6L 1s - Revision history

Lucius Chiaraviglio: /* Scale tree */ 37edo also fits mediantone

2026-05-03T23:38:59Z

Scale tree: 37edo also fits mediantone

← Older revision		Revision as of 23:38, 3 May 2026
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	\| 4/1 = Isra/[[leantone]]		\| 4/1 = Isra/[[leantone]]
	\| 5/1 = Didacus/[[hemithirds]]/[[hemiwürschmidt]]		\| 5/1 = Didacus/[[hemithirds]]/[[hemiwürschmidt]]
	\| 6/1 = Didacus/[[roulette]]		\| 6/1 = Didacus/[[mediantone]]/[[roulette]]
	}}		}}

ArrowHead294: substitute deprecated template

2025-05-05T14:01:47Z

substitute deprecated template

← Older revision		Revision as of 14:01, 5 May 2025
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	== Scale properties ==		== Scale properties ==
	{{MOS ~~scale properties~~}}
			=== Intervals ===
			{{MOS intervals}}

			=== Generator chain ===
			{{MOS genchain}}

			=== Modes ===
			{{MOS mode degrees}}

	==== Proposed names ====		==== Proposed names ====

ArrowHead294 at 13:36, 3 March 2025

2025-03-03T13:36:26Z

← Older revision		Revision as of 13:36, 3 March 2025
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	There are two notable harmonic entropy minima with this [[MOS]] pattern. The first is [[Tetracot family\|tetracot]], in which the generator is identified with [[10/9]] and four generators make a [[3/2]]. These produce very soft tunings of archaeotonic, ranging from 4:3 in [[27edo]] to 7:6 in [[48edo]]. The second is known as [[didacus]], which is at a basic level the temperament in the [[2.5.7 subgroup]] defined by [[3136/3125]], where two generators make [[5/4]] and five make [[7/4]], and produces very hard tunings, ranging from 4:1 in [[25edo]] to 7:1 in [[43edo]]; it has various extensions that span portions of this range, including [[Hemimean clan#Roulette\|roulette]] and [[Hemimean clan#Mediantone\|mediantone]] to the no-twos 19-limit, and [[hemithirds]] (along with its 5-limit microtemperament restriction [[luna]]) and [[hemiwürschmidt]] to the full 7-limit.		There are two notable harmonic entropy minima with this [[MOS]] pattern. The first is [[Tetracot family\|tetracot]], in which the generator is identified with [[10/9]] and four generators make a [[3/2]]. These produce very soft tunings of archaeotonic, ranging from 4:3 in [[27edo]] to 7:6 in [[48edo]]. The second is known as [[didacus]], which is at a basic level the temperament in the [[2.5.7 subgroup]] defined by [[3136/3125]], where two generators make [[5/4]] and five make [[7/4]], and produces very hard tunings, ranging from 4:1 in [[25edo]] to 7:1 in [[43edo]]; it has various extensions that span portions of this range, including [[Hemimean clan#Roulette\|roulette]] and [[Hemimean clan#Mediantone\|mediantone]] to the no-twos 19-limit, and [[hemithirds]] (along with its 5-limit microtemperament restriction [[luna]]) and [[hemiwürschmidt]] to the full 7-limit.

	The 6L 1s pattern also houses a temperament of the 11th and 13th harmonics, i.e. [[No-threes subgroup temperaments#Bluebirds\|Bluebirds]], where the generator is identified with [[143/128]]; for example L=7 s=4 (46 edo) is such a scale.		The 6L 1s pattern also houses a temperament of the 11th and 13th harmonics, i.e. [[No-threes subgroup temperaments#Bluebirds\|Bluebirds]], where the generator is identified with [[143/128]]; for example {{nowrap\|L {{=}} 7\|s {{=}} 4}} (46 edo) is such a scale.

