Generator ranges of MOS: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 334544698 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 334772470 - 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- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-14 03:28:19 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>334772470</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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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 < g < v, then we may multiply by P to get C/Q < Pg < 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 < g, and hence C/Q < Pg, with C/N being the lower end of the range of possible generators, where L=s. If the range is C/Q < Pg < 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 > 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]]. | 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 < g < v, then we may multiply by P to get C/Q < Pg < 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 < g, and hence C/Q < Pg, with C/N being the lower end of the range of possible generators, where L=s. If the range is C/Q < Pg < 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 > 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]]. | ||
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=3= | =3= | ||
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step || | || Large-small numbers || Generator range || Range of propriety || Large step || Small step || | ||
|| 1L2s || 2\3 < g < 1 || 2\3 < g < 3\4 || | || 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 || | || 2L1s || 1\3 < g < 1\2 || 1\3 < g < 2\5 || g || -2g+1 || | ||
=4= | =4= | ||
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step || | || Large-small numbers || Generator range || Range of propriety || Large step || Small step || | ||
|| 1L3s | || 1L3s || 3\4 < g < 1 || 3\4 < g < 4\5 || -2+3g || -g+1 || | ||
|| 2L2s | || 2L2s || 1\4 < g < 1\2 || 1\4 < g < 1\3 || g || -g+1\2 || | ||
|| 3L1s | || 3L1s || 1\4 < g < 1\3 || 1\4 < g < 2\7 || g || 1-3g || | ||
=5= | =5= | ||
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step || | || Large-small numbers || Generator range || Range of propriety || Large step || Small step || | ||
|| 1L4s | || 1L4s || 4\5 < g < 1 || 4\5 < g < 5\6 || -3+4g || -g+1 || | ||
|| 2L3s | || 2L3s || 2\5 < g < 1\2 || 2\5 < g < 3\7 || -1+3g || -2g+1 || | ||
|| 3L2s | || 3L2s || 3\5 < g < 2\3 || 3\5 < g < 5\8 || -1+2g || -3g+2 || | ||
|| 4L1s | || 4L1s || 1\5 < g < 1\4 || 1\5 < g < 2\9 || g || -4g+1 || | ||
=6= | =6= | ||
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step || | || Large-small numbers || Generator range || Range of propriety || Large step || Small step || | ||
|| 1L5s | || 1L5s || 5\6 < g < 1 || 5\6 < g < 6\7 || -4+5g || -g+1 || | ||
|| 2L4s | || 2L4s || 1\3 < g < 1\2 || 1\3 < g < 2\5 || -1\2+2g || -g+1\2 || | ||
|| 3L3s | || 3L3s || 1\6 < g < 1\3 || 1\6 < g < 2\9 || g || -g+1\3 || | ||
|| 4L2s | || 4L2s || 1\6 < g < 1\4 || 1\6 < g < 1\5 || g || -2g+1\2 || | ||
|| 5L1s | || 5L1s || 1\6 < g < 1\5 || 1\6 < g < 2\11 || g || -5g+1 || | ||
=7= | =7= | ||
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step || | || Large-small numbers || Generator range || Range of propriety || Large step || Small step || | ||
|| 1L6s | || 1L6s || 6\7 < g < 1 || 6\7 < g < 7\8 || -5+6g || -g+1 || | ||
|| 2L5s | || 2L5s || 3\7 < g < 1\2 || 3\7 < g < 4\9 || -2+5g || -2g+1 || | ||
|| 3L4s | || 3L4s || 2\7 < g < 1\3 || 2\7 < g < 3\10 || -1+4g || 1-3g || | ||
|| 4L3s | || 4L3s || 5\7 < g < 3\4 || 5\7 < g < 8\11 || -2+3g || -4g+3 || | ||
|| 5L2s | || 5L2s || 4\7 < g < 3\5 || 4\7 < g < 7\12 || -1+2g || -5g+3 || | ||
|| 6L1s | || 6L1s || 1\7 < g < 1\6 || 1\7 < g < 2\13 || g || -6g+1 || | ||
=8= | =8= | ||
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step || | || Large-small numbers || Generator range || Range of propriety || Large step || Small step || | ||
|| 1L7s | || 1L7s || 7\8 < g < 1 || 7\8 < g < 8\9 || -6+7g || -g+1 || | ||
|| 2L6s | || 2L6s || 3\8 < g < 1\2 || 3\8 < g < 2\5 || -1+3g || -g+1\2 || | ||
|| 3L5s | || 3L5s || 5\8 < g < 2\3 || 5\8 < g < 7\11 || -3+5g || -3g+2 || | ||
|| 4L4s | || 4L4s || 1\8 < g < 1\4 || 1\8 < g < 1\6 || g || -g+1\4 || | ||
|| 5L3s | || 5L3s || 3\8 < g < 2\5 || 3\8 < g < 5\13 || -1+3g || -5g+2 || | ||
|| 6L2s | || 6L2s || 1\8 < g < 1\6 || 1\8 < g < 1\7 || g || -3g+1\2 || | ||
|| 7L1s | || 7L1s || 1\8 < g < 1\7 || 1\8 < g < 2\15 || g || -7g+1 || | ||
=9= | =9= | ||
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step || | || Large-small numbers || Generator range || Range of propriety || Large step || Small step || | ||
|| 1L8s | || 1L8s || 8\9 < g < 1 || 8\9 < g < 9\10 || -7+8g || -g+1 || | ||
|| 2L7s | || 2L7s || 4\9 < g < 1\2 || 4\9 < g < 5\11 || -3+7g || -2g+1 || | ||
|| 3L6s | || 3L6s || 2\9 < g < 1\3 || 2\9 < g < 1\4 || -1\3+2g || -g+1\3 || | ||
|| 4L5s | || 4L5s || 2\9 < g < 1\4 || 2\9 < g < 3\13 || -1+5g || -4g+1 || | ||
|| 5L4s | || 5L4s || 7\9 < g < 4\5 || 7\9 < g < 11\14 || -3+4g || -5g+4 || | ||
|| 6L3s | || 6L3s || 1\9 < g < 1\6 || 1\9 < g < 2\15 || g || -2g+1\3 || | ||
|| 7L2s | || 7L2s || 5\9 < g < 4\7 || 5\9 < g < 9\16 || -1+2g || -7g+4 || | ||
|| 8L1s | || 8L1s || 1\9 < g < 1\8 || 1\9 < g < 2\17 || g || -8g+1 || | ||
=10= | =10= | ||
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step || | || Large-small numbers || Generator range || Range of propriety || Large step || Small step || | ||
|| 1L9s | || 1L9s || 9\10 < g < 1 || 9\10 < g < 10\11 || -8+9g || -g+1 || | ||
|| 2L8s | || 2L8s || 2\5 < g < 1\2 || 2\5 < g < 3\7 || -3\2+4g || -g+1\2 || | ||
|| 3L7s | || 3L7s || 3\10 < g < 1\3 || 3\10 < g < 4\13 || -2+7g || 1-3g || | ||
|| 4L6s | || 4L6s || 1\5 < g < 1\4 || 1\5 < g < 2\9 || 3g-1\2 || -2g+1\2 || | ||
|| 5L5s | || 5L5s || 1\10 < g < 1\5 || 1\10 < g < 2\15 || g || -g+1\5 || | ||
|| 6L4s | || 6L4s || 3\10 < g < 1\3 || 3\10 < g < 4\13 || -1\2+2g || 1-3g || | ||
|| 7L3s | || 7L3s || 7\10 < g < 5\7 || 7\10 < g < 12\17 || -2+3g || -7g+5 || | ||
|| 8L2s | || 8L2s || 1\10 < g < 1\8 || 1\10 < g < 1\9 || g || -4g+1\2 || | ||
|| 9L1s | || 9L1s || 1\10 < g < 1\9 || 1\10 < g < 2\19 || g || -9g+1 || | ||
=11= | =11= | ||
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step || | || Large-small numbers || Generator range || Range of propriety || Large step || Small step || | ||
|| 1L10s | || 1L10s || 10\11 < g < 1 || 10\11 < g < 11\12 || -9+10g || -g+1 || | ||
|| 2L9s | || 2L9s || 5\11 < g < 1\2 || 5\11 < g < 6\13 || -4+9g || -2g+1 || | ||
|| 3L8s | || 3L8s || 7\11 < g < 2\3 || 7\11 < g < 9\14 || -5+8g || -3g+2 || | ||
|| 4L7s | || 4L7s || 8\11 < g < 3\4 || 8\11 < g < 11\15 || -5+7g || -4g+3 || | ||
|| 5L6s | || 5L6s || 2\11 < g < 1\5 || 2\11 < g < 3\16 || -1+6g || -5g+1 || | ||
|| 6L5s | || 6L5s || 9\11 < g < 5\6 || 9\11 < g < 14\17 || -4+5g || -6g+5 || | ||
|| 7L4s | || 7L4s || 3\11 < g < 2\7 || 3\11 < g < 5\18 || -1+4g || -7g+2 || | ||
|| 8L3s | || 8L3s || 4\11 < g < 3\8 || 4\11 < g < 7\19 || -1+3g || -8g+3 || | ||
|| 9L2s | || 9L2s || 6\11 < g < 5\9 || 6\11 < g < 11\20 || -1+2g || -9g+5 || | ||
|| 10L1s | || 10L1s || 1\11 < g < 1\10 || 1\11 < g < 2\21 || g || -10g+1 || | ||
=12= | =12= | ||
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step || | || Large-small numbers || Generator range || Range of propriety || Large step || Small step || | ||
|| 1L11s | || 1L11s || 11\12 < g < 1 || 11\12 < g < 12\13 || -10+11g || -g+1 || | ||
|| 2L10s | || 2L10s || 5\12 < g < 1\2 || 5\12 < g < 3\7 || -2+5g || -g+1\2 || | ||
|| 3L9s | || 3L9s || 1\4 < g < 1\3 || 1\4 < g < 2\7 || -2\3+3g || -g+1\3 || | ||
|| 4L8s | || 4L8s || 1\6 < g < 1\4 || 1\6 < g < 1\5 || -1\4+2g || -g+1\4 || | ||
|| 5L7s | || 5L7s || 7\12 < g < 3\5 || 7\12 < g < 10\17 || -4+7g || -5g+3 || | ||
|| 6L6s | || 6L6s || 1\12 < g < 1\6 || 1\12 < g < 1\9 || g || -g+1\6 || | ||
|| 7L5s | || 7L5s || 5\12 < g < 3\7 || 5\12 < g < 8\19 || -2+5g || -7g+3 || | ||
|| 8L4s | || 8L4s || 1\12 < g < 1\8 || 1\12 < g < 1\10 || g || -2g+1\4 || | ||
|| 9L3s | || 9L3s || 1\12 < g < 1\9 || 1\12 < g < 2\21 || g || -3g+1\3 || | ||
|| 10L2s | || 10L2s || 1\12 < g < 1\10 || 1\12 < g < 1\11 || g || -5g+1\2 || | ||
|| 11L1s | || 11L1s || 1\12 < g < 1\11 || 1\12 < g < 2\23 || g || -11g+1 || | ||
=13= | =13= | ||
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step || | || Large-small numbers || Generator range || Range of propriety || Large step || Small step || | ||
|| 1L12s | || 1L12s || 12\13 < g < 1 || 12\13 < g < 13\14 || -11+12g || -g+1 || | ||
|| 2L11s | || 2L11s || 6\13 < g < 1\2 || 6\13 < g < 7\15 || -5+11g || -2g+1 || | ||
|| 3L10s | || 3L10s || 4\13 < g < 1\3 || 4\13 < g < 5\16 || -3+10g || 1-3g || | ||
|| 4L9s | || 4L9s || 3\13 < g < 1\4 || 3\13 < g < 4\17 || -2+9g || -4g+1 || | ||
|| 5L8s | || 5L8s || 5\13 < g < 2\5 || 5\13 < g < 7\18 || -3+8g || -5g+2 || | ||
|| 6L7s | || 6L7s || 2\13 < g < 1\6 || 2\13 < g < 3\19 || -1+7g || -6g+1 || | ||
|| 7L6s | || 7L6s || 11\13 < g < 6\7 || 11\13 < g < 17\20 || -5+6g || -7g+6 || | ||
|| 8L5s | || 8L5s || 8\13 < g < 5\8 || 8\13 < g < 13\21 || -3+5g || -8g+5 || | ||
|| 9L4s | || 9L4s || 10\13 < g < 7\9 || 10\13 < g < 17\22 || -3+4g || -9g+7 || | ||
|| 10L3s | || 10L3s || 9\13 < g < 7\10 || 9\13 < g < 16\23 || -2+3g || -10g+7 || | ||
|| 11L2s | || 11L2s || 7\13 < g < 6\11 || 7\13 < g < 13\24 || -1+2g || -11g+6 || | ||
|| 12L1s | || 12L1s || 1\13 < g < 1\12 || 1\13 < g < 2\25 || g || -12g+1 || | ||
=14= | =14= | ||
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step || | || Large-small numbers || Generator range || Range of propriety || Large step || Small step || | ||
|| 1L13s | || 1L13s || 13\14 < g < 1 || 13\14 < g < 14\15 || -12+13g || -g+1 || | ||
|| 2L12s | || 2L12s || 3\7 < g < 1\2 || 3\7 < g < 4\9 || -5\2+6g || -g+1\2 || | ||
|| 3L11s | || 3L11s || 9\14 < g < 2\3 || 9\14 < g < 11\17 || -7+11g || -3g+2 || | ||
|| 4L10s | || 4L10s || 3\14 < g < 1\4 || 3\14 < g < 2\9 || -1+5g || -2g+1\2 || | ||
|| 5L9s | || 5L9s || 11\14 < g < 4\5 || 11\14 < g < 15\19 || -7+9g || -5g+4 || | ||
|| 6L8s | || 6L8s || 1\7 < g < 1\6 || 1\7 < g < 2\13 || 4g-1\2 || -3g+1\2 || | ||
|| 7L7s | || 7L7s || 1\14 < g < 1\7 || 1\14 < g < 2\21 || g || -g+1\7 || | ||
|| 8L6s | || 8L6s || 5\14 < g < 3\8 || 5\14 < g < 4\11 || -1+3g || -4g+3\2 || | ||
|| 9L5s | || 9L5s || 3\14 < g < 2\9 || 3\14 < g < 5\23 || -1+5g || -9g+2 || | ||
|| 10L4s | || 10L4s || 2\7 < g < 3\10 || 2\7 < g < 5\17 || -1\2+2g || -5g+3\2 || | ||
|| 11L3s | || 11L3s || 5\14 < g < 4\11 || 5\14 < g < 9\25 || -1+3g || -11g+4 || | ||
|| 12L2s | || 12L2s || 1\14 < g < 1\12 || 1\14 < g < 1\13 || g || -6g+1\2 || | ||
|| 13L1s | || 13L1s || 1\14 < g < 1\13 || 1\14 < g < 2\27 || g || -13g+1 || | ||
=15= | =15= | ||
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step || | || Large-small numbers || Generator range || Range of propriety || Large step || Small step || | ||
|| 1L14s | || 1L14s || 14\15 < g < 1 || 14\15 < g < 15\16 || -13+14g || -g+1 || | ||
|| 2L13s | || 2L13s || 7\15 < g < 1\2 || 7\15 < g < 8\17 || -6+13g || -2g+1 || | ||
|| 3L12s | || 3L12s || 4\15 < g < 1\3 || 4\15 < g < 5\18 || -1+4g || -g+1\3 || | ||
|| 4L11s | || 4L11s || 11\15 < g < 3\4 || 11\15 < g < 14\19 || -8+11g || -4g+3 || | ||
|| 5L10s | || 5L10s || 2\15 < g < 1\5 || 2\15 < g < 3\20 || -1\5+2g || -g+1\5 || | ||
|| 6L9s | || 6L9s || 2\15 < g < 1\6 || 2\15 < g < 1\7 || -1\3+3g || -2g+1\3 || | ||
|| 7L8s | || 7L8s || 2\15 < g < 1\7 || 2\15 < g < 3\22 || -1+8g || -7g+1 || | ||
|| 8L7s | || 8L7s || 13\15 < g < 7\8 || 13\15 < g < 20\23 || -6+7g || -8g+7 || | ||
|| 9L6s | || 9L6s || 1\5 < g < 2\9 || 1\5 < g < 3\14 || -1\3+2g || -3g+2\3 || | ||
|| 10L5s | || 10L5s || 1\15 < g < 1\10 || 1\15 < g < 2\25 || g || -2g+1\5 || | ||
|| 11L4s | || 11L4s || 4\15 < g < 3\11 || 4\15 < g < 7\26 || -1+4g || -11g+3 || | ||
|| 12L3s | || 12L3s || 1\15 < g < 1\12 || 1\15 < g < 2\27 || g || -4g+1\3 || | ||
|| 13L2s | || 13L2s || 8\15 < g < 7\13 || 8\15 < g < 15\28 || -1+2g || -13g+7 || | ||
|| 14L1s | || 14L1s || 1\15 < g < 1\14 || 1\15 < g < 2\29 || g || -14g+1 || | ||
=16= | =16= | ||
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step || | || Large-small numbers || Generator range || Range of propriety || Large step || Small step || | ||
|| 1L15s | || 1L15s || 15\16 < g < 1 || 15\16 < g < 16\17 || -14+15g || -g+1 || | ||
|| 2L14s | || 2L14s || 7\16 < g < 1\2 || 7\16 < g < 4\9 || -3+7g || -g+1\2 || | ||
|| 3L13s | || 3L13s || 5\16 < g < 1\3 || 5\16 < g < 6\19 || -4+13g || 1-3g || | ||
|| 4L12s | || 4L12s || 3\16 < g < 1\4 || 3\16 < g < 1\5 || 3g-1\2 || -g+1\4 || | ||
|| 5L11s | || 5L11s || 3\16 < g < 1\5 || 3\16 < g < 4\21 || -2+11g || -5g+1 || | ||
|| 6L10s | || 6L10s || 5\16 < g < 1\3 || 5\16 < g < 6\19 || -3\2+5g || 1-3g || | ||
|| 7L9s | || 7L9s || 9\16 < g < 4\7 || 9\16 < g < 13\23 || -5+9g || -7g+4 || | ||
|| 8L8s | || 8L8s || 1\16 < g < 1\8 || 1\16 < g < 1\12 || g || -g+1\8 || | ||
|| 9L7s | || 9L7s || 7\16 < g < 4\9 || 7\16 < g < 11\25 || -3+7g || -9g+4 || | ||
|| 10L6s | || 10L6s || 3\16 < g < 1\5 || 3\16 < g < 4\21 || 3g-1\2 || -5g+1 || | ||
|| 11L5s | || 11L5s || 13\16 < g < 9\11 || 13\16 < g < 22\27 || -4+5g || -11g+9 || | ||
|| 12L4s | || 12L4s || 1\16 < g < 1\12 || 1\16 < g < 1\14 || g || -3g+1\4 || | ||
|| 13L3s | || 13L3s || 11\16 < g < 9\13 || 11\16 < g < 20\29 || -2+3g || -13g+9 || | ||
|| 14L2s | || 14L2s || 1\16 < g < 1\14 || 1\16 < g < 1\15 || g || -7g+1\2 || | ||
|| 15L1s | || 15L1s || 1\16 < g < 1\15 || 1\16 < g < 2\31 || g || -15g+1 || | ||
=17= | =17= | ||
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step || | || Large-small numbers || Generator range || Range of propriety || Large step || Small step || | ||
|| 1L16s | || 1L16s || 16\17 < g < 1 || 16\17 < g < 17\18 || -15+16g || -g+1 || | ||
|| 2L15s | || 2L15s || 8\17 < g < 1\2 || 8\17 < g < 9\19 || -7+15g || -2g+1 || | ||
|| 3L14s | || 3L14s || 11\17 < g < 2\3 || 11\17 < g < 13\20 || -9+14g || -3g+2 || | ||
|| 4L13s | || 4L13s || 4\17 < g < 1\4 || 4\17 < g < 5\21 || -3+13g || -4g+1 || | ||
|| 5L12s | || 5L12s || 10\17 < g < 3\5 || 10\17 < g < 13\22 || -7+12g || -5g+3 || | ||
