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