9edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-~~22 03~~:49:49 UTC</tt>.<br>

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-25 21:08:31 UTC</tt>.<br>

: The original revision id was <tt>~~602737978~~</tt>.<br>

: The original revision id was <tt>602809098</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>

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Here the characterizations are taken from [[http://en.wikipedia.org/wiki/Scala_%28program%29|Scala]], which also describes the scale itself as "Pelog Nawanada: Sunda". Chords such as 1/1 - 7/6 - 49/36 - 12/7/1 are therefore natural ones for 9EDO. The above scale generates the [[Just intonation subgroups|just intonation subgroup]] 2.27/25.7/3, which is closely related to 9EDO.

~~Like 16edo,~~ 9edo can be notated two ways. The first is ~~with~~ sharp ~~higher~~ than flat, to ~~preserve melodic contour~~:

=Notation=

D ~~E * F G A B * C~~ D

~~D -~~ E - E#/~~Fb -~~ F - G - A - B - B#/Cb - C ~~- D~~

9edo can be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first preserves the __melodic__ meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.

~~P1 - m2 - M2~~/~~m3 - M3 - P4 - P5 - m6 - M6~~/~~m7 - M7 - P8~~

The second approach preserves the __harmonic__ meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp is lower in pitch than flat, and major/aug is narrower than minor/dim. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 9edo "on the fly".

||= <span style="color: #660000;">[[xenharmonic/Degree|Degree]]</span> ||= [[xenharmonic/Cent|Cent]]s ||= Approximate

Ratios ||||= Major wider

than minor ||||= Major narrower

than minor ||

||= 0 ||= 0 ||= 1/1 ||= perfect unison ||= D ||= perfect unison ||= D ||

||= 1 ||= 133 ||= 13/12, 12/11 ||= minor 2nd ||= E ||= major 2nd ||= E ||

||= 2 ||= 267 ||= 7/6 ||= major 2nd, minor 3rd ||= E#, Fb ||= minor 2nd, major 3rd ||= Eb, F# ||

||= 3 ||= 400 ||= 5/4, 9/7 ||= major 3rd ||= F ||= minor 3rd ||= F ||

||= 4 ||= 533 ||= 4/3, 11/8 ||= perfect 4th ||= G ||= perfect 4th ||= G ||

||= 5 ||= 667 ||= 16/11, 3/2 ||= perfect 5th ||= A ||= perfect 5th ||= A ||

||= 6 ||= 800 ||= 14/9, 8/5 ||= minor 6th ||= B ||= major 6th ||= B ||

||= 7 ||= 933 ||= 12/7 ||= major 6th, minor 7th ||= B#, Cb ||= minor 6th, major 7th ||= Bb, C# ||

||= 8 ||= 1067 ||= 11/6, 24/13 ||= major 7th ||= C ||= minor 7th ||= C ||

||= 9 ||= 1200 ||= 2/1 ||= octave ||= D ||= octave ||= D ||

~~The second way is with sharp lower than flat, to preserve interval arithmetic and chord names:~~

~~D E * F G A B * C D~~

~~D - E - Eb/F# - F - G - A - B - Bb/C# - C - D~~

~~P1 - M2 - m2/M3 - m3 - P4 - P5 - M6 - m6/M7 - m7 - P8~~

9EDO contains a pentatonic [[MOSScales|MOS scale]] -- 2L 3s (1 3 1 3 1) -- with a heptatonic extension -- 2L 5s (1 1 2 1 1 2 1, sometimes called "mavila" or "antidiatonic"). Indonesian pelog scales sometimes use five-tone subsets of a seven-tone superset in a similar way, and it has been suggested that Indonesian gamelan music stems from a [[http://www.neuroscience-of-music.se/pelog%20historical.htm|9EDO tradition]].

