26edo: Difference between revisions
Wikispaces>guest **Imported revision 203283124 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 214920252 - 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:genewardsmith|genewardsmith]] and made on <tt>2011-03-28 23:24:48 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>214920252</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html"> | <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;white-space: pre-wrap ! important" class="old-revision-html"> | ||
=**Structure**= | =**Structure**= | ||
| Line 20: | Line 15: | ||
- K. | - K. | ||
| Line 84: | Line 48: | ||
|| || || || || 31\115 || | || || || || || 31\115 || | ||
|| 7\26 || || || || || | || 7\26 || || || || || | ||
Orgone tempers out 65539/65219 = |16 0 0 -2 -3>, and has a minimax tuning which sharpens both 7 and 11 by 1/5 of this comma, or 1.679 cents. This makes the generator g a 77/64 sharp by 2/5 of the orgone comma. From this we may conclude that 24/89 or 31/115 would be reasonable alternatives to the 7/26 generator. | Orgone tempers out 65539/65219 = |16 0 0 -2 -3>, and has a minimax tuning which sharpens both 7 and 11 by 1/5 of this comma, or 1.679 cents. This makes the generator g a 77/64 sharp by 2/5 of the orgone comma. From this we may conclude that 24/89 or 31/115 would be reasonable alternatives to the 7/26 generator. | ||
| Line 92: | Line 55: | ||
[[image:orgone_heptatonic.jpg]] | [[image:orgone_heptatonic.jpg]] | ||
=Intervals= | |||
|| degree || cents || | |||
|| 0 || 0 || | |||
|| 1 || 46.15 || | |||
|| 2 || 92.31 || | |||
|| 3 || 138.46 || | |||
|| 4 || 184.62 || | |||
|| 5 || 230.77 || | |||
|| 6 || 276.92 || | |||
|| 7 || 323.08 || | |||
|| 8 || 369.23 || | |||
|| 9 || 415.38 || | |||
|| 10 || 461.54 || | |||
|| 11 || 507.69 || | |||
|| 12 || 553.85 || | |||
|| 13 || 600.00 || | |||
|| 14 || 646.15 || | |||
|| 15 || 692.31 || | |||
|| 16 || 738.46 || | |||
|| 17 || 784.62 || | |||
|| 18 || 830.77 || | |||
|| 19 || 876.92 || | |||
|| 20 || 923.08 || | |||
|| 21 || 969.23 || | |||
|| 22 || 1015.38 || | |||
|| 23 || 1061.54 || | |||
|| 24 || 1107.69 || | |||
|| 25 || 1153.85 || | |||
=****Literature****= | =****Literature****= | ||
[[http://www.ronsword.com|Sword, Ron. **Icosihexaphonic Scales for Guitar**. IAAA Press. 2010 - A Guitar-scale thesaurus for 26-EDO.]]</pre></div> | [[http://www.ronsword.com|Sword, Ron. **Icosihexaphonic Scales for Guitar**. IAAA Press. 2010 - A Guitar-scale thesaurus for 26-EDO.]] | ||
=Compositions= | |||
[[http://soundclick.com/share?songid=5683791|A Time-Yellowed Photo of the Cliffs Hangs on the Wall ]] by [[Igliashon Jones]] | |||
[[http://www.io.com/%7Ehmiller/midi/26tet.mid|Etude in 26-tone equal tuning]] by [[Herman Miller]] | |||
[[http://danielthompson.blogspot.com/2007/04/new-version-of-organ-study-1.html|A New Recording of Organ Study #1]] by [[Daniel Thompson]] | |||
</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>26edo</title></head><body> | <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>26edo</title></head><body><br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Structure"></a><!-- ws:end:WikiTextHeadingRule:0 --><strong>Structure</strong></h1> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule: | |||
<br /> | <br /> | ||
The structure of 26-EDO is an interesting beast, and I find three particular manners of understanding the chords and chordal relationships in it;<br /> | The structure of 26-EDO is an interesting beast, and I find three particular manners of understanding the chords and chordal relationships in it;<br /> | ||
| Line 111: | Line 105: | ||
<br /> | <br /> | ||
- K.<br /> | - K.<br /> | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Orgone Temperament"></a><!-- ws:end:WikiTextHeadingRule:2 -->Orgone Temperament</h1> | |||
<!-- ws:start:WikiTextHeadingRule: | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a> proposes a temperament family which takes advantage of 26edo's excellent 11 &amp; 7 approximations. 7 degrees of 26edo is a wide minor third of approximately 323.077 cents, and that interval taken as a generator produces 7-tone and 11-tone MOS scales:<br /> | <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a> proposes a temperament family which takes advantage of 26edo's excellent 11 &amp; 7 approximations. 7 degrees of 26edo is a wide minor third of approximately 323.077 cents, and that interval taken as a generator produces 7-tone and 11-tone MOS scales:<br /> | ||
| Line 507: | Line 330: | ||
</table> | </table> | ||
<br /> | <br /> | ||
