Generator ranges of MOS

Below are ranges of generators for various L-s patterns of MOS, 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 fir 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
1L2s	2\3 < g < 1	g = 5\6	g = 3\4, 4\5, 5\6	2g-1	1-g
2L1s	1\3 < g < 1\2	g = 5\12	g = 2\5, 3\7, 4\9	g	1-2g
1L3s	3\4 < g < 1	g = 7\8	g = 4\5, 5\6, 6\7	3g-2	1-g
2L2s	1\4 < g < 1\2	g = 3\8	g = 2\6, 3\8, 4\10	g	1\2-g
3L1s	1\4 < g < 1\3	g = 7\24	g = 2\7, 3\10, 4\13	g	1-3g

5

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
2L3s	2\5 < g < 1\2	g = 9\20	g = 3\7, 4\9, 5\11	3g-1	1-2g
3L2s	3\5 < g < 2\3	g = 19\30	g = 5\8, 7\11, 9\14	2g-1	2-3g
4L1s	1\5 < g < 1\4	g = 9\40	g = 2\9, 3\13, 4\17	g	1-4g

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
2L4s	2\6 < g < 1\2	g = 5\12	g = 3\8, 4\10, 5\12	2g-1\2	1\2-g
3L3s	1\6 < g < 1\3	g = 3\12	g = 2\9, 3\12, 4\15	g	1\3-g
4L2s	1\6 < g < 1\4	g = 5\24	g = 2\10, 3\14, 4\18	g	1\2-2g
5L1s	1\6 < g < 1\5	g = 11\60	g = 2\11, 3\16, 4\21	g	1-5g

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
2L5s	3\7 < g < 1\2	g = 13\28	g = 4\9, 5\11, 6\13	5g-2	1-2g
3L4s	2\7 < g < 1\3	g = 13\42	g = 3\10, 4\13, 5\16	4g-1	1-3g
4L3s	5\7 < g < 3\4	g = 41\56	g = 8\11, 11\15, 14\19	3g-2	3-4g
5L2s	4\7 < g < 3\5	g = 41\70	g = 7\12, 10\17, 13\22	2g-1	3-5g
6L1s	1\7 < g < 1\6	g = 13\84	g = 2\13, 3\19, 4\25	g	1-6g

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
2L6s	3\8 < g < 1\2	g = 7\16	g = 4\10, 5\12, 6\14	3g-1	1\2-g
3L5s	5\8 < g < 2\3	g = 31\48	g = 7\11, 9\14, 11\17	5g-3	2-3g
4L4s	1\8 < g < 1\4	g = 3\16	g = 2\12, 3\16, 4\20	g	1\4-g
5L3s	3\8 < g < 2\5	g = 31\80	g = 5\13, 7\18, 9\23	3g-1	2-5g
6L2s	1\8 < g < 1\6	g = 7\48	g = 2\14, 3\20, 4\26	g	1\2-3g
7L1s	1\8 < g < 1\7	g = 15\112	g = 2\15, 3\22, 4\29	g	1-7g

9

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
1L8s	8\9 < g < 1	g = 17\18	g = 9\10, 10\11, 11\12	8g-7	1-g
2L7s	4\9 < g < 1\2	g = 17\36	g = 5\11, 6\13, 7\15	7g-3	1-2g
3L6s	2\9 < g < 1\3	g = 5\18	g = 3\12, 4\15, 5\18	2g-1\3	1\3-g
4L5s	2\9 < g < 1\4	g = 17\72	g = 3\13, 4\17, 5\21	5g-1	1-4g
5L4s	7\9 < g < 4\5	g = 71\90	g = 11\14, 15\19, 18\23	4g-3	4-5g
6L3s	1\9 < g < 1\6	g = 5\36	g = 2\15, 3\21, 4\27	g	1\3-2g
7L2s	5\9 < g < 4\7	g = 71\126	g = 9\16, 10\23, 17\30	2g-1	4-7g
8L1s	1\9 < g < 1\8	g = 17\144	g = 2\17, 3\25, 4\33	g	1-8g

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
2L8s	4\10 < g < 1\2	g = 9\20	g = 5\12, 6\14, 7\16	4g-3\2	1\2-g
3L7s	3\10 < g < 1\3	g = 19\60	g = 4\13, 5\16, 6\19	7g-2	1-3g
4L6s	2\10 < g < 1\4	g = 9\40	g = 3\14, 4\18, 5\22	3g-1\2	1\2-2g
5L5s	1\10 < g < 1\5	g = 3\20	g = 2\15, 3\20, 4\25	g	1\5-g
6L4s	3\10 < g < 2\6	g = 19\60	g = 5\16, 7\22, 9\28	2g-1\2	1-3g
7L3s	7\10 < g < 5\7	g = 99\140	g = 12\17, 17\24, 22\31	3g-2	5-7g
8L2s	1\10 < g < 1\8	g = 9\80	g = 2\18, 3\26, 4\34	g	1\2-4g
9L1s	1\10 < g < 1\9	g = 19\180	g = 2\19, 3\28, 4\37	g	1-9g

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
2L9s	5\11 < g < 1\2	g = 21\44	g = 6\13, 7\15, 8\17	9g-4	1-2g
3L8s	7\11 < g < 2\3	g = 43\66	g = 9\14, 11\17, 13\20	8g-5	2-3g
4L7s	8\11 < g < 3\4	g = 65\88	g = 11\15, 14\19, 17\23	7g-5	3-4g
5L6s	2\11 < g < 1\5	g = 21\110	g = 3\16, 4\21, 5\26	6g-1	1-5g
6L5s	9\11 < g < 5\6	g = 109\132	g = 14\17, 19\23, 24\29	5g-4	5-6g
7L4s	3\11 < g < 2\7	g = 43\154	g = 5\18, 7\25, 9\32	4g-1	2-7g
8L3s	4\11 < g < 3\8	g = 65\176	g = 7\19, 10\27, 13\35	3g-1	3-8g
9L2s	6\11 < g < 5\9	g = 109\198	g = 11\20, 16\29, 21\38	2g-1	5-9g
10L1s	1\11 < g < 1\10	g = 21\220	g = 2\21, 3\31, 4\41	g	1-10g

