Generator ranges of MOS: Difference between revisions

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**Imported revision 334772470 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 334778896 - 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:genewardsmith|genewardsmith]] and made on <tt>2012-05-14 03:28:19 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-14 03:52:43 UTC</tt>.<br>
: The original revision id was <tt>334772470</tt>.<br>
: The original revision id was <tt>334778896</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>
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<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 22. 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.
<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 22. 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.


Suppose we have a scale of N steps to the interval of repetition, with Q steps to a period, so that there are P = N/Q periods to the repetition interval (usually, an octave.) If the generator range in question is u &lt; g &lt; v, then we may multiply by P to get C/Q &lt; Pg &lt; a/b, where C is the number of the [[Interval class|generic interval]] to which the generator g belongs, and both C/Q and a/b are reduced to lowest terms. We have normalized so that C/N &lt; g, and hence C/Q &lt; Pg, with C/N being the lower end of the range of possible generators, where L=s. If the range is C/Q &lt; Pg &lt; a/b, then when Pg = a/b, s has decreased to zero with increasing g, so s = (a - bg)/P. From s we may find L, since if there are e large steps and s small steps, eL + fs = 1, and so L = (1-fs)/e. Another fact worthy of note is that since C/N is the average size of an interval in class C, and since g &gt; C/N, g is larger than average, meaning g is the larger of the two possible sizes in that class. This means that the generator has been normalized to be [[Modal UDP Notation|chroma-positive]].
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 &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 [[Modal UDP Notation|chroma-positive]] generator.
 


=2=
=2=
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|| 20L2s || 1\22 &lt; g &lt; 1\20 || 1\22 &lt; g &lt; 1\21 || g || -10g+1\2 ||
|| 20L2s || 1\22 &lt; g &lt; 1\20 || 1\22 &lt; g &lt; 1\21 || g || -10g+1\2 ||
|| 21L1s || 1\22 &lt; g &lt; 1\21 || 1\22 &lt; g &lt; 2\43 || g || -21g+1 ||
|| 21L1s || 1\22 &lt; g &lt; 1\21 || 1\22 &lt; g &lt; 2\43 || g || -21g+1 ||
</pre></div>
</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Generator ranges of MOS&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Below are ranges of generators for various L-s patterns of MOS, with the number of steps in the scale from 2 to 22. 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.&lt;br /&gt;
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Generator ranges of MOS&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Below are ranges of generators for various L-s patterns of MOS, with the number of steps in the scale from 2 to 22. 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.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Suppose we have a scale of N steps to the interval of repetition, with Q steps to a period, so that there are P = N/Q periods to the repetition interval (usually, an octave.) If the generator range in question is u &amp;lt; g &amp;lt; v, then we may multiply by P to get C/Q &amp;lt; Pg &amp;lt; a/b, where C is the number of the &lt;a class="wiki_link" href="/Interval%20class"&gt;generic interval&lt;/a&gt; to which the generator g belongs, and both C/Q and a/b are reduced to lowest terms. We have normalized so that C/N &amp;lt; g, and hence C/Q &amp;lt; Pg, with C/N being the lower end of the range of possible generators, where L=s. If the range is C/Q &amp;lt; Pg &amp;lt; a/b, then when Pg = a/b, s has decreased to zero with increasing g, so s = (a - bg)/P. From s we may find L, since if there are e large steps and s small steps, eL + fs = 1, and so L = (1-fs)/e. Another fact worthy of note is that since C/N is the average size of an interval in class C, and since g &amp;gt; C/N, g is larger than average, meaning g is the larger of the two possible sizes in that class. This means that the generator has been normalized to be &lt;a class="wiki_link" href="/Modal%20UDP%20Notation"&gt;chroma-positive&lt;/a&gt;.&lt;br /&gt;
If the number of the &lt;a class="wiki_link" href="/Interval%20class"&gt;generic interval&lt;/a&gt; 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 &amp;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 &lt;a class="wiki_link" href="/Modal%20UDP%20Notation"&gt;chroma-positive&lt;/a&gt; generator.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x2"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;2&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x2"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;2&lt;/h1&gt;

Revision as of 03:52, 14 May 2012

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2012-05-14 03:52:43 UTC.
The original revision id was 334778896.
The revision comment was:

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

Original Wikitext content:

Below are ranges of generators for various L-s patterns of MOS, with the number of steps in the scale from 2 to 22. 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 || Large step || Small step ||
|| 1L1s || 1\2 < g < 1 || 1\2 < g < 2\3 || g || -g+1 ||

=3=
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step ||
|| 1L2s || 2\3 < g < 1 || 2\3 < g < 3\4 || -1+2g || -g+1 ||
|| 2L1s || 1\3 < g < 1\2 || 1\3 < g < 2\5 || g || -2g+1 ||

=4=
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step ||
|| 1L3s || 3\4 < g < 1 || 3\4 < g < 4\5 || -2+3g || -g+1 ||
|| 2L2s || 1\4 < g < 1\2 || 1\4 < g < 1\3 || g || -g+1\2 ||
|| 3L1s || 1\4 < g < 1\3 || 1\4 < g < 2\7 || g || 1-3g ||

=5=
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step ||
|| 1L4s || 4\5 < g < 1 || 4\5 < g < 5\6 || -3+4g || -g+1 ||
|| 2L3s || 2\5 < g < 1\2 || 2\5 < g < 3\7 || -1+3g || -2g+1 ||
|| 3L2s || 3\5 < g < 2\3 || 3\5 < g < 5\8 || -1+2g || -3g+2 ||
|| 4L1s || 1\5 < g < 1\4 || 1\5 < g < 2\9 || g || -4g+1 ||

=6=
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step ||
|| 1L5s || 5\6 < g < 1 || 5\6 < g < 6\7 || -4+5g || -g+1 ||
|| 2L4s || 1\3 < g < 1\2 || 1\3 < g < 2\5 || -1\2+2g || -g+1\2 ||
|| 3L3s || 1\6 < g < 1\3 || 1\6 < g < 2\9 || g || -g+1\3 ||
|| 4L2s || 1\6 < g < 1\4 || 1\6 < g < 1\5 || g || -2g+1\2 ||
|| 5L1s || 1\6 < g < 1\5 || 1\6 < g < 2\11 || g || -5g+1 ||

=7=
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step ||
|| 1L6s || 6\7 < g < 1 || 6\7 < g < 7\8 || -5+6g || -g+1 ||
|| 2L5s || 3\7 < g < 1\2 || 3\7 < g < 4\9 || -2+5g || -2g+1 ||
|| 3L4s || 2\7 < g < 1\3 || 2\7 < g < 3\10 || -1+4g || 1-3g ||
|| 4L3s || 5\7 < g < 3\4 || 5\7 < g < 8\11 || -2+3g || -4g+3 ||
|| 5L2s || 4\7 < g < 3\5 || 4\7 < g < 7\12 || -1+2g || -5g+3 ||
|| 6L1s || 1\7 < g < 1\6 || 1\7 < g < 2\13 || g || -6g+1 ||

=8=
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step ||
|| 1L7s || 7\8 < g < 1 || 7\8 < g < 8\9 || -6+7g || -g+1 ||
|| 2L6s || 3\8 < g < 1\2 || 3\8 < g < 2\5 || -1+3g || -g+1\2 ||
|| 3L5s || 5\8 < g < 2\3 || 5\8 < g < 7\11 || -3+5g || -3g+2 ||
|| 4L4s || 1\8 < g < 1\4 || 1\8 < g < 1\6 || g || -g+1\4 ||
|| 5L3s || 3\8 < g < 2\5 || 3\8 < g < 5\13 || -1+3g || -5g+2 ||
|| 6L2s || 1\8 < g < 1\6 || 1\8 < g < 1\7 || g || -3g+1\2 ||
|| 7L1s || 1\8 < g < 1\7 || 1\8 < g < 2\15 || g || -7g+1 ||

=9=
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step ||
|| 1L8s || 8\9 < g < 1 || 8\9 < g < 9\10 || -7+8g || -g+1 ||
|| 2L7s || 4\9 < g < 1\2 || 4\9 < g < 5\11 || -3+7g || -2g+1 ||
|| 3L6s || 2\9 < g < 1\3 || 2\9 < g < 1\4 || -1\3+2g || -g+1\3 ||
|| 4L5s || 2\9 < g < 1\4 || 2\9 < g < 3\13 || -1+5g || -4g+1 ||
|| 5L4s || 7\9 < g < 4\5 || 7\9 < g < 11\14 || -3+4g || -5g+4 ||
|| 6L3s || 1\9 < g < 1\6 || 1\9 < g < 2\15 || g || -2g+1\3 ||
|| 7L2s || 5\9 < g < 4\7 || 5\9 < g < 9\16 || -1+2g || -7g+4 ||
|| 8L1s || 1\9 < g < 1\8 || 1\9 < g < 2\17 || g || -8g+1 ||

=10=
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step ||
|| 1L9s || 9\10 < g < 1 || 9\10 < g < 10\11 || -8+9g || -g+1 ||
|| 2L8s || 2\5 < g < 1\2 || 2\5 < g < 3\7 || -3\2+4g || -g+1\2 ||
|| 3L7s || 3\10 < g < 1\3 || 3\10 < g < 4\13 || -2+7g || 1-3g ||
|| 4L6s || 1\5 < g < 1\4 || 1\5 < g < 2\9 || 3g-1\2 || -2g+1\2 ||
|| 5L5s || 1\10 < g < 1\5 || 1\10 < g < 2\15 || g || -g+1\5 ||
|| 6L4s || 3\10 < g < 1\3 || 3\10 < g < 4\13 || -1\2+2g || 1-3g ||
|| 7L3s || 7\10 < g < 5\7 || 7\10 < g < 12\17 || -2+3g || -7g+5 ||
|| 8L2s || 1\10 < g < 1\8 || 1\10 < g < 1\9 || g || -4g+1\2 ||
|| 9L1s || 1\10 < g < 1\9 || 1\10 < g < 2\19 || g || -9g+1 ||

=11=
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step ||
|| 1L10s || 10\11 < g < 1 || 10\11 < g < 11\12 || -9+10g || -g+1 ||
|| 2L9s || 5\11 < g < 1\2 || 5\11 < g < 6\13 || -4+9g || -2g+1 ||
|| 3L8s || 7\11 < g < 2\3 || 7\11 < g < 9\14 || -5+8g || -3g+2 ||
|| 4L7s || 8\11 < g < 3\4 || 8\11 < g < 11\15 || -5+7g || -4g+3 ||
|| 5L6s || 2\11 < g < 1\5 || 2\11 < g < 3\16 || -1+6g || -5g+1 ||
|| 6L5s || 9\11 < g < 5\6 || 9\11 < g < 14\17 || -4+5g || -6g+5 ||
|| 7L4s || 3\11 < g < 2\7 || 3\11 < g < 5\18 || -1+4g || -7g+2 ||
|| 8L3s || 4\11 < g < 3\8 || 4\11 < g < 7\19 || -1+3g || -8g+3 ||
|| 9L2s || 6\11 < g < 5\9 || 6\11 < g < 11\20 || -1+2g || -9g+5 ||
|| 10L1s || 1\11 < g < 1\10 || 1\11 < g < 2\21 || g || -10g+1 ||

=12=
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step ||
|| 1L11s || 11\12 < g < 1 || 11\12 < g < 12\13 || -10+11g || -g+1 ||
|| 2L10s || 5\12 < g < 1\2 || 5\12 < g < 3\7 || -2+5g || -g+1\2 ||
|| 3L9s || 1\4 < g < 1\3 || 1\4 < g < 2\7 || -2\3+3g || -g+1\3 ||
|| 4L8s || 1\6 < g < 1\4 || 1\6 < g < 1\5 || -1\4+2g || -g+1\4 ||
|| 5L7s || 7\12 < g < 3\5 || 7\12 < g < 10\17 || -4+7g || -5g+3 ||
|| 6L6s || 1\12 < g < 1\6 || 1\12 < g < 1\9 || g || -g+1\6 ||
|| 7L5s || 5\12 < g < 3\7 || 5\12 < g < 8\19 || -2+5g || -7g+3 ||
|| 8L4s || 1\12 < g < 1\8 || 1\12 < g < 1\10 || g || -2g+1\4 ||
|| 9L3s || 1\12 < g < 1\9 || 1\12 < g < 2\21 || g || -3g+1\3 ||
|| 10L2s || 1\12 < g < 1\10 || 1\12 < g < 1\11 || g || -5g+1\2 ||
|| 11L1s || 1\12 < g < 1\11 || 1\12 < g < 2\23 || g || -11g+1 ||

