Meantone family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 325872508 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 327495430 - 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>2012-04- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-30 13:14:34 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>327495430</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: 5, 26, 31, 57, 88 | EDOs: 5, 26, 31, 57, 88 | ||
Badness: 0.0240 | Badness: 0.0240 | ||
==Cynder== | |||
Commas: 45/44, 81/80, 1029/1024 | |||
POTE generator: ~8/7 = 231.317 | |||
Map: [<1 1 0 3 0|, <0 3 12 -1 18|] | |||
EDOs: 26, 57e, 83bce | |||
Badness: 0.0557 | |||
===13-limit=== | |||
Commas: 45/44, 78/77, 81/80, 640/637 | |||
POTE generator: ~8/7 = 231.293 | |||
Map: [<1 1 0 3 0 1|, <0 3 12 -1 18 14|] | |||
EDOs: 26, 57e, 83bce | |||
Badness: 0.0341 | |||
==Mosura== | ==Mosura== | ||
| Line 777: | Line 795: | ||
Map: [<19 30 44 53 0|, <0 0 0 0 1|] | Map: [<19 30 44 53 0|, <0 0 0 0 1|] | ||
EDOs: 19, 38d | EDOs: 19, 38d | ||
Badness: 0.0364 | Badness: 0.0364</pre></div> | ||
</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 | |||
The <a class="wiki_link" href="/5-limit">5-limit</a> parent <a class="wiki_link" href="/Comma">comma</a> of the <a class="wiki_link" href="/meantone">meantone</a> family is the Didymus or <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Syntonic_comma" rel="nofollow">syntonic comma</a>, 81/80. This is the one they all temper out. The <a class="wiki_link" href="/Monzos%20and%20Interval%20Space">monzo</a> for 81/80 goes |-4 4 -1&gt;, and that can be flipped around to the corresponding <a class="wiki_link" href="/Wedgies%20and%20Multivals">wedgie</a>, &lt;&lt;1 4 4||, which tells us that the period is an octave, the generator is a fifth, and four fifths go to make up a 5/1 interval.<br /> | The <a class="wiki_link" href="/5-limit">5-limit</a> parent <a class="wiki_link" href="/Comma">comma</a> of the <a class="wiki_link" href="/meantone">meantone</a> family is the Didymus or <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Syntonic_comma" rel="nofollow">syntonic comma</a>, 81/80. This is the one they all temper out. The <a class="wiki_link" href="/Monzos%20and%20Interval%20Space">monzo</a> for 81/80 goes |-4 4 -1&gt;, and that can be flipped around to the corresponding <a class="wiki_link" href="/Wedgies%20and%20Multivals">wedgie</a>, &lt;&lt;1 4 4||, which tells us that the period is an octave, the generator is a fifth, and four fifths go to make up a 5/1 interval.<br /> | ||
<br /> | <br /> | ||
| Line 1,427: | Line 1,446: | ||
Badness: 0.0240<br /> | Badness: 0.0240<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:108:&lt;h2&gt; --><h2 id="toc54"><a name="Mothra-Mosura"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:108:&lt;h2&gt; --><h2 id="toc54"><a name="Mothra-Cynder"></a><!-- ws:end:WikiTextHeadingRule:108 -->Cynder</h2> | ||
Commas: 45/44, 81/80, 1029/1024 <br /> | |||
<br /> | |||
POTE generator: ~8/7 = 231.317<br /> | |||
<br /> | |||
Map: [&lt;1 1 0 3 0|, &lt;0 3 12 -1 18|]<br /> | |||
EDOs: 26, 57e, 83bce<br /> | |||
Badness: 0.0557<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:110:&lt;h3&gt; --><h3 id="toc55"><a name="Mothra-Cynder-13-limit"></a><!-- ws:end:WikiTextHeadingRule:110 -->13-limit</h3> | |||
Commas: 45/44, 78/77, 81/80, 640/637<br /> | |||
<br /> | |||
POTE generator: ~8/7 = 231.293<br /> | |||
<br /> | |||
Map: [&lt;1 1 0 3 0 1|, &lt;0 3 12 -1 18 14|]<br /> | |||
EDOs: 26, 57e, 83bce<br /> | |||
Badness: 0.0341<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:112:&lt;h2&gt; --><h2 id="toc56"><a name="Mothra-Mosura"></a><!-- ws:end:WikiTextHeadingRule:112 -->Mosura</h2> | |||
Commas: 81/80, 176/175, 1029/1024<br /> | Commas: 81/80, 176/175, 1029/1024<br /> | ||
<br /> | <br /> | ||
