18edo: 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:~~Kosmorsky~~|~~Kosmorsky~~]] and made on <tt>~~2013~~-05-~~09 11~~:58:38 UTC</tt>.

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-03-24 21:25:39 UTC</tt>.

: The original revision id was <tt>~~430237910~~</tt>.

: The original revision id was <tt>545218750</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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===Representations of Just Intervals===

|| Degree || Cents ||= 5L3s Notation || Nearest Ratio || Error (cents) || 17-Limit Ratios* ||

|| Degree || Cents

DMS ||= 5L3s Notation || Nearest Ratio || Error (cents)

(DMS) || 17-Limit Ratios* ||

|| 0 || 0 ||= **C** || 1/1 || 0 || **1/1** ||

|| 1 || 66.667 ||= Db || 27/26 || +1.329 ||> 78/75, 75/72 ||

|| 1 || 66.667

|| 2 || 133.333 ||= C# || 27/25 || +0.096 ||> 51/55, 42/39 ||

20° ||= Db || 27/26 || +1.329

|| 3 || 200 ||= **D** || 9/8 || -3.910 || **9/8** ||

+23'56" ||> 78/75, 75/72 ||

|| 4 || 266.667 ||= Eb || 7/6 || -0.204 || **75/64** ||

|| 2 || 133.333

|| 5 || 333.333 ||= D# || 17/14 or 40/33 || -2.796 +0.293 || **39/32** ||

40° ||= C# || 27/25 || +0.096

|| 6 || 400 ||= **E** || 5/4 or 44/35 || +13.686 +3.822 ||> 64/55 ||

+1'43" ||> 51/55, 42/39 ||

|| 7 || 466.667 ||= **F** || 21/16 || -4.114 || **21/16** ||

|| 3 || 200

|| 8 || 533.333 ||= Gb || 15/11 || -3.617 ||> 102/75 ||

60° ||= **D** || 9/8 || -3.910

|| 9 || 600 ||= F# || 17/12 or 24/17 || -3.000 +3.000 ||> 17/12 ||

-1°10'23" || **9/8** ||

|| 10 || 666.667 ||= **G** || 22/15 || +3.617 ||> 75/51 ||

|| 4 || 266.667

|| 11 || 733.333 ||= Hb || 32/21 || +4.114 ||> 32/21 ||

80° ||= Eb || 7/6 || -0.204

|| 12 || 800 ||= G# || 8/5 or 35/22 || -13.686 -3.8222 || **51/32** ||

-1"50" || **75/64** ||

|| 13 || 866.667 ||= **H** || 28/17 or 33/20 || +2.796 -0.293 ||> 64/39 ||

|| 5 || 333.333

|| 14 || 933.333 ||= **A** || 12/7 || +0.204 || **55/32** ||

100° ||= D# || 17/14 or 40/33 || -2.796 +0.293

|| 15 || 1000 ||= Bb || 16/9 || +3.910 ||> 16/9 ||

-50'20" +5'16" || **39/32** ||

|| 16 || 1066.667 ||= A# || 50/27 || -0.096 ||> 39/21 ||

|| 6 || 400

|| 17 || 1133.333 ||= **B** || 52/27 || -1.329 ||> 75/39 ||

120° ||= **E** || 5/4 or 44/35 || +13.686 +3.822

|| 18 || 1200 ||= **C** || 2/1 || 0 || **2/1** ||

+4°6'21" +1°8'47" ||> 64/55 ||

|| 7 || 466.667

140° ||= **F** || 21/16 || -4.114

-1°14'3" || **21/16** ||

|| 8 || 533.333

160° ||= Gb || 15/11 || -3.617

-1°5'7" ||> 102/75 ||

|| 9 || 600

180° ||= F# || 17/12 or 24/17 || -3.000 +3.000

-54' +54' ||> 17/12 ||

|| 10 || 666.667

200° ||= **G** || 22/15 || +3.617

+1°5'7" ||> 75/51 ||

|| 11 || 733.333

220° ||= Hb || 32/21 || +4.114

+1°14'3" ||> 32/21 ||

|| 12 || 800

240° ||= G# || 8/5 or 35/22 || -13.686 -3.8222

-4°6'21" -1°8'47" || **51/32** ||

|| 13 || 866.667

260° ||= **H** || 28/17 or 33/20 || +2.796 -0.293

+50'20" -5'16" ||> 64/39 ||

|| 14 || 933.333

280° ||= **A** || 12/7 || +0.204

+1"50" || **55/32** ||

|| 15 || 1000

300° ||= Bb || 16/9 || +3.910

+1°10'23" ||> 16/9 ||

|| 16 || 1066.667

