Generator ranges of MOS: Difference between revisions

Revision as of 01:46, 12 May 2012

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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. C/Q is the [[http://en.wikipedia.org/wiki/Mediant_(mathematics)|mediant]] between (C-a)/(Q-b) and a/b, and so there are b large steps and Q-b small steps to a period, so that bL + (Q-b)s = !/P and hence L = (1 - (Q-b)(a-gb))/bP.

=2=

|| 1L1s || 1\2 < g < 1 || 1\2 < g < 2\3 ||

=3=

|| 1L2s || 2\3 < g < 1 || 2\3 < g < 3\4 ||
|| 2L1s || 1\3 < g < 1\2 || 1\3 < g < 2\5 ||

=4=

|| 1L3s  || 3\4 < g < 1 || 3\4 < g < 4\5 ||
|| 2L2s  || 1\4 < g < 1\2 || 1\4 < g < 1\3 ||
|| 3L1s  || 1\4 < g < 1\3 || 1\4 < g < 2\7 ||

=5=

|| 1L4s  || 4\5 < g < 1 || 4\5 < g < 5\6 ||
|| 2L3s  || 2\5 < g < 1\2 || 2\5 < g < 3\7 ||
|| 3L2s  || 3\5 < g < 2\3 || 3\5 < g < 5\8 ||
|| 4L1s  || 1\5 < g < 1\4 || 1\5 < g < 2\9 ||

=6=

|| 1L5s  || 5\6 < g < 1 || 5\6 < g < 6\7 ||
|| 2L4s  || 1\3 < g < 1\2 || 1\3 < g < 2\5 ||
|| 3L3s  || 1\6 < g < 1\3 || 1\6 < g < 2\9 ||
|| 4L2s  || 1\6 < g < 1\4 || 1\6 < g < 1\5 ||
|| 5L1s  || 1\6 < g < 1\5 || 1\6 < g < 2\11 ||

=7=

|| 1L6s  || 6\7 < g < 1 || 6\7 < g < 7\8 ||
|| 2L5s  || 3\7 < g < 1\2 || 3\7 < g < 4\9 ||
|| 3L4s  || 2\7 < g < 1\3 || 2\7 < g < 3\10 ||
|| 4L3s  || 5\7 < g < 3\4 || 5\7 < g < 8\11 ||
|| 5L2s  || 4\7 < g < 3\5 || 4\7 < g < 7\12 ||
|| 6L1s  || 1\7 < g < 1\6 || 1\7 < g < 2\13 ||

=8=

|| 1L7s  || 7\8 < g < 1 || 7\8 < g < 8\9 ||
|| 2L6s  || 3\8 < g < 1\2 || 3\8 < g < 2\5 ||
|| 3L5s  || 5\8 < g < 2\3 || 5\8 < g < 7\11 ||
|| 4L4s  || 1\8 < g < 1\4 || 1\8 < g < 1\6 ||
|| 5L3s  || 3\8 < g < 2\5 || 3\8 < g < 5\13 ||
|| 6L2s  || 1\8 < g < 1\6 || 1\8 < g < 1\7 ||
|| 7L1s  || 1\8 < g < 1\7 || 1\8 < g < 2\15 ||

=9=

|| 1L8s  || 8\9 < g < 1 || 8\9 < g < 9\10 ||
|| 2L7s  || 4\9 < g < 1\2 || 4\9 < g < 5\11 ||
|| 3L6s  || 2\9 < g < 1\3 || 2\9 < g < 1\4 ||
|| 4L5s  || 2\9 < g < 1\4 || 2\9 < g < 3\13 ||
|| 5L4s  || 7\9 < g < 4\5 || 7\9 < g < 11\14 ||
|| 6L3s  || 1\9 < g < 1\6 || 1\9 < g < 2\15 ||
|| 7L2s  || 5\9 < g < 4\7 || 5\9 < g < 9\16 ||
|| 8L1s  || 1\9 < g < 1\8 || 1\9 < g < 2\17 ||

=10=

|| 1L9s  || 9\10 < g < 1 || 9\10 < g < 10\11 ||
|| 2L8s  || 2\5 < g < 1\2 || 2\5 < g < 3\7 ||
|| 3L7s  || 3\10 < g < 1\3 || 3\10 < g < 4\13 ||
|| 4L6s  || 1\5 < g < 1\4 || 1\5 < g < 2\9 ||
|| 5L5s  || 1\10 < g < 1\5 || 1\10 < g < 2\15 ||
|| 6L4s  || 3\10 < g < 1\3 || 3\10 < g < 4\13 ||
|| 7L3s  || 7\10 < g < 5\7 || 7\10 < g < 12\17 ||
|| 8L2s  || 1\10 < g < 1\8 || 1\10 < g < 1\9 ||
|| 9L1s  || 1\10 < g < 1\9 || 1\10 < g < 2\19 ||

=11=

|| 1L10s  || 10\11 < g < 1 || 10\11 < g < 11\12 ||
|| 2L9s  || 5\11 < g < 1\2 || 5\11 < g < 6\13 ||
|| 3L8s  || 7\11 < g < 2\3 || 7\11 < g < 9\14 ||
|| 4L7s  || 8\11 < g < 3\4 || 8\11 < g < 11\15 ||
|| 5L6s  || 2\11 < g < 1\5 || 2\11 < g < 3\16 ||
|| 6L5s  || 9\11 < g < 5\6 || 9\11 < g < 14\17 ||
|| 7L4s  || 3\11 < g < 2\7 || 3\11 < g < 5\18 ||
|| 8L3s  || 4\11 < g < 3\8 || 4\11 < g < 7\19 ||
|| 9L2s  || 6\11 < g < 5\9 || 6\11 < g < 11\20 ||
|| 10L1s  || 1\11 < g < 1\10 || 1\11 < g < 2\21 ||

=12=

|| 1L11s  || 11\12 < g < 1 || 11\12 < g < 12\13 ||
|| 2L10s  || 5\12 < g < 1\2 || 5\12 < g < 3\7 ||
|| 3L9s  || 1\4 < g < 1\3 || 1\4 < g < 2\7 ||
|| 4L8s  || 1\6 < g < 1\4 || 1\6 < g < 1\5 ||
|| 5L7s  || 7\12 < g < 3\5 || 7\12 < g < 10\17 ||
|| 6L6s  || 1\12 < g < 1\6 || 1\12 < g < 1\9 ||
|| 7L5s  || 5\12 < g < 3\7 || 5\12 < g < 8\19 ||
|| 8L4s  || 1\12 < g < 1\8 || 1\12 < g < 1\10 ||
|| 9L3s  || 1\12 < g < 1\9 || 1\12 < g < 2\21 ||
|| 10L2s  || 1\12 < g < 1\10 || 1\12 < g < 1\11 ||
|| 11L1s  || 1\12 < g < 1\11 || 1\12 < g < 2\23 ||

=13=

|| 1L12s  || 12\13 < g < 1 || 12\13 < g < 13\14 ||
|| 2L11s  || 6\13 < g < 1\2 || 6\13 < g < 7\15 ||
|| 3L10s  || 4\13 < g < 1\3 || 4\13 < g < 5\16 ||
|| 4L9s  || 3\13 < g < 1\4 || 3\13 < g < 4\17 ||
|| 5L8s  || 5\13 < g < 2\5 || 5\13 < g < 7\18 ||
|| 6L7s  || 2\13 < g < 1\6 || 2\13 < g < 3\19 ||
|| 7L6s  || 11\13 < g < 6\7 || 11\13 < g < 17\20 ||
|| 8L5s  || 8\13 < g < 5\8 || 8\13 < g < 13\21 ||
|| 9L4s  || 10\13 < g < 7\9 || 10\13 < g < 17\22 ||
|| 10L3s  || 9\13 < g < 7\10 || 9\13 < g < 16\23 ||
|| 11L2s  || 7\13 < g < 6\11 || 7\13 < g < 13\24 ||
|| 12L1s  || 1\13 < g < 1\12 || 1\13 < g < 2\25 ||

