Mint temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 328748252 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 336772140 - 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>2012-05- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-17 15:46:38 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>336772140</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> | ||
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EDOs: [[12edo|12]], [[23edo|23]] | EDOs: [[12edo|12]], [[23edo|23]] | ||
Badness: 0.0597 | Badness: 0.0597 | ||
==11-limit== | |||
Commas: 36/35, 80/77, 126/121 | |||
POTE generator: ~21/20 = ~12/11 = 99.385 | |||
Map: [<1 2 3 3 4|, <0 -5 -8 -2 -6|] | |||
EDOs: 12 | |||
Badness: 0.0388 | |||
==13-limit== | |||
Commas: 36/35, 40/39, 66/65, 147/143 | |||
POTE generator: ~21/20 = ~12/11 = ~14/13 = 98.572 | |||
Map: [<1 2 3 3 4 4|, <0 -5 -8 -2 -6 -3|] | |||
EDOs: 12f | |||
Badness: 0.0316 | |||
=Smate= | =Smate= | ||
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Badness: 0.0331</pre></div> | Badness: 0.0331</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"><html><head><title>Mint temperaments</title></head><body><!-- ws:start:WikiTextTocRule: | <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"><html><head><title>Mint temperaments</title></head><body><!-- ws:start:WikiTextTocRule:54:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><a href="#Progression">Progression</a><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --> | <a href="#Ripple">Ripple</a><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --> | <a href="#Smate">Smate</a><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --> | <a href="#Hemismate">Hemismate</a><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --> | <a href="#Subklei">Subklei</a><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --> | <a href="#Slurpee">Slurpee</a><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:82 --><br /> | ||
These are low complexity, high error temperaments tempering out the septimal quarter-tone, <a class="wiki_link" href="/36_35">36/35</a>. 36 is <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Square_triangular_number" rel="nofollow">both</a> a <a class="wiki_link_ext" href="http://mathworld.wolfram.com/SquareNumber.html" rel="nofollow">square</a> and a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Triangular_number" rel="nofollow">triangular number</a>, and this helps make 36/35 a septimal interval of considerable significance. Temperaments tempering it out include beep, dicot, dominant, father, diminished, august, hystrix, penta, hexadecimal, ripple and gorgo.<br /> | These are low complexity, high error temperaments tempering out the septimal quarter-tone, <a class="wiki_link" href="/36_35">36/35</a>. 36 is <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Square_triangular_number" rel="nofollow">both</a> a <a class="wiki_link_ext" href="http://mathworld.wolfram.com/SquareNumber.html" rel="nofollow">square</a> and a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Triangular_number" rel="nofollow">triangular number</a>, and this helps make 36/35 a septimal interval of considerable significance. Temperaments tempering it out include beep, dicot, dominant, father, diminished, august, hystrix, penta, hexadecimal, ripple and gorgo.<br /> | ||
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Badness: 0.0597<br /> | Badness: 0.0597<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id=" | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Ripple-11-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->11-limit</h2> | ||
Commas: 36/35, 80/77, 126/121<br /> | |||
<br /> | |||
POTE generator: ~21/20 = ~12/11 = 99.385<br /> | |||
<br /> | |||
Map: [&lt;1 2 3 3 4|, &lt;0 -5 -8 -2 -6|]<br /> | |||
EDOs: 12<br /> | |||
Badness: 0.0388<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Ripple-13-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->13-limit</h2> | |||
Commas: 36/35, 40/39, 66/65, 147/143<br /> | |||
<br /> | |||
POTE generator: ~21/20 = ~12/11 = ~14/13 = 98.572<br /> | |||
<br /> | |||
Map: [&lt;1 2 3 3 4 4|, &lt;0 -5 -8 -2 -6 -3|]<br /> | |||
EDOs: 12f<br /> | |||
Badness: 0.0316<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Smate"></a><!-- ws:end:WikiTextHeadingRule:20 -->Smate</h1> | |||
Comma: 2048/1875<br /> | Comma: 2048/1875<br /> | ||
<br /> | <br /> | ||
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Badness: 0.179<br /> | Badness: 0.179<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Smate-7-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->7-limit</h2> | ||
