Ragismic family: Difference between revisions
→Thunor: + scale |
m Units & misc. cleanup. - redundant category |
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{{Mapping|legend=1| 1 0 0 1 | 0 1 0 7 | 0 0 1 -4 }} | {{Mapping|legend=1| 1 0 0 1 | 0 1 0 7 | 0 0 1 -4 }} | ||
: mapping generators: ~2, ~3, ~5 | : mapping generators: ~2, ~3, ~5 | ||
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[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[7-odd-limit]] [[ | * [[7-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7 | ||
* [[9-odd-limit]] [[ | * [[9-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5 | ||
{{Optimal ET sequence|legend=1| 19, 27, 45, 46, 53, 72, 99, 171, 441, 612, 935, 1106, 1277, 1547, 1718, 4983, 6701, 8419, 17279c }} | {{Optimal ET sequence|legend=1| 19, 27, 45, 46, 53, 72, 99, 171, 441, 612, 935, 1106, 1277, 1547, 1718, 4983, 6701, 8419, 17279c }} | ||
[[Projection pair]]: | [[Projection pair]]: <code>7 ~4374/625</code> | ||
Scales: [[Ragismic19]], [[Ragismic chromatic]] | Scales: [[Ragismic19]], [[Ragismic chromatic]] | ||
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{{Optimal ET sequence|legend=1| 7, 19, 26, 45, 46, 53, 72, 118, 190, 315e, 361e, 433de, 623cdee }} | {{Optimal ET sequence|legend=1| 7, 19, 26, 45, 46, 53, 72, 118, 190, 315e, 361e, 433de, 623cdee }} | ||
[[Badness]]: 0.721 × 10<sup>-3</sup> | [[Badness]] (Smith): 0.721 × 10<sup>-3</sup> | ||
=== 13-limit === | === 13-limit === | ||
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Mapping: {{mapping| 1 0 0 1 6 2 | 0 1 0 7 -6 4 | 0 0 1 -4 3 -2 }} | Mapping: {{mapping| 1 0 0 1 6 2 | 0 1 0 7 -6 4 | 0 0 1 -4 3 -2 }} | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 7, 19, 26, 46, 53, 72, 118f, 125f, 171ef, 190ff, 197ef, 243eff }} | ||
Badness: 0.840 × 10<sup>-3</sup> | Badness (Smith): 0.840 × 10<sup>-3</sup> | ||
== Ulmo == | == Ulmo == | ||
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{{Optimal ET sequence|legend=1| 7, 39, 46, 53, 80, 126, 179, 259cd, 385bcd }} | {{Optimal ET sequence|legend=1| 7, 39, 46, 53, 80, 126, 179, 259cd, 385bcd }} | ||
[[Badness]]: 1.23 × 10<sup>-3</sup> | [[Badness]] (Smith): 1.23 × 10<sup>-3</sup> | ||
=== 13-limit === | === 13-limit === | ||
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Mapping: {{mapping| 1 0 0 1 -3 2 | 0 1 0 7 7 4 | 0 0 1 -4 -2 -2 }} | Mapping: {{mapping| 1 0 0 1 -3 2 | 0 1 0 7 7 4 | 0 0 1 -4 -2 -2 }} | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 7, 39, 46, 53, 80, 133d, 179, 312cdf }} | ||
Badness: 0.932 × 10<sup>-3</sup> | Badness (Smith): 0.932 × 10<sup>-3</sup> | ||
== Thor == | == Thor == | ||
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{{Mapping|legend=1| 2 0 0 2 5 | 0 1 0 7 5 | 0 0 1 -4 -3 }} | {{Mapping|legend=1| 2 0 0 2 5 | 0 1 0 7 5 | 0 0 1 -4 -3 }} | ||
: mapping generators: ~99/70, ~3, ~5 | : mapping generators: ~99/70, ~3, ~5 | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[11-odd-limit]] [[ | * [[11-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7.11/5 | ||
{{Optimal ET sequence|legend=1| 26, 34d, 46, 72, 118, 152, 224, 270, 342, 494, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }} | {{Optimal ET sequence|legend=1| 26, 34d, 46, 72, 118, 152, 224, 270, 342, 494, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }} | ||
