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Generator ranges of MOS: Difference between revisions

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Below are ranges of generators for various L-s patterns of [[MOS scale]]s, with the number of steps in the scale from 2 to 29. The ranges are given in fractions of the interval of equivalence, which is normally an octave. The tables give the range of possible generators in the second column, normalized so that the lower end of the range is where L/s = 1 (Nedo). The third column gives the boundaries of propriety, maximum expressiveness and diatonicity (i.e. best, better and good behavior). Finally, the fourth column gives the formula for the size of the chroma.
Below are ranges of generators for various L-s patterns of [[MOS scale]]s, with the number of steps in the scale from 2 to 29. The ranges are given in fractions of the interval of equivalence, which is normally an octave. The tables give the range of possible generators in the second column, normalized so that the lower end of the range is where L/s = 1 (Nedo). The third column gives the boundaries of propriety, maximum expressiveness and diatonicity (i.e. best, better and good behavior). Finally, the fourth column gives the formula for the size of the chroma. We have normalized to the formula for the step size where the leading term is positive.


If the number of the [[Interval_class|generic interval]] to which the generator g belongs is C, and there are N scale steps to the interval of equivalence, then the average the size of an interval in class C is C/N. We have normalized so that C/N is the lower bound of the range of generators; since therefore g > C/N, g is larger than average and hence is the larger of the two sizes of intervals in its class, which means we have normalized to the [[Modal_UDP_Notation|chroma-positive]] generator. We have normalized to the formula for the step size where the leading term is positive.
= 2, 3, and 4-tone =
'''Note 1: These sets are given for the sake of completeness as they are not really scales'''


= 2, 3, and 4-tone =
'''Note 2: monosmall patterns are italicized from here below as the boundary of propriety does apply to them'''
'''Note: These sets are given for the sake of completeness as they are not really scales'''


{| class="wikitable"
{| class="wikitable"
Line 13: Line 13:
! | Large step-Small step
! | Large step-Small step
|-
|-
| | [[1L 1s]]
| |[[1L 1s|''1L 1s'']]
| | 1\2 < g < 1
| | ''1\2 < g < 1''
| | g = 2\3, 3\4, 4\5-5\6
| | ''g = 2\3, 3\4, 4\5-5\6''
| | g-(1-g) = 2g-1
| | ''g-(1-g) = 2g-1''
|-
|-
| | [[1L 2s]]
| |[[1L 2s]]
| | 2\3 < g < 1
| | 2\3 < g < 1
| | g = 3\4, 4\5, 5\6-6\7
| | g = 3\4, 4\5, 5\6-6\7
| | 2g-1-(1-g) = 3g-2
| | 2g-1-(1-g) = 3g-2
|-
|-
| | [[2L 1s]]
| |[[2L 1s|''2L 1s'']]
| | 1\3 < g < 1\2
| | ''1\3 < g < 1\2''
| | g = 2\5, 3\7, 4\9-5\11
| | ''g = 2\5, 3\7, 4\9-5\11''
| | g-(1-2g)= 3g-1
| | ''g-(1-2g)= 3g-1''
|-
|-
| | [[1L 3s]]
| |[[1L 3s]]
| | 3\4 < g < 1
| | 3\4 < g < 1
| | g = 4\5, 5\6, 6\7-7\8
| | g = 4\5, 5\6, 6\7-7\8
| | 3g-2-(1-g) = 4g-3
| | 3g-2-(1-g) = 4g-3
|-
|-
| | [[2L 2s]]
| |[[2L 2s|''2L 2s'']] ''= 1L 1s (2)''
| | 1\4 < g < 1\2
| | ''1\4 < g < 1\2''
| | g = 2\6, 3\8, 4\10-5\12
| | ''g = 2\6, 3\8, 4\10-5\12''
| | g-(1\2-g) = 2g-1\2
| | ''g-(1\2-g) = 2g-1\2''
|-
|-
| | [[3L 1s]]
| |[[3L 1s|''3L 1s'']]
| | 1\4 < g < 1\3
| | ''1\4 < g < 1\3''
| | g = 2\7, 3\10, 4\13-5\16
| | ''g = 2\7, 3\10, 4\13-5\16''
| | g-(1-3g) = 4g-1
| | ''g-(1-3g) = 4g-1''
|}
|}


