Generator ranges of MOS: Difference between revisions

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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.
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, 4=
= 2, 3, and 4-tone =
'''Note: These sets are given for the sake of completeness as they are not really scales'''
'''Note: These sets are given for the sake of completeness as they are not really scales'''


Line 13: Line 13:
! | Large step+Small step
! | Large step+Small step
|-
|-
| | 1L1s
| | [[1L 1s]]
| | 1\2 < g < 1
| | 1\2 < g < 1
| | g = 2\3, 3\4, 4\5
| | g = 2\3, 3\4, 4\5
| | g+1-g = 1
| | g+1-g = 1
|-
|-
| | 1L2s
| | [[1L 2s]]
| | 2\3 < g < 1
| | 2\3 < g < 1
| | g = 3\4, 4\5, 5\6
| | g = 3\4, 4\5, 5\6
| | 2g-1+1-g = g
| | 2g-1+1-g = g
|-
|-
| | 2L1s
| | [[2L 1s]]
| | 1\3 < g < 1\2
| | 1\3 < g < 1\2
| | g = 2\5, 3\7, 4\9
| | g = 2\5, 3\7, 4\9
| | g+1-2g = 1-g
| | g+1-2g = 1-g
|-
|-
| | 1L3s
| | [[1L 3s]]
| | 3\4 < g < 1
| | 3\4 < g < 1
| | g = 4\5, 5\6, 6\7
| | g = 4\5, 5\6, 6\7
| | 3g-2+1-g = 2g-1
| | 3g-2+1-g = 2g-1
|-
|-
| | 2L2s
| | [[2L 2s]]
| | 1\4 < g < 1\2
| | 1\4 < g < 1\2
| | g = 2\6, 3\8, 4\10
| | g = 2\6, 3\8, 4\10
| | g+1\2-g = 1\2
| | g+1\2-g = 1\2
|-
|-
| | 3L1s
| | [[3L 1s]]
| | 1\4 < g < 1\3
| | 1\4 < g < 1\3
| | g = 2\7, 3\10, 4\13
| | g = 2\7, 3\10, 4\13
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|}
|}


=5=
= 5-tone =
'''Note: italicized generators from here below generate scales which are weakly tonal'''
'''Note: italicized generators from here below generate scales which are weakly tonal'''
{| class="wikitable"
{| class="wikitable"
Line 53: Line 53:
! | Large step+Small step
! | Large step+Small step
|-
|-
| | 1L4s
| | [[1L 4s]]
| | 4\5 < g < 1
| | 4\5 < g < 1
| | g = ''5\6'', 6\7, 7\8
| | g = ''5\6'', 6\7, 7\8
| | 4g-3+1-g = 3g-2
| | 4g-3+1-g = 3g-2
|-
|-
| | 2L3s
| | [[2L 3s]]
| | 2\5 < g < 1\2
| | 2\5 < g < 1\2
| | g = 3\7, 4\9, 5\11
| | g = 3\7, 4\9, 5\11
| | 3g-1+1-2g = g
| | 3g-1+1-2g = g
|-
|-
| | 3L2s
| | [[3L 2s]]
| | 3\5 < g < 2\3
| | 3\5 < g < 2\3
| | g = 5\8, 7\11, 9\14
| | g = 5\8, 7\11, 9\14
| | 2g-1+2-3g = 1-g
| | 2g-1+2-3g = 1-g
|-
|-
| | 4L1s
| | [[4L 1s]]
| | 1\5 < g < 1\4
| | 1\5 < g < 1\4
| | g = 2\9, 3\13, 4\17
| | g = 2\9, 3\13, 4\17
Line 74: Line 74:
|}
|}


=6=
= 6-tone =
 
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 83: Line 82:
! | Large step+Small step
! | Large step+Small step
|-
|-
| | 1L5s
| | [[1L 5s]]
| | 5\6 < g < 1
| | 5\6 < g < 1
| | g = ''6\7'', 7\8, 8\9
| | g = ''6\7'', 7\8, 8\9
| | 5g-4+1-g = 4g-3
| | 5g-4+1-g = 4g-3
|-
|-
| | 2L4s
| | [[2L 4s]]
| | 2\6 < g < 1\2
| | 2\6 < g < 1\2
| | g = 3\8, 4\10, 5\12
| | g = 3\8, 4\10, 5\12
| | 2g-1\2+1\2-g = g
| | 2g-1\2+1\2-g = g
|-
|-
| | 3L3s
| | [[3L 3s]]
| | 1\6 < g < 1\3
| | 1\6 < g < 1\3
| | g = 2\9, 3\12, 4\15
| | g = 2\9, 3\12, 4\15
| | g+1\3-g = 1\3
| | g+1\3-g = 1\3
|-
|-
| | 4L2s
| | [[4L 2s]]
| | 1\6 < g < 1\4
| | 1\6 < g < 1\4
| | g = 2\10, 3\14, 4\18
| | g = 2\10, 3\14, 4\18
| | g+1\2-2g = 1\2-g
| | g+1\2-2g = 1\2-g
|-
|-
| | 5L1s
| | [[5L 1s]]
| | 1\6 < g < 1\5
| | 1\6 < g < 1\5
| | g = 2\11, 3\16, 4\21
| | g = 2\11, 3\16, 4\21
Line 109: Line 108:
|}
|}


=7=
= 7-tone =
 
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 118: Line 116:
! | Large step+Small step
! | Large step+Small step
|-
|-
| | 1L6s
| | [[1L 6s]]
| | 6\7 < g < 1
| | 6\7 < g < 1
| | g = ''7\8'', 8\9, 9\10
| | g = ''7\8'', 8\9, 9\10
| | 6g-5+1-g = 5g-4
| | 6g-5+1-g = 5g-4
|-
|-
| | 2L5s
| | [[2L 5s]]
| | 3\7 < g < 1\2
| | 3\7 < g < 1\2
| | g = 4\9, 5\11, 6\13
| | g = 4\9, 5\11, 6\13
| | 5g-2+1-2g = 3g-1
| | 5g-2+1-2g = 3g-1
|-
|-
| | 3L4s
| | [[3L 4s]]
| | 2\7 < g < 1\3
| | 2\7 < g < 1\3
| | g = 3\10, 4\13, 5\16
| | g = 3\10, 4\13, 5\16
| | 4g-1+1-3g = g
| | 4g-1+1-3g = g
|-
|-
| | 4L3s
| | [[4L 3s]]
| | 5\7 < g < 3\4
| | 5\7 < g < 3\4
| | g = 8\11, 11\15, 14\19
| | g = 8\11, 11\15, 14\19
| | 3g-2+3-4g = 1-g
| | 3g-2+3-4g = 1-g
|-
|-
| | 5L2s
| | [[5L 2s]]
| | 4\7 < g < 3\5
| | 4\7 < g < 3\5
| | g = 7\12, 10\17, 13\22
| | g = 7\12, 10\17, 13\22
| | 2g-1+3-5g = 2-3g
| | 2g-1+3-5g = 2-3g
|-
|-
| | 6L1s
| | [[6L 1s]]
| | 1\7 < g < 1\6
| | 1\7 < g < 1\6
| | g = 2\13, 3\19, 4\25
| | g = 2\13, 3\19, 4\25
Line 149: Line 147:
|}
|}


=8=
= 8-tone =
 
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 158: Line 155:
! | Large step+Small step
! | Large step+Small step
|-
|-
| | 1L7s
| | [[1L 7s]]
| | 7\8 < g < 1
| | 7\8 < g < 1
| | g = ''8\9, 9\10'', 10\11
| | g = ''8\9, 9\10'', 10\11
| | 7g-6+1-g = 6g-5
| | 7g-6+1-g = 6g-5
|-
|-
| | 2L6s
| | [[2L 6s]]
| | 3\8 < g < 1\2
| | 3\8 < g < 1\2
| | g = ''4\10'', 5\12, 6\14
| | g = ''4\10'', 5\12, 6\14
| | 3g-1+1\2-g = 2g-1\2
| | 3g-1+1\2-g = 2g-1\2
|-
|-
| | 3L5s
| | [[3L 5s]]
| | 5\8 < g < 2\3
| | 5\8 < g < 2\3
| | g = 7\11, 9\14, 11\17
| | g = 7\11, 9\14, 11\17
| | 5g-3+2-3g = 2g-1
| | 5g-3+2-3g = 2g-1
|-
|-
| | 4L4s
| | [[4L 4s]]
| | 1\8 < g < 1\4
| | 1\8 < g < 1\4
| | g = 2\12, 3\16, 4\20
| | g = 2\12, 3\16, 4\20
| | g+1\4-g = 1\4
| | g+1\4-g = 1\4
|-
|-
| | 5L3s
| | [[5L 3s]]
| | 3\8 < g < 2\5
| | 3\8 < g < 2\5
| | g = 5\13, 7\18, 9\23
| | g = 5\13, 7\18, 9\23
| | 3g-1+2-5g = 1-2g
| | 3g-1+2-5g = 1-2g
|-
|-
| | 6L2s
| | [[6L 2s]]
| | 1\8 < g < 1\6
| | 1\8 < g < 1\6
| | g = 2\14, 3\20, 4\26
| | g = 2\14, 3\20, 4\26
| | g+1\2-3g = 1\2-2g
| | g+1\2-3g = 1\2-2g
|-
|-
| | 7L1s
| | [[7L 1s]]
| | 1\8 < g < 1\7
| | 1\8 < g < 1\7
| | g = 2\15, 3\22, 4\29
| | g = 2\15, 3\22, 4\29
Line 194: Line 191:
|}
|}


=9=
= 9-tone =
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 202: Line 199:
! | Large step+Small step
! | Large step+Small step
|-
|-
| | 1L8s
| | [[1L 8s]]
| | 8\9 < g < 1
| | 8\9 < g < 1
| | g = ''9\10'', ''10\11'', 11\12
| | g = ''9\10'', ''10\11'', 11\12
| | 8g-7+1-g = 7g-6
| | 8g-7+1-g = 7g-6
|-
|-
| | 2L7s
| | [[2L 7s]]
| | 4\9 < g < 1\2
| | 4\9 < g < 1\2
| | g = ''5\11'', 6\13, 7\15
| | g = ''5\11'', 6\13, 7\15
| | 7g-3+1-2g = 5g-2
| | 7g-3+1-2g = 5g-2
|-
|-
| | 3L6s
| | [[3L 6s]]
| | 2\9 < g < 1\3
| | 2\9 < g < 1\3
| | g = 3\12, 4\15, 5\18
| | g = 3\12, 4\15, 5\18
| | 2g-1\3+1\3-g = g
| | 2g-1\3+1\3-g = g
|-
|-
| | 4L5s
| | [[4L 5s]]
| | 2\9 < g < 1\4
| | 2\9 < g < 1\4
| | g = 3\13, 4\17, 5\21
| | g = 3\13, 4\17, 5\21
| | 5g-1+1-4g = g
| | 5g-1+1-4g = g
|-
|-
| | 5L4s
| | [[5L 4s]]
| | 7\9 < g < 4\5
| | 7\9 < g < 4\5
| | g = 11\14, 15\19, 18\23
| | g = 11\14, 15\19, 18\23
| | 4g-3+4-5g = 1-g
| | 4g-3+4-5g = 1-g
|-
|-
| | 6L3s
| | [[6L 3s]]
| | 1\9 < g < 1\6
| | 1\9 < g < 1\6
| | g = 2\15, 3\21, 4\27
| | g = 2\15, 3\21, 4\27
| | g+1\3-2g = 1\3-g
| | g+1\3-2g = 1\3-g
|-
|-
| | 7L2s
| | [[7L 2s]]
| | 5\9 < g < 4\7
| | 5\9 < g < 4\7
| | g = 9\16, 10\23, 17\30
| | g = 9\16, 10\23, 17\30
| | 2g-1+4-7g = 3-7g
| | 2g-1+4-7g = 3-7g
|-
|-
| | 8L1s
| | [[8L 1s]]
| | 1\9 < g < 1\8
| | 1\9 < g < 1\8
| | g = 2\17, 3\25, 4\33
| | g = 2\17, 3\25, 4\33
Line 243: Line 240:
|}
|}


=10=
= 10-tone =
 
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 252: Line 248:
! | Large step+Small step
! | Large step+Small step
|-
|-
| | 1L9s
| | [[1L 9s]]
| | 9\10 < g < 1
| | 9\10 < g < 1
| | g = ''10\11'', ''11\12'', 12\13
| | g = ''10\11'', ''11\12'', 12\13
| | 9g-8+1-g = 8g-7
| | 9g-8+1-g = 8g-7
|-
|-
| | 2L8s
| | [[2L 8s]]
| | 4\10 < g < 1\2
| | 4\10 < g < 1\2
| | g = ''5\12'', 6\14, 7\16
| | g = ''5\12'', 6\14, 7\16
| | 4g-3\2+1\2-g = 3g-1
| | 4g-3\2+1\2-g = 3g-1
|-
|-
| | 3L7s
| | [[3L 7s]]
| | 3\10 < g < 1\3
| | 3\10 < g < 1\3
| | g = 4\13, 5\16, 6\19
| | g = 4\13, 5\16, 6\19
| | 7g-2+1-3g = 4g-1
| | 7g-2+1-3g = 4g-1
|-
|-
| | 4L6s
| | [[4L 6s]]
| | 2\10 < g < 1\4
| | 2\10 < g < 1\4
| | g = 3\14, 4\18, 5\22
| | g = 3\14, 4\18, 5\22
| | 3g-1\2+1\2-2g = g
| | 3g-1\2+1\2-2g = g
|-
|-
| | 5L5s
| | [[5L 5s]]
| | 1\10 < g < 1\5
| | 1\10 < g < 1\5
| | g = 2\15, 3\20, 4\25
| | g = 2\15, 3\20, 4\25
| | g+1\5-g = 1\5  
| | g+1\5-g = 1\5  
|-
|-
| | 6L4s
| | [[6L 4s]]
| | 3\10 < g < 2\6
| | 3\10 < g < 2\6
| | g = 5\16, 7\22, 9\28
| | g = 5\16, 7\22, 9\28
| | 2g-1\2+1-3g = 1\2-g
| | 2g-1\2+1-3g = 1\2-g
|-
|-
| | 7L3s
| | [[7L 3s]]
| | 7\10 < g < 5\7
| | 7\10 < g < 5\7
| | g = 12\17, 17\24, 22\31
| | g = 12\17, 17\24, 22\31
| | 3g-2+5-7g = 3-4g
| | 3g-2+5-7g = 3-4g
|-
|-
| | 8L2s
| | [[8L 2s]]
| | 1\10 < g < 1\8
| | 1\10 < g < 1\8
| | g = 2\18, 3\26, 4\34
| | g = 2\18, 3\26, 4\34
| | g+1\2-4g = 1\2-3g
| | g+1\2-4g = 1\2-3g
|-
|-
| | 9L1s
| | [[9L 1s]]
| | 1\10 < g < 1\9
| | 1\10 < g < 1\9
| | g = 2\19, 3\28, 4\37
| | g = 2\19, 3\28, 4\37
Line 298: Line 294:
|}
|}


=11=
= 11-tone =
 
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 307: Line 302:
! | Large step+Small step
! | Large step+Small step
|-
|-
| | 1L10s
| | [[1L 10s]]
| | 10\11 < g < 1
| | 10\11 < g < 1
| | g = ''11\12'', ''12\13'', 13\14
| | g = ''11\12'', ''12\13'', 13\14
| | 10g-9+1-g = 9g-8
| | 10g-9+1-g = 9g-8
|-
|-
| | 2L9s
| | [[2L 9s]]
| | 5\11 < g < 1\2
| | 5\11 < g < 1\2
| | g = ''6\13'', 7\15, 8\17
| | g = ''6\13'', 7\15, 8\17
| | 9g-4+1-2g = 7g-3
| | 9g-4+1-2g = 7g-3
|-
|-
| | 3L8s
| | [[3L 8s]]
| | 7\11 < g < 2\3
| | 7\11 < g < 2\3
| | g = 9\14, 11\17, 13\20
| | g = 9\14, 11\17, 13\20
| | 8g-5+2-3g = 5g-3
| | 8g-5+2-3g = 5g-3
|-
|-
| | 4L7s
| | [[4L 7s]]
| | 8\11 < g < 3\4
| | 8\11 < g < 3\4
| | g = 11\15, 14\19, 17\23
| | g = 11\15, 14\19, 17\23
| | 7g-5+3-4g = 3g-2
| | 7g-5+3-4g = 3g-2
|-
|-
| | 5L6s
| | [[5L 6s]]
| | 2\11 < g < 1\5
| | 2\11 < g < 1\5
| | g = 3\16, 4\21, 5\26
| | g = 3\16, 4\21, 5\26
| | 6g-1+1-5g = g
| | 6g-1+1-5g = g
|-
|-
| | 6L5s
| | [[6L 5s]]
| | 9\11 < g < 5\6
| | 9\11 < g < 5\6
| | g = 14\17, 19\23, 24\29
| | g = 14\17, 19\23, 24\29
| | 5g-4+5-6g = 1-g
| | 5g-4+5-6g = 1-g
|-
|-
| | 7L4s
| | [[7L 4s]]
| | 3\11 < g < 2\7
| | 3\11 < g < 2\7
| | g = 5\18, 7\25, 9\32
| | g = 5\18, 7\25, 9\32
| | 4g-1+2-7g = 1-3g
| | 4g-1+2-7g = 1-3g
|-
|-
| | 8L3s
| | [[8L 3s]]
| | 4\11 < g < 3\8
| | 4\11 < g < 3\8
| | g = 7\19, 10\27, 13\35
| | g = 7\19, 10\27, 13\35
| | 3g-1+3-8g = 2-5g
| | 3g-1+3-8g = 2-5g
|-
|-
| | 9L2s
| | [[9L 2s]]
| | 6\11 < g < 5\9
| | 6\11 < g < 5\9
| | g = 11\20, 16\29, 21\38
| | g = 11\20, 16\29, 21\38
| | 2g-1+5-9g = 4-7g
| | 2g-1+5-9g = 4-7g
|-
|-
| | 10L1s
| | [[10L 1s]]
| | 1\11 < g < 1\10
| | 1\11 < g < 1\10
| | g = 2\21, 3\31, 4\41
| | g = 2\21, 3\31, 4\41
Line 358: Line 353:
|}
|}


=12=
= 12-tone =
 
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 367: Line 361:
! | Large step+Small step
! | Large step+Small step
|-
|-
| | 1L11s
| | [[1L 11s]]
| | 11\12 < g < 1
| | 11\12 < g < 1
| | g = ''12\13,'' ''13\14, 14\15''
| | g = ''12\13,'' ''13\14, 14\15''
| | 11g-10+1-g = 10g-9
| | 11g-10+1-g = 10g-9
|-
|-
| | 2L10s
| | [[2L 10s]]
| | 5\12 < g < 1\2
| | 5\12 < g < 1\2
| | g = ''6\14'', 7\16, 8\18
| | g = ''6\14'', 7\16, 8\18
| | 5g-2+1\2-g = 4g-3\2
| | 5g-2+1\2-g = 4g-3\2
|-
|-
| | 3L9s
| | [[3L 9s]]
| | 3\12 < g < 1\3
| | 3\12 < g < 1\3
| | g = ''4\15'', 5\18, 6\21
| | g = ''4\15'', 5\18, 6\21
| | 3g-2\3+1\3-g = 2g-1\3
| | 3g-2\3+1\3-g = 2g-1\3
|-
|-
| | 4L8s
| | [[4L 8s]]
| | 2\12 < g < 1\4
| | 2\12 < g < 1\4
| | g = 3\16, 4\20, 5\24
| | g = 3\16, 4\20, 5\24
| | 2g-1\4+1\4-g = g
| | 2g-1\4+1\4-g = g
|-
|-
| | 5L7s
| | [[5L 7s]]
| | 7\12 < g < 3\5
| | 7\12 < g < 3\5
| | g = 10\17, 13\22, 16\27
| | g = 10\17, 13\22, 16\27
| | 7g-4+3-5g = 2g-1
| | 7g-4+3-5g = 2g-1
|-
|-
| | 6L6s
| | [[6L 6s]]
| | 1\12 < g < 1\6
| | 1\12 < g < 1\6
| | g = 2\18, 3\24, 4\30
| | g = 2\18, 3\24, 4\30
| | g+1\6-g = g
| | g+1\6-g = g
|-
|-
| | 7L5s
| | [[7L 5s]]
| | 5\12 < g < 3\7
| | 5\12 < g < 3\7
| | g = 8\19, 11\26, 14\33
| | g = 8\19, 11\26, 14\33
| | 5g-2+3-7g = 1-2g
| | 5g-2+3-7g = 1-2g
|-
|-
| | 8L4s
| | [[8L 4s]]
| | 1\12 < g < 1\8
| | 1\12 < g < 1\8
| | g = 2\20, 3\28, 4\36
| | g = 2\20, 3\28, 4\36
| | g+1\4-2g = 1\4-g
| | g+1\4-2g = 1\4-g
|-
|-
| | 9L3s
| | [[9L 3s]]
| | 1\12 < g < 1\9
| | 1\12 < g < 1\9
| | g = 2\21, 3\30, 4\39
| | g = 2\21, 3\30, 4\39
| | g+1\3-3g = 1\3-2g
| | g+1\3-3g = 1\3-2g
|-
|-
| | 10L2s
| | [[10L 2s]]
| | 1\12 < g < 1\10
| | 1\12 < g < 1\10
| | g = 2\22, 3\32, 4\42
| | g = 2\22, 3\32, 4\42
| | g+1\2-5g = 1\2-4g
| | g+1\2-5g = 1\2-4g
|-
|-
| | 11L1s
| | [[11L 1s]]
| | 1\12 < g < 1\11
| | 1\12 < g < 1\11
| | g = 2\23, 3\34, 4\45
| | g = 2\23, 3\34, 4\45
Line 423: Line 417:
|}
|}


=13=
= 13-tone =
 
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 432: Line 425:
! | Large step+Small step
! | Large step+Small step
|-
|-
| | 1L12s
| | [[1L 12s]]
| | 12\13 < g < 1
| | 12\13 < g < 1
| | ''g = 13\14, 14\15, 15\16''
| | ''g = 13\14, 14\15, 15\16''
| | 12g-11+1-g = 11g-10
| | 12g-11+1-g = 11g-10
|-
|-
| | 2L11s
| | [[2L 11s]]
| | 6\13 < g < 1\2
| | 6\13 < g < 1\2
| | g = ''7\15'', 8\17, 9\19
| | g = ''7\15'', 8\17, 9\19
| | 11g-5-1-2g = 10g-6
| | 11g-5-1-2g = 10g-6
|-
|-
| | 3L10s
| | [[3L 10s]]
| | 4\13 < g < 1\3
| | 4\13 < g < 1\3
| | g = ''5\16'', 6\19, 7/22
| | g = ''5\16'', 6\19, 7/22
| | 10g-3+1-3g = 7g-2
| | 10g-3+1-3g = 7g-2
|-
|-
| | 4L9s
| | [[4L 9s]]
| | 3\13 < g < 1\4
| | 3\13 < g < 1\4
| | g = 4\17, 5\21, 6\25
| | g = 4\17, 5\21, 6\25
| | 9g-2+1-4g = 5g-1
| | 9g-2+1-4g = 5g-1
|-
|-
| | 5L8s
| | [[5L 8s]]
| | 5\13 < g < 2\5
| | 5\13 < g < 2\5
| | g = 7\18, 9\23, 11\28
| | g = 7\18, 9\23, 11\28
| | 8g-3+2-5g = 3g-1
| | 8g-3+2-5g = 3g-1
|-
|-
| | 6L7s
| | [[6L 7s]]
| | 2\13 < g < 1\6
| | 2\13 < g < 1\6
| | g = 3\19, 4\25, 5\31
| | g = 3\19, 4\25, 5\31
| | 7g-1+1-6g = g
| | 7g-1+1-6g = g
|-
|-
| | 7L6s
| | [[7L 6s]]
| | 11\13 < g < 6\7
| | 11\13 < g < 6\7
| | g = 17\20, 23\27, 29\34
| | g = 17\20, 23\27, 29\34
| | 6g-5+6-7g = 1-g
| | 6g-5+6-7g = 1-g
|-
|-
| | 8L5s
| | [[8L 5s]]
| | 8\13 < g < 5\8
| | 8\13 < g < 5\8
| | g = 13\21, 18\29, 23\37
| | g = 13\21, 18\29, 23\37
| | 5g-3+5-8g = 2-3g
| | 5g-3+5-8g = 2-3g
|-
|-
| | 9L4s
| | [[9L 4s]]
| | 10\13 < g < 7\9
| | 10\13 < g < 7\9
| | g = 17\22, 24\31, 31\40
| | g = 17\22, 24\31, 31\40
| | 4g-3+7-9g = 4-5g
| | 4g-3+7-9g = 4-5g
|-
|-
| | 10L3s
| | [[10L 3s]]
| | 9\13 < g < 7\10
| | 9\13 < g < 7\10
| | g = 16\23, 23\33, 30\43
| | g = 16\23, 23\33, 30\43
| | 3g-2+7-10g = 5-7g
| | 3g-2+7-10g = 5-7g
|-
|-
| | 11L2s
| | [[11L 2s]]
| | 7\13 < g < 6\11
| | 7\13 < g < 6\11
| | g = 13\24, 19\35, 25\46
| | g = 13\24, 19\35, 25\46
| | 2g-1+6-11g = 5-9g
| | 2g-1+6-11g = 5-9g
|-
|-
| | 12L1s
| | [[12L 1s]]
| | 1\13 < g < 1\12
| | 1\13 < g < 1\12
| | g = 2\25, 3\37, 4\49
| | g = 2\25, 3\37, 4\49
Line 493: Line 486:
|}
|}


