Werckismic temperaments: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 239766851 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 240548749 - 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>2011-07- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-07-08 15:45:42 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>240548749</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: 12, 26, 46, 58, 72, 118, 130, 248, 320 | EDOs: 12, 26, 46, 58, 72, 118, 130, 248, 320 | ||
Generators: 99/70, 3, 5 | Generators: 99/70, 3, 5 | ||
Badness: 0.000419</pre></div> | Badness: 0.000419 | ||
=Octowerck= | |||
Commas: 420175/419904, 321489/320000 | |||
POTE generator: ~350/243 = 633.738 | |||
Map: [<8 0 -11 14|, <0 3 7 2|] | |||
EDOs: 72, 176, 248, 320 | |||
Badness: 0.1023 | |||
==11-limit== | |||
Commas: 441/440, 8019/8000, 41503/41472 | |||
POTE generator: ~121/84 = 633.355 | |||
Map: [<8 0 -11 14 15|, <0 3 7 2 3|] | |||
EDOs: 72, 176, 248, 320 | |||
Badness: 0.0302 | |||
==13-limit== | |||
Commas: 441/440, 729/728, 1001/1000, 6656/6655 | |||
POTE generator: ~75/52 = 633.742 | |||
Map: [<8 0 -11 14 15 -38|, <0 3 7 2 3 16|] | |||
EDOs: 72, 248, 320 | |||
Badness: 0.0276 | |||
</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>Werckismic 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>Werckismic temperaments</title></head><body><!-- ws:start:WikiTextTocRule:14:&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:14 --><!-- ws:start:WikiTextTocRule:15: --><a href="#Rank four">Rank four</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <a href="#History">History</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Varuna">Varuna</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Octowerck">Octowerck</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:22 --><br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Rank four"></a><!-- ws:end:WikiTextHeadingRule:0 -->Rank four</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Rank four"></a><!-- ws:end:WikiTextHeadingRule:0 -->Rank four</h1> | ||
These are rank three temperaments tempering out 441/440, but we can began by looking at the rank four temperament.<br /> | These are rank three temperaments tempering out 441/440, but we can began by looking at the rank four temperament.<br /> | ||
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EDOs: 12, 26, 46, 58, 72, 118, 130, 248, 320<br /> | EDOs: 12, 26, 46, 58, 72, 118, 130, 248, 320<br /> | ||
Generators: 99/70, 3, 5<br /> | Generators: 99/70, 3, 5<br /> | ||
Badness: 0.000419</body></html></pre></div> | Badness: 0.000419<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Octowerck"></a><!-- ws:end:WikiTextHeadingRule:8 -->Octowerck</h1> | |||
Commas: 420175/419904, 321489/320000<br /> | |||
<br /> | |||
POTE generator: ~350/243 = 633.738<br /> | |||
<br /> | |||
Map: [&lt;8 0 -11 14|, &lt;0 3 7 2|]<br /> | |||
EDOs: 72, 176, 248, 320<br /> | |||
Badness: 0.1023<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Octowerck-11-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->11-limit</h2> | |||
Commas: 441/440, 8019/8000, 41503/41472<br /> | |||
<br /> | |||
POTE generator: ~121/84 = 633.355<br /> | |||
<br /> | |||
Map: [&lt;8 0 -11 14 15|, &lt;0 3 7 2 3|]<br /> | |||
EDOs: 72, 176, 248, 320<br /> | |||
Badness: 0.0302<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Octowerck-13-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->13-limit</h2> | |||
Commas: 441/440, 729/728, 1001/1000, 6656/6655<br /> | |||
<br /> | |||
POTE generator: ~75/52 = 633.742<br /> | |||
<br /> | |||
Map: [&lt;8 0 -11 14 15 -38|, &lt;0 3 7 2 3 16|]<br /> | |||
EDOs: 72, 248, 320<br /> | |||
Badness: 0.0276</body></html></pre></div> | |||
Revision as of 15:45, 8 July 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2011-07-08 15:45:42 UTC.
