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31edo: Difference between revisions

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**Imported revision 601658724 - Original comment: **
Wikispaces>TallKite
**Imported revision 602864796 - 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:TallKite|TallKite]] and made on <tt>2016-12-07 17:08:00 UTC</tt>.<br>
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-28 03:06:58 UTC</tt>.<br>
: The original revision id was <tt>601658724</tt>.<br>
: The original revision id was <tt>602864796</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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Etc.
Etc.


=Notation=


31edo can be notated with [[ups and downs notation]] like so:
31edo can be notated with [[ups and downs notation]] like so:
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0-12-18 = C Fv G = C.v4 = "C down-four"
0-12-18 = C Fv G = C.v4 = "C down-four"
etc.
etc.
For a more complete list, see [[xenharmonic/Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]].


=Harmonic Scale=  
=Harmonic Scale=  
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= =  
= =  
=Commas=  
=Commas=  
31 EDO tempers out the following commas. (Note: This assumes the val &lt; 31 49 72 87 107 115/1 |, comma values rounded to 5 significant digits.)
31 EDO tempers out the following commas. (Note: This assumes the val &lt; 31 49 72 87 107 115 |, comma values rounded to 5 significant digits.)
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 ||
||=  ||&lt; | -25 7 6 &gt; ||&gt; 31.567 ||= [[ampersand|Ampersand's Comma]] ||=  ||=  ||
||=  ||&lt; | -25 7 6 &gt; ||&gt; 31.567 ||= [[ampersand|Ampersand's Comma]] ||=  ||=  ||
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<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;31edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;a class="wiki_link" href="http://xenharmonie.wikispaces.com/31edo"&gt;Deutsch&lt;/a&gt;&lt;br /&gt;
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;31edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;a class="wiki_link" href="http://xenharmonie.wikispaces.com/31edo"&gt;Deutsch&lt;/a&gt;&lt;br /&gt;
&lt;/span&gt;&lt;br /&gt;
&lt;/span&gt;&lt;br /&gt;
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&lt;!-- ws:start:WikiTextTocRule:89:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:89 --&gt;&lt;!-- ws:start:WikiTextTocRule:90: --&gt;&lt;a href="#Linear temperaments"&gt;Linear temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:90 --&gt;&lt;!-- ws:start:WikiTextTocRule:91: --&gt; | &lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:91 --&gt;&lt;!-- ws:start:WikiTextTocRule:92: --&gt;&lt;!-- ws:end:WikiTextTocRule:92 --&gt;&lt;!-- ws:start:WikiTextTocRule:93: --&gt;&lt;!-- ws:end:WikiTextTocRule:93 --&gt;&lt;!-- ws:start:WikiTextTocRule:94: --&gt;&lt;!-- ws:end:WikiTextTocRule:94 --&gt;&lt;!-- ws:start:WikiTextTocRule:95: --&gt;&lt;!-- ws:end:WikiTextTocRule:95 --&gt;&lt;!-- ws:start:WikiTextTocRule:96: --&gt;&lt;!-- ws:end:WikiTextTocRule:96 --&gt;&lt;!-- ws:start:WikiTextTocRule:97: --&gt;&lt;!-- ws:end:WikiTextTocRule:97 --&gt;&lt;!-- ws:start:WikiTextTocRule:98: --&gt;&lt;!-- ws:end:WikiTextTocRule:98 --&gt;&lt;!-- ws:start:WikiTextTocRule:99: --&gt;&lt;!-- ws:end:WikiTextTocRule:99 --&gt;&lt;!-- ws:start:WikiTextTocRule:100: --&gt;&lt;!-- ws:end:WikiTextTocRule:100 --&gt;&lt;!-- ws:start:WikiTextTocRule:101: --&gt;&lt;!-- ws:end:WikiTextTocRule:101 --&gt;&lt;!-- ws:start:WikiTextTocRule:102: --&gt;&lt;!-- ws:end:WikiTextTocRule:102 --&gt;&lt;!-- ws:start:WikiTextTocRule:103: --&gt;&lt;!-- ws:end:WikiTextTocRule:103 --&gt;&lt;!-- ws:start:WikiTextTocRule:104: --&gt;&lt;!-- ws:end:WikiTextTocRule:104 --&gt;&lt;!-- ws:start:WikiTextTocRule:105: --&gt;&lt;!-- ws:end:WikiTextTocRule:105 --&gt;&lt;!-- ws:start:WikiTextTocRule:106: --&gt;&lt;!-- ws:end:WikiTextTocRule:106 --&gt;&lt;!