5L 3s: 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>2015-02-11 14:14:24 UTC</tt>.

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-02-11 14:17:20 UTC</tt>.

: The original revision id was <tt>~~540641396~~</tt>.

: The original revision id was <tt>540641992</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.

<h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">5L 3s refers to the structure of moment of symmetry scales with generators ranging from 2\5 (two degrees of [[5edo]] = 480¢) to 3\8 (three degrees of [[8edo]] = 450¢). In the case of 8edo, L and s are the same size; in the case of 5edo, s becomes so small it disappears (and all that remains are the five equal L's). The spectrum looks like this:

||~ ||~ ||~ ||~ ||~ ||~ ||~ ||~ ||~ tetrachord ||~ g in cents ||~ 2g ||~ 3g ||~ 4g ||~ Comments ||

||||||||||||||||~ generator ||~ tetrachord ||~ g in cents ||~ 2g ||~ 3g ||~ 4g ||~ Comments ||

|| 2\5 || || || || || || || || 1 0 1 || 480.000 || 960.000 || 240.00 || 720.000 ||= ||

|| 2\5 || || || || || || || || 1 0 1 || 480.000 || 960.000 || 240.00 || 720.000 ||= ||

|| 21\53 || || || || || || || || 10 1 10 || 475.472 || 950.943 || 226.415 || 701.887 ||= Vulture/Buzzard is around here ||

|| 21\53 || || || || || || || || 10 1 10 || 475.472 || 950.943 || 226.415 || 701.887 ||= Vulture/Buzzard is around here ||

|| 19\48 || || || || || || || || 9 1 9 || 475 || 950 || 225 || 700 ||= ||

|| 19\48 || || || || || || || || 9 1 9 || 475 || 950 || 225 || 700 ||= ||

|| 17\43 || || || || || || || || 8 1 8 || 474.419 || 948.837 || 223.256 || 697.674 ||= ||

|| 17\43 || || || || || || || || 8 1 8 || 474.419 || 948.837 || 223.256 || 697.674 ||= ||

|| 15\38 || || || || || || || || 7 1 7 || 473.684 || 947.368 || 221.053 || 694.737 ||= ||

|| 15\38 || || || || || || || || 7 1 7 || 473.684 || 947.368 || 221.053 || 694.737 ||= ||

|| 13\33 || || || || || || || || 6 1 6 || 472.727 || 945.455 || 218.181 || 690.909 ||= ||

|| 13\33 || || || || || || || || 6 1 6 || 472.727 || 945.455 || 218.181 || 690.909 ||= ||

|| 11\28 || || || || || || || || 5 1 5 || 471.429 || 942.857 || 214.286 || 685.714 ||= ||

|| 11\28 || || || || || || || || 5 1 5 || 471.429 || 942.857 || 214.286 || 685.714 ||= ||

|| 9\23 || || || || || || || || 4 1 4 || 469.565 || 939.130 || 208.696 || 678.261 ||= L/s = 4 ||

|| 9\23 || || || || || || || || 4 1 4 || 469.565 || 939.130 || 208.696 || 678.261 ||= L/s = 4 ||

|| || || || || || || || || 3.03 1 3.03 || 466.769 || 933.538 || 200.307 || 667.076 ||= L/s = 3*2^(1/75) ||

|| 7\18 || || || || || || || || 3 1 3 || 466.667 || 933.333 || 200.000 || 666.667 ||= L/s = 3 ||

|| 7\18 || || || || || || || || 3 1 3 || 466.667 || 933.333 || 200.000 || 666.667 ||= L/s = 3 ||

|| || || || || || || || || 2.97 1 2.97 || 466.564 || 933.127 || 199.691 || 666.255 ||= L/s = 3/2^(1/75) ||

|| || 12\31 || || || || || || || 5 2 5 || 464.516 || 929.032 || 193.549 || 658.065 ||= ||

|| || 12\31 || || || || || || || 5 2 5 || 464.516 || 929.032 || 193.549 || 658.065 ||= ||

|| 5\13 || || || || || || || || 2 1 2 || 461.538 || 923.077 || 184.615 || 646.154 ||= ||

|| 5\13 || || || || || || || || 2 1 2 || 461.538 || 923.077 || 184.615 || 646.154 ||= ||

