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On this page, I explore some unnamed rank-2 temperaments that catched my interest.
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) ==
== Berkenthin (19 & 239) ==
Line 428: Line 442:


Badness: 2.875
Badness: 2.875
== 31 & 773 ==
Subgroup: 2.3.5.7
Comma list: 2401/2400, {{monzo|60 -3 -25 1}}
Mapping: [{{val|1 49 -3 12}}, {{val|0 -98 11 -19}}]
POTE generator: ~5859375/4194304 = 580.5918
{{Optimal ET sequence|legend=1|31, 556b, 587b, 618, 649, 680, 711, 1453, 3617c}}
Badness: 4.036
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 172032/171875, 820125/819896
Mapping: [{{val|1 49 -3 12 92}}, {{val|0 -98 11 -19 -183}}]
POTE generator: ~7875/5632 = 580.5924
{{Optimal ET sequence|legend=1|31, 618ee, 649e, 680e, 711, 742, 1453, 2195e, 2937e}}
Badness: 1.638


== 31 & 1063 ==
== 31 & 1063 ==
Line 1,171: Line 1,213:
Badness: 40.263
Badness: 40.263


== 53 & 1063 ==
== 53 & 733 ==


Subgroup: 2.3.5
Subgroup: 2.3.5


Comma list: {{monzo|57 -55 13}}
Comma list: {{monzo|42 -47 14}}


Mapping: [{{val|1 6 21}}, {{val|0 -13 -55}}]
Mapping: [{{val|1 0 -3}}, {{val|0 14 47}}]


POTE generator: ~163840000/129140163 = 407.5202
POTE generator: ~64000/59049 = 135.8799


{{Optimal ET sequence|legend=1|50cc, 53, 427c, 480, 533, 586, 639, 692, 745, 798, 851, 2500b, 3351b}}
{{Optimal ET sequence|legend=1| 44c, 53, 415, 468, 521, 574, 627, 680, 733}}


Badness: 22.373
Badness: 18.063
 
== 53 & 1063 ==
 
Subgroup: 2.3.5
 
Comma list: {{monzo|57 -55 13}}
 
Mapping: [{{val|1 6 21}}, {{val|0 -13 -55}}]
 
POTE generator: ~163840000/129140163 = 407.5202
 
{{Optimal ET sequence|legend=1|50cc, 53, 427c, 480, 533, 586, 639, 692, 745, 798, 851, 2500b, 3351b}}
 
Badness: 22.373


== 53 & 1193 ==
== 53 & 1193 ==
Line 1,198: Line 1,254:


Badness: 29.067
Badness: 29.067
== 53 & 1759 ==
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 ==
== 103 & 167 ==
Line 1,348: Line 1,418:


Badness: 1.978
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 ==
== 113 & 409 ==
Line 1,377: Line 1,461:
Badness: 1.829
Badness: 1.829


== 167 & 311 ==
== 113 & 709 ==


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.11.13.17


Comma list: 3025/3024, 6250/6237, 2401/2400, 4225/4224
Comma list: 971074/970299, 2097152/2093663, 60915712/60886809


Mapping: [{{val|1 -13 -14 -9 -8 7}}, {{val|0 84 94 68 66 -19}}]
Mapping: [{{val|1 -44 17 -64 42}}, {{val|0 101 -30 150 -84}}]


POTE generator: ~44/39 = 208.3614
POTE generator: ~33048/24167 = 541.6049


{{Optimal ET sequence|legend=1|23bc, 144, 167, 311}}
{{Optimal ET sequence|legend=1|113, 483f, 596f, 709, 822, 935, 1757e}}


Badness: 1.904
Badness: 3.748


=== 17-limit ===
=== 19-limit ===


Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.11.13.17.19


Comma list: 595/594, 1225/1224, 3025/3024, 2500/2499, 4225/4224
Comma list: 2432/2431, 278528/278179, 793152/793117, 68054272/68049963


Mapping: [{{val|1 -13 -14 -9 -8 7 -23}}, {{val|0 84 94 68 66 -19 156}}]
Mapping: [{{val|1 -44 17 -64 42 -12}}, {{val|0 101 -30 150 -84 36}}]


POTE generator: ~44/39 = 208.3624
POTE generator: ~4199/3072 = 541.6049


{{Optimal ET sequence|legend=1|144g, 167, 311, 1100bef}}
{{Optimal ET sequence|legend=1|113, 483f, 596f, 709, 822, 935, 1757e}}


