13edo: Difference between revisions
Wikispaces>cookiemeows **Imported revision 505651788 - Original comment: ** |
Wikispaces>cookiemeows **Imported revision 505794736 - 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:cookiemeows|cookiemeows]] and made on <tt>2014- | : This revision was by author [[User:cookiemeows|cookiemeows]] and made on <tt>2014-05-01 10:31:54 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>505794736</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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The 2.9.5.11.13 subgroup has commas 45/44, 65/64 and 81/80, leading to a linear temperament with POTE generator 185.728 cents, quite __[[13edo#top|close]]__ to 2\13. Use this as a generator, and at 7 notes (6L1s) two full pentads are available (as well as two more 4:5:9:11 tetrad, and one 4:5:9:13 tetrad). These triads and tetrads can be assumed to likely be the most consonant base sonorities available in 13 edo and act in a similar way to major/minor triads. However, other sonorities such as orwell chords are avaliable as well. | The 2.9.5.11.13 subgroup has commas 45/44, 65/64 and 81/80, leading to a linear temperament with POTE generator 185.728 cents, quite __[[13edo#top|close]]__ to 2\13. Use this as a generator, and at 7 notes (6L1s) two full pentads are available (as well as two more 4:5:9:11 tetrad, and one 4:5:9:13 tetrad). These triads and tetrads can be assumed to likely be the most consonant base sonorities available in 13 edo and act in a similar way to major/minor triads. However, other sonorities such as orwell chords are avaliable as well. | ||
Play the 4:5:9 chord: [[media type="file" key="13 edo 459 chord.wav" width="300" height="50"]] | Play the 4:5:9 (Wholesome) chord: [[media type="file" key="13 edo 459 chord.wav" width="300" height="50"]] | ||
Play the 4:5:9:11 chord: | Play the 4:5:9:11 (Wholesome Tetrad) chord: [[media type="file" key="13 edo 45911 chord.wav"]] | ||
Play the 4:5:9:13 chord: | Play the 4:5:9:13 chord: [[media type="file" key="13 edo 45913 chord.wav"]] | ||
Play the 4:5:9:21 chord: | Play the 4:5:9:21 chord: [[media type="file" key="13 edo 45921 chord.wav"]] | ||
=Scales in 13edo= | =Scales in 13edo= | ||
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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: | <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:28:&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:28 --><!-- ws:start:WikiTextTocRule:29: --><a href="#Best approximates 2.5.9.11.13.21">Best approximates 2.5.9.11.13.21</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#x13 tone equal temperament / 13edo">13 tone equal temperament / 13edo</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Harmony in 13edo">Harmony in 13edo</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --> | <a href="#Scales in 13edo">Scales in 13edo</a><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --> | <a href="#Animism">Animism</a><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | <a href="#Chuckles McGee's 13-EDO diatonic approaches">Chuckles McGee's 13-EDO diatonic approaches</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --> | <a href="#Mapping to Standard Keyboards">Mapping to Standard Keyboards</a><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc0"><a name="Best approximates 2.5.9.11.13.21"></a><!-- ws:end:WikiTextHeadingRule:8 --><em>Best approximates 2.5.9.11.13.21</em></h1> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc1"><a name="x13 tone equal temperament / 13edo"></a><!-- ws:end:WikiTextHeadingRule:10 -->13 tone equal temperament / 13edo</h1> | ||
13edo refers to a tuning system which divides the octave (frequency ratio 2:1) into 13 equal parts. It is the sixth <a class="wiki_link" href="/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="/11edo">11edo</a> and coming before <a class="wiki_link" href="/17edo">17edo</a>. The steps are of similar size to those of 12edo (albeit squashed), while the intervals between a minor third &amp; major sixth are xenharmonic (not similar to anything available in 12edo).<br /> | 13edo refers to a tuning system which divides the octave (frequency ratio 2:1) into 13 equal parts. It is the sixth <a class="wiki_link" href="/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="/11edo">11edo</a> and coming before <a class="wiki_link" href="/17edo">17edo</a>. The steps are of similar size to those of 12edo (albeit squashed), while the intervals between a minor third &amp; major sixth are xenharmonic (not similar to anything available in 12edo).<br /> | ||
<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');">13 edo chromatic ascending and descending scale on C (MIDI)</a><br /> | <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');">13 edo chromatic ascending and descending scale on C (MIDI)</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc2"><a name="Harmony in 13edo"></a><!-- ws:end:WikiTextHeadingRule:12 -->Harmony in 13edo</h1> | ||