|| || 13\34 || || || || || || || 5 3 5 || 458.824 || 917.647 || 176.471 || 635.294 ||= ||

|| || 13\34 || || || || || || || 5 3 5 || 458.824 || 917.647 || 176.471 || 635.294 ||= ||

|| || || || 34\89 || || || || || 13 8 13 || 458.427 || 916.854 || 175.281 || 633.708 ||= ||

|| || || || 34\89 || || || || || 13 8 13 || 458.427 || 916.854 || 175.281 || 633.708 ||= ||

|| || || || || || 89\233 || || || 34 21 34 || 458.369 || 916.738 || 175.107 || 633.473 ||= ||

|| || || || || || 89\233 || || || 34 21 34 || 458.369 || 916.738 || 175.107 || 633.473 ||= ||

|| || || || || || || || 233\610 || 89 55 89 || 458.361 || 916.721 || 175.082 || 633.443 ||= Golden father ||

|| || || || || || || || 233\610 || 89 55 89 || 458.361 || 916.721 || 175.082 || 633.443 ||= Golden father ||

|| || || || || || || 144\377 || || 55 34 55 || 458.355 || 916.711 || 175.066 || 633.422 ||= ||

|| || || || || || || 144\377 || || 55 34 55 || 458.355 || 916.711 || 175.066 || 633.422 ||= ||

|| || || || || 55\144 || || || || 21 13 21 || 458.333 || 916.666 || 175 || 633.333 ||= ||

|| || || || || 55\144 || || || || 21 13 21 || 458.333 || 916.666 || 175 || 633.333 ||= ||

|| || || 21\55 || || || || || || 8 5 8 || 458.182 || 916.364 || 174.545 || 632.727 ||= ||

|| || || 21\55 || || || || || || 8 5 8 || 458.182 || 916.364 || 174.545 || 632.727 ||= ||

|| 8\21 || || || || || || || || 3 2 3 || 457.143 || 914.286 || 171.429 || 628.571 ||= Optimum rank range (L/s=3/2) father ||

|| 8\21 || || || || || || || || 3 2 3 || 457.143 || 914.286 || 171.429 || 628.571 ||= Optimum rank range (L/s=3/2) father ||

|| 11\29 || || || || || || || || 4 3 4 || 455.172 || 910.345 || 165.517 || 620.690 ||= ||

|| 11\29 || || || || || || || || 4 3 4 || 455.172 || 910.345 || 165.517 || 620.690 ||= ||

|| 3\8 || || || || || || || || 1 1 1 || 450.000 || 900.000 || 150.000 || 600.000 ||= ||

|| 3\8 || || || || || || || || 1 1 1 || 450.000 || 900.000 || 150.000 || 600.000 ||= ||

The only notable harmonic entropy minimum is Vulture/[[Hemifamity temperaments|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region is a kind of wasteland in terms of harmonious MOSes.</pre></div>

