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:igliashon|igliashon]] and made on <tt>2011-07-~~19 01~~:23:21 UTC</tt>.

: This revision was by author [[User:igliashon|igliashon]] and made on <tt>2011-07-30 17:50:41 UTC</tt>.

: The original revision id was <tt>~~241890068~~</tt>.

: The original revision id was <tt>243534697</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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==Basic Properties==

18-EDO divides the octave into 18 equal parts of ~66.667 cents each. It does not approximate the 3rd harmonic at all, unless a >30¢-error is considered acceptable, and it approximates the 5th and 7th harmonics equally with 12-TET. It does, however, render a most accurate tuning of 9/8, 7/6, 21/16, 15/11, 12/7, 16/9, and 13/7. It is also the smallest EDO to approximate the harmonic series chord 5:6:7 without tempering out 36/35 (and thus without using the same interval to approximate both 6/5 and 7/6).

In order to access the excellent consonances actually available, one must take a considerably "non-common-practice" approach, meaning to avoid the usual closed-voice "root-3rd-5th" type of chord and instead use chords which are either more compressed or more stretched out. 18-EDO may be treated as a temperament of the 17-limit [[k*N subgroups|4*18 subgroup]] [[Just intonation subgroups|just intonation subgroup]] 2.9.75.21.55.39.51. On this subgroup it tempers out exactly the same commas as 72 does on the full [[17-limit]], and gives precisely the same tunings. The subgroup can be put into a single chord, for example 32:36:39:42:51:55:64:75 (in terms of 18edo, 0-3-5-7-12-14-18-22), and transpositions and inversions of this chord or its subchords provide plenty of harmonic resources.

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===Representations of Just Intervals===

|| Degree || Cents || Nearest Ratio || Error (cents) || 17-Limit Ratios* ||

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

|| 0 || 0 || 1/1 || 0 || **1/1** ||

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

|| 10 || 666.667 || 22/15 || +3.617 ||> 75/51 ||

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

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

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

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

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

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

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

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

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

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

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

|| 16 || 1066.667 || 50/27 || -0.096 ||> 39/21 ||

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

|| 17 || 1133.333 || 52/27 || -1.329 ||> 75/39 ||

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

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

|| 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

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<h2 id="toc1"><a name="x18 Equal Divisions of the Octave-Basic Properties"></a>Basic Properties</h2>

18-EDO divides the octave into 18 equal parts of ~66.667 cents each. It does not approximate the 3rd harmonic at all, unless a &gt;30¢-error is considered acceptable, and it approximates the 5th and 7th harmonics equally with 12-TET. It does, however, render a most accurate tuning of 9/8, 7/6, 21/16, 15/11, 12/7, 16/9, and 13/7. It is also the smallest EDO to approximate the harmonic series chord 5:6:7 without tempering out 36/35 (and thus without using the same interval to approximate both 6/5 and 7/6).

18-EDO divides the octave into 18 equal parts of ~66.667 cents each. It does not approximate the 3rd harmonic at all, unless a &gt;30¢-error is considered acceptable, and it approximates the 5th and 7th harmonics equally with 12-TET. It does, however, render a most accurate tuning of 9/8, 7/6, 21/16, 15/11, 12/7, 16/9, and 13/7. It is also the smallest EDO to approximate the harmonic series chord 5:6:7 without tempering out 36/35 (and thus without using the same interval to approximate both 6/5 and 7/6).

In order to access the excellent consonances actually available, one must take a considerably &quot;non-common-practice&quot; approach, meaning to avoid the usual closed-voice &quot;root-3rd-5th&quot; type of chord and instead use chords which are either more compressed or more stretched out. 18-EDO may be treated as a temperament of the 17-limit <a class="wiki_link" href="/k%2AN%20subgroups">4*18 subgroup</a> <a class="wiki_link" href="/Just%20intonation%20subgroups">just intonation subgroup</a> 2.9.75.21.55.39.51. On this subgroup it tempers out exactly the same commas as 72 does on the full <a class="wiki_link" href="/17-limit">17-limit</a>, and gives precisely the same tunings. The subgroup can be put into a single chord, for example 32:36:39:42:51:55:64:75 (in terms of 18edo, 0-3-5-7-12-14-18-22), and transpositions and inversions of this chord or its subchords provide plenty of harmonic resources.

