OTC 2L ns

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This revision was by author spt3125 and made on 2016-08-28 22:06:21 UTC.
The original revision id was 590311712.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

**Omnitetrachordal scales of the form 2L+//n//s -- a special case?**

An OTC scale of this form (example: LssssLsssssss) has been confirmed for every scale size from 3 to 53 (except 4), and probably exists for any larger scale size as well.  With the exception of the 3-, 5-, and 7-note scales, these patterns are not MOS.

In every case so far studied, the strings of 's' steps come in a small group and a large group.  Let x be the number of 's' steps in the small group, and y the number of 's' steps in the large group.  Then:
* 9/8 = (y-x)s
* 4/3 = L+xs
* 3/2 = L+ys
* If either x or y is odd, the scale has a symmetric mode (ex. sLsLs).
* If both x and y are odd, there are two symmetric modes (ex. sLssssLs and ssLssLss).
* If both x and y are even, no symmetric mode exists (ex. LsLsss).

As scale size increases:
* y/x appears to converge on a value around 0.6 .
* For odd size scales, the generator is large (at least 4/3 = 498 cents), and appears to approach sqrt(2) = 600 cents.
* For even size scales, the period is 1/2 octave, and the generator is small, and appears to approach 1/1 = 0 cents.

Note the patterns in values of [[Gallery of omnitetrachordal scales#perfect|P]]:
* P(3) = P(5)+1 = P(7)+2
* P(6) = P(8)+1 = P(10)+2 = P(12a)+3
* P(9) = P(11)+1 = P(13)+2 = P(15)+3 = P(17)+4
* P(12b) = P(14)+1 = P(16)+2 = P(18)+3 = P(20)+4 = P(22)+5
* P(19) = P(21)+1 = P(23)+2 = P(25)+3 = P(27)+4 = P(29)+5
* etc.
These groups appear to share generators and temperaments.

For some scale sizes (12, 17, 22, 29, 34, 41, 46, 53, and possibly others), more than one class of OTC scale is possible!  In such cases, the two will have different tetrachordal divisions (i.e. representing 4/3 with different numbers of steps). One version will have P very near 1, and the other will have a much higher value of P.  Note that these scale sizes tend to correspond to [[EDO]]s that represent 4/3 and 3/2 with relatively high accuracy.