Commas: 36/35, 2048/1875<br /> | Commas: 36/35, 2048/1875<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0779<br /> | Badness: 0.0779<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Smate-11-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->11-limit</h2> | ||
Commas: 36/35 56/55 243/242<br /> | Commas: 36/35 56/55 243/242<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0425<br /> | Badness: 0.0425<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Smate-13-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->13-limit</h2> | ||
Commas: 26/25, 36/35, 56/55, 243/242 <br /> | Commas: 26/25, 36/35, 56/55, 243/242 <br /> | ||
<br /> | <br /> | ||
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Badness: 0.0368<br /> | Badness: 0.0368<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Hemismate"></a><!-- ws:end:WikiTextHeadingRule:28 -->Hemismate</h1> | ||
commas: 256/245, 392/375 <br /> | commas: 256/245, 392/375 <br /> | ||
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Badness: 0.1543<br /> | Badness: 0.1543<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="Hemismate-11-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->11-limit</h2> | ||
Commas: 56/55, 77/75, 256/245<br /> | Commas: 56/55, 77/75, 256/245<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0655<br /> | Badness: 0.0655<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Hemismate-13-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->13-limit</h2> | ||
Commas: 26/25, 56/55, 77/75, 256/245<br /> | Commas: 26/25, 56/55, 77/75, 256/245<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0505<br /> | Badness: 0.0505<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="Subklei"></a><!-- ws:end:WikiTextHeadingRule:34 -->Subklei</h1> | ||
Comma: 17496/15625<br /> | Comma: 17496/15625<br /> | ||
<br /> | <br /> | ||
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Badness: 0.3559<br /> | Badness: 0.3559<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Subklei-7-limit"></a><!-- ws:end:WikiTextHeadingRule:36 -->7-limit</h2> | ||
Commas: 36/35, 1029/1000<br /> | Commas: 36/35, 1029/1000<br /> | ||
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Badness: 0.0611<br /> | Badness: 0.0611<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Subklei-11-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->11-limit</h2> | ||
Commas: 36/35, 77/75, 352/343<br /> | Commas: 36/35, 77/75, 352/343<br /> | ||
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Badness: 0.0447<br /> | Badness: 0.0447<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Subklei-Subkla"></a><!-- ws:end:WikiTextHeadingRule:40 -->Subkla</h2> | ||
Commas: 36/35, 56/55, 1029/1000<br /> | Commas: 36/35, 56/55, 1029/1000<br /> | ||
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Badness: 0.0472<br /> | Badness: 0.0472<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:42:&lt;h3&gt; --><h3 id="toc21"><a name="Subklei-Subkla-13-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->13-limit</h3> | ||
Commas: 36/35, 56/55, 66/65, 640/637<br /> | Commas: 36/35, 56/55, 66/65, 640/637<br /> | ||
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Badness: 0.0367<br /> | Badness: 0.0367<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Subklei-13-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->13-limit</h2> | ||
Commas: 26/25, 36/35, 66/65, 352/343 <br /> | Commas: 26/25, 36/35, 66/65, 352/343 <br /> | ||
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Badness: 0.0323<br /> | Badness: 0.0323<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:46:&lt;h1&gt; --><h1 id="toc23"><a name="Slurpee"></a><!-- ws:end:WikiTextHeadingRule:46 -->Slurpee</h1> | ||
Comma: 177147/156250 <br /> | Comma: 177147/156250 <br /> | ||
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Badness: 0.6893<br /> | Badness: 0.6893<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Slurpee-7-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->7-limit</h2> | ||
Commas: 36/35, 51200/50421<br /> | Commas: 36/35, 51200/50421<br /> | ||
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Badness: 0.1149<br /> | Badness: 0.1149<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="Slurpee-11-limit"></a><!-- ws:end:WikiTextHeadingRule:50 -->11-limit</h2> | ||
Commas: 36/35, 121/120, 352/343 <br /> | Commas: 36/35, 121/120, 352/343 <br /> | ||
<br /> | <br /> | ||
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Badness: 0.0505<br /> | Badness: 0.0505<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:52:&lt;h2&gt; --><h2 id="toc26"><a name="Slurpee-13-limit"></a><!-- ws:end:WikiTextHeadingRule:52 -->13-limit</h2> | ||
Commas: 36/35. 66/65, 143/140, 352/343<br /> | Commas: 36/35. 66/65, 143/140, 352/343<br /> | ||
<br /> | <br /> | ||