@@ Line 1: / Line 1: @@
 On this page, I explore some unnamed rank-2 temperaments that catched my interest.
+== 7 & 37 ==
+Subgroup: 2.3.5.11.13
+Comma list: [[55/54]], [[100/99]], [[512/507]]
+Mapping: [{{val|1 5 8 8 2}}, {{val|0 -6 -10 -8 3}}]
+POTE generator: ~160/117 = 518.2094
+{{Optimal ET sequence|legend=1|7, 23bc, 30, 37, 44 }}
+Badness: 1.211
 == Berkenthin (19 & 239) ==
@@ Line 251: / Line 265: @@
 Badness: 9.862
-==31 & 449==
+== 31 & 421 ==
-Subgroup: 2.3.5.7
+Subgroup: 2.3.7
-Comma list: 6144/6125, {{monzo|7 -4 -16 13}}
+Comma list: {{monzo|37 5 -16}}
-Mapping: [{{val|1 -3 2 1}}, {{val|0 71 5 28}}]
+Mapping: [{{val|1 -17 -3}}, {{val|0 48 15}}]
-POTE generator: ~256/245 = 77.498
+POTE generator: 464.6264
-{{Optimal ET sequence|legend=1|31, 294bbd, 325bd, 356bd, 387bd, 418d, 449, 480, 991cd}}
+{{Optimal ET sequence|legend=1|25b, 31, 68, 99, 130, 229, 588, 817, 1405d, 2222dd}}
-Badness: 8.502
+Badness: 3.193
-== Adriansonka (31 & 569) ==
+=== 11-limit ===
-Subgroup: 2.3.5.7
+Subgroup: 2.3.7.11
-Comma list: 65625/65536, 678223072849/675000000000
+Comma list: 1362944/1361367, {{monzo|13 13 -6 -6}}
-Mapping: [{{val|1 -35 10 1}}, {{val|0 81 -17 4}}]
+Mapping: [{{val|1 -17 -3 -31}}, {{val|0 48 15 89}}]
-CTE tuning: ~1875/1372 = 542.0577
+POTE generator: ~847/648 = 464.6259
-{{Optimal ET sequence|legend=1|31, 476b, 507, 538, 569, 600, 631}}
+Badness: 2.532
-Badness: 7.921
+== Dakshdua (31 & 431) ==
-=== 11-limit ===
+Subgroup: 2.3.5.7
-Subgroup: 2.3.5.7.11
+Comma list: 2401/2400, 8589934592/8544921875
-Comma list: 42592/42525, 65625/65536, 422576/421875
+Mapping: [{{val|1 19 2 7}}, {{val|0 -54 1 -13}}]
-Mapping: [{{val|1 -35 10 1 -53}}, {{val|0 81 -17 4 125}}]
+POTE generator: ~ 5/4 = 386.9969
-CTE tuning: ~308/225 = 542.0730
+{{Optimal ET sequence|31, 214b, 245b, 276b, 307, 338, 369, 400, 769, 1169c, 1938cc}}
-{{Optimal ET sequence|legend=1|31, 476b, 507, 538, 569, 600e}}
+Badness: 3.038
-Badness: 3.942
+=== 11-limit ===
-== 31 & 577 ==
+Subgroup: 2.3.5.7.11
-Subgroup: 2.5.7
+Comma list: 5632/5625, 2401/2400, 46656/46585
-Comma list: {{monzo|60 -21 -4}}
+Mapping: [{{val|1 19 2 7 37}}, {{val|0 -54 1 -13 -104}}]
-Mapping: [{{val|1 4 -6}}, {{val|0 -4 21}}]
+POTE generator: ~5/4 = 386.9992
-CTE tuning: ~21875/16384 = 503.2464
+{{Optimal ET sequence|legend=1|31, 276bee, 307e, 338e, 369, 400, 1969ccee}}
-{{Optimal ET sequence|legend=1|12d, 19d, 31, 298, 329, 360, 391, 422, 453, 484, 515, 546, 3307ccdd, 3853cccdd}}
+Badness: 1.372
-Badness: 5.455
+=== 13-limit ===
-=== 11-limit ===
+Subgroup: 2.3.5.7.11.13
-Comma list: 4302592/4296875, {{monzo|44 -5 -14 2}}
+Commas: 1001/1000, 1716/1715, 4096/4095, 75816/75625
-Mapping: [{{val|1 4 -6 -54}}, {{val|0 -4 21 137}}]
+Mapping: [{{val|1 19 2 7 37 -35}}, {{val|0 -54 1 -13 -104 120}}]
-CTE tuning: ~21875/16384 = 503.2468
+POTE generator: ~5/4 = 387.0031
-{{Optimal ET sequence|legend=1|31, 391ee, 422ee, 453e, 484e, 515, 546, 2153cde, 2699ccde, 3245ccddee, 3791cccddee}}
+{{Optimal ET sequence|legend=1|31, 369, 400, 831}}
-Badness: 6.490
+Badness: 1.798
-== 37 & 307 ==
+=== 17-limit ===
-Subgroup: 2.5.7
+Subgroup: 2.3.5.7.11.13.17
-Comma list: {{monzo|20 -34 21}}
+Commas: 1001/1000, 936/935, 1377/1375, 1716/1715, 4096/4095
-Mapping: [{{val|1 8 12}}, {{val|0 -21 -34}}]
+Mapping: [{{val|1 19 2 7 37 -35 -33}}, {{val|0 -54 1 -13 -104 120 115}}]
-CTE tuning: ~1475789056/1220703125 = 324.444
+POTE generator: ~5/4 = 387.0028
-{{Optimal ET sequence|legend=1|11cd, 26cdd, 37, 159, 196, 233, 270, 503, 773, 1816, 2589c}}
+{{Optimal ET sequence|legend=1|31, 369, 400, 831}}
-Badness: 7.966
+Badness: 1.515
-=== 11-limit ===
+=== 19-limit ===
-Subgroup: 2.5.7.11
+Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 102487/102400, 4302592/4296875
+Commas: 1001/1000, 936/935, 1377/1375, 1716/1715, 2926/2925, 4096/4095
-Mapping: [{{val|1 8 12 4}}, {{val|0 -21 -34 -2}}]
+Mapping: [{{val|1 19 2 7 37 -35 -33 -38}}, {{val|0 -54 1 -13 -104 120 115 131}}]
-CTE tuning: ~15125/12544 = 324.4587
+POTE generator: ~5/4 = 387.0033
-{{Optimal ET sequence|legend=1|11cd, 37, 159, 196, 233, 270, 503}}
+{{Optimal ET sequence|legend=1|31, 369, 400, 831}}
-Badness: 0.511
+Badness: 1.393
-=== 13-limit ===
+== 31 & 449 ==
-Subgroup: 2.5.7.11.13
+Subgroup: 2.3.5.7
-Comma list: 1001/1000, 6656/6655, 105644/105625
+Comma list: 6144/6125, {{monzo|7 -4 -16 13}}
-Mapping: [{{val|1 8 12 4 11}}, {{val|0 -21 -34 -2 -27}}]
+Mapping: [{{val|1 -3 2 1}}, {{val|0 71 5 28}}]
-CTE tuning: ~650/539 = 324.4626
+POTE generator: ~256/245 = 77.498
-{{Optimal ET sequence|legend=1|11cdf, 37, 159, 196, 233, 270, 503, 773, 1276f}}
+{{Optimal ET sequence|legend=1|31, 294bbd, 325bd, 356bd, 387bd, 418d, 449, 480, 991cd}}
-Badness: 0.290
+Badness: 8.502
-=== 17-limit ===
+== Adriansonka (31 & 569) ==
-Subgroup: 2.5.7.11.13.17
+Subgroup: 2.3.5.7
-Comma list: 1001/1000, 7744/7735, 32768/32725, 105644/105625
+Comma list: 65625/65536, 678223072849/675000000000
-Mapping: [{{val|1 8 12 4 11 -17}}, {{val|0 -21 -34 -2 -27 78}}]
+Mapping: [{{val|1 -35 10 1}}, {{val|0 81 -17 4}}]
-CTE tuning: ~650/539 = 324.4083
+CTE tuning: ~1875/1372 = 542.0577
-{{Optimal ET sequence|legend=1|37, 233g, 270, 307}}
+{{Optimal ET sequence|legend=1|31, 476b, 507, 538, 569, 600, 631}}
-Badness: 0.929
+Badness: 7.921
-=== 19-limit ===
+=== 11-limit ===
-Subgroup: 2.5.7.11.13.17.19
+Subgroup: 2.3.5.7.11
-Comma list: 1001/1000, 3328/3325, 2128/2125, 7744/7735, 105644/105625
+Comma list: 42592/42525, 65625/65536, 422576/421875
-Mapping: [{{val|1 8 12 4 11 -17 -9}}, {{val|0 -21 -34 -2 -27 78 49}}]
+Mapping: [{{val|1 -35 10 1 -53}}, {{val|0 81 -17 4 125}}]
-CTE tuning: ~650/539 = 324.4173
+CTE tuning: ~308/225 = 542.0730
-{{Optimal ET sequence|legend=1|37, 233g, 270, 307, 577g, 884g}}
+{{Optimal ET sequence|legend=1|31, 476b, 507, 538, 569, 600e}}
-Badness: 0.809
+Badness: 3.942
-== 37 & 577 ==
+== 31 & 577 ==
 Subgroup: 2.5.7
-Comma list: {{monzo|20 -34 21}}
+Comma list: {{monzo|60 -21 -4}}
-Mapping: [{{val|1 8 12}}, {{val|0 -42 -68}}]
+Mapping: [{{val|1 4 -6}}, {{val|0 -4 21}}]
-CTE tuning: ~1475789056/1220703125 = 324.444
+CTE tuning: ~21875/16384 = 503.2464
-{{Optimal ET sequence|legend=1|11cd, 26cdd, 37, 159, 196, 233, 270, 503, 773, 1816, 2589c}}
+{{Optimal ET sequence|legend=1|12d, 19d, 31, 298, 329, 360, 391, 422, 453, 484, 515, 546, 3307ccdd, 3853cccdd}}
-Badness: 7.966
+Badness: 5.455
 === 11-limit ===
-Subgroup: 2.5.7.11
+Comma list: 4302592/4296875, {{monzo|44 -5 -14 2}}
-Comma list: 102487/102400, 4302592/4296875
+Mapping: [{{val|1 4 -6 -54}}, {{val|0 -4 21 137}}]
-Mapping: [{{val|1 8 12 4}}, {{val|0 -42 -68 -4}}]
+CTE tuning: ~21875/16384 = 503.2468
-CTE tuning: ~3773/3125 = 324.451
+{{Optimal ET sequence|legend=1|31, 391ee, 422ee, 453e, 484e, 515, 546, 2153cde, 2699ccde, 3245ccddee, 3791cccddee}}
-{{Optimal ET sequence|legend=1|11cd, 37, 159, 196, 233, 270, 503}}
+Badness: 6.490
-Badness: 0.511
+== Audreyglende (31 & 677) ==
-=== 13-limit ===
+Subgroup: 2.3.5.7.11
-Subgroup: 2.5.7.11.13
+Comma list: 3025/3024, 759375/758912, 589824/588245
-Comma list: 1001/1000, 10985/10976, 75712/75625
+Mapping: [{{val|1 19 0 9 35}}, {{val|0 -90 12 -32 -163}}]
-Mapping: [{{val|1 8 12 4 11}}, {{val|0 -42 -68 -4 -54}}]
+CTE tuning: ~4320/3773 = 232.1820
-CTE tuning: ~169/140 = 324.446
+{{Optimal ET sequence|legend=1|31, 553bde, 584de, 615, 646, 1323d}}
-{{Optimal ET sequence|legend=1|11cdf, 37, 159, 196, 233, 270, 503, 773, 1276f}}
+Badness: 2.875
-Badness: 0.290
+== 31 & 773 ==
-==41 & 167==
 Subgroup: 2.3.5.7
-Comma list: 2401/2400, 179200/177147
+Comma list: 2401/2400, {{monzo|60 -3 -25 1}}
-Mapping: [{{val|1 5 17 11}}, {{val|0 -10 -43 -24}}]
+Mapping: [{{val|1 49 -3 12}}, {{val|0 -98 11 -19}}]
-CTE tuning: ~80/63 = 409.639
