@@ 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 274: / Line 270: @@
 == Accord ==
+Accord tempers out [[126/125]], the starling comma, and may be described as the {{nowrap| 39d & 46 }} temperament.
 [[Subgroup]]: 2.3.5.7
@@ Line 295: / 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 306: / Line 304: @@
 == Houborizic ==
-Houborizic tempers out 225/224, the [[marvel comma]], and may be described as the {{nowrap| 53 & 60 }} temperament. It is so named because it is closely related to the ''houboriz tuning'' (generator: 339.774971 cents).
+Houborizic tempers out 225/224, the [[marvel comma]], and may be described as the {{nowrap| 53 & 60 }} temperament. It was named by [[Xenllium]] in 2021 for its close relation to the ''houboriz tuning'' (generator: 339.774971 cents).
 [[Subgroup]]: 2.3.5.7
@@ Line 329: / 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 344: / 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 359: / 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 374: / 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 385: / Line 383: @@
 == Paramity ==
-Paramity tempers out the [[horwell comma]] (65625/65536) and [[garischisma]] (33554432/33480783), and may be described as the {{nowrap| 53 & 311 }} temperament.
+Paramity tempers out the [[horwell comma]] (65625/65536) and [[garischisma]] (33554432/33480783), and may be described as the {{nowrap| 53 & 311 }} temperament. It was named by [[Xenllium]] in 2021, with the prefix ''para-'' signifying its relation to amity.
 [[Subgroup]]: 2.3.5.7
@@ Line 408: / 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 423: / 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 438: / 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 453: / 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 473: / Line 471: @@
 : mapping generators: ~343/240, ~7/6
-Optimal tunings:
+[[Optimal tuning]]s:
-* CTE: ~343/240 = 600.000{{c}}, ~7/6 = 260.563{{c}}
+* [[WE]]: ~343/240 = 600.3379{{c}}, ~7/6 = 260.5488{{c}}
-* POTE: ~343/240 = 600.000{{c}}, ~7/6 = 260.402{{c}}
+: [[error map]]: {{val| +0.676 +1.127 +0.483 -4.519 }}
+* [[CWE]]: ~343/240 = 600.0000{{c}}, ~7/6 = 260.4686{{c}}
+: error map: {{val| 0.000 +0.388 -0.222 -6.014 }}
-{{Optimal ET sequence|legend=1| 14c, 32c, 46, 106d, 152d }}
+{{Optimal ET sequence|legend=1| 14c, 32c, 46, 60, 106d }}
-[[Badness]] (Smith): 0.083601
+[[Badness]] (Sintel): 2.12
 === 11-limit ===
@@ Line 486: / 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:
-* CTE: ~99/70 = 600.000{{c}}, ~7/6 = 260.653{{c}}
+* WE: ~99/70 = 600.5039{{c}}, ~7/6 = 260.6119{{c}}
-* POTE: ~99/70 = 600.000{{c}}, ~7/6 = 260.393{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~7/6 = 260.4948{{c}}
-{{Optimal ET sequence|legend=0| 14c, 32c, 46, 152de, 198, 244dee }}
+{{Optimal ET sequence|legend=0| 14c, 32c, 46, 60e, 106de }}
-Badness (Smith): 0.035504
+Badness (Sintel): 1.17
 === 13-limit ===
@@ Line 501: / 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:
-* CTE: ~55/39 = 600.000{{c}}, ~7/6 = 260.811{{c}}
+* WE: ~55/39 = 600.3896{{c}}, ~7/6 = 260.7874{{c}}
-* POTE: ~55/39 = 600.000{{c}}, ~7/6 = 260.618{{c}}
+* CWE: ~55/39 = 600.0000{{c}}, ~7/6 = 260.6927{{c}}
-{{Optimal ET sequence|legend=0| 14cf, 32cf, 46 }}
+{{Optimal ET sequence|legend=0| 14cf, 32cf, 46, 106deff }}
-Badness (Smith): 0.030885
+Badness (Sintel): 1.28
 == Hamity ==
@@ Line 518: / Line 518: @@
 [[Comma list]]: 2430/2401, 4000/3969
-{{Mapping|legend=1| 1 8 19 15 | 0 -10 -26 -19 }}
+{{Mapping|legend=1| 1 -2 -7 -4 | 0 10 26 19 }}
-: mapping generators: ~2, ~14/9
+: mapping generators: ~2, ~9/7
-Optimal tunings:
+[[Optimal tuning]]s:
-* CTE: ~2 = 1200.000{{c}}, ~9/7 = 430.168{{c}}
+* [[WE]]: ~2 = 1199.5499{{c}}, ~9/7 = 430.0579{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~9/7 = 430.219{{c}}
+: [[error map]]: {{val| -0.450 -0.476 -1.657 +4.075 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~9/7 = 430.1958{{c}}
+: error map: {{val| 0.000 +0.003 -1.222 +4.895 }}
 {{Optimal ET sequence|legend=1| 14c, 39d, 53 }}
-[[Badness]] (Smith): 0.073956
+[[Badness]] (Sintel): 1.87
 === 11-limit ===
@@ Line 534: / Line 536: @@
 Comma list: 99/98, 121/120, 2200/2187
-Mapping: {{mapping| 1 8 19 15 15 | 0 -10 -26 -19 -18 }}
+{{Mapping|legend=0| 1 -2 -7 -4 -3 | 0 10 26 19 18 }}
 Optimal tunings:
