Meantone family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 397940612 - Original comment: ** |
Wikispaces>hstraub **Imported revision 448780312 - 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: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2013-09-05 10:33:27 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>448780312</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"><span style="display: block; text-align: right;">[[toc]] | ||
Other languages: [[xenharmonie/mitteltönig|Deutsch]] | |||
</span> | |||
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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Badness: 0.0234 | Badness: 0.0234 | ||
=Ptolemy= | =Ptolemy= | ||
Commas: 81/80, 121/120, 525/512 | Commas: 81/80, 121/120, 525/512 | ||
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Badness: 0.0588 | Badness: 0.0588 | ||
==13-limit== | ==13-limit== | ||
Commas: 65/64, 81/80, 105/104, 121/120 | Commas: 65/64, 81/80, 105/104, 121/120 | ||
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Badness: 0.0364 | Badness: 0.0364 | ||
==13-limit== | ==13-limit== | ||
Commas: 49/48, 65/64, 81/80, 126/125 | Commas: 49/48, 65/64, 81/80, 126/125 | ||
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Badness: 0.0229</pre></div> | Badness: 0.0229</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>Meantone family</title></head><body><!-- ws:start:WikiTextTocRule:166:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:166 --><!-- ws:start:WikiTextTocRule:167: --><div style="margin-left: 2em;"><a href="#x-Seven limit children">Seven limit children</a></div> | <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>Meantone family</title></head><body><span style="display: block; text-align: right;"><!-- ws:start:WikiTextTocRule:166:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:166 --><!-- ws:start:WikiTextTocRule:167: --><div style="margin-left: 2em;"><a href="#x-Seven limit children">Seven limit children</a></div> | ||
<!-- ws:end:WikiTextTocRule:167 --><!-- ws:start:WikiTextTocRule:168: --><div style="margin-left: 1em;"><a href="#Septimal meantone">Septimal meantone</a></div> | <!-- ws:end:WikiTextTocRule:167 --><!-- ws:start:WikiTextTocRule:168: --><div style="margin-left: 1em;"><a href="#Septimal meantone">Septimal meantone</a></div> | ||
<!-- ws:end:WikiTextTocRule:168 --><!-- ws:start:WikiTextTocRule:169: --><div style="margin-left: 2em;"><a href="#Septimal meantone-Unidecimal meantone aka Huygens">Unidecimal meantone aka Huygens</a></div> | <!-- ws:end:WikiTextTocRule:168 --><!-- ws:start:WikiTextTocRule:169: --><div style="margin-left: 2em;"><a href="#Septimal meantone-Unidecimal meantone aka Huygens">Unidecimal meantone aka Huygens</a></div> | ||
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<!-- ws:end:WikiTextTocRule:248 --><!-- ws:start:WikiTextTocRule:249: --><div style="margin-left: 2em;"><a href="#Undevigintone-13-limit">13-limit</a></div> | <!-- ws:end:WikiTextTocRule:248 --><!-- ws:start:WikiTextTocRule:249: --><div style="margin-left: 2em;"><a href="#Undevigintone-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule:249 --><!-- ws:start:WikiTextTocRule:250: --></div> | <!-- ws:end:WikiTextTocRule:249 --><!-- ws:start:WikiTextTocRule:250: --></div> | ||
<!-- ws:end:WikiTextTocRule:250 -->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 /> | <!-- ws:end:WikiTextTocRule:250 --><br /> | ||
Other languages: <a class="wiki_link" href="http://xenharmonie.wikispaces.com/mittelt%C3%B6nig">Deutsch</a><br /> | |||
</span><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 /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 696.239<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~3/2 = 696.239<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:92:&lt;h1&gt; --><h1 id="toc46"><a name="Ptolemy"></a><!-- ws:end:WikiTextHeadingRule:92 -->Ptolemy</h1> | <!-- ws:start:WikiTextHeadingRule:92:&lt;h1&gt; --><h1 id="toc46"><a name="Ptolemy"></a><!-- ws:end:WikiTextHeadingRule:92 -->Ptolemy</h1> | ||
Commas: 81/80, 121/120, 525/512<br /> | Commas: 81/80, 121/120, 525/512<br /> | ||
<br /> | <br /> | ||
POTE generator: ~11/9 = 346.922<br /> | POTE generator: ~11/9 = 346.922<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:94:&lt;h2&gt; --><h2 id="toc47"><a name="Ptolemy-13-limit"></a><!-- ws:end:WikiTextHeadingRule:94 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:94:&lt;h2&gt; --><h2 id="toc47"><a name="Ptolemy-13-limit"></a><!-- ws:end:WikiTextHeadingRule:94 -->13-limit</h2> | ||
Commas: 65/64, 81/80, 105/104, 121/120<br /> | Commas: 65/64, 81/80, 105/104, 121/120<br /> | ||
<br /> | <br /> | ||
POTE generator: ~11/9 = 346.910<br /> | POTE generator: ~11/9 = 346.910<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:164:&lt;h2&gt; --><h2 id="toc82"><a name="Undevigintone-13-limit"></a><!-- ws:end:WikiTextHeadingRule:164 -->13-limit</h2> | <!-- ws:start:WikiTextHeadingRule:164:&lt;h2&gt; --><h2 id="toc82"><a name="Undevigintone-13-limit"></a><!-- ws:end:WikiTextHeadingRule:164 -->13-limit</h2> | ||
Commas: 49/48, 65/64, 81/80, 126/125<br /> | Commas: 49/48, 65/64, 81/80, 126/125<br /> | ||
<br /> | <br /> | ||
POTE generator: ~11/8 = 537.061<br /> | POTE generator: ~11/8 = 537.061<br /> | ||