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

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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 182: 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 251: 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 ===
=== 11-limit ===


Subgroup: 2.3.5.7.11
Subgroup: 2.5.7.11


Comma list: 540/539, 5632/5625, 166698/166375
Comma list: 5767168/5764801, 537109375/536870912


Mapping: [{{val|1 -11 2 -3 -23}}, {{val|0 39 1 18 82}}]
Mapping: [{{val|1 0 6 29}}, {{val|0 8 -11 -88}}]


POTE generator: ~5/4 = 387.2309
POTE generator: ~16807/13750 = 348.2809


{{Optimal ET sequence|legend=1|31, 158bee, 189ee, 220e, 251e, 282, 877cdee, 1159cddeee}}
{{Optimal ET sequence|legend=1|31, 255e, 286e, 317, 348, 379, 727, 3287, 4014, 4741, 5468 }}


Badness: 1.518
Badness: 0.811


=== 13-limit ===
== 31 & 367 ==


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5


Comma list: 351/350, 540/539, 4096/4095, 166698/166375
Comma list: {{monzo|-156 12 59}}


Mapping: [{{val|1 -11 2 -3 -23 35}}, {{val|0 39 1 18 82 -97}}]
Mapping: [{{val|1 13 0}}, {{val|0 -59 12}}]


POTE generator: ~5/4 = 387.2169
POTE generator: ~2500/2187 = 232.1720


{{Optimal ET sequence|legend=1|31, 282f, 313, 657d}}
{{Optimal ET sequence|legend=1|31, 305b, 336, 367, 398, 429, 460, 889, 1349}}


Badness: 2.592
Badness: 90.743


== 31 & 317 ==
== 31 & 397 ==


Subgroup: 2.5.7
Subgroup: 2.3.5


Comma list: 281484423828125/281474976710656
Comma list: {{monzo|55 -1 -23}}


Mapping: [{{val|1 0 6}}, {{val|0 8 -11}}]
Mapping: [{{val|1 9 2}}, {{val|0 -46 2}}]


POTE generator: ~262144/214375 = 348.2889
POTE generator: ~4096/3645 = 193.4315


{{Optimal ET sequence|legend=1|7, 24, 31, 224, 255, 286, 317, 348, 379, 410, 789, 6691, 7480, 8269, 9058, 9847, 10636}}
{{Optimal ET sequence|legend=1|28b, 31, 90, 121, 152, 335, 822, 1157c, 1492c, 2649cc}}


Badness: 0.015
Badness: 9.862


=== 11-limit ===
== 31 & 419 ==


Subgroup: 2.5.7.11
Subgroup: 2.3.5.7


Comma list: 5767168/5764801, 537109375/536870912
Comma list: 235298/234375, 2100875/2097152


Mapping: [{{val|1 0 6 29}}, {{val|0 8 -11 -88}}]
Mapping: [{{val|1 5 2 3}}, {{val|0 -53 5 -3}}]


POTE generator: ~16807/13750 = 348.2809
POTE generator: ~256/245 = 77.3224


{{Optimal ET sequence|legend=1|31, 255e, 286e, 317, 348, 379, 727, 3287, 4014, 4741, 5468 }}
{{Optimal ET sequence|legend=1|31, 233b, 264b, 295, 326, 357, 388, 807d}}


Badness: 0.811
Badness: 4.426


== 31 & 367 ==
== 31 & 421 ==


Subgroup: 2.3.5
Subgroup: 2.3.7


Comma list: {{monzo|-156 12 59}}
Comma list: {{monzo|37 5 -16}}


Mapping: [{{val|1 13 0}}, {{val|0 -59 12}}]
Mapping: [{{val|1 -17 -3}}, {{val|0 48 15}}]


POTE generator: ~2500/2187 = 232.1720
POTE generator: 464.6264


{{Optimal ET sequence|legend=1|31, 305b, 336, 367, 398, 429, 460, 889, 1349}}
{{Optimal ET sequence|legend=1|25b, 31, 68, 99, 130, 229, 588, 817, 1405d, 2222dd}}


Badness: 90.743
Badness: 3.193


== 31 & 397 ==
=== 11-limit ===


Subgroup: 2.3.5
Subgroup: 2.3.7.11


Comma list: {{monzo|55 -1 -23}}
Comma list: 1362944/1361367, {{monzo|13 13 -6 -6}}


Mapping: [{{val|1 9 2}}, {{val|0 -46 2}}]
Mapping: [{{val|1 -17 -3 -31}}, {{val|0 48 15 89}}]


POTE generator: ~4096/3645 = 193.4315
POTE generator: ~847/648 = 464.6259


{{Optimal ET sequence|legend=1|28b, 31, 90, 121, 152, 335, 822, 1157c, 1492c, 2649cc}}
Badness: 2.532


Badness: 9.862
== Dakshdua (31 & 431) ==
 
== 31 & 419 ==


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Comma list: 235298/234375, 2100875/2097152
Comma list: 2401/2400, 8589934592/8544921875


