5L 3s: Difference between revisions

Revision as of 14:17, 11 February 2015

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This revision was by author JosephRuhf and made on 2015-02-11 14:17:20 UTC.

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Original Wikitext content:

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:
||||||||||||||||~ generator ||~ <span style="display: block; text-align: center;">tetrachord</span> ||~ <span style="display: block; text-align: center;">g in cents</span> ||~ <span style="display: block; text-align: center;">2g</span> ||~ <span style="display: block; text-align: center;">3g</span> ||~ <span style="display: block; text-align: center;">4g</span> ||~ <span style="display: block; text-align: center;">Comments</span> ||
|| 2\5 ||   ||   ||   ||   ||   ||   ||   || <span style="display: block; text-align: center;">1 0 1</span> || 480.000 || 960.000 || 240.00 || <span style="line-height: 15.6000003814697px;">720.000</span> ||=   ||
|| 21\53 ||   ||   ||   ||   ||   ||   ||   || <span style="display: block; text-align: center;">10 1 10</span> || 475.472 || 950.943 || 226.415 || 701.887 ||= <span style="display: block; text-align: center;">Vulture/Buzzard is around here</span> ||
|| 19\48 ||   ||   ||   ||   ||   ||   ||   || <span style="display: block; text-align: center;">9 1 9</span> || 475 || 950 || 225 || 700 ||=   ||
|| 17\43 ||   ||   ||   ||   ||   ||   ||   || <span style="display: block; text-align: center;">8 1 8</span> || 474.419 || 948.837 || 223.256 || 697.674 ||=   ||
|| 15\38 ||   ||   ||   ||   ||   ||   ||   || <span style="display: block; text-align: center;">7 1 7</span> || 473.684 || 947.368 || 221.053 || 694.737 ||=   ||
|| 13\33 ||   ||   ||   ||   ||   ||   ||   || <span style="display: block; text-align: center;">6 1 6</span> || 472.727 || 945.455 || 218.181 || 690.909 ||=   ||
|| 11\28 ||   ||   ||   ||   ||   ||   ||   || <span style="display: block; text-align: center;">5 1 5</span> || 471.429 || 942.857 || 214.286 || 685.714 ||=   ||
|| 9\23 ||   ||   ||   ||   ||   ||   ||   || <span style="display: block; text-align: center;">4 1 4</span> || 469.565 || 939.130 || 208.696 || 678.261 ||= <span style="display: block; text-align: center;">L/s = 4</span> ||
||   ||   ||   ||   ||   ||   ||   ||   || 3.03 1 3.03 || 466.769 || 933.538 || 200.307 || 667.076 ||= <span style="display: block; text-align: center;">L/s = 3*2^(1/75)</span> ||
|| 7\18 ||   ||   ||   ||   ||   ||   ||   || <span style="display: block; text-align: center;">3 1 3</span> || 466.667 || 933.333 || 200.000 || 666.667 ||= <span style="display: block; text-align: center;">L/s = 3</span> ||
||   ||   ||   ||   ||   ||   ||   ||   || 2.97 1 2.97 || 466.564 || 933.127 || 199.691 || 666.255 ||= <span style="display: block; text-align: center;">L/s = 3/2^(1/75)</span> ||
||   || 12\31 ||   ||   ||   ||   ||   ||   || <span style="display: block; text-align: center;">5 2 5</span> || 464.516 || 929.032 || 193.549 || 658.065 ||=   ||
|| 5\13 ||   ||   ||   ||   ||   ||   ||   || <span style="display: block; text-align: center;">2 1 2</span> || 461.538 || 923.077 || 184.615 || 646.154 ||=   ||
||   || 13\34 ||   ||   ||   ||   ||   ||   || <span style="display: block; text-align: center;">5 3 5</span> || 458.824 || 917.647 || 176.471 || 635.294 ||=   ||
||   ||   ||   || 34\89 ||   ||   ||   ||   || <span style="display: block; text-align: center;">13 8 13</span> || 458.427 || 916.854 || 175.281 || 633.708 ||=   ||
||   ||   ||   ||   ||   || 89\233 ||   ||   || <span style="display: block; text-align: center;">34 21 34</span> || <span style="line-height: 15.6000003814697px;">458.369</span> || <span style="display: block; text-align: center;">916.738</span> || 175.107 || <span style="line-height: 15.6000003814697px;">633.473</span> ||=   ||
||   ||   ||   ||   ||   ||   ||   || 233\610 || <span style="display: block; text-align: center;">89 55 89</span> || 458.361 || 916.721 || 175.082 || 633.443 ||= <span style="display: block; text-align: center;">Golden father</span> ||
||   ||   ||   ||   ||   ||   || 144\377 ||   || <span style="display: block; text-align: center;">55 34 55</span> || 458.355 || 916.711 || 175.066 || 633.422 ||=   ||
||   ||   ||   ||   || 55\144 ||   ||   ||   || <span style="display: block; text-align: center;">21 13 21</span> || 458.333 || 916.666 || 175 || 633.333 ||=   ||
||   ||   || 21\55 ||   ||   ||   ||   ||   || <span style="display: block; text-align: center;">8 5 8</span> || 458.182 || 916.364 || 174.545 || 632.727 ||=   ||
|| 8\21 ||   ||   ||   ||   ||   ||   ||   || <span style="display: block; text-align: center;">3 2 3</span> || 457.143 || 914.286 || 171.429 || 628.571 ||= <span style="display: block; text-align: center;">Optimum rank range (L/s=3/2) father</span> ||
|| 11\29 ||   ||   ||   ||   ||   ||   ||   || <span style="display: block; text-align: center;">4 3 4</span> || 455.172 || 910.345 || 165.517 || 620.690 ||=   ||
|| 3\8 ||   ||   ||   ||   ||   ||   ||   || <span style="display: block; text-align: center;">1 1 1</span> || 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.

