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, 4
Note: These sets are given for the sake of completeness as they are not really scales
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L1s
|
1\2 < g < 1
|
g = 3\4
|
g = 2\3, 3\4, 4\5
|
g+1-g = 1
|
| 1L2s
|
2\3 < g < 1
|
g = 5\6
|
g = 3\4, 4\5, 5\6
|
2g-1+1-g = g
|
| 2L1s
|
1\3 < g < 1\2
|
g = 5\12
|
g = 2\5, 3\7, 4\9
|
g+1-2g = 1-g
|
| 1L3s
|
3\4 < g < 1
|
g = 7\8
|
g = 4\5, 5\6, 6\7
|
3g-2+1-g = 2g-1
|
| 2L2s
|
1\4 < g < 1\2
|
g = 3\8
|
g = 2\6, 3\8, 4\10
|
g+1\2-g = 1\2
|
| 3L1s
|
1\4 < g < 1\3
|
g = 7\24
|
g = 2\7, 3\10, 4\13
|
g+1-3g = 1-2g
|
5
Note: italicized generators from here below generate scales which are weakly tonal
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L4s
|
4\5 < g < 1
|
g = 9\10
|
g = 5\6, 6\7, 7\8
|
4g-3+1-g = 3g-2
|
| 2L3s
|
2\5 < g < 1\2
|
g = 9\20
|
g = 3\7, 4\9, 5\11
|
3g-1+1-2g = g
|
| 3L2s
|
3\5 < g < 2\3
|
g = 19\30
|
g = 5\8, 7\11, 9\14
|
2g-1+2-3g = 1-g
|
| 4L1s
|
1\5 < g < 1\4
|
g = 9\40
|
g = 2\9, 3\13, 4\17
|
g+1-4g = 1-3g
|
6
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L5s
|
5\6 < g < 1
|
g = 11\12
|
g = 6\7, 7\8, 8\9
|
5g-4+1-g = 4g-3
|
| 2L4s
|
2\6 < g < 1\2
|
g = 5\12
|
g = 3\8, 4\10, 5\12
|
2g-1\2+1\2-g = g
|
| 3L3s
|
1\6 < g < 1\3
|
g = 3\12
|
g = 2\9, 3\12, 4\15
|
g+1\3-g = 1\3
|
| 4L2s
|
1\6 < g < 1\4
|
g = 5\24
|
g = 2\10, 3\14, 4\18
|
g+1\2-2g = 1\2-g
|
| 5L1s
|
1\6 < g < 1\5
|
g = 11\60
|
g = 2\11, 3\16, 4\21
|
g+1-5g = 1-4g
|
7
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L6s
|
6\7 < g < 1
|
g = 13\14
|
g = 7\8, 8\9, 9\10
|
6g-5+1-g = 5g-4
|
| 2L5s
|
3\7 < g < 1\2
|
g = 13\28
|
g = 4\9, 5\11, 6\13
|
5g-2+1-2g = 3g-1
|
| 3L4s
|
2\7 < g < 1\3
|
g = 13\42
|
g = 3\10, 4\13, 5\16
|
4g-1+1-3g = g
|
| 4L3s
|
5\7 < g < 3\4
|
g = 41\56
|
g = 8\11, 11\15, 14\19
|
3g-2+3-4g = 1-g
|
| 5L2s
|
4\7 < g < 3\5
|
g = 41\70
|
g = 7\12, 10\17, 13\22
|
2g-1+3-5g = 2-3g
|
| 6L1s
|
1\7 < g < 1\6
|
g = 13\84
|
g = 2\13, 3\19, 4\25
|
g+1-6g = 1-5g
|
8
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L7s
|
7\8 < g < 1
|
g = 15\16
|
g = 8\9, 9\10, 10\11
|
7g-6+1-g = 6g-5
|
| 2L6s
|
3\8 < g < 1\2
|
g = 7\16
|
g = 4\10, 5\12, 6\14
|
3g-1+1\2-g = 2g-1\2
|
| 3L5s
|
5\8 < g < 2\3
|
g = 31\48
|
g = 7\11, 9\14, 11\17
|
5g-3+2-3g = 2g-1
|
| 4L4s
|
1\8 < g < 1\4
|
g = 3\16
|
g = 2\12, 3\16, 4\20
|
g+1\4-g = 1\4
|
| 5L3s
|
3\8 < g < 2\5
|
g = 31\80
|
g = 5\13, 7\18, 9\23
|
3g-1+2-5g = 1-2g
|
| 6L2s
|
1\8 < g < 1\6
|
g = 7\48
|
g = 2\14, 3\20, 4\26
|
g+1\2-3g = 1\2-2g
|
| 7L1s
|
1\8 < g < 1\7
|
g = 15\112
|
g = 2\15, 3\22, 4\29
|
g+1-7g = 1-6g
|
9
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L8s
|
8\9 < g < 1
|
g = 17\18
|
g = 9\10, 10\11, 11\12
|
8g-7+1-g = 7g-6
|
| 2L7s
|
4\9 < g < 1\2
|
g = 17\36
|
g = 5\11, 6\13, 7\15
|
7g-3+1-2g = 5g-2
|
| 3L6s
|
2\9 < g < 1\3
|
g = 5\18
|
g = 3\12, 4\15, 5\18
|
2g-1\3+1\3-g = g
|
| 4L5s
|
2\9 < g < 1\4
|
g = 17\72
|
g = 3\13, 4\17, 5\21
|
5g-1+1-4g = g
|
| 5L4s
|
7\9 < g < 4\5
|
g = 71\90
|
g = 11\14, 15\19, 18\23
|
4g-3+4-5g = 1-g
|
| 6L3s
|
1\9 < g < 1\6
|
g = 5\36
|
g = 2\15, 3\21, 4\27
|
g+1\3-2g = 1\3-g
|
| 7L2s
|
5\9 < g < 4\7
|
g = 71\126
|
g = 9\16, 10\23, 17\30
|
2g-1+4-7g = 3-7g
|
| 8L1s
|
1\9 < g < 1\8
|
g = 17\144
|
g = 2\17, 3\25, 4\33
|
g+1-8g = 1-7g
|
10
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L9s
|
9\10 < g < 1
|
g = 19\20
|
g = 10\11, 11\12, 12\13
|
9g-8+1-g = 8g-7
|
| 2L8s
|
4\10 < g < 1\2
|
g = 9\20
|
g = 5\12, 6\14, 7\16
|
4g-3\2+1\2-g = 3g-1
|
| 3L7s
|
3\10 < g < 1\3
|
g = 19\60
|
g = 4\13, 5\16, 6\19
|
7g-2+1-3g = 4g-1
|
| 4L6s
|
2\10 < g < 1\4
|
g = 9\40
|
g = 3\14, 4\18, 5\22
|
3g-1\2+1\2-2g = g
|
| 5L5s
|
1\10 < g < 1\5
|
g = 3\20
|
g = 2\15, 3\20, 4\25
|
g+1\5-g = 1\5
|
| 6L4s
|
3\10 < g < 2\6
|
g = 19\60
|
g = 5\16, 7\22, 9\28
|
2g-1\2+1-3g = 1\2-g
|
| 7L3s
|
7\10 < g < 5\7
|
g = 99\140
|
g = 12\17, 17\24, 22\31
|
3g-2+5-7g = 3-4g
|
| 8L2s
|
1\10 < g < 1\8
|
g = 9\80
|
g = 2\18, 3\26, 4\34
|
g+1\2-4g = 1\2-3g
|
| 9L1s
|
1\10 < g < 1\9
|
g = 19\180
|
g = 2\19, 3\28, 4\37
|
g+1-9g = 1-8g
|
11
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L10s
|
10\11 < g < 1
|
g = 21\22
|
g = 11\12, 12\13, 13\14
|
10g-9+1-g = 9g-8
|
| 2L9s
|
5\11 < g < 1\2
|
g = 21\44
|
g = 6\13, 7\15, 8\17
|
9g-4+1-2g = 7g-3
|
| 3L8s
|
7\11 < g < 2\3
|
g = 43\66
|
g = 9\14, 11\17, 13\20
|
8g-5+2-3g = 5g-3
|
| 4L7s
|
8\11 < g < 3\4
|
g = 65\88
|
g = 11\15, 14\19, 17\23
|
7g-5+3-4g = 3g-2
|
| 5L6s
|
2\11 < g < 1\5
|
g = 21\110
|
g = 3\16, 4\21, 5\26
|
6g-1+1-5g = g
|
| 6L5s
|
9\11 < g < 5\6
|
g = 109\132
|
