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Kalismic temperaments: Difference between revisions

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* ''[[Baldur]]'' (+2401/2400) → [[Breed family #Baldur|Breed family]]
* ''[[Baldur]]'' (+2401/2400) → [[Breed family #Baldur|Breed family]]
* ''[[Thor]]'' (+3025/3024 or 4375/4374) → [[Ragismic family #Thor|Ragismic family]]
* ''[[Thor]]'' (+3025/3024 or 4375/4374) → [[Ragismic family #Thor|Ragismic family]]
* ''[[Semihemimean]]'' (+3136/3125) → [[Hemimean family #Semihemimean|Hemimean family]]
* ''[[Loki]]'' (+5632/5625) → [[Vishdelismic clan #Loki|Vishdelismic clan]]
* ''[[Semiporwell]]'' (+6144/6125) → [[Porwell family #Semiporwell|Porwell family]]
* ''[[Semiporwell]]'' (+6144/6125) → [[Porwell family #Semiporwell|Porwell family]]
* ''[[Semicanou]]'' (+14641/14580) → [[Canou family #Semicanou|Canou family]]
* ''[[Semicathart]]'' (+14641/14580) → [[Cathartic family #Semicathart|Cathartic family]]
* ''[[Pessoal]]'' (+131072/130977) → [[Olympic clan #Pessoal|Olympic clan]]
* ''[[Odin]]'' (+151263/151250) → [[Landscape family #Odin|Landscape family]]


Considered below are lycoris, van gogh, sif, loki, pessoal, and linus, in the order of increasing [[badness]]. For the rank-4 temperament, see [[Rank-4 temperament #Kalismic (9801/9800)]].
Considered below are lycoris, van gogh, sif, diaspheric, and linus, in the order of increasing [[badness]]. For the rank-4 temperament, see [[Rank-4 temperament #Kalismic (9801/9800)]].


== Lycoris ==
== Lycoris ==
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Comma list: 9801/9800, 10648/10647, 1399680/1399489
Comma list: 9801/9800, 10648/10647, 1399680/1399489


Mapping: {{mapping| 2 1 -1 2 2 4 | 0 2 2 6 4 1 | 0 0 6 -5 1 4 }}
{{Mapping|legend=0| 2 1 -1 2 2 4 | 0 2 2 6 4 1 | 0 0 6 -5 1 4 }}
: mapping generators: ~99/70, ~1458/1001, ~81/70
: mapping generators: ~99/70, ~1458/1001, ~81/70


Line 84: Line 88:


{{Mapping|legend=1| 2 0 1 7 11 | 0 1 0 1 -1 | 0 0 4 -5 -1 }}
{{Mapping|legend=1| 2 0 1 7 11 | 0 1 0 1 -1 | 0 0 4 -5 -1 }}
: mapping generators: ~99/70, ~3
: mapping generators: ~99/70, ~3, ~48/35


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
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Comma list: 4096/4095, 6656/6655, 9801/9800
Comma list: 4096/4095, 6656/6655, 9801/9800


Mapping: {{mapping| 2 0 1 7 11 16 | 0 1 0 1 -1 -3 | 0 0 4 -5 -1 1 }}
{{Mapping|legend=0| 2 0 1 7 11 16 | 0 1 0 1 -1 -3 | 0 0 4 -5 -1 1 }}


Optimal tunings:  
Optimal tunings:  
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Badness (Sintel): 0.317
Badness (Sintel): 0.317


== Loki ==
== Diaspheric ==
[[Subgroup]]: 2.3.5.7.11
Diaspheric is notable for detempering [[diaschismic family #Septimal diaschismic|diaschismic]]. It was named by [[Eufalesio]] in 2026 as a variant of ''diaschismic''.  
 
[[Comma list]]: 5632/5625, 9801/9800
 
{{Mapping|legend=1| 2 0 0 -21 -18 | 0 1 0 4 2 | 0 0 1 3 4 }}
: mapping generators: ~99/70, ~3, ~5
 
[[Optimal tuning]]s:
* [[WE]]: ~99/70 = 599.9481{{c}}, ~3/2 = 702.1195{{c}}, ~5/4 = 386.7636{{c}}
: [[error map]]: {{val| -0.104 +0.061 +0.242 -0.005 -0.128 }}
* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 702.1647{{c}}, ~5/4 = 386.7768{{c}}
: error map: {{val| 0.000 +0.210 +0.463 +0.163 +0.119 }}
 
{{Optimal ET sequence|legend=1| 12, 22, 34d, 56d, 74d, 84de, 96d, 118, 130, 152, 248, 270, 670, 822, 940, 1092, 1362c, 2032c, 2302c }}
 
[[Badness]] (Sintel): 0.592
 
== Pessoal ==
{{See also| Pessoalisma }}
 
Pessoal tempers out the [[olympia]]. It was named by [[Aura]] in 2023, meaning [[Wiktionary: pessoal #Portuguese|"personal"]], for the fact that it is associated with [[abigail]], which is in turn a person's name.  


