12edt: Difference between revisions
Wikispaces>genewardsmith **Imported revision 262694422 - Original comment: ** |
Wikispaces>guest **Imported revision 288802419 - 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:guest|guest]] and made on <tt>2011-12-30 00:47:58 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>288802419</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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=A scala formatted description of the tuning= | =A scala formatted description of the tuning= | ||
! C:\Cakewalk\scales\tritave-in-12.scl | ! C:\Cakewalk\scales\tritave-in-12.scl | ||
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[[media type="custom" key="10532830"]] | [[media type="custom" key="10532830"]] | ||
==Compositions | =Exactly analogous to meantone= | ||
In octave land, these simple temperaments, 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 3.13.17 -- 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=13/1. Tempering out the 85293/83521 comma. In fact, even the MOS pattern is the same for this higher limit meantone! Relish the sweet 9:13:17 chords. | |||
Another example of a macrodiatonic scale is [[17ed5|hyperpyth]] which is found in the fifth harmonic and is based on the 5:9:13:(17):(21) chord. | |||
=Compositions= | |||
[[http://www.seraph.it/XenoTunes3.html|Instant Gamelan]] [[http://www.seraph.it/XenoTunes3_files/instant%20gamelan.mp3|play]] by [[Carlo Serafini]] | [[http://www.seraph.it/XenoTunes3.html|Instant Gamelan]] [[http://www.seraph.it/XenoTunes3_files/instant%20gamelan.mp3|play]] by [[Carlo Serafini]] | ||
[[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> | ||
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<!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><h1 id="toc1"><a name="A scala formatted description of the tuning"></a><!-- ws:end:WikiTextHeadingRule:3 -->A scala formatted description of the tuning</h1> | <!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><h1 id="toc1"><a name="A scala formatted description of the tuning"></a><!-- ws:end:WikiTextHeadingRule:3 -->A scala formatted description of the tuning</h1> | ||
<br /> | <br /> | ||
! C:\Cakewalk\scales\tritave-in-12.scl<br /> | ! C:\Cakewalk\scales\tritave-in-12.scl<br /> | ||
!<br /> | !<br /> | ||
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</script><!-- ws:end:WikiTextMediaRule:0 --><br /> | </script><!-- ws:end:WikiTextMediaRule:0 --><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:5:&lt; | <!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id="toc2"><a name="Exactly analogous to meantone"></a><!-- ws:end:WikiTextHeadingRule:5 -->Exactly analogous to meantone</h1> | ||
In octave land, these simple temperaments, 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 3.13.17 -- 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=13/1. Tempering out the 85293/83521 comma. In fact, even the MOS pattern is the same for this higher limit meantone! Relish the sweet 9:13:17 chords.<br /> | |||
<br /> | |||
Another example of a macrodiatonic scale is <a class="wiki_link" href="/17ed5">hyperpyth</a> which is found in the fifth harmonic and is based on the 5:9:13:(17):(21) chord.<br /> | |||
<br /> | |||
<br /> | |||
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<!-- ws:start:WikiTextHeadingRule:7:&lt;h1&gt; --><h1 id="toc3"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:7 -->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> | ||