Gariboh family

The gariboh family of rank-3 temperaments tempers out the gariboh comma, 3125/3087.

Gariboh

Subgroup: 2.3.5.7

Comma list: 3125/3087

Mapping: [⟨1 0 0 0], ⟨0 1 1 1], ⟨0 0 3 5]]

Mapping generators: ~2, ~3, ~25/21

Optimal tuning (POTE): ~2 = 1\1, ~3 = 702.4482, ~25/21 = 293.7397

Optimal ET sequence: 8d, 12, 29, 37, 41, 53, 94

Badness: 0.614 × 10^-3

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]]

Optimal tuning (POTE): ~2 = 1\1, ~3 = 702.7001, ~25/21 = 293.5587

Optimal ET sequence: 8d, 12e, 25bccdd, 33cd, 37ee, 41, 53, 94, 229c

Badness: 1.75 × 10^-3

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 tuning (POTE): ~2 = 1\1, ~3 = 702.5381, ~13/11 = 293.6878

Optimal ET sequence: 8d, 12e, 33cd, 41, 53, 94

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]]

Optimal tuning (POTE): ~2 = 1\1, ~3 = 705.0554, ~25/21 = 293.1102

Optimal ET sequence: 8d, 12, 29, 37, 41, 90e, 131e *

* optimal patent val: 119

Badness: 1.20 × 10^-3

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

Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.5559, ~12/11 = 147.0103

Optimal ET sequence: 8d, 16, 33cd, 41, 49

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 tuning (POTE): ~2 = 1\1, ~3/2 = 702.9404, ~12/11 = 147.1132

Optimal ET sequence: 8d, 16, 33cd, 41, 49f

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 tuning (POTE): ~2 = 1\1, ~3/2 = 703.0799, ~12/11 = 147.2446

Optimal ET sequence: 8d, 16, 33cd, 41, 49fg