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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox ET}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | {{ED intro}} |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-17 12:47:43 UTC</tt>.<br>
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| : The original revision id was <tt>255065588</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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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| <h4>Original Wikitext content:</h4>
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| <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]]
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| =Properties= | | == Theory == |
| The 7 equal division of 3, the tritave, divides it into 7 equal parts of 271.708 cents each, corresponding to 4.4165 edo. The step size is very close to the 271.509 cents of 7-limit [[Orwell|orwell temperament]] and also close to the 271.426 cents of 11-limit orwell. It is almost identical to 12\53, the [[53edo]] orwell generator which is 271.698 cents.
| | Since one step of 7edt approximates a [[7/6]] subminor third (4.84{{c}} sharp) quite nicely, three steps are almost exactly [[8/5]] (tempering out [[1728/1715]], the orwellisma), and four steps are very nearly [[15/8]] (tempering out [[2430/2401]], the nuwell comma). 7edt is the lowest equal division of the tritave to accurately approximate some [[7-limit]] harmony, along with some elements of the [[11-limit]], such as the [[11/8]] major fourth. Seven steps make up a tritave, meaning that 7edt tempers out 839808/823543, the eric comma. |
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| =Scale degrees of 7edt=
| | Due to the proximity of the step size with 7/6, 7edt supports [[orwell]] temperament. One step of 7edt is almost identical to 12\53, the [[53edo]] orwell generator, at about 271.698 cents. 7edt is also a good tuning for [[Electra]] temperament, with two steps of 7edt being a close approximation to [[15/11]]. |
| || Degrees || Cents || Approximate Ratio ||
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| || 0 || 0 || [[1_1|1/1]] ||
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| || 1 || 271.708 || [[7_6|7/6]] ||
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| || 2 || 543.416 || [[15_11|15/11]], [[11_8|11/8]] ||
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| || 3 || 815.124 || [[8_5|8/5]] ||
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| || 4 || 1086.831 || [[15_8|15/8]] ||
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| || 5 || 1358.539 || 11/5 ([[11_10|11/10]] plus an octave) ||
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| || 6 || 1630.247 || 18/7 ([[9_7|9/7]] plus an octave) ||
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| || 7 || 1901.955 || 3/1 ||
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| Since one step of 7edt is a sharp subminor (7/6) third, three steps are almost exactlty 8/5, four steps are very nearly 15/8 and six steps are a bit flat of 18/7, 7edt is the lowest equal division of the tritave to accurately approximate some 7-limit harmony. Seven steps make up a tritave, meaning that 7edt tempers out 839808/823543, the eric comma.
| | === Harmonics === |
| | {{Harmonics in equal|7|3|1|columns=15}} |
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| =7n-edt Family= | | === Subsets and supersets === |
| [[14edt]] | | 7edt is the 4th [[prime equal division|prime edt]], after [[5edt]] and before [[11edt]]. |
| [[21edt]] | |
| [[28edt]] | |
| ...</pre></div>
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| <h4>Original HTML content:</h4>
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| <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>7edt</title></head><body><!-- ws:start:WikiTextTocRule:6:&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:6 --><!-- ws:start:WikiTextTocRule:7: --><a href="#Properties">Properties</a><!-- ws:end:WikiTextTocRule:7 --><!-- ws:start:WikiTextTocRule:8: --> | <a href="#Scale degrees of 7edt">Scale degrees of 7edt</a><!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --> | <a href="#x7n-edt Family">7n-edt Family</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: -->
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| <!-- ws:end:WikiTextTocRule:10 --><br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Properties"></a><!-- ws:end:WikiTextHeadingRule:0 -->Properties</h1>
