Meantone family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 325806804 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 325872508 - 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>2012-04-27 00:09:30 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>325872508</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">[[toc]] | <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;white-space: pre-wrap ! important" class="old-revision-html">[[toc]] | ||
The [[5-limit]] parent [[Comma|comma]] of the [[meantone]] family is the Didymus or [[http://en.wikipedia.org/wiki/Syntonic_comma|syntonic comma]], 81/80. This is the one they all temper out. The [[Monzos and Interval Space|monzo]] for 81/80 goes |-4 4 -1>, and that can be flipped around to the corresponding [[Wedgies and Multivals|wedgie]], <<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. | The [[5-limit]] parent [[Comma|comma]] of the [[meantone]] family is the Didymus or [[http://en.wikipedia.org/wiki/Syntonic_comma|syntonic comma]], 81/80. This is the one they all temper out. The [[Monzos and Interval Space|monzo]] for 81/80 goes |-4 4 -1>, and that can be flipped around to the corresponding [[Wedgies and Multivals|wedgie]], <<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. | ||
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==13-limit== | ==13-limit== | ||
Liesel is a very natural 13-limit tuning, given the generator is so near 13/9. | |||
POTE generator: ~13/9 = 633 | Commas: 56/55, 78/77, 81/80, 91/90 | ||
POTE generator: ~10/7 = ~13/9 = 633.042 | |||
Map: [<1 0 -4 -3 4 0|, <0 3 12 11 -1 7|] | Map: [<1 0 -4 -3 4 0|, <0 3 12 11 -1 7|] | ||
EDOs: | EDOs: 17c, 19, 36, 91cef | ||
Badness | Badness: 0.0273 | ||
==Elisa== | ==Elisa== | ||
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EDOs: 19e, 36e | EDOs: 19e, 36e | ||
Badness: 0.0416 | Badness: 0.0416 | ||
==Lisa== | |||
Commas: 45/44, 81/80, 343/330 | |||
POTE generator: ~10/7 = 631.370 | |||
Map: [<1 0 -4 -3 -6|, <0 3 12 11 18|] | |||
EDOs: 19 | |||
Badness: 0.0548 | |||
==13-limit== | |||
Commas: 45/44, 81/80, 91/88, 147/143 | |||
POTE generator: ~10/7 = 631.221 | |||
Map: [<1 0 -4 -3 -6 0|, <0 3 12 11 18 7|] | |||
EDOs: 19 | |||
Badness: 0.0361 | |||
=Jerome= | =Jerome= | ||
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EDOs: 19, 38d | EDOs: 19, 38d | ||
Badness: 0.0364 | Badness: 0.0364 | ||
</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 /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 696.239<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 696.239<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:128:&lt;h2&gt; --><h2 id="toc64"><a name="Liese-13-limit"></a><!-- ws:end:WikiTextHeadingRule:128 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:128:&lt;h2&gt; --><h2 id="toc64"><a name="Liese-13-limit"></a><!-- ws:end:WikiTextHeadingRule:128 -->13-limit</h2> | ||
Liesel is a very natural 13-limit tuning, given the generator is so near 13/9.<br /> | |||
<br /> | <br /> | ||
POTE generator: ~13/9 = 633 | Commas: 56/55, 78/77, 81/80, 91/90<br /> | ||
<br /> | |||
POTE generator: ~10/7 = ~13/9 = 633.042<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 0 -4 -3 4 0|, &lt;0 3 12 11 -1 7|]<br /> | Map: [&lt;1 0 -4 -3 4 0|, &lt;0 3 12 11 -1 7|]<br /> | ||
EDOs: | EDOs: 17c, 19, 36, 91cef<br /> | ||
Badness | Badness: 0.0273<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:130:&lt;h2&gt; --><h2 id="toc65"><a name="Liese-Elisa"></a><!-- ws:end:WikiTextHeadingRule:130 -->Elisa</h2> | <!-- ws:start:WikiTextHeadingRule:130:&lt;h2&gt; --><h2 id="toc65"><a name="Liese-Elisa"></a><!-- ws:end:WikiTextHeadingRule:130 -->Elisa</h2> | ||
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Badness: 0.0416<br /> | Badness: 0.0416<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:132:&lt;h1&gt; --><h1 id=" | <!-- ws:start:WikiTextHeadingRule:132:&lt;h2&gt; --><h2 id="toc66"><a name="Liese-Lisa"></a><!-- ws:end:WikiTextHeadingRule:132 -->Lisa</h2> | ||
Commas: 45/44, 81/80, 343/330<br /> | |||
<br /> | |||
POTE generator: ~10/7 = 631.370<br /> | |||
<br /> | |||
Map: [&lt;1 0 -4 -3 -6|, &lt;0 3 12 11 18|]<br /> | |||
EDOs: 19<br /> | |||
Badness: 0.0548<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:134:&lt;h2&gt; --><h2 id="toc67"><a name="Liese-13-limit"></a><!-- ws:end:WikiTextHeadingRule:134 -->13-limit</h2> | |||
Commas: 45/44, 81/80, 91/88, 147/143<br /> | |||
<br /> | |||
POTE generator: ~10/7 = 631.221<br /> | |||
<br /> | |||
Map: [&lt;1 0 -4 -3 -6 0|, &lt;0 3 12 11 18 7|]<br /> | |||
EDOs: 19<br /> | |||
Badness: 0.0361<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:136:&lt;h1&gt; --><h1 id="toc68"><a name="Jerome"></a><!-- ws:end:WikiTextHeadingRule:136 -->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 /> | ||
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Badness: 0.1087<br /> | Badness: 0.1087<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:138:&lt;h2&gt; --><h2 id="toc69"><a name="Jerome-11-limit"></a><!-- ws:end:WikiTextHeadingRule:138 -->11-limit</h2> | ||
Commas: 81/80, 99/98, 864/847<br /> | Commas: 81/80, 99/98, 864/847<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0479<br /> | Badness: 0.0479<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:140:&lt;h2&gt; --><h2 id="toc70"><a name="Jerome-13-limit"></a><!-- ws:end:WikiTextHeadingRule:140 -->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 /> | ||
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Badness: 0.0293<br /> | Badness: 0.0293<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:142:&lt;h2&gt; --><h2 id="toc71"><a name="Jerome-17-limit"></a><!-- ws:end:WikiTextHeadingRule:142 -->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 /> | ||
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Badness: 0.0209<br /> | Badness: 0.0209<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:144:&lt;h1&gt; --><h1 id="toc72"><a name="Meanmag"></a><!-- ws:end:WikiTextHeadingRule:144 -->Meanmag</h1> | ||
Commas: 81/80, 3125/3072<br /> | Commas: 81/80, 3125/3072<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0770<br /> | Badness: 0.0770<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:146:&lt;h1&gt; --><h1 id="toc73"><a name="Undevigintone"></a><!-- ws:end:WikiTextHeadingRule:146 -->Undevigintone</h1> | ||
Commas: 49/48, 81/80, 126/125<br /> | Commas: 49/48, 81/80, 126/125<br /> | ||
<br /> | <br /> | ||
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Map: [&lt;19 30 44 53 0|, &lt;0 0 0 0 1|]<br /> | Map: [&lt;19 30 44 53 0|, &lt;0 0 0 0 1|]<br /> | ||
EDOs: 19, 38d<br /> | EDOs: 19, 38d<br /> | ||
Badness: 0.0364 | Badness: 0.0364</body></html></pre></div> | ||
</body></html></pre></div> | |||