Octagar temperaments: Difference between revisions

← Older edit Newer edit →

VisualWikitext

@@ Line 16: / Line 16: @@
 * ''[[Hamity]]'' (+2430/2401) → [[Amity family #Hamity|Amity family]]
 * ''[[Hemikleismic]]'' (+6144/6125) → [[Kleismic family #Hemikleismic|Kleismic family]]
-* ''[[Pluto]]'' (+10976/10935) → [[Mirkwai clan #Pluto|Mirkwai clan]]
 * ''[[Quintupole]]'' (+458752/455625) → [[Quintaleap family #Quintupole|Quintaleap family]]
-Considered below are 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]].
+== Pluto ==
+{{Distinguish| Plutus }}
+Pluto, named by [[Gene Ward Smith]] in 2010<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_18465.html Yahoo! Tuning Group | ''19-limit Pluto temperament'']</ref>, can be described as the {{nowrap| 41 & 80 }} temperament. It is generated by a flattened [[10/7]], and [[121edo|59\121]] is about perfect as a tuning.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 4000/3969, 10976/10935
+{{Mapping|legend=1| 1 -2 -11 -10 | 0 7 26 25 }}
+: mapping generators: ~2, ~10/7
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.4720{{c}}, ~10/7 = 614.5826{{c}}
+: [[error map]]: {{val| -0.528 +1.179 -1.358 +1.020 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 614.8282{{c}}
+: error map: {{val| 0.000 +1.843 -0.780 +1.880 }}
+{{Optimal ET sequence|legend=1| 39d, 41, 80, 121, 283d, 404bd }}
+[[Badness]] (Sintel): 1.46
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 540/539, 896/891, 1375/1372
+Mapping: {{mapping| 1 -2 -11 -10 5 | 0 7 26 25 -3 }}
+Optimal tunings:
+* WE: ~2 = 1200.1835{{c}}, ~10/7 = 614.4677{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.8616{{c}}
+{{Optimal ET sequence|legend=0| 39d, 41, 80, 121 }}
+Badness (Sintel): 0.987
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 325/324, 352/351, 364/363, 540/539
+Mapping: {{mapping| 1 -2 -11 -10 5 16 | 0 7 26 25 -3 -24 }}
+Optimal tunings:
+* WE: ~2 = 1199.2469{{c}}, ~10/7 = 614.4908{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.8684{{c}}
+{{Optimal ET sequence|legend=0| 39d, 41, 80, 121 }}
+Badness (Sintel): 1.06
+===== 17-limit =====
+Subgroup: 2.3.5.7.11.13.17
+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 }}
+Optimal tunings:
+* WE: ~2 = 1199.2009{{c}}, ~10/7 = 614.4746{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.8813{{c}}
+{{Optimal ET sequence|legend=0| 39d, 41, 80, 121 }}
+Badness (Sintel): 1.09
+===== 19-limit =====
+Subgroup: 2.3.5.7.11.13.17.19
+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 }}
+Optimal tunings:
+* WE: ~2 = 1199.2833{{c}}, ~10/7 = 614.5237{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.8876{{c}}
+{{Optimal ET sequence|legend=0| 39d, 41, 80, 121 }}
+Badness (Sintel): 1.07
+==== Orcus ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 144/143, 196/195, 275/273, 896/891
+Mapping: {{mapping| 1 -2 -11 -10 5 -5 | 0 7 26 25 -3 17 }}
+Optimal tunings:
+* WE: ~2 = 1198.7372{{c}}, ~10/7 = 614.2418{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.8502{{c}}
+{{Optimal ET sequence|legend=0| 39df, 41, 80f, 121ff }}
+Badness (Sintel): 1.38
+=== Plutino ===
+Subgroup: 2.3.5.7.11
+Comma list: 100/99, 245/242, 10976/10935
+Mapping: {{mapping| 1 -2 -11 -10 -16 | 0 7 26 25 38 }}
+Optimal tunings:
+* WE: ~2 = 1199.7793{{c}}, ~10/7 = 614.6040{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.7074{{c}}
+{{Optimal ET sequence|legend=0| 39dee, 41 }}
+Badness (Sintel): 1.92
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 100/99, 196/195, 245/242, 729/728
+Mapping: {{mapping| 1 5 15 15 22 12 | 0 7 26 25 38 17 }}
+Optimal tunings:
+* WE: ~2 = 1199.0328{{c}}, ~10/7 = 614.2729{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.7277{{c}}
+{{Optimal ET sequence|legend=0| 39deef, 41 }}
+Badness (Sintel): 1.66
 == Slithy ==
@@ Line 269: / Line 395: @@
 Badness (Sintel): 1.55
+== References ==
 [[Category:Temperament collections]]
 [[Category:Octagar temperaments| ]] <!-- main article -->
 [[Category:Rank 2]]