Badness: 1.547
Badness: 1.676


== 193 & 547 ==
=== 31-limit ===


Subgroup: 2.3.5.7
Subgroup: 2.3.11.13.17.19.31


Comma list: 589824/588245, 23066015625/23018340352
Comma list: 2432/2431, 1024/1023, 25296/25289, 793152/793117, 68054272/68049963


Mapping: [{{val|1 0 4 2}}, {{val|0 51 -54 26}}]
Mapping: [{{val|1 -44 17 -64 42 -12 37}}, {{val|0 101 -30 150 -84 36 -71}}]


POTE generator: ~49/48 = 37.2913
POTE generator: ~4199/3072 = 541.6055


{{Optimal ET sequence|legend=1|32, 129, 161, 193, 354, 547, 901d, 1255d}}
{{Optimal ET sequence|legend=1|113, 483f, 596f, 709, 822k}}


Badness: 7.020
Badness: 1.718


== 193 & 607 ==
=== 37-limit ===


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.11.13.17.19.31.37


Comma list: 625/624, 3025/3024, 78975/78848, 218700/218491
Comma list: 2432/2431, 1024/1023, 3553/3552, 25296/25289, 793152/793117, 681472/681207


Mapping: [{{val|1 26 2 42 60 -22}}, {{val|0 -76 1 -122 -176 80}}
Mapping: [{{val|1 -44 17 -64 42 -12 37 86}}, {{val|0 101 -30 150 -84 36 -71 -179}}]


POTE generator: ~5/4 = 385.5044
POTE generator: ~4199/3072 = 541.6062


{{Optimal ET sequence|legend=1|193, 414, 607, 1021c}}
{{Optimal ET sequence|legend=1|113, 483f, 596f, 709, 822kl}}


Badness: 2.529
Badness: 1.939


=== 17-limit ===
== 167 & 311 ==


Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13


Comma list: 625/624, 1225/1224, 3025/3024, 78975/78848, 5832/5831
Comma list: 3025/3024, 6250/6237, 2401/2400, 4225/4224


Mapping: [{{val|1 26 2 42 60 -22 33}}, {{val|0 -76 1 -122 -176 80 -90}}
Mapping: [{{val|1 -13 -14 -9 -8 7}}, {{val|0 84 94 68 66 -19}}]


POTE generator: ~5/4 = 385.5044
POTE generator: ~44/39 = 208.3614


{{Optimal ET sequence|legend=1|193, 414, 607, 1021c}}
{{Optimal ET sequence|legend=1|23bc, 144, 167, 311}}


Badness: 1.693
Badness: 1.904


=== 19-limit ===
=== 17-limit ===


Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17


Comma list: 625/624, 1225/1224, 3025/3024, 1729/1728, 6669/6664, 26775/26752
Comma list: 595/594, 1225/1224, 3025/3024, 2500/2499, 4225/4224


Mapping: [{{val|1 26 2 42 60 -22 33 64}}, {{val|0 -76 1 -122 -176 80 -90 -186}}]
Mapping: [{{val|1 -13 -14 -9 -8 7 -23}}, {{val|0 84 94 68 66 -19 156}}]


POTE generator: ~5/4 = 385.5037
POTE generator: ~44/39 = 208.3624


{{Optimal ET sequence|legend=1|193, 414h, 607, 1021chh}}
{{Optimal ET sequence|legend=1|144g, 167, 311, 1100bef}}


Badness: 1.618
Badness: 1.547


== 193 & 653 ==
== 193 & 547 ==


Subgroup: 2.3.5.7.11.13.17.19.23
Subgroup: 2.3.5.7


Comma list: 1225/1224, 1540/1539, 3025/3024, 1729/1728, 2025/2024, 3520/3519, 1521/1520
Comma list: 589824/588245, 23066015625/23018340352


Mapping: [{{val|1 -18 16 -46 -64 18 -27 -20 21}}, {{val|0 63 -44 157 217 -46 100 78 -53}}]
Mapping: [{{val|1 0 4 2}}, {{val|0 51 -54 26}}]


POTE generator: ~243/196 = 373.0467
POTE generator: ~49/48 = 37.2913


Badness: 1.271
{{Optimal ET sequence|legend=1|32, 129, 161, 193, 354, 547, 901d, 1255d}}


=== 29-limit ===
Badness: 7.020


Subgroup: 2.3.5.7.11.13.17.19.23.29
== 193 & 607 ==


Comma list: 1225/1224, 1540/1539, 3025/3024, 1729/1728, 2025/2024, 3520/3519, 1521/1520, 2205/2204
Subgroup: 2.3.5.7.11.13