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Here the characterizations are taken from <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Scala_%28program%29" rel="nofollow">Scala</a>, which also describes the scale itself as &quot;Pelog Nawanada: Sunda&quot;. Chords such as 1/1 - 7/6 - 49/36 - 12/7/1 are therefore natural ones for 9EDO. The above scale generates the <a class="wiki_link" href="/Just%20intonation%20subgroups">just intonation subgroup</a> 2.27/25.7/3, which is closely related to 9EDO.<br />

<br />

~~Like 16edo,~~ 9edo can be notated two ways. The first is ~~with~~ sharp ~~higher~~ than flat, to ~~preserve melodic contour~~:<br />

<h1 id="toc0"><a name="Notation"></a>Notation</h1>

D E * F G A B * C D<br />

<br />

D - E - E#/Fb - F - G - A - B - B#/Cb - C - D<br />

9edo can be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first preserves the <u>melodic</u> meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.<br />

P1 - m2 - M2/m3 - M3 - P4 - P5 - m6 - M6/m7 - M7 - P8<br />

<br />

The second approach preserves the <u>harmonic</u> meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp is lower in pitch than flat, and major/aug is narrower than minor/dim. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 9edo &quot;on the fly&quot;.<br />

<br />

<tr>

<td style="text-align: center;"><span style="color: #660000;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Degree">Degree</a></span><br />

</td>

</td>

<td style="text-align: center;">Approximate<br />

Ratios<br />

</td>

<td colspan="2" style="text-align: center;">Major wider<br />

than minor<br />

</td>

<td colspan="2" style="text-align: center;">Major narrower<br />

than minor<br />

</td>

</tr>

<tr>

</td>

</td>

</td>

<td style="text-align: center;">perfect unison<br />

</td>

</td>

<td style="text-align: center;">perfect unison<br />

</td>

</td>

</tr>

<tr>

</td>

</td>

</td>

<td style="text-align: center;">minor 2nd<br />

</td>

</td>

<td style="text-align: center;">major 2nd<br />

</td>

</td>

</tr>

<tr>

</td>

</td>

</td>

<td style="text-align: center;">major 2nd, minor 3rd<br />

</td>

</td>

<td style="text-align: center;">minor 2nd, major 3rd<br />

</td>

</td>

</tr>

<tr>

</td>

</td>

</td>

<td style="text-align: center;">major 3rd<br />

</td>

</td>

<td style="text-align: center;">minor 3rd<br />

</td>

</td>

</tr>

<tr>

</td>

</td>

</td>

<td style="text-align: center;">perfect 4th<br />

</td>

</td>

<td style="text-align: center;">perfect 4th<br />

</td>

</td>

</tr>

<tr>

</td>

</td>

</td>

<td style="text-align: center;">perfect 5th<br />

</td>

</td>

<td style="text-align: center;">perfect 5th<br />

</td>

</td>

</tr>

<tr>

</td>

</td>

</td>

<td style="text-align: center;">minor 6th<br />

</td>

</td>

<td style="text-align: center;">major 6th<br />

</td>

</td>

</tr>

<tr>

</td>

</td>

</td>

<td style="text-align: center;">major 6th, minor 7th<br />

</td>

</td>

<td style="text-align: center;">minor 6th, major 7th<br />

</td>

</td>

</tr>

<tr>

</td>

</td>

</td>

<td style="text-align: center;">major 7th<br />

</td>

</td>

<td style="text-align: center;">minor 7th<br />

</td>

</td>

</tr>

<tr>

</td>

</td>

</td>

<td style="text-align: center;">octave<br />

</td>

</td>

<td style="text-align: center;">octave<br />

</td>

</td>

</tr>

</table>

<br />

~~The second way is with sharp lower than flat, to preserve interval arithmetic and chord names:<br />~~

~~D E * F G A B * C D<br />~~

~~D - E - Eb/F# - F - G - A - B - Bb/C# - C - D<br />~~

~~P1 - M2 - m2/M3 - m3 - P4 - P5 - M6 - m6/M7 - m7 - P8<br />~~

<br />

9EDO contains a pentatonic <a class="wiki_link" href="/MOSScales">MOS scale</a> -- 2L 3s (1 3 1 3 1) -- with a heptatonic extension -- 2L 5s (1 1 2 1 1 2 1, sometimes called &quot;mavila&quot; or &quot;antidiatonic&quot;). Indonesian pelog scales sometimes use five-tone subsets of a seven-tone superset in a similar way, and it has been suggested that Indonesian gamelan music stems from a <a class="wiki_link_ext" href="http://www.neuroscience-of-music.se/pelog%20historical.htm" rel="nofollow">9EDO tradition</a>.<br />

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<object id="example" type="image/svg+xml" data="http://xenharmonic.wikispaces.com/file/view/9ed2-001.svg">alt : Your browser has no SVG support.</object><br />

