Operations on MOSes: Difference between revisions

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== Sistering ==

'''Sistering''' 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 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)~~. A sister of a MOS pattern is often denoted with the prefix ''anti-''~~.

'''Sistering''' 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 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).

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).

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

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

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

== Neutralization ==

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 == Sistering ==
-'''Sistering''' 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 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). A sister of a MOS pattern is often denoted with the prefix ''anti-''.
+'''Sistering''' 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 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).
 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).
+* [[2L 5s]] is the sister of [[5L 2s]] (and is ofteb called the anti-diatonic).
-* [[3L 5s]] is the sister of [[5L 3s]] (anti-oneirotonic).
+* [[3L 5s]] is the sister of [[5L 3s]].
 == Neutralization ==