5L 2s: Difference between revisions

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=5L 2s - "diatonic"= 

One way of distinguishing the "diatonic" scale is by considering it a [[MOSScales|moment of symmetry]] scale produced by a chain of "fifths". This will include [[12edo]]'s diatonic scale along with the Pythagorean diatonic scale and meantone systems, while excluding just intonation scales that use more than one size of "tone".

It may be misleading to call 5L 2s "diatonic," since other scales called diatonic can be arrived at different ways (through just intonation procedures for instance, or with tetrachords). Also, a composer working with a 5L 2s scale may choose to do something very different than typical diatonic music.

==substituting step sizes== 

The 5L 2s MOS scale has this generalized form.
L L s L L L s

Insert 2 for L and 1 for s and you'll get the 12edo diatonic of standard practice.
2 2 1 2 2 2 1

When L=3, s=1, you have [[17edo]]:
3 3 1 3 3 3 1

When L=3, s=2, you have [[19edo]]:
3 3 2 3 3 3 2

When L=4, s=1, you have [[22edo]]:
4 4 1 4 4 4 1

When L=4, s=3, you have [[26edo]]:
4 4 3 4 4 4 3

When L=5, s=1, you have [[27edo]]:
5 5 1 5 5 5 1

When L=5, s=2, you have [[29edo]]:
5 5 2 5 5 5 2

When L=5, s=3, you have [[31edo]]:
5 5 3 5 5 5 3

When L=5, s=4, you have [[33edo]]:
5 5 4 5 5 5 4

So you have scales where L and s are nearly equal, which approach [[7edo]]:
1 1 1 1 1 1 1

And you have scales where s becomes so small it approaches zero, which would give us [[5edo]]:
1 1 0 1 1 1 0 or 1 1 1 1 1

==a continuum of temperaments== 

So if 3\7 (three degrees of 7edo) is at one extreme and 2\5 (two degrees of 5edo) is at the other, all other possible 5L 2s scales exist in a continuum between them. You can chop this continuum up by taking "freshman sums" of the two edges - adding together the numerators, then adding together the denominators. Thus, between 3\7 and 2\5 you have (3+2)\(7+5) = 5\12, five degrees of 12edo:

|| 3\7 ||   ||
||   || 5\12 ||
|| 2\5 ||   ||

If we carry this freshman-summing out a little further, new, larger [[edo]]s pop up in our continuum.
||||||||||||~ generator ||~   ||~ in cents ||~ tetrachord ||~   ||~   ||~   ||~   ||~ comments ||
||< 3\7 ||||<   ||<   ||<   ||=   ||   ||= 514.286 ||= 1 1 1 || 239.2945 || 274.991 || 307.521 || 378.193 ||=   ||
|| 59\138 ||||<   ||   ||   ||   ||   ||= 513.0435 ||= 20 20 19 || 238.673 || 274.370 || 308.142 || 378.8145 ||   ||
|| 56\131 ||||<   ||   ||   ||   ||   ||= 512.977 ||= 19 19 18 || 238.640 || 274.337 || 308.175 || 378.848 ||   ||
|| 53\124 ||||<   ||   ||   ||   ||   ||= 512.903 ||= 18 18 17 || 238.603 || 274.300 || 308.212 || 378.885 ||   ||
|| 50\117 ||||<   ||<   ||<   ||   ||   ||= 512.8205 ||= 17 17 16 || 238.562 || 274.259 || 308.2535 || 378.926 ||   ||
||< 47\110 ||||<   ||<   ||<   ||   ||   ||= 512.727 ||= 16 16 15 || 238.515 || 274.212 || 308.300 || 378.973 ||   ||
||< 44\103 ||||<   ||<   ||<   ||   ||   ||= 512.621 ||= 15 15 14 || 238.462 || 274.159 || 308.353 || 379.0255 ||   ||
||< 41\96 ||||<   ||<   ||<   ||   ||   ||= 512.500 ||= 14 14 13 || 238.402 || 274.098 || 308.414 || 379.086 ||   ||
||< 38\89 ||||<   ||<   ||<   ||   ||   ||= 512.360 ||= 13 13 12 || 238.331 || 274.028 || 308.484 || 379.156 ||   ||
||< 35\82 ||||<   ||<   ||<   ||   ||   ||= 512.195 ||= 12 12 11 || 238.249 || 273.946 || 308.566 || 379.239 ||   ||
||< 32\75 ||||<   ||<   ||<   ||   ||   ||= 512.000 ||= 11 11 10 || 238.152 || 273.848 || 308.664 || 379.336 ||   ||
||< 29\68 ||||<   ||<   ||<   ||   ||   ||= 511.765 ||= 10 10 9 || 238.034 || 273.731 || 308.781 || 379.454 ||   ||
||< 26\61 ||||<   ||<   ||<   ||   ||   ||= 511.475 ||= 9 9 8 || 237.889 || 273.586 || 308.926 || 379.5985 ||   ||
||< 23\54 ||||<   ||<   ||<   ||   ||   ||= 511.111 ||= 8 8 7 || 237.707 || 273.404 || 309.108 || 379.781 ||   ||
||< 20\47 ||||<   ||<   ||<   ||   ||   ||= 510.638 ||= 7 7 6 || 237.471 || 273.168 || 309.345 || 380.017 ||   ||
||< 17\40 ||||<   ||<   ||<   ||=   ||   ||= 510.000 ||= 6 6 5 || 237.152 || 272.848 || 309.664 || 380.336 ||=   ||
||< 14\33 ||||<   ||<   ||<   ||=   ||   ||= 509.091 ||= 5 5 4 || 236.697 || 272.394 || 310.118 || 380.791 ||=   ||
||<   ||||< 25\59 ||<   ||<   ||=   ||   ||= 508.475 ||= 9 9 7 || 236.389 || 272.086 || 310.4265 || 381.0985 ||=   ||
||< 11\26 ||||<   ||<   ||<   ||=   ||   ||= 507.692 ||= 4 4 3 || 235.998 || 271.695 || 310.817 || 381.491 ||=   ||
||<   ||||< 30\71 ||<   ||<   ||=   ||   ||= 507.042 ||= 11 11 8 || 235.672 || 271.3695 || 311.142 || 381.846 ||=   ||
||<   ||||< 19\45 ||<   ||<   ||=   ||   ||= 506.667 ||= 7 7 5 || 235.485 || 271.182 || 311.33 || 382.003 ||=   ||
||<   ||||< 27\64 ||<   ||<   ||=   ||   ||= 506.250 ||= 10 10 7 || 235.277 || 270.973 || 311.539 || 382.211 ||=   ||
||< 8\19 ||||<   ||<   ||<   ||=   ||   ||= 505.263 ||= 3 3 2 || 234.783 || 270.480 || 312.032 || 382.705 ||= Optimum rank range (L/s=3/2) diatonic ||
||   ||||< 37\88 ||   ||   ||   ||   ||= 504.5455 ||= 14 14 9 || 234.424 || 270.121 || 312.391 || 383.0635 ||= LucyTuning ||
||   ||<   ||   ||   ||   ||   ||   ||= 504.356 ||= <span style="display: block; text-align: center;">pi pi 2</span> || 234.329 || 270.026 || 312.486 || 383.158 ||   ||
||<   ||||< 29\69 ||<   ||<   ||=   ||   ||= 504.348 ||= 11 11 7 || 234.3255 || 270.022 || 312.490 || 383.172 ||=   ||
||<   ||||< 21\50 ||<   ||<   ||=   ||   ||= 504.000 ||= 8 8 5 || 234.152 || 269.848 || 312.664 || 383.336 ||=   ||
||   ||||<   || 55\131 ||   ||   ||   ||= 503.817 ||= 21 21 13 || 234.060 || 269.757 || 312.755 || 383.428 ||   ||
||   ||||<   ||   ||   || 144\343 ||   ||= 503.790 ||= 55 55 34 || 234.047 || 269.743 || 312.769 || 383.441 ||   ||
||   ||||<   ||   ||   ||   || 233\555 ||= 503.784 ||= 89 89 55 || 234.0435 || 269.740 || 312.772 || 383.444 ||= Golden meantone ||
||   ||||<   ||   || 89\212 ||   ||   ||= 503.774 ||= 34 34 21 || 234.038 || 269.735 || 312.777 || 383.449 ||=   ||
||<   ||||<   ||< 34\81 ||<   ||=   ||   ||= 503.704 ||= 13 13 8 || 234.003 || 269.700 || 312.811 || 383.485 ||=   ||
||<   ||||< 13\31 ||<   ||<   ||=   ||   ||= 503.226 ||= 5 5 3 || 233.7645 || 269.461 || 313.051 || 383.723 ||= Meantone is in this region ||
||<   ||||<   ||< 31\74 ||<   ||=   ||   ||= 502.703 ||= 12 12 7 || 233.503 || 269.200 || 313.312 || 383.985 ||=   ||
||   ||   ||   ||   ||   ||   ||   ||= 502.5135 ||= <span style="background-color: #ffffff;">√3 √3 1</span> || 233.408 || 269.105 || 313.407 || 384.079 ||   ||
||<   ||||< 18\43 ||<   ||<   ||=   ||   ||= 502.326 ||= 7 7 4 || 233.314 || 269.011 || 313.501 || 384.183 ||=   ||
||<   ||||< 23\55 ||<   ||<   ||=   ||   ||= 501.818 ||= 9 9 5 || 233.061 || 268.7575 || 313.754 || 384.428 ||=   ||
||< 5\12 ||||<   ||<   ||<   ||=   ||   ||= 500.000 ||= 2 2 1 || 232.152 || 267.848 || 314.664 || 385.336 ||= Boundary of propriety
(generators larger than this are proper) ||
||<   ||||< 42\101 ||<   ||<   ||   ||   ||= 499.010 ||= 17 17 8 || 231.6565 || 267.353 || 315.159 || 385.831 ||   ||
||<   ||||< <span style="display: block; text-align: center;">37\89</span> ||<   ||<   ||=   ||=   ||= 498.876 ||= 15 15 7 ||< 231.590 ||< 267.287 ||< 315,226 ||< 385.898 ||=   ||
||<   ||||< <span style="display: block; text-align: center;">32\77</span> ||<   ||<   ||=   ||=   ||= 498.701 ||= 13 13 6 ||< 231.502 ||< 267.199 ||< 315.313 ||< 385.986 ||=   ||
||<   ||||< 27\65 ||<   ||<   ||   ||   ||= 498.4615 ||= 11 11 5 || 231.382 || 267.079 || 315.433 || 386.105 ||   ||
||<   ||||< 22\53 ||<   ||<   ||=   ||   ||= 498.113 ||= 9 9 4 || 231.208 || 266.905 || 315.609 || 386.278 ||= Pythagorean is around here ||
||<   ||||< 17\41 ||<   ||<   ||=   ||   ||= 497.591 ||= 7 7 3 || 230.932 || 266.629 || 315.883 || 386.556 ||=   ||
||<   ||||< 29\70 ||<   ||<   ||=   ||   ||= 497.143 ||= 12 12 5 || 230.723 || 266.420 || 316.092 || 386.765 ||=   ||
||<   ||||< 12\29 ||<   ||<   ||=   ||   ||= 496.552 ||= 5 5 2 || 230.4275 || 266.124 || 316.388 || 387.061 ||=   ||
||<   ||||<   ||< 31\75 ||<   ||=   ||   ||= 496.000 ||= 13 13 5 || 230.152 || 265.848 || 316.664 || 387.336 ||=   ||
||   ||   ||   ||   ||   || 81\196 ||   ||= 495.918 ||= 34 34 13 || 230.111 || 265.808 || 316.705 || 387.377 ||   ||
||   ||   ||   ||   ||   ||   || 131\317 ||= 495.899 ||= 55 55 21 || 230.101 || 265.798 || 316.714 || 387.387 ||   ||
||   ||   ||   ||   || 50\121 ||   ||   ||= 495.868 ||= 21 21 8 || 230.0855 || 265.782 || 316.73 || 387.402 ||   ||
||<   ||||< 19\46 ||<   ||<   ||=   ||   ||= 495.652 ||= 8 8 3 || 229.978 || 265.6745 || 316.837 || 387.511 ||=   ||
||<   ||||<   ||<   ||<   ||=   ||   ||= 495.393 ||= <span style="display: block; text-align: center;">e e 1</span> || 229.848 || 265.545 || 316.967 || 387.639 ||= <span style="display: block; text-align: center;">L/s = e</span> ||
||   ||||< 26\63 ||   ||   ||   ||   ||= <span style="display: block; text-align: center;">495.238</span> ||= 11 11 4 || 229.771 || 265.4675 || 317.045 || 387.717 ||= <span style="display: block; text-align: center;">
</span> ||
||< 7\17 ||||<   ||<   ||<   ||=   ||   ||= 494.118 ||= 3 3 1 || 229.210 || 264.907 || 317.596 || 388.286 ||= L/s = 3 ||
||   ||||<   ||   ||   ||   ||   ||= 493.553 ||= pi pi 1 || 228.928 || 264.625 || 317.887 || 388.56 ||= <span style="display: block; text-align: center;">L/s = pi</span> ||
||<   ||||< 23\56 ||<   ||<   ||=   ||   ||= 492.857 ||= 10 10 3 || 228.580 || 264.277 || 318.235 || 388.908 ||=   ||
||<   ||||< 16\39 ||<   ||<   ||=   ||   ||= 492.308 ||= 7 7 2 || 228.305 || 264.002 || 318.51 || 389.182 ||=   ||
||<   ||||< 25\61 ||<   ||<   ||=   ||   ||= 491.803 ||= 11 11 3 || 228.053 || 263.750 || 318.761 || 389.436 ||=   ||
||< 9\22 ||||<   ||<   ||<   ||=   ||   ||= 490.909 ||= 4 4 1 || 227.606 || 263.303 || 319.209 || 389.882 ||= (No-5's) superpyth is in this region
L/s = 4 ||
||<   ||||< 20\49 ||<   ||<   ||=   ||   ||= 489.796 ||= 9 9 2 || 227.050 || 262.746 || 319.766 || 390.438 ||=   ||
||< 11\27 ||||<   ||<   ||<   ||=   ||   ||= 488.889 ||= 5 5 1 || 226.596 || 262.293 || 320.219 || 390.892 ||=   ||
||< 13\32 ||||<   ||<   ||<   ||=   ||   ||= 487.500 ||= 6 6 1 || 225.9015 || 261.598 || 320.914 || 391.596 ||=   ||
||< 15\37 ||||<   ||<   ||<   ||   ||   ||= 486.4865 ||= 7 7 1 || 225.395 || 261.092 || 321.4205 || 392.093 ||   ||
||< 17\42 ||||<   ||<   ||<   ||=   ||=   ||= 485.714 ||= 8 8 1 ||< 225.009 ||< 260.7055 ||< 321.807 ||< 392.479 ||=   ||
||< 19\47 ||||<   ||<   ||<   ||   ||   ||= 485.106 ||= 9 9 1 || 224.705 || 260.402 || 322.111 || 392.783 ||   ||
||< 21\52 ||||<   ||<   ||<   ||   ||   ||= 484.615 ||= 10 10 1 || 224.459 || 260.156 || 322.356 || 393.0285 ||   ||
||< 23\57 ||||<   ||<   ||<   ||   ||   ||= 484.2105 ||= 11 11 1 || 224.257 || 259.954 || 322.5585 || 393.231 ||   ||
||< 25\62 ||||<   ||<   ||<   ||   ||   ||= 483.871 ||= 12 12 1 || 224.087 || 259.784 || 322.728 || 393.401 ||   ||
||< 27\67 ||||<   ||<   ||<   ||   ||   ||= 483.582 ||= 13 13 1 || 223.943 || 259.6395 || 322.873 || 393.545 ||   ||
||< 29\72 ||||<   ||<   ||<   ||   ||   ||= 483.333 ||= 14 14 1 || 223.818 || 259.515 || 322.997 || 393.6695 ||   ||
||< 31\77 ||||<   ||<   ||<   ||   ||   ||= 483.117 ||= 15 15 1 || 223.710 || 259.407 || 323.105 || 393.778 ||   ||
||< 33\82 ||||<   ||<   ||<   ||   ||   ||= 482.927 ||= 16 16 1 || 223.615 || 259.312 || 323.200 || 393.873 ||   ||
|| 35\87 ||||<   ||<   ||<   ||   ||   ||= 482.759 ||= 17 17 1 || 223.531 || 259.228 || 323.2845 || 393.957 ||   ||
|| 37\92 ||||<   ||<   ||<   ||   ||   ||= 482.609 ||= 18 18 1 || 223.456 || 259.153 || 323.539 || 394.032 ||   ||
|| 39\97 ||||<   ||   ||   ||   ||   ||= 482.474 ||= 19 19 1 || 223.389 || 259.0855 || 323.427 || 394.099 ||   ||
|| 41\102 ||||<   ||   ||   ||   ||   ||= 482.353 ||= 20 20 1 || 223.328 || 259.025 || 323.487 || 394.160 ||   ||
|| 43\107 ||||<   ||   ||   ||   ||   ||= 482.243 ||= 21 21 1 || 223.273 || 258.970 || 323.542 || 394.215 ||   ||
|| 45\112 ||||<   ||   ||   ||   ||   ||= 482.143 ||= 22 22 1 || 223.223 || 258.920 || 323.592 || 394.265 ||   ||
|| 47\117 ||||<   ||   ||   ||   ||   ||= 482.051 ||= 23 23 1 || 223.177 || 258.874 || 323.638 || 394.311 ||   ||
|| 49\122 ||||<   ||   ||   ||   ||   ||= 481.967 ||= 24 24 1 || 223.135 || 258.832 || 322.680 || 394.353 ||   ||
||< 2\5 ||||<   ||<   ||<   ||=   ||   ||= 480.000 ||= 1 1 0 || 222.152 || 257.848 || 324.664 || 395.336 ||=   ||

