Generator ranges of MOS: Difference between revisions
Wikispaces>JosephRuhf **Imported revision 539625988 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 539766998 - 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- | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-02-04 18:42:42 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>539766998</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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|| Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || | || 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 || | || 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 || | || 2L23s || 12\25 < g < 1\2 || 12\25 < g < 13\27 || 13\27 < g < 14\29 || 2g-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 || | || 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 || | || 4L21s || 6\25 < g < 1\4 || 6\25 < g < 7\29 || 7\29 < g < 8\33 || -5+21g || -4g+1 || | ||
| Line 380: | Line 380: | ||
|| 22L3s || 17\25 < g < 15\22 || 17\25 < g < 32\47 || 32\47 < g < 47\69 || 3g-2 || -22g+15 || | || 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 || | || 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> | || 24L1s || 1\25 < g < 1\24 || 1\25 < g < 2\49 || 2\49 < g < 3\73 || g || -24g+1 || | ||
=26= | |||
|| Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || | |||
|| 1L25s || 25\26 < g < 1 || 25\26 < g < 26\27 || 26\27 < g < 27\28 || -24+25g || -g+1 || | |||
|| 2L<span style="line-height: 1.5;">24s</span> || 12\26 (6\13) < g < 1\2 || <span style="line-height: 1.5;">12\26 (6\13)</span> < g < 13\28 || 13\28 < g < 14\30 (7\15) || 12g-11\2 || 1\2-g || | |||
|| 3L<span style="line-height: 1.5;">23s</span> || 17\26 < g < 2\3 || 17\26 < g < 19\29 || 19\29 < g < 21\32 || -15+23g || 2-3g || | |||
|| 4L<span style="line-height: 1.5;">22s</span> || 6\26 (3\13) < g < 1\4 || 6\26 (3\13) < g < 7\30 || 7\30 < g < 8\34 (4\17) || 11g-5\2 || <span style="line-height: 1.5;">-2g+1\2</span> || | |||
|| 5L<span style="line-height: 1.5;">21s</span> || 5\26 < g < 1\5 || 5\26 < g < 6\31 || 6\31 < g < 7\36 || -4+21g || 1-5g || | |||
|| 6L<span style="line-height: 1.5;">20s</span> || 4\26 (2\13) < g < 1\6 || 4\26 (2\13) < g < 5\32 || 5\32 < g < 6\38 (3\19) || -3\2+10g || -3g+1\2 || | |||
|| 7L<span style="line-height: 1.5;">19s</span> || 15\26 < g < 4\7 || 15\26 < g < 19\33 || 19\33 < g < 23\40 || 11-19g || 7g-4 || | |||
|| 8L<span style="line-height: 1.5;">18s</span> || 3\26 < g < 1\8 || 3\26 < g < 4\34 (2\17) || 4\34 (2\17) < g < 5\42 || 9g-1 || 1\2-4g || | |||
|| 9L<span style="line-height: 1.5;">17s</span> || 23\26 < g < 8\9 || 23\26 < g < 31\35 || 31\35 < g < 39\44 || -15+17g || -9g+8 || | |||
|| 10L<span style="line-height: 1.5;">16s</span> || 5\26 < g < 2\10 <span style="line-height: 1.5;">(1\5)</span> || 5\26 < g < 7\36 || 7\36 < g < 9\46 || -3\2+8g || 1-5g || | |||
|| 11L<span style="line-height: 1.5;">15s</span> || 7\26 < g < 3\11 || 7\26 < g < 10\37 || 10\37 < g < 13\48 || 15g-4 || -11g+3 || | |||
|| 12L<span style="line-height: 1.5;">14s</span> || 2\26 (1\13) < g < 1\12 || 2\26 (1\13) < g < 3\38 || 3\38 < g < 4\50 || 7g-1\2 || 1\2-6g || | |||
