Ragismic family: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Wikispaces>genewardsmith
**Imported revision 303438478 - Original comment: **
 
(31 intermediate revisions by 9 users not shown)
Line 1: Line 1:
<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>2012-02-20 16:12:44 UTC</tt>.<br>
: The original revision id was <tt>303438478</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">[[toc]]


=Ragisma=
Temperaments discussed elsewhere include:
Comma: 4375/4374
* ''[[Sensigh]]'' → [[Sensamagic family #Sensigh|Sensamagic family]]
* ''[[Catakleismoid]]'' → [[Marvel family #Catakleismoid|Marvel family]]
* ''[[Ennealimmic]]'' → [[Breed family #Ennealimmic|Breed family]]


7-limit
Considered below are beyla, ulmo, thor, heimdall, bragi, and vidar.
[|1 0 0 0&gt;, |-1/7 0 4/7 1/7&gt;, |0 0 1 0&gt;, |0 0 0 1&gt;]
Eigenmonzos: 2, 8/7, 5/4


9-limit
== Ragismic ==
[|1 0 0 0&gt;, |0 1 0 0&gt;, |1/5 7/5 1/5 -1/5&gt;,
[[Subgroup]]: 2.3.5.7
|1/5 7/5 -4/5 4/5&gt;]
Eigenmonzos: 2, 4/3, 7/5


Lattice basis: 10/9 length=0.789 6/5 length=0.921
[[Comma list]]: [[4375/4374]]
Angle(10/9, 6/5) = 105.299
Map to lattice: [&lt;0 -1 -1 -3|, &lt;0 -1 -2 1|]


Map: [&lt;1 0 0 1|, &lt;0 1 0 7|, &lt;0 0 1 -4|]
{{Mapping|legend=1| 1 0 0 1 | 0 1 0 7 | 0 0 1 -4 }}
Generators: 2, 3, 5
Edos: 9, 19, 26, 27, 45, 46, 53, 72, 80, 91, 99, 171, 270, 441, 494, 612, 665, 935, 1106, 1277, 1376, 1718, 1889, 6279


[[Projection pair]]: 7 4374/625
: mapping generators: ~2, ~3, ~5


Scales: [[ragismic19]]
[[Mapping to lattice]]: [{{val| 0 -1 -1 -3 }}, {{val| 0 -1 -2 1 }}]


==11 limit children==
Lattice basis:
: 10/9 length = 0.789, 6/5 length = 0.921
: Angle (10/9, 6/5) = 105.299°


=Thor=
[[Minimax tuning]]:
Commas: 4375/4374, 3025/3024
* [[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


Minimax tuning
{{Optimal ET sequence|legend=1| 19, 27, 45, 46, 53, 72, 99, 171, 441, 612, 935, 1106, 1277, 1547, 1718, 4983, 6701, 8419, 17279c }}
[|1 0 0 0 0&gt;, |3/4 0 1/2 1/2 -1/2&gt;,  
|25/16 0 7/8 5/8 -7/8&gt;, |0 0 0 1 0&gt;,  
|25/16 0 -1/8 5/8 1/8&gt;]
Eigenmonzos: 2, 11/10, 8/7


Map: [&lt;2 0 0 2 5|, &lt;0 1 0 7 5|, &lt;0 0 1 -4 -3|]
[[Projection pair]]: ~7 = ~4374/625
Generators: 99/70, 3, 5
Badness: 0.0000888


Projection pairs: 2 9801/4900 7 21434787/3062500 11 2310905821257/210087500000 to 3.5.14/11
Scales: [[Ragismic19]], [[Ragismic chromatic]]


==Donar==
== Beyla ==
Commas: 4375/4374, 3025/3024, 4225/4224
[[Subgroup]]: 2.3.5.7.11


13-limit
[[Comma list]]: 385/384, 4375/4374
||1 0 0 0 0 0&gt;, |3/4 0 1/2 1/2 -1/2 0&gt;,
|25/16 0 7/8 5/8 -7/8 0&gt;, |0 0 0 1 0 0&gt;,
|25/16 0 -1/8 5/8 1/8 0&gt;,
|99/32 0 -11/16 -1/16 11/16 0&gt;]
Eigenmonzos: 2, 11/10, 8/7


