Diminished family: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 331608928 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 332260622 - 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>2012-05- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-09 01:09:29 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>332260622</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: 24, 52de, 76cde | EDOs: 24, 52de, 76cde | ||
Badness: 0.039 | Badness: 0.039 | ||
=Semidim= | |||
Commas: 245/243, 392/375 | |||
POTE generator4: ~3/2 = 707.014 | |||
Map: [<8 0 6 -3|, <0 1 1 2|] | |||
Wedgie: <<8 8 16 -6 3 15|| | |||
EDOs: 24, 32c, 56c | |||
Badness: 0.1075 | |||
==11-limit== | |||
Commas: 56/55, 77/75, 245/243 | |||
POTE generator: ~3/2 = 706.645 | |||
Map: [<8 0 6 -3 15|, <0 1 1 2 1|] | |||
EDOs: 24, 32c, 56c | |||
Badness: 0.0476 | |||
==13-limit== | |||
Commas: 56/55, 66/65, 77/75, 507/500 | |||
POTE generator: ~3/2 = 707.376 | |||
Map: [<8 0 6 -3 15 17|, <0 1 1 2 1 1|] | |||
EDOs: 24, 32cf, 56cf | |||
Badness: 0.0306 | |||
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</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" class="old-revision-html"><html><head><title>Dimipent family</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>Dimipent family</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="#Dimipent">Dimipent</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <a href="#Hemidim">Hemidim</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Semidim">Semidim</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 /> | ||
The dimipent family tempers out the major diesis aka diminished comma, 648/625, the amount by which four 6/5 minor thirds exceed an octave, and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as 12edo. <br /> | The dimipent family tempers out the major diesis aka diminished comma, 648/625, the amount by which four 6/5 minor thirds exceed an octave, and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as 12edo. <br /> | ||
<br /> | <br /> | ||
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Map: [&lt;4 0 3 8 -2 -1|, &lt;0 2 2 1 5 5|]<br /> | Map: [&lt;4 0 3 8 -2 -1|, &lt;0 2 2 1 5 5|]<br /> | ||
EDOs: 24, 52de, 76cde<br /> | EDOs: 24, 52de, 76cde<br /> | ||
Badness: 0.039</body></html></pre></div> | Badness: 0.039<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Semidim"></a><!-- ws:end:WikiTextHeadingRule:8 -->Semidim</h1> | |||
Commas: 245/243, 392/375<br /> | |||
<br /> | |||
POTE generator4: ~3/2 = 707.014<br /> | |||
<br /> | |||
Map: [&lt;8 0 6 -3|, &lt;0 1 1 2|]<br /> | |||
Wedgie: &lt;&lt;8 8 16 -6 3 15||<br /> | |||
EDOs: 24, 32c, 56c <br /> | |||
Badness: 0.1075<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Semidim-11-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->11-limit</h2> | |||
Commas: 56/55, 77/75, 245/243<br /> | |||
<br /> | |||
POTE generator: ~3/2 = 706.645<br /> | |||
<br /> | |||
Map: [&lt;8 0 6 -3 15|, &lt;0 1 1 2 1|]<br /> | |||
EDOs: 24, 32c, 56c<br /> | |||
Badness: 0.0476<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Semidim-13-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->13-limit</h2> | |||
Commas: 56/55, 66/65, 77/75, 507/500<br /> | |||
<br /> | |||
POTE generator: ~3/2 = 707.376<br /> | |||
<br /> | |||
Map: [&lt;8 0 6 -3 15 17|, &lt;0 1 1 2 1 1|]<br /> | |||
EDOs: 24, 32cf, 56cf<br /> | |||
Badness: 0.0306</body></html></pre></div> | |||
Revision as of 01:09, 9 May 2012
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 2012-05-09 01:09:29 UTC.
- The original revision id was 332260622.