<br />

<div class="objectEmbed"><a href="/file/view/9ed2-001.svg/480700332/9ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/9ed2-001.svg/480700332/9ed2-001.svg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="9ed2-001.svg" /></a><div><a href="/file/view/9ed2-001.svg/480700332/9ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/9ed2-001.svg/480700332/9ed2-001.svg');" class="filename" title="9ed2-001.svg">9ed2-001.svg</a><br /><ul><li><a href="/file/detail/9ed2-001.svg">Details</a></li><li><a href="/file/view/9ed2-001.svg/480700332/9ed2-001.svg">Download</a></li><li style="color: #666">13 KB</li></ul></div></div><br />

<div class="objectEmbed"><a href="/file/view/9ed2-001.svg/480700332/9ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/9ed2-001.svg/480700332/9ed2-001.svg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="9ed2-001.svg" /></a><div><a href="/file/view/9ed2-001.svg/480700332/9ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/9ed2-001.svg/480700332/9ed2-001.svg');" class="filename" title="9ed2-001.svg">9ed2-001.svg</a><br /><ul><li><a href="/file/detail/9ed2-001.svg">Details</a></li><li><a href="/file/view/9ed2-001.svg/480700332/9ed2-001.svg">Download</a></li><li style="color: #666">13 KB</li></ul></div></div><br />

<br />

<h1 id="~~toc0~~"><a name="Images"></a>Images</h1>

<h1 id="toc1"><a name="Images"></a>Images</h1>

<br />

<img src="/file/view/9edo%20wheel.png/516973334/385x385/9edo%20wheel.png" alt="9edo wheel.png" title="9edo wheel.png" style="height: 385px; width: 385px;" /><br />

<img src="/file/view/9edo%20wheel.png/516973334/385x385/9edo%20wheel.png" alt="9edo wheel.png" title="9edo wheel.png" style="height: 385px; width: 385px;" /><br />

<br />

<h2 id="~~toc1~~"><a name="Images-Commas"></a>Commas</h2>

<h2 id="toc2"><a name="Images-Commas"></a>Commas</h2>

9 EDO tempers out the following commas. (Note: This assumes val &lt; 9 14 21 25 31 33/1 |.)<br />

<br />

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<br />

<h1 id="~~toc2~~"><a name="Compositions"></a>Compositions</h1>

<h1 id="toc3"><a name="Compositions"></a>Compositions</h1>

<br />

<ul><li>Nocturne in 9tet by <a class="wiki_link_ext" href="http://home.snafu.de/djwolf/WorksDescriptive.htm" rel="nofollow">Daniel Wolf</a></li><li><em><a class="wiki_link_ext" href="http://www.h-pi.com/mp3/Prelude9ET.mp3" rel="nofollow">Prelude in 9ET</a></em> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a></li><li><em><a class="wiki_link_ext" href="http://micro.soonlabel.com/9-edo/daily20110629_fts_e_guit_9et.mp3" rel="nofollow">Improvisation for Electric Guitar in 9 edo</a></em> by <a class="wiki_link_ext" href="http://www.chrisvaisvil.com" rel="nofollow">Chris Vaisvil</a><script type="text/javascript" src="http://mediaplayer.yahoo.com/js">

</script></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/08%20-%208.%209%20octave.mp3" rel="nofollow">Comets Over Flatland 8</a> by <a class="wiki_link" href="/Randy%20Winchester">Randy Winchester</a></li><li><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=bDFCsCoaUO4" rel="nofollow">Nine tones per Octave (9-EDO / 9-TET)</a> by <a class="wiki_link" href="/Ivor%20Darreg">Ivor Darreg</a></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/9-edo/daily20111008b_gerbils_at_the_wheel_of_government.mp3" rel="nofollow">Gerbils at the Wheel of Government</a> by <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1402" rel="nofollow" target="_blank">Chris Vaisvil</a> (in 9 and 18 edo simultaneously)</li><li><a class="wiki_link_ext" href="http://www.seraph.it/dep/det/NewWorld.mp3" rel="nofollow">New World</a> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/f533be803cb9ed1efc23fc9e2db10c6f-167.html" rel="nofollow">blog entry</a>)</li><li><a class="wiki_link_ext" href="https://soundcloud.com/santiagocosentino/interdimensional-train-ride" rel="nofollow">Interdimensional Train Ride by Santiago Cosentino</a></li></ul><br />

