Magic Tetrachords: Difference between revisions
Wikispaces>hearneg **Imported revision 507843428 - Original comment: ** |
Wikispaces>hearneg **Imported revision 507845610 - 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:hearneg|hearneg]] and made on <tt>2014-05-09 16: | : This revision was by author [[User:hearneg|hearneg]] and made on <tt>2014-05-09 16:18:41 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>507845610</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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<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;white-space: pre-wrap ! important" class="old-revision-html">=Magic Tetrachords!= | <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;white-space: pre-wrap ! important" class="old-revision-html">=Magic Tetrachords!= | ||
Dissatisfied with Magic[7]? A fan of tetrachordal scales? Try tetrachordal MODMOS of Magic[7], Magic | Dissatisfied with Magic[7]? A fan of tetrachordal scales? Try tetrachordal MODMOS of Magic[7], [[Magic]] [[Tetrachord]]s! | ||
Magic[7] has structure | Magic[7] has structure [[3L 4s]], with a large step of 6/5 and a small step of 25/24~28/27~36/35. The chroma is therefore 7/6, so the diminished second is 8/9 (so like, a tone in the wrong direction. Weird hey). From any mode of Magic[7] with 4/3 or 3/2 can be constructed a 1-[[MODMOS]] with 4/3 and 3/2. | ||
Eg. Take 5|1. We have LsLssLs: 1/1 6/5 5/4 3/2 14/9 8/5 27/14 2/1. | Eg. Take 5|1. We have LsLssLs: 1/1 6/5 5/4 3/2 14/9 8/5 27/14 2/1. | ||
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From 3|3 however, both raising the major fourth to 3/2 and lowering the minor fifth to 4/3 leads us to 3|3 #4 b5, sLLdLLs: 1/1 28/27 5/4 3/2 4/3 8/5 27/14 2/1, a symmetrical scale with chromatic tetrachords of 1/1 28/27 5/4 4/3 and 1/1 16/15 9/7 2/1, inversions of each other. | From 3|3 however, both raising the major fourth to 3/2 and lowering the minor fifth to 4/3 leads us to 3|3 #4 b5, sLLdLLs: 1/1 28/27 5/4 3/2 4/3 8/5 27/14 2/1, a symmetrical scale with chromatic tetrachords of 1/1 28/27 5/4 4/3 and 1/1 16/15 9/7 2/1, inversions of each other. | ||
From the 1-MODMOS above, 2-MODMOS can be obtained with two diminished seconds of 8/9, and one diminished fourth of 10/9, of one diatonic and one chromatic tetrachord, moving us another step closer to the Zarlino-Ptolemy diatonic scale, and from other 1-MODMOS, other, non-diatonic tetrachordal scales can be constructed, but that is outside the scope of this article | From the 1-MODMOS above, 2-MODMOS can be obtained with two diminished seconds of 8/9, and one diminished fourth of 10/9, of one diatonic and one chromatic tetrachord, moving us another step closer to the Zarlino-Ptolemy diatonic scale, and from other 1-MODMOS, other, non-diatonic tetrachordal scales can be constructed, but that is outside the scope of this article and is left as an exercise for the reader. | ||
==Table of Results:== | ==Table of Results:== | ||
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|| 3|3 #4 b5 || sLLdLLs || 1/1 28/27 5/4 3/2 4/3 8/5 27/14 2/1 || Chromatic: 1/1 28/27 5/4 4/3 || Chromatic: 1/1 16/15 9/7 2/1 || | || 3|3 #4 b5 || sLLdLLs || 1/1 28/27 5/4 3/2 4/3 8/5 27/14 2/1 || Chromatic: 1/1 28/27 5/4 4/3 || Chromatic: 1/1 16/15 9/7 2/1 || | ||
Any of the 7 modes of each of these scales can of course be used. | Any of the 7 modes of each of these scales can of course be used. | ||
