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:<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-04-02 12:05:35 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-04-02 12:09:01 UTC</tt>.<br>

: The original revision id was <tt>~~216449964~~</tt>.<br>

: The original revision id was <tt>216450448</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>

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* [[http://qcpages.qc.edu/~howe/articles/19-Tone%20Theory.html|19-Tone Theory and Applications]] by Hubert S. Howe Jr. [[http://www.webcitation.org/5xbMKVaqa|Permalink]]

* [[http://sethares.engr.wisc.edu/tet19/guitarchords19.html|Tunings for 19 Tone Equal Tempered Guitar]] by William A. Sethares [[http://www.webcitation.org/5xeCbEPZ0|Permalink]]

* [[http://www.n-ism.org/Projects/microtonalism.php|~~Rehearsing Microtonal Music~~]] by Bailey, Morrison, Pearson and Parncutt [[http://www.webcitation.org/5xeDFQDvn|Permalink]]

* [[http://www.n-ism.org/Projects/microtonalism.php|Microtonalism]] by Bailey, Morrison, Pearson and Parncutt [[http://www.webcitation.org/5xeDFQDvn|Permalink]]

* [[http://tonalsoft.com/enc/number/19edo.aspx|19-tone equal-temperament and 1/3-comma meantone - Encyclopedia of Microtonal Music Theory]]

* [[http://tonalsoft.com/enc/number/19edo.aspx|19-tone equal-temperament and 1/3-comma meantone - Encyclopedia of Microtonal Music Theory]] [[http://tonalsoft.com/enc/number/19edo.aspx|Permalink]]

* [[http://mtg.redkeylabs.com/index.php?topic=6.0|Forum Discussion with some 19-EDO xenharmonic scales Hanson (Keemun), Liese, Negri, Magic, Semaphore, Sensi played on guitar]].

* [[http://www.ronsword.com/books.html|Enneadecaphonic Scales for Guitar]] by Ron Sword

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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 />

<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, <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 <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 />

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 <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 />

<br />

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

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<h2 id="toc3"><a name="Theory-Articles"></a>Articles</h2>

<br />

<ul><li><a class="wiki_link_ext" href="http://sonic-arts.org/darreg/case.htm" rel="nofollow">A Case For Nineteen</a> by <a class="wiki_link" href="/Ivor%20Darreg">Ivor Darreg</a> <a class="wiki_link_ext" href="http://www.webcitation.org/5xZzBtDGF" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://qcpages.qc.edu/~howe/articles/19-Tone%20Theory.html" rel="nofollow">19-Tone Theory and Applications</a> by Hubert S. Howe Jr. <a class="wiki_link_ext" href="http://www.webcitation.org/5xbMKVaqa" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/tet19/guitarchords19.html" rel="nofollow">Tunings for 19 Tone Equal Tempered Guitar</a> by William A. Sethares <a class="wiki_link_ext" href="http://www.webcitation.org/5xeCbEPZ0" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://www.n-ism.org/Projects/microtonalism.php" rel="nofollow">~~Rehearsing Microtonal Music~~</a> by Bailey, Morrison, Pearson and Parncutt <a class="wiki_link_ext" href="http://www.webcitation.org/5xeDFQDvn" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://tonalsoft.com/enc/number/19edo.aspx" rel="nofollow">19-tone equal-temperament and 1/3-comma meantone - Encyclopedia of Microtonal Music Theory</a></li><li><a class="wiki_link_ext" href="http://mtg.redkeylabs.com/index.php?topic=6.0" rel="nofollow">Forum Discussion with some 19-EDO xenharmonic scales Hanson (Keemun), Liese, Negri, Magic, Semaphore, Sensi played on guitar</a>.</li><li><a class="wiki_link_ext" href="http://www.ronsword.com/books.html" rel="nofollow">Enneadecaphonic Scales for Guitar</a> by Ron Sword</li></ul><br />

<ul><li><a class="wiki_link_ext" href="http://sonic-arts.org/darreg/case.htm" rel="nofollow">A Case For Nineteen</a> by <a class="wiki_link" href="/Ivor%20Darreg">Ivor Darreg</a> <a class="wiki_link_ext" href="http://www.webcitation.org/5xZzBtDGF" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://qcpages.qc.edu/~howe/articles/19-Tone%20Theory.html" rel="nofollow">19-Tone Theory and Applications</a> by Hubert S. Howe Jr. <a class="wiki_link_ext" href="http://www.webcitation.org/5xbMKVaqa" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/tet19/guitarchords19.html" rel="nofollow">Tunings for 19 Tone Equal Tempered Guitar</a> by William A. Sethares <a class="wiki_link_ext" href="http://www.webcitation.org/5xeCbEPZ0" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://www.n-ism.org/Projects/microtonalism.php" rel="nofollow">Microtonalism</a> by Bailey, Morrison, Pearson and Parncutt <a class="wiki_link_ext" href="http://www.webcitation.org/5xeDFQDvn" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://tonalsoft.com/enc/number/19edo.aspx" rel="nofollow">19-tone equal-temperament and 1/3-comma meantone - Encyclopedia of Microtonal Music Theory</a> <a class="wiki_link_ext" href="http://tonalsoft.com/enc/number/19edo.aspx" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://mtg.redkeylabs.com/index.php?topic=6.0" rel="nofollow">Forum Discussion with some 19-EDO xenharmonic scales Hanson (Keemun), Liese, Negri, Magic, Semaphore, Sensi played on guitar</a>.</li><li><a class="wiki_link_ext" href="http://www.ronsword.com/books.html" rel="nofollow">Enneadecaphonic Scales for Guitar</a> by Ron Sword</li></ul><br />