=13=
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step ||
|| 1L12s || 12\13 < g < 1 || 12\13 < g < 13\14 || -11+12g || -g+1 ||
|| 2L11s || 6\13 < g < 1\2 || 6\13 < g < 7\15 || -5+11g || -2g+1 ||
|| 3L10s || 4\13 < g < 1\3 || 4\13 < g < 5\16 || -3+10g || 1-3g ||
|| 4L9s || 3\13 < g < 1\4 || 3\13 < g < 4\17 || -2+9g || -4g+1 ||
|| 5L8s || 5\13 < g < 2\5 || 5\13 < g < 7\18 || -3+8g || -5g+2 ||
|| 6L7s || 2\13 < g < 1\6 || 2\13 < g < 3\19 || -1+7g || -6g+1 ||
|| 7L6s || 11\13 < g < 6\7 || 11\13 < g < 17\20 || -5+6g || -7g+6 ||
|| 8L5s || 8\13 < g < 5\8 || 8\13 < g < 13\21 || -3+5g || -8g+5 ||
|| 9L4s || 10\13 < g < 7\9 || 10\13 < g < 17\22 || -3+4g || -9g+7 ||
|| 10L3s || 9\13 < g < 7\10 || 9\13 < g < 16\23 || -2+3g || -10g+7 ||
|| 11L2s || 7\13 < g < 6\11 || 7\13 < g < 13\24 || -1+2g || -11g+6 ||
|| 12L1s || 1\13 < g < 1\12 || 1\13 < g < 2\25 || g || -12g+1 ||

=14=
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step ||
|| 1L13s || 13\14 < g < 1 || 13\14 < g < 14\15 || -12+13g || -g+1 ||
|| 2L12s || 3\7 < g < 1\2 || 3\7 < g < 4\9 || -5\2+6g || -g+1\2 ||
|| 3L11s || 9\14 < g < 2\3 || 9\14 < g < 11\17 || -7+11g || -3g+2 ||
|| 4L10s || 3\14 < g < 1\4 || 3\14 < g < 2\9 || -1+5g || -2g+1\2 ||
|| 5L9s || 11\14 < g < 4\5 || 11\14 < g < 15\19 || -7+9g || -5g+4 ||
|| 6L8s || 1\7 < g < 1\6 || 1\7 < g < 2\13 || 4g-1\2 || -3g+1\2 ||
|| 7L7s || 1\14 < g < 1\7 || 1\14 < g < 2\21 || g || -g+1\7 ||
|| 8L6s || 5\14 < g < 3\8 || 5\14 < g < 4\11 || -1+3g || -4g+3\2 ||
|| 9L5s || 3\14 < g < 2\9 || 3\14 < g < 5\23 || -1+5g || -9g+2 ||
|| 10L4s || 2\7 < g < 3\10 || 2\7 < g < 5\17 || -1\2+2g || -5g+3\2 ||
|| 11L3s || 5\14 < g < 4\11 || 5\14 < g < 9\25 || -1+3g || -11g+4 ||
|| 12L2s || 1\14 < g < 1\12 || 1\14 < g < 1\13 || g || -6g+1\2 ||
|| 13L1s || 1\14 < g < 1\13 || 1\14 < g < 2\27 || g || -13g+1 ||

=15=
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step ||
|| 1L14s || 14\15 < g < 1 || 14\15 < g < 15\16 || -13+14g || -g+1 ||
|| 2L13s || 7\15 < g < 1\2 || 7\15 < g < 8\17 || -6+13g || -2g+1 ||
|| 3L12s || 4\15 < g < 1\3 || 4\15 < g < 5\18 || -1+4g || -g+1\3 ||
|| 4L11s || 11\15 < g < 3\4 || 11\15 < g < 14\19 || -8+11g || -4g+3 ||
|| 5L10s || 2\15 < g < 1\5 || 2\15 < g < 3\20 || -1\5+2g || -g+1\5 ||
|| 6L9s || 2\15 < g < 1\6 || 2\15 < g < 1\7 || -1\3+3g || -2g+1\3 ||
|| 7L8s || 2\15 < g < 1\7 || 2\15 < g < 3\22 || -1+8g || -7g+1 ||
|| 8L7s || 13\15 < g < 7\8 || 13\15 < g < 20\23 || -6+7g || -8g+7 ||
|| 9L6s || 1\5 < g < 2\9 || 1\5 < g < 3\14 || -1\3+2g || -3g+2\3 ||
|| 10L5s || 1\15 < g < 1\10 || 1\15 < g < 2\25 || g || -2g+1\5 ||
|| 11L4s || 4\15 < g < 3\11 || 4\15 < g < 7\26 || -1+4g || -11g+3 ||
|| 12L3s || 1\15 < g < 1\12 || 1\15 < g < 2\27 || g || -4g+1\3 ||
|| 13L2s || 8\15 < g < 7\13 || 8\15 < g < 15\28 || -1+2g || -13g+7 ||
|| 14L1s || 1\15 < g < 1\14 || 1\15 < g < 2\29 || g || -14g+1 ||

=16=
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step ||
|| 1L15s || 15\16 < g < 1 || 15\16 < g < 16\17 || -14+15g || -g+1 ||
|| 2L14s || 7\16 < g < 1\2 || 7\16 < g < 4\9 || -3+7g || -g+1\2 ||
|| 3L13s || 5\16 < g < 1\3 || 5\16 < g < 6\19 || -4+13g || 1-3g ||
|| 4L12s || 3\16 < g < 1\4 || 3\16 < g < 1\5 || 3g-1\2 || -g+1\4 ||
|| 5L11s || 3\16 < g < 1\5 || 3\16 < g < 4\21 || -2+11g || -5g+1 ||
|| 6L10s || 5\16 < g < 1\3 || 5\16 < g < 6\19 || -3\2+5g || 1-3g ||
|| 7L9s || 9\16 < g < 4\7 || 9\16 < g < 13\23 || -5+9g || -7g+4 ||
|| 8L8s || 1\16 < g < 1\8 || 1\16 < g < 1\12 || g || -g+1\8 ||
|| 9L7s || 7\16 < g < 4\9 || 7\16 < g < 11\25 || -3+7g || -9g+4 ||
|| 10L6s || 3\16 < g < 1\5 || 3\16 < g < 4\21 || 3g-1\2 || -5g+1 ||
|| 11L5s || 13\16 < g < 9\11 || 13\16 < g < 22\27 || -4+5g || -11g+9 ||
|| 12L4s || 1\16 < g < 1\12 || 1\16 < g < 1\14 || g || -3g+1\4 ||
|| 13L3s || 11\16 < g < 9\13 || 11\16 < g < 20\29 || -2+3g || -13g+9 ||
|| 14L2s || 1\16 < g < 1\14 || 1\16 < g < 1\15 || g || -7g+1\2 ||
|| 15L1s || 1\16 < g < 1\15 || 1\16 < g < 2\31 || g || -15g+1 ||

=17=
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step ||
|| 1L16s || 16\17 < g < 1 || 16\17 < g < 17\18 || -15+16g || -g+1 ||
|| 2L15s || 8\17 < g < 1\2 || 8\17 < g < 9\19 || -7+15g || -2g+1 ||
|| 3L14s || 11\17 < g < 2\3 || 11\17 < g < 13\20 || -9+14g || -3g+2 ||
|| 4L13s || 4\17 < g < 1\4 || 4\17 < g < 5\21 || -3+13g || -4g+1 ||
|| 5L12s || 10\17 < g < 3\5 || 10\17 < g < 13\22 || -7+12g || -5g+3 ||
|| 6L11s || 14\17 < g < 5\6 || 14\17 < g < 19\23 || -9+11g || -6g+5 ||
|| 7L10s || 12\17 < g < 5\7 || 12\17 < g < 17\24 || -7+10g || -7g+5 ||
|| 8L9s || 2\17 < g < 1\8 || 2\17 < g < 3\25 || -1+9g || -8g+1 ||
|| 9L8s || 15\17 < g < 8\9 || 15\17 < g < 23\26 || -7+8g || -9g+8 ||
|| 10L7s || 5\17 < g < 3\10 || 5\17 < g < 8\27 || -2+7g || -10g+3 ||
|| 11L6s || 3\17 < g < 2\11 || 3\17 < g < 5\28 || -1+6g || -11g+2 ||
|| 12L5s || 7\17 < g < 5\12 || 7\17 < g < 12\29 || -2+5g || -12g+5 ||
|| 13L4s || 13\17 < g < 10\13 || 13\17 < g <23\30 || -3+4g || -13g+10 ||
|| 14L3s || 6\17 < g < 5\14 || 6\17 < g < 11\31 || -1+3g || -14g+5 ||
|| 15L2s || 9\17 < g < 8\15 || 9\17 < g < 17\32 || -1+2g || -15g+8 ||
|| 16L1s || 1\17 < g < 1\16 || 1\17 < g < 2\33 || g || -16g+1 ||

=18=
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step ||
|| 1L17s || 17\18 < g < 1 || 17\18 < g < 18\19 || -16+17g || -g+1 ||
|| 2L16s || 4\9 < g < 1\2 || 4\9 < g < 5\11 || -7\2+8g || -g+1\2 ||
|| 3L15s || 5\18 < g < 1\3 || 5\18 < g < 2\7 || -4\3+5g || -g+1\3 ||
|| 4L14s || 2\9 < g < 1\4 || 2\9 < g < 3\13 || -3\2+7g || -2g+1\2 ||
|| 5L13s || 7\18 < g < 2\5 || 7\18 < g < 9\23 || -5+13g || -5g+2 ||
|| 6L12s || 1\9 < g < 1\6 || 1\9 < g < 2\15 || -1\6+2g || -g+1\6 ||
|| 7L11s || 5\18 < g < 2\7 || 5\18 < g < 7\25 || -3+11g || -7g+2 ||
|| 8L10s || 1\9 < g < 1\8 || 1\9 < g < 2\17 || -1\2+5g || -4g+1\2 ||
|| 9L9s || 1\18 < g < 1\9 || 1\18 < g < 2\27 || g || -g+1\9 ||
|| 10L8s || 7\18 < g < 2\5 || 7\18 < g < 9\23 || -3\2+4g || -5g+2 ||
|| 11L7s || 13\18 < g < 8\11 || 13\18 < g < 21\29 || -5+7g || -11g+8 ||
|| 12L6s || 1\18 < g < 1\12 || 1\18 < g < 1\15 || g || -2g+1\6 ||
|| 13L5s || 11\18 < g < 8\13 || 11\18 < g < 19\31 || -3+5g || -13g+8 ||
|| 14L4s || 5\18 < g < 2\7 || 5\18 < g < 7\25 || -1\2+2g || -7g+2 ||
|| 15L3s || 1\18 < g < 1\15 || 1\18 < g < 2\33 || g || -5g+1\3 ||
|| 16L2s || 1\18 < g < 1\16 || 1\18 < g < 1\17 || g || -8g+1\2 ||
|| 17L1s || 1\18 < g < 1\17 || 1\18 < g < 2\35 || g || -17g+1 ||

=19=
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step ||
|| 1L18s || 18\19 < g < 1 || 18\19 < g < 19\20 || -17+18g || -g+1 ||
|| 2L17s || 9\19 < g < 1\2 || 9\19 < g < 10\21 || -8+17g || -2g+1 ||
|| 3L16s || 6\19 < g < 1\3 || 6\19 < g < 7\22 || -5+16g || 1-3g ||
|| 4L15s || 14\19 < g < 3\4 || 14\19 < g < 17\23 || -11+15g || -4g+3 ||
|| 5L14s || 15\19 < g < 4\5 || 15\19 < g < 19\24 || -11+14g || -5g+4 ||
|| 6L13s || 3\19 < g < 1\6 || 3\19 < g < 4\25 || -2+13g || -6g+1 ||
|| 7L12s || 8\19 < g < 3\7 || 8\19 < g < 11\26 || -5+12g || -7g+3 ||
|| 8L11s || 7\19 < g < 3\8 || 7\19 < g < 10\27 || -4+11g || -8g+3 ||
|| 9L10s || 2\19 < g < 1\9 || 2\19 < g < 3\28 || -1+10g || -9g+1 ||
|| 10L9s || 17\19 < g < 9\10 || 17\19 < g < 26\29 || -8+9g || -10g+9 ||
|| 11L8s || 12\19 < g < 7\11 || 12\19 < g < 19\30 || -5+8g || -11g+7 ||
|| 12L7s || 11\19 < g < 7\12 || 11\19 < g < 18\31 || -4+7g || -12g+7 ||
|| 13L6s || 16\19 < g < 11\13 || 16\19 < g < 27\32 || -5+6g || -13g+11 ||
|| 14L5s || 4\19 < g < 3\14 || 4\19 < g < 7\33 || -1+5g || -14g+3 ||
|| 15L4s || 5\19 < g < 4\15 || 5\19 < g < 9\34 || -1+4g || -15g+4 ||
|| 16L3s || 13\19 < g < 11\16 || 13\19 < g < 24\35 || -2+3g || -16g+11 ||
|| 17L2s || 10\19 < g < 9\17 || 10\19 < g < 19\36 || -1+2g || -17g+9 ||
|| 18L1s || 1\19 < g < 1\18 || 1\19 < g < 2\37 || g || -18g+1 ||