Temperaments above 5\12 on this chart are called "negative temperaments" (as they lessen the size of the fifth) and include meantone systems such as 1/3-comma (close to 8\19) and 1/4-comma (close to 13\31). As these tunings approach 3\7, the majors become flatter and the minors become sharper.

Temperaments below 5\12 on this chart are called "positive temperaments" and they include Pythagorean tuning itself (well approximated by 22\53) as well as superpyth temperaments such as 7\17 and 9\22. As these tunings approach 2\5, the majors become sharper and the minors become flatter. Around 9\22, the thirds fall closer to 7-limit than 5-limit intervals: 7:6 and 9:7 as opposed to 6:5 and 5:4.

[[image:5L2s.jpg]]

5L 2s contains the pentatonic MOS [[2L 3s]] and (with the sole exception of the 5L 2s of 12edo) is itself contained in a dodecaphonic MOS: either [[7L 5s]] or [[5L 7s]].

Original HTML content:

<html><head><title>5L 2s</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x5L 2s - &quot;diatonic&quot;"></a><!-- ws:end:WikiTextHeadingRule:0 -->5L 2s - &quot;diatonic&quot;</h1>
 <br />
One way of distinguishing the &quot;diatonic&quot; scale is by considering it a <a class="wiki_link" href="/MOSScales">moment of symmetry</a> scale produced by a chain of &quot;fifths&quot;. This will include <a class="wiki_link" href="/12edo">12edo</a>'s diatonic scale along with the Pythagorean diatonic scale and meantone systems, while excluding just intonation scales that use more than one size of &quot;tone&quot;.<br />
<br />
It may be misleading to call 5L 2s &quot;diatonic,&quot; since other scales called diatonic can be arrived at different ways (through just intonation procedures for instance, or with tetrachords). Also, a composer working with a 5L 2s scale may choose to do something very different than typical diatonic music.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x5L 2s - &quot;diatonic&quot;-substituting step sizes"></a><!-- ws:end:WikiTextHeadingRule:2 -->substituting step sizes</h2>
 <br />
The 5L 2s MOS scale has this generalized form.<br />
L L s L L L s<br />
<br />
Insert 2 for L and 1 for s and you'll get the 12edo diatonic of standard practice.<br />
2 2 1 2 2 2 1<br />
<br />
When L=3, s=1, you have <a class="wiki_link" href="/17edo">17edo</a>:<br />
3 3 1 3 3 3 1<br />
<br />
When L=3, s=2, you have <a class="wiki_link" href="/19edo">19edo</a>:<br />
3 3 2 3 3 3 2<br />
<br />
When L=4, s=1, you have <a class="wiki_link" href="/22edo">22edo</a>:<br />
4 4 1 4 4 4 1<br />
<br />
When L=4, s=3, you have <a class="wiki_link" href="/26edo">26edo</a>:<br />
4 4 3 4 4 4 3<br />
<br />
When L=5, s=1, you have <a class="wiki_link" href="/27edo">27edo</a>:<br />
5 5 1 5 5 5 1<br />
<br />
When L=5, s=2, you have <a class="wiki_link" href="/29edo">29edo</a>:<br />
5 5 2 5 5 5 2<br />
<br />
When L=5, s=3, you have <a class="wiki_link" href="/31edo">31edo</a>:<br />
5 5 3 5 5 5 3<br />
<br />
When L=5, s=4, you have <a class="wiki_link" href="/33edo">33edo</a>:<br />
5 5 4 5 5 5 4<br />
<br />
So you have scales where L and s are nearly equal, which approach <a class="wiki_link" href="/7edo">7edo</a>:<br />
1 1 1 1 1 1 1<br />
<br />
And you have scales where s becomes so small it approaches zero, which would give us <a class="wiki_link" href="/5edo">5edo</a>:<br />
1 1 0 1 1 1 0 or 1 1 1 1 1<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x5L 2s - &quot;diatonic&quot;-a continuum of temperaments"></a><!-- ws:end:WikiTextHeadingRule:4 -->a continuum of temperaments</h2>
 <br />
So if 3\7 (three degrees of 7edo) is at one extreme and 2\5 (two degrees of 5edo) is at the other, all other possible 5L 2s scales exist in a continuum between them. You can chop this continuum up by taking &quot;freshman sums&quot; of the two edges - adding together the numerators, then adding together the denominators. Thus, between 3\7 and 2\5 you have (3+2)\(7+5) = 5\12, five degrees of 12edo:<br />
<br />


