21edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 278429854 - Original comment: ** |
Wikispaces>phylingual **Imported revision 322860192 - 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:phylingual|phylingual]] and made on <tt>2012-04-19 17:43:08 UTC</tt>.<br> | ||
: The original revision id was <tt> | : 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> | ||
| Line 20: | Line 20: | ||
**Value** || **7-EDO** | **Value** || **7-EDO** | ||
**Notation** || **5L3s** | **Notation** || **5L3s** | ||
**Notation** ||= **D.-R. Interval** | **Notation** ||= **D.-R. Interval** | ||
**Types** ||= **Approximate** | **Types** ||= **Approximate** | ||
**Ratios*** || | **Ratios*** || | ||
| Line 59: | Line 59: | ||
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== | ||
| Line 119: | Line 134: | ||
<strong>Notation</strong><br /> | <strong>Notation</strong><br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><strong>D.-R. Interval</strong> <br /> | <td style="text-align: center;"><strong>D.-R. Interval</strong><br /> | ||
<strong>Types</strong><br /> | <strong>Types</strong><br /> | ||
</td> | </td> | ||
| Line 451: | Line 466: | ||
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.<br /> | 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.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x21 equal divisions of the octave-13-limit Commas"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x21 equal divisions of the octave-Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:6 -->Rank two temperaments</h2> | ||
<table class="wiki_table"> | |||
<tr> | |||
<th>Periods<br /> | |||
per octave<br /> | |||
</th> | |||
<th>Generator<br /> | |||
</th> | |||
<th>Temperaments<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td>1<br /> | |||
</td> | |||
<td>1\21<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Escapade%20family#Escapade">Escapade</a><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1<br /> | |||
</td> | |||
<td>2\21<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Gamelismic%20clan#Miracle">Miracle</a><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1<br /> | |||
</td> | |||
<td>4\21<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Slendric">Slendric</a>/<a class="wiki_link" href="/Gamelismic%20clan#Gorgo">Gorgo</a>/<a class="wiki_link" href="/Gamelismic%20clan#Gidorah">Gidorah</a><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1<br /> | |||
</td> | |||
<td>5\21<br /> | |||
</td> | |||
<td>Huxley<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1<br /> | |||
</td> | |||
<td>8\21<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Chromatic%20pairs#Tridec">Tridec</a><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1<br /> | |||
</td> | |||
<td>10\21<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Marvel%20temperaments#Triton">Triton</a><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3<br /> | |||
</td> | |||
<td>1\21<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3<br /> | |||
</td> | |||
<td>2\21<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Augmented%20family">Augmented</a>/<a class="wiki_link" href="/August">August</a><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3<br /> | |||
</td> | |||
<td>3\21<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>7<br /> | |||
</td> | |||
<td>1\21<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/Apotome%20family">Whitewood</a><br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x21 equal divisions of the octave-13-limit Commas"></a><!-- ws:end:WikiTextHeadingRule:8 -->13-limit Commas</h2> | |||
21 EDO tempers out the following 13-limit commas. (Note: This assumes the val &lt; 21 33 49 59 73 78 |.)<br /> | 21 EDO tempers out the following 13-limit commas. (Note: This assumes the val &lt; 21 33 49 59 73 78 |.)<br /> | ||
| Line 653: | Line 765: | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Books / Literature:"></a><!-- ws:end:WikiTextHeadingRule:10 --><strong>Books / Literature:</strong></h1> | ||
Sword, Ron. &quot;Icosihenaphonic Scales for Guitar&quot;. IAAA Press. 1st ed: July 2009.<br /> | Sword, Ron. &quot;Icosihenaphonic Scales for Guitar&quot;. IAAA Press. 1st ed: July 2009.<br /> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:622:&lt;img src=&quot;http://www.ronsword.com/images/ron1.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 188px; width: 254px;&quot; /&gt; --><img src="http://www.ronsword.com/images/ron1.jpg" alt="external image ron1.jpg" title="external image ron1.jpg" style="height: 188px; width: 254px;" /><!-- ws:end:WikiTextRemoteImageRule:622 --><!-- ws:start:WikiTextRemoteImageRule:623:&lt;img src=&quot;http://www.swordguitars.com/21tetsm.JPG&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 191px; width: 363px;&quot; /&gt; --><img src="http://www.swordguitars.com/21tetsm.JPG" alt="external image 21tetsm.JPG" title="external image 21tetsm.JPG" style="height: 191px; width: 363px;" /><!-- ws:end:WikiTextRemoteImageRule:623 --><br /> | ||
<strong><em>21-edo Icosihenaphonic Acoustic Guitar (Ron Sword)</em></strong><br /> | <strong><em>21-edo Icosihenaphonic Acoustic Guitar (Ron Sword)</em></strong><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Compositions/Listening:"></a><!-- ws:end:WikiTextHeadingRule:12 --><strong>Compositions/Listening:</strong></h1> | ||
<a class="wiki_link_ext" href="http://www.ronsword.com/sounds/21_improv.mp3" rel="nofollow" target="_blank">Short Clip of 21-edo Acoustic</a> by <a class="wiki_link" href="/Ron%20Sword">Ron Sword</a><br /> | <a class="wiki_link_ext" href="http://www.ronsword.com/sounds/21_improv.mp3" rel="nofollow" target="_blank">Short Clip of 21-edo Acoustic</a> by <a class="wiki_link" href="/Ron%20Sword">Ron Sword</a><br /> | ||
<a class="wiki_link_ext" href="http://www.ronsword.com/sounds/Ron_Sword_21_Tone_improv.mp3" rel="nofollow" target="_blank">Open tuning Drone Improvisation in 21-edo</a> by Ron Sword<br /> | <a class="wiki_link_ext" href="http://www.ronsword.com/sounds/Ron_Sword_21_Tone_improv.mp3" rel="nofollow" target="_blank">Open tuning Drone Improvisation in 21-edo</a> by Ron Sword<br /> | ||