Mapping: [{{val|1 -18 16 -46 -64 18 -27 -20 21 -94}}, {{val|0 63 -44 157 217 -46 100 78 -53 318}}]
Comma list: 625/624, 3025/3024, 78975/78848, 218700/218491


POTE generator: ~243/196 = 373.0471
Mapping: [{{val|1 26 2 42 60 -22}}, {{val|0 -76 1 -122 -176 80}}


Badness: 1.364
POTE generator: ~5/4 = 385.5044


== 233 & 317 ==
{{Optimal ET sequence|legend=1|193, 414, 607, 1021c}}


Subgroup: 2.5.7.11
Badness: 2.529


Comma list: 537109375/536870912, 40353607/40262750
=== 17-limit ===


Mapping: [{{val|1 -1 22 40}}, {{val|0 9 -52 -99}}]
Subgroup: 2.3.5.7.11.13.17


POTE generator: ~15488/12005 = 442.9148
Comma list: 625/624, 1225/1224, 3025/3024, 78975/78848, 5832/5831


{{Optimal ET sequence|legend=1|65e, 84, 149, 233, 783, 1016, 1249, 1482}}
Mapping: [{{val|1 26 2 42 60 -22 33}}, {{val|0 -76 1 -122 -176 80 -90}}


Badness: 3.492
POTE generator: ~5/4 = 385.5044


=== 13-limit ===
{{Optimal ET sequence|legend=1|193, 414, 607, 1021c}}


Subgroup: 2.5.7.11.13
Badness: 1.693


Comma list: 75712/75625, 10985/10976, 5462275/5451776
=== 19-limit ===


Mapping: [{{val|1 -1 22 40 24}}, {{val|0 9 -52 -99 -55}}]
Subgroup: 2.3.5.7.11.13.17.19


POTE generator: ~455/352 = 442.9140
Comma list: 625/624, 1225/1224, 3025/3024, 1729/1728, 6669/6664, 26775/26752


{{Optimal ET sequence|legend=1|65ef, 84, 149, 233, 783, 1016f, 1249f}}
Mapping: [{{val|1 26 2 42 60 -22 33 64}}, {{val|0 -76 1 -122 -176 80 -90 -186}}]


Badness: 1.410
POTE generator: ~5/4 = 385.5037


== 233 & 659 ==
{{Optimal ET sequence|legend=1|193, 414h, 607, 1021chh}}


Subgroup: 2.5.7.11.13.17
Badness: 1.618


Comma list: 6656/6655, 105644/105625, 557375/557056, 22578125/22550528
== 193 & 653 ==


Mapping: [{{val|1 -10 30 40 101 146}}, {{val|0 29 -64 -86 -229 -334}}]
Subgroup: 2.3.5.7.11.13.17.19.23


POTE generator: ~325/242 = 509.8664
Comma list: 1225/1224, 1540/1539, 3025/3024, 1729/1728, 2025/2024, 3520/3519, 1521/1520


{{Optimal ET sequence|legend=1|193fgg, 233, 659, 892, 1125}}
Mapping: [{{val|1 -18 16 -46 -64 18 -27 -20 21}}, {{val|0 63 -44 157 217 -46 100 78 -53}}]


Badness: 2.422
POTE generator: ~243/196 = 373.0467


=== 23-limit ===
Badness: 1.271


Subgroup: 2.5.7.11.13.17.23
=== 29-limit ===


Comma list: 5635/5632, 25025/25024, 6656/6655, 105644/105625, 50575/50531
Subgroup: 2.3.5.7.11.13.17.19.23.29


Mapping: [{{val|1 -10 30 40 101 146 -1}}, {{val|0 29 -64 -86 -229 -334 13}}]
Comma list: 1225/1224, 1540/1539, 3025/3024, 1729/1728, 2025/2024, 3520/3519, 1521/1520, 2205/2204


POTE generator: ~1375/1024 = 509.8663
Mapping: [{{val|1 -18 16 -46 -64 18 -27 -20 21 -94}}, {{val|0 63 -44 157 217 -46 100 78 -53 318}}]


{{Optimal ET sequence|legend=1|233, 659, 892, 1125, 2017}}
POTE generator: ~243/196 = 373.0471


Badness: 1.679
Badness: 1.364


=== 31-limit ===
== 233 & 317 ==


Subgroup: 2.5.7.11.13.17.23.31
Subgroup: 2.5.7.11


Comma list: 5635/5632, 25025/25024, 6656/6655, 3875/3872, 105644/105625, 180625/180544
Comma list: 537109375/536870912, 40353607/40262750