15-limit minimax
{{Mapping|legend=1| 1 0 0 1 6 | 0 1 0 7 -6 | 0 0 1 -4 3 }}
[|1 0 0 0 0 0&gt;, |1/2 1/3 1/3 1/3 -1/3 0&gt;,
|9/8 7/12 7/12 1/3 -7/12 0&gt;, |0 0 0 1 0 0&gt;,
|13/8 -1/12 -1/12 2/3 1/12 0&gt;,
|55/16 -11/24 -11/24 1/6 11/24 0&gt;]
Eigenmonzos: 2, 8/7, 15/11


Lattice basis: 44/39 length = 0.3480 6/5 length = 0.7828
{{Optimal ET sequence|legend=1| 7, 19, 26, 45, 46, 53, 72, 118, 190, 315e, 361e, 433de, 623cdee }}
Angle(44/39, 6/5) = 85.3977
Map to lattice: [&lt;0 2 2 6 4 1|, &lt;0 -1 -2 1 1 2|]


Map: [&lt;2 0 1 -2 2 7|, &lt;0 1 0 7 5 3|, &lt;0 0 2 -8 -6 -5|]
[[Badness]]: 0.721 × 10<sup>-3</sup>
Generators: 99/70, 3, 220/117
Edos: 46, 80, 92, 126, 144, 178, 190, 224, 494, 684, 954, 1178, 1942, 3120, 3390
Badness: 0.000322


Scales: [[donar46]]
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


==Thunor==
Comma list: 169/168, 325/324, 385/384
Commas: 4375/4374, 3025/3024, 1716/1715


13 and 15 limit minimax
Mapping: {{mapping| 1 0 0 1 6 2 | 0 1 0 7 -6 4 | 0 0 1 -4 3 -2 }}
[|1 0 0 0 0 0&gt;, |7/10 4/5 0 -2/5 0 1/5&gt;,
|9/8 3/2 0 -3/4 0 1/4&gt;, |7/5 -2/5 0 1/5 0 2/5&gt;, |21/8 -1/2 0 1/4 0 1/4&gt;, |0 0 0 0 0 1&gt;]
Eigenmonzos: 2, 16/13, 9/7


Lattice basis: 10/9 length 0.4234 6/5 length 0.8426
{{Optimal ET sequence|legend=1| 7, 19, 26, 46, 53, 72, 118f, 125f, 171ef, 190ff, 197ef, 243eff }}
Angle(10/9, 6/5) = 84.126 degrees
Map to lattice: [&lt;0 -1 -2 -3 -2 -7|, &lt;0 -1 -2 1 1 1|] 


Map: [&lt;2 0 0 2 5 -3|, &lt;0 1 0 7 5 15|, &lt;0 0 1 -4 -3 -8|]
Badness: 0.840 × 10<sup>-3</sup>
Generators: 99/70, 3, 5
Edos: 26, 46, 72, 178, 224, 270, 494
Badness: 0.000341


==Rym==
== Ulmo ==
Commas: 4375/4374, 3025/3024, 4096/4095
[[Subgroup]]: 2.3.5.7.11


Map: [&lt;2 0 0 2 5 22|, &lt;0 1 0 7 5 -9|, &lt;0 0 1 -4 -3 3|]
[[Comma list]]: 176/175, 2200/2187
EDOs: 46, 106, 118, 152, 224, 270, 494, 764, 1106, 1376, 1870
Badness: 0.000549


=Vidar=
{{Mapping|legend=1| 1 0 0 1 -3 | 0 1 0 7 7 | 0 0 1 -4 -2 }}
Commas: 4375/4374, 100663296/100656875


=Bragi=
{{Optimal ET sequence|legend=1| 7, 39, 46, 53, 80, 126, 179, 259cd, 385bcd }}
Commas: 4375/4374, 2097152/2096325


=Beyla=
[[Badness]]: 1.23 × 10<sup>-3</sup>
Commas: 4374/4375, 385/384


Map: [&lt;1 0 0 1 6|, &lt;0 1 0 7 -6|, &lt;0 0 1 -4 3|]
=== 13-limit ===
EDOs: 7, 19, 26, 45, 46, 53, 72, 118, 190, 315e, 361e, 433de, 623cde
Subgroup: 2.3.5.7.11.13
Badness: 0.000721


