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Ragismic family: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Technical data page}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
The '''ragismic family''' of temperaments are rank-3 microtemperaments which temper out [[4375/4374]].
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-10-04 19:45:43 UTC</tt>.<br>
: The original revision id was <tt>167763909</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Comma: 4375/4374


7-limit minimax
Temperaments discussed elsewhere include:
[|1 0 0 0&gt;, |-1/7 0 4/7 1/7&gt;,
* ''[[Sensigh]]'' → [[Sensamagic family #Sensigh|Sensamagic family]]
|0 0 1 0&gt;, |0 0 0 1&gt;]
* ''[[Catakleismoid]]'' → [[Marvel family #Catakleismoid|Marvel family]]
Eigenmonzos: 2, 5, 7
* ''[[Ennealimmic]]'' → [[Breed family #Ennealimmic|Breed family]]


9-limit minimax
Considered below are beyla, ulmo, thor, heimdall, bragi, and vidar.
||1 0 0 0&gt;, |0 1 0 0&gt;,  
|1/5 7/5 1/5 -1/5&gt;, |1/5 7/5 -4/5 4/5&gt;]
Eigenmonzos: 2, 3, 7/5


Map: [&lt;1 0 0 1|, &lt;0 1 0 7|, &lt;0 0 1 -4|]
== Ragismic ==
Generators: 2, 3, 5
[[Subgroup]]: 2.3.5.7
Edos: 7, 19, 26, 27, 45, 46, 53, 65, 72, 80, 91, 99, 171, 270, 441, 612, 935, 1106, 1277, 1376, 1547, 1718, 1889, 2923, 3166, 3436, 3877, 3535, 4390, 5496, 5937, 6450, 9058</pre></div>
 
<h4>Original HTML content:</h4>
[[Comma list]]: [[4375/4374]]
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Ragisma family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Comma: 4375/4374&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 1 0 0 1 | 0 1 0 7 | 0 0 1 -4 }}
7-limit minimax&lt;br /&gt;
 
[|1 0 0 0&amp;gt;, |-1/7 0 4/7 1/7&amp;gt;, &lt;br /&gt;
: mapping generators: ~2, ~3, ~5
|0 0 1 0&amp;gt;, |0 0 0 1&amp;gt;]&lt;br /&gt;
 
Eigenmonzos: 2, 5, 7&lt;br /&gt;
[[Mapping to lattice]]: [{{val| 0 -1 -1 -3 }}, {{val| 0 -1 -2 1 }}]
&lt;br /&gt;
 
9-limit minimax&lt;br /&gt;
Lattice basis:
||1 0 0 0&amp;gt;, |0 1 0 0&amp;gt;, &lt;br /&gt;
: 10/9 length = 0.789, 6/5 length = 0.921
|1/5 7/5 1/5 -1/5&amp;gt;, |1/5 7/5 -4/5 4/5&amp;gt;]&lt;br /&gt;
: Angle (10/9, 6/5) = 105.299°
Eigenmonzos: 2, 3, 7/5&lt;br /&gt;
 
&lt;br /&gt;
[[Minimax tuning]]:
Map: [&amp;lt;1 0 0 1|, &amp;lt;0 1 0 7|, &amp;lt;0 0 1 -4|]&lt;br /&gt;
* [[7-odd-limit]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7
Generators: 2, 3, 5&lt;br /&gt;
* [[9-odd-limit]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5
Edos: 7, 19, 26, 27, 45, 46, 53, 65, 72, 80, 91, 99, 171, 270, 441, 612, 935, 1106, 1277, 1376, 1547, 1718, 1889, 2923, 3166, 3436, 3877, 3535, 4390, 5496, 5937, 6450, 9058&lt;/body&gt;&lt;/html&gt;</pre></div>
 
{{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
 
Scales: [[Ragismic19]], [[Ragismic chromatic]]
 
== Beyla ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 385/384, 4375/4374
 
{{Mapping|legend=1| 1 0 0 1 6 | 0 1 0 7 -6 | 0 0 1 -4 3 }}
 
{{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>
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 169/168, 325/324, 385/384
 