+POTE generator: ~5859375/4194304 = 580.5918
-{{Optimal ET sequence|legend=1|38ccd, 41, 126, 167, 208, 375b}}
+{{Optimal ET sequence|legend=1|31, 556b, 587b, 618, 649, 680, 711, 1453, 3617c}}
-Badness: 2.943
+Badness: 4.036
-===11-limit===
+=== 11-limit ===
-Subgroup: 2.3.5.7
+Subgroup: 2.3.5.7.11
-Comma list: 896/891, 2200/2187, 2401/2400
+Comma list: 2401/2400, 172032/171875, 820125/819896
-Mapping: [{{val|1 5 17 11 -2}}, {{val|0 -10 -43 -24 16}}]
+Mapping: [{{val|1 49 -3 12 92}}, {{val|0 -98 11 -19 -183}}]
-CTE tuning: ~80/63 = 409.630
+POTE generator: ~7875/5632 = 580.5924
-{{Optimal ET sequence|legend=1|41, 126, 167, 208, 375be}}
+{{Optimal ET sequence|legend=1|31, 618ee, 649e, 680e, 711, 742, 1453, 2195e, 2937e}}
-Badness: 1.816
+Badness: 1.638
-===13-limit===
+== 31 & 1063 ==
-Subgroup: 2.3.5.7.11.13
+Subgroup: 2.3.5.7
-Comma list: 325/324, 352/351, 896/891, 2401/2400
+Comma list: 2401/2400, {{monzo|-97 7 37 0}}
-Mapping: [{{val|1 5 17 11 -2 -12}}, {{val|0 -10 -43 -24 16 46}}]
+Mapping: [{{val|1 35 -4 8}}, {{val|0 -148 28 -23}}]
-CTE tuning: ~195/154 = 409.617
+POTE generator: ~962072674304/823974609375 = 270.9334
-{{Optimal ET sequence|legend=1|41, 126, 167, 208, 375be}}
+{{Optimal ET sequence|legend=1|31, 970b, 1001, 1032, 1063, 1094, 1125}}
-Badness: 1.782
+Badness: 9.148
-== 41 & 197 ==
+== 37 & 307 ==
-Subgroup: 2.3.5.7
+Subgroup: 2.5.7
-Comma list: 225/224, 4202539929/4194304000
+Comma list: {{monzo|20 -34 21}}
-Mapping: [{{val|1 0 5 5}}, {{val|0 13 -22 -18}}]
+Mapping: [{{val|1 8 12}}, {{val|0 -21 -34}}]
-POTE generator: ~160/147 = 146.1953
+CTE tuning: ~1475789056/1220703125 = 324.444
-{{Optimal ET sequence|legend=1|33, 41, 115, 156, 197}}
+{{Optimal ET sequence|legend=1|11cd, 26cdd, 37, 159, 196, 233, 270, 503, 773, 1816, 2589c}}
-Badness: 3.049
+Badness: 7.966
-== 41 & 227 ==
+=== 11-limit ===
-Subgroup: 2.3.5.7
+Subgroup: 2.5.7.11
-Comma list: 5120/5103, 117649/116640
+Comma list: 102487/102400, 4302592/4296875
-Mapping: [{{val|1 0 -11 -1}}, {{val|0 5 42 12}}]
+Mapping: [{{val|1 8 12 4}}, {{val|0 -21 -34 -2}}]
-POTE generator: ~56/45 = 380.6339
+CTE tuning: ~15125/12544 = 324.4587
-{{Optimal ET sequence|legend=1|19cc, 22c, 41, 104c, 145, 186, 413}}
+{{Optimal ET sequence|legend=1|11cd, 37, 159, 196, 233, 270, 503}}
-Badness: 2.852
+Badness: 0.511
-=== 11-limit ===
+=== 13-limit ===
-Subgroup: 2.3.5.7.11
+Subgroup: 2.5.7.11.13
-Comma list: 385/384, 2200/2187, 67228/66825
+Comma list: 1001/1000, 6656/6655, 105644/105625
-Mapping: [{{val|1 0 -11 -1 19}}, {{val|0 5 42 12 -49}}]
+Mapping: [{{val|1 8 12 4 11}}, {{val|0 -21 -34 -2 -27}}]
-POTE generator: ~96/77 = 380.6090
+CTE tuning: ~650/539 = 324.4626
-{{Optimal ET sequence|legend=1|41, 145e, 186, 227}}
+{{Optimal ET sequence|legend=1|11cdf, 37, 159, 196, 233, 270, 503, 773, 1276f}}
-Badness: 2.774
+Badness: 0.290
-===13-limit===
+=== 17-limit ===
-Subgroup: 2.3.5.7.11.13
+Subgroup: 2.5.7.11.13.17
-Comma list: 385/384, 325/324, 352/351, 67228/66825
+Comma list: 1001/1000, 7744/7735, 32768/32725, 105644/105625
-Mapping: [{{val|1 0 -11 -1 19 24}}, {{val|0 5 42 12 -49 -64}}]
+Mapping: [{{val|1 8 12 4 11 -17}}, {{val|0 -21 -34 -2 -27 78}}]
-POTE generator: ~96/77 = 380.6135
+CTE tuning: ~650/539 = 324.4083
-{{Optimal ET sequence|legend=1|41, 145ef, 186, 227}}
+{{Optimal ET sequence|legend=1|37, 233g, 270, 307}}
-Badness: 2.307
+Badness: 0.929
-==41 & 233==
+=== 19-limit ===
-Subgroup: 2.3.5.7
+Subgroup: 2.5.7.11.13.17.19
-Comma list: 2401/2400, 124556484375/123363917824
+Comma list: 1001/1000, 3328/3325, 2128/2125, 7744/7735, 105644/105625
-Mapping: [{{val|1 9 -19 -6}}, {{val|0 -16 46 19}}]
+Mapping: [{{val|1 8 12 4 11 -17 -9}}, {{val|0 -21 -34 -2 -27 78 49}}]
-POTE generator: ~30375/21952 = 556.1960
+CTE tuning: ~650/539 = 324.4173
-{{Optimal ET sequence|legend=1|41, 151, 192, 233, 274, 315, 589bcd}}
+{{Optimal ET sequence|legend=1|37, 233g, 270, 307, 577g, 884g}}
-Badness: 4.209
+Badness: 0.809
-===11-limit===
+== 37 & 577 ==
-Subgroup: 2.3.5.7.11
+Subgroup: 2.5.7
-Comma list: 441/440, 540/539, 5053640625/5035261952
+Comma list: {{monzo|20 -34 21}}
-Mapping: [{{val|1 9 -19 -6 22}}, {{val|0 -16 46 19 -40}}]
+Mapping: [{{val|1 8 12}}, {{val|0 -42 -68}}]
-POTE generator: ~2475/1792 = 556.2083
+CTE tuning: ~1475789056/1220703125 = 324.444
-{{Optimal ET sequence|41, 151, 192, 233, 274}}
+{{Optimal ET sequence|legend=1|11cd, 26cdd, 37, 159, 196, 233, 270, 503, 773, 1816, 2589c}}
-Badness: 2.494
+Badness: 7.966
-===13-limit===
+=== 11-limit ===
-Subgroup: 2.3.5.7.11.13
+Subgroup: 2.5.7.11
-Comma list: 441/440, 540/539, 21168/21125, 81675/81536
+Comma list: 102487/102400, 4302592/4296875
-Mapping: [{{val|1 9 -19 -6 22 38}}, {{val|0 -16 46 19 -40 -74}}]
+Mapping: [{{val|1 8 12 4}}, {{val|0 -42 -68 -4}}]
-POTE generator: ~91/66 = 556.2131
+CTE tuning: ~3773/3125 = 324.451
-{{Optimal ET sequence|legend=1|41, 192, 233, 274, 507b}}
+{{Optimal ET sequence|legend=1|11cd, 37, 159, 196, 233, 270, 503}}
-Badness: 2.034
+Badness: 0.511
-==41 & 337==
+=== 13-limit ===
-(better described as 41 & 255)
-Subgroup: 2.3.5.7
+Subgroup: 2.5.7.11.13
-Comma list: 16875/16807, 7381125/7340032
+Comma list: 1001/1000, 10985/10976, 75712/75625
-Mapping: [{{val|1 4 -8 -4}}, {{val|0 -11 47 31}}]
+Mapping: [{{val|1 8 12 4 11}}, {{val|0 -42 -68 -4 -54}}]
-POTE generator: ~784/675 = 263.5183
+CTE tuning: ~169/140 = 324.446
-{{Optimal ET sequence|legend=1|41, 173, 214, 255, 296, 551, 847c}}
+{{Optimal ET sequence|legend=1|11cdf, 37, 159, 196, 233, 270, 503, 773, 1276f}}
-Badness: 3.414
+Badness: 0.290
-==41 & 359==
+== 37 & 661 ==
-Subgroup: 2.3.5
+Subgroup: 2.5.7.11.13
-Comma list: {{monzo|155 -89 -6}}
+Comma list: 75712/75625, 10985/10976, 3200000/3195731
-Mapping: [{{val|1 1 11}}, {{val|0 6 -89}}]
+Mapping: [{{val|1 23 32 -1 26}}, {{val|0 -51 -72 11 -55}}]
-POTE generator: ~2187/2048 = 117.0069
+CTE tuning: ~847/640 = 486.5098
-{{Optimal ET sequence|legend=1|41, 236cc, 277c, 318c, 359, 400, 441}}
+{{Optimal ET sequence|legend=1|37, 402df, 439, 476, 513, 550, 587, 624}}
-Badness: 46.849
+Badness: 1.129
-===7-limit===
+=== 17-limit ===
-Subgroup: 2.3.5.7
+Subgroup: 2.5.7.11.13.17
-Comma list: 2401/2400, 11785390260224/11767897353375
+Comma list: 32768/32725, 140800/140777, 286000/285719, 1328125/1328096
-Mapping: [{{val|1 1 11 7}}, {{val|0 6 -89 -43}}]
+Mapping: [{{val|1 23 32 -1 26 -62}}, {{val|0 -51 -72 11 -55 163}}]
-POTE generator: ~15/14 = 117.0067
+CTE tuning: ~847/640 = 486.4954
-{{Optimal ET sequence|legend=1|41, 236cc, 277c, 318c, 359, 400, 441}}
+{{Optimal ET sequence|legend=1|37, 587g, 624, 661, 1285deg}}
-Badness: 1.383
+Badness: 1.843
-===11-limit===
+=== 19-limit ===
-Subgroup: 2.3.5.7.11
+Subgroup: 2.5.7.11.13.17.19
-Comma list: 2401/2400, 200704/200475, 46656/46585
+Comma list: 3328/3325, 2432/2431, 12103/12100, 10985/10976, 190400/190333
-Mapping: [{{val|1 1 11 7 -2}}, {{val|0 6 -89 -43 56}}]
+Mapping: [{{val|1 23 32 -1 26 -62 -44}}, {{val|0 -51 -72 11 -55 163 119}}]
-POTE generator: ~77/72 = 117.0029
+CTE tuning: ~847/640 = 486.4966
-{{Optimal ET sequence|legend=1|41, 318c, 359, 400, 841e, 1241e}}
+{{Optimal ET sequence|legend=1|37, 587g, 624, 661, 1285deg}}
-Badness: 1.716
+Badness: 1.391
-== 41 & 373 ==
+=== 23-limit ===
-Subgroup: 2.3.5.7
+Subgroup: 2.5.7.11.13.17.19.23
-Comma list: 2401/2400, {{monzo|-35 18 4 -1}}
+Comma list: 3328/3325, 2432/2431, 12103/12100, 2300/2299, 36179/36176, 10985/10976
-Mapping: [{{val|1 5 -15 -5}}, {{val|0 -14 71 32}}]
+Mapping: [{{val|1 23 32 -1 26 -62 -44 -94}}, {{val|0 -51 -72 11 -55 163 119 243}}]
-POTE generator: ~1215/1024 = 292.7572
+CTE tuning: ~847/640 = 486.4987
-{{Optimal ET sequence|legend=1|41, 209c, 250c, 291, 332, 373, 414, 787}}