=14=
= 14-tone =
 
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 502: Line 494:
! | Large step+Small step
! | Large step+Small step
|-
|-
| | 1L13s
| | [[1L 13s]]
| | 13\14 < g < 1
| | 13\14 < g < 1
| | ''g = 14\15, 15\16, 16\17''
| | ''g = 14\15, 15\16, 16\17''
| | 13g-12+1-g = 12g-11
| | 13g-12+1-g = 12g-11
|-
|-
| | 2L12s
| | [[2L 12s]]
| | 6\14 < g < 1\2
| | 6\14 < g < 1\2
| | g = ''7\16'', 8\18, 9\20
| | g = ''7\16'', 8\18, 9\20
| | 6g-5\2+1\2-g = 5g-2
| | 6g-5\2+1\2-g = 5g-2
|-
|-
| | 3L11s
| | [[3L 11s]]
| | 9\14 < g < 2\3
| | 9\14 < g < 2\3
| | g = ''11\17'', 13\20, 15\23
| | g = ''11\17'', 13\20, 15\23
| | 11g-7+2-3g = 9g-5
| | 11g-7+2-3g = 9g-5
|-
|-
| | 4L10s
| | [[4L 10s]]
| | 3\14 < g < 1\4
| | 3\14 < g < 1\4
| | g = 4\18, 5\22, 6\26
| | g = 4\18, 5\22, 6\26
| | 5g-1+1\2-2g = 3g-1\2
| | 5g-1+1\2-2g = 3g-1\2
|-
|-
| | 5L9s
| | [[5L 9s]]
| | 11\14 < g < 4\5
| | 11\14 < g < 4\5
| | g = 15\19, 19\24, 23\29
| | g = 15\19, 19\24, 23\29
| | 9g-7+4-5g = 4g-3
| | 9g-7+4-5g = 4g-3
|-
|-
| | 6L8s
| | [[6L 8s]]
| | 2\14 < g < 1\6
| | 2\14 < g < 1\6
| | g = 3\20, 4\26, 5\32
| | g = 3\20, 4\26, 5\32
| | 4g-1\2-1\2-3g = g
| | 4g-1\2-1\2-3g = g
|-
|-
| | 7L7s
| | [[7L 7s]]
| | 1\14 < g < 1\7
| | 1\14 < g < 1\7
| | g = 2\21, 3\28, 4\35
| | g = 2\21, 3\28, 4\35
| | g+1\7-g = 1\7
| | g+1\7-g = 1\7
|-
|-
| | 8L6s
| | [[8L 6s]]
| | 5\14 < g < 3\8
| | 5\14 < g < 3\8
| | g = 8\22, 11\30, 14\38
| | g = 8\22, 11\30, 14\38
| | 3g-1+3\2-4g = 1\2-g
| | 3g-1+3\2-4g = 1\2-g
|-
|-
| | 9L5s
| | [[9L 5s]]
| | 3\14 < g < 2\9
| | 3\14 < g < 2\9
| | g = 5\23, 7\32, 9\41
| | g = 5\23, 7\32, 9\41
| | 5g-1+2-9g = 1-4g
| | 5g-1+2-9g = 1-4g
|-
|-
| | 10L4s
| | [[10L 4s]]
| | 4\14 < g < 3\10
| | 4\14 < g < 3\10
| | g = 7\24, 10\34, 13\44
| | g = 7\24, 10\34, 13\44
| | 2g-1\2+3\2-5g = 1-3g
| | 2g-1\2+3\2-5g = 1-3g
|-
|-
| | 11L3s
| | [[11L 3s]]
| | 5\14 < g < 4\11
| | 5\14 < g < 4\11
| | g = 9\25, 13\36, 17\47
| | g = 9\25, 13\36, 17\47
| | 3g-1+4-11g = 3-8g
| | 3g-1+4-11g = 3-8g
|-
|-
| | 12L2s
| | [[12L 2s]]
| | 1\14 < g < 1\12
| | 1\14 < g < 1\12
| | g = 2\26, 3\38, 4\50
| | g = 2\26, 3\38, 4\50
| | g+1\2-6g = 1\2-5g
| | g+1\2-6g = 1\2-5g
|-
|-
| | 13L1s
| | [[13L 1s]]
| | 1\14 < g < 1\13
| | 1\14 < g < 1\13
| | g = 2\27, 3\40, 4\53
| | g = 2\27, 3\40, 4\53
Line 568: Line 560:
|}
|}


=15=
= 15-tone =
 
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 577: Line 568:
! | Large step+Small step
! | Large step+Small step
|-
|-
| | 1L14s
| | [[1L 14s]]
| | 14\15 < g < 1
| | 14\15 < g < 1
| | ''g = 15\16, 16\17, 17\18''
| | ''g = 15\16, 16\17, 17\18''
| | 14g-13+1-g = 13g-12
| | 14g-13+1-g = 13g-12
|-
|-
| | 2L13s
| | [[2L 13s]]
| | 7\15 < g < 1\2
| | 7\15 < g < 1\2
| | g = ''8\17'', 9\19, 10\21
| | g = ''8\17'', 9\19, 10\21
| | 13g-6+1-2g = 11g-5  
| | 13g-6+1-2g = 11g-5  
|-
|-
| | 3L12s
| | [[3L 12s]]
| | 4\15 < g < 1\3
| | 4\15 < g < 1\3
| | g = ''5\18'', 6\21, 7\24
| | g = ''5\18'', 6\21, 7\24
| | 4g-1+1\3-g = 3g-2\3
| | 4g-1+1\3-g = 3g-2\3
|-
|-
| | 4L11s
| | [[4L 11s]]
| | 11\15 < g < 3\4
| | 11\15 < g < 3\4
| | g = 14\19, 17\23, 20\27
| | g = 14\19, 17\23, 20\27
| | 11g-8+3-4g = 8g-4
| | 11g-8+3-4g = 8g-4
|-
|-
| | 5L10s
| | [[5L 10s]]
| | 2\15 < g < 1\5
| | 2\15 < g < 1\5
| | g = 3\20, 4\25, 5\30
| | g = 3\20, 4\25, 5\30
| | 2g-1\5+1\5-g = g
| | 2g-1\5+1\5-g = g
|-
|-
| | 6L9s
| | [[6L 9s]]
| | 2\15 < g < 1\6
| | 2\15 < g < 1\6
| | g = 3\21, 4\27, 5\33
| | g = 3\21, 4\27, 5\33
| | 3g-1\3+1\3-2g = g
| | 3g-1\3+1\3-2g = g
|-
|-
| | 7L8s
| | [[7L 8s]]
| | 2\15 < g < 1\7
| | 2\15 < g < 1\7
| | g = 3\22, 4\29, 5\36
| | g = 3\22, 4\29, 5\36
| | 8g-1+1-7g = g
| | 8g-1+1-7g = g
|-
|-
| | 8L7s
| | [[8L 7s]]
| | 13\15 < g < 7\8
| | 13\15 < g < 7\8
| | g = 20\23, 27\31, 34\39
| | g = 20\23, 27\31, 34\39
| | 7g-6+7-8g = 1-g
| | 7g-6+7-8g = 1-g
|-
|-
| | 9L6s
| | [[9L 6s]]
| | 3\15 < g < 2\9
| | 3\15 < g < 2\9
| | g = 5\24, 7\33, 9\42
| | g = 5\24, 7\33, 9\42
| | 2g-1\3+2\3-3g = 1\3-g
| | 2g-1\3+2\3-3g = 1\3-g
|-
|-
| | 10L5s
| | [[10L 5s]]
| | 1\15 < g < 1\10
| | 1\15 < g < 1\10
| | g = 2\25, 3\35, 4\45
| | g = 2\25, 3\35, 4\45
| | g+1\5-2g = 1\5-g
| | g+1\5-2g = 1\5-g
|-
|-
| | 11L4s
| | [[11L 4s]]
| | 4\15 < g < 3\11
| | 4\15 < g < 3\11
| | g = 7\26, 10\37, 13\48
| | g = 7\26, 10\37, 13\48
| | 4g-1+3-11g = 2-7g
| | 4g-1+3-11g = 2-7g
|-
|-
| | 12L3s
| | [[12L 3s]]
| | 1\15 < g < 1\12
| | 1\15 < g < 1\12
| | g = 2\27, 3\39, 4\51
| | g = 2\27, 3\39, 4\51
| | g+1\3-4g = 1\3-3g
| | g+1\3-4g = 1\3-3g
|-
|-
| | 13L2s
| | [[13L 2s]]
| | 8\15 < g < 7\13
| | 8\15 < g < 7\13
| | g = 15\28, 22\41, 29\54
| | g = 15\28, 22\41, 29\54
| | 2g-1+7-13g = 6-11g
| | 2g-1+7-13g = 6-11g
|-
|-
| | 14L1s
| | [[14L 1s]]
| | 1\15 < g < 1\14
| | 1\15 < g < 1\14
| | g = 2\29, 3\43, 4\57
| | g = 2\29, 3\43, 4\57
Line 648: Line 639:
|}
|}


=16=
= 16-tone =
 
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 657: Line 647:
! | Large step+Small step
! | Large step+Small step
|-
|-
| | 1L15s
| | [[1L 15s]]
| | 15\16 < g < 1
| | 15\16 < g < 1
| | ''g = 16\17, 17\18, 18\19''
| | ''g = 16\17, 17\18, 18\19''
| | 15g-14+1-g = 14g-13
| | 15g-14+1-g = 14g-13
|-
|-
| | 2L14s
| | [[2L 14s]]
| | 7\16 < g < 1\2
| | 7\16 < g < 1\2
| | g = ''8\18, 9\20'', 10\22
| | g = ''8\18, 9\20'', 10\22
| | 7g-3+1\2-g = 5\2-6g
| | 7g-3+1\2-g = 5\2-6g
|-
|-
| | 3L13s
| | [[3L 13s]]
| | 5\16 < g < 1\3
| | 5\16 < g < 1\3
| | g = ''6\19'', 7\22, 8\25
| | g = ''6\19'', 7\22, 8\25
| | 13g-4+1-3g = 10g-3
| | 13g-4+1-3g = 10g-3
|-
|-
| | 4L12s
| | [[4L 12s]]
| | 3\16 < g < 1\4
| | 3\16 < g < 1\4
| | g = ''4\20'', 5\24, 6\28
| | g = ''4\20'', 5\24, 6\28
| | 3g-1\2+1\4-g = 2g-1\4
| | 3g-1\2+1\4-g = 2g-1\4
|-
|-
| | 5L11s
| | [[5L 11s]]
| | 3\16 < g < 1\5
| | 3\16 < g < 1\5
| | g = 4\21, 5\26, 6\31
| | g = 4\21, 5\26, 6\31
| | 11g-2+1-5g = 6g-1
| | 11g-2+1-5g = 6g-1
|-
|-
| | 6L10s
| | [[6L 10s]]
| | 5\16 < g < 2\6
| | 5\16 < g < 2\6
| | g = 7\22, 9\28, 11\34
| | g = 7\22, 9\28, 11\34
| | 5g-3\2+1-3g = 2g-1\2
| | 5g-3\2+1-3g = 2g-1\2
|-
|-
| | 7L9s
| | [[7L 9s]]
| | 9\16 < g < 4\7
| | 9\16 < g < 4\7
| | g = 13\23, 17\30, 21\37
| | g = 13\23, 17\30, 21\37
| | 9g-5+4-7g = 2g-1
| | 9g-5+4-7g = 2g-1
|-
|-
| | 8L8s
| | [[8L 8s]]
| | 1\16 < g < 1\8
| | 1\16 < g < 1\8
| | g = 2\24, 3\32, 4\40
| | g = 2\24, 3\32, 4\40
| | g+1\8-g = 1\8
| | g+1\8-g = 1\8
|-
|-
| | 9L7s
| | [[9L 7s]]
| | 7\16 < g < 4\9
| | 7\16 < g < 4\9
| | g = 11\25, 15\34, 19\43
| | g = 11\25, 15\34, 19\43
| | 7g-3+4-9g = 1-2g
| | 7g-3+4-9g = 1-2g
|-
|-
| | 10L6s
| | [[10L 6s]]
| | 3\16 < g < 2\10
| | 3\16 < g < 2\10
| | g = 5\26, 7\36, 8\46
| | g = 5\26, 7\36, 8\46
| | 3g-1\2+1-5g = 1\2-2g
| | 3g-1\2+1-5g = 1\2-2g
|-
|-
| | 11L5s
| | [[11L 5s]]
| | 13\16 < g < 9\11
| | 13\16 < g < 9\11
| | g = 22\27, 31\38, 40\49
| | g = 22\27, 31\38, 40\49
| | 5g-4+9-11g = 5-6g
| | 5g-4+9-11g = 5-6g
|-
|-
| | 12L4s
| | [[12L 4s]]
| | 1\16 < g < 1\12
| | 1\16 < g < 1\12
| | g = 2\28, 3\40, 4\52
| | g = 2\28, 3\40, 4\52
| | g+1\4-3g = 1\4-2g
| | g+1\4-3g = 1\4-2g
|-
|-
| | 13L3s
| | [[13L 3s]]
| | 11\16 < g < 9\13
| | 11\16 < g < 9\13
| | g = 20\29, 29\42, 38\55
| | g = 20\29, 29\42, 38\55
| | 3g-2+9-13g = 7-10g
| | 3g-2+9-13g = 7-10g
|-
|-
| | 14L2s
| | [[14L 2s]]
| | 1\16 < g < 1\14
| | 1\16 < g < 1\14
| | g = 2\30, 3\44, 4\58
| | g = 2\30, 3\44, 4\58
| | g+1\2-7g = 1\2-6g
| | g+1\2-7g = 1\2-6g
|-
|-
| | 15L1s
| | [[15L 1s]]
| | 1\16 < g < 1\15
| | 1\16 < g < 1\15
| | g = 2\31, 3\46, 4\61
| | g = 2\31, 3\46, 4\61
Line 733: Line 723:
|}
|}


=17=
= 17-tone =
 
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 742: Line 731:
! | Large step+Small step
! | Large step+Small step
|-
|-
| | 1L16s
| | [[1L 16s]]
| | 16\17 < g < 1
| | 16\17 < g < 1
| | ''g = 17\18, 18\19, 19\20''
| | ''g = 17\18, 18\19, 19\20''
| | 16g-15+1-g = 15g-14
| | 16g-15+1-g = 15g-14
|-
|-
| | 2L15s
| | [[2L 15s]]
| | 8\17 < g < 1\2
| | 8\17 < g < 1\2
| | g = ''9\19'', ''10\21'', 11\23
| | g = ''9\19'', ''10\21'', 11\23
| | 15g-7+1-2g = 13g-6
| | 15g-7+1-2g = 13g-6
|-
|-
| | 3L14s
| | [[3L 14s]]
| | 11\17 < g < 2\3
| | 11\17 < g < 2\3
| | g = ''13\20'', 15\23, 17\26
| | g = ''13\20'', 15\23, 17\26
| | 14g-9+2-3g = 11g-7
| | 14g-9+2-3g = 11g-7
|-
|-
| | 4L13s
| | [[4L 13s]]
| | 4\17 < g < 1\4
| | 4\17 < g < 1\4
| | g = ''5\21'', 6\25, 7\29
| | g = ''5\21'', 6\25, 7\29
| | 13g-3+1-4g = 9g-2
| | 13g-3+1-4g = 9g-2
|-
|-
| | 5L12s
| | [[5L 12s]]
| | 10\17 < g < 3\5
| | 10\17 < g < 3\5
| | g = 13\22, 16\27, 19\32
| | g = 13\22, 16\27, 19\32
| | 12g-7+3-5g = 7g-4
| | 12g-7+3-5g = 7g-4
|-
|-
| | 6L11s
| | [[6L 11s]]
| | 14\17 < g < 5\6
| | 14\17 < g < 5\6
| | g = 19\23, 24\29, 29\35
| | g = 19\23, 24\29, 29\35
| | 11g-9+5-6g = 5g-4
| | 11g-9+5-6g = 5g-4
|-
|-
| | 7L10s
| | [[7L 10s]]
| | 12\17 < g < 5\7
| | 12\17 < g < 5\7
| | g = 17\24, 22\31, 27\38
| | g = 17\24, 22\31, 27\38
| | 10g-7+5-7g = 3g-2
| | 10g-7+5-7g = 3g-2
|-
|-
| | 8L9s
| | [[8L 9s]]
| | 2\17 < g < 1\8
| | 2\17 < g < 1\8
| | g = 3\25, 4\33, 5\41
| | g = 3\25, 4\33, 5\41
| | 9g-1+1-8g = g
| | 9g-1+1-8g = g
|-
|-
| | 9L8s
| | [[9L 8s]]
| | 15\17 < g < 8\9
| | 15\17 < g < 8\9
| | g = 23\26, 31\35, 39\44
| | g = 23\26, 31\35, 39\44
| | 8g-7+8-9g = 1-g
| | 8g-7+8-9g = 1-g
|-
|-
| | 10L7s
| | [[10L 7s]]
| | 5\17 < g < 3\10
| | 5\17 < g < 3\10
| | g = 8\27, 11\37, 14\47
| | g = 8\27, 11\37, 14\47
| | 7g-2+3-10g = 1-3g
| | 7g-2+3-10g = 1-3g
|-
|-
| | 11L6s
| | [[11L 6s]]
| | 3\17 < g < 2\11
| | 3\17 < g < 2\11
| | g = 5\28, 7\39, 9\50
| | g = 5\28, 7\39, 9\50
| | 6g-1+2-11g = 1-5g
| | 6g-1+2-11g = 1-5g
|-
|-
| | 12L5s
| | [[12L 5s]]
| | 7\17 < g < 5\12
| | 7\17 < g < 5\12
| | g = 12\29, 17\41, 22\53
| | g = 12\29, 17\41, 22\53
| | 5g-2+5-12g = 3-7g
| | 5g-2+5-12g = 3-7g
|-
|-
| | 13L4s
| | [[13L 4s]]
| | 13\17 < g < 10\13
| | 13\17 < g < 10\13
| | g = 23\30, 33\43, 43\56
| | g = 23\30, 33\43, 43\56
| | 4g-3+10-13g = 7-9g
| | 4g-3+10-13g = 7-9g
|-
|-
| | 14L3s
| | [[14L 3s]]
| | 6\17 < g < 5\14
| | 6\17 < g < 5\14
| | g = 11\31, 16\45, 21\59
| | g = 11\31, 16\45, 21\59
| | 3g-1+5-14g = 4-11g
| | 3g-1+5-14g = 4-11g
|-
|-
| | 15L2s
| | [[15L 2s]]
| | 9\17 < g < 8\15
| | 9\17 < g < 8\15
| | g = 17\32, 25\47, 33\62
| | g = 17\32, 25\47, 33\62
| | 2g-1+8-15g = 7-13g
| | 2g-1+8-15g = 7-13g
|-
|-
| | 16L1s
| | [[16L 1s]]
| | 1\17 < g < 1\16
| | 1\17 < g < 1\16
| | g = 2\33, 3\49, 4\65
| | g = 2\33, 3\49, 4\65
Line 823: Line 812:
|}
|}


=18=
= 18-tone =
 
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 832: Line 820:
! | Large step+Small step
! | Large step+Small step
|-
|-
| | 1L17s
| | [[1L 17s]]
| | 17\18 < g < 1
| | 17\18 < g < 1
| | ''g = 18\19, 19\20, 20\21''
| | ''g = 18\19, 19\20, 20\21''
| | 17g-16+1-g = 16g-15
| | 17g-16+1-g = 16g-15
|-
|-
| | 2L16s
| | [[2L 16s]]
| | 8\18 < g < 1\2
| | 8\18 < g < 1\2
| | g = ''9\20'', ''10\22'', 11\24
| | g = ''9\20'', ''10\22'', 11\24
| | 8g-7\2+1\2-g = 7g-3
| | 8g-7\2+1\2-g = 7g-3
|-
|-
| | 3L15s
| | [[3L 15s]]
| | 5\18 < g < 1\3
| | 5\18 < g < 1\3
| | g = ''6\21'', 7\24, 8\27
| | g = ''6\21'', 7\24, 8\27
| | 5g-4\3+1\3-g = 4g-3
| | 5g-4\3+1\3-g = 4g-3
|-
|-
| | 4L14s
| | [[4L 14s]]
| | <span style="line-height: 15.6000003814697px;">4\18 &lt; g &lt; 1\4</span>
| | <span style="line-height: 15.6000003814697px;">4\18 &lt; g &lt; 1\4</span>
| | <span style="line-height: 15.6000003814697px;">g = ''5\22'', 6\26,</span> 7\30
| | <span style="line-height: 15.6000003814697px;">g = ''5\22'', 6\26,</span> 7\30
| | 7g-3\2+1\2-2g = 5g-2
| | 7g-3\2+1\2-2g = 5g-2
|-
|-
| | 5L13s
| | [[5L 13s]]
| | 7\18 &lt; g &lt; 2\5
| | 7\18 &lt; g &lt; 2\5
| | g = 9\23, 11\28, 13\33
| | g = 9\23, 11\28, 13\33
| | 13g-5+2-5g = 8g-3
| | 13g-5+2-5g = 8g-3
|-
|-
| | 6L12s
| | [[6L 12s]]
| | 2\18 &lt; g &lt; 1\6
| | 2\18 &lt; g &lt; 1\6
| | g = 3\24, 4\30, 5\36
| | g = 3\24, 4\30, 5\36
| | 2g-1\6+1\6-g = g
| | 2g-1\6+1\6-g = g
|-
|-
| | 7L11s
| | [[7L 11s]]
| | 5\18 &lt; g &lt; 2\7
| | 5\18 &lt; g &lt; 2\7
| | g = 7\25, 9\32, 11\39
| | g = 7\25, 9\32, 11\39
| | 11g-3+2-7g = 4g-1
| | 11g-3+2-7g = 4g-1
|-
|-
| | 8L10s
| | [[8L 10s]]
| | 2\18 &lt; g &lt; 1\8
| | 2\18 &lt; g &lt; 1\8
| | g = 3\26, 4\34, 5\42
| | g = 3\26, 4\34, 5\42
| | 5g-1\2+1\2-4g = g
| | 5g-1\2+1\2-4g = g
|-
|-
| | 9L9s
| | [[9L 9s]]
| | 1\18 &lt; g &lt; 1\9
| | 1\18 &lt; g &lt; 1\9
| | g = 2\27, 3\36, 4\45
| | g = 2\27, 3\36, 4\45
| | g+1\9-g = 1\9
| | g+1\9-g = 1\9
|-
|-
| | 10L8s
| | [[10L 8s]]
| | 7\18 &lt; g &lt; 4\10
| | 7\18 &lt; g &lt; 4\10
| | g = 11\28, 15\38, 19\48
| | g = 11\28, 15\38, 19\48
| | 4g-3\2+2-5g = 1\2-g
| | 4g-3\2+2-5g = 1\2-g
|-
|-
| | 11L7s
| | [[11L 7s]]
| | 13\18 &lt; g &lt; 8\11
| | 13\18 &lt; g &lt; 8\11
| | g = 21\29, 29\40, 37\51
| | g = 21\29, 29\40, 37\51
| | 7g-5+8-11g = 3-4g
| | 7g-5+8-11g = 3-4g
|-
|-
| | 12L6s
| | [[12L 6s]]
| | 1\18 &lt; g &lt; 1\12
| | 1\18 &lt; g &lt; 1\12
| | g = 2\30, 3\42, 4\54
| | g = 2\30, 3\42, 4\54
| | g+1\6-2g = 1\6-g
| | g+1\6-2g = 1\6-g
|-
|-
| | 13L5s
| | [[13L 5s]]
| | 11\18 &lt; g &lt; 8\13
| | 11\18 &lt; g &lt; 8\13
| | g = 19\31, 27\44, 35\57
| | g = 19\31, 27\44, 35\57
| | 5g-3+8-13g = 5-8g
| | 5g-3+8-13g = 5-8g
|-
|-
| | 14L4s
| | [[14L 4s]]
| | 5\18 &lt; g &lt; 4\14
| | 5\18 &lt; g &lt; 4\14
| | g = 9\32, 13\46, 17\60
| | g = 9\32, 13\46, 17\60
| | 2g-1\2+2-7g = 3\2-5g
| | 2g-1\2+2-7g = 3\2-5g
|-
|-
| | 15L3s
| | [[15L 3s]]
| | 1\18 &lt; g &lt; 1\15
| | 1\18 &lt; g &lt; 1\15
| | g = 2\33, 3\48, 4\63
| | g = 2\33, 3\48, 4\63
| | g+1\3-5g = 1\3-4g
| | g+1\3-5g = 1\3-4g
|-
|-
| | 16L2s
| | [[16L 2s]]
| | 1\18 &lt; g &lt; 1\16
| | 1\18 &lt; g &lt; 1\16
| | g = 2\34, 3\50, 4\66
| | g = 2\34, 3\50, 4\66
| | g+1\2-8g = 1\2-7g
| | g+1\2-8g = 1\2-7g
|-
|-
| | 17L1s
| | [[17L 1s]]
| | 1\18 &lt; g &lt; 1\17
| | 1\18 &lt; g &lt; 1\17
| | g = 2\35, 3\52, 4\69
| | g = 2\35, 3\52, 4\69
Line 918: Line 906:
|}
|}


