Even-regular MV3 scale

A diregular scale is a type of scale with even notes. A diregular 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 diregular scale. One example is the achiral variant of diachrome.

In terms of guide frames and interleaved scale, in diregular 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.

The term diregular has been coined by akselai and Inthar.

By the MV3 classification theorem, a balanced MV3 scale that has an even number of notes is always diregular and has step signature aXaYbZ where b is even.