Mapping: [{{val|1 5 2 3}}, {{val|0 -53 5 -3}}]
Mapping: [{{val|1 19 2 7}}, {{val|0 -54 1 -13}}]


POTE generator: ~256/245 = 77.3224
POTE generator: ~ 5/4 = 386.9969


{{Optimal ET sequence|legend=1|31, 233b, 264b, 295, 326, 357, 388, 807d}}
{{Optimal ET sequence|31, 214b, 245b, 276b, 307, 338, 369, 400, 769, 1169c, 1938cc}}


Badness: 4.426
Badness: 3.038


== 31 & 421 ==
=== 11-limit ===


Subgroup: 2.3.7
Subgroup: 2.3.5.7.11


Comma list: {{monzo|37 5 -16}}
Comma list: 5632/5625, 2401/2400, 46656/46585


Mapping: [{{val|1 -17 -3}}, {{val|0 48 15}}]
Mapping: [{{val|1 19 2 7 37}}, {{val|0 -54 1 -13 -104}}]


POTE generator: 464.6264
POTE generator: ~5/4 = 386.9992


{{Optimal ET sequence|legend=1|25b, 31, 68, 99, 130, 229, 588, 817, 1405d, 2222dd}}
{{Optimal ET sequence|legend=1|31, 276bee, 307e, 338e, 369, 400, 1969ccee}}


Badness: 3.193
Badness: 1.372


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


Subgroup: 2.3.7.11
Subgroup: 2.3.5.7.11.13


Comma list: 1362944/1361367, {{monzo|13 13 -6 -6}}
Commas: 1001/1000, 1716/1715, 4096/4095, 75816/75625


Mapping: [{{val|1 -17 -3 -31}}, {{val|0 48 15 89}}]
Mapping: [{{val|1 19 2 7 37 -35}}, {{val|0 -54 1 -13 -104 120}}]


POTE generator: ~847/648 = 464.6259
POTE generator: ~5/4 = 387.0031


Badness: 2.532
{{Optimal ET sequence|legend=1|31, 369, 400, 831}}


== Dakshdua (31 & 431) ==
Badness: 1.798


Subgroup: 2.3.5.7
=== 17-limit ===


Comma list: 2401/2400, 8589934592/8544921875
Subgroup: 2.3.5.7.11.13.17


Mapping: [{{val|1 19 2 7}}, {{val|0 -54 1 -13}}]
Commas: 1001/1000, 936/935, 1377/1375, 1716/1715, 4096/4095


POTE generator: ~ 5/4 = 386.9969
Mapping: [{{val|1 19 2 7 37 -35 -33}}, {{val|0 -54 1 -13 -104 120 115}}]


{{Optimal ET sequence|31, 214b, 245b, 276b, 307, 338, 369, 400, 769, 1169c, 1938cc}}
POTE generator: ~5/4 = 387.0028


Badness: 3.038
{{Optimal ET sequence|legend=1|31, 369, 400, 831}}


=== 11-limit ===
Badness: 1.515


Subgroup: 2.3.5.7.11
=== 19-limit ===


Comma list: 5632/5625, 2401/2400, 46656/46585
Subgroup: 2.3.5.7.11.13.17.19


Mapping: [{{val|1 19 2 7 37}}, {{val|0 -54 1 -13 -104}}]
Commas: 1001/1000, 936/935, 1377/1375, 1716/1715, 2926/2925, 4096/4095


POTE generator: ~5/4 = 386.9992
Mapping: [{{val|1 19 2 7 37 -35 -33 -38}}, {{val|0 -54 1 -13 -104 120 115 131}}]


{{Optimal ET sequence|legend=1|31, 276bee, 307e, 338e, 369, 400, 1969ccee}}
POTE generator: ~5/4 = 387.0033


Badness: 1.372
{{Optimal ET sequence|legend=1|31, 369, 400, 831}}


=== 13-limit ===
Badness: 1.393


Subgroup: 2.3.5.7.11.13
== 31 & 449 ==


Commas: 1001/1000, 1716/1715, 4096/4095, 75816/75625
Subgroup: 2.3.5.7


Mapping: [{{val|1 19 2 7 37 -35}}, {{val|0 -54 1 -13 -104 120}}]
Comma list: 6144/6125, {{monzo|7 -4 -16 13}}


POTE generator: ~5/4 = 387.0031
Mapping: [{{val|1 -3 2 1}}, {{val|0 71 5 28}}]


{{Optimal ET sequence|legend=1|31, 369, 400, 831}}
POTE generator: ~256/245 = 77.498


Badness: 1.798
{{Optimal ET sequence|legend=1|31, 294bbd, 325bd, 356bd, 387bd, 418d, 449, 480, 991cd}}