g = 14\17, 19\23, 24\29
|
5g-4+5-6g = 1-g
|
| 7L4s
|
3\11 < g < 2\7
|
g = 43\154
|
g = 5\18, 7\25, 9\32
|
4g-1+2-7g = 1-3g
|
| 8L3s
|
4\11 < g < 3\8
|
g = 65\176
|
g = 7\19, 10\27, 13\35
|
3g-1+3-8g = 2-5g
|
| 9L2s
|
6\11 < g < 5\9
|
g = 109\198
|
g = 11\20, 16\29, 21\38
|
2g-1+5-9g = 4-7g
|
| 10L1s
|
1\11 < g < 1\10
|
g = 21\220
|
g = 2\21, 3\31, 4\41
|
g+1-10g = 1-9g
|
12
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L11s
|
11\12 < g < 1
|
g = 23\24
|
g = 12\13, 13\14, 14\15
|
11g-10+1-g = 10g-9
|
| 2L10s
|
5\12 < g < 1\2
|
g = 11\24
|
g = 6\14, 7\16, 8\18
|
5g-2+1\2-g = 4g-3\2
|
| 3L9s
|
3\12 < g < 1\3
|
g = 7\24
|
g = 4\15, 5\18, 6\21
|
3g-2\3+1\3-g = 2g-1\3
|
| 4L8s
|
2\12 < g < 1\4
|
g = 5\24
|
g = 3\16, 4\20, 5\24
|
2g-1\4+1\4-g = g
|
| 5L7s
|
7\12 < g < 3\5
|
g = 71\120
|
g = 10\17, 13\22, 16\27
|
7g-4+3-5g = 2g-1
|
| 6L6s
|
1\12 < g < 1\6
|
g = 3\24
|
g = 2\18, 3\24, 4\30
|
g+1\6-g = g
|
| 7L5s
|
5\12 < g < 3\7
|
g = 71\168
|
g = 8\19, 11\26, 14\33
|
5g-2+3-7g = 1-2g
|
| 8L4s
|
1\12 < g < 1\8
|
g = 5\48
|
g = 2\20, 3\28, 4\36
|
g+1\4-2g = 1\4-g
|
| 9L3s
|
1\12 < g < 1\9
|
g = 7\72
|
g = 2\21, 3\30, 4\39
|
g+1\3-3g = 1\3-2g
|
| 10L2s
|
1\12 < g < 1\10
|
g = 11\120
|
g = 2\22, 3\32, 4\42
|
g+1\2-5g = 1\2-4g
|
| 11L1s
|
1\12 < g < 1\11
|
g = 23\264
|
g = 2\23, 3\34, 4\45
|
g+1-11g = 1-10g
|
13
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L12s
|
12\13 < g < 1
|
g = 25\26
|
g = 13\14, 14\15, 15\16
|
12g-11+1-g = 11g-10
|
| 2L11s
|
6\13 < g < 1\2
|
g = 25\52
|
g = 7\15, 8\17, 9\19
|
11g-5-1-2g = 10g-6
|
| 3L10s
|
4\13 < g < 1\3
|
g = 25\78
|
g = 5\16, 6\19, 7/22
|
10g-3+1-3g = 7g-2
|
| 4L9s
|
3\13 < g < 1\4
|
g = 25\104
|
g = 4\17, 5\21, 6\25
|
9g-2+1-4g = 5g-1
|
| 5L8s
|
5\13 < g < 2\5
|
g = 51\130
|
g = 7\18, 9\23, 11\28
|
8g-3+2-5g = 3g-1
|
| 6L7s
|
2\13 < g < 1\6
|
g = 25\156
|
g = 3\19, 4\25, 5\31
|
7g-1+1-6g = g
|
| 7L6s
|
11\13 < g < 6\7
|
g = 155\182
|
g = 17\20, 23\27, 29\34
|
6g-5+6-7g = 1-g
|
| 8L5s
|
8\13 < g < 5\8
|
g = 129\208
|
g = 13\21, 18\29, 23\37
|
5g-3+5-8g = 2-3g
|
| 9L4s
|
10\13 < g < 7\9
|
g = 181\234
|
g = 17\22, 24\31, 31\40
|
4g-3+7-9g = 4-5g
|
| 10L3s
|
9\13 < g < 7\10
|
g = 181\260
|
g = 16\23, 23\33, 30\43
|
3g-2+7-10g = 5-7g
|
| 11L2s
|
7\13 < g < 6\11
|
g = 155\286
|
g = 13\24, 19\35, 25\46
|
2g-1+6-11g = 5-9g
|
| 12L1s
|
1\13 < g < 1\12
|
g = 25\312
|
g = 2\25, 3\37, 4\49
|
g+1-12g = 1-11g
|
14
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L13s
|
13\14 < g < 1
|
g = 27\28
|
g = 14\15, 15\16, 16\17
|
13g-12+1-g = 12g-11
|
| 2L12s
|
6\14 < g < 1\2
|
g = 13\28
|
g = 7\16, 8\18, 9\20
|
6g-5\2+1\2-g = 5g-2
|
| 3L11s
|
9\14 < g < 2\3
|
g = 55\84
|
g = 11\17, 13\20, 15\23
|
11g-7+2-3g = 9g-5
|
| 4L10s
|
3\14 < g < 1\4
|
g = 13\56
|
g = 4\18, 5\22, 6\26
|
5g-1+1\2-2g = 3g-1\2
|
| 5L9s
|
11\14 < g < 4\5
|
g = 111\140
|
g = 15\19, 19\24, 23\29
|
9g-7+4-5g = 4g-3
|
| 6L8s
|
2\14 < g < 1\6
|
g = 13\84
|
g = 3\20, 4\26, 5\32
|
4g-1\2-1\2-3g = g
|
| 7L7s
|
1\14 < g < 1\7
|
g = 3\28
|
g = 2\21, 3\28, 4\35
|
g+1\7-g = 1\7
|
| 8L6s
|
5\14 < g < 3\8
|
g = 41\112
|
g = 8\22, 11\30, 14\38
|
3g-1+3\2-4g = 1\2-g
|
| 9L5s
|
3\14 < g < 2\9
|
g = 55\252
|
g = 5\23, 7\32, 9\41
|
5g-1+2-9g = 1-4g
|
| 10L4s
|
4\14 < g < 3\10
|
g = 41\140
|
g = 7\24, 10\34, 13\44
|
2g-1\2+3\2-5g = 1-3g
|
| 11L3s
|
5\14 < g < 4\11
|
g = 111\308
|
g = 9\25, 13\36, 17\47
|
3g-1+4-11g = 3-8g
|
| 12L2s
|
1\14 < g < 1\12
|
g = 13\168
|
g = 2\26, 3\38, 4\50
|
g+1\2-6g = 1\2-5g
|
| 13L1s
|
1\14 < g < 1\13
|
g = 27\364
|
g = 2\27, 3\40, 4\53
|
g+1-13g = 1-12g
|
15
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L14s
|
14\15 < g < 1
|
g = 29\30
|
g = 15\16, 16\17, 17\18
|
14g-13+1-g = 13g-12
|
| 2L13s
|
7\15 < g < 1\2
|
g = 29\60
|
g = 8\17, 9\19, 10\21
|
13g-6+1-2g = 11g-5
|
| 3L12s
|
4\15 < g < 1\3
|
g = 9\30
|
g = 5\18, 6\21, 7\24
|
4g-1+1\3-g = 3g-2\3
|
| 4L11s
|
11\15 < g < 3\4
|
g = 89\120
|
g = 14\19, 17\23, 20\27
|
11g-8+3-4g = 8g-4
|
| 5L10s
|
2\15 < g < 1\5
|
g = 5\30
|
g = 3\20, 4\25, 5\30
|
2g-1\5+1\5-g = g
|
| 6L9s
|
2\15 < g < 1\6
|
g = 9\60
|
g = 3\21, 4\27, 5\33
|
3g-1\3+1\3-2g = g
|
| 7L8s
|
2\15 < g < 1\7
|
g = 29\210
|
g = 3\22, 4\29, 5\36
|
8g-1+1-7g = g
|
| 8L7s
|
13\15 < g < 7\8
|
g = 209\240
|
g = 20\23, 27\31, 34\39
|
7g-6+7-8g = 1-g
|
| 9L6s
|
3\15 < g < 2\9
|
g = 19\90
|
g = 5\24, 7\33, 9\42
|
2g-1\3+2\3-3g = 1\3-g
|
| 10L5s
|
1\15 < g < 1\10
|
g = 5\60
|
g = 2\25, 3\35, 4\45
|
g+1\5-2g = 1\5-g
|
| 11L4s
|
4\15 < g < 3\11
|
g = 89\330
|
g = 7\26, 10\37, 13\48
|
4g-1+3-11g = 2-7g
|
| 12L3s
|
1\15 < g < 1\12
|
g = 9\120
|
g = 2\27, 3\39, 4\51
|
g+1\3-4g = 1\3-3g
