14edo: Difference between revisions
Wikispaces>TallKite **Imported revision 599946362 - Original comment: ** |
Wikispaces>TallKite **Imported revision 599959722 - 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:TallKite|TallKite]] and made on <tt>2016-11-21 | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-11-21 07:02:40 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>599959722</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** || [[xenharmonic/Ups and Downs Notation|up/down]] | || **DEGREE** ||||= [[xenharmonic/Ups and Downs Notation|up/down]] | ||
[[xenharmonic/Ups and Downs Notation| | [[xenharmonic/Ups and Downs Notation| notation]] || **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 || | ||
|| 0 || C || 0 ||= 1/1 ||= 1/1 ||= 1 || Unison | || 0 ||= C ||= unison || 0 ||= 1/1 ||= 1/1 ||= 1 || Unison || | ||
|| 1 || C^, Dv || 85.714, 102.857 | || 1 ||= C^, Dv ||= up-unison, | ||
25°42'51" ||= 20/19, 19/18, 18/17 ||= 22/21, 28/27, 21/20 ||= 67 || Narrow Minor | down-2nd || 85.714, 102.857 | ||
25°42'51" ||= 20/19, 19/18, 18/17 ||= 22/21, 28/27, 21/20 ||= 67 || Narrow Minor 2nd || | |||
|| 2 || D || 171.429, 205.714 | || 2 ||= D ||= 2nd || 171.429, 205.714 | ||
<span style="background-color: #ffffff;">51°25'43"</span> ||= 11/10, 10/9, | <span style="background-color: #ffffff;">51°25'43"</span> ||= 11/10, 10/9, | ||
19/17 ||= 9/8, 10/9, | 19/17 ||= 9/8, 10/9, | ||
11/10, 12/11 ||= 71 || Neutral 2nd, or | 11/10, 12/11 ||= 71 || Neutral 2nd, or | ||
Narrow Major | Narrow Major 2nd || | ||
|| 3· || D^, Ev || 257.143, 308.571 | || 3· ||= D^, Ev ||= up-2nd, | ||
77°8'34" ||= 22/19, 20/17 ||= 7/6, 8/7 ||= 37 || Subminor | down-3rd || 257.143, 308.571 | ||
77°8'34" ||= 22/19, 20/17 ||= 7/6, 8/7 ||= 37 || Subminor 3rd || | |||
|| 4 || E || 342.857, 411.429 | || 4 ||= E ||= 3rd || 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 | <span style="background-color: #ffffff;">102°51'26"</span> ||= 11/9, 17/14 ||= 11/9, 5/4, 6/5 ||= 39 || Neutral 3rd || | ||
|| 5· || E^, Fv || 428.571, 514.286 | || 5· ||= E^, Fv ||= up-3rd, | ||
<span style="line-height: 15.6000003814697px;">128°34'17"</span> ||= 9/7, 14/11, | down-4th || 428.571, 514.286 | ||
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 || | |||
|| | || 6 ||= F ||= 4th || 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 | <span style="background-color: #ffffff;">154°17'9"</span> ||= 19/14 ||= 4/3, 11/8 ||= 43 || Wide 4th || | ||
|| 7· || F^, Gv || 600, 720 | || 7· ||= F^, Gv ||= up-4th, | ||
180° ||= 7/5, 10/7 ||= 7/5, 10/7 ||= 91 || Tritone || | down-5th || 600, 720 | ||
180° ||= 7/5, 10/7 ||= 7/5, 10/7 ||= 91 || Tritone || | |||
|| | || 8 ||= G ||= 5th || 685.714, 823.857 | ||
<span style="background-color: #ffffff;">205°42'51"</span> ||= 28/19 ||= 3/2, 16/11 ||= 95 || Narrow | <span style="background-color: #ffffff;">205°42'51"</span> ||= 28/19 ||= 3/2, 16/11 ||= 95 || Narrow 5th || | ||
|| 9· || G^, Av || 771.429, 925.714 | || 9· ||= G^, Av ||= up-5th, | ||
231°25'43" ||= 14/9, 11/7, | down-6th || 771.429, 925.714 | ||
17/11 ||= ||= 25 || Subminor 6th || | 231°25'43" ||= 14/9, 11/7, | ||
17/11 ||= ||= 25 || Subminor 6th || | |||
|| | || 10 ||= A ||= 6th || 857.143, 1028.571 | ||