=== 17-limit ===
Badness: 8.502


Subgroup: 2.3.5.7.11.13.17
== 31 & 463 ==


Commas: 1001/1000, 936/935, 1377/1375, 1716/1715, 4096/4095
Subgroup: 2.3.5.7


Mapping: [{{val|1 19 2 7 37 -35 -33}}, {{val|0 -54 1 -13 -104 120 115}}]
Comma list: 703125/702464, 283115520/282475249


POTE generator: ~5/4 = 387.0028
Mapping: [{{val|1 34 -3 12}}, {{val|0 -67 11 -19}}]


{{Optimal ET sequence|legend=1|31, 369, 400, 831}}
POTE tuning: ~480/343 = 580.5677


Badness: 1.515
{{Optimal ET sequence|legend=1|31, 339b, 370b, 401, 432, 463, 494, 1513, 2007d, 2501d}}


=== 19-limit ===
Badness: 3.040


Subgroup: 2.3.5.7.11.13.17.19
=== 11-limit ===


Commas: 1001/1000, 936/935, 1377/1375, 1716/1715, 2926/2925, 4096/4095
Subgroup: 2.3.5.7.11


Mapping: [{{val|1 19 2 7 37 -35 -33 -38}}, {{val|0 -54 1 -13 -104 120 115 131}}]
Comma list: 3025/3024, 759375/758912, 180224/180075
 
Mapping: [{{val|1 34 -3 12 62}}, {{val|0 -67 11 -19 -121}}]


POTE generator: ~5/4 = 387.0033
POTE tuning: ~3773/2700 = 580.5674


{{Optimal ET sequence|legend=1|31, 369, 400, 831}}
{{Optimal ET sequence|legend=1|31, 370bee, 401e, 432e, 463, 494, 2501d}}


Badness: 1.393
Badness: 1.062


== 31 & 449 ==
== 31 & 499 ==


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Comma list: 6144/6125, {{monzo|7 -4 -16 13}}
Comma list: 2401/2400, 3848290697216/3814697265625


Mapping: [{{val|1 -3 2 1}}, {{val|0 71 5 28}}]
Mapping: [{{val|1 -21 2 -3}}, {{val|0 70 1 18}}]


POTE generator: ~256/245 = 77.498
POTE tuning: ~5/4 = 387.1746


{{Optimal ET sequence|legend=1|31, 294bbd, 325bd, 356bd, 387bd, 418d, 449, 480, 991cd}}
{{Optimal ET sequence|legend=1|31, 313b, 344b, 375b, 406b, 437, 468, 499}}


Badness: 8.502
Badness: 6.211


== 31 & 463 ==
== 31 & 523 ==


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Comma list: 703125/702464, 283115520/282475249
Comma list: 2401/2400, 13904571533203125/13792273858822144


Mapping: [{{val|1 34 -3 12}}, {{val|0 -67 11 -19}}]
Mapping: [{{val|1 -17 8 1}}, {{val|0 72 -22 7}}]


POTE tuning: ~480/343 = 580.5677
POTE tuning: ~448/375 = 309.7449


{{Optimal ET sequence|legend=1|31, 339b, 370b, 401, 432, 463, 494, 1513, 2007d, 2501d}}
{{Optimal ET sequence|legend=1|31, 430, 461, 492, 523, 554, 585, 1139cd, 1724ccd}}


Badness: 3.040
Badness: 6.842


=== 11-limit ===
=== 11-limit ===
Line 491: Line 519:
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 3025/3024, 759375/758912, 180224/180075
Comma list: 2401/2400, 496125/495616, 166375/165888


Mapping: [{{val|1 34 -3 12 62}}, {{val|0 -67 11 -19 -121}}]
Mapping: [{{val|1 -17 8 1 -27}}, {{val|0 72 -22 7 118}}]


POTE tuning: ~3773/2700 = 580.5674
POTE tuning: ~448/375 = 309.7469


{{Optimal ET sequence|legend=1|31, 370bee, 401e, 432e, 463, 494, 2501d}}
{{Optimal ET sequence|legend=1|31, 430, 461, 492, 523, 554e}}


Badness: 1.062
Badness: 2,784


== 31 & 499 ==
== Adriansonka (31 & 569) ==
 
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
 
== Adriansonka (31 & 569) ==


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 834: Line 848:


Badness: 1.782
Badness: 1.782
== 41 & 179 ==
Subgroup: 2.3.5.7
Comma list: 10976/10935, 20480000/20253807
Mapping: [{{val|1 4 16 13}}, {{val|0 -9 -51 -38}}]
POTE generator: ~1600/1323 = 321.8267
{{Optimal ET sequence|legend=1|15ccd, 26ccd, 41, 138cd, 179, 220, 481bd, 701bdd}}
Badness: 3.653


== 41 & 197 ==
== 41 & 197 ==
Line 932: 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 1,755: 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: 625/624, 41067/40960, 528125/527076
 
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
Comma list: 3025/3024, 6250/6237, 2401/2400, 4225/4224
Line 2,170: 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 2,454: 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 2,552: 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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