<h4>Original HTML content:</h4>

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<tr>

<th>~~ ~~

<th colspan="8">generator

~~</th>~~

~~<th> ~~

~~</th>~~

~~<th> ~~

~~</th>~~

~~<th> ~~

~~</th>~~

~~<th> ~~

~~</th>~~

~~<th> ~~

~~</th>~~

~~<th> ~~

~~</th>~~

~~<th>~~

</th>

<th>tetrachord

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<td>

</td>

<td>1 0 1

<td>1 0 1

</td>

<td>480.000

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<td>

</td>

<td>10 1 10

<td>10 1 10

</td>

<td>475.472

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<td>701.887

</td>

<td style="text-align: center;">Vulture/Buzzard is around here

<td style="text-align: center;">Vulture/Buzzard is around here

</td>

</tr>

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<td>

</td>

<td>9 1 9

<td>9 1 9

</td>

<td>475

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<td>

</td>

<td>8 1 8

<td>8 1 8

</td>

<td>474.419

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<td>

</td>

<td>7 1 7

<td>7 1 7

</td>

<td>473.684

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<td>

</td>

<td>6 1 6

<td>6 1 6

</td>

<td>472.727

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<td>

</td>

<td>5 1 5

<td>5 1 5

</td>

<td>471.429

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<td>

</td>

<td>4 1 4

<td>4 1 4

</td>

<td>469.565

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<td>678.261

</td>

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

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

</td>

</tr>

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<td>

</td>

<td>3 1 3

<td>3 1 3

</td>

<td>466.667

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<td>666.667

</td>

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

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

</td>

</tr>

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<td>

</td>

<td>5 2 5

<td>5 2 5

</td>

<td>464.516

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<td>

</td>

<td>2 1 2

<td>2 1 2

</td>

<td>461.538

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<td>

</td>

<td>5 3 5

<td>5 3 5

</td>

<td>458.824

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<td>

</td>

<td>13 8 13

<td>13 8 13

</td>

<td>458.427

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<td>

</td>

<td>34 21 34

<td>34 21 34

</td>

<td>458.369

</td>

<td>916.738

<td>916.738

</td>

<td>175.107

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<td>233\610

</td>

<td>89 55 89

<td>89 55 89

</td>

<td>458.361

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<td>633.443

</td>

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

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

</td>

</tr>

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<td>

</td>

<td>55 34 55

<td>55 34 55

</td>

<td>458.355

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<td>

</td>

<td>21 13 21

<td>21 13 21

</td>

<td>458.333

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<td>

</td>

<td>8 5 8

<td>8 5 8

</td>

<td>458.182

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<td>

</td>

<td>3 2 3

<td>3 2 3

</td>

<td>457.143

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<td>628.571

</td>

<td style="text-align: center;">Optimum rank range (L/s=3/2) father

<td style="text-align: center;">Optimum rank range (L/s=3/2) father

</td>

</tr>

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<td>

</td>

<td>4 3 4

<td>4 3 4

</td>

<td>455.172

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<td>

</td>

<td>1 1 1

<td>1 1 1

</td>

<td>450.000

@@ 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>2015-02-11 14:14:24 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-02-11 14:17:20 UTC</tt>.<br>
-: The original revision id was <tt>540641396</tt>.<br>
+: The original revision id was <tt>540641992</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>
 <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">5L 3s refers to the structure of moment of symmetry scales with generators ranging from 2\5 (two degrees of [[5edo]] = 480¢) to 3\8 (three degrees of [[8edo]] = 450¢). In the case of 8edo, L and s are the same size; in the case of 5edo, s becomes so small it disappears (and all that remains are the five equal L's). The spectrum looks like this:
-||~   ||~   ||~   ||~   ||~   ||~   ||~   ||~   ||~ &lt;span style="display: block; text-align: center;"&gt;tetrachord&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;g in cents&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;2g&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;3g&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;4g&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;Comments&lt;/span&gt; ||