-* CTE: ~2 = 1200.000{{c}}, ~9/7 = 430.220{{c}}
+* WE: ~2 = 1200.2215{{c}}, ~9/7 = 430.2713{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~9/7 = 430.192{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~9/7 = 430.2036{{c}}
 {{Optimal ET sequence|legend=0| 14c, 39d, 53 }}
-Badness (Smith): 0.042947
+Badness (Sintel): 1.42
 === 13-limit ===
@@ Line 549: / 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:
-* CTE: ~2 = 1200.000{{c}}, ~9/7 = 430.233{{c}}
+* WE: ~2 = 1200.1379{{c}}, ~9/7 = 430.2658{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~9/7 = 430.216{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~9/7 = 430.2227{{c}}
 {{Optimal ET sequence|legend=0| 14cf, 39df, 53 }}
-Badness (Smith): 0.029753
+Badness (Sintel): 1.23
 == Gamity ==
-Gamity tempers out 1029/1024, the [[gamelisma]], and may be described as the {{nowrap| 46 & 113 }} temperament. It splits the interval of grave major sixth (~400/243, an octave minus acute minor third) in three.
+Gamity tempers out 1029/1024, the [[gamelisma]], and may be described as the {{nowrap| 46 & 113 }} temperament. It splits the interval of the grave major sixth in three. It was named by [[Xenllium]] in 2021 as a contraction of ''gamelismic'' and ''amity''.
 [[Subgroup]]: 2.3.5.7
@@ Line 566: / Line 568: @@
 [[Comma list]]: 1029/1024, 1071875/1062882
-{{Mapping|legend=1| 1 13 32 -1 | 0 -15 -39 5 }}
+{{Mapping|legend=1| 1 -2 -7 4 | 0 15 39 -5 }}
-: mapping generators: ~2, ~320/189
+: mapping generators: ~2, ~189/160
-Optimal tunings:
+[[Optimal tuning]]s:
-* CTE: ~2 = 1200.000{{c}}, ~189/160 = 286.816{{c}}
+* [[WE]]: ~2 = 1200.4434{{c}}, ~189/160 = 286.8930{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~189/160 = 286.787{{c}}
+: [[error map]]: {{val| +0.443 +0.553 -0.591 -1.571 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~189/160 = 286.7955{{c}}
+: error map: {{val| 0.000 -0.022 -1.288 -2.804 }}
-{{Optimal ET sequence|legend=1| 46, 113, 159, 205d, 364d }}
+{{Optimal ET sequence|legend=1| 46, 113, 159 }}
-[[Badness]] (Smith): 0.125733
+[[Badness]] (Sintel): 3.18
 === 11-limit ===
@@ Line 582: / Line 586: @@
 Comma list: 385/384, 441/440, 1071875/1062882
-Mapping: {{mapping| 1 13 32 -1 -11 | 0 -15 -39 5 19 }}
+{{Mapping|legend=0| 1 -2 -7 4 8 | 0 15 39 -5 -19 }}
 Optimal tunings:
-* CTE: ~2 = 1200.000{{c}}, ~33/28 = 286.813{{c}}
+* WE: ~2 = 1200.3315{{c}}, ~33/28 = 286.8764{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~33/28 = 286.797{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~33/28 = 286.8002{{c}}
-{{Optimal ET sequence|legend=0| 46, 113, 159, 205d, 364d }}
+{{Optimal ET sequence|legend=0| 46, 113, 159 }}
-Badness (Smith): 0.051111
+Badness (Sintel): 1.69
 === 13-limit ===
@@ Line 597: / Line 601: @@
 Comma list: 325/324, 364/363, 385/384, 10985/10976
-Mapping: {{mapping| 1 13 32 -1 -11 -10 | 0 -15 -39 5 19 18 }}
+{{Mapping|legend=0| 1 -2 -7 4 8 8 | 0 15 39 -5 -19 -18 }}
 Optimal tunings:
-* CTE: ~2 = 1200.000{{c}}, ~13/11 = 286.803{{c}}
+* WE: ~2 = 1200.4248{{c}}, ~13/11 = 286.8906{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~13/11 = 286.789{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~13/11 = 286.7912{{c}}
 {{Optimal ET sequence|legend=0| 46, 113, 159, 364df, 523ddff }}
-Badness (Smith): 0.030297
+Badness (Sintel): 1.25
 === 17-limit ===
@@ Line 612: / Line 616: @@
 Comma list: 273/272, 325/324, 364/363, 385/384, 3773/3757
-Mapping: {{mapping| 1 13 32 -1 -11 -10 -2 | 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:
-* CTE: ~2 = 1200.000{{c}}, ~13/11 = 286.804{{c}}
+* WE: ~2 = 1200.3287{{c}}, ~13/11 = 286.8731{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~13/11 = 286.795{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~13/11 = 286.7957{{c}}
-{{Optimal ET sequence|legend=0| 46, 113, 159, 364df, 523ddff }}
+{{Optimal ET sequence|legend=0| 46, 113, 159 }}
-Badness (Smith): 0.022036
+Badness (Sintel): 1.12
 == Trinity ==
-Trinity tempers out 703125/702464, the [[meter]], and may be described as the {{nowrap| 152 & 159 }} temperament. It splits the acute minor tenth (~243/100, an octave plus acute minor third) in three. It was so named for the following reason – 133\311 (133 steps of 311edo) is a possible generator, which is placed around 3\7 (1.1{{c}} flat), three of which makes acute minor third of ~243/200 with octave reduction.
