Generator ranges of MOS: Difference between revisions

If the number of the [[Interval_class|generic interval]] to which the generator g belongs is C, and there are N scale steps to the interval of equivalence, then the average the size of an interval in class C is C/N. We have normalized so that C/N is the lower bound of the range of generators; since therefore g > C/N, g is larger than average and hence is the larger of the two sizes of intervals in its class, which means we have normalized to the [[Modal_UDP_Notation|chroma-positive]] generator. We have normalized to the formula for the step size where the leading term is positive.

! | Large-small numbers

! | Generator range

|-

| | [[1L 1s]]

| | 1\2 < g < 1

|-

| | [[1L 2s]]

| | 2\3 < g < 1

|-

| | [[2L 1s]]

| | 1\3 < g < 1\2

|-

| | [[1L 3s]]

| | 3\4 < g < 1

|-

| | [[2L 2s]]

| | 1\4 < g < 1\2

|-

| | [[3L 1s]]

| | 1\4 < g < 1\3

|}

! | Large-small numbers

! | Generator range

|-

| | [[1L 4s]]

| | 4\5 < g < 1

|-

| | [[2L 3s]]

| | 2\5 < g < 1\2

|-

| | [[3L 2s]]

| | 3\5 < g < 2\3

|-

| | [[4L 1s]]

| | 1\5 < g < 1\4

|}

! | Large-small numbers

! | Generator range

|-

| | [[1L 5s]]

| | 5\6 < g < 1

|-

| | [[2L 4s]]

| | 2\6 < g < 1\2

|-

| | [[3L 3s]]

| | 1\6 < g < 1\3

|-

| | [[4L 2s]]

| | 1\6 < g < 1\4

|-

| | [[5L 1s]]

| | 1\6 < g < 1\5

|}

! | Large-small numbers

! | Generator range

|-

| | [[1L 6s]]

| | 6\7 < g < 1

|-

| | [[2L 5s]]

| | 3\7 < g < 1\2

|-

| | [[3L 4s]]

| | 2\7 < g < 1\3

|-

| | [[4L 3s]]

| | 5\7 < g < 3\4

|-

| | [[5L 2s]]

| | 4\7 < g < 3\5

|-

| | [[6L 1s]]

| | 1\7 < g < 1\6

|}

! | Large-small numbers

! | Generator range

|-

| | [[1L 7s]]

| | 7\8 < g < 1

|-

| | [[2L 6s]]

| | 3\8 < g < 1\2

|-

| | [[3L 5s]]

| | 5\8 < g < 2\3

|-

| | [[4L 4s]]

| | 1\8 < g < 1\4

|-

| | [[5L 3s]]

| | 3\8 < g < 2\5

|-

| | [[6L 2s]]

| | 1\8 < g < 1\6

|-

| | [[7L 1s]]

| | 1\8 < g < 1\7

|}

! | Large-small numbers

! | Generator range

|-

| | [[1L 8s]]

| | 8\9 < g < 1

|-

| | [[2L 7s]]

| | 4\9 < g < 1\2

|-

| | [[3L 6s]]

| | 2\9 < g < 1\3

|-

| | [[4L 5s]]

| | 2\9 < g < 1\4

|-

| | [[5L 4s]]

| | 7\9 < g < 4\5

|-

| | [[6L 3s]]

| | 1\9 < g < 1\6

|-

| | [[7L 2s]]

| | 5\9 < g < 4\7

|-

| | [[8L 1s]]

| | 1\9 < g < 1\8

|}

! | Large-small numbers

! | Generator range

|-

| | [[1L 9s]]

| | 9\10 < g < 1

|-

| | [[2L 8s]]

| | 4\10 < g < 1\2

|-

| | [[3L 7s]]

| | 3\10 < g < 1\3

|-

| | [[4L 6s]]

| | 2\10 < g < 1\4

|-

| | [[5L 5s]]

| | 1\10 < g < 1\5

|-

| | [[6L 4s]]

| | 3\10 < g < 2\6

|-

| | [[7L 3s]]

| | 7\10 < g < 5\7

|-

| | [[8L 2s]]

| | 1\10 < g < 1\8

|-

| | [[9L 1s]]

| | 1\10 < g < 1\9

|}

! | Large-small numbers

! | Generator range

|-

| | [[1L 10s]]

| | 10\11 < g < 1

|-

| | [[2L 9s]]

| | 5\11 < g < 1\2

|-

| | [[3L 8s]]

| | 7\11 < g < 2\3

|-

| | [[4L 7s]]

| | 8\11 < g < 3\4

|-

| | [[5L 6s]]

| | 2\11 < g < 1\5

|-

| | [[6L 5s]]

| | 9\11 < g < 5\6

|-

| | [[7L 4s]]

| | 3\11 < g < 2\7

|-

| | [[8L 3s]]

| | 4\11 < g < 3\8

|-

| | [[9L 2s]]

| | 6\11 < g < 5\9

|-

| | [[10L 1s]]

| | 1\11 < g < 1\10

|}

! | Large-small numbers

! | Generator range

|-

| | [[1L 11s]]

