Operations on MOSes: Difference between revisions

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 == Dualization ==
-'''Dualization''' creates new MOS patterns from a MOS pattern in a specific EDO by swapping step sizes with step frequencies.
+Given a MOS pattern ''x''L ''y''s with concrete step sizes L and s, '''dualization''' is the process in which the values of ''x'' and L are swapped, the values of ''y'' and s are swapped, or both are swapped. This is not to be confused with the sister operation.
-xL ys can be read as a formula: ''x'' * ''L'' + ''y'' * ''s'' = edo-size. From this formula it is clear we can swap for example ''x'' (the number of L-steps) with ''L'' (the size of the L-step) to get a new MOS scale in the same EDO, this is called the '''L-dual'''. Similarly we have the '''s-dual''' and when swapping both we get the '''Ls-dual''' (or just the '''dual''').
-For example, take 5L 2s in 43 EDO, with L=7 and s=4:
-* The L-dual is 7L 2s with L=5 and s=4
-* The s-dual is 5L 4s with L=7 and s=2
-* The Ls-dual is 7L 4s with L=5 and s=2
+Depending on which values are swapped, a different MOS scale is produced; however, the relationship between these scales depends on the sizes of L and s, and since ''x * L + y * s'', these relationships also depends on the edo. Additionally, it's possible for a dual to be itself, if either ''x'' and L are the same or ''y'' and s are the same.
+{| class="wikitable"
+|+Example with 5L 2s in 43edo
+!MOS
+!Step pattern
+!Notes about step sizes
+!Step visualization
+|-
+|5L 2s
+|LLLsLLs
+|L = 7, s = 4
+Original scale
+|{{Step vis|7 7 7 4 7 7 4}}
+|-
+|7L 2s
+|LLLLsLLLs
+|L = 5, s = 4
+L-dual, as ''x'' and L are swapped
+|{{Step vis|5 5 5 5 4 5 5 5 4}}
+|-
+|5L 4s
+|LLsLsLsLs
+|L = 7, s = 2
+s-dual, as ''y'' and s are swapped
+|{{Step vis|7 7 2 7 2 7 2 7 2}}
+|-
+|7L 4s
+|LLsLLsLLsLs
+|L = 5, s = 2
+Ls-dual, as ''x'' and L are swapped, as are ''y'' with s
+|{{Step vis|5 5 2 5 5 2 5 5 2 5 2}}
+|}
 [[Category:MOS scale]]