|| 13L13s || 1\26 < g < 1\13 || 1\26 < g < 2\39 || 2\39 < g < 3\52 || g || -g+1\13 || | |||
|| <span style="line-height: 1.5;">14L</span>12s || 11\26 < g < 6\14 (3\7) || 11\26 < g < 17\40 || 17\40 < g < 23\54 || 6g-5\2 || 3-7g || | |||
|| <span style="line-height: 1.5;">15L</span>11s || 19\26 < g < 11\15 || 19\26 < g < 30\41 || 30\41< g < 41\56 || -8+11g || -15g+11 || | |||
|| <span style="line-height: 1.5;">16L</span>10s || 21\26 < g < 13\16 || 21\26 < g < 34\42 (17\21) || 34\42 (17\21) < g < 47\58 || -8g+13\2 || 5g-4 || | |||
|| <span style="line-height: 1.5;">17L</span>9s || 3\26 < g < 2\17 || 3\26 < g < 5\43 || 5\43 < g < 7\60 || 9g-1 || 2-17g || | |||
|| <span style="line-height: 1.5;">18L</span>8s || 10\26 <span style="line-height: 1.5;">(5\13) < g < 7\18 </span> || 10\26 (5\13) < g < 17\44 || 17\44 < g < 24\62 (12\31) || 8g-7 || -9g+7\2 || | |||
|| <span style="line-height: 1.5;">19L</span>7s || 11\26 < g < 8\19 || 11\26 < g < 19\45 || 19\45 < g < 27\64 || 3-7g || -8+19g || | |||
|| <span style="line-height: 1.5;">20L</span>6s || 9\26 < g < 7\20 || 9\26 < g < 16\46 (8\23) || 16\43 (8\23) < g < 23\66 || -1+3g || 7\2-10g || | |||
|| <span style="line-height: 1.5;">21L</span>5s || 21\26 < g < 17\21 || 21\26 < g < 38\47 || 38\47 < g < 55\68 || 5g-4 || -21g+16 || | |||
|| <span style="line-height: 1.5;">22L</span>4s || 7\26 < g < 6\22 (3\11) || 7\26 < g < 13\48 || 13\48 < g < 19\70 || 2g-1\2 || -11g+3 || | |||
|| <span style="line-height: 1.5;">23L</span>3s || 17\26 < g < 15\23 || 17\26 < g < 32\49 || 32\49 < g < 47\72 || -3g+2 || -23g+15 || | |||
|| <span style="line-height: 1.5;">24L</span>2s || 1\26 < g < 1\24 || 1\26 < g < 2\50 (1\25) || 2\50 (1\25) < g < 3\74 || g || -12g+1\2 || | |||
|| 25L1s || 1\26 < g < 1\25 || 1\26 < g < 2\51 || 2\51< g < 3\76 || g || -25g+1 || | |||
=27= | |||
|| Large-small numbers || Generator range || Range of propriety || Range of maximum expressiveness || Large step || Small step || | |||
|| 1L26s || 26\27 < g < 1 || <span style="line-height: 1.5;">26\27</span> < g < <span style="line-height: 1.5;">27\28</span> || 27\28 < g < 28\29 || -25+26g || -g+1 || | |||
|| 2L25s || 13\27 < g < 1\2 || <span style="line-height: 1.5;">13</span>\27 < g < 14\29 || 14\29 < g < 15\31 || 25g-12 || -2g+1 || | |||
|| 3L24s || 8\27 < g < 1\3 || 8\27 < g < 9\30 (3\10) || 9\30 (3\10) < g < 10\33 || -7\3+8g || 1\3-g || | |||
|| 4L23s || 20\27 < g < 3\4 || 20\27 < g < 23\31 || 23\31 < g < 26\35 || 23g-17 || -4g+3 || | |||
|| 5L22s || 16\27 < g < 3\5 || 16\27 < g < 19\32 || 19\32 < g < 22\37 || -13+22g || 3-5g || | |||
|| 6L21s || 4\27 < g < 1\6 || 4\27 < g < 5\33 || 5\33 < g < 6\39 (2\13) || -1+7g || -2g+1\3 || | |||
|| 7L20s || 23\27 < g < 6\7 || 23\27 < g < 29\34 || 29\34 < g < 35\41 || -17+20g || -7g+6 || | |||
|| 8L19s || 10\27 < g < 3\8 || 10\27 < g < 13\35 || 13\35 < g < 16\43 || 19g-7 || 3-8g || | |||
|| 9L18s || 2\27 < g < 1\9 || 2\27 < g < 3\36 (1\12) || 3\36 (1\12) < g < 4\45 || -1\9+2g || -g+1\9 || | |||
|| 10L17s || 8\27 < g < 3\10 || 8\27 < g < 11\37 || 11\37 < g < 14\47 || -5+17g || 3-10g || | |||
