31edo: Difference between revisions
Wikispaces>Andrew_Heathwaite **Imported revision 343336110 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2012-06- | : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2012-06-10 00:00:57 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>344121526</tt>.<br> | ||
: The revision comment was: <tt></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> | 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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by [[Igliashon Jones]] | by [[Igliashon Jones]] | ||
[[http://soonlabel.com/xenharmonic/wp-content/uploads/2012/03/Claudi_Meneghin_Chaconne_G_001.mp3|Chaconna en G=, La Padana, ou la septimala (‘The Padanian, or the septimal’)]] by [[Claudi Meneghin]] | [[http://soonlabel.com/xenharmonic/wp-content/uploads/2012/03/Claudi_Meneghin_Chaconne_G_001.mp3|Chaconna en G=, La Padana, ou la septimala (‘The Padanian, or the septimal’)]] by [[Claudi Meneghin]] | ||
== == | |||
==Thirty-one tone pedagogy== | ==Thirty-one tone pedagogy== | ||
The [[MicroPedagogyCollective]] is currently at work producing demonstrative material which will encourage and enable more people to learn this system. There have been two [[ThirtyOneToneSinginCamp]]s as well. | The [[MicroPedagogyCollective]] is currently at work producing demonstrative material which will encourage and enable more people to learn this system. There have been two [[ThirtyOneToneSinginCamp]]s as well. | ||
See also: [[31edo solfege]]. | |||
=Practical Theory / Books= | =Practical Theory / Books= | ||
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* <span class="wiki_link_ext">[[http://tonalsoft.com/enc/number/31edo.aspx|Tonalsoft Encyclopedia article]]</span> [[http://www.webcitation.org/5xeGYj7QU|Permalink]]</pre></div> | * <span class="wiki_link_ext">[[http://tonalsoft.com/enc/number/31edo.aspx|Tonalsoft Encyclopedia article]]</span> [[http://www.webcitation.org/5xeGYj7QU|Permalink]]</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>31edo</title></head><body><!-- ws:start:WikiTextTocRule: | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>31edo</title></head><body><!-- ws:start:WikiTextTocRule:82:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><a href="#Linear temperaments">Linear temperaments</a><!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --> | <a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --><!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --><!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --><!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --><!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --><!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --><!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --><!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --><!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --><!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --><!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --><!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --><!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --><!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --><!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --><!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --><!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --><!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --><!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --><!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --><!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --><!-- ws:end:WikiTextTocRule:109 --><!-- ws:start:WikiTextTocRule:110: --><!-- ws:end:WikiTextTocRule:110 --><!-- ws:start:WikiTextTocRule:111: --><!-- ws:end:WikiTextTocRule:111 --><!-- ws:start:WikiTextTocRule:112: --><!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextTocRule:113: --><!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --><!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --> | <a href="#Harmonic Scale">Harmonic Scale</a><!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --> | <a href="#Modes">Modes</a><!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --><!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --> | <a href="#Music in 31-edo">Music in 31-edo</a><!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --><!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --><!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --> | <a href="#Practical Theory / Books">Practical Theory / Books</a><!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --> | <a href="#Other Articles">Other Articles</a><!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --> | ||