+{{Optimal ET sequence|legend=1|37, 587gi, 624, 1285deg}}
-Badness: 3.790
+Badness: 1.474
-=== 11-limit ===
+== 41 & 167 ==
-Subgroup: 2.3.5.7.11
+Subgroup: 2.3.5.7
-Comma list: 3025/3024, 2401/2400, 4428675/4415488
+Comma list: 2401/2400, 179200/177147
-Mapping: [{{val|1 5 -15 -5 22}}, {{val|0 -14 71 32 -76}}]
+Mapping: [{{val|1 5 17 11}}, {{val|0 -10 -43 -24}}]
-POTE generator: ~4096/3465 = 292.7564
+CTE tuning: ~80/63 = 409.639
-{{Optimal ET sequence|legend=1|41, 291e, 332e, 373, 414, 787e, 1201bcde, 1988bcddee}}
+{{Optimal ET sequence|legend=1|38ccd, 41, 126, 167, 208, 375b}}
-Badness: 1.849
+Badness: 2.943
-== 41 & 421 ==
+=== 11-limit ===
-Subgroup: 2.3.7
+Subgroup: 2.3.5.7
-Comma list: {{monzo|-125 47 18}}
+Comma list: 896/891, 2200/2187, 2401/2400
-Mapping: [{{val|1 -5 20}}, {{val|0 18 -47}}]
+Mapping: [{{val|1 5 17 11 -2}}, {{val|0 -10 -43 -24 16}}]
-POTE generator: ~9/7 = 438.9747
+CTE tuning: ~80/63 = 409.630
-{{Optimal ET sequence|legend=1|41, 298, 339, 380, 421, 462, 503, 544, 585, 2966bddd}}
+{{Optimal ET sequence|legend=1|41, 126, 167, 208, 375be}}
-Badness: 78.897
+Badness: 1.816
-=== 11-limit ===
+=== 13-limit ===
-Subgroup: 2.3.7.11
+Subgroup: 2.3.5.7.11.13
-Comma list: 2893401/2883584, 208971104256/208422380089
+Comma list: 325/324, 352/351, 896/891, 2401/2400
-Mapping: [{{val|1 -5 20 -28}}, {{val|0 18 -47 86}}]
+Mapping: [{{val|1 5 17 11 -2 -12}}, {{val|0 -10 -43 -24 16 46}}]
-POTE generator: ~9/7 = 438.9681
+CTE tuning: ~195/154 = 409.617
-{{Optimal ET sequence|legend=1|41, 380e, 421, 462, 503, 1047, 1550b}}
+{{Optimal ET sequence|legend=1|41, 126, 167, 208, 375be}}
-Badness: 6.355
+Badness: 1.782
-=== 13-limit ===
+== 41 & 197 ==
-Subgroup: 2.3.7.11.13
+Subgroup: 2.3.5.7
-Comma list: 85293/85184, 53361/53248, 216513/215306
+Comma list: 225/224, 4202539929/4194304000
-Mapping: [{{val|1 -5 20 -28 -38}}, {{val|0 18 -47 86 114}}]
+Mapping: [{{val|1 0 5 5}}, {{val|0 13 -22 -18}}]
-POTE generator: ~156/121 = 438.9595
+POTE generator: ~160/147 = 146.1953
-{{Optimal ET sequence|legend=1|41, 380e, 421, 462}}
+{{Optimal ET sequence|legend=1|33, 41, 115, 156, 197}}
-Badness: 4.703
+Badness: 3.049
-==41 & 509==
+== 41 & 227 ==
 Subgroup: 2.3.5.7
-Comma list: 2401/2400, {{monzo|40 -27 0 1}}
+Comma list: 5120/5103, 117649/116640
-Mapping: [{{val|1 1 -29 -13}}, {{val|0 2 107 54}}]
+Mapping: [{{val|1 0 -11 -1}}, {{val|0 5 42 12}}]
-POTE generator: ~49/40 = 351.278
+POTE generator: ~56/45 = 380.6339
-{{Optimal ET sequence|legend=1|41, 263ccd, 304ccd, 345c, 386c, 427c, 468, 509, 1486bc }}
+{{Optimal ET sequence|legend=1|19cc, 22c, 41, 104c, 145, 186, 413}}
-Badness: 6.884
+Badness: 2.852
-==41 & 523==
+=== 11-limit ===
-(better known as 41 & 441)
-Subgroup: 2.3.5.7
+Subgroup: 2.3.5.7.11
-Comma list: 2401/2400, {{monzo|35 -23 -3 3}}
+Comma list: 385/384, 2200/2187, 67228/66825
-Mapping: [{{val|1 1 11 7}}, {{val|0 6 -89 -43}}]
+Mapping: [{{val|1 0 -11 -1 19}}, {{val|0 5 42 12 -49}}]
-POTE generator: ~15/14 = 117.006
+POTE generator: ~96/77 = 380.6090
-{{Optimal ET sequence|legend=1|41, 236cc, 277c, 318c, 359, 400, 441}}
+{{Optimal ET sequence|legend=1|41, 145e, 186, 227}}
-Badness: 1.383
+Badness: 2.774
-===11-limit===
+===13-limit===
-Subgroup: 2.3.5.7.11
+Subgroup: 2.3.5.7.11.13
-Comma list: 2401/2400, 19712/19683, 166375/165888
+Comma list: 385/384, 325/324, 352/351, 67228/66825
-Mapping: [{{val|1 1 11 7 -6}}, {{val|0 6 -89 -43 97}}]
+Mapping: [{{val|1 0 -11 -1 19 24}}, {{val|0 5 42 12 -49 -64}}]
-POTE generator: ~77/72 = 117.025
+POTE generator: ~96/77 = 380.6135
-{{Optimal ET sequence|legend=1|41, 400e, 441e, 482, 1487cdee}}
+{{Optimal ET sequence|legend=1|41, 145ef, 186, 227}}
-Badness: 3.127
+Badness: 2.307
-==43 & 233==
+==41 & 233==
-Subgroup: 2.3.5.7.11.13
+Subgroup: 2.3.5.7
-Comma list: 441/440, 1001/1000, 21168/21125, 81675/81536
+Comma list: 2401/2400, 124556484375/123363917824
-Mapping: [{{val|1 8 -8 -17 -13 9}}, {{val|0 -23 37 71 59 -19}}]
+Mapping: [{{val|1 9 -19 -6}}, {{val|0 -16 46 19}}]
-POTE generator: ~40/33 = 334.7481
+POTE generator: ~30375/21952 = 556.1960
-{{Optimal ET sequence|legend=1|43, 147de, 190, 423d, 613bde}}
+{{Optimal ET sequence|legend=1|41, 151, 192, 233, 274, 315, 589bcd}}
-Badness: 1.813
+Badness: 4.209
-===17-limit===
+===11-limit===
-Subgroup: 2.3.5.7.11.13.17
+Subgroup: 2.3.5.7.11
-Comma list: 441/440, 561/560, 1275/1274, 1156/1155, 21168/21125
+Comma list: 441/440, 540/539, 5053640625/5035261952
-Mapping: [{{val|1 8 -8 -17 -13 9 -16}}, {{val|0 -23 37 71 59 -19 72}}]
+Mapping: [{{val|1 9 -19 -6 22}}, {{val|0 -16 46 19 -40}}]
-POTE generator: ~17/14 = 334.7511
+POTE generator: ~2475/1792 = 556.2083
-{{Optimal ET sequence|legend=1|43, 147deg, 190g, 233, 423dg}}
+{{Optimal ET sequence|41, 151, 192, 233, 274}}
-Badness: 1.592
+Badness: 2.494
-==Mehlem (53 & 179)==
+===13-limit===
-Subgroup: 2.3.5
+Subgroup: 2.3.5.7.11.13
-Comma list: {{monzo|12 -31 16}}
+Comma list: 441/440, 540/539, 21168/21125, 81675/81536
-Mapping: [{{val|1 4 7}}, {{val|0 -16 -31}}]
+Mapping: [{{val|1 9 -19 -6 22 38}}, {{val|0 -16 46 19 -40 -74}}]
-POTE generator: ~10/9 = 181.0964
+POTE generator: ~91/66 = 556.2131
-{{Optimal ET sequence|legend=1|20c, 33c, 53, 338, 391, 444, 497, 550, 603, 656, 1259b}}
+{{Optimal ET sequence|legend=1|41, 192, 233, 274, 507b}}
-Badness: 10.511
+Badness: 2.034
-===7-limit===
+==41 & 337==
+(better described as 41 & 255)
 Subgroup: 2.3.5.7
-Comma list: 4375/4374, 65536/64827
+Comma list: 16875/16807, 7381125/7340032
-Mapping: [{{val|1 4 7 1}}, {{val|0 -16 -31 12}}]
+Mapping: [{{val|1 4 -8 -4}}, {{val|0 -11 47 31}}]
-POTE generator: ~10/9 = 181.0314
+POTE generator: ~784/675 = 263.5183
-{{Optimal ET sequence|legend=1|20c, 53, 126, 179, 232d}}
+{{Optimal ET sequence|legend=1|41, 173, 214, 255, 296, 551, 847c}}
-Badness: 3.333
+Badness: 3.414
-== 53 & 239 ==
+==41 & 359==
 Subgroup: 2.3.5
-Comma list: 390625000/387420489
+Comma list: {{monzo|155 -89 -6}}
-Mapping: [{{val|1 2 3}}, {{val|0 -11 -18}}]
+Mapping: [{{val|1 1 11}}, {{val|0 6 -89}}]
-POTE generator: ~250/243 = 45.2329
+POTE generator: ~2187/2048 = 117.0069
-{{Optimal ET sequence|legend=1|25bcc, 26, 27, 53, 239, 292, 345, 398, 451}}
+{{Optimal ET sequence|legend=1|41, 236cc, 277c, 318c, 359, 400, 441}}
-Badness: 2.750
+Badness: 46.849
-=== 7-limit ===
+===7-limit===
 Subgroup: 2.3.5.7
-Comma list: 5120/5103, 95703125/95551488
+Comma list: 2401/2400, 11785390260224/11767897353375
-Mapping: [{{val|1 2 3 1}}, {{val|0 -11 -18 48}}]
+Mapping: [{{val|1 1 11 7}}, {{val|0 6 -89 -43}}]
-POTE generator: ~250/243 = 45.1995
+POTE generator: ~15/14 = 117.0067
-{{Optimal ET sequence|legend=1|53, 186, 239, 292, 531, 823bd}}
+{{Optimal ET sequence|legend=1|41, 236cc, 277c, 318c, 359, 400, 441}}
-Badness: 2.937
+Badness: 1.383
-== 53 & 307 ==
+===11-limit===
-Subgroup: 2.9.5
+Subgroup: 2.3.5.7.11
-Comma list: 32805/32768
+Comma list: 2401/2400, 200704/200475, 46656/46585
-Mapping: [{{val|1 0 15}}, {{val|0 7 -28}}]
+Mapping: [{{val|1 1 11 7 -2}}, {{val|0 6 -89 -43 56}}]
-POTE generator: ~512/375 = 543.3531
+POTE generator: ~77/72 = 117.0029
-{{Optimal ET sequence|legend=1|6, 29, 35, 41, 47, 53, 59, 171, 230, 519, 749 }}
+{{Optimal ET sequence|legend=1|41, 318c, 359, 400, 841e, 1241e}}
-Badness: 0.100
+Badness: 1.716
-==53 & 467==
+== 41 & 373 ==
-Subgroup: 2.3.5
+Subgroup: 2.3.5.7
-Comma list: {{monzo|-36 11 8}}
+Comma list: 2401/2400, {{monzo|-35 18 4 -1}}
-Mapping: [{{val|1 4 -1}}, {{val|0 -8 11}}]
+Mapping: [{{val|1 5 -15 -5}}, {{val|0 -14 71 32}}]
-POTE generator: ~10125/8192 = 362.3210
+POTE generator: ~1215/1024 = 292.7572
-{{Optimal ET sequence|legend=1|10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc}}
+{{Optimal ET sequence|legend=1|41, 209c, 250c, 291, 332, 373, 414, 787}}
