Gallery of omnitetrachordal scales - Revision history

BudjarnLambeth: /* Definitions and formulas */ {{Navbox scale gallery}}

2025-09-28T02:58:21Z

Definitions and formulas: {{Navbox scale gallery}}

← Older revision		Revision as of 02:58, 28 September 2025
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	'''"L/s range"''': For any L+s scale pattern, the ratio L/s may range from 1 (L=s, in which case the scale is (L+s)edo ) to ~infinity (s=0, in which case the scale is (L)edo ). A note such as "full L/s range is good" simply means that the approximation of 3/2 or 4/3 is reasonable across the entire range; no other assessment of the scale's "goodness" is intended.		'''"L/s range"''': For any L+s scale pattern, the ratio L/s may range from 1 (L=s, in which case the scale is (L+s)edo ) to ~infinity (s=0, in which case the scale is (L)edo ). A note such as "full L/s range is good" simply means that the approximation of 3/2 or 4/3 is reasonable across the entire range; no other assessment of the scale's "goodness" is intended.

			{{Navbox scale gallery}}
	[[Category:Omnitetrachordal]]		[[Category:Omnitetrachordal]]
	[[Category:Lists of scales]]		[[Category:Lists of scales]]

Fredg999: Outdated todo tag

2025-02-28T02:30:31Z

Outdated todo tag

← Older revision		Revision as of 02:30, 28 February 2025
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	'''"L/s range"''': For any L+s scale pattern, the ratio L/s may range from 1 (L=s, in which case the scale is (L+s)edo ) to ~infinity (s=0, in which case the scale is (L)edo ). A note such as "full L/s range is good" simply means that the approximation of 3/2 or 4/3 is reasonable across the entire range; no other assessment of the scale's "goodness" is intended.		'''"L/s range"''': For any L+s scale pattern, the ratio L/s may range from 1 (L=s, in which case the scale is (L+s)edo ) to ~infinity (s=0, in which case the scale is (L)edo ). A note such as "full L/s range is good" simply means that the approximation of 3/2 or 4/3 is reasonable across the entire range; no other assessment of the scale's "goodness" is intended.
	[[Category:~~omnitetrachordal~~]]
			[[Category:Omnitetrachordal]]
	[[Category:Lists of scales]]		[[Category:Lists of scales]]
	~~[[Category:todo:add_definition]]~~

Cmloegcmluin: add unchanged-intervals along with eigenmonzo, per prior agreement on Xenwiki Work Group

2023-05-05T23:43:18Z

add unchanged-intervals along with eigenmonzo, per prior agreement on Xenwiki Work Group

← Older revision		Revision as of 23:43, 5 May 2023
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	'''"Dual"''' refers to the "inverse" of a L+s scale pattern, where every L is replaced by s, and vice versa. For example, <tt> sLssL </tt> and <tt> LsLLs </tt> are duals. If a scale is OTC, its dual is often OTC as well, but not always!		'''"Dual"''' refers to the "inverse" of a L+s scale pattern, where every L is replaced by s, and vice versa. For example, <tt> sLssL </tt> and <tt> LsLLs </tt> are duals. If a scale is OTC, its dual is often OTC as well, but not always!

	'''"Perfect"''' means that values for L and s exist such that L > s and that every mode of the scale will contain a perfect (just) 3/2 or 4/3 (or both). (See also [[Eigenmonzo_subgroup\|Eigenmonzo subgroup]].)		'''"Perfect"''' means that values for L and s exist such that L > s and that every mode of the scale will contain a perfect (just) 3/2 or 4/3 (or both). (See also [[Eigenmonzo_subgroup\|Eigenmonzo subgroup]], or [[unchanged-interval basis]].)

