21edo: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:~~JosephRuhf~~|~~JosephRuhf~~]] and made on <tt>2016-10-~~30 19~~:01:06 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-11-21 04:58:48 UTC</tt>.

: The original revision id was <tt>~~597508916~~</tt>.

: The original revision id was <tt>599949526</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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|| **Degree** || **Cents coarse/fine, DMS**

**Value** || ~~**7-EDO**~~

**Value** ||||= [[Ups and Downs Notation|Up/down]]

**Notation** || **5L3s**

[[Ups and Downs Notation|Notation]] || **5L3s**

**Notation** ||= **D.-R. Interval**

**Types** ||= **Approximate**

**Ratios *1** ||= **Approximate****Ratios *2** ||= **Approximate****Ratios *3** ||

|| 0 || 0 || C || C ||= Unison ||= 1/1 ||= 1/1 ||= 1/1 ||

|| 0 || 0 ||= C ||= unison || C ||= Unison ||= 1/1 ||= 1/1 ||= 1/1 ||

|| 1 || 57.143, 68.571

17°8'34" || C^/Dvv || C# ||= Subminor 2nd ||= 28/27, 30/29 ||= 35/34, 36/35 ||= 64/63 ||

17°8'34" ||= C^/Dvv ||= up unison || C# ||= Subminor 2nd ||= 28/27, 30/29 ||= 35/34, 36/35 ||= 64/63 ||

|| 2 || 114.286, 137.143

34°17'9" || C^^/Dv || Db ||= Minor 2nd ||= 16/15, 15/14, 29/27 ||= 18/17 ||= 16/15, 25/24 ||

34°17'9" ||= C^^/Dv ||= down 2nd || Db ||= Minor 2nd ||= 16/15, 15/14, 29/27 ||= 18/17 ||= 16/15, 25/24 ||

|| 3 || 171.429, 205.714

51°25'43" || D || D ||= Submajor 2nd ||= 10/9, 32/29 ||= 10/9,11/10 ||= 9/8 ||

51°25'43" ||= D ||= 2nd || D ||= Submajor 2nd ||= 10/9, 32/29 ||= 10/9,11/10 ||= 9/8 ||

|| 4 || 228.571, 274.286

68°34'17" || D^/Evv || D# ||= Supermajor 2nd ||= 8/7 ||= 8/7 ||= 8/7, 10/9, 11/10 ||

68°34'17" ||= D^/Evv ||= up 2nd || D# ||= Supermajor 2nd ||= 8/7 ||= 8/7 ||= 8/7, 10/9, 11/10 ||

|| 5 || 285.714, 342.857

85°42'51" || D^^/Ev || Eb ||= Subminor 3rd ||= 27/23, 32/27 ||= 13/11, 20/17 ||= 6/5, 7/6 ||

85°42'51" ||= D^^/Ev ||= down 3rd || Eb ||= Subminor 3rd ||= 27/23, 32/27 ||= 13/11, 20/17 ||= 6/5, 7/6 ||

|| 6 || 342.857, 411.429

102°51'26" || E || E ||= Neutral 3rd ||= 28/23 ||= 11/9 ||= 16/13 ||

102°51'26" ||= E ||= 3rd || E ||= Neutral 3rd ||= 28/23 ||= 11/9 ||= 16/13 ||

|| 7 || 400, 480

120° || E^/Fvv || E#/Fb ||= Major 3rd ||= 29/23 ||= 44/35 ||= 5/4, 9/7, 11/9, 14/11 ||

120° ||= E^/Fvv ||= up 3rd || E#/Fb ||= Major 3rd ||= 29/23 ||= 44/35 ||= 5/4, 9/7, 11/9, 14/11 ||

|| 8 || 457.143, 548.571

137°8'34" || E^^/Fv || F ||= Third-Fourth ||= 30/23 ||= 13/10, 17/13, 22/17 ||= 13/10 ||

137°8'34" ||= E^^/Fv ||= down 4th || F ||= Third-Fourth ||= 30/23 ||= 13/10, 17/13, 22/17 ||= 13/10 ||

|| 9 || 514.286, 617.143

154°17'9" || F || F# ||= Acute 4th ||= 161/120, 256/189 ||= 35/26 ||= 4/3, 18/13 ||

