Generator ranges of MOS: Difference between revisions
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Wikispaces>JosephRuhf **Imported revision 539535058 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 539625988 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-02-03 | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-02-03 22:14:57 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>539625988</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Below are ranges of generators for various L-s patterns of MOS, with the number of steps in the scale from 2 to | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Below are ranges of generators for various L-s patterns of MOS, with the number of steps in the scale from 2 to 29. The ranges are given in fractions of the interval of equivalence, which is normally an octave. The tables give the range of possible generators in the second column, normalized so that the lower end of the range is where L/s = 1 (Nedo.) The third column gives the range of propriety, where the proper MOS reside. | ||
If the number of the [[Interval class|generic interval]] to which the generator g belongs is C, and there are N scale steps to the interval of equivalence, then the average the size of an interval in class C is C/N. We have normalized so that C/N is the lower bound of the range of generators; since therefore g > C/N, g is larger than average and hence is the larger of the two sizes of intervals in its class, which means we have normalized to the [[Modal UDP Notation|chroma-positive]] generator. | If the number of the [[Interval class|generic interval]] to which the generator g belongs is C, and there are N scale steps to the interval of equivalence, then the average the size of an interval in class C is C/N. We have normalized so that C/N is the lower bound of the range of generators; since therefore g > C/N, g is larger than average and hence is the larger of the two sizes of intervals in its class, which means we have normalized to the [[Modal UDP Notation|chroma-positive]] generator. | ||
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|| 19L3s || 15\22 < g < 13\19 || 15\22 < g < 28\41 || 28\41 < g < 41\60 || -2+3g || -19g+13 || | || 19L3s || 15\22 < g < 13\19 || 15\22 < g < 28\41 || 28\41 < g < 41\60 || -2+3g || -19g+13 || | ||
|| 20L2s || 1\22 < g < 1\20 || 1\22 < g < 2\42 (1\21) || 2\42 (1\21) < g < 3\62 || g || -10g+1\2 || | || 20L2s || 1\22 < g < 1\20 || 1\22 < g < 2\42 (1\21) || 2\42 (1\21) < g < 3\62 || g || -10g+1\2 || | ||
|| 21L1s || 1\22 < g < 1\21 || 1\22 < g < 2\43 || 2\43 < g < 3\64 || g || -21g+1 ||</pre></div> | || 21L1s || 1\22 < g < 1\21 || 1\22 < g < 2\43 || 2\43 < g < 3\64 || g || -21g+1 || | ||
=23= | |||
|| Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || | |||
|| 1L22s || <span style="line-height: 1.5;">22\23 < g < 1</span> || <span style="line-height: 1.5;">22\23</span> < g < 23\24 || <span style="line-height: 1.5;">23\24 </span>< g < 24\25 || -21+22g || -g+1 || | |||
|| 2L21s || 11\23 < g < 1\2 || <span style="line-height: 15.6000003814697px;">11\23</span> < g < <span style="line-height: 1.5;">12\25</span> || 12\25 < g < 13\27 || -10+21g || -2g+1 || | |||
|| 3L20s || 15\23 < g < 2\3 || 15\23 < g < 17\26 || <span style="line-height: 1.5;">17\26</span> < g < 19\29 || -13+20g || 1-3g || | |||
|| 4L19s || 17\23 < g < 3\4 || <span style="line-height: 1.5;">17\23</span> < g < 20\27 || <span style="line-height: 15.6000003814697px;">20</span>\27 < g < 23<span style="line-height: 1.5;">\31</span> || -14+19g || -4g+3 || | |||
|| 5L18s || 9\23 < g < 2\5 || 9\23 < g < 11\28 || 11\28 < g < 13\33 || -7+18g || -5g+2 || | |||
|| 6L17s || 19\23 < g < 5\6 || 19\23 < g < 24\29 || 24\29 < g < 29\35 || -15+17g || 1-6g || | |||
|| 7L16s || 13\23 < g < 4\7 || 13\23 < g < 17\30 || <span style="line-height: 1.5;">17\30</span> < g < 21\37 || -9+16g || -7g+4 || | |||
|| 8L15s || 20\23 < g < 7\8 || 20\23 < g < 27\31 || 27\31 < g < 34\39 || -13+15g || -8g+7 || | |||
|| 9L14s || <span style="line-height: 1.5;">18\23</span> < g < 11<span style="line-height: 1.5;">\14</span> || 18\23 < g < 29\37 || 29\37 < g < 47\60 || 9g-7 || <span style="line-height: 1.5;">11-14g</span> || | |||
|| 10L13s || 16\23 < g < 7\10 || 16\23 < g < 23\33 || 23\33 < g < 30\43 || -9+13g || -10g+7 || | |||
|| 11L12s || 2\23 < g < 1\11 || 2\23 < g < 3\34 || 3\34 < g < 4\45 || -11g+1 || 12g-1 || | |||
|| 12L11s || 21\23 < g < 11\12 || 21\23 < g < 32\35 || 32\35 < g < 43\47 || <span style="line-height: 1.5;">11g-10</span> || 11-12g || | |||
|| 13L10s || 7\23 < g < 4\13 || 7\23 < g < 11\36 || 11\36 < g < 15\49 || 4-13g || 10g-3 || | |||
|| 14L9s || 5\23 < g < 2\9 || 5\23 < g < 7\32 || 7\32 < g < 9\41 || 14g-3 || -9g+2 || | |||
|| 15L8s || 3\23 < g < 2\15 || 3\23 < g < 5\38 || 5\38 < g < 7\53 || 2-15g || 8g-1 || | |||
|| 16L7s || 10\23 < g < 7\16 || 10\23 < g < 17\39 || 17\39 < g < 24\55 || 7g-3 || <span style="line-height: 1.5;">-16g+7</span> || | |||
|| 17L6s || 4\23 < g < 3\17 || 4\23 < g < 7\40 || 7\40 < g < 10\57 || -1+6g || -17g+3 || | |||
|| 18L5s || 14\23 < g < <span style="line-height: 1.5;">11\18</span> || 14\23 < g < 25\41 || 25\41 < g < 36\59 || 11-18g || 5g-4 || | |||
|| 19L4s || 6\23 < g < 5\19 || 6\23 < g < 11\42 || 11\42 < g < 16\61 || -1+4g || -19g+5 || | |||
|| 20L3s || 8\23 < g < 7\20 || 8\23 < g < 15\43 || 15\43 < g < 22\63 || -1+3g || -20g+13 || | |||
|| 21L2s || 12\23 < g < 11\21 || 12\23 < g < 23\44 || 23\44 < g < 34\65 || -1+2g || -21g+1 || | |||
|| 22L1s || 1\23 < g < 1\22 || 1\23 < g < 2\45 || 2\45 < g < 3\67 || g || -22g+1 || | |||
=24= | |||
|| Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || | |||
|| 1L23s || 23\24 < g < 1 || 23\24 < g < 24\25 || 24\25 < g < 25\26 || -22+23g || -g+1 || | |||
|| 2L<span style="line-height: 1.5;">22s</span> || 11\24 < g < 1\2 || 11\24 < g < 12\26 (6\13) || 12\26 (6\13) < g < 15\28 || <span style="line-height: 1.5;">-g+1/2</span> || -5+11g || | |||
|| 3L<span style="line-height: 1.5;">21s</span> || 7\24 < g < 1\3 || 7\24 < g < 8\27 || 8\27 < g < 9\30 (3\10) || -2+7g || <span style="line-height: 1.5;">-</span>1/3+g || | |||
|| 4L<span style="line-height: 1.5;">20s</span> || 5\24 < g < 1\4 || 5\24 < g < 6\28 (3\14) || 6\28 (3\14) < g < 7\32 || -1+5g || -g+1/4 || | |||
|| 5L<span style="line-height: 1.5;">19s</span> || 19\24 < g < 4\5 || 19\24 < g < 23\29 || 23\29 < g < 27\34 || -15+19g || -5g+4 || | |||
|| 6L<span style="line-height: 1.5;">18s</span> || 3\24 (1\8) < g < 1\6 || 3\24 (1\8) < g < 4\30 (2\15) || 4\30 (2\15) < g < 5\36 || -1\3+3g || 1\6-g || | |||
|| 7L<span style="line-height: 1.5;">17s</span> || 17\24 < g < 5\7 || 17\24 < g < 22\31 || 22\31 < g < 27\38 || 5-17g || 7g-2 || | |||
|| 8L<span style="line-height: 1.5;">16s</span> || 2\24 (1\12) < g < 1\8 || 2\24 (1\12) < g < 3\32 || 3\32 < g < 4\40 (1\10) || -1\8+2g || -g+1\8 || | |||
|| 9L<span style="line-height: 1.5;">15s</span> || 5\24 < g < 2\9 || 5\24 < g < 7\33 || 7\33 < g < 9\42 (3\14) || 5g-1 || 2\3-3g || | |||
|| 10L<span style="line-height: 1.5;">14s</span> || 7\24 < g < 3\10 || 7\24 < g < 10\34 (5\17) || 10\34 (5\17) < g < 13\44 || <span style="line-height: 1.5;">-4+7g</span> || -3\2+5g || | |||
|| 11L<span style="line-height: 1.5;">13s</span> || 13\24 < g < 6\11 || 13\24 < g < 19\35 || 19\35 < g < 25\46 || 13g-7 || -11g+6 || | |||
|| 12L12s || 1\24 < g < 1\12 || 1\24 < g < 2\36 (1\18) || 2\36 (1\18) < g < 3\48 (1\16) || g || 1\12-g || | |||
|| <span style="line-height: 1.5;">13L</span>11s || 11\24 < g < 6\13 || 11\24 < g < 17\37 || 17\37 < g < 23\50 || 11g-5 || 6-13g || | |||
|| <span style="line-height: 1.5;">14L</span>10s || 7\24 < g < 4\14 (2\7) || 7\24 < g < 11\38 || 11\38 < g < 15\52 || 3\2-5g || 7g-2 || | |||
|| <span style="line-height: 1.5;">15L</span>9s || 3\24 (1\8) < g < 2\15 || 3\24 (1\8) < g < 5\39 || 5\39 < g < 7\54 || 3g-1\3 || -5g+2\3 || | |||
|| <span style="line-height: 1.5;">16L</span>8s || 1\24 < g < 1\16 || 1\24 < g < 2\40 (1\20) || 2\40 (1\20) < g < 3\56 || g || <span style="line-height: 1.5;">1\8</span>-<span style="line-height: 1.5;">2g</span> || | |||
|| <span style="line-height: 1.5;">17L</span>7s || 17\24 < g < 12\17 || 17\24 < g < 29\41 || 29\41 < g < 41\58 || -7g+4 || 17g-12 || | |||
|| <span style="line-height: 1.5;">18L</span>6s || 1\24 < g < 1\18 || 1\24 < g < 2\42 (1\21) || 2\42 (1\21) < g < 3\60 (1\20) || g || <span style="line-height: 1.5;">1\6-3</span>g || | |||
|| <span style="line-height: 1.5;">19L</span>5s || 19\24 < g < 15\19 || 19\24 < g < 34\43 || 34\43 < g < 49\62 || -5g+4 || <span style="line-height: 1.5;">-15+19g</span> || | |||
|| <span style="line-height: 1.5;">20L</span>4s || 1\24 < g < 1\20 || 1\24 < g < 2\44 (1\22) || 2\44 (1\22) < g < 3\64 || g || -5g+1\4 || | |||
|| <span style="line-height: 1.5;">21L</span>3s || 1\24 < g < 1\21 || 1\24 < g < 2\45 || 2\45 < g < 3\66 (1\22) || g || -7g+1\3 || | |||
|| <span style="line-height: 1.5;">22L</span>2s || 1\24 < g < 1\22 || 1\24 < g < 2\46 (1\23) || 2\46 (1\23) < g < 3\68 || g || -11g+1\2 || | |||
|| 23L1s || 1\24 < g < 1\23 || 1\24 < g < 2\47 || 2\47 < g < 3\70 || g || -23g+1 || | |||
=25= | |||
|| Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || | |||
|| 1L24s || 24\25 < g < 1 || 24\25 < g < 25\26 || 25\26 < g < 26\27 || -23+24g || -g+1 || | |||
|| 2L23s || 12\25 < g < 1\2 || 12\25 < g < 13\27 || 13\27 < g < 14\29 || 23g-11 || 1-2g || | |||
|| 3L22s || 8\25 < g < 1\3 || 8\25 < g < 9\28 || 9\28 < g < <span style="line-height: 1.5;">10\31</span> || -7+22g || 1-3g || | |||
|| 4L21s || 6\25 < g < 1\4 || 6\25 < g < 7\29 || 7\29 < g < 8\33 || -5+21g || -4g+1 || | |||
|| 5L20s || 4\25 < g < 1\5 || 4\25 < g < 5\30 (1\6) || 5\30 (1\6) < g < 6\35 || -3\5+4g || 1\5-g || | |||
|| 6L19s || 4\25 < g < 1\6 || 4\25 < g < 5\31 || 5\31 < g < 6\37 || -3+19g || -6g+1 || | |||
|| 7L18s || 7\25 < g < 2\7 || 7\25 < g < 9\32 || 9\32 < g < 11\39 || -5+18g || -7g+2 || | |||
|| 8L17s || 3\25 < g < 1\8 || 3\25 < g < 4\33 || 4\33 < g < 5\41 || <span style="line-height: 1.5;">17g-2</span> || 1-8g || | |||
|| 9L16s || 11\25 < g < 4\9 || 11\25 < g < 15\34 || 15\34 < g < 19\43 || -7+16g || <span style="line-height: 1.5;">-9g+4</span> || | |||
|| 10L15s || 2\25 < g < 1\10 || 2\25 < g < 3\35 || 3\35 < g < 4\45 || -1\5+3g || 1\5-2g || | |||
|| 11L14s || 9\25 < g < 4\11 || 9\25 < g < 13\36 || 13\36 < g < 17\47 || 14g-5 || -11g+4 || | |||
|| 12L13s || 2\25 < g < 1\12 || 2\25 < g < 3\37 || 3\37 < g < 4\49 || 13g-1 || 1-12g || | |||
|| 13L12s || 23\25 < g < 12\13 || 23\25 < g < 35\38 || 35\38 < g < 47\51 || 12g-11 || 12-13g || | |||
|| 14L11s || 16\25 < g < 9\14 || 16\25 < g < 25\39 || 25\39 < g < 34\53 || -7+11g || -14g+9 || | |||
|| 15L10s || 2\25 < g < 1\15 || 1\25 < g < 3<span style="line-height: 1.5;">\40</span> || <span style="line-height: 1.5;">3\40</span> < g < 4\55 || -2g+1\5 || 3g-1\5 || | |||
|| 16L9s || 14\25 < g < 9\16 || 14\25 < g < 23\41 || 23\41 < g < 32\57 || 9g-5 || 9-16g || | |||
|| 17L8s || 22\25 < g < 15\17 || 22\25 < g < 37\42 || 37\42 < g < 52\59 || 8g-7 || -17g+15 || | |||
|| 18L7s || 18\25 < g < 13\18 || 18\25 < g < 31\43 || 31\43 < g < 44\61 || g || 1\6-3g || | |||
|| 19L6s || 21\25 < g < 16\19 || 21\25 < g < 37\44 || 37\44 < g < 53\63 || -19g+16 || -5+6g || | |||
|| 20L5s || 1\25 < g < 1\20 || 1\25 < g < 2\45 || 2\45 < g < 3\65 || g || -4g+1\5 || | |||
|| 21L4s || 16\21 < g < 19\25 || 19\25 < g < 35\46 || 35\46 < g < 51\67 || 4g-3 || -21g+16 || | |||
|| 22L3s || 17\25 < g < 15\22 || 17\25 < g < 32\47 || 32\47 < g < 47\69 || 3g-2 || -22g+15 || | |||
|| 23L2s || 13\25 < g < 12\23 || 13\25 < g < 23\48 || 23\48 < g < 35\71 || -2g+1 || 23g-11 || | |||
|| 24L1s || 1\25 < g < 1\24 || 1\25 < g < 2\49 || 2\49 < g < 3\73 || g || -24g+1 ||</pre></div> | |||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Generator ranges of MOS</title></head><body>Below are ranges of generators for various L-s patterns of MOS, with the number of steps in the scale from 2 to | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Generator ranges of MOS</title></head><body>Below are ranges of generators for various L-s patterns of MOS, with the number of steps in the scale from 2 to 29. The ranges are given in fractions of the interval of equivalence, which is normally an octave. The tables give the range of possible generators in the second column, normalized so that the lower end of the range is where L/s = 1 (Nedo.) The third column gives the range of propriety, where the proper MOS reside.<br /> | ||
<br /> | <br /> | ||
If the number of the <a class="wiki_link" href="/Interval%20class">generic interval</a> to which the generator g belongs is C, and there are N scale steps to the interval of equivalence, then the average the size of an interval in class C is C/N. We have normalized so that C/N is the lower bound of the range of generators; since therefore g &gt; C/N, g is larger than average and hence is the larger of the two sizes of intervals in its class, which means we have normalized to the <a class="wiki_link" href="/Modal%20UDP%20Notation">chroma-positive</a> generator.<br /> | If the number of the <a class="wiki_link" href="/Interval%20class">generic interval</a> to which the generator g belongs is C, and there are N scale steps to the interval of equivalence, then the average the size of an interval in class C is C/N. We have normalized so that C/N is the lower bound of the range of generators; since therefore g &gt; C/N, g is larger than average and hence is the larger of the two sizes of intervals in its class, which means we have normalized to the <a class="wiki_link" href="/Modal%20UDP%20Notation">chroma-positive</a> generator.<br /> | ||
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</td> | </td> | ||
<td>-21g+1<br /> | <td>-21g+1<br /> | ||
</td> | |||
</tr> | |||
</table> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:42:&lt;h1&gt; --><h1 id="toc21"><a name="x23"></a><!-- ws:end:WikiTextHeadingRule:42 -->23</h1> | |||
<table class="wiki_table"> | |||
<tr> | |||
<td>Large-small numbers<br /> | |||
</td> | |||
<td>Generator range<br /> | |||
</td> | |||
<td>Range of propriety<br /> | |||
</td> | |||
<td>Range of maximum expressiveness<br /> | |||
</td> | |||
<td>Large step<br /> | |||
</td> | |||
<td>Small step<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1L22s<br /> | |||
</td> | |||
<td><span style="line-height: 1.5;">22\23 &lt; g &lt; 1</span><br /> | |||
</td> | |||
<td><span style="line-height: 1.5;">22\23</span> &lt; g &lt; 23\24<br /> | |||
</td> | |||
<td><span style="line-height: 1.5;">23\24 </span>&lt; g &lt; 24\25<br /> | |||
</td> | |||
<td>-21+22g<br /> | |||
</td> | |||
<td>-g+1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>2L21s<br /> | |||
</td> | |||
<td>11\23 &lt; g &lt; 1\2<br /> | |||
</td> | |||
<td><span style="line-height: 15.6000003814697px;">11\23</span> &lt; g &lt; <span style="line-height: 1.5;">12\25</span><br /> | |||
</td> | |||
<td>12\25 &lt; g &lt; 13\27<br /> | |||
</td> | |||
<td>-10+21g<br /> | |||
</td> | |||
<td>-2g+1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3L20s<br /> | |||
</td> | |||
<td>15\23 &lt; g &lt; 2\3<br /> | |||
</td> | |||
<td>15\23 &lt; g &lt; 17\26<br /> | |||
</td> | |||
<td><span style="line-height: 1.5;">17\26</span> &lt; g &lt; 19\29<br /> | |||
</td> | |||
<td>-13+20g<br /> | |||
</td> | |||
<td>1-3g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4L19s<br /> | |||
</td> | |||
<td>17\23 &lt; g &lt; 3\4<br /> | |||
</td> | |||
<td><span style="line-height: 1.5;">17\23</span> &lt; g &lt; 20\27<br /> | |||
</td> | |||
<td><span style="line-height: 15.6000003814697px;">20</span>\27 &lt; g &lt; 23<span style="line-height: 1.5;">\31</span><br /> | |||
</td> | |||
<td>-14+19g<br /> | |||
</td> | |||
<td>-4g+3<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>5L18s<br /> | |||
</td> | |||
<td>9\23 &lt; g &lt; 2\5<br /> | |||
</td> | |||
<td>9\23 &lt; g &lt; 11\28<br /> | |||
</td> | |||
<td>11\28 &lt; g &lt; 13\33<br /> | |||
</td> | |||
<td>-7+18g<br /> | |||
</td> | |||
<td>-5g+2<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>6L17s<br /> | |||
</td> | |||
<td>19\23 &lt; g &lt; 5\6<br /> | |||
</td> | |||
<td>19\23 &lt; g &lt; 24\29<br /> | |||
</td> | |||
<td>24\29 &lt; g &lt; 29\35<br /> | |||
</td> | |||
<td>-15+17g<br /> | |||
</td> | |||
<td>1-6g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>7L16s<br /> | |||
</td> | |||
<td>13\23 &lt; g &lt; 4\7<br /> | |||
</td> | |||
<td>13\23 &lt; g &lt; 17\30<br /> | |||
</td> | |||
<td><span style="line-height: 1.5;">17\30</span> &lt; g &lt; 21\37<br /> | |||
</td> | |||
<td>-9+16g<br /> | |||
</td> | |||
<td>-7g+4<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>8L15s<br /> | |||
</td> | |||
<td>20\23 &lt; g &lt; 7\8<br /> | |||
</td> | |||
<td>20\23 &lt; g &lt; 27\31<br /> | |||
</td> | |||
<td>27\31 &lt; g &lt; 34\39<br /> | |||
</td> | |||
<td>-13+15g<br /> | |||
</td> | |||
<td>-8g+7<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>9L14s<br /> | |||
</td> | |||
<td><span style="line-height: 1.5;">18\23</span> &lt; g &lt; 11<span style="line-height: 1.5;">\14</span><br /> | |||
</td> | |||
<td>18\23 &lt; g &lt; 29\37<br /> | |||
</td> | |||
<td>29\37 &lt; g &lt; 47\60<br /> | |||
</td> | |||
<td>9g-7<br /> | |||
</td> | |||
<td><span style="line-height: 1.5;">11-14g</span><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>10L13s<br /> | |||
</td> | |||
<td>16\23 &lt; g &lt; 7\10<br /> | |||
</td> | |||
<td>16\23 &lt; g &lt; 23\33<br /> | |||
</td> | |||
<td>23\33 &lt; g &lt; 30\43<br /> | |||
</td> | |||
<td>-9+13g<br /> | |||
</td> | |||
<td>-10g+7<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>11L12s<br /> | |||
</td> | |||
<td>2\23 &lt; g &lt; 1\11<br /> | |||
</td> | |||
<td>2\23 &lt; g &lt; 3\34<br /> | |||
</td> | |||
<td>3\34 &lt; g &lt; 4\45<br /> | |||
</td> | |||
<td>-11g+1<br /> | |||
</td> | |||
<td>12g-1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>12L11s<br /> | |||
</td> | |||
<td>21\23 &lt; g &lt; 11\12<br /> | |||
</td> | |||
<td>21\23 &lt; g &lt; 32\35<br /> | |||
</td> | |||
<td>32\35 &lt; g &lt; 43\47<br /> | |||
</td> | |||
<td><span style="line-height: 1.5;">11g-10</span><br /> | |||
</td> | |||
<td>11-12g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>13L10s<br /> | |||
</td> | |||
<td>7\23 &lt; g &lt; 4\13<br /> | |||
</td> | |||
<td>7\23 &lt; g &lt; 11\36<br /> | |||
</td> | |||
<td>11\36 &lt; g &lt; 15\49<br /> | |||
</td> | |||
<td>4-13g<br /> | |||
</td> | |||
