Diminished family: Difference between revisions

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~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~

__FORCETOC__

~~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>2012-05-09 01:09:29 UTC</tt>.<br>~~

~~: The original revision id was <tt>332260622</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>~~

~~<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|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.

Line 16:

Line 8:

Map: [<4 0 3|, <0 1 1|]

EDOs: 8, 12

Badness: 0.0472

Line 25:

Line 19:

Map: [<4 0 3 8|, <0 2 2 1|]

Wedgie: <<8 8 4 -6 -16 -13||

EDOs: 24, 52d, 76cd

Badness: 0.0864

Line 35:

Line 32:

Map: [<4 0 3 8 -2|, <0 2 2 1 5|]

EDOs: 24, 76cde

Badness: 0.0566

Line 44:

Line 43:

Map: [<4 0 3 8 -2 -1|, <0 2 2 1 5 5|]

EDOs: 24, 52de, 76cde

Badness: 0.039

Line 53:

Line 54:

Map: [<8 0 6 -3|, <0 1 1 2|]

Wedgie: <<8 8 16 -6 3 15||

EDOs: 24, 32c, 56c

Badness: 0.1075

Line 63:

Line 67:

Map: [<8 0 6 -3 15|, <0 1 1 2 1|]

EDOs: 24, 32c, 56c

Badness: 0.0476

Line 72:

Line 78:

Map: [<8 0 6 -3 15 17|, <0 1 1 2 1 1|]

EDOs: 24, 32cf, 56cf

Badness: 0.0306

~~</pre></div>~~

~~<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><a href="#Dimipent">Dimipent</a> | <a href="#Hemidim">Hemidim</a> | <a href="#Semidim">Semidim</a>

~~<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 />~~

~~<h1 id="toc0"><a name="Dimipent"></a>Dimipent</h1>~~

~~Comma: 648/625<br />~~

~~<br />~~

~~POTE generator: ~3/2 = 699.507<br />~~

~~<br />~~

~~Map: [&lt;4 0 3|, &lt;0 1 1|]<br />~~

~~EDOs: 8, 12<br />~~

~~Badness: 0.0472<br />~~

~~<br />~~

~~<h1 id="toc1"><a name="Hemidim"></a>Hemidim</h1>~~

~~Commas: 49/48, 648/625<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 252.555<br />~~

~~<br />~~

~~Map: [&lt;4 0 3 8|, &lt;0 2 2 1|]<br />~~

~~Wedgie: &lt;&lt;8 8 4 -6 -16 -13||<br />~~

~~EDOs: 24, 52d, 76cd<br />~~

~~Badness: 0.0864<br />~~

~~<br />~~

~~<h2 id="toc2"><a name="Hemidim-11-limit"></a>11-limit</h2>~~

~~Commas: 49/48, 77/75, 243/242<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 251.658<br />~~

~~<br />~~

~~Map: [&lt;4 0 3 8 -2|, &lt;0 2 2 1 5|]<br />~~

~~EDOs: 24, 76cde<br />~~

~~Badness: 0.0566<br />~~

~~<br />~~

~~<h2 id="toc3"><a name="Hemidim-13-limit"></a>13-limit</h2>~~

~~Commas: 49/48, 66/65, 77/75, 648/625<br />~~

~~<br />~~

~~POTE generator: ~8/7 = 252.225<br />~~

~~<br />~~

~~Map: [&lt;4 0 3 8 -2 -1|, &lt;0 2 2 1 5 5|]<br />~~

~~EDOs: 24, 52de, 76cde<br />~~

~~Badness: 0.039<br />~~

~~<br />~~

~~<h1 id="toc4"><a name="Semidim"></a>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 />~~

~~<h2 id="toc5"><a name="Semidim-11-limit"></a>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 />~~

~~<h2 id="toc6"><a name="Semidim-13-limit"></a>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>~~

