Octagar temperaments: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
__FORCETOC__
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>2014-04-27 14:54:49 UTC</tt>.<br>
: The original revision id was <tt>504840782</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]]
 
Octagar temperaments temper out the octagar comma, |5 -4 3 -2&gt; = 4000/3969.
Octagar temperaments temper out the octagar comma, |5 -4 3 -2&gt; = 4000/3969.


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Map: [&lt;1 2 3 3|, &lt;0 -17 -28 -8|]
Map: [&lt;1 2 3 3|, &lt;0 -17 -28 -8|]
Wedgie: &lt;&lt;17 28 8 5 -35 -60||
Wedgie: &lt;&lt;17 28 8 5 -35 -60||
EDOs: 41, 206, 247bc, 288bcd, 329bcd
EDOs: 41, 206, 247bc, 288bcd, 329bcd
Badness: 0.1429
Badness: 0.1429


Line 26: Line 21:


Map: [&lt;1 2 3 3 4|, &lt;0 -17 -28 -8 -22|]
Map: [&lt;1 2 3 3 4|, &lt;0 -17 -28 -8 -22|]
EDOs: 41, 206e
EDOs: 41, 206e
Badness: 0.0632
Badness: 0.0632


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Map: [&lt;1 2 3 3 4 4|, &lt;0 -17 -28 -8 -22 -12|]
Map: [&lt;1 2 3 3 4 4|, &lt;0 -17 -28 -8 -22 -12|]
EDOs: 41, 124ef, 165ef
EDOs: 41, 124ef, 165ef
Badness: 0.0436
Badness: 0.0436


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Map: [&lt;1 3 5 4|, &lt;0 -19 -36 -16|]
Map: [&lt;1 3 5 4|, &lt;0 -19 -36 -16|]
EDOs: 27, 94, 121, 215, 336d
EDOs: 27, 94, 121, 215, 336d
Badness: 0.1075
Badness: 0.1075


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Map: [&lt;1 3 5 4 8|, &lt;0 -19 -36 -16 -61|]
Map: [&lt;1 3 5 4 8|, &lt;0 -19 -36 -16 -61|]
EDOs: 94, 121, 215, 336de, 551bde
EDOs: 94, 121, 215, 336de, 551bde
Badness: 0.0459
Badness: 0.0459


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Map: [&lt;1 3 5 4 8 4|, &lt;0 -19 -36 -16 -61 -4|]
Map: [&lt;1 3 5 4 8 4|, &lt;0 -19 -36 -16 -61 -4|]
EDOs: 94, 121, 215, 336def
EDOs: 94, 121, 215, 336def
Badness: 0.0285
Badness: 0.0285
</pre></div>
<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;Octagar temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:12:&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:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Slendi"&gt;Slendi&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="#Slendi-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Slendi-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Slithy"&gt;Slithy&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Slithy-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Slithy-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;br /&gt;
Octagar temperaments temper out the octagar comma, |5 -4 3 -2&amp;gt; = 4000/3969.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Slendi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Slendi&lt;/h1&gt;
Commas: 4000/3969, 84035/82944&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~49/48 = 29.181&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 3|, &amp;lt;0 -17 -28 -8|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;17 28 8 5 -35 -60||&lt;br /&gt;
EDOs: 41, 206, 247bc, 288bcd, 329bcd&lt;br /&gt;
Badness: 0.1429&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Slendi-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11-limit&lt;/h2&gt;
Commas: 100/99, 245/242, 46656/46585&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~49/48 = 29.180&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 3 4|, &amp;lt;0 -17 -28 -8 -22|]&lt;br /&gt;
EDOs: 41, 206e&lt;br /&gt;
Badness: 0.0632&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Slendi-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;13-limit&lt;/h2&gt;
Commas: 100/99, 144/143, 245/242, 343/338&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~49/48 = 29.125&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 3 4 4|, &amp;lt;0 -17 -28 -8 -22 -12|]&lt;br /&gt;
EDOs: 41, 124ef, 165ef&lt;br /&gt;
Badness: 0.0436&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Slithy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Slithy&lt;/h1&gt;
Commas: 4000/3969, 420175/419904&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~21/20 = 89.282&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 3 5 4|, &amp;lt;0 -19 -36 -16|]&lt;br /&gt;
EDOs: 27, 94, 121, 215, 336d&lt;br /&gt;
Badness: 0.1075&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Slithy-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;11-limit&lt;/h2&gt;
Commas: 540/539, 2200/2187, 4375/4356&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~21/20 = 89.291&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 3 5 4 8|, &amp;lt;0 -19 -36 -16 -61|]&lt;br /&gt;
EDOs: 94, 121, 215, 336de, 551bde&lt;br /&gt;
Badness: 0.0459&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Slithy-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;13-limit&lt;/h2&gt;
Commas: 325/324, 352/351, 540/539, 1575/1573&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~21/20 = 89.286&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 3 5 4 8 4|, &amp;lt;0 -19 -36 -16 -61 -4|]&lt;br /&gt;
EDOs: 94, 121, 215, 336def&lt;br /&gt;
Badness: 0.0285&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

Octagar temperaments temper out the octagar comma, |5 -4 3 -2> = 4000/3969.

Slendi

Commas: 4000/3969, 84035/82944

POTE generator: ~49/48 = 29.181

Map: [<1 2 3 3|, <0 -17 -28 -8|]

Wedgie: <<17 28 8 5 -35 -60||

EDOs: 41, 206, 247bc, 288bcd, 329bcd

Badness: 0.1429

11-limit

Commas: 100/99, 245/242, 46656/46585

POTE generator: ~49/48 = 29.180

Map: [<1 2 3 3 4|, <0 -17 -28 -8 -22|]

EDOs: 41, 206e

Badness: 0.0632

13-limit

Commas: 100/99, 144/143, 245/242, 343/338

POTE generator: ~49/48 = 29.125

Map: [<1 2 3 3 4 4|, <0 -17 -28 -8 -22 -12|]

EDOs: 41, 124ef, 165ef

Badness: 0.0436

Slithy

Commas: 4000/3969, 420175/419904

POTE generator: ~21/20 = 89.282

Map: [<1 3 5 4|, <0 -19 -36 -16|]

EDOs: 27, 94, 121, 215, 336d

Badness: 0.1075

11-limit

Commas: 540/539, 2200/2187, 4375/4356

POTE generator: ~21/20 = 89.291

Map: [<1 3 5 4 8|, <0 -19 -36 -16 -61|]

EDOs: 94, 121, 215, 336de, 551bde

Badness: 0.0459

13-limit

Commas: 325/324, 352/351, 540/539, 1575/1573

POTE generator: ~21/20 = 89.286

Map: [<1 3 5 4 8 4|, <0 -19 -36 -16 -61 -4|]

EDOs: 94, 121, 215, 336def

Badness: 0.0285

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