29edo: Difference between revisions
Wikispaces>hstraub **Imported revision 614182467 - 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:hstraub|hstraub]] and made on <tt>2017-06- | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2017-06-10 07:46:47 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>614499797</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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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. | 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. | ||
[[media type="file" key="Nautilus14_29edo.mp3"]] | |||
Nautilus[14] scale (Lsssssssssssss) in 29edo | |||
=Nicetone= | =Nicetone= | ||
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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:23:&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:23 --><!-- ws:start:WikiTextTocRule:24: --><a href="#x29 tone equal temperament">29 tone equal temperament</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | <a href="#Intervals and linear temperaments">Intervals and linear temperaments</a><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <a href="#The Tetradecatonic System">The Tetradecatonic System</a><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --> | <a href="#Nicetone">Nicetone</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#Scales">Scales</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:35 --><hr /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:1:&lt;h1&gt; --><h1 id="toc0"><a name="x29 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:1 --><span style="color: #ff4700; font-family: 'Times New Roman',Times,serif; font-size: 113%;">29 tone equal temperament</span></h1> | ||
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29edo divides the 2:1 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/octave">octave</a> into 29 equal steps of approximately 41.37931 <a class="wiki_link" href="/cent">cents</a>. It is the 10th <a class="wiki_link" href="/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="/23edo">23edo</a> and coming before <a class="wiki_link" href="/31edo">31edo</a>.<br /> | 29edo divides the 2:1 <a class="wiki_link" href="http://xenharmonic.wikispaces.com/octave">octave</a> into 29 equal steps of approximately 41.37931 <a class="wiki_link" href="/cent">cents</a>. It is the 10th <a class="wiki_link" href="/prime%20numbers">prime</a> edo, following <a class="wiki_link" href="/23edo">23edo</a> and coming before <a class="wiki_link" href="/31edo">31edo</a>.<br /> | ||
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A more coincidental similarity is that just as the 12-tone scale is also a 1/2-tone scale (the whole tone being divided into 2 semitones), the 29-tone temperament may also be called 2/9-tone. This is because it has two different sizes of whole tone (4 and 5 steps wide, respectively). So the step size of 29edo may be called a 2/9-tone, just as 24edo's step size is called a quarter tone.<br /> | A more coincidental similarity is that just as the 12-tone scale is also a 1/2-tone scale (the whole tone being divided into 2 semitones), the 29-tone temperament may also be called 2/9-tone. This is because it has two different sizes of whole tone (4 and 5 steps wide, respectively). So the step size of 29edo may be called a 2/9-tone, just as 24edo's step size is called a quarter tone.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><h1 id="toc1"><a name="Intervals and linear temperaments"></a><!-- ws:end:WikiTextHeadingRule:3 -->Intervals and linear temperaments</h1> | ||
<a class="wiki_link" href="/List%20of%2029et%20rank%20two%20temperaments%20by%20badness">List of 29et rank two temperaments by badness</a><br /> | <a class="wiki_link" href="/List%20of%2029et%20rank%20two%20temperaments%20by%20badness">List of 29et rank two temperaments by badness</a><br /> | ||
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Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs">Ups and Downs Notation - Chord names in other EDOs</a>.<br /> | Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs">Ups and Downs Notation - Chord names in other EDOs</a>.<br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:947:&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:947 --><br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:5:&lt;h2&gt; --><h2 id="toc2"><a name="Intervals and linear temperaments-Selected just intervals by error"></a><!-- ws:end:WikiTextHeadingRule:5 -->Selected just intervals by error</h2> | ||
The following table shows how <a class="wiki_link" href="/Just-24">some prominent just intervals</a> are represented in 29edo (ordered by absolute error).<br /> | The following table shows how <a class="wiki_link" href="/Just-24">some prominent just intervals</a> are represented in 29edo (ordered by absolute error).<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:7:&lt;h1&gt; --><h1 id="toc3"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:7 -->Commas</h1> | ||