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<em>Thirty-one tone equal temperament</em>, also called <em>31-tET</em>, <em>31-EDO</em>, <em>31-et</em>, or <em>tricesimoprimal meantone temperament</em>, is the scale derived by dividing the octave into 31 <a class="wiki_link" href="/equal">equally</a> large steps. The term 'Tricesimoprimal' was first used by <a class="wiki_link" href="/Adriaan%20Fokker">Adriaan Fokker</a>. Each step is equivalent to a frequency ratio of the 31st root of 2, or 38.71 <a class="wiki_link" href="/cents">cents</a>. 31's perfect fifth is flat of the just interval 3:2 (over five cents), as befits a tuning supporting meantone, but the major third is less than a cent sharp (of just 5:4). 31's approximation of 7:4, a cent flat, is also very close to just. Because of these near-just values 31-et is relatively quite accurate and is in fact the sixth <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta integral edo</a>. Many 7-limit JI scales are well-approximated in 31 (with tempering, of course).It also deals with the 11-limit fairly well, and is consistent through it, but is the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for the rank five temperament tempering out the 13-limit comma 66/65. It also provides the optimal patent val for mohajira, squares and casablance in the 11-limit and huygens/meantone, squares, winston, lupercalia and nightengale in the 13-limit.<br /> | <em>Thirty-one tone equal temperament</em>, also called <em>31-tET</em>, <em>31-EDO</em>, <em>31-et</em>, or <em>tricesimoprimal meantone temperament</em>, is the scale derived by dividing the octave into 31 <a class="wiki_link" href="/equal">equally</a> large steps. The term 'Tricesimoprimal' was first used by <a class="wiki_link" href="/Adriaan%20Fokker">Adriaan Fokker</a>. Each step is equivalent to a frequency ratio of the 31st root of 2, or 38.71 <a class="wiki_link" href="/cents">cents</a>. 31's perfect fifth is flat of the just interval 3:2 (over five cents), as befits a tuning supporting meantone, but the major third is less than a cent sharp (of just 5:4). 31's approximation of 7:4, a cent flat, is also very close to just. Because of these near-just values 31-et is relatively quite accurate and is in fact the sixth <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta integral edo</a>. Many 7-limit JI scales are well-approximated in 31 (with tempering, of course).It also deals with the 11-limit fairly well, and is consistent through it, but is the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a> for the rank five temperament tempering out the 13-limit comma 66/65. It also provides the optimal patent val for mohajira, squares and casablance in the 11-limit and huygens/meantone, squares, winston, lupercalia and nightengale in the 13-limit.<br /> | ||
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by <a class="wiki_link" href="/Igliashon%20Jones">Igliashon Jones</a><br /> | by <a class="wiki_link" href="/Igliashon%20Jones">Igliashon Jones</a><br /> | ||
<a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2012/03/Claudi_Meneghin_Chaconne_G_001.mp3" rel="nofollow">Chaconna en G=, La Padana, ou la septimala (‘The Padanian, or the septimal’)</a> by <a class="wiki_link" href="/Claudi%20Meneghin">Claudi Meneghin</a><br /> | <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2012/03/Claudi_Meneghin_Chaconne_G_001.mp3" rel="nofollow">Chaconna en G=, La Padana, ou la septimala (‘The Padanian, or the septimal’)</a> by <a class="wiki_link" href="/Claudi%20Meneghin">Claudi Meneghin</a><br /> | ||
<!-- ws:start:WikiTextHeadingRule:74:&lt;h2&gt; --><h2 id="toc37"><a name="Music in 31-edo-Thirty-one tone pedagogy"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:74:&lt;h2&gt; --><h2 id="toc37"><!-- ws:end:WikiTextHeadingRule:74 --> </h2> | ||
The <a class="wiki_link" href="/MicroPedagogyCollective">MicroPedagogyCollective</a> is currently at work producing demonstrative material which will encourage and enable more people to learn this system. There have been two <a class="wiki_link" href="/ThirtyOneToneSinginCamp">ThirtyOneToneSinginCamp</a>s as well.<br /> | <!-- ws:start:WikiTextHeadingRule:76:&lt;h2&gt; --><h2 id="toc38"><a name="Music in 31-edo-Thirty-one tone pedagogy"></a><!-- ws:end:WikiTextHeadingRule:76 -->Thirty-one tone pedagogy</h2> | ||
<br /> | |||
