13edo: Difference between revisions
Wikispaces>igliashon **Imported revision 506177958 - Original comment: ** |
Wikispaces>igliashon **Imported revision 506178022 - 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:igliashon|igliashon]] and made on <tt>2014-05-03 07: | : This revision was by author [[User:igliashon|igliashon]] and made on <tt>2014-05-03 07:33:44 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>506178022</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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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"]] | ||
=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. | ||
== | ==The Cryptic Ruse Methods== | ||
13edo offers two main candidates for diatonic-like scales: the 6L1s heptatonic MOS generated by 2\13, and the 5L3s octatonic MOS. Both of these scales are Rothenberg proper, and bear a slightly-twisted resemblance to the 12edo diatonic scale. Specifically, the 6L1s scale resembles the 12edo diatonic with one of its semitones replaced with a whole-tone, while the 5L3s scale resembles the 12edo diatonic with an extra semitone inserted between two adjacent whole-tones. | 13edo offers two main candidates for diatonic-like scales: the 6L1s heptatonic MOS generated by 2\13, and the 5L3s octatonic MOS. Both of these scales are Rothenberg proper, and bear a slightly-twisted resemblance to the 12edo diatonic scale. Specifically, the 6L1s scale resembles the 12edo diatonic with one of its semitones replaced with a whole-tone, while the 5L3s scale resembles the 12edo diatonic with an extra semitone inserted between two adjacent whole-tones. | ||
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[[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/02/Margo-Schulter-For_Claudi-2014-02-17-13edo.mp3|For Claudi]] by [[http://soonlabel.com/xenharmonic/archives/1788|Margo Schulter]]</pre></div> | [[http://soonlabel.com/xenharmonic/wp-content/uploads/2014/02/Margo-Schulter-For_Claudi-2014-02-17-13edo.mp3|For Claudi]] by [[http://soonlabel.com/xenharmonic/archives/1788|Margo Schulter]]</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<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><!-- ws:start:WikiTextTocRule:37:&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:37 --><!-- ws:start:WikiTextTocRule:38: --><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:38 --><!-- ws:start:WikiTextTocRule:39: --> | <a href="#x13edo: 13 equal divisions of the octave">13edo: 13 equal divisions of the octave</a><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> | <a href="#Scales in 13edo">Scales in 13edo</a><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --> | <a href="#Harmony in 13edo">Harmony in 13edo</a><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><!-- 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: --> | <a href="#Mapping to Standard Keyboards">Mapping to Standard Keyboards</a><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --> | <a href="#Animism">Animism</a><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --> | <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><!-- ws:start:WikiTextTocRule:37:&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:37 --><!-- ws:start:WikiTextTocRule:38: --><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:38 --><!-- ws:start:WikiTextTocRule:39: --> | <a href="#x13edo: 13 equal divisions of the octave">13edo: 13 equal divisions of the octave</a><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> | <a href="#Scales in 13edo">Scales in 13edo</a><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --> | <a href="#Harmony in 13edo">Harmony in 13edo</a><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --> | <a href="#Notational and Compositional Approaches to 13edo">Notational and Compositional Approaches to 13edo</a><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><!-- 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: --> | <a href="#Mapping to Standard Keyboards">Mapping to Standard Keyboards</a><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --> | <a href="#Animism">Animism</a><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --> | ||
<!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/23473422?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;23473422&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://webplayer.yahooapis.com/player-beta.js"> | <!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/23473422?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;23473422&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://webplayer.yahooapis.com/player-beta.js"> | ||
</script><!-- ws:end:WikiTextMediaRule:0 --><br /> | </script><!-- ws:end:WikiTextMediaRule:0 --><br /> | ||
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Play the 4:5:9:21 chord:<br /> | Play the 4:5:9:21 chord:<br /> | ||
