Generator ranges of MOS

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 boundaries of propriety, maximum expressiveness and diatonicity (i.e. best, better and good behavior). Finally, the fourth column gives the formula for the size of the chroma.

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

L-s pattern	Generator range	Boundaries of best, better, good behavior	Large step-Small step
1L 1s	1\2 < g < 1	g = 2\3, 3\4, 4\5-5\6	g-(1-g) = 2g-1
1L 2s	2\3 < g < 1	g = 3\4, 4\5, 5\6-6\7	2g-1-(1-g) = 3g-2
2L 1s	1\3 < g < 1\2	g = 2\5, 3\7, 4\9-5\11	g-(1-2g)= 3g-1
1L 3s	3\4 < g < 1	g = 4\5, 5\6, 6\7-7\8	3g-2-(1-g) = 4g-3
2L 2s	1\4 < g < 1\2	g = 2\6, 3\8, 4\10-5\12	g-(1\2-g) = 2g-1\2
3L 1s	1\4 < g < 1\3	g = 2\7, 3\10, 4\13-5\16	g-(1-3g) = 4g-1

5-tone

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

L-s pattern	Generator range	Boundaries of best, better, good behavior	Large step-Small step
1L 4s	4\5 < g < 1	g = 5\6, 6\7, 7\8-8\9	4g-3-(1-g) = 5g-4
2L 3s	2\5 < g < 1\2	g = 3\7, 4\9, 5\11-6\13	3g-1-(1-2g) = 5g-2
3L 2s	3\5 < g < 2\3	g = 5\8, 7\11, 9\14-11\17	2g-1-(2-3g) = 5g-3
4L 1s	1\5 < g < 1\4	g = 2\9, 3\13, 4\17-5\21	g-(1-4g) = 5g-1

6-tone

L-s pattern	Generator range	Boundaries of best, better, good behavior	Large step-Small step
1L 5s	5\6 < g < 1	g = 6\7, 7\8, 8\9-9\10	5g-4-(1-g) = 6g-5
2L 4s	2\6 < g < 1\2	g = 3\8, 4\10, 5\12-6\14	2g-1\2-(1\2-g) = 3g-1
3L 3s	1\6 < g < 1\3	g = 2\9, 3\12, 4\15-5\18	g-(1\3-g) = 2g-1\3
4L 2s	1\6 < g < 1\4	g = 2\10, 3\14, 4\18-5\22	g-(1\2-2g) = 3g-1\2
5L 1s	1\6 < g < 1\5	g = 2\11, 3\16, 4\21-5\26	g-(1-5g) = 6g-1

7-tone

L-s pattern	Generator range	Boundaries of best, better, good behavior	Large step-Small step
1L 6s	6\7 < g < 1	g = 7\8, 8\9, 9\10-10\11	6g-5-(1-g) = 7g-6
2L 5s	3\7 < g < 1\2	g = 4\9, 5\11, 6\13-7\15	5g-2-(1-2g) = 7g-3
3L 4s	2\7 < g < 1\3	g = 3\10, 4\13, 5\16-6\19	4g-1-(1-3g) = 7g-2
4L 3s	5\7 < g < 3\4	g = 8\11, 11\15, 14\19-17\23	3g-2-(3-4g) = 7g-5
5L 2s	4\7 < g < 3\5	g = 7\12, 10\17, 13\22-16\27	2g-1-(3-5g) = 7g-4
6L 1s	1\7 < g < 1\6	g = 2\13, 3\19, 4\25-5\31	g-(1-6g) = 7g-1

8-tone

L-s pattern	Generator range	Boundaries of best, better, good behavior	Large step-Small step
1L 7s	7\8 < g < 1	g = 8\9, 9\10, 10\11-11\12	7g-6-(1-g) = 8g-7
2L 6s	3\8 < g < 1\2	g = 4\10, 5\12, 6\14-7\16	3g-1-(1\2-g) = 4g-3\2
3L 5s	5\8 < g < 2\3	g = 7\11, 9\14, 11\17-13\20	5g-3-(2-3g) = 8g-5
4L 4s	1\8 < g < 1\4	g = 2\12, 3\16, 4\20-5\24	g-(1\4-g) = 2g-1\4
5L 3s	3\8 < g < 2\5	g = 5\13, 7\18, 9\23-11\28	3g-1-(2-5g) = 8g-3
6L 2s	1\8 < g < 1\6	g = 2\14, 3\20, 4\26-5\32	g-(1\2-3g) = 4g-1\2
7L 1s	1\8 < g < 1\7	g = 2\15, 3\22, 4\29-5\36	g-(1-7g) = 8g-1