<h2 id="toc4"><a name="Theory-References"></a>References</h2>

<br />

@@ 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:genewardsmith|genewardsmith]] and made on <tt>2011-04-02 12:05:35 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-04-02 12:09:01 UTC</tt>.<br>
-: The original revision id was <tt>216449964</tt>.<br>
+: The original revision id was <tt>216450448</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 52: / Line 52: @@
 * [[http://qcpages.qc.edu/~howe/articles/19-Tone%20Theory.html|19-Tone Theory and Applications]] by Hubert S. Howe Jr. [[http://www.webcitation.org/5xbMKVaqa|Permalink]]
 * [[http://sethares.engr.wisc.edu/tet19/guitarchords19.html|Tunings for 19 Tone Equal Tempered Guitar]] by William A. Sethares [[http://www.webcitation.org/5xeCbEPZ0|Permalink]]
-* [[http://www.n-ism.org/Projects/microtonalism.php|Rehearsing Microtonal Music]] by Bailey, Morrison, Pearson and Parncutt [[http://www.webcitation.org/5xeDFQDvn|Permalink]]
+* [[http://www.n-ism.org/Projects/microtonalism.php|Microtonalism]] by Bailey, Morrison, Pearson and Parncutt [[http://www.webcitation.org/5xeDFQDvn|Permalink]]
-* [[http://tonalsoft.com/enc/number/19edo.aspx|19-tone equal-temperament and 1/3-comma meantone - Encyclopedia of Microtonal Music Theory]]
+* [[http://tonalsoft.com/enc/number/19edo.aspx|19-tone equal-temperament and 1/3-comma meantone - Encyclopedia of Microtonal Music Theory]] [[http://tonalsoft.com/enc/number/19edo.aspx|Permalink]]
 * [[http://mtg.redkeylabs.com/index.php?topic=6.0|Forum Discussion with some 19-EDO xenharmonic scales Hanson (Keemun), Liese, Negri, Magic, Semaphore, Sensi played on guitar]].
 * [[http://www.ronsword.com/books.html|Enneadecaphonic Scales for Guitar]] by Ron Sword
@@ Line 92: / Line 92: @@
 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:330: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:330 --&gt;. It is less successful with &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; (but still better than 12-et), as it eliminates the distinction between a septimal minor third (&lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt;), and a septimal whole tone (&lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&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:331: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:331 --&gt;. It is less successful with &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; (but still better than 12-et), as it eliminates the distinction between a septimal minor third (&lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt;), and a septimal whole tone (&lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt;).&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;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Theory-Articles"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Articles&lt;/h2&gt;
   &lt;br /&gt;
-&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://sonic-arts.org/darreg/case.htm" rel="nofollow"&gt;A Case For Nineteen&lt;/a&gt; by &lt;a class="wiki_link" href="/Ivor%20Darreg"&gt;Ivor Darreg&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xZzBtDGF" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://qcpages.qc.edu/~howe/articles/19-Tone%20Theory.html" rel="nofollow"&gt;19-Tone Theory and Applications&lt;/a&gt; by Hubert S. Howe Jr. &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xbMKVaqa" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/tet19/guitarchords19.html" rel="nofollow"&gt;Tunings for 19 Tone Equal Tempered Guitar&lt;/a&gt; by William A. Sethares &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeCbEPZ0" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.n-ism.org/Projects/microtonalism.php" rel="nofollow"&gt;Rehearsing Microtonal Music&lt;/a&gt; by Bailey, Morrison, Pearson and Parncutt &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeDFQDvn" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://tonalsoft.com/enc/number/19edo.aspx" rel="nofollow"&gt;19-tone equal-temperament and 1/3-comma meantone - Encyclopedia of Microtonal Music Theory&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://mtg.redkeylabs.com/index.php?topic=6.0" rel="nofollow"&gt;Forum Discussion with some 19-EDO xenharmonic scales Hanson (Keemun), Liese, Negri, Magic, Semaphore, Sensi played on guitar&lt;/a&gt;.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.ronsword.com/books.html" rel="nofollow"&gt;Enneadecaphonic Scales for Guitar&lt;/a&gt; by Ron Sword&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
+&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://sonic-arts.org/darreg/case.htm" rel="nofollow"&gt;A Case For Nineteen&lt;/a&gt; by &lt;a class="wiki_link" href="/Ivor%20Darreg"&gt;Ivor Darreg&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xZzBtDGF" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://qcpages.qc.edu/~howe/articles/19-Tone%20Theory.html" rel="nofollow"&gt;19-Tone Theory and Applications&lt;/a&gt; by Hubert S. Howe Jr. &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xbMKVaqa" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/tet19/guitarchords19.html" rel="nofollow"&gt;Tunings for 19 Tone Equal Tempered Guitar&lt;/a&gt; by William A. Sethares &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeCbEPZ0" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.n-ism.org/Projects/microtonalism.php" rel="nofollow"&gt;Microtonalism&lt;/a&gt; by Bailey, Morrison, Pearson and Parncutt &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeDFQDvn" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://tonalsoft.com/enc/number/19edo.aspx" rel="nofollow"&gt;19-tone equal-temperament and 1/3-comma meantone - Encyclopedia of Microtonal Music Theory&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://tonalsoft.com/enc/number/19edo.aspx" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://mtg.redkeylabs.com/index.php?topic=6.0" rel="nofollow"&gt;Forum Discussion with some 19-EDO xenharmonic scales Hanson (Keemun), Liese, Negri, Magic, Semaphore, Sensi played on guitar&lt;/a&gt;.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.ronsword.com/books.html" rel="nofollow"&gt;Enneadecaphonic Scales for Guitar&lt;/a&gt; by Ron Sword&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Theory-References"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;References&lt;/h2&gt;
   &lt;br /&gt;