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

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Badness: 1.211
Badness: 1.211
== 19 & 233 ==
Subgroup: 2.3.5.7
Comma list: 177147/175616, 78732/78125
Mapping: [{{val|1 6 8 19}}, {{val|0 -21 -27 -77}}]
POTE generator: ~280/243 = 252.3522
{{Optimal ET sequence|legend=1|138cddd, 157dd, 176d, 195d, 214, 233, 447, 680b}}
Badness: 5.012


== Berkenthin (19 & 239) ==
== Berkenthin (19 & 239) ==
Line 70: Line 84:


Badness: 1.422
Badness: 1.422
== 19 & 263 ==
Subgroup: 2.3.5
Comma list: {{monzo|18 37 -33}}
Mapping: [{{val|1 12 14}}, {{val|0 -33 -37}}]
POTE generator: ~390625/314928 = 378.7335
{{Optimal ET sequence|legend=1|19, 149bcc, 168bc, 187bc, 206c, 225c, 244, 263, 282, 301, 583, 884}}
Badness: 378.7335


== 19 & 331 ==
== 19 & 331 ==
Line 168: Line 196:


Badness: 1.796
Badness: 1.796
== 31 & 179 ==
Subgroup: 2.3.5.7
Comma list: 3136/3125, 10616832/10504375
Mapping: [{{val|1 -8 0 -3}}, {{val|0 33 8 20}}]
POTE generator: ~60/49 = 348.5617
{{Optimal ET sequence|legend=1|24bd, 31, 117bd, 148d, 179, 210, 451cd, 661ccdd}}
Badness: 3.282


== 31 & 197 ==
== 31 & 197 ==
Line 237: Line 279:
Badness: 75.296
Badness: 75.296


=== 7-limit ===
== 31 & 317 ==


Subgroup: 2.3.5.7
Subgroup: 2.5.7


Comma list: 6144/6125, 52734375/52706752
Comma list: 281484423828125/281474976710656


Mapping: [{{val|1 -11 2 -3}}, {{val|0 39 1 18}}]
Mapping: [{{val|1 0 6}}, {{val|0 8 -11}}]


POTE generator: ~5/4 = 387.2386
POTE generator: ~262144/214375 = 348.2889


{{Optimal ET sequence|legend=1|31, 158b, 189, 220, 251, 282, 533d, 815cdd}}
{{Optimal ET sequence|legend=1|7, 24, 31, 224, 255, 286, 317, 348, 379, 410, 789, 6691, 7480, 8269, 9058, 9847, 10636}}


Badness: 2.708
Badness: 0.015
 
=== 11-limit ===
 
Subgroup: 2.3.5.7.11
 
Comma list: 540/539, 5632/5625, 166698/166375
 
Mapping: [{{val|1 -11 2 -3 -23}}, {{val|0 39 1 18 82}}]
 
POTE generator: ~5/4 = 387.2309
 
{{Optimal ET sequence|legend=1|31, 158bee, 189ee, 220e, 251e, 282, 877cdee, 1159cddeee}}
 
Badness: 1.518
 
=== 13-limit ===
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 351/350, 540/539, 4096/4095, 166698/166375
 
Mapping: [{{val|1 -11 2 -3 -23 35}}, {{val|0 39 1 18 82 -97}}]
 
POTE generator: ~5/4 = 387.2169
 
{{Optimal ET sequence|legend=1|31, 282f, 313, 657d}}
 
Badness: 2.592
 
== 31 & 317 ==
 
Subgroup: 2.5.7
 
Comma list: 281484423828125/281474976710656
 
Mapping: [{{val|1 0 6}}, {{val|0 8 -11}}]
 
POTE generator: ~262144/214375 = 348.2889
 
{{Optimal ET sequence|legend=1|7, 24, 31, 224, 255, 286, 317, 348, 379, 410, 789, 6691, 7480, 8269, 9058, 9847, 10636}}
 
Badness: 0.015


=== 11-limit ===
=== 11-limit ===
Line 487: Line 487:
Badness: 1.062
Badness: 1.062


== Adriansonka (31 & 569) ==
== 31 & 499 ==
 
Subgroup: 2.3.5.7
 
Comma list: 2401/2400, 3848290697216/3814697265625
 
Mapping: [{{val|1 -21 2 -3}}, {{val|0 70 1 18}}]
 
POTE tuning: ~5/4 = 387.1746
 
{{Optimal ET sequence|legend=1|31, 313b, 344b, 375b, 406b, 437, 468, 499}}
 
Badness: 6.211
 
== 31 & 523 ==
 
Subgroup: 2.3.5.7
 
Comma list:  2401/2400, 13904571533203125/13792273858822144
 
Mapping: [{{val|1 -17 8 1}}, {{val|0 72 -22 7}}]
 
POTE tuning: ~448/375 = 309.7449
 
{{Optimal ET sequence|legend=1|31, 430, 461, 492, 523, 554, 585, 1139cd, 1724ccd}}
 
Badness: 6.842
 
=== 11-limit ===
 
Subgroup: 2.3.5.7.11
 
Comma list:  2401/2400, 496125/495616, 166375/165888
 
Mapping: [{{val|1 -17 8 1 -27}}, {{val|0 72 -22 7 118}}]
 
POTE tuning: ~448/375 = 309.7469
 
{{Optimal ET sequence|legend=1|31, 430, 461, 492, 523, 554e}}
 
Badness: 2,784
 
== Adriansonka (31 & 569) ==


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 807: Line 849:
Badness: 1.782
Badness: 1.782


== 41 & 197 ==
== 41 & 179 ==


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Comma list: 225/224, 4202539929/4194304000
Comma list: 10976/10935, 20480000/20253807


Mapping: [{{val|1 0 5 5}}, {{val|0 13 -22 -18}}]
Mapping: [{{val|1 4 16 13}}, {{val|0 -9 -51 -38}}]


POTE generator: ~160/147 = 146.1953
POTE generator: ~1600/1323 = 321.8267


{{Optimal ET sequence|legend=1|33, 41, 115, 156, 197}}
{{Optimal ET sequence|legend=1|15ccd, 26ccd, 41, 138cd, 179, 220, 481bd, 701bdd}}


Badness: 3.049
Badness: 3.653
 
== 41 & 197 ==
 
Subgroup: 2.3.5.7
 
Comma list: 225/224, 4202539929/4194304000
 
Mapping: [{{val|1 0 5 5}}, {{val|0 13 -22 -18}}]
 
POTE generator: ~160/147 = 146.1953
 
{{Optimal ET sequence|legend=1|33, 41, 115, 156, 197}}
 
Badness: 3.049


== 41 & 227 ==
== 41 & 227 ==
Line 905: Line 961:
Badness: 2.034
Badness: 2.034


==41 & 337==
== 41 & 251 ==
(better described as 41 & 255)


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Comma list: 16875/16807, 7381125/7340032
Comma list: 5120/5103, 184528125/184473632


Mapping: [{{val|1 4 -8 -4}}, {{val|0 -11 47 31}}]
Mapping: [{{val|1 1 -9 -5}}, {{val|0 3 58 40}}]


POTE generator: ~784/675 = 263.5183
POTE generator: ~343/300 = 234.2534


{{Optimal ET sequence|legend=1|41, 173, 214, 255, 296, 551, 847c}}
{{Optimal ET sequence|legend=1|41, 169cd, 210, 251, 292, 543d}}


Badness: 3.414
Badness: 2.966


==41 & 359==
== 41 & 313 ==


Subgroup: 2.3.5
Subgroup: 2.3.5.7


Comma list: {{monzo|155 -89 -6}}
Comma list: 32805/32768, 40500000/40353607


Mapping: [{{val|1 1 11}}, {{val|0 6 -89}}]
Mapping: [{{val|1 4 -17 -9}}, {{val|0 -9 72 44}}]


POTE generator: ~2187/2048 = 117.0069
POTE generator: ~135/112 = 322.0278


{{Optimal ET sequence|legend=1|41, 236cc, 277c, 318c, 359, 400, 441}}
{{Optimal ET sequence|legend=1|41, 231cd, 272, 313, 354, 395, 1144}}


Badness: 46.849
Badness: 3.189


===7-limit===
=== 11-limit ===


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7.11


Comma list: 2401/2400, 11785390260224/11767897353375
Comma list: 540/539, 32805/32768, 166698/166375


Mapping: [{{val|1 1 11 7}}, {{val|0 6 -89 -43}}]
Mapping: [{{val|1 4 -17 -9 15}}, {{val|0 -9 72 44 -43}}]


POTE generator: ~15/14 = 117.0067
POTE generator: ~135/112 = 322.0346


{{Optimal ET sequence|legend=1|41, 236cc, 277c, 318c, 359, 400, 441}}
{{Optimal ET sequence|legend=1|41, 231cd, 272, 313, 354}}


Badness: 1.383
Badness: 2.357


===11-limit===
=== 13-limit ===


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11.13


Comma list: 2401/2400, 200704/200475, 46656/46585
Comma list: 540/539, 2080/2079, 4096/4095, 166698/166375


Mapping: [{{val|1 1 11 7 -2}}, {{val|0 6 -89 -43 56}}]
Mapping: [{{val|1 4 -17 -9 15 30}}, {{val|0 -9 72 44 -43 -98}}]


POTE generator: ~77/72 = 117.0029
POTE generator: ~135/112 = 322.0336


{{Optimal ET sequence|legend=1|41, 318c, 359, 400, 841e, 1241e}}
{{Optimal ET sequence|legend=1|41, 272f, 313, 354}}


Badness: 1.716
Badness: 1.900


== 41 & 373 ==
== 41 & 337 ==
(better described as 41 & 255)


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Comma list: 2401/2400, {{monzo|-35 18 4 -1}}
Comma list: 16875/16807, 7381125/7340032


Mapping: [{{val|1 5 -15 -5}}, {{val|0 -14 71 32}}]
Mapping: [{{val|1 4 -8 -4}}, {{val|0 -11 47 31}}]


