Octagar temperaments: Difference between revisions

← Older edit Newer edit →

VisualWikitext

@@ Line 20: / Line 20: @@
 == 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
@@ Line 25: / Line 29: @@
 {{Mapping|legend=1| 1 2 3 3 | 0 -17 -28 -8 }}
+: mapping generators: ~2, ~49/48
 [[Optimal tuning]]s:
-* [[WE]]: ~2 = 1200.252{{c}}, ~49/48 = 29.187{{c}}
+* [[WE]]: ~2 = 1200.2515{{c}}, ~49/48 = 29.1870{{c}}
-* [[CWE]]: ~2 = 1200.000{{c}}, ~49/48 = 29.172{{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| 41, 206, 247bc, 288bcd, 329bcd }}
+{{Optimal ET sequence|legend=1| 1c, 40c, 41, 206 }}
-[[Badness]] (Sintel): 3.616
+[[Badness]] (Sintel): 3.62
 === 11-limit ===
@@ Line 42: / Line 49: @@
 Optimal tunings:
-* WE: ~2 = 1199.803{{c}}, ~49/48 = 29.175{{c}}
+* WE: ~2 = 1199.8027{{c}}, ~49/48 = 29.1751{{c}}
-* CWE: ~2 = 1200.000{{c}}, ~49/48 = 29.188{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 29.1875{{c}}
-{{Optimal ET sequence|legend=0| 41, 206e }}
+{{Optimal ET sequence|legend=0| 1ce, 40c, 41 }}
-Badness (Sintel): 2.090
+Badness (Sintel): 2.09
 === 13-limit ===
@@ Line 57: / Line 64: @@
 Optimal tunings:
-* WE: ~2 = 1199.091{{c}}, ~40/39 = 29.103{{c}}
+* WE: ~2 = 1199.0915{{c}}, ~49/48 = 29.1033{{c}}
-* CWE: ~2 = 1200.000{{c}}, ~40/39 = 29.158{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 29.1576{{c}}
-{{Optimal ET sequence|legend=0| 41, 124ef, 165ef }}
+{{Optimal ET sequence|legend=0| 1ce, 41 }}
-Badness (Sintel): 1.803
+Badness (Sintel): 1.80
 == Slithy ==