19edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:~~xenwolf~~|~~xenwolf~~]] and made on <tt>2011-03-~~25 15~~:01:11 UTC</tt>.

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-30 17:28:22 UTC</tt>.

: The original revision id was <tt>~~214056672~~</tt>.

: The original revision id was <tt>215611770</tt>.

: The revision comment was: <tt></tt>

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[[http://gewi.uni-graz.at/%7Ecim04/CIM04_paper_pdf/Bucht_Huovinen_CIM04_proceedings.pdf|Bucht, Saku and Huovinen, Erkki, //Perceived consonance of harmonic intervals in 19-tone equal temperament]]

//[[http://sonic-arts.org/darreg/~~CASE~~.~~HTM|Darreg, Ivor,~~ //~~A Case for Nineteen/~~/]]//

//[[Ivor Darreg. A Case For Nineteen. URL:http://sonic-arts.org/darreg/case.htm. Accessed: 2011-03-30. (Archived by WebCite® at http://www.webcitation.org/5xZzBtDGF)]]//

//[[http://qcpages.qc.edu/%7Ehowe/articles/19-Tone%20Theory.html|Howe, Hubert S. Jr., //9-Tone Theory and Applications//]]//

//[[http://eceserv0.ece.wisc.edu/%7Esethares/tet19/guitarchords19.html|Sethares, William A., //Tunings for 19 Tone Equal Tempered Guitar//]]//

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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.

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, <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>. 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 <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, <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>. 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).

<h2 id="toc2"><a name="Theory-Intervals"></a>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>

<a class="wiki_link_ext" href="http://sonic-arts.org/darreg/~~CASE~~.~~HTM~~" rel="nofollow">~~Darreg, Ivor,~~ //~~A Case for Nineteen~~//</a>

[[Ivor Darreg. A Case For Nineteen. URL:<a class="wiki_link_ext" href="http://sonic-arts.org/darreg/case.htm" rel="nofollow">http://sonic-arts.org/darreg/case.htm</a>. Accessed: 2011-03-30. (Archived by WebCite® at <a class="wiki_link_ext" href="http://www.webcitation.org/5xZzBtDGF" rel="nofollow">http://www.webcitation.org/5xZzBtDGF</a>)]]

<a class="wiki_link_ext" href="http://qcpages.qc.edu/%7Ehowe/articles/19-Tone%20Theory.html" rel="nofollow">Howe, Hubert S. Jr., //9-Tone Theory and Applications//</a>

<a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/tet19/guitarchords19.html" rel="nofollow">Sethares, William A., //Tunings for 19 Tone Equal Tempered Guitar//</a>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-03-25 15:01:11 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-30 17:28:22 UTC</tt>.<br>
-: The original revision id was <tt>214056672</tt>.<br>
+: The original revision id was <tt>215611770</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>
@@ Line 50: / Line 50: @@
 [[http://gewi.uni-graz.at/%7Ecim04/CIM04_paper_pdf/Bucht_Huovinen_CIM04_proceedings.pdf|Bucht, Saku and Huovinen, Erkki, //Perceived consonance of harmonic intervals in 19-tone equal temperament]]
-//[[http://sonic-arts.org/darreg/CASE.HTM|Darreg, Ivor, //A Case for Nineteen//]]//
+//[[Ivor Darreg. A Case For Nineteen. URL:http://sonic-arts.org/darreg/case.htm. Accessed: 2011-03-30. (Archived by WebCite® at http://www.webcitation.org/5xZzBtDGF)]]//
 //[[http://qcpages.qc.edu/%7Ehowe/articles/19-Tone%20Theory.html|Howe, Hubert S. Jr., //9-Tone Theory and Applications//]]//
 //[[http://eceserv0.ece.wisc.edu/%7Esethares/tet19/guitarchords19.html|Sethares, William A., //Tunings for 19 Tone Equal Tempered Guitar//]]//
@@ Line 91: / Line 91: @@
 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;
 &lt;br /&gt;
-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 &lt;a class="wiki_link" href="/Harmonic%20Limit"&gt;5-limit&lt;/a&gt; music in a tolerable manner, and is the fifth (after 12) Zeta function integral tuning, &lt;!-- ws:start:WikiTextUrlRule:310:http://www.research.att.com/~njas/sequences/A117538 --&gt;&lt;a class="wiki_link_ext" href="http://www.research.att.com/~njas/sequences/A117538" rel="nofollow"&gt;http://www.research.att.com/~njas/sequences/A117538&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:310 --&gt;. 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).&lt;br /&gt;
+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 &lt;a class="wiki_link" href="/Harmonic%20Limit"&gt;5-limit&lt;/a&gt; music in a tolerable manner, and is the fifth (after 12) Zeta function integral tuning, &lt;!-- ws:start:WikiTextUrlRule:309:http://www.research.att.com/~njas/sequences/A117538 --&gt;&lt;a class="wiki_link_ext" href="http://www.research.att.com/~njas/sequences/A117538" rel="nofollow"&gt;http://www.research.att.com/~njas/sequences/A117538&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:309 --&gt;. 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).&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Theory-Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Intervals&lt;/h2&gt;
@@ Line 266: / Line 266: @@
   &lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://gewi.uni-graz.at/%7Ecim04/CIM04_paper_pdf/Bucht_Huovinen_CIM04_proceedings.pdf" rel="nofollow"&gt;Bucht, Saku and Huovinen, Erkki, //Perceived consonance of harmonic intervals in 19-tone equal temperament&lt;/a&gt;&lt;br /&gt;
-&lt;em&gt;&lt;a class="wiki_link_ext" href="http://sonic-arts.org/darreg/CASE.HTM" rel="nofollow"&gt;Darreg, Ivor, //A Case for Nineteen//&lt;/a&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;em&gt;[[Ivor Darreg. A Case For Nineteen. URL:&lt;!-- ws:start:WikiTextUrlRule:310:http://sonic-arts.org/darreg/case.htm --&gt;&lt;a class="wiki_link_ext" href="http://sonic-arts.org/darreg/case.htm" rel="nofollow"&gt;http://sonic-arts.org/darreg/case.htm&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:310 --&gt;. Accessed: 2011-03-30. (Archived by WebCite® at &lt;!-- ws:start:WikiTextUrlRule:311:http://www.webcitation.org/5xZzBtDGF --&gt;&lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xZzBtDGF" rel="nofollow"&gt;http://www.webcitation.org/5xZzBtDGF&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:311 --&gt;)]]&lt;/em&gt;&lt;br /&gt;
 &lt;em&gt;&lt;a class="wiki_link_ext" href="http://qcpages.qc.edu/%7Ehowe/articles/19-Tone%20Theory.html" rel="nofollow"&gt;Howe, Hubert S. Jr., //9-Tone Theory and Applications//&lt;/a&gt;&lt;/em&gt;&lt;br /&gt;
 &lt;em&gt;&lt;a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/tet19/guitarchords19.html" rel="nofollow"&gt;Sethares, William A., //Tunings for 19 Tone Equal Tempered Guitar//&lt;/a&gt;&lt;/em&gt;&lt;br /&gt;