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+__FORCETOC__
-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>2012-05-09 01:09:29 UTC</tt>.<br>
-: The original revision id was <tt>332260622</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>
-<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|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.
@@ Line 16: / Line 8: @@
 Map: [&lt;4 0 3|, &lt;0 1 1|]
 EDOs: 8, 12
 Badness: 0.0472
@@ Line 25: / Line 19: @@
 Map: [&lt;4 0 3 8|, &lt;0 2 2 1|]
 Wedgie: &lt;&lt;8 8 4 -6 -16 -13||
 EDOs: 24, 52d, 76cd
 Badness: 0.0864
@@ Line 35: / Line 32: @@
 Map: [&lt;4 0 3 8 -2|, &lt;0 2 2 1 5|]
 EDOs: 24, 76cde
 Badness: 0.0566
@@ Line 44: / Line 43: @@
 Map: [&lt;4 0 3 8 -2 -1|, &lt;0 2 2 1 5 5|]
 EDOs: 24, 52de, 76cde
 Badness: 0.039
@@ Line 53: / Line 54: @@
 Map: [&lt;8 0 6 -3|, &lt;0 1 1 2|]
 Wedgie: &lt;&lt;8 8 16 -6 3 15||
 EDOs: 24, 32c, 56c
 Badness: 0.1075
@@ Line 63: / Line 67: @@
 Map: [&lt;8 0 6 -3 15|, &lt;0 1 1 2 1|]
 EDOs: 24, 32c, 56c
 Badness: 0.0476
@@ Line 72: / Line 78: @@
 Map: [&lt;8 0 6 -3 15 17|, &lt;0 1 1 2 1 1|]
 EDOs: 24, 32cf, 56cf
 Badness: 0.0306
-</pre></div>
-<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Dimipent family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:14:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt;&lt;a href="#Dimipent"&gt;Dimipent&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt; | &lt;a href="#Hemidim"&gt;Hemidim&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt; | &lt;a href="#Semidim"&gt;Semidim&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;br /&gt;
-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. &lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Dimipent"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Dimipent&lt;/h1&gt;
-Comma: 648/625&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 =  699.507&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;4 0 3|, &amp;lt;0 1 1|]&lt;br /&gt;
-EDOs: 8, 12&lt;br /&gt;
-Badness: 0.0472&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Hemidim"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Hemidim&lt;/h1&gt;
-Commas: 49/48, 648/625&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~8/7 = 252.555&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;4 0 3 8|, &amp;lt;0 2 2 1|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;8 8 4 -6 -16 -13||&lt;br /&gt;
-EDOs: 24, 52d, 76cd&lt;br /&gt;
-Badness: 0.0864&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Hemidim-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
-Commas: 49/48, 77/75, 243/242&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~8/7 = 251.658&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;4 0 3 8 -2|, &amp;lt;0 2 2 1 5|]&lt;br /&gt;
-EDOs: 24, 76cde&lt;br /&gt;
-Badness: 0.0566&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Hemidim-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
-Commas: 49/48, 66/65, 77/75, 648/625&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~8/7 = 252.225&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;4 0 3 8 -2 -1|, &amp;lt;0 2 2 1 5 5|]&lt;br /&gt;
-EDOs: 24, 52de, 76cde&lt;br /&gt;
-Badness: 0.039&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Semidim"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Semidim&lt;/h1&gt;
-Commas: 245/243, 392/375&lt;br /&gt;
-&lt;br /&gt;
-POTE generator4: ~3/2 = 707.014&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;8 0 6 -3|, &amp;lt;0 1 1 2|]&lt;br /&gt;
-Wedgie: &amp;lt;&amp;lt;8 8 16 -6 3 15||&lt;br /&gt;
-EDOs: 24, 32c, 56c &lt;br /&gt;
-Badness: 0.1075&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Semidim-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;11-limit&lt;/h2&gt;
-Commas: 56/55, 77/75, 245/243&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 706.645&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;8 0 6 -3 15|, &amp;lt;0 1 1 2 1|]&lt;br /&gt;
-EDOs: 24, 32c, 56c&lt;br /&gt;
-Badness: 0.0476&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Semidim-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;13-limit&lt;/h2&gt;
-Commas: 56/55, 66/65, 77/75, 507/500&lt;br /&gt;
-&lt;br /&gt;
-POTE generator: ~3/2 = 707.376&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;8 0 6 -3 15 17|, &amp;lt;0 1 1 2 1 1|]&lt;br /&gt;
-EDOs: 24, 32cf, 56cf&lt;br /&gt;
-Badness: 0.0306&lt;/body&gt;&lt;/html&gt;</pre></div>