-- ws:start:WikiTextTocRule:107: --&gt;&lt;!-- ws:end:WikiTextTocRule:107 --&gt;&lt;!-- ws:start:WikiTextTocRule:108: --&gt;&lt;!-- ws:end:WikiTextTocRule:108 --&gt;&lt;!-- ws:start:WikiTextTocRule:109: --&gt;&lt;!-- ws:end:WikiTextTocRule:109 --&gt;&lt;!-- ws:start:WikiTextTocRule:110: --&gt;&lt;!-- ws:end:WikiTextTocRule:110 --&gt;&lt;!-- ws:start:WikiTextTocRule:111: --&gt;&lt;!-- ws:end:WikiTextTocRule:111 --&gt;&lt;!-- ws:start:WikiTextTocRule:112: --&gt;&lt;!-- ws:end:WikiTextTocRule:112 --&gt;&lt;!-- ws:start:WikiTextTocRule:113: --&gt;&lt;!-- ws:end:WikiTextTocRule:113 --&gt;&lt;!-- ws:start:WikiTextTocRule:114: --&gt;&lt;!-- ws:end:WikiTextTocRule:114 --&gt;&lt;!-- ws:start:WikiTextTocRule:115: --&gt;&lt;!-- ws:end:WikiTextTocRule:115 --&gt;&lt;!-- ws:start:WikiTextTocRule:116: --&gt;&lt;!-- ws:end:WikiTextTocRule:116 --&gt;&lt;!-- ws:start:WikiTextTocRule:117: --&gt;&lt;!-- ws:end:WikiTextTocRule:117 --&gt;&lt;!-- ws:start:WikiTextTocRule:118: --&gt;&lt;!-- ws:end:WikiTextTocRule:118 --&gt;&lt;!-- ws:start:WikiTextTocRule:119: --&gt;&lt;!-- ws:end:WikiTextTocRule:119 --&gt;&lt;!-- ws:start:WikiTextTocRule:120: --&gt;&lt;!-- ws:end:WikiTextTocRule:120 --&gt;&lt;!-- ws:start:WikiTextTocRule:121: --&gt;&lt;!-- ws:end:WikiTextTocRule:121 --&gt;&lt;!-- ws:start:WikiTextTocRule:122: --&gt;&lt;!-- ws:end:WikiTextTocRule:122 --&gt;&lt;!-- ws:start:WikiTextTocRule:123: --&gt; | &lt;a href="#Notation"&gt;Notation&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:123 --&gt;&lt;!-- ws:start:WikiTextTocRule:124: --&gt; | &lt;a href="#Harmonic Scale"&gt;Harmonic Scale&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:124 --&gt;&lt;!-- ws:start:WikiTextTocRule:125: --&gt; | &lt;a href="#toc35"&gt; &lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:125 --&gt;&lt;!-- ws:start:WikiTextTocRule:126: --&gt; | &lt;a href="#Commas"&gt;Commas&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:126 --&gt;&lt;!-- ws:start:WikiTextTocRule:127: --&gt; | &lt;a href="#Modes"&gt;Modes&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:127 --&gt;&lt;!-- ws:start:WikiTextTocRule:128: --&gt;&lt;!-- ws:end:WikiTextTocRule:128 --&gt;&lt;!-- ws:start:WikiTextTocRule:129: --&gt; | &lt;a href="#Music in 31-edo"&gt;Music in 31-edo&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:129 --&gt;&lt;!-- ws:start:WikiTextTocRule:130: --&gt;&lt;!-- ws:end:WikiTextTocRule:130 --&gt;&lt;!-- ws:start:WikiTextTocRule:131: --&gt;&lt;!-- ws:end:WikiTextTocRule:131 --&gt;&lt;!-- ws:start:WikiTextTocRule:132: --&gt; | &lt;a href="#Practical Theory / Books"&gt;Practical Theory / Books&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:132 --&gt;&lt;!-- ws:start:WikiTextTocRule:133: --&gt; | &lt;a href="#Other Articles"&gt;Other Articles&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:133 --&gt;&lt;!-- ws:start:WikiTextTocRule:134: --&gt;
&lt;!-- ws:end:WikiTextTocRule:131 --&gt;&lt;hr /&gt;
&lt;!-- ws:end:WikiTextTocRule:134 --&gt;&lt;hr /&gt;
&lt;em&gt;Thirty-one tone equal temperament&lt;/em&gt;, also called &lt;em&gt;31-tET&lt;/em&gt;, &lt;em&gt;31-EDO&lt;/em&gt;, &lt;em&gt;31-et&lt;/em&gt;, or &lt;em&gt;tricesimoprimal meantone temperament&lt;/em&gt;, is the scale derived by dividing the octave into 31 &lt;a class="wiki_link" href="/equal"&gt;equally&lt;/a&gt; large steps. The term 'Tricesimoprimal' was first used by &lt;a class="wiki_link" href="/Adriaan%20Fokker"&gt;Adriaan Fokker&lt;/a&gt;. Each step is equivalent to a frequency ratio of the 31st root of 2, or 38.71 &lt;a class="wiki_link" href="/cents"&gt;cents&lt;/a&gt;. 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 &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists"&gt;zeta integral edo&lt;/a&gt;. Many &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; JI scales are well-approximated in 31 (with tempering, of course). It also deals with the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; fairly well, and is consistent through it, but is the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for the rank five temperament tempering out the 13-limit comma 66/65. It also provides the optimal patent val for mohajira, squares and casablanca in the 11-limit and huygens/meantone, squares, winston, lupercalia and nightengale in the 13-limit.&lt;br /&gt;