|| 11L16s || 5\27 < g < 2\11 || 5\27 < g < 7\38 || 7\38 < g < 9\49 || -16g+3 || 11g-4 || | |||
|| 12L15s || 2\27 < g < 1\12 || 2\27 < g < 3\39<span style="line-height: 1.5;"> (1\13)</span> || 3\39 (1\13) < g < 4\51 || 5g-1\3 || 1\3-4g || | |||
|| 13L14s || 2\27 < g < 1\13 || 2\27 < g < 3\40 || 3\40 < g < 4\53 || 14g-1 || -<span style="line-height: 1.5;">13g+1</span> || | |||
|| 14L13s || 25\27 < g < 13\14 || 25\27 < g < 38\41 || 38\41 < g < 51\55 || 13g-12 || 13-14g || | |||
|| 15L12s || 25\27 < g < 14\15 || 25\27 < g < 39\42 (13\14) || 39\42 (13\14) < g < 43\57 || -4+4g || -5g+14\3 || | |||
|| 16L11s || 22\27 < g < 13\16 || 22\27 < g < 35\43 || 35\43 < g < 48\59 || -11g+9 || 16g-13 || | |||
|| 17L10s || 19\27 < g < 12\17 || 19\27 < g < 31\44 || 31\44 < g < 43\61 || 10g-7 || 12-17g || | |||
|| 18L9s || 1\27 < g < 1\18 || 1\27 < g < 2\45 || 2\45 < g < 3\63 (1\21) || g || -2g+1\9 || | |||
|| 19L8s || 17\27 < g < 12\19 || 17\27 < g < 29\46 || 29\46 < g < 41\65 || -5+8g || 12-19g || | |||
|| 20L7s || 4\27 < g < 3\20 || 4\27 < g < 7\47 || 7\47 < g < 10\67 || -1+7g || 3-20g || | |||
|| 21L6s || 5\27 < g < 4\21 || 5\27 < g < 9\48 (3\16) || 9\48 (3\16) < g < 13\69 || 2g-1\3 || -7g+4 || | |||
|| 22L5s || <span style="line-height: 1.5;">11</span>\27 < g < 9\22 || 11\27 < g < 20\49 || 20\49 < g < 29\71 || 5g-2 || -22g+9 || | |||
|| 23L4s || 7\27 < g < 6\23 || 7\27 < g < 13\50 || 13\50< g < 19\73 || 4g-1 || -23g+6 || | |||
|| 24L3s || 1\27 < g < 1\24 || 1\27 < g < 2\51 || 2\51 < g < 3\75 <span style="line-height: 1.5;">(1\25)</span> || g || -8g+1\3 || | |||
|| 25L2s || 14\27 < g < 13\25 || 14\27 < g < 27\52 || 27\52< g < 40\77 || 2g-1 || -25g+13 || | |||
|| 26L1s || 1\27 < g < 1\26 || 1\27 < g < 2\53 || 2\53< g < 3\79 || g || -26g+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 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 /> | <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 /> | ||
| Line 4,774: | Line 4,831: | ||
<td>13\27 &lt; g &lt; 14\29<br /> | <td>13\27 &lt; g &lt; 14\29<br /> | ||
</td> | </td> | ||
<td> | <td>2g-11<br /> | ||
</td> | </td> | ||
<td>1-2g<br /> | <td>1-2g<br /> | ||
| Line 5,085: | Line 5,142: | ||
</td> | </td> | ||
<td>-24g+1<br /> | <td>-24g+1<br /> | ||
</td> | |||
</tr> | |||
</table> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:48:&lt;h1&gt; --><h1 id="toc24"><a name="x26"></a><!-- ws:end:WikiTextHeadingRule:48 -->26</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>1L25s<br /> | |||
</td> | |||
<td>25\26 &lt; g &lt; 1<br /> | |||
</td> | |||
<td>25\26 &lt; g &lt; 26\27<br /> | |||
</td> | |||
<td>26\27 &lt; g &lt; 27\28<br /> | |||
</td> | |||
<td>-24+25g<br /> | |||
</td> | |||
<td>-g+1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>2L<span style="line-height: 1.5;">24s</span><br /> | |||
</td> | |||
<td>12\26 (6\13) &lt; g &lt; 1\2<br /> | |||
</td> | |||
<td><span style="line-height: 1.5;">12\26 (6\13)</span> &lt; g &lt; 13\28<br /> | |||
</td> | |||
<td>13\28 &lt; g &lt; 14\30 (7\15)<br /> | |||
</td> | |||
<td>12g-11\2<br /> | |||
</td> | |||