=20=
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step ||
|| 1L19s || 19\20 < g < 1 || 19\20 < g < 20\21 || -18+19g || -g+1 ||
|| 2L18s || 9\20 < g < 1\2 || 9\20 < g < 5\11 || -4+9g || -g+1\2 ||
|| 3L17s || 13\20 < g < 2\3 || 13\20 < g < 15\23 || -11+17g || -3g+2 ||
|| 4L16s || 1\5 < g < 1\4 || 1\5 < g < 2\9 || -3\4+4g || -g+1\4 ||
|| 5L15s || 3\20 < g < 1\5 || 3\20 < g < 4\25 || -2\5+3g || -g+1\5 ||
|| 6L14s || 3\20 < g < 1\6 || 3\20 < g < 2\13 || -1+7g || -3g+1\2 ||
|| 7L13s || 17\20 < g < 6\7 || 17\20 < g < 23\27 || -11+13g || -7g+6 ||
|| 8L12s || 1\10 < g < 1\8 || 1\10 < g < 1\9 || -1\4+3g || -2g+1\4 ||
|| 9L11s || 11\20 < g < 5\9 || 11\20 < g < 16\29 || -6+11g || -9g+5 ||
|| 10L10s || 1\20 < g < 1\10 || 1\20 < g < 1\15 || g || -g+1\10 ||
|| 11L9s || 9\20 < g < 5\11 || 9\20 < g < 14\31 || -4+9g || -11g+5 ||
|| 12L8s || 3\20 < g < 1\6 || 3\20 < g < 2\13 || -1\4+2g || -3g+1\2 ||
|| 13L7s || 3\20 < g < 2\13 || 3\20 < g < 5\33 || -1+7g || -13g+2 ||
|| 14L6s || 7\20 < g < 5\14 || 7\20 < g < 6\17 || -1+3g || -7g+5\2 ||
|| 15L5s || 1\20 < g < 1\15 || 1\20 < g < 2\35 || g || -3g+1\5 ||
|| 16L4s || 1\20 < g < 1\16 || 1\20 < g < 1\18 || g || -4g+1\4 ||
|| 17L3s || 7\20 < g < 6\17 || 7\20 < g < 13\37 || -1+3g || -17g+6 ||
|| 18L2s || 1\20 < g < 1\18 || 1\20 < g < 1\19 || g || -9g+1\2 ||
|| 19L1s || 1\20 < g < 1\19 || 1\20 < g < 2\39 || g || -19g+1 ||

=21=
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step ||
|| 1L20s || 20\21 < g < 1 || 20\21 < g < 21\22 || -19+20g || -g+1 ||
|| 2L19s || 10\21 < g < 1\2 || 10\21 < g < 11\23 || -9+19g || -2g+1 ||
|| 3L18s || 2\7 < g < 1\3 || 2\7 < g < 3\10 || -5\3+6g || -g+1\3 ||
|| 4L17s || 5\21 < g < 1\4 || 5\21 < g < 6\25 || -4+17g || -4g+1 ||
|| 5L16s || 4\21 < g < 1\5 || 4\21 < g < 5\26 || -3+16g || -5g+1 ||
|| 6L15s || 1\7 < g < 1\6 || 1\7 < g < 2\13 || -2\3+5g || -2g+1\3 ||
|| 7L14s || 2\21 < g < 1\7 || 2\21 < g < 3\28 || -1\7+2g || -g+1\7 ||
|| 8L13s || 13\21 < g < 5\8 || 13\21 < g < 18\29 || -8+13g || -8g+5 ||
|| 9L12s || 2\21 < g < 1\9 || 2\21 < g < 1\10 || -1\3+4g || -3g+1\3 ||
|| 10L11s || 2\21 < g < 1\10 || 2\21 < g < 3\31 || -1+11g || -10g+1 ||
|| 11L10s || 19\21 < g < 10\11 || 19\21 < g < 29\32 || -9+10g || -11g+10 ||
|| 12L9s || 5\21 < g < 1\4 || 5\21 < g < 6\25 || -2\3+3g || -4g+1 ||
|| 13L8s || 8\21 < g < 5\13 || 8\21 < g < 13\34 || -3+8g || -13g+5 ||
|| 14L7s || 1\21 < g < 1\14 || 1\21 < g < 2\35 || g || -2g+1\7 ||
|| 15L6s || 4\21 < g < 1\5 || 4\21 < g < 5\26 || -1\3+2g || -5g+1 ||
|| 16L5s || 17\21 < g < 13\16 || 17\21 < g < 30\37 || -4+5g || -16g+13 ||
|| 17L4s || 16\21 < g < 13\17 || 16\21 < g < 29\38 || -3+4g || -17g+13 ||
|| 18L3s || 1\21 < g < 1\18 || 1\21 < g < 2\39 || g || -6g+1\3 ||
|| 19L2s || 11\21 < g < 10\19 || 11\21 < g < 21\40 || -1+2g || -19g+10 ||
|| 20L1s || 1\21 < g < 1\20 || 1\21 < g < 2\41 || g || -20g+1 ||

=22=
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step ||
|| 1L21s || 21\22 < g < 1 || 21\22 < g < 22\23 || -20+21g || -g+1 ||
|| 2L20s || 5\11 < g < 1\2 || 5\11 < g < 6\13 || -9\2+10g || -g+1\2 ||
|| 3L19s || 7\22 < g < 1\3 || 7\22 < g < 8\25 || -6+19g || 1-3g ||
|| 4L18s || 5\22 < g < 1\4 || 5\22 < g < 3\13 || -2+9g || -2g+1\2 ||
|| 5L17s || 13\22 < g < 3\5 || 13\22 < g < 16\27 || -10+17g || -5g+3 ||
|| 6L16s || 7\22 < g < 1\3 || 7\22 < g < 8\25 || -5\2+8g || 1-3g ||
|| 7L15s || 3\22 < g < 1\7 || 3\22 < g < 4\29 || -2+15g || -7g+1 ||
|| 8L14s || 4\11 < g < 3\8 || 4\11 < g < 7\19 || -5\2+7g || -4g+3\2 ||
|| 9L13s || 17\22 < g < 7\9 || 17\22 < g < 24\31 || -10+13g || -9g+7 ||
|| 10L12s || 1\11 < g < 1\10 || 1\11 < g < 2\21 || -1\2+6g || -5g+1\2 ||
|| 11L11s || 1\22 < g < 1\11 || 1\22 < g < 2\33 || g || -g+1\11 ||
|| 12L10s || 9\22 < g < 5\12 || 9\22 < g < 7\17 || -2+5g || -6g+5\2 ||
|| 13L9s || 5\22 < g < 3\13 || 5\22 < g < 8\35 || -2+9g || -13g+3 ||
|| 14L8s || 3\22 < g < 1\7 || 3\22 < g < 4\29 || 4g-1\2 || -7g+1 ||
|| 15L7s || 19\22 < g < 13\15 || 19\22 < g < 32\37 || -6+7g || -15g+13 ||
|| 16L6s || 2\11 < g < 3\16 || 2\11 < g < 5\27 || 3g-1\2 || -8g+3\2 ||
|| 17L5s || 9\22 < g < 7\17 || 9\22 < g < 16\39 || -2+5g || -17g+7 ||
|| 18L4s || 3\11 < g < 5\18 || 3\11 < g < 8\29 || -1\2+2g || -9g+5\2 ||
|| 19L3s || 15\22 < g < 13\19 || 15\22 < g <28\41 || -2+3g || -19g+13 ||
|| 20L2s || 1\22 < g < 1\20 || 1\22 < g < 1\21 || g || -10g+1\2 ||
|| 21L1s || 1\22 < g < 1\21 || 1\22 < g < 2\43 || g || -21g+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 22. 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 &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 />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x2"></a><!-- ws:end:WikiTextHeadingRule:0 -->2</h1>


