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 & 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