Monotone-MOS scale - Revision history

Inthar at 04:48, 3 March 2026

2026-03-03T04:48:04Z

← Older revision		Revision as of 04:48, 3 March 2026
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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~~''.		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 ~~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 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 ~~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 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.		The term ''monotone-MOS'' was coined by Tom Price.

	[[Category:Aberrismic theory]]		[[Category:Aberrismic theory]]

Inthar at 15:03, 4 January 2025

2025-01-04T15:03:12Z

← Older revision		Revision as of 15:03, 4 January 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.

	[[~~Regular~~ MV3 scale]]s and [[~~diregular~~ scale]]s 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 regular, ~~diregular~~ 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, 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]]

Inthar at 16:56, 3 December 2024

2024-12-03T16:56:43Z

← Older revision		Revision as of 16:56, 3 December 2024
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.

	[[Regular MV3 scale]]s and [[diregular scale]]s 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 regular, diregular or MV3; a counterexample is the 7L10m5s scale LmmLsmLmsLmmLsmLmsmLms.		[[Regular MV3 scale]]s and [[diregular scale]]s 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 regular, diregular 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]]

Inthar at 16:55, 3 December 2024

2024-12-03T16:55:49Z

← Older revision		Revision as of 16:55, 3 December 2024
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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 ~~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 condition''.

	[[Regular MV3 scale]]s satisfy all 3 properties and hence are monotone-MOS, from the stronger property that they are both [[pairwise-MOS]] and [[deletion-MOS scale]]s.		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.

			[[Regular MV3 scale]]s and [[diregular scale]]s 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 regular, diregular or MV3; a counterexample is the 7L10m5s scale LmmLsmLmsLmmLsmLmsmLms.

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

	[[Category:Aberrismic theory]]		[[Category:Aberrismic theory]]

Inthar at 21:50, 14 August 2024

2024-08-14T21:50:42Z

← Older revision		Revision as of 21:50, 14 August 2024
Line 1:		Line 1:
	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 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 property''. This property is used in [[aberrismic theory]].

	[[Regular MV3 scale]]s satisfy all 3 properties and hence are monotone-MOS~~. They~~ are ~~also~~ [[pairwise-MOS]] and [[deletion-MOS scale]]s.		[[Regular MV3 scale]]s satisfy all 3 properties and hence are monotone-MOS, from the stronger property that they are both [[pairwise-MOS]] and [[deletion-MOS scale]]s.

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

	[[Category:Aberrismic theory]]		[[Category:Aberrismic theory]]

Inthar at 21:50, 14 August 2024

2024-08-14T21:50:07Z

← Older revision		Revision as of 21:50, 14 August 2024
Line 1:		Line 1:
	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 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 property''. This property is used in [[aberrismic theory]].

	[[Regular MV3 scale]]s satisfy all 3 properties and hence are monotone-MOS. They are also [[deletion-MOS scale]]s.		[[Regular MV3 scale]]s satisfy all 3 properties and hence are monotone-MOS. They are also [[pairwise-MOS]] and [[deletion-MOS scale]]s.

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

	[[Category:Aberrismic theory]]		[[Category:Aberrismic theory]]

Inthar at 21:49, 14 August 2024

2024-08-14T21:49:11Z

← Older revision		Revision as of 21:49, 14 August 2024
Line 1:		Line 1:
	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 property''. This property is used in [[aberrismic theory]].

			[[Regular MV3 scale]]s satisfy all 3 properties and hence are monotone-MOS. They are also [[deletion-MOS scale]]s.

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

	[[Category:Aberrismic theory]]		[[Category:Aberrismic theory]]

Inthar at 21:46, 14 August 2024

2024-08-14T21:46:11Z

← Older revision		Revision as of 21:46, 14 August 2024
Line 1:		Line 1:
	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 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, 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]].

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

	[[Category:Aberrismic theory]]		[[Category:Aberrismic theory]]

Inthar at 18:16, 9 August 2024

2024-08-09T18:16:56Z

← Older revision		Revision as of 18:16, 9 August 2024
Line 2:		Line 2:

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

			[[Category:Aberrismic theory]]

Inthar: Created page with "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 of the identifications make..."

2024-08-09T13:50:38Z

Created page with "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 of the identifications make..."

New page

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 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]].

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