|
| 13L2s
|
8\15 < g < 7\13
|
g = 209\390
|
g = 15\28, 22\41, 29\54
|
2g-1+7-13g = 6-11g
|
| 14L1s
|
1\15 < g < 1\14
|
g = 29\420
|
g = 2\29, 3\43, 4\57
|
g+1-14g = 1-13g
|
16
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L15s
|
15\16 < g < 1
|
g = 31\32
|
g = 16\17, 17\18, 18\19
|
15g-14+1-g = 14g-13
|
| 2L14s
|
7\16 < g < 1\2
|
g = 15\32
|
g = 8\18, 9\20, 10\22
|
7g-3+1\2-g = 5\2-6g
|
| 3L13s
|
5\16 < g < 1\3
|
g = 31\96
|
g = 6\19, 7\22, 8\25
|
13g-4+1-3g = 10g-3
|
| 4L12s
|
3\16 < g < 1\4
|
g = 7\32
|
g = 4\20, 5\24, 6\28
|
3g-1\2+1\4-g = 2g-1\4
|
| 5L11s
|
3\16 < g < 1\5
|
g = 31\160
|
g = 4\21, 5\26, 6\31
|
11g-2+1-5g = 6g-1
|
| 6L10s
|
5\16 < g < 2\6
|
g = 31\96
|
g = 7\22, 9\28, 11\34
|
5g-3\2+1-3g = 2g-1\2
|
| 7L9s
|
9\16 < g < 4\7
|
g = 127\224
|
g = 13\23, 17\30, 21\37
|
9g-5+4-7g = 2g-1
|
| 8L8s
|
1\16 < g < 1\8
|
g = 3\32
|
g = 2\24, 3\32, 4\40
|
g+1\8-g = 1\8
|
| 9L7s
|
7\16 < g < 4\9
|
g = 127\286
|
g = 11\25, 15\34, 19\43
|
7g-3+4-9g = 1-2g
|
| 10L6s
|
3\16 < g < 2\10
|
g = 31\160
|
g = 5\26, 7\36, 8\46
|
3g-1\2+1-5g = 1\2-2g
|
| 11L5s
|
13\16 < g < 9\11
|
g = 287\352
|
g = 22\27, 31\38, 40\49
|
5g-4+9-11g = 5-6g
|
| 12L4s
|
1\16 < g < 1\12
|
g = 7\48
|
g = 2\28, 3\40, 4\52
|
g+1\4-3g = 1\4-2g
|
| 13L3s
|
11\16 < g < 9\13
|
g = 287\416
|
g = 20\29, 29\42, 38\55
|
3g-2+9-13g = 7-10g
|
| 14L2s
|
1\16 < g < 1\14
|
g = 15\224
|
g = 2\30, 3\44, 4\58
|
g+1\2-7g = 1\2-6g
|
| 15L1s
|
1\16 < g < 1\15
|
g = 31\480
|
g = 2\31, 3\46, 4\61
|
g+1-15g = 1-14g
|
17
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L16s
|
16\17 < g < 1
|
g = 33\34
|
g = 17\18, 18\19, 19\20
|
16g-15+1-g = 15g-14
|
| 2L15s
|
8\17 < g < 1\2
|
g = 33\68
|
g = 9\19, 10\21, 11\23
|
15g-7+1-2g = 13g-6
|
| 3L14s
|
11\17 < g < 2\3
|
g = 67\102
|
g = 13\20, 15\23, 17\26
|
14g-9+2-3g = 11g-7
|
| 4L13s
|
4\17 < g < 1\4
|
g = 33\136
|
g = 5\21, 6\25, 7\29
|
13g-3+1-4g = 9g-2
|
| 5L12s
|
10\17 < g < 3\5
|
g = 101\170
|
g = 13\22, 16\27, 19\32
|
12g-7+3-5g = 7g-4
|
| 6L11s
|
14\17 < g < 5\6
|
g = 169\204
|
g = 19\23, 24\29, 29\35
|
11g-9+5-6g = 5g-4
|
| 7L10s
|
12\17 < g < 5\7
|
g = 169\238
|
g = 17\24, 22\31, 27\38
|
10g-7+5-7g = 3g-2
|
| 8L9s
|
2\17 < g < 1\8
|
g = 33\272
|
g = 3\25, 4\33, 5\41
|
9g-1+1-8g = g
|
| 9L8s
|
15\17 < g < 8\9
|
g = 271\306
|
g = 23\26, 31\35, 39\44
|
8g-7+8-9g = 1-g
|
| 10L7s
|
5\17 < g < 3\10
|
g = 101\340
|
g = 8\27, 11\37, 14\47
|
7g-2+3-10g = 1-3g
|
| 11L6s
|
3\17 < g < 2\11
|
g = 67\374
|
g = 5\28, 7\39, 9\50
|
6g-1+2-11g = 1-5g
|
| 12L5s
|
7\17 < g < 5\12
|
g = 169\408
|
g = 12\29, 17\41, 22\53
|
5g-2+5-12g = 3-7g
|
| 13L4s
|
13\17 < g < 10\13
|
g = 339\442
|
g = 23\30, 33\43, 43\56
|
4g-3+10-13g = 7-9g
|
| 14L3s
|
6\17 < g < 5\14
|
g = 169\476
|
g = 11\31, 16\45, 21\59
|
3g-1+5-14g = 4-11g
|
| 15L2s
|
9\17 < g < 8\15
|
g = 271\510
|
g = 17\32, 25\47, 33\62
|
2g-1+8-15g = 7-13g
|
| 16L1s
|
1\17 < g < 1\16
|
g = 33\544
|
g = 2\33, 3\49, 4\65
|
g+1-16g = 1-15g
|
18
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L17s
|
17\18 < g < 1
|
g = 35\36
|
g = 18\19, 19\20, 20\21
|
17g-16+1-g = 16g-15
|
| 2L16s
|
8\18 < g < 1\2
|
g = 17\36
|
g = 9\20, 10\22, 11\24
|
8g-7\2+1\2-g = 7g-3
|
| 3L15s
|
5\18 < g < 1\3
|
g = 11\36
|
g = 6\21, 7\24, 8\27
|
5g-4\3+1\3-g = 4g-3
|
| 4L14s
|
4\18 < g < 1\4
|
g = 17\72
|
g = 5\22, 6\26, 7\30
|
7g-3\2+1\2-2g = 5g-2
|
| 5L13s
|
7\18 < g < 2\5
|
g = 71\180
|
g = 9\23, 11\28, 13\33
|
13g-5+2-5g = 8g-3
|
| 6L12s
|
2\18 < g < 1\6
|
g = 5\36
|
g = 3\24, 4\30, 5\36
|
2g-1\6+1\6-g = g
|
| 7L11s
|
5\18 < g < 2\7
|
g = 71\252
|
g = 7\25, 9\32, 11\39
|
11g-3+2-7g = 4g-1
|
| 8L10s
|
2\18 < g < 1\8
|
g = 17\144
|
g = 3\26, 4\34, 5\42
|
5g-1\2+1\2-4g = g
|
| 9L9s
|
1\18 < g < 1\9
|
g = 3\36
|
g = 2\27, 3\36, 4\45
|
g+1\9-g = 1\9
|
| 10L8s
|
7\18 < g < 4\10
|
g = 71\180
|
g = 11\28, 15\38, 19\48
|
4g-3\2+2-5g = 1\2-g
|
| 11L7s
|
13\18 < g < 8\11
|
g = 287\396
|
g = 21\29, 29\40, 37\51
|
7g-5+8-11g = 3-4g
|
| 12L6s
|
1\18 < g < 1\12
|
g = 5\72
|
g = 2\30, 3\42, 4\54
|
g+1\6-2g = 1\6-g
|
| 13L5s
|
11\18 < g < 8\13
|
g = 287\468
|
g = 19\31, 27\44, 35\57
|
5g-3+8-13g = 5-8g
|
| 14L4s
|
5\18 < g < 4\14
|
g = 71\252
|
g = 9\32, 13\46, 17\60
|
2g-1\2+2-7g = 3\2-5g
|
| 15L3s
|
1\18 < g < 1\15
|
g = 11\180
|
g = 2\33, 3\48, 4\63
|
g+1\3-5g = 1\3-4g
|
| 16L2s
|
1\18 < g < 1\16
|
g = 17\288
|
g = 2\34, 3\50, 4\66
|
g+1\2-8g = 1\2-7g
|
| 17L1s
|
1\18 < g < 1\17
|
g = 35\618
|
g = 2\35, 3\52, 4\69
|
g+1-17g = 1-16g
|
19
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L18s
|
18\19 < g < 1
|
g = 37\38
|
g = 19\20, 20\21, 21\22
|
18g-17+1-g = 17g-16