9-tone

L-s pattern	Generator range	Boundaries of best, better, good behavior	Large step-Small step
1L 8s	8\9 < g < 1	g = 9\10, 10\11, 11\12-12\13	8g-7-(1-g) = 9g-8
2L 7s	4\9 < g < 1\2	g = 5\11, 6\13, 7\15-8\17	7g-3-(1-2g) = 9g-4
3L 6s	2\9 < g < 1\3	g = 3\12, 4\15, 5\18-6\21	2g-1\3-(1\3-g) = 3g-2\3
4L 5s	2\9 < g < 1\4	g = 3\13, 4\17, 5\21-6\25	5g-1-(1-4g) = 9g-2
5L 4s	7\9 < g < 4\5	g = 11\14, 15\19, 19\24-23\29	4g-3-(4-5g) = 9g-7
6L 3s	1\9 < g < 1\6	g = 2\15, 3\21, 4\27-5\33	g-(1\3-2g) = 3g-1\3
7L 2s	5\9 < g < 4\7	g = 9\16, 13\23, 17\30-21\37	2g-1-(4-7g) = 9g-5
8L 1s	1\9 < g < 1\8	g = 2\17, 3\25, 4\33-5\41	g-(1-8g) = 9g-1

10-tone

L-s pattern	Generator range	Boundaries of best, better, good behavior	Large step-Small step
1L 9s	9\10 < g < 1	g = 10\11, 11\12, 12\13-13\14	9g-8-(1-g) = 10g-9
2L 8s	4\10 < g < 1\2	g = 5\12, 6\14, 7\16-8\18	4g-3\2-(1\2-g) = 5g-2
3L 7s	3\10 < g < 1\3	g = 4\13, 5\16, 6\19-7\22	7g-2-(1-3g) = 10g-3
4L 6s	2\10 < g < 1\4	g = 3\14, 4\18, 5\22-6\26	3g-1\2-(1\2-2g) = 5g-1
5L 5s	1\10 < g < 1\5	g = 2\15, 3\20, 4\25-5\30	g-(1\5-g) = 2g-1\5
6L 4s	3\10 < g < 2\6	g = 5\16, 7\22, 9\28-11\34	2g-1\2-(1-3g) = 5g-3\2
7L 3s	7\10 < g < 5\7	g = 12\17, 17\24, 22\31-27\38	3g-2-(5-7g) = 10g-7
8L 2s	1\10 < g < 1\8	g = 2\18, 3\26, 4\34-5\42	g-(1\2-4g) = 5g-1\2
9L 1s	1\10 < g < 1\9	g = 2\19, 3\28, 4\37-5\46	g-(1-9g) = 10g-1

11-tone

L-s pattern	Generator range	Boundaries of best, better, good behavior	Large step-Small step
1L 10s	10\11 < g < 1	g = 11\12, 12\13, 13\14-14\15	10g-9-(1-g) = 11g-10
2L 9s	5\11 < g < 1\2	g = 6\13, 7\15, 8\17-9\19	9g-4-(1-2g) = 11g-5
3L 8s	7\11 < g < 2\3	g = 9\14, 11\17, 13\20-15\23	8g-5-(2-3g) = 11g-7
4L 7s	8\11 < g < 3\4	g = 11\15, 14\19, 17\23-20\27	7g-5-(3-4g) = 11g-8
5L 6s	2\11 < g < 1\5	g = 3\16, 4\21, 5\26-6\31	6g-1-(1-5g) = 11g-2
6L 5s	9\11 < g < 5\6	g = 14\17, 19\23, 24\29-29\35	5g-4-(5-6g) = 11g-9
7L 4s	3\11 < g < 2\7	g = 5\18, 7\25, 9\32-11\39	4g-1-(2-7g) = 11g-3
8L 3s	4\11 < g < 3\8	g = 7\19, 10\27, 13\35-16\43	3g-1-(3-8g) = 11g-4
9L 2s	6\11 < g < 5\9	g = 11\20, 16\29, 21\38-26\47	2g-1-(5-9g) = 11g-6
10L 1s	1\11 < g < 1\10	g = 2\21, 3\31, 4\41-5\51	g+1-10g = 11g-1

