Octagar temperaments: Difference between revisions

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 This is a collection of [[rank-2 temperament|rank-2]] [[regular temperament|temperaments]] [[tempering out]] the [[octagar comma]] ({{monzo|legend=1| 5 -4 3 -2 }}, [[ratio]]: 4000/3969).
-Temperaments considered below are slendi and slithy. Discussed elsewhere are:
+Temperaments discussed elsewhere are:
 * ''[[Sida]]'' (+25/24) → [[Dicot family #Sida|Dicot family]]
 * ''[[Rip]]'' (+36/35) → [[Ripple family #Rip|Ripple family]]
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 * ''[[Quintupole]]'' (+458752/455625) → [[Quintaleap family #Quintupole|Quintaleap family]]
-== Slendi ==
+Considered below are slithy, tridecatonic, slendi and dhaivatic, in the order of increasing [[badness]].
-Slendi may be described as the {{nowrap| 41 & 42 }} temperament. It has a generator of [[49/48]], seventeen of which give [[4/3]]. Its [[ploidacot]] is omega-17-cot.
-The name was likely derived from ''slendro diesis'', one of the names for the interval 49/48.
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 4000/3969, 84035/82944
-{{Mapping|legend=1| 1 2 3 3 | 0 -17 -28 -8 }}
-: mapping generators: ~2, ~49/48
-[[Optimal tuning]]s:
-* [[WE]]: ~2 = 1200.2515{{c}}, ~49/48 = 29.1870{{c}}
-: [[error map]]: {{val| +0.252 +2.368 -2.796 -1.568 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/48 = 29.1715{{c}}
-: error map: {{val| 0.000 +2.129 -3.116 -2.198 }}
-{{Optimal ET sequence|legend=1| 1c, 40c, 41, 206 }}
-[[Badness]] (Sintel): 3.62
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 100/99, 245/242, 46656/46585
-Mapping: {{mapping| 1 2 3 3 4 | 0 -17 -28 -8 -22 }}
-Optimal tunings:
-* WE: ~2 = 1199.8027{{c}}, ~49/48 = 29.1751{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 29.1875{{c}}
-{{Optimal ET sequence|legend=0| 1ce, 40c, 41 }}
-Badness (Sintel): 2.09
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 100/99, 144/143, 245/242, 343/338
-Mapping: {{mapping| 1 2 3 3 4 4 | 0 -17 -28 -8 -22 -12 }}
-Optimal tunings:
-* WE: ~2 = 1199.0915{{c}}, ~49/48 = 29.1033{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 29.1576{{c}}
-{{Optimal ET sequence|legend=0| 1ce, 41 }}
-Badness (Sintel): 1.80
 == Slithy ==
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 Badness (Sintel): 1.56
+== Slendi ==
+Slendi may be described as the {{nowrap| 41 & 42 }} temperament. It has a generator of [[49/48]], seventeen of which give [[4/3]]. Its [[ploidacot]] is omega-17-cot.
+The name was likely derived from ''slendro diesis'', one of the names for the interval 49/48.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 4000/3969, 84035/82944
+{{Mapping|legend=1| 1 2 3 3 | 0 -17 -28 -8 }}
+: mapping generators: ~2, ~49/48
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.2515{{c}}, ~49/48 = 29.1870{{c}}
+: [[error map]]: {{val| +0.252 +2.368 -2.796 -1.568 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/48 = 29.1715{{c}}
+: error map: {{val| 0.000 +2.129 -3.116 -2.198 }}
+{{Optimal ET sequence|legend=1| 1c, 40c, 41, 206 }}
+[[Badness]] (Sintel): 3.62
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 100/99, 245/242, 46656/46585
+Mapping: {{mapping| 1 2 3 3 4 | 0 -17 -28 -8 -22 }}
+Optimal tunings:
+* WE: ~2 = 1199.8027{{c}}, ~49/48 = 29.1751{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 29.1875{{c}}
+{{Optimal ET sequence|legend=0| 1ce, 40c, 41 }}
+Badness (Sintel): 2.09
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 100/99, 144/143, 245/242, 343/338
+Mapping: {{mapping| 1 2 3 3 4 4 | 0 -17 -28 -8 -22 -12 }}
+Optimal tunings:
+* WE: ~2 = 1199.0915{{c}}, ~49/48 = 29.1033{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 29.1576{{c}}
+{{Optimal ET sequence|legend=0| 1ce, 41 }}
+Badness (Sintel): 1.80
 == Dhaivatic ==