320° ||= A# || 50/27 || -0.096

-1'43" ||> 39/21 ||

|| 17 || 1133.333

340° ||= **B** || 52/27 || -1.329

-23'56" ||> 75/39 ||

|| 18 || 1200

360° ||= **C** || 2/1 || 0 || **2/1** ||

*based on the above description of 18-EDO as a 2.9.75.21.55.39.51 subgroup temperament

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==Listen==

* ~~////~~[[http://www.h-pi.com/mp3/18ETPrelude.mp3|18ETPrelude]]~~////~~ by [[Aaron Andrew Hunt]]

* [[http://www.h-pi.com/mp3/18ETPrelude.mp3|18ETPrelude]] by [[Aaron Andrew Hunt]]

* ~~////~~[[http://micro.soonlabel.com/18-ET/prelude-in-18et.mp3|Prelude in 18et]]~~////~~ by [[@http://www.chrisvaisvil.com|Chris Vaisvil]] => [[@http://chrisvaisvil.com/?p=3|composer notes]]

* [[http://micro.soonlabel.com/18-ET/prelude-in-18et.mp3|Prelude in 18et]] by [[@http://www.chrisvaisvil.com|Chris Vaisvil]] => [[@http://chrisvaisvil.com/?p=3|composer notes]]

* ~~////~~[[http://micro.soonlabel.com/18-ET/daily20110401-18c-flippertronics.mp3|Flippertronics]]~~////~~ by Chris Vaisvil

* [[http://micro.soonlabel.com/18-ET/daily20110401-18c-flippertronics.mp3|Flippertronics]] by Chris Vaisvil

* ~~////~~[[http://micro.soonlabel.com/9-edo/daily20111008b_gerbils_at_the_wheel_of_government.mp3|Gerbils at the Wheel of Government]]~~////~~ by [[@http://chrisvaisvil.com/?p=1402|Chris Vaisvil (in 9 and 18 edo simultaneously)]]</pre></div>

* [[http://micro.soonlabel.com/9-edo/daily20111008b_gerbils_at_the_wheel_of_government.mp3|Gerbils at the Wheel of Government]] by [[@http://chrisvaisvil.com/?p=1402|Chris Vaisvil (in 9 and 18 edo simultaneously)]]</pre></div>

<h4>Original HTML content:</h4>

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>18edo</title></head><body><h1 id="toc0"><a name="x18 Equal Divisions of the Octave"></a>18 Equal Divisions of the Octave</h1>

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</td>

<td>Cents

DMS

</td>

<td style="text-align: center;">5L3s Notation

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</td>

<td>Error (cents)

(DMS)

</td>

<td>17-Limit Ratios*

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</td>

<td>66.667

20°

</td>

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

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</td>

<td>+1.329

+23'56&quot;

</td>

<td style="text-align: right;">78/75, 75/72

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</td>

<td>133.333

40°

</td>

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

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</td>

<td>+0.096

+1'43&quot;

</td>

<td style="text-align: right;">51/55, 42/39

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</td>

<td>200

60°

</td>

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

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</td>

<td>-3.910

-1°10'23&quot;

</td>

<td>9/8

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</td>

<td>266.667

80°

</td>

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

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</td>

<td>-0.204

-1&quot;50&quot;

