@@ Line 29: / Line 29: @@
 === Overview to extensions ===
-The second comma to extend the 5-limit amity include [[4375/4374]] for septimal amity, [[225/224]] for houborizic, 65625/65536 for paramity, [[126/125]] for accord, [[245/243]] for bamity, [[2430/2401]] for hamity, [[1029/1024]] for gamity, [[10976/10935]] for chromat, [[703125/702464]] for trinity, [[2401/2400]] for amicable, [[2100875/2097152]] for calamity, [[420175/419904]] for witcher, and [[16875/16807]] for familia.
+The second comma to extend 5-limit amity include [[4375/4374]] for septimal amity, [[65625/65536]] for paramity, [[126/125]] for accord, and [[225/224]] for houborizic. Those all use the same generator as the 5-limit temperament.
-Temperaments discussed elsewhere include:
+Bamity adds [[245/243]] with a 1/2-octave period. Hamity adds [[2430/2401]] and splits the generator in two. Gamity adds [[1029/1024]]. Chromat adds [[10976/10935]]. Trinity adds [[703125/702464]]. Those split the generator in three. Amicable adds [[2401/2400]], splitting the generator in four. Witcher adds [[420175/419904]]. Calamity adds [[2100875/2097152]]. Familia adds [[16875/16807]]. Those split the generator in five.
-* ''[[Chromat]]'' → [[Hemimage temperaments #Chromat]] (+10976/10935)
-* ''[[Witcher]]'' → [[Wizmic microtemperaments #Witcher]] (+420175/419904)
-The rest are considered below.
 == Septimal amity ==
@@ Line 63: / Line 59: @@
 Comma list: 540/539, 4375/4374, 5120/5103
-Mapping: {{mapping| 1 -2 -7 15 -41 | 0 5 13 -17 62 }}
+{{Mapping|legend=0| 1 -2 -7 15 -41 | 0 5 13 -17 62 }}
 Optimal tunings:
@@ Line 78: / Line 74: @@
 Comma list: 352/351, 540/539, 625/624, 729/728
-Mapping: {{mapping| 1 -2 -7 15 -41 -30 | 0 5 13 -17 62 47 }}
+{{Mapping|legend=0| 1 -2 -7 15 -41 -30 | 0 5 13 -17 62 47 }}
 Optimal tunings:
@@ Line 95: / Line 91: @@
 Comma list: 256/255, 352/351, 375/374, 540/539, 729/728
-Mapping: {{mapping| 1 -2 -7 15 -41 -30 17 | 0 5 13 -17 62 47 -18 }}
+{{Mapping|legend=0| 1 -2 -7 15 -41 -30 17 | 0 5 13 -17 62 47 -18 }}
 Optimal tunings:
@@ Line 110: / Line 106: @@
 Comma list: 256/255, 324/323, 352/351, 375/374, 400/399, 456/455
-Mapping: {{mapping| 1 -2 -7 15 -41 -30 17 -23 | 0 5 13 -17 62 47 -18 38 }}
+{{Mapping|legend=0| 1 -2 -7 15 -41 -30 17 -23 | 0 5 13 -17 62 47 -18 38 }}
 Optimal tunings:
@@ Line 125: / Line 121: @@
 Comma list: 121/120, 176/175, 2200/2187
-Mapping: {{mapping| 1 -2 -7 15 -3 | 0 5 13 -17 9 }}
+{{Mapping|legend=0| 1 -2 -7 15 -3 | 0 5 13 -17 9 }}
 Optimal tunings:
@@ Line 140: / Line 136: @@
 Comma list: 121/120, 169/168, 176/175, 325/324
-Mapping: {{mapping| 1 -2 -7 15 -3 8 | 0 5 13 -17 9 -6 }}
+{{Mapping|legend=0| 1 -2 -7 15 -3 8 | 0 5 13 -17 9 -6 }}
 Optimal tunings:
@@ Line 155: / Line 151: @@
 Comma list: 121/120, 154/153, 169/168, 176/175, 273/272
-Mapping: {{mapping| 1 -2 -7 15 -3 8 17 | 0 5 13 -17 9 -6 -18 }}
+{{Mapping|legend=0| 1 -2 -7 15 -3 8 17 | 0 5 13 -17 9 -6 -18 }}
 Optimal tunings:
@@ Line 170: / Line 166: @@
 Comma list: 121/120, 154/153, 169/168, 171/170, 176/175, 190/189
-Mapping: {{mapping| 1 -2 -7 15 -3 8 17 15 | 0 5 13 -17 9 -6 -18 -15 }}
+{{Mapping|legend=0| 1 -2 -7 15 -3 8 17 15 | 0 5 13 -17 9 -6 -18 -15 }}
 Optimal tunings:
@@ Line 187: / Line 183: @@
 Comma list: 441/440, 896/891, 4375/4374
