Maja family: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Wikispaces>genewardsmith
**Imported revision 394448992 - Original comment: **
 
(19 intermediate revisions by 10 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 '''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>2012-12-23 22:53:31 UTC</tt>.<br>
: The original revision id was <tt>394448992</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]]


=Maja=
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]].
Comma: 762939453125/753145430616


POTE generator: ~125/81 = 747.198
== Maja ==
[[Subgroup]]: 2.3.5


Map: [&lt;1 8 11|, &lt;0 -17 -23|]
[[Comma list]]: 762939453125/753145430616
EDOs: 45, 53, 432, 485, 538, 591, 644, 697, 750
Badness: 0.3610


==7-limit==
{{Mapping|legend=1| 1 8 11 | 0 -17 -23 }}
Commas: 2430/2401, 3125/3087


POTE generator: ~125/81 = 747.145
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/81 = 747.198


Map: [&lt;1 8 11 13|, &lt;0 -17 -23 -27|]
{{Optimal ET sequence|legend=1| 8, 45, 53, 432, 485, 538, 591, 644, 697, 750, 803c }}
EDOs: 45, 53, 469cd
Badness: 0.0894


==11-limit==
[[Badness]]: 0.361013
Commas: 99/98, 121/120, 3125/3087


POTE generator: ~125/81 = 747.100
== Septimal maja ==
[[Subgroup]]: 2.3.5.7


Map: [&lt;1 8 11 13 11|, &lt;0 -17 -23 -27 -20|]
[[Comma list]]: 2430/2401, 3125/3087
EDOs: 45e, 53
Badness: 0.0500


==13-limit==
{{Mapping|legend=1| 1 8 11 13 | 0 -17 -23 -27 }}
Commas: 176/175, 275/273, 325/324, 540/539


POTE generator: ~125/81 = 747.095
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~54/35 = 747.145


Map: [&lt;1 8 11 13 11 12|, &lt;0 -17 -23 -27 -20 -22|]
{{Optimal ET sequence|legend=1| 8d, 45, 53 }}
EDOs: 45ef, 53
Badness: 0.0275


=Majo=
[[Badness]]: 0.089454
Commas: 6144/6125, 1250000/1240029


POTE generator: ~125/81 = 747.264
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;1 8 11 -7|, &lt;0 -17 -23 26|]
Comma list: 99/98, 121/120, 3125/3087
Wedgie: &lt;&lt;17 23 -26 -3 -89 -125||
EDOs: 53, 167, 220
Badness: 0.1405


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;!-- ws:start:WikiTextTocRule:10:&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:10 --&gt;&lt;!-- ws:start:WikiTextTocRule:11: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Maja"&gt;Maja&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:11 --&gt;&lt;!-- ws:start:WikiTextTocRule:12: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Maja-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
Comma list: 99/98, 121/120, 169/168, 275/273
&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Maja-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Maja-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
Mapping: {{mapping| 1 8 11 13 11 12 | 0 -17 -23 -27 -20 -22 }}
&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Majo"&gt;Majo&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt;&lt;/div&gt;
Optimal tuning (POTE): ~2 = 1\1, ~20/13 = 747.095
&lt;!-- ws:end:WikiTextTocRule:16 --&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;
{{Optimal ET sequence|legend=1| 8d, 45ef, 53 }}
Comma: 762939453125/753145430616&lt;br /&gt;
 
&lt;br /&gt;
Badness: 0.027532
POTE generator: ~125/81 = 747.198&lt;br /&gt;
 
&lt;br /&gt;
== Majo ==
Map: [&amp;lt;1 8 11|, &amp;lt;0 -17 -23|]&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
EDOs: 45, 53, 432, 485, 538, 591, 644, 697, 750&lt;br /&gt;
 
Badness: 0.3610&lt;br /&gt;
[[Comma list]]: 6144/6125, 1250000/1240029
&lt;br /&gt;
 
&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;
{{Mapping|legend=1| 1 8 11 -7 | 0 -17 -23 26 }}
Commas: 2430/2401, 3125/3087 &lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/81 = 747.264
POTE generator: ~125/81 = 747.145&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 53, 167, 220, 493bd, 713bdd }}
Map: [&amp;lt;1 8 11 13|, &amp;lt;0 -17 -23 -27|]&lt;br /&gt;
 
EDOs: 45, 53, 469cd&lt;br /&gt;
[[Badness]]: 0.140489
Badness: 0.0894&lt;br /&gt;
 