|| **size** ||= **_L+_s** ||= **P** || **pattern** ||
|| 3 ||= 2L+s ||= 2.4424745962 || {{ LsL }} (MOS) ||
|| 4 ||= - ||= - || no OTC scale pattern possible ||
|| 5 ||= [[OTC 2L 3s|2L+3s]] ||= 1.4424745962 || {{ LssLs }} (MOS) ||
|| 6 ||= 2L+4s ||= 3.8849491924 || {{ LsssLs }} ||
|| 7 ||= [[OTC 2L 5s|2L+5s]] ||= 0.4424745962 || {{ LsssLss }} (MOS) ||
|| 8 ||= 2L+6s ||= 2.8849491924 || {{ LssssLss }} ||
|| 9 ||= 2L+7s ||= 5.3274237885 || {{ LsssssLss }} ||
|| 10 ||= [[OTC 2L 8s|2L+8s]] ||= 1.8849491924 || {{ LsssssLsss }} ||
|| 11 ||= 2L+9s ||= 4.3274237885 || {{ LssssssLsss }} ||
|| 12a ||= [[OTC 2L 10s|2L+10s]] ||= 0.8849491924 || {{ LssssssLssss }} ||
|| 12b ||= [[OTC 2L 10s|2L+10s]] ||= 6.7698983847 || {{ LsssssssLsss }} ||
|| 13 ||= 2L+11s ||= 3.3274237885 || {{ LsssssssLssss }} ||
|| 14 ||= 2L+12s ||= 5.7698983847 || {{ LssssssssLssss }} ||
|| 15 ||= 2L+13s ||= 2.3274237885 || {{ LssssssssLsssss }} ||
|| 16 ||= 2L+14s ||= 4.7698983847 || {{ LsssssssssLsssss }} ||
|| 17a ||= 2L+15s ||= 1.3274237885 || {{ LsssssssssLssssss }} ||
|| 17b ||= 2L+15s ||= 7.2123729809 || {{ LssssssssssLsssss }} ||
|| 18 ||= 2L+16s ||= 3.7698983847 || {{ LssssssssssLssssss }} ||
|| 19 ||= 2L+17s ||= 6.2123729809 || {{ LsssssssssssLssssss }} ||
|| 20 ||= 2L+18s ||= 2.7698983847 || {{ LsssssssssssLsssssss }} ||
|| 21 ||= 2L+19s ||= 5.2123729809 || {{ LssssssssssssLsssssss }} ||
|| 22a ||= 2L+20s ||= 1.7698983847 || {{ LssssssssssssLssssssss }} ||
|| 22b ||= 2L+20s ||= 7.6548475771 || {{ LsssssssssssssLsssssss }} ||
|| 23 ||= 2L+21s ||= 4.2123729809 || {{ LsssssssssssssLssssssss }} ||
|| 24 ||= 2L+22s ||= 6.6548475771 || {{ LssssssssssssssLssssssss }} ||
|| 25 ||= 2L+23s ||= 3.2123729809 || {{ LssssssssssssssLsssssssss }} ||
|| 26 ||= 2L+24s ||= 5.6548475771 || {{ LsssssssssssssssLsssssssss }} ||
|| 27 ||= 2L+25s ||= 2.2123729809 || {{ LsssssssssssssssLssssssssss }} ||
|| 28 ||= 2L+26s ||= 4.6548475771 || {{ LssssssssssssssssLssssssssss }} ||
|| 29a ||= 2L+27s ||= 1.2123729809 || {{ LssssssssssssssssLsssssssssss }} ||
|| 29b ||= 2L+27s ||= 7.0973221733 || {{ LsssssssssssssssssLssssssssss }} ||
|| 30 ||= 2L+28s ||= 3.6548475771 || {{ LsssssssssssssssssLsssssssssss }} ||
|| 31 ||= 2L+29s ||= 6.0973221733 || {{ LssssssssssssssssssLsssssssssss }} ||
|| 32 ||= 2L+30s ||= 2.6548475771 || {{ LssssssssssssssssssLssssssssssss }} ||
|| 33 ||= 2L+31s ||= 5.0973221733 || {{ LsssssssssssssssssssLssssssssssss }} ||
|| 34a ||= 2L+32s ||= 1.6548475771 || {{ LsssssssssssssssssssLsssssssssssss }} ||
|| 34b ||= 2L+32s ||= 6.5397967694 || {{ LssssssssssssssssssssLssssssssssss }} ||
|| 35 ||= 2L+33s ||= 4.0973221733 || {{ LssssssssssssssssssssLsssssssssssss }} ||
|| 36 ||= 2L+34s ||= 6.5397967694 || {{ LsssssssssssssssssssssLsssssssssssss }} ||
|| 37 ||= 2L+35s ||= 3.0973221733 || {{ LsssssssssssssssssssssLssssssssssssss }} ||
|| 38 ||= 2L+36s ||= 5.5397967694 || {{ LssssssssssssssssssssssLssssssssssssss }} ||
|| 39 ||= 2L+37s ||= 2.0973221733 || {{ LssssssssssssssssssssssLsssssssssssssss }} ||
|| 40 ||= 2L+38s ||= 4.5397967694 || {{ LsssssssssssssssssssssssLsssssssssssssss }} ||
|| 41a ||= 2L+39s ||= 1.0973221733 || {{ LsssssssssssssssssssssssLssssssssssssssss }} ||
|| 41b ||= 2L+39s ||= 6.9822713656 || {{ LssssssssssssssssssssssssLsssssssssssssss }} ||
|| 42 ||= 2L+40s ||= 3.5397967694 || {{ LssssssssssssssssssssssssLssssssssssssssss }} ||
|| 43 ||= 2L+41s ||= 5.9822713656 || {{ LsssssssssssssssssssssssssLssssssssssssssss }} ||
|| 44 ||= 2L+42s ||= 2.5397967694 || {{ LsssssssssssssssssssssssssLsssssssssssssssss }} ||
|| 45 ||= 2L+43s ||= 4.9822713656 || {{ LssssssssssssssssssssssssssLsssssssssssssssss }} ||
|| 46a ||= 2L+44s ||= 1.5397967694 || {{ LssssssssssssssssssssssssssLssssssssssssssssss }} ||
|| 46b ||= 2L+44s ||= 7.4247459618 || {{ LsssssssssssssssssssssssssssLsssssssssssssssss }} ||
|| 47 ||= 2L+45s ||= 3.9822713656 || {{ LsssssssssssssssssssssssssssLssssssssssssssssss }} ||
|| 48 ||= 2L+46s ||= 6.4247459618 || {{ LssssssssssssssssssssssssssssLssssssssssssssssss }} ||
|| 49 ||= 2L+47s ||= 2.9822713656 || {{ LssssssssssssssssssssssssssssLsssssssssssssssssss }} ||
|| 50 ||= 2L+48s ||= 5.4247459618 || {{ LsssssssssssssssssssssssssssssLsssssssssssssssssss }} ||
|| 51 ||= 2L+49s ||= 1.9822713656 || {{ LsssssssssssssssssssssssssssssLssssssssssssssssssss }} ||
|| 52 ||= 2L+50s ||= 4.4247459618 || {{ LssssssssssssssssssssssssssssssLssssssssssssssssssss }} ||
|| 53a ||= 2L+51s ||= 0.9822713656 || {{ LssssssssssssssssssssssssssssssLsssssssssssssssssssss }} ||
|| 53b ||=  2L+51s  ||=  6.8672205580  || {{ LsssssssssssssssssssssssssssssssLssssssssssssssssssss }} ||
etc.