<table class="wiki_table">
    <tr>
        <td>Large-small numbers<br />
</td>
        <td>Generator range<br />
</td>
        <td>Range of propriety<br />
</td>
        <td>Large step<br />
</td>
        <td>Small step<br />
</td>
    </tr>
    <tr>
        <td>1L1s<br />
</td>
        <td>1\2 &lt; g &lt; 1<br />
</td>
        <td>1\2 &lt; g &lt; 2\3<br />
</td>
        <td>g<br />
</td>
        <td>-g+1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><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>Large step<br />
</td>
        <td>Small step<br />
</td>
    </tr>
    <tr>
        <td>1L2s<br />
</td>
        <td>2\3 &lt; g &lt; 1<br />
</td>
        <td>2\3 &lt; g &lt; 3\4<br />
</td>
        <td>-1+2g<br />
</td>
        <td>-g+1<br />
</td>
    </tr>
    <tr>
        <td>2L1s<br />
</td>
        <td>1\3 &lt; g &lt; 1\2<br />
</td>
        <td>1\3 &lt; g &lt; 2\5<br />
</td>
        <td>g<br />
</td>
        <td>-2g+1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><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>Large step<br />
</td>
        <td>Small step<br />
</td>
    </tr>
    <tr>
        <td>1L3s<br />
</td>
        <td>3\4 &lt; g &lt; 1<br />
</td>
        <td>3\4 &lt; g &lt; 4\5<br />
</td>
        <td>-2+3g<br />
</td>
        <td>-g+1<br />
</td>
    </tr>
    <tr>
        <td>2L2s<br />
</td>
        <td>1\4 &lt; g &lt; 1\2<br />
</td>
        <td>1\4 &lt; g &lt; 1\3<br />
</td>
        <td>g<br />
</td>
        <td>-g+1\2<br />
</td>
    </tr>
    <tr>
        <td>3L1s<br />
</td>
        <td>1\4 &lt; g &lt; 1\3<br />
</td>
        <td>1\4 &lt; g &lt; 2\7<br />
</td>
        <td>g<br />
</td>
        <td>1-3g<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><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>Large step<br />
</td>
        <td>Small step<br />
</td>
    </tr>
    <tr>
        <td>1L4s<br />
</td>
        <td>4\5 &lt; g &lt; 1<br />
</td>
        <td>4\5 &lt; g &lt; 5\6<br />
</td>
        <td>-3+4g<br />
</td>
        <td>-g+1<br />
</td>
    </tr>
    <tr>
        <td>2L3s<br />
</td>
        <td>2\5 &lt; g &lt; 1\2<br />
</td>
        <td>2\5 &lt; g &lt; 3\7<br />
</td>
        <td>-1+3g<br />
</td>
        <td>-2g+1<br />
</td>
    </tr>
    <tr>
        <td>3L2s<br />
</td>
        <td>3\5 &lt; g &lt; 2\3<br />
</td>
        <td>3\5 &lt; g &lt; 5\8<br />
</td>
        <td>-1+2g<br />
</td>
        <td>-3g+2<br />
</td>
    </tr>
    <tr>
        <td>4L1s<br />
</td>
        <td>1\5 &lt; g &lt; 1\4<br />
</td>
        <td>1\5 &lt; g &lt; 2\9<br />
</td>
        <td>g<br />
</td>
        <td>-4g+1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><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>Large step<br />
</td>
        <td>Small step<br />
</td>
    </tr>
    <tr>
        <td>1L5s<br />
</td>
        <td>5\6 &lt; g &lt; 1<br />
</td>
        <td>5\6 &lt; g &lt; 6\7<br />
</td>
        <td>-4+5g<br />
</td>
        <td>-g+1<br />
</td>
    </tr>
    <tr>
        <td>2L4s<br />
</td>
        <td>1\3 &lt; g &lt; 1\2<br />
</td>
        <td>1\3 &lt; g &lt; 2\5<br />
</td>
        <td>-1\2+2g<br />
</td>
        <td>-g+1\2<br />
</td>
    </tr>
    <tr>
        <td>3L3s<br />
</td>
        <td>1\6 &lt; g &lt; 1\3<br />
</td>
        <td>1\6 &lt; g &lt; 2\9<br />
</td>
        <td>g<br />
</td>
        <td>-g+1\3<br />
</td>
    </tr>
    <tr>
        <td>4L2s<br />
</td>
        <td>1\6 &lt; g &lt; 1\4<br />
</td>
        <td>1\6 &lt; g &lt; 1\5<br />
</td>
        <td>g<br />
</td>
        <td>-2g+1\2<br />
</td>
    </tr>
    <tr>
        <td>5L1s<br />
</td>
        <td>1\6 &lt; g &lt; 1\5<br />
</td>
        <td>1\6 &lt; g &lt; 2\11<br />
</td>
        <td>g<br />
</td>
        <td>-5g+1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><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>Large step<br />
</td>
        <td>Small step<br />
</td>
    </tr>
    <tr>
        <td>1L6s<br />
</td>
        <td>6\7 &lt; g &lt; 1<br />
</td>
        <td>6\7 &lt; g &lt; 7\8<br />
</td>
        <td>-5+6g<br />
</td>
        <td>-g+1<br />
</td>
    </tr>
    <tr>
        <td>2L5s<br />
</td>
        <td>3\7 &lt; g &lt; 1\2<br />
</td>
        <td>3\7 &lt; g &lt; 4\9<br />
</td>
        <td>-2+5g<br />
</td>
        <td>-2g+1<br />
</td>
    </tr>
    <tr>
        <td>3L4s<br />
</td>
        <td>2\7 &lt; g &lt; 1\3<br />
</td>
        <td>2\7 &lt; g &lt; 3\10<br />
</td>
        <td>-1+4g<br />
</td>
        <td>1-3g<br />
</td>
    </tr>
    <tr>
        <td>4L3s<br />
</td>
        <td>5\7 &lt; g &lt; 3\4<br />
</td>
        <td>5\7 &lt; g &lt; 8\11<br />
</td>
        <td>-2+3g<br />
</td>
        <td>-4g+3<br />
</td>
    </tr>
    <tr>
        <td>5L2s<br />
</td>
        <td>4\7 &lt; g &lt; 3\5<br />
</td>
        <td>4\7 &lt; g &lt; 7\12<br />
</td>
        <td>-1+2g<br />
</td>
        <td>-5g+3<br />
</td>
    </tr>
    <tr>
        <td>6L1s<br />
</td>
        <td>1\7 &lt; g &lt; 1\6<br />
</td>
        <td>1\7 &lt; g &lt; 2\13<br />
</td>
        <td>g<br />
</td>
        <td>-6g+1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><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>Large step<br />
</td>
        <td>Small step<br />
</td>
    </tr>
    <tr>
        <td>1L7s<br />
</td>
        <td>7\8 &lt; g &lt; 1<br />
</td>
        <td>7\8 &lt; g &lt; 8\9<br />
</td>
        <td>-6+7g<br />
</td>
        <td>-g+1<br />
</td>
    </tr>
    <tr>
        <td>2L6s<br />
</td>
        <td>3\8 &lt; g &lt; 1\2<br />
</td>
        <td>3\8 &lt; g &lt; 2\5<br />
</td>
        <td>-1+3g<br />
</td>
        <td>-g+1\2<br />
</td>
    </tr>
    <tr>
        <td>3L5s<br />
</td>
        <td>5\8 &lt; g &lt; 2\3<br />
</td>
        <td>5\8 &lt; g &lt; 7\11<br />
</td>
        <td>-3+5g<br />
</td>
        <td>-3g+2<br />
</td>
    </tr>
    <tr>
        <td>4L4s<br />
</td>
        <td>1\8 &lt; g &lt; 1\4<br />
</td>
        <td>1\8 &lt; g &lt; 1\6<br />
</td>
        <td>g<br />
</td>
        <td>-g+1\4<br />
</td>
    </tr>
    <tr>
        <td>5L3s<br />
</td>
        <td>3\8 &lt; g &lt; 2\5<br />
</td>
        <td>3\8 &lt; g &lt; 5\13<br />
</td>
        <td>-1+3g<br />
</td>
        <td>-5g+2<br />
</td>
    </tr>
    <tr>
        <td>6L2s<br />
</td>
        <td>1\8 &lt; g &lt; 1\6<br />
</td>
        <td>1\8 &lt; g &lt; 1\7<br />
</td>
        <td>g<br />
</td>
        <td>-3g+1\2<br />
</td>
    </tr>
    <tr>
        <td>7L1s<br />
</td>
        <td>1\8 &lt; g &lt; 1\7<br />
</td>
        <td>1\8 &lt; g &lt; 2\15<br />
</td>
        <td>g<br />
</td>
        <td>-7g+1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><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>Large step<br />
</td>
        <td>Small step<br />
</td>
    </tr>
    <tr>
        <td>1L8s<br />
</td>
        <td>8\9 &lt; g &lt; 1<br />
</td>
        <td>8\9 &lt; g &lt; 9\10<br />
</td>
        <td>-7+8g<br />
</td>
        <td>-g+1<br />
</td>
    </tr>
    <tr>
        <td>2L7s<br />
</td>
        <td>4\9 &lt; g &lt; 1\2<br />
</td>
        <td>4\9 &lt; g &lt; 5\11<br />
</td>
        <td>-3+7g<br />
</td>
        <td>-2g+1<br />
</td>
    </tr>
    <tr>
        <td>3L6s<br />
</td>
        <td>2\9 &lt; g &lt; 1\3<br />
</td>
        <td>2\9 &lt; g &lt; 1\4<br />
</td>
        <td>-1\3+2g<br />
</td>
        <td>-g+1\3<br />
</td>
    </tr>
    <tr>
        <td>4L5s<br />
</td>
        <td>2\9 &lt; g &lt; 1\4<br />
</td>
        <td>2\9 &lt; g &lt; 3\13<br />
</td>
        <td>-1+5g<br />
</td>
        <td>-4g+1<br />
</td>
    </tr>
    <tr>
        <td>5L4s<br />
</td>
        <td>7\9 &lt; g &lt; 4\5<br />
</td>
        <td>7\9 &lt; g &lt; 11\14<br />
</td>
        <td>-3+4g<br />
</td>
        <td>-5g+4<br />
</td>
    </tr>
    <tr>
        <td>6L3s<br />
</td>
        <td>1\9 &lt; g &lt; 1\6<br />
</td>
        <td>1\9 &lt; g &lt; 2\15<br />
</td>
        <td>g<br />
</td>
        <td>-2g+1\3<br />
</td>
    </tr>
    <tr>
        <td>7L2s<br />
</td>
        <td>5\9 &lt; g &lt; 4\7<br />
</td>
        <td>5\9 &lt; g &lt; 9\16<br />
</td>
        <td>-1+2g<br />
</td>
        <td>-7g+4<br />
</td>
    </tr>
    <tr>
        <td>8L1s<br />
</td>
        <td>1\9 &lt; g &lt; 1\8<br />
</td>
        <td>1\9 &lt; g &lt; 2\17<br />
</td>
        <td>g<br />
</td>
        <td>-8g+1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><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>Large step<br />
</td>
        <td>Small step<br />
</td>
    </tr>
    <tr>
        <td>1L9s<br />
</td>
        <td>9\10 &lt; g &lt; 1<br />
</td>
        <td>9\10 &lt; g &lt; 10\11<br />
</td>
        <td>-8+9g<br />
</td>
        <td>-g+1<br />
</td>
    </tr>
    <tr>
        <td>2L8s<br />
</td>
        <td>2\5 &lt; g &lt; 1\2<br />
</td>
        <td>2\5 &lt; g &lt; 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 &lt; g &lt; 1\3<br />
</td>
        <td>3\10 &lt; g &lt; 4\13<br />
</td>
        <td>-2+7g<br />
</td>
        <td>1-3g<br />
</td>
    </tr>
    <tr>
        <td>4L6s<br />
</td>
        <td>1\5 &lt; g &lt; 1\4<br />
</td>
        <td>1\5 &lt; g &lt; 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 &lt; g &lt; 1\5<br />
</td>
        <td>1\10 &lt; g &lt; 2\15<br />
</td>
        <td>g<br />
</td>
        <td>-g+1\5<br />
</td>
    </tr>
    <tr>
        <td>6L4s<br />
</td>
        <td>3\10 &lt; g &lt; 1\3<br />
</td>
        <td>3\10 &lt; g &lt; 4\13<br />
</td>
        <td>-1\2+2g<br />
</td>
        <td>1-3g<br />
</td>
    </tr>
    <tr>
        <td>7L3s<br />
</td>
        <td>7\10 &lt; g &lt; 5\7<br />
</td>
        <td>7\10 &lt; g &lt; 12\17<br />
</td>
        <td>-2+3g<br />
</td>
        <td>-7g+5<br />
</td>