Line 68: Line 68:
| | 2g-1-(2-3g) = 5g-3
| | 2g-1-(2-3g) = 5g-3
|-
|-
| | [[4L 1s]]
| | [[4L 1s|''4L 1s'']]
| | 1\5 < g < 1\4
| | ''1\5 < g < 1\4''
| | g = 2\9, 3\13, 4\17-5\21
| | ''g = 2\9, 3\13, 4\17-5\21''
| | g-(1-4g) = 5g-1
| | ''g-(1-4g) = 5g-1''
|}
|}


Line 92: Line 92:
| | 2g-1\2-(1\2-g) = 3g-1
| | 2g-1\2-(1\2-g) = 3g-1
|-
|-
| | [[3L 3s]]
| | [[3L 3s|''3L 3s'']] ''= 1L 1s (3)''
| | 1\6 < g < 1\3
| | ''1\6 < g < 1\3''
| | g = 2\9, 3\12, 4\15-5\18
| | ''g = 2\9, 3\12, 4\15-5\18''
| | g-(1\3-g) = 2g-1\3
| | ''g-(1\3-g) = 2g-1\3''
|-
|-
| | [[4L 2s]]
| | [[4L 2s|''4L 2s'']] ''= 2L 1s (2)''
| | 1\6 < g < 1\4
| | ''1\6 < g < 1\4''
| | g = 2\10, 3\14, 4\18-5\22
| | ''g = 2\10, 3\14, 4\18-5\22''
| | g-(1\2-2g) = 3g-1\2
| | ''g-(1\2-2g) = 3g-1\2''
|-
|-
| | [[5L 1s]]
| | [[5L 1s|''5L 1s'']]
| | 1\6 < g < 1\5
| | ''1\6 < g < 1\5''
| | g = 2\11, 3\16, 4\21-5\26
| | ''g = 2\11, 3\16, 4\21-5\26''
| | g-(1-5g) = 6g-1
| | ''g-(1-5g) = 6g-1''
|}
|}


Line 141: Line 141:
| | 2g-1-(3-5g) = 7g-4
| | 2g-1-(3-5g) = 7g-4
|-
|-
| | [[6L 1s]]
| | [[6L 1s|''6L 1s'']]
| | 1\7 < g < 1\6
| | ''1\7 < g < 1\6''
| | g = 2\13, 3\19, 4\25-5\31
| | ''g = 2\13, 3\19, 4\25-5\31''
| | g-(1-6g) = 7g-1
| | ''g-(1-6g) = 7g-1''
|}
|}


Line 170: Line 170:
| | 5g-3-(2-3g) = 8g-5
| | 5g-3-(2-3g) = 8g-5
|-
|-
| | [[4L 4s]]
| | [[4L 4s|''4L 4s'']] ''= 1L 1s (4)''
| | 1\8 < g < 1\4
| | ''1\8 < g < 1\4''
| | g = 2\12, 3\16, 4\20-5\24
| | ''g = 2\12, 3\16, 4\20-5\24''
| | g-(1\4-g) = 2g-1\4
| | ''g-(1\4-g) = 2g-1\4''
|-
|-
| | [[5L 3s]]
| | [[5L 3s]]
Line 180: Line 180:
| | 3g-1-(2-5g) = 8g-3
| | 3g-1-(2-5g) = 8g-3
|-
|-
| | [[6L 2s]]
| | [[6L 2s|''6L 2s'']] ''= 3L 1s (2)''
| | 1\8 < g < 1\6
| | ''1\8 < g < 1\6''
| | g = 2\14, 3\20, 4\26-5\32
| | ''g = 2\14, 3\20, 4\26-5\32''
| | g-(1\2-3g) = 4g-1\2
| | ''g-(1\2-3g) = 4g-1\2''
|-
|-
| | [[7L 1s]]
| | [[7L 1s|''7L 1s'']]
| | 1\8 < g < 1\7
| | ''1\8 < g < 1\7''
| | g = 2\15, 3\22, 4\29-5\36
| | ''g = 2\15, 3\22, 4\29-5\36''
| | g-(1-7g) = 8g-1
| | ''g-(1-7g) = 8g-1''
|}
|}