Original HTML content:

<html><head><title>OTC 2L ns</title></head><body><strong>Omnitetrachordal scales of the form 2L+<em>n</em>s -- a special case?</strong><br />
<br />
An OTC scale of this form (example: LssssLsssssss) has been confirmed for every scale size from 3 to 53 (except 4), and probably exists for any larger scale size as well.  With the exception of the 3-, 5-, and 7-note scales, these patterns are not MOS.<br />
<br />
In every case so far studied, the strings of 's' steps come in a small group and a large group.  Let x be the number of 's' steps in the small group, and y the number of 's' steps in the large group.  Then:<br />
<ul><li>9/8 = (y-x)s</li><li>4/3 = L+xs</li><li>3/2 = L+ys</li><li>If either x or y is odd, the scale has a symmetric mode (ex. sLsLs).</li><li>If both x and y are odd, there are two symmetric modes (ex. sLssssLs and ssLssLss).</li><li>If both x and y are even, no symmetric mode exists (ex. LsLsss).</li></ul><br />
As scale size increases:<br />
<ul><li>y/x appears to converge on a value around 0.6 .</li><li>For odd size scales, the generator is large (at least 4/3 = 498 cents), and appears to approach sqrt(2) = 600 cents.</li><li>For even size scales, the period is 1/2 octave, and the generator is small, and appears to approach 1/1 = 0 cents.</li></ul><br />
Note the patterns in values of <a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a>:<br />
<ul><li>P(3) = P(5)+1 = P(7)+2</li><li>P(6) = P(8)+1 = P(10)+2 = P(12a)+3</li><li>P(9) = P(11)+1 = P(13)+2 = P(15)+3 = P(17)+4</li><li>P(12b) = P(14)+1 = P(16)+2 = P(18)+3 = P(20)+4 = P(22)+5</li><li>P(19) = P(21)+1 = P(23)+2 = P(25)+3 = P(27)+4 = P(29)+5</li><li>etc.</li></ul>These groups appear to share generators and temperaments.<br />
<br />
For some scale sizes (12, 17, 22, 29, 34, 41, 46, 53, and possibly others), more than one class of OTC scale is possible!  In such cases, the two will have different tetrachordal divisions (i.e. representing 4/3 with different numbers of steps). One version will have P very near 1, and the other will have a much higher value of P.  Note that these scale sizes tend to correspond to <a class="wiki_link" href="/EDO">EDO</a>s that represent 4/3 and 3/2 with relatively high accuracy.<br />
<br />