+Trinity tempers out 703125/702464, the [[meter]], and may be described as the {{nowrap| 152 & 159 }} temperament. [[311edo|178\311]] is a recommendable generator. It was named by [[Xenllium]] in 2022 for the fact that it splits amity's generator in three.
 [[Subgroup]]: 2.3.5.7
@@ Line 629: / Line 633: @@
 [[Comma list]]: 703125/702464, 1600000/1594323
-{{Mapping|legend=1| 1 8 19 46 | 0 -15 -39 -101 }}
+{{Mapping|legend=1| 1 -7 -20 -55 | 0 15 39 101 }}
+: mapping generators: ~2, ~125/84
-Optimal tunings:
+[[Optimal tuning]]s:
-* CTE: ~2 = 1200.000{{c}}, ~168/125 = 513.180{{c}}
+* [[WE]]: ~2 = 1199.9474{{c}}, ~125/84 = 686.7921{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~168/125 = 513.178{{c}}
+: [[error map]]: {{val| -0.053 +0.295 -0.369 +0.071 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~125/84 = 686.8215{{c}}
+: error map: {{val| 0.000 +0.367 -0.276 +0.144 }}
-{{Optimal ET sequence|legend=1| 7d, …, 145d, 152, 311, 774, 1085 }}
+{{Optimal ET sequence|legend=1| 7d, …, 152, 311, 463, 774 }}
-[[Badness]] (Smith): 0.119453
+[[Badness]] (Sintel): 3.02
 === 11-limit ===
@@ Line 644: / Line 651: @@
 Comma list: 3025/3024, 4000/3993, 19712/19683
-Mapping: {{mapping| 1 8 19 46 18 | 0 -15 -39 -101 -34 }}
+{{Mapping|legend=0| 1 -7 -20 -55 -16 | 0 15 39 101 34 }}
 Optimal tunings:
-* CTE: ~2 = 1200.000{{c}}, ~121/90 = 513.181{{c}}
+* WE: ~2 = 1199.9090{{c}}, ~125/84 = 686.7710{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~121/90 = 513.177{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~125/84 = 686.8218{{c}}
-{{Optimal ET sequence|legend=0| 7d, …, 145d, 152, 311, 774, 1085e, 1396e }}
+{{Optimal ET sequence|legend=0| 7d, …, 152, 311, 463, 774, 1237e }}
-Badness (Smith): 0.031296
+Badness (Sintel): 1.03
 === 13-limit ===
@@ Line 659: / Line 666: @@
 Comma list: 625/624, 1575/1573, 2080/2079, 13720/13689
-Mapping: {{mapping| 1 8 19 46 18 64 | 0 -15 -39 -101 -34 -141 }}
+{{Mapping|legend=0| 1 -7 -20 -55 -16 -77 | 0 15 39 101 34 141 }}
 Optimal tunings:
-* CTE: ~2 = 1200.000{{c}}, ~35/26 = 513.184{{c}}
+* WE: ~2 = 1199.9531{{c}}, ~52/35 = 686.7909{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~35/26 = 513.182{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~52/35 = 686.8172{{c}}
-{{Optimal ET sequence|legend=0| 152f, 159, 311 }}
+{{Optimal ET sequence|legend=0| 7df, …, 152f, 311 }}
-Badness (Smith): 0.026418
+Badness (Sintel): 1.09
 === 17-limit ===
@@ Line 674: / Line 681: @@
 Comma list: 595/594, 625/624, 833/832, 1575/1573, 8624/8619
-Mapping: {{mapping| 1 8 19 46 18 64 -22 | 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:
-* CTE: ~2 = 1200.000{{c}}, ~35/26 = 513.185{{c}}
+* WE: ~2 = 1200.0347{{c}}, ~52/35 = 686.8342{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~35/26 = 513.186{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~52/35 = 686.8146{{c}}
-{{Optimal ET sequence|legend=0| 152f, 159, 311, 1714cdeg, 2025cdefgg, 2336bccdefgg }}
+{{Optimal ET sequence|legend=0| 152f, 159, 311, 1092cdg }}
-Badness (Smith): 0.025588
+Badness (Sintel): 1.30
 === 19-limit ===
@@ Line 689: / Line 696: @@
 Comma list: 595/594, 625/624, 833/832, 969/968, 1216/1215, 1575/1573