=14=

|| 1L13s  || 13\14 < g < 1 || 13\14 < g < 14\15 ||
|| 2L12s  || 3\7 < g < 1\2 || 3\7 < g < 4\9 ||
|| 3L11s  || 9\14 < g < 2\3 || 9\14 < g < 11\17 ||
|| 4L10s  || 3\14 < g < 1\4 || 3\14 < g < 2\9 ||
|| 5L9s  || 11\14 < g < 4\5 || 11\14 < g < 15\19 ||
|| 6L8s  || 1\7 < g < 1\6 || 1\7 < g < 2\13 ||
|| 7L7s  || 1\14 < g < 1\7 || 1\14 < g < 2\21 ||
|| 8L6s  || 5\14 < g < 3\8 || 5\14 < g < 4\11 ||
|| 9L5s  || 3\14 < g < 2\9 || 3\14 < g < 5\23 ||
|| 10L4s  || 2\7 < g < 3\10 || 2\7 < g < 5\17 ||
|| 11L3s  || 5\14 < g < 4\11 || 5\14 < g < 9\25 ||
|| 12L2s  || 1\14 < g < 1\12 || 1\14 < g < 1\13 ||
|| 13L1s  || 1\14 < g < 1\13 || 1\14 < g < 2\27 ||

=15=

|| 1L14s  || 14\15 < g < 1 || 14\15 < g < 15\16 ||
|| 2L13s  || 7\15 < g < 1\2 || 7\15 < g < 8\17 ||
|| 3L12s  || 4\15 < g < 1\3 || 4\15 < g < 5\18 ||
|| 4L11s  || 11\15 < g < 3\4 || 11\15 < g < 14\19 ||
|| 5L10s  || 2\15 < g < 1\5 || 2\15 < g < 3\20 ||
|| 6L9s  || 2\15 < g < 1\6 || 2\15 < g < 1\7 ||
|| 7L8s  || 2\15 < g < 1\7 || 2\15 < g < 3\22 ||
|| 8L7s  || 13\15 < g < 7\8 || 13\15 < g < 20\23 ||
|| 9L6s  || 1\5 < g < 2\9 || 1\5 < g < 3\14 ||
|| 10L5s  || 1\15 < g < 1\10 || 1\15 < g < 2\25 ||
|| 11L4s  || 4\15 < g < 3\11 || 4\15 < g < 7\26 ||
|| 12L3s  || 1\15 < g < 1\12 || 1\15 < g < 2\27 ||
|| 13L2s  || 8\15 < g < 7\13 || 8\15 < g < 15\28 ||
|| 14L1s  || 1\15 < g < 1\14 || 1\15 < g < 2\29 ||

=16=

|| 1L15s  || 15\16 < g < 1 || 15\16 < g < 16\17 ||
|| 2L14s  || 7\16 < g < 1\2 || 7\16 < g < 4\9 ||
|| 3L13s  || 5\16 < g < 1\3 || 5\16 < g < 6\19 ||
|| 4L12s  || 3\16 < g < 1\4 || 3\16 < g < 1\5 ||
|| 5L11s  || 3\16 < g < 1\5 || 3\16 < g < 4\21 ||
|| 6L10s  || 5\16 < g < 1\3 || 5\16 < g < 6\19 ||
|| 7L9s  || 9\16 < g < 4\7 || 9\16 < g < 13\23 ||
|| 8L8s  || 1\16 < g < 1\8 || 1\16 < g < 1\12 ||
|| 9L7s  || 7\16 < g < 4\9 || 7\16 < g < 11\25 ||
|| 10L6s  || 3\16 < g < 1\5 || 3\16 < g < 4\21 ||
|| 11L5s  || 13\16 < g < 9\11 || 13\16 < g < 22\27 ||
|| 12L4s  || 1\16 < g < 1\12 || 1\16 < g < 1\14 ||
|| 13L3s  || 11\16 < g < 9\13 || 11\16 < g < 20\29 ||
|| 14L2s  || 1\16 < g < 1\14 || 1\16 < g < 1\15 ||
|| 15L1s  || 1\16 < g < 1\15 || 1\16 < g < 2\31 ||

=17=

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

=18=

|| 1L17s  || 17\18 < g < 1 || 17\18 < g < 18\19 ||
|| 2L16s  || 4\9 < g < 1\2 || 4\9 < g < 5\11 ||
|| 3L15s  || 5\18 < g < 1\3 || 5\18 < g < 2\7 ||
|| 4L14s  || 2\9 < g < 1\4 || 2\9 < g < 3\13 ||
|| 5L13s  || 7\18 < g < 2\5 || 7\18 < g < 9\23 ||
|| 6L12s  || 1\9 < g < 1\6 || 1\9 < g < 2\15 ||
|| 7L11s  || 5\18 < g < 2\7 || 5\18 < g < 7\25 ||
|| 8L10s  || 1\9 < g < 1\8 || 1\9 < g < 2\17 ||
|| 9L9s  || 1\18 < g < 1\9 || 1\18 < g < 2\27 ||
|| 10L8s  || 7\18 < g < 2\5 || 7\18 < g < 9\23 ||
|| 11L7s  || 13\18 < g < 8\11 || 13\18 < g < 21\29 ||
|| 12L6s  || 1\18 < g < 1\12 || 1\18 < g < 1\15 ||
|| 13L5s  || 11\18 < g < 8\13 || 11\18 < g < 19\31 ||
|| 14L4s  || 5\18 < g < 2\7 || 5\18 < g < 7\25 ||
|| 15L3s  || 1\18 < g < 1\15 || 1\18 < g < 2\33 ||
|| 16L2s  || 1\18 < g < 1\16 || 1\18 < g < 1\17 ||
|| 17L1s  || 1\18 < g < 1\17 || 1\18 < g < 2\35 ||

=19=

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

=20=

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

=21=

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

=22=

|| 1L21s  || 21\22 < g < 1 || 21\22 < g < 22\23 ||
|| 2L20s  || 5\11 < g < 1\2 || 5\11 < g < 6\13 ||
|| 3L19s  || 7\22 < g < 1\3 || 7\22 < g < 8\25 ||
|| 4L18s  || 5\22 < g < 1\4 || 5\22 < g < 3\13 ||
|| 5L17s  || 13\22 < g < 3\5 || 13\22 < g < 16\27 ||
|| 6L16s  || 7\22 < g < 1\3 || 7\22 < g < 8\25 ||
|| 7L15s  || 3\22 < g < 1\7 || 3\22 < g < 4\29 ||
|| 8L14s  || 4\11 < g < 3\8 || 4\11 < g < 7\19 ||
|| 9L13s  || 17\22 < g < 7\9 || 17\22 < g < 24\31 ||
|| 10L12s  || 1\11 < g < 1\10 || 1\11 < g < 2\21 ||
|| 11L11s  || 1\22 < g < 1\11 || 1\22 < g < 2\33 ||
|| 12L10s  || 9\22 < g < 5\12 || 9\22 < g < 7\17 ||
|| 13L9s  || 5\22 < g < 3\13 || 5\22 < g < 8\35 ||
|| 14L8s  || 3\22 < g < 1\7 || 3\22 < g < 4\29 ||
|| 15L7s  || 19\22 < g < 13\15 || 19\22 < g < 32\37 ||
|| 16L6s  || 2\11 < g < 3\16 || 2\11 < g < 5\27 ||
|| 17L5s  || 9\22 < g < 7\17 || 9\22 < g < 16\39 ||
|| 18L4s  || 3\11 < g < 5\18 || 3\11 < g < 8\29 ||
|| 19L3s  || 15\22 < g < 13\19 || 15\22 < g < 28\41 ||
|| 20L2s  || 1\22 < g < 1\20 || 1\22 < g < 1\21 ||
|| 21L1s  || 1\22 < g < 1\21 || 1\22 < g < 2\43 ||

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 &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. C/Q is the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Mediant_(mathematics)" rel="nofollow">mediant</a> between (C-a)/(Q-b) and a/b, and so there are b large steps and Q-b small steps to a period, so that bL + (Q-b)s = !/P and hence L = (1 - (Q-b)(a-gb))/bP.<br />
<br />
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<br />


