Even-regular MV3 scale
An even-regular MV3 scale is a type of ternary scale with an even number of notes. An even-regular MV3 scale consists of two identical generator chains, where all generators are identical and subtend the same step class. The two chains are offset by an interval that subtends k steps in a 2k-note even-regular MV3 scale.
Notable even-regular MV3 scales
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 frames and interleaved scales, in even-regular MV3 scales the 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 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 always satisfy all 3 of the monotone-MOS conditions.
Terminology
The term even-regular MV3 has been coined by Inthar.