26edo: Difference between revisions
Wikispaces>guest **Imported revision 121781907 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 155550183 - Original comment: ** |
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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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2010-08-07 14:11:49 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>155550183</tt>.<br> | ||
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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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3. 26-EDO nearly perfectly approximates the 7th and 11th harmonics, and an entire system may be constructed analogous to that based on the 3rd and 5th harmonics. The resulting scale is jagged, and it perverts common musical rules and conventions, but this particular organisation has its charm -perhaps because of this- and leads to some intriguing music. | 3. 26-EDO nearly perfectly approximates the 7th and 11th harmonics, and an entire system may be constructed analogous to that based on the 3rd and 5th harmonics. The resulting scale is jagged, and it perverts common musical rules and conventions, but this particular organisation has its charm -perhaps because of this- and leads to some intriguing music. | ||
- K.</pre></div> | - K. | ||
=Orgone Temperament= | |||
[[user:Andrew_Heathwaite|1281204709]] proposes a temperament family which takes advantage of 26edo's excellent 11 & 7 approximations. 7 degrees of 26edo is a wide minor third of approximately 323.077 cents, and that interval taken as a generator produces 7-tone and 11-tone MOS scales: | |||
The 7-tone scale in degrees-in-between: 5 2 5 2 5 2 5. | |||
The 7-tone scale in cents: 0 231 323 554 646 877 969 1200. | |||
The 11-tone scale in degrees-in-between: 2 3 2 2 3 2 3 2 2 3 2. | |||
The 11-tone scale in cents: 0 92 231 323 415 554 646 785 877 969 1108. | |||
The primary triad for Orgone temperament is 8:11:14 and its subharmonic inversion, which these scales have in abundance. I would define any temperament where 2g approximates 16/11 and 3g approximates 7/4 as Orgone. [[37edo]] is another excellent Orgone tuning. | |||
If a name already exists for this temperament, I'd be interested to know about it. As far as I know, temperaments which ignore lower primes (in this case 3 and 5) in favor of higher ones (in this case 7 and 11) are still largely uncharted, but I am interested in finding out if someone has walked this path before.</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>26edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:0 -->Compositions</h1> | <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>26edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:0 -->Compositions</h1> | ||
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3. 26-EDO nearly perfectly approximates the 7th and 11th harmonics, and an entire system may be constructed analogous to that based on the 3rd and 5th harmonics. The resulting scale is jagged, and it perverts common musical rules and conventions, but this particular organisation has its charm -perhaps because of this- and leads to some intriguing music.<br /> | 3. 26-EDO nearly perfectly approximates the 7th and 11th harmonics, and an entire system may be constructed analogous to that based on the 3rd and 5th harmonics. The resulting scale is jagged, and it perverts common musical rules and conventions, but this particular organisation has its charm -perhaps because of this- and leads to some intriguing music.<br /> | ||
<br /> | <br /> | ||
- K.</body></html></pre></div> | - K.<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Orgone Temperament"></a><!-- ws:end:WikiTextHeadingRule:4 -->Orgone Temperament</h1> | |||
<!-- ws:start:WikiTextUserlinkRule:00:[[user:Andrew_Heathwaite|1281204709]] --><span class="membersnap">- <a class="userLink" href="http://www.wikispaces.com/user/view/Andrew_Heathwaite" style="outline: none;"><img src="http://www.wikispaces.com/user/pic/Andrew_Heathwaite-lg.jpg" width="16" height="16" alt="Andrew_Heathwaite" class="userPicture" /></a> <a class="userLink" href="http://www.wikispaces.com/user/view/Andrew_Heathwaite" style="outline: none;">Andrew_Heathwaite</a> <small>Aug 7, 2010</small></span><!-- ws:end:WikiTextUserlinkRule:00 --> proposes a temperament family which takes advantage of 26edo's excellent 11 &amp; 7 approximations. 7 degrees of 26edo is a wide minor third of approximately 323.077 cents, and that interval taken as a generator produces 7-tone and 11-tone MOS scales:<br /> | |||
<br /> | |||
The 7-tone scale in degrees-in-between: 5 2 5 2 5 2 5.<br /> | |||
The 7-tone scale in cents: 0 231 323 554 646 877 969 1200.<br /> | |||
<br /> | |||
The 11-tone scale in degrees-in-between: 2 3 2 2 3 2 3 2 2 3 2.<br /> | |||
The 11-tone scale in cents: 0 92 231 323 415 554 646 785 877 969 1108.<br /> | |||
<br /> | |||
The primary triad for Orgone temperament is 8:11:14 and its subharmonic inversion, which these scales have in abundance. I would define any temperament where 2g approximates 16/11 and 3g approximates 7/4 as Orgone. <a class="wiki_link" href="/37edo">37edo</a> is another excellent Orgone tuning.<br /> | |||
<br /> | |||
If a name already exists for this temperament, I'd be interested to know about it. As far as I know, temperaments which ignore lower primes (in this case 3 and 5) in favor of higher ones (in this case 7 and 11) are still largely uncharted, but I am interested in finding out if someone has walked this path before.</body></html></pre></div> | |||