14edo: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 597494574 - Original comment: ** |
Wikispaces>TallKite **Imported revision 599946362 - 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:TallKite|TallKite]] and made on <tt>2016-11-21 03:56:02 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>599946362</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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[[toc|flat]] | [[toc|flat]] | ||
=**Intervals**= | =**Intervals**= | ||
|| **DEGREE** || | || **DEGREE** || [[xenharmonic/Ups and Downs Notation|up/down]] | ||
[[xenharmonic/Ups and Downs Notation| name]] || **CENTS (coarse/fine)** | |||
**<span style="background-color: #ffffff;">DMS</span>** ||= **Approximate** | **<span style="background-color: #ffffff;">DMS</span>** ||= **Approximate** | ||
**Ratios 1``*``** ||= **Approximate** | **Ratios 1``*``** ||= **Approximate** | ||
**Ratios 2** **``**``** ||= Nearest | **Ratios 2** **``**``** ||= Nearest | ||
Harmonic || Interval Type || | Harmonic || Interval Type ||= [[Ups and Downs Notation|up/down name]] || | ||
|| 0 || C || 0 ||= 1/1 ||= 1/1 ||= 1 || Unison || | || 0 || C || 0 ||= 1/1 ||= 1/1 ||= 1 || Unison ||= unison || | ||
|| 1 || C^, Dv || 85.714, 102.857 | || 1 || C^, Dv || 85.714, 102.857 | ||
25°42'51" ||= 20/19, 19/18, 18/17 ||= 22/21, 28/27, 21/20 ||= 67 || Narrow Minor 2nd || | 25°42'51" ||= 20/19, 19/18, 18/17 ||= 22/21, 28/27, 21/20 ||= 67 || Narrow Minor 2nd ||= up-unison, | ||
down-2nd || | |||
|| 2 || D || 171.429, 205.714 | || 2 || D || 171.429, 205.714 | ||
<span style="background-color: #ffffff;">51°25'43"</span> ||= 11/10, 10/9, 19/17 ||= 9/8, 10/9, 11/10, | <span style="background-color: #ffffff;">51°25'43"</span> ||= 11/10, 10/9, | ||
12/11 ||= 71 || Neutral 2nd, or | 19/17 ||= 9/8, 10/9, | ||
Narrow Major 2nd || | 11/10, 12/11 ||= 71 || Neutral 2nd, or | ||
Narrow Major 2nd ||= 2nd || | |||
|| 3· || D^, Ev || 257.143, 308.571 | || 3· || D^, Ev || 257.143, 308.571 | ||
77°8'34" ||= 22/19, 20/17 ||= 7/6, 8/7 ||= 37 || Subminor 3rd || | 77°8'34" ||= 22/19, 20/17 ||= 7/6, 8/7 ||= 37 || Subminor 3rd ||= up-2nd, | ||
down-3rd || | |||
|| 4 || E || 342.857, 411.429 | || 4 || E || 342.857, 411.429 | ||
<span style="background-color: #ffffff;">102°51'26"</span> ||= 11/9, 17/14 ||= 11/9, 5/4, 6/5 ||= 39 || Neutral 3rd || | <span style="background-color: #ffffff;">102°51'26"</span> ||= 11/9, 17/14 ||= 11/9, 5/4, 6/5 ||= 39 || Neutral 3rd ||= 3rd || | ||
|| 5· || E^, Fv || 428.571, 514.286 | || 5· || E^, Fv || 428.571, 514.286 | ||
<span style="line-height: 15.6000003814697px;">128°34'17"</span> ||= 9/7, 14/11, 22/17 ||= 9/7, 14/11 ||= 41 || Supermajor 3rd || | <span style="line-height: 15.6000003814697px;">128°34'17"</span> ||= 9/7, 14/11, | ||
22/17 ||= 9/7, 14/11 ||= 41 || Supermajor 3rd ||= up-3rd, | |||
down-4th || | |||
|| 6 || F || 51<span style="line-height: 1.5;">4.286, 617.143</span> | || 6 || F || 51<span style="line-height: 1.5;">4.286, 617.143</span> | ||
<span style="background-color: #ffffff;">154°17'9"</span> ||= 19/14 ||= 4/3, 11/8 ||= 43 || Wide 4th || | <span style="background-color: #ffffff;">154°17'9"</span> ||= 19/14 ||= 4/3, 11/8 ||= 43 || Wide 4th ||= 4th || | ||
|| 7· || F^, Gv || 600, 720 | || 7· || F^, Gv || 600, 720 | ||
180° ||= 7/5, 10/7 ||= 7/5, 10/7 ||= 91 || Tritone || | 180° ||= 7/5, 10/7 ||= 7/5, 10/7 ||= 91 || Tritone ||= up-4th, | ||
down-5th || | |||
|| 8 || G || 685.714, 823.857 | || 8 || G || 685.714, 823.857 | ||
<span style="background-color: #ffffff;">205°42'51"</span> ||= 28/19 ||= 3/2, 16/11 ||= 95 || Narrow 5th || | <span style="background-color: #ffffff;">205°42'51"</span> ||= 28/19 ||= 3/2, 16/11 ||= 95 || Narrow 5th ||= 5th || | ||