|| 6L11s | || 6L11s || 14\17 < g < 5\6 || 14\17 < g < 19\23 || -9+11g || -6g+5 || | ||
|| 7L10s | || 7L10s || 12\17 < g < 5\7 || 12\17 < g < 17\24 || -7+10g || -7g+5 || | ||
|| 8L9s | || 8L9s || 2\17 < g < 1\8 || 2\17 < g < 3\25 || -1+9g || -8g+1 || | ||
|| 9L8s | || 9L8s || 15\17 < g < 8\9 || 15\17 < g < 23\26 || -7+8g || -9g+8 || | ||
|| 10L7s | || 10L7s || 5\17 < g < 3\10 || 5\17 < g < 8\27 || -2+7g || -10g+3 || | ||
|| 11L6s | || 11L6s || 3\17 < g < 2\11 || 3\17 < g < 5\28 || -1+6g || -11g+2 || | ||
|| 12L5s | || 12L5s || 7\17 < g < 5\12 || 7\17 < g < 12\29 || -2+5g || -12g+5 || | ||
|| 13L4s | || 13L4s || 13\17 < g < 10\13 || 13\17 < g <23\30 || -3+4g || -13g+10 || | ||
|| 14L3s | || 14L3s || 6\17 < g < 5\14 || 6\17 < g < 11\31 || -1+3g || -14g+5 || | ||
|| 15L2s | || 15L2s || 9\17 < g < 8\15 || 9\17 < g < 17\32 || -1+2g || -15g+8 || | ||
|| 16L1s | || 16L1s || 1\17 < g < 1\16 || 1\17 < g < 2\33 || g || -16g+1 || | ||
=18= | =18= | ||
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step || | || Large-small numbers || Generator range || Range of propriety || Large step || Small step || | ||
|| 1L17s | || 1L17s || 17\18 < g < 1 || 17\18 < g < 18\19 || -16+17g || -g+1 || | ||
|| 2L16s | || 2L16s || 4\9 < g < 1\2 || 4\9 < g < 5\11 || -7\2+8g || -g+1\2 || | ||
|| 3L15s | || 3L15s || 5\18 < g < 1\3 || 5\18 < g < 2\7 || -4\3+5g || -g+1\3 || | ||
|| 4L14s | || 4L14s || 2\9 < g < 1\4 || 2\9 < g < 3\13 || -3\2+7g || -2g+1\2 || | ||
|| 5L13s | || 5L13s || 7\18 < g < 2\5 || 7\18 < g < 9\23 || -5+13g || -5g+2 || | ||
|| 6L12s | || 6L12s || 1\9 < g < 1\6 || 1\9 < g < 2\15 || -1\6+2g || -g+1\6 || | ||
|| 7L11s | || 7L11s || 5\18 < g < 2\7 || 5\18 < g < 7\25 || -3+11g || -7g+2 || | ||
|| 8L10s | || 8L10s || 1\9 < g < 1\8 || 1\9 < g < 2\17 || -1\2+5g || -4g+1\2 || | ||
|| 9L9s | || 9L9s || 1\18 < g < 1\9 || 1\18 < g < 2\27 || g || -g+1\9 || | ||
|| 10L8s | || 10L8s || 7\18 < g < 2\5 || 7\18 < g < 9\23 || -3\2+4g || -5g+2 || | ||
|| 11L7s | || 11L7s || 13\18 < g < 8\11 || 13\18 < g < 21\29 || -5+7g || -11g+8 || | ||
|| 12L6s | || 12L6s || 1\18 < g < 1\12 || 1\18 < g < 1\15 || g || -2g+1\6 || | ||
|| 13L5s | || 13L5s || 11\18 < g < 8\13 || 11\18 < g < 19\31 || -3+5g || -13g+8 || | ||
|| 14L4s | || 14L4s || 5\18 < g < 2\7 || 5\18 < g < 7\25 || -1\2+2g || -7g+2 || | ||
|| 15L3s | || 15L3s || 1\18 < g < 1\15 || 1\18 < g < 2\33 || g || -5g+1\3 || | ||
|| 16L2s | || 16L2s || 1\18 < g < 1\16 || 1\18 < g < 1\17 || g || -8g+1\2 || | ||
|| 17L1s | || 17L1s || 1\18 < g < 1\17 || 1\18 < g < 2\35 || g || -17g+1 || | ||
=19= | =19= | ||
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step || | || Large-small numbers || Generator range || Range of propriety || Large step || Small step || | ||
|| 1L18s | || 1L18s || 18\19 < g < 1 || 18\19 < g < 19\20 || -17+18g || -g+1 || | ||
|| 2L17s | || 2L17s || 9\19 < g < 1\2 || 9\19 < g < 10\21 || -8+17g || -2g+1 || | ||
|| 3L16s | || 3L16s || 6\19 < g < 1\3 || 6\19 < g < 7\22 || -5+16g || 1-3g || | ||
|| 4L15s | || 4L15s || 14\19 < g < 3\4 || 14\19 < g < 17\23 || -11+15g || -4g+3 || | ||
|| 5L14s | || 5L14s || 15\19 < g < 4\5 || 15\19 < g < 19\24 || -11+14g || -5g+4 || | ||
|| 6L13s | || 6L13s || 3\19 < g < 1\6 || 3\19 < g < 4\25 || -2+13g || -6g+1 || | ||
|| 7L12s | || 7L12s || 8\19 < g < 3\7 || 8\19 < g < 11\26 || -5+12g || -7g+3 || | ||
|| 8L11s | || 8L11s || 7\19 < g < 3\8 || 7\19 < g < 10\27 || -4+11g || -8g+3 || | ||
|| 9L10s | || 9L10s || 2\19 < g < 1\9 || 2\19 < g < 3\28 || -1+10g || -9g+1 || | ||
|| 10L9s | || 10L9s || 17\19 < g < 9\10 || 17\19 < g < 26\29 || -8+9g || -10g+9 || | ||
|| 11L8s | || 11L8s || 12\19 < g < 7\11 || 12\19 < g < 19\30 || -5+8g || -11g+7 || | ||
|| 12L7s | || 12L7s || 11\19 < g < 7\12 || 11\19 < g < 18\31 || -4+7g || -12g+7 || | ||
|| 13L6s | || 13L6s || 16\19 < g < 11\13 || 16\19 < g < 27\32 || -5+6g || -13g+11 || | ||
|| 14L5s | || 14L5s || 4\19 < g < 3\14 || 4\19 < g < 7\33 || -1+5g || -14g+3 || | ||
|| 15L4s | || 15L4s || 5\19 < g < 4\15 || 5\19 < g < 9\34 || -1+4g || -15g+4 || | ||
|| 16L3s | || 16L3s || 13\19 < g < 11\16 || 13\19 < g < 24\35 || -2+3g || -16g+11 || | ||
|| 17L2s | || 17L2s || 10\19 < g < 9\17 || 10\19 < g < 19\36 || -1+2g || -17g+9 || | ||
|| 18L1s | || 18L1s || 1\19 < g < 1\18 || 1\19 < g < 2\37 || g || -18g+1 || | ||
=20= | =20= | ||
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step || | || Large-small numbers || Generator range || Range of propriety || Large step || Small step || | ||
|| 1L19s | || 1L19s || 19\20 < g < 1 || 19\20 < g < 20\21 || -18+19g || -g+1 || | ||
|| 2L18s | || 2L18s || 9\20 < g < 1\2 || 9\20 < g < 5\11 || -4+9g || -g+1\2 || | ||
|| 3L17s | || 3L17s || 13\20 < g < 2\3 || 13\20 < g < 15\23 || -11+17g || -3g+2 || | ||
|| 4L16s | || 4L16s || 1\5 < g < 1\4 || 1\5 < g < 2\9 || -3\4+4g || -g+1\4 || | ||
|| 5L15s | || 5L15s || 3\20 < g < 1\5 || 3\20 < g < 4\25 || -2\5+3g || -g+1\5 || | ||
|| 6L14s | || 6L14s || 3\20 < g < 1\6 || 3\20 < g < 2\13 || -1+7g || -3g+1\2 || | ||
|| 7L13s | || 7L13s || 17\20 < g < 6\7 || 17\20 < g < 23\27 || -11+13g || -7g+6 || | ||
|| 8L12s | || 8L12s || 1\10 < g < 1\8 || 1\10 < g < 1\9 || -1\4+3g || -2g+1\4 || | ||
|| 9L11s | || 9L11s || 11\20 < g < 5\9 || 11\20 < g < 16\29 || -6+11g || -9g+5 || | ||
|| 10L10s | || 10L10s || 1\20 < g < 1\10 || 1\20 < g < 1\15 || g || -g+1\10 || | ||
|| 11L9s | || 11L9s || 9\20 < g < 5\11 || 9\20 < g < 14\31 || -4+9g || -11g+5 || | ||
|| 12L8s | || 12L8s || 3\20 < g < 1\6 || 3\20 < g < 2\13 || -1\4+2g || -3g+1\2 || | ||
|| 13L7s | || 13L7s || 3\20 < g < 2\13 || 3\20 < g < 5\33 || -1+7g || -13g+2 || | ||
|| 14L6s | || 14L6s || 7\20 < g < 5\14 || 7\20 < g < 6\17 || -1+3g || -7g+5\2 || | ||
|| 15L5s | || 15L5s || 1\20 < g < 1\15 || 1\20 < g < 2\35 || g || -3g+1\5 || | ||
|| 16L4s | || 16L4s || 1\20 < g < 1\16 || 1\20 < g < 1\18 || g || -4g+1\4 || | ||
|| 17L3s | || 17L3s || 7\20 < g < 6\17 || 7\20 < g < 13\37 || -1+3g || -17g+6 || | ||
|| 18L2s | || 18L2s || 1\20 < g < 1\18 || 1\20 < g < 1\19 || g || -9g+1\2 || | ||
|| 19L1s | || 19L1s || 1\20 < g < 1\19 || 1\20 < g < 2\39 || g || -19g+1 || | ||
=21= | =21= | ||
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step || | || Large-small numbers || Generator range || Range of propriety || Large step || Small step || | ||
|| 1L20s | || 1L20s || 20\21 < g < 1 || 20\21 < g < 21\22 || -19+20g || -g+1 || | ||
|| 2L19s | || 2L19s || 10\21 < g < 1\2 || 10\21 < g < 11\23 || -9+19g || -2g+1 || | ||
|| 3L18s | || 3L18s || 2\7 < g < 1\3 || 2\7 < g < 3\10 || -5\3+6g || -g+1\3 || | ||
|| 4L17s | || 4L17s || 5\21 < g < 1\4 || 5\21 < g < 6\25 || -4+17g || -4g+1 || | ||
|| 5L16s | || 5L16s || 4\21 < g < 1\5 || 4\21 < g < 5\26 || -3+16g || -5g+1 || | ||
|| 6L15s | || 6L15s || 1\7 < g < 1\6 || 1\7 < g < 2\13 || -2\3+5g || -2g+1\3 || | ||
|| 7L14s | || 7L14s || 2\21 < g < 1\7 || 2\21 < g < 3\28 || -1\7+2g || -g+1\7 || | ||
|| 8L13s | || 8L13s || 13\21 < g < 5\8 || 13\21 < g < 18\29 || -8+13g || -8g+5 || | ||
|| 9L12s | || 9L12s || 2\21 < g < 1\9 || 2\21 < g < 1\10 || -1\3+4g || -3g+1\3 || | ||
|| 10L11s | || 10L11s || 2\21 < g < 1\10 || 2\21 < g < 3\31 || -1+11g || -10g+1 || | ||
|| 11L10s | || 11L10s || 19\21 < g < 10\11 || 19\21 < g < 29\32 || -9+10g || -11g+10 || | ||
|| 12L9s | || 12L9s || 5\21 < g < 1\4 || 5\21 < g < 6\25 || -2\3+3g || -4g+1 || | ||
|| 13L8s | || 13L8s || 8\21 < g < 5\13 || 8\21 < g < 13\34 || -3+8g || -13g+5 || | ||
|| 14L7s | || 14L7s || 1\21 < g < 1\14 || 1\21 < g < 2\35 || g || -2g+1\7 || | ||
|| 15L6s | || 15L6s || 4\21 < g < 1\5 || 4\21 < g < 5\26 || -1\3+2g || -5g+1 || | ||
|| 16L5s | || 16L5s || 17\21 < g < 13\16 || 17\21 < g < 30\37 || -4+5g || -16g+13 || | ||
|| 17L4s | || 17L4s || 16\21 < g < 13\17 || 16\21 < g < 29\38 || -3+4g || -17g+13 || | ||
|| 18L3s | || 18L3s || 1\21 < g < 1\18 || 1\21 < g < 2\39 || g || -6g+1\3 || | ||
|| 19L2s | || 19L2s || 11\21 < g < 10\19 || 11\21 < g < 21\40 || -1+2g || -19g+10 || | ||
|| 20L1s | || 20L1s || 1\21 < g < 1\20 || 1\21 < g < 2\41 || g || -20g+1 || | ||
=22= | =22= | ||
|| Large-small numbers || Generator range || Range of propriety || Large step || Small step || | || Large-small numbers || Generator range || Range of propriety || Large step || Small step || | ||
|| 1L21s | || 1L21s || 21\22 < g < 1 || 21\22 < g < 22\23 || -20+21g || -g+1 || | ||
|| 2L20s | || 2L20s || 5\11 < g < 1\2 || 5\11 < g < 6\13 || -9\2+10g || -g+1\2 || | ||
|| 3L19s | || 3L19s || 7\22 < g < 1\3 || 7\22 < g < 8\25 || -6+19g || 1-3g || | ||
|| 4L18s | || 4L18s || 5\22 < g < 1\4 || 5\22 < g < 3\13 || -2+9g || -2g+1\2 || | ||
|| 5L17s | || 5L17s || 13\22 < g < 3\5 || 13\22 < g < 16\27 || -10+17g || -5g+3 || | ||
|| 6L16s | || 6L16s || 7\22 < g < 1\3 || 7\22 < g < 8\25 || -5\2+8g || 1-3g || | ||
|| 7L15s | || 7L15s || 3\22 < g < 1\7 || 3\22 < g < 4\29 || -2+15g || -7g+1 || | ||
|| 8L14s | || 8L14s || 4\11 < g < 3\8 || 4\11 < g < 7\19 || -5\2+7g || -4g+3\2 || | ||
|| 9L13s | || 9L13s || 17\22 < g < 7\9 || 17\22 < g < 24\31 || -10+13g || -9g+7 || | ||
|| 10L12s | || 10L12s || 1\11 < g < 1\10 || 1\11 < g < 2\21 || -1\2+6g || -5g+1\2 || | ||
|| 11L11s | || 11L11s || 1\22 < g < 1\11 || 1\22 < g < 2\33 || g || -g+1\11 || | ||
|| 12L10s | || 12L10s || 9\22 < g < 5\12 || 9\22 < g < 7\17 || -2+5g || -6g+5\2 || | ||
|| 13L9s | || 13L9s || 5\22 < g < 3\13 || 5\22 < g < 8\35 || -2+9g || -13g+3 || | ||
|| 14L8s | || 14L8s || 3\22 < g < 1\7 || 3\22 < g < 4\29 || 4g-1\2 || -7g+1 || | ||
|| 15L7s | || 15L7s || 19\22 < g < 13\15 || 19\22 < g < 32\37 || -6+7g || -15g+13 || | ||
|| 16L6s | || 16L6s || 2\11 < g < 3\16 || 2\11 < g < 5\27 || 3g-1\2 || -8g+3\2 || | ||
|| 17L5s | || 17L5s || 9\22 < g < 7\17 || 9\22 < g < 16\39 || -2+5g || -17g+7 || | ||
|| 18L4s | || 18L4s || 3\11 < g < 5\18 || 3\11 < g < 8\29 || -1\2+2g || -9g+5\2 || | ||
|| 19L3s | || 19L3s || 15\22 < g < 13\19 || 15\22 < g <28\41 || -2+3g || -19g+13 || | ||
|| 20L2s | || 20L2s || 1\22 < g < 1\20 || 1\22 < g < 1\21 || g || -10g+1\2 || | ||
|| 21L1s | || 21L1s || 1\22 < g < 1\21 || 1\22 < g < 2\43 || g || -21g+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 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 /> | <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 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 /> | <br /> | ||
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 <a class="wiki_link" href="/Interval%20class">generic interval</a> 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 <a class="wiki_link" href="/Modal%20UDP%20Notation">chroma-positive</a>.<br /> | 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 <a class="wiki_link" href="/Interval%20class">generic interval</a> 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 <a class="wiki_link" href="/Modal%20UDP%20Notation">chroma-positive</a>.<br /> | ||
<br /> | |||
<br /> | <br /> | ||
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| Line 362: | Line 366: | ||
<td>2\3 &lt; g &lt; 3\4<br /> | <td>2\3 &lt; g &lt; 3\4<br /> | ||
</td> | </td> | ||
<td> | <td>-1+2g<br /> | ||
</td> | </td> | ||
<td>-g+1<br /> | <td>-g+1<br /> | ||
| Line 405: | Line 409: | ||
<td>3\4 &lt; g &lt; 4\5<br /> | <td>3\4 &lt; g &lt; 4\5<br /> | ||
</td> | </td> | ||
<td> | <td>-2+3g<br /> | ||
</td> | </td> | ||
<td>-g+1<br /> | <td>-g+1<br /> | ||
| Line 419: | Line 423: | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>-g+1 | <td>-g+1\2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 431: | Line 435: | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>-3g | <td>1-3g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 460: | Line 464: | ||
<td>4\5 &lt; g &lt; 5\6<br /> | <td>4\5 &lt; g &lt; 5\6<br /> | ||
</td> | </td> | ||
<td> | <td>-3+4g<br /> | ||
</td> | </td> | ||
<td>-g+1<br /> | <td>-g+1<br /> | ||
| Line 472: | Line 476: | ||
<td>2\5 &lt; g &lt; 3\7<br /> | <td>2\5 &lt; g &lt; 3\7<br /> | ||
</td> | </td> | ||
<td> | <td>-1+3g<br /> | ||
</td> | </td> | ||
<td>-2g+1<br /> | <td>-2g+1<br /> | ||
| Line 484: | Line 488: | ||
<td>3\5 &lt; g &lt; 5\8<br /> | <td>3\5 &lt; g &lt; 5\8<br /> | ||
</td> | </td> | ||
<td> | <td>-1+2g<br /> | ||
</td> | </td> | ||
<td>-3g+2<br /> | <td>-3g+2<br /> | ||
| Line 527: | Line 531: | ||
<td>5\6 &lt; g &lt; 6\7<br /> | <td>5\6 &lt; g &lt; 6\7<br /> | ||
</td> | </td> | ||
<td> | <td>-4+5g<br /> | ||
</td> | </td> | ||
<td>-g+1<br /> | <td>-g+1<br /> | ||
| Line 539: | Line 543: | ||
<td>1\3 &lt; g &lt; 2\5<br /> | <td>1\3 &lt; g &lt; 2\5<br /> | ||
</td> | </td> | ||
<td> | <td>-1\2+2g<br /> | ||
</td> | </td> | ||
<td>-g+1 | <td>-g+1\2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 553: | Line 557: | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>-g+1 | <td>-g+1\3<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 565: | Line 569: | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>-2g+1 | <td>-2g+1\2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 606: | Line 610: | ||
<td>6\7 &lt; g &lt; 7\8<br /> | <td>6\7 &lt; g &lt; 7\8<br /> | ||
</td> | </td> | ||
<td> | <td>-5+6g<br /> | ||
</td> | </td> | ||
<td>-g+1<br /> | <td>-g+1<br /> | ||
| Line 618: | Line 622: | ||
<td>3\7 &lt; g &lt; 4\9<br /> | <td>3\7 &lt; g &lt; 4\9<br /> | ||
</td> | </td> | ||
<td> | <td>-2+5g<br /> | ||
</td> | </td> | ||
<td>-2g+1<br /> | <td>-2g+1<br /> | ||
| Line 630: | Line 634: | ||
<td>2\7 &lt; g &lt; 3\10<br /> | <td>2\7 &lt; g &lt; 3\10<br /> | ||
</td> | </td> | ||
<td> | <td>-1+4g<br /> | ||
</td> | </td> | ||
<td>-3g | <td>1-3g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 642: | Line 646: | ||
<td>5\7 &lt; g &lt; 8\11<br /> | <td>5\7 &lt; g &lt; 8\11<br /> | ||
</td> | </td> | ||
<td> | <td>-2+3g<br /> | ||
</td> | </td> | ||
<td>-4g+3<br /> | <td>-4g+3<br /> | ||
| Line 654: | Line 658: | ||
<td>4\7 &lt; g &lt; 7\12<br /> | <td>4\7 &lt; g &lt; 7\12<br /> | ||
</td> | </td> | ||
<td> | <td>-1+2g<br /> | ||
</td> | </td> | ||
<td>-5g+3<br /> | <td>-5g+3<br /> | ||
| Line 697: | Line 701: | ||
<td>7\8 &lt; g &lt; 8\9<br /> | <td>7\8 &lt; g &lt; 8\9<br /> | ||
</td> | </td> | ||
<td> | <td>-6+7g<br /> | ||
</td> | </td> | ||
<td>-g+1<br /> | <td>-g+1<br /> | ||
| Line 709: | Line 713: | ||
<td>3\8 &lt; g &lt; 2\5<br /> | <td>3\8 &lt; g &lt; 2\5<br /> | ||