Line 224: Line 224:
| | 4g-3-(4-5g) = 9g-7
| | 4g-3-(4-5g) = 9g-7
|-
|-
| | [[6L 3s]]
| | [[6L 3s|''6L 3s'']] ''= 2L 1s (3)''
| | 1\9 < g < 1\6
| | ''1\9 < g < 1\6''
| | g = 2\15, 3\21, 4\27-5\33
| | ''g = 2\15, 3\21, 4\27-5\33''
| | g-(1\3-2g) = 3g-1\3
| | ''g-(1\3-2g) = 3g-1\3''
|-
|-
| | [[7L 2s]]
| | [[7L 2s]]
Line 234: Line 234:
| | 2g-1-(4-7g) = 9g-5
| | 2g-1-(4-7g) = 9g-5
|-
|-
| | [[8L 1s]]
| | [[8L 1s|''8L 1s'']]
| | 1\9 < g < 1\8
| | ''1\9 < g < 1\8''
| | g = 2\17, 3\25, 4\33-5\41
| | ''g = 2\17, 3\25, 4\33-5\41''
| | g-(1-8g) = 9g-1
| | ''g-(1-8g) = 9g-1''
|}
|}


Line 268: Line 268:
| | 3g-1\2-(1\2-2g) = 5g-1
| | 3g-1\2-(1\2-2g) = 5g-1
|-
|-
| | [[5L 5s]]
| | [[5L 5s|''5L 5s'']] ''= 1L 1s (5)''
| | 1\10 < g < 1\5
| | ''1\10 < g < 1\5''
| | g = 2\15, 3\20, 4\25-5\30
| | ''g = 2\15, 3\20, 4\25-5\30''
| | g-(1\5-g) = 2g-1\5
| | ''g-(1\5-g) = 2g-1\5''
|-
|-
| | [[6L 4s]]
| | [[6L 4s]]
Line 283: Line 283:
| | 3g-2-(5-7g) = 10g-7
| | 3g-2-(5-7g) = 10g-7
|-
|-
| | [[8L 2s]]
| | [[8L 2s|''8L 2s'']] ''= 4L 1s (2)''
| | 1\10 < g < 1\8
| | ''1\10 < g < 1\8''
| | g = 2\18, 3\26, 4\34-5\42
| | ''g = 2\18, 3\26, 4\34-5\42''
| | g-(1\2-4g) = 5g-1\2
| | ''g-(1\2-4g) = 5g-1\2''
|-
|-
| | [[9L 1s]]
| | [[9L 1s|''9L 1s'']]
| | 1\10 < g < 1\9
| | ''1\10 < g < 1\9''
| | g = 2\19, 3\28, 4\37-5\46
| | ''g = 2\19, 3\28, 4\37-5\46''
| | g-(1-9g) = 10g-1
| | ''g-(1-9g) = 10g-1''
|}
|}


Line 347: Line 347:
| | 2g-1-(5-9g) = 11g-6
| | 2g-1-(5-9g) = 11g-6
|-
|-
| | [[10L 1s]]
| | [[10L 1s|''10L 1s'']]
| | 1\11 < g < 1\10
| | ''1\11 < g < 1\10''
| | g = 2\21, 3\31, 4\41-5\51
| | ''g = 2\21, 3\31, 4\41-5\51''
| | g+1-10g = 11g-1
| | ''g+1-10g = 11g-1''
|}
|}