=19=
= 19-tone =
 
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 927: Line 914:
! |Large step+Small step
! |Large step+Small step
|-
|-
| | 1L18s
| | [[1L 18s]]
| | 18\19 &lt; g &lt; 1
| | 18\19 &lt; g &lt; 1
| | ''g = 19\20, 20\21, 21\22''
| | ''g = 19\20, 20\21, 21\22''
| |18g-17+1-g = 17g-16
| |18g-17+1-g = 17g-16
|-
|-
| | 2L17s
| | [[2L 17s]]
| | 9\19 &lt; g &lt; 1\2
| | 9\19 &lt; g &lt; 1\2
| | g = ''10\21'', ''11\23'', 12\25
| | g = ''10\21'', ''11\23'', 12\25
| |17g-8+1-2g = 15g-7
| |17g-8+1-2g = 15g-7
|-
|-
| | 3L16s
| | [[3L 16s]]
| | 6\19 &lt; g &lt; 1\3
| | 6\19 &lt; g &lt; 1\3
| | g = ''7\22'', 8\25, 10\31
| | g = ''7\22'', 8\25, 10\31
| |16g-5+1-3g = 13g-4
| |16g-5+1-3g = 13g-4
|-
|-
| | 4L15s
| | [[4L 15s]]
| | 14\19 &lt; g &lt; 3\4
| | 14\19 &lt; g &lt; 3\4
| | g = ''17\23'', 20\27, 23\31
| | g = ''17\23'', 20\27, 23\31
| |15g-11+3-4g = 11g-8
| |15g-11+3-4g = 11g-8
|-
|-
| | 5L14s
| | [[5L 14s]]
| | 15\19 &lt; g &lt; 4\5
| | 15\19 &lt; g &lt; 4\5
| | g = 19\24, 23\29, 27\34
| | g = 19\24, 23\29, 27\34
| |14g-11+4-5g = 9g-7
| |14g-11+4-5g = 9g-7
|-
|-
| | 6L13s
| | [[6L 13s]]
| | 3\19 &lt; g &lt; 1\6
| | 3\19 &lt; g &lt; 1\6
| | g = 4\25, 5\31, 6/37
| | g = 4\25, 5\31, 6/37
| |13g-2+1-6g = 7g-1
| |13g-2+1-6g = 7g-1
|-
|-
| | 7L12s
| | [[7L 12s]]
| | 8\19 &lt; g &lt; 3\7
| | 8\19 &lt; g &lt; 3\7
| | g = 11\26, 14\33, 17\40
| | g = 11\26, 14\33, 17\40
| |12g-5+3-7g = 5g-2
| |12g-5+3-7g = 5g-2
|-
|-
| | 8L11s
| | [[8L 11s]]
| | 7\19 &lt; g &lt; 3\8
| | 7\19 &lt; g &lt; 3\8
| | g = 10\27, 13\35, 16\43
| | g = 10\27, 13\35, 16\43
| |11g-4+3-8g = 3g-1
| |11g-4+3-8g = 3g-1
|-
|-
| | 9L10s
| | [[9L 10s]]
| | 2\19 &lt; g &lt; 1\9
| | 2\19 &lt; g &lt; 1\9
| | g = 3\28, 4\37, 5\46
| | g = 3\28, 4\37, 5\46
| |10g-1+1-9g = g
| |10g-1+1-9g = g
|-
|-
| | 10L9s
| | [[10L 9s]]
| | 17\19 &lt; g &lt; 9\10
| | 17\19 &lt; g &lt; 9\10
| | g = 26\29, 35\39, 44\49
| | g = 26\29, 35\39, 44\49
| |9g-8+9-10g = 1-g
| |9g-8+9-10g = 1-g
|-
|-
| | 11L8s
| | [[11L 8s]]
| | 12\19 &lt; g &lt; 7\11
| | 12\19 &lt; g &lt; 7\11
| | g = 19\30, 26\41, 33\52
| | g = 19\30, 26\41, 33\52
| |8g-5+7-11g = 2-3g
| |8g-5+7-11g = 2-3g
|-
|-
| | 12L7s
| | [[12L 7s]]
| | 11\19 &lt; g &lt; 7\12
| | 11\19 &lt; g &lt; 7\12
| | g = 18\31, 25\43, 32\55
| | g = 18\31, 25\43, 32\55
| |7g-4+7-12g = 3-5g
| |7g-4+7-12g = 3-5g
|-
|-
| | 13L6s
| | [[13L 6s]]
| | 16\19 &lt; g &lt; 11\13
| | 16\19 &lt; g &lt; 11\13
| | g = 27\32, 38\45, 49\58
| | g = 27\32, 38\45, 49\58
| |6g-5+11-13g = 6-7g
| |6g-5+11-13g = 6-7g
|-
|-
| | 14L5s
| | [[14L 5s]]
| | 4\19 &lt; g &lt; 3\14
| | 4\19 &lt; g &lt; 3\14
| | g = 7\33, 10\47, 13\61
| | g = 7\33, 10\47, 13\61
| |5g-1+3-14g = 2-9g
| |5g-1+3-14g = 2-9g
|-
|-
| | 15L4s
| | [[15L 4s]]
| | 5\19 &lt; g &lt; 4\15
| | 5\19 &lt; g &lt; 4\15
| | g = 9\34, 13\49, 17\64
| | g = 9\34, 13\49, 17\64
| |4g-1+4-15g = 3-11g
| |4g-1+4-15g = 3-11g
|-
|-
| | 16L3s
| | [[16L 3s]]
| | 13\19 &lt; g &lt; 11\16
| | 13\19 &lt; g &lt; 11\16
| | g = 24\35, 35\51, 46\67
| | g = 24\35, 35\51, 46\67
| |3g-2+11-16g = 9-13g
| |3g-2+11-16g = 9-13g
|-
|-
| | 17L2s
| | [[17L 2s]]
| | 10\19 &lt; g &lt; 9\17
| | 10\19 &lt; g &lt; 9\17
| | g = 19\36, 28\53, 37\70
| | g = 19\36, 28\53, 37\70
| |2g-1+9-17g = 8-15g
| |2g-1+9-17g = 8-15g
|-
|-
| | 18L1s
| | [[18L 1s]]
| | 1\19 &lt; g &lt; 1\18
| | 1\19 &lt; g &lt; 1\18
| | g = 2\37, 3\55, 4\73
| | g = 2\37, 3\55, 4\73
Line 1,018: Line 1,005:
|}
|}


=20=
= 20-tone =
 
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 1,027: Line 1,013:
! | Large step+Small step
! | Large step+Small step
|-
|-
| | 1L19s
| | [[1L 19s]]
| | 19\20 &lt; g &lt; 1
| | 19\20 &lt; g &lt; 1
| | ''g = 20\21, 21\22, 22\23''
| | ''g = 20\21, 21\22, 22\23''
| | 19g-18+1-g = 18g-17
| | 19g-18+1-g = 18g-17
|-
|-
| | 2L18s
| | [[2L 18s]]
| | 9\20 &lt; g &lt; 1\2
| | 9\20 &lt; g &lt; 1\2
| | g = ''10\22'', ''11\24'', 12\26
| | g = ''10\22'', ''11\24'', 12\26
| | 9g-4+1\2-g = 8g-7\2
| | 9g-4+1\2-g = 8g-7\2
|-
|-
| | 3L17s
| | [[3L 17s]]
| | 13\20 &lt; g &lt; 2\3
| | 13\20 &lt; g &lt; 2\3
| | g = ''15\23'', 17\26, 20\29
| | g = ''15\23'', 17\26, 20\29
| | 17g-11+2-3g = 14g-9
| | 17g-11+2-3g = 14g-9
|-
|-
| | 4L16s
| | [[4L 16s]]
| | 4\20 &lt; g &lt; 1\4
| | 4\20 &lt; g &lt; 1\4
| | g = ''5\24'', 6\28, 7\32
| | g = ''5\24'', 6\28, 7\32
| | 4g-3\4+1\4-g = 3g-1\4
| | 4g-3\4+1\4-g = 3g-1\4
|-
|-
| | 5L15s
| | [[5L 15s]]
| | 3\20 &lt; g &lt; 1\5
| | 3\20 &lt; g &lt; 1\5
| | g = ''4\25'', 5\30, 6\35
| | g = ''4\25'', 5\30, 6\35
| | 3g-2\5+1\5-g = 2g-1\5
| | 3g-2\5+1\5-g = 2g-1\5
|-
|-
| | 6L14s
| | [[6L 14s]]
| | 3\20 &lt; g &lt; 1\6
| | 3\20 &lt; g &lt; 1\6
| | g = 4\26, 5\32, 6\38
| | g = 4\26, 5\32, 6\38
| | 7g-1+1\2-3g = 4g-1\2
| | 7g-1+1\2-3g = 4g-1\2
|-
|-
| | 7L13s
| | [[7L 13s]]
| | 17\20 &lt; g &lt; 6\7
| | 17\20 &lt; g &lt; 6\7
| | g = 23\27, 29\34, 35\41
| | g = 23\27, 29\34, 35\41
| | 13g-11+6-7g = 6g-5
| | 13g-11+6-7g = 6g-5
|-
|-
| | 8L12s
| | [[8L 12s]]
| | 2\20 &lt; g &lt; 1\8
| | 2\20 &lt; g &lt; 1\8
| | g = 3\28, 4\36, 5\44
| | g = 3\28, 4\36, 5\44
| | 3g-1\4+1\4-2g = g
| | 3g-1\4+1\4-2g = g
|-
|-
| | 9L11s
| | [[9L 11s]]
| | 11\20 &lt; g &lt; 5\9
| | 11\20 &lt; g &lt; 5\9
| | g = 16\29, 21\38, 26\47
| | g = 16\29, 21\38, 26\47
| | 11g-6+5-9g =2g-1  
| | 11g-6+5-9g =2g-1  
|-
|-
| | 10L10s
| | [[10L 10s]]
| | 1\20 &lt; g &lt; 1\10
| | 1\20 &lt; g &lt; 1\10
| | g = 2\30, 3\40, 4\50
| | g = 2\30, 3\40, 4\50
| | g+1\10-g = 1\10
| | g+1\10-g = 1\10
|-
|-
| | 11L9s
| | [[11L 9s]]
| | 9\20 &lt; g &lt; 5\11
| | 9\20 &lt; g &lt; 5\11
| | g = 14\31, 19\42, 24\53
| | g = 14\31, 19\42, 24\53
| | 9g-4+5-11g = 1-2g
| | 9g-4+5-11g = 1-2g
|-
|-
| | 12L8s
| | [[12L 8s]]
| | 3\20 &lt; g &lt; 2\12
| | 3\20 &lt; g &lt; 2\12
| | g = 5\32, 7\44, 9\56
| | g = 5\32, 7\44, 9\56
| | 2g-1\4+1\2-3g = 1\4-g
| | 2g-1\4+1\2-3g = 1\4-g
|-
|-
| | 13L7s
| | [[13L 7s]]
| | 3\20 &lt; g &lt; 2\13
| | 3\20 &lt; g &lt; 2\13
| | g = 5\33, 7\46, 9\59
| | g = 5\33, 7\46, 9\59
| | 7g-1+2-13g = 1-6g
| | 7g-1+2-13g = 1-6g
|-
|-
| | 14L6s
| | [[14L 6s]]
| | 7\20 &lt; g &lt; 5\14
| | 7\20 &lt; g &lt; 5\14
| | g = 12\34, 17\48, 22\62
| | g = 12\34, 17\48, 22\62
| | 3g-1+5\2-7g = 2-4g
| | 3g-1+5\2-7g = 2-4g
|-
|-
| | 15L5s
| | [[15L 5s]]
| | 1\20 &lt; g &lt; 1\15
| | 1\20 &lt; g &lt; 1\15
| | g = 2\35, 3\50, 4\65
| | g = 2\35, 3\50, 4\65
| | g+1\5-3g = 1\5-2g
| | g+1\5-3g = 1\5-2g
|-
|-
| | 16L4s
| | [[16L 4s]]
| | 1\20 &lt; g &lt; 1\16
| | 1\20 &lt; g &lt; 1\16
| | g = 2\36, 3\52, 4\68
| | g = 2\36, 3\52, 4\68
| | g+1\4-4g = 1\4-3g
| | g+1\4-4g = 1\4-3g
|-
|-
| | 17L3s
| | [[17L 3s]]
| | 7\20 &lt; g &lt; 6\17
| | 7\20 &lt; g &lt; 6\17
| | g = 13\37, 19\54, 25\71
| | g = 13\37, 19\54, 25\71
| | 3g-1+6-17g = 5-14g
| | 3g-1+6-17g = 5-14g
|-
|-
| | 18L2s
| | [[18L 2s]]
| | 1\20 &lt; g &lt; 1\18
| | 1\20 &lt; g &lt; 1\18
| | g = 2\38, 3\56, 4\74
| | g = 2\38, 3\56, 4\74
| | g+1\2-9g = 1\2-8g
| | g+1\2-9g = 1\2-8g
|-
|-
| | 19L1s
| | [[19L 1s]]
| | 1\20 &lt; g &lt; 1\19
| | 1\20 &lt; g &lt; 1\19
| | g = 2\39, 3\58, 4\77
| | g = 2\39, 3\58, 4\77
Line 1,123: Line 1,109:
|}
|}


=21=
= 21-tone =
 
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 1,132: Line 1,117:
! | Large step+Small step
! | Large step+Small step
|-
|-
| | 1L20s
| | [[1L 20s]]
| | 20\21 &lt; g &lt; 1
| | 20\21 &lt; g &lt; 1
| | ''g = 21\22, 22\23, 23\24''
| | ''g = 21\22, 22\23, 23\24''
| | 20g-19+1-g = 19g-18
| | 20g-19+1-g = 19g-18
|-
|-
| | 2L19s
| | [[2L 19s]]
| | 10\21 &lt; g &lt; 1\2
| | 10\21 &lt; g &lt; 1\2
| | g = ''11\23, 12\25'', 13\27
| | g = ''11\23, 12\25'', 13\27
| | 19g-9+1-2g = 17g-8
| | 19g-9+1-2g = 17g-8
|-
|-
| | 3L18s
| | [[3L 18s]]
| | 6\21 &lt; g &lt; 1\3
| | 6\21 &lt; g &lt; 1\3
| | g = ''7\24'', 8\27, 9\30
| | g = ''7\24'', 8\27, 9\30
| | 6g-5\3+1\3-g = 5g-4\3
| | 6g-5\3+1\3-g = 5g-4\3
|-
|-
| | 4L17s
| | [[4L 17s]]
| | 5\21 &lt; g &lt; 1\4
| | 5\21 &lt; g &lt; 1\4
| | g = ''6\25'', 7\29, 8\33
| | g = ''6\25'', 7\29, 8\33
| | 17g-2+1-4g = 13g-1
| | 17g-2+1-4g = 13g-1
|-
|-
| | 5L16s
| | [[5L 16s]]
| | 4\21 &lt; g &lt; 1\5
| | 4\21 &lt; g &lt; 1\5
| | g = ''5\26'', 6\31, 7\36
| | g = ''5\26'', 6\31, 7\36
| | 16g-3+1-5g = 11g-2
| | 16g-3+1-5g = 11g-2
|-
|-
| | 6L15s
| | [[6L 15s]]
| | 3\21 &lt; g &lt; 1\6
| | 3\21 &lt; g &lt; 1\6
| | g = 4\27, 5\33, 6\39
| | g = 4\27, 5\33, 6\39
| | 5g-2\3+1\3-2g = 3g-1\3
| | 5g-2\3+1\3-2g = 3g-1\3
|-
|-
| | 7L14s
| | [[7L 14s]]
| | 2\21 &lt; g &lt; 1\7
| | 2\21 &lt; g &lt; 1\7
| | g = 3\28, 4\35, 5\42
| | g = 3\28, 4\35, 5\42
| | 2g-1\7+1\7-g = g
| | 2g-1\7+1\7-g = g
|-
|-
| | 8L13s
| | [[8L 13s]]
| | 13\21 &lt; g &lt; 5\8
| | 13\21 &lt; g &lt; 5\8
| | g = 18\29, 23\37, 28\45
| | g = 18\29, 23\37, 28\45
| | 13g-8+5-8g = 5g-3
| | 13g-8+5-8g = 5g-3
|-
|-
| | 9L12s
| | [[9L 12s]]
| | 2\21 &lt; g &lt; 1\9
| | 2\21 &lt; g &lt; 1\9
| | g = 3\30, 4\39, 5\48
| | g = 3\30, 4\39, 5\48
| | 4g-1\3+1\3-3g = g
| | 4g-1\3+1\3-3g = g
|-
|-
| | 10L11s
| | [[10L 11s]]
| | 2\21 &lt; g &lt; 1\10
| | 2\21 &lt; g &lt; 1\10
| | g = 3\31, 4\41, 5\51
| | g = 3\31, 4\41, 5\51
| | 11g-1+1-10g = g
| | 11g-1+1-10g = g
|-
|-
| | 11L10s
| | [[11L 10s]]
| | 19\21 &lt; g &lt; 10\11
| | 19\21 &lt; g &lt; 10\11
| | g = 29\32, 39\43, 49\54
| | g = 29\32, 39\43, 49\54
| | 10g-9+10-11g = 1-g
| | 10g-9+10-11g = 1-g
|-
|-
| | 12L9s
| | [[12L 9s]]
| | 5\21 &lt; g &lt; 3\12
| | 5\21 &lt; g &lt; 3\12
| | g = 8\33, 11\45, 14\57
| | g = 8\33, 11\45, 14\57
| | 3g-2\3+1-4g = 1\3-3g
| | 3g-2\3+1-4g = 1\3-3g
|-
|-
| | 13L8s
| | [[13L 8s]]
| | 8\21 &lt; g &lt; 5\13
| | 8\21 &lt; g &lt; 5\13
| | g = 13\34, 18\47, 23\70
| | g = 13\34, 18\47, 23\70
| | 8g-3+5-13g = 2-5g
| | 8g-3+5-13g = 2-5g
|-
|-
| | 14L7s
| | [[14L 7s]]
| | 1\21 &lt; g &lt; 1\14
| | 1\21 &lt; g &lt; 1\14
| | g = 2\35, 3\49, 4\63
| | g = 2\35, 3\49, 4\63
| | g+1\7-2g = 1\7-g
| | g+1\7-2g = 1\7-g
|-
|-
| | 15L6s
| | [[15L 6s]]
| | 4\21 &lt; g &lt; 3\15
| | 4\21 &lt; g &lt; 3\15
| | g = 7\36, 10\51, 13\66
| | g = 7\36, 10\51, 13\66
| | 2g-1\3+1-5g = 2\3-3g
| | 2g-1\3+1-5g = 2\3-3g
|-
|-
| | 16L5s
| | [[16L 5s]]
| | 17\21 &lt; g &lt; 13\16
| | 17\21 &lt; g &lt; 13\16
| | g = 30\37, 43\53, 56\69
| | g = 30\37, 43\53, 56\69
| | 5g-4+13-16g = 9-11g
| | 5g-4+13-16g = 9-11g
|-
|-
| | 17L4s
| | [[17L 4s]]
| | 16\21 &lt; g &lt; 13\17
| | 16\21 &lt; g &lt; 13\17
| | g = 29\38, 42\55, 55\72
| | g = 29\38, 42\55, 55\72
| | 4g-3+13-17g = 10-13g
| | 4g-3+13-17g = 10-13g
|-
|-
| | 18L3s
| | [[18L 3s]]
| | 1\21 &lt; g &lt; 1\18
| | 1\21 &lt; g &lt; 1\18
| | g = 2\39, 3\57, 4\75
| | g = 2\39, 3\57, 4\75
| | g+1\3-6g = 1\3-5g
| | g+1\3-6g = 1\3-5g
|-
|-
| | 19L2s
| | [[19L 2s]]
| | 11\21 &lt; g &lt; 10\19
| | 11\21 &lt; g &lt; 10\19
| | g = 21\40, 31\59, 41\78
| | g = 21\40, 31\59, 41\78
| | 2g-1+10-19g = 9-17g
| | 2g-1+10-19g = 9-17g
|-
|-
| | 20L1s
| | [[20L 1s]]
| | 1\21 &lt; g &lt; 1\20
| | 1\21 &lt; g &lt; 1\20
| | g = 2\41, 3\61, 4/81
| | g = 2\41, 3\61, 4/81
Line 1,233: Line 1,218:
|}
|}