Orgone tempers out 65539/65219 = |16 0 0 -2 -3&gt;, and has a minimax tuning which sharpens both 7 and 11 by 1/5 of this comma, or 1.679 cents. This makes the generator g a 77/64 sharp by 2/5 of the orgone comma. From this we may conclude that 24/89 or 31/115 would be reasonable alternatives to the 7/26 generator.<br /> | Orgone tempers out 65539/65219 = |16 0 0 -2 -3&gt;, and has a minimax tuning which sharpens both 7 and 11 by 1/5 of this comma, or 1.679 cents. This makes the generator g a 77/64 sharp by 2/5 of the orgone comma. From this we may conclude that 24/89 or 31/115 would be reasonable alternatives to the 7/26 generator.<br /> | ||
| Line 515: | Line 337: | ||
<!-- ws:start:WikiTextLocalImageRule:380:&lt;img src=&quot;/file/view/orgone_heptatonic.jpg/155606933/orgone_heptatonic.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/orgone_heptatonic.jpg/155606933/orgone_heptatonic.jpg" alt="orgone_heptatonic.jpg" title="orgone_heptatonic.jpg" /><!-- ws:end:WikiTextLocalImageRule:380 --><br /> | <!-- ws:start:WikiTextLocalImageRule:380:&lt;img src=&quot;/file/view/orgone_heptatonic.jpg/155606933/orgone_heptatonic.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/orgone_heptatonic.jpg/155606933/orgone_heptatonic.jpg" alt="orgone_heptatonic.jpg" title="orgone_heptatonic.jpg" /><!-- ws:end:WikiTextLocalImageRule:380 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h1> | |||
<br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<td>degree<br /> | |||
</td> | |||
<td>cents<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>0<br /> | |||
</td> | |||
<td>0<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1<br /> | |||
</td> | |||
<td>46.15<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>2<br /> | |||
</td> | |||
<td>92.31<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3<br /> | |||
</td> | |||
<td>138.46<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4<br /> | |||
</td> | |||
<td>184.62<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>5<br /> | |||
</td> | |||
<td>230.77<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>6<br /> | |||
</td> | |||
<td>276.92<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>7<br /> | |||
</td> | |||
<td>323.08<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>8<br /> | |||
</td> | |||
<td>369.23<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>9<br /> | |||
</td> | |||
<td>415.38<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>10<br /> | |||
</td> | |||
<td>461.54<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>11<br /> | |||
</td> | |||
<td>507.69<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>12<br /> | |||
</td> | |||
<td>553.85<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>13<br /> | |||
</td> | |||
<td>600.00<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>14<br /> | |||
</td> | |||
<td>646.15<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>15<br /> | |||
</td> | |||
<td>692.31<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>16<br /> | |||
</td> | |||
<td>738.46<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>17<br /> | |||
</td> | |||
<td>784.62<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>18<br /> | |||
</td> | |||
<td>830.77<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>19<br /> | |||
</td> | |||
<td>876.92<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>20<br /> | |||
</td> | |||
<td>923.08<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>21<br /> | |||
</td> | |||
<td>969.23<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>22<br /> | |||
</td> | |||
<td>1015.38<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>23<br /> | |||
</td> | |||
<td>1061.54<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>24<br /> | |||
</td> | |||
<td>1107.69<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>25<br /> | |||
</td> | |||
<td>1153.85<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="x**Literature**"></a><!-- ws:end:WikiTextHeadingRule:6 -->Literature</h1> | |||
<br /> | |||
<a class="wiki_link_ext" href="http://www.ronsword.com" rel="nofollow">Sword, Ron. **Icosihexaphonic Scales for Guitar**. IAAA Press. 2010 - A Guitar-scale thesaurus for 26-EDO.</a><br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name=" | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:8 -->Compositions</h1> | ||
<br /> | <br /> | ||
<a class="wiki_link_ext" href="http://www. | <a class="wiki_link_ext" href="http://soundclick.com/share?songid=5683791" rel="nofollow">A Time-Yellowed Photo of the Cliffs Hangs on the Wall </a> by <a class="wiki_link" href="/Igliashon%20Jones">Igliashon Jones</a><br /> | ||
<a class="wiki_link_ext" href="http://www.io.com/%7Ehmiller/midi/26tet.mid" rel="nofollow">Etude in 26-tone equal tuning</a> by <a class="wiki_link" href="/Herman%20Miller">Herman Miller</a><br /> | |||
<a class="wiki_link_ext" href="http://danielthompson.blogspot.com/2007/04/new-version-of-organ-study-1.html" rel="nofollow">A New Recording of Organ Study #1</a> by <a class="wiki_link" href="/Daniel%20Thompson">Daniel Thompson</a></body></html></pre></div> | |||