-Mapping: {{mapping| 1 -2 -7 15 30 | 0 5 13 -17 -37 }}
+{{Mapping|legend=0| 1 -2 -7 15 30 | 0 5 13 -17 -37 }}
 Optimal tunings:
@@ Line 202: / Line 198: @@
 Comma list: 196/195, 352/351, 364/363, 4375/4374
-Mapping: {{mapping| 1 -2 -7 15 30 41 | 0 5 13 -17 -37 -52 }}
+{{Mapping|legend=0| 1 -2 -7 15 30 41 | 0 5 13 -17 -37 -52 }}
 Optimal tunings:
@@ Line 217: / Line 213: @@
 Comma list: 196/195, 256/255, 352/351, 364/363, 1156/1155
-Mapping: {{mapping| 1 -2 -7 15 30 41 17 | 0 5 13 -17 -37 -52 -18 }}
+{{Mapping|legend=0| 1 -2 -7 15 30 41 17 | 0 5 13 -17 -37 -52 -18 }}
 Optimal tunings:
@@ Line 232: / Line 228: @@
 Comma list: 196/195, 256/255, 343/342, 352/351, 364/363, 476/475
-Mapping: {{mapping| 1 -2 -7 15 30 41 17 48 | 0 5 13 -17 -37 -52 -18 -61 }}
+{{Mapping|legend=0| 1 -2 -7 15 30 41 17 48 | 0 5 13 -17 -37 -52 -18 -61 }}
 Optimal tunings:
@@ Line 247: / Line 243: @@
 Comma list: 3025/3024, 4375/4374, 5120/5103
-Mapping: {{mapping| 2 1 -1 13 13 | 0 5 13 -17 -14 }}
+{{Mapping|legend=0| 2 1 -1 13 13 | 0 5 13 -17 -14 }}
 : mapping generators: ~99/70, ~64/55
@@ Line 263: / Line 259: @@
 Comma list: 352/351, 847/845, 1716/1715, 3025/3024
-Mapping: {{mapping| 2 1 -1 13 13 20 | 0 5 13 -17 -14 -29 }}
+{{Mapping|legend=0| 2 1 -1 13 13 20 | 0 5 13 -17 -14 -29 }}
 Optimal tunings:
@@ Line 297: / Line 293: @@
 Comma list: 121/120, 126/125, 896/891
-Mapping: {{mapping| 1 -2 -7 -18 -3 | 0 5 13 29 9 }}
+{{Mapping|legend=0| 1 -2 -7 -18 -3 | 0 5 13 29 9 }}
 Optimal tunings:
@@ Line 331: / Line 327: @@
 Comma list: 225/224, 385/384, 1250000/1240029
-Mapping: {{mapping| 1 -2 -7 -23 35 | 0 5 13 36 -44 }}
+{{Mapping|legend=0| 1 -2 -7 -23 35 | 0 5 13 36 -44 }}
 Optimal tunings:
@@ Line 346: / Line 342: @@
 Comma list: 225/224, 325/324, 385/384, 2200/2197
-Mapping: {{mapping| 1 -2 -7 -23 35 8 | 0 5 13 36 -44 -6 }}
+{{Mapping|legend=0| 1 -2 -7 -23 35 8 | 0 5 13 36 -44 -6 }}
 Optimal tunings:
@@ Line 361: / Line 357: @@
 Comma list: 121/120, 225/224, 2200/2187
-Mapping: {{mapping| 1 -2 -7 -23 -3 | 0 5 13 36 9 }}
+{{Mapping|legend=0| 1 -2 -7 -23 -3 | 0 5 13 36 9 }}
 Optimal tunings:
@@ Line 376: / Line 372: @@
 Comma list: 121/120, 225/224, 275/273, 325/324
-Mapping: {{mapping| 1 -2 -7 -23 -3 8 | 0 -5 -13 -36 -9 6 }}
+{{Mapping|legend=0| 1 -2 -7 -23 -3 8 | 0 -5 -13 -36 -9 6 }}
 Optimal tunings:
@@ Line 410: / Line 406: @@
 Comma list: 6250/6237, 19712/19683, 41503/41472
-Mapping: {{mapping| 1 -2 -7 53 -79 | 0 5 13 -70 115 }}
+{{Mapping|legend=0| 1 -2 -7 53 -79 | 0 5 13 -70 115 }}
 Optimal tunings:
@@ Line 425: / Line 421: @@
 Comma list: 625/624, 2080/2079, 2200/2197, 19712/19683
-Mapping: {{mapping| 1 -2 -7 53 -79 -30 | 0 5 13 -70 115 47 }}
+{{Mapping|legend=0| 1 -2 -7 53 -79 -30 | 0 5 13 -70 115 47 }}
 Optimal tunings:
@@ Line 440: / Line 436: @@
 Comma list: 625/624, 1225/1224, 2080/2079, 2200/2197, 2431/2430
-Mapping: {{mapping| 1 -2 -7 53 -79 -30 93 | 0 5 13 -70 115 47 -124 }}
+{{Mapping|legend=0| 1 -2 -7 53 -79 -30 93 | 0 5 13 -70 115 47 -124 }}
 Optimal tunings:
@@ Line 455: / Line 451: @@
 Comma list: 625/624, 1225/1224, 1540/1539, 1729/1728, 2080/2079, 2200/2197
-Mapping: {{mapping| 1 -2 -7 53 -79 -30 93 -23 | 0 5 13 -70 115 47 -124 38 }}
+{{Mapping|legend=0| 1 -2 -7 53 -79 -30 93 -23 | 0 5 13 -70 115 47 -124 38 }}