<span style="background-color: #ffffff;">257°8'34"</span> ||= 18/11 ||= 18/11, 8/5, 5/3 ||= 105 || Neutral | <span style="background-color: #ffffff;">257°8'34"</span> ||= 18/11 ||= 18/11, 8/5, 5/3 ||= 105 || Neutral 6th || | ||
|| 11· || A^, Bv || 942.857, 1131.429 | || 11· ||= A^, Bv ||= up-6th, | ||
282°51'26" ||= 19/11, 17/10 ||= 12/7, 7/4 ||= 55 || Supermajor 6th || | down-7th || 942.857, 1131.429 | ||
282°51'26" ||= 19/11, 17/10 ||= 12/7, 7/4 ||= 55 || Supermajor 6th || | |||
|| | || 12 ||= B ||= 7th || 1028.571, 1234.286 | ||
<span style="background-color: #ffffff;">308°34'17"</span> ||= 20/11, 9/5, | <span style="background-color: #ffffff;">308°34'17"</span> ||= 20/11, 9/5, | ||
34/19 ||= 16/9, 9/5, | 34/19 ||= 16/9, 9/5, | ||
20/11, 11/6 ||= 29 || Neutral 7th, or | 20/11, 11/6 ||= 29 || Neutral 7th, or | ||
Wide Minor | Wide Minor 7th || | ||
|| 13 || B^, Cv || 1114.286, 1337.143 | || 13 ||= B^, Cv ||= up-7th, | ||
334°17'9" ||= 19/10, 36/19, | down-8ve || 1114.286, 1337.143 | ||
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 || | |||
|| 14··(or 0) || C || 1200, 1440 | || 14··(or 0) ||= C ||= 8ve || 1200, 1440 | ||
360° ||= 2/1 ||= 2/1 ||= 2 || Octave | 360° ||= 2/1 ||= 2/1 ||= 2 || Octave || | ||
``*``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><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation">up/down</a><br /> | <td colspan="2" style="text-align: center;"><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"> | <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"> notation</a><br /> | ||
</td> | </td> | ||
<td><strong>CENTS (coarse/fine)</strong><br /> | <td><strong>CENTS (coarse/fine)</strong><br /> | ||
Line 197: | Line 197: | ||
</td> | </td> | ||
<td>Interval Type<br /> | <td>Interval Type<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 204: | Line 202: | ||
<td>0<br /> | <td>0<br /> | ||
</td> | </td> | ||
<td>C<br /> | <td style="text-align: center;">C<br /> | ||
</td> | |||
<td style="text-align: center;">unison<br /> | |||
</td> | </td> | ||
<td>0<br /> | <td>0<br /> | ||
Line 215: | Line 215: | ||
</td> | </td> | ||
<td>Unison<br /> | <td>Unison<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 222: | Line 220: | ||
<td>1<br /> | <td>1<br /> | ||
</td> | </td> | ||
<td>C^, Dv<br /> | <td style="text-align: center;">C^, Dv<br /> | ||
</td> | |||
<td style="text-align: center;">up-unison,<br /> | |||
down-2nd<br /> | |||
</td> | </td> | ||
<td>85.714, 102.857<br /> | <td>85.714, 102.857<br /> | ||
Line 234: | Line 235: | ||
</td> | </td> | ||
<td>Narrow Minor 2nd<br /> | <td>Narrow Minor 2nd<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 242: | Line 240: | ||
<td>2<br /> | <td>2<br /> | ||
</td> | </td> | ||
<td>D<br /> | <td style="text-align: center;">D<br /> | ||
</td> | |||
<td style="text-align: center;">2nd<br /> | |||
</td> | </td> | ||
<td>171.429, 205.714<br /> | <td>171.429, 205.714<br /> | ||
<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, <br /> | <td style="text-align: center;">11/10, 10/9,<br /> | ||
19/17<br /> | 19/17<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">9/8, 10/9, <br /> | <td style="text-align: center;">9/8, 10/9,<br /> | ||
11/10, 12/11<br /> | 11/10, 12/11<br /> | ||
</td> | </td> | ||
Line 257: | Line 257: | ||
<td>Neutral 2nd, or<br /> | <td>Neutral 2nd, or<br /> | ||