<td>1\2-g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3L<span style="line-height: 1.5;">23s</span><br /> | |||
</td> | |||
<td>17\26 &lt; g &lt; 2\3<br /> | |||
</td> | |||
<td>17\26 &lt; g &lt; 19\29<br /> | |||
</td> | |||
<td>19\29 &lt; g &lt; 21\32<br /> | |||
</td> | |||
<td>-15+23g<br /> | |||
</td> | |||
<td>2-3g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4L<span style="line-height: 1.5;">22s</span><br /> | |||
</td> | |||
<td>6\26 (3\13) &lt; g &lt; 1\4<br /> | |||
</td> | |||
<td>6\26 (3\13) &lt; g &lt; 7\30<br /> | |||
</td> | |||
<td>7\30 &lt; g &lt; 8\34 (4\17)<br /> | |||
</td> | |||
<td>11g-5\2<br /> | |||
</td> | |||
<td><span style="line-height: 1.5;">-2g+1\2</span><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>5L<span style="line-height: 1.5;">21s</span><br /> | |||
</td> | |||
<td>5\26 &lt; g &lt; 1\5<br /> | |||
</td> | |||
<td>5\26 &lt; g &lt; 6\31<br /> | |||
</td> | |||
<td>6\31 &lt; g &lt; 7\36<br /> | |||
</td> | |||
<td>-4+21g<br /> | |||
</td> | |||
<td>1-5g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>6L<span style="line-height: 1.5;">20s</span><br /> | |||
</td> | |||
<td>4\26 (2\13) &lt; g &lt; 1\6<br /> | |||
</td> | |||
<td>4\26 (2\13) &lt; g &lt; 5\32<br /> | |||
</td> | |||
<td>5\32 &lt; g &lt; 6\38 (3\19)<br /> | |||
</td> | |||
<td>-3\2+10g<br /> | |||
</td> | |||
<td>-3g+1\2<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>7L<span style="line-height: 1.5;">19s</span><br /> | |||
</td> | |||
<td>15\26 &lt; g &lt; 4\7<br /> | |||
</td> | |||
<td>15\26 &lt; g &lt; 19\33<br /> | |||
</td> | |||
<td>19\33 &lt; g &lt; 23\40<br /> | |||
</td> | |||
<td>11-19g<br /> | |||
</td> | |||
<td>7g-4<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>8L<span style="line-height: 1.5;">18s</span><br /> | |||
</td> | |||
<td>3\26 &lt; g &lt; 1\8<br /> | |||
</td> | |||
<td>3\26 &lt; g &lt; 4\34 (2\17)<br /> | |||
</td> | |||
<td>4\34 (2\17) &lt; g &lt; 5\42<br /> | |||
</td> | |||
<td>9g-1<br /> | |||
</td> | |||
<td>1\2-4g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>9L<span style="line-height: 1.5;">17s</span><br /> | |||
</td> | |||
<td>23\26 &lt; g &lt; 8\9<br /> | |||
</td> | |||
<td>23\26 &lt; g &lt; 31\35<br /> | |||
</td> | |||
<td>31\35 &lt; g &lt; 39\44<br /> | |||
</td> | |||
<td>-15+17g<br /> | |||
</td> | |||
<td>-9g+8<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>10L<span style="line-height: 1.5;">16s</span><br /> | |||
</td> | |||
<td>5\26 &lt; g &lt; 2\10 <span style="line-height: 1.5;">(1\5)</span><br /> | |||
</td> | |||
<td>5\26 &lt; g &lt; 7\36<br /> | |||
</td> | |||
<td>7\36 &lt; g &lt; 9\46<br /> | |||
</td> | |||
<td>-3\2+8g<br /> | |||
</td> | |||
<td>1-5g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>11L<span style="line-height: 1.5;">15s</span><br /> | |||
</td> | |||
<td>7\26 &lt; g &lt; 3\11<br /> | |||
</td> | |||
<td>7\26 &lt; g &lt; 10\37<br /> | |||
</td> | |||
<td>10\37 &lt; g &lt; 13\48<br /> | |||
</td> | |||
<td>15g-4<br /> | |||
</td> | |||
<td>-11g+3<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>12L<span style="line-height: 1.5;">14s</span><br /> | |||
