Ragismic microtemperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 342103580 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 454886848 - 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> | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-09-28 08:37:37 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>454886848</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: 53, 99e, 152, 555de, 707de, 859bde | EDOs: 53, 99e, 152, 555de, 707de, 859bde | ||
Badness: 0.0315 | Badness: 0.0315 | ||
==13-limit== | |||
Commas: 352/351, 540/539, 625/624, 847/845 | |||
POTE generator: ~243/200 = 339.481 | |||
Map: [<1 3 6 -2 21 17|, <0 -5 -13 17 -62 -47|] | |||
EDOS: 53, 99ef, 152f, 205 | |||
Badness: 0.0280 | |||
==Accord== | ==Accord== | ||
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Badness: 0.0152</pre></div> | Badness: 0.0152</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 ! | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Ennealimmal"></a><!-- ws:end:WikiTextHeadingRule:0 -->Ennealimmal</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Ennealimmal"></a><!-- ws:end:WikiTextHeadingRule:0 -->Ennealimmal</h1> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:100:&lt;h2&gt; --><h2 id="toc50"><a name="Octoid-Music"></a><!-- ws:end:WikiTextHeadingRule:100 -->Music</h2> | <!-- ws:start:WikiTextHeadingRule:100:&lt;h2&gt; --><h2 id="toc50"><a name="Octoid-Music"></a><!-- ws:end:WikiTextHeadingRule:100 -->Music</h2> | ||
<!-- ws:start:WikiTextUrlRule: | <!-- ws:start:WikiTextUrlRule:854:http://www.archive.org/details/Dreyfus --><a class="wiki_link_ext" href="http://www.archive.org/details/Dreyfus" rel="nofollow">http://www.archive.org/details/Dreyfus</a><!-- ws:end:WikiTextUrlRule:854 --><br /> | ||
<a class="wiki_link_ext" href="http://www.archive.org/download/Dreyfus/Genewardsmith-Dreyfus.mp3" rel="nofollow">play</a><br /> | <a class="wiki_link_ext" href="http://www.archive.org/download/Dreyfus/Genewardsmith-Dreyfus.mp3" rel="nofollow">play</a><br /> | ||
<br /> | <br /> | ||
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Badness: 0.0315<br /> | Badness: 0.0315<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:112:&lt;h2&gt; --><h2 id="toc56"><a name="Amity-Accord"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:112:&lt;h2&gt; --><h2 id="toc56"><a name="Amity-13-limit"></a><!-- ws:end:WikiTextHeadingRule:112 -->13-limit</h2> | ||
Commas: 352/351, 540/539, 625/624, 847/845<br /> | |||
<br /> | |||
POTE generator: ~243/200 = 339.481<br /> | |||
<br /> | |||
Map: [&lt;1 3 6 -2 21 17|, &lt;0 -5 -13 17 -62 -47|]<br /> | |||
EDOS: 53, 99ef, 152f, 205<br /> | |||
Badness: 0.0280<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:114:&lt;h2&gt; --><h2 id="toc57"><a name="Amity-Accord"></a><!-- ws:end:WikiTextHeadingRule:114 -->Accord</h2> | |||
Commas: 126/125, 100352/98415<br /> | Commas: 126/125, 100352/98415<br /> | ||
<br /> | <br /> | ||
| Line 1,278: | Line 1,297: | ||
Badness: 0.0956<br /> | Badness: 0.0956<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:116:&lt;h3&gt; --><h3 id="toc58"><a name="Amity-Accord-11-limit"></a><!-- ws:end:WikiTextHeadingRule:116 -->11-limit</h3> | ||
Commas: 121/120, 126/125, 896/891<br /> | Commas: 121/120, 126/125, 896/891<br /> | ||
<br /> | <br /> | ||
| Line 1,287: | Line 1,306: | ||
Badness: 0.0425<br /> | Badness: 0.0425<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:118:&lt;h2&gt; --><h2 id="toc59"><a name="Amity-Hitchcock"></a><!-- ws:end:WikiTextHeadingRule:118 -->Hitchcock</h2> | ||
Commas: 121/120, 176/175, 2200/2187<br /> | Commas: 121/120, 176/175, 2200/2187<br /> | ||
