26edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 232317066 - Original comment: ** |
Wikispaces>jdfreivald **Imported revision 233348666 - Original comment: Added comma table.** |
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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:jdfreivald|jdfreivald]] and made on <tt>2011-05-31 22:21:07 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>233348666</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>Added comma table.</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> | ||
| Line 15: | Line 15: | ||
- K. | - K. | ||
=Commas= | |||
26 EDO tempers out the following commas. (Note: This assumes the val < 26 41 60 73 90 96 |.) | |||
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || | |||
|| 81/80 || | -4 4 -1 > || 21.51 || Syntonic Comma || Didymos Comma || Meantone Comma || | |||
|| 5696703/5695946 || | -17 62 -35 > || 0.23 || Senior || || || | |||
|| 525/512 || | -9 1 2 1 > || 43.41 || Avicennma || Avicenna's Enharmonic Diesis || || | |||
|| 50/49 || | 1 0 2 -2 > || 34.98 || Tritonic Diesis || Jubilisma || || | |||
|| 875/864 || | -5 -3 3 1 > || 21.90 || Keema || || || | |||
|| 4000/3969 || | 5 -4 3 -2 > || 13.47 || Octagar || || || | |||
|| 1728/1715 || | 6 3 -1 -3 > || 13.07 || Orwellisma || Orwell Comma || || | |||
|| 1029/1024 || | -10 1 0 3 > || 8.43 || Gamelisma || || || | |||
|| 321489/320000 || | -9 8 -4 2 > || 8.04 || Varunisma || || || | |||
|| 1065875/1063543 || | -26 -1 1 9 > || 3.79 || Wadisma || || || | |||
|| 4375/4374 || | -1 -7 4 1 > || 0.40 || Ragisma || || || | |||
|| 99/98 || | -1 2 0 -2 1 > || 17.58 || Mothwellsma || || || | |||
|| 100/99 || | 2 -2 2 0 -1 > || 17.40 || Ptolemisma || || || | |||
|| 65536/65219 || | 16 0 0 -2 -3 > || 8.39 || Orgonisma || || || | |||
|| 385/384 || | -7 -1 1 1 1 > || 4.50 || Keenanisma || || || | |||
|| 441/440 || | -3 2 -1 2 -1 > || 3.93 || Werckisma || || || | |||
|| 3025/3024 || | -4 -3 2 -1 2 > || 0.57 || Lehmerisma || || || | |||
|| 9801/9800 || | -3 4 -2 -2 2 > || 0.18 || Kalisma || Gauss' Comma || || | |||
=Orgone Temperament= | =Orgone Temperament= | ||
| Line 108: | Line 128: | ||
- K.<br /> | - K.<br /> | ||
<br /> | <br /> | ||
<br /> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:2 -->Commas</h1> | ||
<!-- ws:start:WikiTextHeadingRule: | 26 EDO tempers out the following commas. (Note: This assumes the val &lt; 26 41 60 73 90 96 |.)<br /> | ||
<table class="wiki_table"> | |||
<tr> | |||
<th>Comma<br /> | |||
</th> | |||
<th>Monzo<br /> | |||
</th> | |||
<th>Value (Cents)<br /> | |||
</th> | |||
<th>Name 1<br /> | |||
</th> | |||
<th>Name 2<br /> | |||
</th> | |||
<th>Name 3<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td>81/80<br /> | |||
</td> | |||
<td>| -4 4 -1 &gt;<br /> | |||
</td> | |||
<td>21.51<br /> | |||
</td> | |||
<td>Syntonic Comma<br /> | |||
</td> | |||
<td>Didymos Comma<br /> | |||
</td> | |||
<td>Meantone Comma<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>5696703/5695946<br /> | |||
</td> | |||
<td>| -17 62 -35 &gt;<br /> | |||
</td> | |||
<td>0.23<br /> | |||
</td> | |||
<td>Senior<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>525/512<br /> | |||
</td> | |||
<td>| -9 1 2 1 &gt;<br /> | |||
</td> | |||
<td>43.41<br /> | |||
</td> | |||
<td>Avicennma<br /> | |||
</td> | |||
<td>Avicenna's Enharmonic Diesis<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>50/49<br /> | |||
</td> | |||
<td>| 1 0 2 -2 &gt;<br /> | |||
</td> | |||
<td>34.98<br /> | |||
</td> | |||
<td>Tritonic Diesis<br /> | |||
</td> | |||
<td>Jubilisma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>875/864<br /> | |||
</td> | |||
<td>| -5 -3 3 1 &gt;<br /> | |||
</td> | |||
<td>21.90<br /> | |||
</td> | |||
<td>Keema<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4000/3969<br /> | |||
</td> | |||
<td>| 5 -4 3 -2 &gt;<br /> | |||
</td> | |||
<td>13.47<br /> | |||
</td> | |||
<td>Octagar<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1728/1715<br /> | |||
</td> | |||
<td>| 6 3 -1 -3 &gt;<br /> | |||
</td> | |||
<td>13.07<br /> | |||
</td> | |||
<td>Orwellisma<br /> | |||
</td> | |||
<td>Orwell Comma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1029/1024<br /> | |||
</td> | |||
<td>| -10 1 0 3 &gt;<br /> | |||
</td> | |||
<td>8.43<br /> | |||
</td> | |||
<td>Gamelisma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>321489/320000<br /> | |||
</td> | |||
<td>| -9 8 -4 2 &gt;<br /> | |||
</td> | |||