</td> | |||
<td>2\26 (1\13) &lt; g &lt; 1\12<br /> | |||
</td> | |||
<td>2\26 (1\13) &lt; g &lt; 3\38<br /> | |||
</td> | |||
<td>3\38 &lt; g &lt; 4\50<br /> | |||
</td> | |||
<td>7g-1\2<br /> | |||
</td> | |||
<td>1\2-6g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>13L13s<br /> | |||
</td> | |||
<td>1\26 &lt; g &lt; 1\13<br /> | |||
</td> | |||
<td>1\26 &lt; g &lt; 2\39<br /> | |||
</td> | |||
<td>2\39 &lt; g &lt; 3\52<br /> | |||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>-g+1\13<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><span style="line-height: 1.5;">14L</span>12s<br /> | |||
</td> | |||
<td>11\26 &lt; g &lt; 6\14 (3\7)<br /> | |||
</td> | |||
<td>11\26 &lt; g &lt; 17\40<br /> | |||
</td> | |||
<td>17\40 &lt; g &lt; 23\54<br /> | |||
</td> | |||
<td>6g-5\2<br /> | |||
</td> | |||
<td>3-7g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><span style="line-height: 1.5;">15L</span>11s<br /> | |||
</td> | |||
<td>19\26 &lt; g &lt; 11\15<br /> | |||
</td> | |||
<td>19\26 &lt; g &lt; 30\41<br /> | |||
</td> | |||
<td>30\41&lt; g &lt; 41\56<br /> | |||
</td> | |||
<td>-8+11g<br /> | |||
</td> | |||
<td>-15g+11<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><span style="line-height: 1.5;">16L</span>10s<br /> | |||
</td> | |||
<td>21\26 &lt; g &lt; 13\16<br /> | |||
</td> | |||
<td>21\26 &lt; g &lt; 34\42 (17\21)<br /> | |||
</td> | |||
<td>34\42 (17\21) &lt; g &lt; 47\58<br /> | |||
</td> | |||
<td>-8g+13\2<br /> | |||
</td> | |||
<td>5g-4<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><span style="line-height: 1.5;">17L</span>9s<br /> | |||
</td> | |||
<td>3\26 &lt; g &lt; 2\17<br /> | |||
</td> | |||
<td>3\26 &lt; g &lt; 5\43<br /> | |||
</td> | |||
<td>5\43 &lt; g &lt; 7\60<br /> | |||
</td> | |||
<td>9g-1<br /> | |||
</td> | |||
<td>2-17g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><span style="line-height: 1.5;">18L</span>8s<br /> | |||
</td> | |||
<td>10\26 <span style="line-height: 1.5;">(5\13) &lt; g &lt; 7\18 </span><br /> | |||
</td> | |||
<td>10\26 (5\13) &lt; g &lt; 17\44<br /> | |||
</td> | |||
<td>17\44 &lt; g &lt; 24\62 (12\31)<br /> | |||
</td> | |||
<td>8g-7<br /> | |||
</td> | |||
<td>-9g+7\2<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><span style="line-height: 1.5;">19L</span>7s<br /> | |||
</td> | |||
<td>11\26 &lt; g &lt; 8\19<br /> | |||
</td> | |||
<td>11\26 &lt; g &lt; 19\45<br /> | |||
</td> | |||
<td>19\45 &lt; g &lt; 27\64<br /> | |||
</td> | |||
<td>3-7g<br /> | |||
</td> | |||
<td>-8+19g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><span style="line-height: 1.5;">20L</span>6s<br /> | |||
</td> | |||
<td>9\26 &lt; g &lt; 7\20<br /> | |||
</td> | |||
<td>9\26 &lt; g &lt; 16\46 (8\23)<br /> | |||
</td> | |||
<td>16\43 (8\23) &lt; g &lt; 23\66<br /> | |||
</td> | |||
<td>-1+3g<br /> | |||
</td> | |||
<td>7\2-10g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><span style="line-height: 1.5;">21L</span>5s<br /> | |||
</td> | |||
<td>21\26 &lt; g &lt; 17\21<br /> | |||
</td> | |||
<td>21\26 &lt; g &lt; 38\47<br /> | |||
