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> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-06-20 05: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-06-20 05:46:26 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>237682215</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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==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# | 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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<!-- ws:start:WikiTextHeadingRule:3:&lt;h2&gt; --><h2 id="toc1"><a name="Theory-As an approximation of other temperaments"></a><!-- ws:end:WikiTextHeadingRule:3 -->As an approximation of other temperaments</h2> | <!-- ws:start:WikiTextHeadingRule:3:&lt;h2&gt; --><h2 id="toc1"><a name="Theory-As an approximation of other temperaments"></a><!-- ws:end:WikiTextHeadingRule:3 -->As an approximation of other temperaments</h2> | ||
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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 <a class="wiki_link" href="/Meantone# | 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 <a class="wiki_link" href="/Meantone# ">meantone</a> temperament. It is also a suitable for <a class="wiki_link" href="/Regular%20Temperaments#magic">magic</a> temperament, because five of its major thirds are equivalent to one of its <em>twelfths</em>.<br /> | ||
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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 <a class="wiki_link" href="/31edo">31 equal temperament</a>. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; <a class="wiki_link" href="/41edo">41 equal temperament</a> more closely matches it.<br /> | 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 <a class="wiki_link" href="/31edo">31 equal temperament</a>. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; <a class="wiki_link" href="/41edo">41 equal temperament</a> more closely matches it.<br /> | ||