- 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]] The dimipent family tempers out the major diesis aka diminished comma, 648/625, the amount by which four 6/5 minor thirds exceed an octave, and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as 12edo. =Dimipent= Comma: 648/625 POTE generator: ~3/2 = 699.507 Map: [<4 0 3|, <0 1 1|] EDOs: 8, 12 Badness: 0.0472 =Hemidim= Commas: 49/48, 648/625 POTE generator: ~8/7 = 252.555 Map: [<4 0 3 8|, <0 2 2 1|] Wedgie: <<8 8 4 -6 -16 -13|| EDOs: 24, 52d, 76cd Badness: 0.0864 ==11-limit== Commas: 49/48, 77/75, 243/242 POTE generator: ~8/7 = 251.658 Map: [<4 0 3 8 -2|, <0 2 2 1 5|] EDOs: 24, 76cde Badness: 0.0566 ==13-limit== Commas: 49/48, 66/65, 77/75, 648/625 POTE generator: ~8/7 = 252.225 Map: [<4 0 3 8 -2 -1|, <0 2 2 1 5 5|] EDOs: 24, 52de, 76cde Badness: 0.039 =Semidim= Commas: 245/243, 392/375 POTE generator4: ~3/2 = 707.014 Map: [<8 0 6 -3|, <0 1 1 2|] Wedgie: <<8 8 16 -6 3 15|| EDOs: 24, 32c, 56c Badness: 0.1075 ==11-limit== Commas: 56/55, 77/75, 245/243 POTE generator: ~3/2 = 706.645 Map: [<8 0 6 -3 15|, <0 1 1 2 1|] EDOs: 24, 32c, 56c Badness: 0.0476 ==13-limit== Commas: 56/55, 66/65, 77/75, 507/500 POTE generator: ~3/2 = 707.376 Map: [<8 0 6 -3 15 17|, <0 1 1 2 1 1|] EDOs: 24, 32cf, 56cf Badness: 0.0306
Original HTML content:
<html><head><title>Dimipent family</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="#Dimipent">Dimipent</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <a href="#Hemidim">Hemidim</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Semidim">Semidim</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 /> The dimipent family tempers out the major diesis aka diminished comma, 648/625, the amount by which four 6/5 minor thirds exceed an octave, and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as 12edo. <br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Dimipent"></a><!-- ws:end:WikiTextHeadingRule:0 -->Dimipent</h1> Comma: 648/625<br /> <br /> POTE generator: ~3/2 = 699.507<br /> <br /> Map: [<4 0 3|, <0 1 1|]<br /> EDOs: 8, 12<br /> Badness: 0.0472<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Hemidim"></a><!-- ws:end:WikiTextHeadingRule:2 -->Hemidim</h1> Commas: 49/48, 648/625<br /> <br /> POTE generator: ~8/7 = 252.555<br /> <br /> Map: [<4 0 3 8|, <0 2 2 1|]<br /> Wedgie: <<8 8 4 -6 -16 -13||<br /> EDOs: 24, 52d, 76cd<br /> Badness: 0.0864<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Hemidim-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2> Commas: 49/48, 77/75, 243/242<br /> <br /> POTE generator: ~8/7 = 251.658<br /> <br /> Map: [<4 0 3 8 -2|, <0 2 2 1 5|]<br /> EDOs: 24, 76cde<br /> Badness: 0.0566<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="Hemidim-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2> Commas: 49/48, 66/65, 77/75, 648/625<br /> <br /> POTE generator: ~8/7 = 252.225<br /> <br /> Map: [<4 0 3 8 -2 -1|, <0 2 2 1 5 5|]<br /> EDOs: 24, 52de, 76cde<br /> Badness: 0.039<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="Semidim"></a><!-- ws:end:WikiTextHeadingRule:8 -->Semidim</h1> Commas: 245/243, 392/375<br /> <br /> POTE generator4: ~3/2 = 707.014<br /> <br /> Map: [<8 0 6 -3|, <0 1 1 2|]<br /> Wedgie: <<8 8 16 -6 3 15||<br /> EDOs: 24, 32c, 56c <br /> Badness: 0.1075<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="Semidim-11-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->11-limit</h2> Commas: 56/55, 77/75, 245/243<br /> <br /> POTE generator: ~3/2 = 706.645<br /> <br /> Map: [<8 0 6 -3 15|, <0 1 1 2 1|]<br /> EDOs: 24, 32c, 56c<br /> Badness: 0.0476<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="Semidim-13-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->13-limit</h2> Commas: 56/55, 66/65, 77/75, 507/500<br /> <br /> POTE generator: ~3/2 = 707.376<br /> <br /> Map: [<8 0 6 -3 15 17|, <0 1 1 2 1 1|]<br /> EDOs: 24, 32cf, 56cf<br /> Badness: 0.0306</body></html>