</td> | |||
<td>38\47 &lt; g &lt; 55\68<br /> | |||
</td> | |||
<td>5g-4<br /> | |||
</td> | |||
<td>-21g+16<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><span style="line-height: 1.5;">22L</span>4s<br /> | |||
</td> | |||
<td>7\26 &lt; g &lt; 6\22 (3\11)<br /> | |||
</td> | |||
<td>7\26 &lt; g &lt; 13\48<br /> | |||
</td> | |||
<td>13\48 &lt; g &lt; 19\70<br /> | |||
</td> | |||
<td>2g-1\2<br /> | |||
</td> | |||
<td>-11g+3<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><span style="line-height: 1.5;">23L</span>3s<br /> | |||
</td> | |||
<td>17\26 &lt; g &lt; 15\23<br /> | |||
</td> | |||
<td>17\26 &lt; g &lt; 32\49<br /> | |||
</td> | |||
<td>32\49 &lt; g &lt; 47\72<br /> | |||
</td> | |||
<td>-3g+2<br /> | |||
</td> | |||
<td>-23g+15<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td><span style="line-height: 1.5;">24L</span>2s<br /> | |||
</td> | |||
<td>1\26 &lt; g &lt; 1\24<br /> | |||
</td> | |||
<td>1\26 &lt; g &lt; 2\50 (1\25)<br /> | |||
</td> | |||
<td>2\50 (1\25) &lt; g &lt; 3\74<br /> | |||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>-12g+1\2<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>25L1s<br /> | |||
</td> | |||
<td>1\26 &lt; g &lt; 1\25<br /> | |||
</td> | |||
<td>1\26 &lt; g &lt; 2\51<br /> | |||
</td> | |||
<td>2\51&lt; g &lt; 3\76<br /> | |||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>-25g+1<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:50:&lt;h1&gt; --><h1 id="toc25"><a name="x27"></a><!-- ws:end:WikiTextHeadingRule:50 -->27</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>1L26s<br /> | |||
</td> | |||
<td>26\27 &lt; g &lt; 1<br /> | |||
</td> | |||
<td><span style="line-height: 1.5;">26\27</span> &lt; g &lt; <span style="line-height: 1.5;">27\28</span><br /> | |||
</td> | |||
<td>27\28 &lt; g &lt; 28\29<br /> | |||
</td> | |||
<td>-25+26g<br /> | |||
</td> | |||
<td>-g+1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>2L25s<br /> | |||
</td> | |||
<td>13\27 &lt; g &lt; 1\2<br /> | |||
</td> | |||
<td><span style="line-height: 1.5;">13</span>\27 &lt; g &lt; 14\29<br /> | |||
</td> | |||
<td>14\29 &lt; g &lt; 15\31<br /> | |||
</td> | |||
<td>25g-12<br /> | |||
</td> | |||
<td>-2g+1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3L24s<br /> | |||
</td> | |||
<td>8\27 &lt; g &lt; 1\3<br /> | |||
</td> | |||
<td>8\27 &lt; g &lt; 9\30 (3\10)<br /> | |||
</td> | |||
<td>9\30 (3\10) &lt; g &lt; 10\33<br /> | |||
</td> | |||
<td>-7\3+8g<br /> | |||
</td> | |||
<td>1\3-g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4L23s<br /> | |||
</td> | |||
<td>20\27 &lt; g &lt; 3\4<br /> | |||
</td> | |||
<td>20\27 &lt; g &lt; 23\31<br /> | |||
</td> | |||
<td>23\31 &lt; g &lt; 26\35<br /> | |||
</td> | |||
<td>23g-17<br /> | |||
</td> | |||
<td>-4g+3<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>5L22s<br /> | |||
</td> | |||
<td>16\27 &lt; g &lt; 3\5<br /> | |||
</td> | |||
<td>16\27 &lt; g &lt; 19\32<br /> | |||
</td> | |||
<td>19\32 &lt; g &lt; 22\37<br /> | |||
</td> | |||
<td>-13+22g<br /> | |||
</td> | |||