 Optimal tunings:
@@ Line 490: / Line 486: @@
 Comma list: 121/120, 245/243, 441/440
-Mapping: {{mapping| 2 1 -1 3 3 | 0 5 13 6 9 }}
+{{Mapping|legend=0| 2 1 -1 3 3 | 0 5 13 6 9 }}
 Optimal tunings:
@@ Line 505: / Line 501: @@
 Comma list: 91/90, 121/120, 245/243, 441/440
-Mapping: {{mapping| 2 1 -1 3 3 0 | 0 5 13 6 9 17 }}
+{{Mapping|legend=0| 2 1 -1 3 3 0 | 0 5 13 6 9 17 }}
 Optimal tunings:
@@ Line 540: / Line 536: @@
 Comma list: 99/98, 121/120, 2200/2187
-Mapping: {{mapping| 1 -2 -7 -4 -3 | 0 10 26 19 18 }}
+{{Mapping|legend=0| 1 -2 -7 -4 -3 | 0 10 26 19 18 }}
 Optimal tunings:
@@ Line 555: / Line 551: @@
 Comma list: 99/98, 121/120, 275/273, 572/567
-Mapping: {{mapping| 1 8 19 15 15 30 | 0 -10 -26 -19 -18 -41 }}
+{{Mapping|legend=0| 1 8 19 15 15 30 | 0 -10 -26 -19 -18 -41 }}
 Optimal tunings:
@@ Line 590: / Line 586: @@
 Comma list: 385/384, 441/440, 1071875/1062882
-Mapping: {{mapping| 1 -2 -7 4 8 | 0 15 39 -5 -19 }}
+{{Mapping|legend=0| 1 -2 -7 4 8 | 0 15 39 -5 -19 }}
 Optimal tunings:
@@ Line 605: / Line 601: @@
 Comma list: 325/324, 364/363, 385/384, 10985/10976
-Mapping: {{mapping| 1 -2 -7 4 8 8 | 0 15 39 -5 -19 -18 }}
+{{Mapping|legend=0| 1 -2 -7 4 8 8 | 0 15 39 -5 -19 -18 }}
 Optimal tunings:
@@ Line 620: / Line 616: @@
 Comma list: 273/272, 325/324, 364/363, 385/384, 3773/3757
-Mapping: {{mapping| 1 -2 -7 4 8 8 6 | 0 15 39 -5 -19 -18 -8 }}
+{{Mapping|legend=0| 1 -2 -7 4 8 8 6 | 0 15 39 -5 -19 -18 -8 }}
 Optimal tunings:
@@ Line 655: / Line 651: @@
 Comma list: 3025/3024, 4000/3993, 19712/19683
-Mapping: {{mapping| 1 -7 -20 -55 -16 | 0 15 39 101 34 }}
+{{Mapping|legend=0| 1 -7 -20 -55 -16 | 0 15 39 101 34 }}
 Optimal tunings:
@@ Line 670: / Line 666: @@
 Comma list: 625/624, 1575/1573, 2080/2079, 13720/13689
-Mapping: {{mapping| 1 -7 -20 -55 -16 -77 | 0 15 39 101 34 141 }}
+{{Mapping|legend=0| 1 -7 -20 -55 -16 -77 | 0 15 39 101 34 141 }}
 Optimal tunings:
@@ Line 685: / Line 681: @@
 Comma list: 595/594, 625/624, 833/832, 1575/1573, 8624/8619
-Mapping: {{mapping| 1 -7 -20 -55 -16 -77 39 | 0 15 39 101 34 141 -61 }}
+{{Mapping|legend=0| 1 -7 -20 -55 -16 -77 39 | 0 15 39 101 34 141 -61 }}
 Optimal tunings:
@@ Line 700: / Line 696: @@
 Comma list: 595/594, 625/624, 833/832, 969/968, 1216/1215, 1575/1573
-Mapping: {{mapping| 1 -7 -20 -55 -16 -77 39 -61 | 0 15 39 101 34 141 -61 114 }}
+{{Mapping|legend=0| 1 -7 -20 -55 -16 -77 39 -61 | 0 15 39 101 34 141 -61 114 }}
 Optimal tunings:
@@ Line 715: / Line 711: @@
 Comma list: 595/594, 625/624, 760/759, 833/832, 875/874, 969/968, 1105/1104
-Mapping: {{mapping| 1 -7 -20 -55 -16 -77 39 -61 -55 | 0 15 39 101 34 141 -61 114 104 }}
+{{Mapping|legend=0| 1 -7 -20 -55 -16 -77 39 -61 -55 | 0 15 39 101 34 141 -61 114 104 }}
 Optimal tunings:
@@ Line 730: / Line 726: @@
 Comma list: 595/594, 625/624, 760/759, 784/783, 833/832, 875/874, 969/968, 1045/1044
-Mapping: {{mapping| 1 -7 -20 -55 -16 -77 39 -61 -55 -85 | 0 15 39 101 34 141 -61 114 104 157 }}
+{{Mapping|legend=0| 1 -7 -20 -55 -16 -77 39 -61 -55 -85 | 0 15 39 101 34 141 -61 114 104 157 }}
 Optimal tunings:
@@ Line 740: / Line 736: @@
 Badness (Sintel): 1.01
-== Amicable ==
+== Chromat ==
-Amicable tempers out the [[breedsma]] as well as the [[canousma]], and may be described as the {{nowrap| 99 & 311 }} temperament.
