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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 ==
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]], [[septiennealimmic 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.
 
=== Decitonic aka decoid ===
{{see also| Breedsmic temperaments #Decoid}}
 
Subgroup: 2.3.5.7.11.13
 
[[Comma list]]: 676/675, 1001/1000, 1716/1715, 4096/4095
 
[[Mapping]]: [{{val| 10 0 47 36 98 37 }}, {{val| 0 2 -3 -1 -8 0 }}]
 
[[POTE generator]]: ~15/13 = 248.917
 
{{Optimal ET sequence|legend=1| 130, 270, 940, 1210f }}
 
[[Badness]]: 0.013475
 
=== Avicenna ===
{{see also| Landscape microtemperaments #Avicenna }}
 
Subgroup: 2.3.5.7.11.13
 
[[Comma list]]: 676/675, 1001/1000, 3025/3024, 4096/4095
 
[[Mapping]]: [{{val| 3 2 8 16 9 8 }}, {{val| 0 8 -3 -22 4 9 }}]
 
[[CTE|CTE generator]]: ~13/12 = 137.777
 
[[POTE generator]]: ~13/12 = 137.777
 
{{Optimal ET sequence|legend=1| 87, 183, 270 }}
 
[[Badness]]: 0.015557
 
=== Tertiathirds ===
{{see also| Wizmic microtemperaments #Tertiathirds }}
 
Subgroup: 2.3.5.7.11.13
 
[[Comma list]]: 676/675, 1716/1715, 3025/3024, 4225/4224
 
[[Mapping]]: [{{val| 1 -4 2 -6 -9 -5 }}, {{val| 0 52 3 82 116 81 }}]
 
[[POTE generator]]: ~14/13 = 128.8902
 
{{Optimal ET sequence|legend=1| 121, 149, 270, 1741bc, 2011bcf, 2281bcf, 2551bcf, 2821bcf, 3091bcff, 3361bcff }}
 
[[Badness]]: 0.019494
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 676/675, 715/714, 1716/1715, 2025/2023, 4225/4224
 
Mapping: [{{val| 1 -4 2 -6 -9 -5 -3 }}, {{val| 0 52 3 82 116 81 66 }}]
 
POTE generator: ~14/13 = 128.8912
 
{{Optimal ET sequence|legend=1| 121, 149, 270 }}
 
Badness: 0.019107


== Subgroup temperaments ==
== Subgroup temperaments ==
=== Barbados ===
=== Barbados ===
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.
{{See also|Extraclassical tonality}}


[[Subgroup]]: 2.3.13/5
See [[Subgroup temperaments#Barbados]].  


[[Comma list]]: 676/675 = {{monzo| 2 -3 2 }}
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]].
 
[[Sval]] [[mapping]]: [{{val| 1 0 -1 }}, {{val| 0 2 3 }}]
 
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~15/13 = 248.621
 
{{Optimal ET sequence|legend=1| 5, 9, 14, 19, 24, 29, 53, 82, 111, 140, 251, 362 }}
 
[[Badness]]: 0.002335
 
; Music
* [http://micro.soonlabel.com/gene_ward_smith/Others/Sevish/Sevish%20-%20Desert%20Island%20Rain.mp3 ''Desert Island Rain''] in 313edo tuned Barbados[9], by [https://soundcloud.com/sevish/desert-island-rain Sevish]


==== Pinkan ====
==== Pinkan ====
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[[Sval]] [[mapping]]: [{{val| 1 0 -1 -7 }}, {{val| 0 2 3 10 }}]
[[Sval]] [[mapping]]: [{{val| 1 0 -1 -7 }}, {{val| 0 2 3 10 }}]


[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~15/13 = 248.868
[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~2 = 1\1, ~26/15 = 951.132
 
[[Optimal tuning]] ([[CWE]]): ~2 = 1\1, ~26/15 = 951.097


{{Optimal ET sequence|legend=1| 5, 24, 29, 53, 82, 111, 135 }}
{{Optimal ET sequence|legend=1| 5, 24, 29, 53, 82, 111, 135 }}


[[Badness]]: ?
[[Badness]] (Sintel): 0.039


==== Tobago ====
==== Tobago ====
{{See also| Chromatic pairs #Tobago }}
{{See also| Chromatic pairs #Tobago }}


Tobago uses the semioctave period. It can be described as the 10 & 14 temperament and is related to [[neutral]] and [[barbados]].  
Tobago uses the semioctave period. It can be described as the 10 & 14 temperament and is related to [[neutral]] and [[barbados]]. It is related to [[hemipyth]].


[[Subgroup]]: 2.3.11.13/5
[[Subgroup]]: 2.3.11.13/5
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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 }}
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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:  
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<nowiki>*</nowiki> wart for 13/5
<nowiki>*</nowiki> wart for 13/5
==== Crete ====
Crete is a strong extension of Barbados tempering out [[64/63]], thus mapping [[7/4]] to a stack of 4 semifourths, and favoring a flat semifourth near 1 step of [[5edo]]. It is a weak extension of [[archy]]. This is a somewhat peculiar temperament as most archy systems do not have interseptimals or equate them with septimal intervals as in [[oceanfront]], but crete can be used in [[34edo|34d-edo]], [[39edo|39d-edo]], [[44edo]], and [[49edo]] (with 34d and 39d often considered better than 34edo and 39edo's [[semaphore]] patent vals). Some other notable non-patent vals are [[54edo]] using its second-best 13/5 and [[93edo|93b-edo]]. Crete can be seen as a version of [[pseudo-semaphore]] with a singular mapping for 3, making pseudo-semaphore's flat fifth [[52/35]] and pseudo-semaphore's sharp fifth [[3/2]]. It was discovered and named by {{u|CompactStar}} in 2026. Since it is the combination of [[Archy]] (which is named after an Ancient Greek music theorist) and island, Crete is named after a Greek island.
[[Subgroup]]: 2.3.7.13/5
[[Comma list]]: 64/63 = {{monzo| 6 -2 -1 0 }}, 676/675 = {{monzo| 2 -3 0 2 }}
[[Sval]] [[mapping]]: [{{val| 1 0 6 -1 }}, {{val| 0 2 -4 3 }}]
: Mapping generators: ~2, ~26/15
[[Optimal tuning]] ([[CWE]]): ~2 = 1\1, ~26/15 = 954.438
{{Optimal ET sequence|legend=1|5, 24d, 29d, 34d, 39d, 44}}
[[Badness]] (Sintel): 0.457


=== Cata ===
=== Cata ===
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