12-tone

L-s pattern	Generator range	Boundaries of best, better, good behavior	Large step-Small step
1L 11s	11\12 < g < 1	g = 12\13, 13\14, 14\15-15\16	11g-10-(1-g) = 12g-11
2L 10s	5\12 < g < 1\2	g = 6\14, 7\16, 8\18-9\20	5g-2-(1\2-g) = 6g-5\2
3L 9s	3\12 < g < 1\3	g = 4\15, 5\18, 6\21-7\24	3g-2\3-(1\3-g) = 4g-1
4L 8s	2\12 < g < 1\4	g = 3\16, 4\20, 5\24-6\28	2g-1\4-(1\4-g) = 3g-1\2
5L 7s	7\12 < g < 3\5	g = 10\17, 13\22, 16\27-19\32	7g-4-(3-5g) = 12g-7
6L 6s	1\12 < g < 1\6	g = 2\18, 3\24, 4\30-5\36	g-(1\6-g) = 2g-1\6
7L 5s	5\12 < g < 3\7	g = 8\19, 11\26, 14\33-17\40	5g-2-(3-7g) = 12g-5
8L 4s	1\12 < g < 1\8	g = 2\20, 3\28, 4\36-5\44	g-(1\4-2g) = 3g-1\4
9L 3s	1\12 < g < 1\9	g = 2\21, 3\30, 4\39-5\48	g-(1\3-3g) = 4g-1\3
10L 2s	1\12 < g < 1\10	g = 2\22, 3\32, 4\42-5\52	g-(1\2-5g) = 6g-1\2
11L 1s	1\12 < g < 1\11	g = 2\23, 3\34, 4\45-5\56	g-(1-11g) = 12g-1

13-tone

L-s pattern	Generator range	Boundaries of best, better, good behavior	Large step-Small step
1L 12s	12\13 < g < 1	g = 13\14, 14\15, 15\16-16\17	12g-11-(1-g) = 13g-12
2L 11s	6\13 < g < 1\2	g = 7\15, 8\17, 9\19-10\21	11g-5-(1-2g) = 13g-6
3L 10s	4\13 < g < 1\3	g = 5\16, 6\19, 7\22-8\25	10g-3-(1-3g) = 13g-4
4L 9s	3\13 < g < 1\4	g = 4\17, 5\21, 6\25-7\28	9g-2-(1-4g) = 13g-3
5L 8s	5\13 < g < 2\5	g = 7\18, 9\23, 11\28-13\33	8g-3-(2-5g) = 13g-5
6L 7s	2\13 < g < 1\6	g = 3\19, 4\25, 5\31-6\37	7g-1-(1-6g) = 13g-2
7L 6s	11\13 < g < 6\7	g = 17\20, 23\27, 29\34-35\41	6g-5-(6-7g) = 13g-11
8L 5s	8\13 < g < 5\8	g = 13\21, 18\29, 23\37-28\45	5g-3-(5-8g) = 13g-8
9L 4s	10\13 < g < 7\9	g = 17\22, 24\31, 31\40-38\49	4g-3-(7-9g) = 13g-10
10L 3s	9\13 < g < 7\10	g = 16\23, 23\33, 30\43-37\53	3g-2-(7-10g) = 13g-9
11L 2s	7\13 < g < 6\11	g = 13\24, 19\35, 25\46-31\57	2g-1-(6-11g) = 13g-7
12L 1s	1\13 < g < 1\12	g = 2\25, 3\37, 4\49-5\61	g-(1-12g) = 13g-1