|
| 2L17s
|
9\19 < g < 1\2
|
g = 37\76
|
g = 10\21, 11\23, 12\25
|
17g-8+1-2g = 15g-7
|
| 3L16s
|
6\19 < g < 1\3
|
g = 37\114
|
g = 7\22, 8\25, 10\31
|
16g-5+1-3g = 13g-4
|
| 4L15s
|
14\19 < g < 3\4
|
g = 113\152
|
g = 17\23, 20\27, 23\31
|
15g-11+3-4g = 11g-8
|
| 5L14s
|
15\19 < g < 4\5
|
g = 151\190
|
g = 19\24, 23\29, 27\34
|
14g-11+4-5g = 9g-7
|
| 6L13s
|
3\19 < g < 1\6
|
g = 37\228
|
g = 4\25, 5\31, 6/37
|
13g-2+1-6g = 7g-1
|
| 7L12s
|
8\19 < g < 3\7
|
g = 113\266
|
g = 11\26, 14\33, 17\40
|
12g-5+3-7g = 5g-2
|
| 8L11s
|
7\19 < g < 3\8
|
g = 113\304
|
g = 10\27, 13\35, 16\43
|
11g-4+3-8g = 3g-1
|
| 9L10s
|
2\19 < g < 1\9
|
g = 37\342
|
g = 3\28, 4\37, 5\46
|
10g-1+1-9g = g
|
| 10L9s
|
17\19 < g < 9\10
|
g = 341\380
|
g = 26\29, 35\39, 44\49
|
9g-8+9-10g = 1-g
|
| 11L8s
|
12\19 < g < 7\11
|
g = 265\418
|
g = 19\30, 26\41, 33\52
|
8g-5+7-11g = 2-3g
|
| 12L7s
|
11\19 < g < 7\12
|
g = 265\456
|
g = 18\31, 25\43, 32\55
|
7g-4+7-12g = 3-5g
|
| 13L6s
|
16\19 < g < 11\13
|
g = 417\494
|
g = 27\32, 38\45, 49\58
|
6g-5+11-13g = 6-7g
|
| 14L5s
|
4\19 < g < 3\14
|
g = 113\532
|
g = 7\33, 10\47, 13\61
|
5g-1+3-14g = 2-9g
|
| 15L4s
|
5\19 < g < 4\15
|
g = 151\570
|
g = 9\34, 13\49, 17\64
|
4g-1+4-15g = 3-11g
|
| 16L3s
|
13\19 < g < 11\16
|
g = 417\608
|
g = 24\35, 35\51, 46\67
|
3g-2+11-16g = 9-13g
|
| 17L2s
|
10\19 < g < 9\17
|
g = 341\646
|
g = 19\36, 28\53, 37\70
|
2g-1+9-17g = 8-15g
|
| 18L1s
|
1\19 < g < 1\18
|
g = 37\684
|
g = 2\37, 3\55, 4\73
|
g+1-18g = 1-17g
|
20
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L19s
|
19\20 < g < 1
|
g = 39\40
|
g = 20\21, 21\22, 22\23
|
19g-18+1-g = 18g-17
|
| 2L18s
|
9\20 < g < 1\2
|
g = 19\40
|
g = 10\22, 11\24, 12\26
|
9g-4+1\2-g = 8g-7\2
|
| 3L17s
|
13\20 < g < 2\3
|
g = 79\120
|
g = 15\23, 17\26, 20\29
|
17g-11+2-3g = 14g-9
|
| 4L16s
|
4\20 < g < 1\4
|
g = 9\40
|
g = 5\24, 6\28, 7\32
|
4g-3\4+1\4-g = 3g-1\4
|
| 5L15s
|
3\20 < g < 1\5
|
g = 7\40
|
g = 4\25, 5\30, 6\35
|
3g-2\5+1\5-g = 2g-1\5
|
| 6L14s
|
3\20 < g < 1\6
|
g = 19\120
|
g = 4\26, 5\32, 6\38
|
7g-1+1\2-3g = 4g-1\2
|
| 7L13s
|
17\20 < g < 6\7
|
g = 239\280
|
g = 23\27, 29\34, 35\41
|
13g-11+6-7g = 6g-5
|
| 8L12s
|
2\20 < g < 1\8
|
g = 9\80
|
g = 3\28, 4\36, 5\44
|
3g-1\4+1\4-2g = g
|
| 9L11s
|
11\20 < g < 5\9
|
g = 199\360
|
g = 16\29, 21\38, 26\47
|
11g-6+5-9g =2g-1
|
| 10L10s
|
1\20 < g < 1\10
|
g = 3\40
|
g = 2\30, 3\40, 4\50
|
g+1\10-g = 1\10
|
| 11L9s
|
9\20 < g < 5\11
|
g = 199\440
|
g = 14\31, 19\42, 24\53
|
9g-4+5-11g = 1-2g
|
| 12L8s
|
3\20 < g < 2\12
|
g = 19\120
|
g = 5\32, 7\44, 9\56
|
2g-1\4+1\2-3g = 1\4-g
|
| 13L7s
|
3\20 < g < 2\13
|
g = 79\520
|
g = 5\33, 7\46, 9\59
|
7g-1+2-13g = 1-6g
|
| 14L6s
|
7\20 < g < 5\14
|
g = 99\280
|
g = 12\34, 17\48, 22\62
|
3g-1+5\2-7g = 2-4g
|
| 15L5s
|
1\20 < g < 1\15
|
g = 7\120
|
g = 2\35, 3\50, 4\65
|
g+1\5-3g = 1\5-2g
|
| 16L4s
|
1\20 < g < 1\16
|
g = 9\160
|
g = 2\36, 3\52, 4\68
|
g+1\4-4g = 1\4-3g
|
| 17L3s
|
7\20 < g < 6\17
|
g = 239\680
|
g = 13\37, 19\54, 25\71
|
3g-1+6-17g = 5-14g
|
| 18L2s
|
1\20 < g < 1\18
|
g = 19\360
|
g = 2\38, 3\56, 4\74
|
g+1\2-9g = 1\2-8g
|
| 19L1s
|
1\20 < g < 1\19
|
g = 39\760
|
g = 2\39, 3\58, 4\77
|
g+1-19g = 1-18g
|
21
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L20s
|
20\21 < g < 1
|
g = 41\42
|
g = 21\22, 22\23, 23\24
|
20g-19+1-g = 19g-18
|
| 2L19s
|
10\21 < g < 1\2
|
g = 41\84
|
g = 11\23, 12\25, 13\27
|
19g-9+1-2g = 17g-8
|
| 3L18s
|
6\21 < g < 1\3
|
g = 13\42
|
g = 7\24, 8\27, 9\30
|
6g-5\3+1\3-g = 5g-4\3
|
| 4L17s
|
5\21 < g < 1\4
|
g = 41\168
|
g = 6\25, 7\29, 8\33
|
17g-2+1-4g = 13g-1
|
| 5L16s
|
4\21 < g < 1\5
|
g = 41\210
|
g = 5\26, 6\31, 7\36
|
16g-3+1-5g = 11g-2
|
| 6L15s
|
3\21 < g < 1\6
|
g = 13\84
|
g = 4\27, 5\33, 6\39
|
5g-2\3+1\3-2g = 3g-1\3
|
| 7L14s
|
2\21 < g < 1\7
|
g = 5\42
|
g = 3\28, 4\35, 5\42
|
2g-1\7+1\7-g = g
|
| 8L13s
|
13\21 < g < 5\8
|
g = 209\336
|
g = 18\29, 23\37, 28\45
|
13g-8+5-8g = 5g-3
|
| 9L12s
|
2\21 < g < 1\9
|
g = 13\126
|
g = 3\30, 4\39, 5\48
|
4g-1\3+1\3-3g = g
|
| 10L11s
|
2\21 < g < 1\10
|
g = 41\420
|
g = 3\31, 4\41, 5\51
|
11g-1+1-10g = g
|
| 11L10s
|
19\21 < g < 10\11
|
g = 419\462
|
g = 29\32, 39\43, 49\54
|
10g-9+10-11g = 1-g
|
| 12L9s
|
5\21 < g < 3\12
|
g = 41\168
|
g = 8\33, 11\45, 14\57
|
3g-2\3+1-4g = 1\3-3g
|
| 13L8s
|
8\21 < g < 5\13
|
g = 209\546
|
g = 13\34, 18\47, 23\70
|
8g-3+5-13g = 2-5g
|
| 14L7s
|
1\21 < g < 1\14
|
g = 5\84
|
g = 2\35, 3\49, 4\63
|
g+1\7-2g = 1\7-g
|
| 15L6s
|
4\21 < g < 3\15
|
g = 41\210
|
g = 7\36, 10\51, 13\66
|
2g-1\3+1-5g = 2\3-3g
|
| 16L5s
|
17\21 < g < 13\16
|
g = 545\672
|
