Canousmic temperaments: Difference between revisions

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 * ''[[kleischismic]]'', {32805/32768, 1562500/1492992} → [[Schismatic family #Kleischismic]]
-Discussed below are satin and semiluna.
+Discussed below are satin, superlimmal and semiluna.
-= Satin =
+== Satin ==
-== 5-limit ==
+=== 5-limit ===
 Subgroup: 2.3.5
@@ Line 30: / Line 30: @@
 [[Badness]]: 2.8530
-== 7-limit ==
+=== 7-limit ===
 Subgroup: 2.3.5.7
@@ Line 44: / Line 44: @@
 [[Badness]]: 0.1972
-== 11-limit ==
+=== 11-limit ===
 Subgroup: 2.3.5.7.11
@@ Line 58: / Line 58: @@
 Badness: 0.0580
-== 13-limit ==
+=== 13-limit ===
 Subgroup: 2.3.5.7.11.13
@@ Line 72: / Line 72: @@
 Badness: 0.0303
-== 17-limit ==
+=== 17-limit ===
 Subgroup: 2.3.5.7.11.13.17
@@ Line 86: / Line 86: @@
 Badness: 0.0200
-== 19-limit ==
+=== 19-limit ===
 Subgroup: 2.3.5.7.11.13.17.19
@@ Line 100: / Line 100: @@
 Badness: 0.0145
-== 23-limit ==
+=== 23-limit ===
 Subgroup: 2.3.5.7.11.13.17.19.23
@@ Line 114: / Line 114: @@
 Badness: 0.0122
-= Semiluna =
+== Superlimmal ==
+The superlimmal temperament uses an ever slightly sharpened [[27/25|large limma]] as the generator, nine exceed the octave by [[126/125]]. It can be described as 80 & 311. It gets all the primes up to 29 reasonably covered, but still acceptible just as a 13-limit microtemperament, judging from its comma basis. The 80-tone [[MOS scale]] is presumably the place to start, and a 151-tone MOS is possible.
+Subgroup: 2.3.5.7
+[[Comma list]]: 4802000/4782969, 52734375/52706752
+[[Mapping]]: [{{val| 1 8 12 18 }}, {{val| 0 -57 -86 -135 }}]
+{{Multival|legend=1| 57 86 135 3 53 72 }}
+[[POTE generator]]: ~27/25 = 135.0464
+{{Val list|legend=1| 80, 231, 311, 1324b, 1635b }}
+[[Badness]]: 0.2524
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 3025/3024, 4000/3993, 1479016/1476225
+Mapping: [{{val| 1 8 12 18 11 }}, {{val| 0 -57 -86 -135 -67 }}]
+POTE generator: ~27/25 = 135.0455
+Vals: {{val list| 80, 231, 311, 1013e, 1324be }}
+Badness: 0.06067
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 3025/3024, 4000/3993, 4225/4224, 4459/4455
+Mapping: [{{val| 1 8 12 18 11 1 }}, {{val| 0 -57 -86 -135 -67 24 }}]
+POTE generator: ~27/25 = 135.0446
+Vals: {{val list| 80, 231, 311, 702, 1013e }}
+Badness: 0.03902
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 595/594, 1275/1274, 2500/2499, 3025/3024, 4225/4224
+Mapping: [{{val| 1 8 12 18 11 1 6 }}, {{val| 0 -57 -86 -135 -67 24 -17 }}]
+POTE generator: ~27/25 = 135.0462
+Vals: {{val list| 80, 231, 311 }}
+Badness: 0.03008
+=== 19-limit ===
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 595/594, 969/968, 1275/1274, 1445/1444, 1729/1728, 2500/2499
+Mapping: [{{val| 1 8 12 18 11 1 6 11 }}, {{val| 0 -57 -86 -135 -67 24 -17 -60 }}]
+POTE generator: ~27/25 = 135.0464
+Vals: {{val list| 80, 231, 311 }}
+Badness: 0.02046
+=== 23-limit ===
+Subgroup: 2.3.5.7.11.13.17.19.23
+Comma list: 595/594, 760/759, 969/968, 1105/1104, 1275/1274, 1445/1444, 1496/1495
+Mapping: [{{val| 1 8 12 18 11 1 6 11 7 }}, {{val| 0 -57 -86 -135 -67 24 -17 -60 -22 }}]
+POTE generator: ~27/25 = 135.0458
+Vals: {{val list| 80, 231, 311 }}
+Badness: 0.01615
+=== 29-limit ===
+Subgroup: 2.3.5.7.11.13.17.19.23.29
+Comma list: 595/594, 760/759, 784/783, 969/968, 1045/1044, 1105/1104, 1275/1274, 1496/1495
+Mapping: [{{val| 1 8 12 18 11 1 6 11 7 16 }}, {{val| 0 -57 -86 -135 -67 24 -17 -60 -22 -99 }}]
+POTE generator: ~27/25 = 135.0460
+Vals: {{val list| 80, 231, 311 }}
+Badness: 0.01305
+== Semiluna ==
 {{see also|Luna family #Semiluna}}
@@ Line 129: / Line 224: @@
 [[Badness]]: 0.1922
-== 11-limit ==
+=== 11-limit ===
 Subgroup: 2.3.5.7.11