The Archipelago - Revision history

FloraC: Text replacement - "{{Mapping|legend=2| " to "{{Mapping|legend=3| "

2026-09-30T17:38:27Z

Text replacement - "{{Mapping|legend=2| " to "{{Mapping|legend=3| "

← Older revision		Revision as of 17:38, 30 September 2026
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	[[Comma list]]: 221/220, 243/242, 289/288		[[Comma list]]: 221/220, 243/242, 289/288

	{{Mapping\|legend=2\| 2 0 -1 -2 5 \| 0 2 5 3 2 }}		{{Mapping\|legend=3\| 2 0 -1 -2 5 \| 0 2 5 3 2 }}

	[[Optimal tuning]]s:		[[Optimal tuning]]s:

FloraC: /* Rank-2 temperaments */ - duplicate data; update links

2026-09-08T13:48:28Z

Rank-2 temperaments: - duplicate data; update links

@@ Line 121: / Line 121: @@
 == Rank-2 temperaments ==
-Rank two temperaments tempering out 676/675 include the 13-limit versions of [[Ragismic microtemperaments #Hemiennealimmal|hemiennealimmal]], [[Breedsmic temperaments #Harry|harry]], [[Kleismic family #Tritikleismic|tritikleismic]], [[Kleismic family #Catakleismic|catakleimsic]], [[Marvel temperaments #Negri|negri]], [[Hemifamity temperaments #Mystery|mystery]], [[Hemifamity temperaments #Buzzard|buzzard]], [[Kleismic family #Quadritikleismic|quadritikleismic]].
+Rank-2 temperaments tempering out 676/675 include the 13-limit versions of [[semaphoresmic clan #Negri|negri]], [[buzzardsmic clan #Buzzard|buzzard]], [[kleismic family #Catakleismic|catakleismic]], [[gravity family #Harry|harry]], [[kleismic family #Tritikleismic|tritikleismic]], [[quintosec family #Decoid|decoid]], [[kleismic family #Quadritikleismic|quadritikleismic]], [[landscape microtemperaments #Avicenna|avicenna]], [[septiennealimmal clan #Hemiennealimmal|hemiennealimmal]], [[wizmic microtemperaments #Tertiathirds|tertiathirds]], and [[aberschismic temperaments #Mystery|mystery]].
-It is interesting to note the Graham complexity of 15/13 in these temperaments. This is 18 in hemiennealimmal, 6 in harry, 9 in tritikleismic, 3 in catakleismic, 2 in negri, 2 in buzzard, 12 in quadritikleismic. Catakleismic and buzzard are particularly interesting from an archipelago point of view. Mystery is special case, since the 15/13 part of it belongs to [[29edo]] alone.
+It is interesting to note the Graham complexity of 15/13 in these temperaments. This is 2 in negri, 2 in buzzard, 3 in catakleismic, 6 in harry, 9 in tritikleismic, 10 in decoid, 12 in quadritikleismic, 12 in avicenna, 18 in hemiennealimmal, 26 in tertiathirds. Catakleismic and buzzard are particularly interesting from an archipelago point of view. Mystery is special case, since the 15/13 part of it belongs to [[29edo]] alone.
 == Subgroup temperaments ==

FloraC: /* Rank-3 temperaments */ update

2026-09-08T13:38:46Z

Rank-3 temperaments: update

← Older revision		Revision as of 13:38, 8 September 2026
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	* [[History (temperament)\|History]] → [[Werckismic temperaments #History\|Werckismic temperaments]]		* [[History (temperament)\|History]] → [[Werckismic temperaments #History\|Werckismic temperaments]]
	: +364/363, 441/440		: +364/363, 441/440
	* [[Borneo]] → [[~~Lehmerismic temperaments~~ #Borneo\|~~Lehmerismic temperaments~~]]		* [[Borneo]] → [[Landscape family #Borneo\|Landscape family]]
	: +1001/1000, 3025/3024		: +1001/1000, 3025/3024
	* [[Enlil\|Enlil ~~aka~~ sumatra]] → [[Kleismic rank-3 family #Enlil\|Kleismic rank-3 family]]		* [[Enlil\|Enlil a.k.a. sumatra]] → [[Kleismic rank-3 family #Enlil\|Kleismic rank-3 family]]
	: +325/324, 385/384		: +325/324, 385/384
	* [[Madagascar]] → [[Cataharry family #Madagascar\|Cataharry family]]		* [[Madagascar]] → [[Cataharry family #Madagascar\|Cataharry family]]
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	* [[Hagrid]] → [[Cataharry family #Hagrid\|Cataharry family]]		* [[Hagrid]] → [[Cataharry family #Hagrid\|Cataharry family]]
	: +243/242, 351/350		: +243/242, 351/350
	* [[Baffin]] → [[~~Olympic~~ clan #Baffin\|~~Olympic~~ clan]]		* [[Baffin]] → [[Vishdelismic clan #Baffin\|Vishdelismic clan]]
	: +1001/1000, 4096/4095		: +1001/1000, 4096/4095
	* [[Kujuku]] → [[Pentacircle clan #Kujuku\|Pentacircle clan]]		* [[Kujuku]] → [[Pentacircle clan #Kujuku\|Pentacircle clan]]
	: +352/351, 364/363		: +352/351, 364/363
	* [[Namaka]] → [[~~Hemifamity~~ family#Namaka\|~~Hemifamity~~ family]]		* [[Namaka]] → [[Aberschismic family #Namaka\|Aberschismic family]]
	: +352/351, ~~1001~~/~~1000~~		: +352/351, 847/845