Narrow Major 2nd<br /> | Narrow Major 2nd<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 264: | Line 262: | ||
<td>3·<br /> | <td>3·<br /> | ||
</td> | </td> | ||
<td>D^, Ev<br /> | <td style="text-align: center;">D^, Ev<br /> | ||
</td> | |||
<td style="text-align: center;">up-2nd,<br /> | |||
down-3rd<br /> | |||
</td> | </td> | ||
<td>257.143, 308.571<br /> | <td>257.143, 308.571<br /> | ||
Line 276: | Line 277: | ||
</td> | </td> | ||
<td>Subminor 3rd<br /> | <td>Subminor 3rd<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 284: | Line 282: | ||
<td>4<br /> | <td>4<br /> | ||
</td> | </td> | ||
<td>E<br /> | <td style="text-align: center;">E<br /> | ||
</td> | |||
<td style="text-align: center;">3rd<br /> | |||
</td> | </td> | ||
<td>342.857, 411.429<br /> | <td>342.857, 411.429<br /> | ||
Line 296: | Line 296: | ||
</td> | </td> | ||
<td>Neutral 3rd<br /> | <td>Neutral 3rd<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 303: | Line 301: | ||
<td>5·<br /> | <td>5·<br /> | ||
</td> | </td> | ||
<td>E^, Fv<br /> | <td style="text-align: center;">E^, Fv<br /> | ||
</td> | |||
<td style="text-align: center;">up-3rd,<br /> | |||
down-4th<br /> | |||
</td> | </td> | ||
<td>428.571, 514.286<br /> | <td>428.571, 514.286<br /> | ||
<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, <br /> | <td style="text-align: center;">9/7, 14/11,<br /> | ||
22/17<br /> | 22/17<br /> | ||
</td> | </td> | ||
Line 316: | Line 317: | ||
</td> | </td> | ||
<td>Supermajor 3rd<br /> | <td>Supermajor 3rd<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 324: | Line 322: | ||
<td>6<br /> | <td>6<br /> | ||
</td> | </td> | ||
<td>F<br /> | <td style="text-align: center;">F<br /> | ||
</td> | |||
<td style="text-align: center;">4th<br /> | |||
</td> | </td> | ||
<td>51<span style="line-height: 1.5;">4.286, 617.143</span><br /> | <td>51<span style="line-height: 1.5;">4.286, 617.143</span><br /> | ||
Line 336: | Line 336: | ||
</td> | </td> | ||
<td>Wide 4th<br /> | <td>Wide 4th<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 343: | Line 341: | ||
<td>7·<br /> | <td>7·<br /> | ||
</td> | </td> | ||
<td>F^, Gv<br /> | <td style="text-align: center;">F^, Gv<br /> | ||
</td> | |||
<td style="text-align: center;">up-4th,<br /> | |||
down-5th<br /> | |||
</td> | </td> | ||
<td>600, 720<br /> | <td>600, 720<br /> | ||
Line 355: | Line 356: | ||
</td> | </td> | ||
<td>Tritone<br /> | <td>Tritone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 363: | Line 361: | ||
<td>8<br /> | <td>8<br /> | ||
</td> | </td> | ||
<td>G<br /> | <td style="text-align: center;">G<br /> | ||
</td> | |||
<td style="text-align: center;">5th<br /> | |||
</td> | </td> | ||
<td>685.714, 823.857<br /> | <td>685.714, 823.857<br /> | ||
Line 375: | Line 375: | ||
</td> | </td> | ||
<td>Narrow 5th<br /> | <td>Narrow 5th<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 382: | Line 380: | ||
<td>9·<br /> | <td>9·<br /> | ||
</td> | </td> | ||
<td>G^, Av<br /> | <td style="text-align: center;">G^, Av<br /> | ||
</td> | |||
<td style="text-align: center;">up-5th,<br /> | |||
down-6th<br /> | |||
</td> | </td> | ||
<td>771.429, 925.714<br /> | <td>771.429, 925.714<br /> | ||
231°25'43&quot;<br /> | 231°25'43&quot;<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">14/9, 11/7, <br /> | <td style="text-align: center;">14/9, 11/7,<br /> | ||