154°17'9" ||= F ||= 4th || F# ||= Acute 4th ||= 161/120, 256/189 ||= 35/26 ||= 4/3, 18/13 ||

|| 10 || 571.429, 685.714

171°25'43" || F^/Gvv || Gb ||= Narrow Tritone ||= 32/23 ||= 18/13 ||= 7/5, 11/8 ||

171°25'43" ||= F^/Gvv ||= up 4th || Gb ||= Narrow Tritone ||= 32/23 ||= 18/13 ||= 7/5, 11/8 ||

|| 11 || 628.571, 754.286

188°34'17" || F^^/Gv || G ||= Wide Tritone ||= 23/16 ||= 13/9 ||= 10/7, 16/11 ||

188°34'17" ||= F^^/Gv ||= down 5th || G ||= Wide Tritone ||= 23/16 ||= 13/9 ||= 10/7, 16/11 ||

|| 12 || 685.714, 824.857

205°42'51" || G || G# ||= Grave 5th ||= 189/128, 240/161 ||= 52/35 ||= 3/2, 13/9 ||

205°42'51" ||= G ||= 5th || G# ||= Grave 5th ||= 189/128, 240/161 ||= 52/35 ||= 3/2, 13/9 ||

|| 13 || 742.857, 891.428

222°51'26" || G^/Avv || Hb ||= Fifth-Sixth ||= 23/15 ||= 17/11, 20/13, 26/17 ||= 20/13 ||

222°51'26" ||= G^/Avv ||= up 5th || Hb ||= Fifth-Sixth ||= 23/15 ||= 17/11, 20/13, 26/17 ||= 20/13 ||

|| 14 || 800, 960

240° || G^^/Av || H ||= Minor 6th ||= 46/29 ||= 35/22 ||= 8/5, 11/7, 14/9, 18/11 ||

240° ||= G^^/Av ||= down 6th || H ||= Minor 6th ||= 46/29 ||= 35/22 ||= 8/5, 11/7, 14/9, 18/11 ||

|| 15 || 857.143, 1028.571

257°8'34" || A || H#/Ab ||= Neutral 6th ||= 23/14 ||= 18/11 ||= 13/8 ||

257°8'34" ||= A ||= 6th || H#/Ab ||= Neutral 6th ||= 23/14 ||= 18/11 ||= 13/8 ||

|| 16 || 914.286, 1097.143

274°17'9" || A^/Bvv || A ||= Supermajor 6th ||= 27/16, 46/27 ||= 17/10, 22/13 ||= 5/3, 12/7 ||

274°17'9" ||= A^/Bvv ||= up 6th || A ||= Supermajor 6th ||= 27/16, 46/27 ||= 17/10, 22/13 ||= 5/3, 12/7 ||

|| 17 || 971.429, 1165.714

391°25'43" || A^^/Bv || A# ||= Subminor 7th ||= 7/4 ||= 7/4 ||= 7/4, 9/5, 20/11 ||

391°25'43" ||= A^^/Bv ||= down 7th || A# ||= Subminor 7th ||= 7/4 ||= 7/4 ||= 7/4, 9/5, 20/11 ||

|| 18 || 1028.571, 1234.286

308°34'17" || B || Bb ||= Supraminor 7th ||= 29/16, 9/5 ||= 9/5, 20/11 ||= 16/9 ||

308°34'17" ||= B ||= 7th || Bb ||= Supraminor 7th ||= 29/16, 9/5 ||= 9/5, 20/11 ||= 16/9 ||

|| 19 || 1085.714, 1302.857

325°42'51" || B^/Cvv || B ||= Major 7th ||= 15/8 ||= 17/9 ||= 15/8, 48/25 ||

325°42'51" ||= B^/Cvv ||= up 7th || B ||= Major 7th ||= 15/8 ||= 17/9 ||= 15/8, 48/25 ||

|| 20 || 1142.857, 1371.429

342°8'34" || B^^/Cv || B#/Cb ||= Supermajor 7th ||= 27/14, 29/15 ||= 35/18, 68/35 ||= 63/32 ||