	== Scales ==		== Scales ==
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	== Scale tree ==		== Scale tree ==
	{{~~Scale tree~~\|~~Comments=~~		{{MOS tuning spectrum
	5/4: [[Tetracot]] is in this region;		\| 5/4 = [[Tetracot]] is in this region
	9/7: Tetracot/[[modus]]/[[wollemia]];		\| 9/7 = Tetracot/[[modus]]/[[wollemia]]
	13/8: Wilson Golden 2 (181.~~3227¢~~);		\| 13/8 = Wilson Golden 2 (181.3227{{c}})
	12/7: [[Bluebirds]];		\| 12/7 = [[Bluebirds]]
	13/5: Golden [[glacial]] (188.~~0298¢~~);		\| 13/5 = Golden [[glacial]] (188.0298{{c}})
	3/1: [[Spell]];		\| 3/1 = [[Spell]]
	7/2: [[Isra]]/[[deutone]];		\| 7/2 = [[Isra]]/[[deutone]]
	4/1: Isra/[[leantone]];		\| 4/1 = Isra/[[leantone]]
	5/1: Didacus/[[hemithirds]]/[[hemiwürschmidt]];		\| 5/1 = Didacus/[[hemithirds]]/[[hemiwürschmidt]]
	6/1: Didacus/[[roulette]]		\| 6/1 = Didacus/[[roulette]]
	}}		}}

Lériendil: added info on what the 2.11.13 temp is and more details on didacus.

2024-12-18T20:38:30Z

added info on what the 2.11.13 temp is and more details on didacus.

← Older revision		Revision as of 20:38, 18 December 2024
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	== Temperaments ==		== Temperaments ==
	There are two notable harmonic entropy minima with this [[MOS]] pattern. The first is [[Tetracot family\|tetracot]], in which four generators make a 3/2, ~~and the~~ second is known as [[~~roulette7~~]], the ~~seven note albitonic scale for~~ the 2.5.7~~.11.13~~ subgroup ~~temperament~~ [[~~Chromatic pairs~~#Roulette\|roulette]]~~. (Other temperaments like~~ [[~~didacus~~]], [[~~luna~~]], [[~~hemithirds~~]], and [[hemiwürschmidt]] ~~have very similar~~ 7-~~note MOSes~~.)		There are two notable harmonic entropy minima with this [[MOS]] pattern. The first is [[Tetracot family\|tetracot]], in which the generator is identified with [[10/9]] and four generators make a [[3/2]]. These produce very soft tunings of archaeotonic, ranging from 4:3 in [[27edo]] to 7:6 in [[48edo]]. The second is known as [[didacus]], which is at a basic level the temperament in the [[2.5.7 subgroup]] defined by [[3136/3125]], where two generators make [[5/4]] and five make [[7/4]], and produces very hard tunings, ranging from 4:1 in [[25edo]] to 7:1 in [[43edo]]; it has various extensions that span portions of this range, including [[Hemimean clan#Roulette\|roulette]] and [[Hemimean clan#Mediantone\|mediantone]] to the no-twos 19-limit, and [[hemithirds]] (along with its 5-limit microtemperament restriction [[luna]]) and [[hemiwürschmidt]] to the full 7-limit.

	The 6L 1s pattern also houses a temperament of the 11th and 13th harmonics, for example L=7 s=4 (46 edo) is such a scale.		The 6L 1s pattern also houses a temperament of the 11th and 13th harmonics, i.e. [[No-threes subgroup temperaments#Bluebirds\|Bluebirds]], where the generator is identified with [[143/128]]; for example L=7 s=4 (46 edo) is such a scale.

