7edo: Difference between revisions

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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]]

**7 Equal Divisions of the Octave**

7-edo divides the 1200-cent [[octave]] into 7 equal parts, making its smallest interval [[cent|171.428¢]], or the seventh root of 2. It is the fourth [[prime numbers|prime]] edo, after [[2edo]], [[3edo]] and [[5edo]].

A Thai xylophone measured by Morton (1974) "varied only plus or minus 5 cents," from 7-TET. A Ugandan Chopi xylophone measured by Haddon (1952) was also tuned to this system.

|| **Interval** || **Interval**

**size**

|| 7 (0) || 1200.0 || eighth || exactly 2/1 ||

* Related in a lateral way to traditional Thai music.

==Notation==  

=== ===  

[[http://sethares.engr.wisc.edu/mp3s/PagansRevenge.mp3|Pagan's Revenge]] by Bill Sethares (synthetic gamelan)

[[http://www.seraph.it/dep/det/7edo%20dance.mp3|7edo Dance]] by Carlo Serafini

[[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/06%20-%206.%207%20octave.mp3|Comets Over Flatland 6]] by [[Randy Winchester]]

=Commas=  

<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;7edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:20:&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:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;a href="#x&amp;quot;neutral diatonic&amp;quot;"&gt;&amp;quot;neutral diatonic&amp;quot;&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt; | &lt;a href="#Intervals in 7-edo"&gt;Intervals in 7-edo&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt; | &lt;a href="#Related scales"&gt;Related scales&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt; | &lt;a href="#Music"&gt;Music&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt; | &lt;a href="#Commas"&gt;Commas&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt;

&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;br /&gt;

&lt;strong&gt;7 Equal Divisions of the Octave&lt;/strong&gt;&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="x&amp;quot;neutral diatonic&amp;quot;"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&amp;quot;neutral diatonic&amp;quot;&lt;/h1&gt;

7-edo divides the 1200-cent &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 7 equal parts, making its smallest interval &lt;a class="wiki_link" href="/cent"&gt;171.428¢&lt;/a&gt;, or the seventh root of 2. It is the fourth &lt;a class="wiki_link" href="/prime%20numbers"&gt;prime&lt;/a&gt; edo, after &lt;a class="wiki_link" href="/2edo"&gt;2edo&lt;/a&gt;, &lt;a class="wiki_link" href="/3edo"&gt;3edo&lt;/a&gt; and &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt;.&lt;br /&gt;

&lt;br /&gt;

&lt;br /&gt;

Similarly, in equi-heptatonic systems the desire for harmonic sound may dictate constant adjustments of intonation away from the theoretical interval of 171 cents. One of the most impressive areas in Africa in which a pen-equidistant heptatonic scale is combined with a distinctively harmonic style based on singing in intervals of thirds plus fifths, or thirds plus fourths, is the eastern Angolan culture area. This music is heptatonic and non-modal; i.e., there is no concept of major or minor thirds as distinctive intervals. In principle all the thirds are neutral, but in practice the thirds rendered by the singers often approximate natural major thirds (386 cents), especially at points of rest. In this manner, the principles of equidistance and harmonic euphony are accommodated within one tonal-harmonic system. For the notation of such music, a seven-line stave is most appropriate, with each horizontal line representing one pitch level.&lt;br /&gt;

&lt;br /&gt;

A Thai xylophone measured by Morton (1974) &amp;quot;varied only plus or minus 5 cents,&amp;quot; from 7-TET. A Ugandan Chopi xylophone measured by Haddon (1952) was also tuned to this system.&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="Intervals in 7-edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Intervals in 7-edo&lt;/h1&gt;

&lt;table class="wiki_table"&gt;

&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Related scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Related scales&lt;/h1&gt;

  &lt;ul&gt;&lt;li&gt;Notatable on a five-line staff without accidentals.&lt;/li&gt;&lt;/ul&gt;&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Related scales-Harmony"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Harmony&lt;/h2&gt;

  There is no distinction between Major or Minor; each pitch class is unique.&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt; &lt;/h3&gt;

  &lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Music&lt;/h1&gt;

&lt;a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/mp3s/PagansRevenge.mp3" rel="nofollow"&gt;Pagan's Revenge&lt;/a&gt; by Bill Sethares (synthetic gamelan)&lt;br /&gt;

&lt;a class="wiki_link_ext" href="http://www.akjmusic.com/audio/i_dream_of_tibet.mp3" rel="nofollow"&gt;I dream of Tibet&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://www.akjmusic.com/works.html" rel="nofollow"&gt;Aaron K. Johnson&lt;/a&gt; (electronic swirlies)&lt;br /&gt;

&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/7edo%20dance.mp3" rel="nofollow"&gt;7edo Dance&lt;/a&gt; by Carlo Serafini&lt;br /&gt;

&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/06%20-%206.%207%20octave.mp3" rel="nofollow"&gt;Comets Over Flatland 6&lt;/a&gt; by &lt;a class="wiki_link" href="/Randy%20Winchester"&gt;Randy Winchester&lt;/a&gt;&lt;br /&gt;

&lt;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Commas&lt;/h1&gt;