18edo: Difference between revisions
Wikispaces>Kosmorsky **Imported revision 430231004 - Original comment: ** |
Wikispaces>Kosmorsky **Imported revision 430237910 - 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:Kosmorsky|Kosmorsky]] and made on <tt>2013-05-09 11: | : This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2013-05-09 11:58:38 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>430237910</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 14: | Line 14: | ||
In order to access the excellent consonances actually available, one must take a considerably "non-common-practice" approach, meaning to avoid the usual closed-voice "root-3rd-5th" type of chord and instead use chords which are either more compressed or more stretched out. 18-EDO may be treated as a temperament of the 17-limit [[k*N subgroups|4*18 subgroup]] [[Just intonation subgroups|just intonation subgroup]] 2.9.75.21.55.39.51. On this subgroup it tempers out exactly the same commas as 72 does on the full [[17-limit]], and gives precisely the same tunings. The subgroup can be put into a single chord, for example 32:36:39:42:51:55:64:75 (in terms of 18edo, 0-3-5-7-12-14-18-22), and transpositions and inversions of this chord or its subchords provide plenty of harmonic resources. | In order to access the excellent consonances actually available, one must take a considerably "non-common-practice" approach, meaning to avoid the usual closed-voice "root-3rd-5th" type of chord and instead use chords which are either more compressed or more stretched out. 18-EDO may be treated as a temperament of the 17-limit [[k*N subgroups|4*18 subgroup]] [[Just intonation subgroups|just intonation subgroup]] 2.9.75.21.55.39.51. On this subgroup it tempers out exactly the same commas as 72 does on the full [[17-limit]], and gives precisely the same tunings. The subgroup can be put into a single chord, for example 32:36:39:42:51:55:64:75 (in terms of 18edo, 0-3-5-7-12-14-18-22), and transpositions and inversions of this chord or its subchords provide plenty of harmonic resources. | ||
However, less accurate approximations can be used. 18 equal does temper out 28/27, which makes three "fifths" (ie. 3/2) up, a 7/4. Thus 9/8 = a near just 7/6 (and what the relatively accurate 200 cents as 9/8, is in fact 8/7 - what do you make of that? Music.) This treatment applies to the scale generated by the large fifth, known as Father | However, less accurate approximations can be used. 18 equal does temper out 28/27, which makes three "fifths" (ie. 3/2) up, a 7/4. Thus 9/8 = a near just 7/6 (and what the relatively accurate 200 cents as 9/8, is in fact 8/7 - what do you make of that? Music.) This treatment applies to the scale generated by the large fifth, known as Father. One, if one really gets into it, can generate scales from the 3/2 and the half octave: with all the sharpness, what's 18e going to hurt? Call 600 cents 11/8 and 866 cents 13/8. Hey it's possible, lots of people like mavila. | ||
18-EDO contains sub-EDOs 2, 3, 6, and 9, and itself is half of 36-EDO and one-fourth of 72-EDO. It bears some similarities to 13-EDO (with its very flat 4ths and nice subminor 3rds), 11-EDO (with its very sharp minor 3rds, two of which span a very flat 5th), 16-EDO (with its sharp 4ths and flat 5ths), and 17-EDO and 19-EDO (with its narrow semitone, three of which comprise a whole-tone). It is an excellent tuning for those seeking a forceful deviation from the common practice. | 18-EDO contains sub-EDOs 2, 3, 6, and 9, and itself is half of 36-EDO and one-fourth of 72-EDO. It bears some similarities to 13-EDO (with its very flat 4ths and nice subminor 3rds), 11-EDO (with its very sharp minor 3rds, two of which span a very flat 5th), 16-EDO (with its sharp 4ths and flat 5ths), and 17-EDO and 19-EDO (with its narrow semitone, three of which comprise a whole-tone). It is an excellent tuning for those seeking a forceful deviation from the common practice. | ||
| Line 81: | Line 81: | ||
==Listen== | ==Listen== | ||
* //[[http://www.h-pi.com/mp3/18ETPrelude.mp3|18ETPrelude]]// by [[Aaron Andrew Hunt]] | * ////[[http://www.h-pi.com/mp3/18ETPrelude.mp3|18ETPrelude]]//// by [[Aaron Andrew Hunt]] | ||
* //[[http://micro.soonlabel.com/18-ET/prelude-in-18et.mp3|Prelude in 18et]]// by [[@http://www.chrisvaisvil.com|Chris Vaisvil]] => [[@http://chrisvaisvil.com/?p=3|composer notes]] | * ////[[http://micro.soonlabel.com/18-ET/prelude-in-18et.mp3|Prelude in 18et]]//// by [[@http://www.chrisvaisvil.com|Chris Vaisvil]] => [[@http://chrisvaisvil.com/?p=3|composer notes]] | ||
* //[[http://micro.soonlabel.com/18-ET/daily20110401-18c-flippertronics.mp3|Flippertronics]]// by Chris Vaisvil | * ////[[http://micro.soonlabel.com/18-ET/daily20110401-18c-flippertronics.mp3|Flippertronics]]//// by Chris Vaisvil | ||
* //[[http://micro.soonlabel.com/9-edo/daily20111008b_gerbils_at_the_wheel_of_government.mp3|Gerbils at the Wheel of Government]]// by [[@http://chrisvaisvil.com/?p=1402|Chris Vaisvil (in 9 and 18 edo simultaneously)]]</pre></div> | * ////[[http://micro.soonlabel.com/9-edo/daily20111008b_gerbils_at_the_wheel_of_government.mp3|Gerbils at the Wheel of Government]]//// by [[@http://chrisvaisvil.com/?p=1402|Chris Vaisvil (in 9 and 18 edo simultaneously)]]</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>18edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x18 Equal Divisions of the Octave"></a><!-- ws:end:WikiTextHeadingRule:0 -->18 Equal Divisions of the Octave</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>18edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x18 Equal Divisions of the Octave"></a><!-- ws:end:WikiTextHeadingRule:0 -->18 Equal Divisions of the Octave</h1> | ||
