EDO: Difference between revisions
Wikispaces>genewardsmith **Imported revision 244521297 - Original comment: ** |
Wikispaces>Kosmorsky **Imported revision 245821255 - 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:Kosmorsky|Kosmorsky]] and made on <tt>2011-08-13 22:50:26 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>245821255</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 abbreviation **EDO** stands for **[[Equal]] Divisions of the [[Octave]]** (not to be confused with the [[http://en.wikipedia.org/wiki/Edo_period|Edo period]] in Japanese history). | The abbreviation **EDO** stands for **[[Equal]] Divisions of the [[Octave]]** (not to be confused with the [[http://en.wikipedia.org/wiki/Edo_period|Edo period]] in Japanese history). | ||
= EDO FAQ = | =EDO FAQ= | ||
==What are EDO scales like?== | ==What are EDO scales like?== | ||
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The [[MOSScales|Moments of Symmetry]] paradigm is a fascinating way of thinking about building sub-scales of EDOs and relating them to non-EDO scales, as well as finding common melodic patterns between multiple EDOs. | The [[MOSScales|Moments of Symmetry]] paradigm is a fascinating way of thinking about building sub-scales of EDOs and relating them to non-EDO scales, as well as finding common melodic patterns between multiple EDOs. | ||
Interesting phenomena may be observed when adding the cardinality of one equal division to that of another (octave or not). Most obviously, an interval that they both approximate will also be approximated. (Since there is only one sum, you could call this "Chinese Parenting" har har har). Taking this further, any MOS they both support, may be found in the child - this is because of the nature of the Moment of SymmetryrtemmyS fo tnemoM as a X(L)+Y(s). The breakthrough here would be figuring out mathematically how multiple-limit harmony interacts rather than the dual-limit perspective of MOSes, but that is more important and less immediately obvious. | |||
Dissimilar pairings have less mathematically well defined (yet) results. FFFF pointed out that 15+16=31, which triggered my insight. The tip of the iceberg in this example is that 15edo, a multiple of 5, tunes the fifth sharp 20 cents and 16 edo tunes the fifth flat 25 cents. More importantly would be the higher limit implications, and the route of tempering between them (and thus, I suspect, the mood) are hybrid too, though certainly not chimeric. While many pairs add up to the same number, it seems that in each case that heritage could be seen as relevant. | |||
When an edo divides the octave into fewer than 12 divisions (so that each step exceeds 100 cents), you might call it a [[macrotonal edos|macrotonal edo]]. Of these, 1, 2, 3, 4 and 6 divide 12 and so are already available to anyone wishing to explore them. The 5, 7 and 9 edos have arguably been used in various kinds of musical traditions in different parts of the world. | When an edo divides the octave into fewer than 12 divisions (so that each step exceeds 100 cents), you might call it a [[macrotonal edos|macrotonal edo]]. Of these, 1, 2, 3, 4 and 6 divide 12 and so are already available to anyone wishing to explore them. The 5, 7 and 9 edos have arguably been used in various kinds of musical traditions in different parts of the world. | ||
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* [[http://www.webcitation.org/5xZz8RtQB|Teen Tunes]] by [[Ivor Darreg]]</pre></div> | * [[http://www.webcitation.org/5xZz8RtQB|Teen Tunes]] by [[Ivor Darreg]]</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>EDO</title></head><body><!-- ws:start:WikiTextTocRule:14:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><div style="margin-left: 1em;"><a href="#EDO FAQ"> EDO FAQ </a></div> | <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>EDO</title></head><body><!-- ws:start:WikiTextTocRule:14:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><div style="margin-left: 1em;"><a href="#EDO FAQ">EDO FAQ</a></div> | ||
<!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --><div style="margin-left: 2em;"><a href="#EDO FAQ-What are EDO scales like?">What are EDO scales like?</a></div> | <!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --><div style="margin-left: 2em;"><a href="#EDO FAQ-What are EDO scales like?">What are EDO scales like?</a></div> | ||
<!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><div style="margin-left: 2em;"><a href="#EDO FAQ-Why would I want to use an EDO?">Why would I want to use an EDO?</a></div> | <!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><div style="margin-left: 2em;"><a href="#EDO FAQ-Why would I want to use an EDO?">Why would I want to use an EDO?</a></div> | ||
