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Keemic temperaments: Difference between revisions

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Undeka 13-limit -> no-13 17-limit. Pentadecal 13-limit -> no-11 13-limit
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Named by [[Xenllium]] in 2021, pentadecal tempers out the 15-5/3-comma ({{monzo| -11 -15 15 }}) in the 5-limit. This temperament can be described as {{nowrap| 15 & 60 }} temperament, tempering out the [[cloudy comma]], 16807/16384 and the [[keema]], 875/864 in the 7-limit.
Named by [[Xenllium]] in 2021, pentadecal tempers out the 15-5/3-comma ({{monzo| -11 -15 15 }}) in the 5-limit. This temperament can be described as {{nowrap| 15 & 60 }} temperament, tempering out the [[cloudy comma]], 16807/16384 and the [[keema]], 875/864 in the 7-limit.


=== 7-limit ===
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


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[[Badness]] (Sintel): 2.91
[[Badness]] (Sintel): 2.91


=== 11-limit ===
==== 2.3.5.7.13 subgroup ====
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.13
 
Comma list: 100/99, 385/384, 1372/1331


Mapping: {{mapping| 15 0 11 42 52 | 0 1 1 0 0 }}
Comma list: 105/104, 325/324, 15625/15379
 
Optimal tunings:
* WE: ~21/20 = 80.0213{{c}}, ~3/2 = 702.9194{{c}} (~56/55 = 17.2721{{c}})
* CWE: ~21/20 = 80.0000{{c}}, ~3/2 = 702.8751{{c}} (~56/55 = 17.1249{{c}})
 
{{Optimal ET sequence|legend=0| 15, 45, 60, 75de, 135de }}
 
Badness (Sintel): 2.56
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 100/99, 105/104, 144/143, 1372/1331


Mapping: {{mapping| 15 0 11 42 52 8 | 0 1 1 0 0 2 }}
Mapping: {{mapping| 15 0 11 42 52 8 | 0 1 1 0 0 2 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~21/20 = 80.0207{{c}}, ~3/2 = 701.8966{{c}} (~91/90 = 18.2900{{c}})
* WE: ~21/20 = 80.1133{{c}}, ~3/2 = 700.1871{{c}} (~91/90 = 20.8325{{c}})
* CWE: ~21/20 = 80.0000{{c}}, ~3/2 = 701.8545{{c}} (~91/90 = 18.1455{{c}})
* CWE: ~21/20 = 80.0000{{c}}, ~3/2 = 700.2086{{c}} (~91/90 = 19.7914{{c}})


{{Optimal ET sequence|legend=0| 15, 45f, 60, 135de, 195cddee }}
{{Optimal ET sequence|legend=0| 15, 30bcff, 45f, 60 }}


Badness (Sintel): 2.14
Badness (Sintel): 1.80


=== Quindecal ===
=== Quindecal ===
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Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 121/120, 196/195, 352/351, 875/864
Comma list: 105/104, 121/120, 275/273, 325/324


Mapping: {{mapping| 15 0 11 42 28 103 | 0 1 1 0 1 -2 }}
Mapping: {{mapping| 15 0 11 42 28 8 | 0 1 1 0 1 2 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~21/20 = 80.1015{{c}}, ~3/2 = 702.5374{{c}} (~126/125 = 18.3763{{c}})
* WE: ~21/20 = 80.1359{{c}}, ~3/2 = 700.2567{{c}} (~91/90 = 20.9661{{c}})
* CWE: ~21/20 = 80.0000{{c}}, ~3/2 = 701.8504{{c}} (~126/125 = 18.1496{{c}})
* CWE: ~21/20 = 80.0000{{c}}, ~3/2 = 700.2955{{c}} (~91/90 = 19.7045{{c}})


{{Optimal ET sequence|legend=0| 15f, 60e, 135deef }}
{{Optimal ET sequence|legend=0| 15, 30bceff, 45ef, 60e }}


Badness (Sintel): 2.29
Badness (Sintel): 1.34


== Undeka ==
== Undeka ==
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Badness (Sintel): 2.27
Badness (Sintel): 2.27


=== 13-limit ===
=== 2.3.5.7.11.17 subgroup ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.17


Comma list: 65/63, 100/99, 169/165, 352/343
Comma list: 85/84, 100/99, 121/119, 385/384


Mapping: {{mapping| 11 0 8 31 38 23 | 0 1 1 0 0 1 }}
Mapping: {{mapping| 11 0 8 31 38 45 | 0 1 1 0 0 0 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~13/12 = 109.1184{{c}}, ~3/2 = 707.9422{{c}}
* WE: ~17/16 = 109.0232{{c}}, ~3/2 = 706.5074{{c}}
* CWE: ~13/12 = 109.0909{{c}}, ~3/2 = 707.9065{{c}}
* CWE: ~17/16 = 109.0909{{c}}, ~3/2 = 706.6786{{c}}


{{Optimal ET sequence|legend=0| 11cf, 22 }}
{{Optimal ET sequence|legend=0| 11c, 22 }}


Badness (Sintel): 2.34
Badness (Sintel): 1.82


== Hyperkleismic ==
== Hyperkleismic ==
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