342°8'34" ||= B^^/Cv ||= down 8ve || B#/Cb ||= Supermajor 7th ||= 27/14, 29/15 ||= 35/18, 68/35 ||= 63/32 ||

|| 21 || 1200, 1440

360° || C || C ||= Octave ||= 2/1 ||= 2/1 ||= 2/1 ||

360° ||= C ||= 8ve || C ||= Octave ||= 2/1 ||= 2/1 ||= 2/1 ||

*1: based on treating 21-EDO as a 2.7.15.23.27.29 subgroup temperament

Line 186:

Value

</td>

<~~strong~~>Notation</~~strong~~>

<a class="wiki_link" href="/Ups%20and%20Downs%20Notation">Notation</a>

</td>

<td>5L3s

Line 208:

<td>0

</td>

<td>C

<td style="text-align: center;">C

</td>

<td style="text-align: center;">unison

</td>

<td>C

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17°8'34&quot;

</td>

<td>C^/Dvv

<td style="text-align: center;">C^/Dvv

</td>

<td style="text-align: center;">up unison

</td>

<td>C#

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34°17'9&quot;

</td>

<td>C^^/Dv

<td style="text-align: center;">C^^/Dv

</td>

<td style="text-align: center;">down 2nd

</td>

<td>Db

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51°25'43&quot;

</td>

<td>D

<td style="text-align: center;">D

</td>

<td style="text-align: center;">2nd

</td>

<td>D

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68°34'17&quot;

</td>

<td>D^/Evv

<td style="text-align: center;">D^/Evv

</td>

<td style="text-align: center;">up 2nd

</td>

<td>D#

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85°42'51&quot;

</td>

<td>D^^/Ev

<td style="text-align: center;">D^^/Ev

</td>

<td style="text-align: center;">down 3rd

</td>

<td>Eb

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102°51'26&quot;

</td>

<td>E

<td style="text-align: center;">E

</td>

<td style="text-align: center;">3rd

</td>

<td>E

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Line 355:

120°

</td>

<td>E^/Fvv

<td style="text-align: center;">E^/Fvv

</td>

<td style="text-align: center;">up 3rd

</td>

<td>E#/Fb

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137°8'34&quot;

</td>

<td>E^^/Fv

<td style="text-align: center;">E^^/Fv

</td>

<td style="text-align: center;">down 4th

</td>

<td>F

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Line 397:

154°17'9&quot;

</td>

<td>F

<td style="text-align: center;">F

</td>

<td style="text-align: center;">4th

</td>

<td>F#

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171°25'43&quot;

</td>

<td>F^/Gvv

<td style="text-align: center;">F^/Gvv

</td>

<td style="text-align: center;">up 4th

</td>

<td>Gb

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188°34'17&quot;

</td>

<td>F^^/Gv

<td style="text-align: center;">F^^/Gv

</td>

<td style="text-align: center;">down 5th

</td>

<td>G

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205°42'51&quot;

</td>

<td>G

<td style="text-align: center;">G

</td>

<td style="text-align: center;">5th

</td>

<td>G#

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222°51'26&quot;

</td>

<td>G^/Avv

<td style="text-align: center;">G^/Avv

</td>

<td style="text-align: center;">up 5th

</td>

<td>Hb

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240°

</td>

<td>G^^/Av

<td style="text-align: center;">G^^/Av

</td>

<td style="text-align: center;">down 6th

</td>

<td>H

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257°8'34&quot;

</td>

<td>A

<td style="text-align: center;">A

</td>

<td style="text-align: center;">6th

</td>

<td>H#/Ab

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Line 544:

274°17'9&quot;

</td>

<td>A^/Bvv

<td style="text-align: center;">A^/Bvv

</td>

<td style="text-align: center;">up 6th

</td>

<td>A

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391°25'43&quot;

</td>

<td>A^^/Bv

<td style="text-align: center;">A^^/Bv

</td>

<td style="text-align: center;">down 7th

</td>

<td>A#

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308°34'17&quot;

