7edo
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Original Wikitext content:
=7 Equal Divisions of the Octave= ==="neutral diatonic"=== 7-edo divides the 1200-[[cents|cent]] octave into 7 equal parts, making its smallest interval [[171.428¢]], or the seventh root of 2. ==Intervals in 7-edo== || **Interval, in fifths of an octave** || **Interval in ¢** || **Closest diatonic interval name** || **The "neighborhood" of just intervals** || || 1 || 0.0 || unison / prime || exactly 1/1 || || 2 || 171,429 || second || 6,424 c from Ptolemy (neutral) second 11/10 3,215 c from second 54/49 -10,976 c from (Didymus) major second (small whole tone) 10/9 || || 3 || 342,857 || third || -4,551 c from neutral third 11/9 || || 4 || 514,286 || fourth || 16,241 c from just fourth 4/3 (498,045 c) -5,265 c from wide fourth 27/20 || || 5 || 685,714 || fifth || 5,265 c from narrow fifth 40/27 -16,241 c from just fifth 3/2 (701,955 c) || || 6 || 857,143 || sixth || 4,551 c from neutral sixth 18/11 || || 7 || 1028,571 || seventh || 10,975 c from (Didymus) minor seventh 9/5 -3,216 c from seventh 49/27 -6,425 c from neutral seventh 20/11 || || 8 || 1200.0 || eighth || exactly 2/1 || ==Related scales== * Related in a lateral way to traditional Thai music. ==Notation== * Notatable on a five-line staff without accidentals. ==Harmony== Major and minor collide in every way. ==Melody== Neutral feel betweem whole tone scale and major/minor diatonic scale. The second 171,429 c works well as a basic step for melodic progression. Step from seventh to octave is too large for the leading tone. === === ===Music=== [[http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/pagans.html|Pagan's Revenge]] by Bill Sethares (synthetic gamelan) [[http://www.akjmusic.com/works.html|I dream of Tibet]] by Aaron K. Johnson (electronic swirlies) [[http://www.mp3.com.au/album.asp?id=3227|Seven Equal Trio]] by Robert Walker ((synth) violin, viola, glockenspiel) [[http://www.h-pi.com/midi/7ET.mid|Two-part Invention in 7TET]] by Aaron Hunt (two parts!) [[http://www.uvnitr.cz/flao/pavouci.html|Pavouci]], [[http://www.uvnitr.cz/flao/kelt.html|Kelt]] by Milan Guštar
Original HTML content:
<html><head><title>7edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x7 Equal Divisions of the Octave"></a><!-- ws:end:WikiTextHeadingRule:0 -->7 Equal Divisions of the Octave</h1>
<!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x7 Equal Divisions of the Octave--"neutral diatonic""></a><!-- ws:end:WikiTextHeadingRule:2 -->"neutral diatonic"</h3>
<br />
7-edo divides the 1200-<a class="wiki_link" href="/cents">cent</a> octave into 7 equal parts, making its smallest interval <a class="wiki_link" href="/171.428%C2%A2">171.428¢</a>, or the seventh root of 2.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x7 Equal Divisions of the Octave-Intervals in 7-edo"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals in 7-edo</h2>
<table class="wiki_table">
<tr>
<td><strong>Interval,<br />
in fifths of<br />
an octave</strong><br />
</td>
<td><strong>Interval<br />
in ¢</strong><br />
</td>
<td><strong>Closest<br />
diatonic<br />
interval name</strong><br />
</td>
<td><strong>The "neighborhood" of just intervals</strong><br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>0.0<br />
</td>
<td>unison / prime<br />
</td>
<td>exactly 1/1<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>171,429<br />
</td>
<td>second<br />
</td>
<td>6,424 c from Ptolemy (neutral) second 11/10<br />
3,215 c from second 54/49<br />
-10,976 c from (Didymus) major second (small whole tone) 10/9<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>342,857<br />
</td>
<td>third<br />
</td>
<td>-4,551 c from neutral third 11/9<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>514,286<br />
</td>
<td>fourth<br />
</td>
<td>16,241 c from just fourth 4/3 (498,045 c)<br />
-5,265 c from wide fourth 27/20<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>685,714<br />
</td>
<td>fifth<br />
</td>
<td>5,265 c from narrow fifth 40/27<br />
-16,241 c from just fifth 3/2 (701,955 c)<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>857,143<br />
</td>
<td>sixth<br />
</td>
<td>4,551 c from neutral sixth 18/11<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>1028,571<br />
</td>
<td>seventh<br />
</td>
<td>10,975 c from (Didymus) minor seventh 9/5<br />
-3,216 c from seventh 49/27<br />
-6,425 c from neutral seventh 20/11<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>1200.0<br />
</td>
<td>eighth<br />
</td>
<td>exactly 2/1<br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="x7 Equal Divisions of the Octave-Related scales"></a><!-- ws:end:WikiTextHeadingRule:6 -->Related scales</h2>
<ul><li>Related in a lateral way to traditional Thai music.</li></ul><br />
<!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="x7 Equal Divisions of the Octave-Notation"></a><!-- ws:end:WikiTextHeadingRule:8 -->Notation</h2>
<ul><li>Notatable on a five-line staff without accidentals.</li></ul><br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="x7 Equal Divisions of the Octave-Harmony"></a><!-- ws:end:WikiTextHeadingRule:10 -->Harmony</h2>
<br />
Major and minor collide in every way.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="x7 Equal Divisions of the Octave-Melody"></a><!-- ws:end:WikiTextHeadingRule:12 -->Melody</h2>
Neutral feel betweem whole tone scale and major/minor diatonic scale. The second 171,429 c works well as a basic step for melodic progression.<br />
Step from seventh to octave is too large for the leading tone.<br />
<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:<h3> --><h3 id="toc7"><!-- ws:end:WikiTextHeadingRule:14 --> </h3>
<!-- ws:start:WikiTextHeadingRule:16:<h3> --><h3 id="toc8"><a name="x7 Equal Divisions of the Octave-Melody-Music"></a><!-- ws:end:WikiTextHeadingRule:16 -->Music</h3>
<a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/pagans.html" rel="nofollow">Pagan's Revenge</a> by Bill Sethares (synthetic gamelan)<br />
<a class="wiki_link_ext" href="http://www.akjmusic.com/works.html" rel="nofollow">I dream of Tibet</a> by Aaron K. Johnson (electronic swirlies)<br />
<a class="wiki_link_ext" href="http://www.mp3.com.au/album.asp?id=3227" rel="nofollow">Seven Equal Trio</a> by Robert Walker ((synth) violin, viola, glockenspiel)<br />
<a class="wiki_link_ext" href="http://www.h-pi.com/midi/7ET.mid" rel="nofollow">Two-part Invention in 7TET</a> by Aaron Hunt (two parts!)<br />
<a class="wiki_link_ext" href="http://www.uvnitr.cz/flao/pavouci.html" rel="nofollow">Pavouci</a>, <a class="wiki_link_ext" href="http://www.uvnitr.cz/flao/kelt.html" rel="nofollow">Kelt</a> by Milan Guštar</body></html>