22edo: 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:~~genewardsmith~~|~~genewardsmith~~]] and made on <tt>~~2014~~-02-~~22 03~~:39:56 UTC</tt>.

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-03-27 10:16:32 UTC</tt>.

: The original revision id was <tt>~~491178528~~</tt>.

: The original revision id was <tt>545554374</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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22-et can also be treated as adding harmonics 3 and 5 to 11-EDO's 2.7.9.11.15.17 subgroup, making it a (rather accurate) 2.3.5.7.11.17 subgroup temperament. Let us also mind it's approximation of the 31st harmonic is within half a cent, which is fairly accurate.

==Intervals by degree==

|| Degree || Cents ||= Approximate

Ratios* ||

|| 0 || 0 ||= 1/1 ||

|| 1 || 54.55 ||= 33/32, 34/33 ||

|| 1 || 54.55

|| 2 || 109.09 ||= 18/17, 17/16, 16/15, 15/14 ||

16°21'49" ||= 33/32, 34/33 ||

|| 3 || 163.64 ||= 11/10, 10/9 ||

|| 2 || 109.09

|| 4 || 218.18 ||= 9/8, 8/7, 17/15 ||

32°43'38" ||= 18/17, 17/16, 16/15, 15/14 ||

|| 5 || 272.73 ||= 7/6, 20/17 ||

|| 3 || 163.64

|| 6 || 327.27 ||= 6/5, 17/14, 11/9 ||

49°5'27" ||= 11/10, 10/9 ||

|| 7 || 381.82 ||= 5/4 ||

|| 4 || 218.18

|| 8 || 436.36 ||= 9/7, 14/11, 22/17 ||

65°27'16" ||= 9/8, 8/7, 17/15 ||

|| 9 || 490.91 ||= 4/3 ||

|| 5 || 272.73

|| 10 || 545.45 ||= 11/8, 15/11 ||

81°49'5" ||= 7/6, 20/17 ||

|| 11 || 600 ||= 7/5, 10/7, 17/12, 24/17 ||

|| 6 || 327.27

|| 12 || 654.55 ||= 16/11, 22/15 ||

98°10'55" ||= 6/5, 17/14, 11/9 ||

|| 13 || 709.09 ||= 3/2 ||

|| 7 || 381.82

|| 14 || 763.64 ||= 11/7, 14/9, 17/11 ||

114°31'44" ||= 5/4 ||

|| 15 || 818.18 ||= 8/5 ||

|| 8 || 436.36

|| 16 || 872.73 ||= 5/3, 18/11, 28/17 ||

130°54'33" ||= 9/7, 14/11, 22/17 ||

|| 17 || 927.27 ||= 12/7, 17/10 ||

|| 9 || 490.91

|| 18 || 981.82 ||= 7/4, 16/9, 30/17 ||

147°16'22" ||= 4/3 ||

|| 19 || 1036.36 ||= 20/11, 9/5 ||

|| 10 || 545.45

|| 20 || 1090.91 ||= 15/8, 32/17, 17/9, 28/15 ||

163°38'11" ||= 11/8, 15/11 ||

|| 21 || 1145.45 ||= 33/17, 64/33, 31/16 ||

|| 11 || 600

|| 22 || 1200 ||= 2/1 ||

180° ||= 7/5, 10/7, 17/12, 24/17 ||

|| 12 || 654.55

196°21'49" ||= 16/11, 22/15 ||

|| 13 || 709.09

212°43'38" ||= 3/2 ||

|| 14 || 763.64

229°5'27" ||= 11/7, 14/9, 17/11 ||

|| 15 || 818.18

245°16'22" ||= 8/5 ||

|| 16 || 872.73

261°49'5" ||= 5/3, 18/11, 28/17 ||

|| 17 || 927.27

278°10'55" ||= 12/7, 17/10 ||

|| 18 || 981.82

294°31'44" ||= 7/4, 16/9, 30/17 ||

|| 19 || 1036.36

310°54'33" ||= 20/11, 9/5 ||

|| 20 || 1090.91

327°16'22" ||= 15/8, 32/17, 17/9, 28/15 ||

|| 21 || 1145.45

343°38'11" ||= 33/17, 64/33, 31/16 ||

|| 22 || 1200

360° ||= 2/1 ||

==Intervals by error==

|| Interval || Error ||

|| 9/7 || 1.280 ||

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<h2 id="toc1"><a name="Theory-Intervals by degree"></a>Intervals by degree</h2>

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</td>

<td>54.55

16°21'49&quot;