<table class="wiki_table">
    <tr>
        <td>3\7<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td>5\12<br />
</td>
    </tr>
    <tr>
        <td>2\5<br />
</td>
        <td><br />
</td>
    </tr>
</table>

<br />
If we carry this freshman-summing out a little further, new, larger <a class="wiki_link" href="/edo">edo</a>s pop up in our continuum.<br />


<table class="wiki_table">
    <tr>
        <th colspan="6">generator<br />
</th>
        <th><br />
</th>
        <th>in cents<br />
</th>
        <th>tetrachord<br />
</th>
        <th><br />
</th>
        <th><br />
</th>
        <th><br />
</th>
        <th><br />
</th>
        <th>comments<br />
</th>
    </tr>
    <tr>
        <td style="text-align: left;">3\7<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">514.286<br />
</td>
        <td style="text-align: center;">1 1 1<br />
</td>
        <td>239.2945<br />
</td>
        <td>274.991<br />
</td>
        <td>307.521<br />
</td>
        <td>378.193<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td>59\138<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">513.0435<br />
</td>
        <td style="text-align: center;">20 20 19<br />
</td>
        <td>238.673<br />
</td>
        <td>274.370<br />
</td>
        <td>308.142<br />
</td>
        <td>378.8145<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>56\131<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">512.977<br />
</td>
        <td style="text-align: center;">19 19 18<br />
</td>
        <td>238.640<br />
</td>
        <td>274.337<br />
</td>
        <td>308.175<br />
</td>
        <td>378.848<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>53\124<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">512.903<br />
</td>
        <td style="text-align: center;">18 18 17<br />
</td>
        <td>238.603<br />
</td>
        <td>274.300<br />
</td>
        <td>308.212<br />
</td>
        <td>378.885<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>50\117<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">512.8205<br />
</td>
        <td style="text-align: center;">17 17 16<br />
</td>
        <td>238.562<br />
</td>
        <td>274.259<br />
</td>
        <td>308.2535<br />
</td>
        <td>378.926<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">47\110<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">512.727<br />
</td>
        <td style="text-align: center;">16 16 15<br />
</td>
        <td>238.515<br />
</td>
        <td>274.212<br />
</td>
        <td>308.300<br />
</td>
        <td>378.973<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">44\103<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">512.621<br />
</td>
        <td style="text-align: center;">15 15 14<br />
</td>
        <td>238.462<br />
</td>
        <td>274.159<br />
</td>
        <td>308.353<br />
</td>
        <td>379.0255<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">41\96<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">512.500<br />
</td>
        <td style="text-align: center;">14 14 13<br />
</td>
        <td>238.402<br />
</td>
        <td>274.098<br />
</td>
        <td>308.414<br />
</td>
        <td>379.086<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">38\89<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">512.360<br />
</td>
        <td style="text-align: center;">13 13 12<br />
</td>
        <td>238.331<br />
</td>
        <td>274.028<br />
</td>
        <td>308.484<br />
</td>
        <td>379.156<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">35\82<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">512.195<br />
</td>
        <td style="text-align: center;">12 12 11<br />
</td>
        <td>238.249<br />
</td>
        <td>273.946<br />
</td>
        <td>308.566<br />
</td>
        <td>379.239<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">32\75<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">512.000<br />
</td>
        <td style="text-align: center;">11 11 10<br />
</td>
        <td>238.152<br />
</td>
        <td>273.848<br />
</td>
        <td>308.664<br />
</td>
        <td>379.336<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">29\68<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">511.765<br />
</td>
        <td style="text-align: center;">10 10 9<br />
</td>
        <td>238.034<br />
</td>
        <td>273.731<br />
</td>
        <td>308.781<br />
</td>
        <td>379.454<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">26\61<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">511.475<br />
</td>
        <td style="text-align: center;">9 9 8<br />
</td>
        <td>237.889<br />
</td>
        <td>273.586<br />
</td>
        <td>308.926<br />
</td>
        <td>379.5985<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">23\54<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">511.111<br />
</td>
        <td style="text-align: center;">8 8 7<br />
</td>
        <td>237.707<br />
</td>
        <td>273.404<br />
</td>
        <td>309.108<br />
</td>
        <td>379.781<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">20\47<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">510.638<br />
</td>
        <td style="text-align: center;">7 7 6<br />
</td>
        <td>237.471<br />
</td>
        <td>273.168<br />
</td>
        <td>309.345<br />
</td>
        <td>380.017<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">17\40<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">510.000<br />
</td>
        <td style="text-align: center;">6 6 5<br />
</td>
        <td>237.152<br />
</td>
        <td>272.848<br />
</td>
        <td>309.664<br />
</td>
        <td>380.336<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">14\33<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">509.091<br />
</td>
        <td style="text-align: center;">5 5 4<br />
</td>
        <td>236.697<br />
</td>
        <td>272.394<br />
</td>
        <td>310.118<br />
</td>
        <td>380.791<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;">25\59<br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">508.475<br />
</td>
        <td style="text-align: center;">9 9 7<br />
</td>
        <td>236.389<br />
</td>
        <td>272.086<br />
</td>
        <td>310.4265<br />
</td>
        <td>381.0985<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">11\26<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">507.692<br />
</td>
        <td style="text-align: center;">4 4 3<br />
</td>
        <td>235.998<br />
</td>
        <td>271.695<br />
</td>
        <td>310.817<br />
</td>
        <td>381.491<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;">30\71<br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">507.042<br />
</td>
        <td style="text-align: center;">11 11 8<br />
</td>
        <td>235.672<br />
</td>
        <td>271.3695<br />
</td>
        <td>311.142<br />
</td>
        <td>381.846<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;">19\45<br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">506.667<br />
</td>
        <td style="text-align: center;">7 7 5<br />
</td>
        <td>235.485<br />
</td>
        <td>271.182<br />
</td>
        <td>311.33<br />
</td>
        <td>382.003<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;">27\64<br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">506.250<br />
</td>
        <td style="text-align: center;">10 10 7<br />
</td>
        <td>235.277<br />
</td>
        <td>270.973<br />
</td>
        <td>311.539<br />
</td>
        <td>382.211<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">8\19<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">505.263<br />
</td>
        <td style="text-align: center;">3 3 2<br />
</td>
        <td>234.783<br />
</td>
        <td>270.480<br />
</td>
        <td>312.032<br />
</td>
        <td>382.705<br />
</td>
        <td style="text-align: center;">Optimum rank range (L/s=3/2) diatonic<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td colspan="2" style="text-align: left;">37\88<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">504.5455<br />
</td>
        <td style="text-align: center;">14 14 9<br />
</td>
        <td>234.424<br />
</td>
        <td>270.121<br />
</td>
        <td>312.391<br />
</td>
        <td>383.0635<br />
</td>
        <td style="text-align: center;">LucyTuning<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">504.356<br />
</td>
        <td style="text-align: center;"><span style="display: block; text-align: center;">pi pi 2</span><br />
</td>
        <td>234.329<br />
</td>
        <td>270.026<br />
</td>
        <td>312.486<br />
</td>
        <td>383.158<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;">29\69<br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">504.348<br />
</td>
        <td style="text-align: center;">11 11 7<br />
</td>
        <td>234.3255<br />
</td>
        <td>270.022<br />
</td>
        <td>312.490<br />
</td>
        <td>383.172<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;">21\50<br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">504.000<br />
</td>
        <td style="text-align: center;">8 8 5<br />
</td>
        <td>234.152<br />
</td>
        <td>269.848<br />
</td>
        <td>312.664<br />
</td>
        <td>383.336<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td>55\131<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">503.817<br />
</td>
        <td style="text-align: center;">21 21 13<br />
</td>
        <td>234.060<br />
</td>
        <td>269.757<br />
</td>
        <td>312.755<br />
</td>
        <td>383.428<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>144\343<br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">503.790<br />
</td>
        <td style="text-align: center;">55 55 34<br />
</td>
        <td>234.047<br />
</td>
        <td>269.743<br />
</td>
        <td>312.769<br />
</td>
        <td>383.441<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>233\555<br />
</td>
        <td style="text-align: center;">503.784<br />
</td>
        <td style="text-align: center;">89 89 55<br />
</td>
        <td>234.0435<br />
</td>
        <td>269.740<br />
</td>
        <td>312.772<br />
</td>
        <td>383.444<br />
</td>
        <td style="text-align: center;">Golden meantone<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td>89\212<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">503.774<br />
</td>
        <td style="text-align: center;">34 34 21<br />
</td>
        <td>234.038<br />
</td>
        <td>269.735<br />
</td>
        <td>312.777<br />
</td>
        <td>383.449<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;">34\81<br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">503.704<br />
</td>
        <td style="text-align: center;">13 13 8<br />
</td>
        <td>234.003<br />
</td>
        <td>269.700<br />
</td>
        <td>312.811<br />
</td>
        <td>383.485<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;">13\31<br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">503.226<br />
</td>
        <td style="text-align: center;">5 5 3<br />
</td>
        <td>233.7645<br />
</td>
        <td>269.461<br />
</td>
        <td>313.051<br />
</td>
        <td>383.723<br />
</td>
        <td style="text-align: center;">Meantone is in this region<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;">31\74<br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">502.703<br />
</td>
        <td style="text-align: center;">12 12 7<br />
</td>
        <td>233.503<br />
</td>
        <td>269.200<br />
</td>
        <td>313.312<br />
</td>
        <td>383.985<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 style="text-align: center;">502.5135<br />
</td>
        <td style="text-align: center;"><span style="background-color: #ffffff;">√3 √3 1</span><br />
</td>
        <td>233.408<br />
</td>
        <td>269.105<br />
</td>
        <td>313.407<br />
</td>
        <td>384.079<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;">18\43<br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">502.326<br />
</td>
        <td style="text-align: center;">7 7 4<br />
</td>
        <td>233.314<br />
</td>
        <td>269.011<br />
</td>
        <td>313.501<br />
</td>
        <td>384.183<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;">23\55<br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">501.818<br />
</td>
        <td style="text-align: center;">9 9 5<br />
</td>
        <td>233.061<br />
</td>
        <td>268.7575<br />
</td>
        <td>313.754<br />
</td>
        <td>384.428<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">5\12<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">500.000<br />
</td>
        <td style="text-align: center;">2 2 1<br />
</td>
        <td>232.152<br />
</td>
        <td>267.848<br />
</td>
        <td>314.664<br />
</td>
        <td>385.336<br />
</td>
        <td style="text-align: center;">Boundary of propriety<br />
(generators larger than this are proper)<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;">42\101<br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">499.010<br />
</td>
        <td style="text-align: center;">17 17 8<br />
</td>
        <td>231.6565<br />
</td>
        <td>267.353<br />
</td>
        <td>315.159<br />
</td>
        <td>385.831<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;"><span style="display: block; text-align: center;">37\89</span><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">498.876<br />
</td>
        <td style="text-align: center;">15 15 7<br />
</td>
        <td style="text-align: left;">231.590<br />
</td>
        <td style="text-align: left;">267.287<br />
</td>
        <td style="text-align: left;">315,226<br />
</td>
        <td style="text-align: left;">385.898<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;"><span style="display: block; text-align: center;">32\77</span><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">498.701<br />
