Gariboh family: Difference between revisions

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-The '''gariboh family''' of [[planar temperament]]s tempers out the gariboh comma, [[3125/3087]].
+{{Technical data page}}
+The '''gariboh family''' of [[Rank-3 temperament|rank-3]] [[temperament]]s [[Tempering out|tempers out]] the gariboh comma, [[3125/3087]].
 == Gariboh ==
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: [[3125/3087]]
-[[Mapping]]: [{{val| 1 0 0 0 }}, {{val| 0 1 1 1 }}, {{val| 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
+: Mapping generators: ~2, ~3, ~25/21
-{{Val list|legend=1| 8d, 12, 29, 37, 41, 53, 94 }}
+[[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 }}
+[[Badness]]: 0.614 × 10<sup>-3</sup>
 [[Projection pair]]s: 5 – 15625/3087, 7 – 9765625/1361367 to 2.3.25/7
 == Undecimal gariboh ==
-Subgroup: 2.3.5.7.11
+[[Subgroup]]: 2.3.5.7.11
 [[Comma list]]: 540/539, 3125/3087
-[[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 1 1 2 }}, {{val| 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 }}
+[[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
-{{Val list|legend=1| 8d, 12e, 25bccdd, 33cd, 37ee, 41, 53, 94, 229c }}
+{{Optimal ET sequence|legend=1| 8d, 12e, 33cd, 41, 53, 94 }}
 == Androboh ==
-Subgroup: 2.3.5.7.11
+[[Subgroup]]: 2.3.5.7.11
 [[Comma list]]: 100/99, 1375/1372
-[[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 1 1 0 }}, {{val| 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
-{{Val list|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]]
+[[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, 33cd, 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, 33cd, 41, 49f }}
+=== 17-limit ===
+[[Subgroup]]: 2.3.5.7.11.13.17
+[[Comma list]]: 120/119, 144/143, 170/169, 847/845
+{{Mapping|legend=1| 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|legend=1| 8d, 16, 33cd, 41, 49fg }}
 [[Category:Temperament families]]
+[[Category:Pages with mostly numerical content]]
 [[Category:Gariboh family| ]] <!-- main article -->
+[[Category:Gariboh| ]] <!-- key article -->
 [[Category:Rank 3]]