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Maja 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 '''maja family''' of [[Rank-2 temperament|rank-2]] [[temperament]]s [[Tempering out|tempers out]] the [[maja comma]], {{monzo| -3 -23 17 }} = 762939453125/753145430616.
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-04 13:13:40 UTC</tt>.<br>
: The original revision id was <tt>330089396</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">
=Maja=
Comma: 762939453125/753145430616


POTE generator: ~125/81 = 747.198
Maja was named by [[Petr Pařízek]] in 2011 for 13/10 is a generator and that ''M'' and ''J'' are the 13th letter and the 10th letter, respectively<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>. It is unrelated to either the [[interval quality|major quality]] or [[magic|magic temperament]].  


Map: [&lt;1 8 11|, &lt;0 -17 -23|]
== Maja ==
EDOs: 45, 53, 432, 485, 538, 591, 644, 697, 750
[[Subgroup]]: 2.3.5
Badness: 0.3610


==7-limit==
[[Comma list]]: 762939453125/753145430616
Commas: 2430/2401, 3125/3087


POTE generator: ~125/81 = 747.145
{{Mapping|legend=1| 1 8 11 | 0 -17 -23 }}


Map: [&lt;1 8 11 13|, &lt;0 -17 -23 -27|]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/81 = 747.198
EDOs: 45, 53, 469cd
Badness: 0.0894


==Majo==
{{Optimal ET sequence|legend=1| 8, 45, 53, 432, 485, 538, 591, 644, 697, 750, 803c }}
Commas: 6144/6125, 1250000/1240029


POTE generator: ~125/81 = 747.264
[[Badness]]: 0.361013


Map: [&lt;1 8 11 -7|, &lt;0 -17 -23 26|]
== Septimal maja ==
Wedgie: &lt;&lt;17 23 -26 -3 -89 -125||
[[Subgroup]]: 2.3.5.7
EDOs: 53, 167, 220
Badness: 0.1405


==11-limit==
[[Comma list]]: 2430/2401, 3125/3087  
Commas: 99/98, 121/120, 3125/3087


POTE generator: ~125/81 = 747.100
{{Mapping|legend=1| 1 8 11 13 | 0 -17 -23 -27 }}


Map: [&lt;1 8 11 13 11|, &lt;0 -17 -23 -27 -20|]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~54/35 = 747.145
EDOs: 45e, 53
Badness: 0.0500


==13-limit==
{{Optimal ET sequence|legend=1| 8d, 45, 53 }}
Commas: 176/175, 275/273, 325/324, 540/539


POTE generator: ~125/81 = 747.095
[[Badness]]: 0.089454


Map: [&lt;1 8 11 13 11 12|, &lt;0 -17 -23 -27 -20 -22|]
=== 11-limit ===
EDOs: 45ef, 53
Subgroup: 2.3.5.7.11
Badness: 0.0275


Comma list: 99/98, 121/120, 3125/3087


Mapping: {{mapping| 1 8 11 13 11 | 0 -17 -23 -27 -20 }}


Optimal tuning (POTE): ~2 = 1\1, ~54/35 = 747.100


{{Optimal ET sequence|legend=1| 8d, 45e, 53 }}


Badness: 0.049991


</pre></div>
=== 13-limit ===
<h4>Original HTML content:</h4>
Subgroup: 2.3.5.7.11.13
<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;Maja family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Maja"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Maja&lt;/h1&gt;
Comma list: 99/98, 121/120, 169/168, 275/273
Comma: 762939453125/753145430616&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 8 11 13 11 12 | 0 -17 -23 -27 -20 -22 }}
POTE generator: ~125/81 = 747.198&lt;br /&gt;
 
&lt;br /&gt;
Optimal tuning (POTE): ~2 = 1\1, ~20/13 = 747.095
Map: [&amp;lt;1 8 11|, &amp;lt;0 -17 -23|]&lt;br /&gt;
 
EDOs: 45, 53, 432, 485, 538, 591, 644, 697, 750&lt;br /&gt;
{{Optimal ET sequence|legend=1| 8d, 45ef, 53 }}
Badness: 0.3610&lt;br /&gt;
 
&lt;br /&gt;
Badness: 0.027532
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Maja-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;7-limit&lt;/h2&gt;
 
Commas: 2430/2401, 3125/3087 &lt;br /&gt;
== Majo ==
&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
POTE generator: ~125/81 = 747.145&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 6144/6125, 1250000/1240029
Map: [&amp;lt;1 8 11 13|, &amp;lt;0 -17 -23 -27|]&lt;br /&gt;
 
EDOs: 45, 53, 469cd&lt;br /&gt;
{{Mapping|legend=1| 1 8 11 -7 | 0 -17 -23 26 }}
Badness: 0.0894&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/81 = 747.264
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Maja-Majo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Majo&lt;/h2&gt;
 
Commas: 6144/6125, 1250000/1240029&lt;br /&gt;
{{Optimal ET sequence|legend=1| 53, 167, 220, 493bd, 713bdd }}
&lt;br /&gt;
 
POTE generator: ~125/81 = 747.264&lt;br /&gt;
[[Badness]]: 0.140489
&lt;br /&gt;
 
Map: [&amp;lt;1 8 11 -7|, &amp;lt;0 -17 -23 26|]&lt;br /&gt;
=== 11-limit ===
Wedgie: &amp;lt;&amp;lt;17 23 -26 -3 -89 -125||&lt;br /&gt;
Subgroup: 2.3.5.7.11
EDOs: 53, 167, 220&lt;br /&gt;
 
Badness: 0.1405&lt;br /&gt;
Comma list: 2200/2187, 3388/3375, 6144/6125
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Maja-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;11-limit&lt;/h2&gt;
Mapping: {{mapping| 1 8 11 -7 31 | 0 -17 -23 26 -73 }}
Commas: 99/98, 121/120, 3125/3087&lt;br /&gt;
 
&lt;br /&gt;
Optimal tuning (POTE): ~2 = 1\1, ~77/50 = 747.287
POTE generator: ~125/81 = 747.100&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 53, 114e, 167, 220, 387bd }}
Map: [&amp;lt;1 8 11 13 11|, &amp;lt;0 -17 -23 -27 -20|]&lt;br /&gt;
 
EDOs: 45e, 53&lt;br /&gt;
Badness: 0.081931
Badness: 0.0500&lt;br /&gt;
 
&lt;br /&gt;
=== 13-limit ===
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Maja-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;13-limit&lt;/h2&gt;
Subgroup: 2.3.5.7.11.13
Commas: 176/175, 275/273, 325/324, 540/539&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 325/324, 352/351, 1001/1000, 2704/2695
POTE generator: ~125/81 = 747.095&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 8 11 -7 31 12 | 0 -17 -23 26 -73 -22 }}
Map: [&amp;lt;1 8 11 13 11 12|, &amp;lt;0 -17 -23 -27 -20 -22|]&lt;br /&gt;
 
EDOs: 45ef, 53&lt;br /&gt;
Optimal tuning (POTE): ~2 = 1\1, ~20/13 = 747.286
Badness: 0.0275&lt;/body&gt;&lt;/html&gt;</pre></div>
 
{{Optimal ET sequence|legend=1| 53, 114e, 167, 220, 387bd }}
 
Badness: 0.043128
 
== Notes ==
 
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Maja family| ]] <!-- main article -->
[[Category:Maja| ]] <!-- key article -->
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Maja_family"