=22=
= 22-tone =
 
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 1,242: Line 1,226:
! |Large step+Small step
! |Large step+Small step
|-
|-
| | 1L21s
| | [[1L 21s]]
| | 21\22 &lt; g &lt; 1
| | 21\22 &lt; g &lt; 1
| | ''g = 22\23, 23\24, 24/25''
| | ''g = 22\23, 23\24, 24/25''
| |21g-20+1-g = 20g-19
| |21g-20+1-g = 20g-19
|-
|-
| | 2L20s
| | [[2L 20s]]
| | 10\22 &lt; g &lt; 1\2
| | 10\22 &lt; g &lt; 1\2
| | g = ''11\24,'' ''12\26'', 13\28
| | g = ''11\24,'' ''12\26'', 13\28
| |10g-9\2+1\2-g = 9g-4
| |10g-9\2+1\2-g = 9g-4
|-
|-
| | 3L19s
| | [[3L 19s]]
| | 7\22 &lt; g &lt; 1\3
| | 7\22 &lt; g &lt; 1\3
| | g = ''8\25'', 9\28, 10\31
| | g = ''8\25'', 9\28, 10\31
| |19g-6+1-3g = 16g-5
| |19g-6+1-3g = 16g-5
|-
|-
| | 4L18s
| | [[4L 18s]]
| | 5\22 &lt; g &lt; 1\4
| | 5\22 &lt; g &lt; 1\4
| | g = ''6\26'', 7\30, 8\34
| | g = ''6\26'', 7\30, 8\34
| |9g-2+1\2-2g = 7g-3\2
| |9g-2+1\2-2g = 7g-3\2
|-
|-
| | 5L17s
| | [[5L 17s]]
| | 13\22 &lt; g &lt; 3\5
| | 13\22 &lt; g &lt; 3\5
| | g = ''16\27'', 19\32, 22\37
| | g = ''16\27'', 19\32, 22\37
| |17g-10+3-5g = 12g-7
| |17g-10+3-5g = 12g-7
|-
|-
| | 6L16s
| | [[6L 16s]]
| | 7\22 &lt; g &lt; 2\6
| | 7\22 &lt; g &lt; 2\6
| | g = 9\28, 11\34, 13\40
| | g = 9\28, 11\34, 13\40
| |8g-5\2+1-3g = 5g-2
| |8g-5\2+1-3g = 5g-2
|-
|-
| | 7L15s
| | [[7L 15s]]
| | 3\22 &lt; g &lt; 1\7
| | 3\22 &lt; g &lt; 1\7
| | g = 4\29, 5\36, 6\43
| | g = 4\29, 5\36, 6\43
| |15g-2+1-7g = 8g-1
| |15g-2+1-7g = 8g-1
|-
|-
| | 8L14s
| | [[8L 14s]]
| | 8\22 &lt; g &lt; 3\8
| | 8\22 &lt; g &lt; 3\8
| | g = 11\30, 14\38, 17\46
| | g = 11\30, 14\38, 17\46
| |7g-5\2+3\2-4g = 3g-2
| |7g-5\2+3\2-4g = 3g-2
|-
|-
| | 9L13s
| | [[9L 13s]]
| | 17\22 &lt; g &lt; 7\9
| | 17\22 &lt; g &lt; 7\9
| | g = 24\31, 31\40, 38\49
| | g = 24\31, 31\40, 38\49
| |13g-10+7-9g = 4g-3
| |13g-10+7-9g = 4g-3
|-
|-
| | 10L12s
| | [[10L 12s]]
| | 2\22 &lt; g &lt; 1\10
| | 2\22 &lt; g &lt; 1\10
| | g = 3\32, 4\42, 5\52
| | g = 3\32, 4\42, 5\52
| |6g-1\2+1\2-5g = g
| |6g-1\2+1\2-5g = g
|-
|-
| | 11L11s
| | [[11L 11s]]
| | 1\22 &lt; g &lt; 1\11
| | 1\22 &lt; g &lt; 1\11
| | g = 2\33, 3\44, 4\55
| | g = 2\33, 3\44, 4\55
| |g + 1\11-g = 1\11
| |g + 1\11-g = 1\11
|-
|-
| | 12L10s
| | [[12L 10s]]
| | 9\22 &lt; g &lt; 5\12
| | 9\22 &lt; g &lt; 5\12
| | g = 14\34, 19\46, 24\58
| | g = 14\34, 19\46, 24\58
| |5g-2+5\2-6g = 1\2-g
| |5g-2+5\2-6g = 1\2-g
|-
|-
| | 13L9s
| | [[13L 9s]]
| | 5\22 &lt; g &lt; 3\13
| | 5\22 &lt; g &lt; 3\13
| | g = 8\35, 11\48, 14\61
| | g = 8\35, 11\48, 14\61
| |9g-2+3-13g = 1-4g
| |9g-2+3-13g = 1-4g
|-
|-
| | 14L8s
| | [[14L 8s]]
| | 3\22 &lt; g &lt; 2\14
| | 3\22 &lt; g &lt; 2\14
| | g = 5\36, 7\50, 9\64
| | g = 5\36, 7\50, 9\64
| |4g-1\2+1-7g = 1\2-3g
| |4g-1\2+1-7g = 1\2-3g
|-
|-
| | 15L7s
| | [[15L 7s]]
| | 19\22 &lt; g &lt; 13\15
| | 19\22 &lt; g &lt; 13\15
| | g = 32\37, 45\52, 58\67
| | g = 32\37, 45\52, 58\67
| |7g-6+13-15g = 7-8g
| |7g-6+13-15g = 7-8g
|-
|-
| | 16L6s
| | [[16L 6s]]
| | 4\22 &lt; g &lt; 3\16
| | 4\22 &lt; g &lt; 3\16
| | g = 7\38, 10\54, 13\70
| | g = 7\38, 10\54, 13\70
| |3g-1\2+3\2-8g = 1-5g
| |3g-1\2+3\2-8g = 1-5g
|-
|-
| | 17L5s
| | [[17L 5s]]
| | 9\22 &lt; g &lt; 7\17
| | 9\22 &lt; g &lt; 7\17
| | g = 16\39, 23\56, 30\73
| | g = 16\39, 23\56, 30\73
| |5g-2+7-17g = 5-12g
| |5g-2+7-17g = 5-12g
|-
|-
| | 18L4s
| | [[18L 4s]]
| | 6\22 &lt; g &lt; 5\18
| | 6\22 &lt; g &lt; 5\18
| | g = 11\40, 16\58, 21\76
| | g = 11\40, 16\58, 21\76
| |2g-1\2+5\2-9g = 2-7g
| |2g-1\2+5\2-9g = 2-7g
|-
|-
| | 19L3s
| | [[19L 3s]]
| | 15\22 &lt; g &lt; 13\19
| | 15\22 &lt; g &lt; 13\19
| | g = 28\41, 41\60, 54\79
| | g = 28\41, 41\60, 54\79
| |3g-2+13-19g = 11-16g
| |3g-2+13-19g = 11-16g
|-
|-
| | 20L2s
| | [[20L 2s]]
| | 1\22 &lt; g &lt; 1\20
| | 1\22 &lt; g &lt; 1\20
| | g = 2\42, 3\62, 4\72
| | g = 2\42, 3\62, 4\72
| |g+1\2-10g = 1\2-9g
| |g+1\2-10g = 1\2-9g
|-
|-
| | 21L1s
| | [[21L 1s]]
| | 1\22 &lt; g &lt; 1\21
| | 1\22 &lt; g &lt; 1\21
| | g = 2\43, 3\64, 4\85
| | g = 2\43, 3\64, 4\85
Line 1,348: Line 1,332:
|}
|}


=23=
= 23-tone =
 
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 1,357: Line 1,340:
! | Large step+Small step
! | Large step+Small step
|-
|-
| | 1L22s
| | [[1L 22s]]
| | <span style="line-height: 15.6000003814697px;">22\23 &lt; g &lt; 1</span>
| | 22\23 &lt; g &lt; 1
| | ''g = 23\24, 24\25, 25\26''
| | ''g = 23\24, 24\25, 25\26''
| | 22g-21+1-g = 21g-20
| | 22g-21+1-g = 21g-20
|-
|-
| | 2L21s
| | [[2L 21s]]
| | 11\23 &lt; g &lt; 1\2
| | 11\23 &lt; g &lt; 1\2
| | g = ''12\25, 13\27'', 14\29
| | g = ''12\25, 13\27'', 14\29
| | 21g-10+1-2g = 19g-9
| | 21g-10+1-2g = 19g-9
|-
|-
| | 3L20s
| | [[3L 20s]]
| | 15\23 &lt; g &lt; 2\3
| | 15\23 &lt; g &lt; 2\3
| | g = ''17\26'', 19\29, 21\32
| | g = ''17\26'', 19\29, 21\32
| | 20g-13+1-3g = 17g-12
| | 20g-13+1-3g = 17g-12
|-
|-
| | 4L19s
| | [[4L 19s]]
| | 17\23 &lt; g &lt; 3\4
| | 17\23 &lt; g &lt; 3\4
| | g = ''20\27'', 23\31, 26\35
| | g = ''20\27'', 23\31, 26\35
| | 19g-14+3-4g = 15g-11
| | 19g-14+3-4g = 15g-11
|-
|-
| | 5L18s
| | [[5L 18s]]
| | 9\23 &lt; g &lt; 2\5
| | 9\23 &lt; g &lt; 2\5
| | g = ''11\28'', 13\33, 15\38
| | g = ''11\28'', 13\33, 15\38
| | 18g-7+2-5g = 13g-5
| | 18g-7+2-5g = 13g-5
|-
|-
| | 6L17s
| | [[6L 17s]]
| | 19\23 &lt; g &lt; 5\6
| | 19\23 &lt; g &lt; 5\6
| | g = 24\29, 29\35, 34\41
| | g = 24\29, 29\35, 34\41
| | 17g-15+1-6g = 11g-14
| | 17g-15+1-6g = 11g-14
|-
|-
| | 7L16s
| | [[7L 16s]]
| | 13\23 &lt; g &lt; 4\7
| | 13\23 &lt; g &lt; 4\7
| | g = 17\30,<span style="line-height: 15.6000003814697px;"> 21\37,</span> 25\44
| | g = 17\30, 21\37, 25\44
| | 16g-9+4-7g = 9g-5
| | 16g-9+4-7g = 9g-5
|-
|-
| | 8L15s
| | [[8L 15s]]
| | 20\23 &lt; g &lt; 7\8
| | 20\23 &lt; g &lt; 7\8
| | g = 27\31, 34\39, 41\47
| | g = 27\31, 34\39, 41\47
| | 15g-13+7-8g = 7g-6
| | 15g-13+7-8g = 7g-6
|-
|-
| | 9L14s
| | [[9L 14s]]
| | 5\23 &lt; g &lt; 2\9
| | 5\23 &lt; g &lt; 2\9
| | g = 7\32, 9\41, 11\50
| | g = 7\32, 9\41, 11\50
| | 14g-7+<span style="line-height: 15.6000003814697px;">2-9g = 5g-5</span>
| | 14g-7+2-9g = 5g-5
|-
|-
| | 10L13s
| | [[10L 13s]]
| | 16\23 &lt; g &lt; 7\10
| | 16\23 &lt; g &lt; 7\10
| | g = 23\33, 30\43, 37\53
| | g = 23\33, 30\43, 37\53
| | 13g-9+7-10g = 3g-2
| | 13g-9+7-10g = 3g-2
|-
|-
| | 11L12s
| | [[11L 12s]]
| | 2\23 &lt; g &lt; 1\11
| | 2\23 &lt; g &lt; 1\11
| | g = 3\34, 4\45, 5\56
| | g = 3\34, 4\45, 5\56
| | 12g-1+1-11g = g
| | 12g-1+1-11g = g
|-
|-
| | 12L11s
| | [[12L 11s]]
| | 21\23 &lt; g &lt; 11\12
| | 21\23 &lt; g &lt; 11\12
| | g = 32\35, 43\47, 54\59
| | g = 32\35, 43\47, 54\59
| | <span style="line-height: 15.6000003814697px;">11g-10+11-12g = 1-g</span>
| | 11g-10+11-12g = 1-g
|-
|-
| | 13L10s
| | [[13L 10s]]
| | 7\23 &lt; g &lt; 4\13
| | 7\23 &lt; g &lt; 4\13
| | g = 11\36, 15\49, 19\62
| | g = 11\36, 15\49, 19\62
| | 10g-3+4-13g =1-3g
| | 10g-3+4-13g =1-3g
|-
|-
| | 14L9s
| | [[14L 9s]]
| | 18\23 &lt; g &lt; 11\14
| | 18\23 &lt; g &lt; 11\14
| | g = 29\37, 40\51, 51\65
| | g = 29\37, 40\51, 51\65
| | 9g-7+11-14g = 4-5g
| | 9g-7+11-14g = 4-5g
|-
|-
| | 15L8s
| | [[15L 8s]]
| | 3\23 &lt; g &lt; 2\15
| | 3\23 &lt; g &lt; 2\15
| | g = 5\38, 7\53, 9\68
| | g = 5\38, 7\53, 9\68
| | 8g-1+2-15g = 1-7g
| | 8g-1+2-15g = 1-7g
|-
|-
| | 16L7s
| | [[16L 7s]]
| | 10\23 &lt; g &lt; 7\16
| | 10\23 &lt; g &lt; 7\16
| | g = 17\39, 24\55, 31\71
| | g = 17\39, 24\55, 31\71
| | 7g-3+<span style="line-height: 15.6000003814697px;">7-16g = 4-9g</span>
| | 7g-3+7-16g = 4-9g
|-
|-
| | 17L6s
| | [[17L 6s]]
| | 4\23 &lt; g &lt; 3\17
| | 4\23 &lt; g &lt; 3\17
| | g = 7\40, 10\57, 13\74
| | g = 7\40, 10\57, 13\74
| | 6g-1+3-17g = 2-11g
| | 6g-1+3-17g = 2-11g
|-
|-
| | 18L5s
| | [[18L 5s]]
| | 14\23 &lt; g &lt; 11\18
| | 14\23 &lt; g &lt; 11\18
| | g = 25\41, 36\59, 47\77
| | g = 25\41, 36\59, 47\77
| | 5g-4+11-18g = 7-13g
| | 5g-4+11-18g = 7-13g
|-
|-
| | 19L4s
| | [[19L 4s]]
| | 6\23 &lt; g &lt; 5\19
| | 6\23 &lt; g &lt; 5\19
| | g = 11\42, 16\61, 21\80
| | g = 11\42, 16\61, 21\80
| | 4g-1+5-19g = 4-15g
| | 4g-1+5-19g = 4-15g
|-
|-
| | 20L3s
| | [[20L 3s]]
| | 8\23 &lt; g &lt; 7\20
| | 8\23 &lt; g &lt; 7\20
| | g = 15\43, 22\63, 29\83
| | g = 15\43, 22\63, 29\83
| | 3g-1+13-20g = 12-17g
| | 3g-1+13-20g = 12-17g
|-
|-
| | 21L2s
| | [[21L 2s]]
| | 12\23 &lt; g &lt; 11\21
| | 12\23 &lt; g &lt; 11\21
| | g = 23\44, 34\65, 45\86
| | g = 23\44, 34\65, 45\86
| | 2g-1+11-21g = 10-19g
| | 2g-1+11-21g = 10-19g
|-
|-
| | 22L1s
| | [[22L 1s]]
| | 1\23 &lt; g &lt; 1\22
| | 1\23 &lt; g &lt; 1\22
| | g = 2\45, 3\67, 4\89
| | g = 2\45, 3\67, 4\89
Line 1,468: Line 1,451:
|}
|}


=24=
= 24-tone =
 
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 1,477: Line 1,459:
! | Large step+Small step
! | Large step+Small step
|-
|-
| | 1L23s
| | [[1L 23s]]
| | 23\24 &lt; g &lt; 1
| | 23\24 &lt; g &lt; 1
| | ''g = 24\25, 25\26, 26\27''
| | ''g = 24\25, 25\26, 26\27''
| | 23g-22+1-g = 22g-21
| | 23g-22+1-g = 22g-21
|-
|-
| | 2L22s
| | [[2L 22s]]
| | 11\24 &lt; g &lt; 1\2
| | 11\24 &lt; g &lt; 1\2
| | g = ''12\26, 13\28, 14\30''
| | g = ''12\26, 13\28, 14\30''
| | 11g-5+1/2-g = 10g-9/2
| | 11g-5+1/2-g = 10g-9/2
|-
|-
| | 3L21s
| | [[3L 21s]]
| | 7\24 &lt; g &lt; 1\3
| | 7\24 &lt; g &lt; 1\3
| | g = ''8\27, 9\30'', 10\33
| | g = ''8\27, 9\30'', 10\33
| | 7g-2+1/3-g = 6g-5/3
| | 7g-2+1/3-g = 6g-5/3
|-
|-
| | 4L20s
| | [[4L 20s]]
| | 5\24 &lt; g &lt; 1\4
| | 5\24 &lt; g &lt; 1\4
| | g = ''6\28'', 7\32, 8\36
| | g = ''6\28'', 7\32, 8\36
| | 5g-1+1/4-g = 4g-3/4
| | 5g-1+1/4-g = 4g-3/4
|-
|-
| | 5L19s
| | [[5L 19s]]
| | 19\24 &lt; g &lt; 4\5
| | 19\24 &lt; g &lt; 4\5
| | g = ''23\29'', 27\34, 31\39
| | g = ''23\29'', 27\34, 31\39
| | 19g-15+4-5g  = 14g-11
| | 19g-15+4-5g  = 14g-11
|-
|-
| | 6L18s
| | [[6L 18s]]
| | 3\24 &lt; g &lt; 1\6
| | 3\24 &lt; g &lt; 1\6
| | g = ''4\30'', 5\36, 6\42
| | g = ''4\30'', 5\36, 6\42
| | 3g-1\3+1\6-g = 2g-1\6
| | 3g-1\3+1\6-g = 2g-1\6
|-
|-
| | 7L17s
| | [[7L 17s]]
| | 17\24 &lt; g &lt; 5\7
| | 17\24 &lt; g &lt; 5\7
| | g = 22\31, 27\38, 32\45
| | g = 22\31, 27\38, 32\45
| | 17g-12+5-7g = 10g-7
| | 17g-12+5-7g = 10g-7
|-
|-
| | 8L16s
| | [[8L 16s]]
| | 2\24 &lt; g &lt; 1\8
| | 2\24 &lt; g &lt; 1\8
| | g = 3\32, 4\40, 5\48
| | g = 3\32, 4\40, 5\48
| | 2g-1\8+1\8-g = g
| | 2g-1\8+1\8-g = g
|-
|-
| | 9L15s
| | [[9L 15s]]
| | 5\24 &lt; g &lt; 2\9
| | 5\24 &lt; g &lt; 2\9
| | g = 7\33, 9\42, 11\51
| | g = 7\33, 9\42, 11\51
| | 5g-1+2\3-3g = 2g-1\3
| | 5g-1+2\3-3g = 2g-1\3
|-
|-
| | 10L14s
| | [[10L 14s]]
| | 7\24 &lt; g &lt; 3\10
| | 7\24 &lt; g &lt; 3\10
| | g = 10\34, 13\44, 16\54
| | g = 10\34, 13\44, 16\54
| | 7g-2+3\2-5g = 2g-1\2
| | 7g-2+3\2-5g = 2g-1\2
|-
|-
| | 11L13s
| | [[11L 13s]]
| | 13\24 &lt; g &lt; 6\11
| | 13\24 &lt; g &lt; 6\11
| | g = 19\35, 25\46, 31\57
| | g = 19\35, 25\46, 31\57
| | 13g-7+6-11g = 2g-1
| | 13g-7+6-11g = 2g-1
|-
|-
| | 12L12s
| | [[12L 12s]]
| | 1\24 &lt; g &lt; 1\12
| | 1\24 &lt; g &lt; 1\12
| | g = 2\36, 3\48, 4\60
| | g = 2\36, 3\48, 4\60
| | g+1\12-g = 1\12
| | g+1\12-g = 1\12
|-
|-
| | 13L11s
| | [[13L 11s]]
| | 11\24 &lt; g &lt; 6\13
| | 11\24 &lt; g &lt; 6\13
| | g = 17\37, 23\50, 29\63
| | g = 17\37, 23\50, 29\63
| | 11g-5+6-13g = 1-2g
| | 11g-5+6-13g = 1-2g
|-
|-
| | 14L10s
| | [[14L 10s]]
| | 17\24 &lt; g &lt; 10\14
| | 17\24 &lt; g &lt; 10\14
| | g = 27\38, 37\52, 47\66
| | g = 27\38, 37\52, 47\66
| | 5g-7\2+5-7g = 3\2-2g
| | 5g-7\2+5-7g = 3\2-2g
|-
|-
| | 15L9s
| | [[15L 9s]]
| | 3\24 &lt; g &lt; 2\15
| | 3\24 &lt; g &lt; 2\15
| | g = 5\39, 7\54, 9\69
| | g = 5\39, 7\54, 9\69
| | 3g-1\3+2\3-5g = 1\3-2g
| | 3g-1\3+2\3-5g = 1\3-2g
|-
|-
| | 16L8s
| | [[16L 8s]]
| | 1\24 &lt; g &lt; 1\16
| | 1\24 &lt; g &lt; 1\16
| | g = 2\40, 3\56, 4\72
| | g = 2\40, 3\56, 4\72
| | g+1\8-2g = 1\8-g
| | g+1\8-2g = 1\8-g
|-
|-
| | 17L7s
| | [[17L 7s]]
| | 7\24 &lt; g &lt; 5\17
| | 7\24 &lt; g &lt; 5\17
| | g = 12\41, 17\58, 22\75
| | g = 12\41, 17\58, 22\75
| | 7g-2+5-17g = 3-10g
| | 7g-2+5-17g = 3-10g
|-
|-
| | 18L6s
| | [[18L 6s]]
| | 1\24 &lt; g &lt; 1\18
| | 1\24 &lt; g &lt; 1\18
| | g = 2\42, 3\60, 4\78
| | g = 2\42, 3\60, 4\78
| | g+1\6-3g = 1\6-2g
| | g+1\6-3g = 1\6-2g
|-
|-
| | 19L5s
| | [[19L 5s]]
| | 5\24 &lt; g &lt; 4\19
| | 5\24 &lt; g &lt; 4\19
| | g = 9\43, 13\62, 17\81
| | g = 9\43, 13\62, 17\81
| | 5g-5+4-19g = 1-18g
| | 5g-5+4-19g = 1-18g
|-
|-
| | 20L4s
| | [[20L 4s]]
| | 1\24 &lt; g &lt; 1\20
| | 1\24 &lt; g &lt; 1\20
| | g = 2\44, 3\64, 4\84
| | g = 2\44, 3\64, 4\84
| | g+1\4-5g = 1\4-4g
| | g+1\4-5g = 1\4-4g
|-
|-
| | 21L3s
| | [[21L 3s]]
| | 1\24 &lt; g &lt; 1\21
| | 1\24 &lt; g &lt; 1\21
| | g = 2\45, 3\66, 4\87
| | g = 2\45, 3\66, 4\87
| | g+1\3-7g = 1\3-6g
| | g+1\3-7g = 1\3-6g
|-
|-
| | 22L2s
| | [[22L 2s]]
| | 1\24 &lt; g &lt; 1\22
| | 1\24 &lt; g &lt; 1\22
| | g = 2\46, 3\68, 4\90
| | g = 2\46, 3\68, 4\90
| | g+1\2-11g = 1\2-10g
| | g+1\2-11g = 1\2-10g
|-
|-
| | 23L1s
| | [[23L 1s]]
| | 1\24 &lt; g &lt; 1\23
| | 1\24 &lt; g &lt; 1\23
| | g = 2\47, 3\70, 4\93
| | g = 2\47, 3\70, 4\93
Line 1,593: Line 1,575:
|}
|}