+||||||||||||||||~ generator ||~ &lt;span style="display: block; text-align: center;"&gt;tetrachord&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;g in cents&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;2g&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;3g&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;4g&lt;/span&gt; ||~ &lt;span style="display: block; text-align: center;"&gt;Comments&lt;/span&gt; ||
-|| 2\5 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="text-align: center;"&gt;1 0 1&lt;/span&gt; || 480.000 || 960.000 || 240.00 || &lt;span style="line-height: 15.6000003814697px;"&gt;720.000&lt;/span&gt; ||=   ||
+|| 2\5 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;1 0 1&lt;/span&gt; || 480.000 || 960.000 || 240.00 || &lt;span style="line-height: 15.6000003814697px;"&gt;720.000&lt;/span&gt; ||=   ||
-|| 21\53 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="text-align: center;"&gt;10 1 10&lt;/span&gt; || 475.472 || 950.943 || 226.415 || 701.887 ||= &lt;span style="text-align: center;"&gt;Vulture/Buzzard is around here&lt;/span&gt; ||
+|| 21\53 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;10 1 10&lt;/span&gt; || 475.472 || 950.943 || 226.415 || 701.887 ||= &lt;span style="display: block; text-align: center;"&gt;Vulture/Buzzard is around here&lt;/span&gt; ||
-|| 19\48 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="text-align: center;"&gt;9 1 9&lt;/span&gt; || 475 || 950 || 225 || 700 ||=   ||
+|| 19\48 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;9 1 9&lt;/span&gt; || 475 || 950 || 225 || 700 ||=   ||
-|| 17\43 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="text-align: center;"&gt;8 1 8&lt;/span&gt; || 474.419 || 948.837 || 223.256 || 697.674 ||=   ||
+|| 17\43 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;8 1 8&lt;/span&gt; || 474.419 || 948.837 || 223.256 || 697.674 ||=   ||
-|| 15\38 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="text-align: center;"&gt;7 1 7&lt;/span&gt; || 473.684 || 947.368 || 221.053 || 694.737 ||=   ||
+|| 15\38 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;7 1 7&lt;/span&gt; || 473.684 || 947.368 || 221.053 || 694.737 ||=   ||
-|| 13\33 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="text-align: center;"&gt;6 1 6&lt;/span&gt; || 472.727 || 945.455 || 218.181 || 690.909 ||=   ||
+|| 13\33 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;6 1 6&lt;/span&gt; || 472.727 || 945.455 || 218.181 || 690.909 ||=   ||
-|| 11\28 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="text-align: center;"&gt;5 1 5&lt;/span&gt; || 471.429 || 942.857 || 214.286 || 685.714 ||=   ||
+|| 11\28 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;5 1 5&lt;/span&gt; || 471.429 || 942.857 || 214.286 || 685.714 ||=   ||
-|| 9\23 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="text-align: center;"&gt;4 1 4&lt;/span&gt; || 469.565 || 939.130 || 208.696 || 678.261 ||= &lt;span style="text-align: center;"&gt;L/s = 4&lt;/span&gt; ||
+|| 9\23 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;4 1 4&lt;/span&gt; || 469.565 || 939.130 || 208.696 || 678.261 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = 4&lt;/span&gt; ||
 ||   ||   ||   ||   ||   ||   ||   ||   || 3.03 1 3.03 || 466.769 || 933.538 || 200.307 || 667.076 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = 3*2^(1/75)&lt;/span&gt; ||
-|| 7\18 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="text-align: center;"&gt;3 1 3&lt;/span&gt; || 466.667 || 933.333 || 200.000 || 666.667 ||= &lt;span style="text-align: center;"&gt;L/s = 3&lt;/span&gt; ||
+|| 7\18 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;3 1 3&lt;/span&gt; || 466.667 || 933.333 || 200.000 || 666.667 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = 3&lt;/span&gt; ||
 ||   ||   ||   ||   ||   ||   ||   ||   || 2.97 1 2.97 || 466.564 || 933.127 || 199.691 || 666.255 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = 3/2^(1/75)&lt;/span&gt; ||
-||   || 12\31 ||   ||   ||   ||   ||   ||   || &lt;span style="text-align: center;"&gt;5 2 5&lt;/span&gt; || 464.516 || 929.032 || 193.549 || 658.065 ||=   ||
+||   || 12\31 ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;5 2 5&lt;/span&gt; || 464.516 || 929.032 || 193.549 || 658.065 ||=   ||
-|| 5\13 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="text-align: center;"&gt;2 1 2&lt;/span&gt; || 461.538 || 923.077 || 184.615 || 646.154 ||=   ||
+|| 5\13 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;2 1 2&lt;/span&gt; || 461.538 || 923.077 || 184.615 || 646.154 ||=   ||
-||   || 13\34 ||   ||   ||   ||   ||   ||   || &lt;span style="text-align: center;"&gt;5 3 5&lt;/span&gt; || 458.824 || 917.647 || 176.471 || 635.294 ||=   ||