POTE generator: ~1215/1024 = 292.7572
POTE generator: ~784/675 = 263.5183


{{Optimal ET sequence|legend=1|41, 209c, 250c, 291, 332, 373, 414, 787}}
{{Optimal ET sequence|legend=1|41, 173, 214, 255, 296, 551, 847c}}


Badness: 3.790
Badness: 3.414


=== 11-limit ===
==41 & 359==


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5


Comma list: 3025/3024, 2401/2400, 4428675/4415488
Comma list: {{monzo|155 -89 -6}}


Mapping: [{{val|1 5 -15 -5 22}}, {{val|0 -14 71 32 -76}}]
Mapping: [{{val|1 1 11}}, {{val|0 6 -89}}]


POTE generator: ~4096/3465 = 292.7564
POTE generator: ~2187/2048 = 117.0069


{{Optimal ET sequence|legend=1|41, 291e, 332e, 373, 414, 787e, 1201bcde, 1988bcddee}}
{{Optimal ET sequence|legend=1|41, 236cc, 277c, 318c, 359, 400, 441}}


Badness: 1.849
Badness: 46.849


== 41 & 421 ==
===7-limit===


Subgroup: 2.3.7
Subgroup: 2.3.5.7


Comma list: {{monzo|-125 47 18}}
Comma list: 2401/2400, 11785390260224/11767897353375


Mapping: [{{val|1 -5 20}}, {{val|0 18 -47}}]
Mapping: [{{val|1 1 11 7}}, {{val|0 6 -89 -43}}]


POTE generator: ~9/7 = 438.9747
POTE generator: ~15/14 = 117.0067


{{Optimal ET sequence|legend=1|41, 298, 339, 380, 421, 462, 503, 544, 585, 2966bddd}}
{{Optimal ET sequence|legend=1|41, 236cc, 277c, 318c, 359, 400, 441}}


Badness: 78.897
Badness: 1.383


=== 11-limit ===
===11-limit===


Subgroup: 2.3.7.11
Subgroup: 2.3.5.7.11


Comma list: 2893401/2883584, 208971104256/208422380089
Comma list: 2401/2400, 200704/200475, 46656/46585


Mapping: [{{val|1 -5 20 -28}}, {{val|0 18 -47 86}}]
Mapping: [{{val|1 1 11 7 -2}}, {{val|0 6 -89 -43 56}}]


POTE generator: ~9/7 = 438.9681
POTE generator: ~77/72 = 117.0029


{{Optimal ET sequence|legend=1|41, 380e, 421, 462, 503, 1047, 1550b}}
{{Optimal ET sequence|legend=1|41, 318c, 359, 400, 841e, 1241e}}


Badness: 6.355
Badness: 1.716


=== 13-limit ===
== 41 & 373 ==


Subgroup: 2.3.7.11.13
Subgroup: 2.3.5.7


Comma list: 85293/85184, 53361/53248, 216513/215306
Comma list: 2401/2400, {{monzo|-35 18 4 -1}}


Mapping: [{{val|1 -5 20 -28 -38}}, {{val|0 18 -47 86 114}}]
Mapping: [{{val|1 5 -15 -5}}, {{val|0 -14 71 32}}]


POTE generator: ~156/121 = 438.9595
POTE generator: ~1215/1024 = 292.7572


{{Optimal ET sequence|legend=1|41, 380e, 421, 462}}
{{Optimal ET sequence|legend=1|41, 209c, 250c, 291, 332, 373, 414, 787}}


Badness: 4.703
Badness: 3.790


== 41 & 463 ==
=== 11-limit ===


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7.11


Comma list: 4096000/4084101, 359661568/358722675
Comma list: 3025/3024, 2401/2400, 4428675/4415488


Mapping: [{{val|1 2 -35 -20}}, {{val|0 -1 90 55}}]
Mapping: [{{val|1 5 -15 -5 22}}, {{val|0 -14 71 32 -76}}]


POTE generator: ~4/3 = 497.6285
POTE generator: ~4096/3465 = 292.7564


{{Optimal ET sequence|legend=1|41, 217ccd, 258cd, 299cd, 340c, 381, 422, 885, 1307d, 1729bdd}}
{{Optimal ET sequence|legend=1|41, 291e, 332e, 373, 414, 787e, 1201bcde, 1988bcddee}}


Badness: 4.045
Badness: 1.849


=== 11-limit ===
== 41 & 421 ==


Subgroup: 2.3.5.7.11
Subgroup: 2.3.7


Comma list: 3025/3024, 19712/19683, 1296000/1294139
Comma list: {{monzo|-125 47 18}}


Mapping: [{{val|1 2 -35 -20 30}}, {{val|0 -1 90 55 -64}}]
Mapping: [{{val|1 -5 20}}, {{val|0 18 -47}}]


POTE generator: ~4/3 = 497.6281
POTE generator: ~9/7 = 438.9747


{{Optimal ET sequence|legend=1|41, 340c, 381, 422, 885, 1307de}}
{{Optimal ET sequence|legend=1|41, 298, 339, 380, 421, 462, 503, 544, 585, 2966bddd}}


Badness: 1.883
Badness: 78.897


== 41 & 509 ==
=== 11-limit ===


Subgroup: 2.3.5.7
Subgroup: 2.3.7.11


Comma list: 2401/2400, {{monzo|40 -27 0 1}}
Comma list: 2893401/2883584, 208971104256/208422380089


Mapping: [{{val|1 1 -29 -13}}, {{val|0 2 107 54}}]
Mapping: [{{val|1 -5 20 -28}}, {{val|0 18 -47 86}}]


POTE generator: ~49/40 = 351.278
POTE generator: ~9/7 = 438.9681


{{Optimal ET sequence|legend=1|41, 263ccd, 304ccd, 345c, 386c, 427c, 468, 509, 1486bc }}
{{Optimal ET sequence|legend=1|41, 380e, 421, 462, 503, 1047, 1550b}}


Badness: 6.884
Badness: 6.355


==41 & 523==
=== 13-limit ===
(better known as 41 & 441)


Subgroup: 2.3.5.7
Subgroup: 2.3.7.11.13


Comma list: 2401/2400, {{monzo|35 -23 -3 3}}
Comma list: 85293/85184, 53361/53248, 216513/215306


Mapping: [{{val|1 1 11 7}}, {{val|0 6 -89 -43}}]
Mapping: [{{val|1 -5 20 -28 -38}}, {{val|0 18 -47 86 114}}]


POTE generator: ~15/14 = 117.006
POTE generator: ~156/121 = 438.9595


{{Optimal ET sequence|legend=1|41, 236cc, 277c, 318c, 359, 400, 441}}
{{Optimal ET sequence|legend=1|41, 380e, 421, 462}}


Badness: 1.383
Badness: 4.703


===11-limit===
== 41 & 463 ==


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7


Comma list: 2401/2400, 19712/19683, 166375/165888
Comma list: 4096000/4084101, 359661568/358722675


Mapping: [{{val|1 1 11 7 -6}}, {{val|0 6 -89 -43 97}}]
Mapping: [{{val|1 2 -35 -20}}, {{val|0 -1 90 55}}]


POTE generator: ~77/72 = 117.025
POTE generator: ~4/3 = 497.6285


{{Optimal ET sequence|legend=1|41, 400e, 441e, 482, 1487cdee}}
{{Optimal ET sequence|legend=1|41, 217ccd, 258cd, 299cd, 340c, 381, 422, 885, 1307d, 1729bdd}}


Badness: 3.127
Badness: 4.045


== 41 & 571 ==
=== 11-limit ===


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7.11


Comma list: 2401/2400, {{monzo|50 -31 -4 3}}
Comma list: 3025/3024, 19712/19683, 1296000/1294139


Mapping: [{{val|1 5 -39 -17}}, {{val|0 -10 121 58}}]
Mapping: [{{val|1 2 -35 -20 30}}, {{val|0 -1 90 55 -64}}]


POTE generator: ~2657205/2097152 = 409.8044
POTE generator: ~4/3 = 497.6281


{{Optimal ET sequence|legend=1|41, 407c, 448, 489c, 530, 571, 612, 2407, 3019, 3631d, 4243d}}
{{Optimal ET sequence|legend=1|41, 340c, 381, 422, 885, 1307de}}


Badness: 1.987
Badness: 1.883


=== 11-limit ===
== 41 & 503 ==
 
Subgroup: 2.3.5.7


Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 7943330713528125/7881299347898368


Comma list: 3025/3024, 2401/2400, 645922816/645700815
Mapping: [{{val|1 -5 40 20}}, {{val|0 18 -103 -47}}]


Mapping: [{{val|1 5 -39 -17 40}}, {{val|0 -10 121 58 -107}}]
POTE generator: ~66430125/51380224 = 438.9721


POTE generator: ~308/243 = 409.8034
{{Optimal ET sequence|legend=1|41, 380c, 421, 462, 503, 544, 1129d, 1673bcd, 2802bbccdd}}


Badness: 1.291
Badness: 6.307


== 41 & 607 ==
== 41 & 509 ==


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7


Comma list: 2080/2079, 3025/3024, 78975/78848, 218700/218491
Comma list: 2401/2400, {{monzo|40 -27 0 1}}


Mapping: [{{val|1 0 15 10 -8 -18}}, {{val|0 13 -104 -59 94 178}}]
Mapping: [{{val|1 1 -29 -13}}, {{val|0 2 107 54}}]


POTE generator: ~160/147 = 146.2905
POTE generator: ~49/40 = 351.278


{{Optimal ET sequence|legend=1|41, 525f, 566}}
{{Optimal ET sequence|legend=1|41, 263ccd, 304ccd, 345c, 386c, 427c, 468, 509, 1486bc }}


Badness: 2.398
Badness: 6.884


== 41 & 1063 ==
==41 & 523==
(better known as 41 & 441)


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Comma list: 2401/2400, {{monzo|80 -52 -5 5}}
Comma list: 2401/2400, {{monzo|35 -23 -3 3}}


Mapping: [{{val|1 5 -67 -31}}, {{val|0 -10 203 99}}]
Mapping: [{{val|1 1 11 7}}, {{val|0 6 -89 -43}}]


