Even-regular MV3 scale: Difference between revisions
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* 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]]. | * 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]]. | ||
* 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. | * 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. | ||
* Even-regular MV3 scales are [[chirality|achiral]]. | * Even-regular MV3 scales are [[chirality|achiral]]. There is only one even-regular MV3 scale pattern for a given scale signature if it exists. | ||
== Terminology == | == Terminology == | ||