Generator ranges of MOS: Difference between revisions

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Line 1,606: Line 1,606:
! | <span style="background-color: #ffffff;">Midpoint</span>
! | <span style="background-color: #ffffff;">Midpoint</span>
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step
! | Large step+Small step
! | Small step
|-
|-
| | 1L22s
| | 1L22s
Line 1,613: Line 1,612:
| | g = 45\46
| | g = 45\46
| | ''g = 23\24, 24\25, 25\26''
| | ''g = 23\24, 24\25, 25\26''
| | 22g-21
| | 22g-21+1-g = 21g-20
| | 1-g
|-
|-
| | 2L21s
| | 2L21s
Line 1,620: Line 1,618:
| | g = 45\92
| | g = 45\92
| | g = ''12\25, 13\27'', 14\29
| | g = ''12\25, 13\27'', 14\29
| | 21g-10
| | 21g-10+1-2g = 19g-9
| | 1-2g
|-
|-
| | 3L20s
| | 3L20s
Line 1,627: Line 1,624:
| | g = 91\138
| | g = 91\138
| | g = ''17\26'', 19\29, 21\32
| | g = ''17\26'', 19\29, 21\32
| | 20g-13
| | 20g-13+1-3g = 17g-12
| | 1-3g
|-
|-
| | 4L19s
| | 4L19s
Line 1,634: Line 1,630:
| | g = 137\184
| | g = 137\184
| | g = ''20\27'', 23\31, 26\35
| | g = ''20\27'', 23\31, 26\35
| | 19g-14
| | 19g-14+3-4g = 15g-11
| | 3-4g
|-
|-
| | 5L18s
| | 5L18s
Line 1,641: Line 1,636:
| | g = 91\230
| | g = 91\230
| | g = ''11\28'', 13\33, 15\38
| | g = ''11\28'', 13\33, 15\38
| | 18g-7
| | 18g-7+2-5g = 13g-5
| | 2-5g
|-
|-
| | 6L17s
| | 6L17s
Line 1,648: Line 1,642:
| | g = 229\276
| | g = 229\276
| | g = 24\29, 29\35, 34\41
| | g = 24\29, 29\35, 34\41
| | 17g-15
| | 17g-15+1-6g = 11g-14
| | 1-6g
|-
|-
| | 7L16s
| | 7L16s
Line 1,655: Line 1,648:
| | g = 183\322
| | g = 183\322
| | g = 17\30,<span style="line-height: 15.6000003814697px;"> 21\37,</span> 25\44
| | g = 17\30,<span style="line-height: 15.6000003814697px;"> 21\37,</span> 25\44
| | 16g-9
| | 16g-9+4-7g = 9g-5
| | 4-7g
|-
|-
| | 8L15s
| | 8L15s
Line 1,662: Line 1,654:
| | g = 321\368
| | g = 321\368
| | g = 27\31, 34\39, 41\47
| | g = 27\31, 34\39, 41\47
| | 15g-13
| | 15g-13+7-8g = 7g-6
| | 7-8g
|-
|-
| | 9L14s
| | 9L14s
Line 1,669: Line 1,660:
| | g = 91\414
| | g = 91\414
| | g = 7\32, 9\41, 11\50
| | g = 7\32, 9\41, 11\50
| | 14g-7
| | 14g-7+<span style="line-height: 15.6000003814697px;">2-9g = 5g-5</span>  
| | <span style="line-height: 15.6000003814697px;">11-9g</span>
|-
|-
| | 10L13s
| | 10L13s
Line 1,676: Line 1,666:
| | g = 321\460
| | g = 321\460
| | g = 23\33, 30\43, 37\53
| | g = 23\33, 30\43, 37\53
| | 13g-9
