Gariboh family: Difference between revisions
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The '''gariboh family''' of [[ | The '''gariboh family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperament]]s [[tempering out|tempers out]] the gariboh comma, [[3125/3087]]. | ||
== Gariboh == | == Gariboh == | ||
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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 = 1200.0000{{c}}, ~3 = 702.4482{{c}}, ~25/21 = 293.7397{{c}} | |||
[[Optimal tuning]] ([[POTE]]): ~2 = | |||
{{Optimal ET sequence|legend=1| 8d, 12, 29, 37, 41, 53, 94 }} | {{Optimal ET sequence|legend=1| 8d, 12, 29, 37, 41, 53, 94 }} | ||
[[Badness]]: 0.614 × 10<sup>-3</sup> | [[Badness]] (Smith): 0.614 × 10<sup>-3</sup> | ||
[[Projection pair]]s: 5 – 15625/3087, 7 – 9765625/1361367 to 2.3.25/7 | [[Projection pair]]s: 5 – 15625/3087, 7 – 9765625/1361367 to 2.3.25/7 | ||
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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 = | [[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3 = 702.7001{{c}}, ~25/21 = 293.5587{{c}} | ||
{{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]] (Smith): 1.75 × 10<sup>-3</sup> | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 275/273, 325/324, 540/539 | |||
{{ | Mapping: {{mapping| 1 0 0 0 2 2 | 0 1 1 1 2 2 | 0 0 3 5 -7 -6 }} | ||
Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3 = 702.5381{{c}}, ~13/11 = 293.6878{{c}} | |||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 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 = | [[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3 = 705.0554{{c}}, ~25/21 = 293.1102{{c}} | ||
{{Optimal ET sequence|legend=1| 8d, 12, 29, 37, 41, 90e, 131e }} * | {{Optimal ET sequence|legend=1| 8d, 12, 29, 37, 41, 90e, 131e }} * | ||
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<nowiki>*</nowiki> [[optimal patent val]]: [[119edo|119]] | <nowiki>*</nowiki> [[optimal patent val]]: [[119edo|119]] | ||
[[Badness]]: 1.20 × 10<sup>-3</sup> | [[Badness]] (Smith): 1.20 × 10<sup>-3</sup> | ||
== Trismegiboh == | == Trismegiboh == | ||
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{{Mapping|legend=1| 1 0 0 0 2 | 0 1 1 1 1 | 0 0 6 10 -1 }} | {{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 = 1200.0000{{c}}, ~3/2 = 702.5559{{c}}, ~12/11 = 147.0103{{c}} | |||
[[Optimal tuning]] ([[POTE]]): ~2 = | |||
{{Optimal ET sequence|legend=1| 8d, 16, 33cd, 41, 49 }} | {{Optimal ET sequence|legend=1| 8d, 16, 33cd, 41, 49 }} | ||
=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 144/143, 275/273, 847/845 | |||
{{ | Mapping: {{mapping| 1 0 0 0 2 2 | 0 1 1 1 1 1 | 0 0 6 10 -1 1 }} | ||
Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 702.9404{{c}}, ~12/11 = 147.1132{{c}} | |||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 8d, 16, 33cd, 41, 49f }} | ||
=== 17-limit === | === 17-limit === | ||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 120/119, 144/143, 170/169, 847/845 | |||
{{ | Mapping: {{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 = 1200.0000{{c}}, ~3/2 = 703.0799{{c}}, ~12/11 = 147.2446{{c}} | |||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 8d, 16, 33cd, 41, 49fg }} | ||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||