+Chromat has a period of 1/3 octave and tempers out the [[hemimage comma]] (10976/10935) and the [[triwellisma]].
-While it extends well into 2.3.5.7.13/11, there are multiple reasonable places for the prime 11 and 13 in the interval chain. Amical (311 & 410) does this with no compromise of accuracy, but is enormously complex. Amorous (212 & 311) has the new primes placed on the same side of the interval chain so blends smarter with the other harmonics. Pseudoamical (99 & 113) and pseudoamorous (14cf & 99ef) are the corresponding low-complexity interpretations. Floral (198 & 212) shares the semioctave period and the ~21/20 generator with harry, but in a complementary style, including a characteristic flat 11. Finally, humorous (198 & 311) is one of the best extensions out there and it splits the generator in two.
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 2401/2400, 1600000/1594323
+[[Comma list]]: 10976/10935, 235298/234375
-{{Mapping|legend=1| 1 -17 -46 -26 | 0 20 52 31 }}
+{{Mapping|legend=1| 3 4 5 6 | 0 5 13 16 }}
-: mapping generators: ~2, ~40/21
+: mapping generators: ~63/50, ~28/27
 [[Optimal tuning]]s:
-* [[WE]]: ~2 = 1199.9463{{c}}, ~40/21 = 1115.0701{{c}}
+* [[WE]]: ~63/50 = 399.9549{{c}}, ~28/27 = 60.5216{{c}}
-: [[error map]]: {{val| -0.054 +0.361 -0.195 -0.254 }}
+: [[error map]]: {{val| -0.135 +0.473 +0.241 -0.751 }}
-* [[CWE]]: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1187{{c}}
+* [[CWE]]: ~63/50 = 400.0000{{c}}, ~28/27 = 60.5162{{c}}
-: error map: {{val| 0.000 +0.419 -0.142 -0.146 }}
+: error map: {{val| 0.000 +0.626 +0.397 -0.567 }}
-{{Optimal ET sequence|legend=1| 14c, …, 85c, 99, 212, 311, 410, 1131, 1541b }}
+{{Optimal ET sequence|legend=1| 39d, 60, 99, 258, 357, 456 }}
-[[Badness]] (Sintel): 1.15
+[[Badness]] (Sintel): 1.46
-=== Amical ===
+=== 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 2401/2400, 131072/130977, 1600000/1594323
+Comma list: 441/440, 4375/4356, 10976/10935
-Mapping: {{mapping| 1 -17 -46 -26 154 | 0 20 52 31 -162 }}
+{{Mapping|legend=0| 3 4 5 6 6 | 0 5 13 16 29 }}
 Optimal tunings:
-* WE: ~2 = 1200.0008{{c}}, ~40/21 = 1115.1165{{c}}
+* WE: ~44/35 = 400.0359{{c}}, ~28/27 = 60.4357{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1157{{c}}
+* CWE: ~44/35 = 400.0000{{c}}, ~28/27 = 60.4375{{c}}
-{{Optimal ET sequence|legend=0| 99, 212e, 311, 721, 1032, 1343 }}
+{{Optimal ET sequence|legend=0| 60e, 99e, 159, 258 }}
-Badness (Sintel): 3.33
+Badness (Sintel): 1.67
 ==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
-Comma list: 2080/2079, 2401/2400, 4096/4095, 741125/739206
+Comma list: 364/363, 441/440, 625/624, 10976/10935
+{{Mapping|legend=0| 3 4 5 6 6 4 | 0 5 13 16 29 47 }}
+Optimal tunings:
+* WE: ~44/35 = 400.0382{{c}}, ~28/27 = 60.4342{{c}}
+* CWE: ~44/35 = 400.0000{{c}}, ~28/27 = 60.4331{{c}}
+{{Optimal ET sequence|legend=0| 60eff, 99ef, 159, 258, 417d }}
+Badness (Sintel): 1.90