==13-limit==
Comma list: 169/168, 176/175, 325/324
Commas: 169/168, 325/324, 385/384


Map: [&lt;1 0 0 1 6 2|, &lt;0 1 0 7 -6 4|, &lt;0 0 1 -4 3 -2|]
Mapping: {{mapping| 1 0 0 1 -3 2 | 0 1 0 7 7 4 | 0 0 1 -4 -2 -2 }}
EDOs: 7, 19, 26, 46, 53, 72, 118f, 125f, 171ef, 190f, 197ef, 243ef
 
Badness: 0.000840
{{Optimal ET sequence|legend=1| 7, 39, 46, 53, 80, 133d, 179, 312cdf }}
</pre></div>
 
<h4>Original HTML content:</h4>
Badness: 0.932 × 10<sup>-3</sup>
<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;&lt;!-- ws:start:WikiTextTocRule:20:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Ragisma"&gt;Ragisma&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Ragisma-11 limit children"&gt;11 limit children&lt;/a&gt;&lt;/div&gt;
== Thor ==
&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Thor"&gt;Thor&lt;/a&gt;&lt;/div&gt;
[[Subgroup]]: 2.3.5.7.11
&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Thor-Donar"&gt;Donar&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Thor-Thunor"&gt;Thunor&lt;/a&gt;&lt;/div&gt;
[[Comma list]]: 3025/3024, 4375/4374
&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Thor-Rym"&gt;Rym&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Vidar"&gt;Vidar&lt;/a&gt;&lt;/div&gt;
{{Mapping|legend=1| 2 0 0 2 5 | 0 1 0 7 5 | 0 0 1 -4 -3 }}
&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Bragi"&gt;Bragi&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Beyla"&gt;Beyla&lt;/a&gt;&lt;/div&gt;
: mapping generators: ~99/70, ~3, ~5
&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Beyla-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt;&lt;/div&gt;
[[Minimax tuning]]:
&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;br /&gt;
* [[11-odd-limit]] [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7.11/5
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Ragisma"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Ragisma&lt;/h1&gt;
 
Comma: 4375/4374&lt;br /&gt;
{{Optimal ET sequence|legend=1| 26, 34d, 46, 72, 118, 152, 224, 270, 342, 494, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }}
&lt;br /&gt;
 
7-limit&lt;br /&gt;
[[Badness]]: 0.0888 × 10<sup>-3</sup>
[|1 0 0 0&amp;gt;, |-1/7 0 4/7 1/7&amp;gt;, |0 0 1 0&amp;gt;, |0 0 0 1&amp;gt;]&lt;br /&gt;
 
Eigenmonzos: 2, 8/7, 5/4&lt;br /&gt;
[[Projection pair]]s: 2 = ~9801/4900, ~7 = ~21434787/3062500, ~11 = ~2310905821257/210087500000 to 3.5.14/11
&lt;br /&gt;
 
9-limit&lt;br /&gt;
=== Thunor ===
[|1 0 0 0&amp;gt;, |0 1 0 0&amp;gt;, |1/5 7/5 1/5 -1/5&amp;gt;, &lt;br /&gt;
Subgroup: 2.3.5.7.11.13
|1/5 7/5 -4/5 4/5&amp;gt;]&lt;br /&gt;
 
Eigenmonzos: 2, 4/3, 7/5&lt;br /&gt;
Comma list: 1716/1715, 2080/2079, 3025/3024
&lt;br /&gt;
 
Lattice basis: 10/9 length=0.789 6/5 length=0.921&lt;br /&gt;
Mapping: {{mapping| 2 0 0 2 5 -3 | 0 1 0 7 5 15 | 0 0 1 -4 -3 -8 }}
Angle(10/9, 6/5) = 105.299&lt;br /&gt;
 
Map to lattice: [&amp;lt;0 -1 -1 -3|, &amp;lt;0 -1 -2 1|]&lt;br /&gt;
Mapping to lattice: [{{val| 0 -1 -2 -3 -2 -7 }}, {{val| 0 -1 -2 1 1 1 }}] 
&lt;br /&gt;
 
