Syntonic–diatonic equivalence continuum: Difference between revisions

← Older edit

VisualWikitext

@@ Line 179: / Line 179: @@
 |}
-== Superpyth ==
+== Superpyth (5-limit) ==
 : ''For extensions, see [[Archytas clan #Superpyth]] and [[Jubilismic clan #Bipyth]].''
@@ Line 202: / Line 202: @@
 [[Badness]] (Sintel): 3.17
-== Uncle ==
+== Uncle (5-limit) ==
 : ''For extensions, see [[Trienstonic clan #Uncle]].''
@@ Line 225: / Line 225: @@
 [[Badness]] (Sintel): 6.33
-== Ultrapyth ==
+== Ultrapyth (5-limit) ==
 : ''For extensions, see [[Archytas clan #Ultrapyth]].''
@@ Line 271: / Line 271: @@
 [[Badness]] (Sintel): 55.3
-== Rodan ==
+== Rodan (5-limit) ==
 : ''For extensions, see [[Gamelismic clan #Rodan]].''
@@ Line 361: / Line 361: @@
 -->
-== Hemiseven ==
+== Hemiseven (5-limit) ==
 : ''For extensions, see [[Gamelismic clan #Hemiseven]].''
@@ Line 403: / Line 403: @@
 [[Badness]] (Sintel): 35.2
-== Septiquarter ==
+== Septiquarter (5-limit) ==
 : ''For extensions, see [[Hemifamity temperaments #Septiquarter]].''
@@ Line 424: / Line 424: @@
 [[Badness]] (Sintel): 22.8
-== Tokko ==
+== Tokko (5-limit) ==
 : ''For extensions, see [[Wizmic microtemperaments #Tokko]].''
@@ Line 431: / Line 431: @@
 [[Comma list]]: {{monzo| -76 67 -13 }}
-{{Mapping|legend=1| 1 12 56 | 0 -13 -67 }}
+{{Mapping|legend=1| 1 -1 -11 | 0 13 67 }}
+: mapping generators: ~2, ~{{monzo| -35 31 -6 }}
-: mapping generators: ~2, ~{{monzo| 36 -31 6 }}
 [[Optimal tuning]]s:
-* [[WE]]: ~2 = 1200.0377{{c}}, ~{{monzo| 36 -31 6 }} = 961.4293{{c}}
+* [[WE]]: ~2 = 1200.0377{{c}}, ~{{monzo| -35 31 -6 }} = 238.6084{{c}}
 : [[error map]]: {{val| +0.038 -0.083 +0.035 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~{{monzo| 36 -31 6 }} = 961.3985{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~{{monzo| -35 31 -6 }} = 238.6015{{c}}
 : error map: {{val| 0.000 -0.135 -0.011 }}
-{{Optimal ET sequence|legend=1| 5, …, 166, 171, 860, 1031, 1202, 1373, 1544 }}
+{{Optimal ET sequence|legend=1| 5, …, 166, 171, 860, 1031, 1202, 1373, 1544, 3259, 4803b, 6347b }}
 [[Badness]] (Sintel): 20.9
@@ Line 452: / Line 451: @@
 {{Mapping|legend=1| 1 -2 -16 | 0 9 46 }}
 : mapping generators: ~2, ~320/243
@@ Line 460: / Line 458: @@
 {{Optimal ET sequence|legend=1| 5, 108c, 113, 118, 1057, 1175, 1293, 1411, 1529, 1647, 1765, 1883, 2001b, 3884b }}
-[[Badness]] (Smith): 0.617683
+[[Badness]] (Sintel): 14.5
 == Tribilalegu (5 & 137) ==
@@ Line 467: / Line 465: @@
 [[Comma list]]: {{Monzo| -60 54 -11 }}
-{{Mapping|legend=1| 1 6 24 | 0 -11 -54 }}
+{{Mapping|legend=1| 1 -5 -30 | 0 11 54 }}
+: mapping generators: ~2, ~243/160
-: mapping generators: ~2, ~320/243
 [[Optimal tuning]]s:
-* [[POTE]]: ~2 = 1200.000{{c}}, ~320/243 = 481.742{{c}}
+* [[POTE]]: ~2 = 1200.000{{c}}, ~243/160 = 718.258{{c}}
 {{Optimal ET sequence|legend=1| 5, 127c, 132, 137, 553, 690b, 827b, 964b }}
-[[Badness]] (Smith): 3.620981
+[[Badness]] (Sintel): 84.9
-[http://x31eq.com/cgi-bin/rt.cgi?ets=5_137&limit=5 The temperament finder - 5-limit 5 & 137]
 == 559 & 2513 ==
@@ Line 485: / Line 480: @@
 [[Comma list]]: {{monzo| -124 109 -21 }}
-{{Mapping|legend=1| 1 10 46 | 0 -21 -109 }}
+{{Mapping|legend=1| 1 -11 -63 | 0 21 109 }}
+: mapping generators: ~2, ~{{monzo| -29 26 -5 }}
-: mapping generators: ~2, ~3355443200000/2541865828329
 [[Optimal tuning]]s:
-* [[POTE]]: ~2 = 1200.0000{{c}}, ~3355443200000/2541865828329 = 480.8595{{c}}
+* [[POTE]]: ~2 = 1200.0000{{c}}, ~{{monzo| -29 26 -5 }} = 719.1405{{c}}
-{{Optimal ET sequence|legend=1| 5, 267c, 272c, 277, 559, 1395, 1954, 2513, 40767, 43280, 45793, 48306, 50819, 53332, 55845, 58358, 60871, 63384, 65897, 68410, 70923, 73436, 75949, 78462 }}
-[[Badness]] (Smith): 0.134523
+{{Optimal ET sequence|legend=1| 5, …, 277, 559, 1395, 1954, 2513, 40767, 43280, 45793, 48306, 50819, 53332, 55845, 58358, 60871, 63384, 65897, 68410, 70923, 73436, 75949, 78462, 154411b }}
-[http://x31eq.com/cgi-bin/rt.cgi?ets=2513_559&limit=5 The temperament finder - 5-limit 2513 & 559]
+[[Badness]] (Sintel): 3.16
 -->
 [[Category:5edo]]
 [[Category:Equivalence continua]]