<td>8.04<br /> | |||
</td> | |||
<td>Varunisma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1065875/1063543<br /> | |||
</td> | |||
<td>| -26 -1 1 9 &gt;<br /> | |||
</td> | |||
<td>3.79<br /> | |||
</td> | |||
<td>Wadisma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4375/4374<br /> | |||
</td> | |||
<td>| -1 -7 4 1 &gt;<br /> | |||
</td> | |||
<td>0.40<br /> | |||
</td> | |||
<td>Ragisma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>99/98<br /> | |||
</td> | |||
<td>| -1 2 0 -2 1 &gt;<br /> | |||
</td> | |||
<td>17.58<br /> | |||
</td> | |||
<td>Mothwellsma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>100/99<br /> | |||
</td> | |||
<td>| 2 -2 2 0 -1 &gt;<br /> | |||
</td> | |||
<td>17.40<br /> | |||
</td> | |||
<td>Ptolemisma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>65536/65219<br /> | |||
</td> | |||
<td>| 16 0 0 -2 -3 &gt;<br /> | |||
</td> | |||
<td>8.39<br /> | |||
</td> | |||
<td>Orgonisma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>385/384<br /> | |||
</td> | |||
<td>| -7 -1 1 1 1 &gt;<br /> | |||
</td> | |||
<td>4.50<br /> | |||
</td> | |||
<td>Keenanisma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>441/440<br /> | |||
</td> | |||
<td>| -3 2 -1 2 -1 &gt;<br /> | |||
</td> | |||
<td>3.93<br /> | |||
</td> | |||
<td>Werckisma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3025/3024<br /> | |||
</td> | |||
<td>| -4 -3 2 -1 2 &gt;<br /> | |||
</td> | |||
<td>0.57<br /> | |||
</td> | |||
<td>Lehmerisma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>9801/9800<br /> | |||
</td> | |||
<td>| -3 4 -2 -2 2 &gt;<br /> | |||
</td> | |||
<td>0.18<br /> | |||
</td> | |||
<td>Kalisma<br /> | |||
</td> | |||
<td>Gauss' Comma<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Orgone Temperament"></a><!-- ws:end:WikiTextHeadingRule:4 -->Orgone Temperament</h1> | |||
<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 337: | Line 629: | ||
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:652:&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:652 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:6 -->Intervals</h1> | ||
<br /> | <br /> | ||
| Line 509: | Line 801: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Additional Scalar Bases Available in 26-EDO:"></a><!-- ws:end:WikiTextHeadingRule:8 -->Additional Scalar Bases Available in 26-EDO:</h1> | ||
Since the perfect 5th in 26-EDO spans 15 degrees, it can be divided into three equal parts (each approximately an 8/7) as well as five equal parts (each approximately a 13/12). The former approach produces MOS at 1L+4s, 5L+1s, and 5L+6s (5 5 5 5 6, 5 5 5 5 5 1, and 4 1 4 1 4 1 4 1 4 1 1 respectively), and is excellent for 4:6:7 triads. The latter produces MOS at 1L+7s and 8L+1s (3 3 3 3 3 3 3 5 and 3 3 3 3 3 3 3 3 2 respectively), and is fairly well-supplied with 4:6:7:11:13 pentads. It also works well for more conventional (thought further from Just) 6:7:9 triads, as well as 4:5:6 triads that use the worse mapping for 5 (making 5/4 the 415.38-cent interval).<br /> | Since the perfect 5th in 26-EDO spans 15 degrees, it can be divided into three equal parts (each approximately an 8/7) as well as five equal parts (each approximately a 13/12). The former approach produces MOS at 1L+4s, 5L+1s, and 5L+6s (5 5 5 5 6, 5 5 5 5 5 1, and 4 1 4 1 4 1 4 1 4 1 1 respectively), and is excellent for 4:6:7 triads. The latter produces MOS at 1L+7s and 8L+1s (3 3 3 3 3 3 3 5 and 3 3 3 3 3 3 3 3 2 respectively), and is fairly well-supplied with 4:6:7:11:13 pentads. It also works well for more conventional (thought further from Just) 6:7:9 triads, as well as 4:5:6 triads that use the worse mapping for 5 (making 5/4 the 415.38-cent interval).<br /> | ||
<br /> | <br /> | ||
-Igs<br /> | -Igs<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Literature"></a><!-- ws:end:WikiTextHeadingRule:10 -->Literature</h1> | ||
<br /> | <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 /> | <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: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:12 -->Compositions</h1> | ||
<br /> | <br /> | ||
<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="/IgliashonJones">Igliashon Jones</a><br /> | <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="/IgliashonJones">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://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> | <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> | ||