	== Rank-2 temperaments ==		== Rank-2 temperaments ==

BudjarnLambeth: /* Tobago */ correction

2026-04-29T13:13:05Z

Tobago: correction

← Older revision		Revision as of 13:13, 29 April 2026
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	: [[gencom]]: [55/39 15/13; 243/242 676/675]		: [[gencom]]: [55/39 15/13; 243/242 676/675]

	[[Optimal tuning]] ([[Tp tuning\|subgroup POTE]]): ~2 = 1\1, ~15/13 = 249.312		[[Optimal tuning]] ([[Tp tuning\|subgroup POTE]]): ~55/39 = 1\2, ~15/13 = 249.312

	{{Optimal ET sequence\|legend=1\| 10, 14, 24, 58, 82, 130 }}		{{Optimal ET sequence\|legend=1\| 10, 14, 24, 58, 82, 130 }}

Overthink: /* Barbados */ + see also

2025-12-22T08:18:54Z

Barbados: + see also

← Older revision		Revision as of 08:18, 22 December 2025
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	== Subgroup temperaments ==		== Subgroup temperaments ==
	=== Barbados ===		=== Barbados ===
			{{See also\|Extraclassical tonality}}
	Perhaps the simplest method of making use of the barbados triad and other characteristic island harmonies is to strip things down to essentials by tempering the 2.3.13/5 [[just intonation subgroup]]. The [[minimax tuning]] for this makes the generator the cube root of 20/13, or 248.5953 cents. Edos which may be used for it are [[24edo]], [[29edo]], [[53edo]] and [[111edo]], with [[mos scale]]s of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales.		Perhaps the simplest method of making use of the barbados triad and other characteristic island harmonies is to strip things down to essentials by tempering the 2.3.13/5 [[just intonation subgroup]]. The [[minimax tuning]] for this makes the generator the cube root of 20/13, or 248.5953 cents. Edos which may be used for it are [[24edo]], [[29edo]], [[53edo]] and [[111edo]], with [[mos scale]]s of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales.

Tristanbay: /* Rank-3 temperaments */Added Namaka temperament

2025-09-16T07:35:33Z

Rank-3 temperaments: Added Namaka temperament

← Older revision		Revision as of 07:35, 16 September 2025
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	* [[Kujuku]] → [[Pentacircle clan #Kujuku\|Pentacircle clan]]		* [[Kujuku]] → [[Pentacircle clan #Kujuku\|Pentacircle clan]]
	: +352/351, 364/363		: +352/351, 364/363
			* [[Namaka]] → [[Hemifamity family#Namaka\|Hemifamity family]]
			: +352/351, 1001/1000

	== Rank-2 temperaments ==		== Rank-2 temperaments ==

FloraC: Fix linking

2025-08-27T13:33:16Z

Fix linking

← Older revision		Revision as of 13:33, 27 August 2025
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	* [[Borneo]] → [[Lehmerismic temperaments #Borneo\|Lehmerismic temperaments]]		* [[Borneo]] → [[Lehmerismic temperaments #Borneo\|Lehmerismic temperaments]]
	: +1001/1000, 3025/3024		: +1001/1000, 3025/3024
	* [[Enlil\|Enlil aka sumatra]] → [[Kleismic rank ~~three~~ family #Enlil\|Kleismic rank-3 family]]		* [[Enlil\|Enlil aka sumatra]] → [[Kleismic rank-3 family #Enlil\|Kleismic rank-3 family]]
	: +325/324, 385/384		: +325/324, 385/384
	* [[Madagascar]] → [[Cataharry family #Madagascar\|Cataharry family]]		* [[Madagascar]] → [[Cataharry family #Madagascar\|Cataharry family]]

Tristanbay: /* Rank-3 temperaments */ Added Hagrid to notable rank-3 temperaments