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<!-- ws:end:WikiTextTocRule:22 -->The abbreviation <strong>EDO</strong> stands for <strong><a class="wiki_link" href="/Equal">Equal</a> Divisions of the <a class="wiki_link" href="/Octave">Octave</a></strong> (not to be confused with the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Edo_period" rel="nofollow">Edo period</a> in Japanese history).<br /> | <!-- ws:end:WikiTextTocRule:22 -->The abbreviation <strong>EDO</strong> stands for <strong><a class="wiki_link" href="/Equal">Equal</a> Divisions of the <a class="wiki_link" href="/Octave">Octave</a></strong> (not to be confused with the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Edo_period" rel="nofollow">Edo period</a> in Japanese history).<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="EDO FAQ"></a><!-- ws:end:WikiTextHeadingRule:0 --> EDO FAQ </h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="EDO FAQ"></a><!-- ws:end:WikiTextHeadingRule:0 -->EDO FAQ</h1> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="EDO FAQ-What are EDO scales like?"></a><!-- ws:end:WikiTextHeadingRule:2 -->What are EDO scales like?</h2> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="EDO FAQ-What are EDO scales like?"></a><!-- ws:end:WikiTextHeadingRule:2 -->What are EDO scales like?</h2> | ||
<br /> | <br /> | ||
Very straightforward to work with, the step size being so even and all. Some find the monotony bland, others find it a safe stable footing for musicmaking. The only property shared by all of them is the equality of their step-sizes; otherwise, their individual properties are as different as can be. The lower-numbered EDOs, especially 5 to 24, possess very strong and unique &quot;characters&quot;, which some composers have found to be inspiring in their own right.<br /> | Very straightforward to work with, the step size being so even and all. Some find the monotony bland, others find it a safe stable footing for musicmaking. The only property shared by all of them is the equality of their step-sizes; otherwise, their individual properties are as different as can be. The lower-numbered EDOs, especially 5 to 24, possess very strong and unique &quot;characters&quot;, which some composers have found to be inspiring in their own right.<br /> | ||
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<br /> | <br /> | ||
The <a class="wiki_link" href="/MOSScales">Moments of Symmetry</a> paradigm is a fascinating way of thinking about building sub-scales of EDOs and relating them to non-EDO scales, as well as finding common melodic patterns between multiple EDOs.<br /> | The <a class="wiki_link" href="/MOSScales">Moments of Symmetry</a> paradigm is a fascinating way of thinking about building sub-scales of EDOs and relating them to non-EDO scales, as well as finding common melodic patterns between multiple EDOs.<br /> | ||
<br /> | |||
Interesting phenomena may be observed when adding the cardinality of one equal division to that of another (octave or not). Most obviously, an interval that they both approximate will also be approximated. (Since there is only one sum, you could call this &quot;Chinese Parenting&quot; har har har). Taking this further, any MOS they both support, may be found in the child - this is because of the nature of the Moment of SymmetryrtemmyS fo tnemoM as a X(L)+Y(s). The breakthrough here would be figuring out mathematically how multiple-limit harmony interacts rather than the dual-limit perspective of MOSes, but that is more important and less immediately obvious.<br /> | |||
<br /> | |||
Dissimilar pairings have less mathematically well defined (yet) results. FFFF pointed out that 15+16=31, which triggered my insight. The tip of the iceberg in this example is that 15edo, a multiple of 5, tunes the fifth sharp 20 cents and 16 edo tunes the fifth flat 25 cents. More importantly would be the higher limit implications, and the route of tempering between them (and thus, I suspect, the mood) are hybrid too, though certainly not chimeric. While many pairs add up to the same number, it seems that in each case that heritage could be seen as relevant.<br /> | |||
<br /> | <br /> | ||
When an edo divides the octave into fewer than 12 divisions (so that each step exceeds 100 cents), you might call it a <a class="wiki_link" href="/macrotonal%20edos">macrotonal edo</a>. Of these, 1, 2, 3, 4 and 6 divide 12 and so are already available to anyone wishing to explore them. The 5, 7 and 9 edos have arguably been used in various kinds of musical traditions in different parts of the world.<br /> | When an edo divides the octave into fewer than 12 divisions (so that each step exceeds 100 cents), you might call it a <a class="wiki_link" href="/macrotonal%20edos">macrotonal edo</a>. Of these, 1, 2, 3, 4 and 6 divide 12 and so are already available to anyone wishing to explore them. The 5, 7 and 9 edos have arguably been used in various kinds of musical traditions in different parts of the world.<br /> | ||