Xenharmonic Wiki

13edo: Difference between revisions

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VisualWikitext
Wikispaces>xenwolf
**Imported revision 602900924 - Original comment: **
Wikispaces>michaelwayneharwood
**Imported revision 609238651 - 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:xenwolf|xenwolf]] and made on <tt>2016-12-29 17:22:00 UTC</tt>.<br>
: This revision was by author [[User:michaelwayneharwood|michaelwayneharwood]] and made on <tt>2017-03-21 11:04:18 UTC</tt>.<br>
: The original revision id was <tt>602900924</tt>.<br>
: The original revision id was <tt>609238651</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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||~ Degree ||~ Cents ||~ Approximated 21-limit Ratios* ||~ Erv Wilson ||~ Archaeotonic ||~ Oneirotonic ||~ [[26edo]] names ||~ Kentaku ||
||~ Degree ||~ Cents ||~ Approximated 21-limit Ratios* ||~ Erv Wilson ||~ Archaeotonic ||~ Oneirotonic ||~ [[26edo]] names ||~ Kentaku ||
||= 0 ||&gt;   0.00 ||= 1/1 ||= H ||= C ||= C ||= C ||= J ||
||= 0 ||&gt; 0.00 ||= 1/1 ||= H ||= C ||= C ||= C ||= J ||
||= 1 ||&gt;   92.31 ||= 17/16, 18/17, 19/18, 20/19, 21/20, 22/21 ||= &lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;β&lt;/span&gt; ||= C#/Db ||= C#/Db ||= Cx/Dbb ||= J#/Kb ||
||= 1 ||&gt; 92.31 ||= 17/16, 18/17, 19/18, 20/19, 21/20, 22/21 ||= &lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;β&lt;/span&gt; ||= C#/Db ||= C#/Db ||= Cx/Dbb ||= J#/Kb ||
||= 2 ||&gt; 184.62 ||= 9/8, 10/9, 11/10, 19/17, 21/19 ||= A ||= D ||= D ||= D ||= K ||
||= 2 ||&gt; 184.62 ||= 9/8, 10/9, 11/10, 19/17, 21/19 ||= A ||= D ||= D ||= D ||= K ||
||= 3 ||&gt; 276.92 ||= 7/6, 13/11, 20/17, 19/16, 22/19 ||= &lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;δ&lt;/span&gt; ||= D#/Eb ||= D#/Eb ||= Dx/Ebb ||= K#/Lb ||
||= 3 ||&gt; 276.92 ||= 7/6, 13/11, 20/17, 19/16, 22/19 ||= &lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;δ&lt;/span&gt; ||= D#/Eb ||= D#/Eb ||= Dx/Ebb ||= K#/Lb ||
||= 4 ||&gt; 369.23 ||= 5/4, 11/9, 16/13, 26/21 ||= C ||= E ||= E ||= E ||= L ||
||= 4 ||&gt; 369.23 ||= 5/4, 11/9, 16/13, 26/21 ||= C ||= E ||= E ||= E ||= L ||
||= 5 ||&gt; 461.54 ||= 13/10, 17/13, 21/16, 22/17 ||= B ||= E#/Fb ||= F ||= Ex/Fb ||= M ||
||= 5 ||&gt; 461.54 ||= 13/10, 17/13, 21/16, 22/17 ||= B ||= E#/Fb ||= F ||= Ex/Fb ||= M ||
||= 6 ||&gt; 553.85 ||= 11/8, 18/13, 26/19 ||= &lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;ε&lt;/span&gt; ||= F ||= F#/Gb ||= F# ||= M#/Nb ||
||= 6 ||&gt; 553.85 ||= 11/8, 18/13, 26/19 ||= &lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;ε&lt;/span&gt; ||= F ||= F#/Gb ||= F# ||= M#/Nb ||
||= 7 ||&gt; 646.15 ||= 16/11, 13/9, 19/13 ||= D ||= F#/Gb ||= G ||= Gb ||= N ||
||= 7 ||&gt; 646.15 ||= 16/11, 13/9, 19/13 ||= D ||= F#/Gb ||= G ||= Gb ||= N ||
||= 8 ||&gt; 738.46 ||= 17/11, 20/13, 26/17, 32/21 ||= &lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;γ&lt;/span&gt; ||= G ||= G#/Hb ||= G# ||= N#/Ob ||
||= 8 ||&gt; 738.46 ||= 17/11, 20/13, 26/17, 32/21 ||= &lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;γ&lt;/span&gt; ||= G ||= G#/Hb ||= G# ||= N#/Ob ||