<br /> | <br /> | ||
| Line 1,296: | Line 1,315: | ||
Badness: 0.0352<br /> | Badness: 0.0352<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:120:&lt;h3&gt; --><h3 id="toc60"><a name="Amity-Hitchcock-13-limit"></a><!-- ws:end:WikiTextHeadingRule:120 -->13-limit</h3> | ||
Commas: 121/120, 169/168, 176/175, 325/324<br /> | Commas: 121/120, 169/168, 176/175, 325/324<br /> | ||
<br /> | <br /> | ||
| Line 1,305: | Line 1,324: | ||
Badness: 0.0224<br /> | Badness: 0.0224<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:122:&lt;h2&gt; --><h2 id="toc61"><a name="Amity-Hemiamity"></a><!-- ws:end:WikiTextHeadingRule:122 -->Hemiamity</h2> | ||
Commas: 4375/4374, 5120/5103, 3025/3024<br /> | Commas: 4375/4374, 5120/5103, 3025/3024<br /> | ||
<br /> | <br /> | ||
| Line 1,313: | Line 1,332: | ||
EDOs: 14, 46, 106, 152, 350<br /> | EDOs: 14, 46, 106, 152, 350<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:124:&lt;h1&gt; --><h1 id="toc62"><a name="Parakleismic"></a><!-- ws:end:WikiTextHeadingRule:124 -->Parakleismic</h1> | ||
In the 5-limit, parakleismic is an undoubted microtemperament, tempering out the parakleisma, |8 14 -13&gt;, with the <a class="wiki_link" href="/118edo">118edo</a> tuning giving errors well under a cent. It has a generator a very slightly (half a cent or less) flat 6/5, 13 of which give 32/3, and 14 64/5. However while 118 no longer has better than a cent of accuracy in the 7 or 11 limits, it is a decent temperament there nonetheless, and this allows an extension, with the 7-limit wedgie being &lt;&lt;13 14 35 -8 19 42|| and adding 3136/3125 and 4375/4374, and the 11-limit wedgie &lt;&lt;13 14 35 -36 ...|| adding 385/384. For the 7-limit <a class="wiki_link" href="/99edo">99edo</a> may be preferred, but in the 11-limit it is best to stick with 118.<br /> | In the 5-limit, parakleismic is an undoubted microtemperament, tempering out the parakleisma, |8 14 -13&gt;, with the <a class="wiki_link" href="/118edo">118edo</a> tuning giving errors well under a cent. It has a generator a very slightly (half a cent or less) flat 6/5, 13 of which give 32/3, and 14 64/5. However while 118 no longer has better than a cent of accuracy in the 7 or 11 limits, it is a decent temperament there nonetheless, and this allows an extension, with the 7-limit wedgie being &lt;&lt;13 14 35 -8 19 42|| and adding 3136/3125 and 4375/4374, and the 11-limit wedgie &lt;&lt;13 14 35 -36 ...|| adding 385/384. For the 7-limit <a class="wiki_link" href="/99edo">99edo</a> may be preferred, but in the 11-limit it is best to stick with 118.<br /> | ||
<br /> | <br /> | ||
| Line 1,324: | Line 1,343: | ||
Badness: 0.0433<br /> | Badness: 0.0433<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:126:&lt;h2&gt; --><h2 id="toc63"><a name="Parakleismic-7-limit"></a><!-- ws:end:WikiTextHeadingRule:126 -->7-limit</h2> | ||
Commas: 3136/3125, 4375/4374<br /> | Commas: 3136/3125, 4375/4374<br /> | ||
<br /> | <br /> | ||
| Line 1,333: | Line 1,352: | ||
Badness: 0.0274<br /> | Badness: 0.0274<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:128:&lt;h2&gt; --><h2 id="toc64"><a name="Parakleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:128 -->11-limit</h2> | ||
Commas: 385/384, 3136/3125, 4375/4374<br /> | Commas: 385/384, 3136/3125, 4375/4374<br /> | ||
<br /> | <br /> | ||
| Line 1,342: | Line 1,361: | ||
Badness: 0.0497<br /> | Badness: 0.0497<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:130:&lt;h2&gt; --><h2 id="toc65"><a name="Parakleismic-Parkleismic"></a><!-- ws:end:WikiTextHeadingRule:130 -->Parkleismic</h2> | ||
