31edo: Difference between revisions
Wikispaces>xenwolf **Imported revision 549284250 - Original comment: ** |
Wikispaces>MasonGreen1 **Imported revision 574848367 - 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: | : This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-02-15 01:28:43 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>574848367</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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|| Nearest degree of 31edo: || 0 || 5 || 10 || 14 || 18 || 22 || 25 || 28 || 31 || | || Nearest degree of 31edo: || 0 || 5 || 10 || 14 || 18 || 22 || 25 || 28 || 31 || | ||
|| ...in cents: || 0 || 193.5 || 387.1 || 541.9 || 696.8 || 851.6 || 967.7 || 1083.9 || 1200.0 || | || ...in cents: || 0 || 193.5 || 387.1 || 541.9 || 696.8 || 851.6 || 967.7 || 1083.9 || 1200.0 || | ||
In mode 16, the most closely-matched harmonics are the composite ones, 21 and 25. Of the other harmonics: | |||
* 17 is sharp, like 13. In fact, the 17:13 ratio is matched within a tenth of a cent. | |||
* 19 is also sharp, like 13 and 17. The 19:17 ratio is about one cent sharp. | |||
* 23 is about as flat as 11. The chromatic semitone is about half a cent off from 23:22. 31edo could be considered a tuning of the 2.3.5.7.11.23 subset, on which it is consistent. | |||
* 27 is quite flat, as it's 3^3 and the error from the meantone fifths accumulates. | |||
* 29 and 31 are both //very// sharp, and intervals involving them are unlikely to play any major role. | |||
|| Odd overtones in "Mode 16": || 17 || 19 || 21 || 23 || 25 || 27 || 29 || 31 || | |||
|| ...as JI Ratio from 1/1: || 17/16 || 19/16 || 21/16 || 23/16 || 25/16 || 27/16 || 29/16 || 31/16 || | |||
|| ...in cents: || 105.0 || 297.5 || 470.8 || 628.3 || 772.6 || 905.9 || 1029.6 || 1145.0 || | |||
|| Nearest degree of 31edo: || 3 || 8 || 12 || 16 || 20 || 23 || 27 || 28 || | |||
|| ...in cents: || 116.1 || 309.7 || 464.5 || 619.4 || 774.2 || 890.3 || 1045.1 || 1161.3 || | |||
= = | |||
=Commas= | =Commas= | ||
31 EDO tempers out the following commas. (Note: This assumes the val < 31 49 72 87 107 115 |, comma values roundet to 5 significant digits.) | 31 EDO tempers out the following commas. (Note: This assumes the val < 31 49 72 87 107 115 |, comma values roundet to 5 significant digits.) | ||
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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:86:&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:86 --><!-- ws:start:WikiTextTocRule:87: --><a href="#Linear temperaments">Linear temperaments</a><!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --> | <a href="#Intervals">Intervals</a><!-- 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: --><!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --><!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --><!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --><!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --><!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --> | <a href="#Harmonic Scale">Harmonic Scale</a><!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --> | <a href="#toc34"> </a><!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --> | <a href="#Modes">Modes</a><!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --><!-- ws:end:WikiTextTocRule:124 --><!-- ws:start:WikiTextTocRule:125: --> | <a href="#Music in 31-edo">Music in 31-edo</a><!-- ws:end:WikiTextTocRule:125 --><!-- ws:start:WikiTextTocRule:126: --><!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --><!-- ws:end:WikiTextTocRule:127 --><!-- ws:start:WikiTextTocRule:128: --> | <a href="#Practical Theory / Books">Practical Theory / Books</a><!-- ws:end:WikiTextTocRule:128 --><!-- ws:start:WikiTextTocRule:129: --> | <a href="#Other Articles">Other Articles</a><!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:130 --><hr /> | ||
<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 casablanca 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 casablanca in the 11-limit and huygens/meantone, squares, winston, lupercalia and nightengale in the 13-limit.<br /> | ||
<br /> | <br /> | ||
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</table> | </table> | ||
<!-- ws:start:WikiTextHeadingRule:68:&lt;h1&gt; --><h1 id="toc34"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule: | <br /> | ||