    </tr>
    <tr>
        <td>8L2s<br />
</td>
        <td>1\10 &lt; g &lt; 1\8<br />
</td>
        <td>1\10 &lt; g &lt; 1\9<br />
</td>
        <td>g<br />
</td>
        <td>-4g+1\2<br />
</td>
    </tr>
    <tr>
        <td>9L1s<br />
</td>
        <td>1\10 &lt; g &lt; 1\9<br />
</td>
        <td>1\10 &lt; g &lt; 2\19<br />
</td>
        <td>g<br />
</td>
        <td>-9g+1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><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>Large step<br />
</td>
        <td>Small step<br />
</td>
    </tr>
    <tr>
        <td>1L10s<br />
</td>
        <td>10\11 &lt; g &lt; 1<br />
</td>
        <td>10\11 &lt; g &lt; 11\12<br />
</td>
        <td>-9+10g<br />
</td>
        <td>-g+1<br />
</td>
    </tr>
    <tr>
        <td>2L9s<br />
</td>
        <td>5\11 &lt; g &lt; 1\2<br />
</td>
        <td>5\11 &lt; g &lt; 6\13<br />
</td>
        <td>-4+9g<br />
</td>
        <td>-2g+1<br />
</td>
    </tr>
    <tr>
        <td>3L8s<br />
</td>
        <td>7\11 &lt; g &lt; 2\3<br />
</td>
        <td>7\11 &lt; g &lt; 9\14<br />
</td>
        <td>-5+8g<br />
</td>
        <td>-3g+2<br />
</td>
    </tr>
    <tr>
        <td>4L7s<br />
</td>
        <td>8\11 &lt; g &lt; 3\4<br />
</td>
        <td>8\11 &lt; g &lt; 11\15<br />
</td>
        <td>-5+7g<br />
</td>
        <td>-4g+3<br />
</td>
    </tr>
    <tr>
        <td>5L6s<br />
</td>
        <td>2\11 &lt; g &lt; 1\5<br />
</td>
        <td>2\11 &lt; g &lt; 3\16<br />
</td>
        <td>-1+6g<br />
</td>
        <td>-5g+1<br />
</td>
    </tr>
    <tr>
        <td>6L5s<br />
</td>
        <td>9\11 &lt; g &lt; 5\6<br />
</td>
        <td>9\11 &lt; g &lt; 14\17<br />
</td>
        <td>-4+5g<br />
</td>
        <td>-6g+5<br />
</td>
    </tr>
    <tr>
        <td>7L4s<br />
</td>
        <td>3\11 &lt; g &lt; 2\7<br />
</td>
        <td>3\11 &lt; g &lt; 5\18<br />
</td>
        <td>-1+4g<br />
</td>
        <td>-7g+2<br />
</td>
    </tr>
    <tr>
        <td>8L3s<br />
</td>
        <td>4\11 &lt; g &lt; 3\8<br />
</td>
        <td>4\11 &lt; g &lt; 7\19<br />
</td>
        <td>-1+3g<br />
</td>
        <td>-8g+3<br />
</td>
    </tr>
    <tr>
        <td>9L2s<br />
</td>
        <td>6\11 &lt; g &lt; 5\9<br />
</td>
        <td>6\11 &lt; g &lt; 11\20<br />
</td>
        <td>-1+2g<br />
</td>
        <td>-9g+5<br />
</td>
    </tr>
    <tr>
        <td>10L1s<br />
</td>
        <td>1\11 &lt; g &lt; 1\10<br />
</td>
        <td>1\11 &lt; g &lt; 2\21<br />
</td>
        <td>g<br />
</td>
        <td>-10g+1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><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>Large step<br />
</td>
        <td>Small step<br />
</td>
    </tr>
    <tr>
        <td>1L11s<br />
</td>
        <td>11\12 &lt; g &lt; 1<br />
</td>
        <td>11\12 &lt; g &lt; 12\13<br />
</td>
        <td>-10+11g<br />
</td>
        <td>-g+1<br />
</td>
    </tr>
    <tr>
        <td>2L10s<br />
</td>
        <td>5\12 &lt; g &lt; 1\2<br />
</td>
        <td>5\12 &lt; g &lt; 3\7<br />
</td>
        <td>-2+5g<br />
</td>
        <td>-g+1\2<br />
</td>
    </tr>
    <tr>
        <td>3L9s<br />
</td>
        <td>1\4 &lt; g &lt; 1\3<br />
</td>
        <td>1\4 &lt; g &lt; 2\7<br />
</td>
        <td>-2\3+3g<br />
</td>
        <td>-g+1\3<br />
</td>
    </tr>
    <tr>
        <td>4L8s<br />
</td>
        <td>1\6 &lt; g &lt; 1\4<br />
</td>
        <td>1\6 &lt; g &lt; 1\5<br />
</td>
        <td>-1\4+2g<br />
</td>
        <td>-g+1\4<br />
</td>
    </tr>
    <tr>
        <td>5L7s<br />
</td>
        <td>7\12 &lt; g &lt; 3\5<br />
</td>
        <td>7\12 &lt; g &lt; 10\17<br />
</td>
        <td>-4+7g<br />
</td>
        <td>-5g+3<br />
</td>
    </tr>
    <tr>
        <td>6L6s<br />
</td>
        <td>1\12 &lt; g &lt; 1\6<br />
</td>
        <td>1\12 &lt; g &lt; 1\9<br />
</td>
        <td>g<br />
</td>
        <td>-g+1\6<br />
</td>
    </tr>
    <tr>
        <td>7L5s<br />
</td>
        <td>5\12 &lt; g &lt; 3\7<br />
</td>
        <td>5\12 &lt; g &lt; 8\19<br />
</td>
        <td>-2+5g<br />
</td>
        <td>-7g+3<br />
</td>
    </tr>
    <tr>
        <td>8L4s<br />
</td>
        <td>1\12 &lt; g &lt; 1\8<br />
</td>
        <td>1\12 &lt; g &lt; 1\10<br />
</td>
        <td>g<br />
</td>
        <td>-2g+1\4<br />
</td>
    </tr>
    <tr>
        <td>9L3s<br />
</td>
        <td>1\12 &lt; g &lt; 1\9<br />
</td>
        <td>1\12 &lt; g &lt; 2\21<br />
</td>
        <td>g<br />
</td>
        <td>-3g+1\3<br />
</td>
    </tr>
    <tr>
        <td>10L2s<br />
</td>
        <td>1\12 &lt; g &lt; 1\10<br />
</td>
        <td>1\12 &lt; g &lt; 1\11<br />
</td>
        <td>g<br />
</td>
        <td>-5g+1\2<br />
</td>
    </tr>
    <tr>
        <td>11L1s<br />
</td>
        <td>1\12 &lt; g &lt; 1\11<br />
</td>
        <td>1\12 &lt; g &lt; 2\23<br />
</td>
        <td>g<br />
</td>
        <td>-11g+1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><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>Large step<br />
</td>
        <td>Small step<br />
</td>
    </tr>
    <tr>
        <td>1L12s<br />
</td>
        <td>12\13 &lt; g &lt; 1<br />
</td>
        <td>12\13 &lt; g &lt; 13\14<br />
</td>
        <td>-11+12g<br />
</td>
        <td>-g+1<br />
</td>
    </tr>
    <tr>
        <td>2L11s<br />
</td>
        <td>6\13 &lt; g &lt; 1\2<br />
</td>
        <td>6\13 &lt; g &lt; 7\15<br />
</td>
        <td>-5+11g<br />
</td>
        <td>-2g+1<br />
</td>
    </tr>
    <tr>
        <td>3L10s<br />
</td>
        <td>4\13 &lt; g &lt; 1\3<br />
</td>
        <td>4\13 &lt; g &lt; 5\16<br />
</td>
        <td>-3+10g<br />
</td>
        <td>1-3g<br />
</td>
    </tr>
    <tr>
        <td>4L9s<br />
</td>
        <td>3\13 &lt; g &lt; 1\4<br />
</td>
        <td>3\13 &lt; g &lt; 4\17<br />
</td>
        <td>-2+9g<br />
</td>
        <td>-4g+1<br />
</td>
    </tr>
    <tr>
        <td>5L8s<br />
</td>
        <td>5\13 &lt; g &lt; 2\5<br />
</td>
        <td>5\13 &lt; g &lt; 7\18<br />
</td>
        <td>-3+8g<br />
</td>
        <td>-5g+2<br />
</td>
    </tr>
    <tr>
        <td>6L7s<br />
</td>
        <td>2\13 &lt; g &lt; 1\6<br />
</td>
        <td>2\13 &lt; g &lt; 3\19<br />
</td>
        <td>-1+7g<br />
</td>
        <td>-6g+1<br />
</td>
    </tr>
    <tr>
        <td>7L6s<br />
</td>
        <td>11\13 &lt; g &lt; 6\7<br />
</td>
        <td>11\13 &lt; g &lt; 17\20<br />
</td>
        <td>-5+6g<br />
</td>
        <td>-7g+6<br />
</td>
    </tr>
    <tr>
        <td>8L5s<br />
</td>
        <td>8\13 &lt; g &lt; 5\8<br />
</td>
        <td>8\13 &lt; g &lt; 13\21<br />
</td>
        <td>-3+5g<br />
</td>
        <td>-8g+5<br />
</td>
    </tr>
    <tr>
        <td>9L4s<br />
</td>
        <td>10\13 &lt; g &lt; 7\9<br />
</td>
        <td>10\13 &lt; g &lt; 17\22<br />
</td>
        <td>-3+4g<br />
</td>
        <td>-9g+7<br />
</td>
    </tr>
    <tr>
        <td>10L3s<br />
</td>
        <td>9\13 &lt; g &lt; 7\10<br />
</td>
        <td>9\13 &lt; g &lt; 16\23<br />
</td>
        <td>-2+3g<br />
</td>
        <td>-10g+7<br />
</td>
    </tr>
    <tr>
        <td>11L2s<br />
</td>
        <td>7\13 &lt; g &lt; 6\11<br />
</td>
        <td>7\13 &lt; g &lt; 13\24<br />
</td>
        <td>-1+2g<br />
</td>
        <td>-11g+6<br />
</td>
    </tr>
    <tr>
        <td>12L1s<br />
</td>
        <td>1\13 &lt; g &lt; 1\12<br />
</td>
        <td>1\13 &lt; g &lt; 2\25<br />
</td>
        <td>g<br />
</td>
        <td>-12g+1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><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>Large step<br />
</td>
        <td>Small step<br />
</td>
    </tr>
    <tr>
        <td>1L13s<br />
</td>
        <td>13\14 &lt; g &lt; 1<br />
</td>
        <td>13\14 &lt; g &lt; 14\15<br />
</td>
        <td>-12+13g<br />
</td>
        <td>-g+1<br />
</td>
    </tr>
    <tr>
        <td>2L12s<br />
</td>
        <td>3\7 &lt; g &lt; 1\2<br />
</td>
        <td>3\7 &lt; g &lt; 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 &lt; g &lt; 2\3<br />
</td>
        <td>9\14 &lt; g &lt; 11\17<br />
</td>
        <td>-7+11g<br />
</td>
        <td>-3g+2<br />
</td>
    </tr>
    <tr>
        <td>4L10s<br />
</td>
        <td>3\14 &lt; g &lt; 1\4<br />
</td>
        <td>3\14 &lt; g &lt; 2\9<br />
</td>
        <td>-1+5g<br />
</td>
        <td>-2g+1\2<br />
</td>
    </tr>
    <tr>
        <td>5L9s<br />
</td>
        <td>11\14 &lt; g &lt; 4\5<br />
</td>
        <td>11\14 &lt; g &lt; 15\19<br />
</td>
        <td>-7+9g<br />
</td>
        <td>-5g+4<br />
</td>
    </tr>
    <tr>
        <td>6L8s<br />
</td>
        <td>1\7 &lt; g &lt; 1\6<br />
</td>
        <td>1\7 &lt; g &lt; 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 &lt; g &lt; 1\7<br />
</td>
        <td>1\14 &lt; g &lt; 2\21<br />
</td>
        <td>g<br />
</td>
        <td>-g+1\7<br />
</td>
    </tr>
    <tr>
        <td>8L6s<br />
</td>
        <td>5\14 &lt; g &lt; 3\8<br />
</td>
        <td>5\14 &lt; g &lt; 4\11<br />
</td>
        <td>-1+3g<br />
</td>
        <td>-4g+3\2<br />
</td>
    </tr>
    <tr>
        <td>9L5s<br />
</td>
        <td>3\14 &lt; g &lt; 2\9<br />
</td>
        <td>3\14 &lt; g &lt; 5\23<br />
</td>
        <td>-1+5g<br />
</td>
        <td>-9g+2<br />
</td>
    </tr>
    <tr>
        <td>10L4s<br />
</td>
        <td>2\7 &lt; g &lt; 3\10<br />
</td>
        <td>2\7 &lt; g &lt; 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 &lt; g &lt; 4\11<br />
</td>
        <td>5\14 &lt; g &lt; 9\25<br />
</td>
        <td>-1+3g<br />
</td>
        <td>-11g+4<br />
</td>
    </tr>
    <tr>
        <td>12L2s<br />
</td>
        <td>1\14 &lt; g &lt; 1\12<br />
</td>
        <td>1\14 &lt; g &lt; 1\13<br />
</td>
        <td>g<br />