-Badness: 3.055
+Badness: 3.790
-===7-limit===
+=== 11-limit ===
-Subgroup: 2.3.5.7
+Subgroup: 2.3.5.7.11
-Comma list: 4375/4374, 69198046875/68719476736
+Comma list: 3025/3024, 2401/2400, 4428675/4415488
-Mapping: [{{val|1 4 -1 33}}, {{val|0 -8 11 -100}}]
+Mapping: [{{val|1 5 -15 -5 22}}, {{val|0 -14 71 32 -76}}]
-POTE generator: ~10125/8192 = 362.3181
+POTE generator: ~4096/3465 = 292.7564
-{{Optimal ET sequence|legend=1|53, 255d, 308d, 361, 414, 2123bccdd}}
+{{Optimal ET sequence|legend=1|41, 291e, 332e, 373, 414, 787e, 1201bcde, 1988bcddee}}
-Badness: 4.674
+Badness: 1.849
-==53 & 499==
+== 41 & 421 ==
-Subgroup: 2.3.5
+Subgroup: 2.3.7
-Comma list: {{monzo|63 -50 7}}
+Comma list: {{monzo|-125 47 18}}
-Mapping: [{{val|1 0 -9}}, {{val|0 7 50}}
+Mapping: [{{val|1 -5 20}}, {{val|0 18 -47}}]
-POTE generator: ~2560/2187 = 271.7276
+POTE generator: ~9/7 = 438.9747
-{{Optimal ET sequence|legend=1|22c, 31c, 53, 393, 446, 499, 552, 605, 658, 711, 764, 6165b, 6929b, 7693b, 8457b, 9221bbc, 9985bbc, 10749bbc}}
+{{Optimal ET sequence|legend=1|41, 298, 339, 380, 421, 462, 503, 544, 585, 2966bddd}}
-Badness: 8.860
+Badness: 78.897
-===7-limit===
+=== 11-limit ===
-Subgroup: 2.3.5.7
+Subgroup: 2.3.7.11
-Comma list: 26873856/26796875, 33554432/33480783
+Comma list: 2893401/2883584, 208971104256/208422380089
-Mapping: [{{val|1 0 -9 25}}, {{val|0 7 50 -98}}]
+Mapping: [{{val|1 -5 20 -28}}, {{val|0 18 -47 86}}]
-POTE generator: ~1024/875 = 271.7017
+POTE generator: ~9/7 = 438.9681
-{{Optimal ET sequence|legend=1|53, 393, 446, 499, 552, 2155ccdd, 2707bcccdd}}
+{{Optimal ET sequence|legend=1|41, 380e, 421, 462, 503, 1047, 1550b}}
-Badness: 6.432
+Badness: 6.355
-==103 & 167==
+=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
+Subgroup: 2.3.7.11.13
-Comma list: 1001/1000, 3025/3024, 1716/1715, 4225/4224
+Comma list: 85293/85184, 53361/53248, 216513/215306
-Mapping: [{{val|1 -25 -16 -13 -26 -6}}, {{val|0 74 51 44 82 27}}]
+Mapping: [{{val|1 -5 20 -28 -38}}, {{val|0 18 -47 86 114}}]
-POTE generator: ~440/343 = 431.1062
+POTE generator: ~156/121 = 438.9595
-Badness: 0.662
+{{Optimal ET sequence|legend=1|41, 380e, 421, 462}}
-===17-limit===
+Badness: 4.703
-Subgroup: 2.3.5.7.11.13.17
+== 41 & 463 ==
-Comma list: 1001/1000, 1225/1224, 715/714, 936/935, 4225/4224
+Subgroup: 2.3.5.7
-Mapping: [{{val|1 -25 -16 -13 -26 -6 -11}}, {{val|0 74 51 44 82 27 42}}]
+Comma list: 4096000/4084101, 359661568/358722675
-POTE generator: ~440/343 = 431.1087
+Mapping: [{{val|1 2 -35 -20}}, {{val|0 -1 90 55}}]
-{{Optimal ET sequence|legend=1|39bce, 64be, 103, 167, 270}}
+POTE generator: ~4/3 = 497.6285
-Badness: 1.068
+{{Optimal ET sequence|legend=1|41, 217ccd, 258cd, 299cd, 340c, 381, 422, 885, 1307d, 1729bdd}}
-== 103 & 227 ==
+Badness: 4.045
-Subgroup: 2.3.5.7.11.13
+=== 11-limit ===
-Comma list: 385/384, 1001/1000, 4225/4224, 50421/50336
+Subgroup: 2.3.5.7.11
-Mapping: [{{val|1 -36 -11 -1 -17 -12}}, {{val|0 79 28 8 43 33}}]
+Comma list: 3025/3024, 19712/19683, 1296000/1294139
-POTE generator: ~490/352 = 570.9053
+Mapping: [{{val|1 2 -35 -20 30}}, {{val|0 -1 90 55 -64}}]
-{{Optimal ET sequence|legend=1|21b, 103, 227, 330e}}
+POTE generator: ~4/3 = 497.6281
-Badness: 2.198
+{{Optimal ET sequence|legend=1|41, 340c, 381, 422, 885, 1307de}}
-== 103 & 503 ==
+Badness: 1.883
-Subgroup: 2.3.5.7.11
+== 41 & 509 ==
-Comma list: 2401/2400, 46656/46585, 766656/765625
+Subgroup: 2.3.5.7
-Mapping: [{{val|1 -41 -34 -26 -60}}, {{val|0 102 87 69 152}}]
+Comma list: 2401/2400, {{monzo|40 -27 0 1}}
-POTE generator: ~4/3 = 500.9986
+Mapping: [{{val|1 1 -29 -13}}, {{val|0 2 107 54}}]
-{{Optimal ET sequence|legend=1|91bcdee, 103, 297e, 400, 1303c, 1703ce}}
+POTE generator: ~49/40 = 351.278
-Badness: 2.344
+{{Optimal ET sequence|legend=1|41, 263ccd, 304ccd, 345c, 386c, 427c, 468, 509, 1486bc }}
-=== 13-limit ===
+Badness: 6.884
-Subgroup: 2.3.5.7.11.13
+==41 & 523==
+(better known as 41 & 441)
-Comma list: 1001/1000, 1716/1715, 4225/4224, 75816/75625
+Subgroup: 2.3.5.7
-Mapping: [{{val|1 -41 -34 -26 -60 -13}}, {{val|0 102 87 69 152 40}}]
+Comma list: 2401/2400, {{monzo|35 -23 -3 3}}
-POTE generator: ~4/3 = 500.9970
+Mapping: [{{val|1 1 11 7}}, {{val|0 6 -89 -43}}]
-{{Optimal ET sequence|legend=1|91bcdee, 103, 297e, 400, 503, 903}}
+POTE generator: ~15/14 = 117.006
-Badness: 1.735
+{{Optimal ET sequence|legend=1|41, 236cc, 277c, 318c, 359, 400, 441}}
-=== 17-limit ===
+Badness: 1.383
-Subgroup: 2.3.5.7.11.13.17
+===11-limit===
-Comma list: 1001/1000, 936/935, 1377/1375, 1716/1715, 4225/4224
+Subgroup: 2.3.5.7.11
-Mapping: [{{val|1 -41 -34 -26 -60 -13 2}}, {{val|0 102 87 69 152 40 5}}]
+Comma list: 2401/2400, 19712/19683, 166375/165888
-POTE generator: ~4/3 = 500.9972
+Mapping: [{{val|1 1 11 7 -6}}, {{val|0 6 -89 -43 97}}]
-Badness: 1.402
+POTE generator: ~77/72 = 117.025
-==113 & 409==
+{{Optimal ET sequence|legend=1|41, 400e, 441e, 482, 1487cdee}}
-Subgroup: 2.3.7.11
+Badness: 3.127
-Comma list: 5038848/5021863, 235782657/234881024
+== 41 & 571 ==
-Mapping: [{{val|1 4 16 -1}}, {{val|0 -13 -71 24}}]
+Subgroup: 2.3.5.7
-POTE generator: ~8192/7203 = 222.9728
+Comma list: 2401/2400, {{monzo|50 -31 -4 3}}
-{{Optimal ET sequence|legend=1|70, 113, 183, 296}}
+Mapping: [{{val|1 5 -39 -17}}, {{val|0 -10 121 58}}]
-Badness: 5.092
+POTE generator: ~2657205/2097152 = 409.8044
-===13-limit===
+{{Optimal ET sequence|legend=1|41, 407c, 448, 489c, 530, 571, 612, 2407, 3019, 3631d, 4243d}}
-Subgroup: 2.3.7.11.13
+Badness: 1.987
-Comma list: 729/728, 19773/19712, 718848/717409
+=== 11-limit ===
-Mapping: [{{val|1 4 16 -1 5}}, {{val|0 -13 -71 24 -7}}]
+Subgroup: 2.3.5.7.11
-POTE generator: ~91/80 = 222.9746
+Comma list: 3025/3024, 2401/2400, 645922816/645700815
-{{Optimal ET sequence|legend=1|70, 113, 183, 296}}
+Mapping: [{{val|1 5 -39 -17 40}}, {{val|0 -10 121 58 -107}}]
-Badness: 1.829
+POTE generator: ~308/243 = 409.8034
-==193 & 547==
+Badness: 1.291
-Subgroup: 2.3.5.7
+== 41 & 607 ==
-Comma list: 589824/588245, 23066015625/23018340352
+Subgroup: 2.3.5.7.11.13
-Mapping: [{{val|1 0 4 2}}, {{val|0 51 -54 26}}]
+Comma list: 2080/2079, 3025/3024, 78975/78848, 218700/218491
-POTE generator: ~49/48 = 37.2913
+Mapping: [{{val|1 0 15 10 -8 -18}}, {{val|0 13 -104 -59 94 178}}]
-{{Optimal ET sequence|legend=1|32, 129, 161, 193, 354, 547, 901d, 1255d}}
+POTE generator: ~160/147 = 146.2905
-Badness: 7.020
+{{Optimal ET sequence|legend=1|41, 525f, 566}}
-== 193 & 607 ==
+Badness: 2.398
-Subgroup: 2.3.5.7.11.13
+== 41 & 1063 ==
-Comma list: 625/624, 3025/3024, 78975/78848, 218700/218491
+Subgroup: 2.3.5.7
-Mapping: [{{val|1 26 2 42 60 -22}}, {{val|0 -76 1 -122 -176 80}}
+Comma list: 2401/2400, {{monzo|80 -52 -5 5}}
-POTE generator: ~5/4 = 385.5044
+Mapping: [{{val|1 5 -67 -31}}, {{val|0 -10 203 99}}]
-{{Optimal ET sequence|legend=1|193, 414, 607, 1021c}}
+POTE generator: ~524288/413343 = 409.7856
-Badness: 2.529
+{{Optimal ET sequence|legend=1|41, 776cc, 817c, 858c, 899c, 940, 981, 2984, 3965bc}}
-=== 17-limit ===
+Badness: 10.520
-Subgroup: 2.3.5.7.11.13.17
+== 43 & 233 ==
-Comma list: 625/624, 1225/1224, 3025/3024, 78975/78848, 5832/5831
+Subgroup: 2.3.5.7.11.13
-Mapping: [{{val|1 26 2 42 60 -22 33}}, {{val|0 -76 1 -122 -176 80 -90}}
+Comma list: 441/440, 1001/1000, 21168/21125, 81675/81536
-POTE generator: ~5/4 = 385.5044
+Mapping: [{{val|1 8 -8 -17 -13 9}}, {{val|0 -23 37 71 59 -19}}]
-{{Optimal ET sequence|legend=1|193, 414, 607, 1021c}}
+POTE generator: ~40/33 = 334.7481
-Badness: 1.693
+{{Optimal ET sequence|legend=1|43, 147de, 190, 423d, 613bde}}
-=== 19-limit ===
+Badness: 1.813
-Subgroup: 2.3.5.7.11.13.17.19
+=== 17-limit ===
-Comma list: 625/624, 1225/1224, 3025/3024, 1729/1728, 6669/6664, 26775/26752