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
2L10s	5\12 < g < 1\2	g = 11\24	g = 6\14, 7\16, 8\18	5g-2	1\2-g
3L9s	3\12 < g < 1\3	g = 7\24	g = 4\15, 5\18, 6\21	3g-2\3	1\3-g
4L8s	2\12 < g < 1\4	g = 5\24	g = 3\16, 4\20, 5\24	2g-1\4	1\4-g
5L7s	7\12 < g < 3\5	g = 71\120	g = 10\17, 13\22, 16\27	7g-4	3-5g
6L6s	1\12 < g < 1\6	g = 3\24	g = 2\18, 3\24, 4\30	g	1\6-g
7L5s	5\12 < g < 3\7	g = 71\168	g = 8\19, 11\26, 14\33	5g-2	3-7g
8L4s	1\12 < g < 1\8	g = 5\48	g = 2\20, 3\28, 4\36	g	1\4-2g
9L3s	1\12 < g < 1\9	g = 7\72	g = 2\21, 3\30, 4\39	g	1\3-3g
10L2s	1\12 < g < 1\10	g = 11\120	g = 2\22, 3\32, 4\42	g	1\2-5g
11L1s	1\12 < g < 1\11	g = 23\264	g = 2\23, 3\34, 4\45	g	1-11g

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
2L11s	6\13 < g < 1\2	g = 25\52	g = 7\15, 8\17, 9\19	11g-5	1-2g
3L10s	4\13 < g < 1\3	g = 25\78	g = 5\16, 6\19, 7/22	10g-3	1-3g
4L9s	3\13 < g < 1\4	g = 25\104	g = 4\17, 5\21, 6\25	9g-2	1-4g
5L8s	5\13 < g < 2\5	g = 51\130	g = 7\18, 9\23, 11\28	8g-3	2-5g
6L7s	2\13 < g < 1\6	g = 25\156	g = 3\19, 4\25, 5\31	7g-1	1-6g
7L6s	11\13 < g < 6\7	g = 155\182	g = 17\20, 23\27, 29\34	6g-5	6-7g
8L5s	8\13 < g < 5\8	g = 129\208	g = 13\21, 18\29, 23\37	5g-3	5-8g
9L4s	10\13 < g < 7\9	g = 181\234	g = 17\22, 24\31, 31\40	4g-3	7-9g
10L3s	9\13 < g < 7\10	g = 181\260	g = 16\23, 23\33, 30\43	3g-2	7-10g
11L2s	7\13 < g < 6\11	g = 155\286	g = 13\24, 19\35, 25\46	2g-1	6-11g
12L1s	1\13 < g < 1\12	g = 25\312	g = 2\25, 3\37, 4\49	g	1-12g

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
2L12s	6\14 < g < 1\2	g = 13\28	g = 7\16, 8\18, 9\20	6g-5\2	1\2-g
3L11s	9\14 < g < 2\3	g = 55\84	g = 11\17, 13\20, 15\23	11g-7	2-3g
4L10s	3\14 < g < 1\4	g = 13\56	g = 4\18, 5\22, 6\26	5g-1	1\2-2g
5L9s	11\14 < g < 4\5	g = 111\140	g = 15\19, 19\24, 23\29	9g-7	4-5g
6L8s	2\14 < g < 1\6	g = 13\84	g = 3\20, 4\26, 5\32	4g-1\2	1\2-3g
7L7s	1\14 < g < 1\7	g = 3\28	g = 2\21, 3\28, 4\35	g	1\7-g
8L6s	5\14 < g < 3\8	g = 41\112	g = 8\22, 11\30, 14\38	3g-1	3\2-4g
9L5s	3\14 < g < 2\9	g = 55\252	g = 5\23, 7\32, 9\41	5g-1	2-9g
10L4s	4\14 < g < 3\10	g = 41\140	g = 7\24, 10\34, 13\44	2g-1\2	3\2-5g
11L3s	5\14 < g < 4\11	g = 111\308	g = 9\25, 13\36, 17\47	3g-1	4-11g
12L2s	1\14 < g < 1\12	g = 13\168	g = 2\26, 3\38, 4\50	g	1\2-6g
13L1s	1\14 < g < 1\13	g = 27\364	g = 2\27, 3\40, 4\53	g	1-13g

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
2L13s	7\15 < g < 1\2	g = 29\60	g = 8\17, 9\19, 10\21	13g-6	1-2g
3L12s	4\15 < g < 1\3	g = 9\30	g = 5\18, 6\21, 7\24	4g-1	1\3-g
4L11s	11\15 < g < 3\4	g = 89\120	g = 14\19, 17\23, 20\27	11g-8	3-4g
5L10s	2\15 < g < 1\5	g = 5\30	g = 3\20, 4\25, 5\30	2g-1\5	1\5-g
6L9s	2\15 < g < 1\6	g = 9\60	g = 3\21, 4\27, 5\33	3g-1\3	1\3-2g
7L8s	2\15 < g < 1\7	g = 29\210	g = 3\22, 4\29, 5\36	8g-1	1-7g
8L7s	13\15 < g < 7\8	g = 209\240	g = 20\23, 27\31, 34\39	7g-6	7-8g
9L6s	3\15 < g < 2\9	g = 19\90	g = 5\24, 7\33, 9\42	2g-1\3	2\3-3g
10L5s	1\15 < g < 1\10	g = 5\60	g = 2\25, 3\35, 4\45	g	1\5-2g
11L4s	4\15 < g < 3\11	g = 89\330	g = 7\26, 10\37, 13\48	4g-1	3-11g
12L3s	1\15 < g < 1\12	g = 9\120	g = 2\27, 3\39, 4\51	g	1\3-4g
13L2s	8\15 < g < 7\13	g = 209\390	g = 15\28, 22\41, 29\54	2g-1	7-13g
14L1s	1\15 < g < 1\14	g = 29\420	g = 2\29, 3\43, 4\57	g	1-14g

