7edt: Difference between revisions

Revision as of 16:43, 6 September 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 2011-09-06 16:43:08 UTC.

The original revision id was 251313418.

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]]

=Properties=
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.

=Scale degrees of 7edt= 
|| Degrees || Cents || Approximate Ratio ||
|| 0 || 0 || [[1_1|1/1]] ||
|| 1 || 271.708 || [[7_6|7/6]] ||
|| 2 || 543.416 || [[15_11|15/11]], [[11_8|11/8]] ||
|| 3 || 815.124 || [[8_5|8/5]] ||
|| 4 || 1086.831 || [[15_8|15/8]] ||
|| 5 || 1358.539 || 11/5 ([[11_10|11/10]] plus an octave) ||
|| 6 || 1630.247 || 18/7 ([[9_7|9/7]] plus an octave) ||
|| 7 || 1901.955 || 3/1 ||

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 blair comma.

=7n-edt Family=
[[14edt]]
[[21edt]]
[[28edt]]
...

Original HTML content:

<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: -->
<!-- ws:end:WikiTextTocRule:10 --><br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Properties"></a><!-- ws:end:WikiTextHeadingRule:0 -->Properties</h1>
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 />
<br />
<!-- 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>
 

<table class="wiki_table">
    <tr>
        <td>Degrees<br />
</td>
        <td>Cents<br />
</td>
        <td>Approximate Ratio<br />
</td>
    </tr>
    <tr>
        <td>0<br />
</td>
        <td>0<br />
</td>
        <td><a class="wiki_link" href="/1_1">1/1</a><br />
</td>
    </tr>
    <tr>
        <td>1<br />
</td>
        <td>271.708<br />
</td>
        <td><a class="wiki_link" href="/7_6">7/6</a><br />
</td>
    </tr>
    <tr>
        <td>2<br />
</td>
        <td>543.416<br />
</td>
        <td><a class="wiki_link" href="/15_11">15/11</a>, <a class="wiki_link" href="/11_8">11/8</a><br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td>815.124<br />
</td>
        <td><a class="wiki_link" href="/8_5">8/5</a><br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td>1086.831<br />
</td>
        <td><a class="wiki_link" href="/15_8">15/8</a><br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td>1358.539<br />
</td>
        <td>11/5 (<a class="wiki_link" href="/11_10">11/10</a> plus an octave)<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td>1630.247<br />
</td>
        <td>18/7 (<a class="wiki_link" href="/9_7">9/7</a> plus an octave)<br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td>1901.955<br />
</td>
        <td>3/1<br />
</td>
    </tr>
</table>

<br />
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 blair comma.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="x7n-edt Family"></a><!-- ws:end:WikiTextHeadingRule:4 -->7n-edt Family</h1>
<a class="wiki_link" href="/14edt">14edt</a><br />
<a class="wiki_link" href="/21edt">21edt</a><br />
<a class="wiki_link" href="/28edt">28edt</a><br />
...</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2011-09-06 16:42:37 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-06 16:43:08 UTC</tt>.<br>
-: The original revision id was <tt>251313288</tt>.<br>
+: The original revision id was <tt>251313418</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>
@@ Line 24: / Line 24: @@
 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 blair comma.
-=7n-edt Family:=
+=7n-edt Family=
 [[14edt]]
 [[21edt]]
@@ Line 30: / Line 30: @@
 ...</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;7edt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:6:&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:6 --&gt;&lt;!-- ws:start:WikiTextTocRule:7: --&gt;&lt;a href="#Properties"&gt;Properties&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:7 --&gt;&lt;!-- ws:start:WikiTextTocRule:8: --&gt; | &lt;a href="#Scale degrees of 7edt"&gt;Scale degrees of 7edt&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt; | &lt;a href="#x7n-edt Family:"&gt;7n-edt Family:&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt;
+<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;7edt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:6:&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:6 --&gt;&lt;!-- ws:start:WikiTextTocRule:7: --&gt;&lt;a href="#Properties"&gt;Properties&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:7 --&gt;&lt;!-- ws:start:WikiTextTocRule:8: --&gt; | &lt;a href="#Scale degrees of 7edt"&gt;Scale degrees of 7edt&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt; | &lt;a href="#x7n-edt Family"&gt;7n-edt Family&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt;
 &lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Properties"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Properties&lt;/h1&gt;
@@ Line 116: / Line 116: @@
 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 blair comma.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="x7n-edt Family:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;7n-edt Family:&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="x7n-edt Family"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;7n-edt Family&lt;/h1&gt;
 &lt;a class="wiki_link" href="/14edt"&gt;14edt&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link" href="/21edt"&gt;21edt&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link" href="/28edt"&gt;28edt&lt;/a&gt;&lt;br /&gt;
 ...&lt;/body&gt;&lt;/html&gt;</pre></div>

7edt: Difference between revisions

Revision as of 16:43, 6 September 2011

IMPORTED REVISION FROM WIKISPACES

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