g = 30\37, 43\53, 56\69
|
5g-4+13-16g = 9-11g
|
| 17L4s
|
16\21 < g < 13\17
|
g = 545\714
|
g = 29\38, 42\55, 55\72
|
4g-3+13-17g = 10-13g
|
| 18L3s
|
1\21 < g < 1\18
|
g = 13\252
|
g = 2\39, 3\57, 4\75
|
g+1\3-6g = 1\3-5g
|
| 19L2s
|
11\21 < g < 10\19
|
g = 419\798
|
g = 21\40, 31\59, 41\78
|
2g-1+10-19g = 9-17g
|
| 20L1s
|
1\21 < g < 1\20
|
g = 41\840
|
g = 2\41, 3\61, 4/81
|
g+1-20g = 1-19g
|
22
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L21s
|
21\22 < g < 1
|
g = 43\44
|
g = 22\23, 23\24, 24/25
|
21g-20+1-g = 20g-19
|
| 2L20s
|
10\22 < g < 1\2
|
g = 21\44
|
g = 11\24, 12\26, 13\28
|
10g-9\2+1\2-g = 9g-4
|
| 3L19s
|
7\22 < g < 1\3
|
g = 43\132
|
g = 8\25, 9\28, 10\31
|
19g-6+1-3g = 16g-5
|
| 4L18s
|
5\22 < g < 1\4
|
g = 21\88
|
g = 6\26, 7\30, 8\34
|
9g-2+1\2-2g = 7g-3\2
|
| 5L17s
|
13\22 < g < 3\5
|
g = 131\220
|
g = 16\27, 19\32, 22\37
|
17g-10+3-5g = 12g-7
|
| 6L16s
|
7\22 < g < 2\6
|
g = 43\132
|
g = 9\28, 11\34, 13\40
|
8g-5\2+1-3g = 5g-2
|
| 7L15s
|
3\22 < g < 1\7
|
g = 43\308
|
g = 4\29, 5\36, 6\43
|
15g-2+1-7g = 8g-1
|
| 8L14s
|
8\22 < g < 3\8
|
g = 65\176
|
g = 11\30, 14\38, 17\46
|
7g-5\2+3\2-4g = 3g-2
|
| 9L13s
|
17\22 < g < 7\9
|
g = 307\396
|
g = 24\31, 31\40, 38\49
|
13g-10+7-9g = 4g-3
|
| 10L12s
|
2\22 < g < 1\10
|
g = 21\220
|
g = 3\32, 4\42, 5\52
|
6g-1\2+1\2-5g = g
|
| 11L11s
|
1\22 < g < 1\11
|
g = 3\44
|
g = 2\33, 3\44, 4\55
|
g + 1\11-g = 1\11
|
| 12L10s
|
9\22 < g < 5\12
|
g = 109\264
|
g = 14\34, 19\46, 24\58
|
5g-2+5\2-6g = 1\2-g
|
| 13L9s
|
5\22 < g < 3\13
|
g = 131\572
|
g = 8\35, 11\48, 14\61
|
9g-2+3-13g = 1-4g
|
| 14L8s
|
3\22 < g < 2\14
|
g = 43\308
|
g = 5\36, 7\50, 9\64
|
4g-1\2+1-7g = 1\2-3g
|
| 15L7s
|
19\22 < g < 13\15
|
g = 571\660
|
g = 32\37, 45\52, 58\67
|
7g-6+13-15g = 7-8g
|
| 16L6s
|
4\22 < g < 3\16
|
g = 65\352
|
g = 7\38, 10\54, 13\70
|
3g-1\2+3\2-8g = 1-5g
|
| 17L5s
|
9\22 < g < 7\17
|
g = 207\748
|
g = 16\39, 23\56, 30\73
|
5g-2+7-17g = 5-12g
|
| 18L4s
|
6\22 < g < 5\18
|
g = 109\396
|
g = 11\40, 16\58, 21\76
|
2g-1\2+5\2-9g = 2-7g
|
| 19L3s
|
15\22 < g < 13\19
|
g = 571\836
|
g = 28\41, 41\60, 54\79
|
3g-2+13-19g = 11-16g
|
| 20L2s
|
1\22 < g < 1\20
|
g = 21\440
|
g = 2\42, 3\62, 4\72
|
g+1\2-10g = 1\2-9g
|
| 21L1s
|
1\22 < g < 1\21
|
g = 43\924
|
g = 2\43, 3\64, 4\85
|
g+1-21g = 1-20g
|
23
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L22s
|
22\23 < g < 1
|
g = 45\46
|
g = 23\24, 24\25, 25\26
|
22g-21+1-g = 21g-20
|
| 2L21s
|
11\23 < g < 1\2
|
g = 45\92
|
g = 12\25, 13\27, 14\29
|
21g-10+1-2g = 19g-9
|
| 3L20s
|
15\23 < g < 2\3
|
g = 91\138
|
g = 17\26, 19\29, 21\32
|
20g-13+1-3g = 17g-12
|
| 4L19s
|
17\23 < g < 3\4
|
g = 137\184
|
g = 20\27, 23\31, 26\35
|
19g-14+3-4g = 15g-11
|
| 5L18s
|
9\23 < g < 2\5
|
g = 91\230
|
g = 11\28, 13\33, 15\38
|
18g-7+2-5g = 13g-5
|
| 6L17s
|
19\23 < g < 5\6
|
g = 229\276
|
g = 24\29, 29\35, 34\41
|
17g-15+1-6g = 11g-14
|
| 7L16s
|
13\23 < g < 4\7
|
g = 183\322
|
g = 17\30, 21\37, 25\44
|
16g-9+4-7g = 9g-5
|
| 8L15s
|
20\23 < g < 7\8
|
g = 321\368
|
g = 27\31, 34\39, 41\47
|
15g-13+7-8g = 7g-6
|
| 9L14s
|
5\23 < g < 2\9
|
g = 91\414
|
g = 7\32, 9\41, 11\50
|
14g-7+2-9g = 5g-5
|
| 10L13s
|
16\23 < g < 7\10
|
g = 321\460
|
g = 23\33, 30\43, 37\53
|
13g-9+7-10g = 3g-2
|
| 11L12s
|
2\23 < g < 1\11
|
g = 45\506
|
g = 3\34, 4\45, 5\56
|
12g-1+1-11g = g
|
| 12L11s
|
21\23 < g < 11\12
|
g = 505\552
|
g = 32\35, 43\47, 54\59
|
11g-10+11-12g = 1-g
|
| 13L10s
|
7\23 < g < 4\13
|
g = 183\598
|
g = 11\36, 15\49, 19\62
|
10g-3+4-13g =1-3g
|
| 14L9s
|
18\23 < g < 11\14
|
g = 505\644
|
g = 29\37, 40\51, 51\65
|
9g-7+11-14g = 4-5g
|
| 15L8s
|
3\23 < g < 2\15
|
g = 91\690
|
g = 5\38, 7\53, 9\68
|
8g-1+2-15g = 1-7g
|
| 16L7s
|
10\23 < g < 7\16
|
g = 321\736
|
g = 17\39, 24\55, 31\71
|
7g-3+7-16g = 4-9g
|
| 17L6s
|
4\23 < g < 3\17
|
g = 137\782
|
g = 7\40, 10\57, 13\74
|
6g-1+3-17g = 2-11g
|
| 18L5s
|
14\23 < g < 11\18
|
g = 505\828
|
g = 25\41, 36\59, 47\77
|
5g-4+11-18g = 7-13g
|
| 19L4s
|
6\23 < g < 5\19
|
g = 229\874
|
g = 11\42, 16\61, 21\80
|
4g-1+5-19g = 4-15g
|
| 20L3s
|
8\23 < g < 7\20
|
g = 321\920
|
g = 15\43, 22\63, 29\83
|
3g-1+13-20g = 12-17g
|
| 21L2s
|
12\23 < g < 11\21
|
g = 505\966
|
g = 23\44, 34\65, 45\86
|
2g-1+11-21g = 10-19g
|
| 22L1s
|
1\23 < g < 1\22
|
g = 45\1012
|
g = 2\45, 3\67, 4\89
|
g+1-22g = 1-221
|
24
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L23s
|
23\24 < g < 1
|
g = 47\48
|
g = 24\25, 25\26, 26\27
|
23g-22+1-g = 22g-21
|
| 2L22s
|
11\24 < g < 1\2
|
g = 23\48
|
g = 12\26, 13\28, 14\30
|
11g-5+1/2-g = 10g-9/2
|
| 3L21s
|
7\24 < g < 1\3
|
g = 15\48
|