Contrary to popular belief, consonant harmony is possible in 13-EDO, but it requires a radically different approach than that used in 12-EDO (or other Pythagorean or Meantone-based tunings). Trying to approximate the usual major and minor triads of 12-EDO within 13-EDO is usually a disappointment if consonance is the goal; 0-3-7, 0-4-7, 0-3-8, and 0-4-8 are all rather rough in 13-EDO. Typically, the most consonant harmonies do not use a &quot;stack of 3rds&quot; the way they do in 12-TET, since the strongest dissonances in 13-EDO are near the middle of the octave (<u><a class="wiki_link" href="/13edo#top">degree</a>s</u> 6, 7, and 8). Instead, a stack of whole-tones, or a mixture of whole-tones and minor 3rds, often yields good results. For example, one way to view 13-EDO is as a subgroup temperament of harmonics 2.5.9.11.13. It actually performs quite admirably in this regard, and a chord of 0-4-15-19-22 (approximating 4:5:9:11:13) sounds very convincing. An even larger subgroup is the <a class="wiki_link" href="/k%2AN%20subgroups">2*13 subgroup</a> 2.9.5.21.11.13, on which 13 has the same tuning and commas as 26et.<br /> | Contrary to popular belief, consonant harmony is possible in 13-EDO, but it requires a radically different approach than that used in 12-EDO (or other Pythagorean or Meantone-based tunings). Trying to approximate the usual major and minor triads of 12-EDO within 13-EDO is usually a disappointment if consonance is the goal; 0-3-7, 0-4-7, 0-3-8, and 0-4-8 are all rather rough in 13-EDO. Typically, the most consonant harmonies do not use a &quot;stack of 3rds&quot; the way they do in 12-TET, since the strongest dissonances in 13-EDO are near the middle of the octave (<u><a class="wiki_link" href="/13edo#top">degree</a>s</u> 6, 7, and 8). Instead, a stack of whole-tones, or a mixture of whole-tones and minor 3rds, often yields good results. For example, one way to view 13-EDO is as a subgroup temperament of harmonics 2.5.9.11.13. It actually performs quite admirably in this regard, and a chord of 0-4-15-19-22 (approximating 4:5:9:11:13) sounds very convincing. An even larger subgroup is the <a class="wiki_link" href="/k%2AN%20subgroups">2*13 subgroup</a> 2.9.5.21.11.13, on which 13 has the same tuning and commas as 26et.<br /> | ||
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The 2.9.5.11.13 subgroup has commas 45/44, 65/64 and 81/80, leading to a linear temperament with POTE generator 185.728 cents, quite <u><a class="wiki_link" href="/13edo#top">close</a></u> to 2\13. Use this as a generator, and at 7 notes (6L1s) two full pentads are available (as well as two more 4:5:9:11 tetrad, and one 4:5:9:13 tetrad). These triads and tetrads can be assumed to likely be the most consonant base sonorities available in 13 edo and act in a similar way to major/minor triads. However, other sonorities such as orwell chords are avaliable as well.<br /> | The 2.9.5.11.13 subgroup has commas 45/44, 65/64 and 81/80, leading to a linear temperament with POTE generator 185.728 cents, quite <u><a class="wiki_link" href="/13edo#top">close</a></u> to 2\13. Use this as a generator, and at 7 notes (6L1s) two full pentads are available (as well as two more 4:5:9:11 tetrad, and one 4:5:9:13 tetrad). These triads and tetrads can be assumed to likely be the most consonant base sonorities available in 13 edo and act in a similar way to major/minor triads. However, other sonorities such as orwell chords are avaliable as well.<br /> | ||
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Play the 4:5:9 chord: <!-- ws:start:WikiTextMediaRule:2:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%20459%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 459 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+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/"></embed><!-- ws:end:WikiTextMediaRule:2 --><br /> | Play the 4:5:9 (Wholesome) chord: <!-- ws:start:WikiTextMediaRule:2:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%20459%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 459 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+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/"></embed><!-- ws:end:WikiTextMediaRule:2 --><br /> | ||
Play the 4:5:9:11 chord:<br /> | Play the 4:5:9:11 (Wholesome Tetrad) chord: <!-- ws:start:WikiTextMediaRule:3:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%2045911%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 45911 chord.wav&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+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/"></embed><!-- ws:end:WikiTextMediaRule:3 --><br /> | ||
Play the 4:5:9:13 chord:<br /> | Play the 4:5:9:13 chord: <!-- ws:start:WikiTextMediaRule:4:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%2045913%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 45913 chord.wav&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+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/"></embed><!-- ws:end:WikiTextMediaRule:4 --><br /> | ||
Play the 4:5:9:21 chord:<br /> | Play the 4:5:9:21 chord: <!-- ws:start:WikiTextMediaRule:5:&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;&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:5 --><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc3"><a name="Scales in 13edo"></a><!-- ws:end:WikiTextHeadingRule:14 -->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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Another neat facet of 13-EDO is the fact that any 12-EDO scale can be &quot;turned into&quot; a 13-EDO scale by either adding an extra semitone, or turning an existent semitone into a whole-tone. Because of this, melody in 13-EDO can be quite mind-bending and uncanny, and phrases that begin in a familiar way quickly lead to something totally unexpected.<br /> | Another neat facet of 13-EDO is the fact that any 12-EDO scale can be &quot;turned into&quot; a 13-EDO scale by either adding an extra semitone, or turning an existent semitone into a whole-tone. Because of this, melody in 13-EDO can be quite mind-bending and uncanny, and phrases that begin in a familiar way quickly lead to something totally unexpected.<br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc4"><!-- ws:end:WikiTextHeadingRule:16 --> </h2> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc5"><a name="Animism"></a><!-- ws:end:WikiTextHeadingRule:18 -->Animism</h1> | ||
