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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.


==Berkenthin (19 & 239)==
== 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) ==


Subgroup: 2.3.5
Subgroup: 2.3.5
Line 15: Line 29:
Badness: 19.828
Badness: 19.828


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


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 29: Line 43:
Badness: 3.566
Badness: 3.566


==19 & 251==
== Totziens (19 & 251) ==


Subgroup: 2.3.5
Subgroup: 2.3.5
Line 43: Line 57:
Badness: 2.830
Badness: 2.830


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


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 57: Line 71:
Badness: 1.422
Badness: 1.422


==19 & 349==
== Denjoy (19 & 349) ==


Subgroup: 2.3.5
Subgroup: 2.3.5
Line 71: Line 85:
Badness: 40.121
Badness: 40.121


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


Subgroup: 2.3.5.11
Subgroup: 2.3.5.11
Line 85: Line 99:
Badness: 12.504
Badness: 12.504


==19 & 563==
== Brzezinska (19 & 563) ==


Subgroup: 2.3.5
Subgroup: 2.3.5
Line 99: Line 113:
Badness: 49.390
Badness: 49.390


== 29 & 227 ==
== Greensleeves (19 & 631) ==
 
Subgroup: 2.3.5
 
Comma list: {{monzo|-50 -71 70}}
 
Mapping: [{{val|1 20 21}}, {{val|0 -70 -71}}]
 
POTE generator: ~6/5 = 315.6862
 
{{Optimal ET sequence|legend=1|19, 403bbcc, 422bbcc, 441bbcc, 460bc, 479bc, 498bc, 517bc, 536, 555, 574, 593, 612}}
 
Badness: 17.150
 
=== 7-limit ===
 
Subgroup: 2.3.5.7
 
Comma list: 4375/4374, {{monzo|37 -20 -18 13}}
 
Mapping: [{{val|1 20 21 57}}, {{val|0 -70 -71 -206}}]
 
POTE generator: ~6/5 = 315.6854
 
{{Optimal ET sequence|legend=1|19, 517bcddd, 536dd, 555d, 574d, 593, 612, 1205, 1817, 2429, 4246, 6675}}
 
Badness: 1.798
 
== Wegener (29 & 227) ==


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 223: Line 265:
Badness: 9.862
Badness: 9.862


==31 & 449==
== 31 & 421 ==
 
Subgroup: 2.3.7
 
Comma list: {{monzo|37 5 -16}}
 
Mapping: [{{val|1 -17 -3}}, {{val|0 48 15}}]
 
POTE generator: 464.6264
 
{{Optimal ET sequence|legend=1|25b, 31, 68, 99, 130, 229, 588, 817, 1405d, 2222dd}}
 
Badness: 3.193
 
=== 11-limit ===
 
Subgroup: 2.3.7.11
 
Comma list: 1362944/1361367, {{monzo|13 13 -6 -6}}
 
Mapping: [{{val|1 -17 -3 -31}}, {{val|0 48 15 89}}]
 
POTE generator: ~847/648 = 464.6259
 
Badness: 2.532
 
== Dakshdua (31 & 431) ==
 
Subgroup: 2.3.5.7
 
Comma list: 2401/2400, 8589934592/8544921875
 
Mapping: [{{val|1 19 2 7}}, {{val|0 -54 1 -13}}]
 
POTE generator: ~ 5/4 = 386.9969
 
{{Optimal ET sequence|31, 214b, 245b, 276b, 307, 338, 369, 400, 769, 1169c, 1938cc}}
 
Badness: 3.038
 
=== 11-limit ===
 
Subgroup: 2.3.5.7.11
 
Comma list: 5632/5625, 2401/2400, 46656/46585
 
Mapping: [{{val|1 19 2 7 37}}, {{val|0 -54 1 -13 -104}}]
 
POTE generator: ~5/4 = 386.9992
 
{{Optimal ET sequence|legend=1|31, 276bee, 307e, 338e, 369, 400, 1969ccee}}
 
Badness: 1.372
 
=== 13-limit ===
 
Subgroup: 2.3.5.7.11.13
 
Commas: 1001/1000, 1716/1715, 4096/4095, 75816/75625
 
Mapping: [{{val|1 19 2 7 37 -35}}, {{val|0 -54 1 -13 -104 120}}]
 
