Monotone-MOS property - Revision history

Inthar: Redirected page to Aberrisma#Glossary

2025-12-17T21:38:23Z

← Older revision		Revision as of 21:38, 17 December 2025
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	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''.		#redirect [[Aberrisma#Glossary]]

	~~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. 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 terms~~]]

Inthar at 21:31, 17 December 2025

2025-12-17T21:31:20Z

← Older revision		Revision as of 21:31, 17 December 2025
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	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.		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. 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)).		Both [[odd-regular]] and [[even-regular]] MV3 scales satisfy all 3 properties and hence are monotone-MOS. 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 terms]]		[[Category:Aberrismic terms]]

Inthar at 21:01, 17 December 2025

2025-12-17T21:01:04Z

← Older revision		Revision as of 21:01, 17 December 2025
Line 3:		Line 3:
	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.		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)).		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. 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 terms]]		[[Category:Aberrismic terms]]

Inthar at 21:00, 17 December 2025

2025-12-17T21:00:33Z

← Older revision		Revision as of 21:00, 17 December 2025
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	The term ''monotone-MOS'' was coined by Tom Price.		The term ''monotone-MOS'' was coined by Tom Price.

	[[Category:Aberrismic ~~theory~~]]		[[Category:Aberrismic terms]]

Inthar: Created page with "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...."

2025-12-17T21:00:06Z

Created page with "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...."

New page

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.

[[Category:Aberrismic theory]]