Odd-regular MV3 scale: Difference between revisions

@@ Line 1: / Line 1: @@
-An [[Interval variety|SV3]] 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 SV3 scales are regular with the sole exception of '''XYXZXYX''' up to permutation.
+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]]