-Mapping: {{mapping| 1 8 19 46 18 64 -22 53 | 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:
-* CTE: ~2 = 1200.000{{c}}, ~35/26 = 513.184{{c}}
+* WE: ~2 = 1200.0406{{c}}, ~52/35 = 686.8382{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~35/26 = 513.185{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~52/35 = 686.8152{{c}}
 {{Optimal ET sequence|legend=0| 152f, 159, 311 }}
-Badness (Smith): 0.018412
+Badness (Sintel): 1.12
 === 23-limit ===
@@ Line 704: / Line 711: @@
 Comma list: 595/594, 625/624, 760/759, 833/832, 875/874, 969/968, 1105/1104
-Mapping: {{mapping| 1 8 19 46 18 64 -22 53 49 | 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:
-* CTE: ~2 = 1200.000{{c}}, ~35/26 = 513.184{{c}}
+* WE: ~2 = 1200.0311{{c}}, ~52/35 = 686.8324{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~35/26 = 513.185{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~52/35 = 686.8148{{c}}
-{{Optimal ET sequence|legend=0| 152f, 159, 311, 1714cdeghi, 2025cdefgghhi, 2336bccdefgghhi }}
+{{Optimal ET sequence|legend=0| 152f, 159, 311 }}
-Badness (Smith): 0.014343
+Badness (Sintel): 1.03
 === 29-limit ===
@@ Line 719: / Line 726: @@
 Comma list: 595/594, 625/624, 760/759, 784/783, 833/832, 875/874, 969/968, 1045/1044
-Mapping: {{mapping| 1 8 19 46 18 64 -22 53 49 72 | 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:
-* CTE: ~2 = 1200.000{{c}}, ~35/26 = 513.185{{c}}
+* WE: ~2 = 1200.0311{{c}}, ~52/35 = 686.8318{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~35/26 = 513.186{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~52/35 = 686.8142{{c}}
+{{Optimal ET sequence|legend=0| 152fj, 159, 311, 781dh }}
-{{Optimal ET sequence|legend=0| 152fj, 159, 311, 1403cdgh, 1714cdeghi, 2025cdefgghhij, 2336bccdefgghhij }}
+Badness (Sintel): 1.01
-Badness (Smith): 0.012038
+== Chromat ==
+Chromat has a period of 1/3 octave and tempers out the [[hemimage comma]] (10976/10935) and the [[triwellisma]].
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 10976/10935, 235298/234375
+{{Mapping|legend=1| 3 4 5 6 | 0 5 13 16 }}
+: mapping generators: ~63/50, ~28/27
+[[Optimal tuning]]s:
+* [[WE]]: ~63/50 = 399.9549{{c}}, ~28/27 = 60.5216{{c}}
+: [[error map]]: {{val| -0.135 +0.473 +0.241 -0.751 }}
+* [[CWE]]: ~63/50 = 400.0000{{c}}, ~28/27 = 60.5162{{c}}
+: error map: {{val| 0.000 +0.626 +0.397 -0.567 }}
+{{Optimal ET sequence|legend=1| 39d, 60, 99, 258, 357, 456 }}
+[[Badness]] (Sintel): 1.46
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 441/440, 4375/4356, 10976/10935
+{{Mapping|legend=0| 3 4 5 6 6 | 0 5 13 16 29 }}
+Optimal tunings:
+* WE: ~44/35 = 400.0359{{c}}, ~28/27 = 60.4357{{c}}
+* CWE: ~44/35 = 400.0000{{c}}, ~28/27 = 60.4375{{c}}
+{{Optimal ET sequence|legend=0| 60e, 99e, 159, 258 }}
+Badness (Sintel): 1.67
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+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|legend=0| 3 4 5 6 6 9 | 0 5 13 16 29 14 }}
+Optimal tunings:
+* WE: ~44/35 = 399.9082{{c}}, ~28/27 = 60.4425{{c}}
+* CWE: ~44/35 = 400.0000{{c}}, ~28/27 = 60.4380{{c}}
+{{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.
-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.