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</td>

<td>Cents

</td>

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

</td>

<td>Nearest Ratio

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</td>

<td>0

</td>

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

</td>

<td>1/1

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</td>

<td>66.667

</td>

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

</td>

<td>27/26

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</td>

<td>133.333

</td>

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

</td>

<td>27/25

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</td>

<td>200

</td>

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

</td>

<td>9/8

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</td>

<td>266.667

</td>

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

</td>

<td>7/6

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</td>

<td>333.333

</td>

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

</td>

<td>17/14 or 40/33

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</td>

<td>400

</td>

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

</td>

<td>5/4 or 44/35

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</td>

<td>466.667

</td>

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

</td>

<td>21/16

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</td>

<td>533.333

</td>

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

</td>

<td>15/11

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</td>

<td>600

</td>

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

</td>

<td>17/12 or 24/17

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</td>

<td>666.667

</td>

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

</td>

<td>22/15

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</td>

<td>733.333

</td>

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

</td>

<td>32/21

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</td>

<td>800

</td>

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

</td>

<td>8/5 or 35/22

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</td>

<td>866.667

</td>

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

</td>

<td>28/17 or 33/20

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</td>

<td>933.333

</td>

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

</td>

<td>12/7

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</td>

<td>1000

</td>

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

</td>

<td>16/9

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</td>

<td>1066.667

</td>

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

</td>

<td>50/27

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</td>

<td>1133.333

</td>

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

</td>

<td>52/27

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</td>

<td>1200

</td>

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

</td>

<td>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:igliashon|igliashon]] and made on <tt>2011-07-19 01:23:21 UTC</tt>.<br>
+: This revision was by author [[User:igliashon|igliashon]] and made on <tt>2011-07-30 17:50:41 UTC</tt>.<br>
-: The original revision id was <tt>241890068</tt>.<br>
+: The original revision id was <tt>243534697</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 10: / Line 10: @@
 ==Basic Properties==
 -EDO divides the octave into 18 equal parts of ~66.667 cents each. It does not approximate the 3rd harmonic at all, unless a &gt;30¢-error is considered acceptable, and it approximates the 5th and 7th harmonics equally with 12-TET. It does, however, render a most accurate tuning of 9/8, 7/6, 21/16, 15/11, 12/7, 16/9, and 13/7. It is also the smallest EDO to approximate the harmonic series chord 5:6:7 without tempering out 36/35 (and thus without using the same interval to approximate both 6/5 and 7/6).
 In order to access the excellent consonances actually available, one must take a considerably "non-common-practice" approach, meaning to avoid the usual closed-voice "root-3rd-5th" type of chord and instead use chords which are either more compressed or more stretched out. 18-EDO may be treated as a temperament of the 17-limit [[k*N subgroups|4*18 subgroup]] [[Just intonation subgroups|just intonation subgroup]] 2.9.75.21.55.39.51. On this subgroup it tempers out exactly the same commas as 72 does on the full [[17-limit]], and gives precisely the same tunings. The subgroup can be put into a single chord, for example 32:36:39:42:51:55:64:75 (in terms of 18edo, 0-3-5-7-12-14-18-22), and transpositions and inversions of this chord or its subchords provide plenty of harmonic resources.