- The original revision id was 240548749.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
[[toc|flat]] =Rank four= These are rank three temperaments tempering out 441/440, but we can began by looking at the rank four temperament. Minimax tuning [|1 0 0 0 0>, |1/2 2/3 1/6 -1/3 1/6>, |0 0 1 0 0>, |1 -2/3 1/3 1/3 1/3>, |0 0 0 0 1>] Eigenmonzos: 2, 5, 11, 9/7 Map: [<1 0 0 0 -3|, <0 1 0 0 2|, <0 0 1 0 -1|, <0 0 0 1 2|] EDOs: 72, 118, 130, 159, 171, 190, 248, 289, 320 =History= Commas: 441/400, 4000/3993 Minimax tuning [|1 0 0 0 0>, |4/17 12/17 0 -6/17 6/17>, |-27/17 4/17 0 -2/17 19/17>, |8/17 -10/17 0 5/17 12/17>, |0 0 0 0 1>] Eigenmonzos: 2, 11, 9/7 Map: [<1 2 0 0 1|, <0 -6 0 7 2|, <0 0 1 1 1|] Generators: 2, 21/20, 5 EDOs: 58, 72, 130, 202, 217, 289, 491 Badness: 0.000604 ==13-limit== Commas: 364/363, 441/440, 1001/1000 Minimax tuning [|1 0 0 0 0 0>, |5/4 0 0 -3/8 0 3/8>, |0 0 1 0 0 0>, |7/8 0 1 7/16 0 -7/16>, |5/4 0 1 1/8 0 -1/8>, |7/8 0 1 -9/16 0 9/16>] Eigenmonzos: 2, 5, 13/7 Map: [<1 2 0 0 1 2|, <0 -6 0 7 2 -9|, <0 0 1 1 1 1|] Generators: 2, 21/20, 5 EDOs: 58, 72, 87, 130, 217, 289 Badness: 0.000540 [[Spectrum of a temperament|Spectrum]]: 11/10, 15/13, 14/11, 4/3, 7/5, 5/4, 11/8, 18/13, 15/11, 13/12, 13/10, 6/5, 8/7, 16/15, 12/11, 13/11, 9/8, 16/13, 15/14, 10/9, 7/6, 11/9, 14/13, 9/7 =Varuna= Commas: 441/440, 8019/8000 Map: [<2 0 0 9 12|, <0 1 0 -4 -6|, <0 0 1 2 3|] EDOs: 12, 26, 46, 58, 72, 118, 130, 248, 320 Generators: 99/70, 3, 5 Badness: 0.000419 =Octowerck= Commas: 420175/419904, 321489/320000 POTE generator: ~350/243 = 633.738 Map: [<8 0 -11 14|, <0 3 7 2|] EDOs: 72, 176, 248, 320 Badness: 0.1023 ==11-limit== Commas: 441/440, 8019/8000, 41503/41472 POTE generator: ~121/84 = 633.355 Map: [<8 0 -11 14 15|, <0 3 7 2 3|] EDOs: 72, 176, 248, 320 Badness: 0.0302 ==13-limit== Commas: 441/440, 729/728, 1001/1000, 6656/6655 POTE generator: ~75/52 = 633.742 Map: [<8 0 -11 14 15 -38|, <0 3 7 2 3 16|] EDOs: 72, 248, 320 Badness: 0.0276
Original HTML content:
<html><head><title>Werckismic temperaments</title></head><body><!-- ws:start:WikiTextTocRule:14:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><a href="#Rank four">Rank four</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <a href="#History">History</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Varuna">Varuna</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Octowerck">Octowerck</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> <!-- ws:end:WikiTextTocRule:22 --><br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Rank four"></a><!-- ws:end:WikiTextHeadingRule:0 -->Rank four</h1> These are rank three temperaments tempering out 441/440, but we can began by looking at the rank four temperament.