+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
@@ Line 738: / Line 900: @@
 [[Comma list]]: 2401/2400, 1600000/1594323
-{{Mapping|legend=1| 1 3 6 5 | 0 -20 -52 -31 }}
+{{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 ===
+Subgroup: 2.3.5.7.11
+Comma list: 2401/2400, 6250/6237, 19712/19683
+{{Mapping|legend=0| 1 -17 -46 -26 -135 | 0 20 52 31 149 }}
 Optimal tunings:
-* CTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.8831{{c}}
+* WE: ~2 = 1200.0380{{c}}, ~40/21 = 1115.1458{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~21/20 = 84.880{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1109{{c}}
-{{Optimal ET sequence|legend=1| 14c, …, 85c, 99, 212, 311, 721, 1032, 1753b }}
+{{Optimal ET sequence|legend=0| 99e, 212, 311, 1145c, 1456cd }}
-[[Badness]] (Smith): 0.045473
+Badness (Sintel): 1.62
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 625/624, 2080/2079, 2401/2400, 10648/10647
+apping: {{mapping| 1 -17 -46 -26 -135 -171 | 0 20 52 31 149 188 }}
+Optimal tunings:
+* WE: ~2 = 1200.0543{{c}}, ~40/21 = 1115.1594{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1095{{c}}
+{{Optimal ET sequence|legend=0| 99ef, 212, 311, 834, 1145c }}
+Badness (Sintel): 1.43
 === Amical ===
@@ Line 753: / Line 948: @@
 Comma list: 2401/2400, 131072/130977, 1600000/1594323
-Mapping: {{mapping| 1 3 6 5 -8 | 0 -20 -52 -31 162 }}
+{{Mapping|legend=0| 1 -17 -46 -26 154 | 0 20 52 31 -162 }}
 Optimal tunings:
-* CTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.8843{{c}}
+* WE: ~2 = 1200.0008{{c}}, ~40/21 = 1115.1165{{c}}
-* POTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.8843{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1157{{c}}
-{{Optimal ET sequence|legend=0| 99, 212e, 311, 721, 1032, 1343, 2375bc }}
+{{Optimal ET sequence|legend=0| 99, 212e, 311, 721, 1032, 1343 }}
-Badness (Smith): 0.100668
+Badness (Sintel): 3.33
 ==== 13-limit ====
@@ Line 768: / Line 963: @@
 Comma list: 2080/2079, 2401/2400, 4096/4095, 741125/739206
-Mapping: {{mapping| 1 3 6 5 -8 -5 | 0 -20 -52 -31 162 123 }}
+{{Mapping|legend=0| 1 -17 -46 -26 154 118 | 0 20 52 31 -162 -123 }}
 Optimal tunings:
-* CTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.8837{{c}}
+* WE: ~2 = 1199.9926{{c}}, ~40/21 = 1115.1094{{c}}
-* POTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.8838{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.1162{{c}}
 {{Optimal ET sequence|legend=0| 99, 212ef, 311, 721, 1032 }}
-Badness (Smith): 0.049893
+Badness (Sintel): 2.06
-=== Amorous ===
+=== Pseudoamorous ===
 Subgroup: 2.3.5.7.11
-Comma list: 2401/2400, 6250/6237, 19712/19683
+Comma list: 243/242, 441/440, 980000/970299
-Mapping: {{mapping| 1 3 6 5 14 | 0 -20 -52 -31 -149 }}
+{{Mapping|legend=0| 1 -17 -46 -26 -43 | 0 20 52 31 50 }}
 Optimal tunings:
-* CTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.8883{{c}}
+* WE: ~2 = 1199.8269{{c}}, ~21/11 = 1114.9475{{c}}
-* POTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.8896{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~21/11 = 1115.1038{{c}}
+{{Optimal ET sequence|legend=0| 99e, 212e }} *
-{{Optimal ET sequence|legend=0| 99e, 212, 311, 2389bccd, 2700bccde, 3011bccde, 3322bccdde }}
+<nowiki/>* optimal patent val: [[113edo|113]]
-Badness (Smith): 0.048924
+Badness (Sintel): 1.87
 ==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
-Comma list: 625/624, 2080/2079, 2401/2400, 10648/10647
+Comma list: 243/242, 364/363, 441/440, 1875/1859