POTE generator: ~524288/413343 = 409.7856
POTE generator: ~15/14 = 117.006


{{Optimal ET sequence|legend=1|41, 776cc, 817c, 858c, 899c, 940, 981, 2984, 3965bc}}
{{Optimal ET sequence|legend=1|41, 236cc, 277c, 318c, 359, 400, 441}}


Badness: 10.520
Badness: 1.383


== 43 & 233 ==
===11-limit===


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11


Comma list: 441/440, 1001/1000, 21168/21125, 81675/81536
Comma list: 2401/2400, 19712/19683, 166375/165888


Mapping: [{{val|1 8 -8 -17 -13 9}}, {{val|0 -23 37 71 59 -19}}]
Mapping: [{{val|1 1 11 7 -6}}, {{val|0 6 -89 -43 97}}]


POTE generator: ~40/33 = 334.7481
POTE generator: ~77/72 = 117.025


{{Optimal ET sequence|legend=1|43, 147de, 190, 423d, 613bde}}
{{Optimal ET sequence|legend=1|41, 400e, 441e, 482, 1487cdee}}


Badness: 1.813
Badness: 3.127


=== 17-limit ===
== 41 & 571 ==


Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7


Comma list: 441/440, 561/560, 1275/1274, 1156/1155, 21168/21125
Comma list: 2401/2400, {{monzo|50 -31 -4 3}}


Mapping: [{{val|1 8 -8 -17 -13 9 -16}}, {{val|0 -23 37 71 59 -19 72}}]
Mapping: [{{val|1 5 -39 -17}}, {{val|0 -10 121 58}}]


POTE generator: ~17/14 = 334.7511
POTE generator: ~2657205/2097152 = 409.8044


{{Optimal ET sequence|legend=1|43, 147deg, 190g, 233, 423dg}}
{{Optimal ET sequence|legend=1|41, 407c, 448, 489c, 530, 571, 612, 2407, 3019, 3631d, 4243d}}


Badness: 1.592
Badness: 1.987


==Mehlem (53 & 179)==
=== 11-limit ===


Subgroup: 2.3.5
Subgroup: 2.3.5.7.11


Comma list: {{monzo|12 -31 16}}
Comma list: 3025/3024, 2401/2400, 645922816/645700815


Mapping: [{{val|1 4 7}}, {{val|0 -16 -31}}]
Mapping: [{{val|1 5 -39 -17 40}}, {{val|0 -10 121 58 -107}}]


POTE generator: ~10/9 = 181.0964
POTE generator: ~308/243 = 409.8034


{{Optimal ET sequence|legend=1|20c, 33c, 53, 338, 391, 444, 497, 550, 603, 656, 1259b}}
Badness: 1.291


Badness: 10.511
== 41 & 607 ==


===7-limit===
Subgroup: 2.3.5.7.11.13


Subgroup: 2.3.5.7
Comma list: 2080/2079, 3025/3024, 78975/78848, 218700/218491


Comma list: 4375/4374, 65536/64827
Mapping: [{{val|1 0 15 10 -8 -18}}, {{val|0 13 -104 -59 94 178}}]


Mapping: [{{val|1 4 7 1}}, {{val|0 -16 -31 12}}]
POTE generator: ~160/147 = 146.2905


POTE generator: ~10/9 = 181.0314
{{Optimal ET sequence|legend=1|41, 525f, 566}}


{{Optimal ET sequence|legend=1|20c, 53, 126, 179, 232d}}
Badness: 2.398


Badness: 3.333
== 41 & 1063 ==


== 53 & 239 ==
Subgroup: 2.3.5.7


Subgroup: 2.3.5
Comma list: 2401/2400, {{monzo|80 -52 -5 5}}


Comma list: 390625000/387420489
Mapping: [{{val|1 5 -67 -31}}, {{val|0 -10 203 99}}]


Mapping: [{{val|1 2 3}}, {{val|0 -11 -18}}]
POTE generator: ~524288/413343 = 409.7856


POTE generator: ~250/243 = 45.2329
{{Optimal ET sequence|legend=1|41, 776cc, 817c, 858c, 899c, 940, 981, 2984, 3965bc}}


{{Optimal ET sequence|legend=1|25bcc, 26, 27, 53, 239, 292, 345, 398, 451}}
Badness: 10.520


Badness: 2.750
== 43 & 233 ==


=== 7-limit ===
Subgroup: 2.3.5.7.11.13


Subgroup: 2.3.5.7
Comma list: 441/440, 1001/1000, 21168/21125, 81675/81536


Comma list: 5120/5103, 95703125/95551488
Mapping: [{{val|1 8 -8 -17 -13 9}}, {{val|0 -23 37 71 59 -19}}]


Mapping: [{{val|1 2 3 1}}, {{val|0 -11 -18 48}}]
POTE generator: ~40/33 = 334.7481


POTE generator: ~250/243 = 45.1995
{{Optimal ET sequence|legend=1|43, 147de, 190, 423d, 613bde}}


{{Optimal ET sequence|legend=1|53, 186, 239, 292, 531, 823bd}}
Badness: 1.813


Badness: 2.937
=== 17-limit ===


== 53 & 307 ==
Subgroup: 2.3.5.7.11.13.17


Subgroup: 2.9.5
Comma list: 441/440, 561/560, 1275/1274, 1156/1155, 21168/21125


Comma list: 32805/32768
Mapping: [{{val|1 8 -8 -17 -13 9 -16}}, {{val|0 -23 37 71 59 -19 72}}]


Mapping: [{{val|1 0 15}}, {{val|0 7 -28}}]
POTE generator: ~17/14 = 334.7511


POTE generator: ~512/375 = 543.3531
{{Optimal ET sequence|legend=1|43, 147deg, 190g, 233, 423dg}}


{{Optimal ET sequence|legend=1|6, 29, 35, 41, 47, 53, 59, 171, 230, 519, 749 }}
Badness: 1.592


Badness: 0.100
==Mehlem (53 & 179)==
 
== 53 & 331 ==


Subgroup: 2.3.5
Subgroup: 2.3.5


Comma list: {{monzo|21 -44 21}}
Comma list: {{monzo|12 -31 16}}


Mapping: [{{val|1 0 -1}}, {{val|0 21 44}}]
Mapping: [{{val|1 4 7}}, {{val|0 -16 -31}}]


POTE generator: ~10460353203/10000000000 = 90.5930
POTE generator: ~10/9 = 181.0964


{{Optimal ET sequence|legend=1|13c, 40c, 53, 437, 490, 543, 596, 649, 702, 755, 808, 861}}
{{Optimal ET sequence|legend=1|20c, 33c, 53, 338, 391, 444, 497, 550, 603, 656, 1259b}}


Badness: 26.682
Badness: 10.511


== 53 & 419 ==
===7-limit===


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Comma list: 32805/32768, 117546246144/117236328125
Comma list: 4375/4374, 65536/64827


Mapping: [{{val|1 0 15 -38}}, {{val|0 4 -32 103}}]
Mapping: [{{val|1 4 7 1}}, {{val|0 -16 -31 12}}]


POTE generator: ~1152/875 = 475.4255
POTE generator: ~10/9 = 181.0314


{{Optimal ET sequence|legend=1|53, 313d, 366, 419, 472, 997, 1469}}
{{Optimal ET sequence|legend=1|20c, 53, 126, 179, 232d}}


Badness: 3.544
Badness: 3.333


== 53 & 463 ==
== 53 & 239 ==


Subgroup: 2.3.5.7
Subgroup: 2.3.5


Comma list: 1600000/1594323, 95703125/95551488
Comma list: 390625000/387420489


Mapping: [{{val|1 -2 -7 34}}, {{val|0 10 26 -87}}]
Mapping: [{{val|1 2 3}}, {{val|0 -11 -18}}]


POTE generator: ~32768/25515 = 430.2406
POTE generator: ~250/243 = 45.2329


{{Optimal ET sequence|legend=1|53, 251d, 304, 357, 410, 463, 873}}
{{Optimal ET sequence|legend=1|25bcc, 26, 27, 53, 239, 292, 345, 398, 451}}


Badness: 4.524
Badness: 2.750


== 53 & 467 ==
=== 7-limit ===


Subgroup: 2.3.5
Subgroup: 2.3.5.7


Comma list: {{monzo|-36 11 8}}
Comma list: 5120/5103, 95703125/95551488


Mapping: [{{val|1 4 -1}}, {{val|0 -8 11}}]
Mapping: [{{val|1 2 3 1}}, {{val|0 -11 -18 48}}]


POTE generator: ~10125/8192 = 362.3210
POTE generator: ~250/243 = 45.1995


{{Optimal ET sequence|legend=1|10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc}}
{{Optimal ET sequence|legend=1|53, 186, 239, 292, 531, 823bd}}


Badness: 3.055
Badness: 2.937


=== 7-limit ===
== 53 & 307 ==


Subgroup: 2.3.5.7
Subgroup: 2.9.5


Comma list: 4375/4374, 69198046875/68719476736
Comma list: 32805/32768


Mapping: [{{val|1 4 -1 33}}, {{val|0 -8 11 -100}}]
Mapping: [{{val|1 0 15}}, {{val|0 7 -28}}]  


POTE generator: ~10125/8192 = 362.3181
POTE generator: ~512/375 = 543.3531


{{Optimal ET sequence|legend=1|53, 255d, 308d, 361, 414, 2123bccdd}}
{{Optimal ET sequence|legend=1|6, 29, 35, 41, 47, 53, 59, 171, 230, 519, 749 }}


Badness: 4.674
Badness: 0.100


==53 & 499==
== 53 & 331 ==


Subgroup: 2.3.5
Subgroup: 2.3.5


Comma list: {{monzo|63 -50 7}}
Comma list: {{monzo|21 -44 21}}


Mapping: [{{val|1 0 -9}}, {{val|0 7 50}}
Mapping: [{{val|1 0 -1}}, {{val|0 21 44}}]


