Fifive 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 fifive family of temperaments tempers out the fifive comma (monzo: [-1 -14 10⟩, ratio: 9765625/9565938).
The name fifive was given by Petr Pařízek in 2011 for it splits the perfect fifth in five.[1]
Considered below are crepuscular, fifives, and fourfives.
Fifive
Subgroup: 2.3.5
Comma list: 9765625/9565938
Mapping: [⟨2 2 3], ⟨0 5 7]]
- mapping generators: ~78125/50421, ~27/25
- WE: ~78125/50421 = 600.0168 ¢, ~27/25 = 140.6276 ¢
- error map: ⟨+0.034 +1.217 -1.870]
- CWE: ~78125/50421 = 600.0000 ¢, ~27/25 = 140.6291 ¢
- error map: ⟨0.000 +1.191 -1.910]
Optimal ET sequence: 8, 18bc, 26, 34, 94, 128
Badness (Sintel): 4.83
2.3.5.13 subgroup
Subgroup: 2.3.5.13
Comma list: 325/324, 20000/19773
Mapping: [⟨2 2 3 6], ⟨0 5 7 6]]
Optimal tunings:
- WE: ~351/250 = 599.8593 ¢, ~13/12 = 140.6362 ¢
- CWE: ~351/250 = 600.0000 ¢, ~13/12 = 140.6232 ¢
Optimal ET sequence: 8, 18bcf, 26, 34, 94, 128
Badness (Sintel): 0.800
2.3.5.13.17 subgroup
Subgroup: 2.3.5.13.17
Comma list: 170/169, 289/288, 325/324
Mapping: [⟨2 2 3 6 7], ⟨0 5 7 6 5]]
Optimal tunings:
- CTE: ~17/12 = 599.9773 ¢, ~13/12 = 140.6075 ¢
- CWE: ~17/12 = 600.0000 ¢, ~13/12 = 140.6057 ¢
Optimal ET sequence: 8, 18bcfg, 26, 34, 94, 128
Badness (Sintel): 0.488
Crepuscular
Subgroup: 2.3.5.7
Comma list: 50/49, 4375/4374
Mapping: [⟨2 2 3 4], ⟨0 5 7 7]]
- WE: ~7/5 = 600.000 ¢, ~27/25 = 140.349 ¢
- error map: ⟨-0.787 -1.458 -5.696 +11.398]
- CWE: ~7/5 = 600.000 ¢, ~27/25 = 140.349 ¢
- error map: ⟨0.000 -0.876 -4.803 +12.685]
Optimal ET sequence: 8d, 18bcd, 26, 34d, 60d
Badness (Sintel): 2.19
11-limit
Subgroup: 2.3.5.7.11
Comma list: 50/49, 99/98, 864/847
Mapping: [⟨2 2 3 4 6], ⟨0 5 7 7 4]]
Optimal tunings:
- WE: ~7/5 = 599.1577 ¢, ~12/11 = 140.3893 ¢
- CWE: ~7/5 = 600.0000 ¢, ~12/11 = 140.3244 ¢
Optimal ET sequence: 8d, 18bcd, 26, 34d, 60d
Badness (Sintel): 1.35
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 50/49, 78/77, 99/98, 144/143
Mapping: [⟨2 2 3 4 6 6], ⟨0 5 7 7 4 6]]
Optimal tunings:
- WE: ~7/5 = 599.2598 ¢, ~13/12 = 140.3805 ¢
- CWE: ~7/5 = 600.0000 ¢, ~13/12 = 140.3237 ¢
Optimal ET sequence: 8d, 18bcdf, 26, 34d, 60d
Badness (Sintel): 1.01
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 50/49, 78/77, 85/84, 99/98, 144/143
Mapping: [⟨2 2 3 4 6 6 7], ⟨0 5 7 7 4 6 5]]
Optimal tunings:
- WE: ~7/5 = 599.5348 ¢, ~13/12 = 140.2961 ¢
- CWE: ~7/5 = 600.0000 ¢, ~13/12 = 140.2668 ¢
Optimal ET sequence: 8d, 18bcdfg, 26, 34d, 60d
Badness (Sintel): 0.946
Fifives
Subgroup: 2.3.5.7
Comma list: 875/864, 83349/81920
Mapping: [⟨2 2 3 7], ⟨0 5 7 -6]]
- WE: ~567/400 = 600.9312 ¢, ~27/25 = 140.1261 ¢
- error map: ⟨+1.862 +0.538 -2.637 -3.064]
- CWE: ~567/400 = 600.0000 ¢, ~27/25 = 139.9826 ¢
- error map: ⟨0.000 -2.042 -6.435 -8.722]
Optimal ET sequence: 8, 26, 34, 60, 266bcccddd
Badness (Sintel): 3.30