||= 9 ||&gt; 830.77 ||= 8/5, 13/8, 18/11, 21/13 ||= F ||= G#/Ab ||= H ||= Ab ||= O ||
||= 9 ||&gt; 830.77 ||= 8/5, 13/8, 18/11, 21/13 ||= F ||= G#/Ab ||= H ||= Ab ||= O ||
||= 10 ||&gt; 923.08 ||= [[17_10|17/10]], [[12_7|12/7]], [[22_13|22/13]], [[19_11|19/11]] ||= E ||= A ||= A ||= A# ||= P ||
||= 10 ||&gt; 923.08 ||= [[17_10|17/10]], [[12_7|12/7]], [[22_13|22/13]], [[19_11|19/11]] ||= E ||= A ||= A ||= A# ||= P ||
||= 11 ||&gt; 1015.38 ||= 9/5, 16/9, 20/11, 34/19, 38/21 ||= &lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;α&lt;/span&gt; ||= A#/Bb ||= A#/Bb ||= Bb ||= P#/Qb ||
||= 11 ||&gt; 1015.38 ||= 9/5, 16/9, 20/11, 34/19, 38/21 ||= &lt;span style="background-color: #ffffff; color: #333333; font-family: Verdana; font-size: 12px;"&gt;α&lt;/span&gt; ||= A#/Bb ||= A#/Bb ||= Bb ||= P#/Qb ||
||= 12 ||&gt; 1107.69 ||= 17/9, 19/10, 21/11, 32/17, 36/19, 40/21 ||= G ||= B/Cb ||= B ||= B#/Cbb ||= Q ||
||= 12 ||&gt; 1107.69 ||= 17/9, 19/10, 21/11, 32/17, 36/19, 40/21 ||= G ||= B/Cb ||= B ||= B#/Cbb ||= Q ||
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with major wider than minor ||||||~ Up/down notation using the narrow 5th of 7\13,
with major wider than minor ||||||~ Up/down notation using the narrow 5th of 7\13,
with major narrower than minor ||
with major narrower than minor ||
||= 0 ||&gt;   0 ||= perfect unison ||= P1 ||= D ||= perfect unison ||= P1 ||= D ||
||= 0 ||&gt; 0 ||= perfect unison ||= P1 ||= D ||= perfect unison ||= P1 ||= D ||
||= 1 ||&gt;   92 ||= up unison, minor 2nd ||= ^1, m2 ||= D^, E ||= up unison, major 2nd ||= ^1, M2 ||= D^, E ||
||= 1 ||&gt; 92 ||= up unison, minor 2nd ||= ^1, m2 ||= D^, E ||= up unison, major 2nd ||= ^1, M2 ||= D^, E ||
||= 2 ||&gt; 185 ||= upminor 2nd, minor 3rd ||= ^m2, m3 ||= E^, Fb ||= upmajor 2nd, major 3rd ||= ^M2, M3 ||= E^, F# ||
||= 2 ||&gt; 185 ||= upminor 2nd, minor 3rd ||= ^m2, m3 ||= E^, Fb ||= upmajor 2nd, major 3rd ||= ^M2, M3 ||= E^, F# ||
||= 3 ||&gt; 277 ||= downmajor 2nd, upminor 3rd ||= vM2, ^m3 ||= E#v, Fb^ ||= downminor 2nd, upmajor 3rd ||= vm2, ^M3 ||= Ebv, F#^ ||
||= 3 ||&gt; 277 ||= downmajor 2nd, upminor 3rd ||= vM2, ^m3 ||= E#v, Fb^ ||= downminor 2nd, upmajor 3rd ||= vm2, ^M3 ||= Ebv, F#^ ||
||= 4 ||&gt; 369 ||= major 2nd, downmajor 3rd ||= M2, vM3 ||= E#, Fv ||= minor 2nd, downminor 3rd ||= m2, vm3 ||= Eb, Fv ||
||= 4 ||&gt; 369 ||= major 2nd, downmajor 3rd ||= M2, vM3 ||= E#, Fv ||= minor 2nd, downminor 3rd ||= m2, vm3 ||= Eb, Fv ||
||= 5 ||&gt; 462 ||= major 3rd, down 4th ||= M3, v4 ||= F, Gv ||= minor 3rd, down 4th ||= m3, v4 ||= F, Gv ||
||= 5 ||&gt; 462 ||= major 3rd, down 4th ||= M3, v4 ||= F, Gv ||= minor 3rd, down 4th ||= m3, v4 ||= F, Gv ||
||= 6 ||&gt; 554 ||= perfect 4th, down 5th ||= P4, v5 ||= G, Av ||= perfect 4th, down 5th ||= P4, v5 ||= G, Av ||
||= 6 ||&gt; 554 ||= perfect 4th, down 5th ||= P4, v5 ||= G, Av ||= perfect 4th, down 5th ||= P4, v5 ||= G, Av ||
||= 7 ||&gt; 646 ||= up 4th, perfect 5th ||= ^4, P5 ||= G^, A ||= up 4th, perfect 5th ||= ^4, P5 ||= G^, A ||