POTE generator: ~2560/2187 = 271.7276
POTE generator: ~10460353203/10000000000 = 90.5930


{{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|13c, 40c, 53, 437, 490, 543, 596, 649, 702, 755, 808, 861}}


Badness: 8.860
Badness: 26.682


===7-limit===
== 53 & 419 ==


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Comma list: 26873856/26796875, 33554432/33480783
Comma list: 32805/32768, 117546246144/117236328125


Mapping: [{{val|1 0 -9 25}}, {{val|0 7 50 -98}}]
Mapping: [{{val|1 0 15 -38}}, {{val|0 4 -32 103}}]


POTE generator: ~1024/875 = 271.7017
POTE generator: ~1152/875 = 475.4255


{{Optimal ET sequence|legend=1|53, 393, 446, 499, 552, 2155ccdd, 2707bcccdd}}
{{Optimal ET sequence|legend=1|53, 313d, 366, 419, 472, 997, 1469}}


Badness: 6.432
Badness: 3.544


== 53 & 673 ==
== 53 & 463 ==


Subgroup: 2.3.5
Subgroup: 2.3.5.7


Comma list: {{monzo|51 -60 19}}
Comma list: 1600000/1594323, 95703125/95551488


Mapping: [{{val|1 -2 -9}}, {{val|0 19 60}}]
Mapping: [{{val|1 -2 -7 34}}, {{val|0 10 26 -87}}]


POTE generator: ~1162261467/1024000000 = 226.4390
POTE generator: ~32768/25515 = 430.2406


{{Optimal ET sequence|legend=1|16cc, 37cc, 53, 514c, 567, 620, 673, 726, 779, 832, 885, 938}}
{{Optimal ET sequence|legend=1|53, 251d, 304, 357, 410, 463, 873}}


Badness: 40.263
Badness: 4.524


== 53 & 733 ==
== 53 & 467 ==


Subgroup: 2.3.5
Subgroup: 2.3.5


Comma list: {{monzo|42 -47 14}}
Comma list: {{monzo|-36 11 8}}


Mapping: [{{val|1 0 -3}}, {{val|0 14 47}}]
Mapping: [{{val|1 4 -1}}, {{val|0 -8 11}}]


POTE generator: ~64000/59049 = 135.8799
POTE generator: ~10125/8192 = 362.3210


{{Optimal ET sequence|legend=1| 44c, 53, 415, 468, 521, 574, 627, 680, 733}}
{{Optimal ET sequence|legend=1|10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc}}


Badness: 18.063
Badness: 3.055


== 53 & 1063 ==
=== 7-limit ===


Subgroup: 2.3.5
Subgroup: 2.3.5.7


Comma list: {{monzo|57 -55 13}}
Comma list: 4375/4374, 69198046875/68719476736


Mapping: [{{val|1 6 21}}, {{val|0 -13 -55}}]
Mapping: [{{val|1 4 -1 33}}, {{val|0 -8 11 -100}}]


POTE generator: ~163840000/129140163 = 407.5202
POTE generator: ~10125/8192 = 362.3181


{{Optimal ET sequence|legend=1|50cc, 53, 427c, 480, 533, 586, 639, 692, 745, 798, 851, 2500b, 3351b}}
{{Optimal ET sequence|legend=1|53, 255d, 308d, 361, 414, 2123bccdd}}


Badness: 22.373
Badness: 4.674


== 53 & 1193 ==
==53 & 499==


Subgroup: 2.3.5
Subgroup: 2.3.5


Comma list: {{monzo|87 -71 11}}
Comma list: {{monzo|63 -50 7}}


Mapping: [{{val|1 2 5}}, {{val|0 -11 -71}}]
Mapping: [{{val|1 0 -9}}, {{val|0 7 50}}


POTE generator: ~1638400/1594323 = 45.2622
POTE generator: ~2560/2187 = 271.7276


{{Optimal ET sequence|legend=1|26cc, 27cc, 53, 557c, 610c, 663c, 716, 769, 822, 875, 928, 981, 1034, 1087}}
{{Optimal ET sequence|legend=1|22c, 31c, 53, 393, 446, 499, 552, 605, 658, 711, 764, 6165b, 6929b, 7693b, 8457b, 9221bbc, 9985bbc, 10749bbc}}


Badness: 29.067
Badness: 8.860


== 53 & 1759 ==
===7-limit===


Subgroup: 2.3.5
Subgroup: 2.3.5.7


Comma list: {{monzo|132 -95 8}}
Comma list: 26873856/26796875, 33554432/33480783


Mapping: {{val|1 4 31}}, {{val|0 -8 -95}}]
Mapping: [{{val|1 0 -9 25}}, {{val|0 7 50 -98}}]


POTE generator: ~655360/531441 = 362.2490
POTE generator: ~1024/875 = 271.7017


{{Optimal ET sequence|legend=1|53, 752c, 805c, 858c, 911c, 964c, 1017c, 1070c, 1123, 1176, 1229, 1282, 1335, 1388, 1441, 1494}}
{{Optimal ET sequence|legend=1|53, 393, 446, 499, 552, 2155ccdd, 2707bcccdd}}


Badness: 25.296
Badness: 6.432


== 103 & 167 ==
== 53 & 673 ==


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5


Comma list: 1001/1000, 3025/3024, 1716/1715, 4225/4224
Comma list: {{monzo|51 -60 19}}


Mapping: [{{val|1 -25 -16 -13 -26 -6}}, {{val|0 74 51 44 82 27}}]
Mapping: [{{val|1 -2 -9}}, {{val|0 19 60}}]


POTE generator: ~440/343 = 431.1062
POTE generator: ~1162261467/1024000000 = 226.4390


Badness: 0.662
{{Optimal ET sequence|legend=1|16cc, 37cc, 53, 514c, 567, 620, 673, 726, 779, 832, 885, 938}}


=== 17-limit ===
Badness: 40.263


Subgroup: 2.3.5.7.11.13.17
== 53 & 733 ==


Comma list: 1001/1000, 1225/1224, 715/714, 936/935, 4225/4224
Subgroup: 2.3.5


Mapping: [{{val|1 -25 -16 -13 -26 -6 -11}}, {{val|0 74 51 44 82 27 42}}]
Comma list: {{monzo|42 -47 14}}


POTE generator: ~440/343 = 431.1087
Mapping: [{{val|1 0 -3}}, {{val|0 14 47}}]


{{Optimal ET sequence|legend=1|39bce, 64be, 103, 167, 270}}
POTE generator: ~64000/59049 = 135.8799


Badness: 1.068
{{Optimal ET sequence|legend=1| 44c, 53, 415, 468, 521, 574, 627, 680, 733}}


== 103 & 227 ==
Badness: 18.063


Subgroup: 2.3.5.7.11.13
== 53 & 1063 ==


Comma list: 385/384, 1001/1000, 4225/4224, 50421/50336
Subgroup: 2.3.5


Mapping: [{{val|1 -36 -11 -1 -17 -12}}, {{val|0 79 28 8 43 33}}]
Comma list: {{monzo|57 -55 13}}


POTE generator: ~490/352 = 570.9053
Mapping: [{{val|1 6 21}}, {{val|0 -13 -55}}]


{{Optimal ET sequence|legend=1|21b, 103, 227, 330e}}
POTE generator: ~163840000/129140163 = 407.5202


Badness: 2.198
{{Optimal ET sequence|legend=1|50cc, 53, 427c, 480, 533, 586, 639, 692, 745, 798, 851, 2500b, 3351b}}


== 103 & 457 ==
Badness: 22.373
 
== 53 & 1193 ==


Subgroup: 2.3.5.7
Subgroup: 2.3.5


Comma list: 26873856/26796875, 40500000/40353607
Comma list: {{monzo|87 -71 11}}


Mapping: [{{val|1 -11 -7 -9}}, {{val|0 81 60 76}}]
Mapping: [{{val|1 2 5}}, {{val|0 -11 -71}}]


POTE generator: ~2401/2160 = 186.4436
POTE generator: ~1638400/1594323 = 45.2622


{{Optimal ET sequence|legend=1|45bcd, 103, 251, 354, 605d, 959d, 1313d}}
{{Optimal ET sequence|legend=1|26cc, 27cc, 53, 557c, 610c, 663c, 716, 769, 822, 875, 928, 981, 1034, 1087}}


Badness: 5.981
Badness: 29.067


=== 11-limit ===
== 53 & 1759 ==


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5


Comma list: 540/539, 166698/166375, 2737152/2734375
Comma list: {{monzo|132 -95 8}}


Mapping: [{{val|1 -11 -7 -9 -20}}, {{val|0 81 60 76 151}}]
Mapping: {{val|1 4 31}}, {{val|0 -8 -95}}]


POTE generator: ~49/44 = 186.4402
POTE generator: ~655360/531441 = 362.2490


{{Optimal ET sequence|legend=1|45bcdee, 103, 251e, 354}}
{{Optimal ET sequence|legend=1|53, 752c, 805c, 858c, 911c, 964c, 1017c, 1070c, 1123, 1176, 1229, 1282, 1335, 1388, 1441, 1494}}


Badness: 2.869
Badness: 25.296


=== 13-limit ===
== 103 & 167 ==


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 540/539, 1716/1715, 4225/4224, 34398/34375
Comma list: 1001/1000, 3025/3024, 1716/1715, 4225/4224


Mapping: [{{val|1 -11 -7 -9 -20 -5}}, {{val|0 81 60 76 151 56}}]
Mapping: [{{val|1 -25 -16 -13 -26 -6}}, {{val|0 74 51 44 82 27}}]


POTE generator: ~39/35 = 186.4399
POTE generator: ~440/343 = 431.1062


{{Optimal ET sequence|legend=1|45bcdee, 103, 251e, 354}}
Badness: 0.662
 
Badness: 1.642


=== 17-limit ===
=== 17-limit ===
Line 1,509: Line 1,565:
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Comma list: 540/539, 936/935, 1377/1375, 1716/1715, 4225/4224
Comma list: 1001/1000, 1225/1224, 715/714, 936/935, 4225/4224