Original HTML content:

<html><head><title>5L 3s</title></head><body>5L 3s refers to the structure of moment of symmetry scales with generators ranging from 2\5 (two degrees of <a class="wiki_link" href="/5edo">5edo</a> = 480¢) to 3\8 (three degrees of <a class="wiki_link" href="/8edo">8edo</a> = 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:<br />


<table class="wiki_table">
    <tr>
        <th colspan="8">generator<br />
</th>
        <th><span style="display: block; text-align: center;">tetrachord</span><br />
</th>
        <th><span style="display: block; text-align: center;">g in cents</span><br />
</th>
        <th><span style="display: block; text-align: center;">2g</span><br />
</th>
        <th><span style="display: block; text-align: center;">3g</span><br />
</th>
        <th><span style="display: block; text-align: center;">4g</span><br />
</th>
        <th><span style="display: block; text-align: center;">Comments</span><br />
</th>
    </tr>
    <tr>
        <td>2\5<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><span style="display: block; text-align: center;">1 0 1</span><br />
</td>
        <td>480.000<br />
</td>
        <td>960.000<br />
</td>
        <td>240.00<br />
</td>
        <td><span style="line-height: 15.6000003814697px;">720.000</span><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td>21\53<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><span style="display: block; text-align: center;">10 1 10</span><br />
</td>
        <td>475.472<br />
</td>
        <td>950.943<br />
</td>
        <td>226.415<br />
</td>
        <td>701.887<br />
</td>
        <td style="text-align: center;"><span style="display: block; text-align: center;">Vulture/Buzzard is around here</span><br />
</td>
    </tr>
    <tr>
        <td>19\48<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><span style="display: block; text-align: center;">9 1 9</span><br />
</td>
        <td>475<br />
</td>
        <td>950<br />
</td>
        <td>225<br />
</td>
        <td>700<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td>17\43<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><span style="display: block; text-align: center;">8 1 8</span><br />
</td>
        <td>474.419<br />
</td>
        <td>948.837<br />
</td>
        <td>223.256<br />
</td>
        <td>697.674<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td>15\38<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><span style="display: block; text-align: center;">7 1 7</span><br />
</td>
        <td>473.684<br />
</td>
        <td>947.368<br />
</td>
        <td>221.053<br />
</td>
        <td>694.737<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td>13\33<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><span style="display: block; text-align: center;">6 1 6</span><br />
</td>
        <td>472.727<br />
</td>
        <td>945.455<br />
</td>
        <td>218.181<br />
</td>
        <td>690.909<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td>11\28<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><span style="display: block; text-align: center;">5 1 5</span><br />
</td>
        <td>471.429<br />
</td>
        <td>942.857<br />
</td>
        <td>214.286<br />
</td>
        <td>685.714<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td>9\23<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><span style="display: block; text-align: center;">4 1 4</span><br />
</td>
        <td>469.565<br />
</td>
        <td>939.130<br />
</td>
        <td>208.696<br />
</td>
        <td>678.261<br />
</td>
        <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = 4</span><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>3.03 1 3.03<br />
</td>
        <td>466.769<br />
</td>
        <td>933.538<br />
</td>
        <td>200.307<br />
</td>
        <td>667.076<br />
</td>
        <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = 3*2^(1/75)</span><br />
</td>
    </tr>
    <tr>
        <td>7\18<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><span style="display: block; text-align: center;">3 1 3</span><br />
</td>
        <td>466.667<br />
</td>
        <td>933.333<br />
</td>
        <td>200.000<br />
</td>
        <td>666.667<br />
</td>
        <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = 3</span><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>2.97 1 2.97<br />
</td>
        <td>466.564<br />
</td>
        <td>933.127<br />
</td>
        <td>199.691<br />
</td>
        <td>666.255<br />
</td>
        <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = 3/2^(1/75)</span><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>12\31<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><span style="display: block; text-align: center;">5 2 5</span><br />
</td>
        <td>464.516<br />
</td>
        <td>929.032<br />
</td>
        <td>193.549<br />
</td>
        <td>658.065<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td>5\13<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><span style="display: block; text-align: center;">2 1 2</span><br />
</td>
        <td>461.538<br />
</td>
        <td>923.077<br />
</td>
        <td>184.615<br />
</td>
        <td>646.154<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>13\34<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><span style="display: block; text-align: center;">5 3 5</span><br />
</td>
        <td>458.824<br />
</td>
        <td>917.647<br />
</td>
        <td>176.471<br />
</td>
        <td>635.294<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>34\89<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><span style="display: block; text-align: center;">13 8 13</span><br />
</td>
        <td>458.427<br />
</td>
        <td>916.854<br />
</td>
        <td>175.281<br />
</td>
        <td>633.708<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>89\233<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><span style="display: block; text-align: center;">34 21 34</span><br />
</td>
        <td><span style="line-height: 15.6000003814697px;">458.369</span><br />
</td>
        <td><span style="display: block; text-align: center;">916.738</span><br />
</td>
        <td>175.107<br />
</td>
        <td><span style="line-height: 15.6000003814697px;">633.473</span><br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>233\610<br />
</td>
        <td><span style="display: block; text-align: center;">89 55 89</span><br />
</td>
        <td>458.361<br />
</td>
        <td>916.721<br />
</td>
        <td>175.082<br />
</td>
        <td>633.443<br />
</td>
        <td style="text-align: center;"><span style="display: block; text-align: center;">Golden father</span><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>144\377<br />
</td>
        <td><br />
</td>
        <td><span style="display: block; text-align: center;">55 34 55</span><br />
</td>
        <td>458.355<br />
</td>
        <td>916.711<br />
</td>
        <td>175.066<br />
</td>
        <td>633.422<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>55\144<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><span style="display: block; text-align: center;">21 13 21</span><br />
</td>
        <td>458.333<br />
</td>
        <td>916.666<br />
</td>
        <td>175<br />
</td>
        <td>633.333<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td>21\55<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><span style="display: block; text-align: center;">8 5 8</span><br />
</td>
        <td>458.182<br />
</td>
        <td>916.364<br />
</td>
        <td>174.545<br />
</td>
        <td>632.727<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td>8\21<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><span style="display: block; text-align: center;">3 2 3</span><br />
</td>
        <td>457.143<br />
</td>
        <td>914.286<br />
</td>
        <td>171.429<br />
</td>
        <td>628.571<br />
</td>
        <td style="text-align: center;"><span style="display: block; text-align: center;">Optimum rank range (L/s=3/2) father</span><br />
</td>
    </tr>
    <tr>
        <td>11\29<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><span style="display: block; text-align: center;">4 3 4</span><br />
</td>
        <td>455.172<br />
</td>
        <td>910.345<br />
</td>
        <td>165.517<br />
</td>
        <td>620.690<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td>3\8<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><span style="display: block; text-align: center;">1 1 1</span><br />
</td>
        <td>450.000<br />
</td>
        <td>900.000<br />
</td>
        <td>150.000<br />
</td>
        <td>600.000<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
</table>