Line 386: Line 386:
| | 7g-4-(3-5g) = 12g-7
| | 7g-4-(3-5g) = 12g-7
|-
|-
| | [[6L 6s]]
| | [[6L 6s|''6L 6s'']] ''= 1L 1s (6)''
| | 1\12 < g < 1\6
| | ''1\12 < g < 1\6''
| | g = 2\18, 3\24, 4\30-5\36
| | ''g = 2\18, 3\24, 4\30-5\36''
| | g-(1\6-g) = 2g-1\6
| | ''g-(1\6-g) = 2g-1\6''
|-
|-
| | [[7L 5s]]
| | [[7L 5s]]
Line 396: Line 396:
| | 5g-2-(3-7g) = 12g-5
| | 5g-2-(3-7g) = 12g-5
|-
|-
| | [[8L 4s]]
| | [[8L 4s|''8L 4s'']] ''= 2L 1s (4)''
| | 1\12 < g < 1\8
| | ''1\12 < g < 1\8''
| | g = 2\20, 3\28, 4\36-5\44
| | ''g = 2\20, 3\28, 4\36-5\44''
| | g-(1\4-2g) = 3g-1\4
| | ''g-(1\4-2g) = 3g-1\4''
|-
|-
| | [[9L 3s]]
| | [[9L 3s|''9L 3s'']] ''= 3L 1s (3)''
| | 1\12 < g < 1\9
| | ''1\12 < g < 1\9''
| | g = 2\21, 3\30, 4\39-5\48
| | ''g = 2\21, 3\30, 4\39-5\48''
| | g-(1\3-3g) = 4g-1\3
| | ''g-(1\3-3g) = 4g-1\3''
|-
|-
| | [[10L 2s]]
| | [[10L 2s|''10L 2s'']] ''= 5L 1s (2)''
| | 1\12 < g < 1\10
| | ''1\12 < g < 1\10''
| | g = 2\22, 3\32, 4\42-5\52
| | ''g = 2\22, 3\32, 4\42-5\52''
| | g-(1\2-5g) = 6g-1\2
| | ''g-(1\2-5g) = 6g-1\2''
|-
|-
| | [[11L 1s]]
| | [[11L 1s|''11L 1s'']]
| | 1\12 < g < 1\11
| | ''1\12 < g < 1\11''
| | g = 2\23, 3\34, 4\45-5\56
| | ''g = 2\23, 3\34, 4\45-5\56''
| | g-(1-11g) = 12g-1
| | ''g-(1-11g) = 12g-1''
|}
|}


Line 480: Line 480:
| | 2g-1-(6-11g) = 13g-7
| | 2g-1-(6-11g) = 13g-7
|-
|-
| | [[12L 1s]]
| | [[12L 1s|''12L 1s'']]
| | 1\13 < g < 1\12
| | ''1\13 < g < 1\12''
| | g = 2\25, 3\37, 4\49-5\61
| | ''g = 2\25, 3\37, 4\49-5\61''
| | g-(1-12g) = 13g-1
| | ''g-(1-12g) = 13g-1''
|}
|}


Line 524: Line 524:
| | 4g-1\2-(1\2-3g) = 7g-1
| | 4g-1\2-(1\2-3g) = 7g-1
|-
|-
| | [[7L 7s]]
| | [[7L 7s|''7L 7s'']] ''= 1L 1s (7)''
| | 1\14 < g < 1\7
| | ''1\14 < g < 1\7''
| | g = 2\21, 3\28, 4\35-5\42
| | ''g = 2\21, 3\28, 4\35-5\42''
| | g-(1\7-g) = 2g-1\7
| | ''g-(1\7-g) = 2g-1\7''
|-
|-
| | [[8L 6s]]
| | [[8L 6s]]
Line 549: Line 549:
| | 3g-1-(4-11g) = 14g-5
| | 3g-1-(4-11g) = 14g-5
|-
|-
| | [[12L 2s]]
| | [[12L 2s|''12L 2s'']] ''= 6L 1s (2)''
| | 1\14 < g < 1\12
| | ''1\14 < g < 1\12''
| | g = 2\26, 3\38, 4\50-5\62
| | ''g = 2\26, 3\38, 4\50-5\62''
| | g-(1\2-6g) = 7g-1\2
| | ''g-(1\2-6g) = 7g-1\2''
|-
|-
| | [[13L 1s]]
| | [[13L 1s|''13L 1s'']]
| | 1\14 < g < 1\13
| | ''1\14 < g < 1\13''
| | g = 2\27, 3\40, 4\53-5\66
| | ''g = 2\27, 3\40, 4\53-5\66''
| | g+1-13g = 14g-1
| | ''g+1-13g = 14g-1''
|}
|}