| | 13g-9+7-10g = 3g-2
| | 7-10g
|-
|-
| | 11L12s
| | 11L12s
Line 1,683: Line 1,672:
| | g = 45\506
| | g = 45\506
| | g = 3\34, 4\45, 5\56
| | g = 3\34, 4\45, 5\56
| | 12g-1
| | 12g-1+1-11g = g
| | 1-11g
|-
|-
| | 12L11s
| | 12L11s
Line 1,690: Line 1,678:
| | g = 505\552
| | g = 505\552
| | g = 32\35, 43\47, 54\59
| | g = 32\35, 43\47, 54\59
| | <span style="line-height: 15.6000003814697px;">11g-10</span>
| | <span style="line-height: 15.6000003814697px;">11g-10+11-12g = 1-g</span>
| | 11-12g
|-
|-
| | 13L10s
| | 13L10s
Line 1,697: Line 1,684:
| | g = 183\598
| | g = 183\598
| | g = 11\36, 15\49, 19\62
| | g = 11\36, 15\49, 19\62
| | 10g-3
| | 10g-3+4-13g =1-3g
| | 4-13g
|-
|-
| | 14L9s
| | 14L9s
Line 1,704: Line 1,690:
| | g = 505\644
| | g = 505\644
| | g = 29\37, 40\51, 51\65
| | g = 29\37, 40\51, 51\65
| | 9g-7
| | 9g-7+11-14g = 4-5g
| | 11-14g
|-
|-
| | 15L8s
| | 15L8s
Line 1,711: Line 1,696:
| | g = 91\690
| | g = 91\690
| | g = 5\38, 7\53, 9\68
| | g = 5\38, 7\53, 9\68
| | 8g-1
| | 8g-1+2-15g = 1-7g
| | 2-15g
|-
|-
| | 16L7s
| | 16L7s
Line 1,718: Line 1,702:
| | g = 321\736
| | g = 321\736
| | g = 17\39, 24\55, 31\71
| | g = 17\39, 24\55, 31\71
| | 7g-3
| | 7g-3+<span style="line-height: 15.6000003814697px;">7-16g = 4-9g</span>
| | <span style="line-height: 15.6000003814697px;">7-16g</span>
|-
|-
| | 17L6s
| | 17L6s
Line 1,725: Line 1,708:
| | g = 137\782
| | g = 137\782
| | g = 7\40, 10\57, 13\74
| | g = 7\40, 10\57, 13\74
| | 6g-1
| | 6g-1+3-17g = 2-11g
| | 3-17g
|-
|-
| | 18L5s
| | 18L5s
Line 1,732: Line 1,714:
| | g = 505\828
| | g = 505\828
| | g = 25\41, 36\59, 47\77
| | g = 25\41, 36\59, 47\77
| | 5g-4
| | 5g-4+11-18g = 7-13g
| | 11-18g
|-
|-
| | 19L4s
| | 19L4s
Line 1,739: Line 1,720:
| | g = 229\874
| | g = 229\874
| | g = 11\42, 16\61, 21\80
| | g = 11\42, 16\61, 21\80
| | 4g-1
| | 4g-1+5-19g = 4-15g
| | 5-19g
|-
|-
| | 20L3s
| | 20L3s
Line 1,746: Line 1,726:
| | g = 321\920
| | g = 321\920
| | g = 15\43, 22\63, 29\83
| | g = 15\43, 22\63, 29\83
| | 3g-1
| | 3g-1+13-20g = 12-17g
| | 13-20g
|-
|-
| | 21L2s
| | 21L2s
Line 1,753: Line 1,732:
| | g = 505\966
| | g = 505\966
| | g = 23\44, 34\65, 45\86
| | g = 23\44, 34\65, 45\86
| | 2g-1
| | 2g-1+11-21g = 10-19g
| | 1-21g
|-
|-
| | 22L1s
| | 22L1s
Line 1,760: Line 1,738:
| | g = 45\1012
| | g = 45\1012
| | g = 2\45, 3\67, 4\89
| | g = 2\45, 3\67, 4\89
| | g