<h1 id="~~toc3~~"><a name="Ear Training"></a>Ear Training</h1>

<h1 id="toc4"><a name="Ear Training"></a>Ear Training</h1>

9 EDO ear-training exercises by Alex Ness available <a class="wiki_link_ext" href="https://drive.google.com/a/playgroundsessions.com/folderview?id=0BwsXD8q2VCYUamtVWEgyRFA5alU&amp;usp=sharing#list" rel="nofollow" target="_blank">here</a>.<br />

<br />

<h3 id="~~toc4~~"><a name="Ear Training--Instruments"></a><strong>Instruments</strong></h3>

<h3 id="toc5"><a name="Ear Training--Instruments"></a><strong>Instruments</strong></h3>

<br />

<img src="/file/view/IMG_2223-800x600.jpg/248485599/IMG_2223-800x600.jpg" alt="IMG_2223-800x600.jpg" title="IMG_2223-800x600.jpg" style="width: 400px;" /><br />

<img src="/file/view/IMG_2223-800x600.jpg/248485599/IMG_2223-800x600.jpg" alt="IMG_2223-800x600.jpg" title="IMG_2223-800x600.jpg" style="width: 400px;" /><br />

<br />

Ukulele (MicroUke 1.2) set to 9 EDO with 40 lb. test fishing line (by cenobyte)</body></html></pre></div>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-22 03:49:49 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-25 21:08:31 UTC</tt>.<br>
-: The original revision id was <tt>602737978</tt>.<br>
+: The original revision id was <tt>602809098</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>
@@ Line 22: / Line 22: @@
 Here the characterizations are taken from [[http://en.wikipedia.org/wiki/Scala_%28program%29|Scala]], which also describes the scale itself as "Pelog Nawanada: Sunda". Chords such as 1/1 - 7/6 - 49/36 - 12/7/1 are therefore natural ones for 9EDO. The above scale generates the [[Just intonation subgroups|just intonation subgroup]] 2.27/25.7/3, which is closely related to 9EDO.
-Like 16edo, 9edo can be notated two ways. The first is with sharp higher than flat, to preserve melodic contour:
+=Notation=
-D E * F G A B * C D
-D - E - E#/Fb - F - G - A - B - B#/Cb - C - D
+edo can be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first preserves the __melodic__ meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.
-P1 - m2 - M2/m3 - M3 - P4 - P5 - m6 - M6/m7 - M7 - P8
+The second approach preserves the __harmonic__ meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp is lower in pitch than flat, and major/aug is narrower than minor/dim. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 9edo "on the fly".
+||= &lt;span style="color: #660000;"&gt;[[xenharmonic/Degree|Degree]]&lt;/span&gt; ||= [[xenharmonic/Cent|Cent]]s ||= Approximate
+Ratios ||||= Major wider
+than minor ||||= Major narrower
+than minor ||
+||= 0 ||= 0 ||= 1/1 ||= perfect unison ||= D ||= perfect unison ||= D ||
+||= 1 ||= 133 ||= 13/12, 12/11 ||= minor 2nd ||= E ||= major 2nd ||= E ||
+||= 2 ||= 267 ||= 7/6 ||= major 2nd, minor 3rd ||= E#, Fb ||= minor 2nd, major 3rd ||= Eb, F# ||
+||= 3 ||= 400 ||= 5/4, 9/7 ||= major 3rd ||= F ||= minor 3rd ||= F ||
+||= 4 ||= 533 ||= 4/3, 11/8 ||= perfect 4th ||= G ||= perfect 4th ||= G ||
+||= 5 ||= 667 ||= 16/11, 3/2 ||= perfect 5th ||= A ||= perfect 5th ||= A ||
+||= 6 ||= 800 ||= 14/9, 8/5 ||= minor 6th ||= B ||= major 6th ||= B ||
+||= 7 ||= 933 ||= 12/7 ||= major 6th, minor 7th ||= B#, Cb ||= minor 6th, major 7th ||= Bb, C# ||
+||= 8 ||= 1067 ||= 11/6, 24/13 ||= major 7th ||= C ||= minor 7th ||= C ||
+||= 9 ||= 1200 ||= 2/1 ||= octave ||= D ||= octave ||= D ||
-The second way is with sharp lower than flat, to preserve interval arithmetic and chord names:
-D E * F G A B * C D
-D - E - Eb/F# - F - G - A - B - Bb/C# - C - D
-P1 - M2 - m2/M3 - m3 - P4 - P5 - M6 - m6/M7 - m7 - P8
 EDO contains a pentatonic [[MOSScales|MOS scale]] -- 2L 3s (1 3 1 3 1) -- with a heptatonic extension -- 2L 5s (1 1 2 1 1 2 1, sometimes called "mavila" or "antidiatonic"). Indonesian pelog scales sometimes use five-tone subsets of a seven-tone superset in a similar way, and it has been suggested that Indonesian gamelan music stems from a [[http://www.neuroscience-of-music.se/pelog%20historical.htm|9EDO tradition]].
@@ Line 103: / Line 115: @@
 Here the characterizations are taken from &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Scala_%28program%29" rel="nofollow"&gt;Scala&lt;/a&gt;, which also describes the scale itself as &amp;quot;Pelog Nawanada: Sunda&amp;quot;. Chords such as 1/1 - 7/6 - 49/36 - 12/7/1 are therefore natural ones for 9EDO. The above scale generates the &lt;a class="wiki_link" href="/Just%20intonation%20subgroups"&gt;just intonation subgroup&lt;/a&gt; 2.27/25.7/3, which is closely related to 9EDO.&lt;br /&gt;
 &lt;br /&gt;
