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Octagar temperaments: Difference between revisions

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* ''[[Quartonic]]'' (+1728/1715) → [[Quartonic family #Septimal quartonic|Quartonic family]]
* ''[[Quartonic]]'' (+1728/1715) → [[Quartonic family #Septimal quartonic|Quartonic family]]
* ''[[Hemikleismic]]'' (+6144/6125) → [[Kleismic family #Hemikleismic|Kleismic family]]
* ''[[Hemikleismic]]'' (+6144/6125) → [[Kleismic family #Hemikleismic|Kleismic family]]
* ''[[Trisedodge]]'' (+110592/109375) → [[Trisedodge family #Septimal trisedodge|Trisedodge family]]


Considered below are pluto, slithy, tridecatonic, slendi and dhaivatic, in the order of increasing [[badness]].  
Considered below are pluto, slithy, tridecatonic, slendi and dhaivatic, in the order of increasing [[badness]].  
Line 47: Line 48:
Comma list: 540/539, 896/891, 1375/1372
Comma list: 540/539, 896/891, 1375/1372


Mapping: {{mapping| 1 -2 -11 -10 5 | 0 7 26 25 -3 }}
{{Mapping|legend=0| 1 -2 -11 -10 5 | 0 7 26 25 -3 }}


Optimal tunings:  
Optimal tunings:  
Line 62: Line 63:
Comma list: 325/324, 352/351, 364/363, 540/539
Comma list: 325/324, 352/351, 364/363, 540/539


Mapping: {{mapping| 1 -2 -11 -10 5 16 | 0 7 26 25 -3 -24 }}
{{Mapping|legend=0| 1 -2 -11 -10 5 16 | 0 7 26 25 -3 -24 }}


Optimal tunings:  
Optimal tunings:  
Line 77: Line 78:
Comma list: 256/255, 325/324, 352/351, 364/363, 540/539
Comma list: 256/255, 325/324, 352/351, 364/363, 540/539


Mapping: {{mapping| 1 -2 -11 -10 5 16 21 | 0 7 26 25 -3 -24 -33 }}
{{Mapping|legend=0| 1 -2 -11 -10 5 16 21 | 0 7 26 25 -3 -24 -33 }}


Optimal tunings:  
Optimal tunings:  
Line 92: Line 93:
Comma list: 190/189, 256/255, 325/324, 352/351, 361/360, 595/594
Comma list: 190/189, 256/255, 325/324, 352/351, 361/360, 595/594


Mapping: {{mapping| 1 -2 -11 -10 5 16 21 -6 | 0 7 26 25 -3 -24 -33 20 }}
{{Mapping|legend=0| 1 -2 -11 -10 5 16 21 -6 | 0 7 26 25 -3 -24 -33 20 }}


Optimal tunings:  
Optimal tunings:  
Line 107: Line 108:
Comma list: 144/143, 196/195, 275/273, 896/891
Comma list: 144/143, 196/195, 275/273, 896/891


Mapping: {{mapping| 1 -2 -11 -10 5 -5 | 0 7 26 25 -3 17 }}
{{Mapping|legend=0| 1 -2 -11 -10 5 -5 | 0 7 26 25 -3 17 }}


Optimal tunings:  
Optimal tunings:  
Line 122: Line 123:
Comma list: 100/99, 245/242, 10976/10935
Comma list: 100/99, 245/242, 10976/10935


Mapping: {{mapping| 1 -2 -11 -10 -16 | 0 7 26 25 38 }}
{{Mapping|legend=0| 1 -2 -11 -10 -16 | 0 7 26 25 38 }}


Optimal tunings:  
Optimal tunings:  
Line 137: Line 138:
Comma list: 100/99, 196/195, 245/242, 729/728
Comma list: 100/99, 196/195, 245/242, 729/728


Mapping: {{mapping| 1 5 15 15 22 12 | 0 7 26 25 38 17 }}
{{Mapping|legend=0| 1 5 15 15 22 12 | 0 7 26 25 38 17 }}


Optimal tunings:  
Optimal tunings:  
Line 172: Line 173:
Comma list: 540/539, 2200/2187, 4375/4356
Comma list: 540/539, 2200/2187, 4375/4356


