Countercomp family
The countercomp family tempers out the Pythagorean countercomma, [65 -41⟩, and hence the fifths form a closed 41-note circle of fifths, identical to 41edo.
Countercomp
Subgroup: 2.3.5
Comma list: [65 -41⟩
Mapping: [⟨41 65 0], ⟨0 0 1]]
Mapping generators: ~531441/524288, ~5/1
Optimal tuning (POTE): ~531441/524288 = 1\41, ~5/4 = 386.668
Optimal ET sequence: 41, 123, 164, 205, 369, 574, 779, 2132bc
Badness: 0.934310
Gamelacomp
Subgroup: 2.3.5.7
Comma list: 1029/1024, 537824/531441
Mapping: [⟨41 65 0 115], ⟨0 0 1 0]]
Wedgie: ⟨⟨0 41 0 65 0 -115]]
Optimal tuning (POTE): ~64/63 = 1\41, ~5/4 = 385.731
Optimal ET sequence: 41, 123, 164, 205d, 246d, 451dd
Badness: 0.161056
11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 537824/531441
Mapping: [⟨41 65 0 115 237], ⟨0 0 1 0 -1]]
Optimal tuning (POTE): ~56/55 = 1\41, ~5/4 = 385.871
Optimal ET sequence: 41, 123e, 164, 205d, 451dd
Badness: 0.076537
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 385/384, 59150/59049
Mapping: [⟨41 65 0 115 237 247], ⟨0 0 1 0 -1 -1]]
Optimal tuning (POTE): ~56/55 = 1\41, ~5/4 = 386.604
Optimal ET sequence: 41, 123e, 164, 205d
Badness: 0.054921
Mermacomp
Subgroup: 2.3.5.7
Comma list: 5120/5103, 2500000/2470629
Mapping: [⟨41 65 0 20], ⟨0 0 1 1]]
Wedgie: ⟨⟨0 41 41 65 65 -20]]
Optimal tuning (POTE): ~50/49 = 1\41, ~5/4 = 385.667
Optimal ET sequence: 41, 123d, 164d, 205, 246, 451d, 697dd
Badness: 0.142344
11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 5120/5103, 75625/75264
Mapping: [⟨41 65 0 20 237], ⟨0 0 1 1 -1]]
Optimal tuning (POTE): ~55/54 = 1\41, ~5/4 = 385.309
Optimal ET sequence: 41, 164d, 205, 246
Badness: 0.076588
Hemicountercomp
Subgroup: 2.3.5.7
Comma list: 2401/2400, 52613349376/52301766015
Mapping: [⟨41 65 1 68], ⟨0 0 2 1]]
Mapping generators: ~100352/98415, ~567/256
Optimal tuning (CTE): ~100352/98415 = 1\41, ~567/512 = 178.5314 (~5120/5103 = 2.9216)
Optimal ET sequence: 41, …, 328, 369, 779, 1927bc
Badness: 0.134559
Hemicocomp
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 16384/16335, 19712/19683
Mapping: [⟨41 65 1 68 189], ⟨0 0 2 1 -1]]
Optimal tuning (CTE): ~56/55 = 1\41, ~567/512 = 178.6944 (~3025/3024 = 3.0846)
Optimal ET sequence: 41, …, 328, 369, 1066cee
Badness: 0.064400
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 2401/2400, 3584/3575, 10648/10647
Mapping: [⟨41 65 1 68 189 246], ⟨0 0 2 1 -1 -2]]
Optimal tuning (CTE): ~56/55 = 1\41, ~72/65 = 178.9389 (~352/351 = 3.3291)
Optimal ET sequence: 41, …, 328, 369f, 697cef
Badness: 0.0416
Hemermacomp
Subgroup: 2.3.5.7.11
Comma list: 2401/2400, 59290/59049, 131072/130977
Mapping: [⟨41 65 1 68 236], ⟨0 0 2 1 -2]]
Optimal tuning (CTE): ~55/54 = 1\41, ~256/231 = 178.3836 (~3024/3025 = 2.7738)
Optimal ET sequence: 41, …, 410, 451, 861e
Badness: 0.100152
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 2401/2400, 4096/4095, 59290/59049
Mapping: [⟨41 65 1 68 236 293], ⟨0 0 2 1 -2 -3]]
Optimal tuning (CTE): ~55/54 = 1\41, ~72/65 = 178.3755 (~352/351 = 2.7657)
Optimal ET sequence: 41, …, 410, 451, 861e
Badness: 0.0605