13edo: Difference between revisions
Wikispaces>Kosmorsky **Imported revision 311590024 - Original comment: ** |
Wikispaces>Kosmorsky **Imported revision 311591194 - 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:Kosmorsky|Kosmorsky]] and made on <tt>2012-03-15 22: | : This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2012-03-15 22:16:45 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>311591194</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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=Mapping to Standard Keyboards= | =Mapping to Standard Keyboards= | ||
The 5L+3s scale (Oneirotonic) can be mapped to the standard keyboard effectively, although somewhat awkwardly. | The 5L+3s scale (Oneirotonic) can be mapped to the standard keyboard effectively, although somewhat awkwardly. Consider the sequence of 730-cent intervals that it derives from: 1 6 11 3 8 (13) 5 10 2 7 12 4 9 1. One of these must be absent, so it might as well be the last. So, there are at most five of the full octatonic scales on different keys. Of the four mappings that keep the major pentatonic on the white keys, which ironically look like ordinary minor-pentatonics, the latter which begins on B might be the most straightforward to learn and use. | ||
Consider the sequence of 730-cent intervals that it derives from: 1 6 11 3 8 (13) 5 10 2 7 12 4 9 1. One of these must be absent, so it might as well be the last. So, there are at most five of the full octatonic scales on different keys. | |||
Of the four mappings that keep the major pentatonic on the white keys, which ironically look like ordinary minor-pentatonics, the latter which begins on B might be the most straightforward to learn and use. | |||
|| 1 || 6 || 11 || 3 || 8 || (13) || 5 || 10 || 2 || 7 || 12 || 4 || 9 || 1 || Place in Chain of 730 cent intervals || | || 1 || 6 || 11 || 3 || 8 || (13) || 5 || 10 || 2 || 7 || 12 || 4 || 9 || 1 || Place in Chain of 730 cent intervals || | ||
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|| || * || * || || * || || X || * || || * || * || || * || || || | || || * || * || || * || || X || * || || * || * || || * || || || | ||
|| **D** || Eb || E || **F** || Gb || || **G** || Ab || **A** || Bb || B || **C** || Db || **D** || Keeps the pentatonic scale on the white keys || | || **D** || Eb || E || **F** || Gb || || **G** || Ab || **A** || Bb || B || **C** || Db || **D** || Keeps the pentatonic scale on the white keys || | ||
|| **A** || Bb || B || **C** || Db || || **D** || Eb || **E** || F || Gb || **G** || Ab || **A** || | || **A** || Bb || B || **C** || Db || || **D** || Eb || **E** || F || Gb || **G** || Ab || **A** || || | ||
|| **E** || F || Gb || **G** || Ab || || **A** || Bb || **B** || C || Db || **D** || Eb || **E** || | || **E** || F || Gb || **G** || Ab || || **A** || Bb || **B** || C || Db || **D** || Eb || **E** || || | ||
|| **B** || C || Db || **D** || Eb || || **E** || F || **Gb** || G || Ab || **A** || Bb || **B** || | || **B** || C || Db || **D** || Eb || || **E** || F || **Gb** || G || Ab || **A** || Bb || **B** || || | ||
|| C || Db || D || Eb || E || || F || Gb || G || Ab || A || Bb || B || C || Puts the missing key between a semitone || | || C || Db || D || Eb || E || || F || Gb || G || Ab || A || Bb || B || C || Puts the missing key between a semitone || | ||
|| G || Ab || A || Bb || B || || C || Db || D || Eb || E || F || Gb || G || | || G || Ab || A || Bb || B || || C || Db || D || Eb || E || F || Gb || G || (if that were to be valuable in any way) || | ||
The archeotonic tonality is much simpler to deal with, you just leave out a tone and remember which one. Although, for diatonic use it may be more convenient to put the missing tone between E/F or B/C | |||
to keep it on the white keys, with the remaining small step where it looks like it should be. | |||
= = | = = | ||
=Commas= | =Commas= | ||
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||= 441/440 ||< | -3 2 -1 2 -1 > ||> 3.93 ||= Werckisma ||= ||= ||</pre></div> | ||= 441/440 ||< | -3 2 -1 2 -1 > ||> 3.93 ||= Werckisma ||= ||= ||</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: | <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:21:&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:21 --><!-- ws:start:WikiTextTocRule:22: --><a href="#x13 tone equal temperament / 13edo">13 tone equal temperament / 13edo</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --> | <a href="#Harmony in 13edo">Harmony in 13edo</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Scales in 13edo">Scales in 13edo</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> | <a href="#Animism">Animism</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <a href="#Igliashon's 13-EDO diatonic approaches">Igliashon's 13-EDO diatonic approaches</a><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --> | <a href="#Mapping to Standard Keyboards">Mapping to Standard Keyboards</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#toc8"> </a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/12670900?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;12670900&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://webplayer.yahooapis.com/player.js"> | ||
