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== Rank-3 temperaments ==
== Rank-3 temperaments ==
=== [[Breed_family|Greenland]] ===
Notable rank-3 temperaments of island include greenland, history, borneo, sumatra, madagascar, baffin, and kujuku, all shown below.
Commas: 676/675, 1001/1000, 1716/1715


Map: [<2 0 1 3 7 -1|, <0 2 1 1 -2 4|, <0 0 2 1 3 2|]
=== Greenland ===
{{See also| Breed family #Greenland }}


Edos: 58, 72, 130, 198, 270, 940
Subgroup: 2.3.5.7.11.13


[[Optimal_patent_val|Optimal patent val]]: [[940edo|940edo]]
[[Comma list]]: 676/675, 1001/1000, 1716/1715


Badness: 0.000433
[[Mapping]]: [{{val| 2 0 1 3 7 -1 }}, {{val| 0 2 1 1 -2 4 }}, {{val| 0 0 2 1 3 2 }}]


[[Spectrum_of_a_temperament|Spectrum]]: 15/13, 7/5, 8/7, 7/6, 4/3, 15/14, 5/4, 18/13, 13/12, 14/13, 13/10, 6/5, 16/15, 11/10, 9/7, 9/8, 16/13, 10/9, 14/11, 11/8, 15/11, 12/11, 13/11, 11/9
{{Val list|legend=1| 58, 72, 130, 198, 270, 940, 1210f }}


=== [[Werckismic_temperaments|History]] ===
[[Badness]]: 0.433 × 10<sup>-3</sup>
Commas: 364/363, 441/440, 1001/1000


EDOs: 15, 29, 43, 58, 72, 87, 130, 217, 289
[[Complexity spectrum]]: 15/13, 7/5, 8/7, 7/6, 4/3, 15/14, 5/4, 18/13, 13/12, 14/13, 13/10, 6/5, 16/15, 11/10, 9/7, 9/8, 16/13, 10/9, 14/11, 11/8, 15/11, 12/11, 13/11, 11/9


[[Optimal_patent_val|Optimal patent val]]: [[289edo|289edo]]
=== History ===
{{See also| Werckismic temperaments #History }}


Badness: 0.000540
Subgroup: 2.3.5.7.11.13


Spectrum: 11/10, 15/13, 14/11, 4/3, 7/5, 5/4, 11/8, 18/13, 15/11, 13/12, 13/10, 6/5, 8/7, 16/15, 12/11, 13/11, 9/8, 16/13, 15/14, 10/9, 7/6, 11/9, 14/13, 9/7
[[Comma list]]: 364/363, 441/440, 676/675
 
[[Mapping]]: [{{val| 1 2 0 0 1 2 }}, {{val| 0 -6 0 7 2 -9 }}, {{val| 0 0 1 1 1 1 }}]
 
{{Val list|legend=1| 14cf, 15, 29, 43, 58, 72, 87, 130, 217, 289 }}
 
[[Badness]]: 0.540 × 10<sup>-3</sup>
 
[[Complexity spectrum]]: 11/10, 15/13, 14/11, 4/3, 7/5, 5/4, 11/8, 18/13, 15/11, 13/12, 13/10, 6/5, 8/7, 16/15, 12/11, 13/11, 9/8, 16/13, 15/14, 10/9, 7/6, 11/9, 14/13, 9/7


=== Borneo ===
=== Borneo ===
Commas: 676/675, 1001/1000, 3025/3024
{{See also| Lehmerismic temperaments #Borneo }}


Map: [&lt;3 0 0 4 8 -3|, &lt;0 2 0 -4 1 3|, &lt;0 0 1 2 0 1|]
Subgroup: 2.3.5.7.11.13


EDOs: 15, 72, 87, 111, 159, 183, 198, 270
[[Comma list]]: 676/675, 1001/1000, 3025/3024


[[Optimal_patent_val|Optimal patent val]]: [[270edo|270edo]]
[[Mapping]]: [{{val| 3 0 0 4 8 -3 }}, {{val| 0 2 0 -4 1 3 }}, {{val| 0 0 1 2 0 1 }}]


Badness: 0.000549
{{Val list|legend=1| 15, 24d, 33cdff, 39df, 57f, 72, 111, 159, 183, 198, 270 }}


Spectrum: 12/11, 15/13, 11/8, 4/3, 11/10, 18/13, 6/5, 5/4, 13/12, 15/11, 11/9, 13/10, 10/9, 7/5, 16/15, 13/11, 9/8, 16/13, 8/7, 14/11, 15/14, 7/6, 14/13, 9/7
[[Badness]]: 0.549 × 10<sup>-3</sup>
 
[[Complexity spectrum]]: 12/11, 15/13, 11/8, 4/3, 11/10, 18/13, 6/5, 5/4, 13/12, 15/11, 11/9, 13/10, 10/9, 7/5, 16/15, 13/11, 9/8, 16/13, 8/7, 14/11, 15/14, 7/6, 14/13, 9/7


=== Sumatra ===
=== Sumatra ===
Commas: 325/324, 385/384, 625/624
{{See also| Kleismic rank three family #13-limit (aka sumatra) }}
 