|| 9· || G^, Av || 771.429, 925.714 | || 9· || G^, Av || 771.429, 925.714 | ||
231°25'43" ||= 14/9, 11/7, 17/11 ||= ||= 25 || Subminor 6th || | 231°25'43" ||= 14/9, 11/7, | ||
17/11 ||= ||= 25 || Subminor 6th ||= up-fifth, | |||
down-6th || | |||
|| 10 || A || 857.143, 1028.571 | || 10 || A || 857.143, 1028.571 | ||
<span style="background-color: #ffffff;">257°8'34"</span> ||= 18/11 ||= 18/11, 8/5, 5/3 ||= 105 || Neutral 6th || | <span style="background-color: #ffffff;">257°8'34"</span> ||= 18/11 ||= 18/11, 8/5, 5/3 ||= 105 || Neutral 6th ||= 6th || | ||
|| 11· || A^, Bv || 942.857, 1131.429 | || 11· || A^, Bv || 942.857, 1131.429 | ||
282°51'26" ||= 19/11, 17/10 ||= 12/7, 7/4 ||= 55 || Supermajor 6th || | 282°51'26" ||= 19/11, 17/10 ||= 12/7, 7/4 ||= 55 || Supermajor 6th ||= up-6th, | ||
down-7th || | |||
|| 12 || B || 1028.571, 1234.286 | || 12 || B || 1028.571, 1234.286 | ||
<span style="background-color: #ffffff;">308°34'17"</span> ||= 20/11, 9/5, 34/19 ||= 16/9, 9/5, 20/11, | <span style="background-color: #ffffff;">308°34'17"</span> ||= 20/11, 9/5, | ||
11/6 ||= 29 || Neutral 7th, or | 34/19 ||= 16/9, 9/5, | ||
Wide Minor 7th || | 20/11, 11/6 ||= 29 || Neutral 7th, or | ||
Wide Minor 7th ||= 7th || | |||
|| 13 || B^, Cv || 1114.286, 1337.143 | || 13 || B^, Cv || 1114.286, 1337.143 | ||
334°17'9" ||= 19/10, 36/19, 17/9 ||= 21/11, 27/14, 40/21 ||= 61 || Wide Major 7th || | 334°17'9" ||= 19/10, 36/19, | ||
17/9 ||= 21/11, 27/14, 40/21 ||= 61 || Wide Major 7th ||= up-7th, | |||
down-8ve || | |||
|| 14··(or 0) || C || 1200, 1440 | || 14··(or 0) || C || 1200, 1440 | ||
360° ||= 2/1 ||= 2/1 ||= 2 || Octave || | 360° ||= 2/1 ||= 2/1 ||= 2 || Octave ||= 8ve || | ||
``*``based on treating 14-EDO as a 2.7/5.9/5.11/5.17/5.19/5 [[subgroup]]; other approaches are possible. | ``*``based on treating 14-EDO as a 2.7/5.9/5.11/5.17/5.19/5 [[subgroup]]; other approaches are possible. | ||
<span style="display: block; text-align: center;">``**``</span> | <span style="display: block; text-align: center;">``**``</span> | ||
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<td><strong>DEGREE</strong><br /> | <td><strong>DEGREE</strong><br /> | ||
</td> | </td> | ||
<td>< | <td><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation">up/down</a><br /> | ||
< | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"> name</a><br /> | ||
</td> | </td> | ||
<td><strong>CENTS (coarse/fine)</strong><br /> | <td><strong>CENTS (coarse/fine)</strong><br /> | ||
| Line 185: | Line 197: | ||
</td> | </td> | ||
<td>Interval Type<br /> | <td>Interval Type<br /> | ||
</td> | |||
<td style="text-align: center;"><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">up/down name</a><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 201: | Line 215: | ||
</td> | </td> | ||
<td>Unison<br /> | <td>Unison<br /> | ||
</td> | |||
<td style="text-align: center;">unison<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td>Narrow Minor 2nd<br /> | <td>Narrow Minor 2nd<br /> | ||
</td> | |||
<td style="text-align: center;">up-unison,<br /> | |||
down-2nd<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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<span style="background-color: #ffffff;">51°25'43&quot;</span><br /> | <span style="background-color: #ffffff;">51°25'43&quot;</span><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">11/10, 10/9, 19/17<br /> | <td style="text-align: center;">11/10, 10/9, <br /> | ||
19/17<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">9/8, 10/9 | <td style="text-align: center;">9/8, 10/9, <br /> | ||
12/11<br /> | 11/10, 12/11<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">71<br /> | <td style="text-align: center;">71<br /> | ||
