xL ys has a generator range between a\x and b\(x+y) (it always holds that a < b), then its sister yL xs has a generator range between b\(x+y) and (b-a)\y.

Examples:

* [[2L 5s]] is the sister of [[5L 2s]] (anti-diatonic)

* [[3L 5s]] is the sister [[5L 3s]] (anti-oneirotonic)

== Neutralization ==

'''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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 == Sisterization ==
-'''Sisterization''' is the operation of taking a MOS pattern xL ys and reversing the roles of large and small steps, thus creating a yL xs pattern, called the ''sister'' of xL ys. Inverted MOS patterns are often denoted with the prefix ''anti-''.
+'''Sisterization''' is the operation of taking a MOS pattern xL ys and reversing the roles of large and small steps, thus creating a yL xs pattern, called the ''sister'' of xL ys. It is called thus because they share the same MOS as a subset (for example, [[5L 2s]] and [[2L 5s]] both have [[2L 3s]] subsets), which is the parent on the tree of MOS patterns (closely related to the Stern-Brocot tree). A sister of a MOS pattern are often denoted with the prefix ''anti-''.
-If xL ys has a generator range between a\x and b\(x+y) (it always holds that a < b), then its inversion yL xs has a generator range between b\(x+y) and (b-a)\y.
+If xL ys has a generator range between a\x and b\(x+y) (it always holds that a < b), then its sister yL xs has a generator range between b\(x+y) and (b-a)\y.
 Examples:
 * [[2L 5s]] is the sister of [[5L 2s]] (anti-diatonic)
 * [[3L 5s]] is the sister [[5L 3s]] (anti-oneirotonic)
 == Neutralization ==
 '''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.