Xenharmonic Wiki

Augmented family: Difference between revisions

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VisualWikitext
Wikispaces>genewardsmith
**Imported revision 539738324 - Original comment: **
Wikispaces>clamengh
**Imported revision 564624523 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2015-02-04 15:03:45 UTC</tt>.<br>
: This revision was by author [[User:clamengh|clamengh]] and made on <tt>2015-11-01 06:24:59 UTC</tt>.<br>
: The original revision id was <tt>539738324</tt>.<br>
: The original revision id was <tt>564624523</tt>.<br>
: The revision comment was: <tt></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>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
Line 86: Line 86:
Badness: 0.0229
Badness: 0.0229


===Agene===
===Agene===  
Commas: 56/55, 64/63, 78/77, 100/99
Commas: 56/55, 64/63, 78/77, 100/99


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Badness: 0.0423
Badness: 0.0423


=Trug=
=Trug=  
Commas: 128/125, 360/343
Commas: 128/125, 360/343


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Map: [&lt;9 0 21 11 17 19|, &lt;0 1 0 1 1 1|]
Map: [&lt;9 0 21 11 17 19|, &lt;0 1 0 1 1 1|]
EDOs: 9, 27e, 36, 63ce
EDOs: 9, 27e, 36, 63ce
Badness: 0.0241</pre></div>
Badness: 0.0241
 