In mode 16, the most closely-matched harmonics are the composite ones, 21 and 25. Of the other harmonics:<br /> | |||
<br /> | |||
<ul><li>17 is sharp, like 13. In fact, the 17:13 ratio is matched within a tenth of a cent.</li><li>19 is also sharp, like 13 and 17. The 19:17 ratio is about one cent sharp.</li><li>23 is about as flat as 11. The chromatic semitone is about half a cent off from 23:22. 31edo could be considered a tuning of the 2.3.5.7.11.23 subset, on which it is consistent.</li><li>27 is quite flat, as it's 3^3 and the error from the meantone fifths accumulates.</li><li>29 and 31 are both <em>very</em> sharp, and intervals involving them are unlikely to play any major role.</li></ul><br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<td>Odd overtones in &quot;Mode 16&quot;:<br /> | |||
</td> | |||
<td>17<br /> | |||
</td> | |||
<td>19<br /> | |||
</td> | |||
<td>21<br /> | |||
</td> | |||
<td>23<br /> | |||
</td> | |||
<td>25<br /> | |||
</td> | |||
<td>27<br /> | |||
</td> | |||
<td>29<br /> | |||
</td> | |||
<td>31<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>...as JI Ratio from 1/1:<br /> | |||
</td> | |||
<td>17/16<br /> | |||
</td> | |||
<td>19/16<br /> | |||
</td> | |||
<td>21/16<br /> | |||
</td> | |||
<td>23/16<br /> | |||
</td> | |||
<td>25/16<br /> | |||
</td> | |||
<td>27/16<br /> | |||
</td> | |||
<td>29/16<br /> | |||
</td> | |||
<td>31/16<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>...in cents:<br /> | |||
</td> | |||
<td>105.0<br /> | |||
</td> | |||
<td>297.5<br /> | |||
</td> | |||
<td>470.8<br /> | |||
</td> | |||
<td>628.3<br /> | |||
</td> | |||
<td>772.6<br /> | |||
</td> | |||
<td>905.9<br /> | |||
</td> | |||
<td>1029.6<br /> | |||
</td> | |||
<td>1145.0<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>Nearest degree of 31edo:<br /> | |||
</td> | |||
<td>3<br /> | |||
</td> | |||
<td>8<br /> | |||
</td> | |||
<td>12<br /> | |||
</td> | |||
<td>16<br /> | |||
</td> | |||
<td>20<br /> | |||
</td> | |||
<td>23<br /> | |||
</td> | |||
<td>27<br /> | |||
</td> | |||
<td>28<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>...in cents:<br /> | |||
</td> | |||
<td>116.1<br /> | |||
</td> | |||
<td>309.7<br /> | |||
</td> | |||
<td>464.5<br /> | |||
</td> | |||
<td>619.4<br /> | |||
</td> | |||
<td>774.2<br /> | |||
</td> | |||
<td>890.3<br /> | |||
</td> | |||
<td>1045.1<br /> | |||
</td> | |||
<td>1161.3<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<!-- ws:start:WikiTextHeadingRule:68:&lt;h1&gt; --><h1 id="toc34"><!-- ws:end:WikiTextHeadingRule:68 --> </h1> | |||
<!-- ws:start:WikiTextHeadingRule:70:&lt;h1&gt; --><h1 id="toc35"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:70 -->Commas</h1> | |||
31 EDO tempers out the following commas. (Note: This assumes the val &lt; 31 49 72 87 107 115 |, comma values roundet to 5 significant digits.)<br /> | 31 EDO tempers out the following commas. (Note: This assumes the val &lt; 31 49 72 87 107 115 |, comma values roundet to 5 significant digits.)<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:72:&lt;h1&gt; --><h1 id="toc36"><a name="Modes"></a><!-- ws:end:WikiTextHeadingRule:72 -->Modes</h1> | ||
<br /> | <br /> | ||
A large open list of modes (subsets) from 31edo that people have named: <a class="wiki_link" href="/31edo%20modes">31edo modes</a>. <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Rothenberg_propriety" rel="nofollow">Strictly proper</a> <a class="wiki_link" href="/Strictly%20proper%207-note%2031edo%20scales">7-note 31edo scales</a> in the sense of <a class="wiki_link" href="/David%20Rothenberg">David Rothenberg</a>. Interesting (to somebody) <a class="wiki_link" href="/9-note%2031edo%20scales">9-note 31edo scales</a>. See also <a class="wiki_link" href="/31edo%20MOS%20scales">31edo MOS scales</a>. Some of the popular ones:<br /> | A large open list of modes (subsets) from 31edo that people have named: <a class="wiki_link" href="/31edo%20modes">31edo modes</a>. <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Rothenberg_propriety" rel="nofollow">Strictly proper</a> <a class="wiki_link" href="/Strictly%20proper%207-note%2031edo%20scales">7-note 31edo scales</a> in the sense of <a class="wiki_link" href="/David%20Rothenberg">David Rothenberg</a>. Interesting (to somebody) <a class="wiki_link" href="/9-note%2031edo%20scales">9-note 31edo scales</a>. See also <a class="wiki_link" href="/31edo%20MOS%20scales">31edo MOS scales</a>. Some of the popular ones:<br /> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td colspan="2"><!-- ws:start:WikiTextHeadingRule: | <td colspan="2"><!-- ws:start:WikiTextHeadingRule:74:&lt;h4&gt; --><h4 id="toc37"><a name="Modes---Some 31 tone equal modes:"></a><!-- ws:end:WikiTextHeadingRule:74 -->Some 31 tone equal modes:</h4> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:76:&lt;h1&gt; --><h1 id="toc38"><a name="Music in 31-edo"></a><!-- ws:end:WikiTextHeadingRule:76 -->Music in 31-edo</h1> | ||
