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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 904: Line 960:


Badness: 2.034
Badness: 2.034
== 41 & 251 ==
Subgroup: 2.3.5.7
Comma list: 5120/5103, 184528125/184473632
Mapping: [{{val|1 1 -9 -5}}, {{val|0 3 58 40}}]
POTE generator: ~343/300 = 234.2534
{{Optimal ET sequence|legend=1|41, 169cd, 210, 251, 292, 543d}}
Badness: 2.966


== 41 & 313 ==
== 41 & 313 ==
Line 1,101: Line 1,171:


Badness: 1.883
Badness: 1.883
== 41 & 503 ==
Subgroup: 2.3.5.7
Comma list: 2401/2400, 7943330713528125/7881299347898368
Mapping: [{{val|1 -5 40 20}}, {{val|0 18 -103 -47}}]
POTE generator: ~66430125/51380224 = 438.9721
{{Optimal ET sequence|legend=1|41, 380c, 421, 462, 503, 544, 1129d, 1673bcd, 2802bbccdd}}
Badness: 6.307


== 41 & 509 ==
== 41 & 509 ==
Line 1,713: Line 1,797:
Badness: 1.939
Badness: 1.939


== 167 & 311 ==
== 137 & 349 ==


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.11.13


Comma list: 3025/3024, 6250/6237, 2401/2400, 4225/4224
Comma list: 625/624, 41067/40960, 528125/527076


Mapping: [{{val|1 -13 -14 -9 -8 7}}, {{val|0 84 94 68 66 -19}}]
Mapping: [{{val|1 -7 6 24 27}}, {{val|0 28 -12 -67 -76}}]
 
POTE generator: ~99/80 = 367.9050
 
{{Optimal ET sequence|legend=1|62ef, 75f, 137, 212, 349, 835cef, 1184bcceff}}
 
Badness: 2.198
 
== 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
POTE generator: ~44/39 = 208.3614
Line 2,128: Line 2,226:


Badness: 1.111
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 ==
== 311 & 571 ==
Line 2,412: 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 2,510: 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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