</td> | </td> | ||
<td> | <td>-1+3g<br /> | ||
</td> | </td> | ||
<td>-g+1 | <td>-g+1\2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 721: | Line 725: | ||
<td>5\8 &lt; g &lt; 7\11<br /> | <td>5\8 &lt; g &lt; 7\11<br /> | ||
</td> | </td> | ||
<td> | <td>-3+5g<br /> | ||
</td> | </td> | ||
<td>-3g+2<br /> | <td>-3g+2<br /> | ||
| Line 735: | Line 739: | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>-g+1 | <td>-g+1\4<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 745: | Line 749: | ||
<td>3\8 &lt; g &lt; 5\13<br /> | <td>3\8 &lt; g &lt; 5\13<br /> | ||
</td> | </td> | ||
<td> | <td>-1+3g<br /> | ||
</td> | </td> | ||
<td>-5g+2<br /> | <td>-5g+2<br /> | ||
| Line 759: | Line 763: | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>-3g+1 | <td>-3g+1\2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 800: | Line 804: | ||
<td>8\9 &lt; g &lt; 9\10<br /> | <td>8\9 &lt; g &lt; 9\10<br /> | ||
</td> | </td> | ||
<td> | <td>-7+8g<br /> | ||
</td> | </td> | ||
<td>-g+1<br /> | <td>-g+1<br /> | ||
| Line 812: | Line 816: | ||
<td>4\9 &lt; g &lt; 5\11<br /> | <td>4\9 &lt; g &lt; 5\11<br /> | ||
</td> | </td> | ||
<td> | <td>-3+7g<br /> | ||
</td> | </td> | ||
<td>-2g+1<br /> | <td>-2g+1<br /> | ||
| Line 824: | Line 828: | ||
<td>2\9 &lt; g &lt; 1\4<br /> | <td>2\9 &lt; g &lt; 1\4<br /> | ||
</td> | </td> | ||
<td> | <td>-1\3+2g<br /> | ||
</td> | </td> | ||
<td>-g+1 | <td>-g+1\3<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 836: | Line 840: | ||
<td>2\9 &lt; g &lt; 3\13<br /> | <td>2\9 &lt; g &lt; 3\13<br /> | ||
</td> | </td> | ||
<td> | <td>-1+5g<br /> | ||
</td> | </td> | ||
<td>-4g+1<br /> | <td>-4g+1<br /> | ||
| Line 848: | Line 852: | ||
<td>7\9 &lt; g &lt; 11\14<br /> | <td>7\9 &lt; g &lt; 11\14<br /> | ||
</td> | </td> | ||
<td> | <td>-3+4g<br /> | ||
</td> | </td> | ||
<td>-5g+4<br /> | <td>-5g+4<br /> | ||
| Line 862: | Line 866: | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>-2g+1 | <td>-2g+1\3<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 872: | Line 876: | ||
<td>5\9 &lt; g &lt; 9\16<br /> | <td>5\9 &lt; g &lt; 9\16<br /> | ||
</td> | </td> | ||
<td> | <td>-1+2g<br /> | ||
</td> | </td> | ||
<td>-7g+4<br /> | <td>-7g+4<br /> | ||
| Line 915: | Line 919: | ||
<td>9\10 &lt; g &lt; 10\11<br /> | <td>9\10 &lt; g &lt; 10\11<br /> | ||
</td> | </td> | ||
<td> | <td>-8+9g<br /> | ||
</td> | </td> | ||
<td>-g+1<br /> | <td>-g+1<br /> | ||
| Line 927: | Line 931: | ||
<td>2\5 &lt; g &lt; 3\7<br /> | <td>2\5 &lt; g &lt; 3\7<br /> | ||
</td> | </td> | ||
<td> | <td>-3\2+4g<br /> | ||
</td> | </td> | ||
<td>-g+1 | <td>-g+1\2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 939: | Line 943: | ||
<td>3\10 &lt; g &lt; 4\13<br /> | <td>3\10 &lt; g &lt; 4\13<br /> | ||
</td> | </td> | ||
<td> | <td>-2+7g<br /> | ||
</td> | </td> | ||
<td>-3g | <td>1-3g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 951: | Line 955: | ||
<td>1\5 &lt; g &lt; 2\9<br /> | <td>1\5 &lt; g &lt; 2\9<br /> | ||
</td> | </td> | ||
<td>3g-1 | <td>3g-1\2<br /> | ||
</td> | </td> | ||
<td>-2g+1 | <td>-2g+1\2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 965: | Line 969: | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>-g+1 | <td>-g+1\5<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 975: | Line 979: | ||
<td>3\10 &lt; g &lt; 4\13<br /> | <td>3\10 &lt; g &lt; 4\13<br /> | ||
</td> | </td> | ||
<td> | <td>-1\2+2g<br /> | ||
</td> | </td> | ||
<td>- | <td>1-3g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 987: | Line 991: | ||
<td>7\10 &lt; g &lt; 12\17<br /> | <td>7\10 &lt; g &lt; 12\17<br /> | ||
</td> | </td> | ||
<td> | <td>-2+3g<br /> | ||
</td> | </td> | ||
<td>-7g+5<br /> | <td>-7g+5<br /> | ||
| Line 1,001: | Line 1,005: | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>-4g+1 | <td>-4g+1\2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,042: | Line 1,046: | ||
<td>10\11 &lt; g &lt; 11\12<br /> | <td>10\11 &lt; g &lt; 11\12<br /> | ||
</td> | </td> | ||
<td> | <td>-9+10g<br /> | ||
</td> | </td> | ||
<td>-g+1<br /> | <td>-g+1<br /> | ||
| Line 1,054: | Line 1,058: | ||
<td>5\11 &lt; g &lt; 6\13<br /> | <td>5\11 &lt; g &lt; 6\13<br /> | ||
</td> | </td> | ||
<td> | <td>-4+9g<br /> | ||
</td> | </td> | ||
<td>-2g+1<br /> | <td>-2g+1<br /> | ||
| Line 1,066: | Line 1,070: | ||
<td>7\11 &lt; g &lt; 9\14<br /> | <td>7\11 &lt; g &lt; 9\14<br /> | ||
</td> | </td> | ||
<td> | <td>-5+8g<br /> | ||
</td> | </td> | ||
<td>-3g+2<br /> | <td>-3g+2<br /> | ||
| Line 1,078: | Line 1,082: | ||
<td>8\11 &lt; g &lt; 11\15<br /> | <td>8\11 &lt; g &lt; 11\15<br /> | ||
</td> | </td> | ||
<td> | <td>-5+7g<br /> | ||
</td> | </td> | ||
<td>-4g+3<br /> | <td>-4g+3<br /> | ||
| Line 1,090: | Line 1,094: | ||
<td>2\11 &lt; g &lt; 3\16<br /> | <td>2\11 &lt; g &lt; 3\16<br /> | ||
</td> | </td> | ||
<td> | <td>-1+6g<br /> | ||
</td> | </td> | ||
<td>-5g+1<br /> | <td>-5g+1<br /> | ||
| Line 1,102: | Line 1,106: | ||
<td>9\11 &lt; g &lt; 14\17<br /> | <td>9\11 &lt; g &lt; 14\17<br /> | ||
</td> | </td> | ||
<td> | <td>-4+5g<br /> | ||
</td> | </td> | ||
<td>-6g+5<br /> | <td>-6g+5<br /> | ||
| Line 1,114: | Line 1,118: | ||
<td>3\11 &lt; g &lt; 5\18<br /> | <td>3\11 &lt; g &lt; 5\18<br /> | ||
</td> | </td> | ||
<td> | <td>-1+4g<br /> | ||
</td> | </td> | ||
<td>-7g+2<br /> | <td>-7g+2<br /> | ||
| Line 1,126: | Line 1,130: | ||
<td>4\11 &lt; g &lt; 7\19<br /> | <td>4\11 &lt; g &lt; 7\19<br /> | ||
</td> | </td> | ||
<td> | <td>-1+3g<br /> | ||
</td> | </td> | ||
<td>-8g+3<br /> | <td>-8g+3<br /> | ||
| Line 1,138: | Line 1,142: | ||
<td>6\11 &lt; g &lt; 11\20<br /> | <td>6\11 &lt; g &lt; 11\20<br /> | ||
</td> | </td> | ||
<td> | <td>-1+2g<br /> | ||
</td> | </td> | ||
<td>-9g+5<br /> | <td>-9g+5<br /> | ||
| Line 1,181: | Line 1,185: | ||
<td>11\12 &lt; g &lt; 12\13<br /> | <td>11\12 &lt; g &lt; 12\13<br /> | ||
</td> | </td> | ||
<td> | <td>-10+11g<br /> | ||
</td> | </td> | ||
<td>-g+1<br /> | <td>-g+1<br /> | ||
| Line 1,193: | Line 1,197: | ||
<td>5\12 &lt; g &lt; 3\7<br /> | <td>5\12 &lt; g &lt; 3\7<br /> | ||
</td> | </td> | ||
<td> | <td>-2+5g<br /> | ||
</td> | </td> | ||
<td>-g+1 | <td>-g+1\2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,205: | Line 1,209: | ||
<td>1\4 &lt; g &lt; 2\7<br /> | <td>1\4 &lt; g &lt; 2\7<br /> | ||
</td> | </td> | ||
<td> | <td>-2\3+3g<br /> | ||
</td> | </td> | ||
<td>-g+1 | <td>-g+1\3<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,217: | Line 1,221: | ||
<td>1\6 &lt; g &lt; 1\5<br /> | <td>1\6 &lt; g &lt; 1\5<br /> | ||
</td> | </td> | ||
<td> | <td>-1\4+2g<br /> | ||
</td> | </td> | ||
<td>-g+1 | <td>-g+1\4<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,229: | Line 1,233: | ||
<td>7\12 &lt; g &lt; 10\17<br /> | <td>7\12 &lt; g &lt; 10\17<br /> | ||
</td> | </td> | ||
<td> | <td>-4+7g<br /> | ||
</td> | </td> | ||
<td>-5g+3<br /> | <td>-5g+3<br /> | ||
| Line 1,243: | Line 1,247: | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>-g+1 | <td>-g+1\6<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,253: | Line 1,257: | ||
<td>5\12 &lt; g &lt; 8\19<br /> | <td>5\12 &lt; g &lt; 8\19<br /> | ||
</td> | </td> | ||
<td> | <td>-2+5g<br /> | ||
</td> | </td> | ||
<td>-7g+3<br /> | <td>-7g+3<br /> | ||
| Line 1,267: | Line 1,271: | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>-2g+1 | <td>-2g+1\4<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,279: | Line 1,283: | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>-3g+1 | <td>-3g+1\3<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,291: | Line 1,295: | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>-5g+1 | <td>-5g+1\2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,332: | Line 1,336: | ||
<td>12\13 &lt; g &lt; 13\14<br /> | <td>12\13 &lt; g &lt; 13\14<br /> | ||
</td> | </td> | ||
<td> | <td>-11+12g<br /> | ||
</td> | </td> | ||
<td>-g+1<br /> | <td>-g+1<br /> | ||
| Line 1,344: | Line 1,348: | ||
<td>6\13 &lt; g &lt; 7\15<br /> | <td>6\13 &lt; g &lt; 7\15<br /> | ||
</td> | </td> | ||
<td> | <td>-5+11g<br /> | ||
</td> | </td> | ||
<td>-2g+1<br /> | <td>-2g+1<br /> | ||
| Line 1,356: | Line 1,360: | ||
<td>4\13 &lt; g &lt; 5\16<br /> | <td>4\13 &lt; g &lt; 5\16<br /> | ||
</td> | </td> | ||
<td> | <td>-3+10g<br /> | ||
</td> | </td> | ||
<td>-3g | <td>1-3g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,368: | Line 1,372: | ||
<td>3\13 &lt; g &lt; 4\17<br /> | <td>3\13 &lt; g &lt; 4\17<br /> | ||
</td> | </td> | ||
<td> | <td>-2+9g<br /> | ||
</td> | </td> | ||
<td>-4g+1<br /> | <td>-4g+1<br /> | ||
| Line 1,380: | Line 1,384: | ||
<td>5\13 &lt; g &lt; 7\18<br /> | <td>5\13 &lt; g &lt; 7\18<br /> | ||
</td> | </td> | ||
<td> | <td>-3+8g<br /> | ||
</td> | </td> | ||
<td>-5g+2<br /> | <td>-5g+2<br /> | ||
| Line 1,392: | Line 1,396: | ||
<td>2\13 &lt; g &lt; 3\19<br /> | <td>2\13 &lt; g &lt; 3\19<br /> | ||
</td> | </td> | ||
<td> | <td>-1+7g<br /> | ||
</td> | </td> | ||
<td>-6g+1<br /> | <td>-6g+1<br /> | ||
| Line 1,404: | Line 1,408: | ||
<td>11\13 &lt; g &lt; 17\20<br /> | <td>11\13 &lt; g &lt; 17\20<br /> | ||
</td> | </td> | ||
<td> | <td>-5+6g<br /> | ||
</td> | </td> | ||
<td>-7g+6<br /> | <td>-7g+6<br /> | ||
| Line 1,416: | Line 1,420: | ||
<td>8\13 &lt; g &lt; 13\21<br /> | <td>8\13 &lt; g &lt; 13\21<br /> | ||
</td> | </td> | ||
<td> | <td>-3+5g<br /> | ||
</td> | </td> | ||
<td>-8g+5<br /> | <td>-8g+5<br /> | ||
| Line 1,428: | Line 1,432: | ||
<td>10\13 &lt; g &lt; 17\22<br /> | <td>10\13 &lt; g &lt; 17\22<br /> | ||
</td> | </td> | ||
<td> | <td>-3+4g<br /> | ||
</td> | </td> | ||
<td>-9g+7<br /> | <td>-9g+7<br /> | ||
| Line 1,440: | Line 1,444: | ||
<td>9\13 &lt; g &lt; 16\23<br /> | <td>9\13 &lt; g &lt; 16\23<br /> | ||
</td> | </td> | ||
<td> | <td>-2+3g<br /> | ||
</td> | </td> | ||
<td>-10g+7<br /> | <td>-10g+7<br /> | ||
| Line 1,452: | Line 1,456: | ||
<td>7\13 &lt; g &lt; 13\24<br /> | <td>7\13 &lt; g &lt; 13\24<br /> | ||
</td> | </td> | ||
<td> | <td>-1+2g<br /> | ||
</td> | </td> | ||
<td>-11g+6<br /> | <td>-11g+6<br /> | ||
| Line 1,495: | Line 1,499: | ||
<td>13\14 &lt; g &lt; 14\15<br /> | <td>13\14 &lt; g &lt; 14\15<br /> | ||
</td> | </td> | ||
<td> | <td>-12+13g<br /> | ||
</td> | </td> | ||
<td>-g+1<br /> | <td>-g+1<br /> | ||
| Line 1,507: | Line 1,511: | ||
<td>3\7 &lt; g &lt; 4\9<br /> | <td>3\7 &lt; g &lt; 4\9<br /> | ||
</td> | </td> | ||
<td> | <td>-5\2+6g<br /> | ||
</td> | </td> | ||
<td>-g+1 | <td>-g+1\2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,519: | Line 1,523: | ||
<td>9\14 &lt; g &lt; 11\17<br /> | <td>9\14 &lt; g &lt; 11\17<br /> | ||
</td> | </td> | ||
<td> | <td>-7+11g<br /> | ||
</td> | </td> | ||
<td>-3g+2<br /> | <td>-3g+2<br /> | ||
| Line 1,531: | Line 1,535: | ||
<td>3\14 &lt; g &lt; 2\9<br /> | <td>3\14 &lt; g &lt; 2\9<br /> | ||
</td> | </td> | ||
<td> | <td>-1+5g<br /> | ||
</td> | </td> | ||
<td>-2g+1 | <td>-2g+1\2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,543: | Line 1,547: | ||
<td>11\14 &lt; g &lt; 15\19<br /> | <td>11\14 &lt; g &lt; 15\19<br /> | ||
</td> | </td> | ||
<td> | <td>-7+9g<br /> | ||
</td> | </td> | ||
<td>-5g+4<br /> | <td>-5g+4<br /> | ||
| Line 1,555: | Line 1,559: | ||
<td>1\7 &lt; g &lt; 2\13<br /> | <td>1\7 &lt; g &lt; 2\13<br /> | ||
</td> | </td> | ||
<td>4g-1 | <td>4g-1\2<br /> | ||
</td> | </td> | ||
<td>-3g+1 | <td>-3g+1\2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,569: | Line 1,573: | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>-g+1 | <td>-g+1\7<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,579: | Line 1,583: | ||
<td>5\14 &lt; g &lt; 4\11<br /> | <td>5\14 &lt; g &lt; 4\11<br /> | ||
</td> | </td> | ||
<td> | <td>-1+3g<br /> | ||
</td> | </td> | ||
<td>-4g+3 | <td>-4g+3\2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,591: | Line 1,595: | ||
<td>3\14 &lt; g &lt; 5\23<br /> | <td>3\14 &lt; g &lt; 5\23<br /> | ||
</td> | </td> | ||
<td> | <td>-1+5g<br /> | ||
</td> | </td> | ||
<td>-9g+2<br /> | <td>-9g+2<br /> | ||
| Line 1,603: | Line 1,607: | ||
<td>2\7 &lt; g &lt; 5\17<br /> | <td>2\7 &lt; g &lt; 5\17<br /> | ||
</td> | </td> | ||
<td> | <td>-1\2+2g<br /> | ||
</td> | </td> | ||
<td>-5g+3 | <td>-5g+3\2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,615: | Line 1,619: | ||
<td>5\14 &lt; g &lt; 9\25<br /> | <td>5\14 &lt; g &lt; 9\25<br /> | ||
</td> | </td> | ||
<td> | <td>-1+3g<br /> | ||
</td> | </td> | ||
<td>-11g+4<br /> | <td>-11g+4<br /> | ||
| Line 1,629: | Line 1,633: | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>-6g+1 | <td>-6g+1\2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,670: | Line 1,674: | ||
<td>14\15 &lt; g &lt; 15\16<br /> | <td>14\15 &lt; g &lt; 15\16<br /> | ||
</td> | </td> | ||
<td> | <td>-13+14g<br /> | ||
</td> | </td> | ||
<td>-g+1<br /> | <td>-g+1<br /> | ||
| Line 1,682: | Line 1,686: | ||
<td>7\15 &lt; g &lt; 8\17<br /> | <td>7\15 &lt; g &lt; 8\17<br /> | ||
</td> | </td> | ||
<td> | <td>-6+13g<br /> | ||
</td> | </td> | ||
<td>-2g+1<br /> | <td>-2g+1<br /> | ||
| Line 1,694: | Line 1,698: | ||
<td>4\15 &lt; g &lt; 5\18<br /> | <td>4\15 &lt; g &lt; 5\18<br /> | ||
</td> | </td> | ||
<td> | <td>-1+4g<br /> | ||
</td> | </td> | ||
<td>-g+1 | <td>-g+1\3<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,706: | Line 1,710: | ||
<td>11\15 &lt; g &lt; 14\19<br /> | <td>11\15 &lt; g &lt; 14\19<br /> | ||
</td> | </td> | ||
<td> | <td>-8+11g<br /> | ||
</td> | </td> | ||
<td>-4g+3<br /> | <td>-4g+3<br /> | ||
| Line 1,718: | Line 1,722: | ||
<td>2\15 &lt; g &lt; 3\20<br /> | <td>2\15 &lt; g &lt; 3\20<br /> | ||
</td> | </td> | ||
<td> | <td>-1\5+2g<br /> | ||
</td> | </td> | ||
<td>-g+1 | <td>-g+1\5<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,730: | Line 1,734: | ||
<td>2\15 &lt; g &lt; 1\7<br /> | <td>2\15 &lt; g &lt; 1\7<br /> | ||
</td> | </td> | ||
<td> | <td>-1\3+3g<br /> | ||
</td> | </td> | ||
<td>-2g+1 | <td>-2g+1\3<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,742: | Line 1,746: | ||
<td>2\15 &lt; g &lt; 3\22<br /> | <td>2\15 &lt; g &lt; 3\22<br /> | ||
</td> | </td> | ||
<td> | <td>-1+8g<br /> | ||