&lt;br /&gt;
=== 11-limit ===
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Maja-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
Subgroup: 2.3.5.7.11
Commas: 99/98, 121/120, 3125/3087&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 2200/2187, 3388/3375, 6144/6125
POTE generator: ~125/81 = 747.100&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 8 11 -7 31 | 0 -17 -23 26 -73 }}
Map: [&amp;lt;1 8 11 13 11|, &amp;lt;0 -17 -23 -27 -20|]&lt;br /&gt;
 
EDOs: 45e, 53&lt;br /&gt;
Optimal tuning (POTE): ~2 = 1\1, ~77/50 = 747.287
Badness: 0.0500&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 53, 114e, 167, 220, 387bd }}
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Maja-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
 
Commas: 176/175, 275/273, 325/324, 540/539&lt;br /&gt;
Badness: 0.081931
&lt;br /&gt;
 
POTE generator: ~125/81 = 747.095&lt;br /&gt;
=== 13-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
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;
Comma list: 325/324, 352/351, 1001/1000, 2704/2695
Badness: 0.0275&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 8 11 -7 31 12 | 0 -17 -23 26 -73 -22 }}
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Majo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Majo&lt;/h1&gt;
 
Commas: 6144/6125, 1250000/1240029&lt;br /&gt;
Optimal tuning (POTE): ~2 = 1\1, ~20/13 = 747.286
&lt;br /&gt;
 
POTE generator: ~125/81 = 747.264&lt;br /&gt;
{{Optimal ET sequence|legend=1| 53, 114e, 167, 220, 387bd }}
&lt;br /&gt;
 
Map: [&amp;lt;1 8 11 -7|, &amp;lt;0 -17 -23 26|]&lt;br /&gt;
Badness: 0.043128
Wedgie: &amp;lt;&amp;lt;17 23 -26 -3 -89 -125||&lt;br /&gt;
 
EDOs: 53, 167, 220&lt;br /&gt;
== Notes ==
Badness: 0.1405&lt;/body&gt;&lt;/html&gt;</pre></div>
 
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Maja family| ]] <!-- main article -->
[[Category:Maja| ]] <!-- key article -->
[[Category:Rank 2]]

Latest revision as of 00:26, 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 maja family of rank-2 temperaments tempers out the maja comma, [-3 -23 17⟩ = 762939453125/753145430616.

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[1]. It is unrelated to either the major quality or magic temperament.

Maja

Subgroup: 2.3.5

Comma list: 762939453125/753145430616

Mapping: [⟨1 8 11], ⟨0 -17 -23]]

Optimal tuning (POTE): ~2 = 1\1, ~125/81 = 747.198

Optimal ET sequence: 8, 45, 53, 432, 485, 538, 591, 644, 697, 750, 803c

Badness: 0.361013

Septimal maja

Subgroup: 2.3.5.7

Comma list: 2430/2401, 3125/3087

Mapping: [⟨1 8 11 13], ⟨0 -17 -23 -27]]

Optimal tuning (POTE): ~2 = 1\1, ~54/35 = 747.145

Optimal ET sequence: 8d, 45, 53

Badness: 0.089454

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 8 11 13 11], ⟨0 -17 -23 -27 -20]]

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

Optimal ET sequence: 8d, 45e, 53

Badness: 0.049991

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 99/98, 121/120, 169/168, 275/273

Mapping: [⟨1 8 11 13 11 12], ⟨0 -17 -23 -27 -20 -22]]

Optimal tuning (POTE): ~2 = 1\1, ~20/13 = 747.095

Optimal ET sequence: 8d, 45ef, 53

Badness: 0.027532

Majo

Subgroup: 2.3.5.7

Comma list: 6144/6125, 1250000/1240029

Mapping: [⟨1 8 11 -7], ⟨0 -17 -23 26]]

Optimal tuning (POTE): ~2 = 1\1, ~125/81 = 747.264

Optimal ET sequence: 53, 167, 220, 493bd, 713bdd

Badness: 0.140489

11-limit

Subgroup: 2.3.5.7.11

Comma list: 2200/2187, 3388/3375, 6144/6125

Mapping: [⟨1 8 11 -7 31], ⟨0 -17 -23 26 -73]]

Optimal tuning (POTE): ~2 = 1\1, ~77/50 = 747.287

Optimal ET sequence: 53, 114e, 167, 220, 387bd

Badness: 0.081931

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 352/351, 1001/1000, 2704/2695

Mapping: [⟨1 8 11 -7 31 12], ⟨0 -17 -23 26 -73 -22]]

Optimal tuning (POTE): ~2 = 1\1, ~20/13 = 747.286

Optimal ET sequence: 53, 114e, 167, 220, 387bd

Badness: 0.043128

Notes

  1. ↑ Yahoo! Tuning Group | Suggested names for the unclasified temperaments
Retrieved from "https://en.xen.wiki/index.php?title=Maja_family&oldid=200718"