<td>10g-3<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>14L9s<br /> | |||
</td> | |||
<td>5\23 &lt; g &lt; 2\9<br /> | |||
</td> | |||
<td>5\23 &lt; g &lt; 7\32<br /> | |||
</td> | |||
<td>7\32 &lt; g &lt; 9\41<br /> | |||
</td> | |||
<td>14g-3<br /> | |||
</td> | |||
<td>-9g+2<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>15L8s<br /> | |||
</td> | |||
<td>3\23 &lt; g &lt; 2\15<br /> | |||
</td> | |||
<td>3\23 &lt; g &lt; 5\38<br /> | |||
</td> | |||
<td>5\38 &lt; g &lt; 7\53<br /> | |||
</td> | |||
<td>2-15g<br /> | |||
</td> | |||
<td>8g-1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>16L7s<br /> | |||
</td> | |||
<td>10\23 &lt; g &lt; 7\16<br /> | |||
</td> | |||
<td>10\23 &lt; g &lt; 17\39<br /> | |||
</td> | |||
<td>17\39 &lt; g &lt; 24\55<br /> | |||
</td> | |||
<td>7g-3<br /> | |||
</td> | |||
<td><span style="line-height: 1.5;">-16g+7</span><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>17L6s<br /> | |||
</td> | |||
<td>4\23 &lt; g &lt; 3\17<br /> | |||
</td> | |||
<td>4\23 &lt; g &lt; 7\40<br /> | |||
</td> | |||
<td>7\40 &lt; g &lt; 10\57<br /> | |||
</td> | |||
<td>-1+6g<br /> | |||
</td> | |||
<td>-17g+3<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>18L5s<br /> | |||
</td> | |||
<td>14\23 &lt; g &lt; <span style="line-height: 1.5;">11\18</span><br /> | |||
</td> | |||
<td>14\23 &lt; g &lt; 25\41<br /> | |||
</td> | |||
<td>25\41 &lt; g &lt; 36\59<br /> | |||
</td> | |||
<td>11-18g<br /> | |||
</td> | |||
<td>5g-4<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>19L4s<br /> | |||
</td> | |||
<td>6\23 &lt; g &lt; 5\19<br /> | |||
</td> | |||
<td>6\23 &lt; g &lt; 11\42<br /> | |||
</td> | |||
<td>11\42 &lt; g &lt; 16\61<br /> | |||
</td> | |||
<td>-1+4g<br /> | |||
</td> | |||
<td>-19g+5<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>20L3s<br /> | |||
</td> | |||
<td>8\23 &lt; g &lt; 7\20<br /> | |||
</td> | |||
<td>8\23 &lt; g &lt; 15\43<br /> | |||
</td> | |||
<td>15\43 &lt; g &lt; 22\63<br /> | |||
</td> | |||
<td>-1+3g<br /> | |||
</td> | |||
<td>-20g+13<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>21L2s<br /> | |||
</td> | |||
<td>12\23 &lt; g &lt; 11\21<br /> | |||
</td> | |||
<td>12\23 &lt; g &lt; 23\44<br /> | |||
</td> | |||
<td>23\44 &lt; g &lt; 34\65<br /> | |||
</td> | |||
<td>-1+2g<br /> | |||
</td> | |||
<td>-21g+1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>22L1s<br /> | |||
</td> | |||
<td>1\23 &lt; g &lt; 1\22<br /> | |||
</td> | |||
<td>1\23 &lt; g &lt; 2\45<br /> | |||
</td> | |||
<td>2\45 &lt; g &lt; 3\67<br /> | |||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>-22g+1<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:44:&lt;h1&gt; --><h1 id="toc22"><a name="x24"></a><!-- ws:end:WikiTextHeadingRule:44 -->24</h1> | |||
<table class="wiki_table"> | |||
<tr> | |||
<td>Large-small numbers<br /> | |||
</td> | |||
<td>Generator range<br /> | |||
</td> | |||
<td>Range of propriety<br /> | |||
</td> | |||
<td>Range of maximum expressiveness<br /> | |||
</td> | |||
<td>Large step<br /> | |||
</td> | |||
<td>Small step<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1L23s<br /> | |||
</td> | |||
<td>23\24 &lt; g &lt; 1<br /> | |||
</td> | |||
<td>23\24 &lt; g &lt; 24\25<br /> | |||
</td> | |||
<td>24\25 &lt; g &lt; 25\26<br /> | |||
</td> | |||
<td>-22+23g<br /> | |||
</td> | |||
<td>-g+1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>2L<span style="line-height: 1.5;">22s</span><br /> | |||
</td> | |||
<td>11\24 &lt; g &lt; 1\2<br /> | |||
</td> | |||
<td>11\24 &lt; g &lt; 12\26 (6\13)<br /> | |||
</td> | |||
<td>12\26 (6\13) &lt; g &lt; 15\28<br /> | |||
</td> | |||
<td><span style="line-height: 1.5;">-g+1/2</span><br /> | |||
</td> | |||
<td>-5+11g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3L<span style="line-height: 1.5;">21s</span><br /> | |||
</td> | |||
<td>7\24 &lt; g &lt; 1\3<br /> | |||
</td> | |||
<td>7\24 &lt; g &lt; 8\27<br /> | |||
</td> | |||
<td>8\27 &lt; g &lt; 9\30 (3\10)<br /> | |||
</td> | |||
<td>-2+7g<br /> | |||
</td> | |||
<td><span style="line-height: 1.5;">-</span>1/3+g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4L<span style="line-height: 1.5;">20s</span><br /> | |||
</td> | |||
<td>5\24 &lt; g &lt; 1\4<br /> | |||
</td> | |||
<td>5\24 &lt; g &lt; 6\28 (3\14)<br /> | |||
</td> | |||
<td>6\28 (3\14) &lt; g &lt; 7\32<br /> | |||
</td> | |||
<td>-1+5g<br /> | |||
</td> | |||
<td>-g+1/4<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>5L<span style="line-height: 1.5;">19s</span><br /> | |||
</td> | |||
<td>19\24 &lt; g &lt; 4\5<br /> | |||
</td> | |||
<td>19\24 &lt; g &lt; 23\29<br /> | |||
</td> | |||
<td>23\29 &lt; g &lt; 27\34<br /> | |||
</td> | |||
<td>-15+19g<br /> | |||
</td> | |||
<td>-5g+4<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>6L<span style="line-height: 1.5;">18s</span><br /> | |||
</td> | |||
<td>3\24 (1\8) &lt; g &lt; 1\6<br /> | |||
</td> | |||
<td>3\24 (1\8) &lt; g &lt; 4\30 (2\15)<br /> | |||
</td> | |||
<td>4\30 (2\15) &lt; g &lt; 5\36<br /> | |||
</td> | |||
<td>-1\3+3g<br /> | |||
</td> | |||
<td>1\6-g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>7L<span style="line-height: 1.5;">17s</span><br /> | |||
</td> | |||
<td>17\24 &lt; g &lt; 5\7<br /> | |||
</td> | |||
<td>17\24 &lt; g &lt; 22\31<br /> | |||
</td> | |||
<td>22\31 &lt; g &lt; 27\38<br /> | |||
</td> | |||
<td>5-17g<br /> | |||
</td> | |||
<td>7g-2<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>8L<span style="line-height: 1.5;">16s</span><br /> | |||
</td> | |||
<td>2\24 (1\12) &lt; g &lt; 1\8<br /> | |||
</td> | |||
<td>2\24 (1\12) &lt; g &lt; 3\32<br /> | |||
</td> | |||
<td>3\32 &lt; g &lt; 4\40 (1\10)<br /> | |||
</td> | |||
<td>-1\8+2g<br /> | |||
</td> | |||
<td>-g+1\8<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>9L<span style="line-height: 1.5;">15s</span><br /> | |||
</td> | |||
<td>5\24 &lt; g &lt; 2\9<br /> | |||
</td> | |||
<td>5\24 &lt; g &lt; 7\33<br /> | |||
</td> | |||
<td>7\33 &lt; g &lt; 9\42 (3\14)<br /> | |||
</td> | |||
<td>5g-1<br /> | |||
</td> | |||
<td>2\3-3g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>10L<span style="line-height: 1.5;">14s</span><br /> | |||
</td> | |||
<td>7\24 &lt; g &lt; 3\10<br /> | |||
</td> | |||
<td>7\24 &lt; g &lt; 10\34 (5\17)<br /> | |||
</td> | |||
<td>10\34 (5\17) &lt; g &lt; 13\44<br /> | |||
</td> | |||
<td><span style="line-height: 1.5;">-4+7g</span><br /> | |||
</td> | |||
<td>-3\2+5g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>11L<span style="line-height: 1.5;">13s</span><br /> | |||
</td> | |||
<td>13\24 &lt; g &lt; 6\11<br /> | |||
</td> | |||
<td>13\24 &lt; g &lt; 19\35<br /> | |||
</td> | |||
<td>19\35 &lt; g &lt; 25\46<br /> | |||
</td> | |||
<td>13g-7<br /> | |||
</td> | |||
<td>-11g+6<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>12L12s<br /> | |||
</td> | |||
<td>1\24 &lt; g &lt; 1\12<br /> | |||
</td> | |||
<td>1\24 &lt; g &lt; 2\36 (1\18)<br /> | |||
</td> | |||
<td>2\36 (1\18) &lt; g &lt; 3\48 (1\16)<br /> | |||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>1\12-g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><span style="line-height: 1.5;">13L</span>11s<br /> | |||
</td> | |||
<td>11\24 &lt; g &lt; 6\13<br /> | |||
</td> | |||
<td>11\24 &lt; g &lt; 17\37<br /> | |||
</td> | |||
<td>17\37 &lt; g &lt; 23\50<br /> | |||
</td> | |||
<td>11g-5<br /> | |||
</td> | |||
<td>6-13g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><span style="line-height: 1.5;">14L</span>10s<br /> | |||
</td> | |||
<td>7\24 &lt; g &lt; 4\14 (2\7)<br /> | |||
</td> | |||
<td>7\24 &lt; g &lt; 11\38<br /> | |||
</td> | |||
<td>11\38 &lt; g &lt; 15\52<br /> | |||
</td> | |||
<td>3\2-5g<br /> | |||
</td> | |||
<td>7g-2<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><span style="line-height: 1.5;">15L</span>9s<br /> | |||
</td> | |||
<td>3\24 (1\8) &lt; g &lt; 2\15<br /> | |||
</td> | |||
<td>3\24 (1\8) &lt; g &lt; 5\39<br /> | |||
</td> | |||
<td>5\39 &lt; g &lt; 7\54<br /> | |||
</td> | |||
<td>3g-1\3<br /> | |||
</td> | |||
<td>-5g+2\3<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><span style="line-height: 1.5;">16L</span>8s<br /> | |||
</td> | |||
<td>1\24 &lt; g &lt; 1\16<br /> | |||
</td> | |||
<td>1\24 &lt; g &lt; 2\40 (1\20)<br /> | |||
</td> | |||
<td>2\40 (1\20) &lt; g &lt; 3\56<br /> | |||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td><span style="line-height: 1.5;">1\8</span>-<span style="line-height: 1.5;">2g</span><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><span style="line-height: 1.5;">17L</span>7s<br /> | |||
</td> | |||
<td>17\24 &lt; g &lt; 12\17<br /> | |||
</td> | |||
<td>17\24 &lt; g &lt; 29\41<br /> | |||
</td> | |||
<td>29\41 &lt; g &lt; 41\58<br /> | |||
</td> | |||
<td>-7g+4<br /> | |||
</td> | |||
<td>17g-12<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><span style="line-height: 1.5;">18L</span>6s<br /> | |||
</td> | |||
<td>1\24 &lt; g &lt; 1\18<br /> | |||
</td> | |||
<td>1\24 &lt; g &lt; 2\42 (1\21)<br /> | |||
</td> | |||
<td>2\42 (1\21) &lt; g &lt; 3\60 (1\20)<br /> | |||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td><span style="line-height: 1.5;">1\6-3</span>g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><span style="line-height: 1.5;">19L</span>5s<br /> | |||
</td> | |||
<td>19\24 &lt; g &lt; 15\19<br /> | |||
</td> | |||
<td>19\24 &lt; g &lt; 34\43<br /> | |||
</td> | |||
<td>34\43 &lt; g &lt; 49\62<br /> | |||
</td> | |||
<td>-5g+4<br /> | |||
</td> | |||
<td><span style="line-height: 1.5;">-15+19g</span><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><span style="line-height: 1.5;">20L</span>4s<br /> | |||
</td> | |||
<td>1\24 &lt; g &lt; 1\20<br /> | |||
</td> | |||
<td>1\24 &lt; g &lt; 2\44 (1\22)<br /> | |||
</td> | |||
<td>2\44 (1\22) &lt; g &lt; 3\64<br /> | |||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>-5g+1\4<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><span style="line-height: 1.5;">21L</span>3s<br /> | |||
</td> | |||
<td>1\24 &lt; g &lt; 1\21<br /> | |||
</td> | |||
<td>1\24 &lt; g &lt; 2\45<br /> | |||
</td> | |||
<td>2\45 &lt; g &lt; 3\66 (1\22)<br /> | |||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>-7g+1\3<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><span style="line-height: 1.5;">22L</span>2s<br /> | |||
</td> | |||
<td>1\24 &lt; g &lt; 1\22<br /> | |||
</td> | |||
<td>1\24 &lt; g &lt; 2\46 (1\23)<br /> | |||
</td> | |||
<td>2\46 (1\23) &lt; g &lt; 3\68<br /> | |||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>-11g+1\2<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>23L1s<br /> | |||
</td> | |||
<td>1\24 &lt; g &lt; 1\23<br /> | |||
</td> | |||
<td>1\24 &lt; g &lt; 2\47<br /> | |||
</td> | |||
<td>2\47 &lt; g &lt; 3\70<br /> | |||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>-23g+1<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:46:&lt;h1&gt; --><h1 id="toc23"><a name="x25"></a><!-- ws:end:WikiTextHeadingRule:46 -->25</h1> | |||
<table class="wiki_table"> | |||
<tr> | |||
<td>Large-small numbers<br /> | |||
</td> | |||
<td>Generator range<br /> | |||
</td> | |||
<td>Range of propriety<br /> | |||
</td> | |||
<td>Range of maximum expressiveness<br /> | |||
</td> | |||
<td>Large step<br /> | |||
</td> | |||
<td>Small step<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1L24s<br /> | |||
</td> | |||
<td>24\25 &lt; g &lt; 1<br /> | |||
</td> | |||
<td>24\25 &lt; g &lt; 25\26<br /> | |||
</td> | |||
<td>25\26 &lt; g &lt; 26\27<br /> | |||
</td> | |||
<td>-23+24g<br /> | |||
</td> | |||
<td>-g+1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>2L23s<br /> | |||
</td> | |||
<td>12\25 &lt; g &lt; 1\2<br /> | |||
</td> | |||
<td>12\25 &lt; g &lt; 13\27<br /> | |||
</td> | |||
<td>13\27 &lt; g &lt; 14\29<br /> | |||
</td> | |||
<td>23g-11<br /> | |||
</td> | |||
<td>1-2g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3L22s<br /> | |||
</td> | |||
<td>8\25 &lt; g &lt; 1\3<br /> | |||
</td> | |||
<td>8\25 &lt; g &lt; 9\28<br /> | |||
</td> | |||
<td>9\28 &lt; g &lt; <span style="line-height: 1.5;">10\31</span><br /> | |||
</td> | |||
<td>-7+22g<br /> | |||
</td> | |||
<td>1-3g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4L21s<br /> | |||
</td> | |||
<td>6\25 &lt; g &lt; 1\4<br /> | |||
</td> | |||
<td>6\25 &lt; g &lt; 7\29<br /> | |||
</td> | |||
<td>7\29 &lt; g &lt; 8\33<br /> | |||
</td> | |||
<td>-5+21g<br /> | |||
</td> | |||
<td>-4g+1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>5L20s<br /> | |||
</td> | |||
<td>4\25 &lt; g &lt; 1\5<br /> | |||
</td> | |||
<td>4\25 &lt; g &lt; 5\30 (1\6)<br /> | |||
</td> | |||
<td>5\30 (1\6) &lt; g &lt; 6\35<br /> | |||
</td> | |||
<td>-3\5+4g<br /> | |||
</td> | |||
<td>1\5-g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>6L19s<br /> | |||
</td> | |||
<td>4\25 &lt; g &lt; 1\6<br /> | |||
</td> | |||
<td>4\25 &lt; g &lt; 5\31<br /> | |||
</td> | |||
<td>5\31 &lt; g &lt; 6\37<br /> | |||
</td> | |||
<td>-3+19g<br /> | |||
</td> | |||
<td>-6g+1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>7L18s<br /> | |||
</td> | |||
<td>7\25 &lt; g &lt; 2\7<br /> | |||
</td> | |||
<td>7\25 &lt; g &lt; 9\32<br /> | |||
</td> | |||
<td>9\32 &lt; g &lt; 11\39<br /> | |||
</td> | |||
<td>-5+18g<br /> | |||
</td> | |||
<td>-7g+2<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>8L17s<br /> | |||
</td> | |||
<td>3\25 &lt; g &lt; 1\8<br /> | |||
</td> | |||
<td>3\25 &lt; g &lt; 4\33<br /> | |||
</td> | |||
<td>4\33 &lt; g &lt; 5\41<br /> | |||
</td> | |||
<td><span style="line-height: 1.5;">17g-2</span><br /> | |||
</td> | |||
<td>1-8g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>9L16s<br /> | |||
</td> | |||
<td>11\25 &lt; g &lt; 4\9<br /> | |||
</td> | |||
<td>11\25 &lt; g &lt; 15\34<br /> | |||
</td> | |||
<td>15\34 &lt; g &lt; 19\43<br /> | |||
</td> | |||
<td>-7+16g<br /> | |||
</td> | |||
<td><span style="line-height: 1.5;">-9g+4</span><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>10L15s<br /> | |||
</td> | |||
<td>2\25 &lt; g &lt; 1\10<br /> | |||
</td> | |||
<td>2\25 &lt; g &lt; 3\35<br /> | |||
</td> | |||
<td>3\35 &lt; g &lt; 4\45<br /> | |||
</td> | |||
<td>-1\5+3g<br /> | |||
</td> | |||
<td>1\5-2g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>11L14s<br /> | |||
</td> | |||
<td>9\25 &lt; g &lt; 4\11<br /> | |||
</td> | |||
<td>9\25 &lt; g &lt; 13\36<br /> | |||
</td> | |||
<td>13\36 &lt; g &lt; 17\47<br /> | |||
</td> | |||
<td>14g-5<br /> | |||
</td> | |||
<td>-11g+4<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>12L13s<br /> | |||
</td> | |||
<td>2\25 &lt; g &lt; 1\12<br /> | |||
</td> | |||
<td>2\25 &lt; g &lt; 3\37<br /> | |||
</td> | |||
<td>3\37 &lt; g &lt; 4\49<br /> | |||
</td> | |||
<td>13g-1<br /> | |||
</td> | |||
<td>1-12g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>13L12s<br /> | |||
</td> | |||
<td>23\25 &lt; g &lt; 12\13<br /> | |||
</td> | |||
<td>23\25 &lt; g &lt; 35\38<br /> | |||
</td> | |||
<td>35\38 &lt; g &lt; 47\51<br /> | |||
</td> | |||
<td>12g-11<br /> | |||
</td> | |||
<td>12-13g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>14L11s<br /> | |||
</td> | |||
<td>16\25 &lt; g &lt; 9\14<br /> | |||
</td> | |||
<td>16\25 &lt; g &lt; 25\39<br /> | |||
</td> | |||
<td>25\39 &lt; g &lt; 34\53<br /> | |||
</td> | |||
<td>-7+11g<br /> | |||
</td> | |||
<td>-14g+9<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>15L10s<br /> | |||
</td> | |||
<td>2\25 &lt; g &lt; 1\15<br /> | |||
</td> | |||
<td>1\25 &lt; g &lt; 3<span style="line-height: 1.5;">\40</span><br /> | |||
</td> | |||
<td><span style="line-height: 1.5;">3\40</span> &lt; g &lt; 4\55<br /> | |||
</td> | |||
<td>-2g+1\5<br /> | |||
</td> | |||
<td>3g-1\5<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>16L9s<br /> | |||
</td> | |||
<td>14\25 &lt; g &lt; 9\16<br /> | |||
</td> | |||
<td>14\25 &lt; g &lt; 23\41<br /> | |||
</td> | |||
<td>23\41 &lt; g &lt; 32\57<br /> | |||
</td> | |||
<td>9g-5<br /> | |||
</td> | |||
<td>9-16g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>17L8s<br /> | |||
</td> | |||
<td>22\25 &lt; g &lt; 15\17<br /> | |||
</td> | |||
<td>22\25 &lt; g &lt; 37\42<br /> | |||
</td> | |||
<td>37\42 &lt; g &lt; 52\59<br /> | |||
</td> | |||
<td>8g-7<br /> | |||
</td> | |||
<td>-17g+15<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>18L7s<br /> | |||
</td> | |||
<td>18\25 &lt; g &lt; 13\18<br /> | |||
</td> | |||
<td>18\25 &lt; g &lt; 31\43<br /> | |||
</td> | |||
<td>31\43 &lt; g &lt; 44\61<br /> | |||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>1\6-3g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>19L6s<br /> | |||
</td> | |||
<td>21\25 &lt; g &lt; 16\19<br /> | |||
</td> | |||
<td>21\25 &lt; g &lt; 37\44<br /> | |||
</td> | |||
<td>37\44 &lt; g &lt; 53\63<br /> | |||
</td> | |||
<td>-19g+16<br /> | |||
</td> | |||
<td>-5+6g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>20L5s<br /> | |||
</td> | |||
<td>1\25 &lt; g &lt; 1\20<br /> | |||
</td> | |||
<td>1\25 &lt; g &lt; 2\45<br /> | |||
</td> | |||
<td>2\45 &lt; g &lt; 3\65<br /> | |||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>-4g+1\5<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>21L4s<br /> | |||
</td> | |||
<td>16\21 &lt; g &lt; 19\25<br /> | |||
</td> | |||
<td>19\25 &lt; g &lt; 35\46<br /> | |||
</td> | |||
<td>35\46 &lt; g &lt; 51\67<br /> | |||
</td> | |||
<td>4g-3<br /> | |||
</td> | |||
<td>-21g+16<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>22L3s<br /> | |||
</td> | |||
<td>17\25 &lt; g &lt; 15\22<br /> | |||
</td> | |||
<td>17\25 &lt; g &lt; 32\47<br /> | |||
</td> | |||
<td>32\47 &lt; g &lt; 47\69<br /> | |||
</td> | |||
<td>3g-2<br /> | |||
</td> | |||
<td>-22g+15<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>23L2s<br /> | |||
</td> | |||
<td>13\25 &lt; g &lt; 12\23<br /> | |||
</td> | |||
<td>13\25 &lt; g &lt; 23\48<br /> | |||
</td> | |||
<td>23\48 &lt; g &lt; 35\71<br /> | |||
</td> | |||
<td>-2g+1<br /> | |||
</td> | |||
<td>23g-11<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>24L1s<br /> | |||
</td> | |||
<td>1\25 &lt; g &lt; 1\24<br /> | |||
</td> | |||
<td>1\25 &lt; g &lt; 2\49<br /> | |||
</td> | |||
<td>2\49 &lt; g &lt; 3\73<br /> | |||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>-24g+1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
Revision as of 22:14, 3 February 2015
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author JosephRuhf and made on 2015-02-03 22:14:57 UTC.
- The original revision id was 539625988.