<td>3-5g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>6L21s<br /> | |||
</td> | |||
<td>4\27 &lt; g &lt; 1\6<br /> | |||
</td> | |||
<td>4\27 &lt; g &lt; 5\33<br /> | |||
</td> | |||
<td>5\33 &lt; g &lt; 6\39 (2\13)<br /> | |||
</td> | |||
<td>-1+7g<br /> | |||
</td> | |||
<td>-2g+1\3<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>7L20s<br /> | |||
</td> | |||
<td>23\27 &lt; g &lt; 6\7<br /> | |||
</td> | |||
<td>23\27 &lt; g &lt; 29\34<br /> | |||
</td> | |||
<td>29\34 &lt; g &lt; 35\41<br /> | |||
</td> | |||
<td>-17+20g<br /> | |||
</td> | |||
<td>-7g+6<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>8L19s<br /> | |||
</td> | |||
<td>10\27 &lt; g &lt; 3\8<br /> | |||
</td> | |||
<td>10\27 &lt; g &lt; 13\35<br /> | |||
</td> | |||
<td>13\35 &lt; g &lt; 16\43<br /> | |||
</td> | |||
<td>19g-7<br /> | |||
</td> | |||
<td>3-8g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>9L18s<br /> | |||
</td> | |||
<td>2\27 &lt; g &lt; 1\9<br /> | |||
</td> | |||
<td>2\27 &lt; g &lt; 3\36 (1\12)<br /> | |||
</td> | |||
<td>3\36 (1\12) &lt; g &lt; 4\45<br /> | |||
</td> | |||
<td>-1\9+2g<br /> | |||
</td> | |||
<td>-g+1\9<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>10L17s<br /> | |||
</td> | |||
<td>8\27 &lt; g &lt; 3\10<br /> | |||
</td> | |||
<td>8\27 &lt; g &lt; 11\37<br /> | |||
</td> | |||
<td>11\37 &lt; g &lt; 14\47<br /> | |||
</td> | |||
<td>-5+17g<br /> | |||
</td> | |||
<td>3-10g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>11L16s<br /> | |||
</td> | |||
<td>5\27 &lt; g &lt; 2\11<br /> | |||
</td> | |||
<td>5\27 &lt; g &lt; 7\38<br /> | |||
</td> | |||
<td>7\38 &lt; g &lt; 9\49<br /> | |||
</td> | |||
<td>-16g+3<br /> | |||
</td> | |||
<td>11g-4<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>12L15s<br /> | |||
</td> | |||
<td>2\27 &lt; g &lt; 1\12<br /> | |||
</td> | |||
<td>2\27 &lt; g &lt; 3\39<span style="line-height: 1.5;"> (1\13)</span><br /> | |||
</td> | |||
<td>3\39 (1\13) &lt; g &lt; 4\51<br /> | |||
</td> | |||
<td>5g-1\3<br /> | |||
</td> | |||
<td>1\3-4g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>13L14s<br /> | |||
</td> | |||
<td>2\27 &lt; g &lt; 1\13<br /> | |||
</td> | |||
<td>2\27 &lt; g &lt; 3\40<br /> | |||
</td> | |||
<td>3\40 &lt; g &lt; 4\53<br /> | |||
</td> | |||
<td>14g-1<br /> | |||
</td> | |||
<td>-<span style="line-height: 1.5;">13g+1</span><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>14L13s<br /> | |||
</td> | |||
<td>25\27 &lt; g &lt; 13\14<br /> | |||
</td> | |||
<td>25\27 &lt; g &lt; 38\41<br /> | |||
</td> | |||
<td>38\41 &lt; g &lt; 51\55<br /> | |||
</td> | |||
<td>13g-12<br /> | |||
</td> | |||
<td>13-14g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>15L12s<br /> | |||
</td> | |||
<td>25\27 &lt; g &lt; 14\15<br /> | |||
</td> | |||
<td>25\27 &lt; g &lt; 39\42 (13\14)<br /> | |||
</td> | |||
<td>39\42 (13\14) &lt; g &lt; 43\57<br /> | |||
</td> | |||
<td>-4+4g<br /> | |||
</td> | |||
<td>-5g+14\3<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>16L11s<br /> | |||
</td> | |||
<td>22\27 &lt; g &lt; 13\16<br /> | |||
</td> | |||
<td>22\27 &lt; g &lt; 35\43<br /> | |||