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
2L14s	7\16 < g < 1\2	g = 15\32	g = 8\18, 9\20, 10\22	7g-3	1\2-g
3L13s	5\16 < g < 1\3	g = 31\96	g = 6\19, 7\22, 8\25	13g-4	1-3g
4L12s	3\16 < g < 1\4	g = 7\32	g = 4\20, 5\24, 6\28	3g-1\2	1\4-g
5L11s	3\16 < g < 1\5	g = 31\160	g = 4\21, 5\26, 6\31	11g-2	1-5g
6L10s	5\16 < g < 2\6	g = 31\96	g = 7\22, 9\28, 11\34	5g-3\2	1-3g
7L9s	9\16 < g < 4\7	g = 127\224	g = 13\23, 17\30, 21\37	9g-5	4-7g
8L8s	1\16 < g < 1\8	g = 3\32	g = 2\24, 3\32, 4\40	g	1\8-g
9L7s	7\16 < g < 4\9	g = 127\286	g = 11\25, 15\34, 19\43	7g-3	4-9g
10L6s	3\16 < g < 2\10	g = 31\160	g = 5\26, 7\36, 8\46	3g-1\2	1-5g
11L5s	13\16 < g < 9\11	g = 287\352	g = 22\27, 31\38, 40\49	5g-4	9-11g
12L4s	1\16 < g < 1\12	g = 7\48	g = 2\28, 3\40, 4\52	g	1\4-3g
13L3s	11\16 < g < 9\13	g = 287\416	g = 20\29, 29\42, 38\55	3g-2	9-13g
14L2s	1\16 < g < 1\14	g = 15\224	g = 2\30, 3\44, 4\58	g	1\2-7g
15L1s	1\16 < g < 1\15	g = 31\480	g = 2\31, 3\46, 4\61	g	1-15g

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
2L15s	8\17 < g < 1\2	g = 33\68	g = 9\19, 10\21, 11\23	15g-7	1-2g
3L14s	11\17 < g < 2\3	g = 67\102	g = 13\20, 15\23, 17\26	14g-9	2-3g
4L13s	4\17 < g < 1\4	g = 33\136	g = 5\21, 6\25, 7\29	13g-3	1-4g
5L12s	10\17 < g < 3\5	g = 101\170	g = 13\22, 16\27, 19\32	12g-7	3-5g
6L11s	14\17 < g < 5\6	g = 169\204	g = 19\23, 24\29, 29\35	11g-9	5-6g
7L10s	12\17 < g < 5\7	g = 169\238	g = 17\24, 22\31, 27\38	10g-7	5-7g
8L9s	2\17 < g < 1\8	g = 33\272	g = 3\25, 4\33, 5\41	9g-1	1-8g
9L8s	15\17 < g < 8\9	g = 271\306	g = 23\26, 31\35, 39\44	8g-7	8-9g
10L7s	5\17 < g < 3\10	g = 101\340	g = 8\27, 11\37, 14\47	7g-2	3-10g
11L6s	3\17 < g < 2\11	g = 67\374	g = 5\28, 7\39, 9\50	6g-1	2-11g
12L5s	7\17 < g < 5\12	g = 169\408	g = 12\29, 17\41, 22\53	5g-2	5-12g
13L4s	13\17 < g < 10\13	g = 339\442	g = 23\30, 33\43, 43\56	4g-3	10-13g
14L3s	6\17 < g < 5\14	g = 169\476	g = 11\31, 16\45, 21\59	3g-1	5-14g
15L2s	9\17 < g < 8\15	g = 271\510	g = 17\32, 25\47, 33\62	2g-1	8-15g
16L1s	1\17 < g < 1\16	g = 33\544	g = 2\33, 3\49, 4\65	g	1-16g

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
2L16s	8\18 < g < 1\2	g = 17\36	g -= 9\20, 10\22, 11\24	8g-7\2	1\2-g
3L15s	5\18 < g < 1\3	g = 11\36	g = 6\21, 7\24, 8\27	5g-4\3	1\3-g
4L14s	4\18 < g < 1\4	g = 17\72	g = 5\22, 6\26, 7\30	7g-3\2	1\2-2g
5L13s	7\18 < g < 2\5	g = 71\180	g = 9\23, 11\28, 13\33	13g-5	2-5g
6L12s	2\18 < g < 1\6	g = 5\36	g = 3\24, 4\30, 5\36	2g-1\6	1\6-g
7L11s	5\18 < g < 2\7	g = 71\252	g = 7\25, 9\32, 11\39	11g-3	2-7g
8L10s	2\18 < g < 1\8	g = 17\144	g = 3\26, 4\34, 5\42	5g-1\2	1\2-4g
9L9s	1\18 < g < 1\9	g = 3\36	g = 2\27, 3\36, 4\45	g	1\9-g
10L8s	7\18 < g < 4\10	g = 71\180	g = 11\28, 15\38, 19\48	4g-3\2	2-5g
11L7s	13\18 < g < 8\11	g = 287\396	g = 21\29, 29\40, 37\51	7g-5	8-11g
12L6s	1\18 < g < 1\12	g = 5\72	g = 2\30, 3\42, 4\54	g	1\6-2g
13L5s	11\18 < g < 8\13	g = 287\468	g = 19\31, 27\44, 35\57	5g-3	8-13g
14L4s	5\18 < g < 4\14	g = 71\252	g = 9\32, 13\46, 17\60	2g-1\2	2-7g
15L3s	1\18 < g < 1\15	g = 11\180	g = 2\33, 3\48, 4\63	g	1\3-5g
16L2s	1\18 < g < 1\16	g = 17\288	g = 2\34, 3\50, 4\66	g	1\2-8g
17L1s	1\18 < g < 1\17	g = 35\618	g = 2\35, 3\52, 4\69	g	1-17g