14-tone

L-s pattern	Generator range	Boundaries of best, better, good behavior	Large step-Small step
1L 13s	13\14 < g < 1	g = 14\15, 15\16, 16\17-17\18	13g-12-(1-g) = 14g-13
2L 12s	6\14 < g < 1\2	g = 7\16, 8\18, 9\20-10\22	6g-5\2-(1\2-g) = 7g-3
3L 11s	9\14 < g < 2\3	g = 11\17, 13\20, 15\23-17\26	11g-7-(2-3g) = 14g-9
4L 10s	3\14 < g < 1\4	g = 4\18, 5\22, 6\26-7\30	5g-1-(1\2-2g) = 7g-3\2
5L 9s	11\14 < g < 4\5	g = 15\19, 19\24, 23\29-27\34	9g-7-(4-5g) = 14g-11
6L 8s	2\14 < g < 1\6	g = 3\20, 4\26, 5\32-6\38	4g-1\2-(1\2-3g) = 7g-1
7L 7s	1\14 < g < 1\7	g = 2\21, 3\28, 4\35-5\42	g-(1\7-g) = 2g-1\7
8L 6s	5\14 < g < 3\8	g = 8\22, 11\30, 14\38-17\46	3g-1-(3\2-4g) = 7g-5\2
9L 5s	3\14 < g < 2\9	g = 5\23, 7\32, 9\41-11\50	5g-1-(2-9g) = 14g-3
10L 4s	4\14 < g < 3\10	g = 7\24, 10\34, 13\44-16\54	2g-1\2-(3\2-5g) = 7g-2
11L 3s	5\14 < g < 4\11	g = 9\25, 13\36, 17\47-21\58	3g-1-(4-11g) = 14g-5
12L 2s	1\14 < g < 1\12	g = 2\26, 3\38, 4\50-5\62	g-(1\2-6g) = 7g-1\2
13L 1s	1\14 < g < 1\13	g = 2\27, 3\40, 4\53-5\66	g+1-13g = 14g-1

15-tone

L-s pattern	Generator range	Boundaries of best, better, good behavior	Large step-Small step
1L 14s	14\15 < g < 1	g = 15\16, 16\17, 17\18-18\19	14g-13-(1-g) = 15g-14
2L 13s	7\15 < g < 1\2	g = 8\17, 9\19, 10\21-11\23	13g-6-(1-2g) = 15g-7
3L 12s	4\15 < g < 1\3	g = 5\18, 6\21, 7\24-8\27	4g-1-(1\3-g) = 5g-4\3
4L 11s	11\15 < g < 3\4	g = 14\19, 17\23, 20\27-23\31	11g-8-(3-4g) = 15g-11
5L 10s	2\15 < g < 1\5	g = 3\20, 4\25, 5\30-6\35	2g-1\5-(1\5-g) = 3g-2\5
6L 9s	2\15 < g < 1\6	g = 3\21, 4\27, 5\33-6\39	3g-1\3-(1\3-2g) = 5g-2\3
7L 8s	2\15 < g < 1\7	g = 3\22, 4\29, 5\36-6\43	8g-1-(1-7g) = 15g-2
8L 7s	13\15 < g < 7\8	g = 20\23, 27\31, 34\39-41\47	7g-6-(7-8g) = 15g-13
9L 6s	3\15 < g < 2\9	g = 5\24, 7\33, 9\42-11\51	2g-1\3-(2\3-3g) = 5g-1
10L 5s	1\15 < g < 1\10	g = 2\25, 3\35, 4\45-5\55	g-(1\5-2g) = 3g-1\5
11L 4s	4\15 < g < 3\11	g = 7\26, 10\37, 13\48-16\59	4g-1-(3-11g) = 15g-4
12L 3s	1\15 < g < 1\12	g = 2\27, 3\39, 4\51-5\63	g-(1\3-4g) = 5g-1\3
13L 2s	8\15 < g < 7\13	g = 15\28, 22\41, 29\54-36\67	2g-1-(7-13g) = 15g-8
14L 1s	1\15 < g < 1\14	g = 2\29, 3\43, 4\57-5\71	g-(1-14g) = 15g-1

16-tone

L-s pattern	Generator range	Boundaries of best, better, good behavior	Large step-Small step
1L 15s	15\16 < g < 1	g = 16\17, 17\18, 18\19-19\20	15g-14-(1-g) = 16g-15
2L 14s	7\16 < g < 1\2	g = 8\18, 9\20, 10\22-11\24	7g-3-(1\2-g) = 8g-7\2
3L 13s	5\16 < g < 1\3	g = 6\19, 7\22, 8\25-9\28	13g-4-(1-3g) = 16g-5
4L 12s	3\16 < g < 1\4	g = 4\20, 5\24, 6\28-7\32	3g-1\2-(1\4-g) = 4g-3\4
5L 11s	3\16 < g < 1\5	g = 4\21, 5\26, 6\31-7\36	11g-2-(1-5g) = 16g-3
6L 10s	5\16 < g < 2\6	g = 7\22, 9\28, 11\34-13\40	5g-3\2-(1-3g) = 8g-5\2
7L 9s	9\16 < g < 4\7	g = 13\23, 17\30, 21\37-25\44	9g-5-(4-7g) = 16g-9
8L 8s	1\16 < g < 1\8	g = 2\24, 3\32, 4\40-5\48	g-(1\8-g) = 2g-1\8
9L 7s	7\16 < g < 4\9	g = 11\25, 15\34, 19\43-23\52	7g-3-(4-9g) = 16g-7
10L 6s	3\16 < g < 2\10	g = 5\26, 7\36, 9\46-11\56	3g-1\2-(1-5g) = 8g-3\2
11L 5s	13\16 < g < 9\11	g = 22\27, 31\38, 40\49-49\60	5g-4-(9-11g) = 16g-13
12L 4s	1\16 < g < 1\12	g = 2\28, 3\40, 4\52-5\64	g-(1\4-3g) = 4g-1\4
13L 3s	11\16 < g < 9\13	g = 20\29, 29\42, 38\55-47\68	3g-2-(9-13g) = 16g-11
14L 2s	1\16 < g < 1\14	g = 2\30, 3\44, 4\58-5\72	g-(1\2-7g) = 8g-1\2
15L 1s	1\16 < g < 1\15	g = 2\31, 3\46, 4\61-5\76	g-(1-15g) = 16g-1