==Music==
[[https://www.prismnet.com/~hmiller/music/temp-augmented.html|Herman's Miller page about augmented temperament]]</pre></div>
<h4>Original HTML content:</h4>
<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Augmented family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:76:&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:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Seven limit children"&gt;Seven limit children&lt;/a&gt;&lt;/div&gt;
<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;Augmented family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:78:&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:78 --&gt;&lt;!-- ws:start:WikiTextTocRule:79: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Seven limit children"&gt;Seven limit children&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:77 --&gt;&lt;!-- ws:start:WikiTextTocRule:78: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#August"&gt;August&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:79 --&gt;&lt;!-- ws:start:WikiTextTocRule:80: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#August"&gt;August&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:78 --&gt;&lt;!-- ws:start:WikiTextTocRule:79: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#August-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#August-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:79 --&gt;&lt;!-- ws:start:WikiTextTocRule:80: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#August-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:81 --&gt;&lt;!-- ws:start:WikiTextTocRule:82: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#August-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#August-Augustus"&gt;Augustus&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:82 --&gt;&lt;!-- ws:start:WikiTextTocRule:83: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#August-Augustus"&gt;Augustus&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:81 --&gt;&lt;!-- ws:start:WikiTextTocRule:82: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Augene"&gt;Augene&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:83 --&gt;&lt;!-- ws:start:WikiTextTocRule:84: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Augene"&gt;Augene&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:82 --&gt;&lt;!-- ws:start:WikiTextTocRule:83: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Augene-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:84 --&gt;&lt;!-- ws:start:WikiTextTocRule:85: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Augene-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:83 --&gt;&lt;!-- ws:start:WikiTextTocRule:84: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Augene-11-limit-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:85 --&gt;&lt;!-- ws:start:WikiTextTocRule:86: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Augene-11-limit-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:84 --&gt;&lt;!-- ws:start:WikiTextTocRule:85: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Augene-11-limit-Ogene"&gt;Ogene&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:86 --&gt;&lt;!-- ws:start:WikiTextTocRule:87: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Augene-11-limit-Ogene"&gt;Ogene&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:85 --&gt;&lt;!-- ws:start:WikiTextTocRule:86: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Augene-11-limit-Agene"&gt;Agene&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:87 --&gt;&lt;!-- ws:start:WikiTextTocRule:88: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Augene-11-limit-Agene"&gt;Agene&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:86 --&gt;&lt;!-- ws:start:WikiTextTocRule:87: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Augene-Eugene"&gt;Eugene&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;!-- ws:start:WikiTextTocRule:89: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Augene-Eugene"&gt;Eugene&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:87 --&gt;&lt;!-- ws:start:WikiTextTocRule:88: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Inflated"&gt;Inflated&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:89 --&gt;&lt;!-- ws:start:WikiTextTocRule:90: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Inflated"&gt;Inflated&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;!-- ws:start:WikiTextTocRule:89: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Inflated-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:90 --&gt;&lt;!-- ws:start:WikiTextTocRule:91: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Inflated-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:89 --&gt;&lt;!-- ws:start:WikiTextTocRule:90: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Deflated"&gt;Deflated&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:91 --&gt;&lt;!-- ws:start:WikiTextTocRule:92: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Deflated"&gt;Deflated&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:90 --&gt;&lt;!-- ws:start:WikiTextTocRule:91: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Hexe"&gt;Hexe&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:92 --&gt;&lt;!-- ws:start:WikiTextTocRule:93: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Hexe"&gt;Hexe&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:91 --&gt;&lt;!-- ws:start:WikiTextTocRule:92: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hexe-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:93 --&gt;&lt;!-- ws:start:WikiTextTocRule:94: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hexe-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:92 --&gt;&lt;!-- ws:start:WikiTextTocRule:93: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hexe-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:94 --&gt;&lt;!-- ws:start:WikiTextTocRule:95: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hexe-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:93 --&gt;&lt;!-- ws:start:WikiTextTocRule:94: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Hemiaug"&gt;Hemiaug&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:95 --&gt;&lt;!-- ws:start:WikiTextTocRule:96: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Hemiaug"&gt;Hemiaug&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:94 --&gt;&lt;!-- ws:start:WikiTextTocRule:95: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hemiaug-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:96 --&gt;&lt;!-- ws:start:WikiTextTocRule:97: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hemiaug-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:95 --&gt;&lt;!-- ws:start:WikiTextTocRule:96: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hemiaug-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:97 --&gt;&lt;!-- ws:start:WikiTextTocRule:98: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hemiaug-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:96 --&gt;&lt;!-- ws:start:WikiTextTocRule:97: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Triforce"&gt;Triforce&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:98 --&gt;&lt;!-- ws:start:WikiTextTocRule:99: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Triforce"&gt;Triforce&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:97 --&gt;&lt;!-- ws:start:WikiTextTocRule:98: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Triforce-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:99 --&gt;&lt;!-- ws:start:WikiTextTocRule:100: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Triforce-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:98 --&gt;&lt;!-- ws:start:WikiTextTocRule:99: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Triforce-11-limit-Musical example:"&gt;Musical example:&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:100 --&gt;&lt;!-- ws:start:WikiTextTocRule:101: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Triforce-11-limit-Musical example:"&gt;Musical example:&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:99 --&gt;&lt;!-- ws:start:WikiTextTocRule:100: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Triforce-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:101 --&gt;&lt;!-- ws:start:WikiTextTocRule:102: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Triforce-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:100 --&gt;&lt;!-- ws:start:WikiTextTocRule:101: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Triforce-Semitriforce"&gt;Semitriforce&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:102 --&gt;&lt;!-- ws:start:WikiTextTocRule:103: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Triforce-Semitriforce"&gt;Semitriforce&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:101 --&gt;&lt;!