||= 7 ||&gt; 646 ||= up 4th, perfect 5th ||= ^4, P5 ||= G^, A ||= up 4th, perfect 5th ||= ^4, P5 ||= G^, A ||
||= 8 ||&gt; 738 ||= up 5th, minor 6th ||= ^5, m6 ||= A^, B ||= up 5th, major 6th ||= ^5, M6 ||= A^, B ||
||= 8 ||&gt; 738 ||= up 5th, minor 6th ||= ^5, m6 ||= A^, B ||= up 5th, major 6th ||= ^5, M6 ||= A^, B ||
||= 9 ||&gt; 831 ||= upminor 6th, minor 7th ||= ^m6, m7 ||= B^, Cb ||= upmajor 6th, major 7th ||= ^M6, M7 ||= B^, C# ||
||= 9 ||&gt; 831 ||= upminor 6th, minor 7th ||= ^m6, m7 ||= B^, Cb ||= upmajor 6th, major 7th ||= ^M6, M7 ||= B^, C# ||
||= 10 ||&gt; 923 ||= downmajor 6th, upminor 7th ||= vM6, ^m7 ||= B#v, Cb^ ||= downminor 6th, upmajor 7th ||= vm6, ^M7 ||= Bbv, C#^ ||
||= 10 ||&gt; 923 ||= downmajor 6th, upminor 7th ||= vM6, ^m7 ||= B#v, Cb^ ||= downminor 6th, upmajor 7th ||= vm6, ^M7 ||= Bbv, C#^ ||
||= 11 ||&gt; 1015 ||= major 6th, downmajor 7th ||= M6, vM7 ||= B#, Cv ||= minor 6th, downminor 7th ||= m6, vm7 ||= Bb, Cv ||
||= 11 ||&gt; 1015 ||= major 6th, downmajor 7th ||= M6, vM7 ||= B#, Cv ||= minor 6th, downminor 7th ||= m6, vm7 ||= Bb, Cv ||
||= 12 ||&gt; 1108 ||= major 7th, down 8ve ||= M7, v8 ||= C, Dv ||= minor 7th, down 8ve ||= m7, v8 ||= C, Dv ||
||= 12 ||&gt; 1108 ||= major 7th, down 8ve ||= M7, v8 ||= C, Dv ||= minor 7th, down 8ve ||= m7, v8 ||= C, Dv ||
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[[file:13edo-chromatic-scale.mid|13 edo chromatic ascending and descending scale on C (MIDI)]]
[[file:13edo-chromatic-scale.mid|13 edo chromatic ascending and descending scale on C (MIDI)]]
[[media type="file" key="13 Edo chromatic scale on J.wav" width="300" height="50"]]
[[media type="file" key="13 Edo chromatic scale on J.wav" width="300" height="50" AUTOPLAY="false"]]


[[media type="custom" key="24802800"]]
[[media type="custom" key="24802800"]]
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Play the 4:5:9 chord:
Play the 4:5:9 chord:
[[media type="file" key="13 edo 459 chord.wav" width="300" height="50"]]
[[media type="file" key="13 edo 459 chord.wav" width="300" height="50" AUTOPLAY="false"]]
Play the 4:5:9:11 chord:
Play the 4:5:9:11 chord:
[[media type="file" key="13 edo 45911 chord.wav" width="300" height="50"]]
[[media type="file" key="13 edo 45911 chord.wav" width="300" height="50" AUTOPLAY="false"]]
Play the 4:5:9:13 chord:
Play the 4:5:9:13 chord:
[[media type="file" key="13 edo 45913 chord.wav" width="300" height="50"]]
[[media type="file" key="13 edo 45913 chord.wav" width="300" height="50" AUTOPLAY="false"]]
Play the 4:5:9:21 chord:
Play the 4:5:9:21 chord:
[[media type="file" key="13 edo 45921 chord.wav" width="300" height="50"]]
[[media type="file" key="13 edo 45921 chord.wav" width="300" height="50" AUTOPLAY="false"]]
=Notational and Compositional Approaches to 13edo=  
=Notational and Compositional Approaches to 13edo=  
13edo has drawn the attention of numerous composers and theorists, some of whom have devoted some effort to provide a notation and an outline of a compositional approach to it. Some of these are described below.