17-tone

L-s pattern	Generator range	Boundaries of best, better, good behavior	Large step-Small step
1L 16s	16\17 < g < 1	g = 17\18, 18\19, 19\20-20\21	16g-15-(1-g) = 17g-16
2L 15s	8\17 < g < 1\2	g = 9\19, 10\21, 11\23-13\25	15g-7-(1-2g) = 17g-8
3L 14s	11\17 < g < 2\3	g = 13\20, 15\23, 17\26-19\29	14g-9-(2-3g) = 17g-11
4L 13s	4\17 < g < 1\4	g = 5\21, 6\25, 7\29-8\33	13g-3-(1-4g) = 17g-4
5L 12s	10\17 < g < 3\5	g = 13\22, 16\27, 19\32-22\37	12g-7-(3-5g) = 17g-10
6L 11s	14\17 < g < 5\6	g = 19\23, 24\29, 29\35-34\41	11g-9-(5-6g) = 17g-14
7L 10s	12\17 < g < 5\7	g = 17\24, 22\31, 27\38-32\45	10g-7-(5-7g) = 17g-12
8L 9s	2\17 < g < 1\8	g = 3\25, 4\33, 5\41-6\49	9g-1-(1-8g) = 17g-2
9L 8s	15\17 < g < 8\9	g = 23\26, 31\35, 39\44-47\53	8g-7-(8-9g) = 17g-15
10L 7s	5\17 < g < 3\10	g = 8\27, 11\37, 14\47-17\57	7g-2-(3-10g) = 17g-5
11L 6s	3\17 < g < 2\11	g = 5\28, 7\39, 9\50-11\61	6g-1-(2-11g) = 17g-3
12L 5s	7\17 < g < 5\12	g = 12\29, 17\41, 22\53-27\65	5g-2-(5-12g) = 17g-7
13L 4s	13\17 < g < 10\13	g = 23\30, 33\43, 43\56-53\69	4g-3-(10-13g) = 17g-13
14L 3s	6\17 < g < 5\14	g = 11\31, 16\45, 21\59-26\73	3g-1-(5-14g) = 17g-6
15L 2s	9\17 < g < 8\15	g = 17\32, 25\47, 33\62-41\77	2g-1-(8-15g) = 17g-9
16L 1s	1\17 < g < 1\16	g = 2\33, 3\49, 4\65-5\81	g-(1-16g) = 17g-1

