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:genewardsmith|genewardsmith]] and made on <tt>2011-06-06 20:11:16 UTC</tt>.

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-06 20:40:16 UTC</tt>.

: The original revision id was <tt>~~234717640~~</tt>.

: The original revision id was <tt>234723232</tt>.

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

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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[[http://works.music.columbia.edu/%7Echris/19mix1.mp3|Walking Down the Hillside at Cortona, and Seeing its Towers Rise Before Me]] by Christopher Bailey

[[http://www.emcollective.org/chris/items/ditty/ditty_fast.mp3|Ditty]] by Christopher Bailey

[[http://sethares.engr.wisc.edu/mp3s/sympathetic.html|Sympathetic Metaphor]] by William Sethares

[[http://sethares.engr.wisc.edu/mp3s/sympathetic.html|Sympathetic Metaphor]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/SympatheticMetaphor.mp3|play]] by William Sethares [[http://www.webcitation.org/5zFdC6u4V|Permalink]]

[[http://sethares.engr.wisc.edu/mp3s/truthonabus.html|Truth on a bus]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Truth_on_a_Bus.mp3|play]] by William Sethares

[[http://sethares.engr.wisc.edu/mp3s/truthonabus.html|Truth on a bus]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Truth_on_a_Bus.mp3|play]] by William Sethares [[http://www.webcitation.org/5zFdSw1g4|Permalink]]

[[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.

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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://works.music.columbia.edu/%7Echris/19mix1.mp3" rel="nofollow">Walking Down the Hillside at Cortona, and Seeing its Towers Rise Before Me</a> by Christopher Bailey

<a class="wiki_link_ext" href="http://www.emcollective.org/chris/items/ditty/ditty_fast.mp3" rel="nofollow">Ditty</a> by Christopher Bailey

<a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/mp3s/sympathetic.html" rel="nofollow">Sympathetic Metaphor</a> by William Sethares

<a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/mp3s/sympathetic.html" rel="nofollow">Sympathetic Metaphor</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/SympatheticMetaphor.mp3" rel="nofollow">play</a> by William Sethares <a class="wiki_link_ext" href="http://www.webcitation.org/5zFdC6u4V" rel="nofollow">Permalink</a>

<a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/mp3s/truthonabus.html" rel="nofollow">Truth on a bus</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Truth_on_a_Bus.mp3" rel="nofollow">play</a> by William Sethares

<a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/mp3s/truthonabus.html" rel="nofollow">Truth on a bus</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Truth_on_a_Bus.mp3" rel="nofollow">play</a> by William Sethares <a class="wiki_link_ext" href="http://www.webcitation.org/5zFdSw1g4" rel="nofollow">Permalink</a>

<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.

@@ 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>2011-06-06 20:11:16 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-06 20:40:16 UTC</tt>.<br>
-: The original revision id was <tt>234717640</tt>.<br>
+: The original revision id was <tt>234723232</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 103: / Line 103: @@
 &lt;span class="ymp-btn-page-play ymp-media-1ec26b280d7788ac0e790719d577a218"&gt;[[http://works.music.columbia.edu/%7Echris/19mix1.mp3|Walking Down the Hillside at Cortona, and Seeing its Towers Rise Before Me]] &lt;/span&gt; by Christopher Bailey
 &lt;span class="ymp-btn-page-play ymp-media-cd7d3a983dce091a8096cb87d6862820"&gt;[[http://www.emcollective.org/chris/items/ditty/ditty_fast.mp3|Ditty]] &lt;/span&gt; by Christopher Bailey
-[[http://sethares.engr.wisc.edu/mp3s/sympathetic.html|Sympathetic Metaphor]] by William Sethares
+[[http://sethares.engr.wisc.edu/mp3s/sympathetic.html|Sympathetic Metaphor]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/SympatheticMetaphor.mp3|play]] by William Sethares [[http://www.webcitation.org/5zFdC6u4V|Permalink]]
-[[http://sethares.engr.wisc.edu/mp3s/truthonabus.html|Truth on a bus]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Truth_on_a_Bus.mp3|play]] by William Sethares
+[[http://sethares.engr.wisc.edu/mp3s/truthonabus.html|Truth on a bus]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Truth_on_a_Bus.mp3|play]] by William Sethares [[http://www.webcitation.org/5zFdSw1g4|Permalink]]
 &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.
@@ Line 134: / 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:943: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:943 --&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:946: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:946 --&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 723: / Line 723: @@
 &lt;span class="ymp-btn-page-play ymp-media-1ec26b280d7788ac0e790719d577a218"&gt;&lt;a class="wiki_link_ext" href="http://works.music.columbia.edu/%7Echris/19mix1.mp3" rel="nofollow"&gt;Walking Down the Hillside at Cortona, and Seeing its Towers Rise Before Me&lt;/a&gt; &lt;/span&gt; by Christopher Bailey&lt;br /&gt;
 &lt;span class="ymp-btn-page-play ymp-media-cd7d3a983dce091a8096cb87d6862820"&gt;&lt;a class="wiki_link_ext" href="http://www.emcollective.org/chris/items/ditty/ditty_fast.mp3" rel="nofollow"&gt;Ditty&lt;/a&gt; &lt;/span&gt; by Christopher Bailey&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/mp3s/sympathetic.html" rel="nofollow"&gt;Sympathetic Metaphor&lt;/a&gt; by William Sethares&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/mp3s/sympathetic.html" rel="nofollow"&gt;Sympathetic Metaphor&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/SympatheticMetaphor.mp3" rel="nofollow"&gt;play&lt;/a&gt; by William Sethares &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5zFdC6u4V" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/mp3s/truthonabus.html" rel="nofollow"&gt;Truth on a bus&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Truth_on_a_Bus.mp3" rel="nofollow"&gt;play&lt;/a&gt; by William Sethares&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://sethares.engr.wisc.edu/mp3s/truthonabus.html" rel="nofollow"&gt;Truth on a bus&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Sethares/Truth_on_a_Bus.mp3" rel="nofollow"&gt;play&lt;/a&gt; by William Sethares &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5zFdSw1g4" rel="nofollow"&gt;Permalink&lt;/a&gt;&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;