</td>

<td>75/64

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</td>

<td>333.333

100°

</td>

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

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</td>

<td>-2.796 +0.293

-50'20&quot; +5'16&quot;

</td>

<td>39/32

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</td>

<td>400

120°

</td>

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

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</td>

<td>+13.686 +3.822

+4°6'21&quot; +1°8'47&quot;

</td>

<td style="text-align: right;">64/55

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</td>

<td>466.667

140°

</td>

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

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</td>

<td>-4.114

-1°14'3&quot;

</td>

<td>21/16

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</td>

<td>533.333

160°

</td>

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

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</td>

<td>-3.617

-1°5'7&quot;

</td>

<td style="text-align: right;">102/75

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</td>

<td>600

180°

</td>

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

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</td>

<td>-3.000 +3.000

-54' +54'

</td>

<td style="text-align: right;">17/12

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</td>

<td>666.667

200°

</td>

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

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</td>

<td>+3.617

+1°5'7&quot;

</td>

<td style="text-align: right;">75/51

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</td>

<td>733.333

220°

</td>

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

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</td>

<td>+4.114

+1°14'3&quot;

</td>

<td style="text-align: right;">32/21

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</td>

<td>800

240°

</td>

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

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</td>

<td>-13.686 -3.8222

-4°6'21&quot; -1°8'47&quot;

</td>

<td>51/32

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</td>

<td>866.667

260°

</td>

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

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</td>

<td>+2.796 -0.293

+50'20&quot; -5'16&quot;

</td>

<td style="text-align: right;">64/39

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</td>

<td>933.333

280°

</td>

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

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</td>

<td>+0.204

+1&quot;50&quot;

</td>

<td>55/32

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</td>

<td>1000

300°

</td>

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

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</td>

<td>+3.910

+1°10'23&quot;

</td>

<td style="text-align: right;">16/9

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</td>

<td>1066.667

320°

</td>

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

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</td>

<td>-0.096

-1'43&quot;

</td>

<td style="text-align: right;">39/21

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</td>

<td>1133.333

340°

</td>

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

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</td>

<td>-1.329

-23'56&quot;