POTE generator: ~5/4 = 387.0031
 
{{Optimal ET sequence|legend=1|31, 369, 400, 831}}
 
Badness: 1.798
 
=== 17-limit ===
 
Subgroup: 2.3.5.7.11.13.17
 
Commas: 1001/1000, 936/935, 1377/1375, 1716/1715, 4096/4095
 
Mapping: [{{val|1 19 2 7 37 -35 -33}}, {{val|0 -54 1 -13 -104 120 115}}]
 
POTE generator: ~5/4 = 387.0028
 
{{Optimal ET sequence|legend=1|31, 369, 400, 831}}
 
Badness: 1.515
 
=== 19-limit ===
 
Subgroup: 2.3.5.7.11.13.17.19
 
Commas: 1001/1000, 936/935, 1377/1375, 1716/1715, 2926/2925, 4096/4095
 
Mapping: [{{val|1 19 2 7 37 -35 -33 -38}}, {{val|0 -54 1 -13 -104 120 115 131}}]
 
POTE generator: ~5/4 = 387.0033
 
{{Optimal ET sequence|legend=1|31, 369, 400, 831}}
 
Badness: 1.393
 
== 31 & 449 ==


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 236: Line 374:


Badness: 8.502
Badness: 8.502
== Adriansonka (31 & 569) ==
Subgroup: 2.3.5.7
Comma list: 65625/65536, 678223072849/675000000000
Mapping: [{{val|1 -35 10 1}}, {{val|0 81 -17 4}}]
CTE tuning: ~1875/1372 = 542.0577
{{Optimal ET sequence|legend=1|31, 476b, 507, 538, 569, 600, 631}}
Badness: 7.921
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 42592/42525, 65625/65536, 422576/421875
Mapping: [{{val|1 -35 10 1 -53}}, {{val|0 81 -17 4 125}}]
CTE tuning: ~308/225 = 542.0730
{{Optimal ET sequence|legend=1|31, 476b, 507, 538, 569, 600e}}
Badness: 3.942
== 31 & 577 ==
Subgroup: 2.5.7
Comma list: {{monzo|60 -21 -4}}
Mapping: [{{val|1 4 -6}}, {{val|0 -4 21}}]
CTE tuning: ~21875/16384 = 503.2464
{{Optimal ET sequence|legend=1|12d, 19d, 31, 298, 329, 360, 391, 422, 453, 484, 515, 546, 3307ccdd, 3853cccdd}}
Badness: 5.455
=== 11-limit ===
Comma list: 4302592/4296875, {{monzo|44 -5 -14 2}}
Mapping: [{{val|1 4 -6 -54}}, {{val|0 -4 21 137}}]
CTE tuning: ~21875/16384 = 503.2468
{{Optimal ET sequence|legend=1|31, 391ee, 422ee, 453e, 484e, 515, 546, 2153cde, 2699ccde, 3245ccddee, 3791cccddee}}
Badness: 6.490
== Audreyglende (31 & 677) ==
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 759375/758912, 589824/588245
Mapping: [{{val|1 19 0 9 35}}, {{val|0 -90 12 -32 -163}}]
CTE tuning: ~4320/3773 = 232.1820
{{Optimal ET sequence|legend=1|31, 553bde, 584de, 615, 646, 1323d}}
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 ==
Subgroup: 2.3.5.7
Comma list: 2401/2400, {{monzo|-97 7 37 0}}
Mapping: [{{val|1 35 -4 8}}, {{val|0 -148 28 -23}}]
POTE generator: ~962072674304/823974609375 = 270.9334
{{Optimal ET sequence|legend=1|31, 970b, 1001, 1032, 1063, 1094, 1125}}
Badness: 9.148


== 37 & 307 ==
== 37 & 307 ==
Line 349: Line 597:
Badness: 0.290
Badness: 0.290


==41 & 167==
== 37 & 661 ==
 
Subgroup: 2.5.7.11.13
 
Comma list: 75712/75625, 10985/10976, 3200000/3195731
 
Mapping: [{{val|1 23 32 -1 26}}, {{val|0 -51 -72 11 -55}}]
 