- The revision comment was:
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Original Wikitext content:
Below are ranges of generators for various L-s patterns of MOS, with the number of steps in the scale from 2 to 29. The ranges are given in fractions of the interval of equivalence, which is normally an octave. The tables give the range of possible generators in the second column, normalized so that the lower end of the range is where L/s = 1 (Nedo.) The third column gives the range of propriety, where the proper MOS reside. If the number of the [[Interval class|generic interval]] to which the generator g belongs is C, and there are N scale steps to the interval of equivalence, then the average the size of an interval in class C is C/N. We have normalized so that C/N is the lower bound of the range of generators; since therefore g > C/N, g is larger than average and hence is the larger of the two sizes of intervals in its class, which means we have normalized to the [[Modal UDP Notation|chroma-positive]] generator. =2= || Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || || 1L1s || 1\2 < g < 1 || 1\2 < g < 2\3 || 2\3 < g < 3\4 || g || 1-g || =3= || Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || || 1L2s || 2\3 < g < 1 || 2\3 < g < 3\4 || 3\4 < g < 4\5 || 2g-1 || 1-g || || 2L1s || 1\3 < g < 1\2 || 1\3 < g < 2\5 || 2\5 < g < 3\7 || g || 1-2g || =4= || Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || || 1L3s || 3\4 < g < 1 || 3\4 < g < 4\5 || 4\5 < g < 5\6 || 3g-2 || 1-g || || 2L2s || 1\4 < g < 1\2 || 1\4 < g < 2\6 (1\3) || 2\6 (1/3) < g < 3\8 || g || 1\2-g || || 3L1s || 1\4 < g < 1\3 || 1\4 < g < 2\7 || 2\7 < g < 3\10 || g || 1-3g || =5= || Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || || 1L4s || 4\5 < g < 1 || 4\5 < g < 5\6 || 5\6 < g < 6\7 || -3+4g || -g+1 || || 2L3s || 2\5 < g < 1\2 || 2\5 < g < 3\7 || 3\7 < g < 4\9 || -1+3g || -2g+1 || || 3L2s || 3\5 < g < 2\3 || 3\5 < g < 5\8 || 5\8 < g < 7\11 || -1+2g || -3g+2 || || 4L1s || 1\5 < g < 1\4 || 1\5 < g < 2\9 || 2\9 < g < 3\13 || g || -4g+1 || =6= || Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || || 1L5s || 5\6 < g < 1 || 5\6 < g < 6\7 || 6\7 < g < 7\8 || 5g-4 || 1-g || || 2L4s || 2\6 (1\3) < g < 1\2 || 2\6 (1\3) < g < 4\10 (2\5) || 4\10 (2\5) < g < 5\12 || 2g-1\2 || 1\2-g || || 3L3s || 1\6 < g < 1\3 || 1\6 < g < 2\9 || 2\9 < g < 3\12 (1\4) || g || 1\3-g || || 4L2s || 1\6 < g < 1\4 || 1\6 < g < 2\10 (1\5) || 2\10 (1\5) < g < 3\14 || g || 1\2-2g || || 5L1s || 1\6 < g < 1\5 || 1\6 < g < 2\11 || 2\11 < g < 3\16 || g || 1-5g || =7= || Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || || 1L6s || 6\7 < g < 1 || 6\7 < g < 7\8 || 7\8 < g < 8\9 || 6g-5 || 1-g || || 2L5s || 3\7 < g < 1\2 || 3\7 < g < 4\9 || 4\9 < g < 5\11 || 5g-2 || 1-2g || || 3L4s || 2\7 < g < 1\3 || 2\7 < g < 3\10 || 3\10 < g < 4\13 || 4g-1 || 1-3g || || 4L3s || 5\7 < g < 3\4 || 5\7 < g < 8\11 || 8\11 < g < 11\15 || 3g-2 || 3-4g || || 5L2s || 4\7 < g < 3\5 || 4\7 < g < 7\12 || 7\12 < g < 10\17 || 2g-1 || 3-5g || || 6L1s || 1\7 < g < 1\6 || 1\7 < g < 2\13 || 2\13 < g < 3\19 || g || 1-6g || =8= || Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || || 1L7s || 7\8 < g < 1 || 7\8 < g < 8\9 || 8\9 < g < 9\10 || 7g-6 || 1-g || || 2L6s || 3\8 < g < 1\2 || 3\8 < g < 4\10 (2\5) || 4\10 (2\5) < g < 5\12 || 3g-1 || 1\2-g || || 3L5s || 5\8 < g < 2\3 || 5\8 < g < 7\11 || 7\11 < g < 9\14 || 5g-3 || 2-3g || || 4L4s || 1\8 < g < 1\4 || 1\8 < g < 2\12 (1\6) || 2\12 (1\6) < g < 3\16 || g || 1\4-g || || 5L3s || 3\8 < g < 2\5 || 3\8 < g < 5\13 || 5\13 < g < 7\18 || 3g-1 || 2-5g || || 6L2s || 1\8 < g < 1\6 || 1\8 < g < 2\14 (1\7) || 2\14 (1\7) < g < 3\20 || g || 1\2-3g || || 7L1s || 1\8 < g < 1\7 || 1\8 < g < 2\15 || 2\15 < g < 3\22 || g || 1-7g || =9= || Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || || 1L8s || 8\9 < g < 1 || 8\9 < g < 9\10 || 9\10 < g < 10\11 || 8g-7 || 1-g || || 2L7s || 4\9 < g < 1\2 || 4\9 < g < 5\11 || 5\11 < g < 6\13 || 7g-3 || 1-2g || || 3L6s || 2\9 < g < 1\3 || 2\9 < g < 3\12 (1\4) || 3\12 (1\4) < g < 4\15 || 2g-1\3 || 1\3-g || || 4L5s || 2\9 < g < 1\4 || 2\9 < g < 3\13 || 3\13 < g < 4\17 || 5g-1 || 1-4g || || 5L4s || 7\9 < g < 4\5 || 7\9 < g < 11\14 || 11\14 < g < 15\19 || 4g-3 || 4-5g || || 6L3s || 1\9 < g < 1\6 || 1\9 < g < 2\15 || 2\15 < g < 3\21 (1\7) || g || 1\3-2g || || 7L2s || 5\9 < g < 4\7 || 5\9 < g < 9\16 || 9\16 < g < 10\23 || 2g-1 || 4-7g || || 8L1s || 1\9 < g < 1\8 || 1\9 < g < 2\17 || 217 < g < 3\25 || g || 1-8g || =10= || Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || || 1L9s || 9\10 < g < 1 || 9\10 < g < 10\11 || 10\11 < g < 11\12 || -8+9g || -g+1 || || 2L8s || 4\10 (2\5) < g < 1\2 || 4\10 (2\5) < g < 5\12 || 5\12 < g < 6\14 (3\7) || -3\2+4g || -g+1\2 || || 3L7s || 3\10 < g < 1\3 || 3\10 < g < 4\13 || 4\13 < g < 5\16 || -2+7g || 1-3g || || 4L6s || 2\10 (1\5) < g < 1\4 || 2\10 (1\5) < g < 3\14 || 3\14 < g < 4\18 (2\9) || 3g-1\2 || -2g+1\2 || || 5L5s || 1\10 < g < 1\5 || 1\10 < g < 2\15 || 2\15 < g < 3\20 || g || -g+1\5 || || 6L4s || 3\10 < g < 2\6 (1\3) || 3\10 < g < 5\16 || 5\16 < g < 7\22 || -1\2+2g || 1-3g || || 7L3s || 7\10 < g < 5\7 || 7\10 < g < 12\17 || 12\17 < g < 17\24 || -2+3g || -7g+5 || || 8L2s || 1\10 < g < 1\8 || 1\10 < g < 2\18 (1\9) || 2\18 (1\9) < g < 3\26 || g || -4g+1\2 || || 9L1s || 1\10 < g < 1\9 || 1\10 < g < 2\19 || 2\19 < g < 3\28 || g || -9g+1 || =11= || Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || || 1L10s || 10\11 < g < 1 || 10\11 < g < 11\12 || 11\12 < g < 12\13 || -9+10g || -g+1 || || 2L9s || 5\11 < g < 1\2 || 5\11 < g < 6\13 || 6\13 < g < 7\15 || -4+9g || -2g+1 || || 3L8s || 7\11 < g < 2\3 || 7\11 < g < 9\14 || 9\14 < g < 11\17 || -5+8g || -3g+2 || || 4L7s || 8\11 < g < 3\4 || 8\11 < g < 11\15 || 11\15 < g < 14\19 || -5+7g || -4g+3 || || 5L6s || 2\11 < g < 1\5 || 2\11 < g < 3\16 || 3\16 < g < 4\21 || -1+6g || -5g+1 || || 6L5s || 9\11 < g < 5\6 || 9\11 < g < 14\17 || 14\17 < g < 19\23 || -4+5g || -6g+5 || || 7L4s || 3\11 < g < 2\7 || 3\11 < g < 5\18 || 5\18 < g < 7\25 || -1+4g || -7g+2 || || 8L3s || 4\11 < g < 3\8 || 4\11 < g < 7\19 || 7\19 < g < 10\27 || -1+3g || -8g+3 || || 9L2s || 6\11 < g < 5\9 || 6\11 < g < 11\20 || 11\20 < g < 16\29 || -1+2g || -9g+5 || || 10L1s || 1\11 < g < 1\10 || 1\11 < g < 2\21 || 2\21 < g < 3\31 || g || -10g+1 || =12= || Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || || 1L11s || 11\12 < g < 1 || 11\12 < g < 12\13 || 12\13 < g < 13\14 || 11g-10 || 1-g || || 2L10s || 5\12 < g < 1\2 || 5\12 < g < 6\14 (3\7) || 6\14 (3\7) < g < 7\16 || 5g-2 || 1\2-g || || 3L9s || 3\12 (1\4) < g < 3\9 (1\3) || 3\12 (1\4) < g < 4\15 || 4\15 < g < 5\18 || 3g-2\3 || 1\3-g || || 4L8s || 2\12 (1\6) < g < 1\4 || 2/12 (1\6) < g < 3\16 || 3\16 < g < 4\20 (1\5) || 2g-1\4 || 1\4-g || || 5L7s || 7\12 < g < 3\5 || 7\12 < g < 10\17 || 10\17 < g < 13\22 || 7g-4 || 3-5g || || 6L6s || 1\12 < g < 1\6 || 1\12 < g < 2\18 (1\9) || 2\18 (1\9) < g < 3\24 (1\8) || g || 1\6-g || || 7L5s || 5\12 < g < 3\7 || 5\12 < g < 8\19 || 8\19 < g < 11\26 || 5g-2 || 3-7g || || 8L4s || 1\12 < g < 1\8 || 1\12 < g < 2\20 (1\10) || 2\20 (1\10) < g < 3\28 || g || 1\4-2g || || 9L3s || 1\12 < g < 1\9 || 1\12 < g < 2\21 || 2\21 < g < 3\30 (1\10) || g || 1\3-3g || || 10L2s || 1\12 < g < 1\10 || 1\12 < g < 2\22 (1\11) || 2\22 (1/11) < g < 3\32 || g || 1\2-5g || || 11L1s || 1\12 < g < 1\11 || 1\12 < g < 2\23 || 2\23 < g < 3\34 || g || 1-11g || =13= || Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || || 1L12s || 12\13 < g < 1 || 12\13 < g < 13\14 || 13\14 < g < 14\15 || 12g-11 || 1-g || || 2L11s || 6\13 < g < 1\2 || 6\13 < g < 7\15 || 7\15 < g < 8\17 || 11g-5 || 1-2g || || 3L10s || 4\13 < g < 1\3 || 4\13 < g < 5\16 || 5\16 < g < 6\19 || 10g-3 || 1-3g || || 4L9s || 3\13 < g < 1\4 || 3\13 < g < 4\17 || 4\17 < g < 5\21 || 9g-2 || 1-4g || || 5L8s || 5\13 < g < 2\5 || 5\13 < g < 7\18 || 7\18 < g < 9\23 || 8g-3 || 2-5g || || 6L7s || 2\13 < g < 1\6 || 2\13 < g < 3\19 || 3\19 < g < 4\25 || 7g-1 || 1-6g || || 7L6s || 11\13 < g < 6\7 || 11\13 < g < 17\20 || 17\20 < g < 23\27 || 6g-5 || 6-7g || || 8L5s || 8\13 < g < 5\8 || 8\13 < g < 13\21 || 13\21 < g < 18\29 || 5g-3 || 5-8g || || 9L4s || 10\13 < g < 7\9 || 10\13 < g < 17\22 || 17\22 < g < 24\31 || 4g-3 || 7-9g || || 10L3s || 9\13 < g < 7\10 || 9\13 < g < 16\23 || 16\23 < g < 23\33 || 3g-2 || 7-10g || || 11L2s || 7\13 < g < 6\11 || 7\13 < g < 13\24 || 13\24 < g < 19\35 || 2g-1 || 6-11g || || 12L1s || 1\13 < g < 1\12 || 1\13 < g < 2\25 || 2\25 < g < 3\37 || g || 1-12g || =14= || Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || || 1L13s || 13\14 < g < 1 || 13\14 < g < 14\15 || 14\15 < g < 15\16 || -12+13g || -g+1 || || 2L12s || 6\14 (3\7) < g < 1\2 || 6\14 (3\7) < g < 7\16 || 7\16 < g < 8\18 (4\9) || -5\2+6g || -g+1\2 || || 3L11s || 9\14 < g < 2\3 || 9\14 < g < 11\17 || 11\17 < g < 13\20 || -7+11g || -3g+2 || || 4L10s || 3\14 < g < 1\4 || 3\14 < g < 4\18 (2\9) || 4\18 (2\9) < g < 5\22 || -1+5g || -2g+1\2 || || 5L9s || 11\14 < g < 4\5 || 11\14 < g < 15\19 || 15\19 < g < 19\24 || -7+9g || -5g+4 || || 6L8s || 2\14 (1\7) < g < 1\6 || 2\14 (1\7) < g < 3\20 || 3\20 < g < 4\26 (2\13) || 4g-1\2 || -3g+1\2 || || 7L7s || 1\14 < g < 1\7 || 1\14 < g < 2\21 || 2\21 < g < 3\28 || g || -g+1\7 || || 8L6s || 5\14 < g < 3\8 || 5\14 < g < 8\22 (4\11) || 8\22 (4\11) < g < 11\30 || -1+3g || -4g+3\2 || || 9L5s || 3\14 < g < 2\9 || 3\14 < g < 5\23 || 5\23 < g < 7\32 || -1+5g || -9g+2 || || 10L4s || 4\14 (2\7) < g < 3\10 || 4\14 (2\7) < g < 7\24 || 7\24 < g < 10\34 (5\17) || -1\2+2g || -5g+3\2 || || 11L3s || 5\14 < g < 4\11 || 5\14 < g < 9\25 || 9\25 < g < 13\36 || -1+3g || -11g+4 || || 12L2s || 1\14 < g < 1\12 || 1\14 < g < 2\26 (1\13) || 2\26 (1\13) < g < 3\38 || g || -6g+1\2 || || 13L1s || 1\14 < g < 1\13 || 1\14 < g < 2\27 || 2\27 < g < 3\40 || g || -13g+1 || =15= || Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || || 1L14s || 14\15 < g < 1 || 14\15 < g < 15\16 || 15\16 < g < 16\17 || -13+14g || -g+1 || || 2L13s || 7\15 < g < 1\2 || 7\15 < g < 8\17 || 8\17 < g < 9\19 || -6+13g || -2g+1 || || 3L12s || 4\15 < g < 1\3 || 4\15 < g < 5\18 || 5\18 < g < 6\21 (2\7) || -1+4g || -g+1\3 || || 4L11s || 11\15 < g < 3\4 || 11\15 < g < 14\19 || 14\19 < g < 17\23 || -8+11g || -4g+3 || || 5L10s || 2\15 < g < 1\5 || 2\15 < g < 3\20 || 3\20 < g < 4\25 || -1\5+2g || -g+1\5 || || 6L9s || 2\15 < g < 1\6 || 2\15 < g < 3\21 (1\7) || 3\21 (1\7) < g < 4\27 || -1\3+3g || -2g+1\3 || || 7L8s || 2\15 < g < 1\7 || 2\15 < g < 3\22 || 3\22 < g < 4\29 || -1+8g || -7g+1 || || 8L7s || 13\15 < g < 7\8 || 13\15 < g < 20\23 || 20\23 < g < 27\31 || -6+7g || -8g+7 || || 9L6s || 3\15 (1\5) < g < 2\9 || 3\15 (1\5) < g < 5\24 || 5\24 < g < 7\33 || -1\3+2g || -3g+2\3 || || 10L5s || 1\15 < g < 1\10 || 1\15 < g < 2\25 || 2\25 < g < 3\35 || g || -2g+1\5 || || 11L4s || 4\15 < g < 3\11 || 4\15 < g < 7\26 || 7\26 < g < 10\37 || -1+4g || -11g+3 || || 12L3s || 1\15 < g < 1\12 || 1\15 < g < 2\27 || 2\27 < g < 3\39 (1\13) || g || -4g+1\3 || || 13L2s || 8\15 < g < 7\13 || 8\15 < g < 15\28 || 15\28 < g < 22\41 || -1+2g || -13g+7 || || 14L1s || 1\15 < g < 1\14 || 1\15 < g < 2\29 || 2\29 < g < 3\43 || g || -14g+1 || =16= || Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || || 1L15s || 15\16 < g < 1 || 15\16 < g < 16\17 || 16\17 < g < 17\18 || -14+15g || -g+1 || || 2L14s || 7\16 < g < 1\2 || 7\16 < g < 8\18 (4\9) || 8\18 (4\9) < g < 9\20 || -3+7g || -g+1\2 || || 3L13s || 5\16 < g < 1\3 || 5\16 < g < 6\19 || 6\19 < g < 7\22 || -4+13g || 1-3g || || 4L12s || 3\16 < g < 1\4 || 3\16 < g < 4\20 (1\5) || 4\20 (1\5) < g < 5\24 || 3g-1\2 || -g+1\4 || || 5L11s || 3\16 < g < 1\5 || 3\16 < g < 4\21 || 4\21 < g < 5\26 || -2+11g || -5g+1 || || 6L10s || 5\16 < g < 2\6 (1\3) || 5\16 < g < 7\22 || 7\22 < g < 9\28 || -3\2+5g || 1-3g || || 7L9s || 9\16 < g < 4\7 || 9\16 < g < 13\23 || 13\23 < g < 17\30 || -5+9g || -7g+4 || || 8L8s || 1\16 < g < 1\8 || 1\16 < g < 2\24 (1\12) || 2\24 (1\12) < g < 3\32 || g || -g+1\8 || || 9L7s || 7\16 < g < 4\9 || 7\16 < g < 11\25 || 11\25 < g < 15\34 || -3+7g || -9g+4 || || 10L6s || 3\16 < g < 2\10 (1\5) || 3\16 < g < 5\26 || 5\26 < g < 7\36 || 3g-1\2 || -5g+1 || || 11L5s || 13\16 < g < 9\11 || 13\16 < g < 22\27 || 22\27 < g < 31\38 || -4+5g || -11g+9 || || 12L4s || 1\16 < g < 1\12 || 1\16 < g < 2\28 (1\14) || 2\28 (1\14) < g < 3\40 || g || -3g+1\4 || || 13L3s || 11\16 < g < 9\13 || 11\16 < g < 20\29 || 20\29 < g < 29\42 || -2+3g || -13g+9 || || 14L2s || 1\16 < g < 1\14 || 1\16 < g < 2\30 (1\15) || 2\30 (1\15) < g < 3\44 || g || -7g+1\2 || || 15L1s || 1\16 < g < 1\15 || 1\16 < g < 2\31 || 2\31 < g < 3\46 || g || -15g+1 || =17= || Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || || 1L16s || 16\17 < g < 1 || 16\17 < g < 17\18 || 17\18 < g < 18\19 || -15+16g || -g+1 || || 2L15s || 8\17 < g < 1\2 || 8\17 < g < 9\19 || 9\19 < g < 10\21 || -7+15g || -2g+1 || || 3L14s || 11\17 < g < 2\3 || 11\17 < g < 13\20 || 13\20 < g < 15\23 || -9+14g || -3g+2 || || 4L13s || 4\17 < g < 1\4 || 4\17 < g < 5\21 || 5\21 < g < 6\25 || -3+13g || -4g+1 || || 5L12s || 10\17 < g < 3\5 || 10\17 < g < 13\22 || 13\22 < g < 16\27 || -7+12g || -5g+3 || || 6L11s || 14\17 < g < 5\6 || 14\17 < g < 19\23 || 19\23 < g < 24\29 || -9+11g || -6g+5 || || 7L10s || 12\17 < g < 5\7 || 12\17 < g < 17\24 || 17\24 < g < 22\31 || -7+10g || -7g+5 || || 8L9s || 2\17 < g < 1\8 || 2\17 < g < 3\25 || 3\25 < g < 4\33 || -1+9g || -8g+1 || || 9L8s || 15\17 < g < 8\9 || 15\17 < g < 23\26 || 23\26 < g < 31\35 || -7+8g || -9g+8 || || 10L7s || 5\17 < g < 3\10 || 5\17 < g < 8\27 || 8\27 < g < 11\37 || -2+7g || -10g+3 || || 11L6s || 3\17 < g < 2\11 || 3\17 < g < 5\28 || 5\28 < g < 7\39 || -1+6g || -11g+2 || || 12L5s || 7\17 < g < 5\12 || 7\17 < g < 12\29 || 12\29 < g < 17\41 || -2+5g || -12g+5 || || 13L4s || 13\17 < g < 10\13 || 13\17 < g < 23\30 || 23\30 < g < 33\43 || -3+4g || -13g+10 || || 14L3s || 6\17 < g < 5\14 || 6\17 < g < 11\31 || 11\31 < g < 16\45 || -1+3g || -14g+5 || || 15L2s || 9\17 < g < 8\15 || 9\17 < g < 17\32 || 17\32 < g < 25\47 || -1+2g || -15g+8 || || 16L1s || 1\17 < g < 1\16 || 1\17 < g < 2\33 || 2\33 < g < 3\49 || g || -16g+1 || =18= || Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || || 1L17s || 17\18 < g < 1 || 17\18 < g < 18\19 || 18\19 < g < 19\20 || -16+17g || -g+1 || || 2L16s || 8\18 (4\9) < g < 1\2 || 8\18 (4\9) < g < 9\20 || 9\20 < g < 10\22 (5\11) || -7\2+8g || -g+1\2 || || 3L15s || 5\18 < g < 1\3 || 5\18 < g < 6\21 (2\7) || 6\21 (2\7) < g < 7\24 || -4\3+5g || -g+1\3 || || 4L14s || <span style="line-height: 1.5;">4\18</span> (<span style="line-height: 1.5;">2\9) < g < 1\4</span> || <span style="line-height: 1.5;">4\18</span> (<span style="line-height: 1.5;">2\9) < g < 5\22</span> || <span style="line-height: 15.6000003814697px;">5\22 < g < 6\26 (3\13)</span> || -3\2+7g || -2g+1\2 || || 5L13s || 7\18 < g < 2\5 || 7\18 < g < 9\23 || 9\23 < g < 11\28 || -5+13g || -5g+2 || || 6L12s || 2\18 (1\9) < g < 1\6 || 2\18 (1\9) < g < 3\24 (1\8) || 3\24 (1\8) < g < 4\30 (2\15) || -1\6+2g || -g+1\6 || || 7L11s || 5\18 < g < 2\7 || 5\18 < g < 7\25 || 7\25 < g < 9\32 || -3+11g || -7g+2 || || 8L10s || 2\18 (1\9) < g < 1\8 || 2\18 (1\9) < g < 3\26 || 3\26 < g < 4\34 (2\17) || -1\2+5g || -4g+1\2 || || 9L9s || 1\18 < g < 1\9 || 1\18 < g < 2\27 || 2\27 < g < 3\36 (1\12) || g || -g+1\9 || || 10L8s || 7\18 < g < 4\10 (2\5) || 7\18 < g < 11\28 || 11\28 < g < 15\38 || -3\2+4g || -5g+2 || || 11L7s || 13\18 < g < 8\11 || 13\18 < g < 21\29 || 21\29 < g < 29\37 || -5+7g || -11g+8 || || 12L6s || 1\18 < g < 1\12 || 1\18 < g < 2\30 (1\15) || 2\30 (1\15) < g < 3\42 (1\14) || g || -2g+1\6 || || 13L5s || 11\18 < g < 8\13 || 11\18 < g < 19\31 || 19\31 < g < 27\44 || -3+5g || -13g+8 || || 14L4s || 5\18 < g < 4\14 (2\7) || 5\18 < g < 9\32 || 9\32 < g < 11\46 || -1\2+2g || -7g+2 || || 15L3s || 1\18 < g < 1\15 || 