Map: [&amp;lt;1 0 0 1|, &amp;lt;0 1 0 7|, &amp;lt;0 0 1 -4|]&lt;br /&gt;
Lattice basis:  
Generators: 2, 3, 5&lt;br /&gt;
: 10/9 length = 0.4234, 6/5 length = 0.8426
Edos: 9, 19, 26, 27, 45, 46, 53, 72, 80, 91, 99, 171, 270, 441, 494, 612, 665, 935, 1106, 1277, 1376, 1718, 1889, 6279 &lt;br /&gt;
: Angle (10/9, 6/5) = 84.126°
&lt;br /&gt;
 
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;: 7 4374/625&lt;br /&gt;
Minimax tuning:
&lt;br /&gt;
* 13- and 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.9/7.13
Scales: &lt;a class="wiki_link" href="/ragismic19"&gt;ragismic19&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 26, 46, 72, 152f, 198, 224, 270, 494, 764, 1258 }}
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Ragisma-11 limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11 limit children&lt;/h2&gt;
 
&lt;br /&gt;
Badness: 0.341 × 10<sup>-3</sup>
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Thor"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Thor&lt;/h1&gt;
 
Commas: 4375/4374, 3025/3024&lt;br /&gt;
=== Rym ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
Minimax tuning&lt;br /&gt;
 
[|1 0 0 0 0&amp;gt;, |3/4 0 1/2 1/2 -1/2&amp;gt;, &lt;br /&gt;
Comma list: 3025/3024, 4096/4095, 4375/4374
|25/16 0 7/8 5/8 -7/8&amp;gt;, |0 0 0 1 0&amp;gt;, &lt;br /&gt;
 
|25/16 0 -1/8 5/8 1/8&amp;gt;]&lt;br /&gt;
Mapping: {{mapping| 2 0 0 2 5 22 | 0 1 0 7 5 -9 | 0 0 1 -4 -3 3 }}
Eigenmonzos: 2, 11/10, 8/7&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 46, 72f, 106, 118, 152, 224, 270, 494, 764, 1106, 1376, 1870 }}
Map: [&amp;lt;2 0 0 2 5|, &amp;lt;0 1 0 7 5|, &amp;lt;0 0 1 -4 -3|]&lt;br /&gt;
 
Generators: 99/70, 3, 5&lt;br /&gt;
Badness: 0.549 × 10<sup>-3</sup>
Badness: 0.0000888&lt;br /&gt;
 
&lt;br /&gt;
=== Donar ===
Projection pairs: 2 9801/4900 7 21434787/3062500 11 2310905821257/210087500000 to 3.5.14/11&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Thor-Donar"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Donar&lt;/h2&gt;
Comma list: 3025/3024, 4225/4224, 4375/4374
Commas: 4375/4374, 3025/3024, 4225/4224&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 2 0 1 -2 2 7 | 0 1 0 7 5 3 | 0 0 2 -8 -6 -5 }}
13-limit&lt;br /&gt;
 
||1 0 0 0 0 0&amp;gt;, |3/4 0 1/2 1/2 -1/2 0&amp;gt;, &lt;br /&gt;
: mapping generators: ~99/70, ~3, ~220/117
|25/16 0 7/8 5/8 -7/8 0&amp;gt;, |0 0 0 1 0 0&amp;gt;, &lt;br /&gt;
 
|25/16 0 -1/8 5/8 1/8 0&amp;gt;, &lt;br /&gt;
Mapping to lattice: [{{val| 0 2 2 6 4 1 }}, {{val| 0 -1 -2 1 1 2 }}]
|99/32 0 -11/16 -1/16 11/16 0&amp;gt;]&lt;br /&gt;
 
