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
- CTE: ~531441/524288 = 29.2683¢ (1 ⧵ 41), ~5/4 = 386.3137¢
- CWE: ~531441/524288 = 29.2683¢ (1 ⧵ 41), ~5/4 = 386.5501¢
Optimal ET sequence: 41, 123, 164, 205, 369, 574, 779, 2132bc
Badness (Sintel): 21.917
Gamelacomp
Subgroup: 2.3.5.7
Comma list: 1029/1024, 537824/531441
Mapping: [⟨41 65 0 115], ⟨0 0 1 0]]
Optimal ET sequence: 41, 123, 164, 205d, 246d, 451dd
Badness (Sintel): 4.076
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 tunings:
- CTE: ~56/55 = 29.2683¢ (1 ⧵ 41), ~5/4 = 385.9888¢
- CWE: ~56/55 = 29.2683¢ (1 ⧵ 41), ~5/4 = 385.8909¢
Optimal ET sequence: 41, 123e, 164, 205d, 451dd
Badness (Sintel): 2.530
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 tunings:
- CTE: ~56/55 = 29.2683¢ (1 ⧵ 41), ~5/4 = 386.5763¢
- CWE: ~56/55 = 29.2683¢ (1 ⧵ 41), ~5/4 = 386.5997¢
Optimal ET sequence: 41, 123e, 164, 205d
Badness (Sintel): 2.269
Mermacomp
Subgroup: 2.3.5.7
Comma list: 5120/5103, 2500000/2470629
Mapping: [⟨41 65 0 20], ⟨0 0 1 1]]
Optimal ET sequence: 41, 123d, 164d, 205, 246, 451d, 697dd
Badness (Sintel): 3.602
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 tunings:
- CTE: ~55/54 = 29.2683¢ (1 ⧵ 41), ~5/4 = 385.1784¢
- CWE: ~55/54 = 29.2683¢ (1 ⧵ 41), ~5/4 = 385.2847¢
Optimal ET sequence: 41, 164d, 205, 246
Badness (Sintel): 2.532
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 540/539, 729/728, 75625/75264
Mapping: [⟨41 65 0 20 237 247], ⟨0 0 1 1 -1 -1]]
Optimal tunings:
- CTE: ~55/54 = 29.2683¢ (1 ⧵ 41), ~5/4 = 385.7331¢
- CWE: ~55/54 = 29.2683¢ (1 ⧵ 41), ~5/4 = 385.8418¢
Optimal ET sequence: 41, 164d, 205, 246f
Badness (Sintel): 2.293
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
- CTE: ~100352/98415 = 29.2683¢ (1 ⧵ 41), ~567/512 = 178.5314¢
- CWE: ~100352/98415 = 29.2683¢ (1 ⧵ 41), ~567/512 = 178.6568¢
Optimal ET sequence: 41, …, 328, 369, 779, 1927bc
Badness (Sintel): 3.405
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 tunings:
- CTE: ~56/55 = 29.2683¢ (1 ⧵ 41), ~567/512 = 178.6944¢
- CWE: ~56/55 = 29.2683¢ (1 ⧵ 41), ~567/512 = 178.8825¢
Optimal ET sequence: 41, …, 328, 369, 1066cee
Badness (Sintel): 2.129
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 tunings:
- CTE: ~56/55 = 29.2683¢ (1 ⧵ 41), ~72/65 = 178.9389¢
- CWE: ~56/55 = 29.2683¢ (1 ⧵ 41), ~72/65 = 179.0133¢
Optimal ET sequence: 41, …, 328, 369f, 697cef
Badness (Sintel): 1.718
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 tunings:
- CTE: ~55/54 = 29.2683¢ (1 ⧵ 41), ~256/231 = 178.3836¢
- CWE: ~55/54 = 29.2683¢ (1 ⧵ 41), ~256/231 = 178.3736¢
Optimal ET sequence: 41, …, 410, 451, 861e
Badness (Sintel): 3.311
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 tunings:
- CTE: ~55/54 = 29.2683¢ (1 ⧵ 41), ~72/65 = 178.3755¢
- CWE: ~55/54 = 29.2683¢ (1 ⧵ 41), ~72/65 = 178.3772¢
Optimal ET sequence: 41, …, 410, 451, 861e
Badness (Sintel): 2.500