36edo: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 545673762 - Original comment: ** |
Wikispaces>MasonGreen1 **Imported revision 567108037 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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>2015-11-19 14:54:06 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>567108037</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> | ||
| Line 22: | Line 22: | ||
Heinz Bohlen proposed it as a suitable temperament for approximating his 833-cents scale. | Heinz Bohlen proposed it as a suitable temperament for approximating his 833-cents scale. | ||
=**Relation to 12edo**= | |||
For people accustomed to 12edo, 36edo is one of the easiest (if not //the// easiest) higher edo to become accustomed to. This is because one way to envision it is as an extended 12edo to which [[https://en.wikipedia.org/wiki/Blue_note|blue notes]] (which are a sixth-tone lower than normal) and "red notes" (a sixth-tone higher) have been added. | |||
The intervals in 36edo are all either the familiar 12edo intervals, or else "red" and "blue" versions of them. Unlike [[24edo]], which has genuinely foreign intervals such as 250 cents (halfway between a tone and a third) and 450 cents (halfway between a fourth and a third), the new intervals in 36edo all variations on existing ones. Unlike 24edo, 36edo is also relatively free of what Easley Blackwood called "discordant" intervals. | |||
An easy way of notating 36edo (at least for people who aren't colorblind) is to use colors. For example, **A** is 33.333 cents above **<span style="background-color: #6ee8e8; color: #071ac7;">A</span>** and 33.333 cents below **<span style="background-color: #eda2a2; color: #ff0000;">A</span>**. Or the colors could be written out (red A, blue C#, etc.) | |||
Because of the presence of blue notes, and the closeness with which intervals such as 4:7 are matched, 36edo is an ideal scale to use for African-American styles of music such as blues and jazz, in which chords containing the seventh harmonic are frequently used. The 5th and 11th harmonic fall almost halfway in between scale degrees of 36edo, and thus intervals containing them can be approximated two different ways, one of which is significantly sharp and the other significantly flat. The 333.333-cent interval (the "red major third") sharply approximates 5:4 and flatly approximates 9:11, for instance. However, 10:11 and 11:15 are both approximated uniquely, and very closely. | |||
36edo is fairly cosmopolitan because many other genres of world music can be played in it too. Because it contains 9edo as a subset, pelog (and mavila) easily adapt to it. Slendro can be approximated in several different ways. 36edo can function as a "bridge" between these genres and Western music. Arabic music does not adapt as well, however, since many versions contain quarter tones. | |||
The "red unison" and "blue unison" are in fact the same interval (33.333 cents), which is actually fairly consonant as a result of being so narrow (it is perceived as a unison, albeit noticeably "out of tune", but still pleasing). In contrast, the smallest interval in 24edo, which is 50 cents, sounds very bad to most ears. | |||
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. | |||
=Approximations= | =Approximations= | ||
| Line 142: | Line 158: | ||
* [[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:17:&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:17 --><!-- ws:start:WikiTextTocRule:18: --><a href="#As a harmonic temperament">As a harmonic temperament</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Relation to 12edo">Relation to 12edo</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Approximations">Approximations</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:26 -->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 /> | ||
| Line 159: | Line 175: | ||
Heinz Bohlen proposed it as a suitable temperament for approximating his 833-cents scale.<br /> | Heinz Bohlen proposed it as a suitable temperament for approximating his 833-cents scale.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><h1 id="toc1"><a name="Approximations"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><h1 id="toc1"><a name="Relation to 12edo"></a><!-- ws:end:WikiTextHeadingRule:3 --><strong>Relation to 12edo</strong></h1> | ||
<!-- ws:start:WikiTextHeadingRule: | <br /> | ||
For people accustomed to 12edo, 36edo is one of the easiest (if not <em>the</em> easiest) higher edo to become accustomed to. This is because one way to envision it is as an extended 12edo to which <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Blue_note" rel="nofollow">blue notes</a> (which are a sixth-tone lower than normal) and &quot;red notes&quot; (a sixth-tone higher) have been added.<br /> | |||
<br /> | |||
The intervals in 36edo are all either the familiar 12edo intervals, or else &quot;red&quot; and &quot;blue&quot; versions of them. Unlike <a class="wiki_link" href="/24edo">24edo</a>, which has genuinely foreign intervals such as 250 cents (halfway between a tone and a third) and 450 cents (halfway between a fourth and a third), the new intervals in 36edo all variations on existing ones. Unlike 24edo, 36edo is also relatively free of what Easley Blackwood called &quot;discordant&quot; intervals.<br /> | |||
<br /> | |||
An easy way of notating 36edo (at least for people who aren't colorblind) is to use colors. For example, <strong>A</strong> is 33.333 cents above <strong><span style="background-color: #6ee8e8; color: #071ac7;">A</span></strong> and 33.333 cents below <strong><span style="background-color: #eda2a2; color: #ff0000;">A</span></strong>. Or the colors could be written out (red A, blue C#, etc.)<br /> | |||
<br /> | |||
Because of the presence of blue notes, and the closeness with which intervals such as 4:7 are matched, 36edo is an ideal scale to use for African-American styles of music such as blues and jazz, in which chords containing the seventh harmonic are frequently used. The 5th and 11th harmonic fall almost halfway in between scale degrees of 36edo, and thus intervals containing them can be approximated two different ways, one of which is significantly sharp and the other significantly flat. The 333.333-cent interval (the &quot;red major third&quot;) sharply approximates 5:4 and flatly approximates 9:11, for instance. However, 10:11 and 11:15 are both approximated uniquely, and very closely.<br /> | |||
<br /> | |||
36edo is fairly cosmopolitan because many other genres of world music can be played in it too. Because it contains 9edo as a subset, pelog (and mavila) easily adapt to it. Slendro can be approximated in several different ways. 36edo can function as a &quot;bridge&quot; between these genres and Western music. Arabic music does not adapt as well, however, since many versions contain quarter tones.<br /> | |||
<br /> | |||
The &quot;red unison&quot; and &quot;blue unison&quot; are in fact the same interval (33.333 cents), which is actually fairly consonant as a result of being so narrow (it is perceived as a unison, albeit noticeably &quot;out of tune&quot;, but still pleasing). In contrast, the smallest interval in 24edo, which is 50 cents, sounds very bad to most ears.<br /> | |||
<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 /> | |||
<!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id="toc2"><a name="Approximations"></a><!-- ws:end:WikiTextHeadingRule:5 -->Approximations</h1> | |||
<!-- ws:start:WikiTextHeadingRule:7:&lt;h2&gt; --><h2 id="toc3"><a name="Approximations-3-limit (Pythagorean) approximations (same as 12edo):"></a><!-- ws:end:WikiTextHeadingRule:7 -->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 /> | ||
| Line 172: | Line 204: | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:9:&lt;h2&gt; --><h2 id="toc4"><a name="Approximations-7-limit approximations:"></a><!-- ws:end:WikiTextHeadingRule:9 -->7-limit approximations:</h2> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:11:&lt;h3&gt; --><h3 id="toc5"><a name="Approximations-7-limit approximations:-7 only:"></a><!-- ws:end:WikiTextHeadingRule:11 -->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 /> | ||
| Line 180: | Line 212: | ||
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:13:&lt;h3&gt; --><h3 id="toc6"><a name="Approximations-7-limit approximations:-3 and 7:"></a><!-- ws:end:WikiTextHeadingRule:13 -->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 /> | ||
| Line 610: | Line 642: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:15:&lt;h1&gt; --><h1 id="toc7"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:15 -->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> | ||