</td>

<td style="text-align: center;">33/32, 34/33

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Line 274:

</td>

<td>109.09

32°43'38&quot;

</td>

<td style="text-align: center;">18/17, 17/16, 16/15, 15/14

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</td>

<td>163.64

49°5'27&quot;

</td>

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

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</td>

<td>218.18

65°27'16&quot;

</td>

<td style="text-align: center;">9/8, 8/7, 17/15

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</td>

<td>272.73

81°49'5&quot;

</td>

<td style="text-align: center;">7/6, 20/17

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</td>

<td>327.27

98°10'55&quot;

</td>

<td style="text-align: center;">6/5, 17/14, 11/9

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</td>

<td>381.82

114°31'44&quot;

</td>

<td style="text-align: center;">5/4

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</td>

<td>436.36

130°54'33&quot;

</td>

<td style="text-align: center;">9/7, 14/11, 22/17

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Line 337:

</td>

<td>490.91

147°16'22&quot;

</td>

<td style="text-align: center;">4/3

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Line 346:

</td>

<td>545.45

163°38'11&quot;

</td>

<td style="text-align: center;">11/8, 15/11

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</td>

<td>600

180°

</td>

<td style="text-align: center;">7/5, 10/7, 17/12, 24/17

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</td>

<td>654.55

196°21'49&quot;

</td>

<td style="text-align: center;">16/11, 22/15

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</td>

<td>709.09

212°43'38&quot;

</td>

<td style="text-align: center;">3/2

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</td>

<td>763.64

229°5'27&quot;

</td>

<td style="text-align: center;">11/7, 14/9, 17/11

Line 355:

Line 391:

</td>

<td>818.18

245°16'22&quot;

</td>

<td style="text-align: center;">8/5

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</td>

<td>872.73

261°49'5&quot;

</td>

<td style="text-align: center;">5/3, 18/11, 28/17

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Line 409:

</td>

<td>927.27

278°10'55&quot;

</td>

<td style="text-align: center;">12/7, 17/10

Line 379:

Line 418:

</td>

<td>981.82

294°31'44&quot;

</td>

<td style="text-align: center;">7/4, 16/9, 30/17

Line 387:

Line 427:

</td>

<td>1036.36

310°54'33&quot;

</td>

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

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Line 436:

</td>

<td>1090.91

327°16'22&quot;

</td>

<td style="text-align: center;">15/8, 32/17, 17/9, 28/15

Line 403:

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</td>

<td>1145.45

343°38'11&quot;

</td>

<td style="text-align: center;">33/17, 64/33, 31/16

Line 411:

Line 454:

</td>

<td>1200

360°

</td>

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

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<h2 id="toc2"><a name="Theory-Intervals by error"></a>Intervals by error</h2>