Line 613: Line 613:
| | 2g-1\3-(2\3-3g) = 5g-1
| | 2g-1\3-(2\3-3g) = 5g-1
|-
|-
| | [[10L 5s]]
| | [[10L 5s|''10L 5s'']] ''= 2L 1s (5)''
| | 1\15 < g < 1\10
| | ''1\15 < g < 1\10''
| | g = 2\25, 3\35, 4\45-5\55
| | ''g = 2\25, 3\35, 4\45-5\55''
| | g-(1\5-2g) = 3g-1\5
| | ''g-(1\5-2g) = 3g-1\5''
|-
|-
| | [[11L 4s]]
| | [[11L 4s]]
Line 623: Line 623:
| | 4g-1-(3-11g) = 15g-4
| | 4g-1-(3-11g) = 15g-4
|-
|-
| | [[12L 3s]]
| | [[12L 3s|''12L 3s'']] ''= 4L 1s (3)''
| | 1\15 < g < 1\12
| | ''1\15 < g < 1\12''
| | g = 2\27, 3\39, 4\51-5\63
| | ''g = 2\27, 3\39, 4\51-5\63''
| | g-(1\3-4g) = 5g-1\3
| | ''g-(1\3-4g) = 5g-1\3''
|-
|-
| | [[13L 2s]]
| | [[13L 2s]]
Line 633: Line 633:
| | 2g-1-(7-13g) = 15g-8
| | 2g-1-(7-13g) = 15g-8
|-
|-
| | [[14L 1s]]
| | [[14L 1s|''14L 1s'']]
| | 1\15 < g < 1\14
| | ''1\15 < g < 1\14''
| | g = 2\29, 3\43, 4\57-5\71
| | ''g = 2\29, 3\43, 4\57-5\71''
| | g-(1-14g) = 15g-1
| | ''g-(1-14g) = 15g-1''
|}
|}


Line 682: Line 682:
| | 9g-5-(4-7g) = 16g-9
| | 9g-5-(4-7g) = 16g-9
|-
|-
| | [[8L 8s]]
| | [[8L 8s|''8L 8s'']] = ''1L 1s (8)''
| | 1\16 < g < 1\8
| | ''1\16 < g < 1\8''
| | g = 2\24, 3\32, 4\40-5\48
| | ''g = 2\24, 3\32, 4\40-5\48''
| | g-(1\8-g) = 2g-1\8
| | ''g-(1\8-g) = 2g-1\8''
|-
|-
| | [[9L 7s]]
| | [[9L 7s]]
Line 702: Line 702:
| | 5g-4-(9-11g) = 16g-13
| | 5g-4-(9-11g) = 16g-13
|-
|-
| | [[12L 4s]]
| | [[12L 4s|''12L 4s'']] ''= 3L 1s (4)''
| | 1\16 < g < 1\12
| | ''1\16 < g < 1\12''
| | g = 2\28, 3\40, 4\52-5\64
| | ''g = 2\28, 3\40, 4\52-5\64''
| | g-(1\4-3g) = 4g-1\4
| | ''g-(1\4-3g) = 4g-1\4''
|-
|-
| | [[13L 3s]]
| | [[13L 3s]]
Line 712: Line 712:
| | 3g-2-(9-13g) = 16g-11
| | 3g-2-(9-13g) = 16g-11
|-
|-
| | [[14L 2s]]
| | [[14L 2s|''14L 2s'']] ''= 7L 1s (2)''
| | 1\16 < g < 1\14
| | ''1\16 < g < 1\14''
| | g = 2\30, 3\44, 4\58-5\72
| | ''g = 2\30, 3\44, 4\58-5\72''
| | g-(1\2-7g) = 8g-1\2
| | ''g-(1\2-7g) = 8g-1\2''
|-
|-
| | [[15L 1s]]
| | [[15L 1s|''15L 1s'']]
| | 1\16 < g < 1\15
| | ''1\16 < g < 1\15''
| | g = 2\31, 3\46, 4\61-5\76
| | ''g = 2\31, 3\46, 4\61-5\76''
| | g-(1-15g) = 16g-1
| | ''g-(1-15g) = 16g-1''
|}
|}