| | g+1-22g = 1-221
| | 1-22g
|}
|}


Line 1,772: Line 1,749:
! | <span style="background-color: #ffffff;">Midpoint</span>
! | <span style="background-color: #ffffff;">Midpoint</span>
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step
! | Large step+Small step
! | Small step
|-
|-
| | 1L23s
| | 1L23s
Line 1,779: Line 1,755:
| | g = 47\48
| | g = 47\48
| | ''g = 24\25, 25\26, 26\27''
| | ''g = 24\25, 25\26, 26\27''
| | 23g-22
| | 23g-22+1-g = 22g-21
| | 1-g
|-
|-
| | 2L22s
| | 2L22s
Line 1,786: Line 1,761:
| | g = 23\48
| | g = 23\48
| | g = ''12\26, 13\28'', 14\30
| | g = ''12\26, 13\28'', 14\30
| | 1/2-g
| | 11g-5+1/2-g = 10g-9/2
| | 11g-5
|-
|-
| | 3L21s
| | 3L21s
Line 1,793: Line 1,767:
| | g = 15\48
| | g = 15\48
| | g = ''8\27'', 9\30, 10\33
| | g = ''8\27'', 9\30, 10\33
| | 2/3-2g
| | 7g-2+1/3-g = 6g-5/3
| | g-1/3
|-
|-
| | 4L20s
| | 4L20s
Line 1,800: Line 1,773:
| | g = 11\48
| | g = 11\48
| | g = ''6\28'', 7\32, 8\36
| | g = ''6\28'', 7\32, 8\36
| | 5g-1
| | 5g-1+1/4-g = 4g-3/4
| | 1/4-g
|-
|-
| | 5L19s
| | 5L19s
Line 1,807: Line 1,779:
| | g = 191\240
| | g = 191\240
| | g = ''23\29'', 27\34, 31\39
| | g = ''23\29'', 27\34, 31\39
| | 19g-15
| | 19g-15+4-5g = 14g-11
| | 4-5g
|-
|-
| | 6L18s
| | 6L18s
Line 1,814: Line 1,785:
| | g = 7\48
| | g = 7\48
| | g = 4\30, 5\36, 6\42
| | g = 4\30, 5\36, 6\42
| | 3g-1\3
| | 3g-1\3+1\6-g = 2g-1\6
| | 1\6-g
|-
|-
| | 7L17s
| | 7L17s
Line 1,821: Line 1,791:
| | g = 239\336
| | g = 239\336
| | g = 22\31, 27\38, 32\45
| | g = 22\31, 27\38, 32\45
| | 5-17g
| | 17g-12+5-7g = 10g-7
| | 7g-2
|-
|-
| | 8L16s
| | 8L16s
Line 1,828: Line 1,797:
| | g = 5\48
| | g = 5\48
| | g = 3\32, 4\40, 5\48
| | g = 3\32, 4\40, 5\48
| | 2g-1\8
| | 2g-1\8+1\8-g = g
| | 1\8-g
|-
|-
| | 9L15s
| | 9L15s
Line 1,835: Line 1,803:
| | g = 31\144
| | g = 31\144
| | g = 7\33, 9\42, 11\51
| | g = 7\33, 9\42, 11\51
| | 5g-1
| | 5g-1+2\3-3g = 2g-1\3
| | 2\3-3g
|-
|-
| | 10L14s
| | 10L14s
Line 1,842: Line 1,809:
| | g = 71\240
| | g = 71\240
| | g = 10\34, 13\44, 16\54
| | g = 10\34, 13\44, 16\54
| | 7g-2
| | 7g-2+3\2-5g = 2g-1\2
| | 3\2-5g
|-
|-
| | 11L13s
| | 11L13s
Line 1,849: Line 1,815:
| | g = 287\528
| | g = 287\528
| | g = 19\35, 25\46, 31\57
| | g = 19\35, 25\46, 31\57
| | 13g-7
| | 13g-7+6-11g = 2g-1
| | 6-11g
|-
|-
| | 12L12s
| | 12L12s
Line 1,856: Line 1,821:
| | g = 3\48
| | g = 3\48
| | g = 2\36, 3\48, 4\60
