Ragismic family: Difference between revisions

Overthink (talk | contribs)
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]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7
* [[7-odd-limit]] [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7
* [[9-odd-limit]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5
* [[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]]: ~7 = ~4374/625
[[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=1| 7, 19, 26, 46, 53, 72, 118f, 125f, 171ef, 190ff, 197ef, 243eff }}
{{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=1| 7, 39, 46, 53, 80, 133d, 179, 312cdf }}
{{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]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7.11/5
* [[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 = ~9801/4900, ~7 = ~21434787/3062500, ~11 = ~2310905821257/210087500000 to 3.5.14/11
[[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=1| 26, 46, 72, 152f, 198, 224, 270, 494, 764, 1258 }}
{{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=1| 46, 72f, 106, 118, 152, 224, 270, 494, 764, 1106, 1376, 1870 }}
{{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=1| 34d, 46, 80, 144, 178, 190, 224, 494, 684, 764, 954, 1178, 1448, 6970ceeff, 8418ceeff }}
{{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=1| 46, 111df, 159df, 178, 205, 224, 270, 494, 764, 1258, 1771, 2041f, 2265, 2535f }}
{{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=1| 46, 87d, 91, 133d, 137d, 178, 224, 270, 494, 764, 1125, 1395, 1619, 1665, 1889, 4048, 4542, 6431f }}
{{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:Ragismic| ]] <!-- key article -->
[[Category:Rank 3]]
[[Category:Rank 3]]