Odd-regular MV3 scale: Difference between revisions
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An [[Interval variety|MV3]] (maximum variety 3) scale is '''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]]. | ||
== Properties == | |||
* Odd-regular MV3 scales always satisfy all 3 of the [[monotone-MOS scale|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 [[chirality|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]] | |||
[[Category:Terms]][[Category:Scale]][[Category:Aberrismic theory]] | |||
Latest revision as of 15:37, 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.
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.