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
2L17s	9\19 < g < 1\2	g = 37\76	g = 10\21, 11\23, 12\25	17g-8	1-2g
3L16s	6\19 < g < 1\3	g = 37\114	g = 7\22, 8\25, 10\31	16g-5	1-3g
4L15s	14\19 < g < 3\4	g = 113\152	g = 17\23, 20\27, 23\31	15g-11	3-4g
5L14s	15\19 < g < 4\5	g = 151\190	g = 19\24, 23\29, 27\34	14g-11	4-5g
6L13s	3\19 < g < 1\6	g = 37\228	g = 4\25, 5\31, 6/37	13g-2	1-6g
7L12s	8\19 < g < 3\7	g = 113\266	g = 11\26, 14\33, 17\40	12g-5	3-7g
8L11s	7\19 < g < 3\8	g = 113\304	g = 10\27, 13\35, 16\43	11g-4	3-8g
9L10s	2\19 < g < 1\9	g = 37\342	g = 3\28, 4\37, 5\46	10g-1	1-9g
10L9s	17\19 < g < 9\10	g = 341\380	g = 26\29, 35\39, 44\49	9g-8	9-10g
11L8s	12\19 < g < 7\11	g = 265\418	g = 19\30, 26\41, 33\52	8g-5	7-11g
12L7s	11\19 < g < 7\12	g = 265\456	g = 18\31, 25\43, 32\55	7g-4	7-12g
13L6s	16\19 < g < 11\13	g = 417\494	g = 27\32, 38\45, 49\58	6g-5	11-13g
14L5s	4\19 < g < 3\14	g = 113\532	g = 7\33, 10\47, 13\61	5g-1	3-14g
15L4s	5\19 < g < 4\15	g = 151\570	g = 9\34, 13\49, 17\64	4g-1	4-15g
16L3s	13\19 < g < 11\16	g = 417\608	g = 24\35, 35\51, 46\67	3g-2	11-16g
17L2s	10\19 < g < 9\17	g = 341\646	g = 19\36, 28\53, 37\70	2g-1	9-17g
18L1s	1\19 < g < 1\18	g = 37\684	g = 2\37, 3\55, 4\73	g	1-18g

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
2L18s	9\20 < g < 1\2	g = 19\40	g = 10\22, 11\24, 12\26	9g-4	1\2-g
3L17s	13\20 < g < 2\3	g = 79\120	g = 15\23, 17\26, 20\29	17g-11	2-3g
4L16s	4\20 < g < 1\4	g = 9\40	g = 5\24, 6\28, 7\32	4g-3\4	1\4-g
5L15s	3\20 < g < 1\5	g = 7\40	g = 4\25, 5\30, 6\35	3g-2\5	1\5-g
6L14s	3\20 < g < 1\6	g = 19\120	g = 4\26, 5\32, 6\38	7g-1	1\2-3g
7L13s	17\20 < g < 6\7	g = 239\280	g = 23\27, 29\34, 35\41	13g-11	6-7g
8L12s	2\20 < g < 1\8	g = 9\80	g = 3\28, 4\36, 5\44	3g-1\4	1\4-2g
9L11s	11\20 < g < 5\9	g = 199\360	g = 16\29, 21\38, 26\47	11g-6	5-9g
10L10s	1\20 < g < 1\10	g = 3\40	g = 2\30, 3\40, 4\50	g	1\10-g
11L9s	9\20 < g < 5\11	g = 199\440	g = 14\31, 19\42, 24\53	9g-4	5-11g
12L8s	3\20 < g < 2\12	g = 19\120	g = 5\32, 7\44, 9\56	2g-1\4	1\2-3g
13L7s	3\20 < g < 2\13	g = 79\520	g = 5\33, 7\46, 9\59	7g-1	2-13g
14L6s	7\20 < g < 5\14	g = 99\280	g = 12\34, 17\48, 22\62	3g-1	5\2-7g
15L5s	1\20 < g < 1\15	g = 7\120	g = 2\35, 3\50, 4\65	g	1\5-3g
16L4s	1\20 < g < 1\16	g = 9\160	g = 2\36, 3\52, 4\68	g	1\4-4g
17L3s	7\20 < g < 6\17	g = 239\680	g = 13\37, 19\54, 25\71	3g-1	6-17g
18L2s	1\20 < g < 1\18	g = 19\360	g = 2\38, 3\56, 4\74	g	1\2-9g
19L1s	1\20 < g < 1\19	g = 39\760	g = 2\39, 3\58, 4\77	g	-19g+1

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
2L19s	10\21 < g < 1\2	g = 41\84	g = 11\23, 12\25, 13\27	19g-9	1-2g
3L18s	6\21 < g < 1\3	g = 13\42	g = 7\24, 8\27, 9\30	6g-5\3	1\3-g
4L17s	5\21 < g < 1\4	g = 41\168	g = 6\25, 7\29, 8\33	17g-2	1-4g
5L16s	4\21 < g < 1\5	g = 41\210	g = 5\26, 6\31, 7\36	16g-3	1-5g
6L15s	3\21 < g < 1\6	g = 13\84	g = 4\27, 5\33, 6\39	5g-2\3	1\3-2g
7L14s	2\21 < g < 1\7	g = 5\42	g = 3\28, 4\35, 5\42	2g-1\7	1\7-g
8L13s	13\21 < g < 5\8	g = 209\336	g = 18\29, 23\37, 28\45	13g-8	5-8g
9L12s	2\21 < g < 1\9	g = 13\126	g = 3\30, 4\39, 5\48	4g-1\3	1\3-3g
10L11s	2\21 < g < 1\10	g = 41\420	g = 3\31, 4\41, 5\51	11g-1	1-10g
11L10s	19\21 < g < 10\11	g = 419\462	g = 29\32, 39\43, 49\54	10g-9	10-11g
12L9s	5\21 < g < 3\12	g = 41\168	g = 8\33, 11\45, 14\57	3g-2\3	1-4g
13L8s	8\21 < g < 5\13	g = 209\546	g = 13\34, 18\47, 23\70	8g-3	5-13g
14L7s	1\21 < g < 1\14	g = 5\84	g = 2\35, 3\49, 4\63	g	1\7-2g
15L6s	4\21 < g < 3\15	g = 41\210	g = 7\36, 10\51, 13\66	2g-1\3	1-5g
16L5s	17\21 < g < 13\16	g = 545\672	g = 30\37, 43\53, 56\69	5g-4	13-16g
17L4s	16\21 < g < 13\17	g = 545\714	g = 29\38, 42\55, 55\72	4g-3	13-17g
18L3s	1\21 < g < 1\18	g = 13\252	g = 2\39, 3\57, 4\75	g	1\3-6g
19L2s	11\21 < g < 10\19	g = 419\798	g = 21\40, 31\59, 41\78	2g-1	10-19g
20L1s	1\21 < g < 1\20	g = 41\840	g = 2\41, 3\61, 4/81	g	1-20g

