7edt: 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>
=Properties=
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-17 12:47:43 UTC</tt>.<br>
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|53edo]] orwell generator which is 271.698 cents.
: The original revision id was <tt>255065588</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]]


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


=7n-edt Family=
=7n-edt Family=
[[14edt]]
[[14edt|14edt]]
[[21edt]]
 
[[28edt]]
[[21edt|21edt]]
...</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;
&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;
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 &lt;a class="wiki_link" href="/Orwell"&gt;orwell temperament&lt;/a&gt; and also close to the 271.426 cents of 11-limit orwell. It is almost identical to 12\53, the &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; orwell generator which is 271.698 cents.&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="Scale degrees of 7edt"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Scale degrees of 7edt&lt;/h1&gt;


&lt;table class="wiki_table"&gt;
[[28edt|28edt]]
    &lt;tr&gt;
        &lt;td&gt;Degrees&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Cents&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Approximate Ratio&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/1_1"&gt;1/1&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;271.708&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;543.416&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/15_11"&gt;15/11&lt;/a&gt;, &lt;a class="wiki_link" href="/11_8"&gt;11/8&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;815.124&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/8_5"&gt;8/5&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1086.831&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/15_8"&gt;15/8&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1358.539&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/5 (&lt;a class="wiki_link" href="/11_10"&gt;11/10&lt;/a&gt; plus an octave)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1630.247&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18/7 (&lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt; plus an octave)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1901.955&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
...
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.&lt;br /&gt;
[[Category:53edo]]
&lt;br /&gt;
[[Category:orwell]]
&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;
[[Category:subminor_third]]
&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>