@@ Line 17: / Line 17: @@
 ===Representations of Just Intervals===
-|| Degree || Cents || Nearest Ratio || Error (cents) || 17-Limit Ratios* ||
+|| Degree || Cents ||= 5L3s Notation || Nearest Ratio || Error (cents) || 17-Limit Ratios* ||
-|| 0 || 0 || 1/1 || 0 || **1/1** ||
+|| 0 || 0 ||= **C** || 1/1 || 0 || **1/1** ||
-|| 1 || 66.667 || 27/26 || +1.329 ||&gt; 78/75, 75/72 ||
+|| 1 || 66.667 ||= Db || 27/26 || +1.329 ||&gt; 78/75, 75/72 ||
-|| 2 || 133.333 || 27/25 || +0.096 ||&gt; 51/55, 42/39 ||
+|| 2 || 133.333 ||= C# || 27/25 || +0.096 ||&gt; 51/55, 42/39 ||
-|| 3 || 200 || 9/8 || -3.910 || **9/8** ||
+|| 3 || 200 ||= **D** || 9/8 || -3.910 || **9/8** ||
-|| 4 || 266.667 || 7/6 || -0.204 || **75/64** ||
+|| 4 || 266.667 ||= Eb || 7/6 || -0.204 || **75/64** ||
-|| 5 || 333.333 || 17/14 or 40/33 || -2.796 +0.293 || **39/32** ||
+|| 5 || 333.333 ||= D# || 17/14 or 40/33 || -2.796 +0.293 || **39/32** ||
-|| 6 || 400 || 5/4 or 44/35 || +13.686 +3.822 ||&gt; 64/55 ||
+|| 6 || 400 ||= **E** || 5/4 or 44/35 || +13.686 +3.822 ||&gt; 64/55 ||
-|| 7 || 466.667 || 21/16 || -4.114 || **21/16** ||
+|| 7 || 466.667 ||= **F** || 21/16 || -4.114 || **21/16** ||
-|| 8 || 533.333 || 15/11 || -3.617 ||&gt; 102/75 ||
+|| 8 || 533.333 ||= Gb || 15/11 || -3.617 ||&gt; 102/75 ||
-|| 9 || 600 || 17/12 or 24/17 || -3.000 +3.000 ||&gt; 17/12 ||
+|| 9 || 600 ||= F# || 17/12 or 24/17 || -3.000 +3.000 ||&gt; 17/12 ||
-|| 10 || 666.667 || 22/15 || +3.617 ||&gt; 75/51 ||
+|| 10 || 666.667 ||= **G** || 22/15 || +3.617 ||&gt; 75/51 ||
-|| 11 || 733.333 || 32/21 || +4.114 ||&gt; 32/21 ||
+|| 11 || 733.333 ||= Hb || 32/21 || +4.114 ||&gt; 32/21 ||
-|| 12 || 800 || 8/5 or 35/22 || -13.686 -3.8222 || **51/32** ||
+|| 12 || 800 ||= G# || 8/5 or 35/22 || -13.686 -3.8222 || **51/32** ||
-|| 13 || 866.667 || 28/17 or 33/20 || +2.796 -0.293 ||&gt; 64/39 ||
+|| 13 || 866.667 ||= **H** || 28/17 or 33/20 || +2.796 -0.293 ||&gt; 64/39 ||
-|| 14 || 933.333 || 12/7 || +0.204 || **55/32** ||
+|| 14 || 933.333 ||= **A** || 12/7 || +0.204 || **55/32** ||
-|| 15 || 1000 || 16/9 || +3.910 ||&gt; 16/9 ||
+|| 15 || 1000 ||= Bb || 16/9 || +3.910 ||&gt; 16/9 ||
-|| 16 || 1066.667 || 50/27 || -0.096 ||&gt; 39/21 ||
+|| 16 || 1066.667 ||= A# || 50/27 || -0.096 ||&gt; 39/21 ||
-|| 17 || 1133.333 || 52/27 || -1.329 ||&gt; 75/39 ||
+|| 17 || 1133.333 ||= **B** || 52/27 || -1.329 ||&gt; 75/39 ||
-|| 18 || 1200 || 2/1 || 0 || **2/1** ||
+|| 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 87: / Line 87: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x18 Equal Divisions of the Octave-Basic Properties"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Basic Properties&lt;/h2&gt;
--EDO divides the octave into 18 equal parts of ~66.667 cents each. It does not approximate the 3rd harmonic at all, unless a &amp;gt;30¢-error is considered acceptable, and it approximates the 5th and 7th harmonics equally with 12-TET. It does, however, render a most accurate tuning of 9/8, 7/6, 21/16, 15/11, 12/7, 16/9, and 13/7. It is also the smallest EDO to approximate the harmonic series chord 5:6:7 without tempering out 36/35 (and thus without using the same interval to approximate both 6/5 and 7/6). &lt;br /&gt;
+-EDO divides the octave into 18 equal parts of ~66.667 cents each. It does not approximate the 3rd harmonic at all, unless a &amp;gt;30¢-error is considered acceptable, and it approximates the 5th and 7th harmonics equally with 12-TET. It does, however, render a most accurate tuning of 9/8, 7/6, 21/16, 15/11, 12/7, 16/9, and 13/7. It is also the smallest EDO to approximate the harmonic series chord 5:6:7 without tempering out 36/35 (and thus without using the same interval to approximate both 6/5 and 7/6).&lt;br /&gt;
 &lt;br /&gt;
 In order to access the excellent consonances actually available, one must take a considerably &amp;quot;non-common-practice&amp;quot; approach, meaning to avoid the usual closed-voice &amp;quot;root-3rd-5th&amp;quot; type of chord and instead use chords which are either more compressed or more stretched out. 18-EDO may be treated as a temperament of the 17-limit &lt;a class="wiki_link" href="/k%2AN%20subgroups"&gt;4*18 subgroup&lt;/a&gt; &lt;a class="wiki_link" href="/Just%20intonation%20subgroups"&gt;just intonation subgroup&lt;/a&gt; 2.9.75.21.55.39.51. On this subgroup it tempers out exactly the same commas as 72 does on the full &lt;a class="wiki_link" href="/17-limit"&gt;17-limit&lt;/a&gt;, and gives precisely the same tunings. The subgroup can be put into a single chord, for example 32:36:39:42:51:55:64:75 (in terms of 18edo, 0-3-5-7-12-14-18-22), and transpositions and inversions of this chord or its subchords provide plenty of harmonic resources.&lt;br /&gt;