g = 8\27, 9\30, 10\33
|
7g-2+1/3-g = 6g-5/3
|
| 4L20s
|
5\24 < g < 1\4
|
g = 11\48
|
g = 6\28, 7\32, 8\36
|
5g-1+1/4-g = 4g-3/4
|
| 5L19s
|
19\24 < g < 4\5
|
g = 191\240
|
g = 23\29, 27\34, 31\39
|
19g-15+4-5g = 14g-11
|
| 6L18s
|
3\24 < g < 1\6
|
g = 7\48
|
g = 4\30, 5\36, 6\42
|
3g-1\3+1\6-g = 2g-1\6
|
| 7L17s
|
17\24 < g < 5\7
|
g = 239\336
|
g = 22\31, 27\38, 32\45
|
17g-12+5-7g = 10g-7
|
| 8L16s
|
2\24 < g < 1\8
|
g = 5\48
|
g = 3\32, 4\40, 5\48
|
2g-1\8+1\8-g = g
|
| 9L15s
|
5\24 < g < 2\9
|
g = 31\144
|
g = 7\33, 9\42, 11\51
|
5g-1+2\3-3g = 2g-1\3
|
| 10L14s
|
7\24 < g < 3\10
|
g = 71\240
|
g = 10\34, 13\44, 16\54
|
7g-2+3\2-5g = 2g-1\2
|
| 11L13s
|
13\24 < g < 6\11
|
g = 287\528
|
g = 19\35, 25\46, 31\57
|
13g-7+6-11g = 2g-1
|
| 12L12s
|
1\24 < g < 1\12
|
g = 3\48
|
g = 2\36, 3\48, 4\60
|
g+1\12-g = 1\12
|
| 13L11s
|
11\24 < g < 6\13
|
g = 287\624
|
g = 17\37, 23\50, 29\63
|
11g-5+6-13g = 1-2g
|
| 14L10s
|
17\24 < g < 10\14
|
g = 239\336
|
g = 27\38, 37\52, 47\66
|
5g-7\2+5-7g = 3\2-2g
|
| 15L9s
|
3\24 < g < 2\15
|
g = 31\240
|
g = 5\39, 7\54, 9\69
|
3g-1\3+2\3-5g = 1\3-2g
|
| 16L8s
|
1\24 < g < 1\16
|
g = 5\96
|
g = 2\40, 3\56, 4\72
|
g+1\8-2g = 1\8-g
|
| 17L7s
|
7\24 < g < 5\17
|
g = 239\816
|
g = 12\41, 17\58, 22\75
|
7g-2+5-17g = 3-10g
|
| 18L6s
|
1\24 < g < 1\18
|
g = 7\144
|
g = 2\42, 3\60, 4\78
|
g+1\6-3g = 1\6-2g
|
| 19L5s
|
5\24 < g < 4\19
|
g = 191\912
|
g = 9\43, 13\62, 17\81
|
5g-5+4-19g = 1-18g
|
| 20L4s
|
1\24 < g < 1\20
|
g = 11\240
|
g = 2\44, 3\64, 4\84
|
g+1\4-5g = 1\4-4g
|
| 21L3s
|
1\24 < g < 1\21
|
g = 15\336
|
g = 2\45, 3\66, 4\87
|
g+1\3-7g = 1\3-6g
|
| 22L2s
|
1\24 < g < 1\22
|
g = 23\264
|
g = 2\46, 3\68, 4\90
|
g+1\2-11g = 1\2-10g
|
| 23L1s
|
1\24 < g < 1\23
|
g = 47\1104
|
g = 2\47, 3\70, 4\93
|
g+1-23g = 1-22g
|
25
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L24s
|
24\25 < g < 1
|
g = 49\50
|
g = 25\26, 26\27, 27\28
|
24g-23+1-g = 23g-22
|
| 2L23s
|
12\25 < g < 1\2
|
g = 49\100
|
g = 13\27, 14\29, 15\31
|
23g-11+1-2g = 21g-10
|
| 3L22s
|
8\25 < g < 1\3
|
g = 49\150
|
g = 9\28, 10\31, 11\34
|
22g-7+1-3g = 19g-6
|
| 4L21s
|
6\25 < g < 1\4
|
g = 49\200
|
g = 7\29, 8\33, 9\37
|
21g-5+1-4g = 17g-4
|
| 5L20s
|
4\25 < g < 1\5
|
g = 9\50
|
g = 5\30, 6\35, 7\40
|
4g-3\5+1\5-g = 3g-2\5
|
| 6L19s
|
4\25 < g < 1\6
|
g = 49\300
|
g = 5\31, 6\37, 7\43
|
19g-3+1-6g = 13g-2
|
| 7L18s
|
7\25 < g < 2\7
|
g = 99\350
|
g = 9\32, 11\39, 13\46
|
18g-5+2-7g = 11g-3
|
| 8L17s
|
3\25 < g < 1\8
|
g = 49\400
|
g = 4\33, 5\41, 6\47
|
17g-2+1-8g = 9g-1
|
| 9L16s
|
11\25 < g < 4\9
|
g = 199\450
|
g = 15\34, 19\43, 23\52
|
16g-7+4-9g = 3-7g
|
| 10L15s
|
2\25 < g < 1\10
|
g = 9\100
|
g = 3\35, 4\45, 5\55
|
3g-1\5+1\5-2g = g
|
| 11L14s
|
9\25 < g < 4\11
|
g = 199\550
|
g = 13\36, 17\47, 21\58
|
14g-5+4-11g = 3g-1
|
| 12L13s
|
2\25 < g < 1\12
|
g = 49\600
|
g = 3\37, 4\49, 5\61
|
13g-1+1-12g = g
|
| 13L12s
|
23\25 < g < 12\13
|
g = 599\650
|
g = 35\38, 47\51, 59\64
|
12g-11+12-13g = 1-g
|
| 14L11s
|
16\25 < g < 9\14
|
g = 449\700
|
g = 25\39, 34\53, 43\67
|
11g-7+9-14g = 2-3g
|
| 15L10s
|
3\25 < g < 2\15
|
g = 19\150
|
g = 5\40, 7\55, 9\70
|
2g-1\5+2\5-3g = 1\5-g
|
| 16L9s
|
14\25 < g < 9\16
|
g = 449\800
|
g = 23\41, 32\57, 41\73
|
9g-5+9-16g = 4-7g
|
| 17L8s
|
22\25 < g < 15\17
|
g = 749\850
|
g = 37\42, 52\59, 67\76
|
8g-7+15-17g = 8-9g
|
| 18L7s
|
18\25 < g < 13\18
|
g = 649\900
|
g = 31\43, 44\61, 57\79
|
7g-5+13-18g = 8-11g
|
| 19L6s
|
21\25 < g < 16\19
|
g = 799\950
|
g = 37\44, 53\63, 69\82
|
6g-5+16-19g = 11-13g
|
| 20L5s
|
1\25 < g < 1\20
|
g = 9\200
|
g = 2\45, 3\65, 4\85
|
g+1\5-4g = 1\5-3g
|
| 21L4s
|
16\21 < g < 19\25
|
g = 799\1050
|
g = 35\46, 51\67, 71\88
|
4g-3+16-21g = 13-17g
|
| 22L3s
|
17\25 < g < 15\22
|
g = 749\1100
|
g = 32\47, 47\69, 62\91
|
3g-2+15-22g = 13-19g
|
| 23L2s
|
13\25 < g < 12\23
|
g = 599\1150
|
g = 25\48, 37\71, 49\94
|
2g-1+11-23g = 10-21g
|
| 24L1s
|
1\25 < g < 1\24
|
g = 49\1200
|
g = 2\49, 3\73, 4\97
|
g+1-24g = 1-23g
|
26
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L25s
|
25\26 < g < 1
|
g = 51\52
|
g = 26\27, 27\28, 28\29
|
25g-24+1-g = 24g-23
|
| 2L24s
|
12\26 < g < 1\2
|
g = 25\52
|
g = 13\28, 14\30, 15\32
|
12g-11\2+1\2-g = 11g-5
|
| 3L23s
|
17\26 < g < 2\3
|
g = 103\156
|
g = 19\29, 21\32, 23\35
|
23g-15+2-3g = 20g-13
|
| 4L22s
|
6\26 < g < 1\4
|
g = 25\104
|
g = 7\30, 8\34, 9\38
|
11g-5\2+1\2-2g = 9g-2
|
| 5L21s
|
5\26 < g < 1\5
|
g = 51\260
|
g = 6\31, 7\36, 8\41
|
21g-4+1-5g = 16g-3
|
| 6L20s
|
4\26 < g < 1\6
|
g = 25\156
|
g = 5\32, 6\38, 7\44
|
10g-3\2+1\2-3g = 7g-1
|
| 7L19s
|
11\26 < g < 3\7
|
g = 155\364
|