18-tone

L-s pattern	Generator range	Boundaries of best, better, good behavior	Large step-Small step
1L 17s	17\18 < g < 1	g = 18\19, 19\20, 20\21-21\22	17g-16-(1-g) = 18g-17
2L 16s	8\18 < g < 1\2	g = 9\20, 10\22, 11\24-12\26	8g-7\2-(1\2-g) = 9g-4
3L 15s	5\18 < g < 1\3	g = 6\21, 7\24, 8\27-9\30	5g-4\3-(1\3-g) = 6g-5\3
4L 14s	4\18 < g < 1\4	g = 5\22, 6\26, 7\30-8\34	7g-3\2-(1\2-2g) = 9g-2
5L 13s	7\18 < g < 2\5	g = 9\23, 11\28, 13\33-15\38	13g-5-(2-5g) = 18g-7
6L 12s	2\18 < g < 1\6	g = 3\24, 4\30, 5\36-6\42	2g-1\6-(1\6-g) = 3g-1\3
7L 11s	5\18 < g < 2\7	g = 7\25, 9\32, 11\39-13\46	11g-3-(2-7g) = 18g-5
8L 10s	2\18 < g < 1\8	g = 3\26, 4\34, 5\42-6\50	5g-1\2-(1\2-4g) = 9g-1
9L 9s	1\18 < g < 1\9	g = 2\27, 3\36, 4\45-5\54	g-(1\9-g) = 2g-1\9
10L 8s	7\18 < g < 4\10	g = 11\28, 15\38, 19\48-23\58	4g-3\2-(2-5g) = 9g-7\2
11L 7s	13\18 < g < 8\11	g = 21\29, 29\40, 37\51-41\62	7g-5-(8-11g) = 18g-13
12L 6s	1\18 < g < 1\12	g = 2\30, 3\42, 4\54-5\66	g-(1\6-2g) = 3g-1\6
13L 5s	11\18 < g < 8\13	g = 19\31, 27\44, 35\57-43\70	5g-3-(8-13g) = 18g-11
14L 4s	5\18 < g < 4\14	g = 9\32, 13\46, 17\60-21\74	2g-1\2-(2-7g) = 9g-5\2
15L 3s	1\18 < g < 1\15	g = 2\33, 3\48, 4\63-5\78	g-(1\3-5g) = 6g-1\3
16L 2s	1\18 < g < 1\16	g = 2\34, 3\50, 4\66-5\82	g-(1\2-8g) = 9g-1\2
17L 1s	1\18 < g < 1\17	g = 2\35, 3\52, 4\69-5\86	g-(1-17g) = 18g-1

19-tone

L-s pattern	Generator range	Boundaries of best, better, good behavior	Large step-Small step
1L 18s	18\19 < g < 1	g = 19\20, 20\21, 21\22-22\23	18g-17-(1-g) = 19g-18
2L 17s	9\19 < g < 1\2	g = 10\21, 11\23, 12\25-13\27	17g-8-(1-2g) = 19g-9
3L 16s	6\19 < g < 1\3	g = 7\22, 8\25, 9\28-10\31	16g-5-(1-3g) = 19g-6
4L 15s	14\19 < g < 3\4	g = 17\23, 20\27, 23\31-27\35	15g-11-(3-4g) = 19g-14
5L 14s	15\19 < g < 4\5	g = 19\24, 23\29, 27\34-31\39	14g-11-(4-5g) = 19g-15
6L 13s	3\19 < g < 1\6	g = 4\25, 5\31, 6/37-7\43	13g-2-(1-6g) = 19g-3
7L 12s	8\19 < g < 3\7	g = 11\26, 14\33, 17\40-20\47	12g-5-(3-7g) = 19g-8
8L 11s	7\19 < g < 3\8	g = 10\27, 13\35, 16\43-19\51	11g-4-(3-8g) = 19g-7
9L 10s	2\19 < g < 1\9	g = 3\28, 4\37, 5\46-6\55	10g-1-(1-9g) = 19g-2
10L 9s	17\19 < g < 9\10	g = 26\29, 35\39, 44\49-53\59	9g-8-(9-10g) = 19g-17
11L 8s	12\19 < g < 7\11	g = 19\30, 26\41, 33\52-40\63	8g-5-(7-11g) = 19g-12
12L 7s	11\19 < g < 7\12	g = 18\31, 25\43, 32\55-39\67	7g-4-(7-12g) = 19g-11
13L 6s	16\19 < g < 11\13	g = 27\32, 38\45, 49\58-60\71	6g-5-(11-13g) = 19g-16
14L 5s	4\19 < g < 3\14	g = 7\33, 10\47, 13\61-16\75	5g-1-(3-14g) = 19g-4
15L 4s	5\19 < g < 4\15	g = 9\34, 13\49, 17\64-21\79	4g-1-(4-15g) = 19g-5
16L 3s	13\19 < g < 11\16	g = 24\35, 35\51, 46\67-57\83	3g-2-(11-16g) = 19g-13
17L 2s	10\19 < g < 9\17	g = 19\36, 28\53, 37\70-46\87	2g-1-(9-17g) = 19g-10
18L 1s	1\19 < g < 1\18	g = 2\37, 3\55, 4\73-5\91	g-(1-18g) = 19g-1

20-tone

L-s pattern	Generator range	Boundaries of best, better, good behavior	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