+===== 17-limit =====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 364/363, 375/374, 441/440, 595/594, 3773/3757
+{{Mapping|legend=0| 3 4 5 6 6 4 10 | 0 5 13 16 29 47 15 }}
+Optimal tunings:
+* WE: ~44/35 = 399.9982{{c}}, ~28/27 = 60.4374{{c}}
+* CWE: ~44/35 = 400.0000{{c}}, ~28/27 = 60.4375{{c}}
+{{Optimal ET sequence|legend=0| 99ef, 159, 258, 417dg }}
+Badness (Sintel): 1.61
+==== Catachrome ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 325/324, 441/440, 1001/1000, 10976/10935
+{{Mapping|legend=0| 3 4 5 6 6 12 | 0 5 13 16 29 -6 }}
+Optimal tunings:
+* WE: ~44/35 = 400.1386{{c}}, ~28/27 = 60.3986{{c}}
+* CWE: ~44/35 = 400.0000{{c}}, ~28/27 = 60.3929{{c}}
+{{Optimal ET sequence|legend=0| 60e, 99e, 159 }}
+Badness (Sintel): 1.81
+===== 17-limit =====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 273/272, 325/324, 375/374, 441/440, 4928/4913
+{{Mapping|legend=0| 3 4 5 6 6 12 10 | 0 5 13 16 29 -6 15 }}
+Optimal tunings:
+* WE: ~44/35 = 400.1115{{c}}, ~28/27 = 60.3935{{c}}
+* CWE: ~44/35 = 400.0000{{c}}, ~28/27 = 60.3893{{c}}
+{{Optimal ET sequence|legend=0| 60e, 99e, 159 }}
+Badness (Sintel): 1.54
+==== Chromic ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 196/195, 352/351, 729/728, 1875/1859
-Mapping: {{mapping| 1 -17 -46 -26 154 118 | 0 20 52 31 -162 -123 }}
+{{Mapping|legend=0| 3 4 5 6 6 9 | 0 5 13 16 29 14 }}
 Optimal tunings:
-* WE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1094{{c}}
+* WE: ~44/35 = 399.9082{{c}}, ~28/27 = 60.4425{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1162{{c}}
+* CWE: ~44/35 = 400.0000{{c}}, ~28/27 = 60.4380{{c}}
-{{Optimal ET sequence|legend=0| 99, 212ef, 311, 721, 1032 }}
+{{Optimal ET sequence|legend=0| 60e, 99ef, 159f }}
 Badness (Sintel): 2.06
+===== 17-limit =====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 170/169, 196/195, 352/351, 375/374, 595/594
+{{Mapping|legend=0| 3 4 5 6 6 9 10 | 0 5 13 16 29 14 15 }}
+Optimal tunings:
+* WE: ~44/35 = 399.8948{{c}}, ~28/27 = 60.4435{{c}}
+* CWE: ~44/35 = 400.0000{{c}}, ~28/27 = 60.4385{{c}}
+{{Optimal ET sequence|legend=0| 60e, 99ef, 159f }}
+Badness (Sintel): 1.58
+=== Hemichromat ===
+Subgroup: 2.3.5.7.11
+Comma list: 3025/3024, 10976/10935, 102487/102400
+{{Mapping|legend=0| 3 4 5 6 10 | 0 10 26 32 5 }}
+Optimal tunings:
+* WE: ~63/50 = 399.9750{{c}}, ~55/54 = 30.2568{{c}}
+* CWE: ~63/50 = 400.0000{{c}}, ~55/54 = 30.2561{{c}}
+{{Optimal ET sequence|legend=0| 39d, 120cd, 159, 198, 357, 912b }}
+Badness (Sintel): 2.22
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 676/675, 1001/1000, 3025/3024, 10976/10935
+{{Mapping|legend=0| 3 4 5 6 10 8 | 0 10 26 32 5 41 }}
+Optimal tunings:
+* WE: ~63/50 = 399.9741{{c}}, ~55/54 = 30.2584{{c}}
+* CWE: ~63/50 = 400.0000{{c}}, ~55/54 = 30.2577{{c}}
+{{Optimal ET sequence|legend=0| 39df, 120cdff, 159, 198, 357, 912b }}
+Badness (Sintel): 1.38
+== Amicable ==
+Amicable tempers out the [[breedsma]] as well as the [[canousma]], and may be described as the {{nowrap| 99 & 311 }} temperament.