Mapping: [{{val|1 -11 -7 -9 -20 -5 3}}, {{val|0 81 60 76 151 56 7}}]
Mapping: [{{val|1 -25 -16 -13 -26 -6 -11}}, {{val|0 74 51 44 82 27 42}}]


POTE generator: ~39/35 =186.4396
POTE generator: ~440/343 = 431.1087


{{Optimal ET sequence|legend=1|103, 251e, 354}}
{{Optimal ET sequence|legend=1|39bce, 64be, 103, 167, 270}}


Badness: 1.399
Badness: 1.068


== 103 & 503 ==
== 103 & 227 ==


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11.13


Comma list: 2401/2400, 46656/46585, 766656/765625
Comma list: 385/384, 1001/1000, 4225/4224, 50421/50336


Mapping: [{{val|1 -41 -34 -26 -60}}, {{val|0 102 87 69 152}}]
Mapping: [{{val|1 -36 -11 -1 -17 -12}}, {{val|0 79 28 8 43 33}}]


POTE generator: ~4/3 = 500.9986
POTE generator: ~490/352 = 570.9053


{{Optimal ET sequence|legend=1|91bcdee, 103, 297e, 400, 1303c, 1703ce}}
{{Optimal ET sequence|legend=1|21b, 103, 227, 330e}}


Badness: 2.344
Badness: 2.198


=== 13-limit ===
== 103 & 457 ==


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7


Comma list: 1001/1000, 1716/1715, 4225/4224, 75816/75625
Comma list: 26873856/26796875, 40500000/40353607


Mapping: [{{val|1 -41 -34 -26 -60 -13}}, {{val|0 102 87 69 152 40}}]
Mapping: [{{val|1 -11 -7 -9}}, {{val|0 81 60 76}}]


POTE generator: ~4/3 = 500.9970
POTE generator: ~2401/2160 = 186.4436


{{Optimal ET sequence|legend=1|91bcdee, 103, 297e, 400, 503, 903}}
{{Optimal ET sequence|legend=1|45bcd, 103, 251, 354, 605d, 959d, 1313d}}


Badness: 1.735
Badness: 5.981


=== 17-limit ===
=== 11-limit ===


Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11


Comma list: 1001/1000, 936/935, 1377/1375, 1716/1715, 4225/4224
Comma list: 540/539, 166698/166375, 2737152/2734375


Mapping: [{{val|1 -41 -34 -26 -60 -13 2}}, {{val|0 102 87 69 152 40 5}}]
Mapping: [{{val|1 -11 -7 -9 -20}}, {{val|0 81 60 76 151}}]


POTE generator: ~4/3 = 500.9972
POTE generator: ~49/44 = 186.4402


Badness: 1.402
{{Optimal ET sequence|legend=1|45bcdee, 103, 251e, 354}}


== 103 & 647 ==
Badness: 2.869


Subgroup: 2.5.7.11.13
=== 13-limit ===


Comma list: 105644/105625, 5462275/5451776, 200000/199927
Subgroup: 2.3.5.7.11.13


Mapping: [{{val|1 25 23 60 27}}, {{val|0 -73 -65 -182 -75}}]
Comma list: 540/539, 1716/1715, 4225/4224, 34398/34375


POTE generator: ~3872/3125 = 372.7948
Mapping: [{{val|1 -11 -7 -9 -20 -5}}, {{val|0 81 60 76 151 56}}]


{{Optimal ET sequence|legend=1|103, 338e, 441, 544, 1735cd}}
POTE generator: ~39/35 = 186.4399


Badness: 1.978
{{Optimal ET sequence|legend=1|45bcdee, 103, 251e, 354}}


== Wiloliquy (103 & 700) ==
Badness: 1.642


Subgroup: 2.5.7.13.17
=== 17-limit ===


Comma list: 31250/31213, 10985/10976, 177482125/177209344
Subgroup: 2.3.5.7.11.13.17


Mapping: [{{val|1 38 48 37 -4}}, {{val|0 -75 -95 -70 17}}]
Comma list: 540/539, 936/935, 1377/1375, 1716/1715, 4225/4224


POTE generator: ~50176/36125 = 570.8538
Mapping: [{{val|1 -11 -7 -9 -20 -5 3}}, {{val|0 81 60 76 151 56 7}}]


{{Optimal ET sequence|legend=1|103, 391, 494, 597, 2285cfg}}
POTE generator: ~39/35 =186.4396


Badness: 1.690
{{Optimal ET sequence|legend=1|103, 251e, 354}}


== 113 & 409 ==
Badness: 1.399


Subgroup: 2.3.7.11
== 103 & 503 ==


Comma list: 5038848/5021863, 235782657/234881024
Subgroup: 2.3.5.7.11


Mapping: [{{val|1 4 16 -1}}, {{val|0 -13 -71 24}}]
Comma list: 2401/2400, 46656/46585, 766656/765625


POTE generator: ~8192/7203 = 222.9728
Mapping: [{{val|1 -41 -34 -26 -60}}, {{val|0 102 87 69 152}}]


{{Optimal ET sequence|legend=1|70, 113, 183, 296}}
POTE generator: ~4/3 = 500.9986


Badness: 5.092
{{Optimal ET sequence|legend=1|91bcdee, 103, 297e, 400, 1303c, 1703ce}}
 
Badness: 2.344


=== 13-limit ===
=== 13-limit ===


Subgroup: 2.3.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 729/728, 19773/19712, 718848/717409
Comma list: 1001/1000, 1716/1715, 4225/4224, 75816/75625


Mapping: [{{val|1 4 16 -1 5}}, {{val|0 -13 -71 24 -7}}]
Mapping: [{{val|1 -41 -34 -26 -60 -13}}, {{val|0 102 87 69 152 40}}]


POTE generator: ~91/80 = 222.9746
POTE generator: ~4/3 = 500.9970


{{Optimal ET sequence|legend=1|70, 113, 183, 296}}
{{Optimal ET sequence|legend=1|91bcdee, 103, 297e, 400, 503, 903}}


Badness: 1.829
Badness: 1.735


== 113 & 709 ==
=== 17-limit ===


Subgroup: 2.3.11.13.17
Subgroup: 2.3.5.7.11.13.17


Comma list: 971074/970299, 2097152/2093663, 60915712/60886809
Comma list: 1001/1000, 936/935, 1377/1375, 1716/1715, 4225/4224


Mapping: [{{val|1 -44 17 -64 42}}, {{val|0 101 -30 150 -84}}]
Mapping: [{{val|1 -41 -34 -26 -60 -13 2}}, {{val|0 102 87 69 152 40 5}}]


POTE generator: ~33048/24167 = 541.6049
POTE generator: ~4/3 = 500.9972


{{Optimal ET sequence|legend=1|113, 483f, 596f, 709, 822, 935, 1757e}}
Badness: 1.402


Badness: 3.748
== 103 & 647 ==


=== 19-limit ===
Subgroup: 2.5.7.11.13


Subgroup: 2.3.11.13.17.19
Comma list: 105644/105625, 5462275/5451776, 200000/199927


Comma list: 2432/2431, 278528/278179, 793152/793117, 68054272/68049963
Mapping: [{{val|1 25 23 60 27}}, {{val|0 -73 -65 -182 -75}}]


Mapping: [{{val|1 -44 17 -64 42 -12}}, {{val|0 101 -30 150 -84 36}}]
POTE generator: ~3872/3125 = 372.7948


POTE generator: ~4199/3072 = 541.6049
{{Optimal ET sequence|legend=1|103, 338e, 441, 544, 1735cd}}


{{Optimal ET sequence|legend=1|113, 483f, 596f, 709, 822, 935, 1757e}}
Badness: 1.978


Badness: 1.676
== Wiloliquy (103 & 700) ==


=== 31-limit ===
Subgroup: 2.5.7.13.17


Subgroup: 2.3.11.13.17.19.31
Comma list: 31250/31213, 10985/10976, 177482125/177209344


Comma list: 2432/2431, 1024/1023, 25296/25289, 793152/793117, 68054272/68049963
Mapping: [{{val|1 38 48 37 -4}}, {{val|0 -75 -95 -70 17}}]


Mapping: [{{val|1 -44 17 -64 42 -12 37}}, {{val|0 101 -30 150 -84 36 -71}}]
POTE generator: ~50176/36125 = 570.8538


POTE generator: ~4199/3072 = 541.6055
{{Optimal ET sequence|legend=1|103, 391, 494, 597, 2285cfg}}


{{Optimal ET sequence|legend=1|113, 483f, 596f, 709, 822k}}
Badness: 1.690


Badness: 1.718
== 113 & 409 ==


=== 37-limit ===
Subgroup: 2.3.7.11


Subgroup: 2.3.11.13.17.19.31.37
Comma list: 5038848/5021863, 235782657/234881024


Comma list: 2432/2431, 1024/1023, 3553/3552, 25296/25289, 793152/793117, 681472/681207
Mapping: [{{val|1 4 16 -1}}, {{val|0 -13 -71 24}}]


Mapping: [{{val|1 -44 17 -64 42 -12 37 86}}, {{val|0 101 -30 150 -84 36 -71 -179}}]
POTE generator: ~8192/7203 = 222.9728


POTE generator: ~4199/3072 = 541.6062
{{Optimal ET sequence|legend=1|70, 113, 183, 296}}


{{Optimal ET sequence|legend=1|113, 483f, 596f, 709, 822kl}}
Badness: 5.092


Badness: 1.939
=== 13-limit ===


== 167 & 311 ==
Subgroup: 2.3.7.11.13


Subgroup: 2.3.5.7.11.13
Comma list: 729/728, 19773/19712, 718848/717409


Comma list: 3025/3024, 6250/6237, 2401/2400, 4225/4224
Mapping: [{{val|1 4 16 -1 5}}, {{val|0 -13 -71 24 -7}}]


Mapping: [{{val|1 -13 -14 -9 -8 7}}, {{val|0 84 94 68 66 -19}}]
POTE generator: ~91/80 = 222.9746