</td>

<td>B

<td style="text-align: center;">B

</td>

<td style="text-align: center;">7th

</td>

<td>Bb

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325°42'51&quot;

</td>

<td>B^/Cvv

<td style="text-align: center;">B^/Cvv

</td>

<td style="text-align: center;">up 7th

</td>

<td>B

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Line 628:

342°8'34&quot;

</td>

<td>B^^/Cv

<td style="text-align: center;">B^^/Cv

</td>

<td style="text-align: center;">down 8ve

</td>

<td>B#/Cb

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360°

</td>

<td>C

<td style="text-align: center;">C

</td>

<td style="text-align: center;">8ve

</td>

<td>C

Line 1,083:

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<h1 id="toc7"><a name="Books / Literature:"></a>Books / Literature:</h1>

Sword, Ron. &quot;Icosihenaphonic Scales for Guitar&quot;. IAAA Press. 1st ed: July 2009.

<img src="http://www.ronsword.com/images/ron1.jpg" alt="external image ron1.jpg" title="external image ron1.jpg" style="height: 188px; width: 254px;" /><img src="http://www.swordguitars.com/21tetsm.JPG" alt="external image 21tetsm.JPG" title="external image 21tetsm.JPG" style="height: 191px; width: 363px;" />

<img src="http://www.ronsword.com/images/ron1.jpg" alt="external image ron1.jpg" title="external image ron1.jpg" style="height: 188px; width: 254px;" /><img src="http://www.swordguitars.com/21tetsm.JPG" alt="external image 21tetsm.JPG" title="external image 21tetsm.JPG" style="height: 191px; width: 363px;" />

21-edo Icosihenaphonic Acoustic Guitar (Ron Sword)