CTE tuning: ~847/640 = 486.5098
 
{{Optimal ET sequence|legend=1|37, 402df, 439, 476, 513, 550, 587, 624}}
 
Badness: 1.129
 
=== 17-limit ===
 
Subgroup: 2.5.7.11.13.17
 
Comma list: 32768/32725, 140800/140777, 286000/285719, 1328125/1328096
 
Mapping: [{{val|1 23 32 -1 26 -62}}, {{val|0 -51 -72 11 -55 163}}]
 
CTE tuning: ~847/640 = 486.4954
 
{{Optimal ET sequence|legend=1|37, 587g, 624, 661, 1285deg}}
 
Badness: 1.843
 
=== 19-limit ===
 
Subgroup: 2.5.7.11.13.17.19
 
Comma list: 3328/3325, 2432/2431, 12103/12100, 10985/10976, 190400/190333
 
Mapping: [{{val|1 23 32 -1 26 -62 -44}}, {{val|0 -51 -72 11 -55 163 119}}]
 
CTE tuning: ~847/640 = 486.4966
 
{{Optimal ET sequence|legend=1|37, 587g, 624, 661, 1285deg}}
 
Badness: 1.391
 
=== 23-limit ===
 
Subgroup: 2.5.7.11.13.17.19.23
 
Comma list: 3328/3325, 2432/2431, 12103/12100, 2300/2299, 36179/36176, 10985/10976
 
Mapping: [{{val|1 23 32 -1 26 -62 -44 -94}}, {{val|0 -51 -72 11 -55 163 119 243}}]
 
CTE tuning: ~847/640 = 486.4987
 
{{Optimal ET sequence|legend=1|37, 587gi, 624, 1285deg}}
 
Badness: 1.474
 
== 41 & 167 ==


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 363: Line 667:
Badness: 2.943
Badness: 2.943


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


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 377: Line 681:
Badness: 1.816
Badness: 1.816


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


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 616: Line 920:
Badness: 4.703
Badness: 4.703


==41 & 509==
== 41 & 463 ==
 
Subgroup: 2.3.5.7
 
Comma list: 4096000/4084101, 359661568/358722675
 
Mapping: [{{val|1 2 -35 -20}}, {{val|0 -1 90 55}}]
 
POTE generator: ~4/3 = 497.6285
 
{{Optimal ET sequence|legend=1|41, 217ccd, 258cd, 299cd, 340c, 381, 422, 885, 1307d, 1729bdd}}
 
Badness: 4.045
 
=== 11-limit ===
 
Subgroup: 2.3.5.7.11
 
Comma list: 3025/3024, 19712/19683, 1296000/1294139
 
Mapping: [{{val|1 2 -35 -20 30}}, {{val|0 -1 90 55 -64}}]
 
POTE generator: ~4/3 = 497.6281
 
{{Optimal ET sequence|legend=1|41, 340c, 381, 422, 885, 1307de}}
 
Badness: 1.883
 
== 41 & 509 ==


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 659: Line 991:
Badness: 3.127
Badness: 3.127


==43 & 233==
== 41 & 571 ==
 
Subgroup: 2.3.5.7
 
Comma list: 2401/2400, {{monzo|50 -31 -4 3}}
 
Mapping: [{{val|1 5 -39 -17}}, {{val|0 -10 121 58}}]
 
POTE generator: ~2657205/2097152 = 409.8044
 
{{Optimal ET sequence|legend=1|41, 407c, 448, 489c, 530, 571, 612, 2407, 3019, 3631d, 4243d}}
 
Badness: 1.987
 
=== 11-limit ===
 
Subgroup: 2.3.5.7.11
 
Comma list: 3025/3024, 2401/2400, 645922816/645700815
 
Mapping: [{{val|1 5 -39 -17 40}}, {{val|0 -10 121 58 -107}}]
 
POTE generator: ~308/243 = 409.8034
 
Badness: 1.291
 
== 41 & 607 ==
 
Subgroup: 2.3.5.7.11.13
 
Comma list: 2080/2079, 3025/3024, 78975/78848, 218700/218491
 
Mapping: [{{val|1 0 15 10 -8 -18}}, {{val|0 13 -104 -59 94 178}}]
 