=25=
= 25-tone =
 
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 1,602: Line 1,583:
! | Large step+Small step
! | Large step+Small step
|-
|-
| | 1L24s
| | [[1L 24s]]
| | 24\25 &lt; g &lt; 1
| | 24\25 &lt; g &lt; 1
| | ''g = 25\26, 26\27, 27\28''
| | ''g = 25\26, 26\27, 27\28''
| | 24g-23+1-g = 23g-22
| | 24g-23+1-g = 23g-22
|-
|-
| | 2L23s
| | [[2L 23s]]
| | 12\25 &lt; g &lt; 1\2
| | 12\25 &lt; g &lt; 1\2
| | ''g = 13\27, 14\29, 15\31''
| | ''g = 13\27, 14\29, 15\31''
| | 23g-11+1-2g = 21g-10
| | 23g-11+1-2g = 21g-10
|-
|-
| | 3L22s
| | [[3L 22s]]
| | 8\25 &lt; g &lt; 1\3
| | 8\25 &lt; g &lt; 1\3
| | g = ''9\28'', ''10\31'', 11\34
| | g = ''9\28'', ''10\31'', 11\34
| | 22g-7+1-3g = 19g-6
| | 22g-7+1-3g = 19g-6
|-
|-
| | 4L21s
| | [[4L 21s]]
| | 6\25 &lt; g &lt; 1\4
| | 6\25 &lt; g &lt; 1\4
| | g = ''7\29'', 8\33, 9\37
| | g = ''7\29'', 8\33, 9\37
| | 21g-5+1-4g = 17g-4
| | 21g-5+1-4g = 17g-4
|-
|-
| | 5L20s
| | [[5L 20s]]
| | 4\25 &lt; g &lt; 1\5
| | 4\25 &lt; g &lt; 1\5
| | g = ''5\30'', 6\35, 7\40
| | g = ''5\30'', 6\35, 7\40
| | 4g-3\5+1\5-g = 3g-2\5
| | 4g-3\5+1\5-g = 3g-2\5
|-
|-
| | 6L19s
| | [[6L 19s]]
| | 4\25 &lt; g &lt; 1\6
| | 4\25 &lt; g &lt; 1\6
| | g = ''5\31'', 6\37, 7\43
| | g = ''5\31'', 6\37, 7\43
| | 19g-3+1-6g = 13g-2
| | 19g-3+1-6g = 13g-2
|-
|-
| | 7L18s
| | [[7L 18s]]
| | 7\25 &lt; g &lt; 2\7
| | 7\25 &lt; g &lt; 2\7
| | g = 9\32, 11\39, 13\46
| | g = 9\32, 11\39, 13\46
| | 18g-5+2-7g = 11g-3
| | 18g-5+2-7g = 11g-3
|-
|-
| | 8L17s
| | [[8L 17s]]
| | 3\25 &lt; g &lt; 1\8
| | 3\25 &lt; g &lt; 1\8
| | g = 4\33, 5\41, 6\47
| | g = 4\33, 5\41, 6\47
| | <span style="line-height: 15.6000003814697px;">17g-2+1-8g = 9g-1</span>
| | 17g-2+1-8g = 9g-1
|-
|-
| | 9L16s
| | [[9L 16s]]
| | 11\25 &lt; g &lt; 4\9
| | 11\25 &lt; g &lt; 4\9
| | g = 15\34, 19\43, 23\52
| | g = 15\34, 19\43, 23\52
| | 16g-7<span style="line-height: 15.6000003814697px;">+4-9g = 3-7g</span>
| | 16g-7+4-9g = 3-7g
|-
|-
| | 10L15s
| | [[10L 15s]]
| | 2\25 &lt; g &lt; 1\10
| | 2\25 &lt; g &lt; 1\10
| | g = 3\35, 4\45, 5\55
| | g = 3\35, 4\45, 5\55
| | 3g-1\5+1\5-2g = g
| | 3g-1\5+1\5-2g = g
|-
|-
| | 11L14s
| | [[11L 14s]]
| | 9\25 &lt; g &lt; 4\11
| | 9\25 &lt; g &lt; 4\11
| | g = 13\36, 17\47, 21\58
| | g = 13\36, 17\47, 21\58
| | 14g-5+4-11g = 3g-1
| | 14g-5+4-11g = 3g-1
|-
|-
| | 12L13s
| | [[12L 13s]]
| | 2\25 &lt; g &lt; 1\12
| | 2\25 &lt; g &lt; 1\12
| | g = 3\37, 4\49, 5\61
| | g = 3\37, 4\49, 5\61
| | 13g-1+1-12g = g
| | 13g-1+1-12g = g
|-
|-
| | 13L12s
| | [[13L 12s]]
| | 23\25 &lt; g &lt; 12\13
| | 23\25 &lt; g &lt; 12\13
| | g = 35\38, 47\51, 59\64
| | g = 35\38, 47\51, 59\64
| | 12g-11+12-13g = 1-g
| | 12g-11+12-13g = 1-g
|-
|-
| | 14L11s
| | [[14L 11s]]
| | 16\25 &lt; g &lt; 9\14
| | 16\25 &lt; g &lt; 9\14
| | g = 25\39, 34\53, 43\67
| | g = 25\39, 34\53, 43\67
| | 11g-7+9-14g = 2-3g
| | 11g-7+9-14g = 2-3g
|-
|-
| | 15L10s
| | [[15L 10s]]
| | 3\25 &lt; g &lt; 2\15
| | 3\25 &lt; g &lt; 2\15
| | g = 5\40, 7\55, 9\70
| | g = 5\40, 7\55, 9\70
| | 2g-1\5+2\5-3g = 1\5-g
| | 2g-1\5+2\5-3g = 1\5-g
|-
|-
| | 16L9s
| | [[16L 9s]]
| | 14\25 &lt; g &lt; 9\16
| | 14\25 &lt; g &lt; 9\16
| | g = 23\41, 32\57, 41\73
| | g = 23\41, 32\57, 41\73
| | 9g-5+9-16g = 4-7g
| | 9g-5+9-16g = 4-7g
|-
|-
| | 17L8s
| | [[17L 8s]]
| | 22\25 &lt; g &lt; 15\17
| | 22\25 &lt; g &lt; 15\17
| | g = 37\42, 52\59, 67\76
| | g = 37\42, 52\59, 67\76
| | 8g-7+15-17g = 8-9g
| | 8g-7+15-17g = 8-9g
|-
|-
| | 18L7s
| | [[18L 7s]]
| | 18\25 &lt; g &lt; 13\18
| | 18\25 &lt; g &lt; 13\18
| | g = 31\43, 44\61, 57\79
| | g = 31\43, 44\61, 57\79
| | 7g-5+13-18g = 8-11g
| | 7g-5+13-18g = 8-11g
|-
|-
| | 19L6s
| | [[19L 6s]]
| | 21\25 &lt; g &lt; 16\19
| | 21\25 &lt; g &lt; 16\19
| | g = 37\44, 53\63, 69\82
| | g = 37\44, 53\63, 69\82
| | 6g-5+16-19g = 11-13g
| | 6g-5+16-19g = 11-13g
|-
|-
| | 20L5s
| | [[20L 5s]]
| | 1\25 &lt; g &lt; 1\20
| | 1\25 &lt; g &lt; 1\20
| | g = 2\45, 3\65, 4\85
| | g = 2\45, 3\65, 4\85
| | g+1\5-4g = 1\5-3g
| | g+1\5-4g = 1\5-3g
|-
|-
| | 21L4s
| | [[21L 4s]]
| | 16\21 &lt; g &lt; 19\25
| | 16\21 &lt; g &lt; 19\25
| | g = 35\46, 51\67, 71\88
| | g = 35\46, 51\67, 71\88
| | 4g-3+16-21g = 13-17g
| | 4g-3+16-21g = 13-17g
|-
|-
| | 22L3s
| | [[22L 3s]]
| | 17\25 &lt; g &lt; 15\22
| | 17\25 &lt; g &lt; 15\22
| | g = 32\47, 47\69, 62\91
| | g = 32\47, 47\69, 62\91
| | 3g-2+15-22g = 13-19g
| | 3g-2+15-22g = 13-19g
|-
|-
| | 23L2s
| | [[23L 2s]]
| | 13\25 &lt; g &lt; 12\23
| | 13\25 &lt; g &lt; 12\23
| | g = 25\48, 37\71, 49\94
| | g = 25\48, 37\71, 49\94
| | 2g-1+11-23g = 10-21g
| | 2g-1+11-23g = 10-21g
|-
|-
| | 24L1s
| | [[24L 1s]]
| | 1\25 &lt; g &lt; 1\24
| | 1\25 &lt; g &lt; 1\24
| | g = 2\49, 3\73, 4\97
| | g = 2\49, 3\73, 4\97
Line 1,723: Line 1,704:
|}
|}


=26=
= 26-tone =
 
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 1,732: Line 1,712:
! | Large step+Small step
! | Large step+Small step
|-
|-
| | 1L25s
| | [[1L 25s]]
| | 25\26 &lt; g &lt; 1
| | 25\26 &lt; g &lt; 1
| | ''g = 26\27, 27\28, 28\29''
| | ''g = 26\27, 27\28, 28\29''
| | 25g-24+1-g = 24g-23
| | 25g-24+1-g = 24g-23
|-
|-
| | 2L24s
| | [[2L 24s]]
| | 12\26 &lt; g &lt; 1\2
| | 12\26 &lt; g &lt; 1\2
| | ''g = 13\28, 14\30, 15\32''
| | ''g = 13\28, 14\30, 15\32''
| | 12g-11\2+1\2-g = 11g-5
| | 12g-11\2+1\2-g = 11g-5
|-
|-
| | 3L23s
| | [[3L 23s]]
| | 17\26 &lt; g &lt; 2\3
| | 17\26 &lt; g &lt; 2\3
| | g = ''19\29'', ''21\32'', 23\35
| | g = ''19\29'', ''21\32'', 23\35
| | 23g-15+2-3g = 20g-13
| | 23g-15+2-3g = 20g-13
|-
|-
| | 4L22s
| | [[4L 22s]]
| | 6\26 &lt; g &lt; 1\4
| | 6\26 &lt; g &lt; 1\4
| | g = ''7\30'', 8\34, 9\38
| | g = ''7\30'', 8\34, 9\38
| | 11g-5\2+<span style="line-height: 15.6000003814697px;">1\2-2g = 9g-2</span>
| | 11g-5\2+1\2-2g = 9g-2
|-
|-
| | 5L21s
| | [[5L 21s]]
| | 5\26 &lt; g &lt; 1\5
| | 5\26 &lt; g &lt; 1\5
| | g = ''6\31'', 7\36, 8\41
| | g = ''6\31'', 7\36, 8\41
| | 21g-4+1-5g = 16g-3
| | 21g-4+1-5g = 16g-3
|-
|-
| | 6L20s
| | [[6L 20s]]
| | 4\26 &lt; g &lt; 1\6
| | 4\26 &lt; g &lt; 1\6
| | g = ''5\32'', 6\38, 7\44
| | g = ''5\32'', 6\38, 7\44
| | 10g-3\2+1\2-3g = 7g-1
| | 10g-3\2+1\2-3g = 7g-1
|-
|-
| | 7L19s
| | [[7L 19s]]
| | 11\26 &lt; g &lt; 3\7
| | 11\26 &lt; g &lt; 3\7
| | g = 14\33, 17\40, 20\47
| | g = 14\33, 17\40, 20\47
| | 19g-8+3-7g = 12g-5
| | 19g-8+3-7g = 12g-5
|-
|-
| | 8L18s
| | [[8L 18s]]
| | 3\26 &lt; g &lt; 1\8
| | 3\26 &lt; g &lt; 1\8
| | g = 4\34, 5\42, 6\50
| | g = 4\34, 5\42, 6\50
| | 9g-1+1\2-4g = 5g-1\2
| | 9g-1+1\2-4g = 5g-1\2
|-
|-
| | 9L17s
| | [[9L 17s]]
| | 23\26 &lt; g &lt; 8\9
| | 23\26 &lt; g &lt; 8\9
| | g = 31\35, 39\44, 47\53
| | g = 31\35, 39\44, 47\53
| | 17g-15+8-9g = 8g-7
| | 17g-15+8-9g = 8g-7
|-
|-
| | 10L16s
| | [[10L 16s]]
| | 5\26 &lt; g &lt; 2\10
| | 5\26 &lt; g &lt; 2\10
| | g = 7\36, 9\46, 11\56
| | g = 7\36, 9\46, 11\56
| | 8g-3\2+1-5g = 3g-1\2
| | 8g-3\2+1-5g = 3g-1\2
|-
|-
| | 11L15s
| | [[11L 15s]]
| | 7\26 &lt; g &lt; 3\11
| | 7\26 &lt; g &lt; 3\11
| | g = 10\37, 13\48, 16\59
| | g = 10\37, 13\48, 16\59
| | 15g-4+3-11g = 4g-1
| | 15g-4+3-11g = 4g-1
|-
|-
| | 12L14s
| | [[12L 14s]]
| | 2\26 &lt; g &lt; 1\12
| | 2\26 &lt; g &lt; 1\12
| | g = 3\38, 4\50, 5\62
| | g = 3\38, 4\50, 5\62
| | 7g-1\2+1\2-6g = g
| | 7g-1\2+1\2-6g = g
|-
|-
| | 13L13s
| | [[13L 13s]]
| | 1\26 &lt; g &lt; 1\13
| | 1\26 &lt; g &lt; 1\13
| | g = 2\39, 3\52, 4\65
| | g = 2\39, 3\52, 4\65
| | g+1\13-g = 1\13
| | g+1\13-g = 1\13
|-
|-
| | <span style="line-height: 15.6000003814697px;">14L12s</span>
| | [[14L 12s]]
| | 11\26 &lt; g &lt; 6\14
| | 11\26 &lt; g &lt; 6\14
| | g = 17\40, 23\54, 29\68
| | g = 17\40, 23\54, 29\68
| | 6g-5\2+3-7g = 1\2-g
| | 6g-5\2+3-7g = 1\2-g
|-
|-
| | <span style="line-height: 15.6000003814697px;">15L11s</span>
| | [[15L 11s]]
| | 19\26 &lt; g &lt; 11\15
| | 19\26 &lt; g &lt; 11\15
| | g = 30\41, 41\56, 52\71
| | g = 30\41, 41\56, 52\71
| | 11g-8+11-15g = 3-4g
| | 11g-8+11-15g = 3-4g
|-
|-
| | <span style="line-height: 15.6000003814697px;">16L10s</span>
| | [[16L 10s]]
| | 8\26 &lt; g &lt; 5\16
| | 8\26 &lt; g &lt; 5\16
| | g = 13\42, 18\58, 23\74
| | g = 13\42, 18\58, 23\74
| | 5g-3\2+5\2-8g = 1-3g
| | 5g-3\2+5\2-8g = 1-3g
|-
|-
| | <span style="line-height: 15.6000003814697px;">17L9s</span>
| | [[17L 9s]]
| | 3\26 &lt; g &lt; 2\17
| | 3\26 &lt; g &lt; 2\17
| | g = 5\43, 7\60, 9\77
| | g = 5\43, 7\60, 9\77
| | 9g-1+2-17g = 1-8g
| | 9g-1+2-17g = 1-8g
|-
|-
| | <span style="line-height: 15.6000003814697px;">18L</span>8s
| | [[18L 8s]]
| | 10\26 &lt; g &lt; 7\18
| | 10\26 &lt; g &lt; 7\18
| | g = 17\44, 24\62, 31\80
| | g = 17\44, 24\62, 31\80
| | 4g-7\2+7-9g = 7\2-5g
| | 4g-7\2+7-9g = 7\2-5g
|-
|-
| | <span style="line-height: 15.6000003814697px;">19L</span>7s
| | [[19L 7s]]
| | 15\26 &lt; g &lt; 11\19
| | 15\26 &lt; g &lt; 11\19
| | g = 26\45, 37\64, 48\83
| | g = 26\45, 37\64, 48\83
| | 7g-4+11-19g = 7-12g
| | 7g-4+11-19g = 7-12g
|-
|-
| | <span style="line-height: 15.6000003814697px;">20L</span>6s
| | [[20L 6s]]
| | 9\26 &lt; g &lt; 7\20
| | 9\26 &lt; g &lt; 7\20
| | g = 16\46, 23\66, 30\86
| | g = 16\46, 23\66, 30\86
| | 3g-1+7\2-10g = 5\2-7g
| | 3g-1+7\2-10g = 5\2-7g
|-
|-
| | <span style="line-height: 15.6000003814697px;">21L</span>5s
| | [[21L 5s]]
| | 21\26 &lt; g &lt; 17\21
| | 21\26 &lt; g &lt; 17\21
| | g = 38\47, 55\68, 72\89
| | g = 38\47, 55\68, 72\89
| | 5g-4+16-21g = 12-16g
| | 5g-4+16-21g = 12-16g
|-
|-
| | <span style="line-height: 15.6000003814697px;">22L</span>4s
| | [[22L 4s]]
| | 7\26 &lt; g &lt; 6\22
| | 7\26 &lt; g &lt; 6\22
| | g = 13\48, 19\70, 25\92
| | g = 13\48, 19\70, 25\92
| | 2g-1\2+3-11g = 5\2-9g
| | 2g-1\2+3-11g = 5\2-9g
|-
|-
| | <span style="line-height: 15.6000003814697px;">23L</span>3s
| | [[23L 3s]]
| | 9\26 &lt; g &lt; 8\23
| | 9\26 &lt; g &lt; 8\23
| | g = 17\49, 25\72, 33/95
| | g = 17\49, 25\72, 33/95
| | 3g-1+8-23g = 7-20g
| | 3g-1+8-23g = 7-20g
|-
|-
| | <span style="line-height: 15.6000003814697px;">24L</span>2s
| | [[24L 2s]]
| | 1\26 &lt; g &lt; 1\24
| | 1\26 &lt; g &lt; 1\24
| | g = 2\50, 3\74, 4\98
| | g = 2\50, 3\74, 4\98
| | g+1\2-12g = 1\2-11g
| | g+1\2-12g = 1\2-11g
|-
|-
| | 25L1s
| | [[25L 1s]]
| | 1\26 &lt; g &lt; 1\25
| | 1\26 &lt; g &lt; 1\25
| | g = 2\51, 3\76, 4\101
| | g = 2\51, 3\76, 4\101
Line 1,858: Line 1,838:
|}
|}


=27=
= 27-tone =
 
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 1,867: Line 1,846:
! | Large step+Small step
! | Large step+Small step
|-
|-
| | 1L26s
| | [[1L 26s]]
| | 26\27 &lt; g &lt; 1
| | 26\27 &lt; g &lt; 1
| | <span style="line-height: 15.6000003814697px;">''g = 27\28,''</span> ''28\29, 29\30''
| | ''g = 27\28,'' ''28\29, 29\30''
| | 26g-25+1-g = 25g-24
| | 26g-25+1-g = 25g-24
|-
|-
| | 2L25s
| | [[2L 25s]]
| | 13\27 &lt; g &lt; 1\2
| | 13\27 &lt; g &lt; 1\2
| | ''g = 14\29, 15\31, 16\33''
| | ''g = 14\29, 15\31, 16\33''
| | 25g-12+1-2g = 23g-11
| | 25g-12+1-2g = 23g-11
|-
|-
| | 3L24s
| | [[3L 24s]]
| | 8\27 &lt; g &lt; 1\3
| | 8\27 &lt; g &lt; 1\3
| | g = ''9\30'', ''10\33'', 11\36
| | g = ''9\30'', ''10\33'', 11\36
| | 8g-7\3+1-3g = 5g-2
| | 8g-7\3+1-3g = 5g-2
|-
|-
| | 4L23s
| | [[4L 23s]]
| | 20\27 &lt; g &lt; 3\4
| | 20\27 &lt; g &lt; 3\4
| | g = ''23\31'', 26\35, 29\39
| | g = ''23\31'', 26\35, 29\39
| | 23g-17+3-4g = 19g-14
| | 23g-17+3-4g = 19g-14
|-
|-
| | 5L22s
| | [[5L 22s]]
| | 16\27 &lt; g &lt; 3\5
| | 16\27 &lt; g &lt; 3\5
| | g = ''19\32'', 22\37, 25\42
| | g = ''19\32'', 22\37, 25\42
| | 22g-13+3-5g = 17g-10
| | 22g-13+3-5g = 17g-10
|-
|-
| | 6L21s
| | [[6L 21s]]
| | 4\27 &lt; g &lt; 1\6
| | 4\27 &lt; g &lt; 1\6
| | g = ''5\33'', 6\39, 7\45
| | g = ''5\33'', 6\39, 7\45
| | 7g-1+1\3-2g = 5g-2\3
| | 7g-1+1\3-2g = 5g-2\3
|-
|-
| | 7L20s
| | [[7L 20s]]
| | 23\27 &lt; g &lt; 6\7
| | 23\27 &lt; g &lt; 6\7
| | g = 29\34, 35\41, 41\48
| | g = 29\34, 35\41, 41\48
| | 20g-17+6-7g = 13g-11
| | 20g-17+6-7g = 13g-11
|-
|-
| | 8L19s
| | [[8L 19s]]
| | 10\27 &lt; g &lt; 3\8
| | 10\27 &lt; g &lt; 3\8
| | g = 13\35, 16\43, 19\51
| | g = 13\35, 16\43, 19\51
| | 19g-7+3-8g = 11g-4
| | 19g-7+3-8g = 11g-4
|-
|-
| | 9L18s
| | [[9L 18s]]
| | 2\27 &lt; g &lt; 1\9
| | 2\27 &lt; g &lt; 1\9
| | g = 3\36, 4\45, 5\54
| | g = 3\36, 4\45, 5\54
| | 2g-1\9+1\9-g = g
| | 2g-1\9+1\9-g = g
|-
|-
| | 10L17s
| | [[10L 17s]]
| | 8\27 &lt; g &lt; 3\10
| | 8\27 &lt; g &lt; 3\10
| | g = 11\37, 14\47, 17\57
| | g = 11\37, 14\47, 17\57
| | 17g-5+3-10g = 7g-2
| | 17g-5+3-10g = 7g-2
|-
|-
| | 11L16s
| | [[11L 16s]]
| | 22\27 &lt; g &lt; 9\11
| | 22\27 &lt; g &lt; 9\11
| | g = 31\38, 40\49, 49\60
| | g = 31\38, 40\49, 49\60
| | 16g-13+9-11g = 5g-4
| | 16g-13+9-11g = 5g-4
|-
|-
| | 12L15s
| | [[12L 15s]]
| | 2\27 &lt; g &lt; 1\12
| | 2\27 &lt; g &lt; 1\12
| | g = 3\39, 4\51, 5\63
| | g = 3\39, 4\51, 5\63
| | 5g-1\3+1\3-4g = g
| | 5g-1\3+1\3-4g = g
|-
|-
| | 13L14s
| | [[13L 14s]]
| | 2\27 &lt; g &lt; 1\13
| | 2\27 &lt; g &lt; 1\13
| | g = 3\40, 4\53, 5\66
| | g = 3\40, 4\53, 5\66
| | 14g-1+1-13g = g
| | 14g-1+1-13g = g
|-
|-
| | 14L13s
| | [[14L 13s]]
| | 25\27 &lt; g &lt; 13\14
| | 25\27 &lt; g &lt; 13\14
| | g = 38\41, 51\55, 64\69
| | g = 38\41, 51\55, 64\69
| | 13g-12+13-14g = 1-g
| | 13g-12+13-14g = 1-g
|-
|-
| | 15L12s
| | [[15L 12s]]
| | 7\27 &lt; g &lt; 4\15
| | 7\27 &lt; g &lt; 4\15
| | g = 11\42, 15\57, 19\72
| | g = 11\42, 15\57, 19\72
| | 4g-1+4\3-5g = 1\3-g
| | 4g-1+4\3-5g = 1\3-g
|-
|-
| | 16L11s
| | [[16L 11s]]
| | 5\27 &lt; g &lt; 3\16
| | 5\27 &lt; g &lt; 3\16
| | g = 8\43, 11\59, 14\75
| | g = 8\43, 11\59, 14\75
| | 11g-2+3-16g = 1-5g
| | 11g-2+3-16g = 1-5g
|-
|-
| | 17L10s
| | [[17L 10s]]
| | 19\27 &lt; g &lt; 12\17
| | 19\27 &lt; g &lt; 12\17
| | g = 31\44, 43\61, 55\78
| | g = 31\44, 43\61, 55\78
| | 10g-7+12-17g = 5-7g
| | 10g-7+12-17g = 5-7g
|-
|-
| | 18L9s
| | [[18L 9s]]
| | 1\27 &lt; g &lt; 1\18
| | 1\27 &lt; g &lt; 1\18
| | g = 2\45, 3\63, 4\81
| | g = 2\45, 3\63, 4\81
| | g+1\9-2g = 1\9-g
| | g+1\9-2g = 1\9-g
|-
|-
| | 19L8s
| | [[19L 8s]]
| | 17\27 &lt; g &lt; 12\19
| | 17\27 &lt; g &lt; 12\19
| | g = 29\46, 41\65, 53\84
| | g = 29\46, 41\65, 53\84
| | 8g-5+12-19g = 7-11g
| | 8g-5+12-19g = 7-11g
|-
|-
| | 20L7s
| | [[20L 7s]]
| | 4\27 &lt; g &lt; 3\20
| | 4\27 &lt; g &lt; 3\20
| | g = 7\47, 10\67, 13\87
| | g = 7\47, 10\67, 13\87
| | 7g-1+3-20g = 2-13g
| | 7g-1+3-20g = 2-13g
|-
|-
| | 21L6s
| | [[21L 6s]]
| | 5\27 &lt; g &lt; 4\21
| | 5\27 &lt; g &lt; 4\21
| | g = 9\48, 13\69, 17\90
| | g = 9\48, 13\69, 17\90
| | 2g-1\3+4\3-7g = 1-5g
| | 2g-1\3+4\3-7g = 1-5g
|-
|-
| | 22L5s
| | [[22L 5s]]
| | <span style="line-height: 15.6000003814697px;">11</span>\27 &lt; g &lt; 9\22
| | 11\27 &lt; g &lt; 9\22
| | g = 20\49, 29\71, 38\93
| | g = 20\49, 29\71, 38\93
| | 5g-2+9-22g = 7-17g
| | 5g-2+9-22g = 7-17g
|-
|-
| | 23L4s
| | [[23L 4s]]
| | 7\27 &lt; g &lt; 6\23
| | 7\27 &lt; g &lt; 6\23
| | g = 13\50, 19\73, 25\96
| | g = 13\50, 19\73, 25\96
| | 4g-1+6-23g = 5-19g
| | 4g-1+6-23g = 5-19g
|-
|-
| | 24L3s
| | [[24L 3s]]
| | 1\27 &lt; g &lt; 1\24
| | 1\27 &lt; g &lt; 1\24
| | g = 2\51, 3\75, 4\99
| | g = 2\51, 3\75, 4\99
| | g+1\3-8g = 1\3-7g
| | g+1\3-8g = 1\3-7g
|-
|-
| | 25L2s
| | [[25L 2s]]
| | 14\27 &lt; g &lt; 13\25
| | 14\27 &lt; g &lt; 13\25
| | g = 27\52, 40\77, 53\102
| | g = 27\52, 40\77, 53\102
| | 2g-1+13-25g = 12-23g
| | 2g-1+13-25g = 12-23g
|-
|-
| | 26L1s
| | [[26L 1s]]
| | 1\27 &lt; g &lt; 1\26
| | 1\27 &lt; g &lt; 1\26
| | g = 2\53, 3\79, 4\105
| | g = 2\53, 3\79, 4\105
Line 1,998: Line 1,977:
|}
|}


