Mint temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 328363894 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 328409568 - 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- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-02 02:32:57 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>328409568</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 66: | Line 66: | ||
=Ripple= | =Ripple= | ||
Comma: 6561/6250 | |||
POTE generator: ~27/25 = 100.838 | |||
Map: [<1 2 3|, <0 -5 -8|] | |||
EDOs: 12, 71b, 83b, 95b, 107bc, 119bc | |||
Badness: 0.1389 | |||
==7-limit== | |||
Commas: 36/35, 2560/2401 | Commas: 36/35, 2560/2401 | ||
| Line 165: | Line 174: | ||
Map: [<1 3 4 4 7 7|, <0 -6 -7 -5 -15 -14|] | Map: [<1 3 4 4 7 7|, <0 -6 -7 -5 -15 -14|] | ||
EDOs: 17c | EDOs: 17c | ||
Badness: 0.0323</pre></div> | Badness: 0.0323 | ||
= = | |||
Comma: 177147/156250 | |||
POTE generator: ~27/25 = 72.742 | |||
Map: [<1 2 3|, <0 -7 -11|] | |||
EDOs: 16, 17c, 33 | |||
Badness: 0.6893 | |||
==7-limit== | |||
Commas: 36/35, 51200/50421 | |||
POTE generator: ~21/20 = 72.303 | |||
Map: [<1 2 3 3|, <0 -7 -11 -3|] | |||
Wedgie: <<7 11 3 1 -15 -24|| | |||
EDOs: 16, 17c, 33, 50cd, 83bcd | |||
Badness: 0.1149 | |||
</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:40:&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:40 --><!-- ws:start:WikiTextTocRule:41: --><a href="#Progression">Progression</a><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><!-- 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: --><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --> | <a href="#Ripple">Ripple</a><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --> | <a href="#Smate">Smate</a><!-- 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:52 --><!-- ws:start:WikiTextTocRule:53: --> | <a href="#Subklei">Subklei</a><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><!-- 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: --> | <a href="#toc18"> </a><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:61 --><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 /> | ||
| Line 227: | Line 256: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Ripple"></a><!-- ws:end:WikiTextHeadingRule:12 -->Ripple</h1> | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Ripple"></a><!-- ws:end:WikiTextHeadingRule:12 -->Ripple</h1> | ||
Comma: 6561/6250<br /> | |||
<br /> | |||
POTE generator: ~27/25 = 100.838<br /> | |||
<br /> | |||
Map: [&lt;1 2 3|, &lt;0 -5 -8|]<br /> | |||
EDOs: 12, 71b, 83b, 95b, 107bc, 119bc<br /> | |||
Badness: 0.1389<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Ripple-7-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->7-limit</h2> | |||
Commas: 36/35, 2560/2401<br /> | Commas: 36/35, 2560/2401<br /> | ||
<br /> | <br /> | ||
| Line 236: | Line 274: | ||
Badness: 0.0597<br /> | Badness: 0.0597<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Smate"></a><!-- ws:end:WikiTextHeadingRule:16 -->Smate</h1> | ||
Comma: 2048/1875<br /> | Comma: 2048/1875<br /> | ||
<br /> | <br /> | ||
| Line 245: | Line 283: | ||
Badness: 0.179<br /> | Badness: 0.179<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Smate-7-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->7-limit</h2> | ||
Commas: 36/35, 2048/1875<br /> | Commas: 36/35, 2048/1875<br /> | ||
<br /> | <br /> | ||
| Line 255: | Line 293: | ||
Badness: 0.0779<br /> | Badness: 0.0779<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Smate-11-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->11-limit</h2> | ||
Commas: 36/35 56/55 243/242<br /> | Commas: 36/35 56/55 243/242<br /> | ||
<br /> | <br /> | ||
| Line 264: | Line 302: | ||
Badness: 0.0425<br /> | Badness: 0.0425<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Smate-13-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->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 273: | Line 311: | ||
Badness: 0.0368<br /> | Badness: 0.0368<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Subklei"></a><!-- ws:end:WikiTextHeadingRule:24 -->Subklei</h1> | ||
Comma: 17496/15625<br /> | Comma: 17496/15625<br /> | ||
<br /> | <br /> | ||
| Line 282: | Line 320: | ||
Badness: 0.3559<br /> | Badness: 0.3559<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Subklei-7-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->7-limit</h2> | ||
Commas: 36/35, 1029/1000<br /> | Commas: 36/35, 1029/1000<br /> | ||
<br /> | <br /> | ||
| Line 292: | Line 330: | ||
Badness: 0.0611<br /> | Badness: 0.0611<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Subklei-11-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->11-limit</h2> | ||
Commas: 36/35, 77/75, 352/343<br /> | Commas: 36/35, 77/75, 352/343<br /> | ||
<br /> | <br /> | ||
| Line 301: | Line 339: | ||
Badness: 0.0447<br /> | Badness: 0.0447<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="Subklei-Subkla"></a><!-- ws:end:WikiTextHeadingRule:30 -->Subkla</h2> | ||
Commas: 36/35, 56/55, 1029/1000<br /> | Commas: 36/35, 56/55, 1029/1000<br /> | ||
<br /> | <br /> | ||
| Line 310: | Line 348: | ||
Badness: 0.0472<br /> | Badness: 0.0472<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h3&gt; --><h3 id="toc16"><a name="Subklei-Subkla-13-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->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 319: | Line 357: | ||
Badness: 0.0367<br /> | Badness: 0.0367<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Subklei-13-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->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 /> | ||
| Line 326: | Line 364: | ||
Map: [&lt;1 3 4 4 7 7|, &lt;0 -6 -7 -5 -15 -14|]<br /> | Map: [&lt;1 3 4 4 7 7|, &lt;0 -6 -7 -5 -15 -14|]<br /> | ||
EDOs: 17c<br /> | EDOs: 17c<br /> | ||
Badness: 0.0323</body></html></pre></div> | Badness: 0.0323<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:36:&lt;h1&gt; --><h1 id="toc18"><!-- ws:end:WikiTextHeadingRule:36 --> </h1> | |||
Comma: 177147/156250 <br /> | |||
<br /> | |||
POTE generator: ~27/25 = 72.742<br /> | |||
<br /> | |||
Map: [&lt;1 2 3|, &lt;0 -7 -11|]<br /> | |||
EDOs: 16, 17c, 33<br /> | |||
Badness: 0.6893<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Subklei-7-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->7-limit</h2> | |||
Commas: 36/35, 51200/50421<br /> | |||
<br /> | |||
POTE generator: ~21/20 = 72.303<br /> | |||
<br /> | |||
Map: [&lt;1 2 3 3|, &lt;0 -7 -11 -3|]<br /> | |||
Wedgie: &lt;&lt;7 11 3 1 -15 -24||<br /> | |||
EDOs: 16, 17c, 33, 50cd, 83bcd<br /> | |||
Badness: 0.1149</body></html></pre></div> | |||