User:Francium/Miscellaneous rank-2 temperaments: Difference between revisions
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Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
Comma list: [[2401/2400]], {{monzo|40 -27 0 1 | Comma list: [[2401/2400]], {{monzo|40 -27 0 1}} | ||
Mapping: [{{val|1 1 -29 -13}}, {{val|0 2 107 54}}] | Mapping: [{{val|1 1 -29 -13}}, {{val|0 2 107 54}}] | ||
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Badness: 6.884 | Badness: 6.884 | ||
==41 & 523== | |||
(better known as 41 & 441) | |||
Subgroup: 2.3.5.7 | |||
Comma list: 2401/2400, {{monzo|35 -23 -3 3}} | |||
Mapping: [{{val|1 1 11 7}}, {{val|0 6 -89 -43}}] | |||
POTE generator: ~15/14 = 117.006 | |||
{{Optimal ET sequence|legend=1|41, 236cc, 277c, 318c, 359, 400, 441}} | |||
Badness: 1.383 | |||
===11-limit=== | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 2401/2400, 19712/19683, 166375/165888 | |||
Mapping: [{{val|1 1 11 7 -6}}, {{val|0 6 -89 -43 97}}] | |||
POTE generator: ~77/72 = 117.025 | |||
{{Optimal ET sequence|legend=1|41, 400e, 441e, 482, 1487cdee}} | |||
Badness: 3.127 | |||
==53 & 307== | ==53 & 307== | ||
Revision as of 08:26, 21 November 2023
In this page I explore some unnamed rank-2 temperaments, that catched my interest.
19 & 251
Subgroup: 2.3.5
Comma list: [22 33 -32⟩
Mapping: [⟨1 10 11], ⟨0 -32 -33]]
POTE generator: ~6/5 = 315.5643
Optimal ET sequence: 19, 156bc, 175bc, 194bc, 213, 232, 251, 270, 289, 559, 1407, 1966, 2525, 10659c
Badness: 2.830
7-limit
Subgroup: 2.3.5.7
Comma list: 4375/4374, 7710244864/7688671875
Mapping: [⟨1 10 11 27], ⟨0 -32 -33 -92]]
POTE generator: ~6/5 = 315.5565
Badness: 1.422
31 & 317
Subgroup: 2.5.7
Comma list: 281484423828125/281474976710656
Mapping: [⟨1 0 6], ⟨0 8 -11]]
POTE generator: ~49/40 = 348.2889
Optimal ET sequence: 7, 24, 31, 224, 255, 286, 317, 348, 379, 410, 789, 6691, 7480, 8269, 9058, 9847, 10636
Badness: 0.015
11-limit
Subgroup: 2.5.7.11
Comma list: 5767168/5764801, 537109375/536870912
Mapping: [⟨1 0 6 29], ⟨0 8 -11 -88]]
POTE generator: ~11/9 = 348.2809
Optimal ET sequence: 31, 255e, 286e, 317, 348, 379, 727, 3287, 4014, 4741, 5468
Badness: 0.811
31 & 449
Subgroup: 2.3.5.7
Comma list: 6144/6125, [-4 -5 -13 15⟩, [7 -4 -16 13⟩, [15 6 10 -17⟩
Mapping: [⟨1 -3 2 1], ⟨0 71 5 28]]
POTE generator: ~256/245 = 77.498
Optimal ET sequence: 31, 294bbd, 325bd, 356bd, 387bd, 418d, 449, 480, 991cd
Badness: 8.502
41 & 337
(better described as 41 & 255)
Subgroup: 2.3.5.7
Comma list: 16875/16807, 5250987/5242880, 7381125/7340032, [20 -4 5 -9⟩
Mapping: [⟨1 4 -8 -4], ⟨0 -11 47 31]]
POTE generator: ~7/6 = 263.5183
Optimal ET sequence: 41, 173, 214, 255, 296, 551, 847c
Badness: 3.414
41 & 509
Subgroup: 2.3.5.7
Comma list: 2401/2400, [40 -27 0 1⟩
Mapping: [⟨1 1 -29 -13], ⟨0 2 107 54]]
POTE generator: ~49/40 = 351.278
Optimal ET sequence: 41, 263ccd, 304ccd, 345c, 386c, 427c, 468, 509, 1486bc
Badness: 6.884
41 & 523
(better known as 41 & 441)
Subgroup: 2.3.5.7
Comma list: 2401/2400, [35 -23 -3 3⟩
Mapping: [⟨1 1 11 7], ⟨0 6 -89 -43]]
POTE generator: ~15/14 = 117.006
Optimal ET sequence: 41, 236cc, 277c, 318c, 359, 400, 441
Badness: 1.383
11-limit
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 19712/19683, 166375/165888
Mapping: [⟨1 1 11 7 -6], ⟨0 6 -89 -43 97]]
POTE generator: ~77/72 = 117.025
Optimal ET sequence: 41, 400e, 441e, 482, 1487cdee
Badness: 3.127
53 & 307
Subgroup: 2.9.5
Comma list: 32805/32768
Mapping: [⟨1 0 15], ⟨0 7 -28]]
POTE generator: ~512/375 = 543.3531
Optimal ET sequence: 6, 29, 35, 41, 47, 53, 59, 171, 230, 519, 749
Badness: 0.100