+Subgroup: 2.3.5.7.11.13.17
-Mapping: [{{val|1 26 2 42 60 -22 33 64}}, {{val|0 -76 1 -122 -176 80 -90 -186}}]
+Comma list: 441/440, 561/560, 1275/1274, 1156/1155, 21168/21125
-POTE generator: ~5/4 = 385.5037
+Mapping: [{{val|1 8 -8 -17 -13 9 -16}}, {{val|0 -23 37 71 59 -19 72}}]
-{{Optimal ET sequence|legend=1|193, 414h, 607, 1021chh}}
+POTE generator: ~17/14 = 334.7511
-Badness: 1.618
+{{Optimal ET sequence|legend=1|43, 147deg, 190g, 233, 423dg}}
-== 233 & 317 ==
+Badness: 1.592
-Subgroup: 2.5.7.11
+==Mehlem (53 & 179)==
-Comma list: 537109375/536870912, 40353607/40262750
+Subgroup: 2.3.5
-Mapping: [{{val|1 -1 22 40}}, {{val|0 9 -52 -99}}]
+Comma list: {{monzo|12 -31 16}}
-POTE generator: ~15488/12005 = 442.9148
+Mapping: [{{val|1 4 7}}, {{val|0 -16 -31}}]
-{{Optimal ET sequence|legend=1|65e, 84, 149, 233, 783, 1016, 1249, 1482}}
+POTE generator: ~10/9 = 181.0964
-Badness: 3.492
+{{Optimal ET sequence|legend=1|20c, 33c, 53, 338, 391, 444, 497, 550, 603, 656, 1259b}}
-=== 13-limit ===
+Badness: 10.511
-Subgroup: 2.5.7.11.13
+===7-limit===
-Comma list: 75712/75625, 10985/10976, 5462275/5451776
+Subgroup: 2.3.5.7
-Mapping: [{{val|1 -1 22 40 24}}, {{val|0 9 -52 -99 -55}}]
+Comma list: 4375/4374, 65536/64827
-POTE generator: ~455/352 = 442.9140
+Mapping: [{{val|1 4 7 1}}, {{val|0 -16 -31 12}}]
-{{Optimal ET sequence|legend=1|65ef, 84, 149, 233, 783, 1016f, 1249f}}
+POTE generator: ~10/9 = 181.0314
-Badness: 1.410
+{{Optimal ET sequence|legend=1|20c, 53, 126, 179, 232d}}
-== 239 & 569 ==
+Badness: 3.333
-Subgroup: 2.3.5.7
+== 53 & 239 ==
-Comma list: 823543/820125, 68359375/68024448
+Subgroup: 2.3.5
-Mapping: [{{val|1 8 9 13}}, {{val|0 -73 -76 -116}}]
+Comma list: 390625000/387420489
-POTE generator: ~729/686 = 105.4479
+Mapping: [{{val|1 2 3}}, {{val|0 -11 -18}}]
-{{Optimal ET sequence|legend=1|34bcdd, 57bcd, 91, 148d, 239, 330, 569}}
+POTE generator: ~250/243 = 45.2329
-Badness: 8.274
+{{Optimal ET sequence|legend=1|25bcc, 26, 27, 53, 239, 292, 345, 398, 451}}
-=== 11-limit ===
+Badness: 2.750
-Subgroup: 2.3.5.7.11
+=== 7-limit ===
-Comma list: 42875/42768, 42592/42525, 151263/151250
+Subgroup: 2.3.5.7
-Mapping: [{{val|1 8 9 13 22}}, {{val|0 -73 -76 -116 -211}}]
+Comma list: 5120/5103, 95703125/95551488
-POTE generator: ~729/686 = 105.4456
+Mapping: [{{val|1 2 3 1}}, {{val|0 -11 -18 48}}]
-{{Optimal ET sequence|legend=1|57bcdeee, 91e, 148dee, 239, 569, 808}}
+POTE generator: ~250/243 = 45.1995
-Badness: 3.518
+{{Optimal ET sequence|legend=1|53, 186, 239, 292, 531, 823bd}}
-== 311 & 503 ==
+Badness: 2.937
-Subgroup: 2.3.5.7
+== 53 & 307 ==
-Comma list:  2401/2400, {{monzo|-95 21 29 -2}}
+Subgroup: 2.9.5
-Mapping: [{{val|1 43 -28 -2}}, {{val|0 -112 82 13}}]
+Comma list: 32805/32768
-POTE generator: ~18984375/14680064 = 443.7335
+Mapping: [{{val|1 0 15}}, {{val|0 7 -28}}]
-{{Optimal ET sequence|legend=1|119, 192, 311, 814, 1125, 3064d, 4189cdd, 5314cdd}}
+POTE generator: ~512/375 = 543.3531
-Badness: 7.820
+{{Optimal ET sequence|legend=1|6, 29, 35, 41, 47, 53, 59, 171, 230, 519, 749 }}
-=== 11-limit ===
+Badness: 0.100
-Subgroup: 2.3.5.7.11
+==53 & 467==
-Comma list: 2401/2400, 496125/495616, 100663296/100656875
+Subgroup: 2.3.5
-Mapping: [{{val|1 43 -28 -2 36}}, {{val|0 -112 82 13 -88}}]
+Comma list: {{monzo|-36 11 8}}
-POTE generator: ~21175/16384 = 443.7337
+Mapping: [{{val|1 4 -1}}, {{val|0 -8 11}}]
-{{Optimal ET sequence|legend=1|119, 192, 311, 503, 814, 1125, 1939}}
+POTE generator: ~10125/8192 = 362.3210
-Badness: 2.599
+{{Optimal ET sequence|legend=1|10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc}}
-=== 13-limit ===
+Badness: 3.055
-Subgroup: 2.3.5.7.11.13
+===7-limit===
-Comma list: 2401/2400, 4225/4224, 59535/59488, 6656/6655
+Subgroup: 2.3.5.7
-Mapping: [{{val|1 43 -28 -2 36 71}}, {{val|0 -112 82 13 -88 -182}}]
+Comma list: 4375/4374, 69198046875/68719476736
-POTE generator: ~84/65 = 443.7338
+Mapping: [{{val|1 4 -1 33}}, {{val|0 -8 11 -100}}]
-{{Optimal ET sequence|legend=1|119f, 192, 311, 503, 814, 1125, 1939}}
+POTE generator: ~10125/8192 = 362.3181
-Badness: 1.410
+{{Optimal ET sequence|legend=1|53, 255d, 308d, 361, 414, 2123bccdd}}
-=== 17-limit ===
+Badness: 4.674
-Subgroup: 2.3.5.7.11.13.17
+==53 & 499==
-Comma list: 12376/12375, 2401/2400, 14400/14399, 4225/4224, 11016/11011
+Subgroup: 2.3.5
-Mapping: [{{val|1 43 -28 -2 36 71 -34}}, {{val|0 -112 82 13 -88 -182 103}}]
+Comma list: {{monzo|63 -50 7}}
-POTE generator: ~84/65 = 443.7340
+Mapping: [{{val|1 0 -9}}, {{val|0 7 50}}
-{{Optimal ET sequence|legend=1|192, 311, 503, 814, 1939g, 2753dg}}
+POTE generator: ~2560/2187 = 271.7276
-Badness: 1.111
+{{Optimal ET sequence|legend=1|22c, 31c, 53, 393, 446, 499, 552, 605, 658, 711, 764, 6165b, 6929b, 7693b, 8457b, 9221bbc, 9985bbc, 10749bbc}}
-== 311 & 571 ==
+Badness: 8.860
-Subgroup: 2.3.5.7.11
+===7-limit===
-Comma list: 3025/3024, 2401/2400, 294885080956928/294197433834375
+Subgroup: 2.3.5.7
-Mapping: [{{val|1 11 -22 -7 37}}, {{val|0 -48 124 50 -171}}]
+Comma list: 26873856/26796875, 33554432/33480783
-POTE generator: ~63/55 = 235.3736
+Mapping: [{{val|1 0 -9 25}}, {{val|0 7 50 -98}}]
-{{Optimal ET sequence|legend=1|10, 18bcd, 21e, 23bc, 31, 41, 72, 167, 198, 239, 270, 342, 612, 954, 1566, 3101de, 3443de, 4055de, 4397cdee, 4667dee, 5009cddee}}
+POTE generator: ~1024/875 = 271.7017
-Badness: 2.441
+{{Optimal ET sequence|legend=1|53, 393, 446, 499, 552, 2155ccdd, 2707bcccdd}}
-=== 13-limit ===
+Badness: 6.432
-Subgroup: 2.3.5.7.11.13
+== 53 & 673 ==
-Comma list: 3025/3024, 2401/2400, 47432/47385, 114345/114244
+Subgroup: 2.3.5
-Mapping: [{{val|1 11 -22 -7 37 19}}, {{val|0 -48 124 50 -171 -78}}]
+Comma list: {{monzo|51 -60 19}}
-POTE generator: ~63/55 = 235.3738
+Mapping: [{{val|1 -2 -9}}, {{val|0 19 60}}]
-Badness: 1.528
+POTE generator: ~1162261467/1024000000 = 226.4390
-=== 17-limit ===
+{{Optimal ET sequence|legend=1|16cc, 37cc, 53, 514c, 567, 620, 673, 726, 779, 832, 885, 938}}
-Subgroup: 2.3.5.7.11.13.17
+Badness: 40.263
-Comma list: 2431/2430, 12376/12375, 2601/2600, 8624/8619, 2401/2400
+== 53 & 733 ==
-Mapping: [{{val|1 11 -22 -7 37 19 -22}}, {{val|0 -48 124 50 -171 -78 133}}]
+Subgroup: 2.3.5
-POTE generator: ~63/55 = 235.3741
+Comma list: {{monzo|42 -47 14}}
-{{Optimal ET sequence|legend=1|260, 311, 571, 882}}
+Mapping: [{{val|1 0 -3}}, {{val|0 14 47}}]
-Badness: 1.212
+POTE generator: ~64000/59049 = 135.8799
-== 311 & 1063 ==
+{{Optimal ET sequence|legend=1| 44c, 53, 415, 468, 521, 574, 627, 680, 733}}
-Subgroup: 2.3.5.7
+Badness: 18.063
-Comma list: 2401/2400, 3367254360064/3363025078125
+== 53 & 1063 ==
-Mapping: [{{val|1 11 -22 -7}}, {{val|0 -24 62 25}}]
+Subgroup: 2.3.5
-POTE generator: ~21/16 = 470.7489
+Comma list: {{monzo|57 -55 13}}
-{{Optimal ET sequence|legend=1|51, 79c, 130, 311, 441, 2776, 3217, 3658, 4099, 4540, 4981}}
+Mapping: [{{val|1 6 21}}, {{val|0 -13 -55}}]
-Badness: 1.127
+POTE generator: ~163840000/129140163 = 407.5202
-=== 11-limit ===
+{{Optimal ET sequence|legend=1|50cc, 53, 427c, 480, 533, 586, 639, 692, 745, 798, 851, 2500b, 3351b}}
-Subgroup: 2.3.5.7.11
+Badness: 22.373
-Comma list: 2401/2400, 19712/19683, 9453125/9437184
+== 53 & 1193 ==
-Mapping: [{{val|1 11 -22 -7 98}}, {{val|0 -24 62 25 -241}}]
+Subgroup: 2.3.5
-POTE generator: ~21/16 = 470.7429
+Comma list: {{monzo|87 -71 11}}
-{{Optimal ET sequence|legend=1|130e, 181e, 311, 752, 1063}}
+Mapping: [{{val|1 2 5}}, {{val|0 -11 -71}}]
-Badness: 4.158
+POTE generator: ~1638400/1594323 = 45.2622
-== 379 & 577 ==
+{{Optimal ET sequence|legend=1|26cc, 27cc, 53, 557c, 610c, 663c, 716, 769, 822, 875, 928, 981, 1034, 1087}}
-Subgroup: 2.5.7
+Badness: 29.067
-Comma list: {{monzo|40 -13 25}}
+== 53 & 1759 ==
-Mapping: [{{val|1 20 12}}, {{val|0 -100 -52}}]