</td>
        <td style="text-align: center;">13 13 6<br />
</td>
        <td style="text-align: left;">231.502<br />
</td>
        <td style="text-align: left;">267.199<br />
</td>
        <td style="text-align: left;">315.313<br />
</td>
        <td style="text-align: left;">385.986<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;">27\65<br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">498.4615<br />
</td>
        <td style="text-align: center;">11 11 5<br />
</td>
        <td>231.382<br />
</td>
        <td>267.079<br />
</td>
        <td>315.433<br />
</td>
        <td>386.105<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;">22\53<br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">498.113<br />
</td>
        <td style="text-align: center;">9 9 4<br />
</td>
        <td>231.208<br />
</td>
        <td>266.905<br />
</td>
        <td>315.609<br />
</td>
        <td>386.278<br />
</td>
        <td style="text-align: center;">Pythagorean is around here<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;">17\41<br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">497.591<br />
</td>
        <td style="text-align: center;">7 7 3<br />
</td>
        <td>230.932<br />
</td>
        <td>266.629<br />
</td>
        <td>315.883<br />
</td>
        <td>386.556<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;">29\70<br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">497.143<br />
</td>
        <td style="text-align: center;">12 12 5<br />
</td>
        <td>230.723<br />
</td>
        <td>266.420<br />
</td>
        <td>316.092<br />
</td>
        <td>386.765<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;">12\29<br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">496.552<br />
</td>
        <td style="text-align: center;">5 5 2<br />
</td>
        <td>230.4275<br />
</td>
        <td>266.124<br />
</td>
        <td>316.388<br />
</td>
        <td>387.061<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;">31\75<br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">496.000<br />
</td>
        <td style="text-align: center;">13 13 5<br />
</td>
        <td>230.152<br />
</td>
        <td>265.848<br />
</td>
        <td>316.664<br />
</td>
        <td>387.336<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>81\196<br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">495.918<br />
</td>
        <td style="text-align: center;">34 34 13<br />
</td>
        <td>230.111<br />
</td>
        <td>265.808<br />
</td>
        <td>316.705<br />
</td>
        <td>387.377<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>131\317<br />
</td>
        <td style="text-align: center;">495.899<br />
</td>
        <td style="text-align: center;">55 55 21<br />
</td>
        <td>230.101<br />
</td>
        <td>265.798<br />
</td>
        <td>316.714<br />
</td>
        <td>387.387<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td>50\121<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">495.868<br />
</td>
        <td style="text-align: center;">21 21 8<br />
</td>
        <td>230.0855<br />
</td>
        <td>265.782<br />
</td>
        <td>316.73<br />
</td>
        <td>387.402<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;">19\46<br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">495.652<br />
</td>
        <td style="text-align: center;">8 8 3<br />
</td>
        <td>229.978<br />
</td>
        <td>265.6745<br />
</td>
        <td>316.837<br />
</td>
        <td>387.511<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">495.393<br />
</td>
        <td style="text-align: center;"><span style="display: block; text-align: center;">e e 1</span><br />
</td>
        <td>229.848<br />
</td>
        <td>265.545<br />
</td>
        <td>316.967<br />
</td>
        <td>387.639<br />
</td>
        <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = e</span><br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td colspan="2" style="text-align: left;">26\63<br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;"><span style="display: block; text-align: center;">495.238</span><br />
</td>
        <td style="text-align: center;">11 11 4<br />
</td>
        <td>229.771<br />
</td>
        <td>265.4675<br />
</td>
        <td>317.045<br />
</td>
        <td>387.717<br />
</td>
        <td style="text-align: center;"><span style="display: block; text-align: center;"><br />
</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">7\17<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">494.118<br />
</td>
        <td style="text-align: center;">3 3 1<br />
</td>
        <td>229.210<br />
</td>
        <td>264.907<br />
</td>
        <td>317.596<br />
</td>
        <td>388.286<br />
</td>
        <td style="text-align: center;">L/s = 3<br />
</td>
    </tr>
    <tr>
        <td><br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">493.553<br />
</td>
        <td style="text-align: center;">pi pi 1<br />
</td>
        <td>228.928<br />
</td>
        <td>264.625<br />
</td>
        <td>317.887<br />
</td>
        <td>388.56<br />
</td>
        <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = pi</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;">23\56<br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">492.857<br />
</td>
        <td style="text-align: center;">10 10 3<br />
</td>
        <td>228.580<br />
</td>
        <td>264.277<br />
</td>
        <td>318.235<br />
</td>
        <td>388.908<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;">16\39<br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">492.308<br />
</td>
        <td style="text-align: center;">7 7 2<br />
</td>
        <td>228.305<br />
</td>
        <td>264.002<br />
</td>
        <td>318.51<br />
</td>
        <td>389.182<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;">25\61<br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">491.803<br />
</td>
        <td style="text-align: center;">11 11 3<br />
</td>
        <td>228.053<br />
</td>
        <td>263.750<br />
</td>
        <td>318.761<br />
</td>
        <td>389.436<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">9\22<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">490.909<br />
</td>
        <td style="text-align: center;">4 4 1<br />
</td>
        <td>227.606<br />
</td>
        <td>263.303<br />
</td>
        <td>319.209<br />
</td>
        <td>389.882<br />
</td>
        <td style="text-align: center;">(No-5's) superpyth is in this region<br />
L/s = 4<br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;"><br />
</td>
        <td colspan="2" style="text-align: left;">20\49<br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">489.796<br />
</td>
        <td style="text-align: center;">9 9 2<br />
</td>
        <td>227.050<br />
</td>
        <td>262.746<br />
</td>
        <td>319.766<br />
</td>
        <td>390.438<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">11\27<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">488.889<br />
</td>
        <td style="text-align: center;">5 5 1<br />
</td>
        <td>226.596<br />
</td>
        <td>262.293<br />
</td>
        <td>320.219<br />
</td>
        <td>390.892<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">13\32<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">487.500<br />
</td>
        <td style="text-align: center;">6 6 1<br />
</td>
        <td>225.9015<br />
</td>
        <td>261.598<br />
</td>
        <td>320.914<br />
</td>
        <td>391.596<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">15\37<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">486.4865<br />
</td>
        <td style="text-align: center;">7 7 1<br />
</td>
        <td>225.395<br />
</td>
        <td>261.092<br />
</td>
        <td>321.4205<br />
</td>
        <td>392.093<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">17\42<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td style="text-align: center;">485.714<br />
</td>
        <td style="text-align: center;">8 8 1<br />
</td>
        <td style="text-align: left;">225.009<br />
</td>
        <td style="text-align: left;">260.7055<br />
</td>
        <td style="text-align: left;">321.807<br />
</td>
        <td style="text-align: left;">392.479<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">19\47<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">485.106<br />
</td>
        <td style="text-align: center;">9 9 1<br />
</td>
        <td>224.705<br />
</td>
        <td>260.402<br />
</td>
        <td>322.111<br />
</td>
        <td>392.783<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">21\52<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">484.615<br />
</td>
        <td style="text-align: center;">10 10 1<br />
</td>
        <td>224.459<br />
</td>
        <td>260.156<br />
</td>
        <td>322.356<br />
</td>
        <td>393.0285<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">23\57<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">484.2105<br />
</td>
        <td style="text-align: center;">11 11 1<br />
</td>
        <td>224.257<br />
</td>
        <td>259.954<br />
</td>
        <td>322.5585<br />
</td>
        <td>393.231<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">25\62<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">483.871<br />
</td>
        <td style="text-align: center;">12 12 1<br />
</td>
        <td>224.087<br />
</td>
        <td>259.784<br />
</td>
        <td>322.728<br />
</td>
        <td>393.401<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">27\67<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">483.582<br />
</td>
        <td style="text-align: center;">13 13 1<br />
</td>
        <td>223.943<br />
</td>
        <td>259.6395<br />
</td>
        <td>322.873<br />
</td>
        <td>393.545<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">29\72<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">483.333<br />
</td>
        <td style="text-align: center;">14 14 1<br />
</td>
        <td>223.818<br />
</td>
        <td>259.515<br />
</td>
        <td>322.997<br />
</td>
        <td>393.6695<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">31\77<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">483.117<br />
</td>
        <td style="text-align: center;">15 15 1<br />
</td>
        <td>223.710<br />
</td>
        <td>259.407<br />
</td>
        <td>323.105<br />
</td>
        <td>393.778<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">33\82<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">482.927<br />
</td>
        <td style="text-align: center;">16 16 1<br />
</td>
        <td>223.615<br />
</td>
        <td>259.312<br />
</td>
        <td>323.200<br />
</td>
        <td>393.873<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>35\87<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">482.759<br />
</td>
        <td style="text-align: center;">17 17 1<br />
</td>
        <td>223.531<br />
</td>
        <td>259.228<br />
</td>
        <td>323.2845<br />
</td>
        <td>393.957<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>37\92<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">482.609<br />
</td>
        <td style="text-align: center;">18 18 1<br />
</td>
        <td>223.456<br />
</td>
        <td>259.153<br />
</td>
        <td>323.539<br />
</td>
        <td>394.032<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>39\97<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">482.474<br />
</td>
        <td style="text-align: center;">19 19 1<br />
</td>
        <td>223.389<br />
</td>
        <td>259.0855<br />
</td>
        <td>323.427<br />
</td>
        <td>394.099<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>41\102<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">482.353<br />
</td>
        <td style="text-align: center;">20 20 1<br />
</td>
        <td>223.328<br />
</td>
        <td>259.025<br />
</td>
        <td>323.487<br />
</td>
        <td>394.160<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>43\107<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">482.243<br />
</td>
        <td style="text-align: center;">21 21 1<br />
</td>
        <td>223.273<br />
</td>
        <td>258.970<br />
</td>
        <td>323.542<br />
</td>
        <td>394.215<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>45\112<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">482.143<br />
</td>
        <td style="text-align: center;">22 22 1<br />
</td>
        <td>223.223<br />
</td>
        <td>258.920<br />
</td>
        <td>323.592<br />
</td>
        <td>394.265<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>47\117<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">482.051<br />
</td>
        <td style="text-align: center;">23 23 1<br />
</td>
        <td>223.177<br />
</td>
        <td>258.874<br />
</td>
        <td>323.638<br />
</td>
        <td>394.311<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td>49\122<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">481.967<br />
</td>
        <td style="text-align: center;">24 24 1<br />
</td>
        <td>223.135<br />
</td>
        <td>258.832<br />
</td>
        <td>322.680<br />
</td>
        <td>394.353<br />
</td>
        <td><br />
</td>
    </tr>
    <tr>
        <td style="text-align: left;">2\5<br />
</td>
        <td colspan="2" style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: left;"><br />
</td>
        <td style="text-align: center;"><br />
</td>
        <td><br />
</td>
        <td style="text-align: center;">480.000<br />
</td>
        <td style="text-align: center;">1 1 0<br />
</td>
        <td>222.152<br />
</td>
        <td>257.848<br />
</td>
        <td>324.664<br />
</td>
        <td>395.336<br />
</td>
        <td style="text-align: center;"><br />
</td>
    </tr>
</table>

