Operations on MOSes: Difference between revisions

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-== Sistering ==
+== Sister MOS ==
-'''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).
+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).
 The ''sisterhood'' of xL ys is the set {xL ys, yL xs}. More generally, given an r-step 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