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<td>Neutral 2nd, or<br /> | <td>Neutral 2nd, or<br /> | ||
Narrow Major 2nd<br /> | Narrow Major 2nd<br /> | ||
</td> | |||
<td style="text-align: center;">2nd<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td>Subminor 3rd<br /> | <td>Subminor 3rd<br /> | ||
</td> | |||
<td style="text-align: center;">up-2nd, <br /> | |||
down-3rd<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td>Neutral 3rd<br /> | <td>Neutral 3rd<br /> | ||
</td> | |||
<td style="text-align: center;">3rd<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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<span style="line-height: 15.6000003814697px;">128°34'17&quot;</span><br /> | <span style="line-height: 15.6000003814697px;">128°34'17&quot;</span><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">9/7, 14/11, 22/17<br /> | <td style="text-align: center;">9/7, 14/11, <br /> | ||
22/17<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">9/7, 14/11<br /> | <td style="text-align: center;">9/7, 14/11<br /> | ||
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</td> | </td> | ||
<td>Supermajor 3rd<br /> | <td>Supermajor 3rd<br /> | ||
</td> | |||
<td style="text-align: center;">up-3rd, <br /> | |||
down-4th<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td>Wide 4th<br /> | <td>Wide 4th<br /> | ||
</td> | |||
<td style="text-align: center;">4th<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td>Tritone<br /> | <td>Tritone<br /> | ||
</td> | |||
<td style="text-align: center;">up-4th, <br /> | |||
down-5th<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td>Narrow 5th<br /> | <td>Narrow 5th<br /> | ||
</td> | |||
<td style="text-align: center;">5th<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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231°25'43&quot;<br /> | 231°25'43&quot;<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">14/9, 11/7, 17/11<br /> | <td style="text-align: center;">14/9, 11/7, <br /> | ||
17/11<br /> | |||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;"><br /> | ||
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</td> | </td> | ||
<td>Subminor 6th<br /> | <td>Subminor 6th<br /> | ||
</td> | |||
<td style="text-align: center;">up-fifth, <br /> | |||
down-6th<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td>Neutral 6th<br /> | <td>Neutral 6th<br /> | ||
</td> | |||
<td style="text-align: center;">6th<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td>Supermajor 6th<br /> | <td>Supermajor 6th<br /> | ||
</td> | |||
<td style="text-align: center;">up-6th, <br /> | |||
down-7th<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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<span style="background-color: #ffffff;">308°34'17&quot;</span><br /> | <span style="background-color: #ffffff;">308°34'17&quot;</span><br /> | ||
</td> | </td> | ||
<td style="text-align: center;">20/11, 9/5, 34/19<br /> | <td style="text-align: center;">20/11, 9/5, <br /> | ||
34/19<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">16/9, 9/5 | <td style="text-align: center;">16/9, 9/5, <br /> | ||
11/6<br /> | 20/11, 11/6<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">29<br /> | <td style="text-align: center;">29<br /> | ||
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<td>Neutral 7th, or<br /> | <td>Neutral 7th, or<br /> | ||
Wide Minor 7th<br /> | Wide Minor 7th<br /> | ||
</td> | |||
<td style="text-align: center;">7th<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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334°17'9&quot;<br /> | 334°17'9&quot;<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">19/10, 36/19, 17/9<br /> | <td style="text-align: center;">19/10, 36/19, <br /> | ||