	In this case the value '''P''' is given, where P = L/s. For a perfect scale, P > 1. Note that if a scale "a" is perfect (P<span style="vertical-align: sub;">a</span> = L/s), its dual "b" will have the value P<span style="vertical-align: sub;">b</span> = s/L = 1/P<span style="vertical-align: sub;">a</span>, and therefore must be imperfect (if P<span style="vertical-align: sub;">a</span> > 1, then P<span style="vertical-align: sub;">b</span> < 1 ).		In this case the value '''P''' is given, where P = L/s. For a perfect scale, P > 1. Note that if a scale "a" is perfect (P<span style="vertical-align: sub;">a</span> = L/s), its dual "b" will have the value P<span style="vertical-align: sub;">b</span> = s/L = 1/P<span style="vertical-align: sub;">a</span>, and therefore must be imperfect (if P<span style="vertical-align: sub;">a</span> > 1, then P<span style="vertical-align: sub;">b</span> < 1 ).

Fredg999 category edits: Removing from Category:Gallery using Cat-a-lot

2023-04-13T21:43:31Z

Removing from Category:Gallery using Cat-a-lot

← Older revision		Revision as of 21:43, 13 April 2023
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	'''"L/s range"''': For any L+s scale pattern, the ratio L/s may range from 1 (L=s, in which case the scale is (L+s)edo ) to ~infinity (s=0, in which case the scale is (L)edo ). A note such as "full L/s range is good" simply means that the approximation of 3/2 or 4/3 is reasonable across the entire range; no other assessment of the scale's "goodness" is intended.		'''"L/s range"''': For any L+s scale pattern, the ratio L/s may range from 1 (L=s, in which case the scale is (L+s)edo ) to ~infinity (s=0, in which case the scale is (L)edo ). A note such as "full L/s range is good" simply means that the approximation of 3/2 or 4/3 is reasonable across the entire range; no other assessment of the scale's "goodness" is intended.
	~~[[Category:gallery]]~~
	[[Category:omnitetrachordal]]		[[Category:omnitetrachordal]]
	[[Category:Lists of scales]]		[[Category:Lists of scales]]
	[[Category:todo:add_definition]]		[[Category:todo:add_definition]]

Fredg999 category edits: Moving from Category:Scales to Category:Lists of scales using Cat-a-lot

2022-02-26T03:10:25Z

Moving from Category:Scales to Category:Lists of scales using Cat-a-lot

← Older revision		Revision as of 03:10, 26 February 2022
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	[[Category:gallery]]		[[Category:gallery]]
	[[Category:omnitetrachordal]]		[[Category:omnitetrachordal]]
	[[Category:scales]]		[[Category:Lists of scales]]
	[[Category:todo:add_definition]]		[[Category:todo:add_definition]]

Lhearne: /* 17 tones */ completed unfinished bits

2022-02-06T13:07:15Z

17 tones: completed unfinished bits

← Older revision		Revision as of 13:07, 6 February 2022
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	ABAABCAABAABCAABA		ABAABCAABAABCAABA

	2L+5M+10s -		2L+5M+10s - sMssMLssMssMLssMs

	2L+10M+5s -		2L+10M+5s - MsMMsLMMsMMsLMMsM

	5L+2M+10s -		5L+2M+10s - sLssLMssLssLMssLs

	10L+2M+5s -		10L+2M+5s - LsLLsMLLsLLsMLLsL

	ABACABCABACABCABC ([[Fokker block]])		ABACABCABACABCABC ([[Fokker block]])
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	ABCABCAABCABCAABC ([[Fokker block]])		ABCABCAABCABCAABC ([[Fokker block]])

	5L+7M+5s		5L+7M+5s - MLsMLsMMLsMLsMMLs, sLMMsLMsLMMsLMsLM

	7L+5M+5s		7L+5M+5s - LMsLMsLLMsLMsLLMs, sMLLsMLsMLLsMLsML

	== 19 tones ==		== 19 tones ==

Lhearne: /* Scales with 3 step sizes */ added 46-tone

2021-05-09T19:29:44Z

Scales with 3 step sizes: added 46-tone

← Older revision		Revision as of 19:29, 9 May 2021
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	2L+29M+10s: MsMMMsMMLMMsMMMsMMsMMMsMMsMMMsMMLMMsMMMsM		2L+29M+10s: MsMMMsMMLMMsMMMsMMsMMMsMMsMMMsMMLMMsMMMsM

			== 46 tones ==
			CACACBCACACACBCACACCACACBCACACACBCACACCACACBCA (3-[[SN scale\|SN]])