Subgroup: 2.3.5.7.11.13
 
[[Comma list]]: 325/324, 385/384, 625/624
 
[[Mapping]]: [{{val| 1 0 1 0 6 0 }}, {{val| 0 6 5 0 1 14 }}, {{val| 0 0 0 1 -1 0 }}]
 
{{Val list|legend=1| 15, 19, 34, 53, 72, 87, 125f, 140, 159, 212, 299 }}


EDOs: 15, 19, 34, 53, 72, 87, 140, 159, 212, 299
[[Badness]]: 0.680 × 10<sup>-3</sup>


Optimal patent val: [[299edo|299edo]]
=== Madagascar ===
{{See also| Cataharry family #Madagascar }}


Badness: 0.000680
Subgroup: 2.3.5.7.11.13


=== [[Cataharry_family|Madagascar]] ===
[[Comma list]]: 351/350, 540/539, 676/675
Commas: 351/350, 540/539, 676/675


EDOs: 19, 53, 58, 72, 111, 130, 183, 313
[[Mapping]]: [{{val| 1 0 0 -2 6 -1 }}, {{val| 0 2 0 9 -12 3 }}, {{val| 0 0 1 -1 3 1 }}]


[[Optimal_patent_val|Optimal patent val]]: [[313edo|313edo]]
{{Val list|legend=1| 19, 33cdff, 39df, 53, 58, 72, 111, 130, 183, 313 }}


Badness: 0.000560
[[Badness]]: 0.560 × 10<sup>-3</sup>


Spectrum: 15/13, 4/3, 13/10, 10/9, 6/5, 9/7, 18/13, 9/8, 5/4, 7/6, 13/12, 15/14, 16/15, 14/13, 8/7, 7/5, 16/13, 11/10, 15/11, 11/8, 12/11, 13/11, 11/9, 14/11
[[Complexity spectrum]]: 15/13, 4/3, 13/10, 10/9, 6/5, 9/7, 18/13, 9/8, 5/4, 7/6, 13/12, 15/14, 16/15, 14/13, 8/7, 7/5, 16/13, 11/10, 15/11, 11/8, 12/11, 13/11, 11/9, 14/11


[[madagascar19]]
Scales: [[madagascar19]]


=== Baffin ===
=== Baffin ===
Commas: 676/675, 1001/1000, 4225/4224
Subgroup: 2.3.5.7.11.13


Map: [&lt;1 0 0 13 -9 1|, &lt;0 2 0 -7 4 3|, &lt;0 0 1 -2 4 1|]
[[Comma list]]: 676/675, 1001/1000, 4096/4095


EDOs: 34, 43, 53, 87, 130, 183, 217, 270, 940
[[Mapping]]: [{{val| 1 0 0 13 -9 1 }}, {{val| 0 2 0 -7 4 3 }}, {{val| 0 0 1 -2 4 1 }}]


[[Optimal_patent_val|Optimal patent val]]: [[940edo|940edo]]
{{Val list|legend=1| 34, 43, 53, 87, 130, 183, 217, 270, 940 }}


Badness: 0.000604
[[Badness]]: 0.604 × 10<sup>-3</sup>


Spectrum: 15/13, 16/15, 13/12, 4/3, 16/13, 5/4, 18/13, 13/10, 6/5, 9/8, 11/10, 8/7, 7/5, 15/11, 10/9, 13/11, 15/14, 11/8, 7/6, 14/13, 12/11, 9/7, 11/9, 14/11
[[Complexity spectrum]]: 15/13, 16/15, 13/12, 4/3, 16/13, 5/4, 18/13, 13/10, 6/5, 9/8, 11/10, 8/7, 7/5, 15/11, 10/9, 13/11, 15/14, 11/8, 7/6, 14/13, 12/11, 9/7, 11/9, 14/11


=== Kujuku ===
=== Kujuku ===
Commas: 352/351, 364/363, 676/675
Subgroup: 2.3.5.7.11.13


Map: [&lt;1 0 0 -13 -6 -1|, &lt;0 2 0 17 9 3|, &lt;0 0 1 1 1 1|]
[[Comma list]]: 352/351, 364/363, 676/675


EDOs: 24, 29, 58, 87, 121, 145, 208, 266ef, 474bef
[[Mapping]]: [{{val| 1 0 0 -13 -6 -1 }}, {{val| 0 2 0 17 9 3 }}, {{val| 0 0 1 1 1 1 }}]


[[Optimal_patent_val|Optimal patent val]]: [[208edo|208edo]]
{{Val list|legend=1| 24, 29, 58, 87, 121, 145, 208, 266ef, 474bef }}


Badness: 0.001060
[[Badness]]: 1.060 × 10<sup>-3</sup>


Spectrum: 15/13, 4/3, 13/10, 9/8, 13/11, 15/11, 12/11, 11/9, 11/8, 14/11, 16/13, 16/15, 11/10, 13/12, 9/7, 5/4, 18/13, 7/6, 6/5, 8/7, 10/9, 14/13, 15/14, 7/5
[[Complexity spectrum]]: 15/13, 4/3, 13/10, 9/8, 13/11, 15/11, 12/11, 11/9, 11/8, 14/11, 16/13, 16/15, 11/10, 13/12, 9/7, 5/4, 18/13, 7/6, 6/5, 8/7, 10/9, 14/13, 15/14, 7/5


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