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Compton family: Difference between revisions

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Line 59: Line 59:
Comma list: 225/224, 441/440, 4375/4356
Comma list: 225/224, 441/440, 4375/4356


Mapping: {{mapping| 12 19 0 -22 -42 | 0 0 1 2 3 }}
{{Mapping|legend=0| 12 19 0 -22 -42 | 0 0 1 2 3 }}


Optimal tunings:  
Optimal tunings:  
Line 74: Line 74:
Comma list: 225/224, 351/350, 364/363, 441/440
Comma list: 225/224, 351/350, 364/363, 441/440


Mapping: {{mapping| 12 19 0 -22 -42 -67 | 0 0 1 2 3 4 }}
{{Mapping|legend=0| 12 19 0 -22 -42 -67 | 0 0 1 2 3 4 }}


Optimal tunings:  
Optimal tunings:  
Line 89: Line 89:
Comma list: 221/220, 225/224, 289/288, 351/350, 441/440
Comma list: 221/220, 225/224, 289/288, 351/350, 441/440


Mapping: {{mapping| 12 19 0 -22 -42 -67 49 | 0 0 1 2 3 4 0 }}
{{Mapping|legend=0| 12 19 0 -22 -42 -67 49 | 0 0 1 2 3 4 0 }}


Optimal tunings:  
Optimal tunings:  
Line 104: Line 104:
Comma list: 225/224, 325/324, 441/440, 1001/1000
Comma list: 225/224, 325/324, 441/440, 1001/1000


Mapping: {{mapping| 12 19 0 -22 -42 100 | 0 0 1 2 3 -2 }}
{{Mapping|legend=0| 12 19 0 -22 -42 100 | 0 0 1 2 3 -2 }}


Optimal tunings:  
Optimal tunings:  
Line 119: Line 119:
Comma list: 225/224, 273/272, 289/288, 325/324, 441/440
Comma list: 225/224, 273/272, 289/288, 325/324, 441/440


Mapping: {{mapping| 12 19 0 -22 -42 100 49 | 0 0 1 2 3 -2 0 }}
{{Mapping|legend=0| 12 19 0 -22 -42 100 49 | 0 0 1 2 3 -2 0 }}


Optimal tunings:  
Optimal tunings:  
Line 155: Line 155:
Comma list: 81/80, 99/98, 128/125
Comma list: 81/80, 99/98, 128/125


Mapping: {{mapping| 12 19 28 0 -26 | 0 0 0 1 2 }}
{{Mapping|legend=0| 12 19 28 0 -26 | 0 0 0 1 2 }}


Optimal tunings:  
Optimal tunings:  
Line 170: Line 170:
Comma list: 81/80, 128/125, 540/539
Comma list: 81/80, 128/125, 540/539


Mapping: {{mapping| 12 19 28 0 109 | 0 0 0 1 -2 }}
{{Mapping|legend=0| 12 19 28 0 109 | 0 0 0 1 -2 }}


Optimal tunings:  
Optimal tunings:  
Line 185: Line 185:
Comma list: 56/55, 81/80, 128/125
Comma list: 56/55, 81/80, 128/125


Mapping: {{mapping| 12 19 28 0 8 | 0 0 0 1 1 }}
{{Mapping|legend=0| 12 19 28 0 8 | 0 0 0 1 1 }}


Optimal tunings:  
Optimal tunings:  
Line 200: Line 200:
Comma list: 56/55, 66/65, 81/80, 105/104
Comma list: 56/55, 66/65, 81/80, 105/104


Mapping: {{mapping| 12 19 28 0 8 11 | 0 0 0 1 1 1 }}
{{Mapping|legend=0| 12 19 28 0 8 11 | 0 0 0 1 1 1 }}


Optimal tunings:  
Optimal tunings:  
Line 215: Line 215:
Comma list: 51/50, 56/55, 66/65, 81/80, 105/104
Comma list: 51/50, 56/55, 66/65, 81/80, 105/104


Mapping: {{mapping| 12 19 28 0 8 11 49 | 0 0 0 1 1 1 0 }}
{{Mapping|legend=0| 12 19 28 0 8 11 49 | 0 0 0 1 1 1 0 }}


Optimal tunings:  
Optimal tunings:  
Line 230: Line 230:
Comma list: 51/50, 56/55, 66/65, 76/75, 81/80, 96/95
Comma list: 51/50, 56/55, 66/65, 76/75, 81/80, 96/95


Mapping: {{mapping| 12 19 28 0 8 11 49 51 | 0 0 0 1 1 1 0 0 }}
{{Mapping|legend=0| 12 19 28 0 8 11 49 51 | 0 0 0 1 1 1 0 0 }}


Optimal tunings:  
Optimal tunings:  
Line 241: Line 241:


