7edo: Difference between revisions
Wikispaces>aum-milan **Imported revision 27416153 - Original comment: ** |
Wikispaces>aum-milan **Imported revision 28569671 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:aum-milan|aum-milan]] and made on <tt>2008-06 | : This revision was by author [[User:aum-milan|aum-milan]] and made on <tt>2008-07-22 06:04:57 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>28569671</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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7-edo divides the 1200-[[cents|cent]] octave into 7 equal parts, making its smallest interval [[171.428¢]], or the seventh root of 2. | 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 scales== | ||
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==Notation== | ==Notation== | ||
* Notatable on a five-line staff without accidentals. | * Notatable on a five-line staff without accidentals. | ||
==Harmony== | ==Harmony== | ||
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==Melody== | ==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. | |||
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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 /> | 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 /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x7 Equal Divisions of the Octave-Related scales"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><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 &quot;neighborhood&quot; 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:&lt;h2&gt; --><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 /> | <ul><li>Related in a lateral way to traditional Thai music.</li></ul><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><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 /> | <ul><li>Notatable on a five-line staff without accidentals.</li></ul><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x7 Equal Divisions of the Octave-Harmony"></a><!-- ws:end:WikiTextHeadingRule:10 -->Harmony</h2> | |||
<br /> | <br /> | ||
Major and minor collide in every way.<br /> | Major and minor collide in every way.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x7 Equal Divisions of the Octave-Melody"></a><!-- ws:end:WikiTextHeadingRule:12 -->Melody</h2> | ||
<br /> | 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 /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><!-- ws:end:WikiTextHeadingRule:14 --> </h3> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><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://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.akjmusic.com/works.html" rel="nofollow">I dream of Tibet</a> by Aaron K. Johnson (electronic swirlies)<br /> | ||