29 EDO tempers out the following commas. (Note: This assumes the val &lt; <a class="wiki_link" href="http://tel.wikispaces.com/29%2046%2067%2081%20100%20107">29 46 67 81 100 107</a> |, cent values rounded to 5 digits.)<br /> | 29 EDO tempers out the following commas. (Note: This assumes the val &lt; <a class="wiki_link" href="http://tel.wikispaces.com/29%2046%2067%2081%20100%20107">29 46 67 81 100 107</a> |, cent values rounded to 5 digits.)<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:9:&lt;h1&gt; --><h1 id="toc4"><a name="The Tetradecatonic System"></a><!-- ws:end:WikiTextHeadingRule:9 -->The Tetradecatonic System</h1> | ||
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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 /> | 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 /> | ||
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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 /> | 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 /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/Nautilus14_29edo.mp3?h=20&amp;w=240&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;Nautilus14_29edo.mp3&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;20&quot; width=&quot;240&quot;/&gt; --><embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252FNautilus14_29edo.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=240&height=20"></embed><!-- ws:end:WikiTextMediaRule:0 --><br /> | ||
Nautilus[14] scale (Lsssssssssssss) in 29edo<br /> | |||
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<!-- ws:start:WikiTextHeadingRule:11:&lt;h1&gt; --><h1 id="toc5"><a name="Nicetone"></a><!-- ws:end:WikiTextHeadingRule:11 -->Nicetone</h1> | |||
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29edo is not a meantone system, but it could nonetheless be used as a basis for common-practice music if one considers the superfourth as a consonant, alternative type of fourth, and the 11:13:16 as an alternative type of consonant &quot;doubly minor&quot; triad. We can then use a diatonic scale such as 5435453 (which resembles Didymus' 5-limit JI diatonic scale, but with the syntonic comma being exaggerated in size). This scale has a very similar harmonic structure to a meantone diatonic scale, except that one of its minor triads is doubly-minor.<br /> | 29edo is not a meantone system, but it could nonetheless be used as a basis for common-practice music if one considers the superfourth as a consonant, alternative type of fourth, and the 11:13:16 as an alternative type of consonant &quot;doubly minor&quot; triad. We can then use a diatonic scale such as 5435453 (which resembles Didymus' 5-limit JI diatonic scale, but with the syntonic comma being exaggerated in size). This scale has a very similar harmonic structure to a meantone diatonic scale, except that one of its minor triads is doubly-minor.<br /> | ||
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Such a scale could be called &quot;nicetone&quot; as a play on meantone. Since it preserves most of the same 5-limit relationships, nicetone is only slightly xenharmonic (in contrast to <a class="wiki_link" href="/superpyth">superpyth</a>, which is quite blatantly so). The fact that 29edo's superfourth is within a cent of 15:11, and its 13:11 is within half a cent of a just 13:11, are both happy accidents. One just has to make that one is using a timbre that allows these higher-limit harmonic relationships to sound apparent and consonant enough to substitute for their simpler counterparts.<br /> | Such a scale could be called &quot;nicetone&quot; as a play on meantone. Since it preserves most of the same 5-limit relationships, nicetone is only slightly xenharmonic (in contrast to <a class="wiki_link" href="/superpyth">superpyth</a>, which is quite blatantly so). The fact that 29edo's superfourth is within a cent of 15:11, and its 13:11 is within half a cent of a just 13:11, are both happy accidents. One just has to make that one is using a timbre that allows these higher-limit harmonic relationships to sound apparent and consonant enough to substitute for their simpler counterparts.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:13:&lt;h1&gt; --><h1 id="toc6"><a name="Scales"></a><!-- ws:end:WikiTextHeadingRule:13 -->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:15:&lt;h1&gt; --><h1 id="toc7"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:15 -->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 /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:17:&lt;h2&gt; --><h2 id="toc8"><a name="Music-Instruments"></a><!-- ws:end:WikiTextHeadingRule:17 -->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:19:&lt;h4&gt; --><h4 id="toc9"><a name="Music-Instruments--Guitar 29EDO from Peruvian - Charles Loli and Antonio Huamani"></a><!-- ws:end:WikiTextHeadingRule:19 --><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> | ||
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<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:21:&lt;h4&gt; --><h4 id="toc10"><a name="Music-Instruments--Bass 29EDO from Peruvian - Charles Loli and Antonio Huamani"></a><!-- ws:end:WikiTextHeadingRule:21 --><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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