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-30 19:01:06 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-11-21 04:58:48 UTC</tt>.<br>
-: The original revision id was <tt>597508916</tt>.<br>
+: The original revision id was <tt>599949526</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>
@@ Line 20: / Line 20: @@
 || **Degree** || **Cents coarse/fine, DMS**
-**Value** || **7-EDO**
+**Value** ||||= [[Ups and Downs Notation|Up/down]]
-**Notation** || **5L3s**
+[[Ups and Downs Notation|Notation]] || **5L3s**
 **Notation** ||= **D.-R. Interval**
 **Types** ||= **Approximate**
 **Ratios *1** ||= &lt;span style="display: block; text-align: center;"&gt;**Approximate****Ratios *2**&lt;/span&gt; ||= &lt;span style="display: block; text-align: center;"&gt;**Approximate**&lt;/span&gt;**Ratios *3** ||
-|| 0 || 0 || C || C ||= Unison ||= 1/1 ||= 1/1 ||= 1/1 ||
+|| 0 || 0 ||= C ||= unison || C ||= Unison ||= 1/1 ||= 1/1 ||= 1/1 ||
 || 1 || 57.143, 68.571
-°&lt;span style="background-color: #ffffff;"&gt;8'34"&lt;/span&gt; || C^/Dvv || C# ||= Subminor 2nd ||= 28/27, 30/29 ||= 35/34, 36/35 ||= 64/63 ||
+°&lt;span style="background-color: #ffffff;"&gt;8'34"&lt;/span&gt; ||= C^/Dvv ||= up unison || C# ||= Subminor 2nd ||= 28/27, 30/29 ||= 35/34, 36/35 ||= 64/63 ||
 || 2 || 114.286, 137.143
-°&lt;span style="background-color: #ffffff;"&gt;17'9"&lt;/span&gt; || C^^/Dv || Db ||= Minor 2nd ||= 16/15, 15/14, 29/27 ||= 18/17 ||= 16/15, 25/24 ||
+°&lt;span style="background-color: #ffffff;"&gt;17'9"&lt;/span&gt; ||= C^^/Dv ||= down 2nd || Db ||= Minor 2nd ||= 16/15, 15/14, 29/27 ||= 18/17 ||= 16/15, 25/24 ||
 || 3 || 171.429, 205.714
-&lt;span style="background-color: #ffffff;"&gt;51°25'43"&lt;/span&gt; || D || D ||= Submajor 2nd ||= 10/9, 32/29 ||= 10/9,11/10 ||= 9/8 ||
+&lt;span style="background-color: #ffffff;"&gt;51°25'43"&lt;/span&gt; ||= D ||= 2nd || D ||= Submajor 2nd ||= 10/9, 32/29 ||= 10/9,11/10 ||= 9/8 ||
 || 4 || 228.571, 274.286
-°&lt;span style="background-color: #ffffff;"&gt;34'17"&lt;/span&gt; || D^/Evv || D# ||= Supermajor 2nd ||= 8/7 ||= 8/7 ||= 8/7, 10/9, 11/10 ||
+°&lt;span style="background-color: #ffffff;"&gt;34'17"&lt;/span&gt; ||= D^/Evv ||= up 2nd || D# ||= Supermajor 2nd ||= 8/7 ||= 8/7 ||= 8/7, 10/9, 11/10 ||
 || 5 || 285.714, 342.857
-°&lt;span style="background-color: #ffffff;"&gt;42'51"&lt;/span&gt; || D^^/Ev || Eb ||= Subminor 3rd ||= 27/23, 32/27 ||= 13/11, 20/17 ||= 6/5, 7/6 ||
+°&lt;span style="background-color: #ffffff;"&gt;42'51"&lt;/span&gt; ||= D^^/Ev ||= down 3rd || Eb ||= Subminor 3rd ||= 27/23, 32/27 ||= 13/11, 20/17 ||= 6/5, 7/6 ||
 || 6 || 342.857, 411.429
-&lt;span style="background-color: #ffffff;"&gt;102°51'26"&lt;/span&gt; || E || E ||= Neutral 3rd ||= 28/23 ||= 11/9 ||= 16/13 ||
+&lt;span style="background-color: #ffffff;"&gt;102°51'26"&lt;/span&gt; ||= E ||= 3rd || E ||= Neutral 3rd ||= 28/23 ||= 11/9 ||= 16/13 ||
 || 7 || 400, 480
-° || E^/Fvv || E#/Fb ||= Major 3rd ||= 29/23 ||= 44/35 ||= 5/4, 9/7, 11/9, 14/11 ||
+° ||= E^/Fvv ||= up 3rd || E#/Fb ||= Major 3rd ||= 29/23 ||= 44/35 ||= 5/4, 9/7, 11/9, 14/11 ||
 || 8 || 457.143, 548.571
-°&lt;span style="background-color: #ffffff; line-height: 1.5;"&gt;8'34"&lt;/span&gt; || E^^/Fv || F ||= Third-Fourth ||= 30/23 ||= 13/10, 17/13, 22/17 ||= 13/10 ||
+°&lt;span style="background-color: #ffffff; line-height: 1.5;"&gt;8'34"&lt;/span&gt; ||= E^^/Fv ||= down 4th || F ||= Third-Fourth ||= 30/23 ||= 13/10, 17/13, 22/17 ||= 13/10 ||
 || 9 || 514.286, 617.143
-&lt;span style="background-color: #ffffff;"&gt;154°17'9"&lt;/span&gt; || F || F# ||= Acute 4th ||= 161/120, 256/189 ||= 35/26 ||= 4/3, 18/13 ||
+&lt;span style="background-color: #ffffff;"&gt;154°17'9"&lt;/span&gt; ||= F ||= 4th || F# ||= Acute 4th ||= 161/120, 256/189 ||= 35/26 ||= 4/3, 18/13 ||
 || 10 || 571.429, 685.714
-°&lt;span style="background-color: #ffffff;"&gt;25'43"&lt;/span&gt; || F^/Gvv || Gb ||= Narrow Tritone ||= 32/23 ||= 18/13 ||= 7/5, 11/8 ||
+°&lt;span style="background-color: #ffffff;"&gt;25'43"&lt;/span&gt; ||= F^/Gvv ||= up 4th || Gb ||= Narrow Tritone ||= 32/23 ||= 18/13 ||= 7/5, 11/8 ||
 || 11 || 628.571, 754.286
-°&lt;span style="background-color: #ffffff;"&gt;34'17"&lt;/span&gt; || F^^/Gv || G ||= Wide Tritone ||= 23/16 ||= 13/9 ||= 10/7, 16/11 ||