</td> | </td> | ||
<td>-7g+1<br /> | <td>-7g+1<br /> | ||
| Line 1,754: | Line 1,758: | ||
<td>13\15 &lt; g &lt; 20\23<br /> | <td>13\15 &lt; g &lt; 20\23<br /> | ||
</td> | </td> | ||
<td> | <td>-6+7g<br /> | ||
</td> | </td> | ||
<td>-8g+7<br /> | <td>-8g+7<br /> | ||
| Line 1,766: | Line 1,770: | ||
<td>1\5 &lt; g &lt; 3\14<br /> | <td>1\5 &lt; g &lt; 3\14<br /> | ||
</td> | </td> | ||
<td> | <td>-1\3+2g<br /> | ||
</td> | </td> | ||
<td>-3g+2 | <td>-3g+2\3<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,780: | Line 1,784: | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>-2g+1 | <td>-2g+1\5<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,790: | Line 1,794: | ||
<td>4\15 &lt; g &lt; 7\26<br /> | <td>4\15 &lt; g &lt; 7\26<br /> | ||
</td> | </td> | ||
<td> | <td>-1+4g<br /> | ||
</td> | </td> | ||
<td>-11g+3<br /> | <td>-11g+3<br /> | ||
| Line 1,804: | Line 1,808: | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>-4g+1 | <td>-4g+1\3<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,814: | Line 1,818: | ||
<td>8\15 &lt; g &lt; 15\28<br /> | <td>8\15 &lt; g &lt; 15\28<br /> | ||
</td> | </td> | ||
<td> | <td>-1+2g<br /> | ||
</td> | </td> | ||
<td>-13g+7<br /> | <td>-13g+7<br /> | ||
| Line 1,857: | Line 1,861: | ||
<td>15\16 &lt; g &lt; 16\17<br /> | <td>15\16 &lt; g &lt; 16\17<br /> | ||
</td> | </td> | ||
<td> | <td>-14+15g<br /> | ||
</td> | </td> | ||
<td>-g+1<br /> | <td>-g+1<br /> | ||
| Line 1,869: | Line 1,873: | ||
<td>7\16 &lt; g &lt; 4\9<br /> | <td>7\16 &lt; g &lt; 4\9<br /> | ||
</td> | </td> | ||
<td> | <td>-3+7g<br /> | ||
</td> | </td> | ||
<td>-g+1 | <td>-g+1\2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,881: | Line 1,885: | ||
<td>5\16 &lt; g &lt; 6\19<br /> | <td>5\16 &lt; g &lt; 6\19<br /> | ||
</td> | </td> | ||
<td> | <td>-4+13g<br /> | ||
</td> | </td> | ||
<td>-3g | <td>1-3g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,893: | Line 1,897: | ||
<td>3\16 &lt; g &lt; 1\5<br /> | <td>3\16 &lt; g &lt; 1\5<br /> | ||
</td> | </td> | ||
<td>3g-1 | <td>3g-1\2<br /> | ||
</td> | </td> | ||
<td>-g+1 | <td>-g+1\4<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,905: | Line 1,909: | ||
<td>3\16 &lt; g &lt; 4\21<br /> | <td>3\16 &lt; g &lt; 4\21<br /> | ||
</td> | </td> | ||
<td> | <td>-2+11g<br /> | ||
</td> | </td> | ||
<td>-5g+1<br /> | <td>-5g+1<br /> | ||
| Line 1,917: | Line 1,921: | ||
<td>5\16 &lt; g &lt; 6\19<br /> | <td>5\16 &lt; g &lt; 6\19<br /> | ||
</td> | </td> | ||
<td> | <td>-3\2+5g<br /> | ||
</td> | </td> | ||
<td>- | <td>1-3g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,929: | Line 1,933: | ||
<td>9\16 &lt; g &lt; 13\23<br /> | <td>9\16 &lt; g &lt; 13\23<br /> | ||
</td> | </td> | ||
<td> | <td>-5+9g<br /> | ||
</td> | </td> | ||
<td>-7g+4<br /> | <td>-7g+4<br /> | ||
| Line 1,943: | Line 1,947: | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>-g+1 | <td>-g+1\8<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,953: | Line 1,957: | ||
<td>7\16 &lt; g &lt; 11\25<br /> | <td>7\16 &lt; g &lt; 11\25<br /> | ||
</td> | </td> | ||
<td> | <td>-3+7g<br /> | ||
</td> | </td> | ||
<td>-9g+4<br /> | <td>-9g+4<br /> | ||
| Line 1,965: | Line 1,969: | ||
<td>3\16 &lt; g &lt; 4\21<br /> | <td>3\16 &lt; g &lt; 4\21<br /> | ||
</td> | </td> | ||
<td> | <td>3g-1\2<br /> | ||
</td> | </td> | ||
<td>- | <td>-5g+1<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 1,977: | Line 1,981: | ||
<td>13\16 &lt; g &lt; 22\27<br /> | <td>13\16 &lt; g &lt; 22\27<br /> | ||
</td> | </td> | ||
<td> | <td>-4+5g<br /> | ||
</td> | </td> | ||
<td>-11g+9<br /> | <td>-11g+9<br /> | ||
| Line 1,991: | Line 1,995: | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>-3g+1 | <td>-3g+1\4<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,001: | Line 2,005: | ||
<td>11\16 &lt; g &lt; 20\29<br /> | <td>11\16 &lt; g &lt; 20\29<br /> | ||
</td> | </td> | ||
<td> | <td>-2+3g<br /> | ||
</td> | </td> | ||
<td>-13g+9<br /> | <td>-13g+9<br /> | ||
| Line 2,015: | Line 2,019: | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>-7g+1 | <td>-7g+1\2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,056: | Line 2,060: | ||
<td>16\17 &lt; g &lt; 17\18<br /> | <td>16\17 &lt; g &lt; 17\18<br /> | ||
</td> | </td> | ||
<td> | <td>-15+16g<br /> | ||
</td> | </td> | ||
<td>-g+1<br /> | <td>-g+1<br /> | ||
| Line 2,068: | Line 2,072: | ||
<td>8\17 &lt; g &lt; 9\19<br /> | <td>8\17 &lt; g &lt; 9\19<br /> | ||
</td> | </td> | ||
<td> | <td>-7+15g<br /> | ||
</td> | </td> | ||
<td>-2g+1<br /> | <td>-2g+1<br /> | ||
| Line 2,080: | Line 2,084: | ||
<td>11\17 &lt; g &lt; 13\20<br /> | <td>11\17 &lt; g &lt; 13\20<br /> | ||
</td> | </td> | ||
<td> | <td>-9+14g<br /> | ||
</td> | </td> | ||
<td>-3g+2<br /> | <td>-3g+2<br /> | ||
| Line 2,092: | Line 2,096: | ||
<td>4\17 &lt; g &lt; 5\21<br /> | <td>4\17 &lt; g &lt; 5\21<br /> | ||
</td> | </td> | ||
<td> | <td>-3+13g<br /> | ||
</td> | </td> | ||
<td>-4g+1<br /> | <td>-4g+1<br /> | ||
| Line 2,104: | Line 2,108: | ||
<td>10\17 &lt; g &lt; 13\22<br /> | <td>10\17 &lt; g &lt; 13\22<br /> | ||
</td> | </td> | ||
<td> | <td>-7+12g<br /> | ||
</td> | </td> | ||
<td>-5g+3<br /> | <td>-5g+3<br /> | ||
| Line 2,116: | Line 2,120: | ||
<td>14\17 &lt; g &lt; 19\23<br /> | <td>14\17 &lt; g &lt; 19\23<br /> | ||
</td> | </td> | ||
<td> | <td>-9+11g<br /> | ||
</td> | </td> | ||
<td>-6g+5<br /> | <td>-6g+5<br /> | ||
| Line 2,128: | Line 2,132: | ||
<td>12\17 &lt; g &lt; 17\24<br /> | <td>12\17 &lt; g &lt; 17\24<br /> | ||
</td> | </td> | ||
<td> | <td>-7+10g<br /> | ||
</td> | </td> | ||
<td>-7g+5<br /> | <td>-7g+5<br /> | ||
| Line 2,140: | Line 2,144: | ||
<td>2\17 &lt; g &lt; 3\25<br /> | <td>2\17 &lt; g &lt; 3\25<br /> | ||
</td> | </td> | ||
<td> | <td>-1+9g<br /> | ||
</td> | </td> | ||
<td>-8g+1<br /> | <td>-8g+1<br /> | ||
| Line 2,152: | Line 2,156: | ||
<td>15\17 &lt; g &lt; 23\26<br /> | <td>15\17 &lt; g &lt; 23\26<br /> | ||
</td> | </td> | ||
<td> | <td>-7+8g<br /> | ||
</td> | </td> | ||
<td>-9g+8<br /> | <td>-9g+8<br /> | ||
| Line 2,164: | Line 2,168: | ||
<td>5\17 &lt; g &lt; 8\27<br /> | <td>5\17 &lt; g &lt; 8\27<br /> | ||
</td> | </td> | ||
<td> | <td>-2+7g<br /> | ||
</td> | </td> | ||
<td>-10g+3<br /> | <td>-10g+3<br /> | ||
| Line 2,176: | Line 2,180: | ||
<td>3\17 &lt; g &lt; 5\28<br /> | <td>3\17 &lt; g &lt; 5\28<br /> | ||
</td> | </td> | ||
<td> | <td>-1+6g<br /> | ||
</td> | </td> | ||
<td>-11g+2<br /> | <td>-11g+2<br /> | ||
| Line 2,188: | Line 2,192: | ||
<td>7\17 &lt; g &lt; 12\29<br /> | <td>7\17 &lt; g &lt; 12\29<br /> | ||
</td> | </td> | ||
<td> | <td>-2+5g<br /> | ||
</td> | </td> | ||
<td>-12g+5<br /> | <td>-12g+5<br /> | ||
| Line 2,198: | Line 2,202: | ||
<td>13\17 &lt; g &lt; 10\13<br /> | <td>13\17 &lt; g &lt; 10\13<br /> | ||
</td> | </td> | ||
<td>13\17 &lt; g &lt; 23\30<br /> | <td>13\17 &lt; g &lt;23\30<br /> | ||
</td> | </td> | ||
<td> | <td>-3+4g<br /> | ||
</td> | </td> | ||
<td>-13g+10<br /> | <td>-13g+10<br /> | ||
| Line 2,212: | Line 2,216: | ||
<td>6\17 &lt; g &lt; 11\31<br /> | <td>6\17 &lt; g &lt; 11\31<br /> | ||
</td> | </td> | ||
<td> | <td>-1+3g<br /> | ||
</td> | </td> | ||
<td>-14g+5<br /> | <td>-14g+5<br /> | ||
| Line 2,224: | Line 2,228: | ||
<td>9\17 &lt; g &lt; 17\32<br /> | <td>9\17 &lt; g &lt; 17\32<br /> | ||
</td> | </td> | ||
<td> | <td>-1+2g<br /> | ||
</td> | </td> | ||
<td>-15g+8<br /> | <td>-15g+8<br /> | ||
| Line 2,267: | Line 2,271: | ||
<td>17\18 &lt; g &lt; 18\19<br /> | <td>17\18 &lt; g &lt; 18\19<br /> | ||
</td> | </td> | ||
<td> | <td>-16+17g<br /> | ||
</td> | </td> | ||
<td>-g+1<br /> | <td>-g+1<br /> | ||
| Line 2,279: | Line 2,283: | ||
<td>4\9 &lt; g &lt; 5\11<br /> | <td>4\9 &lt; g &lt; 5\11<br /> | ||
</td> | </td> | ||
<td> | <td>-7\2+8g<br /> | ||
</td> | </td> | ||
<td>-g+1 | <td>-g+1\2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,291: | Line 2,295: | ||
<td>5\18 &lt; g &lt; 2\7<br /> | <td>5\18 &lt; g &lt; 2\7<br /> | ||
</td> | </td> | ||
<td> | <td>-4\3+5g<br /> | ||
</td> | </td> | ||
<td>-g+1 | <td>-g+1\3<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,303: | Line 2,307: | ||
<td>2\9 &lt; g &lt; 3\13<br /> | <td>2\9 &lt; g &lt; 3\13<br /> | ||
</td> | </td> | ||
<td> | <td>-3\2+7g<br /> | ||
</td> | </td> | ||
<td>-2g+1 | <td>-2g+1\2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,315: | Line 2,319: | ||
<td>7\18 &lt; g &lt; 9\23<br /> | <td>7\18 &lt; g &lt; 9\23<br /> | ||
</td> | </td> | ||
<td> | <td>-5+13g<br /> | ||
</td> | </td> | ||
<td>-5g+2<br /> | <td>-5g+2<br /> | ||
| Line 2,327: | Line 2,331: | ||
<td>1\9 &lt; g &lt; 2\15<br /> | <td>1\9 &lt; g &lt; 2\15<br /> | ||
</td> | </td> | ||
<td> | <td>-1\6+2g<br /> | ||
</td> | </td> | ||
<td>-g+1 | <td>-g+1\6<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,339: | Line 2,343: | ||
<td>5\18 &lt; g &lt; 7\25<br /> | <td>5\18 &lt; g &lt; 7\25<br /> | ||
</td> | </td> | ||
<td> | <td>-3+11g<br /> | ||
</td> | </td> | ||
<td>-7g+2<br /> | <td>-7g+2<br /> | ||
| Line 2,351: | Line 2,355: | ||
<td>1\9 &lt; g &lt; 2\17<br /> | <td>1\9 &lt; g &lt; 2\17<br /> | ||
</td> | </td> | ||
<td> | <td>-1\2+5g<br /> | ||
</td> | </td> | ||
<td>-4g+1 | <td>-4g+1\2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,365: | Line 2,369: | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>-g+1 | <td>-g+1\9<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,375: | Line 2,379: | ||
<td>7\18 &lt; g &lt; 9\23<br /> | <td>7\18 &lt; g &lt; 9\23<br /> | ||
</td> | </td> | ||
<td> | <td>-3\2+4g<br /> | ||
</td> | </td> | ||
<td>- | <td>-5g+2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,387: | Line 2,391: | ||
<td>13\18 &lt; g &lt; 21\29<br /> | <td>13\18 &lt; g &lt; 21\29<br /> | ||
</td> | </td> | ||
<td> | <td>-5+7g<br /> | ||
</td> | </td> | ||
<td>-11g+8<br /> | <td>-11g+8<br /> | ||
| Line 2,401: | Line 2,405: | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>-2g+1 | <td>-2g+1\6<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,411: | Line 2,415: | ||
<td>11\18 &lt; g &lt; 19\31<br /> | <td>11\18 &lt; g &lt; 19\31<br /> | ||
</td> | </td> | ||
<td> | <td>-3+5g<br /> | ||
</td> | </td> | ||
<td>-13g+8<br /> | <td>-13g+8<br /> | ||
| Line 2,423: | Line 2,427: | ||
<td>5\18 &lt; g &lt; 7\25<br /> | <td>5\18 &lt; g &lt; 7\25<br /> | ||
</td> | </td> | ||
<td> | <td>-1\2+2g<br /> | ||
</td> | </td> | ||
<td>- | <td>-7g+2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,437: | Line 2,441: | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>-5g+1 | <td>-5g+1\3<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,449: | Line 2,453: | ||
<td>g<br /> | <td>g<br /> | ||
</td> | </td> | ||
<td>-8g+1 | <td>-8g+1\2<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,490: | Line 2,494: | ||
<td>18\19 &lt; g &lt; 19\20<br /> | <td>18\19 &lt; g &lt; 19\20<br /> | ||
</td> | </td> | ||
<td> | <td>-17+18g<br /> | ||
</td> | </td> | ||
<td>-g+1<br /> | <td>-g+1<br /> | ||
| Line 2,502: | Line 2,506: | ||
<td>9\19 &lt; g &lt; 10\21<br /> | <td>9\19 &lt; g &lt; 10\21<br /> | ||
</td> | </td> | ||
<td> | <td>-8+17g<br /> | ||
</td> | </td> | ||
<td>-2g+1<br /> | <td>-2g+1<br /> | ||
| Line 2,514: | Line 2,518: | ||
<td>6\19 &lt; g &lt; 7\22<br /> | <td>6\19 &lt; g &lt; 7\22<br /> | ||
</td> | </td> | ||
<td> | <td>-5+16g<br /> | ||
</td> | </td> | ||
<td>-3g | <td>1-3g<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,526: | Line 2,530: | ||
<td>14\19 &lt; g &lt; 17\23<br /> | <td>14\19 &lt; g &lt; 17\23<br /> | ||
</td> | </td> | ||
<td> | <td>-11+15g<br /> | ||
</td> | </td> | ||
<td>-4g+3<br /> | <td>-4g+3<br /> | ||
| Line 2,538: | Line 2,542: | ||
<td>15\19 &lt; g &lt; 19\24<br /> | <td>15\19 &lt; g &lt; 19\24<br /> | ||
</td> | </td> | ||
<td> | <td>-11+14g<br /> | ||
</td> | </td> | ||
<td>-5g+4<br /> | <td>-5g+4<br /> | ||
| Line 2,550: | Line 2,554: | ||
<td>3\19 &lt; g &lt; 4\25<br /> | <td>3\19 &lt; g &lt; 4\25<br /> | ||
</td> | </td> | ||
<td> | <td>-2+13g<br /> | ||
</td> | </td> | ||
<td>-6g+1<br /> | <td>-6g+1<br /> | ||
| Line 2,562: | Line 2,566: | ||
<td>8\19 &lt; g &lt; 11\26<br /> | <td>8\19 &lt; g &lt; 11\26<br /> | ||
</td> | </td> | ||
<td> | <td>-5+12g<br /> | ||
</td> | </td> | ||
<td>-7g+3<br /> | <td>-7g+3<br /> | ||
| Line 2,574: | Line 2,578: | ||
<td>7\19 &lt; g &lt; 10\27<br /> | <td>7\19 &lt; g &lt; 10\27<br /> | ||
</td> | </td> | ||
<td> | <td>-4+11g<br /> | ||
</td> | </td> | ||
<td>-8g+3<br /> | <td>-8g+3<br /> | ||
| Line 2,586: | Line 2,590: | ||
<td>2\19 &lt; g &lt; 3\28<br /> | <td>2\19 &lt; g &lt; 3\28<br /> | ||
</td> | </td> | ||
<td> | <td>-1+10g<br /> | ||
</td> | </td> | ||
<td>-9g+1<br /> | <td>-9g+1<br /> | ||
| Line 2,598: | Line 2,602: | ||
<td>17\19 &lt; g &lt; 26\29<br /> | <td>17\19 &lt; g &lt; 26\29<br /> | ||
</td> | </td> | ||
<td> | <td>-8+9g<br /> | ||
</td> | </td> | ||
<td>-10g+9<br /> | <td>-10g+9<br /> | ||
| Line 2,610: | Line 2,614: | ||
<td>12\19 &lt; g &lt; 19\30<br /> | <td>12\19 &lt; g &lt; 19\30<br /> | ||
</td> | </td> | ||
<td> | <td>-5+8g<br /> | ||
</td> | </td> | ||
<td>-11g+7<br /> | <td>-11g+7<br /> | ||
| Line 2,622: | Line 2,626: | ||
<td>11\19 &lt; g &lt; 18\31<br /> | <td>11\19 &lt; g &lt; 18\31<br /> | ||
</td> | </td> | ||
<td> | <td>-4+7g<br /> | ||
</td> | </td> | ||
<td>-12g+7<br /> | <td>-12g+7<br /> | ||
| Line 2,634: | Line 2,638: | ||
<td>16\19 &lt; g &lt; 27\32<br /> | <td>16\19 &lt; g &lt; 27\32<br /> | ||
</td> | </td> | ||
<td> | <td>-5+6g<br /> | ||
</td> | </td> | ||
<td>-13g+11<br /> | <td>-13g+11<br /> | ||
| Line 2,646: | Line 2,650: | ||
<td>4\19 &lt; g &lt; 7\33<br /> | <td>4\19 &lt; g &lt; 7\33<br /> | ||
</td> | </td> | ||
<td> | <td>-1+5g<br /> | ||
</td> | </td> | ||
<td>-14g+3<br /> | <td>-14g+3<br /> | ||
| Line 2,658: | Line 2,662: | ||
<td>5\19 &lt; g &lt; 9\34<br /> | <td>5\19 &lt; g &lt; 9\34<br /> | ||
</td> | </td> | ||
<td> | <td>-1+4g<br /> | ||
</td> | </td> | ||
<td>-15g+4<br /> | <td>-15g+4<br /> | ||
| Line 2,670: | Line 2,674: | ||
<td>13\19 &lt; g &lt; 24\35<br /> | <td>13\19 &lt; g &lt; 24\35<br /> | ||
</td> | </td> | ||
<td> | <td>-2+3g<br /> | ||