17/9<br /> | |||
</td> | </td> | ||
<td style="text-align: center;">21/11, 27/14, 40/21<br /> | <td style="text-align: center;">21/11, 27/14, 40/21<br /> | ||
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</td> | </td> | ||
<td>Wide Major 7th<br /> | <td>Wide Major 7th<br /> | ||
</td> | |||
<td style="text-align: center;">up-7th, <br /> | |||
down-8ve<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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</td> | </td> | ||
<td>Octave<br /> | <td>Octave<br /> | ||
</td> | |||
<td style="text-align: center;">8ve<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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<!-- ws:start:WikiTextHeadingRule:7:&lt;h1&gt; --><h1 id="toc1"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:7 -->Rank two temperaments</h1> | <!-- ws:start:WikiTextHeadingRule:7:&lt;h1&gt; --><h1 id="toc1"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:7 -->Rank two temperaments</h1> | ||
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The following chart (made by <a class="wiki_link" href="/T%C3%BAtim%20Dennsuul%20Wafiil">TDW</a>) shows this recommendation as &quot;standard notation&quot; as well as a proposed alternative.<br /> | The following chart (made by <a class="wiki_link" href="/T%C3%BAtim%20Dennsuul%20Wafiil">TDW</a>) shows this recommendation as &quot;standard notation&quot; as well as a proposed alternative.<br /> | ||
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<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:485:&lt;img src=&quot;/file/view/Ciclo_Tetradecafon%C3%ADa.png/233692646/456x468/Ciclo_Tetradecafon%C3%ADa.png&quot; alt=&quot;Intervallic Cycle of 14 steps Equal per Octave&quot; title=&quot;Intervallic Cycle of 14 steps Equal per Octave&quot; style=&quot;height: 468px; width: 456px;&quot; /&gt; --><table class="captionBox"><tr><td class="captionedImage"><img src="/file/view/Ciclo_Tetradecafon%C3%ADa.png/233692646/456x468/Ciclo_Tetradecafon%C3%ADa.png" alt="Ciclo_Tetradecafonía.png" title="Ciclo_Tetradecafonía.png" style="height: 468px; width: 456px;" /></td></tr><tr><td class="imageCaption">Intervallic Cycle of 14 steps Equal per Octave</td></tr></table><!-- ws:end:WikiTextLocalImageRule:485 --><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:15:&lt;h1&gt; --><h1 id="toc5"><a name="Images"></a><!-- ws:end:WikiTextHeadingRule:15 -->Images</h1> | <!-- ws:start:WikiTextHeadingRule:15:&lt;h1&gt; --><h1 id="toc5"><a name="Images"></a><!-- ws:end:WikiTextHeadingRule:15 -->Images</h1> | ||
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<!-- ws:start:WikiTextHeadingRule:17:&lt;h1&gt; --><h1 id="toc6"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:17 -->Commas</h1> | <!-- ws:start:WikiTextHeadingRule:17:&lt;h1&gt; --><h1 id="toc6"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:17 -->Commas</h1> | ||
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<!-- ws:start:WikiTextHeadingRule:21:&lt;h1&gt; --><h1 id="toc8"><a name="Books"></a><!-- ws:end:WikiTextHeadingRule:21 -->Books</h1> | <!-- ws:start:WikiTextHeadingRule:21:&lt;h1&gt; --><h1 id="toc8"><a name="Books"></a><!-- ws:end:WikiTextHeadingRule:21 -->Books</h1> | ||
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<em>Sword, Ron. &quot;Tetradecaphonic Scales for Guitar&quot; IAAA Press. First Ed: June 2009.</em><br /> | <em>Sword, Ron. &quot;Tetradecaphonic Scales for Guitar&quot; IAAA Press. First Ed: June 2009.</em><br /> | ||
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