</td>
        <td>-6g+1\2<br />
</td>
    </tr>
    <tr>
        <td>13L1s<br />
</td>
        <td>1\14 &lt; g &lt; 1\13<br />
</td>
        <td>1\14 &lt; g &lt; 2\27<br />
</td>
        <td>g<br />
</td>
        <td>-13g+1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><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>Large step<br />
</td>
        <td>Small step<br />
</td>
    </tr>
    <tr>
        <td>1L14s<br />
</td>
        <td>14\15 &lt; g &lt; 1<br />
</td>
        <td>14\15 &lt; g &lt; 15\16<br />
</td>
        <td>-13+14g<br />
</td>
        <td>-g+1<br />
</td>
    </tr>
    <tr>
        <td>2L13s<br />
</td>
        <td>7\15 &lt; g &lt; 1\2<br />
</td>
        <td>7\15 &lt; g &lt; 8\17<br />
</td>
        <td>-6+13g<br />
</td>
        <td>-2g+1<br />
</td>
    </tr>
    <tr>
        <td>3L12s<br />
</td>
        <td>4\15 &lt; g &lt; 1\3<br />
</td>
        <td>4\15 &lt; g &lt; 5\18<br />
</td>
        <td>-1+4g<br />
</td>
        <td>-g+1\3<br />
</td>
    </tr>
    <tr>
        <td>4L11s<br />
</td>
        <td>11\15 &lt; g &lt; 3\4<br />
</td>
        <td>11\15 &lt; g &lt; 14\19<br />
</td>
        <td>-8+11g<br />
</td>
        <td>-4g+3<br />
</td>
    </tr>
    <tr>
        <td>5L10s<br />
</td>
        <td>2\15 &lt; g &lt; 1\5<br />
</td>
        <td>2\15 &lt; g &lt; 3\20<br />
</td>
        <td>-1\5+2g<br />
</td>
        <td>-g+1\5<br />
</td>
    </tr>
    <tr>
        <td>6L9s<br />
</td>
        <td>2\15 &lt; g &lt; 1\6<br />
</td>
        <td>2\15 &lt; g &lt; 1\7<br />
</td>
        <td>-1\3+3g<br />
</td>
        <td>-2g+1\3<br />
</td>
    </tr>
    <tr>
        <td>7L8s<br />
</td>
        <td>2\15 &lt; g &lt; 1\7<br />
</td>
        <td>2\15 &lt; g &lt; 3\22<br />
</td>
        <td>-1+8g<br />
</td>
        <td>-7g+1<br />
</td>
    </tr>
    <tr>
        <td>8L7s<br />
</td>
        <td>13\15 &lt; g &lt; 7\8<br />
</td>
        <td>13\15 &lt; g &lt; 20\23<br />
</td>
        <td>-6+7g<br />
</td>
        <td>-8g+7<br />
</td>
    </tr>
    <tr>
        <td>9L6s<br />
</td>
        <td>1\5 &lt; g &lt; 2\9<br />
</td>
        <td>1\5 &lt; g &lt; 3\14<br />
</td>
        <td>-1\3+2g<br />
</td>
        <td>-3g+2\3<br />
</td>
    </tr>
    <tr>
        <td>10L5s<br />
</td>
        <td>1\15 &lt; g &lt; 1\10<br />
</td>
        <td>1\15 &lt; g &lt; 2\25<br />
</td>
        <td>g<br />
</td>
        <td>-2g+1\5<br />
</td>
    </tr>
    <tr>
        <td>11L4s<br />
</td>
        <td>4\15 &lt; g &lt; 3\11<br />
</td>
        <td>4\15 &lt; g &lt; 7\26<br />
</td>
        <td>-1+4g<br />
</td>
        <td>-11g+3<br />
</td>
    </tr>
    <tr>
        <td>12L3s<br />
</td>
        <td>1\15 &lt; g &lt; 1\12<br />
</td>
        <td>1\15 &lt; g &lt; 2\27<br />
</td>
        <td>g<br />
</td>
        <td>-4g+1\3<br />
</td>
    </tr>
    <tr>
        <td>13L2s<br />
</td>
        <td>8\15 &lt; g &lt; 7\13<br />
</td>
        <td>8\15 &lt; g &lt; 15\28<br />
</td>
        <td>-1+2g<br />
</td>
        <td>-13g+7<br />
</td>
    </tr>
    <tr>
        <td>14L1s<br />
</td>
        <td>1\15 &lt; g &lt; 1\14<br />
</td>
        <td>1\15 &lt; g &lt; 2\29<br />
</td>
        <td>g<br />
</td>
        <td>-14g+1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><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>Large step<br />
</td>
        <td>Small step<br />
</td>
    </tr>
    <tr>
        <td>1L15s<br />
</td>
        <td>15\16 &lt; g &lt; 1<br />
</td>
        <td>15\16 &lt; g &lt; 16\17<br />
</td>
        <td>-14+15g<br />
</td>
        <td>-g+1<br />
</td>
    </tr>
    <tr>
        <td>2L14s<br />
</td>
        <td>7\16 &lt; g &lt; 1\2<br />
</td>
        <td>7\16 &lt; g &lt; 4\9<br />
</td>
        <td>-3+7g<br />
</td>
        <td>-g+1\2<br />
</td>
    </tr>
    <tr>
        <td>3L13s<br />
</td>
        <td>5\16 &lt; g &lt; 1\3<br />
</td>
        <td>5\16 &lt; g &lt; 6\19<br />
</td>
        <td>-4+13g<br />
</td>
        <td>1-3g<br />
</td>
    </tr>
    <tr>
        <td>4L12s<br />
</td>
        <td>3\16 &lt; g &lt; 1\4<br />
</td>
        <td>3\16 &lt; g &lt; 1\5<br />
</td>
        <td>3g-1\2<br />
</td>
        <td>-g+1\4<br />
</td>
    </tr>
    <tr>
        <td>5L11s<br />
</td>
        <td>3\16 &lt; g &lt; 1\5<br />
</td>
        <td>3\16 &lt; g &lt; 4\21<br />
</td>
        <td>-2+11g<br />
</td>
        <td>-5g+1<br />
</td>
    </tr>
    <tr>
        <td>6L10s<br />
</td>
        <td>5\16 &lt; g &lt; 1\3<br />
</td>
        <td>5\16 &lt; g &lt; 6\19<br />
</td>
        <td>-3\2+5g<br />
</td>
        <td>1-3g<br />
</td>
    </tr>
    <tr>
        <td>7L9s<br />
</td>
        <td>9\16 &lt; g &lt; 4\7<br />
</td>
        <td>9\16 &lt; g &lt; 13\23<br />
</td>
        <td>-5+9g<br />
</td>
        <td>-7g+4<br />
</td>
    </tr>
    <tr>
        <td>8L8s<br />
</td>
        <td>1\16 &lt; g &lt; 1\8<br />
</td>
        <td>1\16 &lt; g &lt; 1\12<br />
</td>
        <td>g<br />
</td>
        <td>-g+1\8<br />
</td>
    </tr>
    <tr>
        <td>9L7s<br />
</td>
        <td>7\16 &lt; g &lt; 4\9<br />
</td>
        <td>7\16 &lt; g &lt; 11\25<br />
</td>
        <td>-3+7g<br />
</td>
        <td>-9g+4<br />
</td>
    </tr>
    <tr>
        <td>10L6s<br />
</td>
        <td>3\16 &lt; g &lt; 1\5<br />
</td>
        <td>3\16 &lt; g &lt; 4\21<br />
</td>
        <td>3g-1\2<br />
</td>
        <td>-5g+1<br />
</td>
    </tr>
    <tr>
        <td>11L5s<br />
</td>
        <td>13\16 &lt; g &lt; 9\11<br />
</td>
        <td>13\16 &lt; g &lt; 22\27<br />
</td>
        <td>-4+5g<br />
</td>
        <td>-11g+9<br />
</td>
    </tr>
    <tr>
        <td>12L4s<br />
</td>
        <td>1\16 &lt; g &lt; 1\12<br />
</td>
        <td>1\16 &lt; g &lt; 1\14<br />
</td>
        <td>g<br />
</td>
        <td>-3g+1\4<br />
</td>
    </tr>
    <tr>
        <td>13L3s<br />
</td>
        <td>11\16 &lt; g &lt; 9\13<br />
</td>
        <td>11\16 &lt; g &lt; 20\29<br />
</td>
        <td>-2+3g<br />
</td>
        <td>-13g+9<br />
</td>
    </tr>
    <tr>
        <td>14L2s<br />
</td>
        <td>1\16 &lt; g &lt; 1\14<br />
</td>
        <td>1\16 &lt; g &lt; 1\15<br />
</td>
        <td>g<br />
</td>
        <td>-7g+1\2<br />
</td>
    </tr>
    <tr>
        <td>15L1s<br />
</td>
        <td>1\16 &lt; g &lt; 1\15<br />
</td>
        <td>1\16 &lt; g &lt; 2\31<br />
</td>
        <td>g<br />
</td>
        <td>-15g+1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><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>Large step<br />
</td>
        <td>Small step<br />
</td>
    </tr>
    <tr>
        <td>1L16s<br />
</td>
        <td>16\17 &lt; g &lt; 1<br />
</td>
        <td>16\17 &lt; g &lt; 17\18<br />
</td>
        <td>-15+16g<br />
</td>
        <td>-g+1<br />
</td>
    </tr>
    <tr>
        <td>2L15s<br />
</td>
        <td>8\17 &lt; g &lt; 1\2<br />
</td>
        <td>8\17 &lt; g &lt; 9\19<br />
</td>
        <td>-7+15g<br />
</td>
        <td>-2g+1<br />
</td>
    </tr>
    <tr>
        <td>3L14s<br />
</td>
        <td>11\17 &lt; g &lt; 2\3<br />
</td>
        <td>11\17 &lt; g &lt; 13\20<br />
</td>
        <td>-9+14g<br />
</td>
        <td>-3g+2<br />
</td>
    </tr>
    <tr>
        <td>4L13s<br />
</td>
        <td>4\17 &lt; g &lt; 1\4<br />
</td>
        <td>4\17 &lt; g &lt; 5\21<br />
</td>
        <td>-3+13g<br />
</td>
        <td>-4g+1<br />
</td>
    </tr>
    <tr>
        <td>5L12s<br />
</td>
        <td>10\17 &lt; g &lt; 3\5<br />
</td>
        <td>10\17 &lt; g &lt; 13\22<br />
</td>
        <td>-7+12g<br />
</td>
        <td>-5g+3<br />
</td>
    </tr>
    <tr>
        <td>6L11s<br />
</td>
        <td>14\17 &lt; g &lt; 5\6<br />
</td>
        <td>14\17 &lt; g &lt; 19\23<br />
</td>
        <td>-9+11g<br />
</td>
        <td>-6g+5<br />
</td>
    </tr>
    <tr>
        <td>7L10s<br />
</td>
        <td>12\17 &lt; g &lt; 5\7<br />
</td>
        <td>12\17 &lt; g &lt; 17\24<br />
</td>
        <td>-7+10g<br />
</td>
        <td>-7g+5<br />
</td>
    </tr>
    <tr>
        <td>8L9s<br />
</td>
        <td>2\17 &lt; g &lt; 1\8<br />
</td>
        <td>2\17 &lt; g &lt; 3\25<br />
</td>
        <td>-1+9g<br />
</td>
        <td>-8g+1<br />
</td>
    </tr>
    <tr>
        <td>9L8s<br />
</td>
        <td>15\17 &lt; g &lt; 8\9<br />
</td>
        <td>15\17 &lt; g &lt; 23\26<br />
</td>
        <td>-7+8g<br />
</td>
        <td>-9g+8<br />
</td>
    </tr>
    <tr>
        <td>10L7s<br />
</td>
        <td>5\17 &lt; g &lt; 3\10<br />
</td>
        <td>5\17 &lt; g &lt; 8\27<br />
</td>
        <td>-2+7g<br />
</td>
        <td>-10g+3<br />
</td>
    </tr>
    <tr>
        <td>11L6s<br />
</td>
        <td>3\17 &lt; g &lt; 2\11<br />
</td>
        <td>3\17 &lt; g &lt; 5\28<br />
</td>
        <td>-1+6g<br />
</td>
        <td>-11g+2<br />
</td>
    </tr>
    <tr>
        <td>12L5s<br />
</td>
        <td>7\17 &lt; g &lt; 5\12<br />
</td>
        <td>7\17 &lt; g &lt; 12\29<br />
</td>
        <td>-2+5g<br />
</td>
        <td>-12g+5<br />
</td>
    </tr>
    <tr>
        <td>13L4s<br />
</td>
        <td>13\17 &lt; g &lt; 10\13<br />
</td>
        <td>13\17 &lt; g &lt;23\30<br />
</td>
        <td>-3+4g<br />
</td>
        <td>-13g+10<br />
</td>
    </tr>
    <tr>
        <td>14L3s<br />
</td>
        <td>6\17 &lt; g &lt; 5\14<br />
</td>
        <td>6\17 &lt; g &lt; 11\31<br />
</td>
        <td>-1+3g<br />
</td>
        <td>-14g+5<br />
</td>
    </tr>
    <tr>
        <td>15L2s<br />
</td>
        <td>9\17 &lt; g &lt; 8\15<br />
</td>
        <td>9\17 &lt; g &lt; 17\32<br />
</td>
        <td>-1+2g<br />
</td>
        <td>-15g+8<br />
</td>
    </tr>
    <tr>
        <td>16L1s<br />
</td>
        <td>1\17 &lt; g &lt; 1\16<br />
</td>
        <td>1\17 &lt; g &lt; 2\33<br />