POTE generator: ~160/147 = 146.2905
 
{{Optimal ET sequence|legend=1|41, 525f, 566}}
 
Badness: 2.398
 
== 41 & 1063 ==
 
Subgroup: 2.3.5.7
 
Comma list: 2401/2400, {{monzo|80 -52 -5 5}}
 
Mapping: [{{val|1 5 -67 -31}}, {{val|0 -10 203 99}}]
 
POTE generator: ~524288/413343 = 409.7856
 
{{Optimal ET sequence|legend=1|41, 776cc, 817c, 858c, 899c, 940, 981, 2984, 3965bc}}
 
Badness: 10.520
 
== 43 & 233 ==


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 673: Line 1,059:
Badness: 1.813
Badness: 1.813


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


Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17
Line 813: Line 1,199:
Badness: 6.432
Badness: 6.432


==103 & 167==
== 53 & 673 ==
 
Subgroup: 2.3.5
 
Comma list: {{monzo|51 -60 19}}
 
Mapping: [{{val|1 -2 -9}}, {{val|0 19 60}}]
 
POTE generator: ~1162261467/1024000000 = 226.4390
 
{{Optimal ET sequence|legend=1|16cc, 37cc, 53, 514c, 567, 620, 673, 726, 779, 832, 885, 938}}
 
Badness: 40.263
 
== 53 & 733 ==
 
Subgroup: 2.3.5
 
Comma list: {{monzo|42 -47 14}}
 
Mapping: [{{val|1 0 -3}}, {{val|0 14 47}}]
 
POTE generator: ~64000/59049 = 135.8799
 
{{Optimal ET sequence|legend=1| 44c, 53, 415, 468, 521, 574, 627, 680, 733}}
 
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 ==
 
Subgroup: 2.3.5
 
Comma list: {{monzo|87 -71 11}}
 
Mapping: [{{val|1 2 5}}, {{val|0 -11 -71}}]
 
POTE generator: ~1638400/1594323 = 45.2622
 
{{Optimal ET sequence|legend=1|26cc, 27cc, 53, 557c, 610c, 663c, 716, 769, 822, 875, 928, 981, 1034, 1087}}
 
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 ==


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 825: Line 1,281:
Badness: 0.662
Badness: 0.662


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


Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17
Line 852: Line 1,308:


Badness: 2.198
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 ==
== 103 & 503 ==
Line 893: Line 1,405:
Badness: 1.402
Badness: 1.402


==113 & 409==
== 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
Subgroup: 2.3.7.11
Line 907: Line 1,447:
Badness: 5.092
Badness: 5.092


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


Subgroup: 2.3.7.11.13
Subgroup: 2.3.7.11.13
Line 921: Line 1,461:
Badness: 1.829
Badness: 1.829


==193 & 547==
== 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
Subgroup: 2.3.5.7
Line 940: Line 1,564:


Comma list: 625/624, 3025/3024, 78975/78848, 218700/218491
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
POTE generator: ~5/4 = 385.5044
Line 952: Line 1,578:


Comma list: 625/624, 1225/1224, 3025/3024, 78975/78848, 5832/5831
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
POTE generator: ~5/4 = 385.5044
Line 964: Line 1,592:


Comma list: 625/624, 1225/1224, 3025/3024, 1729/1728, 6669/6664, 26775/26752
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
POTE generator: ~5/4 = 385.5037
Line 970: Line 1,600:


Badness: 1.618
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 ==
== 233 & 317 ==
Line 998: Line 1,652:


Badness: 1.410
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 ==
== 239 & 569 ==
Line 1,027: Line 1,737:
Badness: 3.518
Badness: 3.518


==311 & 571==
== 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
Subgroup: 2.3.5.7.11
Line 1,041: Line 1,947:
Badness: 2.441
Badness: 2.441


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


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
Line 1,053: Line 1,959:
Badness: 1.528
Badness: 1.528


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


Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17
Line 1,066: Line 1,972:


Badness: 1.212
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 ==
== 311 & 1063 ==
Line 1,094: Line 2,070:


Badness: 4.158
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 ==
== 379 & 577 ==
Line 1,122: Line 2,272:


Badness: 3.762
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
Retrieved from "https://en.xen.wiki/w/User:Francium/Miscellaneous_rank-2_temperaments"