POTE generator: ~44/39 = 208.3614
{{Optimal ET sequence|legend=1|70, 113, 183, 296}}


{{Optimal ET sequence|legend=1|23bc, 144, 167, 311}}
Badness: 1.829


Badness: 1.904
== 113 & 709 ==


=== 17-limit ===
Subgroup: 2.3.11.13.17


Subgroup: 2.3.5.7.11.13.17
Comma list: 971074/970299, 2097152/2093663, 60915712/60886809


Comma list: 595/594, 1225/1224, 3025/3024, 2500/2499, 4225/4224
Mapping: [{{val|1 -44 17 -64 42}}, {{val|0 101 -30 150 -84}}]


Mapping: [{{val|1 -13 -14 -9 -8 7 -23}}, {{val|0 84 94 68 66 -19 156}}]
POTE generator: ~33048/24167 = 541.6049


POTE generator: ~44/39 = 208.3624
{{Optimal ET sequence|legend=1|113, 483f, 596f, 709, 822, 935, 1757e}}


{{Optimal ET sequence|legend=1|144g, 167, 311, 1100bef}}
Badness: 3.748


Badness: 1.547
=== 19-limit ===


== 193 & 547 ==
Subgroup: 2.3.11.13.17.19


Subgroup: 2.3.5.7
Comma list: 2432/2431, 278528/278179, 793152/793117, 68054272/68049963


Comma list: 589824/588245, 23066015625/23018340352
Mapping: [{{val|1 -44 17 -64 42 -12}}, {{val|0 101 -30 150 -84 36}}]


Mapping: [{{val|1 0 4 2}}, {{val|0 51 -54 26}}]
POTE generator: ~4199/3072 = 541.6049


POTE generator: ~49/48 = 37.2913
{{Optimal ET sequence|legend=1|113, 483f, 596f, 709, 822, 935, 1757e}}


{{Optimal ET sequence|legend=1|32, 129, 161, 193, 354, 547, 901d, 1255d}}
Badness: 1.676


Badness: 7.020
=== 31-limit ===


== 193 & 607 ==
Subgroup: 2.3.11.13.17.19.31


Subgroup: 2.3.5.7.11.13
Comma list: 2432/2431, 1024/1023, 25296/25289, 793152/793117, 68054272/68049963


Comma list: 625/624, 3025/3024, 78975/78848, 218700/218491
Mapping: [{{val|1 -44 17 -64 42 -12 37}}, {{val|0 101 -30 150 -84 36 -71}}]


Mapping: [{{val|1 26 2 42 60 -22}}, {{val|0 -76 1 -122 -176 80}}
POTE generator: ~4199/3072 = 541.6055


POTE generator: ~5/4 = 385.5044
{{Optimal ET sequence|legend=1|113, 483f, 596f, 709, 822k}}


{{Optimal ET sequence|legend=1|193, 414, 607, 1021c}}
Badness: 1.718


Badness: 2.529
=== 37-limit ===


=== 17-limit ===
Subgroup: 2.3.11.13.17.19.31.37


Subgroup: 2.3.5.7.11.13.17
Comma list: 2432/2431, 1024/1023, 3553/3552, 25296/25289, 793152/793117, 681472/681207


Comma list: 625/624, 1225/1224, 3025/3024, 78975/78848, 5832/5831
Mapping: [{{val|1 -44 17 -64 42 -12 37 86}}, {{val|0 101 -30 150 -84 36 -71 -179}}]


Mapping: [{{val|1 26 2 42 60 -22 33}}, {{val|0 -76 1 -122 -176 80 -90}}
POTE generator: ~4199/3072 = 541.6062


POTE generator: ~5/4 = 385.5044
{{Optimal ET sequence|legend=1|113, 483f, 596f, 709, 822kl}}


{{Optimal ET sequence|legend=1|193, 414, 607, 1021c}}
Badness: 1.939


Badness: 1.693
== 137 & 349 ==


=== 19-limit ===
Subgroup: 2.3.5.11.13


Subgroup: 2.3.5.7.11.13.17.19
Comma list: 625/624, 41067/40960, 528125/527076


Comma list: 625/624, 1225/1224, 3025/3024, 1729/1728, 6669/6664, 26775/26752
Mapping: [{{val|1 -7 6 24 27}}, {{val|0 28 -12 -67 -76}}]


Mapping: [{{val|1 26 2 42 60 -22 33 64}}, {{val|0 -76 1 -122 -176 80 -90 -186}}]
POTE generator: ~99/80 = 367.9050


POTE generator: ~5/4 = 385.5037
{{Optimal ET sequence|legend=1|62ef, 75f, 137, 212, 349, 835cef, 1184bcceff}}


{{Optimal ET sequence|legend=1|193, 414h, 607, 1021chh}}
Badness: 2.198


Badness: 1.618
== 167 & 311 ==


== 193 & 653 ==
Subgroup: 2.3.5.7.11.13


Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 3025/3024, 6250/6237, 2401/2400, 4225/4224


Comma list: 1225/1224, 1540/1539, 3025/3024, 1729/1728, 2025/2024, 3520/3519, 1521/1520
Mapping: [{{val|1 -13 -14 -9 -8 7}}, {{val|0 84 94 68 66 -19}}]


Mapping: [{{val|1 -18 16 -46 -64 18 -27 -20 21}}, {{val|0 63 -44 157 217 -46 100 78 -53}}]
POTE generator: ~44/39 = 208.3614


POTE generator: ~243/196 = 373.0467
{{Optimal ET sequence|legend=1|23bc, 144, 167, 311}}


Badness: 1.271
Badness: 1.904


=== 29-limit ===
=== 17-limit ===


Subgroup: 2.3.5.7.11.13.17.19.23.29
Subgroup: 2.3.5.7.11.13.17


Comma list: 1225/1224, 1540/1539, 3025/3024, 1729/1728, 2025/2024, 3520/3519, 1521/1520, 2205/2204
Comma list: 595/594, 1225/1224, 3025/3024, 2500/2499, 4225/4224


Mapping: [{{val|1 -18 16 -46 -64 18 -27 -20 21 -94}}, {{val|0 63 -44 157 217 -46 100 78 -53 318}}]
Mapping: [{{val|1 -13 -14 -9 -8 7 -23}}, {{val|0 84 94 68 66 -19 156}}]


POTE generator: ~243/196 = 373.0471
POTE generator: ~44/39 = 208.3624


Badness: 1.364
{{Optimal ET sequence|legend=1|144g, 167, 311, 1100bef}}


== 233 & 317 ==
Badness: 1.547


Subgroup: 2.5.7.11
== 193 & 547 ==


Comma list: 537109375/536870912, 40353607/40262750
Subgroup: 2.3.5.7


Mapping: [{{val|1 -1 22 40}}, {{val|0 9 -52 -99}}]
Comma list: 589824/588245, 23066015625/23018340352


POTE generator: ~15488/12005 = 442.9148
Mapping: [{{val|1 0 4 2}}, {{val|0 51 -54 26}}]


{{Optimal ET sequence|legend=1|65e, 84, 149, 233, 783, 1016, 1249, 1482}}
POTE generator: ~49/48 = 37.2913


Badness: 3.492
{{Optimal ET sequence|legend=1|32, 129, 161, 193, 354, 547, 901d, 1255d}}


=== 13-limit ===
Badness: 7.020


Subgroup: 2.5.7.11.13
== 193 & 607 ==


Comma list: 75712/75625, 10985/10976, 5462275/5451776
Subgroup: 2.3.5.7.11.13


Mapping: [{{val|1 -1 22 40 24}}, {{val|0 9 -52 -99 -55}}]
Comma list: 625/624, 3025/3024, 78975/78848, 218700/218491


POTE generator: ~455/352 = 442.9140
Mapping: [{{val|1 26 2 42 60 -22}}, {{val|0 -76 1 -122 -176 80}}


{{Optimal ET sequence|legend=1|65ef, 84, 149, 233, 783, 1016f, 1249f}}
POTE generator: ~5/4 = 385.5044


Badness: 1.410
{{Optimal ET sequence|legend=1|193, 414, 607, 1021c}}


== 233 & 659 ==
Badness: 2.529


Subgroup: 2.5.7.11.13.17
=== 17-limit ===


Comma list: 6656/6655, 105644/105625, 557375/557056, 22578125/22550528
Subgroup: 2.3.5.7.11.13.17


Mapping: [{{val|1 -10 30 40 101 146}}, {{val|0 29 -64 -86 -229 -334}}]
Comma list: 625/624, 1225/1224, 3025/3024, 78975/78848, 5832/5831


POTE generator: ~325/242 = 509.8664
Mapping: [{{val|1 26 2 42 60 -22 33}}, {{val|0 -76 1 -122 -176 80 -90}}


{{Optimal ET sequence|legend=1|193fgg, 233, 659, 892, 1125}}
POTE generator: ~5/4 = 385.5044


Badness: 2.422
{{Optimal ET sequence|legend=1|193, 414, 607, 1021c}}


=== 23-limit ===
Badness: 1.693


Subgroup: 2.5.7.11.13.17.23
=== 19-limit ===


Comma list: 5635/5632, 25025/25024, 6656/6655, 105644/105625, 50575/50531
Subgroup: 2.3.5.7.11.13.17.19


Mapping: [{{val|1 -10 30 40 101 146 -1}}, {{val|0 29 -64 -86 -229 -334 13}}]
Comma list: 625/624, 1225/1224, 3025/3024, 1729/1728, 6669/6664, 26775/26752


POTE generator: ~1375/1024 = 509.8663
Mapping: [{{val|1 26 2 42 60 -22 33 64}}, {{val|0 -76 1 -122 -176 80 -90 -186}}]


{{Optimal ET sequence|legend=1|233, 659, 892, 1125, 2017}}
POTE generator: ~5/4 = 385.5037


