14edo: 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:TallKite|TallKite]] and made on <tt>2016-12-~~13 06~~:51:47 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-22 04:04:36 UTC</tt>.

: The original revision id was <tt>~~602052384~~</tt>.

: The original revision id was <tt>602738348</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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=**Intervals**=

|| **DEGREE** ||||= [[xenharmonic/Ups and Downs Notation|up/down]]

[[xenharmonic/Ups and Downs Notation| notation]] || **CENTS (coarse/fine)**

[[xenharmonic/Ups and Downs Notation| notation]] || **CENTS** ||= **Approximate**

**DMS** ||= **Approximate**

**Ratios 1``*``** ||= **Approximate**

**Ratios 2** **``**``** ||= Nearest

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

|| 1 ||= C^, Dv ||= up-unison,

down-2nd || 85.714~~, 102.857~~

down-2nd || 85.714 ||= 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 ||

|| 2 ||= D ||= 2nd || 171.429 ||= 11/10, 10/9,

|| 2 ||= D ||= 2nd || 171.429~~, 205.714~~

~~51°25'43"~~ ||= 11/10, 10/9,

19/17 ||= 9/8, 10/9,

11/10, 12/11 ||= 71 || Neutral 2nd, or

Narrow Major 2nd ||

|| 3· ||= D^, Ev ||= up-2nd,

down-3rd || 257.143~~, 308.571~~

down-3rd || 257.143 ||= 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 ||

|| 4 ||= E ||= 3rd || 342.857 ||= 11/9, 17/14 ||= 11/9, 5/4, 6/5 ||= 39 || Neutral 3rd ||

|| 4 ||= E ||= 3rd || 342.857~~, 411.429~~

~~102°51'26"~~ ||= 11/9, 17/14 ||= 11/9, 5/4, 6/5 ||= 39 || Neutral 3rd ||

|| 5· ||= E^, Fv ||= up-3rd,

down-4th || 428.571~~, 514.286~~

down-4th || 428.571 ||= 9/7, 14/11,

~~128°34'17"~~ ||= 9/7, 14/11,

22/17 ||= 9/7, 14/11 ||= 41 || Supermajor 3rd ||

|| 6 ||= F ||= 4th || 514.286~~, 617.143~~

|| 6 ||= F ||= 4th || 514.286 ||= 19/14 ||= 4/3, 11/8 ||= 43 || Wide 4th ||

~~154°17'9"~~ ||= 19/14 ||= 4/3, 11/8 ||= 43 || Wide 4th ||

|| 7· ||= F^, Gv ||= up-4th,

down-5th || 600~~, 720~~

down-5th || 600 ||= 7/5, 10/7 ||= 7/5, 10/7 ||= 91 || Tritone ||

~~180°~~ ||= 7/5, 10/7 ||= 7/5, 10/7 ||= 91 || Tritone ||

|| 8 ||= G ||= 5th || 685.714 ||= 28/19 ||= 3/2, 16/11 ||= 95 || Narrow 5th ||

|| 8 ||= G ||= 5th || 685.714~~, 823.857~~

~~205°42'51"~~ ||= 28/19 ||= 3/2, 16/11 ||= 95 || Narrow 5th ||

|| 9· ||= G^, Av ||= up-5th,

down-6th || 771.429~~, 925.714~~

down-6th || 771.429 ||= 14/9, 11/7,

~~231°25'43"~~ ||= 14/9, 11/7,

17/11 ||= ||= 25 || Subminor 6th ||

|| 10 ||= A ||= 6th || 857.143~~, 1028.571~~

|| 10 ||= A ||= 6th || 857.143 ||= 18/11 ||= 18/11, 8/5, 5/3 ||= 105 || Neutral 6th ||

~~257°8'34"~~ ||= 18/11 ||= 18/11, 8/5, 5/3 ||= 105 || Neutral 6th ||

|| 11· ||= A^, Bv ||= up-6th,

down-7th || 942.857~~, 1131.429~~

down-7th || 942.857 ||= 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 ||

|| 12 ||= B ||= 7th || 1028.571 ||= 20/11, 9/5,

|| 12 ||= B ||= 7th || 1028.571~~, 1234.286~~

~~308°34'17"~~ ||= 20/11, 9/5,

34/19 ||= 16/9, 9/5,

20/11, 11/6 ||= 29 || Neutral 7th, or

Wide Minor 7th ||

|| 13 ||= B^, Cv ||= up-7th,

down-8ve || 1114.286~~, 1337.143~~

down-8ve || 1114.286 ||= 19/10, 36/19,

~~334°17'9"~~ ||= 19/10, 36/19,

17/9 ||= 21/11, 27/14, 40/21 ||= 61 || Wide Major 7th ||

|| 14··(or 0) ||= C ||= 8ve || 1200~~, 1440~~

|| 14··(or 0) ||= C ||= 8ve || 1200 ||= 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 14edo as an 11-limit temperament