</td> | </td> | ||
<td>-16g+11<br /> | <td>-16g+11<br /> | ||
| Line 2,682: | Line 2,686: | ||
<td>10\19 &lt; g &lt; 19\36<br /> | <td>10\19 &lt; g &lt; 19\36<br /> | ||
</td> | </td> | ||
<td> | <td>-1+2g<br /> | ||
</td> | </td> | ||
<td>-17g+9<br /> | <td>-17g+9<br /> | ||
| Line 2,724: | Line 2,728: | ||
</td> | </td> | ||
<td>19\20 &lt; g &lt; 20\21<br /> | <td>19\20 &lt; g &lt; 20\21<br /> | ||
</td> | |||
<td>-18+19g<br /> | |||
</td> | |||
<td>-g+1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,732: | Line 2,740: | ||
</td> | </td> | ||
<td>9\20 &lt; g &lt; 5\11<br /> | <td>9\20 &lt; g &lt; 5\11<br /> | ||
</td> | |||
<td>-4+9g<br /> | |||
</td> | |||
<td>-g+1\2<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,740: | Line 2,752: | ||
</td> | </td> | ||
<td>13\20 &lt; g &lt; 15\23<br /> | <td>13\20 &lt; g &lt; 15\23<br /> | ||
</td> | |||
<td>-11+17g<br /> | |||
</td> | |||
<td>-3g+2<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,748: | Line 2,764: | ||
</td> | </td> | ||
<td>1\5 &lt; g &lt; 2\9<br /> | <td>1\5 &lt; g &lt; 2\9<br /> | ||
</td> | |||
<td>-3\4+4g<br /> | |||
</td> | |||
<td>-g+1\4<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,756: | Line 2,776: | ||
</td> | </td> | ||
<td>3\20 &lt; g &lt; 4\25<br /> | <td>3\20 &lt; g &lt; 4\25<br /> | ||
</td> | |||
<td>-2\5+3g<br /> | |||
</td> | |||
<td>-g+1\5<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,764: | Line 2,788: | ||
</td> | </td> | ||
<td>3\20 &lt; g &lt; 2\13<br /> | <td>3\20 &lt; g &lt; 2\13<br /> | ||
</td> | |||
<td>-1+7g<br /> | |||
</td> | |||
<td>-3g+1\2<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,772: | Line 2,800: | ||
</td> | </td> | ||
<td>17\20 &lt; g &lt; 23\27<br /> | <td>17\20 &lt; g &lt; 23\27<br /> | ||
</td> | |||
<td>-11+13g<br /> | |||
</td> | |||
<td>-7g+6<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,780: | Line 2,812: | ||
</td> | </td> | ||
<td>1\10 &lt; g &lt; 1\9<br /> | <td>1\10 &lt; g &lt; 1\9<br /> | ||
</td> | |||
<td>-1\4+3g<br /> | |||
</td> | |||
<td>-2g+1\4<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,788: | Line 2,824: | ||
</td> | </td> | ||
<td>11\20 &lt; g &lt; 16\29<br /> | <td>11\20 &lt; g &lt; 16\29<br /> | ||
</td> | |||
<td>-6+11g<br /> | |||
</td> | |||
<td>-9g+5<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,796: | Line 2,836: | ||
</td> | </td> | ||
<td>1\20 &lt; g &lt; 1\15<br /> | <td>1\20 &lt; g &lt; 1\15<br /> | ||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>-g+1\10<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,804: | Line 2,848: | ||
</td> | </td> | ||
<td>9\20 &lt; g &lt; 14\31<br /> | <td>9\20 &lt; g &lt; 14\31<br /> | ||
</td> | |||
<td>-4+9g<br /> | |||
</td> | |||
<td>-11g+5<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,812: | Line 2,860: | ||
</td> | </td> | ||
<td>3\20 &lt; g &lt; 2\13<br /> | <td>3\20 &lt; g &lt; 2\13<br /> | ||
</td> | |||
<td>-1\4+2g<br /> | |||
</td> | |||
<td>-3g+1\2<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,820: | Line 2,872: | ||
</td> | </td> | ||
<td>3\20 &lt; g &lt; 5\33<br /> | <td>3\20 &lt; g &lt; 5\33<br /> | ||
</td> | |||
<td>-1+7g<br /> | |||
</td> | |||
<td>-13g+2<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,828: | Line 2,884: | ||
</td> | </td> | ||
<td>7\20 &lt; g &lt; 6\17<br /> | <td>7\20 &lt; g &lt; 6\17<br /> | ||
</td> | |||
<td>-1+3g<br /> | |||
</td> | |||
<td>-7g+5\2<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,836: | Line 2,896: | ||
</td> | </td> | ||
<td>1\20 &lt; g &lt; 2\35<br /> | <td>1\20 &lt; g &lt; 2\35<br /> | ||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>-3g+1\5<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,844: | Line 2,908: | ||
</td> | </td> | ||
<td>1\20 &lt; g &lt; 1\18<br /> | <td>1\20 &lt; g &lt; 1\18<br /> | ||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>-4g+1\4<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,852: | Line 2,920: | ||
</td> | </td> | ||
<td>7\20 &lt; g &lt; 13\37<br /> | <td>7\20 &lt; g &lt; 13\37<br /> | ||
</td> | |||
<td>-1+3g<br /> | |||
</td> | |||
<td>-17g+6<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,860: | Line 2,932: | ||
</td> | </td> | ||
<td>1\20 &lt; g &lt; 1\19<br /> | <td>1\20 &lt; g &lt; 1\19<br /> | ||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>-9g+1\2<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,868: | Line 2,944: | ||
</td> | </td> | ||
<td>1\20 &lt; g &lt; 2\39<br /> | <td>1\20 &lt; g &lt; 2\39<br /> | ||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>-19g+1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,895: | Line 2,975: | ||
</td> | </td> | ||
<td>20\21 &lt; g &lt; 21\22<br /> | <td>20\21 &lt; g &lt; 21\22<br /> | ||
</td> | |||
<td>-19+20g<br /> | |||
</td> | |||
<td>-g+1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,903: | Line 2,987: | ||
</td> | </td> | ||
<td>10\21 &lt; g &lt; 11\23<br /> | <td>10\21 &lt; g &lt; 11\23<br /> | ||
</td> | |||
<td>-9+19g<br /> | |||
</td> | |||
<td>-2g+1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,911: | Line 2,999: | ||
</td> | </td> | ||
<td>2\7 &lt; g &lt; 3\10<br /> | <td>2\7 &lt; g &lt; 3\10<br /> | ||
</td> | |||
<td>-5\3+6g<br /> | |||
</td> | |||
<td>-g+1\3<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,919: | Line 3,011: | ||
</td> | </td> | ||
<td>5\21 &lt; g &lt; 6\25<br /> | <td>5\21 &lt; g &lt; 6\25<br /> | ||
</td> | |||
<td>-4+17g<br /> | |||
</td> | |||
<td>-4g+1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,927: | Line 3,023: | ||
</td> | </td> | ||
<td>4\21 &lt; g &lt; 5\26<br /> | <td>4\21 &lt; g &lt; 5\26<br /> | ||
</td> | |||
<td>-3+16g<br /> | |||
</td> | |||
<td>-5g+1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,935: | Line 3,035: | ||
</td> | </td> | ||
<td>1\7 &lt; g &lt; 2\13<br /> | <td>1\7 &lt; g &lt; 2\13<br /> | ||
</td> | |||
<td>-2\3+5g<br /> | |||
</td> | |||
<td>-2g+1\3<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,943: | Line 3,047: | ||
</td> | </td> | ||
<td>2\21 &lt; g &lt; 3\28<br /> | <td>2\21 &lt; g &lt; 3\28<br /> | ||
</td> | |||
<td>-1\7+2g<br /> | |||
</td> | |||
<td>-g+1\7<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,951: | Line 3,059: | ||
</td> | </td> | ||
<td>13\21 &lt; g &lt; 18\29<br /> | <td>13\21 &lt; g &lt; 18\29<br /> | ||
</td> | |||
<td>-8+13g<br /> | |||
</td> | |||
<td>-8g+5<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,959: | Line 3,071: | ||
</td> | </td> | ||
<td>2\21 &lt; g &lt; 1\10<br /> | <td>2\21 &lt; g &lt; 1\10<br /> | ||
</td> | |||
<td>-1\3+4g<br /> | |||
</td> | |||
<td>-3g+1\3<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,967: | Line 3,083: | ||
</td> | </td> | ||
<td>2\21 &lt; g &lt; 3\31<br /> | <td>2\21 &lt; g &lt; 3\31<br /> | ||
</td> | |||
<td>-1+11g<br /> | |||
</td> | |||
<td>-10g+1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,975: | Line 3,095: | ||
</td> | </td> | ||
<td>19\21 &lt; g &lt; 29\32<br /> | <td>19\21 &lt; g &lt; 29\32<br /> | ||
</td> | |||
<td>-9+10g<br /> | |||
</td> | |||
<td>-11g+10<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,983: | Line 3,107: | ||
</td> | </td> | ||
<td>5\21 &lt; g &lt; 6\25<br /> | <td>5\21 &lt; g &lt; 6\25<br /> | ||
</td> | |||
<td>-2\3+3g<br /> | |||
</td> | |||
<td>-4g+1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,991: | Line 3,119: | ||
</td> | </td> | ||
<td>8\21 &lt; g &lt; 13\34<br /> | <td>8\21 &lt; g &lt; 13\34<br /> | ||
</td> | |||
<td>-3+8g<br /> | |||
</td> | |||
<td>-13g+5<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 2,999: | Line 3,131: | ||
</td> | </td> | ||
<td>1\21 &lt; g &lt; 2\35<br /> | <td>1\21 &lt; g &lt; 2\35<br /> | ||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>-2g+1\7<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,007: | Line 3,143: | ||
</td> | </td> | ||
<td>4\21 &lt; g &lt; 5\26<br /> | <td>4\21 &lt; g &lt; 5\26<br /> | ||
</td> | |||
<td>-1\3+2g<br /> | |||
</td> | |||
<td>-5g+1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,015: | Line 3,155: | ||
</td> | </td> | ||
<td>17\21 &lt; g &lt; 30\37<br /> | <td>17\21 &lt; g &lt; 30\37<br /> | ||
</td> | |||
<td>-4+5g<br /> | |||
</td> | |||
<td>-16g+13<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,023: | Line 3,167: | ||
</td> | </td> | ||
<td>16\21 &lt; g &lt; 29\38<br /> | <td>16\21 &lt; g &lt; 29\38<br /> | ||
</td> | |||
<td>-3+4g<br /> | |||
</td> | |||
<td>-17g+13<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,031: | Line 3,179: | ||
</td> | </td> | ||
<td>1\21 &lt; g &lt; 2\39<br /> | <td>1\21 &lt; g &lt; 2\39<br /> | ||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>-6g+1\3<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,039: | Line 3,191: | ||
</td> | </td> | ||
<td>11\21 &lt; g &lt; 21\40<br /> | <td>11\21 &lt; g &lt; 21\40<br /> | ||
</td> | |||
<td>-1+2g<br /> | |||
</td> | |||
<td>-19g+10<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,047: | Line 3,203: | ||
</td> | </td> | ||
<td>1\21 &lt; g &lt; 2\41<br /> | <td>1\21 &lt; g &lt; 2\41<br /> | ||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>-20g+1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,074: | Line 3,234: | ||
</td> | </td> | ||
<td>21\22 &lt; g &lt; 22\23<br /> | <td>21\22 &lt; g &lt; 22\23<br /> | ||
</td> | |||
<td>-20+21g<br /> | |||
</td> | |||
<td>-g+1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,082: | Line 3,246: | ||
</td> | </td> | ||
<td>5\11 &lt; g &lt; 6\13<br /> | <td>5\11 &lt; g &lt; 6\13<br /> | ||
</td> | |||
<td>-9\2+10g<br /> | |||
</td> | |||
<td>-g+1\2<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,090: | Line 3,258: | ||
</td> | </td> | ||
<td>7\22 &lt; g &lt; 8\25<br /> | <td>7\22 &lt; g &lt; 8\25<br /> | ||
</td> | |||
<td>-6+19g<br /> | |||
</td> | |||
<td>1-3g<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,098: | Line 3,270: | ||
</td> | </td> | ||
<td>5\22 &lt; g &lt; 3\13<br /> | <td>5\22 &lt; g &lt; 3\13<br /> | ||
</td> | |||
<td>-2+9g<br /> | |||
</td> | |||
<td>-2g+1\2<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,106: | Line 3,282: | ||
</td> | </td> | ||
<td>13\22 &lt; g &lt; 16\27<br /> | <td>13\22 &lt; g &lt; 16\27<br /> | ||
</td> | |||
<td>-10+17g<br /> | |||
</td> | |||
<td>-5g+3<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,114: | Line 3,294: | ||
</td> | </td> | ||
<td>7\22 &lt; g &lt; 8\25<br /> | <td>7\22 &lt; g &lt; 8\25<br /> | ||
</td> | |||
<td>-5\2+8g<br /> | |||
</td> | |||
<td>1-3g<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,122: | Line 3,306: | ||
</td> | </td> | ||
<td>3\22 &lt; g &lt; 4\29<br /> | <td>3\22 &lt; g &lt; 4\29<br /> | ||
</td> | |||
<td>-2+15g<br /> | |||
</td> | |||
<td>-7g+1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,130: | Line 3,318: | ||
</td> | </td> | ||
<td>4\11 &lt; g &lt; 7\19<br /> | <td>4\11 &lt; g &lt; 7\19<br /> | ||
</td> | |||
<td>-5\2+7g<br /> | |||
</td> | |||
<td>-4g+3\2<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,138: | Line 3,330: | ||
</td> | </td> | ||
<td>17\22 &lt; g &lt; 24\31<br /> | <td>17\22 &lt; g &lt; 24\31<br /> | ||
</td> | |||
<td>-10+13g<br /> | |||
</td> | |||
<td>-9g+7<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,146: | Line 3,342: | ||
</td> | </td> | ||
<td>1\11 &lt; g &lt; 2\21<br /> | <td>1\11 &lt; g &lt; 2\21<br /> | ||
</td> | |||
<td>-1\2+6g<br /> | |||
</td> | |||
<td>-5g+1\2<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,154: | Line 3,354: | ||
</td> | </td> | ||
<td>1\22 &lt; g &lt; 2\33<br /> | <td>1\22 &lt; g &lt; 2\33<br /> | ||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>-g+1\11<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,162: | Line 3,366: | ||
</td> | </td> | ||
<td>9\22 &lt; g &lt; 7\17<br /> | <td>9\22 &lt; g &lt; 7\17<br /> | ||
</td> | |||
<td>-2+5g<br /> | |||
</td> | |||
<td>-6g+5\2<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,170: | Line 3,378: | ||
</td> | </td> | ||
<td>5\22 &lt; g &lt; 8\35<br /> | <td>5\22 &lt; g &lt; 8\35<br /> | ||
</td> | |||
<td>-2+9g<br /> | |||
</td> | |||
<td>-13g+3<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,178: | Line 3,390: | ||
</td> | </td> | ||
<td>3\22 &lt; g &lt; 4\29<br /> | <td>3\22 &lt; g &lt; 4\29<br /> | ||
</td> | |||
<td>4g-1\2<br /> | |||
</td> | |||
<td>-7g+1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,186: | Line 3,402: | ||
</td> | </td> | ||
<td>19\22 &lt; g &lt; 32\37<br /> | <td>19\22 &lt; g &lt; 32\37<br /> | ||
</td> | |||
<td>-6+7g<br /> | |||
</td> | |||
<td>-15g+13<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,194: | Line 3,414: | ||
</td> | </td> | ||
<td>2\11 &lt; g &lt; 5\27<br /> | <td>2\11 &lt; g &lt; 5\27<br /> | ||
</td> | |||
<td>3g-1\2<br /> | |||
</td> | |||
<td>-8g+3\2<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,202: | Line 3,426: | ||
</td> | </td> | ||
<td>9\22 &lt; g &lt; 16\39<br /> | <td>9\22 &lt; g &lt; 16\39<br /> | ||
</td> | |||
<td>-2+5g<br /> | |||
</td> | |||
<td>-17g+7<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,210: | Line 3,438: | ||
</td> | </td> | ||
<td>3\11 &lt; g &lt; 8\29<br /> | <td>3\11 &lt; g &lt; 8\29<br /> | ||
</td> | |||
<td>-1\2+2g<br /> | |||
</td> | |||
<td>-9g+5\2<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,217: | Line 3,449: | ||
<td>15\22 &lt; g &lt; 13\19<br /> | <td>15\22 &lt; g &lt; 13\19<br /> | ||
</td> | </td> | ||
<td>15\22 &lt; g &lt; 28\41<br /> | <td>15\22 &lt; g &lt;28\41<br /> | ||
</td> | |||
<td>-2+3g<br /> | |||
</td> | |||
<td>-19g+13<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,226: | Line 3,462: | ||
</td> | </td> | ||
<td>1\22 &lt; g &lt; 1\21<br /> | <td>1\22 &lt; g &lt; 1\21<br /> | ||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>-10g+1\2<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 3,234: | Line 3,474: | ||
</td> | </td> | ||
<td>1\22 &lt; g &lt; 2\43<br /> | <td>1\22 &lt; g &lt; 2\43<br /> | ||
</td> | |||
<td>g<br /> | |||
</td> | |||
<td>-21g+1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
Revision as of 03:28, 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 03:28:19 UTC.