-Like 16edo, 9edo can be notated two ways. The first is with sharp higher than flat, to preserve melodic contour:&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Notation&lt;/h1&gt;
-D E * F G A B * C D&lt;br /&gt;
+ &lt;br /&gt;
-D - E - E#/Fb - F - G - A - B - B#/Cb - C - D&lt;br /&gt;
+edo can be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first preserves the &lt;u&gt;melodic&lt;/u&gt; meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.&lt;br /&gt;
-P1 - m2 - M2/m3 - M3 - P4 - P5 - m6 - M6/m7 - M7 - P8&lt;br /&gt;
+&lt;br /&gt;
+The second approach preserves the &lt;u&gt;harmonic&lt;/u&gt; meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter. Sharp is lower in pitch than flat, and major/aug is narrower than minor/dim. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 9edo &amp;quot;on the fly&amp;quot;.&lt;br /&gt;
+&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;&lt;span style="color: #660000;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Degree"&gt;Degree&lt;/a&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Cent"&gt;Cent&lt;/a&gt;s&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Approximate&lt;br /&gt;
+Ratios&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td colspan="2" style="text-align: center;"&gt;Major wider&lt;br /&gt;
+than minor&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td colspan="2" style="text-align: center;"&gt;Major narrower&lt;br /&gt;
+than minor&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;1/1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;perfect unison&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;perfect unison&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;133&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;13/12, 12/11&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;minor 2nd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;E&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;major 2nd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;E&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;267&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;7/6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;major 2nd, minor 3rd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;E#, Fb&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;minor 2nd, major 3rd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Eb, F#&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;400&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;5/4, 9/7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;major 3rd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;F&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;minor 3rd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;F&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;533&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;4/3, 11/8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;perfect 4th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;G&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;perfect 4th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;G&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;667&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;16/11, 3/2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;perfect 5th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;A&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;perfect 5th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;A&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;6&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;800&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;14/9, 8/5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;minor 6th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;B&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;major 6th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;B&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;933&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;12/7&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;major 6th, minor 7th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;B#, Cb&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;minor 6th, major 7th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Bb, C#&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;1067&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;11/6, 24/13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;major 7th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;minor 7th&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: center;"&gt;9&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;1200&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;2/1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;octave&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;octave&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