+Subgroup: 2.3.5
+Comma list: {{monzo|132 -95 8}}
+Mapping: {{val|1 4 31}}, {{val|0 -8 -95}}]
+POTE generator: ~655360/531441 = 362.2490
+{{Optimal ET sequence|legend=1|53, 752c, 805c, 858c, 911c, 964c, 1017c, 1070c, 1123, 1176, 1229, 1282, 1335, 1388, 1441, 1494}}
+Badness: 25.296
+== 103 & 167 ==
-POTE generator: ~80/49 = 848.548
+Subgroup: 2.3.5.7.11.13
-{{Optimal ET sequence|legend=1|17c, 24c, 41, 99, 140, 239, 379, 1376, 1755, 2134, 6023, 8157, 10291d}}
+Comma list: 1001/1000, 3025/3024, 1716/1715, 4225/4224
-Badness: 0.785
+Mapping: [{{val|1 -25 -16 -13 -26 -6}}, {{val|0 74 51 44 82 27}}]
-=== 11-limit ===
+POTE generator: ~440/343 = 431.1062
-Subgroup: 2.5.7.11
+Badness: 0.662
-Comma list: 102487/102400, {{monzo|28 11 -24 4}}
+=== 17-limit ===
-Mapping: [{{val|1 20 12 10}}, {{val|0 -100 -52 -37}}]
+Subgroup: 2.3.5.7.11.13.17
-POTE generator: ~133100/117649 = 212.1377
+Comma list: 1001/1000, 1225/1224, 715/714, 936/935, 4225/4224
-{{Optimal ET sequence|legend=1|17c, 164c, 181, 198, 379}}
+Mapping: [{{val|1 -25 -16 -13 -26 -6 -11}}, {{val|0 74 51 44 82 27 42}}]
+POTE generator: ~440/343 = 431.1087
+{{Optimal ET sequence|legend=1|39bce, 64be, 103, 167, 270}}
+Badness: 1.068
+== 103 & 227 ==
+Subgroup: 2.3.5.7.11.13
+Comma list: 385/384, 1001/1000, 4225/4224, 50421/50336
+Mapping: [{{val|1 -36 -11 -1 -17 -12}}, {{val|0 79 28 8 43 33}}]
+POTE generator: ~490/352 = 570.9053
+{{Optimal ET sequence|legend=1|21b, 103, 227, 330e}}
+Badness: 2.198
+== 103 & 457 ==
+Subgroup: 2.3.5.7
+Comma list: 26873856/26796875, 40500000/40353607
+Mapping: [{{val|1 -11 -7 -9}}, {{val|0 81 60 76}}]
+POTE generator: ~2401/2160 = 186.4436
+{{Optimal ET sequence|legend=1|45bcd, 103, 251, 354, 605d, 959d, 1313d}}
+Badness: 5.981
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 540/539, 166698/166375, 2737152/2734375
+Mapping: [{{val|1 -11 -7 -9 -20}}, {{val|0 81 60 76 151}}]
+POTE generator: ~49/44 = 186.4402
+{{Optimal ET sequence|legend=1|45bcdee, 103, 251e, 354}}
+Badness: 2.869
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 540/539, 1716/1715, 4225/4224, 34398/34375
+Mapping: [{{val|1 -11 -7 -9 -20 -5}}, {{val|0 81 60 76 151 56}}]
+POTE generator: ~39/35 = 186.4399
+{{Optimal ET sequence|legend=1|45bcdee, 103, 251e, 354}}
+Badness: 1.642
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 540/539, 936/935, 1377/1375, 1716/1715, 4225/4224
+Mapping: [{{val|1 -11 -7 -9 -20 -5 3}}, {{val|0 81 60 76 151 56 7}}]
+POTE generator: ~39/35 =186.4396
+{{Optimal ET sequence|legend=1|103, 251e, 354}}
+Badness: 1.399
+== 103 & 503 ==
+Subgroup: 2.3.5.7.11
+Comma list: 2401/2400, 46656/46585, 766656/765625
+Mapping: [{{val|1 -41 -34 -26 -60}}, {{val|0 102 87 69 152}}]
+POTE generator: ~4/3 = 500.9986
+{{Optimal ET sequence|legend=1|91bcdee, 103, 297e, 400, 1303c, 1703ce}}
+Badness: 2.344
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 1001/1000, 1716/1715, 4225/4224, 75816/75625
+Mapping: [{{val|1 -41 -34 -26 -60 -13}}, {{val|0 102 87 69 152 40}}]
+POTE generator: ~4/3 = 500.9970
+{{Optimal ET sequence|legend=1|91bcdee, 103, 297e, 400, 503, 903}}
+Badness: 1.735
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 1001/1000, 936/935, 1377/1375, 1716/1715, 4225/4224
+Mapping: [{{val|1 -41 -34 -26 -60 -13 2}}, {{val|0 102 87 69 152 40 5}}]
+POTE generator: ~4/3 = 500.9972
+Badness: 1.402
+== 103 & 647 ==
+Subgroup: 2.5.7.11.13
+Comma list: 105644/105625, 5462275/5451776, 200000/199927
+Mapping: [{{val|1 25 23 60 27}}, {{val|0 -73 -65 -182 -75}}]
+POTE generator: ~3872/3125 = 372.7948
+{{Optimal ET sequence|legend=1|103, 338e, 441, 544, 1735cd}}
+Badness: 1.978
+== Wiloliquy (103 & 700) ==
+Subgroup: 2.5.7.13.17
+Comma list: 31250/31213, 10985/10976, 177482125/177209344
+Mapping: [{{val|1 38 48 37 -4}}, {{val|0 -75 -95 -70 17}}]
+POTE generator: ~50176/36125 = 570.8538
+{{Optimal ET sequence|legend=1|103, 391, 494, 597, 2285cfg}}
+Badness: 1.690
+== 113 & 409 ==
+Subgroup: 2.3.7.11
+Comma list: 5038848/5021863, 235782657/234881024
+Mapping: [{{val|1 4 16 -1}}, {{val|0 -13 -71 24}}]
+POTE generator: ~8192/7203 = 222.9728
+{{Optimal ET sequence|legend=1|70, 113, 183, 296}}
+Badness: 5.092
+=== 13-limit ===
+Subgroup: 2.3.7.11.13
+Comma list: 729/728, 19773/19712, 718848/717409
+Mapping: [{{val|1 4 16 -1 5}}, {{val|0 -13 -71 24 -7}}]
+POTE generator: ~91/80 = 222.9746
+{{Optimal ET sequence|legend=1|70, 113, 183, 296}}
+Badness: 1.829
+== 113 & 709 ==
+Subgroup: 2.3.11.13.17
+Comma list: 971074/970299, 2097152/2093663, 60915712/60886809
+Mapping: [{{val|1 -44 17 -64 42}}, {{val|0 101 -30 150 -84}}]
+POTE generator: ~33048/24167 = 541.6049
+{{Optimal ET sequence|legend=1|113, 483f, 596f, 709, 822, 935, 1757e}}
+Badness: 3.748
+=== 19-limit ===
+Subgroup: 2.3.11.13.17.19
+Comma list: 2432/2431, 278528/278179, 793152/793117, 68054272/68049963
+Mapping: [{{val|1 -44 17 -64 42 -12}}, {{val|0 101 -30 150 -84 36}}]
+POTE generator: ~4199/3072 = 541.6049
+{{Optimal ET sequence|legend=1|113, 483f, 596f, 709, 822, 935, 1757e}}
+Badness: 1.676
+=== 31-limit ===
+Subgroup: 2.3.11.13.17.19.31
+Comma list: 2432/2431, 1024/1023, 25296/25289, 793152/793117, 68054272/68049963
+Mapping: [{{val|1 -44 17 -64 42 -12 37}}, {{val|0 101 -30 150 -84 36 -71}}]
+POTE generator: ~4199/3072 = 541.6055
+{{Optimal ET sequence|legend=1|113, 483f, 596f, 709, 822k}}
+Badness: 1.718
+=== 37-limit ===
+Subgroup: 2.3.11.13.17.19.31.37
+Comma list: 2432/2431, 1024/1023, 3553/3552, 25296/25289, 793152/793117, 681472/681207
+Mapping: [{{val|1 -44 17 -64 42 -12 37 86}}, {{val|0 101 -30 150 -84 36 -71 -179}}]
+POTE generator: ~4199/3072 = 541.6062
+{{Optimal ET sequence|legend=1|113, 483f, 596f, 709, 822kl}}
+Badness: 1.939
+== 167 & 311 ==
+Subgroup: 2.3.5.7.11.13
+Comma list: 3025/3024, 6250/6237, 2401/2400, 4225/4224
+Mapping: [{{val|1 -13 -14 -9 -8 7}}, {{val|0 84 94 68 66 -19}}]
+POTE generator: ~44/39 = 208.3614
+{{Optimal ET sequence|legend=1|23bc, 144, 167, 311}}
+Badness: 1.904
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 595/594, 1225/1224, 3025/3024, 2500/2499, 4225/4224
+Mapping: [{{val|1 -13 -14 -9 -8 7 -23}}, {{val|0 84 94 68 66 -19 156}}]
+POTE generator: ~44/39 = 208.3624
+{{Optimal ET sequence|legend=1|144g, 167, 311, 1100bef}}
+Badness: 1.547
+== 193 & 547 ==
+Subgroup: 2.3.5.7
+Comma list: 589824/588245, 23066015625/23018340352
+Mapping: [{{val|1 0 4 2}}, {{val|0 51 -54 26}}]
+POTE generator: ~49/48 = 37.2913
+{{Optimal ET sequence|legend=1|32, 129, 161, 193, 354, 547, 901d, 1255d}}
+Badness: 7.020
+== 193 & 607 ==
+Subgroup: 2.3.5.7.11.13
+Comma list: 625/624, 3025/3024, 78975/78848, 218700/218491
+Mapping: [{{val|1 26 2 42 60 -22}}, {{val|0 -76 1 -122 -176 80}}
+POTE generator: ~5/4 = 385.5044
+{{Optimal ET sequence|legend=1|193, 414, 607, 1021c}}
+Badness: 2.529
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 625/624, 1225/1224, 3025/3024, 78975/78848, 5832/5831
+Mapping: [{{val|1 26 2 42 60 -22 33}}, {{val|0 -76 1 -122 -176 80 -90}}
+POTE generator: ~5/4 = 385.5044
+{{Optimal ET sequence|legend=1|193, 414, 607, 1021c}}
+Badness: 1.693
+=== 19-limit ===
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 625/624, 1225/1224, 3025/3024, 1729/1728, 6669/6664, 26775/26752
+Mapping: [{{val|1 26 2 42 60 -22 33 64}}, {{val|0 -76 1 -122 -176 80 -90 -186}}]
+POTE generator: ~5/4 = 385.5037
+{{Optimal ET sequence|legend=1|193, 414h, 607, 1021chh}}
+Badness: 1.618
+== 193 & 653 ==
+Subgroup: 2.3.5.7.11.13.17.19.23
+Comma list: 1225/1224, 1540/1539, 3025/3024, 1729/1728, 2025/2024, 3520/3519, 1521/1520
+Mapping: [{{val|1 -18 16 -46 -64 18 -27 -20 21}}, {{val|0 63 -44 157 217 -46 100 78 -53}}]
+POTE generator: ~243/196 = 373.0467
+Badness: 1.271
+=== 29-limit ===