| Line 1,436: | Line 1,473: | ||
Badness: 0.0313<br /> | Badness: 0.0313<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:114:&lt;h3&gt; --><h3 id="toc57"><a name="Mothra-Mosura-13-limit"></a><!-- ws:end:WikiTextHeadingRule:114 -->13-limit</h3> | ||
Commas: 81/80, 144/143, 176/175, 1029/1024<br /> | Commas: 81/80, 144/143, 176/175, 1029/1024<br /> | ||
<br /> | <br /> | ||
| Line 1,445: | Line 1,482: | ||
Badness: 0.0369<br /> | Badness: 0.0369<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:116:&lt;h1&gt; --><h1 id="toc58"><a name="Squares"></a><!-- ws:end:WikiTextHeadingRule:116 -->Squares</h1> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 2401/2400<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 2401/2400<br /> | ||
<br /> | <br /> | ||
| Line 1,467: | Line 1,504: | ||
<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/tuning-survey/daily20100603-squares8piano.mp3" rel="nofollow">Square 8</a><br /> | <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/tuning-survey/daily20100603-squares8piano.mp3" rel="nofollow">Square 8</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:118:&lt;h2&gt; --><h2 id="toc59"><a name="Squares-11-limit"></a><!-- ws:end:WikiTextHeadingRule:118 -->11-limit</h2> | ||
Commas: 81/80, 99/98, 121/120<br /> | Commas: 81/80, 99/98, 121/120<br /> | ||
<br /> | <br /> | ||
| Line 1,476: | Line 1,513: | ||
<a class="wiki_link" href="/Badness">Badness</a>: 0.0216<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0216<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:120:&lt;h2&gt; --><h2 id="toc60"><a name="Squares-13-limit"></a><!-- ws:end:WikiTextHeadingRule:120 -->13-limit</h2> | ||
Commas: 81/80, 99/98, 121/120, 66/65<br /> | Commas: 81/80, 99/98, 121/120, 66/65<br /> | ||
<br /> | <br /> | ||
| Line 1,485: | Line 1,522: | ||
<a class="wiki_link" href="/Badness">Badness</a>: 0.0255<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0255<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:122:&lt;h2&gt; --><h2 id="toc61"><a name="Squares-Agora"></a><!-- ws:end:WikiTextHeadingRule:122 -->Agora</h2> | ||
Commas: 81/80, 99/98, 105/104, 121/120<br /> | Commas: 81/80, 99/98, 105/104, 121/120<br /> | ||
<br /> | <br /> | ||
| Line 1,494: | Line 1,531: | ||
Badness: 0.0245<br /> | Badness: 0.0245<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:124:&lt;h1&gt; --><h1 id="toc62"><a name="Cuboctahedra"></a><!-- ws:end:WikiTextHeadingRule:124 -->Cuboctahedra</h1> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:126:&lt;h2&gt; --><h2 id="toc63"><a name="Cuboctahedra-11-limit"></a><!-- ws:end:WikiTextHeadingRule:126 -->11-limit</h2> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 385/384, 1375/1372<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 385/384, 1375/1372<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Badness">Badness</a>: 0.0568<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0568<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:128:&lt;h1&gt; --><h1 id="toc64"><a name="Liese"></a><!-- ws:end:WikiTextHeadingRule:128 -->Liese</h1> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 686/675<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 686/675<br /> | ||
<br /> | <br /> | ||
| Line 1,522: | Line 1,559: | ||
<a class="wiki_link" href="/Badness">Badness</a>: 0.0467<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0467<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:130:&lt;h2&gt; --><h2 id="toc65"><a name="Liese-Liesel"></a><!-- ws:end:WikiTextHeadingRule:130 -->Liesel</h2> | ||
Commas: 56/55, 81/80, 540/539<br /> | Commas: 56/55, 81/80, 540/539<br /> | ||
<br /> | <br /> | ||
| Line 1,531: | Line 1,568: | ||
Badness: 0.0407<br /> | Badness: 0.0407<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:132:&lt;h2&gt; --><h2 id="toc66"><a name="Liese-13-limit"></a><!-- ws:end:WikiTextHeadingRule:132 -->13-limit</h2> | ||
