Gariboh 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 gariboh family of rank-3 temperaments tempers out the gariboh comma, 3125/3087.
Gariboh
Gariboh is generated by a perfect fifth and a narrow minor third of ~25/21, three make ~5/3 and five make ~7/3. 94edo makes for an excellent tuning for it.
Another notable tuning is given by TE, CTE and POTE, all coinciding at 702.4482 ¢, 293.7397 ¢ with pure octaves since prime 2 is not involved in the comma to begin with, though its difference from CWE is practically unnoticeable.
Subgroup: 2.3.5.7
Mapping: [⟨1 0 0 0], ⟨0 1 1 1], ⟨0 0 3 5]]
- mapping generators: ~2, ~3, ~25/21
- WE: ~2 = 1199.9983 ¢, ~3/2 = 702.4472 ¢, ~25/21 = 293.7393 ¢
- error map: ⟨-0.002 +0.490 -2.650 +2.316]
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.4468 ¢, ~25/21 = 293.7395 ¢
- error map: ⟨0.000 +0.492 -2.648 +2.319]
Optimal ET sequence: 8d, 12, 29, 37, 41, 53, 94
Badness (Sintel): 2.71
Projection pairs: 5 – 15625/3087, 7 – 9765625/1361367 to 2.3.25/7
Undecimal gariboh
Subgroup: 2.3.5.7.11
Comma list: 540/539, 3125/3087
Mapping: [⟨1 0 0 0 2], ⟨0 1 1 1 2], ⟨0 0 3 5 -7]]
- WE: ~2 = 1199.9983 ¢, ~3/2 = 702.4472 ¢, ~25/21 = 293.7393 ¢
- error map: ⟨+0.086 +0.881 -2.738 +1.909 -0.531]
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.7792 ¢, ~25/21 = 293.5634 ¢
- error map: ⟨0.000 +0.824 -2.844 +1.770 -0.703]
Optimal ET sequence: 8d, 12e, 25bccdd, 33cd, 37ee, 41, 53, 90e, 94, 229c
Badness (Sintel): 2.10
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 275/273, 325/324, 540/539
Mapping: [⟨1 0 0 0 2 2], ⟨0 1 1 1 2 2], ⟨0 0 3 5 -7 -6]]
Optimal tunings:
- WE: ~2 = 1199.9929 ¢, ~3/2 = 702.5339 ¢, ~13/11 = 293.6861 ¢
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.5314 ¢, ~13/11 = 293.6875 ¢
Optimal ET sequence: 8d, 12e, 25bccddf, 33cd, 41, 53, 94
Badness (Sintel): 1.22
Androboh
Subgroup: 2.3.5.7.11
Comma list: 100/99, 1375/1372
Mapping: [⟨1 0 0 0 2], ⟨0 1 1 1 0], ⟨0 0 3 5 6]]
- WE: ~2 = 1199.2176 ¢, ~3/2 = 704.5957 ¢, ~25/21 = 292.9191 ¢
- error map: ⟨-0.782 +1.858 -3.743 -0.417 +4.632]
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 704.5845 ¢, ~25/21 = 292.9597 ¢
- error map: ⟨0.000 +2.630 -2.850 +0.557 +6.440]
Optimal ET sequence: 8d, 12, 29, 37, 41, 90e, 131e *
Badness (Sintel): 1.44
Trismegiboh
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 3125/3087
Mapping: [⟨1 0 0 0 2], ⟨0 1 1 1 1], ⟨0 0 6 10 -1]]
- mapping generators: ~2, ~3, ~12/11
- WE: ~2 = 1199.5499 ¢, ~3/2 = 702.2924 ¢, ~12/11 = 146.9551 ¢
- error map: ⟨-0.450 -0.113 -2.741 +2.568 +2.669]
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.1698 ¢, ~12/11 = 146.9960 ¢
- error map: ⟨0.000 +0.215 -2.168 +3.304 +3.856]
Optimal ET sequence: 8d, 16, 24d, 33cd, 41, 65d, 90e, 106, 147
Badness (Sintel): 3.38
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 275/273, 847/845
Mapping: [⟨1 0 0 0 2 2], ⟨0 1 1 1 1 1], ⟨0 0 6 10 -1 1]]
Optimal tunings:
- WE: ~2 = 1198.9833 ¢, ~3/2 = 702.3448 ¢, ~12/11 = 146.9886 ¢
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.0567 ¢, ~12/11 = 147.0902 ¢
Optimal ET sequence: 8d, 16, 24d, 33cd, 41, 65d, 106f
Badness (Sintel): 1.83
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 120/119, 144/143, 170/169, 847/845
Mapping: [⟨1 0 0 0 2 2 3], ⟨0 1 1 1 1 1 1], ⟨0 0 6 10 -1 1 -4]]
Optimal tunings:
- WE: ~2 = 1198.6534 ¢, ~3/2 = 702.2909 ¢, ~12/11 = 147.0794 ¢
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.8744 ¢, ~12/11 = 147.2433 ¢
Optimal ET sequence: 8d, 16, 24d, 33cd, 41, 49fg, 65d, 106fg
Badness (Sintel): 1.55