- The original revision id was 334772470.
- 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. 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 < g < v, then we may multiply by P to get C/Q < Pg < 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 < g, and hence C/Q < Pg, with C/N being the lower end of the range of possible generators, where L=s. If the range is C/Q < Pg < 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 > 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]]. =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 />
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 < g < v, then we may multiply by P to get C/Q < Pg < a/b, where C is the number of the <a class="wiki_link" href="/Interval%20class">generic interval</a> 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 < g, and hence C/Q < Pg, with C/N being the lower end of the range of possible generators, where L=s. If the range is C/Q < Pg < 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 > 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 <a class="wiki_link" href="/Modal%20UDP%20Notation">chroma-positive</a>.<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><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 < g < 1<br />
</td>
<td>1\2 < g < 2\3<br />
</td>
<td>g<br />
</td>
<td>-g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="x3"></a><!-- ws:end:WikiTextHeadingRule:2 -->3</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L2s<br />
</td>
<td>2\3 < g < 1<br />
</td>
<td>2\3 < g < 3\4<br />
</td>
<td>-1+2g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L1s<br />
</td>
<td>1\3 < g < 1\2<br />
</td>
<td>1\3 < g < 2\5<br />
</td>
<td>g<br />
</td>
<td>-2g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="x4"></a><!-- ws:end:WikiTextHeadingRule:4 -->4</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L3s<br />
</td>
<td>3\4 < g < 1<br />
</td>
<td>3\4 < g < 4\5<br />
</td>
<td>-2+3g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L2s<br />
</td>
<td>1\4 < g < 1\2<br />
</td>
<td>1\4 < g < 1\3<br />
</td>
<td>g<br />
</td>
<td>-g+1\2<br />
</td>
</tr>
<tr>
<td>3L1s<br />
</td>
<td>1\4 < g < 1\3<br />
</td>
<td>1\4 < g < 2\7<br />
</td>
<td>g<br />
</td>
<td>1-3g<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="x5"></a><!-- ws:end:WikiTextHeadingRule:6 -->5</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L4s<br />
</td>
<td>4\5 < g < 1<br />
</td>
<td>4\5 < g < 5\6<br />
</td>
<td>-3+4g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L3s<br />
</td>
<td>2\5 < g < 1\2<br />
</td>
<td>2\5 < g < 3\7<br />
</td>
<td>-1+3g<br />
</td>
<td>-2g+1<br />
</td>
</tr>
<tr>
<td>3L2s<br />
</td>
<td>3\5 < g < 2\3<br />
</td>
<td>3\5 < g < 5\8<br />
</td>
<td>-1+2g<br />
</td>
<td>-3g+2<br />
</td>
</tr>
<tr>
<td>4L1s<br />
</td>
<td>1\5 < g < 1\4<br />
</td>
<td>1\5 < g < 2\9<br />
</td>
<td>g<br />
</td>
<td>-4g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="x6"></a><!-- ws:end:WikiTextHeadingRule:8 -->6</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L5s<br />
</td>
<td>5\6 < g < 1<br />
</td>
<td>5\6 < g < 6\7<br />
</td>
<td>-4+5g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L4s<br />
</td>
<td>1\3 < g < 1\2<br />
</td>
<td>1\3 < g < 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 < g < 1\3<br />
</td>
<td>1\6 < g < 2\9<br />
</td>
<td>g<br />
</td>
<td>-g+1\3<br />
</td>
</tr>
<tr>
<td>4L2s<br />
</td>
<td>1\6 < g < 1\4<br />
</td>
<td>1\6 < g < 1\5<br />
</td>
<td>g<br />
</td>
<td>-2g+1\2<br />
</td>
</tr>
<tr>
<td>5L1s<br />
</td>
<td>1\6 < g < 1\5<br />
</td>
<td>1\6 < g < 2\11<br />
</td>
<td>g<br />
</td>
<td>-5g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:10:<h1> --><h1 id="toc5"><a name="x7"></a><!-- ws:end:WikiTextHeadingRule:10 -->7</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L6s<br />
</td>
<td>6\7 < g < 1<br />
</td>
<td>6\7 < g < 7\8<br />
</td>
<td>-5+6g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L5s<br />
</td>
<td>3\7 < g < 1\2<br />
</td>
<td>3\7 < g < 4\9<br />
</td>
<td>-2+5g<br />
</td>
<td>-2g+1<br />
</td>
</tr>
<tr>
<td>3L4s<br />
</td>
<td>2\7 < g < 1\3<br />
</td>
<td>2\7 < g < 3\10<br />
</td>
<td>-1+4g<br />
</td>
<td>1-3g<br />
</td>
</tr>
<tr>
<td>4L3s<br />
</td>
<td>5\7 < g < 3\4<br />
</td>
<td>5\7 < g < 8\11<br />
</td>
<td>-2+3g<br />
</td>
<td>-4g+3<br />
</td>
</tr>
<tr>
<td>5L2s<br />
</td>
<td>4\7 < g < 3\5<br />
</td>
<td>4\7 < g < 7\12<br />
</td>
<td>-1+2g<br />
</td>
<td>-5g+3<br />
</td>
</tr>
<tr>
<td>6L1s<br />
</td>
<td>1\7 < g < 1\6<br />
</td>
<td>1\7 < g < 2\13<br />
</td>
<td>g<br />
</td>
<td>-6g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:12:<h1> --><h1 id="toc6"><a name="x8"></a><!-- ws:end:WikiTextHeadingRule:12 -->8</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L7s<br />
</td>
<td>7\8 < g < 1<br />
</td>
<td>7\8 < g < 8\9<br />
</td>
<td>-6+7g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L6s<br />
</td>
<td>3\8 < g < 1\2<br />
</td>
<td>3\8 < g < 2\5<br />
</td>
<td>-1+3g<br />
</td>
<td>-g+1\2<br />
</td>
</tr>
<tr>
<td>3L5s<br />
</td>
<td>5\8 < g < 2\3<br />
</td>
<td>5\8 < g < 7\11<br />
</td>
<td>-3+5g<br />
</td>
<td>-3g+2<br />
</td>
</tr>
<tr>
<td>4L4s<br />
</td>
<td>1\8 < g < 1\4<br />
</td>
<td>1\8 < g < 1\6<br />
</td>
<td>g<br />
</td>
<td>-g+1\4<br />
</td>
</tr>
<tr>
<td>5L3s<br />
</td>
<td>3\8 < g < 2\5<br />
</td>
<td>3\8 < g < 5\13<br />
</td>
<td>-1+3g<br />
</td>
<td>-5g+2<br />
</td>
</tr>
<tr>
<td>6L2s<br />
</td>
<td>1\8 < g < 1\6<br />
</td>
<td>1\8 < g < 1\7<br />
</td>
<td>g<br />
</td>
<td>-3g+1\2<br />
</td>
</tr>
<tr>
<td>7L1s<br />
</td>
<td>1\8 < g < 1\7<br />
</td>
<td>1\8 < g < 2\15<br />
</td>
<td>g<br />
</td>
<td>-7g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:14:<h1> --><h1 id="toc7"><a name="x9"></a><!-- ws:end:WikiTextHeadingRule:14 -->9</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L8s<br />
</td>
<td>8\9 < g < 1<br />
</td>
<td>8\9 < g < 9\10<br />
</td>
<td>-7+8g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L7s<br />
</td>
<td>4\9 < g < 1\2<br />
</td>
<td>4\9 < g < 5\11<br />
</td>
<td>-3+7g<br />
</td>
<td>-2g+1<br />
</td>
</tr>
<tr>
<td>3L6s<br />
</td>
<td>2\9 < g < 1\3<br />
</td>
<td>2\9 < g < 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 < g < 1\4<br />
</td>
<td>2\9 < g < 3\13<br />
</td>
<td>-1+5g<br />
</td>
<td>-4g+1<br />
</td>
</tr>
<tr>
<td>5L4s<br />
</td>
<td>7\9 < g < 4\5<br />
</td>
<td>7\9 < g < 11\14<br />
</td>
<td>-3+4g<br />
</td>
<td>-5g+4<br />
</td>
</tr>
<tr>
<td>6L3s<br />
</td>
<td>1\9 < g < 1\6<br />
</td>
<td>1\9 < g < 2\15<br />
</td>
<td>g<br />
</td>
<td>-2g+1\3<br />
</td>
</tr>
<tr>
<td>7L2s<br />
</td>
<td>5\9 < g < 4\7<br />
</td>
<td>5\9 < g < 9\16<br />
</td>
<td>-1+2g<br />
</td>
<td>-7g+4<br />
</td>
</tr>
<tr>
<td>8L1s<br />
</td>
<td>1\9 < g < 1\8<br />
</td>
<td>1\9 < g < 2\17<br />
</td>
<td>g<br />
</td>
<td>-8g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:16:<h1> --><h1 id="toc8"><a name="x10"></a><!-- ws:end:WikiTextHeadingRule:16 -->10</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L9s<br />
</td>
<td>9\10 < g < 1<br />
</td>
<td>9\10 < g < 10\11<br />
</td>
<td>-8+9g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L8s<br />
</td>
<td>2\5 < g < 1\2<br />
</td>
<td>2\5 < g < 3\7<br />
</td>
<td>-3\2+4g<br />
</td>
<td>-g+1\2<br />
</td>
</tr>
<tr>
<td>3L7s<br />
</td>
<td>3\10 < g < 1\3<br />
</td>
<td>3\10 < g < 4\13<br />
</td>
<td>-2+7g<br />
</td>
<td>1-3g<br />
</td>
</tr>
<tr>
<td>4L6s<br />
</td>
<td>1\5 < g < 1\4<br />
</td>
<td>1\5 < g < 2\9<br />
</td>
<td>3g-1\2<br />
</td>
<td>-2g+1\2<br />
</td>
</tr>
<tr>
<td>5L5s<br />
</td>
<td>1\10 < g < 1\5<br />
</td>
<td>1\10 < g < 2\15<br />
</td>
<td>g<br />
</td>
<td>-g+1\5<br />
</td>
</tr>
<tr>
<td>6L4s<br />
</td>
<td>3\10 < g < 1\3<br />
</td>
<td>3\10 < g < 4\13<br />
</td>
<td>-1\2+2g<br />
</td>
<td>1-3g<br />
</td>
</tr>
<tr>
<td>7L3s<br />
</td>
<td>7\10 < g < 5\7<br />
</td>
<td>7\10 < g < 12\17<br />
</td>
<td>-2+3g<br />
</td>
<td>-7g+5<br />
</td>
</tr>
<tr>
<td>8L2s<br />
</td>
<td>1\10 < g < 1\8<br />
</td>
<td>1\10 < g < 1\9<br />
</td>
<td>g<br />
</td>
<td>-4g+1\2<br />
</td>
</tr>
<tr>
<td>9L1s<br />
</td>
<td>1\10 < g < 1\9<br />
</td>
<td>1\10 < g < 2\19<br />
</td>
<td>g<br />
</td>
<td>-9g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:18:<h1> --><h1 id="toc9"><a name="x11"></a><!-- ws:end:WikiTextHeadingRule:18 -->11</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L10s<br />
</td>
<td>10\11 < g < 1<br />
</td>
<td>10\11 < g < 11\12<br />
</td>
<td>-9+10g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L9s<br />
</td>
<td>5\11 < g < 1\2<br />
</td>
<td>5\11 < g < 6\13<br />
</td>
<td>-4+9g<br />
</td>
<td>-2g+1<br />
</td>
</tr>
<tr>
<td>3L8s<br />
</td>
<td>7\11 < g < 2\3<br />
</td>
<td>7\11 < g < 9\14<br />
</td>
<td>-5+8g<br />
</td>
<td>-3g+2<br />
</td>
</tr>
<tr>
<td>4L7s<br />
</td>
<td>8\11 < g < 3\4<br />
</td>
<td>8\11 < g < 11\15<br />
</td>
<td>-5+7g<br />
</td>
<td>-4g+3<br />
</td>
</tr>
<tr>
<td>5L6s<br />
</td>
<td>2\11 < g < 1\5<br />
</td>
<td>2\11 < g < 3\16<br />
</td>
<td>-1+6g<br />
</td>
<td>-5g+1<br />
</td>
</tr>
<tr>
<td>6L5s<br />
</td>
<td>9\11 < g < 5\6<br />
</td>
<td>9\11 < g < 14\17<br />
</td>
<td>-4+5g<br />
</td>
<td>-6g+5<br />
</td>
</tr>
<tr>
<td>7L4s<br />
</td>
<td>3\11 < g < 2\7<br />
</td>
<td>3\11 < g < 5\18<br />
</td>
<td>-1+4g<br />
</td>
<td>-7g+2<br />
</td>
</tr>
<tr>
<td>8L3s<br />
</td>
<td>4\11 < g < 3\8<br />
</td>
<td>4\11 < g < 7\19<br />
</td>
<td>-1+3g<br />
</td>
<td>-8g+3<br />
</td>
</tr>
<tr>
<td>9L2s<br />
</td>
<td>6\11 < g < 5\9<br />
</td>
<td>6\11 < g < 11\20<br />
</td>
<td>-1+2g<br />
</td>
<td>-9g+5<br />
</td>
</tr>
<tr>
<td>10L1s<br />
</td>
<td>1\11 < g < 1\10<br />
</td>
<td>1\11 < g < 2\21<br />
</td>
<td>g<br />
</td>
<td>-10g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:20:<h1> --><h1 id="toc10"><a name="x12"></a><!-- ws:end:WikiTextHeadingRule:20 -->12</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L11s<br />
</td>
<td>11\12 < g < 1<br />
</td>
<td>11\12 < g < 12\13<br />
</td>
<td>-10+11g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L10s<br />
</td>
<td>5\12 < g < 1\2<br />
</td>
<td>5\12 < g < 3\7<br />
</td>
<td>-2+5g<br />
</td>
<td>-g+1\2<br />
</td>
</tr>
<tr>
<td>3L9s<br />
</td>
<td>1\4 < g < 1\3<br />
</td>
<td>1\4 < g < 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 < g < 1\4<br />
</td>
<td>1\6 < g < 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 < g < 3\5<br />
</td>
<td>7\12 < g < 10\17<br />
</td>
<td>-4+7g<br />
</td>
<td>-5g+3<br />
</td>
</tr>
<tr>
<td>6L6s<br />
</td>
<td>1\12 < g < 1\6<br />
</td>
<td>1\12 < g < 1\9<br />
</td>
<td>g<br />
</td>
<td>-g+1\6<br />
</td>
</tr>
<tr>
<td>7L5s<br />
</td>
<td>5\12 < g < 3\7<br />
</td>
<td>5\12 < g < 8\19<br />
</td>
<td>-2+5g<br />
</td>
<td>-7g+3<br />
</td>
</tr>
<tr>
<td>8L4s<br />
</td>
<td>1\12 < g < 1\8<br />
</td>
<td>1\12 < g < 1\10<br />
</td>
<td>g<br />
</td>
<td>-2g+1\4<br />
</td>
</tr>
<tr>
<td>9L3s<br />
</td>
<td>1\12 < g < 1\9<br />
</td>
<td>1\12 < g < 2\21<br />
</td>
<td>g<br />
</td>
<td>-3g+1\3<br />
</td>
</tr>
<tr>
<td>10L2s<br />
</td>
<td>1\12 < g < 1\10<br />
</td>
<td>1\12 < g < 1\11<br />
</td>
<td>g<br />
</td>
<td>-5g+1\2<br />
</td>
</tr>
<tr>
<td>11L1s<br />
</td>
<td>1\12 < g < 1\11<br />
</td>
<td>1\12 < g < 2\23<br />
</td>
<td>g<br />
</td>
<td>-11g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:22:<h1> --><h1 id="toc11"><a name="x13"></a><!-- ws:end:WikiTextHeadingRule:22 -->13</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L12s<br />
</td>
<td>12\13 < g < 1<br />
</td>
<td>12\13 < g < 13\14<br />
</td>
<td>-11+12g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L11s<br />
</td>
<td>6\13 < g < 1\2<br />
</td>
<td>6\13 < g < 7\15<br />
</td>
<td>-5+11g<br />
</td>
<td>-2g+1<br />
</td>
</tr>
<tr>
<td>3L10s<br />
</td>
<td>4\13 < g < 1\3<br />
</td>
<td>4\13 < g < 5\16<br />