+°&lt;span style="background-color: #ffffff;"&gt;34'17"&lt;/span&gt; ||= F^^/Gv ||= down 5th || G ||= Wide Tritone ||= 23/16 ||= 13/9 ||= 10/7, 16/11 ||
 || 12 || 685.714, 824.857
-&lt;span style="background-color: #ffffff;"&gt;205°42'51"&lt;/span&gt; || G || G# ||= Grave 5th ||= 189/128, 240/161 ||= 52/35 ||= 3/2, 13/9 ||
+&lt;span style="background-color: #ffffff;"&gt;205°42'51"&lt;/span&gt; ||= G ||= 5th || G# ||= Grave 5th ||= 189/128, 240/161 ||= 52/35 ||= 3/2, 13/9 ||
 || 13 || 742.857, 891.428
-°&lt;span style="background-color: #ffffff;"&gt;51'26"&lt;/span&gt; || G^/Avv || Hb ||= Fifth-Sixth ||= 23/15 ||= 17/11, 20/13, 26/17 ||= 20/13 ||
+°&lt;span style="background-color: #ffffff;"&gt;51'26"&lt;/span&gt; ||= G^/Avv ||= up 5th || Hb ||= Fifth-Sixth ||= 23/15 ||= 17/11, 20/13, 26/17 ||= 20/13 ||
 || 14 || 800, 960
-° || G^^/Av || H ||= Minor 6th ||= 46/29 ||= 35/22 ||= 8/5, 11/7, 14/9, 18/11 ||
+° ||= G^^/Av ||= down 6th || H ||= Minor 6th ||= 46/29 ||= 35/22 ||= 8/5, 11/7, 14/9, 18/11 ||
 || 15 || 857.143, 1028.571
-&lt;span style="background-color: #ffffff;"&gt;257°8'34"&lt;/span&gt; || A || H#/Ab ||= Neutral 6th ||= 23/14 ||= 18/11 ||= 13/8 ||
+&lt;span style="background-color: #ffffff;"&gt;257°8'34"&lt;/span&gt; ||= A ||= 6th || H#/Ab ||= Neutral 6th ||= 23/14 ||= 18/11 ||= 13/8 ||
 || 16 || 914.286, 1097.143
-°&lt;span style="background-color: #ffffff;"&gt;17'9"&lt;/span&gt; || A^/Bvv || A ||= Supermajor 6th ||= 27/16, 46/27 ||= 17/10, 22/13 ||= 5/3, 12/7 ||
+°&lt;span style="background-color: #ffffff;"&gt;17'9"&lt;/span&gt; ||= A^/Bvv ||= up 6th || A ||= Supermajor 6th ||= 27/16, 46/27 ||= 17/10, 22/13 ||= 5/3, 12/7 ||
 || 17 || 971.429, 1165.714
-°&lt;span style="background-color: #ffffff;"&gt;25'43"&lt;/span&gt; || A^^/Bv || A# ||= Subminor 7th ||= 7/4 ||= 7/4 ||= 7/4, 9/5, 20/11 ||
+°&lt;span style="background-color: #ffffff;"&gt;25'43"&lt;/span&gt; ||= A^^/Bv ||= down 7th || A# ||= Subminor 7th ||= 7/4 ||= 7/4 ||= 7/4, 9/5, 20/11 ||
 || 18 || 1028.571, 1234.286
-&lt;span style="background-color: #ffffff;"&gt;308°34'17"&lt;/span&gt; || B || Bb ||= Supraminor 7th ||= 29/16, 9/5 ||= 9/5, 20/11 ||= 16/9 ||
+&lt;span style="background-color: #ffffff;"&gt;308°34'17"&lt;/span&gt; ||= B ||= 7th || Bb ||= Supraminor 7th ||= 29/16, 9/5 ||= 9/5, 20/11 ||= 16/9 ||
 || 19 || 1085.714, 1302.857
-°&lt;span style="background-color: #ffffff;"&gt;42'51"&lt;/span&gt; || B^/Cvv || B ||= Major 7th ||= 15/8 ||= 17/9 ||= 15/8, 48/25 ||
+°&lt;span style="background-color: #ffffff;"&gt;42'51"&lt;/span&gt; ||= B^/Cvv ||= up 7th || B ||= Major 7th ||= 15/8 ||= 17/9 ||= 15/8, 48/25 ||
 || 20 || 1142.857, 1371.429
-°&lt;span style="background-color: #ffffff;"&gt;8'34"&lt;/span&gt; || B^^/Cv || B#/Cb ||= Supermajor 7th ||= 27/14, 29/15 ||= 35/18, 68/35 ||= 63/32 ||
+°&lt;span style="background-color: #ffffff;"&gt;8'34"&lt;/span&gt; ||= B^^/Cv ||= down 8ve || B#/Cb ||= Supermajor 7th ||= 27/14, 29/15 ||= 35/18, 68/35 ||= 63/32 ||
 || 21 || 1200, 1440
-° || C || C ||= Octave ||= 2/1 ||= 2/1 ||= 2/1 ||
+° ||= C ||= 8ve || C ||= Octave ||= 2/1 ||= 2/1 ||= 2/1 ||
 *1: based on treating 21-EDO as a 2.7.15.23.27.29 subgroup temperament
@@ Line 186: / Line 186: @@
 &lt;strong&gt;Value&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;7-EDO&lt;/strong&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: center;"&gt;&lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation"&gt;Up/down&lt;/a&gt;&lt;br /&gt;
-&lt;strong&gt;Notation&lt;/strong&gt;&lt;br /&gt;
+&lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation"&gt;Notation&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;strong&gt;5L3s&lt;/strong&gt;&lt;br /&gt;
@@ Line 208: / Line 208: @@
          &lt;td&gt;0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;C&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;unison&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;C&lt;br /&gt;
@@ Line 227: / Line 229: @@
 °&lt;span style="background-color: #ffffff;"&gt;8'34&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;C^/Dvv&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C^/Dvv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;up unison&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;C#&lt;br /&gt;