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
2L20s	10\22 < g < 1\2	g = 21\44	g = 11\24, 12\26, 13\28	10g-9\2	1\2-g
3L19s	7\22 < g < 1\3	g = 43\132	g = 8\25, 9\28, 10\31	19g-6	1-3g
4L18s	5\22 < g < 1\4	g = 21\88	g = 6\26, 7\30, 8\34	9g-2	1\2-2g
5L17s	13\22 < g < 3\5	g = 131\220	g = 16\27, 19\32, 22\37	17g-10	3-5g
6L16s	7\22 < g < 2\6	g = 43\132	g = 9\28, 11\34, 13\40	8g-5\2	1-3g
7L15s	3\22 < g < 1\7	g = 43\308	g = 4\29, 5\36, 6\43	15g-2	1-7g
8L14s	8\22 < g < 3\8	g = 65\176	g = 11\30, 14\38, 17\46	7g-5\2	3\2-4g
9L13s	17\22 < g < 7\9	g = 307\396	g = 24\31, 31\40, 38\49	13g-10	7-9g
10L12s	2\22 < g < 1\10	g = 21\220	g = 3\32, 4\42, 5\52	6g-1\2	1\2-5g
11L11s	1\22 < g < 1\11	g = 3\44	g = 2\33, 3\44, 4\55	g	1\11-g
12L10s	9\22 < g < 5\12	g = 109\264	g = 14\34, 19\46, 24\58	5g-2	5\2-6g
13L9s	5\22 < g < 3\13	g = 131\572	g = 8\35, 11\48, 14\61	9g-2	3-13g
14L8s	3\22 < g < 2\14	g = 43\308	g = 5\36, 7\50, 9\64	4g-1\2	1-7g
15L7s	19\22 < g < 13\15	g = 571\660	g = 32\37, 45\52, 58\67	7g-6	13-15g
16L6s	4\22 < g < 3\16	g = 65\352	g = 7\38, 10\54, 13\70	3g-1\2	3\2-8g
17L5s	9\22 < g < 7\17	g = 207\748	g = 16\39, 23\56, 30\73	5g-2	7-17g
18L4s	6\22 < g < 5\18	g = 109\396	g = 11\40, 16\58, 21\76	2g-1\2	5\2-9g
19L3s	15\22 < g < 13\19	g = 571\836	g = 28\41, 41\60, 54\79	3g-2	13-19g
20L2s	1\22 < g < 1\20	g = 21\440	g = 2\42, 3\62, 4\72	g	1\2-10g
21L1s	1\22 < g < 1\21	g = 43\924	g = 2\43, 3\64, 4\85	g	1-21g

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
2L21s	11\23 < g < 1\2	g = 45\92	g = 12\25, 13\27, 14\29	21g-10	1-2g
3L20s	15\23 < g < 2\3	g = 91\138	g = 17\26, 19\29, 21\32	20g-13	1-3g
4L19s	17\23 < g < 3\4	g = 137\184	g = 20\27, 23\31, 26\35	19g-14	3-4g
5L18s	9\23 < g < 2\5	g = 91\230	g = 11\28, 13\33, 15\38	18g-7	2-5g
6L17s	19\23 < g < 5\6	g = 229\276	g = 24\29, 29\35, 34\41	17g-15	1-6g
7L16s	13\23 < g < 4\7	g = 183\322	g = 17\30, 21\37, 25\44	16g-9	4-7g
8L15s	20\23 < g < 7\8	g = 321\368	g = 27\31, 34\39, 41\47	15g-13	7-8g
9L14s	5\23 < g < 2\9	g = 91\414	g = 7\32, 9\41, 11\50	14g-7	11-9g
10L13s	16\23 < g < 7\10	g = 321\460	g = 23\33, 30\43, 37\53	13g-9	7-10g
11L12s	2\23 < g < 1\11	g = 45\506	g = 3\34, 4\45, 5\56	12g-1	1-11g
12L11s	21\23 < g < 11\12	g = 505\552	g = 32\35, 43\47, 54\59	11g-10	11-12g
13L10s	7\23 < g < 4\13	g = 183\598	g = 11\36, 15\49, 19\62	10g-3	4-13g
14L9s	18\23 < g < 11\14	g = 505\644	g = 29\37, 40\51, 51\65	9g-7	11-14g
15L8s	3\23 < g < 2\15	g = 91\690	g = 5\38, 7\53, 9\68	8g-1	2-15g
16L7s	10\23 < g < 7\16	g = 321\736	g = 17\39, 24\55, 31\71	7g-3	7-16g
17L6s	4\23 < g < 3\17	g = 137\782	g = 7\40, 10\57, 13\74	6g-1	3-17g
18L5s	14\23 < g < 11\18	g = 505\828	g = 25\41, 36\59, 47\77	5g-4	11-18g
19L4s	6\23 < g < 5\19	g = 229\874	g = 11\42, 16\61, 21\80	4g-1	5-19g
20L3s	8\23 < g < 7\20	g = 321\920	g = 15\43, 22\63, 29\83	3g-1	13-20g
21L2s	12\23 < g < 11\21	g = 505\966	g = 23\44, 34\65, 45\86	2g-1	1-21g
22L1s	1\23 < g < 1\22	g = 45\1012	g = 2\45, 3\67, 4\89	g	1-22g

