Even-regular MV3 scale: Difference between revisions

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== Properties ==

Another characterization of even-regular MV3 scales is that it is a ternary one-to-one detempering of a 2-period MOS word M(X, z) which has the form w(x, y, z)w(y, x, z) for some ternary word w and some permutation x, y, z of L, m, s where x and y always alternate in the scale. One even-regular MV3 scale is the achiral variant of [[diachrome]].

In terms of [[guide frame]]s and interleaved scales, in even-regular MV3 scales the [[interleaved scale|interleaving offset]] is generated by the guided generator sequence GS(g), and the 2-note strand scale [0, len(scale)/2-step] is the offset for the guide frame. The other type of generator-offset scale is represented by scales including bipentatonic scales (such as [[blackdye]]), where the strand is generated by GS(g) and the interleaving offset is the offset.

Even-regular MV3 scales are MV3 (but not SV3), and by the [[ternary scale theorems|MV3 classification theorem]] a balanced single-period MV3 scale that has an even number of notes is always even-regular MV3 and has [[step signature]] aXaYbZ where a is odd and b is even.

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== See also ==

* [[Odd-regular MV3 scale]]

* [[Ternary scale theorems]]

[[Category:Aberrismic theory]]

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 == Properties ==
 Another characterization of even-regular MV3 scales is that it is a ternary one-to-one detempering of a 2-period MOS word M(X, z) which has the form w(x, y, z)w(y, x, z) for some ternary word w and some permutation x, y, z of L, m, s where x and y always alternate in the scale. One even-regular MV3 scale is the achiral variant of [[diachrome]].
-In terms of [[guide frame]]s and interleaved scales, in even-regular MV3 scales the [[interleaved scale|interleaving offset]] is generated by the guided generator sequence GS(g), and the 2-note strand scale [0, len(scale)/2-step] is the offset for the guide frame. The other type of generator-offset scale is represented by scales including bipentatonic scales (such as [[blackdye]]), where the strand is generated by GS(g) and the interleaving offset is the offset.
 Even-regular MV3 scales are MV3 (but not SV3), and by the [[ternary scale theorems|MV3 classification theorem]] a balanced single-period MV3 scale that has an even number of notes is always even-regular MV3 and has [[step signature]] aXaYbZ where a is odd and b is even.
@@ Line 20: / Line 18: @@
 == See also ==
 * [[Odd-regular MV3 scale]]
+* [[Ternary scale theorems]]
 [[Category:Aberrismic theory]]