<table class="wiki_table">
    <tr>
        <td><strong>size</strong><br />
</td>
        <td style="text-align: center;"><strong>_L+_s</strong><br />
</td>
        <td style="text-align: center;"><strong>P</strong><br />
</td>
        <td><strong>pattern</strong><br />
</td>
    </tr>
    <tr>
        <td>3<br />
</td>
        <td style="text-align: center;">2L+s<br />
</td>
        <td style="text-align: center;">2.4424745962<br />
</td>
        <td><tt> LsL </tt> (MOS)<br />
</td>
    </tr>
    <tr>
        <td>4<br />
</td>
        <td style="text-align: center;">-<br />
</td>
        <td style="text-align: center;">-<br />
</td>
        <td>no OTC scale pattern possible<br />
</td>
    </tr>
    <tr>
        <td>5<br />
</td>
        <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%203s">2L+3s</a><br />
</td>
        <td style="text-align: center;">1.4424745962<br />
</td>
        <td><tt> LssLs </tt> (MOS)<br />
</td>
    </tr>
    <tr>
        <td>6<br />
</td>
        <td style="text-align: center;">2L+4s<br />
</td>
        <td style="text-align: center;">3.8849491924<br />
</td>
        <td><tt> LsssLs </tt><br />
</td>
    </tr>
    <tr>
        <td>7<br />
</td>
        <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%205s">2L+5s</a><br />
</td>
        <td style="text-align: center;">0.4424745962<br />
</td>
        <td><tt> LsssLss </tt> (MOS)<br />
</td>
    </tr>
    <tr>
        <td>8<br />
</td>
        <td style="text-align: center;">2L+6s<br />
</td>
        <td style="text-align: center;">2.8849491924<br />
</td>
        <td><tt> LssssLss </tt><br />
</td>
    </tr>
    <tr>
        <td>9<br />
</td>
        <td style="text-align: center;">2L+7s<br />
</td>
        <td style="text-align: center;">5.3274237885<br />
</td>
        <td><tt> LsssssLss </tt><br />
</td>
    </tr>
    <tr>
        <td>10<br />
</td>
        <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%208s">2L+8s</a><br />
</td>
        <td style="text-align: center;">1.8849491924<br />
</td>
        <td><tt> LsssssLsss </tt><br />
</td>
    </tr>
    <tr>
        <td>11<br />
</td>
        <td style="text-align: center;">2L+9s<br />
</td>
        <td style="text-align: center;">4.3274237885<br />
</td>
        <td><tt> LssssssLsss </tt><br />
</td>
    </tr>
    <tr>
        <td>12a<br />
</td>
        <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%2010s">2L+10s</a><br />
</td>
        <td style="text-align: center;">0.8849491924<br />
</td>
        <td><tt> LssssssLssss </tt><br />
</td>
    </tr>
    <tr>
        <td>12b<br />
</td>
        <td style="text-align: center;"><a class="wiki_link" href="/OTC%202L%2010s">2L+10s</a><br />
</td>
        <td style="text-align: center;">6.7698983847<br />
</td>
        <td><tt> LsssssssLsss </tt><br />
</td>
    </tr>
    <tr>
        <td>13<br />
</td>
        <td style="text-align: center;">2L+11s<br />
</td>
        <td style="text-align: center;">3.3274237885<br />
</td>
        <td><tt> LsssssssLssss </tt><br />
</td>
    </tr>
    <tr>
        <td>14<br />
</td>
        <td style="text-align: center;">2L+12s<br />
</td>
        <td style="text-align: center;">5.7698983847<br />
</td>
        <td><tt> LssssssssLssss </tt><br />
</td>
    </tr>
    <tr>
        <td>15<br />
</td>
        <td style="text-align: center;">2L+13s<br />
</td>
        <td style="text-align: center;">2.3274237885<br />
</td>
        <td><tt> LssssssssLsssss </tt><br />
</td>
    </tr>
    <tr>
        <td>16<br />
</td>
        <td style="text-align: center;">2L+14s<br />
</td>
        <td style="text-align: center;">4.7698983847<br />
</td>
        <td><tt> LsssssssssLsssss </tt><br />
</td>
    </tr>
    <tr>
        <td>17a<br />
</td>
        <td style="text-align: center;">2L+15s<br />
</td>
        <td style="text-align: center;">1.3274237885<br />
</td>
        <td><tt> LsssssssssLssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>17b<br />
</td>
        <td style="text-align: center;">2L+15s<br />
</td>
        <td style="text-align: center;">7.2123729809<br />
</td>
        <td><tt> LssssssssssLsssss </tt><br />
</td>
    </tr>
    <tr>
        <td>18<br />
</td>
        <td style="text-align: center;">2L+16s<br />
</td>
        <td style="text-align: center;">3.7698983847<br />
</td>
        <td><tt> LssssssssssLssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>19<br />
</td>
        <td style="text-align: center;">2L+17s<br />
</td>
        <td style="text-align: center;">6.2123729809<br />
</td>
        <td><tt> LsssssssssssLssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>20<br />
</td>
        <td style="text-align: center;">2L+18s<br />
</td>
        <td style="text-align: center;">2.7698983847<br />
