13edo: Difference between revisions
Wikispaces>michaelwayneharwood **Imported revision 609290815 - Original comment: ** |
Wikispaces>spt3125 **Imported revision 615832227 - Original comment: added link (deorphaning)** |
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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: | : This revision was by author [[User:spt3125|spt3125]] and made on <tt>2017-07-22 19:49:06 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>615832227</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>added link (deorphaning)</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
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and | and | ||
0 1 3 4 5 8 9 10 12 13 nonatonic | 0 1 3 4 5 8 9 10 12 13 nonatonic | ||
=Guitar= | |||
* [[13EDO Scales and Chords for Guitar]] | |||
=**Compositions**= | =**Compositions**= | ||
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<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>13edo</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="/13%E5%B9%B3%E5%9D%87%E5%BE%8B">日本語</a><br /> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>13edo</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="/13%E5%B9%B3%E5%9D%87%E5%BE%8B">日本語</a><br /> | ||
</span><br /> | </span><br /> | ||
<!-- ws:start:WikiTextTocRule: | <!-- ws:start:WikiTextTocRule:39:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><a href="#Best approximates 2.5.9.11.13.17.19.21">Best approximates 2.5.9.11.13.17.19.21</a><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --> | <a href="#x13edo: 13 equal divisions of the octave">13edo: 13 equal divisions of the octave</a><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --> | <a href="#Scales in 13edo">Scales in 13edo</a><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --> | <a href="#Harmony in 13edo">Harmony in 13edo</a><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --> | <a href="#Notational and Compositional Approaches to 13edo">Notational and Compositional Approaches to 13edo</a><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --> | <a href="#Mapping to Standard Keyboards">Mapping to Standard Keyboards</a><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --> | <a href="#Animism">Animism</a><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --> | <a href="#Guitar">Guitar</a><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --> | ||
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<!-- ws:start:WikiTextFileRule: | <!-- ws:start:WikiTextFileRule:1133:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/13ed2-001.svg?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@13ed2-001.svg&quot; title=&quot;File: 13ed2-001.svg&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/13ed2-001.svg/480712008/13ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/13ed2-001.svg/480712008/13ed2-001.svg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="13ed2-001.svg" /></a><div><a href="/file/view/13ed2-001.svg/480712008/13ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/13ed2-001.svg/480712008/13ed2-001.svg');" class="filename" title="13ed2-001.svg">13ed2-001.svg</a><br /><ul><li><a href="/file/detail/13ed2-001.svg">Details</a></li><li><a href="/file/view/13ed2-001.svg/480712008/13ed2-001.svg">Download</a></li><li style="color: #666">15 KB</li></ul></div></div><!-- ws:end:WikiTextFileRule:1133 --><br /> | ||
<!-- ws:start:WikiTextHeadingRule:13:&lt;h1&gt; --><h1 id="toc2"><a name="Scales in 13edo"></a><!-- ws:end:WikiTextHeadingRule:13 -->Scales in 13edo</h1> | <!-- ws:start:WikiTextHeadingRule:13:&lt;h1&gt; --><h1 id="toc2"><a name="Scales in 13edo"></a><!-- ws:end:WikiTextHeadingRule:13 -->Scales in 13edo</h1> | ||
Due to the prime character of the number 13, 13edo can form several xenharmonic <a class="wiki_link" href="/MOSScales">moment of symmetry scales</a>. The diagram below shows five &quot;families&quot; of MOS scales: those generated by making a chain of 2\13 (two <u><a class="wiki_link" href="/degree">degree</a>s of</u> 13edo), 3\13, 4\13, 5\13, &amp; 6\13, respectively.<br /> | Due to the prime character of the number 13, 13edo can form several xenharmonic <a class="wiki_link" href="/MOSScales">moment of symmetry scales</a>. The diagram below shows five &quot;families&quot; of MOS scales: those generated by making a chain of 2\13 (two <u><a class="wiki_link" href="/degree">degree</a>s of</u> 13edo), 3\13, 4\13, 5\13, &amp; 6\13, respectively.<br /> | ||