&lt;em&gt;Thirty-one tone equal temperament&lt;/em&gt;, also called &lt;em&gt;31-tET&lt;/em&gt;, &lt;em&gt;31-EDO&lt;/em&gt;, &lt;em&gt;31-et&lt;/em&gt;, or &lt;em&gt;tricesimoprimal meantone temperament&lt;/em&gt;, is the scale derived by dividing the octave into 31 &lt;a class="wiki_link" href="/equal"&gt;equally&lt;/a&gt; large steps. The term 'Tricesimoprimal' was first used by &lt;a class="wiki_link" href="/Adriaan%20Fokker"&gt;Adriaan Fokker&lt;/a&gt;. Each step is equivalent to a frequency ratio of the 31st root of 2, or 38.71 &lt;a class="wiki_link" href="/cents"&gt;cents&lt;/a&gt;. 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 &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists"&gt;zeta integral edo&lt;/a&gt;. Many &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; JI scales are well-approximated in 31 (with tempering, of course). It also deals with the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; fairly well, and is consistent through it, but is the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for the rank five temperament tempering out the 13-limit comma 66/65. It also provides the optimal patent val for mohajira, squares and casablanca in the 11-limit and huygens/meantone, squares, winston, lupercalia and nightengale in the 13-limit.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 7,504: Line 7,507:
Etc.&lt;br /&gt;
Etc.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:67:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc33"&gt;&lt;a name="Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:67 --&gt;Notation&lt;/h1&gt;
&lt;br /&gt;
31edo can be notated with &lt;a class="wiki_link" href="/ups%20and%20downs%20notation"&gt;ups and downs notation&lt;/a&gt; like so:&lt;br /&gt;
31edo can be notated with &lt;a class="wiki_link" href="/ups%20and%20downs%20notation"&gt;ups and downs notation&lt;/a&gt; like so:&lt;br /&gt;


Line 7,818: Line 7,822:
etc.&lt;br /&gt;
etc.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:67:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc33"&gt;&lt;a name="Harmonic Scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:67 --&gt;Harmonic Scale&lt;/h1&gt;
For a more complete list, see &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs"&gt;Ups and Downs Notation - Chord names in other EDOs&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:69:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc34"&gt;&lt;a name="Harmonic Scale"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:69 --&gt;Harmonic Scale&lt;/h1&gt;
  31edo approximates Mode 8 of the &lt;a class="wiki_link" href="/OverToneSeries"&gt;harmonic series&lt;/a&gt; O.K., but many intervals between the harmonics aren't distinguished, most importantly 9/8 (major tone) and 10/9 (minor tone), as 31EDO is a meantone temperament. The interval between the 8th and 11th harmonics is approximated O.K., but the intervals between the 11th harmonic and closer harmonics such as the 12th and 9th harmonics are approximated even better. 31's version of 13/8 is quite wide and only vaguely suggests the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt;.&lt;br /&gt;
  31edo approximates Mode 8 of the &lt;a class="wiki_link" href="/OverToneSeries"&gt;harmonic series&lt;/a&gt; O.K., but many intervals between the harmonics aren't distinguished, most importantly 9/8 (major tone) and 10/9 (minor tone), as 31EDO is a meantone temperament. The interval between the 8th and 11th harmonics is approximated O.K., but the intervals between the 11th harmonic and closer harmonics such as the 12th and 9th harmonics are approximated even better. 31's version of 13/8 is quite wide and only vaguely suggests the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 8,045: Line 8,051:
