Passion 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 passion family of temperaments tempers out the passion comma, 262144/253125 ([18 -4 -5⟩) in the 5-limit, which equates five instances of 16/15 with 4/3.
Passion
Subgroup: 2.3.5
Comma list: 262144/253125
Mapping: [⟨1 2 2], ⟨0 -5 4]]
- mapping generators: ~2, ~16/15
- WE: ~2 = 1197.8074 ¢, ~16/15 = 98.4898 ¢
- error map: ⟨-2.193 +1.211 +3.260]
- CWE: ~2 = 1200.0000 ¢, ~16/15 = 98.7335 ¢
- error map: ⟨0.000 +4.378 +8.620]
Optimal ET sequence: 12, 49, 61, 73, 231bccc
Badness (Sintel): 3.95
Septimal passion
Subgroup: 2.3.5.7
Comma list: 64/63, 3125/3087
Mapping: [⟨1 2 2 2], ⟨0 -5 4 10]]
- WE: ~2 = 1197.0350 ¢, ~21/20 = 97.9106 ¢
- error map: ⟨-2.965 +2.562 -0.601 +4.351]
- CWE: ~2 = 1200.0000 ¢, ~16/15 = 98.1019 ¢
- error map: ⟨0.000 +7.535 +6.094 +12.193]
Optimal ET sequence: 12, 37, 49, 110bcd
Badness (Sintel): 1.58
11-limit
Subgroup: 2.3.5.7.11
Comma list: 64/63, 100/99, 1375/1372
Mapping: [⟨1 2 2 2 2], ⟨0 -5 4 10 18]]
Optimal tunings:
- WE: ~2 = 1196.9304 ¢, ~21/20 = 97.7686 ¢
- CWE: ~2 = 1200.0000 ¢, ~21/20 = 97.9333 ¢
Optimal ET sequence: 12, 37, 49
Badness (Sintel): 1.35
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 64/63, 100/99, 196/195, 275/273
Mapping: [⟨1 2 2 2 2 2], ⟨0 -5 4 10 18 21]]
Optimal tunings:
- WE: ~2 = 1196.8712 ¢, ~21/20 = 97.6548 ¢
- CWE: ~2 = 1200.0000 ¢, ~21/20 = 97.8141 ¢
Optimal ET sequence: 12f, 25f, 37, 49f
Badness (Sintel): 1.28
Passionate
Subgroup: 2.3.5.7
Comma list: 126/125, 131072/127575
Mapping: [⟨1 2 2 1], ⟨0 -5 4 22]]
- WE: ~2 = 1197.9486 ¢, ~16/15 = 98.6479 ¢
- error map: ⟨-2.051 +0.703 +4.175 -0.623]
- CWE: ~2 = 1200.0000 ¢, ~16/15 = 98.7770 ¢
- error map: ⟨0.000 +4.160 +8.794 +4.269]
Optimal ET sequence: 12, 49d, 61, 73, 85c
Badness (Sintel): 3.07
11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 176/175, 8192/8019
Mapping: [⟨1 2 2 1 1], ⟨0 -5 4 22 30]]
Optimal tunings:
- WE: ~2 = 1197.8835 ¢, ~16/15 = 98.5469 ¢
- CWE: ~2 = 1200.0000 ¢, ~16/15 = 98.6733 ¢
Optimal ET sequence: 12, 49de, 61, 73, 158bccee
Badness (Sintel): 2.26
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 176/175, 343/338, 364/363
Mapping: [⟨1 2 2 1 1 1], ⟨0 -5 4 22 30 33]]
Optimal tunings:
- WE: ~2 = 1197.8309 ¢, ~16/15 = 98.4485 ¢
- CWE: ~2 = 1200.0000 ¢, ~16/15 = 98.5760 ¢
Optimal ET sequence: 12f, 49de, 61, 73f
Badness (Sintel): 2.16
Pash
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 176/175, 196/195, 1352/1331
Mapping: [⟨1 2 2 1 1 0], ⟨0 -5 4 22 30 45]]
Optimal tunings:
- WE: ~2 = 1197.8306 ¢, ~16/15 = 98.6124 ¢
- CWE: ~2 = 1200.0000 ¢, ~16/15 = 98.7468 ¢
Optimal ET sequence: 12f, 73, 85ce
Badness (Sintel): 2.33
Passive
Subgroup: 2.3.5.7
Comma list: 225/224, 256/245
Mapping: [⟨1 2 2 3], ⟨0 -5 4 -2]]
- WE: ~2 = 1195.3551 ¢, ~16/15 = 98.4266 ¢
- error map: ⟨-4.645 -3.378 -1.897 +20.386]
- CWE: ~2 = 1200.0000 ¢, ~16/15 = 98.9690 ¢
- error map: ⟨0.000 +3.200 +9.562 +33.236]
Optimal ET sequence: 1, 11, 12
Badness (Sintel): 1.90
Freivald
Subgroup: 2.3.5.7
Comma list: 6144/6125, 6272/6075
Mapping: [⟨1 -3 6 -5], ⟨0 10 -8 17]]
- mapping generator: ~2, ~48/35
- WE: ~2 = 1198.4021 ¢, ~48/35 = 550.2038 ¢
- error map: ⟨-4.645 -3.378 -1.897 +20.386]
- CWE: ~2 = 1200.0000 ¢, ~48/35 = 550.8980 ¢
- error map: ⟨0.000 +3.200 +9.562 +33.236]
Optimal ET sequence: 13d, 24, 37, 61, 98b
Badness (Sintel): 5.29
11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 2744/2673
Mapping: [⟨1 -3 6 -5 3], ⟨0 10 -8 17 1]]
Optimal tunings:
- WE: ~2 = 1198.8053 ¢, ~11/8 = 550.3522 ¢
- CWE: ~2 = 1200.0000 ¢, ~11/8 = 550.8760 ¢
Optimal ET sequence: 13d, 24, 37, 61
Badness (Sintel): 2.56
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 121/120, 176/175, 512/507
Mapping: [⟨1 7 -2 12 4 1], ⟨0 -10 8 -17 -1 5]]
Optimal tunings:
- WE: ~2 = 1198.7706 ¢, ~11/8 = 550.3418 ¢
- CWE: ~2 = 1200.0000 ¢, ~11/8 = 550.8892 ¢
Optimal ET sequence: 13d, 24, 37, 61
Badness (Sintel): 1.90