</td>
        <td><tt> LsssssssssssLsssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>21<br />
</td>
        <td style="text-align: center;">2L+19s<br />
</td>
        <td style="text-align: center;">5.2123729809<br />
</td>
        <td><tt> LssssssssssssLsssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>22a<br />
</td>
        <td style="text-align: center;">2L+20s<br />
</td>
        <td style="text-align: center;">1.7698983847<br />
</td>
        <td><tt> LssssssssssssLssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>22b<br />
</td>
        <td style="text-align: center;">2L+20s<br />
</td>
        <td style="text-align: center;">7.6548475771<br />
</td>
        <td><tt> LsssssssssssssLsssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>23<br />
</td>
        <td style="text-align: center;">2L+21s<br />
</td>
        <td style="text-align: center;">4.2123729809<br />
</td>
        <td><tt> LsssssssssssssLssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>24<br />
</td>
        <td style="text-align: center;">2L+22s<br />
</td>
        <td style="text-align: center;">6.6548475771<br />
</td>
        <td><tt> LssssssssssssssLssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>25<br />
</td>
        <td style="text-align: center;">2L+23s<br />
</td>
        <td style="text-align: center;">3.2123729809<br />
</td>
        <td><tt> LssssssssssssssLsssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>26<br />
</td>
        <td style="text-align: center;">2L+24s<br />
</td>
        <td style="text-align: center;">5.6548475771<br />
</td>
        <td><tt> LsssssssssssssssLsssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>27<br />
</td>
        <td style="text-align: center;">2L+25s<br />
</td>
        <td style="text-align: center;">2.2123729809<br />
</td>
        <td><tt> LsssssssssssssssLssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>28<br />
</td>
        <td style="text-align: center;">2L+26s<br />
</td>
        <td style="text-align: center;">4.6548475771<br />
</td>
        <td><tt> LssssssssssssssssLssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>29a<br />
</td>
        <td style="text-align: center;">2L+27s<br />
</td>
        <td style="text-align: center;">1.2123729809<br />
</td>
        <td><tt> LssssssssssssssssLsssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>29b<br />
</td>
        <td style="text-align: center;">2L+27s<br />
</td>
        <td style="text-align: center;">7.0973221733<br />
</td>
        <td><tt> LsssssssssssssssssLssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>30<br />
</td>
        <td style="text-align: center;">2L+28s<br />
</td>
        <td style="text-align: center;">3.6548475771<br />
</td>
        <td><tt> LsssssssssssssssssLsssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>31<br />
</td>
        <td style="text-align: center;">2L+29s<br />
</td>
        <td style="text-align: center;">6.0973221733<br />
</td>
        <td><tt> LssssssssssssssssssLsssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>32<br />
</td>
        <td style="text-align: center;">2L+30s<br />
</td>
        <td style="text-align: center;">2.6548475771<br />
</td>
        <td><tt> LssssssssssssssssssLssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>33<br />
</td>
        <td style="text-align: center;">2L+31s<br />
</td>
        <td style="text-align: center;">5.0973221733<br />
</td>
        <td><tt> LsssssssssssssssssssLssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>34a<br />
</td>
        <td style="text-align: center;">2L+32s<br />
</td>
        <td style="text-align: center;">1.6548475771<br />
</td>
        <td><tt> LsssssssssssssssssssLsssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>34b<br />
</td>
        <td style="text-align: center;">2L+32s<br />
</td>
        <td style="text-align: center;">6.5397967694<br />
</td>
        <td><tt> LssssssssssssssssssssLssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>35<br />
</td>
        <td style="text-align: center;">2L+33s<br />
</td>
        <td style="text-align: center;">4.0973221733<br />
</td>
        <td><tt> LssssssssssssssssssssLsssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>36<br />
</td>
        <td style="text-align: center;">2L+34s<br />
</td>
        <td style="text-align: center;">6.5397967694<br />
</td>
        <td><tt> LsssssssssssssssssssssLsssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>37<br />
</td>
        <td style="text-align: center;">2L+35s<br />
</td>
        <td style="text-align: center;">3.0973221733<br />
</td>
        <td><tt> LsssssssssssssssssssssLssssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>38<br />