&lt;/table&gt;
&lt;/table&gt;


&lt;!-- ws:start:WikiTextHeadingRule:69:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc34"&gt;&lt;!-- ws:end:WikiTextHeadingRule:69 --&gt; &lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:71:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc35"&gt;&lt;!-- ws:end:WikiTextHeadingRule:71 --&gt; &lt;/h1&gt;
  &lt;!-- ws:start:WikiTextHeadingRule:71:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc35"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:71 --&gt;Commas&lt;/h1&gt;
  &lt;!-- ws:start:WikiTextHeadingRule:73:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc36"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:73 --&gt;Commas&lt;/h1&gt;
  31 EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 31 49 72 87 107 115/1 |, comma values rounded to 5 significant digits.)&lt;br /&gt;
  31 EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 31 49 72 87 107 115 |, comma values rounded to 5 significant digits.)&lt;br /&gt;




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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:73:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc36"&gt;&lt;a name="Modes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:73 --&gt;Modes&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:75:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc37"&gt;&lt;a name="Modes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:75 --&gt;Modes&lt;/h1&gt;
  &lt;br /&gt;
  &lt;br /&gt;
A large open list of modes (subsets) from 31edo that people have named: &lt;a class="wiki_link" href="/31edo%20modes"&gt;31edo modes&lt;/a&gt;. &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Rothenberg_propriety" rel="nofollow"&gt;Strictly proper&lt;/a&gt; &lt;a class="wiki_link" href="/Strictly%20proper%207-note%2031edo%20scales"&gt;7-note 31edo scales&lt;/a&gt; in the sense of &lt;a class="wiki_link" href="/David%20Rothenberg"&gt;David Rothenberg&lt;/a&gt;. Interesting (to somebody) &lt;a class="wiki_link" href="/9-note%2031edo%20scales"&gt;9-note 31edo scales&lt;/a&gt;. See also &lt;a class="wiki_link" href="/31edo%20MOS%20scales"&gt;31edo MOS scales&lt;/a&gt;. Some of the popular ones:&lt;br /&gt;
A large open list of modes (subsets) from 31edo that people have named: &lt;a class="wiki_link" href="/31edo%20modes"&gt;31edo modes&lt;/a&gt;. &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Rothenberg_propriety" rel="nofollow"&gt;Strictly proper&lt;/a&gt; &lt;a class="wiki_link" href="/Strictly%20proper%207-note%2031edo%20scales"&gt;7-note 31edo scales&lt;/a&gt; in the sense of &lt;a class="wiki_link" href="/David%20Rothenberg"&gt;David Rothenberg&lt;/a&gt;. Interesting (to somebody) &lt;a class="wiki_link" href="/9-note%2031edo%20scales"&gt;9-note 31edo scales&lt;/a&gt;. See also &lt;a class="wiki_link" href="/31edo%20MOS%20scales"&gt;31edo MOS scales&lt;/a&gt;. Some of the popular ones:&lt;br /&gt;
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&lt;table class="wiki_table"&gt;
&lt;table class="wiki_table"&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td colspan="2"&gt;&lt;!-- ws:start:WikiTextHeadingRule:75:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc37"&gt;&lt;a name="Modes---Some 31 tone equal modes:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:75 --&gt;Some 31 tone equal modes:&lt;/h4&gt;