-Mapping: {{mapping| 1 3 6 5 14 17 | 0 -20 -52 -31 -149 -188 }}
+{{Mapping|legend=0| 1 -17 -46 -26 -43 -79 | 0 20 52 31 50 89 }}
 Optimal tunings:
-* CTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.8895{{c}}
+* WE: ~2 = 1200.0182{{c}}, ~40/21 = 1115.1005{{c}}
-* POTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.8910{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.0840{{c}}
-{{Optimal ET sequence|legend=0| 99ef, 212, 311, 1145c, 1456cd, 1767cd }}
+{{Optimal ET sequence|legend=0| 99ef, 113, 212ef }}
-Badness (Smith): 0.034681
+Badness (Sintel): 1.77
 === Pseudoamical ===
@@ Line 813: / Line 1,010: @@
 Comma list: 385/384, 1375/1372, 1600000/1594323
-Mapping: {{mapping| 1 3 6 5 -1 | 0 -20 -52 -31 63 }}
+{{Mapping|legend=0| 1 -17 -46 -26 62 | 0 20 52 31 -63 }}
 Optimal tunings:
-* CTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.9005{{c}}
+* WE: ~2 = 1200.3436{{c}}, ~40/21 = 1115.4102{{c}}
-* POTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.9091{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~40/21 = 1115.0925{{c}}
-{{Optimal ET sequence|legend=0| 14ce, …, 85cee, 99, 212 }}
+{{Optimal ET sequence|legend=0| 99, 113, 212, 961ccdeee }}
-Badness (Smith): 0.085837
+Badness (Sintel): 2.84
 ==== 13-limit ====
@@ Line 828: / Line 1,025: @@
 Comma list: 325/324, 385/384, 1375/1372, 19773/19712
-Mapping: {{mapping| 1 3 6 5 -1 2 | 0 -20 -52 -31 63 24 }}
+{{Mapping|legend=0| 1 -17 -46 -26 62 26 | 0 20 52 31 -63 -24 }}
 Optimal tunings:
-* CTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.9049{{c}}
+* WE: ~2 = 1200.4212{{c}}, ~40/21 = 1115.4787{{c}}
-* POTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.9127{{c}}
+* CWE: ~2 = 1200.0000{{c}}, 40/21 = 1115.0885{{c}}
-{{Optimal ET sequence|legend=0| 14ce, …, 85ceef, 99, 113, 212 }}
+{{Optimal ET sequence|legend=0| 99, 113, 212, 537cdeff, 749ccdeefff }}
-Badness (Smith): 0.047025
+Badness (Sintel): 1.94
-=== Pseudoamorous ===
+=== Floral ===
 Subgroup: 2.3.5.7.11
-Comma list: 243/242, 441/440, 980000/970299
+Comma list: 2401/2400, 9801/9800, 14641/14580
-Mapping: {{mapping| 1 3 6 5 7 | 0 -20 -52 -31 -50 }}
+{{Mapping|legend=0| 2 -14 -40 -21 -30 | 0 20 52 31 43 }}
+: mapping generators: ~99/70, ~66/49
 Optimal tunings:
-* CTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.9022{{c}}
+* WE: ~99/70 = 600.0052{{c}}, ~66/49 = 515.1257{{c}}
-* POTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.8917{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~66/49 = 515.1215{{c}}
-{{Optimal ET sequence|legend=0| 14c, …, 85ce, 99e, 113, 212e }}
+{{Optimal ET sequence|legend=0| 14c, … 198, 212, 410 }}
-Badness (Smith): 0.056583
+Badness (Sintel): 2.15
 ==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
-Comma list: 243/242, 364/363, 441/440, 1875/1859
+Comma list: 676/675, 1001/1000, 1716/1715, 14641/14580
-Mapping: {{mapping| 1 3 6 5 7 10 | 0 -20 -52 -31 -50 -89 }}
+{{Mapping|legend=0| 2 -14 -40 -21 -30 -63 | 0 20 52 31 43 82 }}
 Optimal tunings:
-* CTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.9153{{c}}
+* WE: ~99/70 = 599.9923{{c}}, ~66/49 = 515.1184{{c}}
-* POTE: ~2 = 1200.0000{{c}}, ~21/20 = 84.9164{{c}}
+* CWE: ~99/70 = 600.0000{{c}}, ~66/49 = 515.1246{{c}}
-{{Optimal ET sequence|legend=0| 14cf, …, 85ceff, 99ef, 113, 212ef, 325ce, 537cdeef }}
+{{Optimal ET sequence|legend=0| 14cf, …, 198, 410 }}
-Badness (Smith): 0.042826
+Badness (Sintel): 1.53
-=== Floral ===
+=== Humorous ===