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<a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"> notation</a>

</td>

<td>CENTS ~~(coarse/fine) ~~

<td>CENTS

~~DMS~~

</td>

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

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down-2nd

</td>

<td>85.714~~, 102.857 ~~

<td>85.714

~~25°42'51&quot;~~

</td>

<td style="text-align: center;">20/19, 19/18, 18/17

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

</td>

<td>171.429~~, 205.714 ~~

<td>171.429

~~51°25'43&quot;~~

</td>

<td style="text-align: center;">11/10, 10/9,

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down-3rd

</td>

<td>257.143~~, 308.571 ~~

<td>257.143

~~77°8'34&quot;~~

</td>

<td style="text-align: center;">22/19, 20/17

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

</td>

<td>342.857~~, 411.429 ~~

<td>342.857

~~102°51'26&quot;~~

</td>

<td style="text-align: center;">11/9, 17/14

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down-4th

</td>

<td>428.571~~, 514.286 ~~

<td>428.571

~~128°34'17&quot;~~

</td>

<td style="text-align: center;">9/7, 14/11,

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

</td>

<td>514.286~~, 617.143 ~~

<td>514.286

~~154°17'9&quot;~~

</td>

<td style="text-align: center;">19/14

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down-5th

</td>

<td>600~~, 720 ~~

<td>600

~~180°~~

</td>

<td style="text-align: center;">7/5, 10/7

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

</td>

<td>685.714~~, 823.857 ~~

<td>685.714

~~205°42'51&quot;~~

</td>

<td style="text-align: center;">28/19

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down-6th

</td>

<td>771.429~~, 925.714 ~~

<td>771.429

~~231°25'43&quot;~~

</td>

<td style="text-align: center;">14/9, 11/7,

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

</td>

<td>857.143~~, 1028.571 ~~

<td>857.143

~~257°8'34&quot;~~

</td>

<td style="text-align: center;">18/11

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down-7th

</td>

<td>942.857~~, 1131.429 ~~

<td>942.857

~~282°51'26&quot;~~

</td>

<td style="text-align: center;">19/11, 17/10

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

</td>

<td>1028.571~~, 1234.286 ~~

<td>1028.571

~~308°34'17&quot;~~

</td>

<td style="text-align: center;">20/11, 9/5,

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down-8ve

</td>

<td>1114.286~~, 1337.143 ~~

<td>1114.286

~~334°17'9&quot;~~

</td>

<td style="text-align: center;">19/10, 36/19,

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

</td>

<td>1200~~, 1440 ~~

<td>1200

~~360°~~

</td>

<td style="text-align: center;">2/1

@@ 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:TallKite|TallKite]] and made on <tt>2016-12-13 06:51:47 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-22 04:04:36 UTC</tt>.<br>
-: The original revision id was <tt>602052384</tt>.<br>
+: The original revision id was <tt>602738348</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 11: / Line 11: @@
 =**Intervals**=
 || **DEGREE** ||||= [[xenharmonic/Ups and Downs Notation|up/down]]
-[[xenharmonic/Ups and Downs Notation| notation]] || **CENTS (coarse/fine)**
+[[xenharmonic/Ups and Downs Notation| notation]] || **CENTS** ||= **Approximate**
-**&lt;span style="background-color: #ffffff;"&gt;DMS&lt;/span&gt;** ||= **Approximate**
 **Ratios 1``*``** ||= **Approximate**
 **Ratios 2** **``**``** ||= Nearest
@@ Line 18: / Line 17: @@
 || 0 ||= C ||= unison || 0 ||= 1/1 ||= 1/1 ||= 1 || Unison ||
 || 1 ||= C^, Dv ||= up-unison,
-down-2nd || 85.714, 102.857
+down-2nd || 85.714 ||= 20/19, 19/18, 18/17 ||= 22/21, 28/27, 21/20 ||= 67 || Narrow Minor 2nd ||
-°42'51" ||= 20/19, 19/18, 18/17 ||= 22/21, 28/27, 21/20 ||= 67 || Narrow Minor 2nd ||