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
2L22s	11\24 < g < 1\2	g = 23\48	g = 12\26, 13\28, 14\30	1/2-g	11g-5
3L21s	7\24 < g < 1\3	g = 15\48	g = 8\27, 9\30, 10\33	2/3-2g	g-1/3
4L20s	5\24 < g < 1\4	g = 11\48	g = 6\28, 7\32, 8\36	5g-1	1/4-g
5L19s	19\24 < g < 4\5	g = 191\240	g = 23\29, 27\34, 31\39	19g-15	4-5g
6L18s	3\24 < g < 1\6	g = 7\48	g = 4\30, 5\36, 6\42	3g-1\3	1\6-g
7L17s	17\24 < g < 5\7	g = 239\336	g = 22\31, 27\38, 32\45	5-17g	7g-2
8L16s	2\24 < g < 1\8	g = 5\48	g = 3\32, 4\40, 5\48	2g-1\8	1\8-g
9L15s	5\24 < g < 2\9	g = 31\144	g = 7\33, 9\42, 11\51	5g-1	2\3-3g
10L14s	7\24 < g < 3\10	g = 71\240	g = 10\34, 13\44, 16\54	7g-2	3\2-5g
11L13s	13\24 < g < 6\11	g = 287\528	g = 19\35, 25\46, 31\57	13g-7	6-11g
12L12s	1\24 < g < 1\12	g = 3\48	g = 2\36, 3\48, 4\60	g	1\12-g
13L11s	11\24 < g < 6\13	g = 287\624	g = 17\37, 23\50, 29\63	11g-5	6-13g
14L10s	17\24 < g < 10\14	g = 239\336	g = 27\38, 37\52, 47\66	3\2-5g	7g-2
15L9s	3\24 < g < 2\15	g = 31\240	g = 5\39, 7\54, 9\69	3g-1\3	2\3-5g
16L8s	1\24 < g < 1\16	g = 5\96	g = 2\40, 3\56, 4\72	g	1\8-2g
17L7s	7\24 < g < 5\17	g = 239\816	g = 12\41, 17\58, 22\75	4-7g	17g-12
18L6s	1\24 < g < 1\18	g = 7\144	g = 2\42, 3\60, 4\78	g	1\6-3g
19L5s	5\24 < g < 4\19	g = 191\912	g = 9\43, 13\62, 17\81	5g-5	4-19g
20L4s	1\24 < g < 1\20	g = 11\240	g = 2\44, 3\64, 4\84	g	1\4-5g
21L3s	1\24 < g < 1\21	g = 15\336	g = 2\45, 3\66, 4\87	g	1\3-7g
22L2s	1\24 < g < 1\22	g = 23\264	g = 2\46, 3\68, 4\90	g	1\2-11g
23L1s	1\24 < g < 1\23	g = 47\1104	g = 2\47, 3\70, 4\93	g	1-23g

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
2L23s	12\25 < g < 1\2	g = 49\100	g = 13\27, 14\29, 15\31	23g-11	1-2g
3L22s	8\25 < g < 1\3	g = 49\150	g = 9\28, 10\31, 11\34	22g-7	1-3g
4L21s	6\25 < g < 1\4	g = 49\200	g = 7\29, 8\33, 9\37	21g-5	1-4g
5L20s	4\25 < g < 1\5	g = 9\50	g = 5\30, 6\35, 7\40	4g-3\5	1\5-g
6L19s	4\25 < g < 1\6	g = 49\300	g = 5\31, 6\37, 7\43	19g-3	1-6g
7L18s	7\25 < g < 2\7	g = 99\350	g = 9\32, 11\39, 13\46	18g-5	2-7g
8L17s	3\25 < g < 1\8	g = 49\400	g = 4\33, 5\41, 6\47	17g-2	1-8g
9L16s	11\25 < g < 4\9	g = 199\450	g = 15\34, 19\43, 23\52	16g-7	-9g+4
10L15s	2\25 < g < 1\10	g = 9\100	g = 3\35, 4\45, 5\55	3g-1\5	1\5-2g
11L14s	9\25 < g < 4\11	g = 199\550	g = 13\36, 17\47, 21\58	14g-5	-11g+4
12L13s	2\25 < g < 1\12	g = 49\600	g = 3\37, 4\49, 5\61	13g-1	1-12g
13L12s	23\25 < g < 12\13	g = 599\650	g = 35\38, 47\51, 59\64	12g-11	12-13g
14L11s	16\25 < g < 9\14	g = 449\700	g = 25\39, 34\53, 43\67	11g-7	-14g+9
15L10s	3\25 < g < 2\15	g = 19\150	g = 5\40, 7\55, 9\70	2g-1\5	2\5-3g
16L9s	14\25 < g < 9\16	g = 449\800	g = 23\41, 32\57, 41\73	9g-5	9-16g
17L8s	22\25 < g < 15\17	g = 749\850	g = 37\42, 52\59, 67\76	8g-7	15-17g
18L7s	18\25 < g < 13\18	g = 649\900	g = 31\43, 44\61, 57\79	7g-5	13-18g
19L6s	21\25 < g < 16\19	g = 799\950	g = 37\44, 53\63, 69\82	6g-5	16-19g
20L5s	1\25 < g < 1\20	g = 9\200	g = 2\45, 3\65, 4\85	g	1\5-4g
21L4s	16\21 < g < 19\25	g = 799\1050	g = 35\46, 51\67, 71\88	4g-3	16-21g
22L3s	17\25 < g < 15\22	g = 749\1100	g = 32\47, 47\69, 62\91	3g-2	15-22g
23L2s	13\25 < g < 12\23	g = 599\1150	g = 25\48, 37\71, 49\94	2g-1	11-23g
24L1s	1\25 < g < 1\24	g = 49\1200	g = 2\49, 3\73, 4\97	g	1-24g