1\18 < g < 2\33 || 2\33 < g < 3\48 (1\16) || g || -5g+1\3 || || 16L2s || 1\18 < g < 1\16 || 1\18 < g < 2\34 (1\17) || 2\34 (1\17) < g < 3\50 || g || -8g+1\2 || || 17L1s || 1\18 < g < 1\17 || 1\18 < g < 2\35 || 2\35 < g < 3\52 || g || -17g+1 || =19= || Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || || 1L18s || 18\19 < g < 1 || 18\19 < g < 19\20 || 19\20 < g < 20\21 || -17+18g || -g+1 || || 2L17s || 9\19 < g < 1\2 || 9\19 < g < 10\21 || 10\21 < g < 11\23 || -8+17g || -2g+1 || || 3L16s || 6\19 < g < 1\3 || 6\19 < g < 7\22 || 7\22 < g < 8\25 || -5+16g || 1-3g || || 4L15s || 14\19 < g < 3\4 || 14\19 < g < 17\23 || 17\23 < g < 20\27 || -11+15g || -4g+3 || || 5L14s || 15\19 < g < 4\5 || 15\19 < g < 19\24 || 19\24 < g < 23\29 || -11+14g || -5g+4 || || 6L13s || 3\19 < g < 1\6 || 3\19 < g < 4\25 || 4\25 < g < 5\31 || -2+13g || -6g+1 || || 7L12s || 8\19 < g < 3\7 || 8\19 < g < 11\26 || 11\26 < g < 14\33 || -5+12g || -7g+3 || || 8L11s || 7\19 < g < 3\8 || 7\19 < g < 10\27 || 10\27 < g < 13\35 || -4+11g || -8g+3 || || 9L10s || 2\19 < g < 1\9 || 2\19 < g < 3\28 || 3\28 < g < 4\37 || -1+10g || -9g+1 || || 10L9s || 17\19 < g < 9\10 || 17\19 < g < 26\29 || 26\29 < g < 35\39 || -8+9g || -10g+9 || || 11L8s || 12\19 < g < 7\11 || 12\19 < g < 19\30 || 19\30 < g < 26\41 || -5+8g || -11g+7 || || 12L7s || 11\19 < g < 7\12 || 11\19 < g < 18\31 || 18\31 < g < 25\43 || -4+7g || -12g+7 || || 13L6s || 16\19 < g < 11\13 || 16\19 < g < 27\32 || 27\32 < g < 38\45< || -5+6g || -13g+11 || || 14L5s || 4\19 < g < 3\14 || 4\19 < g < 7\33 || 7\33 < g < 10\47 || -1+5g || -14g+3 || || 15L4s || 5\19 < g < 4\15 || 5\19 < g < 9\34 || 9\34 < g < 13\49 || -1+4g || -15g+4 || || 16L3s || 13\19 < g < 11\16 || 13\19 < g < 24\35 || 24\35 < g < 35\51 || -2+3g || -16g+11 || || 17L2s || 10\19 < g < 9\17 || 10\19 < g < 19\36 || 19\36 < g < 26\53 || -1+2g || -17g+9 || || 18L1s || 1\19 < g < 1\18 || 1\19 < g < 2\37 || 2\37 < g < 3\55 || g || -18g+1 || =20= || Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || || 1L19s || 19\20 < g < 1 || 19\20 < g < 20\21 || 20\21 < g < 21\22 || -18+19g || -g+1 || || 2L18s || 9\20 < g < 1\2 || 9\20 < g < 10\22 (5\11) || 10\22 (5\11) < g < 11\24 || -4+9g || -g+1\2 || || 3L17s || 13\20 < g < 2\3 || 13\20 < g < 15\23 || 15\23 < g < 17\26 || -11+17g || -3g+2 || || 4L16s || 4\20 (1\5) < g < 1\4 || 4\20 (1\5) < g < 5\24 || 5\24 < g < 6\28 (3\14) || -3\4+4g || -g+1\4 || || 5L15s || 3\20 < g < 1\5 || 3\20 < g < 4\25 || 4\25 < g < 5\30 (1\6) || -2\5+3g || -g+1\5 || || 6L14s || 3\20 < g < 1\6 || 3\20 < g < 4\26 (2\13) || 4\26 (2\13) < g < 5\32 || -1+7g || -3g+1\2 || || 7L13s || 17\20 < g < 6\7 || 17\20 < g < 23\27 || 23\27 < g < 29\34 || -11+13g || -7g+6 || || 8L12s || 2\20 (1\10) < g < 1\8 || 2\20 (1\10) < g < 3\28 || 3\28 < g < 4\36 (1\9) || -1\4+3g || -2g+1\4 || || 9L11s || 11\20 < g < 5\9 || 11\20 < g < 16\29 || 16\29 < g < 21\38 || -6+11g || -9g+5 || || 10L10s || 1\20 < g < 1\10 || 1\20 < g < 2\30 (1\15) || 2\30 (1\15) < g < 3\40 || g || -g+1\10 || || 11L9s || 9\20 < g < 5\11 || 9\20 < g < 14\31 || 14\31 < g < 19\42 || -4+9g || -11g+5 || || 12L8s || 3\20 < g < 2\12 (1\6) || 3\20 < g < 5\32 || 5\32 < g < 7\44 || -1\4+2g || -3g+1\2 || || 13L7s || 3\20 < g < 2\13 || 3\20 < g < 5\33 || 5\33 < g < 7\46 || -1+7g || -13g+2 || || 14L6s || 7\20 < g < 5\14 || 7\20 < g < 12\34 (6\17) || 12\34 (6\17) < g < 17\48 || -1+3g || -7g+5\2 || || 15L5s || 1\20 < g < 1\15 || 1\20 < g < 2\35 || 2\35 < g < 3\50 || g || -3g+1\5 || || 16L4s || 1\20 < g < 1\16 || 1\20 < g < 2\36 (1\18) || 2\36 (1\18) < g < 3\52 || g || -4g+1\4 || || 17L3s || 7\20 < g < 6\17 || 7\20 < g < 13\37 || 13\37 < g < 19\54 || -1+3g || -17g+6 || || 18L2s || 1\20 < g < 1\18 || 1\20 < g < 2\38 (1\19) || 2\38 (1\19) < g < 3\56 || g || -9g+1\2 || || 19L1s || 1\20 < g < 1\19 || 1\20 < g < 2\39 || 2\39 < g < 3\58 || g || -19g+1 || =21= || Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || || 1L20s || 20\21 < g < 1 || 20\21 < g < 21\22 || 21\22 < g < 22\23 || -19+20g || -g+1 || || 2L19s || 10\21 < g < 1\2 || 10\21 < g < 11\23 || 11\23 < g < 12\25 || -9+19g || -2g+1 || || 3L18s || 6\21 (2\7) < g < 1\3 || 6\21 (2\7) < g < 7\24 || 7\24 < g < 8\27 || -5\3+6g || -g+1\3 || || 4L17s || 5\21 < g < 1\4 || 5\21 < g < 6\25 || 6\25 < g < 7\29 || -4+17g || -4g+1 || || 5L16s || 4\21 < g < 1\5 || 4\21 < g < 5\26 || 5\26 < g < 6\31 || -3+16g || -5g+1 || || 6L15s || 3\21 (1\7) < g < 1\6 || 3\21 (1\7) < g < 4\27 || 4\27 < g < 5\33 || -2\3+5g || -2g+1\3 || || 7L14s || 2\21 < g < 1\7 || 2\21 < g < 3\28 || 3\28 < g < 4\35 || -1\7+2g || -g+1\7 || || 8L13s || 13\21 < g < 5\8 || 13\21 < g < 18\29 || 18\29 < g < 23\37 || -8+13g || -8g+5 || || 9L12s || 2\21 < g < 1\9 || 2\21 < g < 3\30 (1\10) || 3\30 (1\10) < g < 4\39 || -1\3+4g || -3g+1\3 || || 10L11s || 2\21 < g < 1\10 || 2\21 < g < 3\31 || 3\31 < g < 4\41 || -1+11g || -10g+1 || || 11L10s || 19\21 < g < 10\11 || 19\21 < g < 29\32 || 29\32 < g < 39\43 || -9+10g || -11g+10 || || 12L9s || 5\21 < g < 3\12 (1\4) || 5\21 < g < 6\33 (2\11) || 6\33 (2\11) < g < 7\45 || -2\3+3g || -4g+1 || || 13L8s || 8\21 < g < 5\13 || 8\21 < g < 13\34 || 13\34 < g < 18\47 || -3+8g || -13g+5 || || 14L7s || 1\21 < g < 1\14 || 1\21 < g < 2\35 || 2\35 < g < 3\49 || g || -2g+1\7 || || 15L6s || 4\21 < g < 3\15 (1\5) || 4\21 < g < 7\36 || 7\36 < g < 10\51 || -1\3+2g || -5g+1 || || 16L5s || 17\21 < g < 13\16 || 17\21 < g < 30\37 || 30\37 < g < 43\53 || -4+5g || -16g+13 || || 17L4s || 16\21 < g < 13\17 || 16\21 < g < 29\38 || 29\38 < g < 42\55 || -3+4g || -17g+13 || || 18L3s || 1\21 < g < 1\18 || 1\21 < g < 2\39 || 2\39 < g < 3\57 (1\19) || g || -6g+1\3 || || 19L2s || 11\21 < g < 10\19 || 11\21 < g < 21\40 || 21\40 < g < 31\59 || -1+2g || -19g+10 || || 20L1s || 1\21 < g < 1\20 || 1\21 < g < 2\41 || 2\41 < g < 3\61 || g || -20g+1 || =22= || Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || || 1L21s || 21\22 < g < 1 || 21\22 < g < 22\23 || 22\23 < g < 23\24 || -20+21g || -g+1 || || 2L20s || 10\22 (5\11) < g < 1\2 || 10\22 (5\11) < g < 11\24 || 11\24 < g < 12\26 (6\13) || -9\2+10g || -g+1\2 || || 3L19s || 7\22 < g < 1\3 || 7\22 < g < 8\25 || 8\25 < g < 9\28 || -6+19g || 1-3g || || 4L18s || 5\22 < g < 1\4 || 5\22 < g < 6\26 (3\13) || 6\26 (3\13) < g < 7\30 || -2+9g || -2g+1\2 || || 5L17s || 13\22 < g < 3\5 || 13\22 < g < 16\27 || 16\27 < g < 19\32 || -10+17g || -5g+3 || || 6L16s || 7\22 < g < 2\6 (1\3) || 7\22 < g < 9\28 || 9\28 < g < 11\34 || -5\2+8g || 1-3g || || 7L15s || 3\22 < g < 1\7 || 3\22 < g < 4\29 || 4\29 < g < 5\36 || -2+15g || -7g+1 || || 8L14s || 8\22 (4\11) < g < 3\8 || 8\22 (4\11) < g < 11\30 || 11\30 < g < 14\38 (7\19) || -5\2+7g || -4g+3\2 || || 9L13s || 17\22 < g < 7\9 || 17\22 < g < 24\31 || 24\31 < g < 31\40 || -10+13g || -9g+7 || || 10L12s || 2\22 (1\11) < g < 1\10 || 2\22 (1\11) < g < 3\32 || 3\32 < g < 4\42 (2\21) || -1\2+6g || -5g+1\2 || || 11L11s || 1\22 < g < 1\11 || 1\22 < g < 2\33 || 2\33 < g < 3\44 || g || -g+1\11 || || 12L10s || 9\22 < g < 5\12 || 9\22 < g < 14\34 (7\17) || 14\34 (7\17) < g < 19\46 || -2+5g || -6g+5\2 || || 13L9s || 5\22 < g < 3\13 || 5\22 < g < 8\35 || 8\35 < g < 11\48 || -2+9g || -13g+3 || || 14L8s || 3\22 < g < 2\14 (1\7) || 3\22 < g < 5\36 || 5\36 < g < 7\50 || 4g-1\2 || -7g+1 || || 15L7s || 19\22 < g < 13\15 || 19\22 < g < 32\37 || 32\37 < g < 45\52 || -6+7g || -15g+13 || || 16L6s || 4\22 (2\11) < g < 3\16 || 4\22 (2\11) < g < 7\38 || 7\38 < g < 10\54 (5\27) || 3g-1\2 || -8g+3\2 || || 17L5s || 9\22 < g < 7\17 || 9\22 < g < 16\39 || 16\39 < g < 23\56 || -2+5g || -17g+7 || || 18L4s || 6\22 (3\11) < g < 5\18 || 6\22 (3\11) < g < 11\40 || 11\40 < g < 16\58 (8\29) || -1\2+2g || -9g+5\2 || || 19L3s || 15\22 < g < 13\19 || 15\22 < g < 28\41 || 28\41 < g < 41\60 || -2+3g || -19g+13 || || 20L2s || 1\22 < g < 1\20 || 1\22 < g < 2\42 (1\21) || 2\42 (1\21) < g < 3\62 || g || -10g+1\2 || || 21L1s || 1\22 < g < 1\21 || 1\22 < g < 2\43 || 2\43 < g < 3\64 || g || -21g+1 || =23= || Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || || 1L22s || <span style="line-height: 1.5;">22\23 < g < 1</span> || <span style="line-height: 1.5;">22\23</span> < g < 23\24 || <span style="line-height: 1.5;">23\24 </span>< g < 24\25 || -21+22g || -g+1 || || 2L21s || 11\23 < g < 1\2 || <span style="line-height: 15.6000003814697px;">11\23</span> < g < <span style="line-height: 1.5;">12\25</span> || 12\25 < g < 13\27 || -10+21g || -2g+1 || || 3L20s || 15\23 < g < 2\3 || 15\23 < g < 17\26 || <span style="line-height: 1.5;">17\26</span> < g < 19\29 || -13+20g || 1-3g || || 4L19s || 17\23 < g < 3\4 || <span style="line-height: 1.5;">17\23</span> < g < 20\27 || <span style="line-height: 15.6000003814697px;">20</span>\27 < g < 23<span style="line-height: 1.5;">\31</span> || -14+19g || -4g+3 || || 5L18s || 9\23 < g < 2\5 || 9\23 < g < 11\28 || 11\28 < g < 13\33 || -7+18g || -5g+2 || || 6L17s || 19\23 < g < 5\6 || 19\23 < g < 24\29 || 24\29 < g < 29\35 || -15+17g || 1-6g || || 7L16s || 13\23 < g < 4\7 || 13\23 < g < 17\30 || <span style="line-height: 1.5;">17\30</span> < g < 21\37 || -9+16g || -7g+4 || || 8L15s || 20\23 < g < 7\8 || 20\23 < g < 27\31 || 27\31 < g < 34\39 || -13+15g || -8g+7 || || 9L14s || <span style="line-height: 1.5;">18\23</span> < g < 11<span style="line-height: 1.5;">\14</span> || 18\23 < g < 29\37 || 29\37 < g < 47\60 || 9g-7 || <span style="line-height: 1.5;">11-14g</span> || || 10L13s || 16\23 < g < 7\10 || 16\23 < g < 23\33 || 23\33 < g < 30\43 || -9+13g || -10g+7 || || 11L12s || 2\23 < g < 1\11 || 2\23 < g < 3\34 || 3\34 < g < 4\45 || -11g+1 || 12g-1 || || 12L11s || 21\23 < g < 11\12 || 21\23 < g < 32\35 || 32\35 < g < 43\47 || <span style="line-height: 1.5;">11g-10</span> || 11-12g || || 13L10s || 7\23 < g < 4\13 || 7\23 < g < 11\36 || 11\36 < g < 15\49 || 4-13g || 10g-3 || || 14L9s || 5\23 < g < 2\9 || 5\23 < g < 7\32 || 7\32 < g < 9\41 || 14g-3 || -9g+2 || || 15L8s || 3\23 < g < 2\15 || 3\23 < g < 5\38 || 5\38 < g < 7\53 || 2-15g || 8g-1 || || 16L7s || 10\23 < g < 7\16 || 10\23 < g < 17\39 || 17\39 < g < 24\55 || 7g-3 || <span style="line-height: 1.5;">-16g+7</span> || || 17L6s || 4\23 < g < 3\17 || 4\23 < g < 7\40 || 7\40 < g < 10\57 || -1+6g || -17g+3 || || 18L5s || 14\23 < g < <span style="line-height: 1.5;">11\18</span> || 14\23 < g < 25\41 || 25\41 < g < 36\59 || 11-18g || 5g-4 || || 19L4s || 6\23 < g < 5\19 || 6\23 < g < 11\42 || 11\42 < g < 16\61 || -1+4g || -19g+5 || || 20L3s || 8\23 < g < 7\20 || 8\23 < g < 15\43 || 15\43 < g < 22\63 || -1+3g || -20g+13 || || 21L2s || 12\23 < g < 11\21 || 12\23 < g < 23\44 || 23\44 < g < 34\65 || -1+2g || -21g+1 || || 22L1s || 1\23 < g < 1\22 || 1\23 < g < 2\45 || 2\45 < g < 3\67 || g || -22g+1 || =24= || Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || || 1L23s || 23\24 < g < 1 || 23\24 < g < 24\25 || 24\25 < g < 25\26 || -22+23g || -g+1 || || 2L<span style="line-height: 1.5;">22s</span> || 11\24 < g < 1\2 || 11\24 < g < 12\26 (6\13) || 12\26 (6\13) < g < 15\28 || <span style="line-height: 1.5;">-g+1/2</span> || -5+11g || || 3L<span style="line-height: 1.5;">21s</span> || 7\24 < g < 1\3 || 7\24 < g < 8\27 || 8\27 < g < 9\30 (3\10) || -2+7g || <span style="line-height: 1.5;">-</span>1/3+g || || 4L<span style="line-height: 1.5;">20s</span> || 5\24 < g < 1\4 || 5\24 < g < 6\28 (3\14) || 6\28 (3\14) < g < 7\32 || -1+5g || -g+1/4 || || 5L<span style="line-height: 1.5;">19s</span> || 19\24 < g < 4\5 || 19\24 < g < 23\29 || 23\29 < g < 27\34 || -15+19g || -5g+4 || || 6L<span style="line-height: 1.5;">18s</span> || 3\24 (1\8) < g < 1\6 || 3\24 (1\8) < g < 4\30 (2\15) || 4\30 (2\15) < g < 5\36 || -1\3+3g || 1\6-g || || 7L<span style="line-height: 1.5;">17s</span> || 17\24 < g < 5\7 || 17\24 < g < 22\31 || 22\31 < g < 27\38 || 5-17g || 7g-2 || || 8L<span style="line-height: 1.5;">16s</span> || 2\24 (1\12) < g < 1\8 || 2\24 (1\12) < g < 3\32 || 3\32 < g < 4\40 (1\10) || -1\8+2g || -g+1\8 || || 9L<span style="line-height: 1.5;">15s</span> || 5\24 < g < 2\9 || 5\24 < g < 7\33 || 7\33 < g < 9\42 (3\14) || 5g-1 || 2\3-3g || || 10L<span style="line-height: 1.5;">14s</span> || 7\24 < g < 3\10 || 7\24 < g < 10\34 (5\17) || 10\34 (5\17) < g < 13\44 || <span style="line-height: 1.5;">-4+7g</span> || -3\2+5g || || 11L<span style="line-height: 1.5;">13s</span> || 13\24 < g < 6\11 || 13\24 < g < 19\35 || 19\35 < g < 25\46 || 13g-7 || -11g+6 || || 12L12s || 1\24 < g < 1\12 || 1\24 < g < 2\36 (1\18) || 2\36 (1\18) < g < 3\48 (1\16) || g || 1\12-g || || <span style="line-height: 1.5;">13L</span>11s || 11\24 < g < 6\13 || 11\24 < g < 17\37 || 17\37 < g < 23\50 || 11g-5 || 6-13g || || <span style="line-height: 1.5;">14L</span>10s || 7\24 < g < 4\14 (2\7) || 7\24 < g < 11\38 || 11\38 < g < 15\52 || 3\2-5g || 7g-2 || || <span style="line-height: 1.5;">15L</span>9s || 3\24 (1\8) < g < 2\15 || 3\24 (1\8) < g < 5\39 || 5\39 < g < 7\54 || 3g-1\3 || -5g+2\3 || || <span style="line-height: 1.5;">16L</span>8s || 1\24 < g < 1\16 || 1\24 < g < 2\40 (1\20) || 2\40 (1\20) < g < 3\56 || g || <span style="line-height: 1.5;">1\8</span>-<span style="line-height: 1.5;">2g</span> || || <span style="line-height: 1.5;">17L</span>7s || 17\24 < g < 12\17 || 17\24 < g < 29\41 || 29\41 < g < 41\58 || -7g+4 || 17g-12 || || <span style="line-height: 1.5;">18L</span>6s || 1\24 < g < 1\18 || 1\24 < g < 2\42 (1\21) || 2\42 (1\21) < g < 3\60 (1\20) || g || <span style="line-height: 1.5;">1\6-3</span>g || || <span style="line-height: 1.5;">19L</span>5s || 19\24 < g < 15\19 || 19\24 < g < 34\43 || 34\43 < g < 49\62 || -5g+4 || <span style="line-height: 1.5;">-15+19g</span> || || <span style="line-height: 1.5;">20L</span>4s || 1\24 < g < 1\20 || 1\24 < g < 2\44 (1\22) || 2\44 (1\22) < g < 3\64 || g || -5g+1\4 || || <span style="line-height: 1.5;">21L</span>3s || 1\24 < g < 1\21 || 1\24 < g < 2\45 || 2\45 < g < 3\66 (1\22) || g || -7g+1\3 || || <span style="line-height: 1.5;">22L</span>2s || 1\24 < g < 1\22 || 1\24 < g < 2\46 (1\23) || 2\46 (1\23) < g < 3\68 || g || -11g+1\2 || || 23L1s || 1\24 < g < 1\23 || 1\24 < g < 2\47 || 2\47 < g < 3\70 || g || -23g+1 || =25= || Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || || 1L24s || 24\25 < g < 1 || 24\25 < g < 25\26 || 25\26 < g < 26\27 || -23+24g || -g+1 || || 2L23s || 12\25 < g < 1\2 || 12\25 < g < 13\27 || 13\27 < g < 14\29 || 23g-11 || 1-2g || || 3L22s || 8\25 < g < 1\3 || 8\25 < g < 9\28 || 9\28 < g < <span style="line-height: 1.5;">10\31</span> || -7+22g || 1-3g || || 4L21s || 6\25 < g < 1\4 || 6\25 < g < 7\29 || 7\29 < g < 8\33 || -5+21g || -4g+1 || || 5L20s || 4\25 < g < 1\5 || 4\25 < g < 5\30 (1\6) || 5\30 (1\6) < g < 6\35 || -3\5+4g || 1\5-g || || 6L19s || 4\25 < g < 1\6 || 4\25 < g < 5\31 || 5\31 < g < 6\37 || -3+19g || -6g+1 || || 7L18s || 7\25 < g < 2\7 || 7\25 < g < 9\32 || 9\32 < g < 11\39 || -5+18g || -7g+2 || || 8L17s || 3\25 < g < 1\8 || 3\25 < g < 4\33 || 4\33 < g < 5\41 || <span style="line-height: 1.5;">17g-2</span> || 1-8g || || 9L16s || 11\25 < g < 4\9 || 11\25 < g < 15\34 || 15\34 < g < 19\43 || -7+16g || <span style="line-height: 1.5;">-9g+4</span> || || 10L15s || 2\25 < g < 1\10 || 2\25 < g < 3\35 || 3\35 < g < 4\45 || -1\5+3g || 1\5-2g || || 11L14s || 9\25 < g < 4\11 || 9\25 < g < 13\36 || 13\36 < g < 17\47 || 14g-5 || -11g+4 || || 12L13s || 2\25 < g < 1\12 || 2\25 < g < 3\37 || 3\37 < g < 4\49 || 13g-1 || 1-12g || || 13L12s || 23\25 < g < 12\13 || 23\25 < g < 35\38 || 35\38 < g < 47\51 || 12g-11 || 12-13g || || 14L11s || 16\25 < g < 9\14 || 16\25 < g < 25\39 || 25\39 < g < 34\53 || -7+11g || -14g+9 || || 15L10s || 2\25 < g < 1\15 || 1\25 < g < 3<span style="line-height: 1.5;">\40</span> || <span style="line-height: 1.5;">3\40</span> < g < 4\55 || -2g+1\5 || 3g-1\5 || || 16L9s || 14\25 < g < 9\16 || 14\25 < g < 23\41 || 23\41 < g < 32\57 || 9g-5 || 9-16g || || 17L8s || 22\25 < g < 15\17 || 22\25 < g < 37\42 || 37\42 < g < 52\59 || 8g-7 || -17g+15 || || 18L7s || 18\25 < g < 13\18 || 18\25 < g < 31\43 || 31\43 < g < 44\61 || g || 1\6-3g || || 19L6s || 21\25 < g < 16\19 || 21\25 < g < 37\44 || 37\44 < g < 53\63 || -19g+16 || -5+6g || || 20L5s || 1\25 < g < 1\20 || 1\25 < g < 2\45 || 2\45 < g < 3\65 || g || -4g+1\5 || || 21L4s || 16\21 < g < 19\25 || 19\25 < g < 35\46 || 35\46 < g < 51\67 || 4g-3 || -21g+16 || || 22L3s || 17\25 < g < 15\22 || 17\25 < g < 32\47 || 32\47 < g < 47\69 || 3g-2 || -22g+15 || || 23L2s || 13\25 < g < 12\23 || 13\25 < g < 23\48 || 23\48 < g < 35\71 || -2g+1 || 23g-11 || || 24L1s || 1\25 < g < 1\24 || 1\25 < g < 2\49 || 2\49 < g < 3\73 || g || -24g+1 ||