Badness: 1.679
{{Optimal ET sequence|legend=1|193, 414h, 607, 1021chh}}


=== 31-limit ===
Badness: 1.618


Subgroup: 2.5.7.11.13.17.23.31
== 193 & 653 ==


Comma list: 5635/5632, 25025/25024, 6656/6655, 3875/3872, 105644/105625, 180625/180544
Subgroup: 2.3.5.7.11.13.17.19.23


Mapping: [{{val|1 -10 30 40 101 146 -1 115}}, {{val|0 29 -64 -86 -229 -334 13 -259}}]
Comma list: 1225/1224, 1540/1539, 3025/3024, 1729/1728, 2025/2024, 3520/3519, 1521/1520


POTE generator: ~1375/1024 = 509.8661
Mapping: [{{val|1 -18 16 -46 -64 18 -27 -20 21}}, {{val|0 63 -44 157 217 -46 100 78 -53}}]


{{Optimal ET sequence|legend=1|233, 659, 892, 1125, 2017k}}
POTE generator: ~243/196 = 373.0467


Badness: 1.405
Badness: 1.271


=== 37-limit ===
=== 29-limit ===


Subgroup: 2.5.7.11.13.17.23.31.37
Subgroup: 2.3.5.7.11.13.17.19.23.29


Comma list: 5635/5632, 25025/25024, 6656/6655, 3875/3872, 1925/1924, 105644/105625, 50575/50531
Comma list: 1225/1224, 1540/1539, 3025/3024, 1729/1728, 2025/2024, 3520/3519, 1521/1520, 2205/2204


Mapping: [{{val|1 -10 30 40 101 146 -1 115 -53}}, {{val|0 29 -64 -86 -229 -334 13 -259 137}}]
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: ~1375/1024 = 509.8657
POTE generator: ~243/196 = 373.0471


{{Optimal ET sequence|legend=1|233, 659, 892}}
Badness: 1.364


Badness: 1.535
== 233 & 317 ==


== 239 & 569 ==
Subgroup: 2.5.7.11


Subgroup: 2.3.5.7
Comma list: 537109375/536870912, 40353607/40262750


Comma list: 823543/820125, 68359375/68024448
Mapping: [{{val|1 -1 22 40}}, {{val|0 9 -52 -99}}]


Mapping: [{{val|1 8 9 13}}, {{val|0 -73 -76 -116}}]
POTE generator: ~15488/12005 = 442.9148


POTE generator: ~729/686 = 105.4479
{{Optimal ET sequence|legend=1|65e, 84, 149, 233, 783, 1016, 1249, 1482}}


{{Optimal ET sequence|legend=1|34bcdd, 57bcd, 91, 148d, 239, 330, 569}}
Badness: 3.492


Badness: 8.274
=== 13-limit ===


=== 11-limit ===
Subgroup: 2.5.7.11.13


Subgroup: 2.3.5.7.11
Comma list: 75712/75625, 10985/10976, 5462275/5451776


Comma list: 42875/42768, 42592/42525, 151263/151250
Mapping: [{{val|1 -1 22 40 24}}, {{val|0 9 -52 -99 -55}}]


Mapping: [{{val|1 8 9 13 22}}, {{val|0 -73 -76 -116 -211}}]
POTE generator: ~455/352 = 442.9140


POTE generator: ~729/686 = 105.4456
{{Optimal ET sequence|legend=1|65ef, 84, 149, 233, 783, 1016f, 1249f}}


{{Optimal ET sequence|legend=1|57bcdeee, 91e, 148dee, 239, 569, 808}}
Badness: 1.410


Badness: 3.518
== 233 & 659 ==


== 239 & 683 ==
Subgroup: 2.5.7.11.13.17


Subgroup: 2.5.11.17.23.29
Comma list: 6656/6655, 105644/105625, 557375/557056, 22578125/22550528


Comma list: 69632/69575, 1048576/1047625, 107648/107525, 244338688/244140625
Mapping: [{{val|1 -10 30 40 101 146}}, {{val|0 29 -64 -86 -229 -334}}]


Mapping: [{{val|1 2 1 4 10 6}}, {{val|0 11 84 3 -187 -39}}]
POTE generator: ~325/242 = 509.8664


POTE generator: ~638/625 = 35.1399
{{Optimal ET sequence|legend=1|193fgg, 233, 659, 892, 1125}}


{{Optimal ET sequence|legend=1|205i, 239, 444i, 683, 1605egi}}
Badness: 2.422


Badness: 1.628
=== 23-limit ===


=== 31-limit ===
Subgroup: 2.5.7.11.13.17.23


Subgroup: 2.5.11.17.23.29.31
Comma list: 5635/5632, 25025/25024, 6656/6655, 105644/105625, 50575/50531


Comma list: 69632/69575, 5800/5797, 14384/14375, 1048576/1047625, 12111616/12109375
Mapping: [{{val|1 -10 30 40 101 146 -1}}, {{val|0 29 -64 -86 -229 -334 13}}]


Mapping: [{{val|1 2 1 4 10 6 8}}, {{val|0 11 84 3 -187 -39 -104}}]
POTE generator: ~1375/1024 = 509.8663


POTE generator: ~253/248 = 35.1400
{{Optimal ET sequence|legend=1|233, 659, 892, 1125, 2017}}


{{Optimal ET sequence|legend=1|205i, 239, 444i, 683, 1605egik}}
Badness: 1.679


Badness: 1.106
=== 31-limit ===


=== 37-limit ===
Subgroup: 2.5.7.11.13.17.23.31


Subgroup: 2.5.11.17.23.29.31.37
Comma list: 5635/5632, 25025/25024, 6656/6655, 3875/3872, 105644/105625, 180625/180544


Comma list: 69632/69575, 5800/5797, 14384/14375, 4625/4624, 1048576/1047625, 1647536/1646875
Mapping: [{{val|1 -10 30 40 101 146 -1 115}}, {{val|0 29 -64 -86 -229 -334 13 -259}}]


Mapping: [{{val|1 2 1 4 10 6 8 6}}, {{val|0 11 84 3 -187 -39 -104 -27}}]
POTE generator: ~1375/1024 = 509.8661


POTE generator: 253/248 = 35.1400
{{Optimal ET sequence|legend=1|233, 659, 892, 1125, 2017k}}


{{Optimal ET sequence|legend=1|205i, 239, 444i, 683, 1605egik}}
Badness: 1.405


Badness: 0.988
=== 37-limit ===


== 239 & 1063 ==
Subgroup: 2.5.7.11.13.17.23.31.37


Subgroup: 2.3.5.7.11
Comma list: 5635/5632, 25025/25024, 6656/6655, 3875/3872, 1925/1924, 105644/105625, 50575/50531


Comma list: 2401/2400, 1953125/1951488, 322102/321489
Mapping: [{{val|1 -10 30 40 101 146 -1 115 -53}}, {{val|0 29 -64 -86 -229 -334 13 -259 137}}]


Mapping: [{{val|1 47 34 30 87}}, {{val|0 -162 -113 -97 -298}}]
POTE generator: ~1375/1024 = 509.8657


POTE generator: ~175/144 = 336.4071
{{Optimal ET sequence|legend=1|233, 659, 892}}


{{Optimal ET sequence|legend=1|107bee, 239, 585e, 824e, 1887e}}
Badness: 1.535


Badness: 4.796
== 239 & 569 ==


== 277 & 641 ==
Subgroup: 2.3.5.7


Subgroup: 2.3.5
Comma list: 823543/820125, 68359375/68024448


Comma list: {{monzo|-56 -13 33}}
Mapping: [{{val|1 8 9 13}}, {{val|0 -73 -76 -116}}]


Mapping: [{{val|1 16 8}}, {{val|0 -33 -13}}]
POTE generator: ~729/686 = 105.4479


POTE generator: ~3125/2304 = 524.1873
{{Optimal ET sequence|legend=1|34bcdd, 57bcd, 91, 148d, 239, 330, 569}}


{{Optimal ET sequence|legend=1|16, 55b, 71, 87, 190, 277}}
Badness: 8.274


Badness: 28.283
=== 11-limit ===


== Focus (307 & 743) ==
Subgroup: 2.3.5.7.11


Subgroup: 2.5.7.11.13.17
Comma list: 42875/42768, 42592/42525, 151263/151250


Comma list: 140800/140777, 40898/40817, 102487/102400, 184960/184877
Mapping: [{{val|1 8 9 13 22}}, {{val|0 -73 -76 -116 -211}}]


Mapping: [{{val|1 -69 -22 -26 -37 -37}}, {{val|0 184 64 76 105 106}}]
POTE generator: ~729/686 = 105.4456


POTE generator: ~17/13 = 465.1430
{{Optimal ET sequence|legend=1|57bcdeee, 91e, 148dee, 239, 569, 808}}


{{Optimal ET sequence|legend=1|129c, 178c, 307, 743, 1050}}
Badness: 3.518


Badness: 2.436
== 239 & 683 ==


=== 19-limit ===
Subgroup: 2.5.11.17.23.29


Subgroup: 2.5.7.11.13.17.19
Comma list: 69632/69575, 1048576/1047625, 107648/107525, 244338688/244140625


Comma list: 10241/10240, 1331/1330, 140800/140777, 64220/64141, 5491/5488
Mapping: [{{val|1 2 1 4 10 6}}, {{val|0 11 84 3 -187 -39}}]


Mapping: [{{val|1 -69 -22 -26 -37 -37 12}}, {{val|0 184 64 76 105 106 -20}}]
POTE generator: ~638/625 = 35.1399


POTE generator: ~17/13 = 465.1425
{{Optimal ET sequence|legend=1|205i, 239, 444i, 683, 1605egi}}


{{Optimal ET sequence|legend=1|129c, 178c, 307, 743, 1050}}
Badness: 1.628


Badness: 1.878
=== 31-limit ===


=== 23-limit ===
Subgroup: 2.5.11.17.23.29.31


Subgroup: 2.5.7.11.13.17.19.23
Comma list: 69632/69575, 5800/5797, 14384/14375, 1048576/1047625, 12111616/12109375


Comma list: 10241/10240, 140800/140777, 27209/27200, 4807/4802, 31603/31556, 608000/607453
Mapping: [{{val|1 2 1 4 10 6 8}}, {{val|0 11 84 3 -187 -39 -104}}]


