29edo: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 597599498 - Original comment: ** |
Wikispaces>MasonGreen1 **Imported revision 599210802 - 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: | : This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-11-11 15:45:02 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>599210802</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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||= 9801/9800 || | -3 4 -2 -2 2 > ||> 0.17665 ||= Kalisma ||= Gauss' Comma || | ||= 9801/9800 || | -3 4 -2 -2 2 > ||> 0.17665 ||= Kalisma ||= Gauss' Comma || | ||
||= 91/90 || | -1 -2 -1 1 0 1 > ||> 19.130 ||= Superleap ||= || | ||= 91/90 || | -1 -2 -1 1 0 1 > ||> 19.130 ||= Superleap ||= || | ||
==The Tetradecatonic System== | |||
A variant of porcupine supported in 29edo is [[xenharmonic/nautilus|nautilus]], which splits the porcupine generator in half (tempering out 50:49 in the process), thus resulting in a different mapping for 7 than standard porcupine. Nautilus also extends to the 13-limit much more easily than does standard porcupine. | |||
The MOS nautilus[14] contains both "even" tetrads (approximating 4:5:6:7 or its inverse) as well as "odd" tetrads (approximating the "Bohlen-Pierce-like" chord 9:11:13:15, or its inverse). Both types are recognizable and consonant, if somewhat heavily tempered. Moreover, one of the four types of tetrads may be built on **each** scale degree of nautilus[14], thus there are as many chords as there are notes, so nautilus[14] has a "circulating" quality to it with as much freedom of modulation as possible. To be exact, there are 4 "major-even", 4 "minor-even", 3 "major-odd", and 3 "minor-odd" chords. | |||
Fourteen-note MOSes are worth looking at because taking every other note of them gives a heptatonic, and in many cases diatonic-like, scale. Nautilus[14] is no exception; although the resulting porcupine "diatonic" scale sounds somewhat different from diatonic scales generated from fifths, it can still provide some degree of familiarity. Furthermore, every diatonic chord progression will have at least one loose analogue in nautilus[14], although the chord types might change (for instance, it is possible to have a I-IV-V chord progression where the I is major-odd, and the IV and V are both major-even; the V in this case being on a narrow or "odd" fifth rather than a perfect or "even" fifth). | |||
The fact that the generator size is also a step size means that nautilus makes a good candidate for a [[https://en.wikipedia.org/wiki/Generalized_keyboard|generalized keyboard]]; the fingering of nautilus[14] becomes very simple as a result, perhaps even simpler than with traditional keyboards, despite there being more notes. | |||
If one can tolerate the tuning error (which is roughly equal to that of 12edo, albeit in the opposite direction for the 5- and 7-limits), this tetradecatonic scale is worth exploring. 29edo is often neglected since it falls so close to the much more popular and well-studied 31edo, but 29 does have its own advantages, and this is one of them. | |||
=Scales= | =Scales= | ||
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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>29edo</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/29edo">Deutsch</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>29edo</title></head><body><span style="display: block; text-align: right;"><a class="wiki_link" href="http://xenharmonie.wikispaces.com/29edo">Deutsch</a><br /> | ||
</span><br /> | </span><br /> | ||
<!-- ws:start:WikiTextTocRule: | <!-- ws:start:WikiTextTocRule:20:&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:20 --><!-- ws:start:WikiTextTocRule:21: --><a href="#x29 tone equal temperament">29 tone equal temperament</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#Intervals and linear temperaments">Intervals and linear temperaments</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> | <a href="#Scales">Scales</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:31 --><hr /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x29 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #ff4700; font-family: 'Times New Roman',Times,serif; font-size: 113%;">29 tone equal temperament</span></h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x29 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #ff4700; font-family: 'Times New Roman',Times,serif; font-size: 113%;">29 tone equal temperament</span></h1> | ||