Eigenmonzos: 2, 11/10, 8/7&lt;br /&gt;
Lattice basis:  
&lt;br /&gt;
: 44/39 length = 0.3480, 6/5 length = 0.7828
15-limit minimax&lt;br /&gt;
: Angle (44/39, 6/5) = 85.3977°
[|1 0 0 0 0 0&amp;gt;, |1/2 1/3 1/3 1/3 -1/3 0&amp;gt;, &lt;br /&gt;
 
|9/8 7/12 7/12 1/3 -7/12 0&amp;gt;, |0 0 0 1 0 0&amp;gt;, &lt;br /&gt;
Minimax tuning:
|13/8 -1/12 -1/12 2/3 1/12 0&amp;gt;, &lt;br /&gt;
* 13-odd-limit unchanged-interval (eigenmonzo) basis: 2.7.11/5
|55/16 -11/24 -11/24 1/6 11/24 0&amp;gt;]&lt;br /&gt;
* 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7.15/11
Eigenmonzos: 2, 8/7, 15/11&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 34d, 46, 80, 144, 178, 190, 224, 494, 684, 764, 954, 1178, 1448, 6970ceeff, 8418ceeff }}
Lattice basis: 44/39 length = 0.3480 6/5 length = 0.7828&lt;br /&gt;
 
Angle(44/39, 6/5) = 85.3977&lt;br /&gt;
Badness: 0.322 × 10<sup>-3</sup>
Map to lattice: [&amp;lt;0 2 2 6 4 1|, &amp;lt;0 -1 -2 1 1 2|]&lt;br /&gt;
 
&lt;br /&gt;
Scales: [[Donar46]]
Map: [&amp;lt;2 0 1 -2 2 7|, &amp;lt;0 1 0 7 5 3|, &amp;lt;0 0 2 -8 -6 -5|]&lt;br /&gt;
 
Generators: 99/70, 3, 220/117&lt;br /&gt;
== Heimdall ==
Edos: 46, 80, 92, 126, 144, 178, 190, 224, 494, 684, 954, 1178, 1942, 3120, 3390&lt;br /&gt;
[[Subgroup]]: 2.3.5.7.11
Badness: 0.000322&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 4375/4374, 117649/117612
Scales: &lt;a class="wiki_link" href="/donar46"&gt;donar46&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 1 0 0 1 2 | 0 2 0 14 37 | 0 0 1 -4 -12 }}
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Thor-Thunor"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Thunor&lt;/h2&gt;
 
Commas: 4375/4374, 3025/3024, 1716/1715&lt;br /&gt;
: mapping generators: ~2, ~343/198, ~5
&lt;br /&gt;
 
13 and 15 limit minimax&lt;br /&gt;
{{Optimal ET sequence|legend=1| 72, 198, 270, 342, 612, 954, 1205, 1475, 1547, 1817, 2159, 4660, 4930, 6819, 7089, 9590d, 11749d }}
[|1 0 0 0 0 0&amp;gt;, |7/10 4/5 0 -2/5 0 1/5&amp;gt;, &lt;br /&gt;
 
|9/8 3/2 0 -3/4 0 1/4&amp;gt;, |7/5 -2/5 0 1/5 0 2/5&amp;gt;, |21/8 -1/2 0 1/4 0 1/4&amp;gt;, |0 0 0 0 0 1&amp;gt;]&lt;br /&gt;
== Bragi ==
Eigenmonzos: 2, 16/13, 9/7&lt;br /&gt;
[[Subgroup]]: 2.3.5.7.11
&lt;br /&gt;
 
Lattice basis: 10/9 length 0.4234 6/5 length 0.8426&lt;br /&gt;
[[Comma list]]: 4375/4374, 2097152/2096325
Angle(10/9, 6/5) = 84.126 degrees&lt;br /&gt;
 
Map to lattice: [&amp;lt;0 -1 -2 -3 -2 -7|, &amp;lt;0 -1 -2 1 1 1|]  &lt;br /&gt;
{{Mapping|legend=1| 1 0 2 -7 8 | 0 1 0 7 -3 | 0 0 3 -12 2 }}
&lt;br /&gt;
 
Map: [&amp;lt;2 0 0 2 5 -3|, &amp;lt;0 1 0 7 5 15|, &amp;lt;0 0 1 -4 -3 -8|]&lt;br /&gt;
: mapping generators: ~2, ~3, ~320/297
Generators: 99/70, 3, 5&lt;br /&gt;
 