Mapping: [{{val|1 -69 -22 -26 -37 -37 12 -73}}, {{val|0 184 64 76 105 106 -20 200}}]
POTE generator: ~253/248 = 35.1400


POTE generator: ~17/13 = 465.1422
{{Optimal ET sequence|legend=1|205i, 239, 444i, 683, 1605egik}}


{{Optimal ET sequence|legend=1|129ci, 307, 743, 1050}}
Badness: 1.106


Badness: 1.538
=== 37-limit ===


== 311 & 379 ==
Subgroup: 2.5.11.17.23.29.31.37


Subgroup: 2.3.5.7
Comma list: 69632/69575, 5800/5797, 14384/14375, 4625/4624, 1048576/1047625, 1647536/1646875


Comma list: 2401/2400, {{monzo|-23 -11 15 2}}
Mapping: [{{val|1 2 1 4 10 6 8 6}}, {{val|0 11 84 3 -187 -39 -104 -27}}]


Mapping: [{{val|1 -5 -2 -1}}, {{val|0 64 42 37}}]
POTE generator: 253/248 = 35.1400


POTE generator: ~78125/72576 = 123.4671
{{Optimal ET sequence|legend=1|205i, 239, 444i, 683, 1605egik}}


{{Optimal ET sequence|legend=1|29bbcd, 39bc, 68, 175, 243, 311, 554, 865, 1419cd}}
Badness: 0.988


Badness: 3.518
== 239 & 1063 ==
 
=== 11-limit ===


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 6250/6237, 2401/2400, 2097152/2096325
Comma list: 2401/2400, 1953125/1951488, 322102/321489


Mapping: [{{val|1 -5 -2 -1 12}}, {{val|0 64 42 37 -83}}]
Mapping: [{{val|1 47 34 30 87}}, {{val|0 -162 -113 -97 -298}}]


POTE generator: ~275/256 = 123.4730
POTE generator: ~175/144 = 336.4071


{{Optimal ET sequence|legend=1|68, 175e, 243, 311}}
{{Optimal ET sequence|legend=1|107bee, 239, 585e, 824e, 1887e}}


Badness: 3.125
Badness: 4.796


== 311 & 503 ==
== 277 & 641 ==


Subgroup: 2.3.5.7
Subgroup: 2.3.5


Comma list: 2401/2400, {{monzo|-95 21 29 -2}}
Comma list: {{monzo|-56 -13 33}}


Mapping: [{{val|1 43 -28 -2}}, {{val|0 -112 82 13}}]
Mapping: [{{val|1 16 8}}, {{val|0 -33 -13}}]


POTE generator: ~18984375/14680064 = 443.7335
POTE generator: ~3125/2304 = 524.1873


{{Optimal ET sequence|legend=1|119, 192, 311, 814, 1125, 3064d, 4189cdd, 5314cdd}}
{{Optimal ET sequence|legend=1|16, 55b, 71, 87, 190, 277}}


Badness: 7.820 
Badness: 28.283


=== 11-limit ===
== Focus (307 & 743) ==


Subgroup: 2.3.5.7.11
Subgroup: 2.5.7.11.13.17


Comma list: 2401/2400, 496125/495616, 100663296/100656875
Comma list: 140800/140777, 40898/40817, 102487/102400, 184960/184877


Mapping: [{{val|1 43 -28 -2 36}}, {{val|0 -112 82 13 -88}}]
Mapping: [{{val|1 -69 -22 -26 -37 -37}}, {{val|0 184 64 76 105 106}}]


POTE generator: ~21175/16384 = 443.7337
POTE generator: ~17/13 = 465.1430


{{Optimal ET sequence|legend=1|119, 192, 311, 503, 814, 1125, 1939}}
{{Optimal ET sequence|legend=1|129c, 178c, 307, 743, 1050}}


Badness: 2.599
Badness: 2.436


=== 13-limit ===
=== 19-limit ===


Subgroup: 2.3.5.7.11.13
Subgroup: 2.5.7.11.13.17.19


Comma list: 2401/2400, 4225/4224, 59535/59488, 6656/6655
Comma list: 10241/10240, 1331/1330, 140800/140777, 64220/64141, 5491/5488


Mapping: [{{val|1 43 -28 -2 36 71}}, {{val|0 -112 82 13 -88 -182}}]
Mapping: [{{val|1 -69 -22 -26 -37 -37 12}}, {{val|0 184 64 76 105 106 -20}}]


POTE generator: ~84/65 = 443.7338
POTE generator: ~17/13 = 465.1425


{{Optimal ET sequence|legend=1|119f, 192, 311, 503, 814, 1125, 1939}}
{{Optimal ET sequence|legend=1|129c, 178c, 307, 743, 1050}}


Badness: 1.410
Badness: 1.878
 
 
=== 17-limit ===
=== 23-limit ===
 
 
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.5.7.11.13.17.19.23
 
 
Comma list: 12376/12375, 2401/2400, 14400/14399, 4225/4224, 11016/11011
Comma list: 10241/10240, 140800/140777, 27209/27200, 4807/4802, 31603/31556, 608000/607453
 
 
Mapping: [{{val|1 43 -28 -2 36 71 -34}}, {{val|0 -112 82 13 -88 -182 103}}]
Mapping: [{{val|1 -69 -22 -26 -37 -37 12 -73}}, {{val|0 184 64 76 105 106 -20 200}}]
 
 
POTE generator: ~84/65 = 443.7340
POTE generator: ~17/13 = 465.1422
 
 
{{Optimal ET sequence|legend=1|192, 311, 503, 814, 1939g, 2753dg}}
{{Optimal ET sequence|legend=1|129ci, 307, 743, 1050}}
 
 
Badness: 1.111
Badness: 1.538
 
 
== 311 & 571 ==
== 311 & 379 ==
 
 
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7
 
 
Comma list: 3025/3024, 2401/2400, 294885080956928/294197433834375
Comma list: 2401/2400, {{monzo|-23 -11 15 2}}
 
 
Mapping: [{{val|1 11 -22 -7 37}}, {{val|0 -48 124 50 -171}}]
Mapping: [{{val|1 -5 -2 -1}}, {{val|0 64 42 37}}]
 
 
POTE generator: ~63/55 = 235.3736
POTE generator: ~78125/72576 = 123.4671
 
 
{{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}}
{{Optimal ET sequence|legend=1|29bbcd, 39bc, 68, 175, 243, 311, 554, 865, 1419cd}}
 
 
Badness: 2.441
Badness: 3.518
 
 
=== 13-limit ===
=== 11-limit ===
 
 
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11
 
 
Comma list: 3025/3024, 2401/2400, 47432/47385, 114345/114244
Comma list: 6250/6237, 2401/2400, 2097152/2096325
 
 
Mapping: [{{val|1 11 -22 -7 37 19}}, {{val|0 -48 124 50 -171 -78}}]
Mapping: [{{val|1 -5 -2 -1 12}}, {{val|0 64 42 37 -83}}]
 
 
POTE generator: ~63/55 = 235.3738
POTE generator: ~275/256 = 123.4730
 
 
Badness: 1.528
{{Optimal ET sequence|legend=1|68, 175e, 243, 311}}
 
 
=== 17-limit ===
Badness: 3.125
 
 
Subgroup: 2.3.5.7.11.13.17
== 311 & 503 ==
 
 
Comma list: 2431/2430, 12376/12375, 2601/2600, 8624/8619, 2401/2400
Subgroup: 2.3.5.7
 
 
Mapping: [{{val|1 11 -22 -7 37 19 -22}}, {{val|0 -48 124 50 -171 -78 133}}]
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 & 509 ==
 
Subgroup: 2.3.5.7.11
 
Comma list: 3025/3024, 2401/2400, 7168000/7144929
 
Mapping: [{{val|1 3 6 5 3}}, {{val|0 -40 -104 -62 13}}]
 
POTE generator: ~6400/6237 = 42.4391
 
{{Optimal ET sequence|legend=1|85c, 113, 198, 311, 509, 820}}
 
Badness: 1.926
 
=== 13-limit ===
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 2080/2079, 3025/3024, 4459/4455, 313600/312741
 
Mapping: [{{val|1 3 6 5 3 6}}, {{val|0 -40 -104 -62 13 -65}}]
 
POTE generator: ~40/39 = 42.4391
 
{{Optimal ET sequence|legend=1|85c, 113, 198, 311, 509, 820f}}
 
Badness: 1.168
 
=== 17-limit ===
 
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 2080/2079, 1225/1224, 2431/2430, 2500/2499, 7616/7605
 
POTE generator: ~40/39 = 42.4389
 
{{Optimal ET sequence|legend=1|113g, 198g, 311, 509, 820f}}
 
Badness: 1.357
 
== 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
POTE generator: ~63/55 = 235.3741
Line 2,370: Line 2,550:


Badness: 1.360
Badness: 1.360
== 373 & 509 ==
Subgroup: 2.3.5.7.11.13
Comma list: 3025/3024, 2401/2400, 40656/40625, 140625/140608
Mapping: [{{val|1 51 26 27 66 84}}, {{val|0 -192 -92 -94 -243 -312}}]
POTE generator: ~1183/990 = 308.8441
{{Optimal ET sequence|legend=1|101bbcdeefff, 136ef, 237beff, 373, 882, 2137e}}
Badness: 1.806


== 373 & 727 ==
== 373 & 727 ==
Line 2,468: Line 2,662:


Badness: 94.681
Badness: 94.681
== 1063 & 5113 ==
Subgroup: 2.3.5.7.11
Comma list: 3294225/3294172, 781258401/781250000, 18889465931478580854784/18885534366318662109375
Mapping: [{{val|1 -256 320 338 560}}, {{val|0 853 -1052 -1110 -1843}}]
POTE generator: ~262144/212625 = 362.3704
{{Optimal ET sequence|legend=1|1063, 2987e, 4050, 5113, 9163}}
Badness: 8.800
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