+Subgroup: 2.3.5.7.11.13.17.19.23.29
+Comma list: 1225/1224, 1540/1539, 3025/3024, 1729/1728, 2025/2024, 3520/3519, 1521/1520, 2205/2204
+Mapping: [{{val|1 -18 16 -46 -64 18 -27 -20 21 -94}}, {{val|0 63 -44 157 217 -46 100 78 -53 318}}]
+POTE generator: ~243/196 = 373.0471
+Badness: 1.364
+== 233 & 317 ==
+Subgroup: 2.5.7.11
+Comma list: 537109375/536870912, 40353607/40262750
+Mapping: [{{val|1 -1 22 40}}, {{val|0 9 -52 -99}}]
+POTE generator: ~15488/12005 = 442.9148
+{{Optimal ET sequence|legend=1|65e, 84, 149, 233, 783, 1016, 1249, 1482}}
+Badness: 3.492
+=== 13-limit ===
+Subgroup: 2.5.7.11.13
+Comma list: 75712/75625, 10985/10976, 5462275/5451776
+Mapping: [{{val|1 -1 22 40 24}}, {{val|0 9 -52 -99 -55}}]
+POTE generator: ~455/352 = 442.9140
+{{Optimal ET sequence|legend=1|65ef, 84, 149, 233, 783, 1016f, 1249f}}
+Badness: 1.410
+== 233 & 659 ==
+Subgroup: 2.5.7.11.13.17
+Comma list: 6656/6655, 105644/105625, 557375/557056, 22578125/22550528
+Mapping: [{{val|1 -10 30 40 101 146}}, {{val|0 29 -64 -86 -229 -334}}]
+POTE generator: ~325/242 = 509.8664
+{{Optimal ET sequence|legend=1|193fgg, 233, 659, 892, 1125}}
+Badness: 2.422
+=== 23-limit ===
+Subgroup: 2.5.7.11.13.17.23
+Comma list: 5635/5632, 25025/25024, 6656/6655, 105644/105625, 50575/50531
+Mapping: [{{val|1 -10 30 40 101 146 -1}}, {{val|0 29 -64 -86 -229 -334 13}}]
+POTE generator: ~1375/1024 = 509.8663
+{{Optimal ET sequence|legend=1|233, 659, 892, 1125, 2017}}
+Badness: 1.679
+=== 31-limit ===
+Subgroup: 2.5.7.11.13.17.23.31
+Comma list: 5635/5632, 25025/25024, 6656/6655, 3875/3872, 105644/105625, 180625/180544
+Mapping: [{{val|1 -10 30 40 101 146 -1 115}}, {{val|0 29 -64 -86 -229 -334 13 -259}}]
+POTE generator: ~1375/1024 = 509.8661
+{{Optimal ET sequence|legend=1|233, 659, 892, 1125, 2017k}}
+Badness: 1.405
+=== 37-limit ===
+Subgroup: 2.5.7.11.13.17.23.31.37
+Comma list: 5635/5632, 25025/25024, 6656/6655, 3875/3872, 1925/1924, 105644/105625, 50575/50531
+Mapping: [{{val|1 -10 30 40 101 146 -1 115 -53}}, {{val|0 29 -64 -86 -229 -334 13 -259 137}}]
+POTE generator: ~1375/1024 = 509.8657
+{{Optimal ET sequence|legend=1|233, 659, 892}}
+Badness: 1.535
+== 239 & 569 ==
+Subgroup: 2.3.5.7
+Comma list: 823543/820125, 68359375/68024448
+Mapping: [{{val|1 8 9 13}}, {{val|0 -73 -76 -116}}]
+POTE generator: ~729/686 = 105.4479
+{{Optimal ET sequence|legend=1|34bcdd, 57bcd, 91, 148d, 239, 330, 569}}
+Badness: 8.274
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 42875/42768, 42592/42525, 151263/151250
+Mapping: [{{val|1 8 9 13 22}}, {{val|0 -73 -76 -116 -211}}]
+POTE generator: ~729/686 = 105.4456
+{{Optimal ET sequence|legend=1|57bcdeee, 91e, 148dee, 239, 569, 808}}
+Badness: 3.518
+== 239 & 683 ==
+Subgroup: 2.5.11.17.23.29
+Comma list: 69632/69575, 1048576/1047625, 107648/107525, 244338688/244140625
+Mapping: [{{val|1 2 1 4 10 6}}, {{val|0 11 84 3 -187 -39}}]
+POTE generator: ~638/625 = 35.1399
+{{Optimal ET sequence|legend=1|205i, 239, 444i, 683, 1605egi}}
+Badness: 1.628
+=== 31-limit ===
+Subgroup: 2.5.11.17.23.29.31
+Comma list: 69632/69575, 5800/5797, 14384/14375, 1048576/1047625, 12111616/12109375
+Mapping: [{{val|1 2 1 4 10 6 8}}, {{val|0 11 84 3 -187 -39 -104}}]
+POTE generator: ~253/248 = 35.1400
+{{Optimal ET sequence|legend=1|205i, 239, 444i, 683, 1605egik}}
+Badness: 1.106
+=== 37-limit ===
+Subgroup: 2.5.11.17.23.29.31.37
+Comma list: 69632/69575, 5800/5797, 14384/14375, 4625/4624, 1048576/1047625, 1647536/1646875
+Mapping: [{{val|1 2 1 4 10 6 8 6}}, {{val|0 11 84 3 -187 -39 -104 -27}}]
+POTE generator: 253/248 = 35.1400
+{{Optimal ET sequence|legend=1|205i, 239, 444i, 683, 1605egik}}
+Badness: 0.988
+== 239 & 1063 ==
+Subgroup: 2.3.5.7.11
+Comma list: 2401/2400, 1953125/1951488, 322102/321489
+Mapping: [{{val|1 47 34 30 87}}, {{val|0 -162 -113 -97 -298}}]
+POTE generator: ~175/144 = 336.4071
+{{Optimal ET sequence|legend=1|107bee, 239, 585e, 824e, 1887e}}
+Badness: 4.796
+== 277 & 641 ==
+Subgroup: 2.3.5
+Comma list: {{monzo|-56 -13 33}}
+Mapping: [{{val|1 16 8}}, {{val|0 -33 -13}}]
+POTE generator: ~3125/2304 = 524.1873
+{{Optimal ET sequence|legend=1|16, 55b, 71, 87, 190, 277}}
+Badness: 28.283
+== Focus (307 & 743) ==
+Subgroup: 2.5.7.11.13.17
+Comma list: 140800/140777, 40898/40817, 102487/102400, 184960/184877
+Mapping: [{{val|1 -69 -22 -26 -37 -37}}, {{val|0 184 64 76 105 106}}]
+POTE generator: ~17/13 = 465.1430
+{{Optimal ET sequence|legend=1|129c, 178c, 307, 743, 1050}}
+Badness: 2.436
+=== 19-limit ===
+Subgroup: 2.5.7.11.13.17.19
+Comma list: 10241/10240, 1331/1330, 140800/140777, 64220/64141, 5491/5488
+Mapping: [{{val|1 -69 -22 -26 -37 -37 12}}, {{val|0 184 64 76 105 106 -20}}]
+POTE generator: ~17/13 = 465.1425
+{{Optimal ET sequence|legend=1|129c, 178c, 307, 743, 1050}}
+Badness: 1.878
+=== 23-limit ===
+Subgroup: 2.5.7.11.13.17.19.23
+Comma list: 10241/10240, 140800/140777, 27209/27200, 4807/4802, 31603/31556, 608000/607453
+Mapping: [{{val|1 -69 -22 -26 -37 -37 12 -73}}, {{val|0 184 64 76 105 106 -20 200}}]
+POTE generator: ~17/13 = 465.1422
+{{Optimal ET sequence|legend=1|129ci, 307, 743, 1050}}
+Badness: 1.538
+== 311 & 379 ==
+Subgroup: 2.3.5.7
+Comma list: 2401/2400, {{monzo|-23 -11 15 2}}
+Mapping: [{{val|1 -5 -2 -1}}, {{val|0 64 42 37}}]
+POTE generator: ~78125/72576 = 123.4671
+{{Optimal ET sequence|legend=1|29bbcd, 39bc, 68, 175, 243, 311, 554, 865, 1419cd}}
+Badness: 3.518
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 6250/6237, 2401/2400, 2097152/2096325
+Mapping: [{{val|1 -5 -2 -1 12}}, {{val|0 64 42 37 -83}}]
+POTE generator: ~275/256 = 123.4730
+{{Optimal ET sequence|legend=1|68, 175e, 243, 311}}
+Badness: 3.125
+== 311 & 503 ==
+Subgroup: 2.3.5.7
+Comma list:  2401/2400, {{monzo|-95 21 29 -2}}
+Mapping: [{{val|1 43 -28 -2}}, {{val|0 -112 82 13}}]
+POTE generator: ~18984375/14680064 = 443.7335
+{{Optimal ET sequence|legend=1|119, 192, 311, 814, 1125, 3064d, 4189cdd, 5314cdd}}
+Badness: 7.820
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 2401/2400, 496125/495616, 100663296/100656875
+Mapping: [{{val|1 43 -28 -2 36}}, {{val|0 -112 82 13 -88}}]
+POTE generator: ~21175/16384 = 443.7337
+{{Optimal ET sequence|legend=1|119, 192, 311, 503, 814, 1125, 1939}}
+Badness: 2.599
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 2401/2400, 4225/4224, 59535/59488, 6656/6655
+Mapping: [{{val|1 43 -28 -2 36 71}}, {{val|0 -112 82 13 -88 -182}}]
+POTE generator: ~84/65 = 443.7338
+{{Optimal ET sequence|legend=1|119f, 192, 311, 503, 814, 1125, 1939}}
+Badness: 1.410
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 12376/12375, 2401/2400, 14400/14399, 4225/4224, 11016/11011
+Mapping: [{{val|1 43 -28 -2 36 71 -34}}, {{val|0 -112 82 13 -88 -182 103}}]
+POTE generator: ~84/65 = 443.7340
+{{Optimal ET sequence|legend=1|192, 311, 503, 814, 1939g, 2753dg}}
+Badness: 1.111
+== 311 & 571 ==
+Subgroup: 2.3.5.7.11
+Comma list: 3025/3024, 2401/2400, 294885080956928/294197433834375
+Mapping: [{{val|1 11 -22 -7 37}}, {{val|0 -48 124 50 -171}}]
+POTE generator: ~63/55 = 235.3736
+{{Optimal ET sequence|legend=1|10, 18bcd, 21e, 23bc, 31, 41, 72, 167, 198, 239, 270, 342, 612, 954, 1566, 3101de, 3443de, 4055de, 4397cdee, 4667dee, 5009cddee}}
+Badness: 2.441
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 3025/3024, 2401/2400, 47432/47385, 114345/114244
+Mapping: [{{val|1 11 -22 -7 37 19}}, {{val|0 -48 124 50 -171 -78}}]
+POTE generator: ~63/55 = 235.3738
+Badness: 1.528
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 2431/2430, 12376/12375, 2601/2600, 8624/8619, 2401/2400
+Mapping: [{{val|1 11 -22 -7 37 19 -22}}, {{val|0 -48 124 50 -171 -78 133}}]
+POTE generator: ~63/55 = 235.3741
+{{Optimal ET sequence|legend=1|260, 311, 571, 882}}
+Badness: 1.212
