Odd-regular MV3 scale

An MV3 (maximum variety 3) scale is regular if it has an odd number of notes per equave and has a step signature of the form aXaYbZ where b is odd. All balanced SV3 (strict variety 3) scales are regular with the sole exception of the ternary Fraenkel word XYXZXYX up to permutation. A balanced MV3 (maximum variety 3) scale is regular (equivalently SV3) if and only if it is not diregular.

Regular MV3 scales always satisfy all 3 of the monotone-MOS conditions.