12edt: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 596362996 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 596363030 - 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:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-21 14:26: | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-21 14:26:52 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>596363030</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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1743.45875 | 1743.45875 | ||
3/1 | 3/1 | ||
=Exactly analogous to meantone= | =Exactly analogous to meantone= | ||
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[[http://micro.soonlabel.com/tritave_in_12/tritavein12_cleaned.mp3|Tritave in 12]] by [[@http://www.chrisvaisvil.com|Chris Vaisvil]]</pre></div> | [[http://micro.soonlabel.com/tritave_in_12/tritavein12_cleaned.mp3|Tritave in 12]] by [[@http://www.chrisvaisvil.com|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>12edt</title></head><body><!-- ws:start:WikiTextHeadingRule: | <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>12edt</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Division of the tritave (3/1) into 12 equal parts"></a><!-- ws:end:WikiTextHeadingRule:0 -->Division of the tritave (3/1) into 12 equal parts</h1> | ||
12edt divides 3, the tritave, into 12 equal parts of 158.496 cents each, corresponding to 7.571 edo, and can be used as a generator chain for <a class="wiki_link" href="/Kleismic%20family#Hemikleismic">hemikleismic temperament</a>. From a no-twos point of view, it tempers out 49/45 and 27/25 in the 7-limit, and 1331/1125 and 1331/1225 in the 11-limit.<br /> | 12edt divides 3, the tritave, into 12 equal parts of 158.496 cents each, corresponding to 7.571 edo, and can be used as a generator chain for <a class="wiki_link" href="/Kleismic%20family#Hemikleismic">hemikleismic temperament</a>. From a no-twos point of view, it tempers out 49/45 and 27/25 in the 7-limit, and 1331/1125 and 1331/1225 in the 11-limit.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="A scala formatted description of the tuning"></a><!-- ws:end:WikiTextHeadingRule:2 -->A scala formatted description of the tuning</h1> | ||
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! C:\Cakewalk\scales\tritave-in-12.scl<br /> | ! C:\Cakewalk\scales\tritave-in-12.scl<br /> | ||
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3/1<br /> | 3/1<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Exactly analogous to meantone"></a><!-- ws:end:WikiTextHeadingRule:4 -->Exactly analogous to meantone</h1> | |||
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In octave land, 12edo handles the 2.3.5 subgroup and 11edo handles the 2.7.11 subgroup - ie. meantone and orgone temperaments. In tritave land however, 13edt handles the 3.5.7 territory (Bohlen-Pierce) and 12edt handles the 2.3.5.13.17.19 -- AND! it is a multiple of 4edt which is the simplest BP equal temperament. Now, exactly analogous to meantone, in which (3/2)^4=5/1, here (17/9)^4=(19/10)^4=13/1, tempering out the 171/170, 85293/83521 and 130321/130000 commas. In fact, even the MOS pattern is the same for this higher limit meantone! Relish the sweet 9:13:17 and 20:27:38 chords.<br /> | In octave land, 12edo handles the 2.3.5 subgroup and 11edo handles the 2.7.11 subgroup - ie. meantone and orgone temperaments. In tritave land however, 13edt handles the 3.5.7 territory (Bohlen-Pierce) and 12edt handles the 2.3.5.13.17.19 -- AND! it is a multiple of 4edt which is the simplest BP equal temperament. Now, exactly analogous to meantone, in which (3/2)^4=5/1, here (17/9)^4=(19/10)^4=13/1, tempering out the 171/170, 85293/83521 and 130321/130000 commas. In fact, even the MOS pattern is the same for this higher limit meantone! Relish the sweet 9:13:17 and 20:27:38 chords.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:6 -->Compositions</h1> | ||
<a class="wiki_link_ext" href="http://www.seraph.it/XenoTunes3.html" rel="nofollow">Instant Gamelan</a> <a class="wiki_link_ext" href="http://www.seraph.it/XenoTunes3_files/instant%20gamelan.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a><br /> | <a class="wiki_link_ext" href="http://www.seraph.it/XenoTunes3.html" rel="nofollow">Instant Gamelan</a> <a class="wiki_link_ext" href="http://www.seraph.it/XenoTunes3_files/instant%20gamelan.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a><br /> | ||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/tritave_in_12/tritavein12_cleaned.mp3" rel="nofollow">Tritave in 12</a> by <a class="wiki_link_ext" href="http://www.chrisvaisvil.com" rel="nofollow" target="_blank">Chris Vaisvil</a></body></html></pre></div> | <a class="wiki_link_ext" href="http://micro.soonlabel.com/tritave_in_12/tritavein12_cleaned.mp3" rel="nofollow">Tritave in 12</a> by <a class="wiki_link_ext" href="http://www.chrisvaisvil.com" rel="nofollow" target="_blank">Chris Vaisvil</a></body></html></pre></div> | ||