Line 806: Line 806:
| | 2g-1-(8-15g) = 17g-9
| | 2g-1-(8-15g) = 17g-9
|-
|-
| | [[16L 1s]]
| | [[16L 1s|''16L 1s'']]
| | 1\17 < g < 1\16
| | ''1\17 < g < 1\16''
| | g = 2\33, 3\49, 4\65-5\81
| | ''g = 2\33, 3\49, 4\65-5\81''
| | g-(1-16g) = 17g-1
| | ''g-(1-16g) = 17g-1''
|}
|}


Line 860: Line 860:
| | 5g-1\2-(1\2-4g) = 9g-1
| | 5g-1\2-(1\2-4g) = 9g-1
|-
|-
| | [[9L 9s]]
| | [[9L 9s|''9L 9s'']] ''= 1L 1s (9)''
| | 1\18 < g < 1\9
| | ''1\18 < g < 1\9''
| | g = 2\27, 3\36, 4\45-5\54
| | ''g = 2\27, 3\36, 4\45-5\54''
| | g-(1\9-g) = 2g-1\9
| | ''g-(1\9-g) = 2g-1\9''
|-
|-
| | [[10L 8s]]
| | [[10L 8s]]
Line 875: Line 875:
| | 7g-5-(8-11g) = 18g-13
| | 7g-5-(8-11g) = 18g-13
|-
|-
| | [[12L 6s]]
| | [[12L 6s|''12L 6s'']] ''= 2L 1s (6)''
| | 1\18 < g < 1\12
| | ''1\18 < g < 1\12''
| | g = 2\30, 3\42, 4\54-5\66
| | ''g = 2\30, 3\42, 4\54-5\66''
| | g-(1\6-2g) = 3g-1\6
| | ''g-(1\6-2g) = 3g-1\6''
|-
|-
| | [[13L 5s]]
| | [[13L 5s]]
Line 890: Line 890:
| | 2g-1\2-(2-7g) = 9g-5\2
| | 2g-1\2-(2-7g) = 9g-5\2
|-
|-
| | [[15L 3s]]
| | [[15L 3s|''15L 3s'']] ''= 5L 1s (3)''
| | 1\18 < g < 1\15
| | ''1\18 < g < 1\15''
| | g = 2\33, 3\48, 4\63-5\78
| | ''g = 2\33, 3\48, 4\63-5\78''
| | g-(1\3-5g) = 6g-1\3
| | ''g-(1\3-5g) = 6g-1\3''
|-
|-
| | [[16L 2s]]
| | [[16L 2s|''16L 2s'']] ''= 8L 1s (2)''
| | 1\18 < g < 1\16
| | ''1\18 < g < 1\16''
| | g = 2\34, 3\50, 4\66-5\82
| | ''g = 2\34, 3\50, 4\66-5\82''
| | g-(1\2-8g) = 9g-1\2
| | ''g-(1\2-8g) = 9g-1\2''
|-
|-
| | [[17L 1s]]
| | [[17L 1s|''17L 1s'']]
| | 1\18 < g < 1\17
| | ''1\18 < g < 1\17''
| | g = 2\35, 3\52, 4\69-5\86
| | ''g = 2\35, 3\52, 4\69-5\86''
| | g-(1-17g) = 18g-1
| | ''g-(1-17g) = 18g-1''
|}
|}