<br />
Temperaments above 5\12 on this chart are called &quot;negative temperaments&quot; (as they lessen the size of the fifth) and include meantone systems such as 1/3-comma (close to 8\19) and 1/4-comma (close to 13\31). As these tunings approach 3\7, the majors become flatter and the minors become sharper.<br />
<br />
Temperaments below 5\12 on this chart are called &quot;positive temperaments&quot; and they include Pythagorean tuning itself (well approximated by 22\53) as well as superpyth temperaments such as 7\17 and 9\22. As these tunings approach 2\5, the majors become sharper and the minors become flatter. Around 9\22, the thirds fall closer to 7-limit than 5-limit intervals: 7:6 and 9:7 as opposed to 6:5 and 5:4.<br />
<br />
<!-- ws:start:WikiTextLocalImageRule:2326:&lt;img src=&quot;/file/view/5L2s.jpg/103741463/5L2s.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/5L2s.jpg/103741463/5L2s.jpg" alt="5L2s.jpg" title="5L2s.jpg" /><!-- ws:end:WikiTextLocalImageRule:2326 --><br />
<br />
5L 2s contains the pentatonic MOS <a class="wiki_link" href="/2L%203s">2L 3s</a> and (with the sole exception of the 5L 2s of 12edo) is itself contained in a dodecaphonic MOS: either <a class="wiki_link" href="/7L%205s">7L 5s</a> or <a class="wiki_link" href="/5L%207s">5L 7s</a>.</body></html>