g = 14\33, 17\40, 20\47
|
19g-8+3-7g = 12g-5
|
| 8L18s
|
3\26 < g < 1\8
|
g = 25\208
|
g = 4\34, 5\42, 6\50
|
9g-1+1\2-4g = 5g-1\2
|
| 9L17s
|
23\26 < g < 8\9
|
g = 415\468
|
g = 31\35, 39\44, 47\53
|
17g-15+8-9g = 8g-7
|
| 10L16s
|
5\26 < g < 2\10
|
g = 51\260
|
g = 7\36, 9\46, 11\56
|
8g-3\2+1-5g = 3g-1\2
|
| 11L15s
|
7\26 < g < 3\11
|
g = 155\572
|
g = 10\37, 13\48, 16\59
|
15g-4+3-11g = 4g-1
|
| 12L14s
|
2\26 < g < 1\12
|
g = 25\312
|
g = 3\38, 4\50, 5\62
|
7g-1\2+1\2-6g = g
|
| 13L13s
|
1\26 < g < 1\13
|
g = 3\52
|
g = 2\39, 3\52, 4\65
|
g+1\13-g = 1\13
|
| 14L12s
|
11\26 < g < 6\14
|
g = 155\364
|
g = 17\40, 23\54, 29\68
|
6g-5\2+3-7g = 1\2-g
|
| 15L11s
|
19\26 < g < 11\15
|
g = 571\780
|
g = 30\41, 41\56, 52\71
|
11g-8+11-15g = 3-4g
|
| 16L10s
|
8\26 < g < 5\16
|
g = 129\416
|
g = 13\42, 18\58, 23\74
|
5g-3\2+5\2-8g = 1-3g
|
| 17L9s
|
3\26 < g < 2\17
|
g = 103\884
|
g = 5\43, 7\60, 9\77
|
9g-1+2-17g = 1-8g
|
| 18L8s
|
10\26 < g < 7\18
|
g = 181\468
|
g = 17\44, 24\62, 31\80
|
4g-7\2+7-9g = 7\2-5g
|
| 19L7s
|
15\26 < g < 11\19
|
g = 571\988
|
g = 26\45, 37\64, 48\83
|
7g-4+11-19g = 7-12g
|
| 20L6s
|
9\26 < g < 7\20
|
g = 181\520
|
g = 16\46, 23\66, 30\86
|
3g-1+7\2-10g = 5\2-7g
|
| 21L5s
|
21\26 < g < 17\21
|
g = 883\1092
|
g = 38\47, 55\68, 72\89
|
5g-4+16-21g = 12-16g
|
| 22L4s
|
7\26 < g < 6\22
|
g = 155\572
|
g = 13\48, 19\70, 25\92
|
2g-1\2+3-11g = 5\2-9g
|
| 23L3s
|
9\26 < g < 8\23
|
g = 415\1196
|
g = 17\49, 25\72, 33/95
|
3g-1+8-23g = 7-20g
|
| 24L2s
|
1\26 < g < 1\24
|
g = 25\312
|
g = 2\50, 3\74, 4\98
|
g+1\2-12g = 1\2-11g
|
| 25L1s
|
1\26 < g < 1\25
|
g = 51\1300
|
g = 2\51, 3\76, 4\101
|
g+1-25g = 1-24g
|
27
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L26s
|
26\27 < g < 1
|
g = 53\54
|
g = 27\28, 28\29, 29\30
|
26g-25+1-g = 25g-24
|
| 2L25s
|
13\27 < g < 1\2
|
g = 53\108
|
g = 14\29, 15\31, 16\33
|
25g-12+1-2g = 23g-11
|
| 3L24s
|
8\27 < g < 1\3
|
g = 17\54
|
g = 9\30, 10\33, 11\36
|
8g-7\3+1-3g = 5g-2
|
| 4L23s
|
20\27 < g < 3\4
|
g = 161\216
|
g = 23\31, 26\35, 29\39
|
23g-17+3-4g = 19g-14
|
| 5L22s
|
16\27 < g < 3\5
|
g = 161\270
|
g = 19\32, 22\37, 25\42
|
22g-13+3-5g = 17g-10
|
| 6L21s
|
4\27 < g < 1\6
|
g = 17\108
|
g = 5\33, 6\39, 7\45
|
7g-1+1\3-2g = 5g-2\3
|
| 7L20s
|
23\27 < g < 6\7
|
g = 323\378
|
g = 29\34, 35\41, 41\48
|
20g-17+6-7g = 13g-11
|
| 8L19s
|
10\27 < g < 3\8
|
g = 161\432
|
g = 13\35, 16\43, 19\51
|
19g-7+3-8g = 11g-4
|
| 9L18s
|
2\27 < g < 1\9
|
g = 5\54
|
g = 3\36, 4\45, 5\54
|
2g-1\9+1\9-g = g
|
| 10L17s
|
8\27 < g < 3\10
|
g = 161\540
|
g = 11\37, 14\47, 17\57
|
17g-5+3-10g = 7g-2
|
| 11L16s
|
22\27 < g < 9\11
|
g = 485\594
|
g = 31\38, 40\49, 49\60
|
16g-13+9-11g = 5g-4
|
| 12L15s
|
2\27 < g < 1\12
|
g = 17\216
|
g = 3\39, 4\51, 5\63
|
5g-1\3+1\3-4g = g
|
| 13L14s
|
2\27 < g < 1\13
|
g = 53\702
|
g = 3\40, 4\53, 5\66
|
14g-1+1-13g = g
|
| 14L13s
|
25\27 < g < 13\14
|
g = 701\756
|
g = 38\41, 51\55, 64\69
|
13g-12+13-14g = 1-g
|
| 15L12s
|
7\27 < g < 4\15
|
g = 71\270
|
g = 11\42, 15\57, 19\72
|
4g-1+4\3-5g = 1\3-g
|
| 16L11s
|
5\27 < g < 3\16
|
g = 161\864
|
g = 8\43, 11\59, 14\75
|
11g-2+3-16g = 1-5g
|
| 17L10s
|
19\27 < g < 12\17
|
g = 647\918
|
g = 31\44, 43\61, 55\78
|
10g-7+12-17g = 5-7g
|
| 18L9s
|
1\27 < g < 1\18
|
g = 5\108
|
g = 2\45, 3\63, 4\81
|
g+1\9-2g = 1\9-g
|
| 19L8s
|
17\27 < g < 12\19
|
g = 647\1026
|
g = 29\46, 41\65, 53\84
|
8g-5+12-19g = 7-11g
|
| 20L7s
|
4\27 < g < 3\20
|
g = 161\1080
|
g = 7\47, 10\67, 13\87
|
7g-1+3-20g = 2-13g
|
| 21L6s
|
5\27 < g < 4\21
|
g = 71\378
|
g = 9\48, 13\69, 17\90
|
2g-1\3+4\3-7g = 1-5g
|
| 22L5s
|
11\27 < g < 9\22
|
g = 485\1188
|
g = 20\49, 29\71, 38\93
|
5g-2+9-22g = 7-17g
|
| 23L4s
|
7\27 < g < 6\23
|
g = 323\1242
|
g = 13\50, 19\73, 25\96
|
4g-1+6-23g = 5-19g
|
| 24L3s
|
1\27 < g < 1\24
|
g = 17\432
|
g = 2\51, 3\75, 4\99
|
g+1\3-8g = 1\3-7g
|
| 25L2s
|
14\27 < g < 13\25
|
g = 701\1350
|
g = 27\52, 40\77, 53\102
|
2g-1+13-25g = 12-23g
|
| 26L1s
|
1\27 < g < 1\26
|
g = 53\1404
|
g = 2\53, 3\79, 4\105
|
g+1-26g = 1-25g
|
28
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L27s
|
27\28 < g < 1
|
g = 55\56
|
g = 28\29, 29\30, 30\31
|
27g-26+1-g = 26g-25
|
| 2L26s
|
13\28 < g < 1\2
|
g = 27\56
|
g = 14\30, 15\32, 16\34
|
13g-6+1\2-g = 12g-11\2
|
| 3L25s
|
9\28 < g < 1\3
|
g = 55\168
|
g = 10\31, 11\34, 12\37
|
25g-8+1-3g = 22g-7
|
| 4L24s
|
6\28 < g < 1\4
|
g = 13\56
|
g = 7\32, 8\36, 9\40
|
6g-5\4+1\4-g = 5g-1
|
| 5L23s
|
11\28 < g < 2\5
|
g = 111\280
|
g = 13\33, 15\38, 17\43
|
23g-9+2-5g = 18g-7
|
| 6L22s
|
9\28 < g < 2\6
|
g = 55\168
|
g = 11\34, 13\40, 15\46