	== 72 tones ==		== 72 tones ==

Lhearne: /* Scales with 3 step sizes */

2021-05-09T19:26:46Z

Scales with 3 step sizes

← Older revision		Revision as of 19:26, 9 May 2021
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	ABCBA=32/27, BC=256/243		ABCBA=32/27, BC=256/243

			10L+2M+7s: LsMsLLsLLsMsLLsLLsL

	ABCABCABABCABCABCAB ([[Fokker block]])		ABCABCABABCABCABCAB ([[Fokker block]])
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	== 29 tones ==		== 29 tones ==
	BABBABABBABCBABBABABBABCBABBA (3-[[SN scale\|SN]])		BABBABABBABCBABBABABBABCBABBA (3-[[SN scale\|SN]])

			2L+10m+17s: smsmssmsLsmssmsmssmsLsmssmsms

	== 31 tones ==		== 31 tones ==
	BABBCBBABABBABABBCBBABABBABABBA (3-[[SN scale\|SN]])		BABBCBBABABBABABBCBBABABBABABBA (3-[[SN scale\|SN]])

			10L+19m+2s: mLmmLmsmLmmLmmLmLmmLmmLmsmLmmLm

			10L+2m+19s: sLssLsmsLssLssLsLssLssLsmsLssLs

	== 41 tones ==		== 41 tones ==
	BABCBABBABBABCBABBABCBABBABBABCBABBABCBAB (3-[[SN scale\|SN]])		BABCBABBABBABCBABBABCBABBABBABCBABBABCBAB (3-[[SN scale\|SN]])

			5L+12M+24s: sMsLsMssMssMsLsMssMsLsMssMssMsLsMssMsLsMs

	BBABBBABBABBBABBCBBABBBABBABBBABBCBBABBBA (3-[[SN scale\|SN]])		BBABBBABBABBBABBCBBABBBABBABBBABBCBBABBBA (3-[[SN scale\|SN]])

			29L+2M+10s: LsLLLsLLMLLsLLLsLLsLLLsLLsLLLsLLMLLsLLLsL

			2L+29M+10s: MsMMMsMMLMMsMMMsMMsMMMsMMsMMMsMMLMMsMMMsM

			== 72 tones ==
			ABAABABABAABABACABABAABABABAABABAABABABAABABAABABABAABABACABABAABABABAAB (3-[[SN scale\|SN]])

			29L+2M+41s: sLssLsLsLssLsLsMsLsLssLsLsLssLsLssLsLsLssLsLssLsLsLssLsLsMsLsLssLsLsLssL

			2L+29M+41s: sMssMsMsMssMsMsLsMsMssMsMsMssMsMssMsMsMssMsMssMsMsMssMsMsLsMssMsMsMssM

	=Definitions and formulas=		=Definitions and formulas=

Lhearne: /* Scales with 3 step sizes */

2021-05-09T17:27:53Z

Scales with 3 step sizes

← Older revision		Revision as of 17:27, 9 May 2021
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	MET-24 has this structure as 5L+12M+7s: MLMsMsMLMsMLMsMsMLMsMLMs		MET-24 has this structure as 5L+12M+7s: MLMsMsMLMsMLMsMsMLMsMLMs

			AABAAABAACAABAAABAACAABA (3-[[SN scale\|SN]])

			== 29 tones ==
			BABBABABBABCBABBABABBABCBABBA (3-[[SN scale\|SN]])

	== 31 tones ==		== 31 tones ==
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	== 41 tones ==		== 41 tones ==
	BABCBABBABBABCBABBABCBABBABBABCBABBABCBAB (3-[[SN scale\|SN]])		BABCBABBABBABCBABBABCBABBABBABCBABBABCBAB (3-[[SN scale\|SN]])

			BBABBBABBABBBABBCBBABBBABBABBBABBCBBABBBA (3-[[SN scale\|SN]])

	=Definitions and formulas=		=Definitions and formulas=

Lhearne: /* Scales with 3 step sizes */ changed 3-SIS to 3-SN, added 31 and 41-note scales

