Gariboh family: Difference between revisions
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{{Mapping|legend=1| 1 0 0 0 | 0 1 1 1 | 0 0 3 5 }} | {{Mapping|legend=1| 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|legend=1| 8d, 12, 29, 37, 41, 53, 94 }} | {{Optimal ET sequence|legend=1| 8d, 12, 29, 37, 41, 53, 94 }} | ||
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{{Mapping|legend=1| 1 0 0 0 2 | 0 1 1 1 2 | 0 0 3 5 -7 }} | {{Mapping|legend=1| 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|legend=1| 8d, 12e, 25bccdd, 33cd, 37ee, 41, 53, 94, 229c }} | {{Optimal ET sequence|legend=1| 8d, 12e, 25bccdd, 33cd, 37ee, 41, 53, 94, 229c }} | ||
[[Badness]]: 1.75 × 10<sup>-3</sup> | [[Badness]]: 1.75 × 10<sup>-3</sup> | ||
=== 13-limit === | |||
[[Subgroup]]: 2.3.5.7.11.13 | |||
[[Comma list]]: 275/273, 325/324, 540/539 | |||
{{Mapping|legend=1| 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|legend=1| 8d, 12e, 33cd, 41, 53, 94 }} | |||
== Androboh == | == Androboh == | ||
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{{Mapping|legend=1| 1 0 0 0 2 | 0 1 1 1 0 | 0 0 3 5 6 }} | {{Mapping|legend=1| 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|legend=1| 8d, 12, 29, 37, 41, 90e, 131e }} * | {{Optimal ET sequence|legend=1| 8d, 12, 29, 37, 41, 90e, 131e }} * | ||
| Line 39: | Line 56: | ||
[[Badness]]: 1.20 × 10<sup>-3</sup> | [[Badness]]: 1.20 × 10<sup>-3</sup> | ||
== Trismegiboh == | |||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: 3025/3024, 3125/3087 | |||
{{Mapping|legend=1| 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|legend=1| 8d, 16, 41, 49 }} | |||
=== 13-limit === | |||
[[Subgroup]]: 2.3.5.7.11.13 | |||
[[Comma list]]: 144/143, 275/273, 847/845 | |||
{{Mapping|legend=1| 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|legend=1| 8d, 16, 41, 49 }} | |||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
Revision as of 23:40, 3 November 2023
The gariboh family of rank-3 temperaments tempers out the gariboh comma, 3125/3087.
Gariboh
Subgroup: 2.3.5.7
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 *
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, 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, 41, 49