Mapping: [{{val|1 -10 30 40 101 146 -1 115}}, {{val|0 29 -64 -86 -229 -334 13 -259}}]
Mapping: [{{val|1 -1 22 40}}, {{val|0 9 -52 -99}}]


POTE generator: ~1375/1024 = 509.8661
POTE generator: ~15488/12005 = 442.9148


{{Optimal ET sequence|legend=1|233, 659, 892, 1125, 2017k}}
{{Optimal ET sequence|legend=1|65e, 84, 149, 233, 783, 1016, 1249, 1482}}


Badness: 1.405
Badness: 3.492


=== 37-limit ===
=== 13-limit ===


Subgroup: 2.5.7.11.13.17.23.31.37
Subgroup: 2.5.7.11.13


Comma list: 5635/5632, 25025/25024, 6656/6655, 3875/3872, 1925/1924, 105644/105625, 50575/50531
Comma list: 75712/75625, 10985/10976, 5462275/5451776


Mapping: [{{val|1 -10 30 40 101 146 -1 115 -53}}, {{val|0 29 -64 -86 -229 -334 13 -259 137}}]
Mapping: [{{val|1 -1 22 40 24}}, {{val|0 9 -52 -99 -55}}]


POTE generator: ~1375/1024 = 509.8657
POTE generator: ~455/352 = 442.9140


{{Optimal ET sequence|legend=1|233, 659, 892}}
{{Optimal ET sequence|legend=1|65ef, 84, 149, 233, 783, 1016f, 1249f}}


Badness: 1.535
Badness: 1.410


== 239 & 569 ==
== 233 & 659 ==


Subgroup: 2.3.5.7
Subgroup: 2.5.7.11.13.17


Comma list: 823543/820125, 68359375/68024448
Comma list: 6656/6655, 105644/105625, 557375/557056, 22578125/22550528


Mapping: [{{val|1 8 9 13}}, {{val|0 -73 -76 -116}}]
Mapping: [{{val|1 -10 30 40 101 146}}, {{val|0 29 -64 -86 -229 -334}}]


POTE generator: ~729/686 = 105.4479
POTE generator: ~325/242 = 509.8664


{{Optimal ET sequence|legend=1|34bcdd, 57bcd, 91, 148d, 239, 330, 569}}
{{Optimal ET sequence|legend=1|193fgg, 233, 659, 892, 1125}}


Badness: 8.274
Badness: 2.422


=== 11-limit ===
=== 23-limit ===


Subgroup: 2.3.5.7.11
Subgroup: 2.5.7.11.13.17.23


Comma list: 42875/42768, 42592/42525, 151263/151250
Comma list: 5635/5632, 25025/25024, 6656/6655, 105644/105625, 50575/50531


Mapping: [{{val|1 8 9 13 22}}, {{val|0 -73 -76 -116 -211}}]
Mapping: [{{val|1 -10 30 40 101 146 -1}}, {{val|0 29 -64 -86 -229 -334 13}}]


POTE generator: ~729/686 = 105.4456
POTE generator: ~1375/1024 = 509.8663


{{Optimal ET sequence|legend=1|57bcdeee, 91e, 148dee, 239, 569, 808}}
{{Optimal ET sequence|legend=1|233, 659, 892, 1125, 2017}}


Badness: 3.518
Badness: 1.679


== 239 & 683 ==
=== 31-limit ===


Subgroup: 2.5.11.17.23.29
Subgroup: 2.5.7.11.13.17.23.31


Comma list: 69632/69575, 1048576/1047625, 107648/107525, 244338688/244140625
Comma list: 5635/5632, 25025/25024, 6656/6655, 3875/3872, 105644/105625, 180625/180544


Mapping: [{{val|1 2 1 4 10 6}}, {{val|0 11 84 3 -187 -39}}]
Mapping: [{{val|1 -10 30 40 101 146 -1 115}}, {{val|0 29 -64 -86 -229 -334 13 -259}}]


POTE generator: ~638/625 = 35.1399
POTE generator: ~1375/1024 = 509.8661


{{Optimal ET sequence|legend=1|205i, 239, 444i, 683, 1605egi}}
{{Optimal ET sequence|legend=1|233, 659, 892, 1125, 2017k}}


Badness: 1.628
Badness: 1.405


=== 31-limit ===
=== 37-limit ===


Subgroup: 2.5.11.17.23.29.31
Subgroup: 2.5.7.11.13.17.23.31.37


Comma list: 69632/69575, 5800/5797, 14384/14375, 1048576/1047625, 12111616/12109375
Comma list: 5635/5632, 25025/25024, 6656/6655, 3875/3872, 1925/1924, 105644/105625, 50575/50531