         &lt;td colspan="2"&gt;&lt;!-- ws:start:WikiTextHeadingRule:77:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc38"&gt;&lt;a name="Modes---Some 31 tone equal modes:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:77 --&gt;Some 31 tone equal modes:&lt;/h4&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:77:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc38"&gt;&lt;a name="Music in 31-edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:77 --&gt;Music in 31-edo&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:79:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc39"&gt;&lt;a name="Music in 31-edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:79 --&gt;Music in 31-edo&lt;/h1&gt;
  &lt;a class="wiki_link" href="/31-edo%20compositions"&gt;An alphabetical list of Tricesimoprimal Compositions&lt;/a&gt;.&lt;br /&gt;
  &lt;a class="wiki_link" href="/31-edo%20compositions"&gt;An alphabetical list of Tricesimoprimal Compositions&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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&lt;a class="wiki_link_ext" href="https://www.youtube.com/watch?v=zZv-jUCynRU" rel="nofollow"&gt;Orphanage of the Dutch Music IX: Sonate no. II in the 31-tone temperament - YouTube&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="https://www.youtube.com/watch?v=zZv-jUCynRU" rel="nofollow"&gt;Orphanage of the Dutch Music IX: Sonate no. II in the 31-tone temperament - YouTube&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:79:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc39"&gt;&lt;!-- ws:end:WikiTextHeadingRule:79 --&gt; &lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:81:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc40"&gt;&lt;!-- ws:end:WikiTextHeadingRule:81 --&gt; &lt;/h2&gt;
  &lt;!-- ws:start:WikiTextHeadingRule:81:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc40"&gt;&lt;a name="Music in 31-edo-Thirty-one tone pedagogy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:81 --&gt;Thirty-one tone pedagogy&lt;/h2&gt;
  &lt;!-- ws:start:WikiTextHeadingRule:83:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc41"&gt;&lt;a name="Music in 31-edo-Thirty-one tone pedagogy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:83 --&gt;Thirty-one tone pedagogy&lt;/h2&gt;
  &lt;br /&gt;
  &lt;br /&gt;
The &lt;a class="wiki_link" href="/MicroPedagogyCollective"&gt;MicroPedagogyCollective&lt;/a&gt; is currently at work producing demonstrative material which will encourage and enable more people to learn this system. There have been two &lt;a class="wiki_link" href="/ThirtyOneToneSinginCamp"&gt;ThirtyOneToneSinginCamp&lt;/a&gt;s as well.&lt;br /&gt;
The &lt;a class="wiki_link" href="/MicroPedagogyCollective"&gt;MicroPedagogyCollective&lt;/a&gt; is currently at work producing demonstrative material which will encourage and enable more people to learn this system. There have been two &lt;a class="wiki_link" href="/ThirtyOneToneSinginCamp"&gt;ThirtyOneToneSinginCamp&lt;/a&gt;s as well.&lt;br /&gt;
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See also: &lt;a class="wiki_link" href="/31edo%20solfege"&gt;31edo solfege&lt;/a&gt;, &lt;a class="wiki_link" href="/Tricesimoprimal%20Tetrachordal%20Tesseract"&gt;Tricesimoprimal Tetrachordal Tesseract&lt;/a&gt;, &lt;a class="wiki_link" href="/Pentachords%20of%2031edo"&gt;Pentachords of 31edo&lt;/a&gt;.&lt;br /&gt;
See also: &lt;a class="wiki_link" href="/31edo%20solfege"&gt;31edo solfege&lt;/a&gt;, &lt;a class="wiki_link" href="/Tricesimoprimal%20Tetrachordal%20Tesseract"&gt;Tricesimoprimal Tetrachordal Tesseract&lt;/a&gt;, &lt;a class="wiki_link" href="/Pentachords%20of%2031edo"&gt;Pentachords of 31edo&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:83:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc41"&gt;&lt;a name="Practical Theory / Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:83 --&gt;Practical Theory / Books&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:85:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc42"&gt;&lt;a name="Practical Theory / Books"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:85 --&gt;Practical Theory / Books&lt;/h1&gt;