</td>

<td style="text-align: right;">75/39

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</td>

<td>1200

360°

</td>

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

@@ 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:Kosmorsky|Kosmorsky]] and made on <tt>2013-05-09 11:58:38 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-03-24 21:25:39 UTC</tt>.<br>
-: The original revision id was <tt>430237910</tt>.<br>
+: The original revision id was <tt>545218750</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 19: / Line 19: @@
 ===Representations of Just Intervals===
-|| Degree || Cents ||= 5L3s Notation || Nearest Ratio || Error (cents) || 17-Limit Ratios* ||
+|| Degree || Cents
+DMS ||= 5L3s Notation || Nearest Ratio || Error (cents)
+(DMS) || 17-Limit Ratios* ||
 || 0 || 0 ||= **C** || 1/1 || 0 || **1/1** ||
-|| 1 || 66.667 ||= Db || 27/26 || +1.329 ||&gt; 78/75, 75/72 ||
+|| 1 || 66.667
-|| 2 || 133.333 ||= C# || 27/25 || +0.096 ||&gt; 51/55, 42/39 ||
+° ||= Db || 27/26 || +1.329
-|| 3 || 200 ||= **D** || 9/8 || -3.910 || **9/8** ||
++23'56" ||&gt; 78/75, 75/72 ||
-|| 4 || 266.667 ||= Eb || 7/6 || -0.204 || **75/64** ||
+|| 2 || 133.333
-|| 5 || 333.333 ||= D# || 17/14 or 40/33 || -2.796 +0.293 || **39/32** ||
+° ||= C# || 27/25 || +0.096
-|| 6 || 400 ||= **E** || 5/4 or 44/35 || +13.686 +3.822 ||&gt; 64/55 ||
++1'43" ||&gt; 51/55, 42/39 ||
-|| 7 || 466.667 ||= **F** || 21/16 || -4.114 || **21/16** ||
+|| 3 || 200
-|| 8 || 533.333 ||= Gb || 15/11 || -3.617 ||&gt; 102/75 ||
+° ||= **D** || 9/8 || -3.910
-|| 9 || 600 ||= F# || 17/12 or 24/17 || -3.000 +3.000 ||&gt; 17/12 ||
+-1°10'23" || **9/8** ||
-|| 10 || 666.667 ||= **G** || 22/15 || +3.617 ||&gt; 75/51 ||
+|| 4 || 266.667
-|| 11 || 733.333 ||= Hb || 32/21 || +4.114 ||&gt; 32/21 ||
+° ||= Eb || 7/6 || -0.204
-|| 12 || 800 ||= G# || 8/5 or 35/22 || -13.686 -3.8222 || **51/32** ||
+-1"50" || **75/64** ||
-|| 13 || 866.667 ||= **H** || 28/17 or 33/20 || +2.796 -0.293 ||&gt; 64/39 ||
+|| 5 || 333.333
-|| 14 || 933.333 ||= **A** || 12/7 || +0.204 || **55/32** ||
+° ||= D# || 17/14 or 40/33 || -2.796 +0.293
-|| 15 || 1000 ||= Bb || 16/9 || +3.910 ||&gt; 16/9 ||
+-50'20" +5'16" || **39/32** ||
-|| 16 || 1066.667 ||= A# || 50/27 || -0.096 ||&gt; 39/21 ||
+|| 6 || 400
-|| 17 || 1133.333 ||= **B** || 52/27 || -1.329 ||&gt; 75/39 ||
+° ||= **E** || 5/4 or 44/35 || +13.686 +3.822
-|| 18 || 1200 ||= **C** || 2/1 || 0 || **2/1** ||
++4°6'21" +1°8'47" ||&gt; 64/55 ||
+|| 7 || 466.667
+° ||= **F** || 21/16 || -4.114
+-1°14'3" || **21/16** ||
+|| 8 || 533.333
+° ||= Gb || 15/11 || -3.617
+-1°5'7" ||&gt; 102/75 ||
+|| 9 || 600
+° ||= F# || 17/12 or 24/17 || -3.000 +3.000
+-54' +54' ||&gt; 17/12 ||
+|| 10 || 666.667
+° ||= **G** || 22/15 || +3.617
++1°5'7" ||&gt; 75/51 ||
+|| 11 || 733.333
+° ||= Hb || 32/21 || +4.114
++1°14'3" ||&gt; 32/21 ||
+|| 12 || 800
+° ||= G# || 8/5 or 35/22 || -13.686 -3.8222
+-4°6'21" -1°8'47" || **51/32** ||
+|| 13 || 866.667
+° ||= **H** || 28/17 or 33/20 || +2.796 -0.293
+&lt;span style="line-height: 15.6000003814697px;"&gt;+&lt;/span&gt;50'20" &lt;span style="line-height: 15.6000003814697px;"&gt;-&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;5'16"&lt;/span&gt; ||&gt; 64/39 ||
+|| 14 || 933.333
+° ||= **A** || 12/7 || +0.204
++1"50" || **55/32** ||
+|| 15 || 1000
+° ||= Bb || 16/9 || +3.910
++1°10'23" ||&gt; 16/9 ||
+|| 16 || 1066.667
+° ||= A# || 50/27 || -0.096
+-1'43" ||&gt; 39/21 ||
+|| 17 || 1133.333
+° ||= **B** || 52/27 || -1.329
+-23'56" ||&gt; 75/39 ||
+|| 18 || 1200
+° ||= **C** || 2/1 || 0 || **2/1** ||
 *based on the above description of 18-EDO as a 2.9.75.21.55.39.51 subgroup temperament
@@ Line 81: / Line 118: @@
 ==Listen==
