Mint temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 328261532 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 328363894 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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>2012-05-01 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-01 23:58:30 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>328363894</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 11: | Line 11: | ||
=Progression= | =Progression= | ||
Comma: 3456/3125 | |||
POTE generator: ~25/24 = 140.995 | |||
Map: [<1 1 2|, <0 5 3|] | |||
EDOs: 8, 9, 17c | |||
Badness: 0.2005 | |||
==7-limit== | |||
Commas: 36/35, 392/375 | Commas: 36/35, 392/375 | ||
| Line 158: | Line 167: | ||
Badness: 0.0323</pre></div> | Badness: 0.0323</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:34:&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:34 --><!-- ws:start:WikiTextTocRule:35: --><a href="#Progression">Progression</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --> | <a href="#Ripple">Ripple</a><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --> | <a href="#Smate">Smate</a><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --> | <a href="#Subklei">Subklei</a><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:52 --><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 both a square and a <a class="wiki_link" href="/triangular%20number">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 both a square and a <a class="wiki_link" href="/triangular%20number">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 /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Progression"></a><!-- ws:end:WikiTextHeadingRule:0 -->Progression</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Progression"></a><!-- ws:end:WikiTextHeadingRule:0 -->Progression</h1> | ||
Comma: 3456/3125<br /> | |||
<br /> | |||
POTE generator: ~25/24 = 140.995<br /> | |||
<br /> | |||
Map: [&lt;1 1 2|, &lt;0 5 3|]<br /> | |||
EDOs: 8, 9, 17c<br /> | |||
Badness: 0.2005<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Progression-7-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->7-limit</h2> | |||
Commas: 36/35, 392/375<br /> | Commas: 36/35, 392/375<br /> | ||
<br /> | <br /> | ||
| Line 172: | Line 190: | ||
Badness: 0.0484<br /> | Badness: 0.0484<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Progression-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2> | ||
Commas: 36/35, 56/55, 77/75<br /> | Commas: 36/35, 56/55, 77/75<br /> | ||
<br /> | <br /> | ||
| Line 181: | Line 199: | ||
Badness: 0.0261<br /> | Badness: 0.0261<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Progression-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2> | ||
Commas: 26/25, 36/35, 56/55, 66/65<br /> | Commas: 26/25, 36/35, 56/55, 66/65<br /> | ||
<br /> | <br /> | ||
| Line 190: | Line 208: | ||
Badness: 0.0182<br /> | Badness: 0.0182<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Progression-17-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->17-limit</h2> | ||
Commas: 26/25, 36/35, 51/50, 56/55, 66/65<br /> | Commas: 26/25, 36/35, 51/50, 56/55, 66/65<br /> | ||
<br /> | <br /> | ||
| Line 199: | Line 217: | ||
Badness: 0.0167<br /> | Badness: 0.0167<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Progression-17-limit-19-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->19-limit</h3> | ||
Commas: 26/25, 36/35, 51/50, 56/55, 57/55, 66/65<br /> | Commas: 26/25, 36/35, 51/50, 56/55, 57/55, 66/65<br /> | ||
<br /> | <br /> | ||
| Line 208: | Line 226: | ||
Badness: 0.0168<br /> | Badness: 0.0168<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Ripple"></a><!-- ws:end:WikiTextHeadingRule:12 -->Ripple</h1> | ||
Commas: 36/35, 2560/2401<br /> | Commas: 36/35, 2560/2401<br /> | ||
<br /> | <br /> | ||
| Line 218: | Line 236: | ||
Badness: 0.0597<br /> | Badness: 0.0597<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Smate"></a><!-- ws:end:WikiTextHeadingRule:14 -->Smate</h1> | ||
Comma: 2048/1875<br /> | Comma: 2048/1875<br /> | ||
<br /> | <br /> | ||
| Line 227: | Line 245: | ||
Badness: 0.179<br /> | Badness: 0.179<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Smate-7-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->7-limit</h2> | ||
Commas: 36/35, 2048/1875<br /> | Commas: 36/35, 2048/1875<br /> | ||
<br /> | <br /> | ||
| Line 237: | Line 255: | ||
Badness: 0.0779<br /> | Badness: 0.0779<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Smate-11-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->11-limit</h2> | ||
Commas: 36/35 56/55 243/242<br /> | Commas: 36/35 56/55 243/242<br /> | ||
<br /> | <br /> | ||
| Line 246: | Line 264: | ||
Badness: 0.0425<br /> | Badness: 0.0425<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Smate-13-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->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 /> | ||
| Line 255: | Line 273: | ||
Badness: 0.0368<br /> | Badness: 0.0368<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Subklei"></a><!-- ws:end:WikiTextHeadingRule:22 -->Subklei</h1> | ||
Comma: 17496/15625<br /> | Comma: 17496/15625<br /> | ||
<br /> | <br /> | ||
| Line 264: | Line 282: | ||
Badness: 0.3559<br /> | Badness: 0.3559<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Subklei-7-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->7-limit</h2> | ||
Commas: 36/35, 1029/1000<br /> | Commas: 36/35, 1029/1000<br /> | ||
<br /> | <br /> | ||
| Line 274: | Line 292: | ||
Badness: 0.0611<br /> | Badness: 0.0611<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Subklei-11-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->11-limit</h2> | ||
Commas: 36/35, 77/75, 352/343<br /> | Commas: 36/35, 77/75, 352/343<br /> | ||
<br /> | <br /> | ||
| Line 283: | Line 301: | ||
Badness: 0.0447<br /> | Badness: 0.0447<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Subklei-Subkla"></a><!-- ws:end:WikiTextHeadingRule:28 -->Subkla</h2> | ||
Commas: 36/35, 56/55, 1029/1000<br /> | Commas: 36/35, 56/55, 1029/1000<br /> | ||
<br /> | <br /> | ||
| Line 292: | Line 310: | ||
Badness: 0.0472<br /> | Badness: 0.0472<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h3&gt; --><h3 id="toc15"><a name="Subklei-Subkla-13-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->13-limit</h3> | ||
Commas: 36/35, 56/55, 66/65, 640/637<br /> | Commas: 36/35, 56/55, 66/65, 640/637<br /> | ||
<br /> | <br /> | ||
| Line 301: | Line 319: | ||
Badness: 0.0367<br /> | Badness: 0.0367<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Subklei-13-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->13-limit</h2> | ||
Commas: 26/25, 36/35, 66/65, 352/343 <br /> | Commas: 26/25, 36/35, 66/65, 352/343 <br /> | ||
<br /> | <br /> | ||