Mapping: [{{val|1 2 1 4 10 6 8}}, {{val|0 11 84 3 -187 -39 -104}}]
Mapping: [{{val|1 -10 30 40 101 146 -1 115 -53}}, {{val|0 29 -64 -86 -229 -334 13 -259 137}}]


POTE generator: ~253/248 = 35.1400
POTE generator: ~1375/1024 = 509.8657


{{Optimal ET sequence|legend=1|205i, 239, 444i, 683, 1605egik}}
{{Optimal ET sequence|legend=1|233, 659, 892}}


Badness: 1.106
Badness: 1.535


=== 37-limit ===
== 239 & 569 ==


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: 823543/820125, 68359375/68024448


Mapping: [{{val|1 2 1 4 10 6 8 6}}, {{val|0 11 84 3 -187 -39 -104 -27}}]
Mapping: [{{val|1 8 9 13}}, {{val|0 -73 -76 -116}}]


POTE generator: 253/248 = 35.1400
POTE generator: ~729/686 = 105.4479


{{Optimal ET sequence|legend=1|205i, 239, 444i, 683, 1605egik}}
{{Optimal ET sequence|legend=1|34bcdd, 57bcd, 91, 148d, 239, 330, 569}}


Badness: 0.988
Badness: 8.274


== 239 & 1063 ==
=== 11-limit ===


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 2401/2400, 1953125/1951488, 322102/321489
Comma list: 42875/42768, 42592/42525, 151263/151250


Mapping: [{{val|1 47 34 30 87}}, {{val|0 -162 -113 -97 -298}}]
Mapping: [{{val|1 8 9 13 22}}, {{val|0 -73 -76 -116 -211}}]


POTE generator: ~175/144 = 336.4071
POTE generator: ~729/686 = 105.4456


{{Optimal ET sequence|legend=1|107bee, 239, 585e, 824e, 1887e}}
{{Optimal ET sequence|legend=1|57bcdeee, 91e, 148dee, 239, 569, 808}}


Badness: 4.796
Badness: 3.518


== 277 & 641 ==
== 239 & 683 ==


Subgroup: 2.3.5
Subgroup: 2.5.11.17.23.29


Comma list: {{monzo|-56 -13 33}}
Comma list: 69632/69575, 1048576/1047625, 107648/107525, 244338688/244140625


Mapping: [{{val|1 16 8}}, {{val|0 -33 -13}}]
Mapping: [{{val|1 2 1 4 10 6}}, {{val|0 11 84 3 -187 -39}}]


POTE generator: ~3125/2304 = 524.1873
POTE generator: ~638/625 = 35.1399


{{Optimal ET sequence|legend=1|16, 55b, 71, 87, 190, 277}}
{{Optimal ET sequence|legend=1|205i, 239, 444i, 683, 1605egi}}


Badness: 28.283
Badness: 1.628


== 311 & 379 ==
=== 31-limit ===


Subgroup: 2.3.5.7
Subgroup: 2.5.11.17.23.29.31


Comma list: 2401/2400, {{monzo|-23 -11 15 2}}
Comma list: 69632/69575, 5800/5797, 14384/14375, 1048576/1047625, 12111616/12109375


Mapping: [{{val|1 -5 -2 -1}}, {{val|0 64 42 37}}]
Mapping: [{{val|1 2 1 4 10 6 8}}, {{val|0 11 84 3 -187 -39 -104}}]


POTE generator: ~78125/72576 = 123.4671
POTE generator: ~253/248 = 35.1400


{{Optimal ET sequence|legend=1|29bbcd, 39bc, 68, 175, 243, 311, 554, 865, 1419cd}}
{{Optimal ET sequence|legend=1|205i, 239, 444i, 683, 1605egik}}


Badness: 3.518
Badness: 1.106


=== 11-limit ===
=== 37-limit ===


Subgroup: 2.3.5.7.11
Subgroup: 2.5.11.17.23.29.31.37


Comma list: 6250/6237, 2401/2400, 2097152/2096325
Comma list: 69632/69575, 5800/5797, 14384/14375, 4625/4624, 1048576/1047625, 1647536/1646875


Mapping: [{{val|1 -5 -2 -1 12}}, {{val|0 64 42 37 -83}}]
Mapping: [{{val|1 2 1 4 10 6 8 6}}, {{val|0 11 84 3 -187 -39 -104 -27}}]


