Monotone-MOS scale: Difference between revisions
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A [[ternary scale]] in L | 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 condition''. | ||
The monotone-MOS conditions are used in [[aberrismic theory]]. An aberrismic scale is required to satisfy the s = 0 monotone-MOS condition and at least one other monotone-MOS condition. | |||
Both [[Odd-regular MV3 scale|odd-regular]] and [[even-regular MV3 scale|even-regular]] MV3 scales satisfy all 3 properties 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. | The term ''monotone-MOS'' was coined by Tom Price. | ||
[[Category:Aberrismic theory]] | [[Category:Aberrismic theory]] | ||
Latest revision as of 15:03, 4 January 2025
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 condition.
The monotone-MOS conditions are used in aberrismic theory. An aberrismic scale is required to satisfy the s = 0 monotone-MOS condition and at least one other monotone-MOS condition.
Both odd-regular and even-regular MV3 scales satisfy all 3 properties and hence are monotone-MOS, from the stronger property that they are both pairwise-MOS and deletion-MOS scales. 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.