+== Sweepaway (311 & 607) ==
+Subgroup: 2.3.5.7.11.13
+Comma list: 2080/2079, 625/624, 3025/3024, 405769/405504
+Mapping: [{{val|1 20 17 -6 12 44}}, {{val|0 -69 -55 33 -32 -151}}]
+POTE generator: ~65/54 = 320.2613
+{{Optimal ET sequence|legend=1|15, 281f, 296, 311, 607, 918c}}
+Badness: 1.583
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 2080/2079, 625/624, 1225/1224, 3025/3024, 270725/270336
+Mapping: [{{val|1 20 17 -6 12 44 -21}}, {{val|0 -69 -55 33 -32 -151 94}}]
+POTE generator: ~65/54 = 320.2617
+{{Optimal ET sequence|legend=1|15, 296, 311, 607, 918c}}
+Badness: 1.503
+=== 19-limit ===
+Subgroup: 2.3.5.7.11.13.17.19
+Commas: 2080/2079, 625/624, 1225/1224, 3025/3024, 1729/1728, 26775/26752
+Mapping: [{{val|1 20 17 -6 12 44 -21 28}}, {{val|0 -69 -55 33 -32 -151 94 -89}}]
+POTE generator: ~65/54 = 320.2615
+{{Optimal ET sequence|legend=1|15, 296, 311, 607, 918ch}}
+Badness: 1.274
+== 311 & 701 ==
+Subgroup: 2.3.5.7.11
+Comma list: 2401/2400, 22478848/22460625, 1395654656/1395032625
+Mapping: [{{val|1 -13 40 18 -17}}, {{val|0 72 -186 -75 101}}]
+POTE generator: ~405/352 = 243.0836
+{{Optimal ET sequence|legend=1|79c, 311, 701, 1012, 1323, 2335, 3658}}
+Badness: 2.442
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 4096/4095, 2401/2400, 6656/6655, 1574640/1574573
+Mapping: [{{val|1 -13 40 18 -17 -20}}, {{val|0 72 -186 -75 101 117}}]
+POTE generator: ~405/352 = 243.0835
+{{Optimal ET sequence|legend=1|79c, 311, 701, 1012, 1323, 2335}}
+Badness: 1.383
+== 311 & 1063 ==
+Subgroup: 2.3.5.7
+Comma list: 2401/2400, 3367254360064/3363025078125
+Mapping: [{{val|1 11 -22 -7}}, {{val|0 -24 62 25}}]
+POTE generator: ~21/16 = 470.7489
+{{Optimal ET sequence|legend=1|51, 79c, 130, 311, 441, 2776, 3217, 3658, 4099, 4540, 4981}}
+Badness: 1.127
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 2401/2400, 19712/19683, 9453125/9437184
+Mapping: [{{val|1 11 -22 -7 98}}, {{val|0 -24 62 25 -241}}]
+POTE generator: ~21/16 = 470.7429
+{{Optimal ET sequence|legend=1|130e, 181e, 311, 752, 1063}}
+Badness: 4.158
+== 311 & 1193 ==
+Subgroup: 2.3.5.7
+Comma list: 2401/2400, {{monzo|36 -16 -7 2}}
+Mapping: [{{val|1 11 -22 -7}}, {{val|0 -48 124 50}}]
+POTE generator: ~8/7 = 235.3744
+{{Optimal ET sequence|legend=1|51, 79c, 130, 311, 441, 2776, 3217, 3658, 4099, 4540, 4981}}
+Badness: 1.127
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list:  3025/3024, 2401/2400, 3637837299712/3632067084375
+Mapping: [{{val|1 11 -22 -7 37}}, {{val|0 -48 124 50 -171}}]
+POTE generator: ~55/48 = 235.3736
+{{Optimal ET sequence|legend=1|51e, 260, 311, 571, 882, 2075}}
+Badness: 2.441
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 3025/3024, 4096/4095, 2401/2400, 492128/492075
+Mapping: [{{val|1 11 -22 -7 37 19}}, {{val|0 -48 124 50 -171 -78}}]
+POTE generator: ~55/48 = 235.3738
+{{Optimal ET sequence|legend=1|51e, 260, 311, 571, 882, 2075f}}
+Badness: 1.528
+== 311 & 1759 ==
+Subgroup: 2.3.5.7.11.13
+Comma list: 3025/3024, 4225/4224, 4100625/4100096, 1664000/1663893
+Mapping: [{{val|1 -34 40 36 -71 -89}}, {{val|0 119 -126 -111 249 310}}]
+POTE generator: ~315/256 = 358.8399
+{{Optimal ET sequence|legend=1|311, 826f, 1137, 1448, 4655cef, 6103cef, 7551ceeff, 8999cceeff}}
+Badness: 1.405
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 3025/3024, 2500/2499, 4225/4224, 56595/56576, 4100625/4100096
+Mapping: [{{val|1 -34 40 36 -71 -89 124}}, {{val|0 119 -126 -111 249 310 -401}}]
+POTE generator: ~315/256 = 358.8402
+{{Optimal ET sequence|legend=1|311, 1137g, 1448, 1759}}
+Badness: 1.903
+=== 19-limit ===
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 1549184/1549125
+Mapping: [{{val|1 -34 40 36 -71 -89 124 50}}, {{val|0 119 -126 -111 249 310 -401 -153}}]
+POTE generator: ~315/256 = 358.8402
+{{Optimal ET sequence|legend=1|311, 1137g, 1448, 1759}}
+Badness: 1.418
+=== 23-limit ===
+Subgroup: 2.3.5.7.11.13.17.19.23
+Comma list: 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 3520/3519, 76545/76544
+Mapping: [{{val|1 -34 40 36 -71 -89 124 50 -81}}, {{val|0 119 -126 -111 249 310 -401 -153 286}}]
+POTE generator: ~315/256 = 358.8402
+{{Optimal ET sequence|legend=1|311, 1137g, 1448, 1759}}
+Badness: 1.239
+=== 29-limit ===
+Subgroup: 2.3.5.7.11.13.17.19.23.29
+Comma list: 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 3520/3519, 5104/5103, 76545/76544
+Mapping: [{{val|1 -34 40 36 -71 -89 124 50 -81 -101}}, {{val|0 119 -126 -111 249 310 -401 -153 286 354}}]
+POTE generator: ~315/256 = 358.8402
+Badness: 1.159
+=== 31-limit ===
+Subgroup: 2.3.5.7.11.13.17.19.23.29.31
+Comma list: 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 3520/3519, 5104/5103, 76545/76544, 6076/6075
+Mapping: [{{val|1 -34 40 36 -71 -89 124 50 -81 -101 -164}}, {{val|0 119 -126 -111 249 310 -401 -153 286 354 565}}]
+POTE generator: ~315/256 = 358.8403
+Badness: 1.303
+=== 37-limit ===
+Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37
+Comma list: 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 3520/3519, 5104/5103, 76545/76544, 6076/6075, 5625/5624
+Mapping: [{{val|1 -34 40 36 -71 -89 124 50 -81 -101 -164 39}}, {{val|0 119 -126 -111 249 310 -401 -153 286 354 565 -113}}]
+POTE generator: ~315/256 = 358.8402
+Badness: 1.301
+=== 41-limit ===
+Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41
+Comma list: 3025/3024, 2500/2499, 5985/5984, 4225/4224, 6175/6174, 3520/3519, 5104/5103, 76545/76544, 6076/6075, 5625/5624, 2625/2624
+Mapping: [{{val|1 -34 40 36 -71 -89 124 50 -81 -101 -164 39 116}}, {{val|0 119 -126 -111 249 310 -401 -153 286 354 565 -113 -370}}]
+POTE generator: ~315/256 = 358.8403
+Badness: 1.360
+== 373 & 727 ==
+Subgroup: 2.3.5.7.11
+Comma list: 24057/24010, 137781/137500, 496125/495616
+Mapping: [{{val|1 18 20 55 115}}, {{val|0 -39 -42 -124 -265}}]
+POTE generator: ~75/56 = 505.0903
+{{Optimal ET sequence|legend=1|19e, 335dee, 354, 373, 727, 1100, 1827b}}
+Badness: 3.365
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 729/728, 1716/1715, 78975/78848, 34398/34375
+Mapping: [{{val|1 18 20 55 115 50}}, {{val|0 -39 -42 -124 -265 -110}}]
+POTE generator: ~75/56 = 505.0903
+{{Optimal ET sequence|legend=1|19e, 335dee, 354, 373, 727, 1100, 1827bf}}
+Badness: 1.677
+== 379 & 577 ==
+Subgroup: 2.5.7
+Comma list: {{monzo|40 -13 25}}
+Mapping: [{{val|1 20 12}}, {{val|0 -100 -52}}]
+POTE generator: ~80/49 = 848.548
+{{Optimal ET sequence|legend=1|17c, 24c, 41, 99, 140, 239, 379, 1376, 1755, 2134, 6023, 8157, 10291d}}
+Badness: 0.785
+=== 11-limit ===
+Subgroup: 2.5.7.11
+Comma list: 102487/102400, {{monzo|28 11 -24 4}}
+Mapping: [{{val|1 20 12 10}}, {{val|0 -100 -52 -37}}]
+POTE generator: ~133100/117649 = 212.1377
+{{Optimal ET sequence|legend=1|17c, 164c, 181, 198, 379}}
 Badness: 3.762
+== 487 & 691 ==
+Subgroup: 2.3.5.11.17.19
+Comma list: 374000/373977, 500000/499851, 632225/632043, 116640/116603
+Mapping: [{{val|1 30 59 65 79 55}}, {{val|0 -187 -373 -405 -493 -334}}]
+POTE generator: ~10/9 = 182.3424
+{{Optimal ET sequence|legend=1|204cegh, 283ceggh, 487, 1178, 1665}}
+Badness: 1.522
+=== 31-limit ===
+Subgroup: 2.3.5.11.17.19.31
+Comma list: 6480/6479, 374000/373977, 500000/499851, 6138/6137, 242000/241893
+Mapping: [{{val|1 30 59 65 79 55 63}}, {{val|0 -187 -373 -405 -493 -334 -382}}]
+POTE generator: ~10/9 = 182.3424
+{{Optimal ET sequence|legend=1|204ceghk, 283cegghk, 487, 1178, 1665}}
+Badness: 1.045
+== Shortcrust (677 & 761) ==
+Subgroup: 2.3.5
+Comma list: {{monzo|159 33 -91}}
+Mapping: [{{val|1 20 9}}, {{val|0 -91 -33}}]
+POTE generator: ~48828125/42467328 = 242.8354
+{{Optimal ET sequence|legend=1|84, 341b, 425, 509, 593, 677, 1947, 2624, 8549c}}
+Badness: 94.681

User:Francium/Miscellaneous rank-2 temperaments: Difference between revisions