POTE generator: ~275/256 = 123.4730
POTE generator: 253/248 = 35.1400


{{Optimal ET sequence|legend=1|68, 175e, 243, 311}}
{{Optimal ET sequence|legend=1|205i, 239, 444i, 683, 1605egik}}


Badness: 3.125
Badness: 0.988


== 311 & 503 ==
== 239 & 1063 ==


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7.11


Comma list: 2401/2400, {{monzo|-95 21 29 -2}}
Comma list: 2401/2400, 1953125/1951488, 322102/321489


Mapping: [{{val|1 43 -28 -2}}, {{val|0 -112 82 13}}]
Mapping: [{{val|1 47 34 30 87}}, {{val|0 -162 -113 -97 -298}}]


POTE generator: ~18984375/14680064 = 443.7335
POTE generator: ~175/144 = 336.4071


{{Optimal ET sequence|legend=1|119, 192, 311, 814, 1125, 3064d, 4189cdd, 5314cdd}}
{{Optimal ET sequence|legend=1|107bee, 239, 585e, 824e, 1887e}}


Badness: 7.820 
Badness: 4.796


=== 11-limit ===
== 277 & 641 ==


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5


Comma list: 2401/2400, 496125/495616, 100663296/100656875
Comma list: {{monzo|-56 -13 33}}


Mapping: [{{val|1 43 -28 -2 36}}, {{val|0 -112 82 13 -88}}]
Mapping: [{{val|1 16 8}}, {{val|0 -33 -13}}]


POTE generator: ~21175/16384 = 443.7337
POTE generator: ~3125/2304 = 524.1873


{{Optimal ET sequence|legend=1|119, 192, 311, 503, 814, 1125, 1939}}
{{Optimal ET sequence|legend=1|16, 55b, 71, 87, 190, 277}}


Badness: 2.599
Badness: 28.283


=== 13-limit ===
== Focus (307 & 743) ==


Subgroup: 2.3.5.7.11.13
Subgroup: 2.5.7.11.13.17


Comma list: 2401/2400, 4225/4224, 59535/59488, 6656/6655
Comma list: 140800/140777, 40898/40817, 102487/102400, 184960/184877


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


POTE generator: ~84/65 = 443.7338
POTE generator: ~17/13 = 465.1430


{{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: 2.436


=== 17-limit ===
=== 19-limit ===


Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.5.7.11.13.17.19


Comma list: 12376/12375, 2401/2400, 14400/14399, 4225/4224, 11016/11011
Comma list: 10241/10240, 1331/1330, 140800/140777, 64220/64141, 5491/5488


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}}, {{val|0 184 64 76 105 106 -20}}]


POTE generator: ~84/65 = 443.7340
POTE generator: ~17/13 = 465.1425


{{Optimal ET sequence|legend=1|192, 311, 503, 814, 1939g, 2753dg}}
{{Optimal ET sequence|legend=1|129c, 178c, 307, 743, 1050}}


Badness: 1.111
Badness: 1.878


== 311 & 571 ==
=== 23-limit ===


Subgroup: 2.3.5.7.11
Subgroup: 2.5.7.11.13.17.19.23


Comma list: 3025/3024, 2401/2400, 294885080956928/294197433834375
Comma list: 10241/10240, 140800/140777, 27209/27200, 4807/4802, 31603/31556, 608000/607453


Mapping: [{{val|1 11 -22 -7 37}}, {{val|0 -48 124 50 -171}}]
Mapping: [{{val|1 -69 -22 -26 -37 -37 12 -73}}, {{val|0 184 64 76 105 106 -20 200}}]


POTE generator: ~63/55 = 235.3736
POTE generator: ~17/13 = 465.1422


{{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|129ci, 307, 743, 1050}}


Badness: 2.441
Badness: 1.538


=== 13-limit ===
== 311 & 379 ==


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7


Comma list: 3025/3024, 2401/2400, 47432/47385, 114345/114244
Comma list: 2401/2400, {{monzo|-23 -11 15 2}}


Mapping: [{{val|1 11 -22 -7 37 19}}, {{val|0 -48 124 50 -171 -78}}]
Mapping: [{{val|1 -5 -2 -1}}, {{val|0 64 42 37}}]


POTE generator: ~63/55 = 235.3738
POTE generator: ~78125/72576 = 123.4671


Badness: 1.528
{{Optimal ET sequence|legend=1|29bbcd, 39bc, 68, 175, 243, 311, 554, 865, 1419cd}}


=== 17-limit ===
Badness: 3.518


Subgroup: 2.3.5.7.11.13.17
=== 11-limit ===


Comma list: 2431/2430, 12376/12375, 2601/2600, 8624/8619, 2401/2400
Subgroup: 2.3.5.7.11