<!-- ws:start:WikiTextMediaRule:6:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%2045921%20chord.wav?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;13 edo 45921 chord.wav&amp;quot; width=&amp;quot;300&amp;quot; height=&amp;quot;50&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><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/"></embed><!-- ws:end:WikiTextMediaRule:6 --><br /> | <!-- ws:start:WikiTextMediaRule:6:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%2045921%20chord.wav?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;13 edo 45921 chord.wav&amp;quot; width=&amp;quot;300&amp;quot; height=&amp;quot;50&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><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/"></embed><!-- ws:end:WikiTextMediaRule:6 --><br /> | ||
<!-- ws:start:WikiTextHeadingRule:17:&lt; | <!-- ws:start:WikiTextHeadingRule:17:&lt;h1&gt; --><h1 id="toc4"><a name="Notational and Compositional Approaches to 13edo"></a><!-- ws:end:WikiTextHeadingRule:17 -->Notational and Compositional Approaches to 13edo</h1> | ||
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.<br /> | 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.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:19:&lt; | <!-- ws:start:WikiTextHeadingRule:19:&lt;h2&gt; --><h2 id="toc5"><a name="Notational and Compositional Approaches to 13edo-The Cryptic Ruse Methods"></a><!-- ws:end:WikiTextHeadingRule:19 -->The Cryptic Ruse Methods</h2> | ||
13edo offers two main candidates for diatonic-like scales: the 6L1s heptatonic MOS generated by 2\13, and the 5L3s octatonic MOS. Both of these scales are Rothenberg proper, and bear a slightly-twisted resemblance to the 12edo diatonic scale. Specifically, the 6L1s scale resembles the 12edo diatonic with one of its semitones replaced with a whole-tone, while the 5L3s scale resembles the 12edo diatonic with an extra semitone inserted between two adjacent whole-tones.<br /> | 13edo offers two main candidates for diatonic-like scales: the 6L1s heptatonic MOS generated by 2\13, and the 5L3s octatonic MOS. Both of these scales are Rothenberg proper, and bear a slightly-twisted resemblance to the 12edo diatonic scale. Specifically, the 6L1s scale resembles the 12edo diatonic with one of its semitones replaced with a whole-tone, while the 5L3s scale resembles the 12edo diatonic with an extra semitone inserted between two adjacent whole-tones.<br /> | ||
<br /> | <br /> | ||
<span style="background-color: #ffffff;">To facilitate discussion of these scales, Cryptic Ruse has ascribed them names based on H.P. Lovecraft's &quot;Dream Cycle&quot; mythos. The 2\13-based heptatonic has been named &quot;archeotonic&quot; after the &quot;Old Ones&quot; that rule the Dreamlands, and the 5\13-based octatonic has been named &quot;oneirotonic&quot; after the Dreamlands themselves. Modes of the archeotonic are named after the individual Old Ones themselves; modes of the oneirotonic are named after cities in the Dreamlands.</span><br /> | <span style="background-color: #ffffff;">To facilitate discussion of these scales, Cryptic Ruse has ascribed them names based on H.P. Lovecraft's &quot;Dream Cycle&quot; mythos. The 2\13-based heptatonic has been named &quot;archeotonic&quot; after the &quot;Old Ones&quot; that rule the Dreamlands, and the 5\13-based octatonic has been named &quot;oneirotonic&quot; after the Dreamlands themselves. Modes of the archeotonic are named after the individual Old Ones themselves; modes of the oneirotonic are named after cities in the Dreamlands.</span><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:21:&lt;h3&gt; --><h3 id="toc6"><a name=" | <!-- 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:855:&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:855 --><br /> | <!-- ws:start:WikiTextLocalImageRule:855:&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:855 --><br /> | ||
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There may be other concordant harmonies possible in this scale that do not represent segments of the overtone series; further exploration is pending.<br /> | There may be other concordant harmonies possible in this scale that do not represent segments of the overtone series; further exploration is pending.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:23:&lt;h3&gt; --><h3 id="toc7"><a name=" | <!-- 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:856:&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:856 --><br /> | <!-- ws:start:WikiTextLocalImageRule:856:&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:856 --><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> | ||
<!-- ws:start:WikiTextHeadingRule:27:&lt;h2&gt; --><h2 id="toc9"><a name=" | <!-- ws:start:WikiTextHeadingRule:27:&lt;h2&gt; --><h2 id="toc9"><a name="Notational and Compositional Approaches to 13edo-The Kentaku (aka William Lynch) Method"></a><!-- ws:end:WikiTextHeadingRule:27 -->The Kentaku (aka William Lynch) Method</h2> | ||
<span style="font-size: 13px; line-height: 1.5;">Normally, 13 edo can be notated by adding an accidental between E and F. For some reading the same staff with the same letters but in different places can be mind boggling and lead to confusion. That's why some have recommended different options. </span><br /> | <span style="font-size: 13px; line-height: 1.5;">Normally, 13 edo can be notated by adding an accidental between E and F. For some reading the same staff with the same letters but in different places can be mind boggling and lead to confusion. That's why some have recommended different options. </span><br /> | ||
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