Gariboh family: Difference between revisions

← Older edit

VisualWikitext

@@ Line 1: / Line 1: @@
-The gariboh family of [[Planar_Temperament|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  ==
+== Gariboh ==
-[[Comma]]: 3125/3087
+[[Subgroup]]: 2.3.5.7
-[[Mapping]]: [{{val|1 0 0 0}}, {{val|0 1 1 1}}, {{val|0 0 3 5}}]
+[[Comma list]]: [[3125/3087]]
-Mapping generators: 2, ~3, ~25/21
+{{Mapping|legend=1| 1 0 0 0 | 0 1 1 1 | 0 0 3 5 }}
-{{Val list|legend=1| 4, 8d, 12, 29, 37, 41, 53, 94 }}
+: Mapping generators: ~2, ~3, ~25/21
-[[Projection_pair|Projection pair]]s: 5 - 15625/3087, 7 - 9765625/1361367 to 2.3.25/7
+[[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
-=== 11-limit  ===
 [[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>
-Mapping generators: 2, ~3, ~25/21
+=== 13-limit ===
+[[Subgroup]]: 2.3.5.7.11.13
-{{Val list|legend=1| 8d, 12e, 41, 53, 94 }}
+[[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 ==
+[[Subgroup]]: 2.3.5.7.11
-== Androboh  ==
 [[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
+{{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 }}
-Mapping generators: 2, ~3, ~25/21
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 703.0799, ~12/11 = 147.2446
-{{Val list|legend=1| 8d, 12, 29, 37, 41}}
+{{Optimal ET sequence|legend=1| 8d, 16, 33cd, 41, 49fg }}
-[[Category:Temperament]]
+[[Category:Temperament families]]
+[[Category:Pages with mostly numerical content]]
+[[Category:Gariboh family| ]] <!-- main article -->
+[[Category:Gariboh| ]] <!-- key article -->
 [[Category:Rank 3]]
-[[Category:todo:expand]]
-[[Category:todo:link]]