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 ~~equave~~ 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 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~~ scale|~~diregular~~]].

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]]

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-An [[Interval variety|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 a'''X'''a'''Y'''b'''Z''' 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 scale|diregular]].
+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]]