Operations on MOSes: Difference between revisions

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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 a1X1 ... arXr with r step sizes X1 > ... > Xr, we call the set of patterns

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

{aπ(1)X1 ... aπ(r)Xr : π a permutation on {1, ..., r}}

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 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
+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
 {a<sub>π(1)</sub>X<sub>1</sub> ... a<sub>π(r)</sub>X<sub>r</sub> : π a permutation on {1, ..., r}}