17/11<br /> | 17/11<br /> | ||
</td> | </td> | ||
Line 395: | Line 396: | ||
</td> | </td> | ||
<td>Subminor 6th<br /> | <td>Subminor 6th<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 403: | Line 401: | ||
<td>10<br /> | <td>10<br /> | ||
</td> | </td> | ||
<td>A<br /> | <td style="text-align: center;">A<br /> | ||
</td> | |||
<td style="text-align: center;">6th<br /> | |||
</td> | </td> | ||
<td>857.143, 1028.571<br /> | <td>857.143, 1028.571<br /> | ||
Line 415: | Line 415: | ||
</td> | </td> | ||
<td>Neutral 6th<br /> | <td>Neutral 6th<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 422: | Line 420: | ||
<td>11·<br /> | <td>11·<br /> | ||
</td> | </td> | ||
<td>A^, Bv<br /> | <td style="text-align: center;">A^, Bv<br /> | ||
</td> | |||
<td style="text-align: center;">up-6th,<br /> | |||
down-7th<br /> | |||
</td> | </td> | ||
<td>942.857, 1131.429<br /> | <td>942.857, 1131.429<br /> | ||
Line 434: | Line 435: | ||
</td> | </td> | ||
<td>Supermajor 6th<br /> | <td>Supermajor 6th<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 442: | Line 440: | ||
<td>12<br /> | <td>12<br /> | ||
</td> | </td> | ||
<td>B<br /> | <td style="text-align: center;">B<br /> | ||
</td> | |||
<td style="text-align: center;">7th<br /> | |||
</td> | </td> | ||
<td>1028.571, 1234.286<br /> | <td>1028.571, 1234.286<br /> | ||
<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, <br /> | <td style="text-align: center;">20/11, 9/5,<br /> | ||
34/19<br /> | 34/19<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">16/9, 9/5, <br /> | <td style="text-align: center;">16/9, 9/5,<br /> | ||
20/11, 11/6<br /> | 20/11, 11/6<br /> | ||
</td> | </td> | ||
Line 457: | Line 457: | ||
<td>Neutral 7th, or<br /> | <td>Neutral 7th, or<br /> | ||
Wide Minor 7th<br /> | Wide Minor 7th<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 464: | Line 462: | ||
<td>13<br /> | <td>13<br /> | ||
</td> | </td> | ||
<td>B^, Cv<br /> | <td style="text-align: center;">B^, Cv<br /> | ||
</td> | |||
<td style="text-align: center;">up-7th,<br /> | |||
down-8ve<br /> | |||
</td> | </td> | ||
<td>1114.286, 1337.143<br /> | <td>1114.286, 1337.143<br /> | ||
334°17'9&quot;<br /> | 334°17'9&quot;<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">19/10, 36/19, <br /> | <td style="text-align: center;">19/10, 36/19,<br /> | ||
17/9<br /> | 17/9<br /> | ||
</td> | </td> | ||
Line 477: | Line 478: | ||
</td> | </td> | ||
<td>Wide Major 7th<br /> | <td>Wide Major 7th<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 485: | Line 483: | ||
<td>14··(or 0)<br /> | <td>14··(or 0)<br /> | ||
</td> | </td> | ||
<td>C<br /> | <td style="text-align: center;">C<br /> | ||
</td> | |||
<td style="text-align: center;">8ve<br /> | |||
</td> | </td> | ||
<td>1200, 1440<br /> | <td>1200, 1440<br /> | ||
Line 497: | Line 497: | ||
</td> | </td> | ||
<td>Octave<br /> | <td>Octave<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 508: | Line 506: | ||
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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:483:&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:483 --><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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