The <a class="wiki_link" href="/MicroPedagogyCollective">MicroPedagogyCollective</a> is currently at work producing demonstrative material which will encourage and enable more people to learn this system. There have been two <a class="wiki_link" href="/ThirtyOneToneSinginCamp">ThirtyOneToneSinginCamp</a>s as well.<br /> | |||
<br /> | |||
See also: <a class="wiki_link" href="/31edo%20solfege">31edo solfege</a>.<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:78:&lt;h1&gt; --><h1 id="toc39"><a name="Practical Theory / Books"></a><!-- ws:end:WikiTextHeadingRule:78 -->Practical Theory / Books</h1> | ||
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<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:7941:&lt;a href=&quot;http://www.ronsword.com/books.html&quot; target=&quot;_blank&quot; rel=&quot;nofollow&quot;&gt;&lt;img src=&quot;http://ronsword.com/images/TSG_sm.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 116px; width: 87px;&quot; /&gt;&lt;/a&gt; --><a href="http://www.ronsword.com/books.html" target="_blank" rel="nofollow"><img src="http://ronsword.com/images/TSG_sm.jpg" alt="external image TSG_sm.jpg" title="external image TSG_sm.jpg" style="height: 116px; width: 87px;" /></a><!-- ws:end:WikiTextRemoteImageRule:7941 --><a class="wiki_link_ext" href="http://www.ronsword.com/books.html" rel="nofollow" target="_blank">Sword, Ronald. &quot;Tricesimoprimal Scales for Guitar.&quot; IAAA Press, UK-USA. First Ed: March 2009.</a> - A comprehensive approach to 31-EDO and all the families associated for Guitar. Features over 300 scale charts / scale examples.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:80:&lt;h1&gt; --><h1 id="toc40"><a name="Other Articles"></a><!-- ws:end:WikiTextHeadingRule:80 -->Other Articles</h1> | ||
<ul><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/beerart.html" rel="nofollow">de Beer, Anton, ''The Development of 31-tone Music</a></span> <a class="wiki_link_ext" href="http://www.webcitation.org/5xeFzBM9b" rel="nofollow">Permalink</a></li><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/fokkerorg.html" rel="nofollow">Fokker, Adriaan Daniël, ''Equal Temperament and the Thirty-one-keyed organ</a></span> <a class="wiki_link_ext" href="http://www.webcitation.org/5xeG6Tmli" rel="nofollow">Permalink</a></li><li>Fokker, A.D., &quot;New Music with 31 Notes&quot; translated by Leigh Gerdine</li><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/rap31.html" rel="nofollow">Rapoport, Paul, ''About 31-tone Equal Temperament</a></span> <a class="wiki_link_ext" href="http://www.webcitation.org/5xeGH4uBH" rel="nofollow">Permalink</a></li><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/terp31.html" rel="nofollow">Terpstra, Siemen, ''Toward a Theory of Meantone (and 31-et) Harmony''</a></span> <a class="wiki_link_ext" href="http://www.webcitation.org/5xeGMeCMd" rel="nofollow">Permalink</a></li><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://tonalsoft.com/enc/number/31edo.aspx" rel="nofollow">Tonalsoft Encyclopedia article</a></span> <a class="wiki_link_ext" href="http://www.webcitation.org/5xeGYj7QU" rel="nofollow">Permalink</a></li></ul></body></html></pre></div> | <ul><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/beerart.html" rel="nofollow">de Beer, Anton, ''The Development of 31-tone Music</a></span> <a class="wiki_link_ext" href="http://www.webcitation.org/5xeFzBM9b" rel="nofollow">Permalink</a></li><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/fokkerorg.html" rel="nofollow">Fokker, Adriaan Daniël, ''Equal Temperament and the Thirty-one-keyed organ</a></span> <a class="wiki_link_ext" href="http://www.webcitation.org/5xeG6Tmli" rel="nofollow">Permalink</a></li><li>Fokker, A.D., &quot;New Music with 31 Notes&quot; translated by Leigh Gerdine</li><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/rap31.html" rel="nofollow">Rapoport, Paul, ''About 31-tone Equal Temperament</a></span> <a class="wiki_link_ext" href="http://www.webcitation.org/5xeGH4uBH" rel="nofollow">Permalink</a></li><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/terp31.html" rel="nofollow">Terpstra, Siemen, ''Toward a Theory of Meantone (and 31-et) Harmony''</a></span> <a class="wiki_link_ext" href="http://www.webcitation.org/5xeGMeCMd" rel="nofollow">Permalink</a></li><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://tonalsoft.com/enc/number/31edo.aspx" rel="nofollow">Tonalsoft Encyclopedia article</a></span> <a class="wiki_link_ext" href="http://www.webcitation.org/5xeGYj7QU" rel="nofollow">Permalink</a></li></ul></body></html></pre></div> | ||