13edo has drawn the attention of numerous composers and theorists, some of whom have devoted some effort to provide a notation and an outline of a compositional approach to it. Some of these are described below.
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Also, this approach allows for a circle of fourths to be produced:
Also, this approach allows for a circle of fourths to be produced:
[[image:xenharmonic/13 ET circle of fourths.PNG]]
[[image:xenharmonic/13 ET circle of fourths.PNG]]
Listen to Ryonian on J (F#) [[media type="file" key="13 edo Ryo mode.wav" width="300" height="50"]]
Listen to Ryonian on J (F#) [[media type="file" key="13 edo Ryo mode.wav" width="300" height="50" AUTOPLAY="false"]]
Listen to Dylathian on J: (F#) [[media type="file" key="13 edo 8 tone mode 1.wav" width="300" height="50"]]
Listen to Dylathian on J: (F#) [[media type="file" key="13 edo 8 tone mode 1.wav" width="300" height="50" AUTOPLAY="false"]]


[[xenharmonic/Kentaku's Approach to 13EDO|More on William Lynch's 13 EDO octatonic approach]]
[[xenharmonic/Kentaku's Approach to 13EDO|More on William Lynch's 13 EDO octatonic approach]]
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&lt;br /&gt;
&lt;br /&gt;
&lt;a href="/file/view/13edo-chromatic-scale.mid/389281456/13edo-chromatic-scale.mid" onclick="ws.common.trackFileLink('/file/view/13edo-chromatic-scale.mid/389281456/13edo-chromatic-scale.mid');"&gt;13 edo chromatic ascending and descending scale on C (MIDI)&lt;/a&gt;&lt;br /&gt;
&lt;a href="/file/view/13edo-chromatic-scale.mid/389281456/13edo-chromatic-scale.mid" onclick="ws.common.trackFileLink('/file/view/13edo-chromatic-scale.mid/389281456/13edo-chromatic-scale.mid');"&gt;13 edo chromatic ascending and descending scale on C (MIDI)&lt;/a&gt;&lt;br /&gt;
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&lt;!-- ws:start:WikiTextMediaRule:1:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20Edo%20chromatic%20scale%20on%20J.wav?h=50&amp;amp;w=300&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;13 Edo chromatic scale on J.wav&amp;amp;quot; width=&amp;amp;quot;300&amp;amp;quot; height=&amp;amp;quot;50&amp;amp;quot; AUTOPLAY=&amp;amp;quot;false&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;50&amp;quot; width=&amp;quot;300&amp;quot;/&amp;gt; --&gt;&lt;embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+Edo+chromatic+scale+on+J.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:1 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextMediaRule:2:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/custom/24802800?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;24802800&amp;amp;quot;&amp;quot; title=&amp;quot;Custom Media&amp;quot;/&amp;gt; --&gt;&lt;object id="example" type="image/svg+xml" data="http://xenharmonic.wikispaces.com/file/view/13ed2-001.svg"&gt;alt : Your browser has no SVG support.&lt;/object&gt;&lt;!-- ws:end:WikiTextMediaRule:2 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextMediaRule:2:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/custom/24802800?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;24802800&amp;amp;quot;&amp;quot; title=&amp;quot;Custom Media&amp;quot;/&amp;gt; --&gt;&lt;object id="example" type="image/svg+xml" data="http://xenharmonic.wikispaces.com/file/view/13ed2-001.svg"&gt;alt : Your browser has no SVG support.&lt;/object&gt;&lt;!-- ws:end:WikiTextMediaRule:2 --&gt;&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
Play the 4:5:9 chord:&lt;br /&gt;
Play the 4:5:9 chord:&lt;br /&gt;
&lt;!-- ws:start:WikiTextMediaRule:3:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%20459%20chord.wav?h=50&amp;amp;w=300&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;13 edo 459 chord.wav&amp;amp;quot; width=&amp;amp;quot;300&amp;amp;quot; height=&amp;amp;quot;50&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;50&amp;quot; width=&amp;quot;300&amp;quot;/&amp;gt; --&gt;&lt;embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+459+chord.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:3 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextMediaRule:3:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%20459%20chord.wav?h=50&amp;amp;w=300&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;13 edo 459 chord.wav&amp;amp;quot; width=&amp;amp;quot;300&amp;amp;quot; height=&amp;amp;quot;50&amp;amp;quot; AUTOPLAY=&amp;amp;quot;false&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;50&amp;quot; width=&amp;quot;300&amp;quot;/&amp;gt; --&gt;&lt;embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+459+chord.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:3 --&gt;&lt;br /&gt;