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See also: <a class="wiki_link" href="/29edo%20solfege">29edo solfege</a><br /> | See also: <a class="wiki_link" href="/29edo%20solfege">29edo solfege</a><br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:751:&lt;img src=&quot;/file/view/29edothumb.png/277524658/29edothumb.png&quot; alt=&quot;this example in Sagittal notation shows 29-edo as a fifth-tone system.&quot; title=&quot;this example in Sagittal notation shows 29-edo as a fifth-tone system.&quot; /&gt; --><table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/29edothumb.png/277524658/29edothumb.png" alt="29edothumb.png" title="29edothumb.png" /></td></tr><tr><td class="imageCaption">this example in Sagittal notation shows 29-edo as a fifth-tone system.</td></tr></table><!-- ws:end:WikiTextLocalImageRule:751 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Intervals and linear temperaments-Selected just intervals by error"></a><!-- ws:end:WikiTextHeadingRule:4 -->Selected just intervals by error</h2> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Intervals and linear temperaments-Selected just intervals by error"></a><!-- ws:end:WikiTextHeadingRule:4 -->Selected just intervals by error</h2> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id=" | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Commas-The Tetradecatonic System"></a><!-- ws:end:WikiTextHeadingRule:8 -->The Tetradecatonic System</h2> | ||
<br /> | |||
A variant of porcupine supported in 29edo is <a class="wiki_link" href="http://xenharmonic.wikispaces.com/nautilus">nautilus</a>, which splits the porcupine generator in half (tempering out 50:49 in the process), thus resulting in a different mapping for 7 than standard porcupine. Nautilus also extends to the 13-limit much more easily than does standard porcupine.<br /> | |||
<br /> | |||
The MOS nautilus[14] contains both &quot;even&quot; tetrads (approximating 4:5:6:7 or its inverse) as well as &quot;odd&quot; tetrads (approximating the &quot;Bohlen-Pierce-like&quot; chord 9:11:13:15, or its inverse). Both types are recognizable and consonant, if somewhat heavily tempered. Moreover, one of the four types of tetrads may be built on <strong>each</strong> scale degree of nautilus[14], thus there are as many chords as there are notes, so nautilus[14] has a &quot;circulating&quot; quality to it with as much freedom of modulation as possible. To be exact, there are 4 &quot;major-even&quot;, 4 &quot;minor-even&quot;, 3 &quot;major-odd&quot;, and 3 &quot;minor-odd&quot; chords. <br /> | |||
<br /> | |||
Fourteen-note MOSes are worth looking at because taking every other note of them gives a heptatonic, and in many cases diatonic-like, scale. Nautilus[14] is no exception; although the resulting porcupine &quot;diatonic&quot; scale sounds somewhat different from diatonic scales generated from fifths, it can still provide some degree of familiarity. Furthermore, every diatonic chord progression will have at least one loose analogue in nautilus[14], although the chord types might change (for instance, it is possible to have a I-IV-V chord progression where the I is major-odd, and the IV and V are both major-even; the V in this case being on a narrow or &quot;odd&quot; fifth rather than a perfect or &quot;even&quot; fifth).<br /> | |||
<br /> | |||
The fact that the generator size is also a step size means that nautilus makes a good candidate for a <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Generalized_keyboard" rel="nofollow">generalized keyboard</a>; the fingering of nautilus[14] becomes very simple as a result, perhaps even simpler than with traditional keyboards, despite there being more notes.<br /> | |||
<br /> | |||
If one can tolerate the tuning error (which is roughly equal to that of 12edo, albeit in the opposite direction for the 5- and 7-limits), this tetradecatonic scale is worth exploring. 29edo is often neglected since it falls so close to the much more popular and well-studied 31edo, but 29 does have its own advantages, and this is one of them.<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:10 -->Scales</h1> | |||