</td> | |||
<td>35\43 &lt; g &lt; 48\59<br /> | |||
</td> | |||
<td>-11g+9<br /> | |||
</td> | |||
<td>16g-13<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>17L10s<br /> | |||
</td> | |||
<td>19\27 &lt; g &lt; 12\17<br /> | |||
</td> | |||
<td>19\27 &lt; g &lt; 31\44<br /> | |||
</td> | |||
<td>31\44 &lt; g &lt; 43\61<br /> | |||
</td> | |||
<td>10g-7<br /> | |||
</td> | |||
<td>12-17g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>18L9s<br /> | |||
</td> | |||
<td>1\27 &lt; g &lt; 1\18<br /> | |||
</td> | |||
<td>1\27 &lt; g &lt; 2\45<br /> | |||
</td> | |||
<td>2\45 &lt; g &lt; 3\63 (1\21)<br /> | |||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>-2g+1\9<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>19L8s<br /> | |||
</td> | |||
<td>17\27 &lt; g &lt; 12\19<br /> | |||
</td> | |||
<td>17\27 &lt; g &lt; 29\46<br /> | |||
</td> | |||
<td>29\46 &lt; g &lt; 41\65<br /> | |||
</td> | |||
<td>-5+8g<br /> | |||
</td> | |||
<td>12-19g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>20L7s<br /> | |||
</td> | |||
<td>4\27 &lt; g &lt; 3\20<br /> | |||
</td> | |||
<td>4\27 &lt; g &lt; 7\47<br /> | |||
</td> | |||
<td>7\47 &lt; g &lt; 10\67<br /> | |||
</td> | |||
<td>-1+7g<br /> | |||
</td> | |||
<td>3-20g<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>21L6s<br /> | |||
</td> | |||
<td>5\27 &lt; g &lt; 4\21<br /> | |||
</td> | |||
<td>5\27 &lt; g &lt; 9\48 (3\16)<br /> | |||
</td> | |||
<td>9\48 (3\16) &lt; g &lt; 13\69<br /> | |||
</td> | |||
<td>2g-1\3<br /> | |||
</td> | |||
<td>-7g+4<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>22L5s<br /> | |||
</td> | |||
<td><span style="line-height: 1.5;">11</span>\27 &lt; g &lt; 9\22<br /> | |||
</td> | |||
<td>11\27 &lt; g &lt; 20\49<br /> | |||
</td> | |||
<td>20\49 &lt; g &lt; 29\71<br /> | |||
</td> | |||
<td>5g-2<br /> | |||
</td> | |||
<td>-22g+9<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>23L4s<br /> | |||
</td> | |||
<td>7\27 &lt; g &lt; 6\23<br /> | |||
</td> | |||
<td>7\27 &lt; g &lt; 13\50<br /> | |||
</td> | |||
<td>13\50&lt; g &lt; 19\73<br /> | |||
</td> | |||
<td>4g-1<br /> | |||
</td> | |||
<td>-23g+6<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>24L3s<br /> | |||
</td> | |||
<td>1\27 &lt; g &lt; 1\24<br /> | |||
</td> | |||
<td>1\27 &lt; g &lt; 2\51<br /> | |||
</td> | |||
<td>2\51 &lt; g &lt; 3\75 <span style="line-height: 1.5;">(1\25)</span><br /> | |||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>-8g+1\3<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>25L2s<br /> | |||
</td> | |||
<td>14\27 &lt; g &lt; 13\25<br /> | |||
</td> | |||
<td>14\27 &lt; g &lt; 27\52<br /> | |||
</td> | |||
<td>27\52&lt; g &lt; 40\77<br /> | |||
</td> | |||
<td>2g-1<br /> | |||
</td> | |||
<td>-25g+13<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>26L1s<br /> | |||
</td> | |||
<td>1\27 &lt; g &lt; 1\26<br /> | |||
</td> | |||
<td>1\27 &lt; g &lt; 2\53<br /> | |||
</td> | |||
<td>2\53&lt; g &lt; 3\79<br /> | |||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>-26g+1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||