Play the 4:5:9:11 chord:&lt;br /&gt;
Play the 4:5:9:11 chord:&lt;br /&gt;
&lt;!-- ws:start:WikiTextMediaRule:4:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%2045911%20chord.wav?h=50&amp;amp;w=300&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;13 edo 45911 chord.wav&amp;amp;quot; width=&amp;amp;quot;300&amp;amp;quot; height=&amp;amp;quot;50&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;50&amp;quot; width=&amp;quot;300&amp;quot;/&amp;gt; --&gt;&lt;embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+45911+chord.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:4 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextMediaRule:4:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%2045911%20chord.wav?h=50&amp;amp;w=300&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;13 edo 45911 chord.wav&amp;amp;quot; width=&amp;amp;quot;300&amp;amp;quot; height=&amp;amp;quot;50&amp;amp;quot; AUTOPLAY=&amp;amp;quot;false&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;50&amp;quot; width=&amp;quot;300&amp;quot;/&amp;gt; --&gt;&lt;embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+45911+chord.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:4 --&gt;&lt;br /&gt;
Play the 4:5:9:13 chord:&lt;br /&gt;
Play the 4:5:9:13 chord:&lt;br /&gt;
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&lt;!-- ws:start:WikiTextMediaRule:5:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%2045913%20chord.wav?h=50&amp;amp;w=300&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;13 edo 45913 chord.wav&amp;amp;quot; width=&amp;amp;quot;300&amp;amp;quot; height=&amp;amp;quot;50&amp;amp;quot; AUTOPLAY=&amp;amp;quot;false&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;50&amp;quot; width=&amp;quot;300&amp;quot;/&amp;gt; --&gt;&lt;embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+45913+chord.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:5 --&gt;&lt;br /&gt;
Play the 4:5:9:21 chord:&lt;br /&gt;
Play the 4:5:9:21 chord:&lt;br /&gt;
&lt;!-- ws:start:WikiTextMediaRule:6:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%2045921%20chord.wav?h=50&amp;amp;w=300&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;13 edo 45921 chord.wav&amp;amp;quot; width=&amp;amp;quot;300&amp;amp;quot; height=&amp;amp;quot;50&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;50&amp;quot; width=&amp;quot;300&amp;quot;/&amp;gt; --&gt;&lt;embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+45921+chord.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:6 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextMediaRule:6:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%2045921%20chord.wav?h=50&amp;amp;w=300&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;13 edo 45921 chord.wav&amp;amp;quot; width=&amp;amp;quot;300&amp;amp;quot; height=&amp;amp;quot;50&amp;amp;quot; AUTOPLAY=&amp;amp;quot;false&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;50&amp;quot; width=&amp;quot;300&amp;quot;/&amp;gt; --&gt;&lt;embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+45921+chord.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:6 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:17:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Notational and Compositional Approaches to 13edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:17 --&gt;Notational and Compositional Approaches to 13edo&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:17:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Notational and Compositional Approaches to 13edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:17 --&gt;Notational and Compositional Approaches to 13edo&lt;/h1&gt;
  13edo has drawn the attention of numerous composers and theorists, some of whom have devoted some effort to provide a notation and an outline of a compositional approach to it. Some of these are described below.&lt;br /&gt;