| | 11\12 < g < 1

|-

| | [[2L 10s]]

| | 5\12 < g < 1\2

|-

| | [[3L 9s]]

| | 3\12 < g < 1\3

|-

| | [[4L 8s]]

| | 2\12 < g < 1\4

|-

| | [[5L 7s]]

| | 7\12 < g < 3\5

|-

| | [[6L 6s]]

| | 1\12 < g < 1\6

|-

| | [[7L 5s]]

| | 5\12 < g < 3\7

|-

| | [[8L 4s]]

| | 1\12 < g < 1\8

|-

| | [[9L 3s]]

| | 1\12 < g < 1\9

|-

| | [[10L 2s]]

| | 1\12 < g < 1\10

|-

| | [[11L 1s]]

| | 1\12 < g < 1\11

|}

! | Large-small numbers

! | Generator range

|-

| | [[1L 12s]]

| | 12\13 < g < 1

|-

| | [[2L 11s]]

| | 6\13 < g < 1\2

|-

| | [[3L 10s]]

| | 4\13 < g < 1\3

|-

| | [[4L 9s]]

| | 3\13 < g < 1\4

|-

| | [[5L 8s]]

| | 5\13 < g < 2\5

|-

| | [[6L 7s]]

| | 2\13 < g < 1\6

|-

| | [[7L 6s]]

| | 11\13 < g < 6\7

|-

| | [[8L 5s]]

| | 8\13 < g < 5\8

|-

| | [[9L 4s]]

| | 10\13 < g < 7\9

|-

| | [[10L 3s]]

| | 9\13 < g < 7\10

|-

| | [[11L 2s]]

| | 7\13 < g < 6\11

|-

| | [[12L 1s]]

| | 1\13 < g < 1\12

|}

! | Large-small numbers

! | Generator range

|-

| | [[1L 13s]]

| | 13\14 < g < 1

|-

| | [[2L 12s]]

| | 6\14 < g < 1\2

|-

| | [[3L 11s]]

| | 9\14 < g < 2\3

|-

| | [[4L 10s]]

| | 3\14 < g < 1\4

|-

| | [[5L 9s]]

| | 11\14 < g < 4\5

|-

| | [[6L 8s]]

| | 2\14 < g < 1\6

|-

| | [[7L 7s]]

| | 1\14 < g < 1\7

|-

| | [[8L 6s]]

| | 5\14 < g < 3\8

|-

| | [[9L 5s]]

| | 3\14 < g < 2\9

|-

| | [[10L 4s]]

| | 4\14 < g < 3\10

|-

| | [[11L 3s]]

| | 5\14 < g < 4\11

|-

| | [[12L 2s]]

| | 1\14 < g < 1\12

|-

| | [[13L 1s]]

| | 1\14 < g < 1\13

|}

! | Large-small numbers

! | Generator range

|-

| | [[1L 14s]]

| | 14\15 < g < 1

|-

| | [[2L 13s]]

| | 7\15 < g < 1\2

|-

| | [[3L 12s]]

| | 4\15 < g < 1\3

|-

| | [[4L 11s]]

| | 11\15 < g < 3\4

|-

| | [[5L 10s]]

| | 2\15 < g < 1\5

|-

| | [[6L 9s]]

| | 2\15 < g < 1\6

|-

| | [[7L 8s]]

| | 2\15 < g < 1\7

|-

| | [[8L 7s]]

| | 13\15 < g < 7\8

|-

| | [[9L 6s]]

| | 3\15 < g < 2\9

|-

| | [[10L 5s]]

| | 1\15 < g < 1\10

|-

| | [[11L 4s]]

| | 4\15 < g < 3\11

|-

| | [[12L 3s]]

| | 1\15 < g < 1\12

|-

| | [[13L 2s]]

| | 8\15 < g < 7\13

|-

| | [[14L 1s]]

| | 1\15 < g < 1\14

|}

! | Large-small numbers

! | Generator range

|-

| | [[1L 15s]]

| | 15\16 < g < 1

|-

| | [[2L 14s]]

| | 7\16 < g < 1\2

|-

| | [[3L 13s]]

| | 5\16 < g < 1\3

|-

| | [[4L 12s]]

| | 3\16 < g < 1\4

|-

| | [[5L 11s]]

| | 3\16 < g < 1\5

|-

| | [[6L 10s]]

| | 5\16 < g < 2\6

|-

| | [[7L 9s]]

| | 9\16 < g < 4\7

|-

| | [[8L 8s]]

| | 1\16 < g < 1\8

|-

| | [[9L 7s]]

| | 7\16 < g < 4\9

|-

| | [[10L 6s]]

| | 3\16 < g < 2\10

|-

| | [[11L 5s]]

| | 13\16 < g < 9\11

|-

| | [[12L 4s]]

| | 1\16 < g < 1\12

|-

| | [[13L 3s]]

| | 11\16 < g < 9\13

|-

| | [[14L 2s]]

| | 1\16 < g < 1\14

|-

| | [[15L 1s]]

| | 1\16 < g < 1\15

|}