The only notable harmonic entropy minimum is Vulture/<a class="wiki_link" href="/Hemifamity%20temperaments">Buzzard</a>, 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.</body></html>

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 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;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;34 21 34&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;34 21 34&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;span style="line-height: 15.6000003814697px;"&gt;458.369&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;916.738&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;916.738&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;175.107&lt;br /&gt;
@@ Line 564: / Line 550: @@
          &lt;td&gt;233\610&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;89 55 89&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;89 55 89&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;458.361&lt;br /&gt;
@@ Line 574: / Line 560: @@
          &lt;td&gt;633.443&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;span style="text-align: center;"&gt;Golden father&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;Golden father&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 594: / Line 580: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;55 34 55&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;55 34 55&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;458.355&lt;br /&gt;
@@ Line 624: / Line 610: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;21 13 21&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;21 13 21&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;458.333&lt;br /&gt;
@@ Line 654: / Line 640: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;8 5 8&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;8 5 8&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;458.182&lt;br /&gt;
@@ Line 684: / Line 670: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;3 2 3&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;3 2 3&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;457.143&lt;br /&gt;
@@ Line 694: / Line 680: @@
          &lt;td&gt;628.571&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;span style="text-align: center;"&gt;Optimum rank range (L/s=3/2) father&lt;/span&gt;&lt;br /&gt;
+         &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;
@@ Line 714: / Line 700: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;span style="text-align: center;"&gt;4 3 4&lt;/span&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;span style="display: block; text-align: center;"&gt;4 3 4&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;455.172&lt;br /&gt;
@@ Line 744: / Line 730: @@
          &lt;td&gt;&lt;br /&gt;
 &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;

5L 3s: Difference between revisions

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