19edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 215955780 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 216001560 - 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:xenwolf|xenwolf]] and made on <tt>2011-03-31 17:11:04 UTC</tt>.<br> | ||
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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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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. | ||
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 [[Harmonic Limit|5-limit]] music in a tolerable manner, and is the fifth (after 12) Zeta function integral tuning, http://www.research.att.com/~njas/sequences/A117538. 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 [[Harmonic Limit|5-limit]] music in a tolerable manner, and is the fifth (after 12) Zeta function integral tuning, http://www.research.att.com/~njas/sequences/A117538. 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|7/6]]), and a septimal whole tone ([[8_7|8/7]]). | ||
==Intervals== | ==Intervals== | ||
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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 /> | ||
<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 <a class="wiki_link" href="/Harmonic%20Limit">5-limit</a> music in a tolerable manner, and is the fifth (after 12) Zeta function integral tuning, <!-- ws:start:WikiTextUrlRule: | 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 <a class="wiki_link" href="/Harmonic%20Limit">5-limit</a> music in a tolerable manner, and is the fifth (after 12) Zeta function integral tuning, <!-- ws:start:WikiTextUrlRule:315:http://www.research.att.com/~njas/sequences/A117538 --><a class="wiki_link_ext" href="http://www.research.att.com/~njas/sequences/A117538" rel="nofollow">http://www.research.att.com/~njas/sequences/A117538</a><!-- ws:end:WikiTextUrlRule:315 -->. It is less successful with <a class="wiki_link" href="/7-limit">7-limit</a> (but still better than 12-et), as it eliminates the distinction between a septimal minor third (<a class="wiki_link" href="/7_6">7/6</a>), and a septimal whole tone (<a class="wiki_link" href="/8_7">8/7</a>).<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Theory-Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h2> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Theory-Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h2> | ||
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<a class="wiki_link_ext" href="http://gewi.uni-graz.at/%7Ecim04/CIM04_paper_pdf/Bucht_Huovinen_CIM04_proceedings.pdf" rel="nofollow">Bucht, Saku and Huovinen, Erkki, //Perceived consonance of harmonic intervals in 19-tone equal temperament</a><br /> | <a class="wiki_link_ext" href="http://gewi.uni-graz.at/%7Ecim04/CIM04_paper_pdf/Bucht_Huovinen_CIM04_proceedings.pdf" rel="nofollow">Bucht, Saku and Huovinen, Erkki, //Perceived consonance of harmonic intervals in 19-tone equal temperament</a><br /> | ||
<em><a class="wiki_link" href="/Ivor%20Darreg">Ivor Darreg</a>. A Case For Nineteen. URL:<!-- ws:start:WikiTextUrlRule: | <em><a class="wiki_link" href="/Ivor%20Darreg">Ivor Darreg</a>. A Case For Nineteen. URL:<!-- ws:start:WikiTextUrlRule:316:http://sonic-arts.org/darreg/case.htm --><a class="wiki_link_ext" href="http://sonic-arts.org/darreg/case.htm" rel="nofollow">http://sonic-arts.org/darreg/case.htm</a><!-- ws:end:WikiTextUrlRule:316 -->. Accessed: 2011-03-30. (Archived by WebCite® at <!-- ws:start:WikiTextUrlRule:317:http://www.webcitation.org/5xZzBtDGF --><a class="wiki_link_ext" href="http://www.webcitation.org/5xZzBtDGF" rel="nofollow">http://www.webcitation.org/5xZzBtDGF</a><!-- ws:end:WikiTextUrlRule:317 -->)</em><br /> | ||
<em><a class="wiki_link_ext" href="http://www.webcitation.org/5xbMKVaqa" rel="nofollow">Howe, Hubert S. Jr., //19-Tone Theory and Applications//</a></em><br /> | <em><a class="wiki_link_ext" href="http://www.webcitation.org/5xbMKVaqa" rel="nofollow">Howe, Hubert S. Jr., //19-Tone Theory and Applications//</a></em><br /> | ||
<em><a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/tet19/guitarchords19.html" rel="nofollow">Sethares, William A., //Tunings for 19 Tone Equal Tempered Guitar//</a></em><br /> | <em><a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/tet19/guitarchords19.html" rel="nofollow">Sethares, William A., //Tunings for 19 Tone Equal Tempered Guitar//</a></em><br /> | ||