36edo: Difference between revisions
Wikispaces>MasonGreen1 **Imported revision 567108443 - Original comment: ** |
Wikispaces>MasonGreen1 **Imported revision 567111481 - 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:MasonGreen1|MasonGreen1]] and made on <tt>2015-11-19 | : This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2015-11-19 15:17:47 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>567111481</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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People with perfect (absolute) pitch often have a harder time listening to xenharmonic and non-12edo scales, which is due to their ability to memorize and become accustomed to the pitches and intervals of 12edo (which results in other pitches and intervals sounding bad). This is not as much of a problem with 36edo, due to its similarity to 12. With practice, it might even be possible to extend one's perfect pitch to be able to recognize blue and red notes too. | People with perfect (absolute) pitch often have a harder time listening to xenharmonic and non-12edo scales, which is due to their ability to memorize and become accustomed to the pitches and intervals of 12edo (which results in other pitches and intervals sounding bad). This is not as much of a problem with 36edo, due to its similarity to 12. With practice, it might even be possible to extend one's perfect pitch to be able to recognize blue and red notes too. | ||
==="Quark"=== | |||
In particle physics, [[https://en.wikipedia.org/wiki/Baryon|baryons]] , which are the main building blocks of atomic nuclei, are always comprised of three quarks. One could draw an analogy between baryons and semitones (the main building block of 12edo); the baryon is comprised of three quarks and the semitone of three sixth-tones. The number of quarks in a [[https://en.wikipedia.org/wiki/Color_charge|colorless]] particle is always a multiple of three; similarly, the width of "colorless" intervals (the 12-edo intervals, which are neither red nor blue), expressed in terms of sixth-tones, is always a multiple of three. Because of this amusing coincidence, I (Mason Green) propose referring to the 33.333-cent sixth-tone interval as a "quark". | |||
=Approximations= | =Approximations= | ||
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* [[http://micro.soonlabel.com/36edo/20120418-36edo.mp3|Thoughts in Legolas Tuning]] by [[Chris Vaisvil]]</pre></div> | * [[http://micro.soonlabel.com/36edo/20120418-36edo.mp3|Thoughts in Legolas Tuning]] by [[Chris Vaisvil]]</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>36edo</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>36edo</title></head><body><!-- ws:start:WikiTextTocRule:19:&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:19 --><!-- ws:start:WikiTextTocRule:20: --><a href="#As a harmonic temperament">As a harmonic temperament</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Relation to 12edo">Relation to 12edo</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --> | <a href="#Approximations">Approximations</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:29 -->36edo, by definition, divides the 2:1 octave into 36 equal steps, each of which is exactly 33.333... cents.<br /> | ||
<br /> | <br /> | ||
36 is a highly composite number, factoring into 2x2x3x3. Since 36 is divisible by 12, it contains the overly-familiar <a class="wiki_link" href="/12edo">12edo</a> as a subset. It divides 12edo's 100-cent half step into three microtonal step of approximately 33 cents, which could be called &quot;sixth tones.&quot; 36edo also contains <a class="wiki_link" href="/18edo">18edo</a> (&quot;third tones&quot;) and <a class="wiki_link" href="/9edo">9edo</a> (&quot;two-thirds tones&quot;) as subsets, not to mention the <a class="wiki_link" href="/6edo">6edo</a> whole tone scale, <a class="wiki_link" href="/4edo">4edo</a> full-diminished seventh chord, and the <a class="wiki_link" href="/3edo">3edo</a> augmented triad, all of which are present in 12edo.<br /> | 36 is a highly composite number, factoring into 2x2x3x3. Since 36 is divisible by 12, it contains the overly-familiar <a class="wiki_link" href="/12edo">12edo</a> as a subset. It divides 12edo's 100-cent half step into three microtonal step of approximately 33 cents, which could be called &quot;sixth tones.&quot; 36edo also contains <a class="wiki_link" href="/18edo">18edo</a> (&quot;third tones&quot;) and <a class="wiki_link" href="/9edo">9edo</a> (&quot;two-thirds tones&quot;) as subsets, not to mention the <a class="wiki_link" href="/6edo">6edo</a> whole tone scale, <a class="wiki_link" href="/4edo">4edo</a> full-diminished seventh chord, and the <a class="wiki_link" href="/3edo">3edo</a> augmented triad, all of which are present in 12edo.<br /> | ||
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People with perfect (absolute) pitch often have a harder time listening to xenharmonic and non-12edo scales, which is due to their ability to memorize and become accustomed to the pitches and intervals of 12edo (which results in other pitches and intervals sounding bad). This is not as much of a problem with 36edo, due to its similarity to 12. With practice, it might even be possible to extend one's perfect pitch to be able to recognize blue and red notes too.<br /> | People with perfect (absolute) pitch often have a harder time listening to xenharmonic and non-12edo scales, which is due to their ability to memorize and become accustomed to the pitches and intervals of 12edo (which results in other pitches and intervals sounding bad). This is not as much of a problem with 36edo, due to its similarity to 12. With practice, it might even be possible to extend one's perfect pitch to be able to recognize blue and red notes too.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id=" | <!-- ws:start:WikiTextHeadingRule:5:&lt;h3&gt; --><h3 id="toc2"><a name="Relation to 12edo--&quot;Quark&quot;"></a><!-- ws:end:WikiTextHeadingRule:5 -->&quot;Quark&quot;</h3> | ||