@@ Line 246: / Line 250: @@
 °&lt;span style="background-color: #ffffff;"&gt;17'9&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;C^^/Dv&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C^^/Dv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;down 2nd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Db&lt;br /&gt;
@@ Line 265: / Line 271: @@
 &lt;span style="background-color: #ffffff;"&gt;51°25'43&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;D&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;2nd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;D&lt;br /&gt;
@@ Line 284: / Line 292: @@
 °&lt;span style="background-color: #ffffff;"&gt;34'17&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;D^/Evv&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;D^/Evv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;up 2nd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;D#&lt;br /&gt;
@@ Line 303: / Line 313: @@
 °&lt;span style="background-color: #ffffff;"&gt;42'51&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;D^^/Ev&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;D^^/Ev&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;down 3rd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Eb&lt;br /&gt;
@@ Line 322: / Line 334: @@
 &lt;span style="background-color: #ffffff;"&gt;102°51'26&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;E&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;E&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;3rd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;E&lt;br /&gt;
@@ Line 341: / Line 355: @@
 °&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;E^/Fvv&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;E^/Fvv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;up 3rd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;E#/Fb&lt;br /&gt;
@@ Line 360: / Line 376: @@
 °&lt;span style="background-color: #ffffff; line-height: 1.5;"&gt;8'34&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;E^^/Fv&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;E^^/Fv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;down 4th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;F&lt;br /&gt;
@@ Line 379: / Line 397: @@
 &lt;span style="background-color: #ffffff;"&gt;154°17'9&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;F&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;F&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;4th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;F#&lt;br /&gt;
@@ Line 398: / Line 418: @@
 °&lt;span style="background-color: #ffffff;"&gt;25'43&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;F^/Gvv&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;F^/Gvv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;up 4th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Gb&lt;br /&gt;
@@ Line 417: / Line 439: @@
 °&lt;span style="background-color: #ffffff;"&gt;34'17&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;F^^/Gv&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;F^^/Gv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;down 5th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;G&lt;br /&gt;
@@ Line 436: / Line 460: @@
 &lt;span style="background-color: #ffffff;"&gt;205°42'51&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;G&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;G&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;5th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;G#&lt;br /&gt;
@@ Line 455: / Line 481: @@
 °&lt;span style="background-color: #ffffff;"&gt;51'26&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;G^/Avv&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;G^/Avv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;up 5th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Hb&lt;br /&gt;
@@ Line 474: / Line 502: @@
 °&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;G^^/Av&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;G^^/Av&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;down 6th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;H&lt;br /&gt;
@@ Line 493: / Line 523: @@
