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Kleismic rank-3 family: Difference between revisions

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Comma list: 325/324, 625/624
Comma list: 325/324, 625/624


Subgroup-val mapping: {{mapping| 1 0 1 0 0 | 0 6 5 0 14 | 0 0 0 1 0 }}
{{Mapping|legend=2| 1 0 1 0 0 | 0 6 5 0 14 | 0 0 0 1 0 }}


Optimal tunings:  
Optimal tunings:  
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Comma list: 325/324, 385/384, 625/624
Comma list: 325/324, 385/384, 625/624


Mapping: {{mapping| 1 0 1 0 6 0 | 0 6 5 0 1 14 | 0 0 0 1 -1 0 }}
{{Mapping|legend=0| 1 0 1 0 6 0 | 0 6 5 0 1 14 | 0 0 0 1 -1 0 }}


Optimal tunings:  
Optimal tunings:  
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Badness (Sintel): 0.636
Badness (Sintel): 0.636
Complexity spectrum: 6/5, 18/13, 15/13, 5/4, 4/3, 10/9, 13/12, 13/10, 16/15, 9/8, 8/7, 11/8, 11/10, 7/5, 12/11, 7/6, 16/13, 15/11, 15/14, 11/9, 9/7, 13/11, 14/13, 14/11


Scales: [[enlil19_13]]
Scales: [[enlil19_13]]
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Comma list: 325/324, 625/624, 1287/1280
Comma list: 325/324, 625/624, 1287/1280


Mapping: {{mapping| 1 0 1 0 9 0 | 0 6 5 0 -21 14 | 0 0 0 1 0 0 }}
{{Mapping|legend=0| 1 0 1 0 9 0 | 0 6 5 0 -21 14 | 0 0 0 1 0 0 }}


Optimal tunings:  
Optimal tunings:  
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Comma list: 325/324, 364/363, 625/624
Comma list: 325/324, 364/363, 625/624


Mapping: {{mapping| 1 0 1 0 1 0 | 0 6 5 0 4 14 | 0 0 0 2 1 0 }}
{{Mapping|legend=0| 1 0 1 0 1 0 | 0 6 5 0 4 14 | 0 0 0 2 1 0 }}


Optimal tunings:  
Optimal tunings:  
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Badness (Sintel): 0.817
Badness (Sintel): 0.817


== Catakleismoid ==
Catakleismoid is the same as catakleismic in the 2.3.5.7.13 subgroup but with an independent generator for prime 11.
[[Subgroup]]: 2.3.5.7.11
[[Comma list]]: 225/224, 4375/4374
{{Mapping|legend=1| 1 0 1 -3 0 | 0 6 5 22 0 | 0 0 0 0 1 }}
: mapping generators: ~2, ~6/5, ~11
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.5965{{c}}, ~6/5 = 316.8893{{c}}, ~11/8 = 549.5258{{c}}
: [[error map]]: {{val| +0.596 -0.619 -1.271 +0.948 -0.003 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 316.7705{{c}}, ~11/8 = 550.0343{{c}}
: error map: {{val| 0.000 -1.332 -2.461 +0.126 -1.284 }}
{{Optimal ET sequence|legend=1| 19, 34d, 53, 72, 197e, 269ce, 341ce }}
[[Badness]] (Sintel): 1.53
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 225/224, 325/324
{{Mapping|legend=0| 1 0 1 -3 0 0 | 0 6 5 22 0 14 | 0 0 0 0 1 0 }}
Optimal tunings:
* WE: ~2 = 1200.8238{{c}}, ~6/5 = 316.9478{{c}}, ~11/8 = 548.9611{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 316.7939{{c}}, ~11/8 = 549.5903{{c}}
{{Optimal ET sequence|legend=0| 19, 34d, 53, 72, 125f, 197ef }}
Badness (Sintel): 0.853
[[Category:Kleismic rank-3 family| ]] <!-- main article -->
[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Kleismic rank-3 family| ]] <!-- main article -->
[[Category:Catalogs of rank-3 temperaments]]
[[Category:Rank 3]]
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