</td>
        <td>g<br />
</td>
        <td>-16g+1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:32:&lt;h1&gt; --><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>Large step<br />
</td>
        <td>Small step<br />
</td>
    </tr>
    <tr>
        <td>1L17s<br />
</td>
        <td>17\18 &lt; g &lt; 1<br />
</td>
        <td>17\18 &lt; g &lt; 18\19<br />
</td>
        <td>-16+17g<br />
</td>
        <td>-g+1<br />
</td>
    </tr>
    <tr>
        <td>2L16s<br />
</td>
        <td>4\9 &lt; g &lt; 1\2<br />
</td>
        <td>4\9 &lt; g &lt; 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 &lt; g &lt; 1\3<br />
</td>
        <td>5\18 &lt; g &lt; 2\7<br />
</td>
        <td>-4\3+5g<br />
</td>
        <td>-g+1\3<br />
</td>
    </tr>
    <tr>
        <td>4L14s<br />
</td>
        <td>2\9 &lt; g &lt; 1\4<br />
</td>
        <td>2\9 &lt; g &lt; 3\13<br />
</td>
        <td>-3\2+7g<br />
</td>
        <td>-2g+1\2<br />
</td>
    </tr>
    <tr>
        <td>5L13s<br />
</td>
        <td>7\18 &lt; g &lt; 2\5<br />
</td>
        <td>7\18 &lt; g &lt; 9\23<br />
</td>
        <td>-5+13g<br />
</td>
        <td>-5g+2<br />
</td>
    </tr>
    <tr>
        <td>6L12s<br />
</td>
        <td>1\9 &lt; g &lt; 1\6<br />
</td>
        <td>1\9 &lt; g &lt; 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 &lt; g &lt; 2\7<br />
</td>
        <td>5\18 &lt; g &lt; 7\25<br />
</td>
        <td>-3+11g<br />
</td>
        <td>-7g+2<br />
</td>
    </tr>
    <tr>
        <td>8L10s<br />
</td>
        <td>1\9 &lt; g &lt; 1\8<br />
</td>
        <td>1\9 &lt; g &lt; 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 &lt; g &lt; 1\9<br />
</td>
        <td>1\18 &lt; g &lt; 2\27<br />
</td>
        <td>g<br />
</td>
        <td>-g+1\9<br />
</td>
    </tr>
    <tr>
        <td>10L8s<br />
</td>
        <td>7\18 &lt; g &lt; 2\5<br />
</td>
        <td>7\18 &lt; g &lt; 9\23<br />
</td>
        <td>-3\2+4g<br />
</td>
        <td>-5g+2<br />
</td>
    </tr>
    <tr>
        <td>11L7s<br />
</td>
        <td>13\18 &lt; g &lt; 8\11<br />
</td>
        <td>13\18 &lt; g &lt; 21\29<br />
</td>
        <td>-5+7g<br />
</td>
        <td>-11g+8<br />
</td>
    </tr>
    <tr>
        <td>12L6s<br />
</td>
        <td>1\18 &lt; g &lt; 1\12<br />
</td>
        <td>1\18 &lt; g &lt; 1\15<br />
</td>
        <td>g<br />
</td>
        <td>-2g+1\6<br />
</td>
    </tr>
    <tr>
        <td>13L5s<br />
</td>
        <td>11\18 &lt; g &lt; 8\13<br />
</td>
        <td>11\18 &lt; g &lt; 19\31<br />
</td>
        <td>-3+5g<br />
</td>
        <td>-13g+8<br />
</td>
    </tr>
    <tr>
        <td>14L4s<br />
</td>
        <td>5\18 &lt; g &lt; 2\7<br />
</td>
        <td>5\18 &lt; g &lt; 7\25<br />
</td>
        <td>-1\2+2g<br />
</td>
        <td>-7g+2<br />
</td>
    </tr>
    <tr>
        <td>15L3s<br />
</td>
        <td>1\18 &lt; g &lt; 1\15<br />
</td>
        <td>1\18 &lt; g &lt; 2\33<br />
</td>
        <td>g<br />
</td>
        <td>-5g+1\3<br />
</td>
    </tr>
    <tr>
        <td>16L2s<br />
</td>
        <td>1\18 &lt; g &lt; 1\16<br />
</td>
        <td>1\18 &lt; g &lt; 1\17<br />
</td>
        <td>g<br />
</td>
        <td>-8g+1\2<br />
</td>
    </tr>
    <tr>
        <td>17L1s<br />
</td>
        <td>1\18 &lt; g &lt; 1\17<br />
</td>
        <td>1\18 &lt; g &lt; 2\35<br />
</td>
        <td>g<br />
</td>
        <td>-17g+1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><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>Large step<br />
</td>
        <td>Small step<br />
</td>
    </tr>
    <tr>
        <td>1L18s<br />
</td>
        <td>18\19 &lt; g &lt; 1<br />
</td>
        <td>18\19 &lt; g &lt; 19\20<br />
</td>
        <td>-17+18g<br />
</td>
        <td>-g+1<br />
</td>
    </tr>
    <tr>
        <td>2L17s<br />
</td>
        <td>9\19 &lt; g &lt; 1\2<br />
</td>
        <td>9\19 &lt; g &lt; 10\21<br />
</td>
        <td>-8+17g<br />
</td>
        <td>-2g+1<br />
</td>
    </tr>
    <tr>
        <td>3L16s<br />
</td>
        <td>6\19 &lt; g &lt; 1\3<br />
</td>
        <td>6\19 &lt; g &lt; 7\22<br />
</td>
        <td>-5+16g<br />
</td>
        <td>1-3g<br />
</td>
    </tr>
    <tr>
        <td>4L15s<br />
</td>
        <td>14\19 &lt; g &lt; 3\4<br />
</td>
        <td>14\19 &lt; g &lt; 17\23<br />
</td>
        <td>-11+15g<br />
</td>
        <td>-4g+3<br />
</td>
    </tr>
    <tr>
        <td>5L14s<br />
</td>
        <td>15\19 &lt; g &lt; 4\5<br />
</td>
        <td>15\19 &lt; g &lt; 19\24<br />
</td>
        <td>-11+14g<br />
</td>
        <td>-5g+4<br />
</td>
    </tr>
    <tr>
        <td>6L13s<br />
</td>
        <td>3\19 &lt; g &lt; 1\6<br />
</td>
        <td>3\19 &lt; g &lt; 4\25<br />
</td>
        <td>-2+13g<br />
</td>
        <td>-6g+1<br />
</td>
    </tr>
    <tr>
        <td>7L12s<br />
</td>
        <td>8\19 &lt; g &lt; 3\7<br />
</td>
        <td>8\19 &lt; g &lt; 11\26<br />
</td>
        <td>-5+12g<br />
</td>
        <td>-7g+3<br />
</td>
    </tr>
    <tr>
        <td>8L11s<br />
</td>
        <td>7\19 &lt; g &lt; 3\8<br />
</td>
        <td>7\19 &lt; g &lt; 10\27<br />
</td>
        <td>-4+11g<br />
</td>
        <td>-8g+3<br />
</td>
    </tr>
    <tr>
        <td>9L10s<br />
</td>
        <td>2\19 &lt; g &lt; 1\9<br />
</td>
        <td>2\19 &lt; g &lt; 3\28<br />
</td>
        <td>-1+10g<br />
</td>
        <td>-9g+1<br />
</td>
    </tr>
    <tr>
        <td>10L9s<br />
</td>
        <td>17\19 &lt; g &lt; 9\10<br />
</td>
        <td>17\19 &lt; g &lt; 26\29<br />
</td>
        <td>-8+9g<br />
</td>
        <td>-10g+9<br />
</td>
    </tr>
    <tr>
        <td>11L8s<br />
</td>
        <td>12\19 &lt; g &lt; 7\11<br />
</td>
        <td>12\19 &lt; g &lt; 19\30<br />
</td>
        <td>-5+8g<br />
</td>
        <td>-11g+7<br />
</td>
    </tr>
    <tr>
        <td>12L7s<br />
</td>
        <td>11\19 &lt; g &lt; 7\12<br />
</td>
        <td>11\19 &lt; g &lt; 18\31<br />
</td>
        <td>-4+7g<br />
</td>
        <td>-12g+7<br />
</td>
    </tr>
    <tr>
        <td>13L6s<br />
</td>
        <td>16\19 &lt; g &lt; 11\13<br />
</td>
        <td>16\19 &lt; g &lt; 27\32<br />
</td>
        <td>-5+6g<br />
</td>
        <td>-13g+11<br />
</td>
    </tr>
    <tr>
        <td>14L5s<br />
</td>
        <td>4\19 &lt; g &lt; 3\14<br />
</td>
        <td>4\19 &lt; g &lt; 7\33<br />
</td>
        <td>-1+5g<br />
</td>
        <td>-14g+3<br />
</td>
    </tr>
    <tr>
        <td>15L4s<br />
</td>
        <td>5\19 &lt; g &lt; 4\15<br />
</td>
        <td>5\19 &lt; g &lt; 9\34<br />
</td>
        <td>-1+4g<br />
</td>
        <td>-15g+4<br />
</td>
    </tr>
    <tr>
        <td>16L3s<br />
</td>
        <td>13\19 &lt; g &lt; 11\16<br />
</td>
        <td>13\19 &lt; g &lt; 24\35<br />
</td>
        <td>-2+3g<br />
</td>
        <td>-16g+11<br />
</td>
    </tr>
    <tr>
        <td>17L2s<br />
</td>
        <td>10\19 &lt; g &lt; 9\17<br />
</td>
        <td>10\19 &lt; g &lt; 19\36<br />
</td>
        <td>-1+2g<br />
</td>
        <td>-17g+9<br />
</td>
    </tr>
    <tr>
        <td>18L1s<br />
</td>
        <td>1\19 &lt; g &lt; 1\18<br />
</td>
        <td>1\19 &lt; g &lt; 2\37<br />
</td>
        <td>g<br />
</td>
        <td>-18g+1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:36:&lt;h1&gt; --><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>Large step<br />
</td>
        <td>Small step<br />
</td>
    </tr>
    <tr>
        <td>1L19s<br />
</td>
        <td>19\20 &lt; g &lt; 1<br />
</td>
        <td>19\20 &lt; g &lt; 20\21<br />
</td>
        <td>-18+19g<br />
</td>
        <td>-g+1<br />
</td>
    </tr>
    <tr>
        <td>2L18s<br />
</td>
        <td>9\20 &lt; g &lt; 1\2<br />
</td>
        <td>9\20 &lt; g &lt; 5\11<br />
</td>
        <td>-4+9g<br />
</td>
        <td>-g+1\2<br />
</td>
    </tr>
    <tr>
        <td>3L17s<br />
</td>
        <td>13\20 &lt; g &lt; 2\3<br />
</td>
        <td>13\20 &lt; g &lt; 15\23<br />
</td>
        <td>-11+17g<br />
</td>
        <td>-3g+2<br />
</td>
    </tr>
    <tr>
        <td>4L16s<br />
</td>
        <td>1\5 &lt; g &lt; 1\4<br />
</td>
        <td>1\5 &lt; g &lt; 2\9<br />
</td>
        <td>-3\4+4g<br />
</td>
        <td>-g+1\4<br />
</td>
    </tr>
    <tr>
        <td>5L15s<br />
</td>
        <td>3\20 &lt; g &lt; 1\5<br />
</td>
        <td>3\20 &lt; g &lt; 4\25<br />
</td>
        <td>-2\5+3g<br />
</td>
        <td>-g+1\5<br />
</td>
    </tr>
    <tr>
        <td>6L14s<br />
</td>
        <td>3\20 &lt; g &lt; 1\6<br />
</td>
        <td>3\20 &lt; g &lt; 2\13<br />
</td>
        <td>-1+7g<br />
</td>
        <td>-3g+1\2<br />
</td>
    </tr>
    <tr>
        <td>7L13s<br />
</td>
        <td>17\20 &lt; g &lt; 6\7<br />
</td>
        <td>17\20 &lt; g &lt; 23\27<br />
</td>
        <td>-11+13g<br />
</td>
        <td>-7g+6<br />
</td>
    </tr>
    <tr>
        <td>8L12s<br />
</td>
        <td>1\10 &lt; g &lt; 1\8<br />
</td>
        <td>1\10 &lt; g &lt; 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 &lt; g &lt; 5\9<br />
</td>
        <td>11\20 &lt; g &lt; 16\29<br />
</td>
        <td>-6+11g<br />
</td>
        <td>-9g+5<br />
</td>
    </tr>
    <tr>
        <td>10L10s<br />
</td>
        <td>1\20 &lt; g &lt; 1\10<br />
</td>
        <td>1\20 &lt; g &lt; 1\15<br />
</td>
        <td>g<br />
</td>
        <td>-g+1\10<br />
</td>
    </tr>
    <tr>
        <td>11L9s<br />
</td>
        <td>9\20 &lt; g &lt; 5\11<br />
</td>
        <td>9\20 &lt; g &lt; 14\31<br />
</td>
        <td>-4+9g<br />
</td>
        <td>-11g+5<br />
</td>
    </tr>
    <tr>
        <td>12L8s<br />
</td>
        <td>3\20 &lt; g &lt; 1\6<br />
</td>
        <td>3\20 &lt; g &lt; 2\13<br />
</td>
        <td>-1\4+2g<br />
</td>