</td>
        <td style="text-align: center;">2L+36s<br />
</td>
        <td style="text-align: center;">5.5397967694<br />
</td>
        <td><tt> LssssssssssssssssssssssLssssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>39<br />
</td>
        <td style="text-align: center;">2L+37s<br />
</td>
        <td style="text-align: center;">2.0973221733<br />
</td>
        <td><tt> LssssssssssssssssssssssLsssssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>40<br />
</td>
        <td style="text-align: center;">2L+38s<br />
</td>
        <td style="text-align: center;">4.5397967694<br />
</td>
        <td><tt> LsssssssssssssssssssssssLsssssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>41a<br />
</td>
        <td style="text-align: center;">2L+39s<br />
</td>
        <td style="text-align: center;">1.0973221733<br />
</td>
        <td><tt> LsssssssssssssssssssssssLssssssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>41b<br />
</td>
        <td style="text-align: center;">2L+39s<br />
</td>
        <td style="text-align: center;">6.9822713656<br />
</td>
        <td><tt> LssssssssssssssssssssssssLsssssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>42<br />
</td>
        <td style="text-align: center;">2L+40s<br />
</td>
        <td style="text-align: center;">3.5397967694<br />
</td>
        <td><tt> LssssssssssssssssssssssssLssssssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>43<br />
</td>
        <td style="text-align: center;">2L+41s<br />
</td>
        <td style="text-align: center;">5.9822713656<br />
</td>
        <td><tt> LsssssssssssssssssssssssssLssssssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>44<br />
</td>
        <td style="text-align: center;">2L+42s<br />
</td>
        <td style="text-align: center;">2.5397967694<br />
</td>
        <td><tt> LsssssssssssssssssssssssssLsssssssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>45<br />
</td>
        <td style="text-align: center;">2L+43s<br />
</td>
        <td style="text-align: center;">4.9822713656<br />
</td>
        <td><tt> LssssssssssssssssssssssssssLsssssssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>46a<br />
</td>
        <td style="text-align: center;">2L+44s<br />
</td>
        <td style="text-align: center;">1.5397967694<br />
</td>
        <td><tt> LssssssssssssssssssssssssssLssssssssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>46b<br />
</td>
        <td style="text-align: center;">2L+44s<br />
</td>
        <td style="text-align: center;">7.4247459618<br />
</td>
        <td><tt> LsssssssssssssssssssssssssssLsssssssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>47<br />
</td>
        <td style="text-align: center;">2L+45s<br />
</td>
        <td style="text-align: center;">3.9822713656<br />
</td>
        <td><tt> LsssssssssssssssssssssssssssLssssssssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>48<br />
</td>
        <td style="text-align: center;">2L+46s<br />
</td>
        <td style="text-align: center;">6.4247459618<br />
</td>
        <td><tt> LssssssssssssssssssssssssssssLssssssssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>49<br />
</td>
        <td style="text-align: center;">2L+47s<br />
</td>
        <td style="text-align: center;">2.9822713656<br />
</td>
        <td><tt> LssssssssssssssssssssssssssssLsssssssssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>50<br />
</td>
        <td style="text-align: center;">2L+48s<br />
</td>
        <td style="text-align: center;">5.4247459618<br />
</td>
        <td><tt> LsssssssssssssssssssssssssssssLsssssssssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>51<br />
</td>
        <td style="text-align: center;">2L+49s<br />
</td>
        <td style="text-align: center;">1.9822713656<br />
</td>
        <td><tt> LsssssssssssssssssssssssssssssLssssssssssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>52<br />
</td>
        <td style="text-align: center;">2L+50s<br />
</td>
        <td style="text-align: center;">4.4247459618<br />
</td>
        <td><tt> LssssssssssssssssssssssssssssssLssssssssssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>53a<br />
</td>
        <td style="text-align: center;">2L+51s<br />
</td>
        <td style="text-align: center;">0.9822713656<br />
</td>
        <td><tt> LssssssssssssssssssssssssssssssLsssssssssssssssssssss </tt><br />
</td>
    </tr>
    <tr>
        <td>53b<br />
</td>
        <td style="text-align: center;"> 2L+51s <br />
</td>
        <td style="text-align: center;"> 6.8672205580 <br />
</td>
        <td><tt> LsssssssssssssssssssssssssssssssLssssssssssssssssssss </tt><br />
</td>
    </tr>
</table>

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