The animist comma, 105/104, appears whenever 3*5*7=13... 13edo does not approximate 3 and 7 individually (26edo does), but 13edo has 21/16 (=3*7) and is also an animist temperament. In 13 edo, the 5th harmonic is tuned so flatly that 5/4 = 16/13, leading to some interesting identities. So two scales stand out through this construction<br /> | The animist comma, 105/104, appears whenever 3*5*7=13... 13edo does not approximate 3 and 7 individually (26edo does), but 13edo has 21/16 (=3*7) and is also an animist temperament. In 13 edo, the 5th harmonic is tuned so flatly that 5/4 = 16/13, leading to some interesting identities. So two scales stand out through this construction<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: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc6"><a name="Chuckles McGee's 13-EDO diatonic approaches"></a><!-- ws:end:WikiTextHeadingRule:20 -->Chuckles McGee's 13-EDO diatonic approaches</h1> | ||
From a temperament perspective, we can probably make the &quot;best&quot; use of 13-EDO as a 2.5.9.11.13.21 subgroup, but assuming our goal is to make reasonably-tonal, triad-based music, we might prefer to think in terms of subsets of this subgroup. The simplest and most accurately-tuned subsets are 2.5.9, 2.5.11, 2.5.13, 2.11.13, and 2.9.21, and for each of these, there is a corresponding MOS generator that is maximally-efficient at producing the desired triad. For 2.5.13, the simplest generator is 4\13, with an octave-equivalent mapping &lt;1 -1| (for 5 and 13), corresponding to the 3rd horagram above. This gives rise to &quot;Sephiroth&quot; modes, in which the generator is any flatly tempered 13th harmonic. For 2.11.13, the simplest generator is 3\13, with an octave-equivalent mapping &lt;2 3| (for 11 and 13). This corresponds to the 2nd horagram above. This scale bears a superficial resemblance to the 9-note MOS of Orwell temperament, although its approximations to the 3rd, 5th, and 7th harmonics are much more distant than in more optimal tunings of the temperament (on the other hand, its approximations to the 11th and 13th harmonics are much better than in optimal tunings of the temperament).<br /> | From a temperament perspective, we can probably make the &quot;best&quot; use of 13-EDO as a 2.5.9.11.13.21 subgroup, but assuming our goal is to make reasonably-tonal, triad-based music, we might prefer to think in terms of subsets of this subgroup. The simplest and most accurately-tuned subsets are 2.5.9, 2.5.11, 2.5.13, 2.11.13, and 2.9.21, and for each of these, there is a corresponding MOS generator that is maximally-efficient at producing the desired triad. For 2.5.13, the simplest generator is 4\13, with an octave-equivalent mapping &lt;1 -1| (for 5 and 13), corresponding to the 3rd horagram above. This gives rise to &quot;Sephiroth&quot; modes, in which the generator is any flatly tempered 13th harmonic. For 2.11.13, the simplest generator is 3\13, with an octave-equivalent mapping &lt;2 3| (for 11 and 13). This corresponds to the 2nd horagram above. This scale bears a superficial resemblance to the 9-note MOS of Orwell temperament, although its approximations to the 3rd, 5th, and 7th harmonics are much more distant than in more optimal tunings of the temperament (on the other hand, its approximations to the 11th and 13th harmonics are much better than in optimal tunings of the temperament).<br /> | ||
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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 /> | ||
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Listen to Ryonian on F#: <!-- ws:start:WikiTextMediaRule: | Listen to Ryonian on F#: <!-- ws:start:WikiTextMediaRule:6:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%20Ryo%20mode.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 Ryo mode.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+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/"></embed><!-- ws:end:WikiTextMediaRule:6 --><br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:783:&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:783 --><br /> | ||
Listen to Dylathian on F#: <!-- ws:start:WikiTextMediaRule: | Listen to Dylathian on F#: <!-- ws:start:WikiTextMediaRule:7:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%208%20tone%20mode%201.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 8 tone mode 1.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+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/"></embed><!-- ws:end:WikiTextMediaRule:7 --><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc7"><a name="Mapping to Standard Keyboards"></a><!-- ws:end:WikiTextHeadingRule:22 -->Mapping to Standard Keyboards</h1> | ||
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 /> | 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 /> | ||
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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.<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 to keep it on the white keys, with the remaining small step where it looks like it should be.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc8"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:24 -->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 /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc9"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:26 --><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><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><br /> | ||