11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 385/384, 3969/3872
Mapping: [⟨2 2 3 7 6], ⟨0 5 7 -6 4]]
Optimal tunings:
- WE: ~63/44 = 600.5091 ¢, ~12/11 = 140.0024 ¢
- CWE: ~63/44 = 600.0000 ¢, ~12/11 = 139.9267 ¢
Optimal ET sequence: 8, 26, 34, 60
Badness (Sintel): 2.65
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 105/104, 144/143, 1352/1331
Mapping: [⟨2 2 3 7 6 6], ⟨0 5 7 -6 4 6]]
Optimal tunings:
- WE: ~55/39 = 600.4600 ¢, ~12/11 = 139.9737 ¢
- CWE: ~55/39 = 600.0000 ¢, ~12/11 = 139.9092 ¢
Optimal ET sequence: 8, 26, 34, 60
Badness (Sintel): 1.83
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 100/99, 105/104, 144/143, 170/169, 221/220
Mapping: [⟨2 2 3 7 6 6 7], ⟨0 5 7 -6 4 6 5]]
Optimal tunings:
- WE: ~17/12 = 600.4903 ¢, ~12/11 = 139.9825 ¢
- CWE: ~17/12 = 600.0000 ¢, ~12/11 = 139.9150 ¢
Optimal tuning (POTE): ~17/12 = 600.000 ¢, ~12/11 = 139.868 ¢
Optimal ET sequence: 8, 26, 34, 60
Badness (Sintel): 1.50
Fourfives
Subgroup: 2.3.5.7
Comma list: 245/243, 235298/234375
Mapping: [⟨4 4 6 7], ⟨0 5 7 9]]
- mapping generators: ~25/21, ~27/25
- WE: ~25/21 = 300.0011 ¢, ~27/25 = 140.7547 ¢
- error map: ⟨+0.004 +1.823 -1.024 -2.026]
- CWE: ~25/21 = 300.0000 ¢, ~27/25 = 140.7549 ¢
- error map: ⟨0.000 +1.819 -1.030 -2.032]
Optimal ET sequence: 8d, …, 60, 68, 128, 196
Badness (Sintel): 2.89
11-limit
Subgroup: 2.3.5.7.11
Comma list: 245/243, 385/384, 235298/234375
Mapping: [⟨4 4 6 7 19], ⟨0 5 7 9 -11]]
Optimal tunings:
- WE: ~25/21 = 299.9901 ¢, ~27/25 = 140.7659 ¢
- CWE: ~25/21 = 300.0000 ¢, ~27/25 = 140.7693 ¢
Optimal ET sequence: 60, 68, 128, 196
Badness (Sintel): 3.97
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 245/243, 385/384, 20000/19773
Mapping: [⟨4 4 6 7 19 12], ⟨0 5 7 9 -11 6]]
Optimal tunings:
- WE: ~25/21 = 299.9488 ¢, ~13/12 = 140.7359 ¢
- CWE: ~25/21 = 300.0000 ¢, ~13/12 = 140.7539 ¢
Optimal ET sequence: 60, 68, 128, 196f
Badness (Sintel): 2.78
Quadrafives
Subgroup: 2.3.5.7.11
Comma list: 121/120, 245/243, 1375/1372
Mapping: [⟨4 4 6 7 11], ⟨0 5 7 9 6]]
Optimal tunings:
- WE: ~25/21 = 300.1673 ¢, ~27/25 = 140.7084 ¢
- CWE: ~25/21 = 300.0000 ¢, ~27/25 = 140.7353 ¢
Optimal ET sequence: 8d, …, 60e, 68, 128e
Badness (Sintel): 1.89
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 196/195, 245/243, 275/273
Mapping: [⟨4 4 6 7 11 12], ⟨0 5 7 9 6 6]]
Optimal tunings:
- WE: ~25/21 = 300.0500 ¢, ~13/12 = 140.7516 ¢
- CWE: ~25/21 = 300.0000 ¢, ~13/12 = 140.7590 ¢
Optimal ET sequence: 8d, …, 60e, 68
Badness (Sintel): 1.49
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 121/120, 154/153, 170/169, 196/195, 245/243
Mapping: [⟨4 4 6 7 11 12 14], ⟨0 5 7 9 6 6 5]]
Optimal tunings:
- WE: ~25/21 = 300.0593 ¢, ~13/12 = 140.7457 ¢
- CWE: ~25/21 = 300.0000 ¢, ~13/12 = 140.7520 ¢
Optimal tuning (POTE): ~25/21 = 300.000 ¢, ~13/12 = 140.718 ¢
Optimal ET sequence: 8d, …, 60e, 68
Badness (Sintel): 1.26