Edos: 26, 46, 72, 178, 224, 270, 494&lt;br /&gt;
{{Optimal ET sequence|legend=1| 46, 111d, 159d, 178, 205, 224, 270, 494, 764, 1053, 1277, 1323, 1547, 1817, 4128, 10073bdee, 14201bdeee }}
Badness: 0.000341&lt;br /&gt;
 
&lt;br /&gt;
=== 13-limit ===
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Thor-Rym"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Rym&lt;/h2&gt;
Subgroup: 2.3.5.7.11.13
Commas: 4375/4374, 3025/3024, 4096/4095&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 2080/2079, 4375/4374, 10985/10976
Map: [&amp;lt;2 0 0 2 5 22|, &amp;lt;0 1 0 7 5 -9|, &amp;lt;0 0 1 -4 -3 3|]&lt;br /&gt;
 
EDOs: 46, 106, 118, 152, 224, 270, 494, 764, 1106, 1376, 1870&lt;br /&gt;
Mapping: {{mapping| 1 0 2 -7 8 -6 | 0 1 0 7 -3 7 | 0 0 3 -12 2 -13 }}
Badness: 0.000549 &lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 46, 111df, 159df, 178, 205, 224, 270, 494, 764, 1258, 1771, 2041f, 2265, 2535f }}
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Vidar"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Vidar&lt;/h1&gt;
 
Commas: 4375/4374, 100663296/100656875&lt;br /&gt;
== Vidar ==
&lt;br /&gt;
[[Subgroup]]: 2.3.5.7.11
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Bragi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Bragi&lt;/h1&gt;
 
Commas: 4375/4374, 2097152/2096325&lt;br /&gt;
[[Comma list]]: 4375/4374, 100663296/100656875
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Beyla"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Beyla&lt;/h1&gt;
{{Mapping|legend=1| 1 0 0 1 5 | 0 1 4 -9 -3 | 0 0 -5 20 4 }}
Commas: 4374/4375, 385/384&lt;br /&gt;
 
&lt;br /&gt;
: mapping generators: ~2, ~3, ~96/55
Map: [&amp;lt;1 0 0 1 6|, &amp;lt;0 1 0 7 -6|, &amp;lt;0 0 1 -4 3|]&lt;br /&gt;
 
EDOs: 7, 19, 26, 45, 46, 53, 72, 118, 190, 315e, 361e, 433de, 623cde&lt;br /&gt;
{{Optimal ET sequence|legend=1| 46, 91, 133d, 137d, 178, 224, 270, 494, 764, 1395, 1619, 1665, 1889, 2159, 2653, 4812, 7735, 9894 }}
Badness: 0.000721&lt;br /&gt;
 
&lt;br /&gt;
=== 13-limit ===
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Beyla-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;13-limit&lt;/h2&gt;
Subgroup: 2.3.5.7.11.13
Commas: 169/168, 325/324, 385/384&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 4225/4224, 4375/4374, 6656/6655
Map: [&amp;lt;1 0 0 1 6 2|, &amp;lt;0 1 0 7 -6 4|, &amp;lt;0 0 1 -4 3 -2|]&lt;br /&gt;
 
EDOs: 7, 19, 26, 46, 53, 72, 118f, 125f, 171ef, 190f, 197ef, 243ef&lt;br /&gt;
Mapping: {{mapping| 1 0 0 1 5 6 | 0 1 4 -9 -3 -5 | 0 0 -5 20 4 7 }}
Badness: 0.000840&lt;/body&gt;&lt;/html&gt;</pre></div>
 
{{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]]

Latest revision as of 00:32, 24 June 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The ragismic family of temperaments are rank-3 microtemperaments which temper out 4375/4374.

Temperaments discussed elsewhere include:

Considered below are beyla, ulmo, thor, heimdall, bragi, and vidar.