2025-08-04T18:49:49Z

Rank-3 temperaments: Added Hagrid to notable rank-3 temperaments

← Older revision		Revision as of 18:49, 4 August 2025
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	* [[Madagascar]] → [[Cataharry family #Madagascar\|Cataharry family]]		* [[Madagascar]] → [[Cataharry family #Madagascar\|Cataharry family]]
	: +351/350, 540/539		: +351/350, 540/539
			* [[Hagrid]] → [[Cataharry family #Hagrid\|Cataharry family]]
			: +243/242, 351/350
	* [[Baffin]] → [[Olympic clan #Baffin\|Olympic clan]]		* [[Baffin]] → [[Olympic clan #Baffin\|Olympic clan]]
	: +1001/1000, 4096/4095		: +1001/1000, 4096/4095

FloraC: Text replacement - "{{Technical data page}}

" to "{{Technical data page}}"

2025-04-13T13:47:58Z

Text replacement - "{{Technical data page}}<br><br>" to "{{Technical data page}}"

← Older revision		Revision as of 13:47, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	The '''archipelago''' is a rag-tag collection of various regular temperaments of different ranks, including subgroup temperaments, associated with island temperament: the rank five thirteen limit temperament tempering out the island comma, [[676/675]]. Common to all of them is the observation that two intervals of 15/13 are equated with a fourth. Hence a 1-15/13-4/3 chord is a characteristic island chord, and 15/13 tends to be of low complexity. Also characteristic is the barbados triad, the 1-13/10-3/2 triad, as well as its inversion 1-15/13-3/2, the barbados tetrad, 1-13/10-3/2-26/15, plus the tetrads 1-13/10-3/2-8/5 and 1-13/10-3/2-9/5. The [[just intonation subgroup]] generated by 2, 4/3 and 15/13 is 2.3.13/5, and the barbados triad and tetrad are found in that, while the other two tetrads are found in the larger 2.3.5.13 subgroup.		The '''archipelago''' is a rag-tag collection of various regular temperaments of different ranks, including subgroup temperaments, associated with island temperament: the rank five thirteen limit temperament tempering out the island comma, [[676/675]]. Common to all of them is the observation that two intervals of 15/13 are equated with a fourth. Hence a 1-15/13-4/3 chord is a characteristic island chord, and 15/13 tends to be of low complexity. Also characteristic is the barbados triad, the 1-13/10-3/2 triad, as well as its inversion 1-15/13-3/2, the barbados tetrad, 1-13/10-3/2-26/15, plus the tetrads 1-13/10-3/2-8/5 and 1-13/10-3/2-9/5. The [[just intonation subgroup]] generated by 2, 4/3 and 15/13 is 2.3.13/5, and the barbados triad and tetrad are found in that, while the other two tetrads are found in the larger 2.3.5.13 subgroup.

BudjarnLambeth: {{Technical data page}}

2025-04-13T06:42:40Z

{{Technical data page}}<br><br>

← Older revision		Revision as of 06:42, 13 April 2025
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			{{Technical data page}}<br><br>
	The '''archipelago''' is a rag-tag collection of various regular temperaments of different ranks, including subgroup temperaments, associated with island temperament: the rank five thirteen limit temperament tempering out the island comma, [[676/675]]. Common to all of them is the observation that two intervals of 15/13 are equated with a fourth. Hence a 1-15/13-4/3 chord is a characteristic island chord, and 15/13 tends to be of low complexity. Also characteristic is the barbados triad, the 1-13/10-3/2 triad, as well as its inversion 1-15/13-3/2, the barbados tetrad, 1-13/10-3/2-26/15, plus the tetrads 1-13/10-3/2-8/5 and 1-13/10-3/2-9/5. The [[just intonation subgroup]] generated by 2, 4/3 and 15/13 is 2.3.13/5, and the barbados triad and tetrad are found in that, while the other two tetrads are found in the larger 2.3.5.13 subgroup.		The '''archipelago''' is a rag-tag collection of various regular temperaments of different ranks, including subgroup temperaments, associated with island temperament: the rank five thirteen limit temperament tempering out the island comma, [[676/675]]. Common to all of them is the observation that two intervals of 15/13 are equated with a fourth. Hence a 1-15/13-4/3 chord is a characteristic island chord, and 15/13 tends to be of low complexity. Also characteristic is the barbados triad, the 1-13/10-3/2 triad, as well as its inversion 1-15/13-3/2, the barbados tetrad, 1-13/10-3/2-26/15, plus the tetrads 1-13/10-3/2-8/5 and 1-13/10-3/2-9/5. The [[just intonation subgroup]] generated by 2, 4/3 and 15/13 is 2.3.13/5, and the barbados triad and tetrad are found in that, while the other two tetrads are found in the larger 2.3.5.13 subgroup.