-* ////[[http://www.h-pi.com/mp3/18ETPrelude.mp3|18ETPrelude]]//// by [[Aaron Andrew Hunt]]
+* [[http://www.h-pi.com/mp3/18ETPrelude.mp3|18ETPrelude]] by [[Aaron Andrew Hunt]]
-* ////[[http://micro.soonlabel.com/18-ET/prelude-in-18et.mp3|Prelude in 18et]]//// by [[@http://www.chrisvaisvil.com|Chris Vaisvil]] =&gt; [[@http://chrisvaisvil.com/?p=3|composer notes]]
+* [[http://micro.soonlabel.com/18-ET/prelude-in-18et.mp3|Prelude in 18et]] by [[@http://www.chrisvaisvil.com|Chris Vaisvil]] =&gt; [[@http://chrisvaisvil.com/?p=3|composer notes]]
-* ////[[http://micro.soonlabel.com/18-ET/daily20110401-18c-flippertronics.mp3|Flippertronics]]//// by Chris Vaisvil
+* [[http://micro.soonlabel.com/18-ET/daily20110401-18c-flippertronics.mp3|Flippertronics]] by Chris Vaisvil
-* ////[[http://micro.soonlabel.com/9-edo/daily20111008b_gerbils_at_the_wheel_of_government.mp3|Gerbils at the Wheel of Government]]//// by [[@http://chrisvaisvil.com/?p=1402|Chris Vaisvil (in 9 and 18 edo simultaneously)]]</pre></div>
+* [[http://micro.soonlabel.com/9-edo/daily20111008b_gerbils_at_the_wheel_of_government.mp3|Gerbils at the Wheel of Government]] by [[@http://chrisvaisvil.com/?p=1402|Chris Vaisvil (in 9 and 18 edo simultaneously)]]</pre></div>
 <h4>Original HTML content:</h4>
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;18edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x18 Equal Divisions of the Octave"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;18 Equal Divisions of the Octave&lt;/h1&gt;
@@ Line 106: / Line 143: @@
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+DMS&lt;br /&gt;
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@@ Line 112: / Line 150: @@
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+(DMS)&lt;br /&gt;
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@@ Line 134: / Line 173: @@
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+°&lt;br /&gt;
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@@ Line 140: / Line 180: @@
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++23'56&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
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@@ Line 148: / Line 189: @@
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+°&lt;br /&gt;
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@@ Line 154: / Line 196: @@
 &lt;/td&gt;
          &lt;td&gt;+0.096&lt;br /&gt;
++1'43&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
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@@ Line 162: / Line 205: @@
 &lt;/td&gt;
          &lt;td&gt;200&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;strong&gt;D&lt;/strong&gt;&lt;br /&gt;
@@ Line 168: / Line 212: @@
 &lt;/td&gt;
          &lt;td&gt;-3.910&lt;br /&gt;
+-1°10'23&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;strong&gt;9/8&lt;/strong&gt;&lt;br /&gt;
@@ Line 176: / Line 221: @@
 &lt;/td&gt;
          &lt;td&gt;266.667&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;Eb&lt;br /&gt;
@@ Line 182: / Line 228: @@
 &lt;/td&gt;
          &lt;td&gt;-0.204&lt;br /&gt;
+-1&amp;quot;50&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;strong&gt;75/64&lt;/strong&gt;&lt;br /&gt;
@@ Line 190: / Line 237: @@
 &lt;/td&gt;
          &lt;td&gt;333.333&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;D#&lt;br /&gt;
@@ Line 196: / Line 244: @@
 &lt;/td&gt;
          &lt;td&gt;-2.796 +0.293&lt;br /&gt;
+-50'20&amp;quot; +5'16&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;strong&gt;39/32&lt;/strong&gt;&lt;br /&gt;
@@ Line 204: / Line 253: @@
 &lt;/td&gt;
          &lt;td&gt;400&lt;br /&gt;
+°&lt;br /&gt;
 &lt;/td&gt;
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18edo: Difference between revisions

Wikispaces>JosephRuhf