Olympic clan: Difference between revisions

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-The '''olympic clan''' of [[rank-3 temperament|rank-3]] [[temperament]]s [[tempering out|tempers out]] the [[olympia]], 131072/130977 = {{monzo| 17 -5 0 -2 -1 }}. This has the effect of equating the [[33/32|undecimal quartertone (33/32)]] with a stack of two [[64/63|septimal commas (64/63)]].
+{{Technical data page}}
+The '''olympic clan''' of [[rank-3 temperament|rank-3]] [[temperament]]s [[tempering out|tempers out]] the [[olympia]] ([[ratio]]: 131072/130977, {{monzo|legend=1| 17 -5 0 -2 -1 }}). This has the effect of equating the [[33/32|undecimal quartertone (33/32)]] with a stack of two [[64/63|septimal commas (64/63)]].
 For the rank-4 olympic temperament, see [[Rank-4 temperament #Olympic (131072/130977)]].
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 Temperaments discussed elsewhere are:
 * ''[[Akea]]'' (+385/384) → [[Hemifamity family #Akea|Hemifamity family]]
+* ''[[Cassaschismic]]'' (+19712/19683) → [[Garischismic family #Cassaschismic|Garischismic family]]
 * ''[[Pessoal]]'' (+9801/9800) → [[Kalismic temperaments #Pessoal|Kalismic temperaments]]
 * ''[[Lif]]'' (+2401/2400) → [[Breed family #Lif|Breed family]]
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 * ''[[Hera]]'' (+6144/6125) → [[Porwell family #Hera|Porwell family]]
-Considered below are orthoschismic, cassaschismic, baffin and sophia.
+Considered below are orthoschismic, baffin and sophia.
 == Orthoschismic ==
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 [[Comma list]]: 540/539, 32805/32768
-{{Mapping|legend=1| 1 0 15 0 17 | 0 1 -8 0 -5 | 0 0 0 1 2 }}
+{{Mapping|legend=1| 1 0 15 0 17 | 0 1 -8 0 -5 | 0 0 0 1 -2 }}
 [[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.7405, ~7/4 = 969.6950
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 Comma list: 540/539, 729/728, 4096/4095
-Mapping: {{mapping| 1 0 15 0 17 -3 | 0 1 -8 0 -5 6 | 0 0 0 1 2 -1 }}
+Mapping: {{mapping| 1 0 15 0 17 -3 | 0 1 -8 0 -5 6 | 0 0 0 1 -2 -1 }}
 Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.7333, ~7/4 = 969.7085
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 Badness: 0.833 × 10<sup>-3</sup>
-== Cassaschismic ==
-=== 7-limit (garischismic) ===
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 33554432/33480783
-{{Mapping|legend=1| 1 0 0 25 | 0 1 0 -14 | 0 0 1 0 }}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.2224, ~5/4 = 386.3137
-{{Optimal ET sequence|legend=1| 12, 29, 41, 53, 94, 164, 176, 217, 229, 270, 593, 863, 1133, 1996d, 2037, 2307, 2900bd, 3170bd, 4303bcd }}
-[[Badness]]: 1.31 × 10<sup>-3</sup>
-=== 11-limit ===
-[[Subgroup]]: 2.3.5.7.11
-[[Comma list]]: 19712/19683, 41503/41472
-{{Mapping|legend=1| 1 0 0 25 -33 | 0 1 0 -14 23 | 0 0 1 0 0 }}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.2280, ~5/4 = 386.3137
-{{Optimal ET sequence|legend=1| 41, 53, 94, 176, 217, 270, 581, 851, 1121 }}
-[[Badness]]: 1.41 × 10<sup>-3</sup>
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 2080/2079, 4096/4095, 19712/19683
-Mapping: {{mapping| 1 0 0 25 -33 -13 | 0 1 0 -14 23 12 | 0 0 1 0 0 -1 }}
-Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.2289, ~5/4 = 386.2869
-{{Optimal ET sequence|legend=1| 41, 53, 94, 176, 217, 270, 581, 851, 2283b }}
-Badness: 0.872 × 10<sup>-3</sup>
-=== 2.3.5.7.11.13.19 subgroup ===
-Subgroup: 2.3.5.7.11.13.19
-Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079
-Sval mapping: {{mapping| 1 0 0 25 -33 -13 -6 | 0 1 0 -14 23 12 5 | 0 0 1 0 0 -1 1 }}
-Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.2293, ~5/4 = 386.3021
-{{Optimal ET sequence|legend=1| 41, 53, 94, 176, 217, 270, 581, 851 }}
-Badness: 0.496 × 10<sup>-3</sup>
 == Baffin ==
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 [[Category:Temperament clans]]
+[[Category:Pages with mostly numerical content]]
 [[Category:Olympic clan| ]] <!-- main article -->
 [[Category:Olympic| ]] <!-- key article -->
 [[Category:Rank 3]]