Original HTML content:
<html><head><title>Generator ranges of MOS</title></head><body>Below are ranges of generators for various L-s patterns of MOS, with the number of steps in the scale from 2 to 29. The ranges are given in fractions of the interval of equivalence, which is normally an octave. The tables give the range of possible generators in the second column, normalized so that the lower end of the range is where L/s = 1 (Nedo.) The third column gives the range of propriety, where the proper MOS reside.<br />
<br />
If the number of the <a class="wiki_link" href="/Interval%20class">generic interval</a> to which the generator g belongs is C, and there are N scale steps to the interval of equivalence, then the average the size of an interval in class C is C/N. We have normalized so that C/N is the lower bound of the range of generators; since therefore g > C/N, g is larger than average and hence is the larger of the two sizes of intervals in its class, which means we have normalized to the <a class="wiki_link" href="/Modal%20UDP%20Notation">chroma-positive</a> generator.<br />
<br />
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<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Range of maximum expressiveness<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L1s<br />
</td>
<td>1\2 < g < 1<br />
</td>
<td>1\2 < g < 2\3<br />
</td>
<td>2\3 < g < 3\4<br />
</td>
<td>g<br />
</td>
<td>1-g<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="x3"></a><!-- ws:end:WikiTextHeadingRule:2 -->3</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Range of maximum expressiveness<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L2s<br />
</td>
<td>2\3 < g < 1<br />
</td>
<td>2\3 < g < 3\4<br />
</td>
<td>3\4 < g < 4\5<br />
</td>
<td>2g-1<br />
</td>
<td>1-g<br />
</td>
</tr>
<tr>
<td>2L1s<br />
</td>
<td>1\3 < g < 1\2<br />
</td>
<td>1\3 < g < 2\5<br />
</td>
<td>2\5 < g < 3\7<br />
</td>
<td>g<br />
</td>
<td>1-2g<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="x4"></a><!-- ws:end:WikiTextHeadingRule:4 -->4</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Range of maximum expressiveness<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L3s<br />
</td>
<td>3\4 < g < 1<br />
</td>
<td>3\4 < g < 4\5<br />
</td>
<td>4\5 < g < 5\6<br />
</td>
<td>3g-2<br />
</td>
<td>1-g<br />
</td>
</tr>
<tr>
<td>2L2s<br />
</td>
<td>1\4 < g < 1\2<br />
</td>
<td>1\4 < g < 2\6 (1\3)<br />
</td>
<td>2\6 (1/3) < g < 3\8<br />
</td>
<td>g<br />
</td>
<td>1\2-g<br />
</td>
</tr>
<tr>
<td>3L1s<br />
</td>
<td>1\4 < g < 1\3<br />
</td>
<td>1\4 < g < 2\7<br />
</td>
<td>2\7 < g < 3\10<br />
</td>
<td>g<br />
</td>
<td>1-3g<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="x5"></a><!-- ws:end:WikiTextHeadingRule:6 -->5</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Range of maximum expressiveness<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L4s<br />
</td>
<td>4\5 < g < 1<br />
</td>
<td>4\5 < g < 5\6<br />
</td>
<td>5\6 < g < 6\7<br />
</td>
<td>-3+4g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L3s<br />
</td>
<td>2\5 < g < 1\2<br />
</td>
<td>2\5 < g < 3\7<br />
</td>
<td>3\7 < g < 4\9<br />
</td>
<td>-1+3g<br />
</td>
<td>-2g+1<br />
</td>
</tr>
<tr>
<td>3L2s<br />
</td>
<td>3\5 < g < 2\3<br />
</td>
<td>3\5 < g < 5\8<br />
</td>
<td>5\8 < g < 7\11<br />
</td>
<td>-1+2g<br />
</td>
<td>-3g+2<br />
</td>
</tr>
<tr>
<td>4L1s<br />
</td>
<td>1\5 < g < 1\4<br />
</td>
<td>1\5 < g < 2\9<br />
</td>
<td>2\9 < g < 3\13<br />
</td>
<td>g<br />
</td>
<td>-4g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="x6"></a><!-- ws:end:WikiTextHeadingRule:8 -->6</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Range of maximum expressiveness<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L5s<br />
</td>
<td>5\6 < g < 1<br />
</td>
<td>5\6 < g < 6\7<br />
</td>
<td>6\7 < g < 7\8<br />
</td>
<td>5g-4<br />
</td>
<td>1-g<br />
</td>
</tr>
<tr>
<td>2L4s<br />
</td>
<td>2\6 (1\3) < g < 1\2<br />
</td>
<td>2\6 (1\3) < g < 4\10 (2\5)<br />
</td>
<td>4\10 (2\5) < g < 5\12<br />
</td>
<td>2g-1\2<br />
</td>
<td>1\2-g<br />
</td>
</tr>
<tr>
<td>3L3s<br />
</td>
<td>1\6 < g < 1\3<br />
</td>
<td>1\6 < g < 2\9<br />
</td>
<td>2\9 < g < 3\12 (1\4)<br />
</td>
<td>g<br />
</td>
<td>1\3-g<br />
</td>
</tr>
<tr>
<td>4L2s<br />
</td>
<td>1\6 < g < 1\4<br />
</td>
<td>1\6 < g < 2\10 (1\5)<br />
</td>
<td>2\10 (1\5) < g < 3\14<br />
</td>
<td>g<br />
</td>
<td>1\2-2g<br />
</td>
</tr>
<tr>
<td>5L1s<br />
</td>
<td>1\6 < g < 1\5<br />
</td>
<td>1\6 < g < 2\11<br />
</td>
<td>2\11 < g < 3\16<br />
</td>
<td>g<br />
</td>
<td>1-5g<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:10:<h1> --><h1 id="toc5"><a name="x7"></a><!-- ws:end:WikiTextHeadingRule:10 -->7</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Range of maximum expressiveness<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L6s<br />
</td>
<td>6\7 < g < 1<br />
</td>
<td>6\7 < g < 7\8<br />
</td>
<td>7\8 < g < 8\9<br />
</td>
<td>6g-5<br />
</td>
<td>1-g<br />
</td>
</tr>
<tr>
<td>2L5s<br />
</td>
<td>3\7 < g < 1\2<br />
</td>
<td>3\7 < g < 4\9<br />
</td>
<td>4\9 < g < 5\11<br />
</td>
<td>5g-2<br />
</td>
<td>1-2g<br />
</td>
</tr>
<tr>
<td>3L4s<br />
</td>
<td>2\7 < g < 1\3<br />
</td>
<td>2\7 < g < 3\10<br />
</td>
<td>3\10 < g < 4\13<br />
</td>
<td>4g-1<br />
</td>
<td>1-3g<br />
</td>
</tr>
<tr>
<td>4L3s<br />
</td>
<td>5\7 < g < 3\4<br />
</td>
<td>5\7 < g < 8\11<br />
</td>
<td>8\11 < g < 11\15<br />
</td>
<td>3g-2<br />
</td>
<td>3-4g<br />
</td>
</tr>
<tr>
<td>5L2s<br />
</td>
<td>4\7 < g < 3\5<br />
</td>
<td>4\7 < g < 7\12<br />
</td>
<td>7\12 < g < 10\17<br />
</td>
<td>2g-1<br />
</td>
<td>3-5g<br />
</td>
</tr>
<tr>
<td>6L1s<br />
</td>
<td>1\7 < g < 1\6<br />
</td>
<td>1\7 < g < 2\13<br />
</td>
<td>2\13 < g < 3\19<br />
</td>
<td>g<br />
</td>
<td>1-6g<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:12:<h1> --><h1 id="toc6"><a name="x8"></a><!-- ws:end:WikiTextHeadingRule:12 -->8</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Range of maximum expressiveness<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L7s<br />
</td>
<td>7\8 < g < 1<br />
</td>
<td>7\8 < g < 8\9<br />
</td>
<td>8\9 < g < 9\10<br />
</td>
<td>7g-6<br />
</td>
<td>1-g<br />
</td>
</tr>
<tr>
<td>2L6s<br />
</td>
<td>3\8 < g < 1\2<br />
</td>
<td>3\8 < g < 4\10 (2\5)<br />
</td>
<td>4\10 (2\5) < g < 5\12<br />
</td>
<td>3g-1<br />
</td>
<td>1\2-g<br />
</td>
</tr>
<tr>
<td>3L5s<br />
</td>
<td>5\8 < g < 2\3<br />
</td>
<td>5\8 < g < 7\11<br />
</td>
<td>7\11 < g < 9\14<br />
</td>
<td>5g-3<br />
</td>
<td>2-3g<br />
</td>
</tr>
<tr>
<td>4L4s<br />
</td>
<td>1\8 < g < 1\4<br />
</td>
<td>1\8 < g < 2\12 (1\6)<br />
</td>
<td>2\12 (1\6) < g < 3\16<br />
</td>
<td>g<br />
</td>
<td>1\4-g<br />
</td>
</tr>
<tr>
<td>5L3s<br />
</td>
<td>3\8 < g < 2\5<br />
</td>
<td>3\8 < g < 5\13<br />
</td>
<td>5\13 < g < 7\18<br />
</td>
<td>3g-1<br />
</td>
<td>2-5g<br />
</td>
</tr>
<tr>
<td>6L2s<br />
</td>
<td>1\8 < g < 1\6<br />
</td>
<td>1\8 < g < 2\14 (1\7)<br />
</td>
<td>2\14 (1\7) < g < 3\20<br />
</td>
<td>g<br />
</td>
<td>1\2-3g<br />
</td>
</tr>
<tr>
<td>7L1s<br />
</td>
<td>1\8 < g < 1\7<br />
</td>
<td>1\8 < g < 2\15<br />
</td>
<td>2\15 < g < 3\22<br />
</td>
<td>g<br />
</td>
<td>1-7g<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:14:<h1> --><h1 id="toc7"><a name="x9"></a><!-- ws:end:WikiTextHeadingRule:14 -->9</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Range of maximum expressiveness<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L8s<br />
</td>
<td>8\9 < g < 1<br />
</td>
<td>8\9 < g < 9\10<br />
</td>
<td>9\10 < g < 10\11<br />
</td>
<td>8g-7<br />
</td>
<td>1-g<br />
</td>
</tr>
<tr>
<td>2L7s<br />
</td>
<td>4\9 < g < 1\2<br />
</td>
<td>4\9 < g < 5\11<br />
</td>
<td>5\11 < g < 6\13<br />
</td>
<td>7g-3<br />
</td>
<td>1-2g<br />
</td>
</tr>
<tr>
<td>3L6s<br />
</td>
<td>2\9 < g < 1\3<br />
</td>
<td>2\9 < g < 3\12 (1\4)<br />
</td>
<td>3\12 (1\4) < g < 4\15<br />
</td>
<td>2g-1\3<br />
</td>
<td>1\3-g<br />
</td>
</tr>
<tr>
<td>4L5s<br />
</td>
<td>2\9 < g < 1\4<br />
</td>
<td>2\9 < g < 3\13<br />
</td>
<td>3\13 < g < 4\17<br />
</td>
<td>5g-1<br />
</td>
<td>1-4g<br />
</td>
</tr>
<tr>
<td>5L4s<br />
</td>
<td>7\9 < g < 4\5<br />
</td>
<td>7\9 < g < 11\14<br />
</td>
<td>11\14 < g < 15\19<br />
</td>
<td>4g-3<br />
</td>
<td>4-5g<br />
</td>
</tr>
<tr>
<td>6L3s<br />
</td>
<td>1\9 < g < 1\6<br />
</td>
<td>1\9 < g < 2\15<br />
</td>
<td>2\15 < g < 3\21 (1\7)<br />
</td>
<td>g<br />
</td>
<td>1\3-2g<br />
</td>
</tr>
<tr>
<td>7L2s<br />
</td>
<td>5\9 < g < 4\7<br />
</td>
<td>5\9 < g < 9\16<br />
</td>
<td>9\16 < g < 10\23<br />
</td>
<td>2g-1<br />
</td>
<td>4-7g<br />
</td>
</tr>
<tr>
<td>8L1s<br />
</td>
<td>1\9 < g < 1\8<br />
</td>
<td>1\9 < g < 2\17<br />
</td>
<td>217 < g < 3\25<br />
</td>
<td>g<br />
</td>
<td>1-8g<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:16:<h1> --><h1 id="toc8"><a name="x10"></a><!-- ws:end:WikiTextHeadingRule:16 -->10</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Range of maximum expressiveness<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L9s<br />
</td>
<td>9\10 < g < 1<br />
</td>
<td>9\10 < g < 10\11<br />
</td>
<td>10\11 < g < 11\12<br />
</td>
<td>-8+9g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L8s<br />
</td>
<td>4\10 (2\5) < g < 1\2<br />
</td>
<td>4\10 (2\5) < g < 5\12<br />
</td>
<td>5\12 < g < 6\14 (3\7)<br />
</td>
<td>-3\2+4g<br />
</td>
<td>-g+1\2<br />
</td>
</tr>
<tr>
<td>3L7s<br />
</td>
<td>3\10 < g < 1\3<br />
</td>
<td>3\10 < g < 4\13<br />
</td>
<td>4\13 < g < 5\16<br />
</td>
<td>-2+7g<br />
</td>
<td>1-3g<br />
</td>
</tr>
<tr>
<td>4L6s<br />
</td>
<td>2\10 (1\5) < g < 1\4<br />
</td>
<td>2\10 (1\5) < g < 3\14<br />
</td>
<td>3\14 < g < 4\18 (2\9)<br />
</td>
<td>3g-1\2<br />
</td>
<td>-2g+1\2<br />
</td>
</tr>
<tr>
<td>5L5s<br />
</td>
<td>1\10 < g < 1\5<br />
</td>
<td>1\10 < g < 2\15<br />
</td>
<td>2\15 < g < 3\20<br />
</td>
<td>g<br />
</td>
<td>-g+1\5<br />
</td>
</tr>
<tr>
<td>6L4s<br />
</td>
<td>3\10 < g < 2\6 (1\3)<br />
</td>
<td>3\10 < g < 5\16<br />
</td>
<td>5\16 < g < 7\22<br />
</td>
<td>-1\2+2g<br />
</td>
<td>1-3g<br />
</td>
</tr>
<tr>
<td>7L3s<br />
</td>
<td>7\10 < g < 5\7<br />
</td>
<td>7\10 < g < 12\17<br />
</td>
<td>12\17 < g < 17\24<br />
</td>
<td>-2+3g<br />
</td>
<td>-7g+5<br />
</td>
</tr>
<tr>
<td>8L2s<br />
</td>
<td>1\10 < g < 1\8<br />
</td>
<td>1\10 < g < 2\18 (1\9)<br />
</td>
<td>2\18 (1\9) < g < 3\26<br />
</td>
<td>g<br />
</td>
<td>-4g+1\2<br />
</td>
</tr>
<tr>
<td>9L1s<br />
</td>
<td>1\10 < g < 1\9<br />
</td>
<td>1\10 < g < 2\19<br />
</td>
<td>2\19 < g < 3\28<br />
</td>
<td>g<br />
</td>
<td>-9g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:18:<h1> --><h1 id="toc9"><a name="x11"></a><!-- ws:end:WikiTextHeadingRule:18 -->11</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Range of maximum expressiveness<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L10s<br />
</td>
<td>10\11 < g < 1<br />
</td>
<td>10\11 < g < 11\12<br />
</td>
<td>11\12 < g < 12\13<br />
</td>
<td>-9+10g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L9s<br />
</td>
<td>5\11 < g < 1\2<br />
</td>
<td>5\11 < g < 6\13<br />
</td>
<td>6\13 < g < 7\15<br />
</td>
<td>-4+9g<br />
</td>
<td>-2g+1<br />
</td>
</tr>
<tr>
<td>3L8s<br />
</td>
<td>7\11 < g < 2\3<br />
</td>
<td>7\11 < g < 9\14<br />
</td>
<td>9\14 < g < 11\17<br />
</td>
<td>-5+8g<br />
</td>
<td>-3g+2<br />
</td>
</tr>
<tr>
<td>4L7s<br />
</td>
<td>8\11 < g < 3\4<br />
</td>
<td>8\11 < g < 11\15<br />
</td>
<td>11\15 < g < 14\19<br />
</td>
<td>-5+7g<br />
</td>
<td>-4g+3<br />
</td>
</tr>
<tr>
<td>5L6s<br />
</td>
<td>2\11 < g < 1\5<br />
</td>
<td>2\11 < g < 3\16<br />
</td>
<td>3\16 < g < 4\21<br />
</td>
<td>-1+6g<br />
</td>
<td>-5g+1<br />
</td>
</tr>
<tr>
<td>6L5s<br />
</td>
<td>9\11 < g < 5\6<br />
</td>
<td>9\11 < g < 14\17<br />
</td>
<td>14\17 < g < 19\23<br />
</td>
<td>-4+5g<br />
</td>
<td>-6g+5<br />
</td>
</tr>
<tr>
<td>7L4s<br />
</td>
<td>3\11 < g < 2\7<br />
</td>
<td>3\11 < g < 5\18<br />
</td>
<td>5\18 < g < 7\25<br />
</td>
<td>-1+4g<br />
</td>
<td>-7g+2<br />
</td>
</tr>
<tr>
<td>8L3s<br />
</td>
<td>4\11 < g < 3\8<br />
</td>
<td>4\11 < g < 7\19<br />
</td>
<td>7\19 < g < 10\27<br />
</td>
<td>-1+3g<br />
</td>
<td>-8g+3<br />
</td>
</tr>
<tr>
<td>9L2s<br />
</td>
<td>6\11 < g < 5\9<br />
</td>
<td>6\11 < g < 11\20<br />
</td>
<td>11\20 < g < 16\29<br />
</td>
<td>-1+2g<br />
</td>
<td>-9g+5<br />
</td>
</tr>
<tr>
<td>10L1s<br />
</td>
<td>1\11 < g < 1\10<br />
</td>
<td>1\11 < g < 2\21<br />
</td>
<td>2\21 < g < 3\31<br />
</td>
<td>g<br />
</td>
<td>-10g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:20:<h1> --><h1 id="toc10"><a name="x12"></a><!-- ws:end:WikiTextHeadingRule:20 -->12</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Range of maximum expressiveness<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L11s<br />
</td>
<td>11\12 < g < 1<br />
</td>
<td>11\12 < g < 12\13<br />
</td>
<td>12\13 < g < 13\14<br />
</td>
<td>11g-10<br />
</td>
<td>1-g<br />
</td>
</tr>
<tr>
<td>2L10s<br />
</td>
<td>5\12 < g < 1\2<br />
</td>
<td>5\12 < g < 6\14 (3\7)<br />
</td>
<td>6\14 (3\7) < g < 7\16<br />
</td>
<td>5g-2<br />
</td>
<td>1\2-g<br />
</td>
</tr>
<tr>
<td>3L9s<br />
</td>
<td>3\12 (1\4) < g < 3\9 (1\3)<br />
</td>
<td>3\12 (1\4) < g < 4\15<br />
</td>
<td>4\15 < g < 5\18<br />
</td>
<td>3g-2\3<br />
</td>
<td>1\3-g<br />
</td>
</tr>
<tr>
<td>4L8s<br />
</td>
<td>2\12 (1\6) < g < 1\4<br />
</td>
<td>2/12 (1\6) < g < 3\16<br />
</td>
<td>3\16 < g < 4\20 (1\5)<br />
</td>
<td>2g-1\4<br />
</td>
<td>1\4-g<br />
</td>
</tr>
<tr>
<td>5L7s<br />
</td>
<td>7\12 < g < 3\5<br />
</td>
<td>7\12 < g < 10\17<br />
</td>
<td>10\17 < g < 13\22<br />
</td>
<td>7g-4<br />
</td>
<td>3-5g<br />
</td>
</tr>
<tr>
<td>6L6s<br />
</td>
<td>1\12 < g < 1\6<br />
</td>
<td>1\12 < g < 2\18 (1\9)<br />
</td>
<td>2\18 (1\9) < g < 3\24 (1\8)<br />
</td>
<td>g<br />
</td>
<td>1\6-g<br />
</td>
</tr>
<tr>
<td>7L5s<br />
</td>
<td>5\12 < g < 3\7<br />
</td>
<td>5\12 < g < 8\19<br />
</td>
<td>8\19 < g < 11\26<br />
</td>
<td>5g-2<br />
</td>
<td>3-7g<br />
</td>
</tr>
<tr>
<td>8L4s<br />
</td>
<td>1\12 < g < 1\8<br />
</td>
<td>1\12 < g < 2\20 (1\10)<br />
</td>
<td>2\20 (1\10) < g < 3\28<br />
</td>
<td>g<br />
</td>
<td>1\4-2g<br />
</td>
</tr>
<tr>
<td>9L3s<br />
</td>
<td>1\12 < g < 1\9<br />
</td>
<td>1\12 < g < 2\21<br />
</td>
<td>2\21 < g < 3\30 (1\10)<br />
</td>
<td>g<br />
</td>
<td>1\3-3g<br />
</td>
</tr>
<tr>
<td>10L2s<br />
</td>
<td>1\12 < g < 1\10<br />
</td>
<td>1\12 < g < 2\22 (1\11)<br />
</td>
<td>2\22 (1/11) < g < 3\32<br />
</td>
<td>g<br />
</td>
<td>1\2-5g<br />
</td>
</tr>
<tr>
<td>11L1s<br />
</td>
<td>1\12 < g < 1\11<br />
</td>
<td>1\12 < g < 2\23<br />
</td>
<td>2\23 < g < 3\34<br />
</td>
<td>g<br />
</td>
