Diaschismic family: Difference between revisions
Wikispaces>guest **Imported revision 212886274 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 213066378 - 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:genewardsmith|genewardsmith]] and made on <tt>2011-03-22 23:27:22 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>213066378</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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Badness: 0.0289 | Badness: 0.0289 | ||
=Shrutar= | |||
Shrutar adds 245/243 to the commas, and also tempers out 6144/6125. With wedgie <<4 -8 14 -22 11 55||, it can also be described as 22&46. Its generator can be taken as either 36/35 or 35/24; the latter is interesting since along with 15/14 and 21/20, it connects opposite sides of a hexany. [[68edo]] makes for a good tuning, but another and excellent choice is a generator of 14^(1/7), making 7s just. | Shrutar adds 245/243 to the commas, and also tempers out 6144/6125. With wedgie <<4 -8 14 -22 11 55||, it can also be described as 22&46. Its generator can be taken as either 36/35 or 35/24; the latter is interesting since along with 15/14 and 21/20, it connects opposite sides of a hexany. [[68edo]] makes for a good tuning, but another and excellent choice is a generator of 14^(1/7), making 7s just. | ||
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EDOs: 22, 46, 68, 250 | EDOs: 22, 46, 68, 250 | ||
==11-limit== | |||
Commas: 2048/2025, 245/243, 121/120 | Commas: 2048/2025, 245/243, 121/120 | ||
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Map: [<2 1 9 -2 8|, <0 2 -4 7 -1|] | Map: [<2 1 9 -2 8|, <0 2 -4 7 -1|] | ||
EDOs: 22, 46, 68, 114, 410 | |||
EDOs: 22, 46, 68, 114, | ==13-limit== | ||
==17-limit== | |||
==19-limit== | |||
Commas: 121/120, 136/135, 154/154, 176/175, 196/195, 343/342 | |||
POTE generator: ~28/27 = 52.730 | |||
Map: [<2 1 9 -2 8 -10 6 -10|, <0 2 -4 7 -1 16 2 17|] | |||
EDOs: 22, 24, 46, 68, 114, 182 | |||
Badness: 0.0175</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>Diaschismic family</title></head><body>The 5-limit parent comma for the diaschismic family is 2048/2025, the diaschisma. Its monzo is |11 -4 -2&gt;, and flipping that yields &lt;&lt;2 -4 -11|| for the wedgie for 5-limit diaschismic, or srutal, temperament. This tells us the period is half an octave, the GCD of 2 and -4, and that the generator is a fifth. Three periods gives 1800 cents, and decreasing this by two fifths gives the major third. <a class="wiki_link" href="/34edo">34edo</a> is a good tuning choice, with <a class="wiki_link" href="/46edo">46edo</a>, <a class="wiki_link" href="/56edo">56edo</a>, <a class="wiki_link" href="/58edo">58edo</a> or <a class="wiki_link" href="/80edo">80edo</a> being other possibilities. Both <a class="wiki_link" href="/12edo">12edo</a> and <a class="wiki_link" href="/22edo">22edo</a> support it, and retuning them to a MOS of diaschismic gives two scale possibilities.<br /> | <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>Diaschismic family</title></head><body>The 5-limit parent comma for the diaschismic family is 2048/2025, the diaschisma. Its monzo is |11 -4 -2&gt;, and flipping that yields &lt;&lt;2 -4 -11|| for the wedgie for 5-limit diaschismic, or srutal, temperament. This tells us the period is half an octave, the GCD of 2 and -4, and that the generator is a fifth. Three periods gives 1800 cents, and decreasing this by two fifths gives the major third. <a class="wiki_link" href="/34edo">34edo</a> is a good tuning choice, with <a class="wiki_link" href="/46edo">46edo</a>, <a class="wiki_link" href="/56edo">56edo</a>, <a class="wiki_link" href="/58edo">58edo</a> or <a class="wiki_link" href="/80edo">80edo</a> being other possibilities. Both <a class="wiki_link" href="/12edo">12edo</a> and <a class="wiki_link" href="/22edo">22edo</a> support it, and retuning them to a MOS of diaschismic gives two scale possibilities.<br /> | ||
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Badness: 0.0289<br /> | Badness: 0.0289<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:32:&lt; | <!-- ws:start:WikiTextHeadingRule:32:&lt;h1&gt; --><h1 id="toc16"><a name="Shrutar"></a><!-- ws:end:WikiTextHeadingRule:32 -->Shrutar</h1> | ||
Shrutar adds 245/243 to the commas, and also tempers out 6144/6125. With wedgie &lt;&lt;4 -8 14 -22 11 55||, it can also be described as 22&amp;46. Its generator can be taken as either 36/35 or 35/24; the latter is interesting since along with 15/14 and 21/20, it connects opposite sides of a hexany. <a class="wiki_link" href="/68edo">68edo</a> makes for a good tuning, but another and excellent choice is a generator of 14^(1/7), making 7s just.<br /> | |||
<br /> | <br /> | ||
By adding 121/120 or 176/175 to the commas, shrutar can be extended to the 11-limit, which loses a bit of accuracy, but picks up low-complexity 11-limit harmony, making shrutar quite an interesting 11-limit system. 68, 114 or a 14^(1/7) generator can again be used as tunings.<br /> | By adding 121/120 or 176/175 to the commas, shrutar can be extended to the 11-limit, which loses a bit of accuracy, but picks up low-complexity 11-limit harmony, making shrutar quite an interesting 11-limit system. 68, 114 or a 14^(1/7) generator can again be used as tunings.<br /> | ||
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EDOs: 22, 46, 68, 250<br /> | EDOs: 22, 46, 68, 250<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:34:&lt; | <!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Shrutar-11-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->11-limit</h2> | ||
Commas: 2048/2025, 245/243, 121/120<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 52.680<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 52.680<br /> | ||
<br /> | <br /> | ||
Map: [&lt;2 1 9 -2 8|, &lt;0 2 -4 7 -1|]<br /> | Map: [&lt;2 1 9 -2 8|, &lt;0 2 -4 7 -1|]<br /> | ||
EDOs: 22, 46, 68, 114, 410<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Shrutar-13-limit"></a><!-- ws:end:WikiTextHeadingRule:36 -->13-limit</h2> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Shrutar-17-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->17-limit</h2> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Shrutar-19-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->19-limit</h2> | |||
Commas: 121/120, 136/135, 154/154, 176/175, 196/195, 343/342<br /> | |||
<br /> | |||
POTE generator: ~28/27 = 52.730<br /> | |||
<br /> | <br /> | ||
EDOs: 22, 46, 68, 114, | Map: [&lt;2 1 9 -2 8 -10 6 -10|, &lt;0 2 -4 7 -1 16 2 17|]<br /> | ||
EDOs: 22, 24, 46, 68, 114, 182<br /> | |||
Badness: 0.0175</body></html></pre></div> | |||