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<hr /> | <hr /> | ||
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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 degrees of 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 degrees of 13edo), 3\13, 4\13, 5\13, &amp; 6\13, respectively.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:774:&lt;img src=&quot;/file/view/13edo_horograms.jpg/104015789/13edo_horograms.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/13edo_horograms.jpg/104015789/13edo_horograms.jpg" alt="13edo_horograms.jpg" title="13edo_horograms.jpg" /><!-- ws:end:WikiTextLocalImageRule:774 --><br /> | ||
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~diagram by Andrew Heathwaite, based on horograms pioneered by Erv Wilson<br /> | ~diagram by Andrew Heathwaite, based on horograms pioneered by Erv Wilson<br /> | ||
<br /> | <br /> | ||
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<br /> | <br /> | ||
To facilitate discussion of these scales, Igliashon 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. See the charts of modes of the two scales below, excerpted from Igliashon's forthcoming paper &quot;The Case for Thirteen&quot;:<br /> | To facilitate discussion of these scales, Igliashon 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. See the charts of modes of the two scales below, excerpted from Igliashon's forthcoming paper &quot;The Case for Thirteen&quot;:<br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:775:&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:775 --><br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:776:&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:776 --><br /> | ||
<!-- ws:start:WikiTextHeadingRule:15:&lt;h1&gt; --><h1 id="toc7"><a name="Mapping to Standard Keyboards"></a><!-- ws:end:WikiTextHeadingRule:15 -->Mapping to Standard Keyboards</h1> | <!-- ws:start:WikiTextHeadingRule:15:&lt;h1&gt; --><h1 id="toc7"><a name="Mapping to Standard Keyboards"></a><!-- ws:end:WikiTextHeadingRule:15 -->Mapping to Standard Keyboards</h1> | ||
<br /> | <br /> | ||
The 5L+3s scale (Oneirotonic) can be mapped to the standard keyboard effectively, although somewhat awkwardly. | The 5L+3s scale (Oneirotonic) can be mapped to the standard keyboard effectively, although somewhat awkwardly. Consider the sequence of 730-cent intervals that it derives from: 1 6 11 3 8 (13) 5 10 2 7 12 4 9 1. One of these must be absent, so it might as well be the last. So, there are at most five of the full octatonic scales on different keys. Of the four mappings that keep the major pentatonic on the white keys, which ironically look like ordinary minor-pentatonics, the latter which begins on B might be the most straightforward to learn and use.<br /> | ||
Consider the sequence of 730-cent intervals that it derives from: 1 6 11 3 8 (13) 5 10 2 7 12 4 9 1. One of these must be absent, so it might as well be the last. So, there are at most five of the full octatonic scales on different keys. | |||
Of the four mappings that keep the major pentatonic on the white keys, which ironically look like ordinary minor-pentatonics, the latter which begins on B might be the most straightforward to learn and use.<br /> | |||
<br /> | <br /> | ||
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<td><strong>A</strong><br /> | <td><strong>A</strong><br /> | ||
</td> | </td> | ||
<td | <td><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td><strong>E</strong><br /> | <td><strong>E</strong><br /> | ||
</td> | </td> | ||
<td | <td><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td><strong>B</strong><br /> | <td><strong>B</strong><br /> | ||
</td> | </td> | ||
<td | <td><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>G<br /> | <td>G<br /> | ||
</td> | </td> | ||
<td | <td>(if that were to be valuable in any way)<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<br /> | <br /> | ||
The archeotonic tonality is much simpler to deal with, you just leave out a tone and remember which one. Although, for diatonic use it may be more convenient to put the missing tone between E/F or B/C<br /> | |||
to keep it on the white keys, with the remaining small step where it looks like it should be.<br /> | |||
<!-- ws:start:WikiTextHeadingRule:17:&lt;h1&gt; --><h1 id="toc8"><!-- ws:end:WikiTextHeadingRule:17 --> </h1> | <!-- ws:start:WikiTextHeadingRule:17:&lt;h1&gt; --><h1 id="toc8"><!-- ws:end:WikiTextHeadingRule:17 --> </h1> | ||
<!-- ws:start:WikiTextHeadingRule:19:&lt;h1&gt; --><h1 id="toc9 | <!-- ws:start:WikiTextHeadingRule:19:&lt;h1&gt; --><h1 id="toc9"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:19 -->Commas</h1> | ||
13 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the val &lt; 13 21 30 36 45 48 |.)<br /> | 13 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the val &lt; 13 21 30 36 45 48 |.)<br /> | ||