Monotone-MOS scale: Difference between revisions

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A [[ternary scale]] in L, M~~, and~~ s is '''monotone-MOS''' if it becomes a MOS under all three of the identifications L = M, M = s, and s = 0. If ''any'' (not necessarily all) of the identifications make the scale a MOS, the scale is said to ''satisfy ~~'''~~a~~'''~~ monotone-MOS ~~property~~''. ~~This property is~~ used in [[aberrismic theory]].

A [[ternary scale]] in L > M > s > 0 is '''monotone-MOS''' if it becomes a MOS under all three of the identifications L = M, M = s, and s = 0. If ''any'' (not necessarily all) of the identifications make the scale a MOS, the scale is said to ''satisfy a monotone-MOS subcondition''.

The monotone-MOS subconditions are used in [[aberrismic theory]]. An aberrismic scale is required to satisfy the s = 0 monotone-MOS subcondition.

Both [[Odd-regular MV3 scale|odd-regular]] and [[even-regular MV3 scale|even-regular]] MV3 scales satisfy all 3 subconditions and hence are monotone-MOS, from the stronger property that they are both [[pairwise-MOS]] and [[deletion-MOS scale]]s. However, scales that are monotone-MOS need not be odd-regular, even-regular or MV3; a counterexample is the 7L10m5s scale LmmLsmLmsLmmLsmLmsmLms (which is, however, a [[MOS substitution]] scale subst 7L(10m5s)).

The term ''monotone-MOS'' was coined by Tom Price.

[[Category:Aberrismic theory]]

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-A [[ternary scale]] in L, M, and s is '''monotone-MOS''' if it becomes a MOS under all three of the identifications L = M, M = s, and s = 0. If ''any'' (not necessarily all) of the identifications make the scale a MOS, the scale is said to ''satisfy '''a''' monotone-MOS property''. This property is used in [[aberrismic theory]].
+A [[ternary scale]] in L > M > s > 0 is '''monotone-MOS''' if it becomes a MOS under all three of the identifications L = M, M = s, and s = 0. If ''any'' (not necessarily all) of the identifications make the scale a MOS, the scale is said to ''satisfy a monotone-MOS subcondition''.
+The monotone-MOS subconditions are used in [[aberrismic theory]]. An aberrismic scale is required to satisfy the s = 0 monotone-MOS subcondition.
+Both [[Odd-regular MV3 scale|odd-regular]] and [[even-regular MV3 scale|even-regular]] MV3 scales satisfy all 3 subconditions and hence are monotone-MOS, from the stronger property that they are both [[pairwise-MOS]] and [[deletion-MOS scale]]s. However, scales that are monotone-MOS need not be odd-regular, even-regular or MV3; a counterexample is the 7L10m5s scale LmmLsmLmsLmmLsmLmsmLms (which is, however, a [[MOS substitution]] scale subst 7L(10m5s)).
 The term ''monotone-MOS'' was coined by Tom Price.
 [[Category:Aberrismic theory]]