<td>1-11g<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:22:<h1> --><h1 id="toc11"><a name="x13"></a><!-- ws:end:WikiTextHeadingRule:22 -->13</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Range of maximum expressiveness<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L12s<br />
</td>
<td>12\13 < g < 1<br />
</td>
<td>12\13 < g < 13\14<br />
</td>
<td>13\14 < g < 14\15<br />
</td>
<td>12g-11<br />
</td>
<td>1-g<br />
</td>
</tr>
<tr>
<td>2L11s<br />
</td>
<td>6\13 < g < 1\2<br />
</td>
<td>6\13 < g < 7\15<br />
</td>
<td>7\15 < g < 8\17<br />
</td>
<td>11g-5<br />
</td>
<td>1-2g<br />
</td>
</tr>
<tr>
<td>3L10s<br />
</td>
<td>4\13 < g < 1\3<br />
</td>
<td>4\13 < g < 5\16<br />
</td>
<td>5\16 < g < 6\19<br />
</td>
<td>10g-3<br />
</td>
<td>1-3g<br />
</td>
</tr>
<tr>
<td>4L9s<br />
</td>
<td>3\13 < g < 1\4<br />
</td>
<td>3\13 < g < 4\17<br />
</td>
<td>4\17 < g < 5\21<br />
</td>
<td>9g-2<br />
</td>
<td>1-4g<br />
</td>
</tr>
<tr>
<td>5L8s<br />
</td>
<td>5\13 < g < 2\5<br />
</td>
<td>5\13 < g < 7\18<br />
</td>
<td>7\18 < g < 9\23<br />
</td>
<td>8g-3<br />
</td>
<td>2-5g<br />
</td>
</tr>
<tr>
<td>6L7s<br />
</td>
<td>2\13 < g < 1\6<br />
</td>
<td>2\13 < g < 3\19<br />
</td>
<td>3\19 < g < 4\25<br />
</td>
<td>7g-1<br />
</td>
<td>1-6g<br />
</td>
</tr>
<tr>
<td>7L6s<br />
</td>
<td>11\13 < g < 6\7<br />
</td>
<td>11\13 < g < 17\20<br />
</td>
<td>17\20 < g < 23\27<br />
</td>
<td>6g-5<br />
</td>
<td>6-7g<br />
</td>
</tr>
<tr>
<td>8L5s<br />
</td>
<td>8\13 < g < 5\8<br />
</td>
<td>8\13 < g < 13\21<br />
</td>
<td>13\21 < g < 18\29<br />
</td>
<td>5g-3<br />
</td>
<td>5-8g<br />
</td>
</tr>
<tr>
<td>9L4s<br />
</td>
<td>10\13 < g < 7\9<br />
</td>
<td>10\13 < g < 17\22<br />
</td>
<td>17\22 < g < 24\31<br />
</td>
<td>4g-3<br />
</td>
<td>7-9g<br />
</td>
</tr>
<tr>
<td>10L3s<br />
</td>
<td>9\13 < g < 7\10<br />
</td>
<td>9\13 < g < 16\23<br />
</td>
<td>16\23 < g < 23\33<br />
</td>
<td>3g-2<br />
</td>
<td>7-10g<br />
</td>
</tr>
<tr>
<td>11L2s<br />
</td>
<td>7\13 < g < 6\11<br />
</td>
<td>7\13 < g < 13\24<br />
</td>
<td>13\24 < g < 19\35<br />
</td>
<td>2g-1<br />
</td>
<td>6-11g<br />
</td>
</tr>
<tr>
<td>12L1s<br />
</td>
<td>1\13 < g < 1\12<br />
</td>
<td>1\13 < g < 2\25<br />
</td>
<td>2\25 < g < 3\37<br />
</td>
<td>g<br />
</td>
<td>1-12g<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:24:<h1> --><h1 id="toc12"><a name="x14"></a><!-- ws:end:WikiTextHeadingRule:24 -->14</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Range of maximum expressiveness<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L13s<br />
</td>
<td>13\14 < g < 1<br />
</td>
<td>13\14 < g < 14\15<br />
</td>
<td>14\15 < g < 15\16<br />
</td>
<td>-12+13g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L12s<br />
</td>
<td>6\14 (3\7) < g < 1\2<br />
</td>
<td>6\14 (3\7) < g < 7\16<br />
</td>
<td>7\16 < g < 8\18 (4\9)<br />
</td>
<td>-5\2+6g<br />
</td>
<td>-g+1\2<br />
</td>
</tr>
<tr>
<td>3L11s<br />
</td>
<td>9\14 < g < 2\3<br />
</td>
<td>9\14 < g < 11\17<br />
</td>
<td>11\17 < g < 13\20<br />
</td>
<td>-7+11g<br />
</td>
<td>-3g+2<br />
</td>
</tr>
<tr>
<td>4L10s<br />
</td>
<td>3\14 < g < 1\4<br />
</td>
<td>3\14 < g < 4\18 (2\9)<br />
</td>
<td>4\18 (2\9) < g < 5\22<br />
</td>
<td>-1+5g<br />
</td>
<td>-2g+1\2<br />
</td>
</tr>
<tr>
<td>5L9s<br />
</td>
<td>11\14 < g < 4\5<br />
</td>
<td>11\14 < g < 15\19<br />
</td>
<td>15\19 < g < 19\24<br />
</td>
<td>-7+9g<br />
</td>
<td>-5g+4<br />
</td>
</tr>
<tr>
<td>6L8s<br />
</td>
<td>2\14 (1\7) < g < 1\6<br />
</td>
<td>2\14 (1\7) < g < 3\20<br />
</td>
<td>3\20 < g < 4\26 (2\13)<br />
</td>
<td>4g-1\2<br />
</td>
<td>-3g+1\2<br />
</td>
</tr>
<tr>
<td>7L7s<br />
</td>
<td>1\14 < g < 1\7<br />
</td>
<td>1\14 < g < 2\21<br />
</td>
<td>2\21 < g < 3\28<br />
</td>
<td>g<br />
</td>
<td>-g+1\7<br />
</td>
</tr>
<tr>
<td>8L6s<br />
</td>
<td>5\14 < g < 3\8<br />
</td>
<td>5\14 < g < 8\22 (4\11)<br />
</td>
<td>8\22 (4\11) < g < 11\30<br />
</td>
<td>-1+3g<br />
</td>
<td>-4g+3\2<br />
</td>
</tr>
<tr>
<td>9L5s<br />
</td>
<td>3\14 < g < 2\9<br />
</td>
<td>3\14 < g < 5\23<br />
</td>
<td>5\23 < g < 7\32<br />
</td>
<td>-1+5g<br />
</td>
<td>-9g+2<br />
</td>
</tr>
<tr>
<td>10L4s<br />
</td>
<td>4\14 (2\7) < g < 3\10<br />
</td>
<td>4\14 (2\7) < g < 7\24<br />
</td>
<td>7\24 < g < 10\34 (5\17)<br />
</td>
<td>-1\2+2g<br />
</td>
<td>-5g+3\2<br />
</td>
</tr>
<tr>
<td>11L3s<br />
</td>
<td>5\14 < g < 4\11<br />
</td>
<td>5\14 < g < 9\25<br />
</td>
<td>9\25 < g < 13\36<br />
</td>
<td>-1+3g<br />
</td>
<td>-11g+4<br />
</td>
</tr>
<tr>
<td>12L2s<br />
</td>
<td>1\14 < g < 1\12<br />
</td>
<td>1\14 < g < 2\26 (1\13)<br />
</td>
<td>2\26 (1\13) < g < 3\38<br />
</td>
<td>g<br />
</td>
<td>-6g+1\2<br />
</td>
</tr>
<tr>
<td>13L1s<br />
</td>
<td>1\14 < g < 1\13<br />
</td>
<td>1\14 < g < 2\27<br />
</td>
<td>2\27 < g < 3\40<br />
</td>
<td>g<br />
</td>
<td>-13g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:26:<h1> --><h1 id="toc13"><a name="x15"></a><!-- ws:end:WikiTextHeadingRule:26 -->15</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Range of maximum expressiveness<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L14s<br />
</td>
<td>14\15 < g < 1<br />
</td>
<td>14\15 < g < 15\16<br />
</td>
<td>15\16 < g < 16\17<br />
</td>
<td>-13+14g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L13s<br />
</td>
<td>7\15 < g < 1\2<br />
</td>
<td>7\15 < g < 8\17<br />
</td>
<td>8\17 < g < 9\19<br />
</td>
<td>-6+13g<br />
</td>
<td>-2g+1<br />
</td>
</tr>
<tr>
<td>3L12s<br />
</td>
<td>4\15 < g < 1\3<br />
</td>
<td>4\15 < g < 5\18<br />
</td>
<td>5\18 < g < 6\21 (2\7)<br />
</td>
<td>-1+4g<br />
</td>
<td>-g+1\3<br />
</td>
</tr>
<tr>
<td>4L11s<br />
</td>
<td>11\15 < g < 3\4<br />
</td>
<td>11\15 < g < 14\19<br />
</td>
<td>14\19 < g < 17\23<br />
</td>
<td>-8+11g<br />
</td>
<td>-4g+3<br />
</td>
</tr>
<tr>
<td>5L10s<br />
</td>
<td>2\15 < g < 1\5<br />
</td>
<td>2\15 < g < 3\20<br />
</td>
<td>3\20 < g < 4\25<br />
</td>
<td>-1\5+2g<br />
</td>
<td>-g+1\5<br />
</td>
</tr>
<tr>
<td>6L9s<br />
</td>
<td>2\15 < g < 1\6<br />
</td>
<td>2\15 < g < 3\21 (1\7)<br />
</td>
<td>3\21 (1\7) < g < 4\27<br />
</td>
<td>-1\3+3g<br />
</td>
<td>-2g+1\3<br />
</td>
</tr>
<tr>
<td>7L8s<br />
</td>
<td>2\15 < g < 1\7<br />
</td>
<td>2\15 < g < 3\22<br />
</td>
<td>3\22 < g < 4\29<br />
</td>
<td>-1+8g<br />
</td>
<td>-7g+1<br />
</td>
</tr>
<tr>
<td>8L7s<br />
</td>
<td>13\15 < g < 7\8<br />
</td>
<td>13\15 < g < 20\23<br />
</td>
<td>20\23 < g < 27\31<br />
</td>
<td>-6+7g<br />
</td>
<td>-8g+7<br />
</td>
</tr>
<tr>
<td>9L6s<br />
</td>
<td>3\15 (1\5) < g < 2\9<br />
</td>
<td>3\15 (1\5) < g < 5\24<br />
</td>
<td>5\24 < g < 7\33<br />
</td>
<td>-1\3+2g<br />
</td>
<td>-3g+2\3<br />
</td>
</tr>
<tr>
<td>10L5s<br />
</td>
<td>1\15 < g < 1\10<br />
</td>
<td>1\15 < g < 2\25<br />
</td>
<td>2\25 < g < 3\35<br />
</td>
<td>g<br />
</td>
<td>-2g+1\5<br />
</td>
</tr>
<tr>
<td>11L4s<br />
</td>
<td>4\15 < g < 3\11<br />
</td>
<td>4\15 < g < 7\26<br />
</td>
<td>7\26 < g < 10\37<br />
</td>
<td>-1+4g<br />
</td>
<td>-11g+3<br />
</td>
</tr>
<tr>
<td>12L3s<br />
</td>
<td>1\15 < g < 1\12<br />
</td>
<td>1\15 < g < 2\27<br />
</td>
<td>2\27 < g < 3\39 (1\13)<br />
</td>
<td>g<br />
</td>
<td>-4g+1\3<br />
</td>
</tr>
<tr>
<td>13L2s<br />
</td>
<td>8\15 < g < 7\13<br />
</td>
<td>8\15 < g < 15\28<br />
</td>
<td>15\28 < g < 22\41<br />
</td>
<td>-1+2g<br />
</td>
<td>-13g+7<br />
</td>
</tr>
<tr>
<td>14L1s<br />
</td>
<td>1\15 < g < 1\14<br />
</td>
<td>1\15 < g < 2\29<br />
</td>
<td>2\29 < g < 3\43<br />
</td>
<td>g<br />
</td>
<td>-14g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:28:<h1> --><h1 id="toc14"><a name="x16"></a><!-- ws:end:WikiTextHeadingRule:28 -->16</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Range of maximum expressiveness<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L15s<br />
</td>
<td>15\16 < g < 1<br />
</td>
<td>15\16 < g < 16\17<br />
</td>
<td>16\17 < g < 17\18<br />
</td>
<td>-14+15g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L14s<br />
</td>
<td>7\16 < g < 1\2<br />
</td>
<td>7\16 < g < 8\18 (4\9)<br />
</td>
<td>8\18 (4\9) < g < 9\20<br />
</td>
<td>-3+7g<br />
</td>
<td>-g+1\2<br />
</td>
</tr>
<tr>
<td>3L13s<br />
</td>
<td>5\16 < g < 1\3<br />
</td>
<td>5\16 < g < 6\19<br />
</td>
<td>6\19 < g < 7\22<br />
</td>
<td>-4+13g<br />
</td>
<td>1-3g<br />
</td>
</tr>
<tr>
<td>4L12s<br />
</td>
<td>3\16 < g < 1\4<br />
</td>
<td>3\16 < g < 4\20 (1\5)<br />
</td>
<td>4\20 (1\5) < g < 5\24<br />
</td>
<td>3g-1\2<br />
</td>
<td>-g+1\4<br />
</td>
</tr>
<tr>
<td>5L11s<br />
</td>
<td>3\16 < g < 1\5<br />
</td>
<td>3\16 < g < 4\21<br />
</td>
<td>4\21 < g < 5\26<br />
</td>
<td>-2+11g<br />
</td>
<td>-5g+1<br />
</td>
</tr>
<tr>
<td>6L10s<br />
</td>
<td>5\16 < g < 2\6 (1\3)<br />
</td>
<td>5\16 < g < 7\22<br />
</td>
<td>7\22 < g < 9\28<br />
</td>
<td>-3\2+5g<br />
</td>
<td>1-3g<br />
</td>
</tr>
<tr>
<td>7L9s<br />
</td>
<td>9\16 < g < 4\7<br />
</td>
<td>9\16 < g < 13\23<br />
</td>
<td>13\23 < g < 17\30<br />
</td>
<td>-5+9g<br />
</td>
<td>-7g+4<br />
</td>
</tr>
<tr>
<td>8L8s<br />
</td>
<td>1\16 < g < 1\8<br />
</td>
<td>1\16 < g < 2\24 (1\12)<br />
</td>
<td>2\24 (1\12) < g < 3\32<br />
</td>
<td>g<br />
</td>
<td>-g+1\8<br />
</td>
</tr>
<tr>
<td>9L7s<br />
</td>
<td>7\16 < g < 4\9<br />
</td>
<td>7\16 < g < 11\25<br />
</td>
<td>11\25 < g < 15\34<br />
</td>
<td>-3+7g<br />
</td>
<td>-9g+4<br />
</td>
</tr>
<tr>
<td>10L6s<br />
</td>
<td>3\16 < g < 2\10 (1\5)<br />
</td>
<td>3\16 < g < 5\26<br />
</td>
<td>5\26 < g < 7\36<br />
</td>
<td>3g-1\2<br />
</td>
<td>-5g+1<br />
</td>
</tr>
<tr>
<td>11L5s<br />
</td>
<td>13\16 < g < 9\11<br />
</td>
<td>13\16 < g < 22\27<br />
</td>
<td>22\27 < g < 31\38<br />
</td>
<td>-4+5g<br />
</td>
<td>-11g+9<br />
</td>
</tr>
<tr>
<td>12L4s<br />
</td>
<td>1\16 < g < 1\12<br />
</td>
<td>1\16 < g < 2\28 (1\14)<br />
</td>
<td>2\28 (1\14) < g < 3\40<br />
</td>
<td>g<br />
</td>
<td>-3g+1\4<br />
</td>
</tr>
<tr>
<td>13L3s<br />
</td>
<td>11\16 < g < 9\13<br />
</td>
<td>11\16 < g < 20\29<br />
</td>
<td>20\29 < g < 29\42<br />
</td>
<td>-2+3g<br />
</td>
<td>-13g+9<br />
</td>
</tr>
<tr>
<td>14L2s<br />
</td>
<td>1\16 < g < 1\14<br />
</td>
<td>1\16 < g < 2\30 (1\15)<br />
</td>
<td>2\30 (1\15) < g < 3\44<br />
</td>
<td>g<br />
</td>
<td>-7g+1\2<br />
</td>
</tr>
<tr>
<td>15L1s<br />
</td>
<td>1\16 < g < 1\15<br />
</td>
<td>1\16 < g < 2\31<br />
</td>
<td>2\31 < g < 3\46<br />
</td>
<td>g<br />
</td>
<td>-15g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:30:<h1> --><h1 id="toc15"><a name="x17"></a><!-- ws:end:WikiTextHeadingRule:30 -->17</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Range of maximum expressiveness<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L16s<br />
</td>
<td>16\17 < g < 1<br />
</td>
<td>16\17 < g < 17\18<br />
</td>
<td>17\18 < g < 18\19<br />
</td>
<td>-15+16g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L15s<br />
</td>
<td>8\17 < g < 1\2<br />
</td>
<td>8\17 < g < 9\19<br />
</td>
<td>9\19 < g < 10\21<br />
</td>
<td>-7+15g<br />
</td>
<td>-2g+1<br />
</td>
</tr>
<tr>
<td>3L14s<br />
</td>
<td>11\17 < g < 2\3<br />
</td>
<td>11\17 < g < 13\20<br />
</td>
<td>13\20 < g < 15\23<br />
</td>
<td>-9+14g<br />
</td>
<td>-3g+2<br />
</td>
</tr>
<tr>
<td>4L13s<br />
</td>
<td>4\17 < g < 1\4<br />
</td>
<td>4\17 < g < 5\21<br />
</td>
<td>5\21 < g < 6\25<br />
</td>
<td>-3+13g<br />
</td>
<td>-4g+1<br />
</td>
</tr>
<tr>
<td>5L12s<br />
</td>
<td>10\17 < g < 3\5<br />
</td>
<td>10\17 < g < 13\22<br />
</td>
<td>13\22 < g < 16\27<br />
</td>
<td>-7+12g<br />
</td>
<td>-5g+3<br />
</td>
</tr>
<tr>
<td>6L11s<br />
</td>
<td>14\17 < g < 5\6<br />
</td>
<td>14\17 < g < 19\23<br />
</td>
<td>19\23 < g < 24\29<br />
</td>
<td>-9+11g<br />
</td>
<td>-6g+5<br />
</td>
</tr>
<tr>
<td>7L10s<br />
</td>
<td>12\17 < g < 5\7<br />
</td>
<td>12\17 < g < 17\24<br />
</td>
<td>17\24 < g < 22\31<br />
</td>
<td>-7+10g<br />
</td>
<td>-7g+5<br />
</td>
</tr>
<tr>
<td>8L9s<br />
</td>
<td>2\17 < g < 1\8<br />
</td>
<td>2\17 < g < 3\25<br />
</td>
<td>3\25 < g < 4\33<br />
</td>
<td>-1+9g<br />
</td>
<td>-8g+1<br />
</td>
</tr>
<tr>
<td>9L8s<br />
</td>
<td>15\17 < g < 8\9<br />
</td>
<td>15\17 < g < 23\26<br />
</td>
<td>23\26 < g < 31\35<br />
</td>
<td>-7+8g<br />
</td>
<td>-9g+8<br />
</td>
</tr>
<tr>
<td>10L7s<br />
</td>
<td>5\17 < g < 3\10<br />
</td>
<td>5\17 < g < 8\27<br />
</td>
<td>8\27 < g < 11\37<br />
</td>
<td>-2+7g<br />
</td>
<td>-10g+3<br />
</td>
</tr>
<tr>
<td>11L6s<br />
</td>
<td>3\17 < g < 2\11<br />
</td>
<td>3\17 < g < 5\28<br />
</td>
<td>5\28 < g < 7\39<br />
</td>
<td>-1+6g<br />
</td>
<td>-11g+2<br />
</td>
</tr>
<tr>
<td>12L5s<br />
</td>
<td>7\17 < g < 5\12<br />
</td>
<td>7\17 < g < 12\29<br />
</td>
<td>12\29 < g < 17\41<br />
</td>
<td>-2+5g<br />
</td>
<td>-12g+5<br />
</td>
</tr>
<tr>
<td>13L4s<br />
</td>
<td>13\17 < g < 10\13<br />
</td>
<td>13\17 < g < 23\30<br />
</td>
<td>23\30 < g < 33\43<br />
</td>
<td>-3+4g<br />
</td>
<td>-13g+10<br />
</td>
</tr>
<tr>
<td>14L3s<br />
</td>
<td>6\17 < g < 5\14<br />
</td>
<td>6\17 < g < 11\31<br />
</td>
<td>11\31 < g < 16\45<br />
</td>
<td>-1+3g<br />
</td>
<td>-14g+5<br />
</td>
</tr>
<tr>
<td>15L2s<br />
</td>
<td>9\17 < g < 8\15<br />
</td>
<td>9\17 < g < 17\32<br />
</td>
<td>17\32 < g < 25\47<br />
</td>
<td>-1+2g<br />
</td>
<td>-15g+8<br />
</td>
</tr>
<tr>
<td>16L1s<br />
</td>
<td>1\17 < g < 1\16<br />
</td>
<td>1\17 < g < 2\33<br />
</td>
<td>2\33 < g < 3\49<br />
</td>
<td>g<br />
</td>
<td>-16g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:32:<h1> --><h1 id="toc16"><a name="x18"></a><!-- ws:end:WikiTextHeadingRule:32 -->18</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Range of maximum expressiveness<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L17s<br />
</td>
<td>17\18 < g < 1<br />
</td>
<td>17\18 < g < 18\19<br />
</td>
<td>18\19 < g < 19\20<br />
</td>
<td>-16+17g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L16s<br />
</td>
<td>8\18 (4\9) < g < 1\2<br />
</td>
<td>8\18 (4\9) < g < 9\20<br />
</td>
<td>9\20 < g < 10\22 (5\11)<br />
</td>
<td>-7\2+8g<br />
</td>
<td>-g+1\2<br />
</td>
</tr>
<tr>
<td>3L15s<br />
</td>
<td>5\18 < g < 1\3<br />
</td>
<td>5\18 < g < 6\21 (2\7)<br />
</td>
<td>6\21 (2\7) < g < 7\24<br />
</td>
<td>-4\3+5g<br />
</td>
<td>-g+1\3<br />
</td>
</tr>
<tr>
<td>4L14s<br />
</td>
<td><span style="line-height: 1.5;">4\18</span> (<span style="line-height: 1.5;">2\9) < g < 1\4</span><br />
</td>
<td><span style="line-height: 1.5;">4\18</span> (<span style="line-height: 1.5;">2\9) < g < 5\22</span><br />
</td>
<td><span style="line-height: 15.6000003814697px;">5\22 < g < 6\26 (3\13)</span><br />
</td>
<td>-3\2+7g<br />
</td>
<td>-2g+1\2<br />
</td>
</tr>
<tr>
<td>5L13s<br />
</td>
<td>7\18 < g < 2\5<br />
</td>
<td>7\18 < g < 9\23<br />
</td>
<td>9\23 < g < 11\28<br />
</td>
<td>-5+13g<br />
</td>
<td>-5g+2<br />
</td>
</tr>
<tr>
<td>6L12s<br />
</td>
<td>2\18 (1\9) < g < 1\6<br />
</td>
<td>2\18 (1\9) < g < 3\24 (1\8)<br />
</td>
<td>3\24 (1\8) < g < 4\30 (2\15)<br />
</td>
<td>-1\6+2g<br />
</td>
<td>-g+1\6<br />
</td>
</tr>
<tr>
<td>7L11s<br />
</td>
<td>5\18 < g < 2\7<br />
</td>
<td>5\18 < g < 7\25<br />
</td>
<td>7\25 < g < 9\32<br />
</td>
<td>-3+11g<br />
</td>
<td>-7g+2<br />
</td>
</tr>
<tr>
<td>8L10s<br />
</td>
<td>2\18 (1\9) < g < 1\8<br />
</td>
<td>2\18 (1\9) < g < 3\26<br />
</td>
<td>3\26 < g < 4\34 (2\17)<br />
</td>
<td>-1\2+5g<br />
</td>
<td>-4g+1\2<br />
</td>
</tr>
<tr>
<td>9L9s<br />
</td>
<td>1\18 < g < 1\9<br />
</td>
<td>1\18 < g < 2\27<br />
</td>
<td>2\27 < g < 3\36 (1\12)<br />
</td>
<td>g<br />
</td>
<td>-g+1\9<br />
</td>
</tr>
<tr>
<td>10L8s<br />
</td>
<td>7\18 < g < 4\10 (2\5)<br />
</td>
<td>7\18 < g < 11\28<br />
</td>