=28=
= 28-tone =
 
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 2,007: Line 1,985:
! | Large step+Small step
! | Large step+Small step
|-
|-
| | 1L27s
| | [[1L 27s]]
| | 27\28 &lt; g &lt; 1
| | 27\28 &lt; g &lt; 1
| | ''g = 28\29, 29\30, 30\31''
| | ''g = 28\29, 29\30, 30\31''
| | 27g-26+1-g = 26g-25
| | 27g-26+1-g = 26g-25
|-
|-
| | 2L26s
| | [[2L 26s]]
| | 13\28 &lt; g &lt; 1\2
| | 13\28 &lt; g &lt; 1\2
| | ''g = 14\30, 15\32, 16\34''
| | ''g = 14\30, 15\32, 16\34''
| | 13g-6+1\2-g = 12g-11\2
| | 13g-6+1\2-g = 12g-11\2
|-
|-
| | 3L25s
| | [[3L 25s]]
| | 9\28 &lt; g &lt; 1\3
| | 9\28 &lt; g &lt; 1\3
| | g = ''10\31'',<span style="line-height: 15.6000003814697px;"> ''11\34'',</span> 12\37
| | g = ''10\31'', ''11\34'', 12\37
| | 25g-8+1-3g = 22g-7
| | 25g-8+1-3g = 22g-7
|-
|-
| | 4L24s
| | [[4L 24s]]
| | 6\28 &lt; g &lt; 1\4
| | 6\28 &lt; g &lt; 1\4
| | g = ''7\32'', 8\36, 9\40
| | g = ''7\32'', 8\36, 9\40
| | 6g-5\4+1\4-g = 5g-1
| | 6g-5\4+1\4-g = 5g-1
|-
|-
| | 5L23s
| | [[5L 23s]]
| | 11\28 &lt; g &lt; 2\5
| | 11\28 &lt; g &lt; 2\5
| | g = ''13\33'', 15\38, 17\43
| | g = ''13\33'', 15\38, 17\43
| | 23g-9+2-5g = 18g-7
| | 23g-9+2-5g = 18g-7
|-
|-
| | 6L22s
| | [[6L 22s]]
| | 9\28 &lt; g &lt; 2\6
| | 9\28 &lt; g &lt; 2\6
| | g = ''11\34'', 13\40, 15\46
| | g = ''11\34'', 13\40, 15\46
| | 11g-7\2+1-3g = 8g-3
| | 11g-7\2+1-3g = 8g-3
|-
|-
| | 7L21s
| | [[7L 21s]]
| | 3\28 &lt; g &lt; 1\7
| | 3\28 &lt; g &lt; 1\7
| | g = 4\35, 5\42, 6\49
| | g = 4\35, 5\42, 6\49
| | 3g-2\7+1\7-g = 2g-1\7
| | 3g-2\7+1\7-g = 2g-1\7
|-
|-
| | 8L20s
| | [[8L 20s]]
| | 3\28 &lt; g &lt; 1\8
| | 3\28 &lt; g &lt; 1\8
| | g = 4\36, 5\44, 6\52
| | g = 4\36, 5\44, 6\52
| | 5g-1\2+1\4-2g = 3g-1\4
| | 5g-1\2+1\4-2g = 3g-1\4
|-
|-
| | 9L19s
| | [[9L 19s]]
| | 3\28 &lt; g &lt; 1\9
| | 3\28 &lt; g &lt; 1\9
| | g = 4\37, 5\46, 6\55
| | g = 4\37, 5\46, 6\55
| | 19g-2+1-9g = 10g-1
| | 19g-2+1-9g = 10g-1
|-
|-
| | 10L18s
| | [[10L 18s]]
| | 11\28 &lt; g &lt; 4\10
| | 11\28 &lt; g &lt; 4\10
| | g = 15\38, 19\48, 23\58
| | g = 15\38, 19\48, 23\58
| | 9g-7\2+2-5g = 4g-3\2
| | 9g-7\2+2-5g = 4g-3\2
|-
|-
| | 11L17s
| | [[11L 17s]]
| | 5\28 &lt; g &lt; 2\11
| | 5\28 &lt; g &lt; 2\11
| | g = 7\39, 9\50, 11\61
| | g = 7\39, 9\50, 11\61
| | 17g-3+2-11g = 6g-1
| | 17g-3+2-11g = 6g-1
|-
|-
| | 12L16s
| | [[12L 16s]]
| | 2\28 &lt; g &lt; 1\12
| | 2\28 &lt; g &lt; 1\12
| | g = 3\40, 4\52, 5\64
| | g = 3\40, 4\52, 5\64
| | 4g-1\4+1\4-3g = g
| | 4g-1\4+1\4-3g = g
|-
|-
| | 13L15s
| | [[13L 15s]]
| | 15\28 &lt; g &lt; 7\13
| | 15\28 &lt; g &lt; 7\13
| | g = 22\41, 29\54, 36\67
| | g = 22\41, 29\54, 36\67
| | 15g-8+7-13g = 2g-1
| | 15g-8+7-13g = 2g-1
|-
|-
| | 14L14s
| | [[14L 14s]]
| | 1\28 &lt; g &lt; 1\14
| | 1\28 &lt; g &lt; 1\14
| | g = 2\42, 3\56, 4\70
| | g = 2\42, 3\56, 4\70
| | g+1\14-g = 1\14
| | g+1\14-g = 1\14
|-
|-
| | <span style="line-height: 15.6000003814697px;">15L13s</span>
| | [[15L 13s]]
| | 13\28 &lt; g &lt; 7\15
| | 13\28 &lt; g &lt; 7\15
| | g = 20\43, 27\58, 34\73
| | g = 20\43, 27\58, 34\73
| | 13g-6+7-15g = 1-2g
| | 13g-6+7-15g = 1-2g
|-
|-
| | <span style="line-height: 15.6000003814697px;">16L12s</span>
| | [[16L 12s]]
| | 5\28 &lt; g &lt; 3\16
| | 5\28 &lt; g &lt; 3\16
| | g = 8\44, 11\60, 14\76
| | g = 8\44, 11\60, 14\76
| | 3g-1\2+3\4-4g = 1\4-g
| | 3g-1\2+3\4-4g = 1\4-g
|-
|-
| | <span style="line-height: 15.6000003814697px;">17L11s</span>
| | [[17L 11s]]
| | 23\28 &lt; g &lt; 14\17
| | 23\28 &lt; g &lt; 14\17
| | g = 37\45, 51\62, 65\79
| | g = 37\45, 51\62, 65\79
| | 11g-9+13-17g = 4-6g
| | 11g-9+13-17g = 4-6g
|-
|-
| | <span style="line-height: 15.6000003814697px;">18L10s</span>
| | [[18L 10s]]
| | 3\28 &lt; g &lt; 2\18
| | 3\28 &lt; g &lt; 2\18
| | g = 5\46, 7\64, 9\82
| | g = 5\46, 7\64, 9\82
| | 5g-1\2+1-9g = 1\2-4g
| | 5g-1\2+1-9g = 1\2-4g
|-
|-
| | <span style="line-height: 15.6000003814697px;">19L9s</span>
| | [[19L 9s]]
| | 25\28 &lt; g &lt; 17\19
| | 25\28 &lt; g &lt; 17\19
| | g = 42\47, 59\66, 76\85
| | g = 42\47, 59\66, 76\85
| | 9g-8+17-19g = 9-10g
| | 9g-8+17-19g = 9-10g
|-
|-
| | <span style="line-height: 15.6000003814697px;">20L</span>8s
| | [[20L 8s]]
| | 4\28 &lt; g &lt; 3\20
| | 4\28 &lt; g &lt; 3\20
| | g = 7\48, 10\68, 13\88
| | g = 7\48, 10\68, 13\88
| | 2g-1\4+3\4-5g = 1\2-3g
| | 2g-1\4+3\4-5g = 1\2-3g
|-
|-
| | <span style="line-height: 15.6000003814697px;">21L7s</span>
| | [[21L 7s]]
| | 1\28 &lt; g &lt; 1\21
| | 1\28 &lt; g &lt; 1\21
| | g = 2\49, 3\70, 4\91
| | g = 2\49, 3\70, 4\91
| | g+<span style="line-height: 15.6000003814697px;">1\7-2g = 1\7-g</span>
| | g+1\7-2g = 1\7-g
|-
|-
| | <span style="line-height: 15.6000003814697px;">22L</span>6s
| | [[22L 6s]]
| | 5\28 &lt; g &lt; 4\22
| | 5\28 &lt; g &lt; 4\22
| | g = 9\50, 13\72, 17\94
| | g = 9\50, 13\72, 17\94
| | 3g-1\2+2-11g = 3\2-8g
| | 3g-1\2+2-11g = 3\2-8g
|-
|-
| | <span style="line-height: 15.6000003814697px;">23L</span>5s
| | [[23L 5s]]
| | 17\28 &lt; g &lt; 14\23
| | 17\28 &lt; g &lt; 14\23
| | g = 31\51, 45\74, 59\97
| | g = 31\51, 45\74, 59\97
| | 5g-3+14-23g = 11-18g
| | 5g-3+14-23g = 11-18g
|-
|-
| | <span style="line-height: 15.6000003814697px;">24L</span>4s
| | [[24L 4s]]
| | 1\28 &lt; g &lt; 1\24
| | 1\28 &lt; g &lt; 1\24
| | g = 2\52, 3\76, 4\100
| | g = 2\52, 3\76, 4\100
| | g+1\4-6g = 1\4-5g
| | g+1\4-6g = 1\4-5g
|-
|-
| | <span style="line-height: 15.6000003814697px;">25L</span>3s
| | [[25L 3s]]
| | 19\28 &lt; g &lt; 17\25
| | 19\28 &lt; g &lt; 17\25
| | g = 36\53, 53\78, 70\103
| | g = 36\53, 53\78, 70\103
| | 3g-2+17-25g = 15+22g
| | 3g-2+17-25g = 15+22g
|-
|-
| | <span style="line-height: 15.6000003814697px;">26L</span>2s
| | [[26L 2s]]
| | 15\28 &lt; g &lt; 14\26
| | 15\28 &lt; g &lt; 14\26
| | g = 29\54, 43\80, 57\106
| | g = 29\54, 43\80, 57\106
| | g-1\2+7-13g = 13\2-12g
| | g-1\2+7-13g = 13\2-12g
|-
|-
| | 27L1s
| | [[27L 1s]]
| | 1\28 &lt; g &lt; 1\27
| | 1\28 &lt; g &lt; 1\27
| | g = 2\55, 3\82, 4\109
| | g = 2\55, 3\82, 4\109
Line 2,143: Line 2,121:
|}
|}


=29=
= 29-tone =
 
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 2,152: Line 2,129:
! | Large step+Small step
! | Large step+Small step
|-
|-
| | 1L28s
| | [[1L 28s]]
| | 28\29 &lt; g &lt; 1
| | 28\29 &lt; g &lt; 1
| | ''g = 29\30, 30\31, 31\32''
| | ''g = 29\30, 30\31, 31\32''
| | 28g-27+1-g = 27g-26
| | 28g-27+1-g = 27g-26
|-
|-
| | 2L27s
| | [[2L 27s]]
| | 14\29 &lt; g &lt; 1\2
| | 14\29 &lt; g &lt; 1\2
| | ''g = 15\31, 16\33, 17\35''
| | ''g = 15\31, 16\33, 17\35''
| | 27g-13+1-2g = 25g-12
| | 27g-13+1-2g = 25g-12
|-
|-
| | 3L26s
| | [[3L 26s]]
| | 19\29 &lt; g &lt; 2\3
| | 19\29 &lt; g &lt; 2\3
| | g = ''21\32'', ''23\35'', 25\38
| | g = ''21\32'', ''23\35'', 25\38
| | 26g-17+2-3g = 23g-15
| | 26g-17+2-3g = 23g-15
|-
|-
| | 4L25s
| | [[4L 25s]]
| | 7\29 &lt; g &lt; 1\4
| | 7\29 &lt; g &lt; 1\4
| | g = ''8\33'', 9\37, 10\41
| | g = ''8\33'', 9\37, 10\41
| | 25g-6+1-4g = 21g-5
| | 25g-6+1-4g = 21g-5
|-
|-
| | 5L24s
| | [[5L 24s]]
| | 23\29 &lt; g &lt; 4\5
| | 23\29 &lt; g &lt; 4\5
| | g = ''27\34'', 31\39, 35\44
| | g = ''27\34'', 31\39, 35\44
| | 24g-19+4-5g = 19g-15
| | 24g-19+4-5g = 19g-15
|-
|-
| | 6L23s
| | [[6L 23s]]
| | 24\29 &lt; g &lt; 5\6
| | 24\29 &lt; g &lt; 5\6
| | g = ''29\35'', 34\41, 39\47
| | g = ''29\35'', 34\41, 39\47
| | 23g-19+5-6g = 17g-14
| | 23g-19+5-6g = 17g-14
|-
|-
| | 7L22s
| | [[7L 22s]]
| | 4\29 &lt; g &lt; 1\7
| | 4\29 &lt; g &lt; 1\7
| | g = ''5\36'', 6\43, 7\50
| | g = ''5\36'', 6\43, 7\50
| | 22g-3+1-7g = 15g-2
| | 22g-3+1-7g = 15g-2
|-
|-
| | 8L21s
| | [[8L 21s]]
| | 18\29 &lt; g &lt; 5\8
| | 18\29 &lt; g &lt; 5\8
| | g = 23\37, 28\45, 33\53
| | g = 23\37, 28\45, 33\53
| | <span style="line-height: 15.6000003814697px;">21g-13+5-8g = 13g-8</span>
| | 21g-13+5-8g = 13g-8
|-
|-
| | 9L20s
| | [[9L 20s]]
| | 16\29 &lt; g &lt; 5\9
| | 16\29 &lt; g &lt; 5\9
| | g = 21\38, 26\47, 31\56
| | g = 21\38, 26\47, 31\56
| | 20g-11+5-9g = 11g-6
| | 20g-11+5-9g = 11g-6
|-
|-
| | 10L19s
| | [[10L 19s]]
| | 26\29 &lt; g &lt; 9\10
| | 26\29 &lt; g &lt; 9\10
| | g = 35\39, 44\49, 53\59
| | g = 35\39, 44\49, 53\59
| | 19g-17+9-10g = 9g-8
| | 19g-17+9-10g = 9g-8
|-
|-
| | 11L18s
| | [[11L 18s]]
| | 21\29 &lt; g &lt; 8\11
| | 21\29 &lt; g &lt; 8\11
| | g = 29\40, 37\51, 45\62
| | g = 29\40, 37\51, 45\62
| | 18g-13+8-11g = 7g-2
| | 18g-13+8-11g = 7g-2
|-
|-
| | 12L17s
| | [[12L 17s]]
| | 12\29 &lt; g &lt; 5\12
| | 12\29 &lt; g &lt; 5\12
| | g = 17\41, 22\53, 27\65
| | g = 17\41, 22\53, 27\65
| | 17g-7+5-12g = 5g-2
| | 17g-7+5-12g = 5g-2
|-
|-
| | 13L16s
| | [[13L 16s]]
| | 20\29 &lt; g &lt; 9\13
| | 20\29 &lt; g &lt; 9\13
| | g = 29\42, 38\55, 47\68
| | g = 29\42, 38\55, 47\68
| | 16g+11+9-13g = 3g-2
| | 16g+11+9-13g = 3g-2
|-
|-
| | 14L15s
| | [[14L 15s]]
| | 2\29 &lt; g &lt; 1\14
| | 2\29 &lt; g &lt; 1\14
| | g = 3\43, 4\57, 5\71
| | g = 3\43, 4\57, 5\71
| | 15g-1+1-14g = g
| | 15g-1+1-14g = g
|-
|-
| | 15L14s
| | [[15L 14s]]
| | 27\29 &lt; g &lt; 14\15
| | 27\29 &lt; g &lt; 14\15
| | g = 41\44, 55\59, 69\74
| | g = 41\44, 55\59, 69\74
| | 14g-13+14-15g = 1-g
| | 14g-13+14-15g = 1-g
|-
|-
| | 16L13s
| | [[16L 13s]]
| | 9\29 &lt; g &lt; 5\16
| | 9\29 &lt; g &lt; 5\16
| | g = 14\45, 19\61, 24\77
| | g = 14\45, 19\61, 24\77
| | 13g-4+5-16g = 1-3g
| | 13g-4+5-16g = 1-3g
|-
|-
| | 17L12s
| | [[17L 12s]]
| | 17\29 &lt; g &lt; 10\17
| | 17\29 &lt; g &lt; 10\17
| | g = 27\46, 37\63, 47\80
| | g = 27\46, 37\63, 47\80
| | 12g-5+7-17g = 2-5g
| | 12g-5+7-17g = 2-5g
|-
|-
| | 18L11s
| | [[18L 11s]]
| | 8\29 &lt; g &lt; 5\18
| | 8\29 &lt; g &lt; 5\18
| | g = 13\47, 18\65, 23\83
| | g = 13\47, 18\65, 23\83
| | 11g-3+5-18g = 2-7g
| | 11g-3+5-18g = 2-7g
|-
|-
| | 19L10s
| | [[19L 10s]]
| | 3\29 &lt; g &lt; 2\19
| | 3\29 &lt; g &lt; 2\19
| | g = 5\48, 7\67, 9\86
| | g = 5\48, 7\67, 9\86
| | 10g-1+2-19g = 1-9g
| | 10g-1+2-19g = 1-9g
|-
|-
| | 20L9s
| | [[20L 9s]]
| | 13\29 &lt; g &lt; 9\20
| | 13\29 &lt; g &lt; 9\20
| | g = 22\49, 31\69, 40\89
| | g = 22\49, 31\69, 40\89
| | 9g-5+9-20g = 4-11g
| | 9g-5+9-20g = 4-11g
|-
|-
| | 21L8s
| | [[21L 8s]]
| | 11\29 &lt; g &lt; 8\21
| | 11\29 &lt; g &lt; 8\21
| | g = 19\50, 27\71, 35\92
| | g = 19\50, 27\71, 35\92
| | 8g-3+8-21g = 5-13g
| | 8g-3+8-21g = 5-13g
|-
|-
| | 22L7s
| | [[22L 7s]]
| | 25\29 &lt; g &lt; 19\22
| | 25\29 &lt; g &lt; 19\22
| | g = 44\51, 63\73, 82\95
| | g = 44\51, 63\73, 82\95
| | 7g-6+9-22g = 3-16g
| | 7g-6+9-22g = 3-16g
|-
|-
| | 23L6s
| | [[23L 6s]]
| | 5\29 &lt; g &lt; 4\23
| | 5\29 &lt; g &lt; 4\23
| | g = 9\52, 13\75, 17\98
| | g = 9\52, 13\75, 17\98
| | 6g-1+4-23g = 3-17g
| | 6g-1+4-23g = 3-17g
|-
|-
| | 24L5s
| | [[24L 5s]]
| | 6\29 &lt; g &lt; 5\24
| | 6\29 &lt; g &lt; 5\24
| | g = 11\53, 16\77, 21\101
| | g = 11\53, 16\77, 21\101
| | 5g-9+5-24g = 4-19g
| | 5g-9+5-24g = 4-19g
|-
|-
| | 25L4s
| | [[25L 4s]]
| | 22\29 &lt; g &lt; 19\25
| | 22\29 &lt; g &lt; 19\25
| | g = 41\54, 60\79, 79\104
| | g = 41\54, 60\79, 79\104
| | 4g-3+19-25g = 16-21g
| | 4g-3+19-25g = 16-21g
|-
|-
| | 26L3s
| | [[26L 3s]]
| | 10\29 &lt; g &lt; 9\26
| | 10\29 &lt; g &lt; 9\26
| | g = 19\55, 28\81, 37\107
| | g = 19\55, 28\81, 37\107
| | 3g-1+9-26g = 8-23g
| | 3g-1+9-26g = 8-23g
|-
|-
| | 27L2s
| | [[27L 2s]]
| | 15\29 &lt; g &lt; 14\27
| | 15\29 &lt; g &lt; 14\27
| | g = 29\56, 43\83, 57\110
| | g = 29\56, 43\83, 57\110
| | 2g-1+17-27g = 16-25g
| | 2g-1+17-27g = 16-25g
|-
|-
| | 28L1s
| | [[28L 1s]]
| | 1\29 &lt; g &lt; 1\28
| | 1\29 &lt; g &lt; 1\28
| | g = 2\57,<span style="line-height: 15.6000003814697px;"> 3\85,</span> 4\113
| | g = 2\57, 3\85, 4\113
| | g+1-28g = 1-27g
| | g+1-28g = 1-27g
|}
|}
[[Category:MOS scales]]

Revision as of 10:11, 19 February 2022

Below are ranges of generators for various L-s patterns of MOS scales, 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 midpoint of the range. Finally, the fourth column gives the boundaries of propriety, maximum expressiveness and diatonicity.