<a class="wiki_link" href="/31-edo%20compositions">An alphabetical list of Tricesimoprimal Compositions</a>.<br /> | <a class="wiki_link" href="/31-edo%20compositions">An alphabetical list of Tricesimoprimal Compositions</a>.<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link_ext" href="https://www.youtube.com/watch?v=r1mat9f1DZ0" rel="nofollow">Fanfare and Toccata</a> by <a class="wiki_link" href="/Juhani%20Nuorvala">Juhani Nuorvala</a><br /> | <a class="wiki_link_ext" href="https://www.youtube.com/watch?v=r1mat9f1DZ0" rel="nofollow">Fanfare and Toccata</a> by <a class="wiki_link" href="/Juhani%20Nuorvala">Juhani Nuorvala</a><br /> | ||
by Johann alias circular17: <a class="wiki_link_ext" href="https://www.youtube.com/watch?v=BBC8wiguN1A&amp;index=5&amp;list=PLRE0IICPofOVS-W5X2Rd7d9d3qzhxMnJN" rel="nofollow" target="_blank">Curieuse planète</a>, <a class="wiki_link_ext" href="https://www.youtube.com/watch?v=8PdJgmDJwu4&amp;index=4&amp;list=PLRE0IICPofOVS-W5X2Rd7d9d3qzhxMnJN" rel="nofollow" target="_blank">Heal</a>, <a class="wiki_link_ext" href="https://www.youtube.com/watch?v=j5eno0ejH0Y&amp;index=2&amp;list=PLRE0IICPofOVS-W5X2Rd7d9d3qzhxMnJN" rel="nofollow" target="_blank">Wave from the past</a>, <a class="wiki_link_ext" href="https://www.youtube.com/watch?v=fyPtr24qBd8&amp;index=1&amp;list=PLRE0IICPofOVS-W5X2Rd7d9d3qzhxMnJN" rel="nofollow" target="_blank">Deep but not too much</a>.<br /> | by Johann alias circular17: <a class="wiki_link_ext" href="https://www.youtube.com/watch?v=BBC8wiguN1A&amp;index=5&amp;list=PLRE0IICPofOVS-W5X2Rd7d9d3qzhxMnJN" rel="nofollow" target="_blank">Curieuse planète</a>, <a class="wiki_link_ext" href="https://www.youtube.com/watch?v=8PdJgmDJwu4&amp;index=4&amp;list=PLRE0IICPofOVS-W5X2Rd7d9d3qzhxMnJN" rel="nofollow" target="_blank">Heal</a>, <a class="wiki_link_ext" href="https://www.youtube.com/watch?v=j5eno0ejH0Y&amp;index=2&amp;list=PLRE0IICPofOVS-W5X2Rd7d9d3qzhxMnJN" rel="nofollow" target="_blank">Wave from the past</a>, <a class="wiki_link_ext" href="https://www.youtube.com/watch?v=fyPtr24qBd8&amp;index=1&amp;list=PLRE0IICPofOVS-W5X2Rd7d9d3qzhxMnJN" rel="nofollow" target="_blank">Deep but not too much</a>.<br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:78:&lt;h2&gt; --><h2 id="toc39"><!-- ws:end:WikiTextHeadingRule:78 --> </h2> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:80:&lt;h2&gt; --><h2 id="toc40"><a name="Music in 31-edo-Thirty-one tone pedagogy"></a><!-- ws:end:WikiTextHeadingRule:80 -->Thirty-one tone pedagogy</h2> | ||
<br /> | <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 /> | 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 /> | ||
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See also: <a class="wiki_link" href="/31edo%20solfege">31edo solfege</a>, <a class="wiki_link" href="/Tricesimoprimal%20Tetrachordal%20Tesseract">Tricesimoprimal Tetrachordal Tesseract</a>, <a class="wiki_link" href="/Pentachords%20of%2031edo">Pentachords of 31edo</a>.<br /> | See also: <a class="wiki_link" href="/31edo%20solfege">31edo solfege</a>, <a class="wiki_link" href="/Tricesimoprimal%20Tetrachordal%20Tesseract">Tricesimoprimal Tetrachordal Tesseract</a>, <a class="wiki_link" href="/Pentachords%20of%2031edo">Pentachords of 31edo</a>.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:82:&lt;h1&gt; --><h1 id="toc41"><a name="Practical Theory / Books"></a><!-- ws:end:WikiTextHeadingRule:82 -->Practical Theory / Books</h1> | ||
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<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:8213:&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:8213 --><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:84:&lt;h1&gt; --><h1 id="toc42"><a name="Other Articles"></a><!-- ws:end:WikiTextHeadingRule:84 -->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> | ||