@@ 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:genewardsmith|genewardsmith]] and made on <tt>2014-02-22 03:39:56 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-03-27 10:16:32 UTC</tt>.<br>
-: The original revision id was <tt>491178528</tt>.<br>
+: The original revision id was <tt>545554374</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: @@
 -et can also be treated as adding harmonics 3 and 5 to 11-EDO's 2.7.9.11.15.17 subgroup, making it a (rather accurate) 2.3.5.7.11.17 subgroup temperament. Let us also mind it's approximation of the 31st harmonic is within half a cent, which is fairly accurate.
 ==Intervals by degree==
 || Degree || Cents ||= Approximate
 Ratios* ||
 || 0 || 0 ||= 1/1 ||
-|| 1 || 54.55 ||= 33/32, 34/33 ||
+|| 1 || 54.55
-|| 2 || 109.09 ||= 18/17, 17/16, 16/15, 15/14 ||
+°&lt;span style="background-color: #ffffff;"&gt;21'49"&lt;/span&gt; ||= 33/32, 34/33 ||
-|| 3 || 163.64 ||= 11/10, 10/9 ||
+|| 2 || 109.09
-|| 4 || 218.18 ||= 9/8, 8/7, 17/15 ||
+&lt;span style="background-color: #ffffff;"&gt;32°43'38"&lt;/span&gt; ||= 18/17, 17/16, 16/15, 15/14 ||
-|| 5 || 272.73 ||= 7/6, 20/17 ||
+|| 3 || 163.64
-|| 6 || 327.27 ||= 6/5, 17/14, 11/9 ||
+°5'27" ||= 11/10, 10/9 ||
-|| 7 || 381.82 ||= 5/4 ||
+|| 4 || 218.18
-|| 8 || 436.36 ||= 9/7, 14/11, 22/17 ||
+&lt;span style="background-color: #ffffff;"&gt;65°27'16"&lt;/span&gt; ||= 9/8, 8/7, 17/15 ||
-|| 9 || 490.91 ||= 4/3 ||
+|| 5 || 272.73
-|| 10 || 545.45 ||= 11/8, 15/11 ||
+°&lt;span style="background-color: #ffffff;"&gt;49'5"&lt;/span&gt; ||= 7/6, 20/17 ||
-|| 11 || 600 ||= 7/5, 10/7, 17/12, 24/17 ||
+|| 6 || 327.27
-|| 12 || 654.55 ||= 16/11, 22/15 ||
+&lt;span style="background-color: #ffffff;"&gt;98°10'55"&lt;/span&gt; ||= 6/5, 17/14, 11/9 ||
-|| 13 || 709.09 ||= 3/2 ||
+|| 7 || 381.82
-|| 14 || 763.64 ||= 11/7, 14/9, 17/11 ||
+°&lt;span style="background-color: #ffffff;"&gt;31'44"&lt;/span&gt; ||= 5/4 ||
-|| 15 || 818.18 ||= 8/5 ||
+|| 8 || 436.36
-|| 16 || 872.73 ||= 5/3, 18/11, 28/17 ||
+&lt;span style="background-color: #ffffff;"&gt;130°54'33"&lt;/span&gt; ||= 9/7, 14/11, 22/17 ||
-|| 17 || 927.27 ||= 12/7, 17/10 ||
+|| 9 || 490.91
-|| 18 || 981.82 ||= 7/4, 16/9, 30/17 ||
+°&lt;span style="background-color: #ffffff;"&gt;16'22"&lt;/span&gt; ||= 4/3 ||
-|| 19 || 1036.36 ||= 20/11, 9/5 ||
+|| 10 || 545.45
-|| 20 || 1090.91 ||= 15/8, 32/17, 17/9, 28/15 ||
+&lt;span style="background-color: #ffffff;"&gt;163°38'11"&lt;/span&gt; ||= 11/8, 15/11 ||
-|| 21 || 1145.45 ||= 33/17, 64/33, 31/16 ||
+|| 11 || 600
-|| 22 || 1200 ||= 2/1 ||
+° ||= 7/5, 10/7, 17/12, 24/17 ||
+|| 12 || 654.55
+&lt;span style="background-color: #ffffff;"&gt;196°21'49"&lt;/span&gt; ||= 16/11, 22/15 ||
+|| 13 || 709.09
+°&lt;span style="background-color: #ffffff;"&gt;43'38"&lt;/span&gt; ||= 3/2 ||
+|| 14 || 763.64
+&lt;span style="background-color: #ffffff;"&gt;229°5'27"&lt;/span&gt; ||= 11/7, 14/9, 17/11 ||
+|| 15 || 818.18
+°&lt;span style="background-color: #ffffff;"&gt;16'22"&lt;/span&gt; ||= 8/5 ||
+|| 16 || 872.73
+&lt;span style="background-color: #ffffff;"&gt;261°49'5"&lt;/span&gt; ||= 5/3, 18/11, 28/17 ||
+|| 17 || 927.27
+°&lt;span style="background-color: #ffffff;"&gt;10'55"&lt;/span&gt; ||= 12/7, 17/10 ||
+|| 18 || 981.82
+&lt;span style="background-color: #ffffff;"&gt;294°31'44"&lt;/span&gt; ||= 7/4, 16/9, 30/17 ||
+|| 19 || 1036.36
+°&lt;span style="background-color: #ffffff;"&gt;54'33"&lt;/span&gt; ||= 20/11, 9/5 ||
+|| 20 || 1090.91
+&lt;span style="background-color: #ffffff;"&gt;327°16'22"&lt;/span&gt; ||= 15/8, 32/17, 17/9, 28/15 ||
+|| 21 || 1145.45
+°&lt;span style="background-color: #ffffff;"&gt;38'11"&lt;/span&gt; ||= 33/17, 64/33, 31/16 ||
+|| 22 || 1200
+° ||= 2/1 ||
 ==Intervals by error==
 || Interval || Error ||
 || 9/7 || 1.280 ||
@@ Line 219: / Line 241: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Theory-Intervals by degree"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Intervals by degree&lt;/h2&gt;
 &lt;table class="wiki_table"&gt;
@@ Line 243: / Line 265: @@
 &lt;/td&gt;
          &lt;td&gt;54.55&lt;br /&gt;
+°&lt;span style="background-color: #ffffff;"&gt;21'49&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;33/32, 34/33&lt;br /&gt;
@@ Line 251: / Line 274: @@
 &lt;/td&gt;
