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7edt: Difference between revisions

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Wikispaces>Sarzadoce
**Imported revision 246275559 - Original comment: **
 
+subsets and supersets; cleanup; -redundant categories
 
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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:Sarzadoce|Sarzadoce]] and made on <tt>2011-08-16 14:09:58 UTC</tt>.<br>
: The original revision id was <tt>246275559</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">=7 Equal Divisions of the Tritave=
|| 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 ||


7edt is the lowest equal division of the tritave to accurately approximate 7-limit harmony. One step of 7edt is a subminor third. Seven of these make up a tritave, meaning that 7edt tempers out 839808/823543, the Orwell comma.
== Theory ==
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.


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]].


=== Harmonics ===
{{Harmonics in equal|7|3|1|columns=15}}


=== Subsets and supersets ===
7edt is the 4th [[prime equal division|prime edt]], after [[5edt]] and before [[11edt]].


==7n-edt Family:==  
== Intervals ==
[[14edt]]
{| class="wikitable center-1 right-2 right-3"
[[21edt]]
|-
[[28edt]]
! #
...</pre></div>
! Cents
<h4>Original HTML content:</h4>
! [[Hekt]]s
<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:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x7 Equal Divisions of the Tritave"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;7 Equal Divisions of the Tritave&lt;/h1&gt;
! Approximate ratios
! [[Electra]] notation<br>({{nowrap|J {{=}} 1/1}})
|-
| 0
| 0
| 0
| [[1/1]]
| J
|-
| 1
| 272
| 186
| [[7/6]]
| K
|-
| 2
| 543
| 371
| [[11/8]], [[15/11]]
| L
|-
| 3
| 815
| 557
| [[8/5]]
| M
|-
| 4
| 1087
| 743
| [[15/8]]
| N
|-
| 5
| 1359
| 929
| [[11/5]]
| O
|-
| 6
| 1630
| 1114
| [[18/7]]
| P
|-
| 7
| 1902
| 1300
| [[3/1]]
| J
|}


&lt;table class="wiki_table"&gt;
[[Category:Orwell]]
    &lt;tr&gt;
[[Category:Subminor third]]
        &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;
7edt is the lowest equal division of the tritave to accurately approximate 7-limit harmony. One step of 7edt is a subminor third. Seven of these make up a tritave, meaning that 7edt tempers out 839808/823543, the Orwell comma.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x7 Equal Divisions of the Tritave-7n-edt Family:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;7n-edt Family:&lt;/h2&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>
Retrieved from "https://en.xen.wiki/w/7edt"