<td>11\28 < g < 15\38<br />
</td>
<td>-3\2+4g<br />
</td>
<td>-5g+2<br />
</td>
</tr>
<tr>
<td>11L7s<br />
</td>
<td>13\18 < g < 8\11<br />
</td>
<td>13\18 < g < 21\29<br />
</td>
<td>21\29 < g < 29\37<br />
</td>
<td>-5+7g<br />
</td>
<td>-11g+8<br />
</td>
</tr>
<tr>
<td>12L6s<br />
</td>
<td>1\18 < g < 1\12<br />
</td>
<td>1\18 < g < 2\30 (1\15)<br />
</td>
<td>2\30 (1\15) < g < 3\42 (1\14)<br />
</td>
<td>g<br />
</td>
<td>-2g+1\6<br />
</td>
</tr>
<tr>
<td>13L5s<br />
</td>
<td>11\18 < g < 8\13<br />
</td>
<td>11\18 < g < 19\31<br />
</td>
<td>19\31 < g < 27\44<br />
</td>
<td>-3+5g<br />
</td>
<td>-13g+8<br />
</td>
</tr>
<tr>
<td>14L4s<br />
</td>
<td>5\18 < g < 4\14 (2\7)<br />
</td>
<td>5\18 < g < 9\32<br />
</td>
<td>9\32 < g < 11\46<br />
</td>
<td>-1\2+2g<br />
</td>
<td>-7g+2<br />
</td>
</tr>
<tr>
<td>15L3s<br />
</td>
<td>1\18 < g < 1\15<br />
</td>
<td>1\18 < g < 2\33<br />
</td>
<td>2\33 < g < 3\48 (1\16)<br />
</td>
<td>g<br />
</td>
<td>-5g+1\3<br />
</td>
</tr>
<tr>
<td>16L2s<br />
</td>
<td>1\18 < g < 1\16<br />
</td>
<td>1\18 < g < 2\34 (1\17)<br />
</td>
<td>2\34 (1\17) < g < 3\50<br />
</td>
<td>g<br />
</td>
<td>-8g+1\2<br />
</td>
</tr>
<tr>
<td>17L1s<br />
</td>
<td>1\18 < g < 1\17<br />
</td>
<td>1\18 < g < 2\35<br />
</td>
<td>2\35 < g < 3\52<br />
</td>
<td>g<br />
</td>
<td>-17g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:34:<h1> --><h1 id="toc17"><a name="x19"></a><!-- ws:end:WikiTextHeadingRule:34 -->19</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Range of maximum expressiveness<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L18s<br />
</td>
<td>18\19 < g < 1<br />
</td>
<td>18\19 < g < 19\20<br />
</td>
<td>19\20 < g < 20\21<br />
</td>
<td>-17+18g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L17s<br />
</td>
<td>9\19 < g < 1\2<br />
</td>
<td>9\19 < g < 10\21<br />
</td>
<td>10\21 < g < 11\23<br />
</td>
<td>-8+17g<br />
</td>
<td>-2g+1<br />
</td>
</tr>
<tr>
<td>3L16s<br />
</td>
<td>6\19 < g < 1\3<br />
</td>
<td>6\19 < g < 7\22<br />
</td>
<td>7\22 < g < 8\25<br />
</td>
<td>-5+16g<br />
</td>
<td>1-3g<br />
</td>
</tr>
<tr>
<td>4L15s<br />
</td>
<td>14\19 < g < 3\4<br />
</td>
<td>14\19 < g < 17\23<br />
</td>
<td>17\23 < g < 20\27<br />
</td>
<td>-11+15g<br />
</td>
<td>-4g+3<br />
</td>
</tr>
<tr>
<td>5L14s<br />
</td>
<td>15\19 < g < 4\5<br />
</td>
<td>15\19 < g < 19\24<br />
</td>
<td>19\24 < g < 23\29<br />
</td>
<td>-11+14g<br />
</td>
<td>-5g+4<br />
</td>
</tr>
<tr>
<td>6L13s<br />
</td>
<td>3\19 < g < 1\6<br />
</td>
<td>3\19 < g < 4\25<br />
</td>
<td>4\25 < g < 5\31<br />
</td>
<td>-2+13g<br />
</td>
<td>-6g+1<br />
</td>
</tr>
<tr>
<td>7L12s<br />
</td>
<td>8\19 < g < 3\7<br />
</td>
<td>8\19 < g < 11\26<br />
</td>
<td>11\26 < g < 14\33<br />
</td>
<td>-5+12g<br />
</td>
<td>-7g+3<br />
</td>
</tr>
<tr>
<td>8L11s<br />
</td>
<td>7\19 < g < 3\8<br />
</td>
<td>7\19 < g < 10\27<br />
</td>
<td>10\27 < g < 13\35<br />
</td>
<td>-4+11g<br />
</td>
<td>-8g+3<br />
</td>
</tr>
<tr>
<td>9L10s<br />
</td>
<td>2\19 < g < 1\9<br />
</td>
<td>2\19 < g < 3\28<br />
</td>
<td>3\28 < g < 4\37<br />
</td>
<td>-1+10g<br />
</td>
<td>-9g+1<br />
</td>
</tr>
<tr>
<td>10L9s<br />
</td>
<td>17\19 < g < 9\10<br />
</td>
<td>17\19 < g < 26\29<br />
</td>
<td>26\29 < g < 35\39<br />
</td>
<td>-8+9g<br />
</td>
<td>-10g+9<br />
</td>
</tr>
<tr>
<td>11L8s<br />
</td>
<td>12\19 < g < 7\11<br />
</td>
<td>12\19 < g < 19\30<br />
</td>
<td>19\30 < g < 26\41<br />
</td>
<td>-5+8g<br />
</td>
<td>-11g+7<br />
</td>
</tr>
<tr>
<td>12L7s<br />
</td>
<td>11\19 < g < 7\12<br />
</td>
<td>11\19 < g < 18\31<br />
</td>
<td>18\31 < g < 25\43<br />
</td>
<td>-4+7g<br />
</td>
<td>-12g+7<br />
</td>
</tr>
<tr>
<td>13L6s<br />
</td>
<td>16\19 < g < 11\13<br />
</td>
<td>16\19 < g < 27\32<br />
</td>
<td>27\32 < g < 38\45<<br />
</td>
<td>-5+6g<br />
</td>
<td>-13g+11<br />
</td>
</tr>
<tr>
<td>14L5s<br />
</td>
<td>4\19 < g < 3\14<br />
</td>
<td>4\19 < g < 7\33<br />
</td>
<td>7\33 < g < 10\47<br />
</td>
<td>-1+5g<br />
</td>
<td>-14g+3<br />
</td>
</tr>
<tr>
<td>15L4s<br />
</td>
<td>5\19 < g < 4\15<br />
</td>
<td>5\19 < g < 9\34<br />
</td>
<td>9\34 < g < 13\49<br />
</td>
<td>-1+4g<br />
</td>
<td>-15g+4<br />
</td>
</tr>
<tr>
<td>16L3s<br />
</td>
<td>13\19 < g < 11\16<br />
</td>
<td>13\19 < g < 24\35<br />
</td>
<td>24\35 < g < 35\51<br />
</td>
<td>-2+3g<br />
</td>
<td>-16g+11<br />
</td>
</tr>
<tr>
<td>17L2s<br />
</td>
<td>10\19 < g < 9\17<br />
</td>
<td>10\19 < g < 19\36<br />
</td>
<td>19\36 < g < 26\53<br />
</td>
<td>-1+2g<br />
</td>
<td>-17g+9<br />
</td>
</tr>
<tr>
<td>18L1s<br />
</td>
<td>1\19 < g < 1\18<br />
</td>
<td>1\19 < g < 2\37<br />
</td>
<td>2\37 < g < 3\55<br />
</td>
<td>g<br />
</td>
<td>-18g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:36:<h1> --><h1 id="toc18"><a name="x20"></a><!-- ws:end:WikiTextHeadingRule:36 -->20</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Range of maximum expressiveness<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L19s<br />
</td>
<td>19\20 < g < 1<br />
</td>
<td>19\20 < g < 20\21<br />
</td>
<td>20\21 < g < 21\22<br />
</td>
<td>-18+19g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L18s<br />
</td>
<td>9\20 < g < 1\2<br />
</td>
<td>9\20 < g < 10\22 (5\11)<br />
</td>
<td>10\22 (5\11) < g < 11\24<br />
</td>
<td>-4+9g<br />
</td>
<td>-g+1\2<br />
</td>
</tr>
<tr>
<td>3L17s<br />
</td>
<td>13\20 < g < 2\3<br />
</td>
<td>13\20 < g < 15\23<br />
</td>
<td>15\23 < g < 17\26<br />
</td>
<td>-11+17g<br />
</td>
<td>-3g+2<br />
</td>
</tr>
<tr>
<td>4L16s<br />
</td>
<td>4\20 (1\5) < g < 1\4<br />
</td>
<td>4\20 (1\5) < g < 5\24<br />
</td>
<td>5\24 < g < 6\28 (3\14)<br />
</td>
<td>-3\4+4g<br />
</td>
<td>-g+1\4<br />
</td>
</tr>
<tr>
<td>5L15s<br />
</td>
<td>3\20 < g < 1\5<br />
</td>
<td>3\20 < g < 4\25<br />
</td>
<td>4\25 < g < 5\30 (1\6)<br />
</td>
<td>-2\5+3g<br />
</td>
<td>-g+1\5<br />
</td>
</tr>
<tr>
<td>6L14s<br />
</td>
<td>3\20 < g < 1\6<br />
</td>
<td>3\20 < g < 4\26 (2\13)<br />
</td>
<td>4\26 (2\13) < g < 5\32<br />
</td>
<td>-1+7g<br />
</td>
<td>-3g+1\2<br />
</td>
</tr>
<tr>
<td>7L13s<br />
</td>
<td>17\20 < g < 6\7<br />
</td>
<td>17\20 < g < 23\27<br />
</td>
<td>23\27 < g < 29\34<br />
</td>
<td>-11+13g<br />
</td>
<td>-7g+6<br />
</td>
</tr>
<tr>
<td>8L12s<br />
</td>
<td>2\20 (1\10) < g < 1\8<br />
</td>
<td>2\20 (1\10) < g < 3\28<br />
</td>
<td>3\28 < g < 4\36 (1\9)<br />
</td>
<td>-1\4+3g<br />
</td>
<td>-2g+1\4<br />
</td>
</tr>
<tr>
<td>9L11s<br />
</td>
<td>11\20 < g < 5\9<br />
</td>
<td>11\20 < g < 16\29<br />
</td>
<td>16\29 < g < 21\38<br />
</td>
<td>-6+11g<br />
</td>
<td>-9g+5<br />
</td>
</tr>
<tr>
<td>10L10s<br />
</td>
<td>1\20 < g < 1\10<br />
</td>
<td>1\20 < g < 2\30 (1\15)<br />
</td>
<td>2\30 (1\15) < g < 3\40<br />
</td>
<td>g<br />
</td>
<td>-g+1\10<br />
</td>
</tr>
<tr>
<td>11L9s<br />
</td>
<td>9\20 < g < 5\11<br />
</td>
<td>9\20 < g < 14\31<br />
</td>
<td>14\31 < g < 19\42<br />
</td>
<td>-4+9g<br />
</td>
<td>-11g+5<br />
</td>
</tr>
<tr>
<td>12L8s<br />
</td>
<td>3\20 < g < 2\12 (1\6)<br />
</td>
<td>3\20 < g < 5\32<br />
</td>
<td>5\32 < g < 7\44<br />
</td>
<td>-1\4+2g<br />
</td>
<td>-3g+1\2<br />
</td>
</tr>
<tr>
<td>13L7s<br />
</td>
<td>3\20 < g < 2\13<br />
</td>
<td>3\20 < g < 5\33<br />
</td>
<td>5\33 < g < 7\46<br />
</td>
<td>-1+7g<br />
</td>
<td>-13g+2<br />
</td>
</tr>
<tr>
<td>14L6s<br />
</td>
<td>7\20 < g < 5\14<br />
</td>
<td>7\20 < g < 12\34 (6\17)<br />
</td>
<td>12\34 (6\17) < g < 17\48<br />
</td>
<td>-1+3g<br />
</td>
<td>-7g+5\2<br />
</td>
</tr>
<tr>
<td>15L5s<br />
</td>
<td>1\20 < g < 1\15<br />
</td>
<td>1\20 < g < 2\35<br />
</td>
<td>2\35 < g < 3\50<br />
</td>
<td>g<br />
</td>
<td>-3g+1\5<br />
</td>
</tr>
<tr>
<td>16L4s<br />
</td>
<td>1\20 < g < 1\16<br />
</td>
<td>1\20 < g < 2\36 (1\18)<br />
</td>
<td>2\36 (1\18) < g < 3\52<br />
</td>
<td>g<br />
</td>
<td>-4g+1\4<br />
</td>
</tr>
<tr>
<td>17L3s<br />
</td>
<td>7\20 < g < 6\17<br />
</td>
<td>7\20 < g < 13\37<br />
</td>
<td>13\37 < g < 19\54<br />
</td>
<td>-1+3g<br />
</td>
<td>-17g+6<br />
</td>
</tr>
<tr>
<td>18L2s<br />
</td>
<td>1\20 < g < 1\18<br />
</td>
<td>1\20 < g < 2\38 (1\19)<br />
</td>
<td>2\38 (1\19) < g < 3\56<br />
</td>
<td>g<br />
</td>
<td>-9g+1\2<br />
</td>
</tr>
<tr>
<td>19L1s<br />
</td>
<td>1\20 < g < 1\19<br />
</td>
<td>1\20 < g < 2\39<br />
</td>
<td>2\39 < g < 3\58<br />
</td>
<td>g<br />
</td>
<td>-19g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:38:<h1> --><h1 id="toc19"><a name="x21"></a><!-- ws:end:WikiTextHeadingRule:38 -->21</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Range of maximum expressiveness<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L20s<br />
</td>
<td>20\21 < g < 1<br />
</td>
<td>20\21 < g < 21\22<br />
</td>
<td>21\22 < g < 22\23<br />
</td>
<td>-19+20g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L19s<br />
</td>
<td>10\21 < g < 1\2<br />
</td>
<td>10\21 < g < 11\23<br />
</td>
<td>11\23 < g < 12\25<br />
</td>
<td>-9+19g<br />
</td>
<td>-2g+1<br />
</td>
</tr>
<tr>
<td>3L18s<br />
</td>
<td>6\21 (2\7) < g < 1\3<br />
</td>
<td>6\21 (2\7) < g < 7\24<br />
</td>
<td>7\24 < g < 8\27<br />
</td>
<td>-5\3+6g<br />
</td>
<td>-g+1\3<br />
</td>
</tr>
<tr>
<td>4L17s<br />
</td>
<td>5\21 < g < 1\4<br />
</td>
<td>5\21 < g < 6\25<br />
</td>
<td>6\25 < g < 7\29<br />
</td>
<td>-4+17g<br />
</td>
<td>-4g+1<br />
</td>
</tr>
<tr>
<td>5L16s<br />
</td>
<td>4\21 < g < 1\5<br />
</td>
<td>4\21 < g < 5\26<br />
</td>
<td>5\26 < g < 6\31<br />
</td>
<td>-3+16g<br />
</td>
<td>-5g+1<br />
</td>
</tr>
<tr>
<td>6L15s<br />
</td>
<td>3\21 (1\7) < g < 1\6<br />
</td>
<td>3\21 (1\7) < g < 4\27<br />
</td>
<td>4\27 < g < 5\33<br />
</td>
<td>-2\3+5g<br />
</td>
<td>-2g+1\3<br />
</td>
</tr>
<tr>
<td>7L14s<br />
</td>
<td>2\21 < g < 1\7<br />
</td>
<td>2\21 < g < 3\28<br />
</td>
<td>3\28 < g < 4\35<br />
</td>
<td>-1\7+2g<br />
</td>
<td>-g+1\7<br />
</td>
</tr>
<tr>
<td>8L13s<br />
</td>
<td>13\21 < g < 5\8<br />
</td>
<td>13\21 < g < 18\29<br />
</td>
<td>18\29 < g < 23\37<br />
</td>
<td>-8+13g<br />
</td>
<td>-8g+5<br />
</td>
</tr>
<tr>
<td>9L12s<br />
</td>
<td>2\21 < g < 1\9<br />
</td>
<td>2\21 < g < 3\30 (1\10)<br />
</td>
<td>3\30 (1\10) < g < 4\39<br />
</td>
<td>-1\3+4g<br />
</td>
<td>-3g+1\3<br />
</td>
</tr>
<tr>
<td>10L11s<br />
</td>
<td>2\21 < g < 1\10<br />
</td>
<td>2\21 < g < 3\31<br />
</td>
<td>3\31 < g < 4\41<br />
</td>
<td>-1+11g<br />
</td>
<td>-10g+1<br />
</td>
</tr>
<tr>
<td>11L10s<br />
</td>
<td>19\21 < g < 10\11<br />
</td>
<td>19\21 < g < 29\32<br />
</td>
<td>29\32 < g < 39\43<br />
</td>
<td>-9+10g<br />
</td>
<td>-11g+10<br />
</td>
</tr>
<tr>
<td>12L9s<br />
</td>
<td>5\21 < g < 3\12 (1\4)<br />
</td>
<td>5\21 < g < 6\33 (2\11)<br />
</td>
<td>6\33 (2\11) < g < 7\45<br />
</td>
<td>-2\3+3g<br />
</td>
<td>-4g+1<br />
</td>
</tr>
<tr>
<td>13L8s<br />
</td>
<td>8\21 < g < 5\13<br />
</td>
<td>8\21 < g < 13\34<br />
</td>
<td>13\34 < g < 18\47<br />
</td>
<td>-3+8g<br />
</td>
<td>-13g+5<br />
</td>
</tr>
<tr>
<td>14L7s<br />
</td>
<td>1\21 < g < 1\14<br />
</td>
<td>1\21 < g < 2\35<br />
</td>
<td>2\35 < g < 3\49<br />
</td>
<td>g<br />
</td>
<td>-2g+1\7<br />
</td>
</tr>
<tr>
<td>15L6s<br />
</td>
<td>4\21 < g < 3\15 (1\5)<br />
</td>
<td>4\21 < g < 7\36<br />
</td>
<td>7\36 < g < 10\51<br />
</td>
<td>-1\3+2g<br />
</td>
<td>-5g+1<br />
</td>
</tr>
<tr>
<td>16L5s<br />
</td>
<td>17\21 < g < 13\16<br />
</td>
<td>17\21 < g < 30\37<br />
</td>
<td>30\37 < g < 43\53<br />
</td>
<td>-4+5g<br />
</td>
<td>-16g+13<br />
</td>
</tr>
<tr>
<td>17L4s<br />
</td>
<td>16\21 < g < 13\17<br />
</td>
<td>16\21 < g < 29\38<br />
</td>
<td>29\38 < g < 42\55<br />
</td>
<td>-3+4g<br />
</td>
<td>-17g+13<br />
</td>
</tr>
<tr>
<td>18L3s<br />
</td>
<td>1\21 < g < 1\18<br />
</td>
<td>1\21 < g < 2\39<br />
</td>
<td>2\39 < g < 3\57 (1\19)<br />
</td>
<td>g<br />
</td>
<td>-6g+1\3<br />
</td>
</tr>
<tr>
<td>19L2s<br />
</td>
<td>11\21 < g < 10\19<br />
</td>
<td>11\21 < g < 21\40<br />
</td>
<td>21\40 < g < 31\59<br />
</td>
<td>-1+2g<br />
</td>
<td>-19g+10<br />
</td>
</tr>
<tr>
<td>20L1s<br />
</td>
<td>1\21 < g < 1\20<br />
</td>
<td>1\21 < g < 2\41<br />
</td>
<td>2\41 < g < 3\61<br />
</td>
<td>g<br />
</td>
<td>-20g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:40:<h1> --><h1 id="toc20"><a name="x22"></a><!-- ws:end:WikiTextHeadingRule:40 -->22</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Range of maximum expressiveness<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L21s<br />
</td>
<td>21\22 < g < 1<br />
</td>
<td>21\22 < g < 22\23<br />
</td>
<td>22\23 < g < 23\24<br />
</td>
<td>-20+21g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L20s<br />
</td>
<td>10\22 (5\11) < g < 1\2<br />
</td>
<td>10\22 (5\11) < g < 11\24<br />
</td>
<td>11\24 < g < 12\26 (6\13)<br />
</td>
<td>-9\2+10g<br />
</td>
<td>-g+1\2<br />
</td>
</tr>
<tr>
<td>3L19s<br />
</td>
<td>7\22 < g < 1\3<br />
</td>
<td>7\22 < g < 8\25<br />
</td>
<td>8\25 < g < 9\28<br />
</td>
<td>-6+19g<br />
</td>
<td>1-3g<br />
</td>
</tr>
<tr>
<td>4L18s<br />
</td>
<td>5\22 < g < 1\4<br />
</td>
<td>5\22 < g < 6\26 (3\13)<br />
</td>
<td>6\26 (3\13) < g < 7\30<br />
</td>
<td>-2+9g<br />
</td>
<td>-2g+1\2<br />
</td>
</tr>
<tr>
<td>5L17s<br />
</td>
<td>13\22 < g < 3\5<br />
</td>
<td>13\22 < g < 16\27<br />
</td>
<td>16\27 < g < 19\32<br />
</td>
<td>-10+17g<br />
</td>
<td>-5g+3<br />
</td>
</tr>
<tr>
<td>6L16s<br />
</td>
<td>7\22 < g < 2\6 (1\3)<br />
</td>
<td>7\22 < g < 9\28<br />
</td>
<td>9\28 < g < 11\34<br />
</td>
<td>-5\2+8g<br />
</td>
<td>1-3g<br />
</td>
</tr>
<tr>
<td>7L15s<br />
</td>
<td>3\22 < g < 1\7<br />
</td>
<td>3\22 < g < 4\29<br />
</td>
<td>4\29 < g < 5\36<br />
</td>
<td>-2+15g<br />
</td>
<td>-7g+1<br />
</td>
</tr>
<tr>
<td>8L14s<br />
</td>
<td>8\22 (4\11) < g < 3\8<br />
</td>
<td>8\22 (4\11) < g < 11\30<br />
</td>
<td>11\30 < g < 14\38 (7\19)<br />
</td>
<td>-5\2+7g<br />
</td>
<td>-4g+3\2<br />
</td>
</tr>
<tr>
<td>9L13s<br />
</td>
<td>17\22 < g < 7\9<br />
</td>
<td>17\22 < g < 24\31<br />
</td>
<td>24\31 < g < 31\40<br />
</td>
<td>-10+13g<br />
</td>
<td>-9g+7<br />
</td>
</tr>
<tr>
<td>10L12s<br />
</td>
<td>2\22 (1\11) < g < 1\10<br />
</td>
<td>2\22 (1\11) < g < 3\32<br />
</td>
<td>3\32 < g < 4\42 (2\21)<br />
</td>
<td>-1\2+6g<br />
</td>
<td>-5g+1\2<br />
</td>
</tr>
<tr>
<td>11L11s<br />
</td>
<td>1\22 < g < 1\11<br />
</td>
<td>1\22 < g < 2\33<br />
</td>
<td>2\33 < g < 3\44<br />
</td>
<td>g<br />
</td>
<td>-g+1\11<br />
</td>
</tr>
<tr>
<td>12L10s<br />
</td>
<td>9\22 < g < 5\12<br />
</td>
<td>9\22 < g < 14\34 (7\17)<br />
</td>
<td>14\34 (7\17) < g < 19\46<br />
</td>
<td>-2+5g<br />
</td>
<td>-6g+5\2<br />
</td>
</tr>
<tr>
<td>13L9s<br />
</td>
<td>5\22 < g < 3\13<br />
</td>
<td>5\22 < g < 8\35<br />
</td>
<td>8\35 < g < 11\48<br />
</td>
<td>-2+9g<br />
</td>
<td>-13g+3<br />
</td>
</tr>
<tr>
<td>14L8s<br />
</td>
<td>3\22 < g < 2\14 (1\7)<br />
</td>
<td>3\22 < g < 5\36<br />
</td>
<td>5\36 < g < 7\50<br />
</td>
<td>4g-1\2<br />
</td>
<td>-7g+1<br />
</td>
</tr>
<tr>
<td>15L7s<br />
</td>
<td>19\22 < g < 13\15<br />
</td>
<td>19\22 < g < 32\37<br />
</td>
<td>32\37 < g < 45\52<br />
</td>
<td>-6+7g<br />
</td>
<td>-15g+13<br />
</td>
</tr>
<tr>
<td>16L6s<br />
</td>
<td>4\22 (2\11) < g < 3\16<br />
</td>
<td>4\22 (2\11) < g < 7\38<br />
</td>
<td>7\38 < g < 10\54 (5\27)<br />
</td>
<td>3g-1\2<br />
</td>
<td>-8g+3\2<br />
</td>
</tr>
<tr>
<td>17L5s<br />
</td>
<td>9\22 < g < 7\17<br />
</td>
<td>9\22 < g < 16\39<br />
</td>
<td>16\39 < g < 23\56<br />
</td>
<td>-2+5g<br />
</td>
<td>-17g+7<br />
</td>
</tr>
<tr>
<td>18L4s<br />
</td>