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| The 7 equal division of 3, the tritave, divides it into 7 equal parts of 271.708 cents each, corresponding to 4.4165 edo. The step size is very close to the 271.509 cents of 7-limit <a class="wiki_link" href="/Orwell">orwell temperament</a> and also close to the 271.426 cents of 11-limit orwell. It is almost identical to 12\53, the <a class="wiki_link" href="/53edo">53edo</a> orwell generator which is 271.698 cents.<br />
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| <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Scale degrees of 7edt"></a><!-- ws:end:WikiTextHeadingRule:2 -->Scale degrees of 7edt</h1>
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| <table class="wiki_table">
| | == Intervals == |
| <tr>
| | {| class="wikitable center-1 right-2 right-3" |
| <td>Degrees<br />
| | |- |
| </td>
| | ! # |
| <td>Cents<br />
| | ! Cents |
| </td>
| | ! [[Hekt]]s |
| <td>Approximate Ratio<br />
| | ! Approximate ratios |
| </td>
| | ! [[Electra]] notation<br>({{nowrap|J {{=}} 1/1}}) |
| </tr>
| | |- |
| <tr>
| | | 0 |
| <td>0<br />
| | | 0 |
| </td>
| | | 0 |
| <td>0<br />
| | | [[1/1]] |
| </td>
| | | J |
| <td><a class="wiki_link" href="/1_1">1/1</a><br />
| | |- |
| </td>
| | | 1 |
| </tr>
| | | 272 |
| <tr>
| | | 186 |
| <td>1<br />
| | | [[7/6]] |
| </td>
| | | K |
| <td>271.708<br />
| | |- |
| </td>
| | | 2 |
| <td><a class="wiki_link" href="/7_6">7/6</a><br />
| | | 543 |
| </td>
| | | 371 |
| </tr>
| | | [[11/8]], [[15/11]] |
| <tr>
| | | L |
| <td>2<br />
| | |- |
| </td>
| | | 3 |
| <td>543.416<br />
| | | 815 |
| </td>
| | | 557 |
| <td><a class="wiki_link" href="/15_11">15/11</a>, <a class="wiki_link" href="/11_8">11/8</a><br />
| | | [[8/5]] |
| </td>
| | | M |
| </tr>
| | |- |
| <tr>
| | | 4 |
| <td>3<br />
| | | 1087 |
| </td>
| | | 743 |
| <td>815.124<br />
| | | [[15/8]] |
| </td>
| | | N |
| <td><a class="wiki_link" href="/8_5">8/5</a><br />
| | |- |
| </td>
| | | 5 |
| </tr>
| | | 1359 |
| <tr>
| | | 929 |
| <td>4<br />
| | | [[11/5]] |
| </td>
| | | O |
| <td>1086.831<br />
| | |- |
| </td>
| | | 6 |
| <td><a class="wiki_link" href="/15_8">15/8</a><br />
| | | 1630 |
| </td>
| | | 1114 |
| </tr>
| | | [[18/7]] |
| <tr>
| | | P |
| <td>5<br />
| | |- |
| </td>
| | | 7 |
| <td>1358.539<br />
| | | 1902 |
| </td>
| | | 1300 |
| <td>11/5 (<a class="wiki_link" href="/11_10">11/10</a> plus an octave)<br />
| | | [[3/1]] |
| </td>
| | | J |
| </tr>
| | |} |
| <tr>
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| <td>6<br />
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| </td>
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| <td>1630.247<br />
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| </td>
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| <td>18/7 (<a class="wiki_link" href="/9_7">9/7</a> plus an octave)<br />
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| </td>
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| </tr>
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| <tr>
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| <td>7<br />
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| </td>
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| <td>1901.955<br />
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| </td>
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| <td>3/1<br />
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| </td>
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| </tr>
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| </table>
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| <br />
| | [[Category:Orwell]] |
| Since one step of 7edt is a sharp subminor (7/6) third, three steps are almost exactlty 8/5, four steps are very nearly 15/8 and six steps are a bit flat of 18/7, 7edt is the lowest equal division of the tritave to accurately approximate some 7-limit harmony. Seven steps make up a tritave, meaning that 7edt tempers out 839808/823543, the eric comma.<br />
| | [[Category:Subminor third]] |
| <br />
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| <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="x7n-edt Family"></a><!-- ws:end:WikiTextHeadingRule:4 -->7n-edt Family</h1>
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| <a class="wiki_link" href="/14edt">14edt</a><br />
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| <a class="wiki_link" href="/21edt">21edt</a><br />
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| <a class="wiki_link" href="/28edt">28edt</a><br />
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| ...</body></html></pre></div>
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