  &lt;br /&gt;
  &lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:8482:&amp;lt;a href=&amp;quot;http://www.ronsword.com/books.html&amp;quot; target=&amp;quot;_blank&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;http://ronsword.com/images/TSG_sm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 116px; width: 87px;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="http://www.ronsword.com/books.html" target="_blank" rel="nofollow"&gt;&lt;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;" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:8482 --&gt;&lt;a class="wiki_link_ext" href="http://www.ronsword.com/books.html" rel="nofollow" target="_blank"&gt;Sword, Ronald. &amp;quot;Tricesimoprimal Scales for Guitar.&amp;quot; IAAA Press, UK-USA. First Ed: March 2009.&lt;/a&gt; - A comprehensive approach to 31-EDO and all the families associated for Guitar. Features over 300 scale charts / scale examples.&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:8485:&amp;lt;a href=&amp;quot;http://www.ronsword.com/books.html&amp;quot; target=&amp;quot;_blank&amp;quot; rel=&amp;quot;nofollow&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;http://ronsword.com/images/TSG_sm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 116px; width: 87px;&amp;quot; /&amp;gt;&amp;lt;/a&amp;gt; --&gt;&lt;a href="http://www.ronsword.com/books.html" target="_blank" rel="nofollow"&gt;&lt;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;" /&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:8485 --&gt;&lt;a class="wiki_link_ext" href="http://www.ronsword.com/books.html" rel="nofollow" target="_blank"&gt;Sword, Ronald. &amp;quot;Tricesimoprimal Scales for Guitar.&amp;quot; IAAA Press, UK-USA. First Ed: March 2009.&lt;/a&gt; - A comprehensive approach to 31-EDO and all the families associated for Guitar. Features over 300 scale charts / scale examples.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:85:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc42"&gt;&lt;a name="Other Articles"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:85 --&gt;Other Articles&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:87:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc43"&gt;&lt;a name="Other Articles"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:87 --&gt;Other Articles&lt;/h1&gt;
  &lt;ul&gt;&lt;li&gt;&lt;span class="wiki_link_ext"&gt;&lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/beerart.html" rel="nofollow"&gt;de Beer, Anton, ''The Development of 31-tone Music&lt;/a&gt;&lt;/span&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeFzBM9b" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="wiki_link_ext"&gt;&lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/fokkerorg.html" rel="nofollow"&gt;Fokker, Adriaan Daniël, ''Equal Temperament and the Thirty-one-keyed organ&lt;/a&gt;&lt;/span&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeG6Tmli" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;Fokker, A.D., &amp;quot;New Music with 31 Notes&amp;quot; translated by Leigh Gerdine&lt;/li&gt;&lt;li&gt;&lt;span class="wiki_link_ext"&gt;&lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/rap31.html" rel="nofollow"&gt;Rapoport, Paul, ''About 31-tone Equal Temperament&lt;/a&gt;&lt;/span&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeGH4uBH" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="wiki_link_ext"&gt;&lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/terp31.html" rel="nofollow"&gt;Terpstra, Siemen, ''Toward a Theory of Meantone (and 31-et) Harmony''&lt;/a&gt;&lt;/span&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeGMeCMd" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="wiki_link_ext"&gt;&lt;a class="wiki_link_ext" href="http://tonalsoft.com/enc/number/31edo.aspx" rel="nofollow"&gt;Tonalsoft Encyclopedia article&lt;/a&gt;&lt;/span&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeGYj7QU" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