<br /> <br /> Minimax tuning<br /> [|1 0 0 0 0>, |1/2 2/3 1/6 -1/3 1/6>, |0 0 1 0 0>, <br /> |1 -2/3 1/3 1/3 1/3>, |0 0 0 0 1>]<br /> Eigenmonzos: 2, 5, 11, 9/7<br /> <br /> Map: [<1 0 0 0 -3|, <0 1 0 0 2|, <0 0 1 0 -1|, <0 0 0 1 2|]<br /> EDOs: 72, 118, 130, 159, 171, 190, 248, 289, 320<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="History"></a><!-- ws:end:WikiTextHeadingRule:2 -->History</h1> Commas: 441/400, 4000/3993<br /> <br /> Minimax tuning<br /> [|1 0 0 0 0>, |4/17 12/17 0 -6/17 6/17>, <br /> |-27/17 4/17 0 -2/17 19/17>, <br /> |8/17 -10/17 0 5/17 12/17>, |0 0 0 0 1>]<br /> Eigenmonzos: 2, 11, 9/7<br /> <br /> Map: [<1 2 0 0 1|, <0 -6 0 7 2|, <0 0 1 1 1|]<br /> Generators: 2, 21/20, 5<br /> EDOs: 58, 72, 130, 202, 217, 289, 491<br /> Badness: 0.000604<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="History-13-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->13-limit</h2> Commas: 364/363, 441/440, 1001/1000<br /> <br /> Minimax tuning<br /> [|1 0 0 0 0 0>, |5/4 0 0 -3/8 0 3/8>, |0 0 1 0 0 0>, <br /> |7/8 0 1 7/16 0 -7/16>, |5/4 0 1 1/8 0 -1/8>, <br /> |7/8 0 1 -9/16 0 9/16>]<br /> Eigenmonzos: 2, 5, 13/7<br /> <br /> Map: [<1 2 0 0 1 2|, <0 -6 0 7 2 -9|, <0 0 1 1 1 1|]<br /> Generators: 2, 21/20, 5<br /> EDOs: 58, 72, 87, 130, 217, 289<br /> Badness: 0.000540<br /> <br /> <a class="wiki_link" href="/Spectrum%20of%20a%20temperament">Spectrum</a>: 11/10, 15/13, 14/11, 4/3, 7/5, 5/4, 11/8, 18/13, 15/11, 13/12, 13/10, 6/5, 8/7, 16/15, 12/11, 13/11, 9/8, 16/13, 15/14, 10/9, 7/6, 11/9, 14/13, 9/7<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Varuna"></a><!-- ws:end:WikiTextHeadingRule:6 -->Varuna</h1> Commas: 441/440, 8019/8000<br /> <br /> Map: [<2 0 0 9 12|, <0 1 0 -4 -6|, <0 0 1 2 3|]<br /> EDOs: 12, 26, 46, 58, 72, 118, 130, 248, 320<br /> Generators: 99/70, 3, 5<br /> Badness: 0.000419<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="Octowerck"></a><!-- ws:end:WikiTextHeadingRule:8 -->Octowerck</h1> Commas: 420175/419904, 321489/320000<br /> <br /> POTE generator: ~350/243 = 633.738<br /> <br /> Map: [<8 0 -11 14|, <0 3 7 2|]<br /> EDOs: 72, 176, 248, 320<br /> Badness: 0.1023<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="Octowerck-11-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->11-limit</h2> Commas: 441/440, 8019/8000, 41503/41472<br /> <br /> POTE generator: ~121/84 = 633.355<br /> <br /> Map: [<8 0 -11 14 15|, <0 3 7 2 3|]<br /> EDOs: 72, 176, 248, 320<br /> Badness: 0.0302<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="Octowerck-13-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->13-limit</h2> Commas: 441/440, 729/728, 1001/1000, 6656/6655<br /> <br /> POTE generator: ~75/52 = 633.742<br /> <br /> Map: [<8 0 -11 14 15 -38|, <0 3 7 2 3 16|]<br /> EDOs: 72, 248, 320<br /> Badness: 0.0276</body></html>