Monotone-MOS scale

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.