Tunings of 19edo, 22edo and 41edo are encouraged.</pre></div> | Tunings of [[19edo]], [[22edo]] and [[41edo]] are encouraged.</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>Magic Tetrachords</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Magic Tetrachords!"></a><!-- ws:end:WikiTextHeadingRule:0 -->Magic Tetrachords!</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>Magic Tetrachords</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Magic Tetrachords!"></a><!-- ws:end:WikiTextHeadingRule:0 -->Magic Tetrachords!</h1> | ||
<br /> | <br /> | ||
Dissatisfied with Magic[7]? A fan of tetrachordal scales? Try tetrachordal MODMOS of Magic[7], Magic | Dissatisfied with Magic[7]? A fan of tetrachordal scales? Try tetrachordal MODMOS of Magic[7], <a class="wiki_link" href="/Magic">Magic</a> <a class="wiki_link" href="/Tetrachord">Tetrachord</a>s!<br /> | ||
<br /> | <br /> | ||
Magic[7] has structure | Magic[7] has structure <a class="wiki_link" href="/3L%204s">3L 4s</a>, with a large step of 6/5 and a small step of 25/24~28/27~36/35. The chroma is therefore 7/6, so the diminished second is 8/9 (so like, a tone in the wrong direction. Weird hey). From any mode of Magic[7] with 4/3 or 3/2 can be constructed a 1-<a class="wiki_link" href="/MODMOS">MODMOS</a> with 4/3 and 3/2.<br /> | ||
<br /> | <br /> | ||
Eg. Take 5|1. We have LsLssLs: 1/1 6/5 5/4 3/2 14/9 8/5 27/14 2/1.<br /> | Eg. Take 5|1. We have LsLssLs: 1/1 6/5 5/4 3/2 14/9 8/5 27/14 2/1.<br /> | ||
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From 3|3 however, both raising the major fourth to 3/2 and lowering the minor fifth to 4/3 leads us to 3|3 #4 b5, sLLdLLs: 1/1 28/27 5/4 3/2 4/3 8/5 27/14 2/1, a symmetrical scale with chromatic tetrachords of 1/1 28/27 5/4 4/3 and 1/1 16/15 9/7 2/1, inversions of each other.<br /> | From 3|3 however, both raising the major fourth to 3/2 and lowering the minor fifth to 4/3 leads us to 3|3 #4 b5, sLLdLLs: 1/1 28/27 5/4 3/2 4/3 8/5 27/14 2/1, a symmetrical scale with chromatic tetrachords of 1/1 28/27 5/4 4/3 and 1/1 16/15 9/7 2/1, inversions of each other.<br /> | ||
<br /> | <br /> | ||
From the 1-MODMOS above, 2-MODMOS can be obtained with two diminished seconds of 8/9, and one diminished fourth of 10/9, of one diatonic and one chromatic tetrachord, moving us another step closer to the Zarlino-Ptolemy diatonic scale, and from other 1-MODMOS, other, non-diatonic tetrachordal scales can be constructed, but that is outside the scope of this article | From the 1-MODMOS above, 2-MODMOS can be obtained with two diminished seconds of 8/9, and one diminished fourth of 10/9, of one diatonic and one chromatic tetrachord, moving us another step closer to the Zarlino-Ptolemy diatonic scale, and from other 1-MODMOS, other, non-diatonic tetrachordal scales can be constructed, but that is outside the scope of this article and is left as an exercise for the reader.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Magic Tetrachords!-Table of Results:"></a><!-- ws:end:WikiTextHeadingRule:2 -->Table of Results:</h2> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Magic Tetrachords!-Table of Results:"></a><!-- ws:end:WikiTextHeadingRule:2 -->Table of Results:</h2> | ||
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Any of the 7 modes of each of these scales can of course be used.<br /> | Any of the 7 modes of each of these scales can of course be used.<br /> | ||
Tunings of 19edo, 22edo and 41edo are encouraged.</body></html></pre></div> | Tunings of <a class="wiki_link" href="/19edo">19edo</a>, <a class="wiki_link" href="/22edo">22edo</a> and <a class="wiki_link" href="/41edo">41edo</a> are encouraged.</body></html></pre></div> | ||