<table class="wiki_table">
    <tr>
        <td>1L1s<br />
</td>
        <td>1\2 &lt; g &lt; 1<br />
</td>
        <td>1\2 &lt; g &lt; 2\3<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="x3"></a><!-- ws:end:WikiTextHeadingRule:2 -->3</h1>
<br />


<table class="wiki_table">
    <tr>
        <td>1L2s<br />
</td>
        <td>2\3 &lt; g &lt; 1<br />
</td>
        <td>2\3 &lt; g &lt; 3\4<br />
</td>
    </tr>
    <tr>
        <td>2L1s<br />
</td>
        <td>1\3 &lt; g &lt; 1\2<br />
</td>
        <td>1\3 &lt; g &lt; 2\5<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="x4"></a><!-- ws:end:WikiTextHeadingRule:4 -->4</h1>
<br />


<table class="wiki_table">
    <tr>
        <td>1L3s<br />
</td>
        <td>3\4 &lt; g &lt; 1<br />
</td>
        <td>3\4 &lt; g &lt; 4\5<br />
</td>
    </tr>
    <tr>
        <td>2L2s<br />
</td>
        <td>1\4 &lt; g &lt; 1\2<br />
</td>
        <td>1\4 &lt; g &lt; 1\3<br />
</td>
    </tr>
    <tr>
        <td>3L1s<br />
</td>
        <td>1\4 &lt; g &lt; 1\3<br />
</td>
        <td>1\4 &lt; g &lt; 2\7<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="x5"></a><!-- ws:end:WikiTextHeadingRule:6 -->5</h1>
<br />


<table class="wiki_table">
    <tr>
        <td>1L4s<br />
</td>
        <td>4\5 &lt; g &lt; 1<br />
</td>
        <td>4\5 &lt; g &lt; 5\6<br />
</td>
    </tr>
    <tr>
        <td>2L3s<br />
</td>
        <td>2\5 &lt; g &lt; 1\2<br />
</td>
        <td>2\5 &lt; g &lt; 3\7<br />
</td>
    </tr>
    <tr>
        <td>3L2s<br />
</td>
        <td>3\5 &lt; g &lt; 2\3<br />
</td>
        <td>3\5 &lt; g &lt; 5\8<br />
</td>
    </tr>
    <tr>
        <td>4L1s<br />
</td>
        <td>1\5 &lt; g &lt; 1\4<br />
</td>
        <td>1\5 &lt; g &lt; 2\9<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="x6"></a><!-- ws:end:WikiTextHeadingRule:8 -->6</h1>
<br />


<table class="wiki_table">
    <tr>
        <td>1L5s<br />
</td>
        <td>5\6 &lt; g &lt; 1<br />
</td>
        <td>5\6 &lt; g &lt; 6\7<br />
</td>
    </tr>
    <tr>
        <td>2L4s<br />
</td>
        <td>1\3 &lt; g &lt; 1\2<br />
</td>
        <td>1\3 &lt; g &lt; 2\5<br />
</td>
    </tr>
    <tr>
        <td>3L3s<br />
</td>
        <td>1\6 &lt; g &lt; 1\3<br />
</td>
        <td>1\6 &lt; g &lt; 2\9<br />
</td>
    </tr>
    <tr>
        <td>4L2s<br />
</td>
        <td>1\6 &lt; g &lt; 1\4<br />
</td>
        <td>1\6 &lt; g &lt; 1\5<br />
</td>
    </tr>
    <tr>
        <td>5L1s<br />
</td>
        <td>1\6 &lt; g &lt; 1\5<br />
</td>
        <td>1\6 &lt; g &lt; 2\11<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="x7"></a><!-- ws:end:WikiTextHeadingRule:10 -->7</h1>
<br />


<table class="wiki_table">
    <tr>
        <td>1L6s<br />
</td>
        <td>6\7 &lt; g &lt; 1<br />
</td>
        <td>6\7 &lt; g &lt; 7\8<br />
</td>
    </tr>
    <tr>
        <td>2L5s<br />
</td>
        <td>3\7 &lt; g &lt; 1\2<br />
</td>
        <td>3\7 &lt; g &lt; 4\9<br />
</td>
    </tr>
    <tr>
        <td>3L4s<br />
</td>
        <td>2\7 &lt; g &lt; 1\3<br />
</td>
        <td>2\7 &lt; g &lt; 3\10<br />
</td>
    </tr>
    <tr>
        <td>4L3s<br />
</td>
        <td>5\7 &lt; g &lt; 3\4<br />
</td>
        <td>5\7 &lt; g &lt; 8\11<br />
</td>
    </tr>
    <tr>
        <td>5L2s<br />
</td>
        <td>4\7 &lt; g &lt; 3\5<br />
</td>
        <td>4\7 &lt; g &lt; 7\12<br />
</td>
    </tr>
    <tr>
        <td>6L1s<br />
</td>
        <td>1\7 &lt; g &lt; 1\6<br />
</td>
        <td>1\7 &lt; g &lt; 2\13<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="x8"></a><!-- ws:end:WikiTextHeadingRule:12 -->8</h1>
<br />


<table class="wiki_table">
    <tr>
        <td>1L7s<br />
</td>
        <td>7\8 &lt; g &lt; 1<br />
</td>
        <td>7\8 &lt; g &lt; 8\9<br />
</td>
    </tr>
    <tr>
        <td>2L6s<br />
</td>
        <td>3\8 &lt; g &lt; 1\2<br />
</td>
        <td>3\8 &lt; g &lt; 2\5<br />
</td>
    </tr>
    <tr>
        <td>3L5s<br />
</td>
        <td>5\8 &lt; g &lt; 2\3<br />
</td>
        <td>5\8 &lt; g &lt; 7\11<br />
</td>
    </tr>
    <tr>
        <td>4L4s<br />
</td>
        <td>1\8 &lt; g &lt; 1\4<br />
</td>
        <td>1\8 &lt; g &lt; 1\6<br />
</td>
    </tr>
    <tr>
        <td>5L3s<br />
</td>
        <td>3\8 &lt; g &lt; 2\5<br />
</td>
        <td>3\8 &lt; g &lt; 5\13<br />
</td>
    </tr>
    <tr>
        <td>6L2s<br />
</td>
        <td>1\8 &lt; g &lt; 1\6<br />
</td>
        <td>1\8 &lt; g &lt; 1\7<br />
</td>
    </tr>
    <tr>
        <td>7L1s<br />
</td>
        <td>1\8 &lt; g &lt; 1\7<br />
</td>
        <td>1\8 &lt; g &lt; 2\15<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="x9"></a><!-- ws:end:WikiTextHeadingRule:14 -->9</h1>
<br />


<table class="wiki_table">
    <tr>
        <td>1L8s<br />
</td>
        <td>8\9 &lt; g &lt; 1<br />
</td>
        <td>8\9 &lt; g &lt; 9\10<br />
</td>
    </tr>
    <tr>
        <td>2L7s<br />
</td>
        <td>4\9 &lt; g &lt; 1\2<br />
</td>
        <td>4\9 &lt; g &lt; 5\11<br />
</td>
    </tr>
    <tr>
        <td>3L6s<br />
</td>
        <td>2\9 &lt; g &lt; 1\3<br />
</td>
        <td>2\9 &lt; g &lt; 1\4<br />
</td>
    </tr>
    <tr>
        <td>4L5s<br />
</td>
        <td>2\9 &lt; g &lt; 1\4<br />
</td>
        <td>2\9 &lt; g &lt; 3\13<br />
</td>
    </tr>
    <tr>
        <td>5L4s<br />
</td>
        <td>7\9 &lt; g &lt; 4\5<br />
</td>
        <td>7\9 &lt; g &lt; 11\14<br />
</td>
    </tr>
    <tr>
        <td>6L3s<br />
</td>
        <td>1\9 &lt; g &lt; 1\6<br />
</td>
        <td>1\9 &lt; g &lt; 2\15<br />
</td>
    </tr>
    <tr>
        <td>7L2s<br />
</td>
        <td>5\9 &lt; g &lt; 4\7<br />
</td>
        <td>5\9 &lt; g &lt; 9\16<br />
</td>
    </tr>
    <tr>
        <td>8L1s<br />
</td>
        <td>1\9 &lt; g &lt; 1\8<br />
</td>
        <td>1\9 &lt; g &lt; 2\17<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="x10"></a><!-- ws:end:WikiTextHeadingRule:16 -->10</h1>
<br />