+|| 2 ||= D ||= 2nd || 171.429 ||= 11/10, 10/9,
-|| 2 ||= D ||= 2nd || 171.429, 205.714
-&lt;span style="background-color: #ffffff;"&gt;51°25'43"&lt;/span&gt; ||= 11/10, 10/9,
 /17 ||= 9/8, 10/9,
 /10, 12/11 ||= 71 || Neutral 2nd, or
 Narrow Major 2nd ||
 || 3· ||= D^, Ev ||= up-2nd,
-down-3rd || 257.143, 308.571
+down-3rd || 257.143 ||= 22/19, 20/17 ||= 7/6, 8/7 ||= 37 || Subminor 3rd ||
-°8'34" ||= 22/19, 20/17 ||= 7/6, 8/7 ||= 37 || Subminor 3rd ||
+|| 4 ||= E ||= 3rd || 342.857 ||= 11/9, 17/14 ||= 11/9, 5/4, 6/5 ||= 39 || Neutral 3rd ||
-|| 4 ||= E ||= 3rd || 342.857, 411.429
-&lt;span style="background-color: #ffffff;"&gt;102°51'26"&lt;/span&gt; ||= 11/9, 17/14 ||= 11/9, 5/4, 6/5 ||= 39 || Neutral 3rd ||
 || 5· ||= E^, Fv ||= up-3rd,
-down-4th || 428.571, 514.286
+down-4th || 428.571 ||= 9/7, 14/11,
-&lt;span style="line-height: 15.6000003814697px;"&gt;128°34'17"&lt;/span&gt; ||= 9/7, 14/11,
 /17 ||= 9/7, 14/11 ||= 41 || Supermajor 3rd ||
-|| 6 ||= F ||= 4th || 51&lt;span style="line-height: 1.5;"&gt;4.286, 617.143&lt;/span&gt;
+|| 6 ||= F ||= 4th || 51&lt;span style="line-height: 1.5;"&gt;4.286&lt;/span&gt; ||= 19/14 ||= 4/3, 11/8 ||= 43 || Wide 4th ||
-&lt;span style="background-color: #ffffff;"&gt;154°17'9"&lt;/span&gt; ||= 19/14 ||= 4/3, 11/8 ||= 43 || Wide 4th ||
 || 7· ||= F^, Gv ||= up-4th,
-down-5th || 600, 720
+down-5th || 600 ||= 7/5, 10/7 ||= 7/5, 10/7 ||= 91 || Tritone ||
-° ||= 7/5, 10/7 ||= 7/5, 10/7 ||= 91 || Tritone ||
+|| 8 ||= G ||= 5th || 685.714 ||= 28/19 ||= 3/2, 16/11 ||= 95 || Narrow 5th ||
-|| 8 ||= G ||= 5th || 685.714, 823.857
-&lt;span style="background-color: #ffffff;"&gt;205°42'51"&lt;/span&gt; ||= 28/19 ||= 3/2, 16/11 ||= 95 || Narrow 5th ||
 || 9· ||= G^, Av ||= up-5th,
-down-6th || 771.429, 925.714
+down-6th || 771.429 ||= 14/9, 11/7,
-°25'43" ||= 14/9, 11/7,
 /11 ||=   ||= 25 || Subminor 6th ||
-|| 10 ||= A ||= 6th || 857.143, 1028.571
+|| 10 ||= A ||= 6th || 857.143 ||= 18/11 ||= 18/11, 8/5, 5/3 ||= 105 || Neutral 6th ||
-&lt;span style="background-color: #ffffff;"&gt;257°8'34"&lt;/span&gt; ||= 18/11 ||= 18/11, 8/5, 5/3 ||= 105 || Neutral 6th ||
 || 11· ||= A^, Bv ||= up-6th,
-down-7th || 942.857, 1131.429
+down-7th || 942.857 ||= 19/11, 17/10 ||= 12/7, 7/4 ||= 55 || Supermajor 6th ||
-°51'26" ||= 19/11, 17/10 ||= 12/7, 7/4 ||= 55 || Supermajor 6th ||
+|| 12 ||= B ||= 7th || 1028.571 ||= 20/11, 9/5,
-|| 12 ||= B ||= 7th || 1028.571, 1234.286
-&lt;span style="background-color: #ffffff;"&gt;308°34'17"&lt;/span&gt; ||= 20/11, 9/5,
 /19 ||= 16/9, 9/5,
 /11, 11/6 ||= 29 || Neutral 7th, or
 Wide Minor 7th ||
 || 13 ||= B^, Cv ||= up-7th,
-down-8ve || 1114.286, 1337.143
+down-8ve || 1114.286 ||= 19/10, 36/19,
-°17'9" ||= 19/10, 36/19,
 /9 ||= 21/11, 27/14, 40/21 ||= 61 || Wide Major 7th ||
-|| 14··(or 0) ||= C ||= 8ve || 1200, 1440
+|| 14··(or 0) ||= C ||= 8ve || 1200 ||= 2/1 ||= 2/1 ||= 2 || Octave ||
-° ||= 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.
 &lt;span style="display: block; text-align: center;"&gt;``**``based on treating 14edo as an 11-limit temperament&lt;/span&gt;
@@ Line 201: / Line 186: @@
 &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt; notation&lt;/a&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;strong&gt;CENTS (coarse/fine)&lt;/strong&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;strong&gt;CENTS&lt;/strong&gt;&lt;br /&gt;
-&lt;strong&gt;&lt;span style="background-color: #ffffff;"&gt;DMS&lt;/span&gt;&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;strong&gt;Approximate&lt;/strong&gt;&lt;br /&gt;
@@ Line 242: / Line 226: @@
 down-2nd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;85.714, 102.857&lt;br /&gt;
+         &lt;td&gt;85.714&lt;br /&gt;
-°42'51&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;20/19, 19/18, 18/17&lt;br /&gt;
@@ Line 261: / Line 244: @@