@@ 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>2015-07-25 16:37:18 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-04 15:05:19 UTC</tt>.<br>
-: The original revision id was <tt>555736879</tt>.<br>
+: The original revision id was <tt>565201449</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 61: / Line 61: @@
 ||||||||||||~ generator ||~   ||~ in cents ||~ tetrachord ||~   ||~   ||~   ||~   ||~ comments ||
 ||&lt; 3\7 ||||&lt;   ||&lt;   ||&lt;   ||=   ||   ||= 514.286 ||= 1 1 1 || 239.2945 || 274.991 || 307.521 || 378.193 ||=   ||
-|| 59\138 ||||   ||   ||   ||   ||   ||= 513.0435 ||= 20 20 19 || 238.673 || 274.370 || 308.142 || 378.8145 ||   ||
+|| 59\138 ||||&lt;   ||   ||   ||   ||   ||= 513.0435 ||= 20 20 19 || 238.673 || 274.370 || 308.142 || 378.8145 ||   ||
-|| 56\131 ||||   ||   ||   ||   ||   ||= 512.977 ||= 19 19 18 || 238.640 || 274.337 || 308.175 || 378.848 ||   ||
+|| 56\131 ||||&lt;   ||   ||   ||   ||   ||= 512.977 ||= 19 19 18 || 238.640 || 274.337 || 308.175 || 378.848 ||   ||
-|| 53\124 ||||   ||   ||   ||   ||   ||= 512.903 ||= 18 18 17 || 238.603 || 274.300 || 308.212 || 378.885 ||   ||
+|| 53\124 ||||&lt;   ||   ||   ||   ||   ||= 512.903 ||= 18 18 17 || 238.603 || 274.300 || 308.212 || 378.885 ||   ||
-|| 50\117 ||||   ||&lt;   ||&lt;   ||   ||   ||= 512.8205 ||= 17 17 16 || 238.562 || 274.259 || 308.2535 || 378.926 ||   ||
+|| 50\117 ||||&lt;   ||&lt;   ||&lt;   ||   ||   ||= 512.8205 ||= 17 17 16 || 238.562 || 274.259 || 308.2535 || 378.926 ||   ||
-||&lt; 47\110 ||||   ||&lt;   ||&lt;   ||   ||   ||= 512.727 ||= 16 16 15 || 238.515 || 274.212 || 308.300 || 378.973 ||   ||
+||&lt; 47\110 ||||&lt;   ||&lt;   ||&lt;   ||   ||   ||= 512.727 ||= 16 16 15 || 238.515 || 274.212 || 308.300 || 378.973 ||   ||
 ||&lt; 44\103 ||||&lt;   ||&lt;   ||&lt;   ||   ||   ||= 512.621 ||= 15 15 14 || 238.462 || 274.159 || 308.353 || 379.0255 ||   ||
 ||&lt; 41\96 ||||&lt;   ||&lt;   ||&lt;   ||   ||   ||= 512.500 ||= 14 14 13 || 238.402 || 274.098 || 308.414 || 379.086 ||   ||
@@ Line 83: / Line 83: @@
 ||&lt;   ||||&lt; 27\64 ||&lt;   ||&lt;   ||=   ||   ||= 506.250 ||= 10 10 7 || 235.277 || 270.973 || 311.539 || 382.211 ||=   ||
 ||&lt; 8\19 ||||&lt;   ||&lt;   ||&lt;   ||=   ||   ||= 505.263 ||= 3 3 2 || 234.783 || 270.480 || 312.032 || 382.705 ||= Optimum rank range (L/s=3/2) diatonic ||
-||   |||| 37\88 ||   ||   ||   ||   ||= 504.5455 ||= 14 14 9 || 234.424 || 270.121 || 312.391 || 383.0635 ||= LucyTuning ||
+||   ||||&lt; 37\88 ||   ||   ||   ||   ||= 504.5455 ||= 14 14 9 || 234.424 || 270.121 || 312.391 || 383.0635 ||= LucyTuning ||
+||   ||&lt;   ||   ||   ||   ||   ||   ||= 504.356 ||= &lt;span style="display: block; text-align: center;"&gt;pi pi 2&lt;/span&gt; || 234.329 || 270.026 || 312.486 || 383.158 ||   ||
 ||&lt;   ||||&lt; 29\69 ||&lt;   ||&lt;   ||=   ||   ||= 504.348 ||= 11 11 7 || 234.3255 || 270.022 || 312.490 || 383.172 ||=   ||
 ||&lt;   ||||&lt; 21\50 ||&lt;   ||&lt;   ||=   ||   ||= 504.000 ||= 8 8 5 || 234.152 || 269.848 || 312.664 || 383.336 ||=   ||
-||   ||||   || 55\131 ||   ||   ||   ||= 503.817 ||= 21 21 13 || 234.060 || 269.757 || 312.755 || 383.428 ||   ||
+||   ||||&lt;   || 55\131 ||   ||   ||   ||= 503.817 ||= 21 21 13 || 234.060 || 269.757 || 312.755 || 383.428 ||   ||
-||   ||||   ||   ||   || 144\343 ||   ||= 503.790 ||= 55 55 34 || 234.047 || 269.743 || 312.769 || 383.441 ||   ||
+||   ||||&lt;   ||   ||   || 144\343 ||   ||= 503.790 ||= 55 55 34 || 234.047 || 269.743 || 312.769 || 383.441 ||   ||
-||   ||||   ||   ||   ||   || 233\555 ||= 503.784 ||= 89 89 55 || 234.0435 || 269.740 || 312.772 || 383.444 ||= Golden meantone ||
+||   ||||&lt;   ||   ||   ||   || 233\555 ||= 503.784 ||= 89 89 55 || 234.0435 || 269.740 || 312.772 || 383.444 ||= Golden meantone ||
-||   ||||   ||   || 89\212 ||   ||   ||= 503.774 ||= 34 34 21 || 234.038 || 269.735 || 312.777 || 383.449 ||=   ||
+||   ||||&lt;   ||   || 89\212 ||   ||   ||= 503.774 ||= 34 34 21 || 234.038 || 269.735 || 312.777 || 383.449 ||=   ||
 ||&lt;   ||||&lt;   ||&lt; 34\81 ||&lt;   ||=   ||   ||= 503.704 ||= 13 13 8 || 234.003 || 269.700 || 312.811 || 383.485 ||=   ||
 ||&lt;   ||||&lt; 13\31 ||&lt;   ||&lt;   ||=   ||   ||= 503.226 ||= 5 5 3 || 233.7645 || 269.461 || 313.051 || 383.723 ||= Meantone is in this region ||
 ||&lt;   ||||&lt;   ||&lt; 31\74 ||&lt;   ||=   ||   ||= 502.703 ||= 12 12 7 || 233.503 || 269.200 || 313.312 || 383.985 ||=   ||
+||   ||   ||   ||   ||   ||   ||   ||= 502.5135 ||= &lt;span style="background-color: #ffffff;"&gt;√3 √3 1&lt;/span&gt; || 233.408 || 269.105 || 313.407 || 384.079 ||   ||
 ||&lt;   ||||&lt; 18\43 ||&lt;   ||&lt;   ||=   ||   ||= 502.326 ||= 7 7 4 || 233.314 || 269.011 || 313.501 || 384.183 ||=   ||
 ||&lt;   ||||&lt; 23\55 ||&lt;   ||&lt;   ||=   ||   ||= 501.818 ||= 9 9 5 || 233.061 || 268.7575 || 313.754 || 384.428 ||=   ||
@@ Line 101: / Line 103: @@
 ||&lt;   ||||&lt; &lt;span style="display: block; text-align: center;"&gt;32\77&lt;/span&gt; ||&lt;   ||&lt;   ||=   ||=   ||= 498.701 ||= 13 13 6 ||&lt; 231.502 ||&lt; 267.199 ||&lt; 315.313 ||&lt; 385.986 ||=   ||
 ||&lt;   ||||&lt; 27\65 ||&lt;   ||&lt;   ||   ||   ||= 498.4615 ||= 11 11 5 || 231.382 || 267.079 || 315.433 || 386.105 ||   ||
-||&lt;   |||| 22\53 ||&lt;   ||&lt;   ||=   ||   ||= 498.113 ||= 9 9 4 || 231.208 || 266.905 || 315.609 || 386.278 ||= Pythagorean is around here ||
+||&lt;   ||||&lt; 22\53 ||&lt;   ||&lt;   ||=   ||   ||= 498.113 ||= 9 9 4 || 231.208 || 266.905 || 315.609 || 386.278 ||= Pythagorean is around here ||
-||&lt;   |||| 17\41 ||&lt;   ||&lt;   ||=   ||   ||= 497.591 ||= 7 7 3 || 230.932 || 266.629 || 315.883 || 386.556 ||=   ||
+||&lt;   ||||&lt; 17\41 ||&lt;   ||&lt;   ||=   ||   ||= 497.591 ||= 7 7 3 || 230.932 || 266.629 || 315.883 || 386.556 ||=   ||
-||&lt;   |||| 29\70 ||&lt;   ||&lt;   ||=   ||   ||= 497.143 ||= 12 12 5 || 230.723 || 266.420 || 316.092 || 386.765 ||=   ||
+||&lt;   ||||&lt; 29\70 ||&lt;   ||&lt;   ||=   ||   ||= 497.143 ||= 12 12 5 || 230.723 || 266.420 || 316.092 || 386.765 ||=   ||
-||&lt;   |||| 12\29 ||&lt;   ||&lt;   ||=   ||   ||= 496.552 ||= 5 5 2 || 230.4275 || 266.124 || 316.388 || 387.061 ||=   ||
+||&lt;   ||||&lt; 12\29 ||&lt;   ||&lt;   ||=   ||   ||= 496.552 ||= 5 5 2 || 230.4275 || 266.124 || 316.388 || 387.061 ||=   ||
-||&lt;   ||||   ||&lt; 31\75 ||&lt;   ||=   ||   ||= 496.000 ||= 13 13 5 || 230.152 || 265.848 || 316.664 || 387.336 ||=   ||
+||&lt;   ||||&lt;   ||&lt; 31\75 ||&lt;   ||=   ||   ||= 496.000 ||= 13 13 5 || 230.152 || 265.848 || 316.664 || 387.336 ||=   ||
-||&lt;   |||| 19\46 ||&lt;   ||&lt;   ||=   ||   ||= 495.652 ||= 8 8 3 || 229.978 || 265.6745 || 316.837 || 387.511 ||=   ||
+||   ||   ||   ||   ||   || 81\196 ||   ||= 495.918 ||= 34 34 13 || 230.111 || 265.808 || 316.705 || 387.377 ||   ||
-||&lt;   ||||   ||&lt;   ||&lt;   ||=   ||   ||= 495.393 ||= &lt;span style="display: block; text-align: center;"&gt;e e 1&lt;/span&gt; || 229.848 || 265.545 || 316.967 || 387.639 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = e&lt;/span&gt; ||
+||   ||   ||   ||   ||   ||   || 131\317 ||= 495.899 ||= 55 55 21 || 230.101 || 265.798 || 316.714 || 387.387 ||   ||
-||   |||| 26\63 ||   ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;495.238&lt;/span&gt; ||= 11 11 4 || 229.771 || 265.4675 || 317.045 || 387.717 ||= &lt;span style="display: block; text-align: center;"&gt;
+||   ||   ||   ||   || 50\121 ||   ||   ||= 495.868 ||= 21 21 8 || 230.0855 || 265.782 || 316.73 || 387.402 ||   ||
+||&lt;   ||||&lt; 19\46 ||&lt;   ||&lt;   ||=   ||   ||= 495.652 ||= 8 8 3 || 229.978 || 265.6745 || 316.837 || 387.511 ||=   ||
+||&lt;   ||||&lt;   ||&lt;   ||&lt;   ||=   ||   ||= 495.393 ||= &lt;span style="display: block; text-align: center;"&gt;e e 1&lt;/span&gt; || 229.848 || 265.545 || 316.967 || 387.639 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = e&lt;/span&gt; ||
+||   ||||&lt; 26\63 ||   ||   ||   ||   ||= &lt;span style="display: block; text-align: center;"&gt;495.238&lt;/span&gt; ||= 11 11 4 || 229.771 || 265.4675 || 317.045 || 387.717 ||= &lt;span style="display: block; text-align: center;"&gt;
 &lt;/span&gt; ||
-||&lt; 7\17 ||||   ||&lt;   ||&lt;   ||=   ||   ||= 494.118 ||= 3 3 1 || 229.210 || 264.907 || 317.596 || 388.286 ||= L/s = 3 ||
+||&lt; 7\17 ||||&lt;   ||&lt;   ||&lt;   ||=   ||   ||= 494.118 ||= 3 3 1 || 229.210 || 264.907 || 317.596 || 388.286 ||= L/s = 3 ||
-||   ||||   ||   ||   ||   ||   ||= 493.553 ||= pi pi 1 || 228.928 || 264.625 || 317.887 || 388.56 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = pi&lt;/span&gt; ||
+||   ||||&lt;   ||   ||   ||   ||   ||= 493.553 ||= pi pi 1 || 228.928 || 264.625 || 317.887 || 388.56 ||= &lt;span style="display: block; text-align: center;"&gt;L/s = pi&lt;/span&gt; ||
-||&lt;   |||| 23\56 ||&lt;   ||&lt;   ||=   ||   ||= 492.857 ||= 10 10 3 || 228.580 || 264.277 || 318.235 || 388.908 ||=   ||
+||&lt;   ||||&lt; 23\56 ||&lt;   ||&lt;   ||=   ||   ||= 492.857 ||= 10 10 3 || 228.580 || 264.277 || 318.235 || 388.908 ||=   ||
-||&lt;   |||| 16\39 ||&lt;   ||&lt;   ||=   ||   ||= 492.308 ||= 7 7 2 || 228.305 || 264.002 || 318.51 || 389.182 ||=   ||
+||&lt;   ||||&lt; 16\39 ||&lt;   ||&lt;   ||=   ||   ||= 492.308 ||= 7 7 2 || 228.305 || 264.002 || 318.51 || 389.182 ||=   ||
-||&lt;   |||| 25\61 ||&lt;   ||&lt;   ||=   ||   ||= 491.803 ||= 11 11 3 || 228.053 || 263.750 || 318.761 || 389.436 ||=   ||
+||&lt;   ||||&lt; 25\61 ||&lt;   ||&lt;   ||=   ||   ||= 491.803 ||= 11 11 3 || 228.053 || 263.750 || 318.761 || 389.436 ||=   ||
-||&lt; 9\22 ||||   ||&lt;   ||&lt;   ||=   ||   ||= 490.909 ||= 4 4 1 || 227.606 || 263.303 || 319.209 || 389.882 ||= (No-5's) superpyth is in this region
+||&lt; 9\22 ||||&lt;   ||&lt;   ||&lt;   ||=   ||   ||= 490.909 ||= 4 4 1 || 227.606 || 263.303 || 319.209 || 389.882 ||= (No-5's) superpyth is in this region
 L/s = 4 ||
-||&lt;   |||| 20\49 ||&lt;   ||&lt;   ||=   ||   ||= 489.796 ||= 9 9 2 || 227.050 || 262.746 || 319.766 || 390.438 ||=   ||
+||&lt;   ||||&lt; 20\49 ||&lt;   ||&lt;   ||=   ||   ||= 489.796 ||= 9 9 2 || 227.050 || 262.746 || 319.766 || 390.438 ||=   ||
-||&lt; 11\27 ||||   ||&lt;   ||&lt;   ||=   ||   ||= 488.889 ||= 5 5 1 || 226.596 || 262.293 || 320.219 || 390.892 ||=   ||
+||&lt; 11\27 ||||&lt;   ||&lt;   ||&lt;   ||=   ||   ||= 488.889 ||= 5 5 1 || 226.596 || 262.293 || 320.219 || 390.892 ||=   ||
-||&lt; 13\32 ||||   ||&lt;   ||&lt;   ||=   ||   ||= 487.500 ||= 6 6 1 || 225.9015 || 261.598 || 320.914 || 391.596 ||=   ||
+||&lt; 13\32 ||||&lt;   ||&lt;   ||&lt;   ||=   ||   ||= 487.500 ||= 6 6 1 || 225.9015 || 261.598 || 320.914 || 391.596 ||=   ||
-||&lt; 15\37 ||||   ||&lt;   ||&lt;   ||   ||   ||= 486.4865 ||= 7 7 1 || 225.395 || 261.092 || 321.4205 || 392.093 ||   ||
+||&lt; 15\37 ||||&lt;   ||&lt;   ||&lt;   ||   ||   ||= 486.4865 ||= 7 7 1 || 225.395 || 261.092 || 321.4205 || 392.093 ||   ||
-||&lt; 17\42 ||||   ||&lt;   ||&lt;   ||=   ||=   ||= 485.714 ||= 8 8 1 ||&lt; 225.009 ||&lt; 260.7055 ||&lt; 321.807 ||&lt; 392.479 ||=   ||
+||&lt; 17\42 ||||&lt;   ||&lt;   ||&lt;   ||=   ||=   ||= 485.714 ||= 8 8 1 ||&lt; 225.009 ||&lt; 260.7055 ||&lt; 321.807 ||&lt; 392.479 ||=   ||
-||&lt; 19\47 ||||   ||&lt;   ||&lt;   ||   ||   ||= 485.106 ||= 9 9 1 || 224.705 || 260.402 || 322.111 || 392.783 ||   ||
+||&lt; 19\47 ||||&lt;   ||&lt;   ||&lt;   ||   ||   ||= 485.106 ||= 9 9 1 || 224.705 || 260.402 || 322.111 || 392.783 ||   ||
-||&lt; 21\52 ||||   ||&lt;   ||&lt;   ||   ||   ||= 484.615 ||= 10 10 1 || 224.459 || 260.156 || 322.356 || 393.0285 ||   ||
+||&lt; 21\52 ||||&lt;   ||&lt;   ||&lt;   ||   ||   ||= 484.615 ||= 10 10 1 || 224.459 || 260.156 || 322.356 || 393.0285 ||   ||
-||&lt; 23\57 ||||   ||&lt;   ||&lt;   ||   ||   ||= 484.2105 ||= 11 11 1 || 224.257 || 259.954 || 322.5585 || 393.231 ||   ||
+||&lt; 23\57 ||||&lt;   ||&lt;   ||&lt;   ||   ||   ||= 484.2105 ||= 11 11 1 || 224.257 || 259.954 || 322.5585 || 393.231 ||   ||
-||&lt; 25\62 ||||   ||&lt;   ||&lt;   ||   ||   ||= 483.871 ||= 12 12 1 || 224.087 || 259.784 || 322.728 || 393.401 ||   ||
+||&lt; 25\62 ||||&lt;   ||&lt;   ||&lt;   ||   ||   ||= 483.871 ||= 12 12 1 || 224.087 || 259.784 || 322.728 || 393.401 ||   ||
-||&lt; 27\67 ||||   ||&lt;   ||&lt;   ||   ||   ||= 483.582 ||= 13 13 1 || 223.943 || 259.6395 || 322.873 || 393.545 ||   ||
+||&lt; 27\67 ||||&lt;   ||&lt;   ||&lt;   ||   ||   ||= 483.582 ||= 13 13 1 || 223.943 || 259.6395 || 322.873 || 393.545 ||   ||
-||&lt; 29\72 ||||   ||&lt;   ||&lt;   ||   ||   ||= 483.333 ||= 14 14 1 || 223.818 || 259.515 || 322.997 || 393.6695 ||   ||
+||&lt; 29\72 ||||&lt;   ||&lt;   ||&lt;   ||   ||   ||= 483.333 ||= 14 14 1 || 223.818 || 259.515 || 322.997 || 393.6695 ||   ||
-||&lt; 31\77 ||||   ||&lt;   ||&lt;   ||   ||   ||= 483.117 ||= 15 15 1 || 223.710 || 259.407 || 323.105 || 393.778 ||   ||
+||&lt; 31\77 ||||&lt;   ||&lt;   ||&lt;   ||   ||   ||= 483.117 ||= 15 15 1 || 223.710 || 259.407 || 323.105 || 393.778 ||   ||
-||&lt; 33\82 ||||   ||&lt;   ||&lt;   ||   ||   ||= 482.927 ||= 16 16 1 || 223.615 || 259.312 || 323.200 || 393.873 ||   ||
+||&lt; 33\82 ||||&lt;   ||&lt;   ||&lt;   ||   ||   ||= 482.927 ||= 16 16 1 || 223.615 || 259.312 || 323.200 || 393.873 ||   ||
-|| 35\87 ||||   ||&lt;   ||&lt;   ||   ||   ||= 482.759 ||= 17 17 1 || 223.531 || 259.228 || 323.2845 || 393.957 ||   ||
+|| 35\87 ||||&lt;   ||&lt;   ||&lt;   ||   ||   ||= 482.759 ||= 17 17 1 || 223.531 || 259.228 || 323.2845 || 393.957 ||   ||
-|| 37\92 ||||   ||&lt;   ||&lt;   ||   ||   ||= 482.609 ||= 18 18 1 || 223.456 || 259.153 || 323.539 || 394.032 ||   ||
+|| 37\92 ||||&lt;   ||&lt;   ||&lt;   ||   ||   ||= 482.609 ||= 18 18 1 || 223.456 || 259.153 || 323.539 || 394.032 ||   ||
-|| 39\97 ||||   ||   ||   ||   ||   ||= 482.474 ||= 19 19 1 || 223.389 || 259.0855 || 323.427 || 394.099 ||   ||
+|| 39\97 ||||&lt;   ||   ||   ||   ||   ||= 482.474 ||= 19 19 1 || 223.389 || 259.0855 || 323.427 || 394.099 ||   ||
-|| 41\102 ||||   ||   ||   ||   ||   ||= 482.353 ||= 20 20 1 || 223.328 || 259.025 || 323.487 || 394.160 ||   ||
+|| 41\102 ||||&lt;   ||   ||   ||   ||   ||= 482.353 ||= 20 20 1 || 223.328 || 259.025 || 323.487 || 394.160 ||   ||
-|| 43\107 ||||   ||   ||   ||   ||   ||= 482.243 ||= 21 21 1 || 223.273 || 258.970 || 323.542 || 394.215 ||   ||
+|| 43\107 ||||&lt;   ||   ||   ||   ||   ||= 482.243 ||= 21 21 1 || 223.273 || 258.970 || 323.542 || 394.215 ||   ||
-|| 45\112 ||||   ||   ||   ||   ||   ||= 482.143 ||= 22 22 1 || 223.223 || 258.920 || 323.592 || 394.265 ||   ||
+|| 45\112 ||||&lt;   ||   ||   ||   ||   ||= 482.143 ||= 22 22 1 || 223.223 || 258.920 || 323.592 || 394.265 ||   ||
-|| 47\117 ||||   ||   ||   ||   ||   ||= 482.051 ||= 23 23 1 || 223.177 || 258.874 || 323.638 || 394.311 ||   ||
+|| 47\117 ||||&lt;   ||   ||   ||   ||   ||= 482.051 ||= 23 23 1 || 223.177 || 258.874 || 323.638 || 394.311 ||   ||