        <td>-3g+1\2<br />
</td>
    </tr>
    <tr>
        <td>13L7s<br />
</td>
        <td>3\20 &lt; g &lt; 2\13<br />
</td>
        <td>3\20 &lt; g &lt; 5\33<br />
</td>
        <td>-1+7g<br />
</td>
        <td>-13g+2<br />
</td>
    </tr>
    <tr>
        <td>14L6s<br />
</td>
        <td>7\20 &lt; g &lt; 5\14<br />
</td>
        <td>7\20 &lt; g &lt; 6\17<br />
</td>
        <td>-1+3g<br />
</td>
        <td>-7g+5\2<br />
</td>
    </tr>
    <tr>
        <td>15L5s<br />
</td>
        <td>1\20 &lt; g &lt; 1\15<br />
</td>
        <td>1\20 &lt; g &lt; 2\35<br />
</td>
        <td>g<br />
</td>
        <td>-3g+1\5<br />
</td>
    </tr>
    <tr>
        <td>16L4s<br />
</td>
        <td>1\20 &lt; g &lt; 1\16<br />
</td>
        <td>1\20 &lt; g &lt; 1\18<br />
</td>
        <td>g<br />
</td>
        <td>-4g+1\4<br />
</td>
    </tr>
    <tr>
        <td>17L3s<br />
</td>
        <td>7\20 &lt; g &lt; 6\17<br />
</td>
        <td>7\20 &lt; g &lt; 13\37<br />
</td>
        <td>-1+3g<br />
</td>
        <td>-17g+6<br />
</td>
    </tr>
    <tr>
        <td>18L2s<br />
</td>
        <td>1\20 &lt; g &lt; 1\18<br />
</td>
        <td>1\20 &lt; g &lt; 1\19<br />
</td>
        <td>g<br />
</td>
        <td>-9g+1\2<br />
</td>
    </tr>
    <tr>
        <td>19L1s<br />
</td>
        <td>1\20 &lt; g &lt; 1\19<br />
</td>
        <td>1\20 &lt; g &lt; 2\39<br />
</td>
        <td>g<br />
</td>
        <td>-19g+1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:38:&lt;h1&gt; --><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>Large step<br />
</td>
        <td>Small step<br />
</td>
    </tr>
    <tr>
        <td>1L20s<br />
</td>
        <td>20\21 &lt; g &lt; 1<br />
</td>
        <td>20\21 &lt; g &lt; 21\22<br />
</td>
        <td>-19+20g<br />
</td>
        <td>-g+1<br />
</td>
    </tr>
    <tr>
        <td>2L19s<br />
</td>
        <td>10\21 &lt; g &lt; 1\2<br />
</td>
        <td>10\21 &lt; g &lt; 11\23<br />
</td>
        <td>-9+19g<br />
</td>
        <td>-2g+1<br />
</td>
    </tr>
    <tr>
        <td>3L18s<br />
</td>
        <td>2\7 &lt; g &lt; 1\3<br />
</td>
        <td>2\7 &lt; g &lt; 3\10<br />
</td>
        <td>-5\3+6g<br />
</td>
        <td>-g+1\3<br />
</td>
    </tr>
    <tr>
        <td>4L17s<br />
</td>
        <td>5\21 &lt; g &lt; 1\4<br />
</td>
        <td>5\21 &lt; g &lt; 6\25<br />
</td>
        <td>-4+17g<br />
</td>
        <td>-4g+1<br />
</td>
    </tr>
    <tr>
        <td>5L16s<br />
</td>
        <td>4\21 &lt; g &lt; 1\5<br />
</td>
        <td>4\21 &lt; g &lt; 5\26<br />
</td>
        <td>-3+16g<br />
</td>
        <td>-5g+1<br />
</td>
    </tr>
    <tr>
        <td>6L15s<br />
</td>
        <td>1\7 &lt; g &lt; 1\6<br />
</td>
        <td>1\7 &lt; g &lt; 2\13<br />
</td>
        <td>-2\3+5g<br />
</td>
        <td>-2g+1\3<br />
</td>
    </tr>
    <tr>
        <td>7L14s<br />
</td>
        <td>2\21 &lt; g &lt; 1\7<br />
</td>
        <td>2\21 &lt; g &lt; 3\28<br />
</td>
        <td>-1\7+2g<br />
</td>
        <td>-g+1\7<br />
</td>
    </tr>
    <tr>
        <td>8L13s<br />
</td>
        <td>13\21 &lt; g &lt; 5\8<br />
</td>
        <td>13\21 &lt; g &lt; 18\29<br />
</td>
        <td>-8+13g<br />
</td>
        <td>-8g+5<br />
</td>
    </tr>
    <tr>
        <td>9L12s<br />
</td>
        <td>2\21 &lt; g &lt; 1\9<br />
</td>
        <td>2\21 &lt; g &lt; 1\10<br />
</td>
        <td>-1\3+4g<br />
</td>
        <td>-3g+1\3<br />
</td>
    </tr>
    <tr>
        <td>10L11s<br />
</td>
        <td>2\21 &lt; g &lt; 1\10<br />
</td>
        <td>2\21 &lt; g &lt; 3\31<br />
</td>
        <td>-1+11g<br />
</td>
        <td>-10g+1<br />
</td>
    </tr>
    <tr>
        <td>11L10s<br />
</td>
        <td>19\21 &lt; g &lt; 10\11<br />
</td>
        <td>19\21 &lt; g &lt; 29\32<br />
</td>
        <td>-9+10g<br />
</td>
        <td>-11g+10<br />
</td>
    </tr>
    <tr>
        <td>12L9s<br />
</td>
        <td>5\21 &lt; g &lt; 1\4<br />
</td>
        <td>5\21 &lt; g &lt; 6\25<br />
</td>
        <td>-2\3+3g<br />
</td>
        <td>-4g+1<br />
</td>
    </tr>
    <tr>
        <td>13L8s<br />
</td>
        <td>8\21 &lt; g &lt; 5\13<br />
</td>
        <td>8\21 &lt; g &lt; 13\34<br />
</td>
        <td>-3+8g<br />
</td>
        <td>-13g+5<br />
</td>
    </tr>
    <tr>
        <td>14L7s<br />
</td>
        <td>1\21 &lt; g &lt; 1\14<br />
</td>
        <td>1\21 &lt; g &lt; 2\35<br />
</td>
        <td>g<br />
</td>
        <td>-2g+1\7<br />
</td>
    </tr>
    <tr>
        <td>15L6s<br />
</td>
        <td>4\21 &lt; g &lt; 1\5<br />
</td>
        <td>4\21 &lt; g &lt; 5\26<br />
</td>
        <td>-1\3+2g<br />
</td>
        <td>-5g+1<br />
</td>
    </tr>
    <tr>
        <td>16L5s<br />
</td>
        <td>17\21 &lt; g &lt; 13\16<br />
</td>
        <td>17\21 &lt; g &lt; 30\37<br />
</td>
        <td>-4+5g<br />
</td>
        <td>-16g+13<br />
</td>
    </tr>
    <tr>
        <td>17L4s<br />
</td>
        <td>16\21 &lt; g &lt; 13\17<br />
</td>
        <td>16\21 &lt; g &lt; 29\38<br />
</td>
        <td>-3+4g<br />
</td>
        <td>-17g+13<br />
</td>
    </tr>
    <tr>
        <td>18L3s<br />
</td>
        <td>1\21 &lt; g &lt; 1\18<br />
</td>
        <td>1\21 &lt; g &lt; 2\39<br />
</td>
        <td>g<br />
</td>
        <td>-6g+1\3<br />
</td>
    </tr>
    <tr>
        <td>19L2s<br />
</td>
        <td>11\21 &lt; g &lt; 10\19<br />
</td>
        <td>11\21 &lt; g &lt; 21\40<br />
</td>
        <td>-1+2g<br />
</td>
        <td>-19g+10<br />
</td>
    </tr>
    <tr>
        <td>20L1s<br />
</td>
        <td>1\21 &lt; g &lt; 1\20<br />
</td>
        <td>1\21 &lt; g &lt; 2\41<br />
</td>
        <td>g<br />
</td>
        <td>-20g+1<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><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>Large step<br />
</td>
        <td>Small step<br />
</td>
    </tr>
    <tr>
        <td>1L21s<br />
</td>
        <td>21\22 &lt; g &lt; 1<br />
</td>
        <td>21\22 &lt; g &lt; 22\23<br />
</td>
        <td>-20+21g<br />
</td>
        <td>-g+1<br />
</td>
    </tr>
    <tr>
        <td>2L20s<br />
</td>
        <td>5\11 &lt; g &lt; 1\2<br />
</td>
        <td>5\11 &lt; g &lt; 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 &lt; g &lt; 1\3<br />
</td>
        <td>7\22 &lt; g &lt; 8\25<br />
</td>
        <td>-6+19g<br />
</td>
        <td>1-3g<br />
</td>
    </tr>
    <tr>
        <td>4L18s<br />
</td>
        <td>5\22 &lt; g &lt; 1\4<br />
</td>
        <td>5\22 &lt; g &lt; 3\13<br />
</td>
        <td>-2+9g<br />
</td>
        <td>-2g+1\2<br />
</td>
    </tr>
    <tr>
        <td>5L17s<br />
</td>
        <td>13\22 &lt; g &lt; 3\5<br />
</td>
        <td>13\22 &lt; g &lt; 16\27<br />
</td>
        <td>-10+17g<br />
</td>
        <td>-5g+3<br />
</td>
    </tr>
    <tr>
        <td>6L16s<br />
</td>
        <td>7\22 &lt; g &lt; 1\3<br />
</td>
        <td>7\22 &lt; g &lt; 8\25<br />
</td>
        <td>-5\2+8g<br />
</td>
        <td>1-3g<br />
</td>
    </tr>
    <tr>
        <td>7L15s<br />
</td>
        <td>3\22 &lt; g &lt; 1\7<br />
</td>
        <td>3\22 &lt; g &lt; 4\29<br />
</td>
        <td>-2+15g<br />
</td>
        <td>-7g+1<br />
</td>
    </tr>
    <tr>
        <td>8L14s<br />
</td>
        <td>4\11 &lt; g &lt; 3\8<br />
</td>
        <td>4\11 &lt; g &lt; 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 &lt; g &lt; 7\9<br />
</td>
        <td>17\22 &lt; g &lt; 24\31<br />
</td>
        <td>-10+13g<br />
</td>
        <td>-9g+7<br />
</td>
    </tr>
    <tr>
        <td>10L12s<br />
</td>
        <td>1\11 &lt; g &lt; 1\10<br />
</td>
        <td>1\11 &lt; g &lt; 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 &lt; g &lt; 1\11<br />
</td>
        <td>1\22 &lt; g &lt; 2\33<br />
</td>
        <td>g<br />
</td>
        <td>-g+1\11<br />
</td>
    </tr>
    <tr>
        <td>12L10s<br />
</td>
        <td>9\22 &lt; g &lt; 5\12<br />
</td>
        <td>9\22 &lt; g &lt; 7\17<br />
</td>
        <td>-2+5g<br />
</td>
        <td>-6g+5\2<br />
</td>
    </tr>
    <tr>
        <td>13L9s<br />
</td>
        <td>5\22 &lt; g &lt; 3\13<br />
</td>
        <td>5\22 &lt; g &lt; 8\35<br />
</td>
        <td>-2+9g<br />
</td>
        <td>-13g+3<br />
</td>
    </tr>
    <tr>
        <td>14L8s<br />
</td>
        <td>3\22 &lt; g &lt; 1\7<br />
</td>
        <td>3\22 &lt; g &lt; 4\29<br />
</td>
        <td>4g-1\2<br />
</td>
        <td>-7g+1<br />
</td>
    </tr>
    <tr>
        <td>15L7s<br />
</td>
        <td>19\22 &lt; g &lt; 13\15<br />
</td>
        <td>19\22 &lt; g &lt; 32\37<br />
</td>
        <td>-6+7g<br />
</td>
        <td>-15g+13<br />
</td>
    </tr>
    <tr>
        <td>16L6s<br />
</td>
        <td>2\11 &lt; g &lt; 3\16<br />
</td>
        <td>2\11 &lt; g &lt; 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 &lt; g &lt; 7\17<br />
</td>
        <td>9\22 &lt; g &lt; 16\39<br />
</td>
        <td>-2+5g<br />
</td>
        <td>-17g+7<br />
</td>
    </tr>
    <tr>
        <td>18L4s<br />
</td>
        <td>3\11 &lt; g &lt; 5\18<br />
</td>
        <td>3\11 &lt; g &lt; 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 &lt; g &lt; 13\19<br />
</td>
        <td>15\22 &lt; g &lt;28\41<br />
</td>
        <td>-2+3g<br />
</td>
        <td>-19g+13<br />
</td>
    </tr>
    <tr>
        <td>20L2s<br />
</td>
        <td>1\22 &lt; g &lt; 1\20<br />
</td>
        <td>1\22 &lt; g &lt; 1\21<br />
</td>
        <td>g<br />
</td>
        <td>-10g+1\2<br />
</td>
    </tr>
    <tr>
        <td>21L1s<br />
</td>
        <td>1\22 &lt; g &lt; 1\21<br />
</td>
        <td>1\22 &lt; g &lt; 2\43<br />
</td>
        <td>g<br />
</td>
        <td>-21g+1<br />
</td>
    </tr>
</table>

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