7edo: Difference between revisions

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7-tet can be thought of as result of stacking seven 11/9s on top of each other, and then tempering to remove the comma 2^(-2) 3^(-14) 11^7.

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.

* Notatable on a five-line staff without accidentals.

==Harmony==  

==Melody==  

==Relative tuning accuracy==  

7-edo is the third [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral edo]].

[[http://www.uvnitr.cz/flaoyg/flao_yg/pavouci.html|Pavouci]], [[http://www.uvnitr.cz/flaoyg/flao_yg/kelt.html|Kelt]] by Milan Guštar

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

==Commas==  

7-tet can be thought of as result of stacking seven 11/9s on top of each other, and then tempering to remove the comma 2^(-2) 3^(-14) 11^7.&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;ul&gt;&lt;li&gt;Related in a lateral way to traditional Thai music.&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="x7 Equal Divisions of the Octave-Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Notation&lt;/h2&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:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x7 Equal Divisions of the Octave-Harmony"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Harmony&lt;/h2&gt;

&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="x7 Equal Divisions of the Octave-Melody"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Melody&lt;/h2&gt;

&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="x7 Equal Divisions of the Octave-Relative tuning accuracy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Relative tuning accuracy&lt;/h2&gt;

  7-edo is the third &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists"&gt;zeta integral edo&lt;/a&gt;.&lt;br /&gt;

&lt;a class="wiki_link_ext" href="http://www.uvnitr.cz/flaoyg/flao_yg/pavouci.html" rel="nofollow"&gt;Pavouci&lt;/a&gt;, &lt;a class="wiki_link_ext" href="http://www.uvnitr.cz/flaoyg/flao_yg/kelt.html" rel="nofollow"&gt;Kelt&lt;/a&gt; by Milan Guštar&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;br /&gt;

&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="x7 Equal Divisions of the Octave-Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Commas&lt;/h2&gt;