If the number of the 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 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: These sets are given for the sake of completeness as they are not really scales

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 1s 1\2 < g < 1 g = 2\3, 3\4, 4\5 g+1-g = 1
1L 2s 2\3 < g < 1 g = 3\4, 4\5, 5\6 2g-1+1-g = g
2L 1s 1\3 < g < 1\2 g = 2\5, 3\7, 4\9 g+1-2g = 1-g
1L 3s 3\4 < g < 1 g = 4\5, 5\6, 6\7 3g-2+1-g = 2g-1
2L 2s 1\4 < g < 1\2 g = 2\6, 3\8, 4\10 g+1\2-g = 1\2
3L 1s 1\4 < g < 1\3 g = 2\7, 3\10, 4\13 g+1-3g = 1-2g

5-tone

Note: italicized generators from here below generate scales which are weakly tonal

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 4s 4\5 < g < 1 g = 5\6, 6\7, 7\8 4g-3+1-g = 3g-2
2L 3s 2\5 < g < 1\2 g = 3\7, 4\9, 5\11 3g-1+1-2g = g
3L 2s 3\5 < g < 2\3 g = 5\8, 7\11, 9\14 2g-1+2-3g = 1-g
4L 1s 1\5 < g < 1\4 g = 2\9, 3\13, 4\17 g+1-4g = 1-3g

6-tone

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 5s 5\6 < g < 1 g = 6\7, 7\8, 8\9 5g-4+1-g = 4g-3
2L 4s 2\6 < g < 1\2 g = 3\8, 4\10, 5\12 2g-1\2+1\2-g = g
3L 3s 1\6 < g < 1\3 g = 2\9, 3\12, 4\15 g+1\3-g = 1\3
4L 2s 1\6 < g < 1\4 g = 2\10, 3\14, 4\18 g+1\2-2g = 1\2-g
5L 1s 1\6 < g < 1\5 g = 2\11, 3\16, 4\21 g+1-5g = 1-4g

7-tone

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 6s 6\7 < g < 1 g = 7\8, 8\9, 9\10 6g-5+1-g = 5g-4
2L 5s 3\7 < g < 1\2 g = 4\9, 5\11, 6\13 5g-2+1-2g = 3g-1
3L 4s 2\7 < g < 1\3 g = 3\10, 4\13, 5\16 4g-1+1-3g = g
4L 3s 5\7 < g < 3\4 g = 8\11, 11\15, 14\19 3g-2+3-4g = 1-g
5L 2s 4\7 < g < 3\5 g = 7\12, 10\17, 13\22 2g-1+3-5g = 2-3g
6L 1s 1\7 < g < 1\6 g = 2\13, 3\19, 4\25 g+1-6g = 1-5g

8-tone

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 7s 7\8 < g < 1 g = 8\9, 9\10, 10\11 7g-6+1-g = 6g-5
2L 6s 3\8 < g < 1\2 g = 4\10, 5\12, 6\14 3g-1+1\2-g = 2g-1\2
3L 5s 5\8 < g < 2\3 g = 7\11, 9\14, 11\17 5g-3+2-3g = 2g-1
4L 4s 1\8 < g < 1\4 g = 2\12, 3\16, 4\20 g+1\4-g = 1\4
5L 3s 3\8 < g < 2\5 g = 5\13, 7\18, 9\23 3g-1+2-5g = 1-2g
6L 2s 1\8 < g < 1\6 g = 2\14, 3\20, 4\26 g+1\2-3g = 1\2-2g
7L 1s 1\8 < g < 1\7 g = 2\15, 3\22, 4\29 g+1-7g = 1-6g

9-tone

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 8s 8\9 < g < 1 g = 9\10, 10\11, 11\12 8g-7+1-g = 7g-6
2L 7s 4\9 < g < 1\2 g = 5\11, 6\13, 7\15 7g-3+1-2g = 5g-2
3L 6s 2\9 < g < 1\3 g = 3\12, 4\15, 5\18 2g-1\3+1\3-g = g
4L 5s 2\9 < g < 1\4 g = 3\13, 4\17, 5\21 5g-1+1-4g = g
5L 4s 7\9 < g < 4\5 g = 11\14, 15\19, 18\23 4g-3+4-5g = 1-g
6L 3s 1\9 < g < 1\6 g = 2\15, 3\21, 4\27 g+1\3-2g = 1\3-g
7L 2s 5\9 < g < 4\7 g = 9\16, 10\23, 17\30 2g-1+4-7g = 3-7g
8L 1s 1\9 < g < 1\8 g = 2\17, 3\25, 4\33 g+1-8g = 1-7g

10-tone

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 9s 9\10 < g < 1 g = 10\11, 11\12, 12\13 9g-8+1-g = 8g-7
2L 8s 4\10 < g < 1\2 g = 5\12, 6\14, 7\16 4g-3\2+1\2-g = 3g-1
3L 7s 3\10 < g < 1\3 g = 4\13, 5\16, 6\19 7g-2+1-3g = 4g-1
4L 6s 2\10 < g < 1\4 g = 3\14, 4\18, 5\22 3g-1\2+1\2-2g = g
5L 5s 1\10 < g < 1\5 g = 2\15, 3\20, 4\25 g+1\5-g = 1\5
6L 4s 3\10 < g < 2\6 g = 5\16, 7\22, 9\28 2g-1\2+1-3g = 1\2-g
7L 3s 7\10 < g < 5\7 g = 12\17, 17\24, 22\31 3g-2+5-7g = 3-4g
8L 2s 1\10 < g < 1\8 g = 2\18, 3\26, 4\34 g+1\2-4g = 1\2-3g
9L 1s 1\10 < g < 1\9 g = 2\19, 3\28, 4\37 g+1-9g = 1-8g

11-tone

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 10s 10\11 < g < 1 g = 11\12, 12\13, 13\14 10g-9+1-g = 9g-8
2L 9s 5\11 < g < 1\2 g = 6\13, 7\15, 8\17 9g-4+1-2g = 7g-3
3L 8s 7\11 < g < 2\3 g = 9\14, 11\17, 13\20 8g-5+2-3g = 5g-3
4L 7s 8\11 < g < 3\4 g = 11\15, 14\19, 17\23 7g-5+3-4g = 3g-2
5L 6s 2\11 < g < 1\5 g = 3\16, 4\21, 5\26 6g-1+1-5g = g
6L 5s 9\11 < g < 5\6 g = 14\17, 19\23, 24\29 5g-4+5-6g = 1-g
7L 4s 3\11 < g < 2\7 g = 5\18, 7\25, 9\32 4g-1+2-7g = 1-3g
8L 3s 4\11 < g < 3\8 g = 7\19, 10\27, 13\35 3g-1+3-8g = 2-5g
9L 2s 6\11 < g < 5\9 g = 11\20, 16\29, 21\38 2g-1+5-9g = 4-7g
10L 1s 1\11 < g < 1\10 g = 2\21, 3\31, 4\41 g+1-10g = 1-9g

12-tone

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 11s 11\12 < g < 1 g = 12\13, 13\14, 14\15 11g-10+1-g = 10g-9
2L 10s 5\12 < g < 1\2 g = 6\14, 7\16, 8\18 5g-2+1\2-g = 4g-3\2
3L 9s 3\12 < g < 1\3 g = 4\15, 5\18, 6\21 3g-2\3+1\3-g = 2g-1\3
4L 8s 2\12 < g < 1\4 g = 3\16, 4\20, 5\24 2g-1\4+1\4-g = g
5L 7s 7\12 < g < 3\5 g = 10\17, 13\22, 16\27 7g-4+3-5g = 2g-1
6L 6s 1\12 < g < 1\6 g = 2\18, 3\24, 4\30 g+1\6-g = g
7L 5s 5\12 < g < 3\7 g = 8\19, 11\26, 14\33 5g-2+3-7g = 1-2g
8L 4s 1\12 < g < 1\8 g = 2\20, 3\28, 4\36 g+1\4-2g = 1\4-g
9L 3s 1\12 < g < 1\9 g = 2\21, 3\30, 4\39 g+1\3-3g = 1\3-2g
10L 2s 1\12 < g < 1\10 g = 2\22, 3\32, 4\42 g+1\2-5g = 1\2-4g
11L 1s 1\12 < g < 1\11 g = 2\23, 3\34, 4\45 g+1-11g = 1-10g

13-tone

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 12s 12\13 < g < 1 g = 13\14, 14\15, 15\16 12g-11+1-g = 11g-10
2L 11s 6\13 < g < 1\2 g = 7\15, 8\17, 9\19 11g-5-1-2g = 10g-6
3L 10s 4\13 < g < 1\3 g = 5\16, 6\19, 7/22 10g-3+1-3g = 7g-2
4L 9s 3\13 < g < 1\4 g = 4\17, 5\21, 6\25 9g-2+1-4g = 5g-1
5L 8s 5\13 < g < 2\5 g = 7\18, 9\23, 11\28 8g-3+2-5g = 3g-1
6L 7s 2\13 < g < 1\6 g = 3\19, 4\25, 5\31 7g-1+1-6g = g
7L 6s 11\13 < g < 6\7 g = 17\20, 23\27, 29\34 6g-5+6-7g = 1-g
8L 5s 8\13 < g < 5\8 g = 13\21, 18\29, 23\37 5g-3+5-8g = 2-3g
9L 4s 10\13 < g < 7\9 g = 17\22, 24\31, 31\40 4g-3+7-9g = 4-5g
10L 3s 9\13 < g < 7\10 g = 16\23, 23\33, 30\43 3g-2+7-10g = 5-7g
11L 2s 7\13 < g < 6\11 g = 13\24, 19\35, 25\46 2g-1+6-11g = 5-9g
12L 1s 1\13 < g < 1\12 g = 2\25, 3\37, 4\49 g+1-12g = 1-11g

14-tone

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 13s 13\14 < g < 1 g = 14\15, 15\16, 16\17 13g-12+1-g = 12g-11
2L 12s 6\14 < g < 1\2 g = 7\16, 8\18, 9\20 6g-5\2+1\2-g = 5g-2
3L 11s 9\14 < g < 2\3 g = 11\17, 13\20, 15\23 11g-7+2-3g = 9g-5
4L 10s 3\14 < g < 1\4 g = 4\18, 5\22, 6\26 5g-1+1\2-2g = 3g-1\2
5L 9s 11\14 < g < 4\5 g = 15\19, 19\24, 23\29 9g-7+4-5g = 4g-3
6L 8s 2\14 < g < 1\6 g = 3\20, 4\26, 5\32 4g-1\2-1\2-3g = g
7L 7s 1\14 < g < 1\7 g = 2\21, 3\28, 4\35 g+1\7-g = 1\7
8L 6s 5\14 < g < 3\8 g = 8\22, 11\30, 14\38 3g-1+3\2-4g = 1\2-g
9L 5s 3\14 < g < 2\9 g = 5\23, 7\32, 9\41 5g-1+2-9g = 1-4g
10L 4s 4\14 < g < 3\10 g = 7\24, 10\34, 13\44 2g-1\2+3\2-5g = 1-3g
11L 3s 5\14 < g < 4\11 g = 9\25, 13\36, 17\47 3g-1+4-11g = 3-8g
12L 2s 1\14 < g < 1\12 g = 2\26, 3\38, 4\50 g+1\2-6g = 1\2-5g
13L 1s 1\14 < g < 1\13 g = 2\27, 3\40, 4\53 g+1-13g = 1-12g

15-tone

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 14s 14\15 < g < 1 g = 15\16, 16\17, 17\18 14g-13+1-g = 13g-12
2L 13s 7\15 < g < 1\2 g = 8\17, 9\19, 10\21 13g-6+1-2g = 11g-5
3L 12s 4\15 < g < 1\3 g = 5\18, 6\21, 7\24 4g-1+1\3-g = 3g-2\3
4L 11s 11\15 < g < 3\4 g = 14\19, 17\23, 20\27 11g-8+3-4g = 8g-4
5L 10s 2\15 < g < 1\5 g = 3\20, 4\25, 5\30 2g-1\5+1\5-g = g
6L 9s 2\15 < g < 1\6 g = 3\21, 4\27, 5\33 3g-1\3+1\3-2g = g
7L 8s 2\15 < g < 1\7 g = 3\22, 4\29, 5\36 8g-1+1-7g = g
8L 7s 13\15 < g < 7\8 g = 20\23, 27\31, 34\39 7g-6+7-8g = 1-g
9L 6s 3\15 < g < 2\9 g = 5\24, 7\33, 9\42 2g-1\3+2\3-3g = 1\3-g
10L 5s 1\15 < g < 1\10 g = 2\25, 3\35, 4\45 g+1\5-2g = 1\5-g
11L 4s 4\15 < g < 3\11 g = 7\26, 10\37, 13\48 4g-1+3-11g = 2-7g
12L 3s 1\15 < g < 1\12 g = 2\27, 3\39, 4\51 g+1\3-4g = 1\3-3g
13L 2s 8\15 < g < 7\13 g = 15\28, 22\41, 29\54 2g-1+7-13g = 6-11g
14L 1s 1\15 < g < 1\14 g = 2\29, 3\43, 4\57 g+1-14g = 1-13g

16-tone

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 15s 15\16 < g < 1 g = 16\17, 17\18, 18\19 15g-14+1-g = 14g-13
2L 14s 7\16 < g < 1\2 g = 8\18, 9\20, 10\22 7g-3+1\2-g = 5\2-6g
3L 13s 5\16 < g < 1\3 g = 6\19, 7\22, 8\25 13g-4+1-3g = 10g-3
4L 12s 3\16 < g < 1\4 g = 4\20, 5\24, 6\28 3g-1\2+1\4-g = 2g-1\4
5L 11s 3\16 < g < 1\5 g = 4\21, 5\26, 6\31 11g-2+1-5g = 6g-1
6L 10s 5\16 < g < 2\6 g = 7\22, 9\28, 11\34 5g-3\2+1-3g = 2g-1\2
7L 9s 9\16 < g < 4\7 g = 13\23, 17\30, 21\37 9g-5+4-7g = 2g-1
8L 8s 1\16 < g < 1\8 g = 2\24, 3\32, 4\40 g+1\8-g = 1\8
9L 7s 7\16 < g < 4\9 g = 11\25, 15\34, 19\43 7g-3+4-9g = 1-2g
10L 6s 3\16 < g < 2\10 g = 5\26, 7\36, 8\46 3g-1\2+1-5g = 1\2-2g
11L 5s 13\16 < g < 9\11 g = 22\27, 31\38, 40\49 5g-4+9-11g = 5-6g
12L 4s 1\16 < g < 1\12 g = 2\28, 3\40, 4\52 g+1\4-3g = 1\4-2g
13L 3s 11\16 < g < 9\13 g = 20\29, 29\42, 38\55 3g-2+9-13g = 7-10g
14L 2s 1\16 < g < 1\14 g = 2\30, 3\44, 4\58 g+1\2-7g = 1\2-6g
15L 1s 1\16 < g < 1\15 g = 2\31, 3\46, 4\61 g+1-15g = 1-14g

17-tone

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 16s 16\17 < g < 1 g = 17\18, 18\19, 19\20 16g-15+1-g = 15g-14
2L 15s 8\17 < g < 1\2 g = 9\19, 10\21, 11\23 15g-7+1-2g = 13g-6
3L 14s 11\17 < g < 2\3 g = 13\20, 15\23, 17\26 14g-9+2-3g = 11g-7
4L 13s 4\17 < g < 1\4 g = 5\21, 6\25, 7\29 13g-3+1-4g = 9g-2
5L 12s 10\17 < g < 3\5 g = 13\22, 16\27, 19\32 12g-7+3-5g = 7g-4
6L 11s 14\17 < g < 5\6 g = 19\23, 24\29, 29\35 11g-9+5-6g = 5g-4
7L 10s 12\17 < g < 5\7 g = 17\24, 22\31, 27\38 10g-7+5-7g = 3g-2
8L 9s 2\17 < g < 1\8 g = 3\25, 4\33, 5\41 9g-1+1-8g = g
9L 8s 15\17 < g < 8\9 g = 23\26, 31\35, 39\44 8g-7+8-9g = 1-g
10L 7s 5\17 < g < 3\10 g = 8\27, 11\37, 14\47 7g-2+3-10g = 1-3g
11L 6s 3\17 < g < 2\11 g = 5\28, 7\39, 9\50 6g-1+2-11g = 1-5g
12L 5s 7\17 < g < 5\12 g = 12\29, 17\41, 22\53 5g-2+5-12g = 3-7g
13L 4s 13\17 < g < 10\13 g = 23\30, 33\43, 43\56 4g-3+10-13g = 7-9g
14L 3s 6\17 < g < 5\14 g = 11\31, 16\45, 21\59 3g-1+5-14g = 4-11g
15L 2s 9\17 < g < 8\15 g = 17\32, 25\47, 33\62 2g-1+8-15g = 7-13g
16L 1s 1\17 < g < 1\16 g = 2\33, 3\49, 4\65 g+1-16g = 1-15g

18-tone

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 17s 17\18 < g < 1 g = 18\19, 19\20, 20\21 17g-16+1-g = 16g-15
2L 16s 8\18 < g < 1\2 g = 9\20, 10\22, 11\24 8g-7\2+1\2-g = 7g-3
3L 15s 5\18 < g < 1\3 g = 6\21, 7\24, 8\27 5g-4\3+1\3-g = 4g-3
4L 14s 4\18 < g < 1\4 g = 5\22, 6\26, 7\30 7g-3\2+1\2-2g = 5g-2
5L 13s 7\18 < g < 2\5 g = 9\23, 11\28, 13\33 13g-5+2-5g = 8g-3
6L 12s 2\18 < g < 1\6 g = 3\24, 4\30, 5\36 2g-1\6+1\6-g = g
7L 11s 5\18 < g < 2\7 g = 7\25, 9\32, 11\39 11g-3+2-7g = 4g-1
8L 10s 2\18 < g < 1\8 g = 3\26, 4\34, 5\42 5g-1\2+1\2-4g = g
9L 9s 1\18 < g < 1\9 g = 2\27, 3\36, 4\45 g+1\9-g = 1\9
10L 8s 7\18 < g < 4\10 g = 11\28, 15\38, 19\48 4g-3\2+2-5g = 1\2-g
11L 7s 13\18 < g < 8\11 g = 21\29, 29\40, 37\51 7g-5+8-11g = 3-4g
12L 6s 1\18 < g < 1\12 g = 2\30, 3\42, 4\54 g+1\6-2g = 1\6-g
13L 5s 11\18 < g < 8\13 g = 19\31, 27\44, 35\57 5g-3+8-13g = 5-8g
14L 4s 5\18 < g < 4\14 g = 9\32, 13\46, 17\60 2g-1\2+2-7g = 3\2-5g
15L 3s 1\18 < g < 1\15 g = 2\33, 3\48, 4\63 g+1\3-5g = 1\3-4g
16L 2s 1\18 < g < 1\16 g = 2\34, 3\50, 4\66 g+1\2-8g = 1\2-7g
17L 1s 1\18 < g < 1\17 g = 2\35, 3\52, 4\69 g+1-17g = 1-16g

19-tone

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 18s 18\19 < g < 1 g = 19\20, 20\21, 21\22 18g-17+1-g = 17g-16
2L 17s 9\19 < g < 1\2 g = 10\21, 11\23, 12\25 17g-8+1-2g = 15g-7
3L 16s 6\19 < g < 1\3 g = 7\22, 8\25, 10\31 16g-5+1-3g = 13g-4
4L 15s 14\19 < g < 3\4 g = 17\23, 20\27, 23\31 15g-11+3-4g = 11g-8
5L 14s 15\19 < g < 4\5 g = 19\24, 23\29, 27\34 14g-11+4-5g = 9g-7
6L 13s 3\19 < g < 1\6 g = 4\25, 5\31, 6/37 13g-2+1-6g = 7g-1
7L 12s 8\19 < g < 3\7 g = 11\26, 14\33, 17\40 12g-5+3-7g = 5g-2
8L 11s 7\19 < g < 3\8 g = 10\27, 13\35, 16\43 11g-4+3-8g = 3g-1
9L 10s 2\19 < g < 1\9 g = 3\28, 4\37, 5\46 10g-1+1-9g = g
10L 9s 17\19 < g < 9\10 g = 26\29, 35\39, 44\49 9g-8+9-10g = 1-g
11L 8s 12\19 < g < 7\11 g = 19\30, 26\41, 33\52 8g-5+7-11g = 2-3g
12L 7s 11\19 < g < 7\12 g = 18\31, 25\43, 32\55 7g-4+7-12g = 3-5g
13L 6s 16\19 < g < 11\13 g = 27\32, 38\45, 49\58 6g-5+11-13g = 6-7g
14L 5s 4\19 < g < 3\14 g = 7\33, 10\47, 13\61 5g-1+3-14g = 2-9g
15L 4s 5\19 < g < 4\15 g = 9\34, 13\49, 17\64 4g-1+4-15g = 3-11g
16L 3s 13\19 < g < 11\16 g = 24\35, 35\51, 46\67 3g-2+11-16g = 9-13g
17L 2s 10\19 < g < 9\17 g = 19\36, 28\53, 37\70 2g-1+9-17g = 8-15g
18L 1s 1\19 < g < 1\18 g = 2\37, 3\55, 4\73 g+1-18g = 1-17g

20-tone

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 19s 19\20 < g < 1 g = 20\21, 21\22, 22\23 19g-18+1-g = 18g-17
2L 18s 9\20 < g < 1\2 g = 10\22, 11\24, 12\26 9g-4+1\2-g = 8g-7\2
3L 17s 13\20 < g < 2\3 g = 15\23, 17\26, 20\29 17g-11+2-3g = 14g-9
4L 16s 4\20 < g < 1\4 g = 5\24, 6\28, 7\32 4g-3\4+1\4-g = 3g-1\4
5L 15s 3\20 < g < 1\5 g = 4\25, 5\30, 6\35 3g-2\5+1\5-g = 2g-1\5
6L 14s 3\20 < g < 1\6 g = 4\26, 5\32, 6\38 7g-1+1\2-3g = 4g-1\2
7L 13s 17\20 < g < 6\7 g = 23\27, 29\34, 35\41 13g-11+6-7g = 6g-5
8L 12s 2\20 < g < 1\8 g = 3\28, 4\36, 5\44 3g-1\4+1\4-2g = g
9L 11s 11\20 < g < 5\9 g = 16\29, 21\38, 26\47 11g-6+5-9g =2g-1
10L 10s 1\20 < g < 1\10 g = 2\30, 3\40, 4\50 g+1\10-g = 1\10
11L 9s 9\20 < g < 5\11 g = 14\31, 19\42, 24\53 9g-4+5-11g = 1-2g
12L 8s 3\20 < g < 2\12 g = 5\32, 7\44, 9\56 2g-1\4+1\2-3g = 1\4-g
13L 7s 3\20 < g < 2\13 g = 5\33, 7\46, 9\59 7g-1+2-13g = 1-6g
14L 6s 7\20 < g < 5\14 g = 12\34, 17\48, 22\62 3g-1+5\2-7g = 2-4g
15L 5s 1\20 < g < 1\15 g = 2\35, 3\50, 4\65 g+1\5-3g = 1\5-2g
16L 4s 1\20 < g < 1\16 g = 2\36, 3\52, 4\68 g+1\4-4g = 1\4-3g
17L 3s 7\20 < g < 6\17 g = 13\37, 19\54, 25\71 3g-1+6-17g = 5-14g
18L 2s 1\20 < g < 1\18 g = 2\38, 3\56, 4\74 g+1\2-9g = 1\2-8g
19L 1s 1\20 < g < 1\19 g = 2\39, 3\58, 4\77 g+1-19g = 1-18g

21-tone

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 20s 20\21 < g < 1 g = 21\22, 22\23, 23\24 20g-19+1-g = 19g-18
2L 19s 10\21 < g < 1\2 g = 11\23, 12\25, 13\27 19g-9+1-2g = 17g-8
3L 18s 6\21 < g < 1\3 g = 7\24, 8\27, 9\30 6g-5\3+1\3-g = 5g-4\3
4L 17s 5\21 < g < 1\4 g = 6\25, 7\29, 8\33 17g-2+1-4g = 13g-1
5L 16s 4\21 < g < 1\5 g = 5\26, 6\31, 7\36 16g-3+1-5g = 11g-2
6L 15s 3\21 < g < 1\6 g = 4\27, 5\33, 6\39 5g-2\3+1\3-2g = 3g-1\3
7L 14s 2\21 < g < 1\7 g = 3\28, 4\35, 5\42 2g-1\7+1\7-g = g
8L 13s 13\21 < g < 5\8 g = 18\29, 23\37, 28\45 13g-8+5-8g = 5g-3
9L 12s 2\21 < g < 1\9 g = 3\30, 4\39, 5\48 4g-1\3+1\3-3g = g
10L 11s 2\21 < g < 1\10 g = 3\31, 4\41, 5\51 11g-1+1-10g = g
11L 10s 19\21 < g < 10\11 g = 29\32, 39\43, 49\54 10g-9+10-11g = 1-g
12L 9s 5\21 < g < 3\12 g = 8\33, 11\45, 14\57 3g-2\3+1-4g = 1\3-3g
13L 8s 8\21 < g < 5\13 g = 13\34, 18\47, 23\70 8g-3+5-13g = 2-5g
14L 7s 1\21 < g < 1\14 g = 2\35, 3\49, 4\63 g+1\7-2g = 1\7-g
15L 6s 4\21 < g < 3\15 g = 7\36, 10\51, 13\66 2g-1\3+1-5g = 2\3-3g
16L 5s 17\21 < g < 13\16 g = 30\37, 43\53, 56\69 5g-4+13-16g = 9-11g
17L 4s 16\21 < g < 13\17 g = 29\38, 42\55, 55\72 4g-3+13-17g = 10-13g
18L 3s 1\21 < g < 1\18 g = 2\39, 3\57, 4\75 g+1\3-6g = 1\3-5g
19L 2s 11\21 < g < 10\19 g = 21\40, 31\59, 41\78 2g-1+10-19g = 9-17g
20L 1s 1\21 < g < 1\20 g = 2\41, 3\61, 4/81 g+1-20g = 1-19g