Liesel is a very natural 13-limit tuning, given the generator is so near 13/9.<br /> | Liesel is a very natural 13-limit tuning, given the generator is so near 13/9.<br /> | ||
<br /> | <br /> | ||
| Line 1,542: | Line 1,579: | ||
Badness: 0.0273<br /> | Badness: 0.0273<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:134:&lt;h2&gt; --><h2 id="toc67"><a name="Liese-Elisa"></a><!-- ws:end:WikiTextHeadingRule:134 -->Elisa</h2> | ||
Commas: 77/75, 81/80, 99/98<br /> | Commas: 77/75, 81/80, 99/98<br /> | ||
<br /> | <br /> | ||
| Line 1,551: | Line 1,588: | ||
Badness: 0.0416<br /> | Badness: 0.0416<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:136:&lt;h2&gt; --><h2 id="toc68"><a name="Liese-Lisa"></a><!-- ws:end:WikiTextHeadingRule:136 -->Lisa</h2> | ||
Commas: 45/44, 81/80, 343/330<br /> | Commas: 45/44, 81/80, 343/330<br /> | ||
<br /> | <br /> | ||
| Line 1,560: | Line 1,597: | ||
Badness: 0.0548<br /> | Badness: 0.0548<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:138:&lt;h2&gt; --><h2 id="toc69"><a name="Liese-13-limit"></a><!-- ws:end:WikiTextHeadingRule:138 -->13-limit</h2> | ||
Commas: 45/44, 81/80, 91/88, 147/143<br /> | Commas: 45/44, 81/80, 91/88, 147/143<br /> | ||
<br /> | <br /> | ||
| Line 1,569: | Line 1,606: | ||
Badness: 0.0361<br /> | Badness: 0.0361<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:140:&lt;h1&gt; --><h1 id="toc70"><a name="Jerome"></a><!-- ws:end:WikiTextHeadingRule:140 -->Jerome</h1> | ||
Jerome is related to <a class="wiki_link" href="/20ed5">Hieronymus' tuning</a>; the Hieronymus generator is 5^(1/20), or 139.316 cents. While the generator represents both 13/12 and 12/11, the POTE and Hieronymus generators are close to 13/12 in size.<br /> | Jerome is related to <a class="wiki_link" href="/20ed5">Hieronymus' tuning</a>; the Hieronymus generator is 5^(1/20), or 139.316 cents. While the generator represents both 13/12 and 12/11, the POTE and Hieronymus generators are close to 13/12 in size.<br /> | ||
<br /> | <br /> | ||
| Line 1,581: | Line 1,618: | ||
Badness: 0.1087<br /> | Badness: 0.1087<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:142:&lt;h2&gt; --><h2 id="toc71"><a name="Jerome-11-limit"></a><!-- ws:end:WikiTextHeadingRule:142 -->11-limit</h2> | ||
Commas: 81/80, 99/98, 864/847<br /> | Commas: 81/80, 99/98, 864/847<br /> | ||
<br /> | <br /> | ||
| Line 1,590: | Line 1,627: | ||
Badness: 0.0479<br /> | Badness: 0.0479<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:144:&lt;h2&gt; --><h2 id="toc72"><a name="Jerome-13-limit"></a><!-- ws:end:WikiTextHeadingRule:144 -->13-limit</h2> | ||
Commas: 77/78, 81/80, 99/98, 144/143<br /> | Commas: 77/78, 81/80, 99/98, 144/143<br /> | ||
<br /> | <br /> | ||
| Line 1,599: | Line 1,636: | ||
Badness: 0.0293<br /> | Badness: 0.0293<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:146:&lt;h2&gt; --><h2 id="toc73"><a name="Jerome-17-limit"></a><!-- ws:end:WikiTextHeadingRule:146 -->17-limit</h2> | ||
Commas: 78/77, 81/80, 99/98, 144/143, 189/187<br /> | Commas: 78/77, 81/80, 99/98, 144/143, 189/187<br /> | ||
<br /> | <br /> | ||
| Line 1,608: | Line 1,645: | ||
Badness: 0.0209<br /> | Badness: 0.0209<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:148:&lt;h1&gt; --><h1 id="toc74"><a name="Meanmag"></a><!-- ws:end:WikiTextHeadingRule:148 -->Meanmag</h1> | ||
Commas: 81/80, 3125/3072<br /> | Commas: 81/80, 3125/3072<br /> | ||
<br /> | <br /> | ||
| Line 1,618: | Line 1,655: | ||
Badness: 0.0770<br /> | Badness: 0.0770<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:150:&lt;h1&gt; --><h1 id="toc75"><a name="Undevigintone"></a><!-- ws:end:WikiTextHeadingRule:150 -->Undevigintone</h1> | ||
Commas: 49/48, 81/80, 126/125<br /> | Commas: 49/48, 81/80, 126/125<br /> | ||
<br /> | <br /> | ||