19edo: Difference between revisions

Wikispaces>hstraub
**Imported revision 237682083 - Original comment: **
Wikispaces>hstraub
**Imported revision 237682215 - 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>
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: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-06-20 05:45:00 UTC</tt>.<br>
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: The original revision id was <tt>237682083</tt>.<br>
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==As an approximation of other temperaments==  
==As an approximation of other temperaments==  


The most salient characteristic of 19-et is that, having an almost just minor third and perfect fifths and major thirds about seven cents narrow, it serves as a good tuning for [[Meantone#meantone|meantone]] temperament. It is also a suitable for [[Regular Temperaments#magic|magic]] temperament, because five of its major thirds are equivalent to one of its //twelfths//.
The most salient characteristic of 19-et is that, having an almost just minor third and perfect fifths and major thirds about seven cents narrow, it serves as a good tuning for [[Meantone# |meantone]] temperament. It is also a suitable for [[Regular Temperaments#magic|magic]] temperament, because five of its major thirds are equivalent to one of its //twelfths//.


For both of these there are more optimal tunings, however. The generating interval for meantone is a fifth, and the fifth of 19-et is flatter than the usual for meantone; a more accurate approximation is [[31edo|31 equal temperament]]. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; [[41edo|41 equal temperament]] more closely matches it.
For both of these there are more optimal tunings, however. The generating interval for meantone is a fifth, and the fifth of 19-et is flatter than the usual for meantone; a more accurate approximation is [[31edo|31 equal temperament]]. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; [[41edo|41 equal temperament]] more closely matches it.
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&lt;!-- ws:start:WikiTextHeadingRule:3:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Theory-As an approximation of other temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:3 --&gt;As an approximation of other temperaments&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:3:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Theory-As an approximation of other temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:3 --&gt;As an approximation of other temperaments&lt;/h2&gt;
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The most salient characteristic of 19-et is that, having an almost just minor third and perfect fifths and major thirds about seven cents narrow, it serves as a good tuning for &lt;a class="wiki_link" href="/Meantone#meantone"&gt;meantone&lt;/a&gt; temperament. It is also a suitable for &lt;a class="wiki_link" href="/Regular%20Temperaments#magic"&gt;magic&lt;/a&gt; temperament, because five of its major thirds are equivalent to one of its &lt;em&gt;twelfths&lt;/em&gt;.&lt;br /&gt;
The most salient characteristic of 19-et is that, having an almost just minor third and perfect fifths and major thirds about seven cents narrow, it serves as a good tuning for &lt;a class="wiki_link" href="/Meantone# "&gt;meantone&lt;/a&gt; temperament. It is also a suitable for &lt;a class="wiki_link" href="/Regular%20Temperaments#magic"&gt;magic&lt;/a&gt; temperament, because five of its major thirds are equivalent to one of its &lt;em&gt;twelfths&lt;/em&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For both of these there are more optimal tunings, however. The generating interval for meantone is a fifth, and the fifth of 19-et is flatter than the usual for meantone; a more accurate approximation is &lt;a class="wiki_link" href="/31edo"&gt;31 equal temperament&lt;/a&gt;. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; &lt;a class="wiki_link" href="/41edo"&gt;41 equal temperament&lt;/a&gt; more closely matches it.&lt;br /&gt;
For both of these there are more optimal tunings, however. The generating interval for meantone is a fifth, and the fifth of 19-et is flatter than the usual for meantone; a more accurate approximation is &lt;a class="wiki_link" href="/31edo"&gt;31 equal temperament&lt;/a&gt;. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; &lt;a class="wiki_link" href="/41edo"&gt;41 equal temperament&lt;/a&gt; more closely matches it.&lt;br /&gt;