Ragismic

Subgroup: 2.3.5.7

Comma list: 4375/4374

Mapping: [⟨1 0 0 1], ⟨0 1 0 7], ⟨0 0 1 -4]]

mapping generators: ~2, ~3, ~5

Mapping to lattice: [⟨0 -1 -1 -3], ⟨0 -1 -2 1]]

Lattice basis:

10/9 length = 0.789, 6/5 length = 0.921
Angle (10/9, 6/5) = 105.299°

Minimax tuning:

Optimal ET sequence: 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: [⟨1 0 0 1 6], ⟨0 1 0 7 -6], ⟨0 0 1 -4 3]]

Optimal ET sequence: 7, 19, 26, 45, 46, 53, 72, 118, 190, 315e, 361e, 433de, 623cdee

Badness: 0.721 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 325/324, 385/384

Mapping: [⟨1 0 0 1 6 2], ⟨0 1 0 7 -6 4], ⟨0 0 1 -4 3 -2]]

Optimal ET sequence: 7, 19, 26, 46, 53, 72, 118f, 125f, 171ef, 190ff, 197ef, 243eff

Badness: 0.840 × 10-3

Ulmo

Subgroup: 2.3.5.7.11

Comma list: 176/175, 2200/2187

Mapping: [⟨1 0 0 1 -3], ⟨0 1 0 7 7], ⟨0 0 1 -4 -2]]

Optimal ET sequence: 7, 39, 46, 53, 80, 126, 179, 259cd, 385bcd

Badness: 1.23 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 176/175, 325/324

Mapping: [⟨1 0 0 1 -3 2], ⟨0 1 0 7 7 4], ⟨0 0 1 -4 -2 -2]]

Optimal ET sequence: 7, 39, 46, 53, 80, 133d, 179, 312cdf

Badness: 0.932 × 10-3

Thor

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 4375/4374

Mapping: [⟨2 0 0 2 5], ⟨0 1 0 7 5], ⟨0 0 1 -4 -3]]

mapping generators: ~99/70, ~3, ~5

Minimax tuning:

Optimal ET sequence: 26, 34d, 46, 72, 118, 152, 224, 270, 342, 494, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee

Badness: 0.0888 × 10-3

Projection pairs: 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: [⟨2 0 0 2 5 -3], ⟨0 1 0 7 5 15], ⟨0 0 1 -4 -3 -8]]

Mapping to lattice: [⟨0 -1 -2 -3 -2 -7], ⟨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: 26, 46, 72, 152f, 198, 224, 270, 494, 764, 1258

Badness: 0.341 × 10-3

Rym

Subgroup: 2.3.5.7.11.13

Comma list: 3025/3024, 4096/4095, 4375/4374

Mapping: [⟨2 0 0 2 5 22], ⟨0 1 0 7 5 -9], ⟨0 0 1 -4 -3 3]]

Optimal ET sequence: 46, 72f, 106, 118, 152, 224, 270, 494, 764, 1106, 1376, 1870

Badness: 0.549 × 10-3

Donar

Subgroup: 2.3.5.7.11.13

Comma list: 3025/3024, 4225/4224, 4375/4374

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: [⟨0 2 2 6 4 1], ⟨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: 34d, 46, 80, 144, 178, 190, 224, 494, 684, 764, 954, 1178, 1448, 6970ceeff, 8418ceeff

Badness: 0.322 × 10-3

Scales: Donar46

Heimdall

Subgroup: 2.3.5.7.11

Comma list: 4375/4374, 117649/117612

Mapping: [⟨1 0 0 1 2], ⟨0 2 0 14 37], ⟨0 0 1 -4 -12]]

mapping generators: ~2, ~343/198, ~5

Optimal ET sequence: 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: [⟨1 0 2 -7 8], ⟨0 1 0 7 -3], ⟨0 0 3 -12 2]]

mapping generators: ~2, ~3, ~320/297

Optimal ET sequence: 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: [⟨1 0 2 -7 8 -6], ⟨0 1 0 7 -3 7], ⟨0 0 3 -12 2 -13]]

Optimal ET sequence: 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: [⟨1 0 0 1 5], ⟨0 1 4 -9 -3], ⟨0 0 -5 20 4]]

mapping generators: ~2, ~3, ~96/55

Optimal ET sequence: 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: [⟨1 0 0 1 5 6], ⟨0 1 4 -9 -3 -5], ⟨0 0 -5 20 4 7]]

Optimal ET sequence: 46, 87d, 91, 133d, 137d, 178, 224, 270, 494, 764, 1125, 1395, 1619, 1665, 1889, 4048, 4542, 6431f

Retrieved from "https://en.xen.wiki/index.php?title=Ragismic_family&oldid=200913"