</td>
<td>-3+10g<br />
</td>
<td>1-3g<br />
</td>
</tr>
<tr>
<td>4L9s<br />
</td>
<td>3\13 < g < 1\4<br />
</td>
<td>3\13 < g < 4\17<br />
</td>
<td>-2+9g<br />
</td>
<td>-4g+1<br />
</td>
</tr>
<tr>
<td>5L8s<br />
</td>
<td>5\13 < g < 2\5<br />
</td>
<td>5\13 < g < 7\18<br />
</td>
<td>-3+8g<br />
</td>
<td>-5g+2<br />
</td>
</tr>
<tr>
<td>6L7s<br />
</td>
<td>2\13 < g < 1\6<br />
</td>
<td>2\13 < g < 3\19<br />
</td>
<td>-1+7g<br />
</td>
<td>-6g+1<br />
</td>
</tr>
<tr>
<td>7L6s<br />
</td>
<td>11\13 < g < 6\7<br />
</td>
<td>11\13 < g < 17\20<br />
</td>
<td>-5+6g<br />
</td>
<td>-7g+6<br />
</td>
</tr>
<tr>
<td>8L5s<br />
</td>
<td>8\13 < g < 5\8<br />
</td>
<td>8\13 < g < 13\21<br />
</td>
<td>-3+5g<br />
</td>
<td>-8g+5<br />
</td>
</tr>
<tr>
<td>9L4s<br />
</td>
<td>10\13 < g < 7\9<br />
</td>
<td>10\13 < g < 17\22<br />
</td>
<td>-3+4g<br />
</td>
<td>-9g+7<br />
</td>
</tr>
<tr>
<td>10L3s<br />
</td>
<td>9\13 < g < 7\10<br />
</td>
<td>9\13 < g < 16\23<br />
</td>
<td>-2+3g<br />
</td>
<td>-10g+7<br />
</td>
</tr>
<tr>
<td>11L2s<br />
</td>
<td>7\13 < g < 6\11<br />
</td>
<td>7\13 < g < 13\24<br />
</td>
<td>-1+2g<br />
</td>
<td>-11g+6<br />
</td>
</tr>
<tr>
<td>12L1s<br />
</td>
<td>1\13 < g < 1\12<br />
</td>
<td>1\13 < g < 2\25<br />
</td>
<td>g<br />
</td>
<td>-12g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:24:<h1> --><h1 id="toc12"><a name="x14"></a><!-- ws:end:WikiTextHeadingRule:24 -->14</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L13s<br />
</td>
<td>13\14 < g < 1<br />
</td>
<td>13\14 < g < 14\15<br />
</td>
<td>-12+13g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L12s<br />
</td>
<td>3\7 < g < 1\2<br />
</td>
<td>3\7 < g < 4\9<br />
</td>
<td>-5\2+6g<br />
</td>
<td>-g+1\2<br />
</td>
</tr>
<tr>
<td>3L11s<br />
</td>
<td>9\14 < g < 2\3<br />
</td>
<td>9\14 < g < 11\17<br />
</td>
<td>-7+11g<br />
</td>
<td>-3g+2<br />
</td>
</tr>
<tr>
<td>4L10s<br />
</td>
<td>3\14 < g < 1\4<br />
</td>
<td>3\14 < g < 2\9<br />
</td>
<td>-1+5g<br />
</td>
<td>-2g+1\2<br />
</td>
</tr>
<tr>
<td>5L9s<br />
</td>
<td>11\14 < g < 4\5<br />
</td>
<td>11\14 < g < 15\19<br />
</td>
<td>-7+9g<br />
</td>
<td>-5g+4<br />
</td>
</tr>
<tr>
<td>6L8s<br />
</td>
<td>1\7 < g < 1\6<br />
</td>
<td>1\7 < g < 2\13<br />
</td>
<td>4g-1\2<br />
</td>
<td>-3g+1\2<br />
</td>
</tr>
<tr>
<td>7L7s<br />
</td>
<td>1\14 < g < 1\7<br />
</td>
<td>1\14 < g < 2\21<br />
</td>
<td>g<br />
</td>
<td>-g+1\7<br />
</td>
</tr>
<tr>
<td>8L6s<br />
</td>
<td>5\14 < g < 3\8<br />
</td>
<td>5\14 < g < 4\11<br />
</td>
<td>-1+3g<br />
</td>
<td>-4g+3\2<br />
</td>
</tr>
<tr>
<td>9L5s<br />
</td>
<td>3\14 < g < 2\9<br />
</td>
<td>3\14 < g < 5\23<br />
</td>
<td>-1+5g<br />
</td>
<td>-9g+2<br />
</td>
</tr>
<tr>
<td>10L4s<br />
</td>
<td>2\7 < g < 3\10<br />
</td>
<td>2\7 < g < 5\17<br />
</td>
<td>-1\2+2g<br />
</td>
<td>-5g+3\2<br />
</td>
</tr>
<tr>
<td>11L3s<br />
</td>
<td>5\14 < g < 4\11<br />
</td>
<td>5\14 < g < 9\25<br />
</td>
<td>-1+3g<br />
</td>
<td>-11g+4<br />
</td>
</tr>
<tr>
<td>12L2s<br />
</td>
<td>1\14 < g < 1\12<br />
</td>
<td>1\14 < g < 1\13<br />
</td>
<td>g<br />
</td>
<td>-6g+1\2<br />
</td>
</tr>
<tr>
<td>13L1s<br />
</td>
<td>1\14 < g < 1\13<br />
</td>
<td>1\14 < g < 2\27<br />
</td>
<td>g<br />
</td>
<td>-13g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:26:<h1> --><h1 id="toc13"><a name="x15"></a><!-- ws:end:WikiTextHeadingRule:26 -->15</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L14s<br />
</td>
<td>14\15 < g < 1<br />
</td>
<td>14\15 < g < 15\16<br />
</td>
<td>-13+14g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L13s<br />
</td>
<td>7\15 < g < 1\2<br />
</td>
<td>7\15 < g < 8\17<br />
</td>
<td>-6+13g<br />
</td>
<td>-2g+1<br />
</td>
</tr>
<tr>
<td>3L12s<br />
</td>
<td>4\15 < g < 1\3<br />
</td>
<td>4\15 < g < 5\18<br />
</td>
<td>-1+4g<br />
</td>
<td>-g+1\3<br />
</td>
</tr>
<tr>
<td>4L11s<br />
</td>
<td>11\15 < g < 3\4<br />
</td>
<td>11\15 < g < 14\19<br />
</td>
<td>-8+11g<br />
</td>
<td>-4g+3<br />
</td>
</tr>
<tr>
<td>5L10s<br />
</td>
<td>2\15 < g < 1\5<br />
</td>
<td>2\15 < g < 3\20<br />
</td>
<td>-1\5+2g<br />
</td>
<td>-g+1\5<br />
</td>
</tr>
<tr>
<td>6L9s<br />
</td>
<td>2\15 < g < 1\6<br />
</td>
<td>2\15 < g < 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 < g < 1\7<br />
</td>
<td>2\15 < g < 3\22<br />
</td>
<td>-1+8g<br />
</td>
<td>-7g+1<br />
</td>
</tr>
<tr>
<td>8L7s<br />
</td>
<td>13\15 < g < 7\8<br />
</td>
<td>13\15 < g < 20\23<br />
</td>
<td>-6+7g<br />
</td>
<td>-8g+7<br />
</td>
</tr>
<tr>
<td>9L6s<br />
</td>
<td>1\5 < g < 2\9<br />
</td>
<td>1\5 < g < 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 < g < 1\10<br />
</td>
<td>1\15 < g < 2\25<br />
</td>
<td>g<br />
</td>
<td>-2g+1\5<br />
</td>
</tr>
<tr>
<td>11L4s<br />
</td>
<td>4\15 < g < 3\11<br />
</td>
<td>4\15 < g < 7\26<br />
</td>
<td>-1+4g<br />
</td>
<td>-11g+3<br />
</td>
</tr>
<tr>
<td>12L3s<br />
</td>
<td>1\15 < g < 1\12<br />
</td>
<td>1\15 < g < 2\27<br />
</td>
<td>g<br />
</td>
<td>-4g+1\3<br />
</td>
</tr>
<tr>
<td>13L2s<br />
</td>
<td>8\15 < g < 7\13<br />
</td>
<td>8\15 < g < 15\28<br />
</td>
<td>-1+2g<br />
</td>
<td>-13g+7<br />
</td>
</tr>
<tr>
<td>14L1s<br />
</td>
<td>1\15 < g < 1\14<br />
</td>
<td>1\15 < g < 2\29<br />
</td>
<td>g<br />
</td>
<td>-14g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:28:<h1> --><h1 id="toc14"><a name="x16"></a><!-- ws:end:WikiTextHeadingRule:28 -->16</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L15s<br />
</td>
<td>15\16 < g < 1<br />
</td>
<td>15\16 < g < 16\17<br />
</td>
<td>-14+15g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L14s<br />
</td>
<td>7\16 < g < 1\2<br />
</td>
<td>7\16 < g < 4\9<br />
</td>
<td>-3+7g<br />
</td>
<td>-g+1\2<br />
</td>
</tr>
<tr>
<td>3L13s<br />
</td>
<td>5\16 < g < 1\3<br />
</td>
<td>5\16 < g < 6\19<br />
</td>
<td>-4+13g<br />
</td>
<td>1-3g<br />
</td>
</tr>
<tr>
<td>4L12s<br />
</td>
<td>3\16 < g < 1\4<br />
</td>
<td>3\16 < g < 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 < g < 1\5<br />
</td>
<td>3\16 < g < 4\21<br />
</td>
<td>-2+11g<br />
</td>
<td>-5g+1<br />
</td>
</tr>
<tr>
<td>6L10s<br />
</td>
<td>5\16 < g < 1\3<br />
</td>
<td>5\16 < g < 6\19<br />
</td>
<td>-3\2+5g<br />
</td>
<td>1-3g<br />
</td>
</tr>
<tr>
<td>7L9s<br />
</td>
<td>9\16 < g < 4\7<br />
</td>
<td>9\16 < g < 13\23<br />
</td>
<td>-5+9g<br />
</td>
<td>-7g+4<br />
</td>
</tr>
<tr>
<td>8L8s<br />
</td>
<td>1\16 < g < 1\8<br />
</td>
<td>1\16 < g < 1\12<br />
</td>
<td>g<br />
</td>
<td>-g+1\8<br />
</td>
</tr>
<tr>
<td>9L7s<br />
</td>
<td>7\16 < g < 4\9<br />
</td>
<td>7\16 < g < 11\25<br />
</td>
<td>-3+7g<br />
</td>
<td>-9g+4<br />
</td>
</tr>
<tr>
<td>10L6s<br />
</td>
<td>3\16 < g < 1\5<br />
</td>
<td>3\16 < g < 4\21<br />
</td>
<td>3g-1\2<br />
</td>
<td>-5g+1<br />
</td>
</tr>
<tr>
<td>11L5s<br />
</td>
<td>13\16 < g < 9\11<br />
</td>
<td>13\16 < g < 22\27<br />
</td>
<td>-4+5g<br />
</td>
<td>-11g+9<br />
</td>
</tr>
<tr>
<td>12L4s<br />
</td>
<td>1\16 < g < 1\12<br />
</td>
<td>1\16 < g < 1\14<br />
</td>
<td>g<br />
</td>
<td>-3g+1\4<br />
</td>
</tr>
<tr>
<td>13L3s<br />
</td>
<td>11\16 < g < 9\13<br />
</td>
<td>11\16 < g < 20\29<br />
</td>
<td>-2+3g<br />
</td>
<td>-13g+9<br />
</td>
</tr>
<tr>
<td>14L2s<br />
</td>
<td>1\16 < g < 1\14<br />
</td>
<td>1\16 < g < 1\15<br />
</td>
<td>g<br />
</td>
<td>-7g+1\2<br />
</td>
</tr>
<tr>
<td>15L1s<br />
</td>
<td>1\16 < g < 1\15<br />
</td>
<td>1\16 < g < 2\31<br />
</td>
<td>g<br />
</td>
<td>-15g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:30:<h1> --><h1 id="toc15"><a name="x17"></a><!-- ws:end:WikiTextHeadingRule:30 -->17</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L16s<br />
</td>
<td>16\17 < g < 1<br />
</td>
<td>16\17 < g < 17\18<br />
</td>
<td>-15+16g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L15s<br />
</td>
<td>8\17 < g < 1\2<br />
</td>
<td>8\17 < g < 9\19<br />
</td>
<td>-7+15g<br />
</td>
<td>-2g+1<br />
</td>
</tr>
<tr>
<td>3L14s<br />
</td>
<td>11\17 < g < 2\3<br />
</td>
<td>11\17 < g < 13\20<br />
</td>
<td>-9+14g<br />
</td>
<td>-3g+2<br />
</td>
</tr>
<tr>
<td>4L13s<br />
</td>
<td>4\17 < g < 1\4<br />
</td>
<td>4\17 < g < 5\21<br />
</td>
<td>-3+13g<br />
</td>
<td>-4g+1<br />
</td>
</tr>
<tr>
<td>5L12s<br />
</td>
<td>10\17 < g < 3\5<br />
</td>
<td>10\17 < g < 13\22<br />
</td>
<td>-7+12g<br />
</td>
<td>-5g+3<br />
</td>
</tr>
<tr>
<td>6L11s<br />
</td>
<td>14\17 < g < 5\6<br />
</td>
<td>14\17 < g < 19\23<br />
</td>
<td>-9+11g<br />
</td>
<td>-6g+5<br />
</td>
</tr>
<tr>
<td>7L10s<br />
</td>
<td>12\17 < g < 5\7<br />
</td>
<td>12\17 < g < 17\24<br />
</td>
<td>-7+10g<br />
</td>
<td>-7g+5<br />
</td>
</tr>
<tr>
<td>8L9s<br />
</td>
<td>2\17 < g < 1\8<br />
</td>
<td>2\17 < g < 3\25<br />
</td>
<td>-1+9g<br />
</td>
<td>-8g+1<br />
</td>
</tr>
<tr>
<td>9L8s<br />
</td>
<td>15\17 < g < 8\9<br />
</td>
<td>15\17 < g < 23\26<br />
</td>
<td>-7+8g<br />
</td>
<td>-9g+8<br />
</td>
</tr>
<tr>
<td>10L7s<br />
</td>
<td>5\17 < g < 3\10<br />
</td>
<td>5\17 < g < 8\27<br />
</td>
<td>-2+7g<br />
</td>
<td>-10g+3<br />
</td>
</tr>
<tr>
<td>11L6s<br />
</td>
<td>3\17 < g < 2\11<br />
</td>
<td>3\17 < g < 5\28<br />
</td>
<td>-1+6g<br />
</td>
<td>-11g+2<br />
</td>
</tr>
<tr>
<td>12L5s<br />
</td>
<td>7\17 < g < 5\12<br />
</td>
<td>7\17 < g < 12\29<br />
</td>
<td>-2+5g<br />
</td>
<td>-12g+5<br />
</td>
</tr>
<tr>
<td>13L4s<br />
</td>
<td>13\17 < g < 10\13<br />
</td>
<td>13\17 < g <23\30<br />
</td>
<td>-3+4g<br />
</td>
<td>-13g+10<br />
</td>
</tr>
<tr>
<td>14L3s<br />
</td>
<td>6\17 < g < 5\14<br />
</td>
<td>6\17 < g < 11\31<br />
</td>
<td>-1+3g<br />
</td>
<td>-14g+5<br />
</td>
</tr>
<tr>
<td>15L2s<br />
</td>
<td>9\17 < g < 8\15<br />
</td>
<td>9\17 < g < 17\32<br />
</td>
<td>-1+2g<br />
</td>
<td>-15g+8<br />
</td>
</tr>
<tr>
<td>16L1s<br />
</td>
<td>1\17 < g < 1\16<br />
</td>
<td>1\17 < g < 2\33<br />
</td>
<td>g<br />
</td>
<td>-16g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:32:<h1> --><h1 id="toc16"><a name="x18"></a><!-- ws:end:WikiTextHeadingRule:32 -->18</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L17s<br />
</td>
<td>17\18 < g < 1<br />
</td>
<td>17\18 < g < 18\19<br />
</td>
<td>-16+17g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L16s<br />
</td>
<td>4\9 < g < 1\2<br />
</td>
<td>4\9 < g < 5\11<br />
</td>
<td>-7\2+8g<br />
</td>
<td>-g+1\2<br />
</td>
</tr>
<tr>
<td>3L15s<br />
</td>
<td>5\18 < g < 1\3<br />
</td>
<td>5\18 < g < 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 < g < 1\4<br />
</td>
<td>2\9 < g < 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 < g < 2\5<br />
</td>
<td>7\18 < g < 9\23<br />
</td>
<td>-5+13g<br />
</td>
<td>-5g+2<br />
</td>
</tr>
<tr>
<td>6L12s<br />
</td>
<td>1\9 < g < 1\6<br />
</td>
<td>1\9 < g < 2\15<br />
</td>
<td>-1\6+2g<br />
</td>
<td>-g+1\6<br />
</td>
</tr>
<tr>
<td>7L11s<br />
</td>
<td>5\18 < g < 2\7<br />
</td>
<td>5\18 < g < 7\25<br />
</td>
<td>-3+11g<br />
</td>
<td>-7g+2<br />
</td>
</tr>
<tr>
<td>8L10s<br />
</td>
<td>1\9 < g < 1\8<br />
</td>
<td>1\9 < g < 2\17<br />
</td>
<td>-1\2+5g<br />
</td>
<td>-4g+1\2<br />
</td>
</tr>
<tr>
<td>9L9s<br />
</td>
<td>1\18 < g < 1\9<br />
</td>
<td>1\18 < g < 2\27<br />
</td>
<td>g<br />
</td>
<td>-g+1\9<br />
</td>
</tr>
<tr>
<td>10L8s<br />
</td>
<td>7\18 < g < 2\5<br />
</td>
<td>7\18 < g < 9\23<br />
</td>
<td>-3\2+4g<br />
</td>
<td>-5g+2<br />
</td>
</tr>
<tr>
<td>11L7s<br />
</td>
<td>13\18 < g < 8\11<br />
</td>
<td>13\18 < g < 21\29<br />
</td>
<td>-5+7g<br />
</td>
<td>-11g+8<br />
</td>
</tr>
<tr>
<td>12L6s<br />
</td>
<td>1\18 < g < 1\12<br />
</td>
<td>1\18 < g < 1\15<br />
</td>
<td>g<br />
</td>
<td>-2g+1\6<br />
</td>
</tr>
<tr>
<td>13L5s<br />
</td>
<td>11\18 < g < 8\13<br />
</td>
<td>11\18 < g < 19\31<br />
</td>
<td>-3+5g<br />
</td>
<td>-13g+8<br />
</td>
</tr>
<tr>
<td>14L4s<br />
</td>
<td>5\18 < g < 2\7<br />
</td>
<td>5\18 < g < 7\25<br />
</td>
<td>-1\2+2g<br />
</td>
