26edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 178017805 - Original comment: ** |
Wikispaces>guest **Imported revision 180145423 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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:guest|guest]] and made on <tt>2010-11-16 15:48:05 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>180145423</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> | ||
| Line 65: | Line 65: | ||
The primary triad for Orgone Temperament is 8:11:14 and its subharmonic inversion, which these scales have in abundance. 2g approximates [[16_11|16:11]] and 3g approximates [[7_4|7:4]] (and I would call that the definition of Orgone Temperament). That also implies that g approximates the difference between 7:4 and 16:11, which is 77:64, about 320.1 cents. | The primary triad for Orgone Temperament is 8:11:14 and its subharmonic inversion, which these scales have in abundance. 2g approximates [[16_11|16:11]] and 3g approximates [[7_4|7:4]] (and I would call that the definition of Orgone Temperament). That also implies that g approximates the difference between 7:4 and 16:11, which is 77:64, about 320.1 cents. | ||
[[37edo]] is another excellent Orgone tuning. [[11edo]] is passable, but barely. If we take 11 and 26 to be the edges of the Orgone Spectrum, | [[37edo]] is another excellent Orgone tuning. [[11edo]] is passable, but barely. If we take 11 and 26 to be the edges of the Orgone Spectrum, we may fill in the rest of the spectrum thus: | ||
|| 3\11 || || || || || | |||
|| || || || || 19\70 || | |||
|| || || || 16\59 || || | |||
|| || || || || 29\107 || | |||
|| || || 13\48 || || || | |||
|| || || || || 36\133 || | |||
|| || || || 23\85 || || | |||
|| || || || || 33\122 || | |||
|| || 10\37 || || || || | |||
|| || || || || 37\137 || | |||
|| || || || 27\100 || || | |||
|| || || || || 44\163 || | |||
|| || || 17\63 || || || | |||
|| || || || || 41\152 || | |||
|| || || || 24\89 || || | |||
|| || || || || 31\115 || | |||
|| 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 272: | Line 291: | ||
The primary triad for Orgone Temperament is 8:11:14 and its subharmonic inversion, which these scales have in abundance. 2g approximates <a class="wiki_link" href="/16_11">16:11</a> and 3g approximates <a class="wiki_link" href="/7_4">7:4</a> (and I would call that the definition of Orgone Temperament). That also implies that g approximates the difference between 7:4 and 16:11, which is 77:64, about 320.1 cents.<br /> | The primary triad for Orgone Temperament is 8:11:14 and its subharmonic inversion, which these scales have in abundance. 2g approximates <a class="wiki_link" href="/16_11">16:11</a> and 3g approximates <a class="wiki_link" href="/7_4">7:4</a> (and I would call that the definition of Orgone Temperament). That also implies that g approximates the difference between 7:4 and 16:11, which is 77:64, about 320.1 cents.<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/37edo">37edo</a> is another excellent Orgone tuning. <a class="wiki_link" href="/11edo">11edo</a> is passable, but barely. If we take 11 and 26 to be the edges of the Orgone Spectrum, | <a class="wiki_link" href="/37edo">37edo</a> is another excellent Orgone tuning. <a class="wiki_link" href="/11edo">11edo</a> is passable, but barely. If we take 11 and 26 to be the edges of the Orgone Spectrum, we may fill in the rest of the spectrum thus:<br /> | ||
<br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<td>3\11<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>19\70<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>16\59<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>29\107<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>13\48<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>36\133<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>23\85<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>33\122<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td>10\37<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>37\137<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>27\100<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>44\163<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>17\63<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>41\152<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>24\89<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>31\115<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>7\26<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | |||
<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 278: | Line 508: | ||
If a name already exists for this temperament, I'd be interested to know about it. As far as I know, temperaments which ignore lower primes (in this case 3 and 5) in favor of higher ones (in this case 7 and 11) are still largely uncharted, but I am interested in finding out if someone has walked this path before.<br /> | If a name already exists for this temperament, I'd be interested to know about it. As far as I know, temperaments which ignore lower primes (in this case 3 and 5) in favor of higher ones (in this case 7 and 11) are still largely uncharted, but I am interested in finding out if someone has walked this path before.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:378:&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:378 --></body></html></pre></div> | ||