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21edo: Difference between revisions

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**Imported revision 242488071 - Original comment: **
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**Imported revision 242633061 - 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:guest|guest]] and made on <tt>2011-07-22 21:13:40 UTC</tt>.<br>
: This revision was by author [[User:igliashon|igliashon]] and made on <tt>2011-07-24 15:17:36 UTC</tt>.<br>
: The original revision id was <tt>242488071</tt>.<br>
: The original revision id was <tt>242633061</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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Twenty-one has a period of 1/3 of the octave and boasts a neat scale dubbed "Whitewood".
Twenty-one has a period of 1/3 of the octave and boasts a neat scale dubbed "Whitewood".


0. 1/1 C
|| Degree || Cents
1. 57.143 cents C^ Dvv
Value || Name ||= Approximate
2. 114.286 cents C^^ Dv
Ratios* ||
3. 171.429 cents D
|| 0 || 0 || C ||= 1/1 ||
4. 228.571 cents D^ Evv
|| 1 || 57.143 || C^/Dvv ||= 28/27, 30/29 ||
5. 285.714 cents D^^ Ev
|| 2 || 114.286 || C^^/Dv ||= 16/15, 15/14, 29/27 ||
6. 342.857 cents E
|| 3 || 171.429 || D ||= 10/9, 32/29 ||
7. 400.000 cents E^ Fvv
|| 4 || 228.571 || D^/Evv ||= 8/7 ||
8. 457.143 cents E^^ Fv
|| 5 || 285.714 || D^^/Ev ||= 27/23, 32/27 ||
9. 514.286 cents F
|| 6 || 342.857 || E ||= 28/23 ||
10. 571.429 cents F^ Gvv
|| 7 || 400 || E^/Fvv ||= 29/23 ||
11. 628.571 cents F^^ Gv
|| 8 || 457.143 || E^^/Fv ||= 30/23 ||
12. 685.714 cents G
|| 9 || 514.286 || F ||= 161/120, 256/189 ||
13. 742.857 cents G^ Avv
|| 10 || 571.429 || F^/Gvv ||= 32/23 ||
14. 800.000 cents G^^ Av
|| 11 || 628.571 || F^^/Gv ||= 23/16 ||
15. 857.143 cents A
|| 12 || 685.714 || G ||= 189/128, 240/161 ||
16. 914.286 cents A^ Bvv
|| 13 || 742.857 || G^/Avv ||= 23/15 ||
17. 971.429 cents A^^ Bv
|| 14 || 800 || G^^/Av ||= 46/29 ||
18. 1028.571 cents B
|| 15 || 857.143 || A ||= 23/14 ||
19. 1085.714 cents B^ Cvv
|| 16 || 914.286 || A^/Bvv ||= 27/16, 46/27 ||
20. 1142.857 cents B^^ Cv
|| 17 || 971.429 || A^^/Bv ||= 7/4 ||
21. 2/1 C
|| 18 || 1028.571 || B ||= 29/16, 9/5 ||
|| 19 || 1085.714 || B^/Cvv ||= 15/8 ||
|| 20 || 1142.857 || B^^/Cv ||= 27/14, 29/15 ||
|| 21 || 1200 || C ||= 2/1 ||
 
*based on treating 21-EDO as a 2.7.15.23.27.29 subgroup temperament; other approaches are possible.


**21-tone scales:**
**21-tone scales:**
Line 79: Line 84:
Twenty-one has a period of 1/3 of the octave and boasts a neat scale dubbed &amp;quot;Whitewood&amp;quot;.&lt;br /&gt;
Twenty-one has a period of 1/3 of the octave and boasts a neat scale dubbed &amp;quot;Whitewood&amp;quot;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
0. 1/1 C&lt;br /&gt;
 
1. 57.143 cents C^ Dvv&lt;br /&gt;
 
2. 114.286 cents C^^ Dv&lt;br /&gt;
&lt;table class="wiki_table"&gt;
3. 171.429 cents D&lt;br /&gt;
    &lt;tr&gt;
4. 228.571 cents D^ Evv&lt;br /&gt;
        &lt;td&gt;Degree&lt;br /&gt;
5. 285.714 cents D^^ Ev&lt;br /&gt;
&lt;/td&gt;
6. 342.857 cents E&lt;br /&gt;
        &lt;td&gt;Cents&lt;br /&gt;
7. 400.000 cents E^ Fvv&lt;br /&gt;
Value&lt;br /&gt;
8. 457.143 cents E^^ Fv&lt;br /&gt;
&lt;/td&gt;
9. 514.286 cents F&lt;br /&gt;
        &lt;td&gt;Name&lt;br /&gt;
10. 571.429 cents F^ Gvv&lt;br /&gt;
&lt;/td&gt;
11. 628.571 cents F^^ Gv&lt;br /&gt;
        &lt;td style="text-align: center;"&gt;Approximate&lt;br /&gt;
12. 685.714 cents G&lt;br /&gt;
Ratios*&lt;br /&gt;
13. 742.857 cents G^ Avv&lt;br /&gt;
&lt;/td&gt;
14. 800.000 cents G^^ Av&lt;br /&gt;
    &lt;/tr&gt;
15. 857.143 cents A&lt;br /&gt;
    &lt;tr&gt;
16. 914.286 cents A^ Bvv&lt;br /&gt;
        &lt;td&gt;0&lt;br /&gt;
17. 971.429 cents A^^ Bv&lt;br /&gt;
&lt;/td&gt;
18. 1028.571 cents B&lt;br /&gt;
        &lt;td&gt;0&lt;br /&gt;
19. 1085.714 cents B^ Cvv&lt;br /&gt;
&lt;/td&gt;
20. 1142.857 cents B^^ Cv&lt;br /&gt;
        &lt;td&gt;C&lt;br /&gt;
21. 2/1 C&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1/1&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;57.143&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C^/Dvv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;28/27, 30/29&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;114.286&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C^^/Dv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;16/15, 15/14, 29/27&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;171.429&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;D&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;10/9, 32/29&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;228.571&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;D^/Evv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;8/7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;285.714&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;D^^/Ev&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;27/23, 32/27&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;342.857&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;E&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;28/23&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;400&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;E^/Fvv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;29/23&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;457.143&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;E^^/Fv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;30/23&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;514.286&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;161/120, 256/189&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;571.429&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;F^/Gvv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;32/23&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;628.571&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;F^^/Gv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;23/16&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;685.714&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;189/128, 240/161&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;742.857&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G^/Avv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;23/15&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;800&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G^^/Av&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;46/29&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;857.143&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;23/14&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;914.286&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A^/Bvv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;27/16, 46/27&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;971.429&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A^^/Bv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7/4&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1028.571&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;B&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;29/16, 9/5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1085.714&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;B^/Cvv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;15/8&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1142.857&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;B^^/Cv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;27/14, 29/15&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1200&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;C&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2/1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
*based on treating 21-EDO as a 2.7.15.23.27.29 subgroup temperament; other approaches are possible.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;strong&gt;21-tone scales:&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;21-tone scales:&lt;/strong&gt;&lt;br /&gt;
Line 313: Line 535:
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Books / Literature:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;&lt;strong&gt;Books / Literature:&lt;/strong&gt;&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Books / Literature:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&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:202:&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:202 --&gt;&lt;!-- ws:start:WikiTextRemoteImageRule:203:&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:203 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:434:&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:434 --&gt;&lt;!-- ws:start:WikiTextRemoteImageRule:435:&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:435 --&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;
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