  13edo has drawn the attention of numerous composers and theorists, some of whom have devoted some effort to provide a notation and an outline of a compositional approach to it. Some of these are described below.&lt;br /&gt;
Line 827: Line 827:
Also, this approach allows for a circle of fourths to be produced:&lt;br /&gt;
Also, this approach allows for a circle of fourths to be produced:&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:1124:&amp;lt;img src=&amp;quot;http://xenharmonic.wikispaces.com/file/view/13%20ET%20circle%20of%20fourths.PNG/506093224/13%20ET%20circle%20of%20fourths.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://xenharmonic.wikispaces.com/file/view/13%20ET%20circle%20of%20fourths.PNG/506093224/13%20ET%20circle%20of%20fourths.PNG" alt="13 ET circle of fourths.PNG" title="13 ET circle of fourths.PNG" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1124 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:1124:&amp;lt;img src=&amp;quot;http://xenharmonic.wikispaces.com/file/view/13%20ET%20circle%20of%20fourths.PNG/506093224/13%20ET%20circle%20of%20fourths.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://xenharmonic.wikispaces.com/file/view/13%20ET%20circle%20of%20fourths.PNG/506093224/13%20ET%20circle%20of%20fourths.PNG" alt="13 ET circle of fourths.PNG" title="13 ET circle of fourths.PNG" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1124 --&gt;&lt;br /&gt;
Listen to Ryonian on J (F#) &lt;!-- ws:start:WikiTextMediaRule:7:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%20Ryo%20mode.wav?h=50&amp;amp;w=300&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;13 edo Ryo mode.wav&amp;amp;quot; width=&amp;amp;quot;300&amp;amp;quot; height=&amp;amp;quot;50&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;50&amp;quot; width=&amp;quot;300&amp;quot;/&amp;gt; --&gt;&lt;embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+Ryo+mode.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:7 --&gt;&lt;br /&gt;
Listen to Ryonian on J (F#) &lt;!-- ws:start:WikiTextMediaRule:7:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%20Ryo%20mode.wav?h=50&amp;amp;w=300&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;13 edo Ryo mode.wav&amp;amp;quot; width=&amp;amp;quot;300&amp;amp;quot; height=&amp;amp;quot;50&amp;amp;quot; AUTOPLAY=&amp;amp;quot;false&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;50&amp;quot; width=&amp;quot;300&amp;quot;/&amp;gt; --&gt;&lt;embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+Ryo+mode.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:7 --&gt;&lt;br /&gt;
Listen to Dylathian on J: (F#) &lt;!-- ws:start:WikiTextMediaRule:8:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%208%20tone%20mode%201.wav?h=50&amp;amp;w=300&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;13 edo 8 tone mode 1.wav&amp;amp;quot; width=&amp;amp;quot;300&amp;amp;quot; height=&amp;amp;quot;50&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;50&amp;quot; width=&amp;quot;300&amp;quot;/&amp;gt; --&gt;&lt;embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+8+tone+mode+1.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:8 --&gt;&lt;br /&gt;
Listen to Dylathian on J: (F#) &lt;!-- ws:start:WikiTextMediaRule:8:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%208%20tone%20mode%201.wav?h=50&amp;amp;w=300&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;13 edo 8 tone mode 1.wav&amp;amp;quot; width=&amp;amp;quot;300&amp;amp;quot; height=&amp;amp;quot;50&amp;amp;quot; AUTOPLAY=&amp;amp;quot;false&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;50&amp;quot; width=&amp;quot;300&amp;quot;/&amp;gt; --&gt;&lt;embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+8+tone+mode+1.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:8 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Kentaku%27s%20Approach%20to%2013EDO"&gt;More on William Lynch's 13 EDO octatonic approach&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Kentaku%27s%20Approach%20to%2013EDO"&gt;More on William Lynch's 13 EDO octatonic approach&lt;/a&gt;&lt;br /&gt;
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