-|| 49\122 ||||   ||   ||   ||   ||   ||= 481.967 ||= 24 24 1 || 223.135 || 258.832 || 322.680 || 394.353 ||   ||
+|| 49\122 ||||&lt;   ||   ||   ||   ||   ||= 481.967 ||= 24 24 1 || 223.135 || 258.832 || 322.680 || 394.353 ||   ||
-||&lt; 2\5 ||||   ||&lt;   ||&lt;   ||=   ||   ||= 480.000 ||= 1 1 0 || 222.152 || 257.848 || 324.664 || 395.336 ||=   ||
+||&lt; 2\5 ||||&lt;   ||&lt;   ||&lt;   ||=   ||   ||= 480.000 ||= 1 1 0 || 222.152 || 257.848 || 324.664 || 395.336 ||=   ||
 Temperaments above 5\12 on this chart are called "negative temperaments" (as they lessen the size of the fifth) and include meantone systems such as 1/3-comma (close to 8\19) and 1/4-comma (close to 13\31). As these tunings approach 3\7, the majors become flatter and the minors become sharper.
@@ Line 275: / Line 280: @@
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-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
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 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
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          &lt;td&gt;&lt;br /&gt;
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-         &lt;td colspan="2"&gt;37\88&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;37\88&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 914: / Line 919: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;LucyTuning&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: left;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;504.356&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;pi pi 2&lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;234.329&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;270.026&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;312.486&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;383.158&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 975: / Line 1,010: @@
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-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
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@@ Line 1,031: / Line 1,066: @@
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-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
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@@ Line 1,059: / Line 1,094: @@
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-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
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@@ Line 1,166: / Line 1,201: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;502.5135&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;span style="background-color: #ffffff;"&gt;√3 √3 1&lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;233.408&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;269.105&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;313.407&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;384.079&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 1,368: / Line 1,433: @@
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 &lt;/td&gt;
-         &lt;td colspan="2"&gt;22\53&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;22\53&lt;br /&gt;
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@@ Line 1,396: / Line 1,461: @@
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 &lt;/td&gt;
-         &lt;td colspan="2"&gt;17\41&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;17\41&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
@@ Line 1,424: / Line 1,489: @@
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 &lt;/td&gt;
-         &lt;td colspan="2"&gt;29\70&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;29\70&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
@@ Line 1,452: / Line 1,517: @@
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 &lt;/td&gt;
-         &lt;td colspan="2"&gt;12\29&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;12\29&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
@@ Line 1,480: / Line 1,545: @@
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 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;31\75&lt;br /&gt;
@@ Line 1,506: / Line 1,571: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: left;"&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;19\46&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;&lt;br /&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;81\196&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;495.918&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;34 34 13&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;230.111&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;265.808&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;316.705&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;387.377&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;131\317&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;495.899&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;55 55 21&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;230.101&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;265.798&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;316.714&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;387.387&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;50\121&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;495.868&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;21 21 8&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;230.0855&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;265.782&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;316.73&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;387.402&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+         &lt;td style="text-align: left;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td colspan="2" style="text-align: left;"&gt;19\46&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: left;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: left;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+         &lt;td style="text-align: center;"&gt;495.652&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;8 8 3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;229.978&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;265.6745&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;316.837&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;387.511&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td style="text-align: left;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: left;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: left;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;495.393&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;e e 1&lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;229.848&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;265.545&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;316.967&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;387.639&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;L/s = e&lt;/span&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td colspan="2" style="text-align: left;"&gt;26\63&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;495.652&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;495.238&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;8 8 3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;11 11 4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;229.978&lt;br /&gt;
+         &lt;td&gt;229.771&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;265.6745&lt;br /&gt;
+         &lt;td&gt;265.4675&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;316.837&lt;br /&gt;
+         &lt;td&gt;317.045&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;387.511&lt;br /&gt;
+         &lt;td&gt;387.717&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;br /&gt;
+&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: left;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;7\17&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
@@ Line 1,546: / Line 1,758: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;495.393&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;494.118&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;e e 1&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;3 3 1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;229.848&lt;br /&gt;
+         &lt;td&gt;229.210&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;265.545&lt;br /&gt;
+         &lt;td&gt;264.907&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;316.967&lt;br /&gt;
+         &lt;td&gt;317.596&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;387.639&lt;br /&gt;
+         &lt;td&gt;388.286&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;L/s = e&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;L/s = 3&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 1,564: / Line 1,776: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;26\63&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 1,574: / Line 1,786: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;495.238&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;493.553&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;11 11 4&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;pi pi 1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;229.771&lt;br /&gt;
+         &lt;td&gt;228.928&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;265.4675&lt;br /&gt;
+         &lt;td&gt;264.625&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;317.045&lt;br /&gt;
+         &lt;td&gt;317.887&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;387.717&lt;br /&gt;
+         &lt;td&gt;388.56&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;L/s = pi&lt;/span&gt;&lt;br /&gt;
-&lt;/span&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: left;"&gt;7\17&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;23\56&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
@@ Line 1,603: / Line 1,814: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;494.118&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;492.857&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;3 3 1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;10 10 3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;229.210&lt;br /&gt;
+         &lt;td&gt;228.580&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;264.907&lt;br /&gt;
+         &lt;td&gt;264.277&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;317.596&lt;br /&gt;
+         &lt;td&gt;318.235&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;388.286&lt;br /&gt;
+         &lt;td&gt;388.908&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;L/s = 3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;16\39&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;493.553&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;492.308&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;pi pi 1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;7 7 2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;228.928&lt;br /&gt;
+         &lt;td&gt;228.305&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;264.625&lt;br /&gt;
+         &lt;td&gt;264.002&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;317.887&lt;br /&gt;
+         &lt;td&gt;318.51&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;388.56&lt;br /&gt;
+         &lt;td&gt;389.182&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;span style="display: block; text-align: center;"&gt;L/s = pi&lt;/span&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 1,649: / Line 1,860: @@
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;23\56&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;25\61&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
@@ Line 1,659: / Line 1,870: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;492.857&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;491.803&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;10 10 3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;11 11 3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;228.580&lt;br /&gt;
+         &lt;td&gt;228.053&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;264.277&lt;br /&gt;
+         &lt;td&gt;263.750&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;318.235&lt;br /&gt;
+         &lt;td&gt;318.761&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;388.908&lt;br /&gt;
+         &lt;td&gt;389.436&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 1,675: / Line 1,886: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: left;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;9\22&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;16\39&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
@@ Line 1,687: / Line 1,898: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;492.308&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;490.909&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;7 7 2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;4 4 1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;228.305&lt;br /&gt;
+         &lt;td&gt;227.606&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;264.002&lt;br /&gt;
+         &lt;td&gt;263.303&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;318.51&lt;br /&gt;
+         &lt;td&gt;319.209&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;389.182&lt;br /&gt;
+         &lt;td&gt;389.882&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;(No-5's) superpyth is in this region&lt;br /&gt;
+L/s = 4&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 1,705: / Line 1,917: @@
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;25\61&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;20\49&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
@@ Line 1,715: / Line 1,927: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;491.803&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;489.796&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;11 11 3&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;9 9 2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;228.053&lt;br /&gt;
+         &lt;td&gt;227.050&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;263.750&lt;br /&gt;
+         &lt;td&gt;262.746&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;318.761&lt;br /&gt;
+         &lt;td&gt;319.766&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;389.436&lt;br /&gt;
+         &lt;td&gt;390.438&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 1,731: / Line 1,943: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: left;"&gt;9\22&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;11\27&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
