7edo
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=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.
Equi-heptitonic scales are used in non-western music in African cultures and it has been speculated in "Indian music:history and structure", that the Indian three-sruti interval of 165 cents is close enough to be mistaken for 171 cents. (or 1.71 semitones).
7-tet can be thought of as result of stacking seven 11/9s on top of each other, and then tempering to remove the Pythagorean comma.
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.
__//("African music." Encyclopædia Britannica. 2009. Encyclopædia Britannica Online. 05 Jul. 2009 <http://www.britannica.com/EBchecked/topic/719112/African-music>.//__)
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.
==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 between 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/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 SerafiniOriginal 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 />
Equi-heptitonic scales are used in non-western music in African cultures and it has been speculated in "Indian music:history and structure", that the Indian three-sruti interval of 165 cents is close enough to be mistaken for 171 cents. (or 1.71 semitones).<br />
7-tet can be thought of as result of stacking seven 11/9s on top of each other, and then tempering to remove the Pythagorean comma.<br />
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.<br />
<u><em>("African music." Encyclopædia Britannica. 2009. Encyclopædia Britannica Online. 05 Jul. 2009 <<!-- ws:start:WikiTextUrlRule:194:http://www.britannica.com/EBchecked/topic/719112/African-music --><a class="wiki_link_ext" href="http://www.britannica.com/EBchecked/topic/719112/African-music" rel="nofollow">http://www.britannica.com/EBchecked/topic/719112/African-music</a><!-- ws:end:WikiTextUrlRule:194 -->>.</em></u>)<br />
<br />
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.<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 />
<!-- 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><!-- 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><!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="x7 Equal Divisions of the Octave-Harmony"></a><!-- ws:end:WikiTextHeadingRule:10 -->Harmony</h2>
Major and minor collide in every way.<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 between 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 />
<!-- 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/flaoyg/flao_yg/pavouci.html" rel="nofollow">Pavouci</a>, <a class="wiki_link_ext" href="http://www.uvnitr.cz/flaoyg/flao_yg/kelt.html" rel="nofollow">Kelt</a> by Milan Guštar<br />
<a class="wiki_link_ext" href="http://www.seraph.it/dep/det/7edo%20dance.mp3" rel="nofollow">7edo Dance</a> by Carlo Serafini</body></html>