21edo: Difference between revisions

Wikispaces>genewardsmith
**Imported revision 278429854 - Original comment: **
Wikispaces>phylingual
**Imported revision 322860192 - 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:genewardsmith|genewardsmith]] and made on <tt>2011-11-23 06:44:32 UTC</tt>.<br>
: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-04-19 17:43:08 UTC</tt>.<br>
: The original revision id was <tt>278429854</tt>.<br>
: The original revision id was <tt>322860192</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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**Value** || **7-EDO**
**Value** || **7-EDO**
**Notation** || **5L3s**
**Notation** || **5L3s**
**Notation** ||= **D.-R. Interval**  
**Notation** ||= **D.-R. Interval**
**Types** ||= **Approximate**
**Types** ||= **Approximate**
**Ratios*** ||
**Ratios*** ||
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For scales with a full-octave period, only 6 degrees of 21-EDO generate unique scales: 1\21, 2\21, 4\21, 5\21, 8\21, and 10\21. Other degrees generate either 7-EDO, 3-EDO, or a repetition of one of the other scales.
For scales with a full-octave period, only 6 degrees of 21-EDO generate unique scales: 1\21, 2\21, 4\21, 5\21, 8\21, and 10\21. Other degrees generate either 7-EDO, 3-EDO, or a repetition of one of the other scales.
==Rank two temperaments==
||~ Periods
per octave ||~ Generator ||~ Temperaments ||
|| 1 || 1\21 || [[Escapade family#Escapade|Escapade]] ||
|| 1 || 2\21 || [[Gamelismic clan#Miracle|Miracle]] ||
|| 1 || 4\21 || [[Slendric]]/[[Gamelismic clan#Gorgo|Gorgo]]/[[Gamelismic clan#Gidorah|Gidorah]] ||
|| 1 || 5\21 || Huxley ||
|| 1 || 8\21 || [[Chromatic pairs#Tridec|Tridec]] ||
|| 1 || 10\21 || [[Marvel temperaments#Triton|Triton]] ||
|| 3 || 1\21 ||  ||
|| 3 || 2\21 || [[Augmented family|Augmented]]/[[August]] ||
|| 3 || 3\21 ||  ||
|| 7 || 1\21 || [[Apotome family|Whitewood]] ||


==13-limit Commas==  
==13-limit Commas==  
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&lt;strong&gt;Notation&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;Notation&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;&lt;strong&gt;D.-R. Interval&lt;/strong&gt; &lt;br /&gt;
         &lt;td style="text-align: center;"&gt;&lt;strong&gt;D.-R. Interval&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;Types&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;Types&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
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For scales with a full-octave period, only 6 degrees of 21-EDO generate unique scales: 1\21, 2\21, 4\21, 5\21, 8\21, and 10\21. Other degrees generate either 7-EDO, 3-EDO, or a repetition of one of the other scales.&lt;br /&gt;
For scales with a full-octave period, only 6 degrees of 21-EDO generate unique scales: 1\21, 2\21, 4\21, 5\21, 8\21, and 10\21. Other degrees generate either 7-EDO, 3-EDO, or a repetition of one of the other scales.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x21 equal divisions of the octave-13-limit Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit Commas&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x21 equal divisions of the octave-Rank two temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Rank two temperaments&lt;/h2&gt;
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;th&gt;Periods&lt;br /&gt;
per octave&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Generator&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Temperaments&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1\21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Escapade%20family#Escapade"&gt;Escapade&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2\21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Gamelismic%20clan#Miracle"&gt;Miracle&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4\21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Slendric"&gt;Slendric&lt;/a&gt;/&lt;a class="wiki_link" href="/Gamelismic%20clan#Gorgo"&gt;Gorgo&lt;/a&gt;/&lt;a class="wiki_link" href="/Gamelismic%20clan#Gidorah"&gt;Gidorah&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5\21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Huxley&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8\21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Chromatic%20pairs#Tridec"&gt;Tridec&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10\21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Marvel%20temperaments#Triton"&gt;Triton&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1\21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2\21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Augmented%20family"&gt;Augmented&lt;/a&gt;/&lt;a class="wiki_link" href="/August"&gt;August&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3\21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1\21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Apotome%20family"&gt;Whitewood&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x21 equal divisions of the octave-13-limit Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;13-limit Commas&lt;/h2&gt;
  21 EDO tempers out the following 13-limit commas. (Note: This assumes the val &amp;lt; 21 33 49 59 73 78 |.)&lt;br /&gt;
  21 EDO tempers out the following 13-limit commas. (Note: This assumes the val &amp;lt; 21 33 49 59 73 78 |.)&lt;br /&gt;


