Gariboh family: Difference between revisions
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The '''gariboh family''' of [[ | The '''gariboh family''' of [[Rank-3 temperament|rank-3]] [[temperament]]s [[Tempering out|tempers out]] the gariboh comma, [[3125/3087]]. | ||
== Gariboh == | == Gariboh == | ||
Subgroup: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
[[Comma list]]: [[3125/3087]] | [[Comma list]]: [[3125/3087]] | ||
{{Mapping|legend=1| 1 0 0 0 | 0 1 1 1 | 0 0 3 5 }} | |||
: mapping generators: ~2, ~3, ~25/21 | |||
{{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> | |||
[[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 | ||
== Undecimal gariboh == | == Undecimal gariboh == | ||
Subgroup: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: 540/539, 3125/3087 | [[Comma list]]: 540/539, 3125/3087 | ||
{{Mapping|legend=1| 1 0 0 0 2 | 0 1 1 1 2 | 0 0 3 5 -7 }} | |||
{{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> | |||
== Androboh == | == Androboh == | ||
Subgroup: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
[[Comma list]]: 100/99, 1375/1372 | [[Comma list]]: 100/99, 1375/1372 | ||
{{Mapping|legend=1| 1 0 0 0 2 | 0 1 1 1 0 | 0 0 3 5 6 }} | |||
{{Optimal ET sequence|legend=1| 8d, 12, 29, 37, 41, 90e, 131e }} * | {{Optimal ET sequence|legend=1| 8d, 12, 29, 37, 41, 90e, 131e }} * | ||
<nowiki>*</nowiki> [[optimal patent val]]: [[119edo|119]] | <nowiki>*</nowiki> [[optimal patent val]]: [[119edo|119]] | ||
[[Badness]]: 1.20 × 10<sup>-3</sup> | |||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Gariboh family| ]] <!-- main article --> | [[Category:Gariboh family| ]] <!-- main article --> | ||
[[Category:Gariboh| ]] <!-- key article --> | |||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||
Revision as of 06:19, 18 September 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 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 ET sequence: 8d, 12e, 25bccdd, 33cd, 37ee, 41, 53, 94, 229c
Badness: 1.75 × 10-3
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 ET sequence: 8d, 12, 29, 37, 41, 90e, 131e *
Badness: 1.20 × 10-3