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~diagram by Andrew Heathwaite, based on horagrams pioneered by Erv Wilson<br /> | ~diagram by Andrew Heathwaite, based on horagrams pioneered by Erv Wilson<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:21:&lt;h3&gt; --><h3 id="toc6"><a name="Notational and Compositional Approaches to 13edo-The Cryptic Ruse Methods-Modes and Harmony in The Archaeotonic Scale"></a><!-- ws:end:WikiTextHeadingRule:21 -->Modes and Harmony in The Archaeotonic Scale</h3> | <!-- ws:start:WikiTextHeadingRule:21:&lt;h3&gt; --><h3 id="toc6"><a name="Notational and Compositional Approaches to 13edo-The Cryptic Ruse Methods-Modes and Harmony in The Archaeotonic Scale"></a><!-- ws:end:WikiTextHeadingRule:21 -->Modes and Harmony in The Archaeotonic Scale</h3> | ||
A 7-nominal notaiton is proposed, using the letters A-G. The &quot;C natural&quot; scale is proposed to be degrees 0-2-4-6-8-10-12-(13), with the note &quot;C&quot; tuned to a reference pitch of concert middle C. The modes are laid out in the following table, excerpted from an unfinished paper on 13edo.<br /> | A 7-nominal notaiton is proposed, using the letters A-G. The &quot;C natural&quot; scale is proposed to be degrees 0-2-4-6-8-10-12-(13), with the note &quot;C&quot; tuned to a reference pitch of concert middle C. The modes are laid out in the following table, excerpted from an unfinished paper on 13edo.<br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:1126:&lt;img src=&quot;/file/view/Archeotonic.png/252639498/Archeotonic.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/Archeotonic.png/252639498/Archeotonic.png" alt="Archeotonic.png" title="Archeotonic.png" /><!-- ws:end:WikiTextLocalImageRule:1126 --><br /> | ||
Treating 13edo as a temperament as proposed above leads to a chord of degrees 0-2-4-6-9 representing the JI harmony 8:9:10:11:13; two such pentads exist in this scale, on E and F. Smaller harmonic units exist as follows: 8:9:10:11 on C, D, E, and F; 8:9:10:13 on E, F and G; 8:9:10 on C, D, E, F, and G; 8:9:11 on C, D, E, and F; 8:9:13 on E, F, G, and A. Finally, on B we have the relatively-discordant 16:17:21:26 (0-1-5-9, or the notes B-C-E-G), which can be octave-inverted into a more concordant 8:13:17:21.<br /> | Treating 13edo as a temperament as proposed above leads to a chord of degrees 0-2-4-6-9 representing the JI harmony 8:9:10:11:13; two such pentads exist in this scale, on E and F. Smaller harmonic units exist as follows: 8:9:10:11 on C, D, E, and F; 8:9:10:13 on E, F and G; 8:9:10 on C, D, E, F, and G; 8:9:11 on C, D, E, and F; 8:9:13 on E, F, G, and A. Finally, on B we have the relatively-discordant 16:17:21:26 (0-1-5-9, or the notes B-C-E-G), which can be octave-inverted into a more concordant 8:13:17:21.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:23:&lt;h3&gt; --><h3 id="toc7"><a name="Notational and Compositional Approaches to 13edo-The Cryptic Ruse Methods-Modes and Harmony in the Oneirotonic Scale"></a><!-- ws:end:WikiTextHeadingRule:23 -->Modes and Harmony in the Oneirotonic Scale</h3> | <!-- ws:start:WikiTextHeadingRule:23:&lt;h3&gt; --><h3 id="toc7"><a name="Notational and Compositional Approaches to 13edo-The Cryptic Ruse Methods-Modes and Harmony in the Oneirotonic Scale"></a><!-- ws:end:WikiTextHeadingRule:23 -->Modes and Harmony in the Oneirotonic Scale</h3> | ||
Here an 8-nominal notation is proposed, using letters A-H. The &quot;C natural&quot; scale is proposed to be degrees 0-2-4-5-7-9-10-12-(13), with the note &quot;C&quot; tuned to concert middle C. The modes are laid out in the following table, excerpted from an unfinished paper on 13edo.<br /> | Here an 8-nominal notation is proposed, using letters A-H. The &quot;C natural&quot; scale is proposed to be degrees 0-2-4-5-7-9-10-12-(13), with the note &quot;C&quot; tuned to concert middle C. The modes are laid out in the following table, excerpted from an unfinished paper on 13edo.<br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:1127:&lt;img src=&quot;/file/view/Oneirotonic.png/252639860/Oneirotonic.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/Oneirotonic.png/252639860/Oneirotonic.png" alt="Oneirotonic.png" title="Oneirotonic.png" /><!-- ws:end:WikiTextLocalImageRule:1127 --><br /> | ||
There is a great number of potential consonant harmonies in this scale. A dedicated article on harmony and tonality in the oneirotonic scale is forthcoming.<br /> | There is a great number of potential consonant harmonies in this scale. A dedicated article on harmony and tonality in the oneirotonic scale is forthcoming.<br /> | ||