| Line 94: | Line 94: | ||
In order to access the excellent consonances actually available, one must take a considerably &quot;non-common-practice&quot; approach, meaning to avoid the usual closed-voice &quot;root-3rd-5th&quot; type of chord and instead use chords which are either more compressed or more stretched out. 18-EDO may be treated as a temperament of the 17-limit <a class="wiki_link" href="/k%2AN%20subgroups">4*18 subgroup</a> <a class="wiki_link" href="/Just%20intonation%20subgroups">just intonation subgroup</a> 2.9.75.21.55.39.51. On this subgroup it tempers out exactly the same commas as 72 does on the full <a class="wiki_link" href="/17-limit">17-limit</a>, and gives precisely the same tunings. The subgroup can be put into a single chord, for example 32:36:39:42:51:55:64:75 (in terms of 18edo, 0-3-5-7-12-14-18-22), and transpositions and inversions of this chord or its subchords provide plenty of harmonic resources.<br /> | In order to access the excellent consonances actually available, one must take a considerably &quot;non-common-practice&quot; approach, meaning to avoid the usual closed-voice &quot;root-3rd-5th&quot; type of chord and instead use chords which are either more compressed or more stretched out. 18-EDO may be treated as a temperament of the 17-limit <a class="wiki_link" href="/k%2AN%20subgroups">4*18 subgroup</a> <a class="wiki_link" href="/Just%20intonation%20subgroups">just intonation subgroup</a> 2.9.75.21.55.39.51. On this subgroup it tempers out exactly the same commas as 72 does on the full <a class="wiki_link" href="/17-limit">17-limit</a>, and gives precisely the same tunings. The subgroup can be put into a single chord, for example 32:36:39:42:51:55:64:75 (in terms of 18edo, 0-3-5-7-12-14-18-22), and transpositions and inversions of this chord or its subchords provide plenty of harmonic resources.<br /> | ||
<br /> | <br /> | ||
However, less accurate approximations can be used. 18 equal does temper out 28/27, which makes three &quot;fifths&quot; (ie. 3/2) up, a 7/4. Thus 9/8 = a near just 7/6 (and what the relatively accurate 200 cents as 9/8, is in fact 8/7 - what do you make of that? Music.) This treatment applies to the scale generated by the large fifth, known as Father | However, less accurate approximations can be used. 18 equal does temper out 28/27, which makes three &quot;fifths&quot; (ie. 3/2) up, a 7/4. Thus 9/8 = a near just 7/6 (and what the relatively accurate 200 cents as 9/8, is in fact 8/7 - what do you make of that? Music.) This treatment applies to the scale generated by the large fifth, known as Father. One, if one really gets into it, can generate scales from the 3/2 and the half octave: with all the sharpness, what's 18e going to hurt? Call 600 cents 11/8 and 866 cents 13/8. Hey it's possible, lots of people like mavila.<br /> | ||
<br /> | <br /> | ||
18-EDO contains sub-EDOs 2, 3, 6, and 9, and itself is half of 36-EDO and one-fourth of 72-EDO. It bears some similarities to 13-EDO (with its very flat 4ths and nice subminor 3rds), 11-EDO (with its very sharp minor 3rds, two of which span a very flat 5th), 16-EDO (with its sharp 4ths and flat 5ths), and 17-EDO and 19-EDO (with its narrow semitone, three of which comprise a whole-tone). It is an excellent tuning for those seeking a forceful deviation from the common practice.<br /> | 18-EDO contains sub-EDOs 2, 3, 6, and 9, and itself is half of 36-EDO and one-fourth of 72-EDO. It bears some similarities to 13-EDO (with its very flat 4ths and nice subminor 3rds), 11-EDO (with its very sharp minor 3rds, two of which span a very flat 5th), 16-EDO (with its sharp 4ths and flat 5ths), and 17-EDO and 19-EDO (with its narrow semitone, three of which comprise a whole-tone). It is an excellent tuning for those seeking a forceful deviation from the common practice.<br /> | ||
| Line 596: | Line 596: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="x18 Equal Divisions of the Octave-Listen"></a><!-- ws:end:WikiTextHeadingRule:22 -->Listen</h2> | <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="x18 Equal Divisions of the Octave-Listen"></a><!-- ws:end:WikiTextHeadingRule:22 -->Listen</h2> | ||
<ul><li | <ul><li><a class="wiki_link_ext" href="http://www.h-pi.com/mp3/18ETPrelude.mp3" rel="nofollow">18ETPrelude</a> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/18-ET/prelude-in-18et.mp3" rel="nofollow">Prelude in 18et</a> by <a class="wiki_link_ext" href="http://www.chrisvaisvil.com" rel="nofollow" target="_blank">Chris Vaisvil</a> =&gt; <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=3" rel="nofollow" target="_blank">composer notes</a></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/18-ET/daily20110401-18c-flippertronics.mp3" rel="nofollow">Flippertronics</a> by Chris Vaisvil</li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/9-edo/daily20111008b_gerbils_at_the_wheel_of_government.mp3" rel="nofollow">Gerbils at the Wheel of Government</a> by <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1402" rel="nofollow" target="_blank">Chris Vaisvil (in 9 and 18 edo simultaneously)</a></li></ul></body></html></pre></div> | ||