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.

Properties

• Odd-regular MV3 scales always satisfy all 3 of the monotone-MOS conditions.
• Odd-regular MV3 scales have a generator sequence of period 2 where both generators subtend the same step class (unlike in even-regular MV3 scales).
• Odd-regular MV3 scales are chiral. Ignoring chirality, there is at most one odd-regular MV3 scale pattern for a given step signature.

See also

• Even-regular MV3 scale
• Ternary scale theorems