+There are multiple reasonable places for primes 11 and 13 in the interval chain. Amorous (99ef & 311) has these primes placed on the same side of the interval chain so it blends smarter with the lower harmonics. Amical (99 & 311) shows a slightly more accurate but much more complex alternative. Pseudoamorous (99ef & 113) and pseudoamical (99 & 113) are the corresponding low-complexity interpretations. Floral (198 & 212) shares the semi-octave period and the ~21/20 generator with [[harry]], but in a complementary style, including a characteristic flat 11. Finally, humorous (198 & 311) is one of the best extensions out there and it splits the generator in two.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 2401/2400, 1600000/1594323
+{{Mapping|legend=1| 1 -17 -46 -26 | 0 20 52 31 }}
+: mapping generators: ~2, ~40/21
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9463{{c}}, ~40/21 = 1115.0701{{c}}
+: [[error map]]: {{val| -0.054 +0.361 -0.195 -0.254 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1187{{c}}
+: error map: {{val| 0.000 +0.419 -0.142 -0.146 }}
+{{Optimal ET sequence|legend=1| 14c, …, 85c, 99, 212, 311, 410, 1131, 1541b }}
+[[Badness]] (Sintel): 1.15
 === Amorous ===
@@ Line 797: / Line 918: @@
 Comma list: 2401/2400, 6250/6237, 19712/19683
-Mapping: {{mapping| 1 -17 -46 -26 -135 | 0 20 52 31 149 }}
+{{Mapping|legend=0| 1 -17 -46 -26 -135 | 0 20 52 31 149 }}
 Optimal tunings:
@@ Line 822: / Line 943: @@
 Badness (Sintel): 1.43
-=== Pseudoamical ===
+=== Amical ===
 Subgroup: 2.3.5.7.11
-Comma list: 385/384, 1375/1372, 1600000/1594323
+Comma list: 2401/2400, 131072/130977, 1600000/1594323
-Mapping: {{mapping| 1 -17 -46 -26 62 | 0 20 52 31 -63 }}
+{{Mapping|legend=0| 1 -17 -46 -26 154 | 0 20 52 31 -162 }}
 Optimal tunings:
-* WE: ~2 = 1200.3436{{c}}, ~40/21 = 1115.4102{{c}}
+* WE: ~2 = 1200.0008{{c}}, ~40/21 = 1115.1165{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.0925{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1157{{c}}
-{{Optimal ET sequence|legend=0| 99, 113, 212, 961ccdeee }}
+{{Optimal ET sequence|legend=0| 99, 212e, 311, 721, 1032, 1343 }}
-Badness (Sintel): 2.84
+Badness (Sintel): 3.33
 ==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
-Comma list: 325/324, 385/384, 1375/1372, 19773/19712
+Comma list: 2080/2079, 2401/2400, 4096/4095, 741125/739206
-Mapping: {{mapping| 1 -17 -46 -26 62 26 | 0 20 52 31 -63 -24 }}
+{{Mapping|legend=0| 1 -17 -46 -26 154 118 | 0 20 52 31 -162 -123 }}
 Optimal tunings:
-* WE: ~2 = 1200.4212{{c}}, ~40/21 = 1115.4787{{c}}
+* WE: ~2 = 1199.9926{{c}}, ~40/21 = 1115.1094{{c}}
-* CWE: ~2 = 1200.0000{{c}}, 40/21 = 1115.0885{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1162{{c}}
-{{Optimal ET sequence|legend=0| 99, 113, 212, 537cdeff, 749ccdeefff }}
+{{Optimal ET sequence|legend=0| 99, 212ef, 311, 721, 1032 }}
-Badness (Sintel): 1.94
+Badness (Sintel): 2.06
 === Pseudoamorous ===
@@ Line 857: / Line 978: @@
 Comma list: 243/242, 441/440, 980000/970299
-Mapping: {{mapping| 1 -17 -46 -26 -43 | 0 20 52 31 50 }}
+{{Mapping|legend=0| 1 -17 -46 -26 -43 | 0 20 52 31 50 }}
 Optimal tunings:
@@ Line 865: / Line 986: @@
 {{Optimal ET sequence|legend=0| 99e, 212e }} *
-* optimal patent val: [[113edo|113]]
+<nowiki/>* optimal patent val: [[113edo|113]]
 Badness (Sintel): 1.87
@@ Line 874: / Line 995: @@
 Comma list: 243/242, 364/363, 441/440, 1875/1859
-Mapping: {{mapping| 1 -17 -46 -26 -43 -79 | 0 20 52 31 50 89 }}
+{{Mapping|legend=0| 1 -17 -46 -26 -43 -79 | 0 20 52 31 50 89 }}
