Countercomp family
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
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]]
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]]
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