 Subgroup: 2.3.5.7.11
-Comma list: 2401/2400, 9801/9800, 14641/14580
+Comma list: 2401/2400, 3025/3024, 1600000/1594323
-Mapping: {{mapping| 2 6 12 10 13 | 0 -20 -52 -31 -43 }}
+{{Mapping|legend=0| 1 -37 -98 -57 16 | 0 40 104 62 -13 }}
+: mapping generators: ~2, ~3993/2048
 Optimal tunings:
-* CTE: ~99/70 = 600.0000{{c}}, ~21/20 = 84.8781{{c}}
+* WE: ~2 = 1199.9189{{c}}, ~3993/2048 = 1157.4826{{c}}
-* POTE: ~99/70 = 600.0000{{c}}, ~21/20 = 84.8788{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3993/2048 = 1157.5602{{c}}
-{{Optimal ET sequence|legend=0| 14c, …, 170bccde, 184c, 198, 212, 410 }}
+{{Optimal ET sequence|legend=0| 85c, 113, 198, 311, 509, 820 }}
-Badness (Smith): 0.065110
+Badness (Sintel): 1.93
 ==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
-Comma list: 676/675, 1001/1000, 1716/1715, 14641/14580
+Comma list: 2080/2079, 2200/2197, 2401/2400, 3025/3024
-Mapping: {{mapping| 2 6 12 10 13 19 | 0 -20 -52 -31 -43 -82 }}
+{{Mapping|legend=0| 1 -37 -98 -57 16 -59 | 0 40 104 62 -13 65 }}
 Optimal tunings:
-* CTE: ~99/70 = 600.0000{{c}}, ~21/20 = 84.8759{{c}}
+* WE: ~2 = 1199.8903{{c}}, ~39/20 = 1157.4551{{c}}
-* POTE: ~99/70 = 600.0000{{c}}, ~21/20 = 84.8750{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~39/20 = 1157.5600{{c}}
+{{Optimal ET sequence|legend=0| 85c, 113, 198, 311, 509, 820f }}
+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| 14c, …, 184cff, 198, 410 }}
+{{Optimal ET sequence|legend=0| 32cf, 166, 198, 364, 562, 926 }}
-Badness (Smith): 0.037013
+Badness (Sintel): 1.57
-=== Humorous ===
+=== Hitch ===
 Subgroup: 2.3.5.7.11
-Comma list: 2401/2400, 3025/3024, 1600000/1594323
+Comma list: 3025/3024, 117649/117612, 1600000/1594323
-Mapping: {{mapping| 1 3 6 5 3 | 0 -40 -104 -62 13 }}
+{{Mapping|legend=0| 1 -32 -85 -16 31 | 0 50 130 28 -41 }}
+: mapping generators: ~2, ~891/560
 Optimal tunings:
-* CTE: ~2 = 1200.0000{{c}}, ~4096/3993 = 42.4414{{c}}
+* WE: ~2 = 1199.8455{{c}}, ~891/560 = 805.9457{{c}}
-* POTE: ~2 = 1200.0000{{c}}, ~4096/3993 = 42.4391{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~891/560 = 806.0488{{c}}
-{{Optimal ET sequence|legend=0| 85c, 113, 198, 311, 1131, 1442, 1753be }}
+{{Optimal ET sequence|legend=0| 67c, 198, 463, 661, 1124bde }}
-Badness (Smith): 0.058249
+Badness (Sintel): 3.09
 ==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
-Comma list: 2080/2079, 2200/2197, 2401/2400, 3025/3024
+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: {{mapping| 1 3 6 5 3 6 | 0 -40 -104 -62 13 -65 }}
+{{Mapping|legend=0| 1 -32 -85 -16 31 -1 | 0 50 130 28 -41 7 }}
 Optimal tunings:
-* CTE: ~2 = 1200.0000{{c}}, ~40/39 = 42.4425{{c}}
+* WE: ~2 = 1199.7690{{c}}, ~78/49 = 805.8958{{c}}
-* POTE: ~2 = 1200.0000{{c}}, ~40/39 = 42.4391{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~78/49 = 806.0500{{c}}
-{{Optimal ET sequence|legend=0| 85c, 113, 198, 311, 1753beff, 2064beff, 2375bceff }}
+{{Optimal ET sequence|legend=0| 67c, 198, 463f, 661ff }}
-Badness (Smith): 0.028267
+Badness (Sintel): 2.46
 == Calamity ==
-Calamity tempers out 2100875/2097152, the [[rainy comma]], and may be described as the {{nowrap| 46 & 311 }} temperament. It splits the interval of two octaves plus an acute minor third into five.
+Named by [[Flora Canou]] in 2023, calamity tempers out 2100875/2097152, the [[rainy comma]], and may be described as the {{nowrap| 46 & 311 }} temperament. It splits the interval of grave major sixth plus an octave into five.