Commas: 176/175, 1375/1372, 2200/2187<br /> | Commas: 176/175, 1375/1372, 2200/2187<br /> | ||
<br /> | <br /> | ||
| Line 1,351: | Line 1,370: | ||
Badness: 0.0559<br /> | Badness: 0.0559<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:132:&lt;h3&gt; --><h3 id="toc66"><a name="Parakleismic-Parkleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:132 -->13-limit</h3> | ||
Commas: 169/168, 176/175, 325/324, 1375/1372<br /> | Commas: 169/168, 176/175, 325/324, 1375/1372<br /> | ||
<br /> | <br /> | ||
| Line 1,360: | Line 1,379: | ||
Badness: 0.0366<br /> | Badness: 0.0366<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:134:&lt;h2&gt; --><h2 id="toc67"><a name="Parakleismic-Paradigmic"></a><!-- ws:end:WikiTextHeadingRule:134 -->Paradigmic</h2> | ||
Commas: 540/539, 896/891, 3136/3125<br /> | Commas: 540/539, 896/891, 3136/3125<br /> | ||
<br /> | <br /> | ||
| Line 1,369: | Line 1,388: | ||
Badness: 0.0417<br /> | Badness: 0.0417<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:136:&lt;h3&gt; --><h3 id="toc68"><a name="Parakleismic-Paradigmic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:136 -->13-limit</h3> | ||
Commas: 169/168, 325/324, 540/539, 832/825<br /> | Commas: 169/168, 325/324, 540/539, 832/825<br /> | ||
<br /> | <br /> | ||
| Line 1,378: | Line 1,397: | ||
Badness: 0.0358<br /> | Badness: 0.0358<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:138:&lt;h1&gt; --><h1 id="toc69"><a name="Semiparakleismic"></a><!-- ws:end:WikiTextHeadingRule:138 -->Semiparakleismic</h1> | ||
Commas: 3025/3024, 3136/3125, 4375/4374<br /> | Commas: 3025/3024, 3136/3125, 4375/4374<br /> | ||
<br /> | <br /> | ||
| Line 1,387: | Line 1,406: | ||
Badness: 0.0342<br /> | Badness: 0.0342<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:140:&lt;h1&gt; --><h1 id="toc70"><a name="Quincy"></a><!-- ws:end:WikiTextHeadingRule:140 -->Quincy</h1> | ||
Commas: 4375/4374, 823543/819200<br /> | Commas: 4375/4374, 823543/819200<br /> | ||
<br /> | <br /> | ||
| Line 1,396: | Line 1,415: | ||
Badness: 0.0797<br /> | Badness: 0.0797<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:142:&lt;h2&gt; --><h2 id="toc71"><a name="Quincy-11-limit"></a><!-- ws:end:WikiTextHeadingRule:142 -->11-limit</h2> | ||
Commas: 441/440, 4000/3993, 41503/41472<br /> | Commas: 441/440, 4000/3993, 41503/41472<br /> | ||
<br /> | <br /> | ||
| Line 1,405: | Line 1,424: | ||
Badness: 0.0309<br /> | Badness: 0.0309<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:144:&lt;h2&gt; --><h2 id="toc72"><a name="Quincy-13-limit"></a><!-- ws:end:WikiTextHeadingRule:144 -->13-limit</h2> | ||
Commas: 364/363, 441/440, 676/675, 4375/4374<br /> | Commas: 364/363, 441/440, 676/675, 4375/4374<br /> | ||
<br /> | <br /> | ||
| Line 1,414: | Line 1,433: | ||
Badness: 0.0239<br /> | Badness: 0.0239<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:146:&lt;h2&gt; --><h2 id="toc73"><a name="Quincy-17-limit"></a><!-- ws:end:WikiTextHeadingRule:146 -->17-limit</h2> | ||
Commas: 364/363, 441/440, 595/594, 1001/1000, 1156/1155<br /> | Commas: 364/363, 441/440, 595/594, 1001/1000, 1156/1155<br /> | ||
<br /> | <br /> | ||
| Line 1,423: | Line 1,442: | ||
Badness: 0.0147<br /> | Badness: 0.0147<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:148:&lt;h2&gt; --><h2 id="toc74"><a name="Quincy-19-limit"></a><!-- ws:end:WikiTextHeadingRule:148 -->19-limit</h2> | ||
Commas: 343/342, 364/363, 441/440, 595/594, 676/675, 2601/2600<br /> | Commas: 343/342, 364/363, 441/440, 595/594, 676/675, 2601/2600<br /> | ||
<br /> | <br /> | ||