[[Badness]]: 0.0888 × 10<sup>-3</sup> | [[Badness]] (Smith): 0.0888 × 10<sup>-3</sup> | ||
[[Projection pair]]s: 2 | [[Projection pair]]s: <code>2 9801/4900, 7 21434787/3062500, 11 2310905821257/210087500000</code> to 3.5.14/11 | ||
=== Thunor === | === Thunor === | ||
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* 13- and 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.9/7.13 | * 13- and 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.9/7.13 | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 26, 46, 72, 152f, 198, 224, 270, 494, 764, 1258 }} | ||
Badness: 0.341 × 10<sup>-3</sup> | Badness (Smith): 0.341 × 10<sup>-3</sup> | ||
Scales: [[Thunor46]] | Scales: [[Thunor46]] | ||
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Mapping: {{mapping| 2 0 0 2 5 22 | 0 1 0 7 5 -9 | 0 0 1 -4 -3 3 }} | Mapping: {{mapping| 2 0 0 2 5 22 | 0 1 0 7 5 -9 | 0 0 1 -4 -3 3 }} | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 46, 72f, 106, 118, 152, 224, 270, 494, 764, 1106, 1376, 1870 }} | ||
Badness: 0.549 × 10<sup>-3</sup> | Badness (Smith): 0.549 × 10<sup>-3</sup> | ||
=== Donar === | === Donar === | ||
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* 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7.15/11 | * 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7.15/11 | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 34d, 46, 80, 144, 178, 190, 224, 494, 684, 764, 954, 1178, 1448, 6970ceeff, 8418ceeff }} | ||
Badness: 0.322 × 10<sup>-3</sup> | Badness (Smith): 0.322 × 10<sup>-3</sup> | ||
Scales: [[Donar46]] | Scales: [[Donar46]] | ||
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{{Mapping|legend=1| 1 0 0 1 2 | 0 2 0 14 37 | 0 0 1 -4 -12 }} | {{Mapping|legend=1| 1 0 0 1 2 | 0 2 0 14 37 | 0 0 1 -4 -12 }} | ||
: mapping generators: ~2, ~343/198, ~5 | : mapping generators: ~2, ~343/198, ~5 | ||
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Mapping: {{mapping| 1 0 2 -7 8 -6 | 0 1 0 7 -3 7 | 0 0 3 -12 2 -13 }} | Mapping: {{mapping| 1 0 2 -7 8 -6 | 0 1 0 7 -3 7 | 0 0 3 -12 2 -13 }} | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 46, 111df, 159df, 178, 205, 224, 270, 494, 764, 1258, 1771, 2041f, 2265, 2535f }} | ||
== Vidar == | == Vidar == | ||
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{{Mapping|legend=1| 1 0 0 1 5 | 0 1 4 -9 -3 | 0 0 -5 20 4 }} | {{Mapping|legend=1| 1 0 0 1 5 | 0 1 4 -9 -3 | 0 0 -5 20 4 }} | ||
: mapping generators: ~2, ~3, ~96/55 | : mapping generators: ~2, ~3, ~96/55 | ||
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Mapping: {{mapping| 1 0 0 1 5 6 | 0 1 4 -9 -3 -5 | 0 0 -5 20 4 7 }} | Mapping: {{mapping| 1 0 0 1 5 6 | 0 1 4 -9 -3 -5 | 0 0 -5 20 4 7 }} | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 46, 87d, 91, 133d, 137d, 178, 224, 270, 494, 764, 1125, 1395, 1619, 1665, 1889, 4048, 4542, 6431f }} | ||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Ragismic family| ]] <!-- main article --> | [[Category:Ragismic family| ]] <!-- main article --> | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||