19edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-06 14:04:58 UTC</tt>.

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-06 19:22:44 UTC</tt>.

: The original revision id was <tt>~~234634536~~</tt>.

: The original revision id was <tt>234708918</tt>.

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

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[[http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/truthonabus.html|Truth on a bus]] by William Sethares

[[http://www.h-pi.com/mp3/Rondo19ET.mp3|Rondo in 19ET]] by Aaron Andrew Hunt

[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Starrett/CitifiedNotions19tet.mp3|Citified Notions]] by John Starrett.

[[http://www.sibeliusmusic.com/cgi-bin/show_score.pl?scoreid=104038|The Light Of My Betelgeuse]] by Mykhaylo Khramov

A number of compositions that were perfomed at the [[http://midwestmicrofest.org/concerts.html|midwestmicrofest concert in 2007]]

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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 <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>).

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>).

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

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<a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/truthonabus.html" rel="nofollow">Truth on a bus</a> by William Sethares

<a class="wiki_link_ext" href="http://www.h-pi.com/mp3/Rondo19ET.mp3" rel="nofollow">Rondo in 19ET</a> by Aaron Andrew Hunt

<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Starrett/CitifiedNotions19tet.mp3" rel="nofollow">Citified Notions</a> by John Starrett.

<a class="wiki_link_ext" href="http://www.sibeliusmusic.com/cgi-bin/show_score.pl?scoreid=104038" rel="nofollow">The Light Of My Betelgeuse</a> by Mykhaylo Khramov

A number of compositions that were perfomed at the <a class="wiki_link_ext" href="http://midwestmicrofest.org/concerts.html" rel="nofollow">midwestmicrofest concert in 2007</a>

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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>2011-06-06 14:04:58 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-06 19:22:44 UTC</tt>.<br>
-: The original revision id was <tt>234634536</tt>.<br>
+: The original revision id was <tt>234708918</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 106: / Line 106: @@
 [[http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/truthonabus.html|Truth on a bus]] by William Sethares
 &lt;span class="ymp-btn-page-play ymp-media-d26b8b4b4beee2371ad7b7c7cc71a9da"&gt;[[http://www.h-pi.com/mp3/Rondo19ET.mp3|Rondo in 19ET]] &lt;/span&gt; by Aaron Andrew Hunt
+[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Starrett/CitifiedNotions19tet.mp3|Citified Notions]] by John Starrett.
 [[http://www.sibeliusmusic.com/cgi-bin/show_score.pl?scoreid=104038|The Light Of My Betelgeuse]] by Mykhaylo Khramov
 A number of compositions that were perfomed at the [[http://midwestmicrofest.org/concerts.html|midwestmicrofest concert in 2007]]
@@ Line 133: / Line 134: @@
 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:940: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:940 --&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:942: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:942 --&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:5:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Theory-Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;Intervals&lt;/h2&gt;
@@ Line 725: / Line 726: @@
 &lt;a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/truthonabus.html" rel="nofollow"&gt;Truth on a bus&lt;/a&gt; by William Sethares&lt;br /&gt;
 &lt;span class="ymp-btn-page-play ymp-media-d26b8b4b4beee2371ad7b7c7cc71a9da"&gt;&lt;a class="wiki_link_ext" href="http://www.h-pi.com/mp3/Rondo19ET.mp3" rel="nofollow"&gt;Rondo in 19ET&lt;/a&gt; &lt;/span&gt; by Aaron Andrew Hunt&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Starrett/CitifiedNotions19tet.mp3" rel="nofollow"&gt;Citified Notions&lt;/a&gt; by John Starrett.&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://www.sibeliusmusic.com/cgi-bin/show_score.pl?scoreid=104038" rel="nofollow"&gt;The Light Of My Betelgeuse&lt;/a&gt; by Mykhaylo Khramov&lt;br /&gt;
 A number of compositions that were perfomed at the &lt;a class="wiki_link_ext" href="http://midwestmicrofest.org/concerts.html" rel="nofollow"&gt;midwestmicrofest concert in 2007&lt;/a&gt;&lt;br /&gt;