22-tone

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 21s 21\22 < g < 1 g = 22\23, 23\24, 24/25 21g-20+1-g = 20g-19
2L 20s 10\22 < g < 1\2 g = 11\24, 12\26, 13\28 10g-9\2+1\2-g = 9g-4
3L 19s 7\22 < g < 1\3 g = 8\25, 9\28, 10\31 19g-6+1-3g = 16g-5
4L 18s 5\22 < g < 1\4 g = 6\26, 7\30, 8\34 9g-2+1\2-2g = 7g-3\2
5L 17s 13\22 < g < 3\5 g = 16\27, 19\32, 22\37 17g-10+3-5g = 12g-7
6L 16s 7\22 < g < 2\6 g = 9\28, 11\34, 13\40 8g-5\2+1-3g = 5g-2
7L 15s 3\22 < g < 1\7 g = 4\29, 5\36, 6\43 15g-2+1-7g = 8g-1
8L 14s 8\22 < g < 3\8 g = 11\30, 14\38, 17\46 7g-5\2+3\2-4g = 3g-2
9L 13s 17\22 < g < 7\9 g = 24\31, 31\40, 38\49 13g-10+7-9g = 4g-3
10L 12s 2\22 < g < 1\10 g = 3\32, 4\42, 5\52 6g-1\2+1\2-5g = g
11L 11s 1\22 < g < 1\11 g = 2\33, 3\44, 4\55 g + 1\11-g = 1\11
12L 10s 9\22 < g < 5\12 g = 14\34, 19\46, 24\58 5g-2+5\2-6g = 1\2-g
13L 9s 5\22 < g < 3\13 g = 8\35, 11\48, 14\61 9g-2+3-13g = 1-4g
14L 8s 3\22 < g < 2\14 g = 5\36, 7\50, 9\64 4g-1\2+1-7g = 1\2-3g
15L 7s 19\22 < g < 13\15 g = 32\37, 45\52, 58\67 7g-6+13-15g = 7-8g
16L 6s 4\22 < g < 3\16 g = 7\38, 10\54, 13\70 3g-1\2+3\2-8g = 1-5g
17L 5s 9\22 < g < 7\17 g = 16\39, 23\56, 30\73 5g-2+7-17g = 5-12g
18L 4s 6\22 < g < 5\18 g = 11\40, 16\58, 21\76 2g-1\2+5\2-9g = 2-7g
19L 3s 15\22 < g < 13\19 g = 28\41, 41\60, 54\79 3g-2+13-19g = 11-16g
20L 2s 1\22 < g < 1\20 g = 2\42, 3\62, 4\72 g+1\2-10g = 1\2-9g
21L 1s 1\22 < g < 1\21 g = 2\43, 3\64, 4\85 g+1-21g = 1-20g

23-tone

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 22s 22\23 < g < 1 g = 23\24, 24\25, 25\26 22g-21+1-g = 21g-20
2L 21s 11\23 < g < 1\2 g = 12\25, 13\27, 14\29 21g-10+1-2g = 19g-9
3L 20s 15\23 < g < 2\3 g = 17\26, 19\29, 21\32 20g-13+1-3g = 17g-12
4L 19s 17\23 < g < 3\4 g = 20\27, 23\31, 26\35 19g-14+3-4g = 15g-11
5L 18s 9\23 < g < 2\5 g = 11\28, 13\33, 15\38 18g-7+2-5g = 13g-5
6L 17s 19\23 < g < 5\6 g = 24\29, 29\35, 34\41 17g-15+1-6g = 11g-14
7L 16s 13\23 < g < 4\7 g = 17\30, 21\37, 25\44 16g-9+4-7g = 9g-5
8L 15s 20\23 < g < 7\8 g = 27\31, 34\39, 41\47 15g-13+7-8g = 7g-6
9L 14s 5\23 < g < 2\9 g = 7\32, 9\41, 11\50 14g-7+2-9g = 5g-5
10L 13s 16\23 < g < 7\10 g = 23\33, 30\43, 37\53 13g-9+7-10g = 3g-2
11L 12s 2\23 < g < 1\11 g = 3\34, 4\45, 5\56 12g-1+1-11g = g
12L 11s 21\23 < g < 11\12 g = 32\35, 43\47, 54\59 11g-10+11-12g = 1-g
13L 10s 7\23 < g < 4\13 g = 11\36, 15\49, 19\62 10g-3+4-13g =1-3g
14L 9s 18\23 < g < 11\14 g = 29\37, 40\51, 51\65 9g-7+11-14g = 4-5g
15L 8s 3\23 < g < 2\15 g = 5\38, 7\53, 9\68 8g-1+2-15g = 1-7g
16L 7s 10\23 < g < 7\16 g = 17\39, 24\55, 31\71 7g-3+7-16g = 4-9g
17L 6s 4\23 < g < 3\17 g = 7\40, 10\57, 13\74 6g-1+3-17g = 2-11g
18L 5s 14\23 < g < 11\18 g = 25\41, 36\59, 47\77 5g-4+11-18g = 7-13g
19L 4s 6\23 < g < 5\19 g = 11\42, 16\61, 21\80 4g-1+5-19g = 4-15g
20L 3s 8\23 < g < 7\20 g = 15\43, 22\63, 29\83 3g-1+13-20g = 12-17g
21L 2s 12\23 < g < 11\21 g = 23\44, 34\65, 45\86 2g-1+11-21g = 10-19g
22L 1s 1\23 < g < 1\22 g = 2\45, 3\67, 4\89 g+1-22g = 1-221

24-tone

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 23s 23\24 < g < 1 g = 24\25, 25\26, 26\27 23g-22+1-g = 22g-21
2L 22s 11\24 < g < 1\2 g = 12\26, 13\28, 14\30 11g-5+1/2-g = 10g-9/2
3L 21s 7\24 < g < 1\3 g = 8\27, 9\30, 10\33 7g-2+1/3-g = 6g-5/3
4L 20s 5\24 < g < 1\4 g = 6\28, 7\32, 8\36 5g-1+1/4-g = 4g-3/4
5L 19s 19\24 < g < 4\5 g = 23\29, 27\34, 31\39 19g-15+4-5g = 14g-11
6L 18s 3\24 < g < 1\6 g = 4\30, 5\36, 6\42 3g-1\3+1\6-g = 2g-1\6
7L 17s 17\24 < g < 5\7 g = 22\31, 27\38, 32\45 17g-12+5-7g = 10g-7
8L 16s 2\24 < g < 1\8 g = 3\32, 4\40, 5\48 2g-1\8+1\8-g = g
9L 15s 5\24 < g < 2\9 g = 7\33, 9\42, 11\51 5g-1+2\3-3g = 2g-1\3
10L 14s 7\24 < g < 3\10 g = 10\34, 13\44, 16\54 7g-2+3\2-5g = 2g-1\2
11L 13s 13\24 < g < 6\11 g = 19\35, 25\46, 31\57 13g-7+6-11g = 2g-1
12L 12s 1\24 < g < 1\12 g = 2\36, 3\48, 4\60 g+1\12-g = 1\12
13L 11s 11\24 < g < 6\13 g = 17\37, 23\50, 29\63 11g-5+6-13g = 1-2g
14L 10s 17\24 < g < 10\14 g = 27\38, 37\52, 47\66 5g-7\2+5-7g = 3\2-2g
15L 9s 3\24 < g < 2\15 g = 5\39, 7\54, 9\69 3g-1\3+2\3-5g = 1\3-2g
16L 8s 1\24 < g < 1\16 g = 2\40, 3\56, 4\72 g+1\8-2g = 1\8-g
17L 7s 7\24 < g < 5\17 g = 12\41, 17\58, 22\75 7g-2+5-17g = 3-10g
18L 6s 1\24 < g < 1\18 g = 2\42, 3\60, 4\78 g+1\6-3g = 1\6-2g
19L 5s 5\24 < g < 4\19 g = 9\43, 13\62, 17\81 5g-5+4-19g = 1-18g
20L 4s 1\24 < g < 1\20 g = 2\44, 3\64, 4\84 g+1\4-5g = 1\4-4g
21L 3s 1\24 < g < 1\21 g = 2\45, 3\66, 4\87 g+1\3-7g = 1\3-6g
22L 2s 1\24 < g < 1\22 g = 2\46, 3\68, 4\90 g+1\2-11g = 1\2-10g
23L 1s 1\24 < g < 1\23 g = 2\47, 3\70, 4\93 g+1-23g = 1-22g

25-tone

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 24s 24\25 < g < 1 g = 25\26, 26\27, 27\28 24g-23+1-g = 23g-22
2L 23s 12\25 < g < 1\2 g = 13\27, 14\29, 15\31 23g-11+1-2g = 21g-10
3L 22s 8\25 < g < 1\3 g = 9\28, 10\31, 11\34 22g-7+1-3g = 19g-6
4L 21s 6\25 < g < 1\4 g = 7\29, 8\33, 9\37 21g-5+1-4g = 17g-4
5L 20s 4\25 < g < 1\5 g = 5\30, 6\35, 7\40 4g-3\5+1\5-g = 3g-2\5
6L 19s 4\25 < g < 1\6 g = 5\31, 6\37, 7\43 19g-3+1-6g = 13g-2
7L 18s 7\25 < g < 2\7 g = 9\32, 11\39, 13\46 18g-5+2-7g = 11g-3
8L 17s 3\25 < g < 1\8 g = 4\33, 5\41, 6\47 17g-2+1-8g = 9g-1
9L 16s 11\25 < g < 4\9 g = 15\34, 19\43, 23\52 16g-7+4-9g = 3-7g
10L 15s 2\25 < g < 1\10 g = 3\35, 4\45, 5\55 3g-1\5+1\5-2g = g
11L 14s 9\25 < g < 4\11 g = 13\36, 17\47, 21\58 14g-5+4-11g = 3g-1
12L 13s 2\25 < g < 1\12 g = 3\37, 4\49, 5\61 13g-1+1-12g = g
13L 12s 23\25 < g < 12\13 g = 35\38, 47\51, 59\64 12g-11+12-13g = 1-g
14L 11s 16\25 < g < 9\14 g = 25\39, 34\53, 43\67 11g-7+9-14g = 2-3g
15L 10s 3\25 < g < 2\15 g = 5\40, 7\55, 9\70 2g-1\5+2\5-3g = 1\5-g
16L 9s 14\25 < g < 9\16 g = 23\41, 32\57, 41\73 9g-5+9-16g = 4-7g
17L 8s 22\25 < g < 15\17 g = 37\42, 52\59, 67\76 8g-7+15-17g = 8-9g
18L 7s 18\25 < g < 13\18 g = 31\43, 44\61, 57\79 7g-5+13-18g = 8-11g
19L 6s 21\25 < g < 16\19 g = 37\44, 53\63, 69\82 6g-5+16-19g = 11-13g
20L 5s 1\25 < g < 1\20 g = 2\45, 3\65, 4\85 g+1\5-4g = 1\5-3g
21L 4s 16\21 < g < 19\25 g = 35\46, 51\67, 71\88 4g-3+16-21g = 13-17g
22L 3s 17\25 < g < 15\22 g = 32\47, 47\69, 62\91 3g-2+15-22g = 13-19g
23L 2s 13\25 < g < 12\23 g = 25\48, 37\71, 49\94 2g-1+11-23g = 10-21g
24L 1s 1\25 < g < 1\24 g = 2\49, 3\73, 4\97 g+1-24g = 1-23g

26-tone

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 25s 25\26 < g < 1 g = 26\27, 27\28, 28\29 25g-24+1-g = 24g-23
2L 24s 12\26 < g < 1\2 g = 13\28, 14\30, 15\32 12g-11\2+1\2-g = 11g-5
3L 23s 17\26 < g < 2\3 g = 19\29, 21\32, 23\35 23g-15+2-3g = 20g-13
4L 22s 6\26 < g < 1\4 g = 7\30, 8\34, 9\38 11g-5\2+1\2-2g = 9g-2
5L 21s 5\26 < g < 1\5 g = 6\31, 7\36, 8\41 21g-4+1-5g = 16g-3
6L 20s 4\26 < g < 1\6 g = 5\32, 6\38, 7\44 10g-3\2+1\2-3g = 7g-1
7L 19s 11\26 < g < 3\7 g = 14\33, 17\40, 20\47 19g-8+3-7g = 12g-5
8L 18s 3\26 < g < 1\8 g = 4\34, 5\42, 6\50 9g-1+1\2-4g = 5g-1\2
9L 17s 23\26 < g < 8\9 g = 31\35, 39\44, 47\53 17g-15+8-9g = 8g-7
10L 16s 5\26 < g < 2\10 g = 7\36, 9\46, 11\56 8g-3\2+1-5g = 3g-1\2
11L 15s 7\26 < g < 3\11 g = 10\37, 13\48, 16\59 15g-4+3-11g = 4g-1
12L 14s 2\26 < g < 1\12 g = 3\38, 4\50, 5\62 7g-1\2+1\2-6g = g
13L 13s 1\26 < g < 1\13 g = 2\39, 3\52, 4\65 g+1\13-g = 1\13
14L 12s 11\26 < g < 6\14 g = 17\40, 23\54, 29\68 6g-5\2+3-7g = 1\2-g
15L 11s 19\26 < g < 11\15 g = 30\41, 41\56, 52\71 11g-8+11-15g = 3-4g
16L 10s 8\26 < g < 5\16 g = 13\42, 18\58, 23\74 5g-3\2+5\2-8g = 1-3g
17L 9s 3\26 < g < 2\17 g = 5\43, 7\60, 9\77 9g-1+2-17g = 1-8g
18L 8s 10\26 < g < 7\18 g = 17\44, 24\62, 31\80 4g-7\2+7-9g = 7\2-5g
19L 7s 15\26 < g < 11\19 g = 26\45, 37\64, 48\83 7g-4+11-19g = 7-12g
20L 6s 9\26 < g < 7\20 g = 16\46, 23\66, 30\86 3g-1+7\2-10g = 5\2-7g
21L 5s 21\26 < g < 17\21 g = 38\47, 55\68, 72\89 5g-4+16-21g = 12-16g
22L 4s 7\26 < g < 6\22 g = 13\48, 19\70, 25\92 2g-1\2+3-11g = 5\2-9g
23L 3s 9\26 < g < 8\23 g = 17\49, 25\72, 33/95 3g-1+8-23g = 7-20g
24L 2s 1\26 < g < 1\24 g = 2\50, 3\74, 4\98 g+1\2-12g = 1\2-11g
25L 1s 1\26 < g < 1\25 g = 2\51, 3\76, 4\101 g+1-25g = 1-24g

27-tone

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 26s 26\27 < g < 1 g = 27\28, 28\29, 29\30 26g-25+1-g = 25g-24
2L 25s 13\27 < g < 1\2 g = 14\29, 15\31, 16\33 25g-12+1-2g = 23g-11
3L 24s 8\27 < g < 1\3 g = 9\30, 10\33, 11\36 8g-7\3+1-3g = 5g-2
4L 23s 20\27 < g < 3\4 g = 23\31, 26\35, 29\39 23g-17+3-4g = 19g-14
5L 22s 16\27 < g < 3\5 g = 19\32, 22\37, 25\42 22g-13+3-5g = 17g-10
6L 21s 4\27 < g < 1\6 g = 5\33, 6\39, 7\45 7g-1+1\3-2g = 5g-2\3
7L 20s 23\27 < g < 6\7 g = 29\34, 35\41, 41\48 20g-17+6-7g = 13g-11
8L 19s 10\27 < g < 3\8 g = 13\35, 16\43, 19\51 19g-7+3-8g = 11g-4
9L 18s 2\27 < g < 1\9 g = 3\36, 4\45, 5\54 2g-1\9+1\9-g = g
10L 17s 8\27 < g < 3\10 g = 11\37, 14\47, 17\57 17g-5+3-10g = 7g-2
11L 16s 22\27 < g < 9\11 g = 31\38, 40\49, 49\60 16g-13+9-11g = 5g-4
12L 15s 2\27 < g < 1\12 g = 3\39, 4\51, 5\63 5g-1\3+1\3-4g = g
13L 14s 2\27 < g < 1\13 g = 3\40, 4\53, 5\66 14g-1+1-13g = g
14L 13s 25\27 < g < 13\14 g = 38\41, 51\55, 64\69 13g-12+13-14g = 1-g
15L 12s 7\27 < g < 4\15 g = 11\42, 15\57, 19\72 4g-1+4\3-5g = 1\3-g
16L 11s 5\27 < g < 3\16 g = 8\43, 11\59, 14\75 11g-2+3-16g = 1-5g
17L 10s 19\27 < g < 12\17 g = 31\44, 43\61, 55\78 10g-7+12-17g = 5-7g
18L 9s 1\27 < g < 1\18 g = 2\45, 3\63, 4\81 g+1\9-2g = 1\9-g
19L 8s 17\27 < g < 12\19 g = 29\46, 41\65, 53\84 8g-5+12-19g = 7-11g
20L 7s 4\27 < g < 3\20 g = 7\47, 10\67, 13\87 7g-1+3-20g = 2-13g
21L 6s 5\27 < g < 4\21 g = 9\48, 13\69, 17\90 2g-1\3+4\3-7g = 1-5g
22L 5s 11\27 < g < 9\22 g = 20\49, 29\71, 38\93 5g-2+9-22g = 7-17g
23L 4s 7\27 < g < 6\23 g = 13\50, 19\73, 25\96 4g-1+6-23g = 5-19g
24L 3s 1\27 < g < 1\24 g = 2\51, 3\75, 4\99 g+1\3-8g = 1\3-7g
25L 2s 14\27 < g < 13\25 g = 27\52, 40\77, 53\102 2g-1+13-25g = 12-23g
26L 1s 1\27 < g < 1\26 g = 2\53, 3\79, 4\105 g+1-26g = 1-25g

28-tone

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 27s 27\28 < g < 1 g = 28\29, 29\30, 30\31 27g-26+1-g = 26g-25
2L 26s 13\28 < g < 1\2 g = 14\30, 15\32, 16\34 13g-6+1\2-g = 12g-11\2
3L 25s 9\28 < g < 1\3 g = 10\31, 11\34, 12\37 25g-8+1-3g = 22g-7
4L 24s 6\28 < g < 1\4 g = 7\32, 8\36, 9\40 6g-5\4+1\4-g = 5g-1
5L 23s 11\28 < g < 2\5 g = 13\33, 15\38, 17\43 23g-9+2-5g = 18g-7
6L 22s 9\28 < g < 2\6 g = 11\34, 13\40, 15\46 11g-7\2+1-3g = 8g-3
7L 21s 3\28 < g < 1\7 g = 4\35, 5\42, 6\49 3g-2\7+1\7-g = 2g-1\7
8L 20s 3\28 < g < 1\8 g = 4\36, 5\44, 6\52 5g-1\2+1\4-2g = 3g-1\4
9L 19s 3\28 < g < 1\9 g = 4\37, 5\46, 6\55 19g-2+1-9g = 10g-1
10L 18s 11\28 < g < 4\10 g = 15\38, 19\48, 23\58 9g-7\2+2-5g = 4g-3\2
11L 17s 5\28 < g < 2\11 g = 7\39, 9\50, 11\61 17g-3+2-11g = 6g-1
12L 16s 2\28 < g < 1\12 g = 3\40, 4\52, 5\64 4g-1\4+1\4-3g = g
13L 15s 15\28 < g < 7\13 g = 22\41, 29\54, 36\67 15g-8+7-13g = 2g-1
14L 14s 1\28 < g < 1\14 g = 2\42, 3\56, 4\70 g+1\14-g = 1\14
15L 13s 13\28 < g < 7\15 g = 20\43, 27\58, 34\73 13g-6+7-15g = 1-2g
16L 12s 5\28 < g < 3\16 g = 8\44, 11\60, 14\76 3g-1\2+3\4-4g = 1\4-g
17L 11s 23\28 < g < 14\17 g = 37\45, 51\62, 65\79 11g-9+13-17g = 4-6g
18L 10s 3\28 < g < 2\18 g = 5\46, 7\64, 9\82 5g-1\2+1-9g = 1\2-4g
19L 9s 25\28 < g < 17\19 g = 42\47, 59\66, 76\85 9g-8+17-19g = 9-10g
20L 8s 4\28 < g < 3\20 g = 7\48, 10\68, 13\88 2g-1\4+3\4-5g = 1\2-3g
21L 7s 1\28 < g < 1\21 g = 2\49, 3\70, 4\91 g+1\7-2g = 1\7-g
22L 6s 5\28 < g < 4\22 g = 9\50, 13\72, 17\94 3g-1\2+2-11g = 3\2-8g
23L 5s 17\28 < g < 14\23 g = 31\51, 45\74, 59\97 5g-3+14-23g = 11-18g
24L 4s 1\28 < g < 1\24 g = 2\52, 3\76, 4\100 g+1\4-6g = 1\4-5g
25L 3s 19\28 < g < 17\25 g = 36\53, 53\78, 70\103 3g-2+17-25g = 15+22g
26L 2s 15\28 < g < 14\26 g = 29\54, 43\80, 57\106 g-1\2+7-13g = 13\2-12g
27L 1s 1\28 < g < 1\27 g = 2\55, 3\82, 4\109 g+1-27g = 1-26g

29-tone

Large-small numbers Generator range Boundaries of propriety, maximum expressiveness, diatonicity Large step+Small step
1L 28s 28\29 < g < 1 g = 29\30, 30\31, 31\32 28g-27+1-g = 27g-26
2L 27s 14\29 < g < 1\2 g = 15\31, 16\33, 17\35 27g-13+1-2g = 25g-12
3L 26s 19\29 < g < 2\3 g = 21\32, 23\35, 25\38 26g-17+2-3g = 23g-15
4L 25s 7\29 < g < 1\4 g = 8\33, 9\37, 10\41 25g-6+1-4g = 21g-5
5L 24s 23\29 < g < 4\5 g = 27\34, 31\39, 35\44 24g-19+4-5g = 19g-15
6L 23s 24\29 < g < 5\6 g = 29\35, 34\41, 39\47 23g-19+5-6g = 17g-14
7L 22s 4\29 < g < 1\7 g = 5\36, 6\43, 7\50 22g-3+1-7g = 15g-2
8L 21s 18\29 < g < 5\8 g = 23\37, 28\45, 33\53 21g-13+5-8g = 13g-8
9L 20s 16\29 < g < 5\9 g = 21\38, 26\47, 31\56 20g-11+5-9g = 11g-6
10L 19s 26\29 < g < 9\10 g = 35\39, 44\49, 53\59 19g-17+9-10g = 9g-8
11L 18s 21\29 < g < 8\11 g = 29\40, 37\51, 45\62 18g-13+8-11g = 7g-2
12L 17s 12\29 < g < 5\12 g = 17\41, 22\53, 27\65 17g-7+5-12g = 5g-2
13L 16s 20\29 < g < 9\13 g = 29\42, 38\55, 47\68 16g+11+9-13g = 3g-2
14L 15s 2\29 < g < 1\14 g = 3\43, 4\57, 5\71 15g-1+1-14g = g
15L 14s 27\29 < g < 14\15 g = 41\44, 55\59, 69\74 14g-13+14-15g = 1-g
16L 13s 9\29 < g < 5\16 g = 14\45, 19\61, 24\77 13g-4+5-16g = 1-3g
17L 12s 17\29 < g < 10\17 g = 27\46, 37\63, 47\80 12g-5+7-17g = 2-5g
18L 11s 8\29 < g < 5\18 g = 13\47, 18\65, 23\83 11g-3+5-18g = 2-7g
19L 10s 3\29 < g < 2\19 g = 5\48, 7\67, 9\86 10g-1+2-19g = 1-9g
20L 9s 13\29 < g < 9\20 g = 22\49, 31\69, 40\89 9g-5+9-20g = 4-11g
21L 8s 11\29 < g < 8\21 g = 19\50, 27\71, 35\92 8g-3+8-21g = 5-13g
22L 7s 25\29 < g < 19\22 g = 44\51, 63\73, 82\95 7g-6+9-22g = 3-16g
23L 6s 5\29 < g < 4\23 g = 9\52, 13\75, 17\98 6g-1+4-23g = 3-17g
24L 5s 6\29 < g < 5\24 g = 11\53, 16\77, 21\101 5g-9+5-24g = 4-19g
25L 4s 22\29 < g < 19\25 g = 41\54, 60\79, 79\104 4g-3+19-25g = 16-21g
26L 3s 10\29 < g < 9\26 g = 19\55, 28\81, 37\107 3g-1+9-26g = 8-23g
27L 2s 15\29 < g < 14\27 g = 29\56, 43\83, 57\110 2g-1+17-27g = 16-25g
28L 1s 1\29 < g < 1\28 g = 2\57, 3\85, 4\113 g+1-28g = 1-27g
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