-- ws:start:WikiTextTocRule:102: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#toc25"&gt; &lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:103 --&gt;&lt;!-- ws:start:WikiTextTocRule:104: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#toc25"&gt; &lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:102 --&gt;&lt;!-- ws:start:WikiTextTocRule:103: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Hemiug"&gt;Hemiug&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:104 --&gt;&lt;!-- ws:start:WikiTextTocRule:105: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Hemiug"&gt;Hemiug&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:103 --&gt;&lt;!-- ws:start:WikiTextTocRule:104: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hemiug-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:105 --&gt;&lt;!-- ws:start:WikiTextTocRule:106: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hemiug-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:104 --&gt;&lt;!-- ws:start:WikiTextTocRule:105: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hemiug-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:106 --&gt;&lt;!-- ws:start:WikiTextTocRule:107: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hemiug-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:105 --&gt;&lt;!-- ws:start:WikiTextTocRule:106: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Trug"&gt;Trug&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:107 --&gt;&lt;!-- ws:start:WikiTextTocRule:108: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Trug"&gt;Trug&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:106 --&gt;&lt;!-- ws:start:WikiTextTocRule:107: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Oodako"&gt;Oodako&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:108 --&gt;&lt;!-- ws:start:WikiTextTocRule:109: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Oodako"&gt;Oodako&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:107 --&gt;&lt;!-- ws:start:WikiTextTocRule:108: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Oodako-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:109 --&gt;&lt;!-- ws:start:WikiTextTocRule:110: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Oodako-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:108 --&gt;&lt;!-- ws:start:WikiTextTocRule:109: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Oodako-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:110 --&gt;&lt;!-- ws:start:WikiTextTocRule:111: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Oodako-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:109 --&gt;&lt;!-- ws:start:WikiTextTocRule:110: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Hemisemiaug"&gt;Hemisemiaug&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:111 --&gt;&lt;!-- ws:start:WikiTextTocRule:112: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Hemisemiaug"&gt;Hemisemiaug&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:110 --&gt;&lt;!-- ws:start:WikiTextTocRule:111: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hemisemiaug-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:112 --&gt;&lt;!-- ws:start:WikiTextTocRule:113: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Hemisemiaug-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:111 --&gt;&lt;!-- ws:start:WikiTextTocRule:112: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Niner"&gt;Niner&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:113 --&gt;&lt;!-- ws:start:WikiTextTocRule:114: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Niner"&gt;Niner&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:112 --&gt;&lt;!-- ws:start:WikiTextTocRule:113: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Niner-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:114 --&gt;&lt;!-- ws:start:WikiTextTocRule:115: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Niner-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:113 --&gt;&lt;!-- ws:start:WikiTextTocRule:114: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Niner-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:115 --&gt;&lt;!-- ws:start:WikiTextTocRule:116: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Niner-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:114 --&gt;&lt;!-- ws:start:WikiTextTocRule:115: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:116 --&gt;&lt;!-- ws:start:WikiTextTocRule:117: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Niner-Music"&gt;Music&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:115 --&gt;The 5-limit parent comma for the &lt;strong&gt;augmented family&lt;/strong&gt; is 128/125, the &lt;a class="wiki_link" href="/128_125"&gt;diesis&lt;/a&gt;. Its &lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt; is |7 0 -3&amp;gt;, and flipping that yields &amp;lt;&amp;lt;3 0 -7|| for the &lt;a class="wiki_link" href="/wedgie"&gt;wedgie&lt;/a&gt;. Hence the period is 1/3 octave, and this is what is used for a major third. The &lt;a class="wiki_link" href="/generator"&gt;generator&lt;/a&gt; can be taken as a fifth or a semitone, and &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, with its excellent fifth, is an obvious tuning for &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; augmented, though a sharper fifth might be preferred to go with the sharp third.&lt;br /&gt;
&lt;!-- ws:end:WikiTextTocRule:117 --&gt;&lt;!-- ws:start:WikiTextTocRule:118: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:118 --&gt;The 5-limit parent comma for the &lt;strong&gt;augmented family&lt;/strong&gt; is 128/125, the &lt;a class="wiki_link" href="/128_125"&gt;diesis&lt;/a&gt;. Its &lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt; is |7 0 -3&amp;gt;, and flipping that yields &amp;lt;&amp;lt;3 0 -7|| for the &lt;a class="wiki_link" href="/wedgie"&gt;wedgie&lt;/a&gt;. Hence the period is 1/3 octave, and this is what is used for a major third. The &lt;a class="wiki_link" href="/generator"&gt;generator&lt;/a&gt; can be taken as a fifth or a semitone, and &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, with its excellent fifth, is an obvious tuning for &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; augmented, though a sharper fifth might be preferred to go with the sharp third.&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Seven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Seven limit children&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Seven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Seven limit children&lt;/h1&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="Augene-11-limit-Agene"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Agene&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="Augene-11-limit-Agene"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Agene&lt;/h3&gt;
Commas: 56/55, 64/63, 78/77, 100/99&lt;br /&gt;
Commas: 56/55, 64/63, 78/77, 100/99&lt;br /&gt;
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POTE generator: ~3/2 = 709.677&lt;br /&gt;
POTE generator: ~3/2 = 709.677&lt;br /&gt;
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Badness: 0.0202&lt;br /&gt;
Badness: 0.0202&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Triforce-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;11-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Triforce-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;11-limit&lt;/h2&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc29"&gt;&lt;a name="Trug"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;Trug&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc29"&gt;&lt;a name="Trug"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;Trug&lt;/h1&gt;
Commas: 128/125, 360/343&lt;br /&gt;
Commas: 128/125, 360/343&lt;br /&gt;
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POTE generator: ~48/35 = 501.980&lt;br /&gt;
POTE generator: ~48/35 = 501.980&lt;br /&gt;
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Map: [&amp;lt;9 0 21 11 17 19|, &amp;lt;0 1 0 1 1 1|]&lt;br /&gt;
Map: [&amp;lt;9 0 21 11 17 19|, &amp;lt;0 1 0 1 1 1|]&lt;br /&gt;
EDOs: 9, 27e, 36, 63ce&lt;br /&gt;
EDOs: 9, 27e, 36, 63ce&lt;br /&gt;
Badness: 0.0241&lt;/body&gt;&lt;/html&gt;</pre></div>
Badness: 0.0241&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:76:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc38"&gt;&lt;a name="Niner-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:76 --&gt;Music&lt;/h2&gt;
&lt;a class="wiki_link_ext" href="https://www.prismnet.com/~hmiller/music/temp-augmented.html" rel="nofollow"&gt;Herman's Miller page about augmented temperament&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
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