[[Subgroup]]: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 9801/9800, 131072/130977
[[Comma list]]: 9801/9800, 2252800/2250423


{{Mapping|legend=1| 2 0 1 10 14 | 0 1 0 -1 -3 | 0 0 3 -1 2 }}
{{Mapping|legend=1| 2 0 1 16 20 | 0 1 0 -5 -7 | 0 0 2 3 5 }}
: mapping generators: ~99/70, ~3, ~32/21
: mapping generators: ~99/70, ~3, ~1323/704


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~99/70 = 599.9711{{c}}, ~3/2 = 702.0265{{c}}, ~32/21 = 728.7942{{c}}
* [[WE]]: ~99/70 = 599.9742{{c}}, ~3/2 = 702.0681{{c}}, ~1323/704 = 1093.1024{{c}}
: [[error map]]: {{val| -0.058 +0.014 +0.040 +0.122 -0.040 }}
: [[error map]]: {{val| -0.052 +0.061 -0.015 +0.166 -0.138 }}
* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 702.0635{{c}}, ~32/21 = 728.8214{{c}}
* [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 702.0803{{c}}, ~1323/704 = 1093.1807{{c}}
: error map: {{val| 0.000 +0.109 +0.150 +0.289 +0.134 }}
: error map: {{val| 0.000 +0.133 +0.048 +0.275 -0.033 }}


{{Optimal ET sequence|legend=1| 36, 46, 84, 94, 130, 224, 270, 494, 764, 1164, 1658, 3586cd, 5244cdde, 6008bcdde }}
{{Optimal ET sequence|legend=1| 46, 58, 104c, 154ce, 166, 212, 224, 270, 494, 764 }}


[[Badness]] (Sintel): 0.599
[[Badness]] (Sintel): 0.950


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 1716/1715, 2080/2079, 4096/4095
Comma list: 1716/1715, 2080/2079, 10648/10647


Mapping: {{mapping| 2 0 1 10 14 13 | 0 1 0 -1 -3 -1 | 0 0 3 -1 2 -2 }}
{{Mapping|legend=0| 2 0 1 16 20 25 | 0 1 0 -5 -7 -9 | 0 0 2 3 5 6 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~99/70 = 599.9835{{c}}, ~3/2 = 702.0253{{c}}, ~32/21 = 728.7700{{c}}
* WE: ~99/70 = 599.9720{{c}}, ~3/2 = 702.0544{{c}}, ~1014/539 = 1093.1699{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 702.0477{{c}}, ~32/21 = 728.7882{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~3/2 = 702.0759{{c}}, ~1014/539 = 1093.1900{{c}}


{{Optimal ET sequence|legend=0| 36, 46, 84, 94, 130, 224, 270, 494, 764, 1258, 1882d, 2152d }}
{{Optimal ET sequence|legend=0| 46, 58, 104c, 154cef, 166, 212, 224, 270, 494, 764, 1258, 1810d, 2304d, 2574d }}


Badness (Sintel): 0.366
Badness (Sintel): 0.454


== Linus ==
== Linus ==
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Comma list: 1001/1000, 4225/4224, 4459/4455
Comma list: 1001/1000, 4225/4224, 4459/4455


Mapping: {{mapping| 10 0 0 -11 4 37 | 0 1 0 1 -1 0 | 0 0 1 1 2 0 }}
{{Mapping|legend=0| 10 0 0 -11 4 37 | 0 1 0 1 -1 0 | 0 0 1 1 2 0 }}


Optimal tunings:  
Optimal tunings:  
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Badness (Sintel): 0.721
Badness (Sintel): 0.721


[[Category:Kalismic temperaments| ]] <!-- main article -->
[[Category:Kalismic| ]] <!-- key article -->
[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Kalismic temperaments| ]] <!-- main article -->
[[Category:Catalogs of rank-3 temperaments]]
[[Category:Rank 3]]
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