@@ Line 101: / Line 101: @@
 &lt;/td&gt;
          &lt;td&gt;Cents&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;5L3s Notation&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Nearest Ratio&lt;br /&gt;
@@ Line 113: / Line 115: @@
 &lt;/td&gt;
          &lt;td&gt;0&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;strong&gt;C&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;1/1&lt;br /&gt;
@@ Line 125: / Line 129: @@
 &lt;/td&gt;
          &lt;td&gt;66.667&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Db&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;27/26&lt;br /&gt;
@@ Line 137: / Line 143: @@
 &lt;/td&gt;
          &lt;td&gt;133.333&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;C#&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;27/25&lt;br /&gt;
@@ Line 149: / Line 157: @@
 &lt;/td&gt;
          &lt;td&gt;200&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;strong&gt;D&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;9/8&lt;br /&gt;
@@ Line 161: / Line 171: @@
 &lt;/td&gt;
          &lt;td&gt;266.667&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Eb&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;7/6&lt;br /&gt;
@@ Line 173: / Line 185: @@
 &lt;/td&gt;
          &lt;td&gt;333.333&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;D#&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;17/14 or 40/33&lt;br /&gt;
@@ Line 185: / Line 199: @@
 &lt;/td&gt;
          &lt;td&gt;400&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;strong&gt;E&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;5/4 or 44/35&lt;br /&gt;
@@ Line 197: / Line 213: @@
 &lt;/td&gt;
          &lt;td&gt;466.667&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;strong&gt;F&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;21/16&lt;br /&gt;
@@ Line 209: / Line 227: @@
 &lt;/td&gt;
          &lt;td&gt;533.333&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Gb&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;15/11&lt;br /&gt;
@@ Line 221: / Line 241: @@
 &lt;/td&gt;
          &lt;td&gt;600&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;F#&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;17/12 or 24/17&lt;br /&gt;
@@ Line 233: / Line 255: @@
 &lt;/td&gt;
          &lt;td&gt;666.667&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;strong&gt;G&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;22/15&lt;br /&gt;
@@ Line 245: / Line 269: @@
 &lt;/td&gt;
          &lt;td&gt;733.333&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Hb&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;32/21&lt;br /&gt;
@@ Line 257: / Line 283: @@
 &lt;/td&gt;
          &lt;td&gt;800&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;G#&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;8/5 or 35/22&lt;br /&gt;
@@ Line 269: / Line 297: @@
 &lt;/td&gt;
          &lt;td&gt;866.667&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;strong&gt;H&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;28/17 or 33/20&lt;br /&gt;
@@ Line 281: / Line 311: @@
 &lt;/td&gt;
          &lt;td&gt;933.333&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;strong&gt;A&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;12/7&lt;br /&gt;
@@ Line 293: / Line 325: @@
 &lt;/td&gt;
          &lt;td&gt;1000&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;Bb&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;16/9&lt;br /&gt;
@@ Line 305: / Line 339: @@
 &lt;/td&gt;
          &lt;td&gt;1066.667&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;A#&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;50/27&lt;br /&gt;
@@ Line 317: / Line 353: @@
 &lt;/td&gt;
          &lt;td&gt;1133.333&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;strong&gt;B&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;52/27&lt;br /&gt;
@@ Line 329: / Line 367: @@
 &lt;/td&gt;
          &lt;td&gt;1200&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;strong&gt;C&lt;/strong&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;2/1&lt;br /&gt;