<td>-7g+2<br />
</td>
</tr>
<tr>
<td>15L3s<br />
</td>
<td>1\18 < g < 1\15<br />
</td>
<td>1\18 < g < 2\33<br />
</td>
<td>g<br />
</td>
<td>-5g+1\3<br />
</td>
</tr>
<tr>
<td>16L2s<br />
</td>
<td>1\18 < g < 1\16<br />
</td>
<td>1\18 < g < 1\17<br />
</td>
<td>g<br />
</td>
<td>-8g+1\2<br />
</td>
</tr>
<tr>
<td>17L1s<br />
</td>
<td>1\18 < g < 1\17<br />
</td>
<td>1\18 < g < 2\35<br />
</td>
<td>g<br />
</td>
<td>-17g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:34:<h1> --><h1 id="toc17"><a name="x19"></a><!-- ws:end:WikiTextHeadingRule:34 -->19</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L18s<br />
</td>
<td>18\19 < g < 1<br />
</td>
<td>18\19 < g < 19\20<br />
</td>
<td>-17+18g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L17s<br />
</td>
<td>9\19 < g < 1\2<br />
</td>
<td>9\19 < g < 10\21<br />
</td>
<td>-8+17g<br />
</td>
<td>-2g+1<br />
</td>
</tr>
<tr>
<td>3L16s<br />
</td>
<td>6\19 < g < 1\3<br />
</td>
<td>6\19 < g < 7\22<br />
</td>
<td>-5+16g<br />
</td>
<td>1-3g<br />
</td>
</tr>
<tr>
<td>4L15s<br />
</td>
<td>14\19 < g < 3\4<br />
</td>
<td>14\19 < g < 17\23<br />
</td>
<td>-11+15g<br />
</td>
<td>-4g+3<br />
</td>
</tr>
<tr>
<td>5L14s<br />
</td>
<td>15\19 < g < 4\5<br />
</td>
<td>15\19 < g < 19\24<br />
</td>
<td>-11+14g<br />
</td>
<td>-5g+4<br />
</td>
</tr>
<tr>
<td>6L13s<br />
</td>
<td>3\19 < g < 1\6<br />
</td>
<td>3\19 < g < 4\25<br />
</td>
<td>-2+13g<br />
</td>
<td>-6g+1<br />
</td>
</tr>
<tr>
<td>7L12s<br />
</td>
<td>8\19 < g < 3\7<br />
</td>
<td>8\19 < g < 11\26<br />
</td>
<td>-5+12g<br />
</td>
<td>-7g+3<br />
</td>
</tr>
<tr>
<td>8L11s<br />
</td>
<td>7\19 < g < 3\8<br />
</td>
<td>7\19 < g < 10\27<br />
</td>
<td>-4+11g<br />
</td>
<td>-8g+3<br />
</td>
</tr>
<tr>
<td>9L10s<br />
</td>
<td>2\19 < g < 1\9<br />
</td>
<td>2\19 < g < 3\28<br />
</td>
<td>-1+10g<br />
</td>
<td>-9g+1<br />
</td>
</tr>
<tr>
<td>10L9s<br />
</td>
<td>17\19 < g < 9\10<br />
</td>
<td>17\19 < g < 26\29<br />
</td>
<td>-8+9g<br />
</td>
<td>-10g+9<br />
</td>
</tr>
<tr>
<td>11L8s<br />
</td>
<td>12\19 < g < 7\11<br />
</td>
<td>12\19 < g < 19\30<br />
</td>
<td>-5+8g<br />
</td>
<td>-11g+7<br />
</td>
</tr>
<tr>
<td>12L7s<br />
</td>
<td>11\19 < g < 7\12<br />
</td>
<td>11\19 < g < 18\31<br />
</td>
<td>-4+7g<br />
</td>
<td>-12g+7<br />
</td>
</tr>
<tr>
<td>13L6s<br />
</td>
<td>16\19 < g < 11\13<br />
</td>
<td>16\19 < g < 27\32<br />
</td>
<td>-5+6g<br />
</td>
<td>-13g+11<br />
</td>
</tr>
<tr>
<td>14L5s<br />
</td>
<td>4\19 < g < 3\14<br />
</td>
<td>4\19 < g < 7\33<br />
</td>
<td>-1+5g<br />
</td>
<td>-14g+3<br />
</td>
</tr>
<tr>
<td>15L4s<br />
</td>
<td>5\19 < g < 4\15<br />
</td>
<td>5\19 < g < 9\34<br />
</td>
<td>-1+4g<br />
</td>
<td>-15g+4<br />
</td>
</tr>
<tr>
<td>16L3s<br />
</td>
<td>13\19 < g < 11\16<br />
</td>
<td>13\19 < g < 24\35<br />
</td>
<td>-2+3g<br />
</td>
<td>-16g+11<br />
</td>
</tr>
<tr>
<td>17L2s<br />
</td>
<td>10\19 < g < 9\17<br />
</td>
<td>10\19 < g < 19\36<br />
</td>
<td>-1+2g<br />
</td>
<td>-17g+9<br />
</td>
</tr>
<tr>
<td>18L1s<br />
</td>
<td>1\19 < g < 1\18<br />
</td>
<td>1\19 < g < 2\37<br />
</td>
<td>g<br />
</td>
<td>-18g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:36:<h1> --><h1 id="toc18"><a name="x20"></a><!-- ws:end:WikiTextHeadingRule:36 -->20</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L19s<br />
</td>
<td>19\20 < g < 1<br />
</td>
<td>19\20 < g < 20\21<br />
</td>
<td>-18+19g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L18s<br />
</td>
<td>9\20 < g < 1\2<br />
</td>
<td>9\20 < g < 5\11<br />
</td>
<td>-4+9g<br />
</td>
<td>-g+1\2<br />
</td>
</tr>
<tr>
<td>3L17s<br />
</td>
<td>13\20 < g < 2\3<br />
</td>
<td>13\20 < g < 15\23<br />
</td>
<td>-11+17g<br />
</td>
<td>-3g+2<br />
</td>
</tr>
<tr>
<td>4L16s<br />
</td>
<td>1\5 < g < 1\4<br />
</td>
<td>1\5 < g < 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 < g < 1\5<br />
</td>
<td>3\20 < g < 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 < g < 1\6<br />
</td>
<td>3\20 < g < 2\13<br />
</td>
<td>-1+7g<br />
</td>
<td>-3g+1\2<br />
</td>
</tr>
<tr>
<td>7L13s<br />
</td>
<td>17\20 < g < 6\7<br />
</td>
<td>17\20 < g < 23\27<br />
</td>
<td>-11+13g<br />
</td>
<td>-7g+6<br />
</td>
</tr>
<tr>
<td>8L12s<br />
</td>
<td>1\10 < g < 1\8<br />
</td>
<td>1\10 < g < 1\9<br />
</td>
<td>-1\4+3g<br />
</td>
<td>-2g+1\4<br />
</td>
</tr>
<tr>
<td>9L11s<br />
</td>
<td>11\20 < g < 5\9<br />
</td>
<td>11\20 < g < 16\29<br />
</td>
<td>-6+11g<br />
</td>
<td>-9g+5<br />
</td>
</tr>
<tr>
<td>10L10s<br />
</td>
<td>1\20 < g < 1\10<br />
</td>
<td>1\20 < g < 1\15<br />
</td>
<td>g<br />
</td>
<td>-g+1\10<br />
</td>
</tr>
<tr>
<td>11L9s<br />
</td>
<td>9\20 < g < 5\11<br />
</td>
<td>9\20 < g < 14\31<br />
</td>
<td>-4+9g<br />
</td>
<td>-11g+5<br />
</td>
</tr>
<tr>
<td>12L8s<br />
</td>
<td>3\20 < g < 1\6<br />
</td>
<td>3\20 < g < 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 < g < 2\13<br />
</td>
<td>3\20 < g < 5\33<br />
</td>
<td>-1+7g<br />
</td>
<td>-13g+2<br />
</td>
</tr>
<tr>
<td>14L6s<br />
</td>
<td>7\20 < g < 5\14<br />
</td>
<td>7\20 < g < 6\17<br />
</td>
<td>-1+3g<br />
</td>
<td>-7g+5\2<br />
</td>
</tr>
<tr>
<td>15L5s<br />
</td>
<td>1\20 < g < 1\15<br />
</td>
<td>1\20 < g < 2\35<br />
</td>
<td>g<br />
</td>
<td>-3g+1\5<br />
</td>
</tr>
<tr>
<td>16L4s<br />
</td>
<td>1\20 < g < 1\16<br />
</td>
<td>1\20 < g < 1\18<br />
</td>
<td>g<br />
</td>
<td>-4g+1\4<br />
</td>
</tr>
<tr>
<td>17L3s<br />
</td>
<td>7\20 < g < 6\17<br />
</td>
<td>7\20 < g < 13\37<br />
</td>
<td>-1+3g<br />
</td>
<td>-17g+6<br />
</td>
</tr>
<tr>
<td>18L2s<br />
</td>
<td>1\20 < g < 1\18<br />
</td>
<td>1\20 < g < 1\19<br />
</td>
<td>g<br />
</td>
<td>-9g+1\2<br />
</td>
</tr>
<tr>
<td>19L1s<br />
</td>
<td>1\20 < g < 1\19<br />
</td>
<td>1\20 < g < 2\39<br />
</td>
<td>g<br />
</td>
<td>-19g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:38:<h1> --><h1 id="toc19"><a name="x21"></a><!-- ws:end:WikiTextHeadingRule:38 -->21</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L20s<br />
</td>
<td>20\21 < g < 1<br />
</td>
<td>20\21 < g < 21\22<br />
</td>
<td>-19+20g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L19s<br />
</td>
<td>10\21 < g < 1\2<br />
</td>
<td>10\21 < g < 11\23<br />
</td>
<td>-9+19g<br />
</td>
<td>-2g+1<br />
</td>
</tr>
<tr>
<td>3L18s<br />
</td>
<td>2\7 < g < 1\3<br />
</td>
<td>2\7 < g < 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 < g < 1\4<br />
</td>
<td>5\21 < g < 6\25<br />
</td>
<td>-4+17g<br />
</td>
<td>-4g+1<br />
</td>
</tr>
<tr>
<td>5L16s<br />
</td>
<td>4\21 < g < 1\5<br />
</td>
<td>4\21 < g < 5\26<br />
</td>
<td>-3+16g<br />
</td>
<td>-5g+1<br />
</td>
</tr>
<tr>
<td>6L15s<br />
</td>
<td>1\7 < g < 1\6<br />
</td>
<td>1\7 < g < 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 < g < 1\7<br />
</td>
<td>2\21 < g < 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 < g < 5\8<br />
</td>
<td>13\21 < g < 18\29<br />
</td>
<td>-8+13g<br />
</td>
<td>-8g+5<br />
</td>
</tr>
<tr>
<td>9L12s<br />
</td>
<td>2\21 < g < 1\9<br />
</td>
<td>2\21 < g < 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 < g < 1\10<br />
</td>
<td>2\21 < g < 3\31<br />
</td>
<td>-1+11g<br />
</td>
<td>-10g+1<br />
</td>
</tr>
<tr>
<td>11L10s<br />
</td>
<td>19\21 < g < 10\11<br />
</td>
<td>19\21 < g < 29\32<br />
</td>
<td>-9+10g<br />
</td>
<td>-11g+10<br />
</td>
</tr>
<tr>
<td>12L9s<br />
</td>
<td>5\21 < g < 1\4<br />
</td>
<td>5\21 < g < 6\25<br />
</td>
<td>-2\3+3g<br />
</td>
<td>-4g+1<br />
</td>
</tr>
<tr>
<td>13L8s<br />
</td>
<td>8\21 < g < 5\13<br />
</td>
<td>8\21 < g < 13\34<br />
</td>
<td>-3+8g<br />
</td>
<td>-13g+5<br />
</td>
</tr>
<tr>
<td>14L7s<br />
</td>
<td>1\21 < g < 1\14<br />
</td>
<td>1\21 < g < 2\35<br />
</td>
<td>g<br />
</td>
<td>-2g+1\7<br />
</td>
</tr>
<tr>
<td>15L6s<br />
</td>
<td>4\21 < g < 1\5<br />
</td>
<td>4\21 < g < 5\26<br />
</td>
<td>-1\3+2g<br />
</td>
<td>-5g+1<br />
</td>
</tr>
<tr>
<td>16L5s<br />
</td>
<td>17\21 < g < 13\16<br />
</td>
<td>17\21 < g < 30\37<br />
</td>
<td>-4+5g<br />
</td>
<td>-16g+13<br />
</td>
</tr>
<tr>
<td>17L4s<br />
</td>
<td>16\21 < g < 13\17<br />
</td>
<td>16\21 < g < 29\38<br />
</td>
<td>-3+4g<br />
</td>
<td>-17g+13<br />
</td>
</tr>
<tr>
<td>18L3s<br />
</td>
<td>1\21 < g < 1\18<br />
</td>
<td>1\21 < g < 2\39<br />
</td>
<td>g<br />
</td>
<td>-6g+1\3<br />
</td>
</tr>
<tr>
<td>19L2s<br />
</td>
<td>11\21 < g < 10\19<br />
</td>
<td>11\21 < g < 21\40<br />
</td>
<td>-1+2g<br />
</td>
<td>-19g+10<br />
</td>
</tr>
<tr>
<td>20L1s<br />
</td>
<td>1\21 < g < 1\20<br />
</td>
<td>1\21 < g < 2\41<br />
</td>
<td>g<br />
</td>
<td>-20g+1<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:40:<h1> --><h1 id="toc20"><a name="x22"></a><!-- ws:end:WikiTextHeadingRule:40 -->22</h1>
<table class="wiki_table">
<tr>
<td>Large-small numbers<br />
</td>
<td>Generator range<br />
</td>
<td>Range of propriety<br />
</td>
<td>Large step<br />
</td>
<td>Small step<br />
</td>
</tr>
<tr>
<td>1L21s<br />
</td>
<td>21\22 < g < 1<br />
</td>
<td>21\22 < g < 22\23<br />
</td>
<td>-20+21g<br />
</td>
<td>-g+1<br />
</td>
</tr>
<tr>
<td>2L20s<br />
</td>
<td>5\11 < g < 1\2<br />
</td>
<td>5\11 < g < 6\13<br />
</td>
<td>-9\2+10g<br />
</td>
<td>-g+1\2<br />
</td>
</tr>
<tr>
<td>3L19s<br />
</td>
<td>7\22 < g < 1\3<br />
</td>
<td>7\22 < g < 8\25<br />
</td>
<td>-6+19g<br />
</td>
<td>1-3g<br />
</td>
</tr>
<tr>
<td>4L18s<br />
</td>
<td>5\22 < g < 1\4<br />
</td>
<td>5\22 < g < 3\13<br />
</td>
<td>-2+9g<br />
</td>
<td>-2g+1\2<br />
</td>
</tr>
<tr>
<td>5L17s<br />
</td>
<td>13\22 < g < 3\5<br />
</td>
<td>13\22 < g < 16\27<br />
</td>
<td>-10+17g<br />
</td>
<td>-5g+3<br />
</td>
</tr>
<tr>
<td>6L16s<br />
</td>
<td>7\22 < g < 1\3<br />
</td>
<td>7\22 < g < 8\25<br />
</td>
<td>-5\2+8g<br />
</td>
<td>1-3g<br />
</td>
</tr>
<tr>
<td>7L15s<br />
</td>
<td>3\22 < g < 1\7<br />
</td>
<td>3\22 < g < 4\29<br />
</td>
<td>-2+15g<br />
</td>
<td>-7g+1<br />
</td>
</tr>
<tr>
<td>8L14s<br />
</td>
<td>4\11 < g < 3\8<br />
</td>
<td>4\11 < g < 7\19<br />
</td>
<td>-5\2+7g<br />
</td>
<td>-4g+3\2<br />
</td>
</tr>
<tr>
<td>9L13s<br />
</td>
<td>17\22 < g < 7\9<br />
</td>
<td>17\22 < g < 24\31<br />
</td>
<td>-10+13g<br />
</td>
<td>-9g+7<br />
</td>
</tr>
<tr>
<td>10L12s<br />
</td>
<td>1\11 < g < 1\10<br />
</td>
<td>1\11 < g < 2\21<br />
</td>
<td>-1\2+6g<br />
</td>
<td>-5g+1\2<br />
</td>
</tr>
<tr>
<td>11L11s<br />
</td>
<td>1\22 < g < 1\11<br />
</td>
<td>1\22 < g < 2\33<br />
</td>
<td>g<br />
</td>
<td>-g+1\11<br />
</td>
</tr>
<tr>
<td>12L10s<br />
</td>
<td>9\22 < g < 5\12<br />
</td>
<td>9\22 < g < 7\17<br />
</td>
<td>-2+5g<br />
</td>
<td>-6g+5\2<br />
</td>
</tr>
<tr>
<td>13L9s<br />
</td>
<td>5\22 < g < 3\13<br />
</td>
<td>5\22 < g < 8\35<br />
</td>
<td>-2+9g<br />
</td>
<td>-13g+3<br />
</td>
</tr>
<tr>
<td>14L8s<br />
</td>
<td>3\22 < g < 1\7<br />
</td>
<td>3\22 < g < 4\29<br />
</td>
<td>4g-1\2<br />
</td>
<td>-7g+1<br />
</td>
</tr>
<tr>
<td>15L7s<br />
</td>
<td>19\22 < g < 13\15<br />
</td>
<td>19\22 < g < 32\37<br />
</td>
<td>-6+7g<br />
</td>
<td>-15g+13<br />
</td>
</tr>
<tr>
<td>16L6s<br />
</td>
<td>2\11 < g < 3\16<br />
</td>
<td>2\11 < g < 5\27<br />
</td>
<td>3g-1\2<br />
</td>
<td>-8g+3\2<br />
</td>
</tr>
<tr>
<td>17L5s<br />
</td>
<td>9\22 < g < 7\17<br />
</td>
<td>9\22 < g < 16\39<br />
</td>
<td>-2+5g<br />
</td>
<td>-17g+7<br />
</td>
</tr>
<tr>
<td>18L4s<br />
</td>
<td>3\11 < g < 5\18<br />
</td>
<td>3\11 < g < 8\29<br />
</td>
<td>-1\2+2g<br />
</td>
<td>-9g+5\2<br />
</td>
</tr>
<tr>
<td>19L3s<br />
</td>
<td>15\22 < g < 13\19<br />
</td>
<td>15\22 < g <28\41<br />
</td>
<td>-2+3g<br />
</td>
<td>-19g+13<br />
</td>
</tr>
<tr>
<td>20L2s<br />
</td>
<td>1\22 < g < 1\20<br />
</td>
<td>1\22 < g < 1\21<br />
</td>
<td>g<br />
</td>
<td>-10g+1\2<br />
</td>
</tr>
<tr>
<td>21L1s<br />
</td>
<td>1\22 < g < 1\21<br />
</td>
<td>1\22 < g < 2\43<br />
</td>
<td>g<br />
</td>
<td>-21g+1<br />
</td>
</tr>
</table>
</body></html>