 [[Subgroup]]: 2.3.5.7
@@ Line 935: / Line 1,231: @@
 [[Comma list]]: 1600000/1594323, 2100875/2097152
-{{Mapping|legend=1| 1 13 32 -15 | 0 -25 -65 39 }}
+{{Mapping|legend=1| 1 -12 -33 24 | 0 25 65 -39 }}
+: mapping generators: ~2, ~35/24
-[[Optimal tuning]] (CTE): ~2 = 1200.000{{c}}, ~48/35 = 547.909{{c}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.0332{{c}}, ~35/24 = 652.1081{{c}}
+: [[error map]]: {{val| +0.033 +0.348 -0.387 -0.243 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~35/24 = 652.0902{{c}}
+: error map: {{val| 0.000 +0.300 -0.452 -0.343 }}
 {{Optimal ET sequence|legend=1| 46, 219c, 265, 311 }}
-[[Badness]] (Smith): 0.198130
+[[Badness]] (Sintel): 5.01
 === 11-limit ===
@@ Line 948: / Line 1,249: @@
 Comma list: 3025/3024, 12005/11979, 131072/130977
-Mapping: {{mapping| 1 13 32 -15 -18 | 0 -25 -65 39 47 }}
+{{Mapping|legend=0| 1 -12 -33 24 29 | 0 25 65 -39 -47 }}
-Optimal tuning (CTE): ~2 = 1200.000{{c}}, ~48/35 = 547.908{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9938{{c}}, ~35/24 = 652.0887{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~35/24 = 652.0920{{c}}
 {{Optimal ET sequence|legend=0| 46, 219c, 265, 311, 979, 1290 }}
-Badness (Smith): 0.060408
+Badness (Sintel): 2.00
 === 13-limit ===
@@ Line 961: / Line 1,264: @@
 Comma list: 2080/2079, 3025/3024, 4096/4095, 12005/11979
-Mapping: {{mapping| 1 13 32 -15 -18 -31 | 0 -25 -65 39 47 76 }}
+{{Mapping|legend=0| 1 -12 -33 24 29 45 | 0 25 65 -39 -47 -76 }}
-Optimal tuning (CTE): ~2 = 1200.000{{c}}, ~48/35 = 547.907{{c}}
+Optimal tunings:
+* WE: ~2 = 1199.9742{{c}}, ~35/24 = 652.0794{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~35/24 = 652.0934{{c}}
 {{Optimal ET sequence|legend=0| 46, 265, 311, 668, 979, 1290 }}
-Badness (Smith): 0.033617
+Badness (Sintel): 1.39
 == Familia ==
-Familia tempers out 16875/16807, the [[mirkwai comma]], and may be described as the {{nowrap| 113 & 152 }} temperament. It splits the interval of acute minor tenth (~243/100) in five.
+Named by [[Xenllium]] in 2021, familia tempers out 16875/16807, the [[mirkwai comma]], and may be described as the {{nowrap| 113 & 152 }} temperament. It is generated by a major sixth, five of which octave reduced make the original generator of amity.
 [[Subgroup]]: 2.3.5.7
@@ Line 976: / Line 1,281: @@
 [[Comma list]]: 16875/16807, 1600000/1594323
-{{Mapping|legend=1| 1 8 19 20 | 0 -25 -65 -67 }}
+{{Mapping|legend=1| 1 -17 -46 -47 | 0 25 65 67 }}
+: mapping generators: ~2, ~6561/3920
-Optimal tunings:
+[[Optimal tuning]]s:
-* CTE: ~2 = 1200.000{{c}}, ~11907/10000 = 307.915{{c}}
+* [[WE]]: ~2 = 1199.9165{{c}}, ~6561/3920 = 892.0267{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~11907/10000 = 307.941{{c}}
+: [[error map]]: {{val| -0.084 +0.132 -0.736 +0.888 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~6561/3920 = 892.0871{{c}}
+: error map: {{val| 0.000 +0.224 -0.649 +1.013 }}
-{{Optimal ET sequence|legend=1| 39d, 74cd, 113, 152, 265, 417, 1516ccdd, 1933ccdd }}
+{{Optimal ET sequence|legend=1| 39d, 74cd, 113, 152, 265, 417 }}
-[[Badness]] (Smith): 0.144551
+[[Badness]] (Sintel): 3.66
 === 11-limit ===
@@ Line 991: / Line 1,299: @@
 Comma list: 540/539, 1375/1372, 1600000/1594323
-Mapping: {{mapping| 1 8 19 20 5 | 0 -25 -65 -67 -6 }}
+{{Mapping|legend=0| 1 -17 -46 -47 -1 | 0 25 65 67 6 }}
 Optimal tunings:
-* CTE: ~2 = 1200.000{{c}}, ~3200/2673 = 307.915{{c}}
+* WE: ~2 = 1199.7927{{c}}, ~2673/1600 = 891.9397{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~3200/2673 = 307.906{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~2673/1600 = 892.0909{{c}}
-{{Optimal ET sequence|legend=0| 39d, 74cd, 113, 152, 265, 417, 1099cdee }}
+{{Optimal ET sequence|legend=0| 39d, 74cd, 113, 152, 417, 569de, 721de }}
-Badness (Smith): 0.051740
+Badness (Sintel): 1.71
 === 13-limit ===
@@ Line 1,006: / Line 1,314: @@
 Comma list: 540/539, 729/728, 1375/1372, 2205/2197
-Mapping: {{mapping| 1 8 19 20 5 25 | 0 -25 -65 -67 -6 -83 }}
+{{Mapping|legend=0| 1 -17 -46 -47 -1 -58 | 0 25 65 67 6 83 }}
 Optimal tunings:
-* CTE: ~2 = 1200.000{{c}}, ~143/120 = 307.922{{c}}
+* WE: ~2 = 1199.7844{{c}}, ~240/143 = 892.9268{{c}}
-* POTE: ~2 = 1200.000{{c}}, ~143/120 = 307.913{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~240/143 = 892.0839{{c}}
 {{Optimal ET sequence|legend=0| 39df, 74cdf, 113, 152f, 265 }}
-Badness (Smith): 0.038473
+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