Countercomp family

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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 GPV sequence41, 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 GPV sequence41, 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 GPV 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 GPV 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 GPV sequence41, 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 GPV 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 GPV sequence41, …, 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 GPV 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 GPV 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 GPV 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 GPV sequence: 41, …, 410, 451, 861e

Badness: 0.0605