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
2L24s	12\26 < g < 1\2	g = 25\52	g = 13\28, 14\30, 15\32	12g-11\2	1\2-g
3L23s	17\26 < g < 2\3	g = 103\156	g = 19\29, 21\32, 23\35	23g-15	2-3g
4L22s	6\26 < g < 1\4	g = 25\104	g = 7\30, 8\34, 9\38	11g-5\2	1\2-2g
5L21s	5\26 < g < 1\5	g = 51\260	g = 6\31, 7\36, 8\41	21g-4	1-5g
6L20s	4\26 < g < 1\6	g = 25\156	g = 5\32, 6\38, 7\44	10g-3\2	1\2-3g
7L19s	11\26 < g < 3\7	g = 155\364	g = 14\33, 17\40, 20\47	19g-8	3-7g
8L18s	3\26 < g < 1\8	g = 25\208	g = 4\34, 5\42, 6\50	9g-1	1\2-4g
9L17s	23\26 < g < 8\9	g = 415\468	g = 31\35, 39\44, 47\53	17g-15	8-9g
10L16s	5\26 < g < 2\10	g = 51\260	g = 7\36, 9\46, 11\56	8g-3\2	1-5g
11L15s	7\26 < g < 3\11	g = 155\572	g = 10\37, 13\48, 16\59	15g-4	3-11g
12L14s	2\26 < g < 1\12	g = 25\312	g = 3\38, 4\50, 5\62	7g-1\2	1\2-6g
13L13s	1\26 < g < 1\13	g = 3\52	g = 2\39, 3\52, 4\65	g	1\13-g
14L12s	11\26 < g < 6\14	g = 155\364	g = 17\40, 23\54, 29\68	6g-5\2	3-7g
15L11s	19\26 < g < 11\15	g = 571\780	g = 30\41, 41\56, 52\71	11g-8	11-15g
16L10s	8\26 < g < 5\16	g = 129\416	g = 13\42, 18\58, 23\74	13\2-8g	5g-4
17L9s	3\26 < g < 2\17	g = 103\884	g = 5\43, 7\60, 9\77	9g-1	2-17g
18L8s	10\26 < g < 7\18	g = 181\468	g = 17\44, 24\62, 31\80	4g-7\2	7-9g
19L7s	15\26 < g < 11\19	g = 571\988	g = 26\45, 37\64, 48\83	7g-4	11-19g
20L6s	9\26 < g < 7\20	g = 181\520	g = 16\46, 23\66, 30\86	3g-1	7\2-10g
21L5s	21\26 < g < 17\21	g = 883\1092	g = 38\47, 55\68, 72\89	5g-4	16-21g
22L4s	7\26 < g < 6\22	g = 155\572	g = 13\48, 19\70, 25\92	2g-1\2	3-11g
23L3s	9\26 < g < 8\23	g = 415\1196	g = 17\49, 25\72, 33/95	3g-1	8-23g
24L2s	1\26 < g < 1\24	g = 25\312	g = 2\50, 3\74, 4\98	g	1\2-12g
25L1s	1\26 < g < 1\25	g = 51\1300	g = 2\51, 3\76, 4\101	g	1-25g

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
2L25s	13\27 < g < 1\2	g = 53\108	g = 14\29, 15\31, 16\33	25g-12	1-2g
3L24s	8\27 < g < 1\3	g = 17\54	g = 9\30, 10\33, 11\36	8g-7\3	1-3g
4L23s	20\27 < g < 3\4	g = 161\216	g = 23\31, 26\35, 29\39	23g-17	3-4g
5L22s	16\27 < g < 3\5	g = 161\270	g = 19\32, 22\37, 25\42	22g-13	3-5g
6L21s	4\27 < g < 1\6	g = 17\108	g = 5\33, 6\39, 7\45	7g-1	1\3-2g
7L20s	23\27 < g < 6\7	g = 323\378	g = 29\34, 35\41, 41\48	20g-17	6-7g
8L19s	10\27 < g < 3\8	g = 161\432	g = 13\35, 16\43, 19\51	19g-7	3-8g
9L18s	2\27 < g < 1\9	g = 5\54	g = 3\36, 4\45, 5\54	2g-1\9	1\9-g
10L17s	8\27 < g < 3\10	g = 161\540	g = 11\37, 14\47, 17\57	17g-5	3-10g
11L16s	22\27 < g < 9\11	g = 485\594	g = 31\38, 40\49, 49\60	16g-13	9-11g
12L15s	2\27 < g < 1\12	g = 17\216	g = 3\39, 4\51, 5\63	5g-1\3	1\3-4g
13L14s	2\27 < g < 1\13	g = 53\702	g = 3\40, 4\53, 5\66	14g-1	1-13g
14L13s	25\27 < g < 13\14	g = 701\756	g = 38\41, 51\55, 64\69	13g-12	13-14g
15L12s	7\27 < g < 4\15	g = 71\270	g = 11\42, 15\57, 19\72	4g-4	14\3-5g
16L11s	5\27 < g < 3\16	g = 161\864	g = 8\43, 11\59, 14\75	11g-2	3-16g
17L10s	19\27 < g < 12\17	g = 647\918	g = 31\44, 43\61, 55\78	10g-7	12-17g
18L9s	1\27 < g < 1\18	g = 5\108	g = 2\45, 3\63, 4\81	g	1\9-2g
19L8s	17\27 < g < 12\19	g = 647\1026	g = 29\46, 41\65, 53\84	8g-5	12-19g
20L7s	4\27 < g < 3\20	g = 161\1080	g = 7\47, 10\67, 13\87	7g-1	3-20g
21L6s	5\27 < g < 4\21	g = 71\378	g = 9\48, 13\69, 17\90	2g-1\3	4-7g
22L5s	11\27 < g < 9\22	g = 485\1188	g = 20\49, 29\71, 38\93	5g-2	9-22g
23L4s	7\27 < g < 6\23	g = 323\1242	g = 13\50, 19\73, 25\96	4g-1	6-23g
24L3s	1\27 < g < 1\24	g = 17\432	g = 2\51, 3\75, 4\99	g	1\3-8g
25L2s	14\27 < g < 13\25	g = 701\1350	g = 27\52, 40\77, 53\102	2g-1	13-25g
26L1s	1\27 < g < 1\26	g = 53\1404	g = 2\53, 3\79, 4\105	g	1-26g