 &lt;span style="background-color: #ffffff;"&gt;257°8'34&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;A&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;A&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;6th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;H#/Ab&lt;br /&gt;
@@ Line 512: / Line 544: @@
 °&lt;span style="background-color: #ffffff;"&gt;17'9&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;A^/Bvv&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;A^/Bvv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;up 6th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;A&lt;br /&gt;
@@ Line 531: / Line 565: @@
 °&lt;span style="background-color: #ffffff;"&gt;25'43&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;A^^/Bv&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;A^^/Bv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;down 7th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;A#&lt;br /&gt;
@@ Line 550: / Line 586: @@
 &lt;span style="background-color: #ffffff;"&gt;308°34'17&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;B&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;B&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;7th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Bb&lt;br /&gt;
@@ Line 569: / Line 607: @@
 °&lt;span style="background-color: #ffffff;"&gt;42'51&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;B^/Cvv&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;B^/Cvv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;up 7th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;B&lt;br /&gt;
@@ Line 588: / Line 628: @@
 °&lt;span style="background-color: #ffffff;"&gt;8'34&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;B^^/Cv&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;B^^/Cv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;down 8ve&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;B#/Cb&lt;br /&gt;
@@ Line 607: / Line 649: @@
 °&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;C&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;8ve&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;C&lt;br /&gt;
@@ Line 1,083: / Line 1,127: @@
 &lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Books / Literature:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;&lt;strong&gt;Books / Literature:&lt;/strong&gt;&lt;/h1&gt;
   Sword, Ron. &amp;quot;Icosihenaphonic Scales for Guitar&amp;quot;. IAAA Press. 1st ed: July 2009.&lt;br /&gt;
-&lt;!-- ws:start:WikiTextRemoteImageRule:842:&amp;lt;img src=&amp;quot;http://www.ronsword.com/images/ron1.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 188px; width: 254px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.ronsword.com/images/ron1.jpg" alt="external image ron1.jpg" title="external image ron1.jpg" style="height: 188px; width: 254px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:842 --&gt;&lt;!-- ws:start:WikiTextRemoteImageRule:843:&amp;lt;img src=&amp;quot;http://www.swordguitars.com/21tetsm.JPG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 191px; width: 363px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.swordguitars.com/21tetsm.JPG" alt="external image 21tetsm.JPG" title="external image 21tetsm.JPG" style="height: 191px; width: 363px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:843 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextRemoteImageRule:886:&amp;lt;img src=&amp;quot;http://www.ronsword.com/images/ron1.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 188px; width: 254px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.ronsword.com/images/ron1.jpg" alt="external image ron1.jpg" title="external image ron1.jpg" style="height: 188px; width: 254px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:886 --&gt;&lt;!-- ws:start:WikiTextRemoteImageRule:887:&amp;lt;img src=&amp;quot;http://www.swordguitars.com/21tetsm.JPG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 191px; width: 363px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.swordguitars.com/21tetsm.JPG" alt="external image 21tetsm.JPG" title="external image 21tetsm.JPG" style="height: 191px; width: 363px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:887 --&gt;&lt;br /&gt;
 &lt;strong&gt;&lt;em&gt;21-edo Icosihenaphonic Acoustic Guitar (Ron Sword)&lt;/em&gt;&lt;/strong&gt;&lt;br /&gt;
 &lt;br /&gt;