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/bridgetown9">bridgetown9</a><br /> | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bridgetown9">bridgetown9</a><br /> | ||
<a class="wiki_link" href="http://xenharmonic.wikispaces.com/bridgetown14">bridgetown14</a><br /> | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/bridgetown14">bridgetown14</a><br /> | ||
<a class="wiki_link_ext" href="http://www.youtube.com/watch?v=uP2Z4Gy8lds" rel="nofollow">Escala Tonal de 17 tonos - Charles Loli</a><br /> | <a class="wiki_link_ext" href="http://www.youtube.com/watch?v=uP2Z4Gy8lds" rel="nofollow">Escala Tonal de 17 tonos - Charles Loli</a><br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:12 -->Music</h1> | ||
<a class="wiki_link_ext" href="http://www.microtonalismo.com/el-teclado-29-edo" rel="nofollow">Mp3 29EDO - Escala tonal de 17 notas</a>by <a class="wiki_link_ext" href="http://musicool.us/musicool/armonia.htm" rel="nofollow">Charles Loli A.</a><br /> | <a class="wiki_link_ext" href="http://www.microtonalismo.com/el-teclado-29-edo" rel="nofollow">Mp3 29EDO - Escala tonal de 17 notas</a>by <a class="wiki_link_ext" href="http://musicool.us/musicool/armonia.htm" rel="nofollow">Charles Loli A.</a><br /> | ||
<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/Paint%20in%20the%20Water%2029.mp3" rel="nofollow">Paint in the Water 29</a> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/IgliashonJones">Igliashon Jones</a><br /> | <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/Paint%20in%20the%20Water%2029.mp3" rel="nofollow">Paint in the Water 29</a> by <a class="wiki_link" href="http://xenharmonic.wikispaces.com/IgliashonJones">Igliashon Jones</a><br /> | ||
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<a class="wiki_link_ext" href="http://www.angelfire.com/mo/oljare/images/stranded.mid" rel="nofollow">Stranded at Sea</a> by Mats Öljare<br /> | <a class="wiki_link_ext" href="http://www.angelfire.com/mo/oljare/images/stranded.mid" rel="nofollow">Stranded at Sea</a> by Mats Öljare<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Music-Instruments"></a><!-- ws:end:WikiTextHeadingRule:14 -->Instruments</h2> | ||
<a class="wiki_link_ext" href="http://www.microtonalismo.com/" rel="nofollow" target="_blank">Guitar 29EDO</a><br /> | <a class="wiki_link_ext" href="http://www.microtonalismo.com/" rel="nofollow" target="_blank">Guitar 29EDO</a><br /> | ||
<ul><li><!-- ws:start:WikiTextHeadingRule: | <ul><li><!-- ws:start:WikiTextHeadingRule:16:&lt;h4&gt; --><h4 id="toc8"><a name="Music-Instruments--Guitar 29EDO from Peruvian - Charles Loli and Antonio Huamani"></a><!-- ws:end:WikiTextHeadingRule:16 --><strong><a class="wiki_link_ext" href="http://www.microtonalismo.com/proyecto-xvii" rel="nofollow">Guitar 29EDO from Peruvian - Charles Loli and Antonio Huamani</a></strong></h4> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:752:&lt;img src=&quot;http://content.pimp-my-profile.com/i116/2/10/29/f_735065b21747.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 891px; width: 321px;&quot; /&gt; --><img src="http://content.pimp-my-profile.com/i116/2/10/29/f_735065b21747.jpg" alt="external image f_735065b21747.jpg" title="external image f_735065b21747.jpg" style="height: 891px; width: 321px;" /><!-- ws:end:WikiTextRemoteImageRule:752 --></li></ul><br /> | ||
<a class="wiki_link_ext" href="http://www.microtonalismo.com/" rel="nofollow" target="_blank">Bass 29EDO</a><br /> | <a class="wiki_link_ext" href="http://www.microtonalismo.com/" rel="nofollow" target="_blank">Bass 29EDO</a><br /> | ||
<ul><li><!-- ws:start:WikiTextHeadingRule: | <ul><li><!-- ws:start:WikiTextHeadingRule:18:&lt;h4&gt; --><h4 id="toc9"><a name="Music-Instruments--Bass 29EDO from Peruvian - Charles Loli and Antonio Huamani"></a><!-- ws:end:WikiTextHeadingRule:18 --><strong><a class="wiki_link_ext" href="http://www.microtonalismo.com/proyecto-xvii" rel="nofollow">Bass 29EDO from Peruvian - Charles Loli and Antonio Huamani</a></strong></h4> | ||
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