==== Duodecic ====
==== Duodecic ====
{{Distinguish|Duodecim}}
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 56/55, 81/80, 91/90, 128/125
Comma list: 56/55, 81/80, 91/90, 128/125


Mapping: {{mapping| 12 19 28 0 8 78 | 0 0 0 1 1 -1 }}
{{Mapping|legend=0| 12 19 28 0 8 78 | 0 0 0 1 1 -1 }}


Optimal tunings:  
Optimal tunings:  
Line 275: Line 277:
Comma list: 51/50, 56/55, 76/75, 81/80, 91/90, 96/95
Comma list: 51/50, 56/55, 76/75, 81/80, 91/90, 96/95


Mapping: {{mapping| 12 19 28 0 8 78 49 51 | 0 0 0 1 1 -1 0 0 }}
{{Mapping|legend=0| 12 19 28 0 8 78 49 51 | 0 0 0 1 1 -1 0 0 }}


Optimal tunings:  
Optimal tunings:  
Line 286: Line 288:


=== Paly ===
=== Paly ===
[[Subgroup]]: 2.3.5.7.11.13.17.19
{{Todo|inline=1|complete section|unify precision|comment= Sort the comma basis. Normalize the mapping. Unify the cent values in optimal tunings to 4 decimal places. Add the optimal ET sequence. <br>Add the data for the 11-, 13-, and 17-limit versions. }}


[[Comma list]]: 81/80, 91/90, 51/50, 128/125, 76/75, 121/120
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19


{{Mapping|24 38 56 48 83 108 98 102|0 0 0 1 0 -1 0 0|legend=1}}
Comma list: 81/80, 91/90, 51/50, 128/125, 76/75, 121/120


[[Optimal tuning|Optimal tunings]]:
{{Mapping| 24 38 56 48 83 108 98 102 | 0 0 0 1 0 -1 0 0 }}


* [[WE]]: ~33/32 = 49.994{{c}}, ~7/4 = 965.340{{c}}
Optimal tunings:
* WE: ~33/32 = 49.994{{c}}, ~7/4 = 965.340{{c}}
: error map: {{val| -0.144 -2.183 +13.350 -3.774 -1.816 -6.516 -5.543 +1.875 }}
* CWE: ~33/32 = 50.000{{c}}, ~7/4 = 965.449{{c}}
: error map: {{val| -0.000 -1.955 +13.686 -3.377 -1.318 -5.977 -4.955 +2.487 }}


: [[error map]]: {{val|-0.144 -2.183 +13.350 -3.774 -1.816 -6.516 -5.543 +1.875}}
Badness (Sintel): 2.383


* [[CWE]]: ~33/32 = 50.000{{c}}, ~7/4 = 965.449{{c}}
== Duodecim ==
{{Distinguish|Duodecic}}


: error map: {{val|-0.000 -1.955 +13.686 -3.377 -1.318 -5.977 -4.955 +2.487}}
Edo join: 24 & 48cf
[[Badness]] (Sintel): 2.383
== Duodecim ==
Duodecim uses exactly the same mapping as the 7-limit of 12edo, only correcting its poor approximation of prime 11.  
Duodecim uses exactly the same mapping as the 7-limit of 12edo, only correcting its poor approximation of prime 11.  


Line 353: Line 354:
Comma list: 243/242, 385/384, 9801/9800
Comma list: 243/242, 385/384, 9801/9800


Mapping: {{mapping| 24 38 0 123 83 | 0 0 1 -1 0 }}
{{Mapping|legend=0| 24 38 0 123 83 | 0 0 1 -1 0 }}


Optimal tunings:  
Optimal tunings:  
Line 368: Line 369:
Comma list: 243/242, 351/350, 364/363, 385/384
Comma list: 243/242, 351/350, 364/363, 385/384


Mapping: {{mapping| 24 38 0 123 83 33 | 0 0 1 -1 0 1 }}
{{Mapping|legend=0| 24 38 0 123 83 33 | 0 0 1 -1 0 1 }}


Optimal tunings:  
Optimal tunings:  
Line 406: Line 407:
Comma list: 540/539, 1029/1024, 4000/3993
Comma list: 540/539, 1029/1024, 4000/3993


Mapping: {{mapping| 36 57 0 101 41 | 0 0 1 0 1 }}
{{Mapping|legend=0| 36 57 0 101 41 | 0 0 1 0 1 }}


Optimal tunings:  
Optimal tunings:  
Line 435: Line 436:
[[Badness]] (Sintel): 1.24
[[Badness]] (Sintel): 1.24


[[Category:Temperament families]]
[[Category:Compton family| ]] <!-- main article -->
[[Category:Compton family| ]] <!-- main article -->
[[Category:Compton| ]] <!-- key article -->
[[Category:Compton| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Temperament families]]
[[Category:Catalogs of rank-2 temperaments]]
Retrieved from "https://en.xen.wiki/w/Compton_family"