<table class="wiki_table">
    <tr>
        <td>1L9s<br />
</td>
        <td>9\10 &lt; g &lt; 1<br />
</td>
        <td>9\10 &lt; g &lt; 10\11<br />
</td>
    </tr>
    <tr>
        <td>2L8s<br />
</td>
        <td>2\5 &lt; g &lt; 1\2<br />
</td>
        <td>2\5 &lt; g &lt; 3\7<br />
</td>
    </tr>
    <tr>
        <td>3L7s<br />
</td>
        <td>3\10 &lt; g &lt; 1\3<br />
</td>
        <td>3\10 &lt; g &lt; 4\13<br />
</td>
    </tr>
    <tr>
        <td>4L6s<br />
</td>
        <td>1\5 &lt; g &lt; 1\4<br />
</td>
        <td>1\5 &lt; g &lt; 2\9<br />
</td>
    </tr>
    <tr>
        <td>5L5s<br />
</td>
        <td>1\10 &lt; g &lt; 1\5<br />
</td>
        <td>1\10 &lt; g &lt; 2\15<br />
</td>
    </tr>
    <tr>
        <td>6L4s<br />
</td>
        <td>3\10 &lt; g &lt; 1\3<br />
</td>
        <td>3\10 &lt; g &lt; 4\13<br />
</td>
    </tr>
    <tr>
        <td>7L3s<br />
</td>
        <td>7\10 &lt; g &lt; 5\7<br />
</td>
        <td>7\10 &lt; g &lt; 12\17<br />
</td>
    </tr>
    <tr>
        <td>8L2s<br />
</td>
        <td>1\10 &lt; g &lt; 1\8<br />
</td>
        <td>1\10 &lt; g &lt; 1\9<br />
</td>
    </tr>
    <tr>
        <td>9L1s<br />
</td>
        <td>1\10 &lt; g &lt; 1\9<br />
</td>
        <td>1\10 &lt; g &lt; 2\19<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="x11"></a><!-- ws:end:WikiTextHeadingRule:18 -->11</h1>
<br />


<table class="wiki_table">
    <tr>
        <td>1L10s<br />
</td>
        <td>10\11 &lt; g &lt; 1<br />
</td>
        <td>10\11 &lt; g &lt; 11\12<br />
</td>
    </tr>
    <tr>
        <td>2L9s<br />
</td>
        <td>5\11 &lt; g &lt; 1\2<br />
</td>
        <td>5\11 &lt; g &lt; 6\13<br />
</td>
    </tr>
    <tr>
        <td>3L8s<br />
</td>
        <td>7\11 &lt; g &lt; 2\3<br />
</td>
        <td>7\11 &lt; g &lt; 9\14<br />
</td>
    </tr>
    <tr>
        <td>4L7s<br />
</td>
        <td>8\11 &lt; g &lt; 3\4<br />
</td>
        <td>8\11 &lt; g &lt; 11\15<br />
</td>
    </tr>
    <tr>
        <td>5L6s<br />
</td>
        <td>2\11 &lt; g &lt; 1\5<br />
</td>
        <td>2\11 &lt; g &lt; 3\16<br />
</td>
    </tr>
    <tr>
        <td>6L5s<br />
</td>
        <td>9\11 &lt; g &lt; 5\6<br />
</td>
        <td>9\11 &lt; g &lt; 14\17<br />
</td>
    </tr>
    <tr>
        <td>7L4s<br />
</td>
        <td>3\11 &lt; g &lt; 2\7<br />
</td>
        <td>3\11 &lt; g &lt; 5\18<br />
</td>
    </tr>
    <tr>
        <td>8L3s<br />
</td>
        <td>4\11 &lt; g &lt; 3\8<br />
</td>
        <td>4\11 &lt; g &lt; 7\19<br />
</td>
    </tr>
    <tr>
        <td>9L2s<br />
</td>
        <td>6\11 &lt; g &lt; 5\9<br />
</td>
        <td>6\11 &lt; g &lt; 11\20<br />
</td>
    </tr>
    <tr>
        <td>10L1s<br />
</td>
        <td>1\11 &lt; g &lt; 1\10<br />
</td>
        <td>1\11 &lt; g &lt; 2\21<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="x12"></a><!-- ws:end:WikiTextHeadingRule:20 -->12</h1>
<br />


<table class="wiki_table">
    <tr>
        <td>1L11s<br />
</td>
        <td>11\12 &lt; g &lt; 1<br />
</td>
        <td>11\12 &lt; g &lt; 12\13<br />
</td>
    </tr>
    <tr>
        <td>2L10s<br />
</td>
        <td>5\12 &lt; g &lt; 1\2<br />
</td>
        <td>5\12 &lt; g &lt; 3\7<br />
</td>
    </tr>
    <tr>
        <td>3L9s<br />
</td>
        <td>1\4 &lt; g &lt; 1\3<br />
</td>
        <td>1\4 &lt; g &lt; 2\7<br />
</td>
    </tr>
    <tr>
        <td>4L8s<br />
</td>
        <td>1\6 &lt; g &lt; 1\4<br />
</td>
        <td>1\6 &lt; g &lt; 1\5<br />
</td>
    </tr>
    <tr>
        <td>5L7s<br />
</td>
        <td>7\12 &lt; g &lt; 3\5<br />
</td>
        <td>7\12 &lt; g &lt; 10\17<br />
</td>
    </tr>
    <tr>
        <td>6L6s<br />
</td>
        <td>1\12 &lt; g &lt; 1\6<br />
</td>
        <td>1\12 &lt; g &lt; 1\9<br />
</td>
    </tr>
    <tr>
        <td>7L5s<br />
</td>
        <td>5\12 &lt; g &lt; 3\7<br />
</td>
        <td>5\12 &lt; g &lt; 8\19<br />
</td>
    </tr>
    <tr>
        <td>8L4s<br />
</td>
        <td>1\12 &lt; g &lt; 1\8<br />
</td>
        <td>1\12 &lt; g &lt; 1\10<br />
</td>
    </tr>
    <tr>
        <td>9L3s<br />
</td>
        <td>1\12 &lt; g &lt; 1\9<br />
</td>
        <td>1\12 &lt; g &lt; 2\21<br />
</td>
    </tr>
    <tr>
        <td>10L2s<br />
</td>
        <td>1\12 &lt; g &lt; 1\10<br />
</td>
        <td>1\12 &lt; g &lt; 1\11<br />
</td>
    </tr>
    <tr>
        <td>11L1s<br />
</td>
        <td>1\12 &lt; g &lt; 1\11<br />
</td>
        <td>1\12 &lt; g &lt; 2\23<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="x13"></a><!-- ws:end:WikiTextHeadingRule:22 -->13</h1>
<br />