  &lt;ul&gt;&lt;li&gt;&lt;span class="wiki_link_ext"&gt;&lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/beerart.html" rel="nofollow"&gt;de Beer, Anton, ''The Development of 31-tone Music&lt;/a&gt;&lt;/span&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeFzBM9b" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="wiki_link_ext"&gt;&lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/fokkerorg.html" rel="nofollow"&gt;Fokker, Adriaan Daniël, ''Equal Temperament and the Thirty-one-keyed organ&lt;/a&gt;&lt;/span&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeG6Tmli" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;Fokker, A.D., &amp;quot;New Music with 31 Notes&amp;quot; translated by Leigh Gerdine&lt;/li&gt;&lt;li&gt;&lt;span class="wiki_link_ext"&gt;&lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/rap31.html" rel="nofollow"&gt;Rapoport, Paul, ''About 31-tone Equal Temperament&lt;/a&gt;&lt;/span&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeGH4uBH" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="wiki_link_ext"&gt;&lt;a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/terp31.html" rel="nofollow"&gt;Terpstra, Siemen, ''Toward a Theory of Meantone (and 31-et) Harmony''&lt;/a&gt;&lt;/span&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeGMeCMd" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="wiki_link_ext"&gt;&lt;a class="wiki_link_ext" href="http://tonalsoft.com/enc/number/31edo.aspx" rel="nofollow"&gt;Tonalsoft Encyclopedia article&lt;/a&gt;&lt;/span&gt; &lt;a class="wiki_link_ext" href="http://www.webcitation.org/5xeGYj7QU" rel="nofollow"&gt;Permalink&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
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&lt;!-- ws:start:WikiTextFileRule:8483:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/31-edo.svg?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@31-edo.svg&amp;quot; title=&amp;quot;File: 31-edo.svg&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/31-edo.svg/591560616/31-edo.svg" onclick="ws.common.trackFileLink('/file/view/31-edo.svg/591560616/31-edo.svg');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="31-edo.svg" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/31-edo.svg/591560616/31-edo.svg" onclick="ws.common.trackFileLink('/file/view/31-edo.svg/591560616/31-edo.svg');" class="filename" title="31-edo.svg"&gt;31-edo.svg&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/31-edo.svg"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/31-edo.svg/591560616/31-edo.svg"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;29 KB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:8483 --&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;!-- ws:start:WikiTextFileRule:8486:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/31-edo.svg?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@31-edo.svg&amp;quot; title=&amp;quot;File: 31-edo.svg&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/31-edo.svg/591560616/31-edo.svg" onclick="ws.common.trackFileLink('/file/view/31-edo.svg/591560616/31-edo.svg');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="31-edo.svg" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/31-edo.svg/591560616/31-edo.svg" onclick="ws.common.trackFileLink('/file/view/31-edo.svg/591560616/31-edo.svg');" class="filename" title="31-edo.svg"&gt;31-edo.svg&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/31-edo.svg"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/31-edo.svg/591560616/31-edo.svg"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;29 KB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:8486 --&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
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