|
11g-7\2+1-3g = 8g-3
|
| 7L21s
|
3\28 < g < 1\7
|
g = 7\56
|
g = 4\35, 5\42, 6\49
|
3g-2\7+1\7-g = 2g-1\7
|
| 8L20s
|
3\28 < g < 1\8
|
g = 13\112
|
g = 4\36, 5\44, 6\52
|
5g-1\2+1\4-2g = 3g-1\4
|
| 9L19s
|
3\28 < g < 1\9
|
g = 55\504
|
g = 4\37, 5\46, 6\55
|
19g-2+1-9g = 10g-1
|
| 10L18s
|
11\28 < g < 4\10
|
g = 111\280
|
g = 15\38, 19\48, 23\58
|
9g-7\2+2-5g = 4g-3\2
|
| 11L17s
|
5\28 < g < 2\11
|
g = 111\616
|
g = 7\39, 9\50, 11\61
|
17g-3+2-11g = 6g-1
|
| 12L16s
|
2\28 < g < 1\12
|
g = 13\168
|
g = 3\40, 4\52, 5\64
|
4g-1\4+1\4-3g = g
|
| 13L15s
|
15\28 < g < 7\13
|
g = 391\728
|
g = 22\41, 29\54, 36\67
|
15g-8+7-13g = 2g-1
|
| 14L14s
|
1\28 < g < 1\14
|
g = 3\56
|
g = 2\42, 3\56, 4\70
|
g+1\14-g = 1\14
|
| 15L13s
|
13\28 < g < 7\15
|
g = 391\840
|
g = 20\43, 27\58, 34\73
|
13g-6+7-15g = 1-2g
|
| 16L12s
|
5\28 < g < 3\16
|
g = 41\224
|
g = 8\44, 11\60, 14\76
|
3g-1\2+3\4-4g = 1\4-g
|
| 17L11s
|
23\28 < g < 14\17
|
g = 783\952
|
g = 37\45, 51\62, 65\79
|
11g-9+13-17g = 4-6g
|
| 18L10s
|
3\28 < g < 2\18
|
g = 55\504
|
g = 5\46, 7\64, 9\82
|
5g-1\2+1-9g = 1\2-4g
|
| 19L9s
|
25\28 < g < 17\19
|
g = 951\1064
|
g = 42\47, 59\66, 76\85
|
9g-8+17-19g = 9-10g
|
| 20L8s
|
4\28 < g < 3\20
|
g = 41\280
|
g = 7\48, 10\68, 13\88
|
2g-1\4+3\4-5g = 1\2-3g
|
| 21L7s
|
1\28 < g < 1\21
|
g = 7\168
|
g = 2\49, 3\70, 4\91
|
g+1\7-2g = 1\7-g
|
| 22L6s
|
5\28 < g < 4\22
|
g = 111\616
|
g = 9\50, 13\72, 17\94
|
3g-1\2+2-11g = 3\2-8g
|
| 23L5s
|
17\28 < g < 14\23
|
g = 783\1288
|
g = 31\51, 45\74, 59\97
|
5g-3+14-23g = 11-18g
|
| 24L4s
|
1\28 < g < 1\24
|
g = 13\336
|
g = 2\52, 3\76, 4\100
|
g+1\4-6g = 1\4-5g
|
| 25L3s
|
19\28 < g < 17\25
|
g = 951\1400
|
g = 36\53, 53\78, 70\103
|
3g-2+17-25g = 15+22g
|
| 26L2s
|
15\28 < g < 14\26
|
g = 391\728
|
g = 29\54, 43\80, 57\106
|
g-1\2+7-13g = 13\2-12g
|
| 27L1s
|
1\28 < g < 1\27
|
g = 55\1512
|
g = 2\55, 3\82, 4\109
|
g+1-27g = 1-26g
|
29
| Large-small numbers
|
Generator range
|
Midpoint
|
Boundaries of propriety, maximum expressiveness, diatonicity
|
Large step+Small step
|
| 1L28s
|
28\29 < g < 1
|
g = 57\58
|
g = 29\30, 30\31, 31\32
|
28g-27+1-g = 27g-26
|
| 2L27s
|
14\29 < g < 1\2
|
g = 57\116
|
g = 15\31, 16\33, 17\35
|
27g-13+1-2g = 25g-12
|
| 3L26s
|
19\29 < g < 2\3
|
g = 115\174
|
g = 21\32, 23\35, 25\38
|
26g-17+2-3g = 23g-15
|
| 4L25s
|
7\29 < g < 1\4
|
g = 57\232
|
g = 8\33, 9\37, 10\41
|
25g-6+1-4g = 21g-5
|
| 5L24s
|
23\29 < g < 4\5
|
g = 231\290
|
g = 27\34, 31\39, 35\44
|
24g-19+4-5g = 19g-15
|
| 6L23s
|
24\29 < g < 5\6
|
g = 289\348
|
g = 29\35, 34\41, 39\47
|
23g-19+5-6g = 17g-14
|
| 7L22s
|
4\29 < g < 1\7
|
g = 57\406
|
g = 5\36, 6\43, 7\50
|
22g-3+1-7g = 15g-2
|
| 8L21s
|
18\29 < g < 5\8
|
g = 289\464
|
g = 23\37, 28\45, 33\53
|
21g-13+5-8g = 13g-8
|
| 9L20s
|
16\29 < g < 5\9
|
g = 289\522
|
g = 21\38, 26\47, 31\56
|
20g-11+5-9g = 11g-6
|
| 10L19s
|
26\29 < g < 9\10
|
g = 521\580
|
g = 35\39, 44\49, 53\59
|
19g-17+9-10g = 9g-8
|
| 11L18s
|
21\29 < g < 8\11
|
g = 463\638
|
g = 29\40, 37\51, 45\62
|
18g-13+8-11g = 7g-2
|
| 12L17s
|
12\29 < g < 5\12
|
g = 289\696
|
g = 17\41, 22\53, 27\65
|
17g-7+5-12g = 5g-2
|
| 13L16s
|
20\29 < g < 9\13
|
g = 521\754
|
g = 29\42, 38\55, 47\68
|
16g+11+9-13g = 3g-2
|
| 14L15s
|
2\29 < g < 1\14
|
g = 57\812
|
g = 3\43, 4\57, 5\71
|
15g-1+1-14g = g
|
| 15L14s
|
27\29 < g < 14\15
|
g = 811\870
|
g = 41\44, 55\59, 69\74
|
14g-13+14-15g = 1-g
|
| 16L13s
|
9\29 < g < 5\16
|
g = 289\928
|
g = 14\45, 19\61, 24\77
|
13g-4+5-16g = 1-3g
|
| 17L12s
|
17\29 < g < 10\17
|
g = 579\986
|
g = 27\46, 37\63, 47\80
|
12g-5+7-17g = 2-5g
|
| 18L11s
|
8\29 < g < 5\18
|
g = 289\1044
|
g = 13\47, 18\65, 23\83
|
11g-3+5-18g = 2-7g
|
| 19L10s
|
3\29 < g < 2\19
|
g = 115\1102
|
g = 5\48, 7\67, 9\86
|
10g-1+2-19g = 1-9g
|
| 20L9s
|
13\29 < g < 9\20
|
g = 521\1160
|
g = 22\49, 31\69, 40\89
|
9g-5+9-20g = 4-11g
|
| 21L8s
|
11\29 < g < 8\21
|
g = 463\1216
|
g = 19\50, 27\71, 35\92
|
8g-3+8-21g = 5-13g
|
| 22L7s
|
25\29 < g < 19\22
|
g = 1001\1274
|
g = 44\51, 63\73, 82\95
|
7g-6+9-22g = 3-16g
|
| 23L6s
|
5\29 < g < 4\23
|
g = 231\1332
|
g = 9\52, 13\75, 17\98
|
6g-1+4-23g = 3-17g
|
| 24L5s
|
6\29 < g < 5\24
|
g = 289\1392
|
g = 11\53, 16\77, 21\101
|
5g-9+5-24g = 4-19g
|
| 25L4s
|
22\29 < g < 19\25
|
g = 1001\1450
|
g = 41\54, 60\79, 79\104
|
4g-3+19-25g = 16-21g
|
| 26L3s
|
10\29 < g < 9\26
|
g = 521\1508
|
g = 19\55, 28\81, 37\107
|
3g-1+9-26g = 8-23g
|
| 27L2s
|
15\29 < g < 14\27
|
g = 811\1564
|
g = 29\56, 43\83, 57\110
|
2g-1+17-27g = 16-25g
|
| 28L1s
|
1\29 < g < 1\28
|
g = 57\1622
|
g = 2\57, 3\85, 4\113
|
g+1-28g = 1-27g
|