Mapping: [{{val|1 11 -22 -7 37 19 -22}}, {{val|0 -48 124 50 -171 -78 133}}]
Comma list: 6250/6237, 2401/2400, 2097152/2096325


POTE generator: ~63/55 = 235.3741
Mapping: [{{val|1 -5 -2 -1 12}}, {{val|0 64 42 37 -83}}]


{{Optimal ET sequence|legend=1|260, 311, 571, 882}}
POTE generator: ~275/256 = 123.4730


Badness: 1.212
{{Optimal ET sequence|legend=1|68, 175e, 243, 311}}


== Sweepaway (311 & 607) ==
Badness: 3.125


Subgroup: 2.3.5.7.11.13
== 311 & 503 ==


Comma list: 2080/2079, 625/624, 3025/3024, 405769/405504
Subgroup: 2.3.5.7


Mapping: [{{val|1 20 17 -6 12 44}}, {{val|0 -69 -55 33 -32 -151}}]
Comma list: 2401/2400, {{monzo|-95 21 29 -2}}


POTE generator: ~65/54 = 320.2613
Mapping: [{{val|1 43 -28 -2}}, {{val|0 -112 82 13}}]


{{Optimal ET sequence|legend=1|15, 281f, 296, 311, 607, 918c}}
POTE generator: ~18984375/14680064 = 443.7335


Badness: 1.583
{{Optimal ET sequence|legend=1|119, 192, 311, 814, 1125, 3064d, 4189cdd, 5314cdd}}


=== 17-limit ===
Badness: 7.820 


Subgroup: 2.3.5.7.11.13.17
=== 11-limit ===


Comma list: 2080/2079, 625/624, 1225/1224, 3025/3024, 270725/270336
Subgroup: 2.3.5.7.11


Mapping: [{{val|1 20 17 -6 12 44 -21}}, {{val|0 -69 -55 33 -32 -151 94}}]
Comma list: 2401/2400, 496125/495616, 100663296/100656875


POTE generator: ~65/54 = 320.2617
Mapping: [{{val|1 43 -28 -2 36}}, {{val|0 -112 82 13 -88}}]


{{Optimal ET sequence|legend=1|15, 296, 311, 607, 918c}}
POTE generator: ~21175/16384 = 443.7337


Badness: 1.503
{{Optimal ET sequence|legend=1|119, 192, 311, 503, 814, 1125, 1939}}


=== 19-limit ===
Badness: 2.599


Subgroup: 2.3.5.7.11.13.17.19
=== 13-limit ===


Commas: 2080/2079, 625/624, 1225/1224, 3025/3024, 1729/1728, 26775/26752
Subgroup: 2.3.5.7.11.13


Mapping: [{{val|1 20 17 -6 12 44 -21 28}}, {{val|0 -69 -55 33 -32 -151 94 -89}}]
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: ~65/54 = 320.2615
POTE generator: ~84/65 = 443.7338


{{Optimal ET sequence|legend=1|15, 296, 311, 607, 918ch}}
{{Optimal ET sequence|legend=1|119f, 192, 311, 503, 814, 1125, 1939}}


Badness: 1.274
Badness: 1.410


== 311 & 1063 ==
=== 17-limit ===


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7.11.13.17


Comma list: 2401/2400, 3367254360064/3363025078125
Comma list: 12376/12375, 2401/2400, 14400/14399, 4225/4224, 11016/11011


Mapping: [{{val|1 11 -22 -7}}, {{val|0 -24 62 25}}]
Mapping: [{{val|1 43 -28 -2 36 71 -34}}, {{val|0 -112 82 13 -88 -182 103}}]


POTE generator: ~21/16 = 470.7489
POTE generator: ~84/65 = 443.7340


{{Optimal ET sequence|legend=1|51, 79c, 130, 311, 441, 2776, 3217, 3658, 4099, 4540, 4981}}
{{Optimal ET sequence|legend=1|192, 311, 503, 814, 1939g, 2753dg}}


Badness: 1.127
Badness: 1.111


=== 11-limit ===
== 311 & 571 ==


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 2401/2400, 19712/19683, 9453125/9437184
Comma list: 3025/3024, 2401/2400, 294885080956928/294197433834375


Mapping: [{{val|1 11 -22 -7 98}}, {{val|0 -24 62 25 -241}}]
Mapping: [{{val|1 11 -22 -7 37}}, {{val|0 -48 124 50 -171}}]