<table class="wiki_table">
    <tr>
        <td>1L12s<br />
</td>
        <td>12\13 &lt; g &lt; 1<br />
</td>
        <td>12\13 &lt; g &lt; 13\14<br />
</td>
    </tr>
    <tr>
        <td>2L11s<br />
</td>
        <td>6\13 &lt; g &lt; 1\2<br />
</td>
        <td>6\13 &lt; g &lt; 7\15<br />
</td>
    </tr>
    <tr>
        <td>3L10s<br />
</td>
        <td>4\13 &lt; g &lt; 1\3<br />
</td>
        <td>4\13 &lt; g &lt; 5\16<br />
</td>
    </tr>
    <tr>
        <td>4L9s<br />
</td>
        <td>3\13 &lt; g &lt; 1\4<br />
</td>
        <td>3\13 &lt; g &lt; 4\17<br />
</td>
    </tr>
    <tr>
        <td>5L8s<br />
</td>
        <td>5\13 &lt; g &lt; 2\5<br />
</td>
        <td>5\13 &lt; g &lt; 7\18<br />
</td>
    </tr>
    <tr>
        <td>6L7s<br />
</td>
        <td>2\13 &lt; g &lt; 1\6<br />
</td>
        <td>2\13 &lt; g &lt; 3\19<br />
</td>
    </tr>
    <tr>
        <td>7L6s<br />
</td>
        <td>11\13 &lt; g &lt; 6\7<br />
</td>
        <td>11\13 &lt; g &lt; 17\20<br />
</td>
    </tr>
    <tr>
        <td>8L5s<br />
</td>
        <td>8\13 &lt; g &lt; 5\8<br />
</td>
        <td>8\13 &lt; g &lt; 13\21<br />
</td>
    </tr>
    <tr>
        <td>9L4s<br />
</td>
        <td>10\13 &lt; g &lt; 7\9<br />
</td>
        <td>10\13 &lt; g &lt; 17\22<br />
</td>
    </tr>
    <tr>
        <td>10L3s<br />
</td>
        <td>9\13 &lt; g &lt; 7\10<br />
</td>
        <td>9\13 &lt; g &lt; 16\23<br />
</td>
    </tr>
    <tr>
        <td>11L2s<br />
</td>
        <td>7\13 &lt; g &lt; 6\11<br />
</td>
        <td>7\13 &lt; g &lt; 13\24<br />
</td>
    </tr>
    <tr>
        <td>12L1s<br />
</td>
        <td>1\13 &lt; g &lt; 1\12<br />
</td>
        <td>1\13 &lt; g &lt; 2\25<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="x14"></a><!-- ws:end:WikiTextHeadingRule:24 -->14</h1>
<br />


<table class="wiki_table">
    <tr>
        <td>1L13s<br />
</td>
        <td>13\14 &lt; g &lt; 1<br />
</td>
        <td>13\14 &lt; g &lt; 14\15<br />
</td>
    </tr>
    <tr>
        <td>2L12s<br />
</td>
        <td>3\7 &lt; g &lt; 1\2<br />
</td>
        <td>3\7 &lt; g &lt; 4\9<br />
</td>
    </tr>
    <tr>
        <td>3L11s<br />
</td>
        <td>9\14 &lt; g &lt; 2\3<br />
</td>
        <td>9\14 &lt; g &lt; 11\17<br />
</td>
    </tr>
    <tr>
        <td>4L10s<br />
</td>
        <td>3\14 &lt; g &lt; 1\4<br />
</td>
        <td>3\14 &lt; g &lt; 2\9<br />
</td>
    </tr>
    <tr>
        <td>5L9s<br />
</td>
        <td>11\14 &lt; g &lt; 4\5<br />
</td>
        <td>11\14 &lt; g &lt; 15\19<br />
</td>
    </tr>
    <tr>
        <td>6L8s<br />
</td>
        <td>1\7 &lt; g &lt; 1\6<br />
</td>
        <td>1\7 &lt; g &lt; 2\13<br />
</td>
    </tr>
    <tr>
        <td>7L7s<br />
</td>
        <td>1\14 &lt; g &lt; 1\7<br />
</td>
        <td>1\14 &lt; g &lt; 2\21<br />
</td>
    </tr>
    <tr>
        <td>8L6s<br />
</td>
        <td>5\14 &lt; g &lt; 3\8<br />
</td>
        <td>5\14 &lt; g &lt; 4\11<br />
</td>
    </tr>
    <tr>
        <td>9L5s<br />
</td>
        <td>3\14 &lt; g &lt; 2\9<br />
</td>
        <td>3\14 &lt; g &lt; 5\23<br />
</td>
    </tr>
    <tr>
        <td>10L4s<br />
</td>
        <td>2\7 &lt; g &lt; 3\10<br />
</td>
        <td>2\7 &lt; g &lt; 5\17<br />
</td>
    </tr>
    <tr>
        <td>11L3s<br />
</td>
        <td>5\14 &lt; g &lt; 4\11<br />
</td>
        <td>5\14 &lt; g &lt; 9\25<br />
</td>
    </tr>
    <tr>
        <td>12L2s<br />
</td>
        <td>1\14 &lt; g &lt; 1\12<br />
</td>
        <td>1\14 &lt; g &lt; 1\13<br />
</td>
    </tr>
    <tr>
        <td>13L1s<br />
</td>
        <td>1\14 &lt; g &lt; 1\13<br />
</td>
        <td>1\14 &lt; g &lt; 2\27<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="x15"></a><!-- ws:end:WikiTextHeadingRule:26 -->15</h1>
<br />


<table class="wiki_table">
    <tr>
        <td>1L14s<br />
</td>
        <td>14\15 &lt; g &lt; 1<br />
</td>
        <td>14\15 &lt; g &lt; 15\16<br />
</td>
    </tr>
    <tr>
        <td>2L13s<br />
</td>
        <td>7\15 &lt; g &lt; 1\2<br />
</td>
        <td>7\15 &lt; g &lt; 8\17<br />
</td>
    </tr>
    <tr>
        <td>3L12s<br />
</td>
        <td>4\15 &lt; g &lt; 1\3<br />
</td>
        <td>4\15 &lt; g &lt; 5\18<br />
</td>
    </tr>
    <tr>
        <td>4L11s<br />
</td>
        <td>11\15 &lt; g &lt; 3\4<br />
</td>
        <td>11\15 &lt; g &lt; 14\19<br />
</td>
    </tr>
    <tr>
        <td>5L10s<br />
</td>
        <td>2\15 &lt; g &lt; 1\5<br />
</td>
        <td>2\15 &lt; g &lt; 3\20<br />
</td>
    </tr>
    <tr>
        <td>6L9s<br />
</td>
        <td>2\15 &lt; g &lt; 1\6<br />
</td>
        <td>2\15 &lt; g &lt; 1\7<br />
</td>
    </tr>
    <tr>
        <td>7L8s<br />
</td>
        <td>2\15 &lt; g &lt; 1\7<br />
</td>
        <td>2\15 &lt; g &lt; 3\22<br />
</td>
    </tr>
    <tr>
        <td>8L7s<br />
</td>
        <td>13\15 &lt; g &lt; 7\8<br />
</td>
        <td>13\15 &lt; g &lt; 20\23<br />
</td>
    </tr>
    <tr>
        <td>9L6s<br />
</td>
        <td>1\5 &lt; g &lt; 2\9<br />
</td>
        <td>1\5 &lt; g &lt; 3\14<br />
</td>
    </tr>
    <tr>
        <td>10L5s<br />
</td>
        <td>1\15 &lt; g &lt; 1\10<br />
</td>
        <td>1\15 &lt; g &lt; 2\25<br />
</td>
    </tr>
    <tr>
        <td>11L4s<br />
</td>
        <td>4\15 &lt; g &lt; 3\11<br />
</td>
        <td>4\15 &lt; g &lt; 7\26<br />
</td>
    </tr>
    <tr>
        <td>12L3s<br />
</td>
        <td>1\15 &lt; g &lt; 1\12<br />
</td>
        <td>1\15 &lt; g &lt; 2\27<br />
</td>
    </tr>
    <tr>
        <td>13L2s<br />
</td>
        <td>8\15 &lt; g &lt; 7\13<br />
</td>
        <td>8\15 &lt; g &lt; 15\28<br />
</td>
    </tr>
    <tr>
        <td>14L1s<br />
</td>
        <td>1\15 &lt; g &lt; 1\14<br />
</td>
        <td>1\15 &lt; g &lt; 2\29<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="x16"></a><!-- ws:end:WikiTextHeadingRule:28 -->16</h1>
<br />