 Optimal tunings:
-* CTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.9153{{c}}
+* WE: ~2 = 1200.0182{{c}}, ~40/21 = 1115.1005{{c}}
-* POTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.9164{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.0840{{c}}
 {{Optimal ET sequence|legend=0| 99ef, 113, 212ef }}
 Badness (Sintel): 1.77
+=== Pseudoamical ===
+Subgroup: 2.3.5.7.11
+Comma list: 385/384, 1375/1372, 1600000/1594323
+{{Mapping|legend=0| 1 -17 -46 -26 62 | 0 20 52 31 -63 }}
+Optimal tunings:
+* WE: ~2 = 1200.3436{{c}}, ~40/21 = 1115.4102{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.0925{{c}}
+{{Optimal ET sequence|legend=0| 99, 113, 212, 961ccdeee }}
+Badness (Sintel): 2.84
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 325/324, 385/384, 1375/1372, 19773/19712
+{{Mapping|legend=0| 1 -17 -46 -26 62 26 | 0 20 52 31 -63 -24 }}
+Optimal tunings:
+* WE: ~2 = 1200.4212{{c}}, ~40/21 = 1115.4787{{c}}
+* CWE: ~2 = 1200.0000{{c}}, 40/21 = 1115.0885{{c}}
+{{Optimal ET sequence|legend=0| 99, 113, 212, 537cdeff, 749ccdeefff }}
+Badness (Sintel): 1.94
 === Floral ===
@@ Line 889: / Line 1,040: @@
 Comma list: 2401/2400, 9801/9800, 14641/14580
-Mapping: {{mapping| 2 -14 -40 -21 -30 | 0 20 52 31 43 }}
+{{Mapping|legend=0| 2 -14 -40 -21 -30 | 0 20 52 31 43 }}
 : mapping generators: ~99/70, ~66/49
 Optimal tunings:
-* WE: ~99/70 = 600.0000{{c}}, ~66/49 = 515.1257{{c}}
+* WE: ~99/70 = 600.0052{{c}}, ~66/49 = 515.1257{{c}}
 * CWE: ~99/70 = 600.0000{{c}}, ~66/49 = 515.1215{{c}}
@@ Line 905: / Line 1,056: @@
 Comma list: 676/675, 1001/1000, 1716/1715, 14641/14580
-Mapping: {{mapping| 2 -14 -40 -21 -30 -63 | 0 20 52 31 43 82 }}
+{{Mapping|legend=0| 2 -14 -40 -21 -30 -63 | 0 20 52 31 43 82 }}
 Optimal tunings:
@@ Line 920: / Line 1,071: @@
 Comma list: 2401/2400, 3025/3024, 1600000/1594323
-Mapping: {{mapping| 1 -37 -98 -57 16 | 0 40 104 62 -13 }}
+{{Mapping|legend=0| 1 -37 -98 -57 16 | 0 40 104 62 -13 }}
 : mapping generators: ~2, ~3993/2048
@@ Line 936: / Line 1,087: @@
 Comma list: 2080/2079, 2200/2197, 2401/2400, 3025/3024
-Mapping: {{mapping| 1 -37 -98 -57 16 -59 | 0 40 104 62 -13 65 }}
+{{Mapping|legend=0| 1 -37 -98 -57 16 -59 | 0 40 104 62 -13 65 }}
 Optimal tunings:
@@ Line 945: / Line 1,096: @@
 Badness (Sintel): 1.17
+== Witcher ==
+Witcher tempers out 420175/419904, the [[wizma]], and may be described as the {{nowrap| 99 & 166 }} temperament.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 420175/419904, 1600000/1594323
+{{Mapping|legend=1| 1 -7 -20 -2 | 0 25 65 14 }}
+: mapping generators: ~2, ~80/63
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.8698{{c}}, ~80/63 = 412.0531{{c}}
+: [[error map]]: {{val| -0.130 +0.283 -0.260 +0.178 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~80/63 = 412.0956{{c}}
+: error map: {{val| 0.000 +0.435 -0.100 +0.512 }}
+{{Optimal ET sequence|legend=1| 32c, 67c, 99, 265, 364, 463, 562, 1025 }}
+[[Badness]] (Sintel): 2.04
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 540/539, 4375/4356, 1240029/1239040
+{{Mapping|legend=0| 1 -7 -20 -2 -35 | 0 25 65 14 112 }}
+Optimal tunings:
+* WE: ~2 = 1199.9909{{c}}, ~80/63 = 412.0758{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~80/63 = 412.0788{{c}}
+{{Optimal ET sequence|legend=0| 99e, 166, 265 }}
+Badness (Sintel): 2.73
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 540/539, 729/728, 4375/4356, 10648/10647
+{{Mapping|legend=0| 1 -7 -20 -2 -35 -43 | 0 25 65 14 112 136 }}