@@ Line 1,743: / Line 1,955: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;490.909&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;488.889&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;4 4 1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;5 5 1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;227.606&lt;br /&gt;
+         &lt;td&gt;226.596&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;263.303&lt;br /&gt;
+         &lt;td&gt;262.293&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;319.209&lt;br /&gt;
+         &lt;td&gt;320.219&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;389.882&lt;br /&gt;
+         &lt;td&gt;390.892&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;(No-5's) superpyth is in this region&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
-L/s = 4&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: left;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;13\32&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;20\49&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
@@ Line 1,772: / Line 1,983: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;489.796&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;487.500&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;9 9 2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;6 6 1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;227.050&lt;br /&gt;
+         &lt;td&gt;225.9015&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;262.746&lt;br /&gt;
+         &lt;td&gt;261.598&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;319.766&lt;br /&gt;
+         &lt;td&gt;320.914&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;390.438&lt;br /&gt;
+         &lt;td&gt;391.596&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 1,788: / Line 1,999: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: left;"&gt;11\27&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;15\37&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
@@ Line 1,796: / Line 2,007: @@
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;488.889&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;486.4865&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;5 5 1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;7 7 1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;226.596&lt;br /&gt;
+         &lt;td&gt;225.395&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;262.293&lt;br /&gt;
+         &lt;td&gt;261.092&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;320.219&lt;br /&gt;
+         &lt;td&gt;321.4205&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;390.892&lt;br /&gt;
+         &lt;td&gt;392.093&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: left;"&gt;13\32&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;17\42&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
@@ Line 1,826: / Line 2,037: @@
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;487.500&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;485.714&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;6 6 1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;8 8 1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;225.9015&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;225.009&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;261.598&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;260.7055&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;320.914&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;321.807&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;391.596&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;392.479&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;&lt;br /&gt;
@@ Line 1,844: / Line 2,055: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: left;"&gt;15\37&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;19\47&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
@@ Line 1,856: / Line 2,067: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;486.4865&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;485.106&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;7 7 1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;9 9 1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;225.395&lt;br /&gt;
+         &lt;td&gt;224.705&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;261.092&lt;br /&gt;
+         &lt;td&gt;260.402&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;321.4205&lt;br /&gt;
+         &lt;td&gt;322.111&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;392.093&lt;br /&gt;
+         &lt;td&gt;392.783&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 1,872: / Line 2,083: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: left;"&gt;17\42&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;21\52&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
@@ Line 1,880: / Line 2,091: @@
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;485.714&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;484.615&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;8 8 1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;10 10 1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;225.009&lt;br /&gt;
+         &lt;td&gt;224.459&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;260.7055&lt;br /&gt;
+         &lt;td&gt;260.156&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;321.807&lt;br /&gt;
+         &lt;td&gt;322.356&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;392.479&lt;br /&gt;
+         &lt;td&gt;393.0285&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: left;"&gt;19\47&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;23\57&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
@@ Line 1,912: / Line 2,123: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;485.106&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;484.2105&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;9 9 1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;11 11 1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;224.705&lt;br /&gt;
+         &lt;td&gt;224.257&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;260.402&lt;br /&gt;
+         &lt;td&gt;259.954&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;322.111&lt;br /&gt;
+         &lt;td&gt;322.5585&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;392.783&lt;br /&gt;
+         &lt;td&gt;393.231&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 1,928: / Line 2,139: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: left;"&gt;21\52&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;25\62&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
@@ Line 1,940: / Line 2,151: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;484.615&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;483.871&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;10 10 1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;12 12 1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;224.459&lt;br /&gt;
+         &lt;td&gt;224.087&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;260.156&lt;br /&gt;
+         &lt;td&gt;259.784&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;322.356&lt;br /&gt;
+         &lt;td&gt;322.728&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;393.0285&lt;br /&gt;
+         &lt;td&gt;393.401&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 1,956: / Line 2,167: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: left;"&gt;23\57&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;27\67&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
@@ Line 1,968: / Line 2,179: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;484.2105&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;483.582&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;11 11 1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;13 13 1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;224.257&lt;br /&gt;
+         &lt;td&gt;223.943&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;259.954&lt;br /&gt;
+         &lt;td&gt;259.6395&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;322.5585&lt;br /&gt;
+         &lt;td&gt;322.873&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;393.231&lt;br /&gt;
+         &lt;td&gt;393.545&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 1,984: / Line 2,195: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: left;"&gt;25\62&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;29\72&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
@@ Line 1,996: / Line 2,207: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;483.871&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;483.333&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;12 12 1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;14 14 1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;224.087&lt;br /&gt;
+         &lt;td&gt;223.818&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;259.784&lt;br /&gt;
+         &lt;td&gt;259.515&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;322.728&lt;br /&gt;
+         &lt;td&gt;322.997&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;393.401&lt;br /&gt;
+         &lt;td&gt;393.6695&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 2,012: / Line 2,223: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: left;"&gt;27\67&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;31\77&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
@@ Line 2,024: / Line 2,235: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;483.582&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;483.117&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;13 13 1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;15 15 1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;223.943&lt;br /&gt;
+         &lt;td&gt;223.710&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;259.6395&lt;br /&gt;
+         &lt;td&gt;259.407&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;322.873&lt;br /&gt;
+         &lt;td&gt;323.105&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;393.545&lt;br /&gt;
+         &lt;td&gt;393.778&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 2,040: / Line 2,251: @@
      &lt;/tr&gt;
      &lt;tr&gt;
-         &lt;td style="text-align: left;"&gt;29\72&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;33\82&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
@@ Line 2,052: / Line 2,263: @@
          &lt;td&gt;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;483.333&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;482.927&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;14 14 1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;16 16 1&lt;br /&gt;
 &lt;/td&gt;
-        &lt;td&gt;223.818&lt;br /&gt;
+         &lt;td&gt;223.615&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;259.515&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;322.997&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;393.6695&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td style="text-align: left;"&gt;31\77&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td colspan="2"&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: left;"&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: left;"&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;483.117&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;15 15 1&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;223.710&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;259.407&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;323.105&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;393.778&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-    &lt;/tr&gt;
-    &lt;tr&gt;
-        &lt;td style="text-align: left;"&gt;33\82&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td colspan="2"&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: left;"&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: left;"&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td&gt;&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;482.927&lt;br /&gt;
-&lt;/td&gt;
-        &lt;td style="text-align: center;"&gt;16 16 1&lt;br /&gt;
-&lt;/td&gt;
-         &lt;td&gt;223.615&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;259.312&lt;br /&gt;
@@ Line 2,126: / Line 2,281: @@
          &lt;td&gt;35\87&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
@@ Line 2,154: / Line 2,309: @@
          &lt;td&gt;37\92&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
@@ Line 2,182: / Line 2,337: @@
          &lt;td&gt;39\97&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 2,210: / Line 2,365: @@
          &lt;td&gt;41\102&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 2,238: / Line 2,393: @@
          &lt;td&gt;43\107&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 2,266: / Line 2,421: @@
          &lt;td&gt;45\112&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 2,294: / Line 2,449: @@
          &lt;td&gt;47\117&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 2,322: / Line 2,477: @@
          &lt;td&gt;49\122&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;
@@ Line 2,350: / Line 2,505: @@
          &lt;td style="text-align: left;"&gt;2\5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2"&gt;&lt;br /&gt;
+         &lt;td colspan="2" style="text-align: left;"&gt;&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: left;"&gt;&lt;br /&gt;
@@ Line 2,382: / Line 2,537: @@
 Temperaments below 5\12 on this chart are called &amp;quot;positive temperaments&amp;quot; and they include Pythagorean tuning itself (well approximated by 22\53) as well as superpyth temperaments such as 7\17 and 9\22. As these tunings approach 2\5, the majors become sharper and the minors become flatter. Around 9\22, the thirds fall closer to 7-limit than 5-limit intervals: 7:6 and 9:7 as opposed to 6:5 and 5:4.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:2176:&amp;lt;img src=&amp;quot;/file/view/5L2s.jpg/103741463/5L2s.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/5L2s.jpg/103741463/5L2s.jpg" alt="5L2s.jpg" title="5L2s.jpg" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:2176 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:2326:&amp;lt;img src=&amp;quot;/file/view/5L2s.jpg/103741463/5L2s.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/5L2s.jpg/103741463/5L2s.jpg" alt="5L2s.jpg" title="5L2s.jpg" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:2326 --&gt;&lt;br /&gt;
 &lt;br /&gt;
 L 2s contains the pentatonic MOS &lt;a class="wiki_link" href="/2L%203s"&gt;2L 3s&lt;/a&gt; and (with the sole exception of the 5L 2s of 12edo) is itself contained in a dodecaphonic MOS: either &lt;a class="wiki_link" href="/7L%205s"&gt;7L 5s&lt;/a&gt; or &lt;a class="wiki_link" href="/5L%207s"&gt;5L 7s&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>

5L 2s: Difference between revisions

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