<td>6\22 (3\11) < g < 5\18<br />
</td>
<td>6\22 (3\11) < g < 11\40<br />
</td>
<td>11\40 < g < 16\58 (8\29)<br />
</td>
<td>-1\2+2g<br />
</td>
<td>-9g+5\2<br />
</td>
</tr>
<tr>
<td>19L3s<br />
</td>
<td>15\22 < g < 13\19<br />
</td>
<td>15\22 < g < 28\41<br />
</td>
<td>28\41 < g < 41\60<br />
</td>
<td>-2+3g<br />
</td>
<td>-19g+13<br />
</td>
</tr>
<tr>
<td>20L2s<br />
</td>
<td>1\22 < g < 1\20<br />
</td>
<td>1\22 < g < 2\42 (1\21)<br />
</td>
<td>2\42 (1\21) < g < 3\62<br />
</td>
<td>g<br />
</td>
<td>-10g+1\2<br />
</td>
</tr>
<tr>
<td>21L1s<br />
</td>
<td>1\22 < g < 1\21<br />
</td>
<td>1\22 < g < 2\43<br />
</td>
<td>2\43 < g < 3\64<br />
</td>
<td>g<br />
</td>
<td>-21g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:42:<h1> --><h1 id="toc21"><a name="x23"></a><!-- ws:end:WikiTextHeadingRule:42 -->23</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Range of maximum expressiveness<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L22s<br />
</td>
<td><span style="line-height: 1.5;">22\23 < g < 1</span><br />
</td>
<td><span style="line-height: 1.5;">22\23</span> < g < 23\24<br />
</td>
<td><span style="line-height: 1.5;">23\24 </span>< g < 24\25<br />
</td>
<td>-21+22g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L21s<br />
</td>
<td>11\23 < g < 1\2<br />
</td>
<td><span style="line-height: 15.6000003814697px;">11\23</span> < g < <span style="line-height: 1.5;">12\25</span><br />
</td>
<td>12\25 < g < 13\27<br />
</td>
<td>-10+21g<br />
</td>
<td>-2g+1<br />
</td>
</tr>
<tr>
<td>3L20s<br />
</td>
<td>15\23 < g < 2\3<br />
</td>
<td>15\23 < g < 17\26<br />
</td>
<td><span style="line-height: 1.5;">17\26</span> < g < 19\29<br />
</td>
<td>-13+20g<br />
</td>
<td>1-3g<br />
</td>
</tr>
<tr>
<td>4L19s<br />
</td>
<td>17\23 < g < 3\4<br />
</td>
<td><span style="line-height: 1.5;">17\23</span> < g < 20\27<br />
</td>
<td><span style="line-height: 15.6000003814697px;">20</span>\27 < g < 23<span style="line-height: 1.5;">\31</span><br />
</td>
<td>-14+19g<br />
</td>
<td>-4g+3<br />
</td>
</tr>
<tr>
<td>5L18s<br />
</td>
<td>9\23 < g < 2\5<br />
</td>
<td>9\23 < g < 11\28<br />
</td>
<td>11\28 < g < 13\33<br />
</td>
<td>-7+18g<br />
</td>
<td>-5g+2<br />
</td>
</tr>
<tr>
<td>6L17s<br />
</td>
<td>19\23 < g < 5\6<br />
</td>
<td>19\23 < g < 24\29<br />
</td>
<td>24\29 < g < 29\35<br />
</td>
<td>-15+17g<br />
</td>
<td>1-6g<br />
</td>
</tr>
<tr>
<td>7L16s<br />
</td>
<td>13\23 < g < 4\7<br />
</td>
<td>13\23 < g < 17\30<br />
</td>
<td><span style="line-height: 1.5;">17\30</span> < g < 21\37<br />
</td>
<td>-9+16g<br />
</td>
<td>-7g+4<br />
</td>
</tr>
<tr>
<td>8L15s<br />
</td>
<td>20\23 < g < 7\8<br />
</td>
<td>20\23 < g < 27\31<br />
</td>
<td>27\31 < g < 34\39<br />
</td>
<td>-13+15g<br />
</td>
<td>-8g+7<br />
</td>
</tr>
<tr>
<td>9L14s<br />
</td>
<td><span style="line-height: 1.5;">18\23</span> < g < 11<span style="line-height: 1.5;">\14</span><br />
</td>
<td>18\23 < g < 29\37<br />
</td>
<td>29\37 < g < 47\60<br />
</td>
<td>9g-7<br />
</td>
<td><span style="line-height: 1.5;">11-14g</span><br />
</td>
</tr>
<tr>
<td>10L13s<br />
</td>
<td>16\23 < g < 7\10<br />
</td>
<td>16\23 < g < 23\33<br />
</td>
<td>23\33 < g < 30\43<br />
</td>
<td>-9+13g<br />
</td>
<td>-10g+7<br />
</td>
</tr>
<tr>
<td>11L12s<br />
</td>
<td>2\23 < g < 1\11<br />
</td>
<td>2\23 < g < 3\34<br />
</td>
<td>3\34 < g < 4\45<br />
</td>
<td>-11g+1<br />
</td>
<td>12g-1<br />
</td>
</tr>
<tr>
<td>12L11s<br />
</td>
<td>21\23 < g < 11\12<br />
</td>
<td>21\23 < g < 32\35<br />
</td>
<td>32\35 < g < 43\47<br />
</td>
<td><span style="line-height: 1.5;">11g-10</span><br />
</td>
<td>11-12g<br />
</td>
</tr>
<tr>
<td>13L10s<br />
</td>
<td>7\23 < g < 4\13<br />
</td>
<td>7\23 < g < 11\36<br />
</td>
<td>11\36 < g < 15\49<br />
</td>
<td>4-13g<br />
</td>
<td>10g-3<br />
</td>
</tr>
<tr>
<td>14L9s<br />
</td>
<td>5\23 < g < 2\9<br />
</td>
<td>5\23 < g < 7\32<br />
</td>
<td>7\32 < g < 9\41<br />
</td>
<td>14g-3<br />
</td>
<td>-9g+2<br />
</td>
</tr>
<tr>
<td>15L8s<br />
</td>
<td>3\23 < g < 2\15<br />
</td>
<td>3\23 < g < 5\38<br />
</td>
<td>5\38 < g < 7\53<br />
</td>
<td>2-15g<br />
</td>
<td>8g-1<br />
</td>
</tr>
<tr>
<td>16L7s<br />
</td>
<td>10\23 < g < 7\16<br />
</td>
<td>10\23 < g < 17\39<br />
</td>
<td>17\39 < g < 24\55<br />
</td>
<td>7g-3<br />
</td>
<td><span style="line-height: 1.5;">-16g+7</span><br />
</td>
</tr>
<tr>
<td>17L6s<br />
</td>
<td>4\23 < g < 3\17<br />
</td>
<td>4\23 < g < 7\40<br />
</td>
<td>7\40 < g < 10\57<br />
</td>
<td>-1+6g<br />
</td>
<td>-17g+3<br />
</td>
</tr>
<tr>
<td>18L5s<br />
</td>
<td>14\23 < g < <span style="line-height: 1.5;">11\18</span><br />
</td>
<td>14\23 < g < 25\41<br />
</td>
<td>25\41 < g < 36\59<br />
</td>
<td>11-18g<br />
</td>
<td>5g-4<br />
</td>
</tr>
<tr>
<td>19L4s<br />
</td>
<td>6\23 < g < 5\19<br />
</td>
<td>6\23 < g < 11\42<br />
</td>
<td>11\42 < g < 16\61<br />
</td>
<td>-1+4g<br />
</td>
<td>-19g+5<br />
</td>
</tr>
<tr>
<td>20L3s<br />
</td>
<td>8\23 < g < 7\20<br />
</td>
<td>8\23 < g < 15\43<br />
</td>
<td>15\43 < g < 22\63<br />
</td>
<td>-1+3g<br />
</td>
<td>-20g+13<br />
</td>
</tr>
<tr>
<td>21L2s<br />
</td>
<td>12\23 < g < 11\21<br />
</td>
<td>12\23 < g < 23\44<br />
</td>
<td>23\44 < g < 34\65<br />
</td>
<td>-1+2g<br />
</td>
<td>-21g+1<br />
</td>
</tr>
<tr>
<td>22L1s<br />
</td>
<td>1\23 < g < 1\22<br />
</td>
<td>1\23 < g < 2\45<br />
</td>
<td>2\45 < g < 3\67<br />
</td>
<td>g<br />
</td>
<td>-22g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:44:<h1> --><h1 id="toc22"><a name="x24"></a><!-- ws:end:WikiTextHeadingRule:44 -->24</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Range of maximum expressiveness<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L23s<br />
</td>
<td>23\24 < g < 1<br />
</td>
<td>23\24 < g < 24\25<br />
</td>
<td>24\25 < g < 25\26<br />
</td>
<td>-22+23g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L<span style="line-height: 1.5;">22s</span><br />
</td>
<td>11\24 < g < 1\2<br />
</td>
<td>11\24 < g < 12\26 (6\13)<br />
</td>
<td>12\26 (6\13) < g < 15\28<br />
</td>
<td><span style="line-height: 1.5;">-g+1/2</span><br />
</td>
<td>-5+11g<br />
</td>
</tr>
<tr>
<td>3L<span style="line-height: 1.5;">21s</span><br />
</td>
<td>7\24 < g < 1\3<br />
</td>
<td>7\24 < g < 8\27<br />
</td>
<td>8\27 < g < 9\30 (3\10)<br />
</td>
<td>-2+7g<br />
</td>
<td><span style="line-height: 1.5;">-</span>1/3+g<br />
</td>
</tr>
<tr>
<td>4L<span style="line-height: 1.5;">20s</span><br />
</td>
<td>5\24 < g < 1\4<br />
</td>
<td>5\24 < g < 6\28 (3\14)<br />
</td>
<td>6\28 (3\14) < g < 7\32<br />
</td>
<td>-1+5g<br />
</td>
<td>-g+1/4<br />
</td>
</tr>
<tr>
<td>5L<span style="line-height: 1.5;">19s</span><br />
</td>
<td>19\24 < g < 4\5<br />
</td>
<td>19\24 < g < 23\29<br />
</td>
<td>23\29 < g < 27\34<br />
</td>
<td>-15+19g<br />
</td>
<td>-5g+4<br />
</td>
</tr>
<tr>
<td>6L<span style="line-height: 1.5;">18s</span><br />
</td>
<td>3\24 (1\8) < g < 1\6<br />
</td>
<td>3\24 (1\8) < g < 4\30 (2\15)<br />
</td>
<td>4\30 (2\15) < g < 5\36<br />
</td>
<td>-1\3+3g<br />
</td>
<td>1\6-g<br />
</td>
</tr>
<tr>
<td>7L<span style="line-height: 1.5;">17s</span><br />
</td>
<td>17\24 < g < 5\7<br />
</td>
<td>17\24 < g < 22\31<br />
</td>
<td>22\31 < g < 27\38<br />
</td>
<td>5-17g<br />
</td>
<td>7g-2<br />
</td>
</tr>
<tr>
<td>8L<span style="line-height: 1.5;">16s</span><br />
</td>
<td>2\24 (1\12) < g < 1\8<br />
</td>
<td>2\24 (1\12) < g < 3\32<br />
</td>
<td>3\32 < g < 4\40 (1\10)<br />
</td>
<td>-1\8+2g<br />
</td>
<td>-g+1\8<br />
</td>
</tr>
<tr>
<td>9L<span style="line-height: 1.5;">15s</span><br />
</td>
<td>5\24 < g < 2\9<br />
</td>
<td>5\24 < g < 7\33<br />
</td>
<td>7\33 < g < 9\42 (3\14)<br />
</td>
<td>5g-1<br />
</td>
<td>2\3-3g<br />
</td>
</tr>
<tr>
<td>10L<span style="line-height: 1.5;">14s</span><br />
</td>
<td>7\24 < g < 3\10<br />
</td>
<td>7\24 < g < 10\34 (5\17)<br />
</td>
<td>10\34 (5\17) < g < 13\44<br />
</td>
<td><span style="line-height: 1.5;">-4+7g</span><br />
</td>
<td>-3\2+5g<br />
</td>
</tr>
<tr>
<td>11L<span style="line-height: 1.5;">13s</span><br />
</td>
<td>13\24 < g < 6\11<br />
</td>
<td>13\24 < g < 19\35<br />
</td>
<td>19\35 < g < 25\46<br />
</td>
<td>13g-7<br />
</td>
<td>-11g+6<br />
</td>
</tr>
<tr>
<td>12L12s<br />
</td>
<td>1\24 < g < 1\12<br />
</td>
<td>1\24 < g < 2\36 (1\18)<br />
</td>
<td>2\36 (1\18) < g < 3\48 (1\16)<br />
</td>
<td>g<br />
</td>
<td>1\12-g<br />
</td>
</tr>
<tr>
<td><span style="line-height: 1.5;">13L</span>11s<br />
</td>
<td>11\24 < g < 6\13<br />
</td>
<td>11\24 < g < 17\37<br />
</td>
<td>17\37 < g < 23\50<br />
</td>
<td>11g-5<br />
</td>
<td>6-13g<br />
</td>
</tr>
<tr>
<td><span style="line-height: 1.5;">14L</span>10s<br />
</td>
<td>7\24 < g < 4\14 (2\7)<br />
</td>
<td>7\24 < g < 11\38<br />
</td>
<td>11\38 < g < 15\52<br />
</td>
<td>3\2-5g<br />
</td>
<td>7g-2<br />
</td>
</tr>
<tr>
<td><span style="line-height: 1.5;">15L</span>9s<br />
</td>
<td>3\24 (1\8) < g < 2\15<br />
</td>
<td>3\24 (1\8) < g < 5\39<br />
</td>
<td>5\39 < g < 7\54<br />
</td>
<td>3g-1\3<br />
</td>
<td>-5g+2\3<br />
</td>
</tr>
<tr>
<td><span style="line-height: 1.5;">16L</span>8s<br />
</td>
<td>1\24 < g < 1\16<br />
</td>
<td>1\24 < g < 2\40 (1\20)<br />
</td>
<td>2\40 (1\20) < g < 3\56<br />
</td>
<td>g<br />
</td>
<td><span style="line-height: 1.5;">1\8</span>-<span style="line-height: 1.5;">2g</span><br />
</td>
</tr>
<tr>
<td><span style="line-height: 1.5;">17L</span>7s<br />
</td>
<td>17\24 < g < 12\17<br />
</td>
<td>17\24 < g < 29\41<br />
</td>
<td>29\41 < g < 41\58<br />
</td>
<td>-7g+4<br />
</td>
<td>17g-12<br />
</td>
</tr>
<tr>
<td><span style="line-height: 1.5;">18L</span>6s<br />
</td>
<td>1\24 < g < 1\18<br />
</td>
<td>1\24 < g < 2\42 (1\21)<br />
</td>
<td>2\42 (1\21) < g < 3\60 (1\20)<br />
</td>
<td>g<br />
</td>
<td><span style="line-height: 1.5;">1\6-3</span>g<br />
</td>
</tr>
<tr>
<td><span style="line-height: 1.5;">19L</span>5s<br />
</td>
<td>19\24 < g < 15\19<br />
</td>
<td>19\24 < g < 34\43<br />
</td>
<td>34\43 < g < 49\62<br />
</td>
<td>-5g+4<br />
</td>
<td><span style="line-height: 1.5;">-15+19g</span><br />
</td>
</tr>
<tr>
<td><span style="line-height: 1.5;">20L</span>4s<br />
</td>
<td>1\24 < g < 1\20<br />
</td>
<td>1\24 < g < 2\44 (1\22)<br />
</td>
<td>2\44 (1\22) < g < 3\64<br />
</td>
<td>g<br />
</td>
<td>-5g+1\4<br />
</td>
</tr>
<tr>
<td><span style="line-height: 1.5;">21L</span>3s<br />
</td>
<td>1\24 < g < 1\21<br />
</td>
<td>1\24 < g < 2\45<br />
</td>
<td>2\45 < g < 3\66 (1\22)<br />
</td>
<td>g<br />
</td>
<td>-7g+1\3<br />
</td>
</tr>
<tr>
<td><span style="line-height: 1.5;">22L</span>2s<br />
</td>
<td>1\24 < g < 1\22<br />
</td>
<td>1\24 < g < 2\46 (1\23)<br />
</td>
<td>2\46 (1\23) < g < 3\68<br />
</td>
<td>g<br />
</td>
<td>-11g+1\2<br />
</td>
</tr>
<tr>
<td>23L1s<br />
</td>
<td>1\24 < g < 1\23<br />
</td>
<td>1\24 < g < 2\47<br />
</td>
<td>2\47 < g < 3\70<br />
</td>
<td>g<br />
</td>
<td>-23g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:46:<h1> --><h1 id="toc23"><a name="x25"></a><!-- ws:end:WikiTextHeadingRule:46 -->25</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Range of maximum expressiveness<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L24s<br />
</td>
<td>24\25 < g < 1<br />
</td>
<td>24\25 < g < 25\26<br />
</td>
<td>25\26 < g < 26\27<br />
</td>
<td>-23+24g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L23s<br />
</td>
<td>12\25 < g < 1\2<br />
</td>
<td>12\25 < g < 13\27<br />
</td>
<td>13\27 < g < 14\29<br />
</td>
<td>23g-11<br />
</td>
<td>1-2g<br />
</td>
</tr>
<tr>
<td>3L22s<br />
</td>
<td>8\25 < g < 1\3<br />
</td>
<td>8\25 < g < 9\28<br />
</td>
<td>9\28 < g < <span style="line-height: 1.5;">10\31</span><br />
</td>
<td>-7+22g<br />
</td>
<td>1-3g<br />
</td>
</tr>
<tr>
<td>4L21s<br />
</td>
<td>6\25 < g < 1\4<br />
</td>
<td>6\25 < g < 7\29<br />
</td>
<td>7\29 < g < 8\33<br />
</td>
<td>-5+21g<br />
</td>
<td>-4g+1<br />
</td>
</tr>
<tr>
<td>5L20s<br />
</td>
<td>4\25 < g < 1\5<br />
</td>
<td>4\25 < g < 5\30 (1\6)<br />
</td>
<td>5\30 (1\6) < g < 6\35<br />
</td>
<td>-3\5+4g<br />
</td>
<td>1\5-g<br />
</td>
</tr>
<tr>
<td>6L19s<br />
</td>
<td>4\25 < g < 1\6<br />
</td>
<td>4\25 < g < 5\31<br />
</td>
<td>5\31 < g < 6\37<br />
</td>
<td>-3+19g<br />
</td>
<td>-6g+1<br />
</td>
</tr>
<tr>
<td>7L18s<br />
</td>
<td>7\25 < g < 2\7<br />
</td>
<td>7\25 < g < 9\32<br />
</td>
<td>9\32 < g < 11\39<br />
</td>
<td>-5+18g<br />
</td>
<td>-7g+2<br />
</td>
</tr>
<tr>
<td>8L17s<br />
</td>
<td>3\25 < g < 1\8<br />
</td>
<td>3\25 < g < 4\33<br />
</td>
<td>4\33 < g < 5\41<br />
</td>
<td><span style="line-height: 1.5;">17g-2</span><br />
</td>
<td>1-8g<br />
</td>
</tr>
<tr>
<td>9L16s<br />
</td>
<td>11\25 < g < 4\9<br />
</td>
<td>11\25 < g < 15\34<br />
</td>
<td>15\34 < g < 19\43<br />
</td>
<td>-7+16g<br />
</td>
<td><span style="line-height: 1.5;">-9g+4</span><br />
</td>
</tr>
<tr>
<td>10L15s<br />
</td>
<td>2\25 < g < 1\10<br />
</td>
<td>2\25 < g < 3\35<br />
</td>
<td>3\35 < g < 4\45<br />
</td>
<td>-1\5+3g<br />
</td>
<td>1\5-2g<br />
</td>
</tr>
<tr>
<td>11L14s<br />
</td>
<td>9\25 < g < 4\11<br />
</td>
<td>9\25 < g < 13\36<br />
</td>
<td>13\36 < g < 17\47<br />
</td>
<td>14g-5<br />
</td>
<td>-11g+4<br />
</td>
</tr>
<tr>
<td>12L13s<br />
</td>
<td>2\25 < g < 1\12<br />
</td>
<td>2\25 < g < 3\37<br />
</td>
<td>3\37 < g < 4\49<br />
</td>
<td>13g-1<br />
</td>
<td>1-12g<br />
</td>
</tr>
<tr>
<td>13L12s<br />
</td>
<td>23\25 < g < 12\13<br />
</td>
<td>23\25 < g < 35\38<br />
</td>
<td>35\38 < g < 47\51<br />
</td>
<td>12g-11<br />
</td>
<td>12-13g<br />
</td>
</tr>
<tr>
<td>14L11s<br />
</td>
<td>16\25 < g < 9\14<br />
</td>
<td>16\25 < g < 25\39<br />
</td>
<td>25\39 < g < 34\53<br />
</td>
<td>-7+11g<br />
</td>
<td>-14g+9<br />
</td>
</tr>
<tr>
<td>15L10s<br />
</td>
<td>2\25 < g < 1\15<br />
</td>
<td>1\25 < g < 3<span style="line-height: 1.5;">\40</span><br />
</td>
<td><span style="line-height: 1.5;">3\40</span> < g < 4\55<br />
</td>
<td>-2g+1\5<br />
</td>
<td>3g-1\5<br />
</td>
</tr>
<tr>
<td>16L9s<br />
</td>
<td>14\25 < g < 9\16<br />
</td>
<td>14\25 < g < 23\41<br />
</td>
<td>23\41 < g < 32\57<br />
</td>
<td>9g-5<br />
</td>
<td>9-16g<br />
</td>
</tr>
<tr>
<td>17L8s<br />
</td>
<td>22\25 < g < 15\17<br />
</td>
<td>22\25 < g < 37\42<br />
</td>
<td>37\42 < g < 52\59<br />
</td>
<td>8g-7<br />
</td>
<td>-17g+15<br />
</td>
</tr>
<tr>
<td>18L7s<br />
</td>
<td>18\25 < g < 13\18<br />
</td>
<td>18\25 < g < 31\43<br />
</td>
<td>31\43 < g < 44\61<br />
</td>
<td>g<br />
</td>
<td>1\6-3g<br />
</td>
</tr>
<tr>
<td>19L6s<br />
</td>
<td>21\25 < g < 16\19<br />
</td>
<td>21\25 < g < 37\44<br />
</td>
<td>37\44 < g < 53\63<br />
</td>
<td>-19g+16<br />
</td>
<td>-5+6g<br />
</td>
</tr>
<tr>
<td>20L5s<br />
</td>
<td>1\25 < g < 1\20<br />
</td>
<td>1\25 < g < 2\45<br />
</td>
<td>2\45 < g < 3\65<br />
</td>
<td>g<br />
</td>
<td>-4g+1\5<br />
</td>
</tr>
<tr>
<td>21L4s<br />
</td>
<td>16\21 < g < 19\25<br />
</td>
<td>19\25 < g < 35\46<br />
</td>
<td>35\46 < g < 51\67<br />
</td>
<td>4g-3<br />
</td>
<td>-21g+16<br />
</td>
</tr>
<tr>
<td>22L3s<br />
</td>
<td>17\25 < g < 15\22<br />
</td>
<td>17\25 < g < 32\47<br />
</td>
<td>32\47 < g < 47\69<br />
</td>
<td>3g-2<br />
</td>
<td>-22g+15<br />
</td>
</tr>
<tr>
<td>23L2s<br />
</td>
<td>13\25 < g < 12\23<br />
</td>
<td>13\25 < g < 23\48<br />
</td>
<td>23\48 < g < 35\71<br />
</td>
<td>-2g+1<br />
</td>
<td>23g-11<br />
</td>
</tr>
<tr>
<td>24L1s<br />
</td>
<td>1\25 < g < 1\24<br />
</td>
<td>1\25 < g < 2\49<br />
</td>
<td>2\49 < g < 3\73<br />
</td>
<td>g<br />
</td>
<td>-24g+1<br />
</td>
</tr>
</table>
</body></html>