Operations on MOSes: Difference between revisions

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== ~~Inversion~~ ==

== Sisterization ==

'''~~Inversion~~''' 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~~. (We also use~~ the ~~term for the resulting MOS pattern~~.) 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. Inverted MOS patterns 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.

Examples:

* [[2L 5s]] is ~~inverted~~ [[5L 2s]] (anti-diatonic)

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

* [[3L 5s]] is ~~inverted~~ [[5L 3s]] (anti-oneirotonic)

* [[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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-== Inversion ==
+== Sisterization ==
-'''Inversion''' 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. (We also use the term for the resulting MOS pattern.) 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. Inverted MOS patterns 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.
 Examples:
-* [[2L 5s]] is inverted [[5L 2s]] (anti-diatonic)
+* [[2L 5s]] is the sister of [[5L 2s]] (anti-diatonic)
-* [[3L 5s]] is inverted [[5L 3s]] (anti-oneirotonic)
+* [[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.