2021-05-09T17:20:47Z

Scales with 3 step sizes: changed 3-SIS to 3-SN, added 31 and 41-note scales

← Older revision		Revision as of 17:20, 9 May 2021
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	== 8 notes ==		== 8 notes ==
	ABCABCAB (Fokker ~~Block~~)		ABCABCAB ([[Fokker block]])

	2L+3M+3s - LMsMsLMs, sMLsMsML		2L+3M+3s - LMsMsLMs, sMLsMsML

	== 10 tones ==		== 10 tones ==
	ABACABACAB (3-~~SIS~~)		ABACABACAB (3-[[SN scale\|SN]])

	2L+3M+5s - sMsLsMsMsL		2L+3M+5s - sMsLsMsMsL
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	== 11 tones ==		== 11 tones ==
	ABACABACABA (3-~~SIS~~)		ABACABACABA (3-[[SN scale\|SN]])

	2L+3M+6s - sMsLsMssMsL		2L+3M+6s - sMsLsMssMsL
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	== 12 tones ==		== 12 tones ==
	ABABCABABCAB (Fokker ~~Block~~)		ABABCABABCAB ([[Fokker block]])

	5L+2M+5s - LsLsMLsLsLsM, MsLsLsLMsLsL		5L+2M+5s - LsLsMLsLsLsM, MsLsLsLMsLsL
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	== 14 tones ==		== 14 tones ==
	ABABACABABACAB (3-~~SIS~~)		ABABACABABACAB (3-[[SN scale\|SN]])

	5L+2M+7s - sLsMsLsLsLsMsL		5L+2M+7s - sLsMsLsLsLsMsL
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	== 15 tones ==		== 15 tones ==
	ABAACAABAACAABA (3-~~SIS~~)		ABAACAABAACAABA (3-[[SN scale\|SN]])

	2L+3M+10s - sMssLssMssMssLs		2L+3M+10s - sMssLssMssMssLs
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	== 17 tones ==		== 17 tones ==
	ABAABACABAABACABA (3-~~SIS~~)		ABAABACABAABACABA (3-[[SN scale\|SN]])

	2L+5M+10s - sMsLsMssMssMsLsMs		2L+5M+10s - sMsLsMssMssMsLsMs
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	10L+2M+5s -		10L+2M+5s -

	ABACABCABACABCABC (Fokker ~~Block~~)		ABACABCABACABCABC ([[Fokker block]])

	5L+7M+5s - MLMsMLsMLsMLMsMLs, sLMsMLMsLMsLMsMLM		5L+7M+5s - MLMsMLsMLsMLMsMLs, sLMsMLMsLMsLMsMLM
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	7L+5M+5s - LMLsLMsLMsLMLsLMs, sMLsLMLsMLsMLsLML		7L+5M+5s - LMLsLMsLMsLMLsLMs, sMLsLMLsMLsMLsLML

	ABCABCAABCABCAABC (Fokker block)		ABCABCAABCABCAABC ([[Fokker block]])

	5L+7M+5s		5L+7M+5s
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	== 19 tones ==		== 19 tones ==
	ABCBAABAABCBAABAABA (3-~~SIS~~)		ABCBAABAABCBAABAABA (3-[[SN scale\|SN]])

	ABA=9/8		ABA=9/8
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	ABCBA=32/27, BC=256/243		ABCBA=32/27, BC=256/243

	ABCABCABABCABCABCAB (Fokker ~~Block~~)		ABCABCABABCABCABCAB ([[Fokker block]])

	== 20 tones ==		== 20 tones ==
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	== 24 tones ==		== 24 tones ==
	ACABABACABACABABACABACAB (3-~~SIS~~)		ACABABACABACABABACABACAB (3-[[SN scale\|SN]])

	MET-24 has this structure		MET-24 has this structure as 5L+12M+7s: MLMsMsMLMsMLMsMsMLMsMLMs

			== 31 tones ==
			BABBCBBABABBABABBCBBABABBABABBA (3-[[SN scale\|SN]])

			== 41 tones ==
			BABCBABBABBABCBABBABCBABBABBABCBABBABCBAB (3-[[SN scale\|SN]])

	=Definitions and formulas=		=Definitions and formulas=