<table class="wiki_table">
    <tr>
        <td>1L15s<br />
</td>
        <td>15\16 &lt; g &lt; 1<br />
</td>
        <td>15\16 &lt; g &lt; 16\17<br />
</td>
    </tr>
    <tr>
        <td>2L14s<br />
</td>
        <td>7\16 &lt; g &lt; 1\2<br />
</td>
        <td>7\16 &lt; g &lt; 4\9<br />
</td>
    </tr>
    <tr>
        <td>3L13s<br />
</td>
        <td>5\16 &lt; g &lt; 1\3<br />
</td>
        <td>5\16 &lt; g &lt; 6\19<br />
</td>
    </tr>
    <tr>
        <td>4L12s<br />
</td>
        <td>3\16 &lt; g &lt; 1\4<br />
</td>
        <td>3\16 &lt; g &lt; 1\5<br />
</td>
    </tr>
    <tr>
        <td>5L11s<br />
</td>
        <td>3\16 &lt; g &lt; 1\5<br />
</td>
        <td>3\16 &lt; g &lt; 4\21<br />
</td>
    </tr>
    <tr>
        <td>6L10s<br />
</td>
        <td>5\16 &lt; g &lt; 1\3<br />
</td>
        <td>5\16 &lt; g &lt; 6\19<br />
</td>
    </tr>
    <tr>
        <td>7L9s<br />
</td>
        <td>9\16 &lt; g &lt; 4\7<br />
</td>
        <td>9\16 &lt; g &lt; 13\23<br />
</td>
    </tr>
    <tr>
        <td>8L8s<br />
</td>
        <td>1\16 &lt; g &lt; 1\8<br />
</td>
        <td>1\16 &lt; g &lt; 1\12<br />
</td>
    </tr>
    <tr>
        <td>9L7s<br />
</td>
        <td>7\16 &lt; g &lt; 4\9<br />
</td>
        <td>7\16 &lt; g &lt; 11\25<br />
</td>
    </tr>
    <tr>
        <td>10L6s<br />
</td>
        <td>3\16 &lt; g &lt; 1\5<br />
</td>
        <td>3\16 &lt; g &lt; 4\21<br />
</td>
    </tr>
    <tr>
        <td>11L5s<br />
</td>
        <td>13\16 &lt; g &lt; 9\11<br />
</td>
        <td>13\16 &lt; g &lt; 22\27<br />
</td>
    </tr>
    <tr>
        <td>12L4s<br />
</td>
        <td>1\16 &lt; g &lt; 1\12<br />
</td>
        <td>1\16 &lt; g &lt; 1\14<br />
</td>
    </tr>
    <tr>
        <td>13L3s<br />
</td>
        <td>11\16 &lt; g &lt; 9\13<br />
</td>
        <td>11\16 &lt; g &lt; 20\29<br />
</td>
    </tr>
    <tr>
        <td>14L2s<br />
</td>
        <td>1\16 &lt; g &lt; 1\14<br />
</td>
        <td>1\16 &lt; g &lt; 1\15<br />
</td>
    </tr>
    <tr>
        <td>15L1s<br />
</td>
        <td>1\16 &lt; g &lt; 1\15<br />
</td>
        <td>1\16 &lt; g &lt; 2\31<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="x17"></a><!-- ws:end:WikiTextHeadingRule:30 -->17</h1>
<br />


<table class="wiki_table">
    <tr>
        <td>1L16s<br />
</td>
        <td>16\17 &lt; g &lt; 1<br />
</td>
        <td>16\17 &lt; g &lt; 17\18<br />
</td>
    </tr>
    <tr>
        <td>2L15s<br />
</td>
        <td>8\17 &lt; g &lt; 1\2<br />
</td>
        <td>8\17 &lt; g &lt; 9\19<br />
</td>
    </tr>
    <tr>
        <td>3L14s<br />
</td>
        <td>11\17 &lt; g &lt; 2\3<br />
</td>
        <td>11\17 &lt; g &lt; 13\20<br />
</td>
    </tr>
    <tr>
        <td>4L13s<br />
</td>
        <td>4\17 &lt; g &lt; 1\4<br />
</td>
        <td>4\17 &lt; g &lt; 5\21<br />
</td>
    </tr>
    <tr>
        <td>5L12s<br />
</td>
        <td>10\17 &lt; g &lt; 3\5<br />
</td>
        <td>10\17 &lt; g &lt; 13\22<br />
</td>
    </tr>
    <tr>
        <td>6L11s<br />
</td>
        <td>14\17 &lt; g &lt; 5\6<br />
</td>
        <td>14\17 &lt; g &lt; 19\23<br />
</td>
    </tr>
    <tr>
        <td>7L10s<br />
</td>
        <td>12\17 &lt; g &lt; 5\7<br />
</td>
        <td>12\17 &lt; g &lt; 17\24<br />
</td>
    </tr>
    <tr>
        <td>8L9s<br />
</td>
        <td>2\17 &lt; g &lt; 1\8<br />
</td>
        <td>2\17 &lt; g &lt; 3\25<br />
</td>
    </tr>
    <tr>
        <td>9L8s<br />
</td>
        <td>15\17 &lt; g &lt; 8\9<br />
</td>
        <td>15\17 &lt; g &lt; 23\26<br />
</td>
    </tr>
    <tr>
        <td>10L7s<br />
</td>
        <td>5\17 &lt; g &lt; 3\10<br />
</td>
        <td>5\17 &lt; g &lt; 8\27<br />
</td>
    </tr>
    <tr>
        <td>11L6s<br />
</td>
        <td>3\17 &lt; g &lt; 2\11<br />
</td>
        <td>3\17 &lt; g &lt; 5\28<br />
</td>
    </tr>
    <tr>
        <td>12L5s<br />
</td>
        <td>7\17 &lt; g &lt; 5\12<br />
</td>
        <td>7\17 &lt; g &lt; 12\29<br />
</td>
    </tr>
    <tr>
        <td>13L4s<br />
</td>
        <td>13\17 &lt; g &lt; 10\13<br />
</td>
        <td>13\17 &lt; g &lt; 23\30<br />
</td>
    </tr>
    <tr>
        <td>14L3s<br />
</td>
        <td>6\17 &lt; g &lt; 5\14<br />
</td>
        <td>6\17 &lt; g &lt; 11\31<br />
</td>
    </tr>
    <tr>
        <td>15L2s<br />
</td>
        <td>9\17 &lt; g &lt; 8\15<br />
</td>
        <td>9\17 &lt; g &lt; 17\32<br />
</td>
    </tr>
    <tr>
        <td>16L1s<br />
</td>
        <td>1\17 &lt; g &lt; 1\16<br />
</td>
        <td>1\17 &lt; g &lt; 2\33<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:32:&lt;h1&gt; --><h1 id="toc16"><a name="x18"></a><!-- ws:end:WikiTextHeadingRule:32 -->18</h1>
<br />