Line 941: Line 941:
| | [[6L 13s]]
| | [[6L 13s]]
| | 3\19 < g < 1\6
| | 3\19 < g < 1\6
| | g = 4\25, 5\31, 6/37-7\43
| | g = 4\25, 5\31, 6\37-7\43
| |13g-2-(1-6g) = 19g-3
| |13g-2-(1-6g) = 19g-3
|-
|-
Line 999: Line 999:
| |2g-1-(9-17g) = 19g-10
| |2g-1-(9-17g) = 19g-10
|-
|-
| | [[18L 1s]]
| | [[18L 1s|''18L 1s'']]
| | 1\19 < g < 1\18
| | ''1\19 < g < 1\18''
| | g = 2\37, 3\55, 4\73-5\91
| | ''g = 2\37, 3\55, 4\73-5\91''
| |g-(1-18g) = 19g-1
| |''g-(1-18g) = 19g-1''
|}
|}


Line 1,015: Line 1,015:
| | [[1L 19s]]
| | [[1L 19s]]
| | 19\20 < g < 1
| | 19\20 < g < 1
| | ''g = 20\21, 21\22, 22\23''
| | ''g = 20\21, 21\22, 22\23-23\24''
| | 19g-18+1-g = 18g-17
| | 19g-18-(1-g) = 20g-19
|-
|-
| | [[2L 18s]]
| | [[2L 18s]]
| | 9\20 < g < 1\2
| | 9\20 < g < 1\2
| | g = ''10\22'', ''11\24'', 12\26
| | g = ''10\22'', ''11\24'', 12\26-13\28
| | 9g-4+1\2-g = 8g-7\2
| | 9g-4-(1\2-g) = 10g-9\2
|-
|-
| | [[3L 17s]]
| | [[3L 17s]]
| | 13\20 < g < 2\3
| | 13\20 < g < 2\3
| | g = ''15\23'', 17\26, 20\29
| | g = ''15\23'', 17\26, 19\29-21\32
| | 17g-11+2-3g = 14g-9
| | 17g-11-(2-3g) = 20g-13
|-
|-
| | [[4L 16s]]
| | [[4L 16s]]
| | 4\20 < g < 1\4
| | 4\20 < g < 1\4
| | g = ''5\24'', 6\28, 7\32
| | g = ''5\24'', 6\28, 7\32-8\36
| | 4g-3\4+1\4-g = 3g-1\4
| | 4g-3\4-(1\4-g) = 5g-1
|-
|-
| | [[5L 15s]]
| | [[5L 15s]]
| | 3\20 < g < 1\5
| | 3\20 < g < 1\5
| | g = ''4\25'', 5\30, 6\35
| | g = ''4\25'', 5\30, 6\35-7\40
| | 3g-2\5+1\5-g = 2g-1\5
| | 3g-2\5-(1\5-g) = 4g-3\5
|-
|-
| | [[6L 14s]]
| | [[6L 14s]]
| | 3\20 < g < 1\6
| | 3\20 < g < 1\6
| | g = 4\26, 5\32, 6\38
| | g = 4\26, 5\32, 6\38-7\44
| | 7g-1+1\2-3g = 4g-1\2
| | 7g-1-(1\2-3g) = 10g-3\2
|-
|-
| | [[7L 13s]]
| | [[7L 13s]]
| | 17\20 < g < 6\7
| | 17\20 < g < 6\7
| | g = 23\27, 29\34, 35\41
| | g = 23\27, 29\34, 35\41-41\48
| | 13g-11+6-7g = 6g-5
| | 13g-11-(6-7g) = 20g-17
|-
|-
| | [[8L 12s]]
| | [[8L 12s]]
| | 2\20 < g < 1\8
| | 2\20 < g < 1\8
| | g = 3\28, 4\36, 5\44
| | g = 3\28, 4\36, 5\44-6\52
| | 3g-1\4+1\4-2g = g
| | 3g-1\4-(1\4-2g) = 5g-1\2
|-
|-
| | [[9L 11s]]
| | [[9L 11s]]
| | 11\20 < g < 5\9
| | 11\20 < g < 5\9
| | g = 16\29, 21\38, 26\47