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
2L26s	13\28 < g < 1\2	g = 27\56	g = 14\30, 15\32, 16\34	13g-6	1\2-g
3L25s	9\28 < g < 1\3	g = 55\168	g = 10\31, 11\34, 12\37	25g-8	1-3g
4L24s	6\28 < g < 1\4	g = 13\56	g = 7\32, 8\36, 9\40	6g-5\4	1\4-g
5L23s	11\28 < g < 2\5	g = 111\280	g = 13\33, 15\38, 17\43	23g-9	2-5g
6L22s	9\28 < g < 2\6	g = 55\168	g = 11\34, 13\40, 15\46	11g-7\2	1-3g
7L21s	3\28 < g < 1\7	g = 7\56	g = 4\35, 5\42, 6\49	3g-2\7	1\7-g
8L20s	3\28 < g < 1\8	g = 13\112	g = 4\36, 5\44, 6\52	5g-1\2	1\4-2g
9L19s	3\28 < g < 1\9	g = 55\504	g = 4\37, 5\46, 6\55	19g-2	1-9g
10L18s	11\28 < g < 4\10	g = 111\280	g = 15\38, 19\48, 23\58	4g-7\2	2-5g
11L17s	5\28 < g < 2\11	g = 111\616	g = 7\39, 9\50, 11\61	17g-3	2-11g
12L16s	2\28 < g < 1\12	g = 13\168	g = 3\40, 4\52, 5\64	4g-1\4	1\4-3g
13L15s	15\28 < g < 7\13	g = 391\728	g = 22\41, 29\54, 36\67	15g-8	7-13g
14L14s	1\28 < g < 1\14	g = 3\56	g = 2\42, 3\56, 4\70	g	1\14-g
15L13s	13\28 < g < 7\15	g = 391\840	g = 20\43, 27\58, 34\73	13g-6	7-15g
16L12s	5\28 < g < 3\16	g = 41\224	g = 8\44, 11\60, 14\76	3g-1\2	3\4-4g
17L11s	23\28 < g < 14\17	g = 783\952	g = 37\45, 51\62, 65\79	11g-9	13-17g
18L10s	3\28 < g < 2\18	g = 55\504	g = 5\46, 7\64, 9\82	5g-1\2	1-9g
19L9s	25\28 < g < 17\19	g = 951\1064	g = 42\47, 59\66, 76\85	9g-8	17-19g
20L8s	4\28 < g < 3\20	g = 41\280	g = 7\48, 10\68, 13\88	2g-1\4	3\4-5g
21L7s	1\28 < g < 1\21	g = 7\168	g = 2\49, 3\70, 4\91	g	1\7-3g
22L6s	5\28 < g < 4\22	g = 111\616	g = 9\50, 13\72, 17\94	3g-1\2	2-11g
23L5s	17\28 < g < 14\23	g = 783\1288	g = 31\51, 45\74, 59\97	5g-3	14-23g
24L4s	1\28 < g < 1\24	g = 13\336	g = 2\52, 3\76, 4\100	g	1\4-6g
25L3s	19\28 < g < 17\25	g = 951\1400	g = 36\53, 53\78, 70\103	3g-2	17-25g
26L2s	15\28 < g < 14\26	g = 391\728	g = 29\54, 43\80, 57\106	g-1\2	19\2-13g
27L1s	1\28 < g < 1\27	g = 55\1512	g = 2\55, 3\82, 4\109	g	1-27g

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
2L27s	14\29 < g < 1\2	g = 57\116	g = 15\31, 16\33, 17\35	27g-13	1-2g
3L26s	19\29 < g < 2\3	g = 115\174	g = 21\32, 23\35, 25\38	26g-17	2-3g
4L25s	7\29 < g < 1\4	g = 57\232	g = 8\33, 9\37, 10\41	25g-6	1-4g
5L24s	23\29 < g < 4\5	g = 231\290	g = 27\34, 31\39, 35\44	24g-19	4-5g
6L23s	24\29 < g < 5\6	g = 289\348	g = 29\35, 34\41, 39\47	23g-19	5-6g
7L22s	4\29 < g < 1\7	g = 57\406	g = 5\36, 6\43, 7\50	22g-3	1-7g
8L21s	18\29 < g < 5\8	g = 289\464	g = 23\37, 28\45, 33\53	21g-13	5-8g
9L20s	16\29 < g < 5\9	g = 289\522	g = 21\38, 26\47, 31\56	20g-11	5-9g
10L19s	26\29 < g < 9\10	g = 521\580	g = 35\39, 44\49, 53\59	19g-17	9-10g
11L18s	21\29 < g < 8\11	g = 463\638	g = 29\40, 37\51, 45\62	18g-13	8-11g
12L17s	12\29 < g < 5\12	g = 289\696	g = 17\41, 22\53, 27\65	17g-7	5-12g
13L16s	20\29 < g < 9\13	g = 521\754	g = 29\42, 38\55, 47\68	16g+11	9-13g
14L15s	2\29 < g < 1\14	g = 57\812	g = 3\43, 4\57, 5\71	15g-1	1-14g
15L14s	27\29 < g < 14\15	g = 811\870	g = 41\44, 55\59, 69\74	14g-13	14-15g
16L13s	9\29 < g < 5\16	g = 289\928	g = 14\45, 19\61, 24\77	13g-4	5-16g
17L12s	17\29 < g < 10\17	g = 579\986	g = 27\46, 37\63, 47\80	12g-5	7-17g
18L11s	8\29 < g < 5\18	g = 289\1044	g = 13\47, 18\65, 23\83	11g-3	5-18g
19L10s	3\29 < g < 2\19	g = 115\1102	g = 5\48, 7\67, 9\86	10g-1	2-19g
20L9s	13\29 < g < 9\20	g = 521\1160	g = 22\49, 31\69, 40\89	9g-5	9-20g
21L8s	11\29 < g < 8\21	g = 463\1216	g = 19\50, 27\71, 35\92	8g-3	8-21g
22L7s	25\29 < g < 19\22	g = 1001\1274	g = 44\51, 63\73, 82\95	7g-6	9-22g
23L6s	5\29 < g < 4\23	g = 231\1332	g = 9\52, 13\75, 17\98	6g-1	4-23g
24L5s	6\29 < g < 5\24	g = 289\1392	g = 11\53, 16\77, 21\101	5g-9	5-24g
25L4s	22\29 < g < 19\25	g = 1001\1450	g = 41\54, 60\79, 79\104	4g-3	19-25g
26L3s	10\29 < g < 9\26	g = 521\1508	g = 19\55, 28\81, 37\107	3g-1	19\2-26g
27L2s	15\29 < g < 14\27	g = 811\1564	g = 29\56, 43\83, 57\110	2g-1	17-27g
28L1s	1\29 < g < 1\28	g = 57\1622	g = 2\57, 3\85, 4\113	g	1-28g