Mapping: {{mapping| 1 -16 -31 -12 -53 | 0 19 36 16 61 }}
{{Mapping|legend=0| 1 -16 -31 -12 -53 | 0 19 36 16 61 }}


Optimal tunings:  
Optimal tunings:  
Line 187: Line 188:
Comma list: 325/324, 352/351, 540/539, 1575/1573
Comma list: 325/324, 352/351, 540/539, 1575/1573


Mapping: {{mapping| 1 -16 -31 -12 -53 0 | 0 19 36 16 61 4 }}
{{Mapping|legend=0| 1 -16 -31 -12 -53 0 | 0 19 36 16 61 4 }}


Optimal tunings:  
Optimal tunings:  
Line 202: Line 203:
Comma list: 325/324, 352/351, 375/374, 540/539, 595/594
Comma list: 325/324, 352/351, 375/374, 540/539, 595/594


Mapping: {{mapping| 1 -16 -31 -12 -53 0 -57 | 0 19 36 16 61 4 66 }}
{{Mapping|legend=0| 1 -16 -31 -12 -53 0 -57 | 0 19 36 16 61 4 66 }}


Optimal tunings:  
Optimal tunings:  
Line 217: Line 218:
Comma list: 190/189, 325/324, 352/351, 361/360, 375/374, 595/594
Comma list: 190/189, 325/324, 352/351, 361/360, 375/374, 595/594


Mapping: {{mapping| 1 -16 -31 -12 -53 0 -57 -30 | 0 19 36 16 61 4 66 37 }}
{{Mapping|legend=0| 1 -16 -31 -12 -53 0 -57 -30 | 0 19 36 16 61 4 66 37 }}


Optimal tunings:  
Optimal tunings:  
Line 232: Line 233:
Comma list: 190/189, 300/299, 323/322, 325/324, 352/351, 361/360, 484/483
Comma list: 190/189, 300/299, 323/322, 325/324, 352/351, 361/360, 484/483


Mapping: {{mapping| 1 -16 -31 -12 -53 0 -57 -30 -76 | 0 19 36 16 61 4 66 37 87 }}
{{Mapping|legend=0| 1 -16 -31 -12 -53 0 -57 -30 -76 | 0 19 36 16 61 4 66 37 87 }}


Optimal tunings:  
Optimal tunings:  
Line 269: Line 270:
Comma list: 99/98, 1944/1925, 2560/2541
Comma list: 99/98, 1944/1925, 2560/2541


Mapping: {{mapping| 13 0 -11 16 45 | 0 1 2 1 0 }}
{{Mapping|legend=0| 13 0 -11 16 45 | 0 1 2 1 0 }}


Optimal tunings:  
Optimal tunings:  
Line 284: Line 285:
Comma list: 99/98, 144/143, 275/273, 1040/1029
Comma list: 99/98, 144/143, 275/273, 1040/1029


Mapping: {{mapping| 13 0 -11 16 45 7 | 0 1 2 1 0 2 }}
{{Mapping|legend=0| 13 0 -11 16 45 7 | 0 1 2 1 0 2 }}


Optimal tunings:  
Optimal tunings:  
Line 321: Line 322:
Comma list: 100/99, 245/242, 46656/46585
Comma list: 100/99, 245/242, 46656/46585


Mapping: {{mapping| 1 2 3 3 4 | 0 -17 -28 -8 -22 }}
{{Mapping|legend=0| 1 2 3 3 4 | 0 -17 -28 -8 -22 }}


Optimal tunings:  
Optimal tunings:  
Line 336: Line 337:
Comma list: 100/99, 144/143, 245/242, 343/338
Comma list: 100/99, 144/143, 245/242, 343/338


Mapping: {{mapping| 1 2 3 3 4 4 | 0 -17 -28 -8 -22 -12 }}
{{Mapping|legend=0| 1 2 3 3 4 4 | 0 -17 -28 -8 -22 -12 }}


Optimal tunings:  
Optimal tunings:  
Line 398: Line 399:
== References ==
== References ==


[[Category:Octagar temperaments| ]] <!-- main article -->
[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Octagar temperaments| ]] <!-- main article -->
[[Category:Catalogs of rank-2 temperaments]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Octagar_temperaments"