| | g = 16\29, 21\38, 26\47-31\56
| | 11g-6+5-9g =2g-1
| | 11g-6-(5-9g) = 20g-11
|-
|-
| | [[10L 10s]]
| | [[10L 10s|''10L 10s'']] ''= 1L 1s (10)''
| | 1\20 < g < 1\10
| | ''1\20 < g < 1\10''
| | g = 2\30, 3\40, 4\50
| | ''g = 2\30, 3\40, 4\50-5\60''
| | g+1\10-g = 1\10
| | ''g-(1\10-g) = 2g-1\10''
|-
|-
| | [[11L 9s]]
| | [[11L 9s]]
| | 9\20 < g < 5\11
| | 9\20 < g < 5\11
| | g = 14\31, 19\42, 24\53
| | g = 14\31, 19\42, 24\53-29\64
| | 9g-4+5-11g = 1-2g
| | 9g-4-(5-11g) = 20g-9
|-
|-
| | [[12L 8s]]
| | [[12L 8s]]
| | 3\20 < g < 2\12
| | 3\20 < g < 2\12
| | g = 5\32, 7\44, 9\56
| | g = 5\32, 7\44, 9\56-11\68
| | 2g-1\4+1\2-3g = 1\4-g
| | 2g-1\4-(1\2-3g) = 5g-3\4
|-
|-
| | [[13L 7s]]
| | [[13L 7s]]
| | 3\20 < g < 2\13
| | 3\20 < g < 2\13
| | g = 5\33, 7\46, 9\59
| | g = 5\33, 7\46, 9\59-11\72
| | 7g-1+2-13g = 1-6g
| | 7g-1-(2-13g) = 20g-3
|-
|-
| | [[14L 6s]]
| | [[14L 6s]]
| | 7\20 < g < 5\14
| | 7\20 < g < 5\14
| | g = 12\34, 17\48, 22\62
| | g = 12\34, 17\48, 22\62-32\76
| | 3g-1+5\2-7g = 2-4g
| | 3g-1-(5\2-7g) = 10g-7\2
|-
|-
| | [[15L 5s]]
| | [[15L 5s|''15L 5s'']] ''= 3L 1s (5)''
| | 1\20 < g < 1\15
| | ''1\20 < g < 1\15''
| | g = 2\35, 3\50, 4\65
| | ''g = 2\35, 3\50, 4\65-5\80''
| | g+1\5-3g = 1\5-2g
| | ''g-(1\5-3g) = 4g-1\5''
|-
|-
| | [[16L 4s]]
| | [[16L 4s|''16L 4s'']] ''= 4L 1s (4)''
| | 1\20 < g < 1\16
| | ''1\20 < g < 1\16''
| | g = 2\36, 3\52, 4\68
| | ''g = 2\36, 3\52, 4\68-5\84''
| | g+1\4-4g = 1\4-3g
| | ''g-(1\4-4g) = 5g-1\4''
|-
|-
| | [[17L 3s]]
| | [[17L 3s]]
| | 7\20 < g < 6\17
| | 7\20 < g < 6\17
| | g = 13\37, 19\54, 25\71
| | g = 13\37, 19\54, 25\71-31\88
| | 3g-1+6-17g = 5-14g
| | 3g-1-(6-17g) = 5-14g
|-
|-
| | [[18L 2s]]
| | [[18L 2s|''18L 2s'']] ''= 9L 1s (2)''
| | 1\20 < g < 1\18
| | ''1\20 < g < 1\18''
| | g = 2\38, 3\56, 4\74
| | ''g = 2\38, 3\56, 4\74-5\92''
| | g+1\2-9g = 1\2-8g
| | ''g-(1\2-9g) = 10g-1\2''
|-
|-
| | [[19L 1s]]
| | [[19L 1s|''19L 1s'']]
| | 1\20 < g < 1\19
| | ''1\20 < g < 1\19''
| | g = 2\39, 3\58, 4\77
| | ''g = 2\39, 3\58, 4\77-5\96''
| | g+1-19g = 1-18g
| | ''g-(1-19g) = 20g-1''
|}
|}


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