<!-- ws:start:WikiTextHeadingRule:25:&lt;h2&gt; --><h2 id="toc8"><!-- ws:end:WikiTextHeadingRule:25 --> </h2> | <!-- ws:start:WikiTextHeadingRule:25:&lt;h2&gt; --><h2 id="toc8"><!-- ws:end:WikiTextHeadingRule:25 --> </h2> | ||
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This new approach simply modifies the way 13 edo is systematized and notated but is based on the exact same 8 tone scale that cryptic ruse uses.<br /> | This new approach simply modifies the way 13 edo is systematized and notated but is based on the exact same 8 tone scale that cryptic ruse uses.<br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:1128:&lt;img src=&quot;/file/view/13%20edo%20alphabet.PNG/506083616/13%20edo%20alphabet.PNG&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/13%20edo%20alphabet.PNG/506083616/13%20edo%20alphabet.PNG" alt="13 edo alphabet.PNG" title="13 edo alphabet.PNG" /><!-- ws:end:WikiTextLocalImageRule:1128 --><br /> | ||
Notation written on the staff looks nearly the same as 12 edo notation except that because there are 8 letters instead of 7, the notes offset themselves to where space to space and line to line is now octaves rather than line to space. This actually makes learning the system much, much easier because a letter that is on a line is always on a line.<br /> | Notation written on the staff looks nearly the same as 12 edo notation except that because there are 8 letters instead of 7, the notes offset themselves to where space to space and line to line is now octaves rather than line to space. This actually makes learning the system much, much easier because a letter that is on a line is always on a line.<br /> | ||
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3 EDO Chromatic Scale in Octatonic Notation:<br /> | 3 EDO Chromatic Scale in Octatonic Notation:<br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:1129:&lt;img src=&quot;/file/view/8%20tone%20scale%2013%20edo.PNG/506382886/8%20tone%20scale%2013%20edo.PNG&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/8%20tone%20scale%2013%20edo.PNG/506382886/8%20tone%20scale%2013%20edo.PNG" alt="8 tone scale 13 edo.PNG" title="8 tone scale 13 edo.PNG" /><!-- ws:end:WikiTextLocalImageRule:1129 --><br /> | ||
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Also, this approach allows for a circle of fourths to be produced:<br /> | Also, this approach allows for a circle of fourths to be produced:<br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:1131:&lt;img src=&quot;http://xenharmonic.wikispaces.com/file/view/13%20ET%20circle%20of%20fourths.PNG/506093224/13%20ET%20circle%20of%20fourths.PNG&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><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" /><!-- ws:end:WikiTextLocalImageRule:1131 --><br /> | ||
Listen to Ryonian on J (F#):<br /> | Listen to Ryonian on J (F#):<br /> | ||
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0 1 3 4 5 8 9 10 12 13 nonatonic<br /> | 0 1 3 4 5 8 9 10 12 13 nonatonic<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:35:&lt;h1&gt; --><h1 id="toc13"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:35:&lt;h1&gt; --><h1 id="toc13"><a name="Guitar"></a><!-- ws:end:WikiTextHeadingRule:35 -->Guitar</h1> | ||
<ul><li><a class="wiki_link" href="/13EDO%20Scales%20and%20Chords%20for%20Guitar">13EDO Scales and Chords for Guitar</a></li></ul><br /> | |||
<!-- ws:start:WikiTextHeadingRule:37:&lt;h1&gt; --><h1 id="toc14"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:37 --><strong>Compositions</strong></h1> | |||
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.microtonalmusic.net/audio/slowdance13edo.mp3" rel="nofollow">Slow Dance</a></span> by <a class="wiki_link_ext" href="http://danielthompson.blogspot.com/" rel="nofollow">Daniel Thompson</a><br /> | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://www.microtonalmusic.net/audio/slowdance13edo.mp3" rel="nofollow">Slow Dance</a></span> by <a class="wiki_link_ext" href="http://danielthompson.blogspot.com/" rel="nofollow">Daniel Thompson</a><br /> | ||
<span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Hunt/Prelude%20in%2013ET.mp3" rel="nofollow">Prelude in 13ET</a></span> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt </a>- <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/2449" rel="nofollow" target="_blank">Organ version</a><br /> | <span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Hunt/Prelude%20in%2013ET.mp3" rel="nofollow">Prelude in 13ET</a></span> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt </a>- <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/2449" rel="nofollow" target="_blank">Organ version</a><br /> | ||