+||   || 13\34 ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;5 3 5&lt;/span&gt; || 458.824 || 917.647 || 176.471 || 635.294 ||=   ||
-||   ||   ||   || 34\89 ||   ||   ||   ||   || &lt;span style="text-align: center;"&gt;13 8 13&lt;/span&gt; || 458.427 || 916.854 || 175.281 || 633.708 ||=   ||
+||   ||   ||   || 34\89 ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;13 8 13&lt;/span&gt; || 458.427 || 916.854 || 175.281 || 633.708 ||=   ||
-||   ||   ||   ||   ||   || 89\233 ||   ||   || &lt;span style="text-align: center;"&gt;34 21 34&lt;/span&gt; || &lt;span style="line-height: 15.6000003814697px;"&gt;458.369&lt;/span&gt; || &lt;span style="text-align: center;"&gt;916.738&lt;/span&gt; || 175.107 || &lt;span style="line-height: 15.6000003814697px;"&gt;633.473&lt;/span&gt; ||=   ||
+||   ||   ||   ||   ||   || 89\233 ||   ||   || &lt;span style="display: block; text-align: center;"&gt;34 21 34&lt;/span&gt; || &lt;span style="line-height: 15.6000003814697px;"&gt;458.369&lt;/span&gt; || &lt;span style="display: block; text-align: center;"&gt;916.738&lt;/span&gt; || 175.107 || &lt;span style="line-height: 15.6000003814697px;"&gt;633.473&lt;/span&gt; ||=   ||
-||   ||   ||   ||   ||   ||   ||   || 233\610 || &lt;span style="text-align: center;"&gt;89 55 89&lt;/span&gt; || 458.361 || 916.721 || 175.082 || 633.443 ||= &lt;span style="text-align: center;"&gt;Golden father&lt;/span&gt; ||
+||   ||   ||   ||   ||   ||   ||   || 233\610 || &lt;span style="display: block; text-align: center;"&gt;89 55 89&lt;/span&gt; || 458.361 || 916.721 || 175.082 || 633.443 ||= &lt;span style="display: block; text-align: center;"&gt;Golden father&lt;/span&gt; ||
-||   ||   ||   ||   ||   ||   || 144\377 ||   || &lt;span style="text-align: center;"&gt;55 34 55&lt;/span&gt; || 458.355 || 916.711 || 175.066 || 633.422 ||=   ||
+||   ||   ||   ||   ||   ||   || 144\377 ||   || &lt;span style="display: block; text-align: center;"&gt;55 34 55&lt;/span&gt; || 458.355 || 916.711 || 175.066 || 633.422 ||=   ||
-||   ||   ||   ||   || 55\144 ||   ||   ||   || &lt;span style="text-align: center;"&gt;21 13 21&lt;/span&gt; || 458.333 || 916.666 || 175 || 633.333 ||=   ||
+||   ||   ||   ||   || 55\144 ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;21 13 21&lt;/span&gt; || 458.333 || 916.666 || 175 || 633.333 ||=   ||
-||   ||   || 21\55 ||   ||   ||   ||   ||   || &lt;span style="text-align: center;"&gt;8 5 8&lt;/span&gt; || 458.182 || 916.364 || 174.545 || 632.727 ||=   ||
+||   ||   || 21\55 ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;8 5 8&lt;/span&gt; || 458.182 || 916.364 || 174.545 || 632.727 ||=   ||
-|| 8\21 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="text-align: center;"&gt;3 2 3&lt;/span&gt; || 457.143 || 914.286 || 171.429 || 628.571 ||= &lt;span style="text-align: center;"&gt;Optimum rank range (L/s=3/2) father&lt;/span&gt; ||
+|| 8\21 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;3 2 3&lt;/span&gt; || 457.143 || 914.286 || 171.429 || 628.571 ||= &lt;span style="display: block; text-align: center;"&gt;Optimum rank range (L/s=3/2) father&lt;/span&gt; ||
-|| 11\29 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="text-align: center;"&gt;4 3 4&lt;/span&gt; || 455.172 || 910.345 || 165.517 || 620.690 ||=   ||
+|| 11\29 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;4 3 4&lt;/span&gt; || 455.172 || 910.345 || 165.517 || 620.690 ||=   ||
-|| 3\8 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="text-align: center;"&gt;1 1 1&lt;/span&gt; || 450.000 || 900.000 || 150.000 || 600.000 ||=   ||
+|| 3\8 ||   ||   ||   ||   ||   ||   ||   || &lt;span style="display: block; text-align: center;"&gt;1 1 1&lt;/span&gt; || 450.000 || 900.000 || 150.000 || 600.000 ||=   ||
 The only notable harmonic entropy minimum is Vulture/[[Hemifamity temperaments|Buzzard]], in which four generators make a 3/1 (and three generators approximate an octave plus 8/7). The rest of this region is a kind of wasteland in terms of harmonious MOSes.</pre></div>
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-         &lt;th&gt;&lt;br /&gt;
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 &lt;/td&gt;
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 &lt;/td&gt;
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+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Optimum rank range (L/s=3/2) father&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
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 &lt;/td&gt;
          &lt;td&gt;455.172&lt;br /&gt;
@@ Line 744: / Line 730: @@
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 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;1 1 1&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;1 1 1&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;450.000&lt;br /&gt;