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&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Books / Literature:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;&lt;strong&gt;Books / Literature:&lt;/strong&gt;&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Books / Literature:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;&lt;strong&gt;Books / Literature:&lt;/strong&gt;&lt;/h1&gt;
  Sword, Ron. &amp;quot;Icosihenaphonic Scales for Guitar&amp;quot;. IAAA Press. 1st ed: July 2009.&lt;br /&gt;
  Sword, Ron. &amp;quot;Icosihenaphonic Scales for Guitar&amp;quot;. IAAA Press. 1st ed: July 2009.&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:530:&amp;lt;img src=&amp;quot;http://www.ronsword.com/images/ron1.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 188px; width: 254px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.ronsword.com/images/ron1.jpg" alt="external image ron1.jpg" title="external image ron1.jpg" style="height: 188px; width: 254px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:530 --&gt;&lt;!-- ws:start:WikiTextRemoteImageRule:531:&amp;lt;img src=&amp;quot;http://www.swordguitars.com/21tetsm.JPG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 191px; width: 363px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.swordguitars.com/21tetsm.JPG" alt="external image 21tetsm.JPG" title="external image 21tetsm.JPG" style="height: 191px; width: 363px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:531 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:622:&amp;lt;img src=&amp;quot;http://www.ronsword.com/images/ron1.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 188px; width: 254px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.ronsword.com/images/ron1.jpg" alt="external image ron1.jpg" title="external image ron1.jpg" style="height: 188px; width: 254px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:622 --&gt;&lt;!-- ws:start:WikiTextRemoteImageRule:623:&amp;lt;img src=&amp;quot;http://www.swordguitars.com/21tetsm.JPG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 191px; width: 363px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.swordguitars.com/21tetsm.JPG" alt="external image 21tetsm.JPG" title="external image 21tetsm.JPG" style="height: 191px; width: 363px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:623 --&gt;&lt;br /&gt;
&lt;strong&gt;&lt;em&gt;21-edo Icosihenaphonic Acoustic Guitar (Ron Sword)&lt;/em&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;&lt;em&gt;21-edo Icosihenaphonic Acoustic Guitar (Ron Sword)&lt;/em&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Compositions/Listening:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;&lt;strong&gt;Compositions/Listening:&lt;/strong&gt;&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Compositions/Listening:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;&lt;strong&gt;Compositions/Listening:&lt;/strong&gt;&lt;/h1&gt;
  &lt;a class="wiki_link_ext" href="http://www.ronsword.com/sounds/21_improv.mp3" rel="nofollow" target="_blank"&gt;Short Clip of 21-edo Acoustic&lt;/a&gt; by &lt;a class="wiki_link" href="/Ron%20Sword"&gt;Ron Sword&lt;/a&gt;&lt;br /&gt;
  &lt;a class="wiki_link_ext" href="http://www.ronsword.com/sounds/21_improv.mp3" rel="nofollow" target="_blank"&gt;Short Clip of 21-edo Acoustic&lt;/a&gt; by &lt;a class="wiki_link" href="/Ron%20Sword"&gt;Ron Sword&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.ronsword.com/sounds/Ron_Sword_21_Tone_improv.mp3" rel="nofollow" target="_blank"&gt;Open tuning Drone Improvisation in 21-edo&lt;/a&gt; by Ron Sword&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.ronsword.com/sounds/Ron_Sword_21_Tone_improv.mp3" rel="nofollow" target="_blank"&gt;Open tuning Drone Improvisation in 21-edo&lt;/a&gt; by Ron Sword&lt;br /&gt;