User:Francium/Miscellaneous rank-2 temperaments: Difference between revisions
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In this page I explore some unnamed rank-2 temperaments, that catched my interest. | In this page I explore some unnamed rank-2 temperaments, that catched my interest. | ||
==19 & 251== | |||
Subgroup: 2.3.5 | |||
Comma list: {{monzo|22 33 -32}} | |||
Mapping: [{{val|1 10 11}}, {{val|0 -32 -33}}] | |||
POTE generator: ~6/5 = 315.5643 | |||
{{Optimal ET sequence|legend=1|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: [{{val|1 10 11 27}}, {{val|0 -32 -33 -92}}] | |||
POTE generator: ~6/5 = 315.5565 | |||
Badness: 1.422 | |||
==31 & 317== | ==31 & 317== | ||
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Comma list: 281484423828125/281474976710656 | Comma list: 281484423828125/281474976710656 | ||
Mapping: [{{val|1 0 6}}, {{val|0 8 -11}} | Mapping: [{{val|1 0 6}}, {{val|0 8 -11}}] | ||
POTE generator: ~49/40 = 348.2889 | POTE generator: ~49/40 = 348.2889 | ||
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Comma list: [[16875/16807]], 5250987/5242880, 7381125/7340032, {{monzo|20 -4 5 -9}} | Comma list: [[16875/16807]], 5250987/5242880, 7381125/7340032, {{monzo|20 -4 5 -9}} | ||
Mapping: [{{val|1 4 -8 -4}}, {{val|0 -11 47 31}} | Mapping: [{{val|1 4 -8 -4}}, {{val|0 -11 47 31}}] | ||
POTE generator: ~7/6 = 263.5183 | POTE generator: ~7/6 = 263.5183 | ||
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Comma list: [[2401/2400]], {{monzo|40 -27 0 1}}, {{monzo|35 -28 -2 5}}, {{monzo| 45 -26 2 -3}} | Comma list: [[2401/2400]], {{monzo|40 -27 0 1}}, {{monzo|35 -28 -2 5}}, {{monzo| 45 -26 2 -3}} | ||
Mapping: [{{val|1 1 -29 -13}}, {{val|0 2 107 54}} | Mapping: [{{val|1 1 -29 -13}}, {{val|0 2 107 54}}] | ||
POTE generator: ~49/40 = 351.278 | POTE generator: ~49/40 = 351.278 | ||
Revision as of 18:24, 11 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
Possible temperament family: Porwell temperaments
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
Possible temperament families: Mirkwai clan, Mitonismic temperaments
41 & 509
Subgroup: 2.3.5.7
Comma list: 2401/2400, [40 -27 0 1⟩, [35 -28 -2 5⟩, [45 -26 2 -3⟩
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
Possible temperament family: Breed temperaments
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
Possible temperament family: Schismatic family