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 }}
 
Badness: 0.840 × 10<sup>-3</sup>
 
== Ulmo ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 176/175, 2200/2187
 
{{Mapping|legend=1| 1 0 0 1 -3 | 0 1 0 7 7 | 0 0 1 -4 -2 }}
 
{{Optimal ET sequence|legend=1| 7, 39, 46, 53, 80, 126, 179, 259cd, 385bcd }}
 
[[Badness]]: 1.23 × 10<sup>-3</sup>
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 169/168, 176/175, 325/324
 
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 }}
 
Badness: 0.932 × 10<sup>-3</sup>
 
== Thor ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 3025/3024, 4375/4374
 
{{Mapping|legend=1| 2 0 0 2 5 | 0 1 0 7 5 | 0 0 1 -4 -3 }}
 
: mapping generators: ~99/70, ~3, ~5
 
[[Minimax tuning]]:
* [[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 }}
 
[[Badness]]: 0.0888 × 10<sup>-3</sup>
 
[[Projection pair]]s: 2 = ~9801/4900, ~7 = ~21434787/3062500, ~11 = ~2310905821257/210087500000 to 3.5.14/11
 
=== Thunor ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 1716/1715, 2080/2079, 3025/3024
 
Mapping: {{mapping| 2 0 0 2 5 -3 | 0 1 0 7 5 15 | 0 0 1 -4 -3 -8 }}
 
Mapping to lattice: [{{val| 0 -1 -2 -3 -2 -7 }}, {{val| 0 -1 -2 1 1 1 }}] 
 
Lattice basis:
: 10/9 length = 0.4234, 6/5 length = 0.8426
: Angle (10/9, 6/5) = 84.126°
 
Minimax tuning:
* 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 }}
 
Badness: 0.341 × 10<sup>-3</sup>
 
=== Rym ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 3025/3024, 4096/4095, 4375/4374
 
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 }}
 
Badness: 0.549 × 10<sup>-3</sup>
 
=== Donar ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 3025/3024, 4225/4224, 4375/4374
 
Mapping: {{mapping| 2 0 1 -2 2 7 | 0 1 0 7 5 3 | 0 0 2 -8 -6 -5 }}
 
: mapping generators: ~99/70, ~3, ~220/117
 
Mapping to lattice: [{{val| 0 2 2 6 4 1 }}, {{val| 0 -1 -2 1 1 2 }}]
 
Lattice basis:
: 44/39 length = 0.3480, 6/5 length = 0.7828
: Angle (44/39, 6/5) = 85.3977°
 
Minimax tuning:
* 13-odd-limit unchanged-interval (eigenmonzo) basis: 2.7.11/5
* 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 }}
 
Badness: 0.322 × 10<sup>-3</sup>
 
Scales: [[Donar46]]
 
== Heimdall ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 4375/4374, 117649/117612
 
{{Mapping|legend=1| 1 0 0 1 2 | 0 2 0 14 37 | 0 0 1 -4 -12 }}
 
: mapping generators: ~2, ~343/198, ~5
 
{{Optimal ET sequence|legend=1| 72, 198, 270, 342, 612, 954, 1205, 1475, 1547, 1817, 2159, 4660, 4930, 6819, 7089, 9590d, 11749d }}
 
== Bragi ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 4375/4374, 2097152/2096325
 
{{Mapping|legend=1| 1 0 2 -7 8 | 0 1 0 7 -3 | 0 0 3 -12 2 }}
 
: mapping generators: ~2, ~3, ~320/297
 
{{Optimal ET sequence|legend=1| 46, 111d, 159d, 178, 205, 224, 270, 494, 764, 1053, 1277, 1323, 1547, 1817, 4128, 10073bdee, 14201bdeee }}
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 2080/2079, 4375/4374, 10985/10976
 
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 }}
 
== Vidar ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 4375/4374, 100663296/100656875
 
{{Mapping|legend=1| 1 0 0 1 5 | 0 1 4 -9 -3 | 0 0 -5 20 4 }}
 
: mapping generators: ~2, ~3, ~96/55
 
{{Optimal ET sequence|legend=1| 46, 91, 133d, 137d, 178, 224, 270, 494, 764, 1395, 1619, 1665, 1889, 2159, 2653, 4812, 7735, 9894 }}
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 4225/4224, 4375/4374, 6656/6655
 
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 }}
 
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Ragismic family| ]] <!-- main article -->
[[Category:Ragismic| ]] <!-- key article -->
[[Category:Rank 3]]
Retrieved from "https://en.xen.wiki/w/Ragismic_family"