 &lt;br /&gt;
-The second way is with sharp lower than flat, to preserve interval arithmetic and chord names:&lt;br /&gt;
-D E * F G A B * C D&lt;br /&gt;
-D - E - Eb/F# - F - G - A - B - Bb/C# - C - D&lt;br /&gt;
-P1 - M2 - m2/M3 - m3 - P4 - P5 - M6 - m6/M7 - m7 - P8&lt;br /&gt;
 &lt;br /&gt;
 EDO contains a pentatonic &lt;a class="wiki_link" href="/MOSScales"&gt;MOS scale&lt;/a&gt; -- 2L 3s (1 3 1 3 1) -- with a heptatonic extension -- 2L 5s (1 1 2 1 1 2 1, sometimes called &amp;quot;mavila&amp;quot; or &amp;quot;antidiatonic&amp;quot;). Indonesian pelog scales sometimes use five-tone subsets of a seven-tone superset in a similar way, and it has been suggested that Indonesian gamelan music stems from a &lt;a class="wiki_link_ext" href="http://www.neuroscience-of-music.se/pelog%20historical.htm" rel="nofollow"&gt;9EDO tradition&lt;/a&gt;.&lt;br /&gt;
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   &lt;br /&gt;
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 EDO tempers out the following commas. (Note: This assumes val &amp;lt; 9 14 21 25 31 33/1 |.)&lt;br /&gt;
 &lt;br /&gt;
@@ Line 426: / Line 616: @@
 &lt;br /&gt;
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+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Compositions&lt;/h1&gt;
   &lt;br /&gt;
 &lt;ul&gt;&lt;li&gt;Nocturne in 9tet by &lt;a class="wiki_link_ext" href="http://home.snafu.de/djwolf/WorksDescriptive.htm" rel="nofollow"&gt;Daniel Wolf&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://www.h-pi.com/mp3/Prelude9ET.mp3" rel="nofollow"&gt;Prelude in 9ET&lt;/a&gt;&lt;/em&gt; by &lt;a class="wiki_link" href="/Aaron%20Andrew%20Hunt"&gt;Aaron Andrew Hunt&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/9-edo/daily20110629_fts_e_guit_9et.mp3" rel="nofollow"&gt;Improvisation for Electric Guitar in 9 edo&lt;/a&gt;&lt;/em&gt; by &lt;a class="wiki_link_ext" href="http://www.chrisvaisvil.com" rel="nofollow"&gt;Chris Vaisvil&lt;/a&gt;&lt;!-- ws:start:WikiTextMediaRule:1:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/custom/10221463?h=0&amp;amp;w=0&amp;quot; class=&amp;quot;WikiMedia WikiMediaCustom&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;custom&amp;amp;quot; key=&amp;amp;quot;10221463&amp;amp;quot;&amp;quot; title=&amp;quot;Custom Media&amp;quot;/&amp;gt; --&gt;&lt;script type="text/javascript" src="http://mediaplayer.yahoo.com/js"&gt;
 &lt;/script&gt;&lt;!-- ws:end:WikiTextMediaRule:1 --&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/08%20-%208.%209%20octave.mp3" rel="nofollow"&gt;Comets Over Flatland 8&lt;/a&gt; by &lt;a class="wiki_link" href="/Randy%20Winchester"&gt;Randy Winchester&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=bDFCsCoaUO4" rel="nofollow"&gt;Nine tones per Octave (9-EDO / 9-TET)&lt;/a&gt; by &lt;a class="wiki_link" href="/Ivor%20Darreg"&gt;Ivor Darreg&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/9-edo/daily20111008b_gerbils_at_the_wheel_of_government.mp3" rel="nofollow"&gt;Gerbils at the Wheel of Government&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1402" rel="nofollow" target="_blank"&gt;Chris Vaisvil&lt;/a&gt; (in 9 and 18 edo simultaneously)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/NewWorld.mp3" rel="nofollow"&gt;New World&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/f533be803cb9ed1efc23fc9e2db10c6f-167.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="https://soundcloud.com/santiagocosentino/interdimensional-train-ride" rel="nofollow"&gt;Interdimensional Train Ride by Santiago Cosentino&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
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+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Ear Training"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Ear Training&lt;/h1&gt;
 EDO ear-training exercises by Alex Ness available &lt;a class="wiki_link_ext" href="https://drive.google.com/a/playgroundsessions.com/folderview?id=0BwsXD8q2VCYUamtVWEgyRFA5alU&amp;amp;usp=sharing#list" rel="nofollow" target="_blank"&gt;here&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
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   &lt;br /&gt;
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 Ukulele (MicroUke 1.2) set to 9 EDO with 40 lb. test fishing line (by cenobyte)&lt;/body&gt;&lt;/html&gt;</pre></div>