User:Francium/Miscellaneous rank-2 temperaments
In this page I explore some unnamed rank-2 temperaments, that catched my interest.
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
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 & 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