          &lt;td&gt;109.09&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;32°43'38&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;18/17, 17/16, 16/15, 15/14&lt;br /&gt;
@@ Line 259: / Line 283: @@
 &lt;/td&gt;
          &lt;td&gt;163.64&lt;br /&gt;
+°5'27&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/10, 10/9&lt;br /&gt;
@@ Line 267: / Line 292: @@
 &lt;/td&gt;
          &lt;td&gt;218.18&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;65°27'16&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;9/8, 8/7, 17/15&lt;br /&gt;
@@ Line 275: / Line 301: @@
 &lt;/td&gt;
          &lt;td&gt;272.73&lt;br /&gt;
+°&lt;span style="background-color: #ffffff;"&gt;49'5&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7/6, 20/17&lt;br /&gt;
@@ Line 283: / Line 310: @@
 &lt;/td&gt;
          &lt;td&gt;327.27&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;98°10'55&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;6/5, 17/14, 11/9&lt;br /&gt;
@@ Line 291: / Line 319: @@
 &lt;/td&gt;
          &lt;td&gt;381.82&lt;br /&gt;
+°&lt;span style="background-color: #ffffff;"&gt;31'44&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;5/4&lt;br /&gt;
@@ Line 299: / Line 328: @@
 &lt;/td&gt;
          &lt;td&gt;436.36&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;130°54'33&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;9/7, 14/11, 22/17&lt;br /&gt;
@@ Line 307: / Line 337: @@
 &lt;/td&gt;
          &lt;td&gt;490.91&lt;br /&gt;
+°&lt;span style="background-color: #ffffff;"&gt;16'22&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;4/3&lt;br /&gt;
@@ Line 315: / Line 346: @@
 &lt;/td&gt;
          &lt;td&gt;545.45&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;163°38'11&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/8, 15/11&lt;br /&gt;
@@ Line 323: / Line 355: @@
 &lt;/td&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, 17/12, 24/17&lt;br /&gt;
@@ Line 331: / Line 364: @@
 &lt;/td&gt;
          &lt;td&gt;654.55&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;196°21'49&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;16/11, 22/15&lt;br /&gt;
@@ Line 339: / Line 373: @@
 &lt;/td&gt;
          &lt;td&gt;709.09&lt;br /&gt;
+°&lt;span style="background-color: #ffffff;"&gt;43'38&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;3/2&lt;br /&gt;
@@ Line 347: / Line 382: @@
 &lt;/td&gt;
          &lt;td&gt;763.64&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;229°5'27&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;11/7, 14/9, 17/11&lt;br /&gt;
@@ Line 355: / Line 391: @@
 &lt;/td&gt;
          &lt;td&gt;818.18&lt;br /&gt;
+°&lt;span style="background-color: #ffffff;"&gt;16'22&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;8/5&lt;br /&gt;
@@ Line 363: / Line 400: @@
 &lt;/td&gt;
          &lt;td&gt;872.73&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;261°49'5&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;5/3, 18/11, 28/17&lt;br /&gt;
@@ Line 371: / Line 409: @@
 &lt;/td&gt;
          &lt;td&gt;927.27&lt;br /&gt;
+°&lt;span style="background-color: #ffffff;"&gt;10'55&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;12/7, 17/10&lt;br /&gt;
@@ Line 379: / Line 418: @@
 &lt;/td&gt;
          &lt;td&gt;981.82&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;294°31'44&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;7/4, 16/9, 30/17&lt;br /&gt;
@@ Line 387: / Line 427: @@
 &lt;/td&gt;
          &lt;td&gt;1036.36&lt;br /&gt;
+°&lt;span style="background-color: #ffffff;"&gt;54'33&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 395: / Line 436: @@
 &lt;/td&gt;
          &lt;td&gt;1090.91&lt;br /&gt;
+&lt;span style="background-color: #ffffff;"&gt;327°16'22&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;15/8, 32/17, 17/9, 28/15&lt;br /&gt;
@@ Line 403: / Line 445: @@
 &lt;/td&gt;
          &lt;td&gt;1145.45&lt;br /&gt;
+°&lt;span style="background-color: #ffffff;"&gt;38'11&amp;quot;&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;33/17, 64/33, 31/16&lt;br /&gt;
@@ Line 411: / Line 454: @@
 &lt;/td&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;
@@ Line 419: / Line 463: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Theory-Intervals by error"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Intervals by error&lt;/h2&gt;
 &lt;table class="wiki_table"&gt;