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>2011-06-~~07 17~~:15:53 UTC</tt>.

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-08 01:55:42 UTC</tt>.

: The original revision id was <tt>~~234969822~~</tt>.

: The original revision id was <tt>235071742</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://www.akjmusic.com/audio/juggler.mp3|The Juggler]] by [[Aaron Krister Johnson]]

[[http://www.soundclick.com/bands/page_songInfo.cfm?bandID=145852&songID=1008195|Foum]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Barton/Foum.mp3|play]] by [[Jacob Barton]]

[[http://music.columbia.edu/%7Echris/sand.html|Sand]] by [[Christopher Bailey]]

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

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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://www.akjmusic.com/audio/juggler.mp3" rel="nofollow">The Juggler</a> by <a class="wiki_link" href="/Aaron%20Krister%20Johnson">Aaron Krister Johnson</a>

<a class="wiki_link_ext" href="http://www.soundclick.com/bands/page_songInfo.cfm?bandID=145852&amp;songID=1008195" rel="nofollow">Foum</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Barton/Foum.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Jacob%20Barton">Jacob Barton</a>

<a class="wiki_link_ext" href="http://music.columbia.edu/%7Echris/sand.html" rel="nofollow">Sand</a> by <a class="wiki_link" href="/Christopher%20Bailey">Christopher Bailey</a>

<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

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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:xenwolf|xenwolf]] and made on <tt>2011-06-07 17:15:53 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-08 01:55:42 UTC</tt>.<br>
-: The original revision id was <tt>234969822</tt>.<br>
+: The original revision id was <tt>235071742</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 100: / Line 100: @@
 &lt;span class="ymp-btn-page-play ymp-media-3e72a120cc21a6d967e20c2712353cac"&gt;[[http://www.akjmusic.com/audio/juggler.mp3|The Juggler]] &lt;/span&gt; by [[Aaron Krister Johnson]]
+[[http://www.soundclick.com/bands/page_songInfo.cfm?bandID=145852&amp;songID=1008195|Foum]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Barton/Foum.mp3|play]] by [[Jacob Barton]]
 [[http://music.columbia.edu/%7Echris/sand.html|Sand]] by [[Christopher Bailey]]
 &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
@@ Line 135: / Line 136: @@
 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:958: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:958 --&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:962: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:962 --&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 721: / Line 722: @@
   &lt;br /&gt;
 &lt;span class="ymp-btn-page-play ymp-media-3e72a120cc21a6d967e20c2712353cac"&gt;&lt;a class="wiki_link_ext" href="http://www.akjmusic.com/audio/juggler.mp3" rel="nofollow"&gt;The Juggler&lt;/a&gt; &lt;/span&gt; by &lt;a class="wiki_link" href="/Aaron%20Krister%20Johnson"&gt;Aaron Krister Johnson&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://www.soundclick.com/bands/page_songInfo.cfm?bandID=145852&amp;amp;songID=1008195" rel="nofollow"&gt;Foum&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Barton/Foum.mp3" rel="nofollow"&gt;play&lt;/a&gt; by &lt;a class="wiki_link" href="/Jacob%20Barton"&gt;Jacob Barton&lt;/a&gt;&lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://music.columbia.edu/%7Echris/sand.html" rel="nofollow"&gt;Sand&lt;/a&gt; by &lt;a class="wiki_link" href="/Christopher%20Bailey"&gt;Christopher Bailey&lt;/a&gt;&lt;br /&gt;
 &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;