Countercomp family

The counterpyth family tempers out counterpyth comma, [65 -41⟩, and hence the fifths form a closed 41-note circle of fifths, identical to 41EDO.

Counterpyth

Subgroup: 2.3.5

Comma list: [65 -41⟩

Mapping: [⟨41 65 0], ⟨0 0 1]]

Mapping generators: ~531441/524288, ~5/1

POTE generator: ~5/4 = 386.668

Badness: 0.934310

Gamelapyth

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 ]]

POTE generator: ~5/4 = 385.731

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]]

POTE generator: ~5/4 = 385.871

Optimal GPV sequence: Template:Val list

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]]

POTE generator: ~5/4 = 386.604

Optimal GPV sequence: Template:Val list

Badness: 0.054921

Mermapyth

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 ]]

POTE generator: ~5/4 = 385.667

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]]

POTE generator: ~5/4 = 385.309

Optimal GPV sequence: Template:Val list

Badness: 0.076588

Hemicounterpyth

Subgroup: 2.3.5.7

Comma list: 2401/2400, 52613349376/52301766015

Mapping: [⟨41 65 1 68], ⟨0 0 2 1]]

Mapping generators: ~531441/524288, ~567/256

POTE generator: ~567/512 = 178.7115

Badness: 0.134559

11-limit

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]]

POTE generator: ~567/512 = 178.9285

Optimal GPV sequence: Template:Val list

Badness: 0.064400

Hemermapyth

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]]

POTE generator: ~567/512 = 178.3714

Optimal GPV sequence: Template:Val list

Badness: 0.100152