User:Recentlymaterialized/Miscellaneous rank-2 temperaments

27e & 87

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 325/324, 441/440, 1001/1000

Mapping: [⟨3 2 2 4 1 10], ⟨0 5 9 8 17 2]]

TE generators: ~63/50 = 399.995, ~91/80 = 220.689

CTE generators: 1\3, ~91/80 = 220.687

Optimal ET sequence: 27e, 60e, 87 (idk how to calculate this)

Badness (Dirichlet): 1.058

130 & 181

Subgroup: 2.3.5.7.13

Comma list: 2401/2400, 4096/4095, 492128/492075

Mapping: [⟨1 11 -22 -7 19], ⟨0 -24 62 25 -39]]

TE generators: ~2/1 = 1199.973, ~21/16 = 470.739

CTE generators: 2/1, ~21/16 = 470.749

Optimal ET sequence: 130, 441, maybe 571, 1012, sorry idk

Badness (Dirichlet): 0.477

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 1575/1573, 2080/2079, 4096/4095, 4459/4455

Mapping: [⟨1 11 -22 -7 -24 19], ⟨0 -24 62 25 70 -39]]

TE generators: ~2/1 = 1199.939, ~21/16 = 470.722

CTE generators: 2/1, ~21/16 = 470.745

Optimal ET sequence: 130, 311, 441, idk

Badness (Dirichlet): 0.897

Badtone (31 & 67)

Subgroup: 2.3.5.7.11.13

Comma list: 81/80, 144/143, 176/175, 196/195

Mapping: [⟨1 1 0 3 -1 7], ⟨0 3 12 -1 23 -17]]

Generator tunings:

	Weil	Tenney	WE	TE
Optimized			1199.935, 232.627	1199.9460, 232.6297
Constrained			1\1, 232.639	1\1, 232.635
Destretched			1\1, 232.6396	1\1, 232.6401

Optimal ET sequence: 31, 67, 98

Errors (WE): -0.065 ¢, -4.138 ¢, 5.216 ¢, -1.649 ¢, -0.821 ¢, 4.348 ¢

Badness (Dirichlet): 1.523

Worsetone (12f & 67)

Subgroup: 2.3.5.7.11.13

Comma list: 81/80, 176/175, 196/195, 364/363

Mapping: [⟨1 1 0 -10 -14 -19], ⟨0 1 4 22 30 39]]

Generator tunings:

	Weil	Tenney	WE	TE
Optimized			1199.788, 698.355	1199.8021, 698.3632
Constrained			1\1, 698.471	1\1, 698.455
Destretched			1\1, 698.4784	1\1, 698.4784

Optimal ET sequence: 12f, 55f, 67

Errors (WE): −0.21 ¢, −3.81 ¢, +7.11 ¢, −2.89 ¢, +2.3 ¢, −0.65 ¢

Badness (Dirichlet): 2.041

2.3.7.11.13(.17.19).23.31.37.41 subgroup

Comma list: 287/286, 297/296, 364/363, 483/481, 621/616, 3627/3626, 4797/4774, (153/152, 273/272)

Mapping: [⟨1 1 0 -10 -14 -19 (-32 -33) -24 -16 -14 -22], ⟨0 1 4 22 30 39 (62 64) 49 36 33 47]]

Generator tunings (no-17 no-19):

	Weil	Tenney	WE	TE
Optimized			1200.984, 698.956	1200.9879, 698.9583
Constrained			1\1, 698.420	1\1, 698.496
Destretched			1\1, 698.3833	1\1, 698.3833

Optimal ET sequence: 43deff(ggghhh)iiikkllmm, 55f(gh)ilm, 67p, 122(g)ilm

Errors (WE): 0.984 ¢, -2.015 ¢, -1.635 ¢, 3.585 ¢, 0.059 ¢, (-1.174 ¢, 3.197 ¢), -3.048 ¢, 1.635 ¢, 0.427 ¢, 0.220 ¢

Badness (Dirichlet): 1.075 (1.353)

Tripierce (b30 & b39)

Subgroup: 3.5.7.13

Comma list: 245/243, 2197/2187

Badness (Dirichlet): 0.269

Hemitripierce (b39 & b60)

Subgroup: 3.5.7.11.13

Comma list: 245/243, 847/845, 1575/1573

Badness (Dirichlet): 0.447

Tridubhe / Semitripierce (b69 & b78)

Subgroup: 3.5.7.13.17.19

Comma list: 245/243, 325/323, 665/663, 3213/3211

Badness (Dirichlet): 0.484

Hemitridubhe / Hemisemitripierce (b60 & b78)

Subgroup: 3.5.7.11.13.17.19

Comma list: 245/243, 325/323, 665/663, 847/845, 1575/1573

Badness (Dirichlet): 0.950

140 & 441

Subgroup: 2.3.5.7.13.23

Comma list: 2401/2400, 4096/4095, 35000/34983, 140625/140608

Badness (Dirichlet): 0.493

13-limit

Subgroup: 2.3.5.7.11.13.23

Comma list: 1288/1287, 2080/2079, 2401/2400, 4096/4095, 35000/34983

Badness (Dirichlet): 1.010

581 & 742 (weak extension)

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 2401/2400, 3136/3135, 4096/4095, 5985/5984, 12376/12375, 14875/14872

Badness (Dirichlet): 0.767