Odd-regular MV3 scale: Difference between revisions
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An [[Interval variety|MV3]] (maximum variety 3) scale is '''odd-regular''' if it has an odd number of notes per | An [[Interval variety|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 a'''X'''a'''Y'''b'''Z''' 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 MV3 scale|even-regular]]. | ||
Odd-regular MV3 scales always satisfy all 3 of the [[monotone-MOS scale|monotone-MOS]] conditions. | Odd-regular MV3 scales always satisfy all 3 of the [[monotone-MOS scale|monotone-MOS]] conditions. | ||
Revision as of 15:12, 4 January 2025
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.