	== Scales ==		== Scales ==

Ganaram inukshuk: Adopt scale properties template

2024-08-08T23:42:53Z

Adopt scale properties template

← Older revision		Revision as of 23:42, 8 August 2024
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	{{TAMNAMS name}}		{{TAMNAMS name}}

	== ~~Modes~~ ==		== Scale properties ==
	{{MOS ~~mode degrees~~}}		{{MOS scale properties}}
	=== Proposed names ===
			==== Proposed names ====
	[[File:Archeotonic.png\|alt=Archeotonic.png\|Archeotonic.png]]		[[File:Archeotonic.png\|alt=Archeotonic.png\|Archeotonic.png]]

Ganaram inukshuk: Dropped unused notation; capitalization

2024-08-08T07:50:25Z

Dropped unused notation; capitalization

← Older revision		Revision as of 07:50, 8 August 2024
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	== Names ==		== Names ==
	{{TAMNAMS name}}		{{TAMNAMS name}}

	~~== Notation ==~~
	~~JKLMNOPJ = LLLsLLL (Horthathian mode), &/@ = chroma up/down~~

	== Modes ==		== Modes ==
	{{MOS mode degrees}}		{{MOS mode degrees}}
	=== Proposed ~~Names~~ ===		=== Proposed names ===
	[[File:Archeotonic.png\|alt=Archeotonic.png\|Archeotonic.png]]		[[File:Archeotonic.png\|alt=Archeotonic.png\|Archeotonic.png]]

Ganaram inukshuk: Adopt tamnams name template

2024-08-08T07:49:50Z

Adopt tamnams name template

← Older revision		Revision as of 07:49, 8 August 2024
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	{{MOS intro}}		{{MOS intro}}
	== Names ==		== Names ==
	~~The [[~~TAMNAMS~~]] system uses the~~ name ~~'''archeotonic'''.~~		{{TAMNAMS name}}

	== Notation ==		== Notation ==

Nick Vuci: /* Modes */ added MOS mode degrees template, added "proposed names" subheading

2024-07-24T23:33:03Z

Modes: added MOS mode degrees template, added "proposed names" subheading

← Older revision		Revision as of 23:33, 24 July 2024
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	== Modes ==		== Modes ==
	=== ~~MOS modes~~ ===		{{MOS mode degrees}}
			=== Proposed Names ===
	[[File:Archeotonic.png\|alt=Archeotonic.png\|Archeotonic.png]]		[[File:Archeotonic.png\|alt=Archeotonic.png\|Archeotonic.png]]
	~~=== MODMOSes ===~~

	== Temperaments ==		== Temperaments ==

FloraC: +more scales

2024-04-17T09:51:46Z

+more scales

← Older revision		Revision as of 09:51, 17 April 2024
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	== Scales ==		== Scales ==
	* [[~~Roulette7~~]]		* [[Tetracot7]] – 34edo, 41edo, and POTE tuning
	* [[Bluebirds7]]		* [[Bluebirds7]] – 329edo tuning
			* [[Glacial7]] – 84edo tuning
			* [[Deutone7]] – 44edo tuning
			* [[Leantone7]] – 81edo tuning
			* [[Roulette7]] – 37edo tuning

	== Scale tree ==		== Scale tree ==

FloraC: /* Scale tree */ I've already forgot what "remainder" is supposed to mean, lol. Replace with module: scale tree

2024-04-17T09:47:45Z

Scale tree: I've already forgot what "remainder" is supposed to mean, lol. Replace with module: scale tree

@@ Line 22: / Line 22: @@
 == Scale tree ==
-Generator ranges:
+{{Scale tree|Comments=
-* Chroma-positive generator: 171.4286 cents (1\7) to 200 cents (1\6)
+/4: [[Tetracot]] is in this region;
-* Chroma-negative generator: 1000 cents (5\6) to 1028.5714 cents (6\7)
+/7: Tetracot/[[modus]]/[[wollemia]];
+/8: Wilson Golden 2 (181.3227¢);
-{| class="wikitable center-all"
+/7: [[Bluebirds]];
-! colspan="6" | Generator
+/5: Golden [[glacial]] (188.0298¢);
-! Cents
+/1: [[Spell]];
-!Remainder
+/2: [[Isra]]/[[deutone]];
-! L
+/1: Isra/[[leantone]];
-! s
+/1: Didacus/[[hemithirds]]/[[hemiwürschmidt]];
-! L/s
+/1: Didacus/[[roulette]]
-! Comments
+}}
 [[Category:Archaeotonic| ]]
 [[Category:7-tone scales]]
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