<!-- ws:start:WikiTextHeadingRule: | <br /> | ||
In particle physics, <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Baryon" rel="nofollow">baryons</a> , which are the main building blocks of atomic nuclei, are always comprised of three quarks. One could draw an analogy between baryons and semitones (the main building block of 12edo); the baryon is comprised of three quarks and the semitone of three sixth-tones. The number of quarks in a <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Color_charge" rel="nofollow">colorless</a> particle is always a multiple of three; similarly, the width of &quot;colorless&quot; intervals (the 12-edo intervals, which are neither red nor blue), expressed in terms of sixth-tones, is always a multiple of three. Because of this amusing coincidence, I (Mason Green) propose referring to the 33.333-cent sixth-tone interval as a &quot;quark&quot;.<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:7:&lt;h1&gt; --><h1 id="toc3"><a name="Approximations"></a><!-- ws:end:WikiTextHeadingRule:7 -->Approximations</h1> | |||
<!-- ws:start:WikiTextHeadingRule:9:&lt;h2&gt; --><h2 id="toc4"><a name="Approximations-3-limit (Pythagorean) approximations (same as 12edo):"></a><!-- ws:end:WikiTextHeadingRule:9 -->3-limit (Pythagorean) approximations (same as 12edo):</h2> | |||
<br /> | <br /> | ||
3/2 = 701.955... cents; 21 degrees of 36edo = 700 cents.<br /> | 3/2 = 701.955... cents; 21 degrees of 36edo = 700 cents.<br /> | ||
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<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:11:&lt;h2&gt; --><h2 id="toc5"><a name="Approximations-7-limit approximations:"></a><!-- ws:end:WikiTextHeadingRule:11 -->7-limit approximations:</h2> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:13:&lt;h3&gt; --><h3 id="toc6"><a name="Approximations-7-limit approximations:-7 only:"></a><!-- ws:end:WikiTextHeadingRule:13 -->7 only:</h3> | ||
7/4 = 968.826... cents; 29 degrees of 36edo = 966.666... cents.<br /> | 7/4 = 968.826... cents; 29 degrees of 36edo = 966.666... cents.<br /> | ||
8/7 = 231.174... cents; 7 degrees of 36edo = 233.333... cents.<br /> | 8/7 = 231.174... cents; 7 degrees of 36edo = 233.333... cents.<br /> | ||
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64/49 = 462.348... cents; 14 degrees of 36edo = 466.666... cents.<br /> | 64/49 = 462.348... cents; 14 degrees of 36edo = 466.666... cents.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:15:&lt;h3&gt; --><h3 id="toc7"><a name="Approximations-7-limit approximations:-3 and 7:"></a><!-- ws:end:WikiTextHeadingRule:15 -->3 and 7:</h3> | ||
7/6 = 266.871... cents; 8 degrees of 36edo = 266.666... cents.<br /> | 7/6 = 266.871... cents; 8 degrees of 36edo = 266.666... cents.<br /> | ||
12/7 = 933.129... cents; 28 degrees of 36 = 933.333... cents.<br /> | 12/7 = 933.129... cents; 28 degrees of 36 = 933.333... cents.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:17:&lt;h1&gt; --><h1 id="toc8"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:17 -->Music</h1> | ||
<ul><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/36edo/something.mp3" rel="nofollow">Something</a></span> by <a class="wiki_link" href="/Herman%20Klein">Herman Klein</a></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/36edo/hay.mp3" rel="nofollow">Hay</a></span> by <a class="wiki_link" href="/Joe%20Hayseed">Joe Hayseed</a></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/36edo/boomers.mp3" rel="nofollow">Boomers</a></span> by <a class="wiki_link" href="/Ivan%20Bratt">Ivan Bratt</a><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/9486498?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;9486498&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://webplayer.yahooapis.com/player.js"> | <ul><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/36edo/something.mp3" rel="nofollow">Something</a></span> by <a class="wiki_link" href="/Herman%20Klein">Herman Klein</a></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/36edo/hay.mp3" rel="nofollow">Hay</a></span> by <a class="wiki_link" href="/Joe%20Hayseed">Joe Hayseed</a></li><li><span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/36edo/boomers.mp3" rel="nofollow">Boomers</a></span> by <a class="wiki_link" href="/Ivan%20Bratt">Ivan Bratt</a><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/9486498?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;9486498&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><script type="text/javascript" src="http://webplayer.yahooapis.com/player.js"> | ||
</script><!-- ws:end:WikiTextMediaRule:0 --></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/36edo/20120418-36edo.mp3" rel="nofollow">Thoughts in Legolas Tuning</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li></ul></body></html></pre></div> | </script><!-- ws:end:WikiTextMediaRule:0 --></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/36edo/20120418-36edo.mp3" rel="nofollow">Thoughts in Legolas Tuning</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a></li></ul></body></html></pre></div> | ||