<table class="wiki_table">
    <tr>
        <td>1L17s<br />
</td>
        <td>17\18 &lt; g &lt; 1<br />
</td>
        <td>17\18 &lt; g &lt; 18\19<br />
</td>
    </tr>
    <tr>
        <td>2L16s<br />
</td>
        <td>4\9 &lt; g &lt; 1\2<br />
</td>
        <td>4\9 &lt; g &lt; 5\11<br />
</td>
    </tr>
    <tr>
        <td>3L15s<br />
</td>
        <td>5\18 &lt; g &lt; 1\3<br />
</td>
        <td>5\18 &lt; g &lt; 2\7<br />
</td>
    </tr>
    <tr>
        <td>4L14s<br />
</td>
        <td>2\9 &lt; g &lt; 1\4<br />
</td>
        <td>2\9 &lt; g &lt; 3\13<br />
</td>
    </tr>
    <tr>
        <td>5L13s<br />
</td>
        <td>7\18 &lt; g &lt; 2\5<br />
</td>
        <td>7\18 &lt; g &lt; 9\23<br />
</td>
    </tr>
    <tr>
        <td>6L12s<br />
</td>
        <td>1\9 &lt; g &lt; 1\6<br />
</td>
        <td>1\9 &lt; g &lt; 2\15<br />
</td>
    </tr>
    <tr>
        <td>7L11s<br />
</td>
        <td>5\18 &lt; g &lt; 2\7<br />
</td>
        <td>5\18 &lt; g &lt; 7\25<br />
</td>
    </tr>
    <tr>
        <td>8L10s<br />
</td>
        <td>1\9 &lt; g &lt; 1\8<br />
</td>
        <td>1\9 &lt; g &lt; 2\17<br />
</td>
    </tr>
    <tr>
        <td>9L9s<br />
</td>
        <td>1\18 &lt; g &lt; 1\9<br />
</td>
        <td>1\18 &lt; g &lt; 2\27<br />
</td>
    </tr>
    <tr>
        <td>10L8s<br />
</td>
        <td>7\18 &lt; g &lt; 2\5<br />
</td>
        <td>7\18 &lt; g &lt; 9\23<br />
</td>
    </tr>
    <tr>
        <td>11L7s<br />
</td>
        <td>13\18 &lt; g &lt; 8\11<br />
</td>
        <td>13\18 &lt; g &lt; 21\29<br />
</td>
    </tr>
    <tr>
        <td>12L6s<br />
</td>
        <td>1\18 &lt; g &lt; 1\12<br />
</td>
        <td>1\18 &lt; g &lt; 1\15<br />
</td>
    </tr>
    <tr>
        <td>13L5s<br />
</td>
        <td>11\18 &lt; g &lt; 8\13<br />
</td>
        <td>11\18 &lt; g &lt; 19\31<br />
</td>
    </tr>
    <tr>
        <td>14L4s<br />
</td>
        <td>5\18 &lt; g &lt; 2\7<br />
</td>
        <td>5\18 &lt; g &lt; 7\25<br />
</td>
    </tr>
    <tr>
        <td>15L3s<br />
</td>
        <td>1\18 &lt; g &lt; 1\15<br />
</td>
        <td>1\18 &lt; g &lt; 2\33<br />
</td>
    </tr>
    <tr>
        <td>16L2s<br />
</td>
        <td>1\18 &lt; g &lt; 1\16<br />
</td>
        <td>1\18 &lt; g &lt; 1\17<br />
</td>
    </tr>
    <tr>
        <td>17L1s<br />
</td>
        <td>1\18 &lt; g &lt; 1\17<br />
</td>
        <td>1\18 &lt; g &lt; 2\35<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="x19"></a><!-- ws:end:WikiTextHeadingRule:34 -->19</h1>
<br />


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

<br />
<!-- ws:start:WikiTextHeadingRule:36:&lt;h1&gt; --><h1 id="toc18"><a name="x20"></a><!-- ws:end:WikiTextHeadingRule:36 -->20</h1>
<br />


<table class="wiki_table">
    <tr>
        <td>1L19s<br />
</td>
        <td>19\20 &lt; g &lt; 1<br />
</td>
        <td>19\20 &lt; g &lt; 20\21<br />
</td>
    </tr>
    <tr>
        <td>2L18s<br />
</td>
        <td>9\20 &lt; g &lt; 1\2<br />
</td>
        <td>9\20 &lt; g &lt; 5\11<br />
</td>
    </tr>
    <tr>
        <td>3L17s<br />
</td>
        <td>13\20 &lt; g &lt; 2\3<br />
</td>
        <td>13\20 &lt; g &lt; 15\23<br />
</td>
    </tr>
    <tr>
        <td>4L16s<br />
</td>
        <td>1\5 &lt; g &lt; 1\4<br />
</td>
        <td>1\5 &lt; g &lt; 2\9<br />
</td>
    </tr>
    <tr>
        <td>5L15s<br />
</td>
        <td>3\20 &lt; g &lt; 1\5<br />
</td>
        <td>3\20 &lt; g &lt; 4\25<br />
</td>
    </tr>
    <tr>
        <td>6L14s<br />
</td>
        <td>3\20 &lt; g &lt; 1\6<br />
</td>
        <td>3\20 &lt; g &lt; 2\13<br />
</td>
    </tr>
    <tr>
        <td>7L13s<br />
</td>
        <td>17\20 &lt; g &lt; 6\7<br />
</td>
        <td>17\20 &lt; g &lt; 23\27<br />
</td>
    </tr>
    <tr>
        <td>8L12s<br />
</td>
        <td>1\10 &lt; g &lt; 1\8<br />
</td>
        <td>1\10 &lt; g &lt; 1\9<br />
</td>
    </tr>
    <tr>
        <td>9L11s<br />
</td>
        <td>11\20 &lt; g &lt; 5\9<br />
</td>
        <td>11\20 &lt; g &lt; 16\29<br />
</td>
    </tr>
    <tr>
        <td>10L10s<br />
</td>
        <td>1\20 &lt; g &lt; 1\10<br />
</td>
        <td>1\20 &lt; g &lt; 1\15<br />
</td>
    </tr>
    <tr>
        <td>11L9s<br />
</td>
        <td>9\20 &lt; g &lt; 5\11<br />
</td>
        <td>9\20 &lt; g &lt; 14\31<br />
</td>
    </tr>
    <tr>
        <td>12L8s<br />
</td>
        <td>3\20 &lt; g &lt; 1\6<br />
</td>
        <td>3\20 &lt; g &lt; 2\13<br />
</td>
    </tr>
    <tr>
        <td>13L7s<br />
</td>
        <td>3\20 &lt; g &lt; 2\13<br />
</td>
        <td>3\20 &lt; g &lt; 5\33<br />
</td>
    </tr>
    <tr>
        <td>14L6s<br />
</td>
        <td>7\20 &lt; g &lt; 5\14<br />
</td>
        <td>7\20 &lt; g &lt; 6\17<br />
</td>
    </tr>
    <tr>
        <td>15L5s<br />
</td>
        <td>1\20 &lt; g &lt; 1\15<br />
</td>
        <td>1\20 &lt; g &lt; 2\35<br />
</td>
    </tr>
    <tr>
        <td>16L4s<br />
</td>
        <td>1\20 &lt; g &lt; 1\16<br />
</td>
        <td>1\20 &lt; g &lt; 1\18<br />
</td>
    </tr>
    <tr>
        <td>17L3s<br />
</td>
        <td>7\20 &lt; g &lt; 6\17<br />
</td>
        <td>7\20 &lt; g &lt; 13\37<br />
</td>
    </tr>
    <tr>
        <td>18L2s<br />
</td>
        <td>1\20 &lt; g &lt; 1\18<br />
</td>
        <td>1\20 &lt; g &lt; 1\19<br />
</td>
    </tr>
    <tr>
        <td>19L1s<br />
</td>
        <td>1\20 &lt; g &lt; 1\19<br />
</td>
        <td>1\20 &lt; g &lt; 2\39<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:38:&lt;h1&gt; --><h1 id="toc19"><a name="x21"></a><!-- ws:end:WikiTextHeadingRule:38 -->21</h1>
<br />


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

<br />
<!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><h1 id="toc20"><a name="x22"></a><!-- ws:end:WikiTextHeadingRule:40 -->22</h1>
<br />


