19edo: Difference between revisions
Wikispaces>hstraub **Imported revision 5478151 - Original comment: link to "magic"** |
Wikispaces>hstraub **Imported revision 5478227 - 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>2007-06-25 09: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2007-06-25 09:13:56 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>5478227</tt>.<br> | ||
: The revision comment was: <tt> | : 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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
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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 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 [[Regular Temperaments#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 [[31 equal temperament]]. Similarly, the generating interval of | 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 [[31 equal temperament]]. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; [[41 equal temperament]] more closely matches it. | ||
However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with 5-limit music in a tolerable manner. It is less successful with 7-limit (but still better than 12-et), as it eliminates the distinction between a septimal minor third(7/6), and a septimal whole tone (8/7). | However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with 5-limit music in a tolerable manner. It is less successful with 7-limit (but still better than 12-et), as it eliminates the distinction between a septimal minor third(7/6), and a septimal whole tone (8/7). | ||
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-As an approximation of other temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 -->As an approximation of other temperaments</h2> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-As an approximation of other temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 -->As an approximation of other temperaments</h2> | ||
<br /> | <br /> | ||
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 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 /> | 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="/Regular%20Temperaments#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 /> | ||
<br /> | <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="/31%20equal%20temperament">31 equal temperament</a>. Similarly, the generating interval of | 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="/31%20equal%20temperament">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="/41%20equal%20temperament">41 equal temperament</a> more closely matches it.<br /> | ||
<br /> | <br /> | ||
However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with 5-limit music in a tolerable manner. It is less successful with 7-limit (but still better than 12-et), as it eliminates the distinction between a septimal minor third(7/6), and a septimal whole tone (8/7).<br /> | However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with 5-limit music in a tolerable manner. It is less successful with 7-limit (but still better than 12-et), as it eliminates the distinction between a septimal minor third(7/6), and a septimal whole tone (8/7).<br /> | ||