POTE generator: ~21/16 = 470.7429
POTE generator: ~63/55 = 235.3736


{{Optimal ET sequence|legend=1|130e, 181e, 311, 752, 1063}}
{{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: 4.158
Badness: 2.441


== 311 & 1193 ==
=== 13-limit ===


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7.11.13


Comma list: 2401/2400, {{monzo|36 -16 -7 2}}
Comma list: 3025/3024, 2401/2400, 47432/47385, 114345/114244


Mapping: [{{val|1 11 -22 -7}}, {{val|0 -48 124 50}}]
Mapping: [{{val|1 11 -22 -7 37 19}}, {{val|0 -48 124 50 -171 -78}}]


POTE generator: ~8/7 = 235.3744
POTE generator: ~63/55 = 235.3738


{{Optimal ET sequence|legend=1|51, 79c, 130, 311, 441, 2776, 3217, 3658, 4099, 4540, 4981}}
Badness: 1.528


Badness: 1.127
=== 17-limit ===


=== 11-limit ===
Subgroup: 2.3.5.7.11.13.17


Subgroup: 2.3.5.7.11
Comma list: 2431/2430, 12376/12375, 2601/2600, 8624/8619, 2401/2400


Comma list: 3025/3024, 2401/2400, 3637837299712/3632067084375
Mapping: [{{val|1 11 -22 -7 37 19 -22}}, {{val|0 -48 124 50 -171 -78 133}}]


Mapping: [{{val|1 11 -22 -7 37}}, {{val|0 -48 124 50 -171}}]
POTE generator: ~63/55 = 235.3741


POTE generator: ~55/48 = 235.3736
{{Optimal ET sequence|legend=1|260, 311, 571, 882}}


{{Optimal ET sequence|legend=1|51e, 260, 311, 571, 882, 2075}}
Badness: 1.212


Badness: 2.441
== Sweepaway (311 & 607) ==
 
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
 
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 625/624, 3025/3024, 405769/405504
 
 
Comma list: 3025/3024, 4096/4095, 2401/2400, 492128/492075
Mapping: [{{val|1 20 17 -6 12 44}}, {{val|0 -69 -55 33 -32 -151}}]
 
 
Mapping: [{{val|1 11 -22 -7 37 19}}, {{val|0 -48 124 50 -171 -78}}]
POTE generator: ~65/54 = 320.2613
 
 
POTE generator: ~55/48 = 235.3738
{{Optimal ET sequence|legend=1|15, 281f, 296, 311, 607, 918c}}
 
 
{{Optimal ET sequence|legend=1|51e, 260, 311, 571, 882, 2075f}}
Badness: 1.583
 
 
Badness: 1.528
=== 17-limit ===
 
 
== 379 & 577 ==
Subgroup: 2.3.5.7.11.13.17
 
 
Subgroup: 2.5.7
Comma list: 2080/2079, 625/624, 1225/1224, 3025/3024, 270725/270336
 
 
Comma list: {{monzo|40 -13 25}}
Mapping: [{{val|1 20 17 -6 12 44 -21}}, {{val|0 -69 -55 33 -32 -151 94}}]
 
 
Mapping: [{{val|1 20 12}}, {{val|0 -100 -52}}]
POTE generator: ~65/54 = 320.2617
 
 
POTE generator: ~80/49 = 848.548
{{Optimal ET sequence|legend=1|15, 296, 311, 607, 918c}}
 
 
{{Optimal ET sequence|legend=1|17c, 24c, 41, 99, 140, 239, 379, 1376, 1755, 2134, 6023, 8157, 10291d}}
Badness: 1.503
 
 
Badness: 0.785
=== 19-limit ===
 
 
=== 11-limit ===
Subgroup: 2.3.5.7.11.13.17.19
 
 
Subgroup: 2.5.7.11
Commas: 2080/2079, 625/624, 1225/1224, 3025/3024, 1729/1728, 26775/26752
 
 
Comma list: 102487/102400, {{monzo|28 11 -24 4}}
Mapping: [{{val|1 20 17 -6 12 44 -21 28}}, {{val|0 -69 -55 33 -32 -151 94 -89}}]
 
 
Mapping: [{{val|1 20 12 10}}, {{val|0 -100 -52 -37}}]
POTE generator: ~65/54 = 320.2615
 
 
POTE generator: ~133100/117649 = 212.1377
{{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}}
{{Optimal ET sequence|legend=1|17c, 164c, 181, 198, 379}}
Line 1,958: Line 2,300:


Badness: 1.045
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
Retrieved from "https://en.xen.wiki/w/User:Francium/Miscellaneous_rank-2_temperaments"