<table class="wiki_table">
    <tr>
        <td>1L21s<br />
</td>
        <td>21\22 &lt; g &lt; 1<br />
</td>
        <td>21\22 &lt; g &lt; 22\23<br />
</td>
    </tr>
    <tr>
        <td>2L20s<br />
</td>
        <td>5\11 &lt; g &lt; 1\2<br />
</td>
        <td>5\11 &lt; g &lt; 6\13<br />
</td>
    </tr>
    <tr>
        <td>3L19s<br />
</td>
        <td>7\22 &lt; g &lt; 1\3<br />
</td>
        <td>7\22 &lt; g &lt; 8\25<br />
</td>
    </tr>
    <tr>
        <td>4L18s<br />
</td>
        <td>5\22 &lt; g &lt; 1\4<br />
</td>
        <td>5\22 &lt; g &lt; 3\13<br />
</td>
    </tr>
    <tr>
        <td>5L17s<br />
</td>
        <td>13\22 &lt; g &lt; 3\5<br />
</td>
        <td>13\22 &lt; g &lt; 16\27<br />
</td>
    </tr>
    <tr>
        <td>6L16s<br />
</td>
        <td>7\22 &lt; g &lt; 1\3<br />
</td>
        <td>7\22 &lt; g &lt; 8\25<br />
</td>
    </tr>
    <tr>
        <td>7L15s<br />
</td>
        <td>3\22 &lt; g &lt; 1\7<br />
</td>
        <td>3\22 &lt; g &lt; 4\29<br />
</td>
    </tr>
    <tr>
        <td>8L14s<br />
</td>
        <td>4\11 &lt; g &lt; 3\8<br />
</td>
        <td>4\11 &lt; g &lt; 7\19<br />
</td>
    </tr>
    <tr>
        <td>9L13s<br />
</td>
        <td>17\22 &lt; g &lt; 7\9<br />
</td>
        <td>17\22 &lt; g &lt; 24\31<br />
</td>
    </tr>
    <tr>
        <td>10L12s<br />
</td>
        <td>1\11 &lt; g &lt; 1\10<br />
</td>
        <td>1\11 &lt; g &lt; 2\21<br />
</td>
    </tr>
    <tr>
        <td>11L11s<br />
</td>
        <td>1\22 &lt; g &lt; 1\11<br />
</td>
        <td>1\22 &lt; g &lt; 2\33<br />
</td>
    </tr>
    <tr>
        <td>12L10s<br />
</td>
        <td>9\22 &lt; g &lt; 5\12<br />
</td>
        <td>9\22 &lt; g &lt; 7\17<br />
</td>
    </tr>
    <tr>
        <td>13L9s<br />
</td>
        <td>5\22 &lt; g &lt; 3\13<br />
</td>
        <td>5\22 &lt; g &lt; 8\35<br />
</td>
    </tr>
    <tr>
        <td>14L8s<br />
</td>
        <td>3\22 &lt; g &lt; 1\7<br />
</td>
        <td>3\22 &lt; g &lt; 4\29<br />
</td>
    </tr>
    <tr>
        <td>15L7s<br />
</td>
        <td>19\22 &lt; g &lt; 13\15<br />
</td>
        <td>19\22 &lt; g &lt; 32\37<br />
</td>
    </tr>
    <tr>
        <td>16L6s<br />
</td>
        <td>2\11 &lt; g &lt; 3\16<br />
</td>
        <td>2\11 &lt; g &lt; 5\27<br />
</td>
    </tr>
    <tr>
        <td>17L5s<br />
</td>
        <td>9\22 &lt; g &lt; 7\17<br />
</td>
        <td>9\22 &lt; g &lt; 16\39<br />
</td>
    </tr>
    <tr>
        <td>18L4s<br />
</td>
        <td>3\11 &lt; g &lt; 5\18<br />
</td>
        <td>3\11 &lt; g &lt; 8\29<br />
</td>
    </tr>
    <tr>
        <td>19L3s<br />
</td>
        <td>15\22 &lt; g &lt; 13\19<br />
</td>
        <td>15\22 &lt; g &lt; 28\41<br />
</td>
    </tr>
    <tr>
        <td>20L2s<br />
</td>
        <td>1\22 &lt; g &lt; 1\20<br />
</td>
        <td>1\22 &lt; g &lt; 1\21<br />
</td>
    </tr>
    <tr>
        <td>21L1s<br />
</td>
        <td>1\22 &lt; g &lt; 1\21<br />
</td>
        <td>1\22 &lt; g &lt; 2\43<br />
</td>
    </tr>
</table>

</body></html>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2012-05-12 01:14:29 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-12 01:46:06 UTC</tt>.<br>
-: The original revision id was <tt>333922658</tt>.<br>
+: The original revision id was <tt>333930922</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>
@@ Line 8: / Line 8: @@
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Below are ranges of generators for various L-s patterns of MOS, with the number of steps in the scale from 2 to 22. The ranges are given in fractions of the interval of equivalence, which is normally an octave. The tables give the range of possible generators in the second column, normalized so that the lower end of the range is where L/s = 1 (Nedo.) The third column gives the range of propriety, where the proper MOS reside.
-Suppose we have a scale of N steps to the interval of repetition, with Q steps to a period, so that there are P = N/Q periods to the repetition interval (usually, an octave.) If the generator range in question is u &lt; g &lt; v, then we may multiply by P to get C/Q &lt; Pg &lt; a/b, where C is the number of the [[Interval class|generic interval]] to which the generator g belongs, and both C/Q and a/b are reduced to lowest terms. We have normalized so that C/N &lt; g, and hence C/Q &lt; Pg, with C/N being the lower end of the range of possible generators, where L=s. If the range is C/Q &lt; Pg &lt; a/b, then when Pg = a/b, s has decreased to zero with increasing g, so s = (a - bg)/P. If there are e large steps and f small steps, then eL + fs = 1, so L = (1 - fs)/e = 1/P - a + bg.
+Suppose we have a scale of N steps to the interval of repetition, with Q steps to a period, so that there are P = N/Q periods to the repetition interval (usually, an octave.) If the generator range in question is u &lt; g &lt; v, then we may multiply by P to get C/Q &lt; Pg &lt; a/b, where C is the number of the [[Interval class|generic interval]] to which the generator g belongs, and both C/Q and a/b are reduced to lowest terms. We have normalized so that C/N &lt; g, and hence C/Q &lt; Pg, with C/N being the lower end of the range of possible generators, where L=s. If the range is C/Q &lt; Pg &lt; a/b, then when Pg = a/b, s has decreased to zero with increasing g, so s = (a - bg)/P. C/Q is the [[http://en.wikipedia.org/wiki/Mediant_(mathematics)|mediant]] between (C-a)/(Q-b) and a/b, and so there are b large steps and Q-b small steps to a period, so that bL + (Q-b)s = !/P and hence L = (1 - (Q-b)(a-gb))/bP.
 =2=
@@ Line 306: / Line 306: @@
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Generator ranges of MOS&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Below are ranges of generators for various L-s patterns of MOS, with the number of steps in the scale from 2 to 22. The ranges are given in fractions of the interval of equivalence, which is normally an octave. The tables give the range of possible generators in the second column, normalized so that the lower end of the range is where L/s = 1 (Nedo.) The third column gives the range of propriety, where the proper MOS reside.&lt;br /&gt;
 &lt;br /&gt;
-Suppose we have a scale of N steps to the interval of repetition, with Q steps to a period, so that there are P = N/Q periods to the repetition interval (usually, an octave.) If the generator range in question is u &amp;lt; g &amp;lt; v, then we may multiply by P to get C/Q &amp;lt; Pg &amp;lt; a/b, where C is the number of the &lt;a class="wiki_link" href="/Interval%20class"&gt;generic interval&lt;/a&gt; to which the generator g belongs, and both C/Q and a/b are reduced to lowest terms. We have normalized so that C/N &amp;lt; g, and hence C/Q &amp;lt; Pg, with C/N being the lower end of the range of possible generators, where L=s. If the range is C/Q &amp;lt; Pg &amp;lt; a/b, then when Pg = a/b, s has decreased to zero with increasing g, so s = (a - bg)/P. If there are e large steps and f small steps, then eL + fs = 1, so L = (1 - fs)/e = 1/P - a + bg.&lt;br /&gt;
+Suppose we have a scale of N steps to the interval of repetition, with Q steps to a period, so that there are P = N/Q periods to the repetition interval (usually, an octave.) If the generator range in question is u &amp;lt; g &amp;lt; v, then we may multiply by P to get C/Q &amp;lt; Pg &amp;lt; a/b, where C is the number of the &lt;a class="wiki_link" href="/Interval%20class"&gt;generic interval&lt;/a&gt; to which the generator g belongs, and both C/Q and a/b are reduced to lowest terms. We have normalized so that C/N &amp;lt; g, and hence C/Q &amp;lt; Pg, with C/N being the lower end of the range of possible generators, where L=s. If the range is C/Q &amp;lt; Pg &amp;lt; a/b, then when Pg = a/b, s has decreased to zero with increasing g, so s = (a - bg)/P. C/Q is the &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Mediant_(mathematics)" rel="nofollow"&gt;mediant&lt;/a&gt; between (C-a)/(Q-b) and a/b, and so there are b large steps and Q-b small steps to a period, so that bL + (Q-b)s = !/P and hence L = (1 - (Q-b)(a-gb))/bP.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x2"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;2&lt;/h1&gt;

Generator ranges of MOS: Difference between revisions

Revision as of 01:46, 12 May 2012

IMPORTED REVISION FROM WIKISPACES

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