          &lt;td style="text-align: center;"&gt;2nd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;171.429, 205.714&lt;br /&gt;
+         &lt;td&gt;171.429&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;51°25'43&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/10, 10/9,&lt;br /&gt;
@@ Line 284: / Line 266: @@
 down-3rd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;257.143, 308.571&lt;br /&gt;
+         &lt;td&gt;257.143&lt;br /&gt;
-°8'34&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;22/19, 20/17&lt;br /&gt;
@@ Line 303: / Line 284: @@
          &lt;td style="text-align: center;"&gt;3rd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;342.857, 411.429&lt;br /&gt;
+         &lt;td&gt;342.857&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;102°51'26&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/9, 17/14&lt;br /&gt;
@@ Line 323: / Line 303: @@
 down-4th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;428.571, 514.286&lt;br /&gt;
+         &lt;td&gt;428.571&lt;br /&gt;
-&lt;span style="line-height: 15.6000003814697px;"&gt;128°34'17&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;9/7, 14/11,&lt;br /&gt;
@@ Line 343: / Line 322: @@
          &lt;td style="text-align: center;"&gt;4th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;51&lt;span style="line-height: 1.5;"&gt;4.286, 617.143&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;51&lt;span style="line-height: 1.5;"&gt;4.286&lt;/span&gt;&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;154°17'9&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;19/14&lt;br /&gt;
@@ Line 363: / Line 341: @@
 down-5th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;600, 720&lt;br /&gt;
+         &lt;td&gt;600&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7/5, 10/7&lt;br /&gt;
@@ Line 382: / Line 359: @@
          &lt;td style="text-align: center;"&gt;5th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;685.714, 823.857&lt;br /&gt;
+         &lt;td&gt;685.714&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;205°42'51&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;28/19&lt;br /&gt;
@@ Line 402: / Line 378: @@
 down-6th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;771.429, 925.714&lt;br /&gt;
+         &lt;td&gt;771.429&lt;br /&gt;
-°25'43&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;14/9, 11/7,&lt;br /&gt;
@@ Line 422: / Line 397: @@
          &lt;td style="text-align: center;"&gt;6th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;857.143, 1028.571&lt;br /&gt;
+         &lt;td&gt;857.143&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;257°8'34&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;18/11&lt;br /&gt;
@@ Line 442: / Line 416: @@
 down-7th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;942.857, 1131.429&lt;br /&gt;
+         &lt;td&gt;942.857&lt;br /&gt;
-°51'26&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;19/11, 17/10&lt;br /&gt;
@@ Line 461: / Line 434: @@
          &lt;td style="text-align: center;"&gt;7th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1028.571, 1234.286&lt;br /&gt;
+         &lt;td&gt;1028.571&lt;br /&gt;
-&lt;span style="background-color: #ffffff;"&gt;308°34'17&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;20/11, 9/5,&lt;br /&gt;
@@ Line 484: / Line 456: @@
 down-8ve&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1114.286, 1337.143&lt;br /&gt;
+         &lt;td&gt;1114.286&lt;br /&gt;
-°17'9&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;19/10, 36/19,&lt;br /&gt;
@@ Line 504: / Line 475: @@
          &lt;td style="text-align: center;"&gt;8ve&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;1200, 1440&lt;br /&gt;
+         &lt;td&gt;1200&lt;br /&gt;
-°&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;2/1&lt;br /&gt;