+Optimal tunings:
+* WE: ~2 = 1200.0660{{c}}, ~33/26 = 412.0928{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~33/26 = 412.0709{{c}}
+{{Optimal ET sequence|legend=0| 99ef, 166, 265 }}
+Badness (Sintel): 2.40
+=== Semiwitcher ===
+Subgroup: 2.3.5.7.11
+Comma list: 9801/9800, 41503/41472, 585640/583443
+{{Mapping|legend=0| 2 -14 -40 -4 -13 | 0 25 65 14 29 }}
+: mapping generators: ~99/70, ~80/63
+Optimal tunings:
+* WE: ~99/70 = 599.9717{{c}}, ~80/63 = 412.0766{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~80/63 = 412.0951{{c}}
+{{Optimal ET sequence|legend=0| 32c, 166, 198, 364, 562, 926 }}
+Badness (Sintel): 2.92
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 1716/1715, 2080/2079, 2200/2197, 17303/17280
+{{Mapping|legend=0| 2 11 25 10 16 24 | 0 25 65 14 29 53 }}
+Optimal tunings:
+* WE: ~99/70 = 599.9666{{c}}, ~33/26 = 412.0726{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~33/26 = 412.0944{{c}}
+{{Optimal ET sequence|legend=0| 32cf, 166, 198, 364, 562, 926 }}
+Badness (Sintel): 1.57
+=== Hitch ===
+Subgroup: 2.3.5.7.11
+Comma list: 3025/3024, 117649/117612, 1600000/1594323
+{{Mapping|legend=0| 1 -32 -85 -16 31 | 0 50 130 28 -41 }}
+: mapping generators: ~2, ~891/560
+Optimal tunings:
+* WE: ~2 = 1199.8455{{c}}, ~891/560 = 805.9457{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~891/560 = 806.0488{{c}}
+{{Optimal ET sequence|legend=0| 67c, 198, 463, 661, 1124bde }}
+Badness (Sintel): 3.09
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 676/675, 1716/1715, 3025/3024, 1600000/1594323
+{{Mapping|legend=0| 1 -32 -85 -16 31 -134 | 0 50 130 28 -41 205 }}
+Optimal tunings:
+* WE: ~2 = 1199.8415{{c}}, ~891/560 = 805.9451{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~891/560 = 806.0508{{c}}
+{{Optimal ET sequence|legend=0| 198, 463, 661 }}
+Badness (Sintel): 2.51
+==== Hitcher ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 2080/2079, 3025/3024, 13720/13689, 28672/28561
+{{Mapping|legend=0| 1 -32 -85 -16 31 -1 | 0 50 130 28 -41 7 }}
+Optimal tunings:
+* WE: ~2 = 1199.7690{{c}}, ~78/49 = 805.8958{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~78/49 = 806.0500{{c}}
+{{Optimal ET sequence|legend=0| 67c, 198, 463f, 661ff }}
+Badness (Sintel): 2.46
 == Calamity ==
@@ Line 971: / Line 1,249: @@
 Comma list: 3025/3024, 12005/11979, 131072/130977
-Mapping: {{mapping| 1 -12 -33 24 29 | 0 25 65 -39 -47 }}
+{{Mapping|legend=0| 1 -12 -33 24 29 | 0 25 65 -39 -47 }}
 Optimal tunings:
@@ Line 986: / Line 1,264: @@
 Comma list: 2080/2079, 3025/3024, 4096/4095, 12005/11979
-Mapping: {{mapping| 1 -12 -33 24 29 45 | 0 25 65 -39 -47 -76 }}
+{{Mapping|legend=0| 1 -12 -33 24 29 45 | 0 25 65 -39 -47 -76 }}
 Optimal tunings:
@@ Line 1,021: / Line 1,299: @@
 Comma list: 540/539, 1375/1372, 1600000/1594323
-Mapping: {{mapping| 1 -17 -46 -47 -1 | 0 25 65 67 6 }}
+{{Mapping|legend=0| 1 -17 -46 -47 -1 | 0 25 65 67 6 }}
 Optimal tunings:
@@ Line 1,036: / Line 1,314: @@
 Comma list: 540/539, 729/728, 1375/1372, 2205/2197
-Mapping: {{mapping| 1 -17 -46 -47 -1 -58 | 0 25 65 67 6 83 }}
+{{Mapping|legend=0| 1 -17 -46 -47 -1 -58 | 0 25 65 67 6 83 }}
 Optimal tunings:
@@ Line 1,046: / Line 1,324: @@
 Badness (Sintel): 1.59
+[[Category:Amity family| ]] <!-- main article -->
+[[Category:Amity| ]] <!-- key article -->
 [[Category:Temperament families]]
-[[Category:Amity family| ]] <!-- main article -->
+[[Category:Catalogs of rank-2 temperaments]]
-[[Category:Rank 2]]

Amity family: Difference between revisions