| | g = 2\36, 3\48, 4\60
| | g
| | g+1\12-g = 1\12
| | 1\12-g
|-
|-
| | 13L11s
| | 13L11s
Line 1,863: Line 1,827:
| | g = 287\624
| | g = 287\624
| | g = 17\37, 23\50, 29\63
| | g = 17\37, 23\50, 29\63
| | 11g-5
| | 11g-5+6-13g = 1-2g
| | 6-13g
|-
|-
| | 14L10s
| | 14L10s
Line 1,870: Line 1,833:
| | g = 239\336
| | g = 239\336
| | g = 27\38, 37\52, 47\66
| | g = 27\38, 37\52, 47\66
| | 3\2-5g
| | 5g-7\2+5-7g = 3\2-2g
| | 7g-2
|-
|-
| | 15L9s
| | 15L9s
Line 1,877: Line 1,839:
| | g = 31\240
| | g = 31\240
| | g = 5\39, 7\54, 9\69
| | g = 5\39, 7\54, 9\69
| | 3g-1\3
| | 3g-1\3+2\3-5g = 1\3-2g
| | 2\3-5g
|-
|-
| | 16L8s
| | 16L8s
Line 1,884: Line 1,845:
| | g = 5\96
| | g = 5\96
| | g = 2\40, 3\56, 4\72
| | g = 2\40, 3\56, 4\72
| | g
| | g+1\8-2g = 1\8-g
| | 1\8-2g
|-
|-
| | 17L7s
| | 17L7s
Line 1,891: Line 1,851:
| | g = 239\816
| | g = 239\816
| | g = 12\41, 17\58, 22\75
| | g = 12\41, 17\58, 22\75
| | 4-7g
| | 7g-2+5-17g = 3-10g
| | 17g-12
|-
|-
| | 18L6s
| | 18L6s
Line 1,898: Line 1,857:
| | g = 7\144
| | g = 7\144
| | g = 2\42, 3\60, 4\78
| | g = 2\42, 3\60, 4\78
| | g
| | g+1\6-3g = 1\6-2g
| | 1\6-3g
|-
|-
| | 19L5s
| | 19L5s
Line 1,905: Line 1,863:
| | g = 191\912
| | g = 191\912
| | g = 9\43, 13\62, 17\81
| | g = 9\43, 13\62, 17\81
| | 5g-5
| | 5g-5+4-19g = 1-18g
| | 4-19g
|-
|-
| | 20L4s
| | 20L4s
Line 1,912: Line 1,869:
| | g = 11\240
| | g = 11\240
| | g = 2\44, 3\64, 4\84
| | g = 2\44, 3\64, 4\84
| | g
| | g+1\4-5g = 1\4-4g
| | 1\4-5g
|-
|-
| | 21L3s
| | 21L3s
Line 1,919: Line 1,875:
| | g = 15\336
| | g = 15\336
| | g = 2\45, 3\66, 4\87
| | g = 2\45, 3\66, 4\87
| | g
| | g+1\3-7g = 1\3-6g
| | 1\3-7g
|-
|-
| | 22L2s
| | 22L2s
Line 1,926: Line 1,881:
| | g = 23\264
| | g = 23\264
| | g = 2\46, 3\68, 4\90
| | g = 2\46, 3\68, 4\90
| | g
| | g+1\2-11g = 1\2-10g
| | 1\2-11g
|-
|-
| | 23L1s
| | 23L1s
Line 1,933: Line 1,887:
| | g = 47\1104
| | g = 47\1104
| | g = 2\47, 3\70, 4\93
| | g = 2\47, 3\70, 4\93
| | g
| | g+1-23g = 1-22g
| | 1-23g
|}
|}


Line 1,945: Line 1,898:
! | <span style="background-color: #ffffff;">Midpoint</span>
! | <span style="background-color: #ffffff;">Midpoint</span>
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step
! | Large step+Small step
! | Small step
|-
|-
| | 1L24s
| | 1L24s
Line 1,952: Line 1,904:
| | g = 49\50
| | g = 49\50
| | ''g = 25\26, 26\27, 27\28''
| | ''g = 25\26, 26\27, 27\28''
| | 24g-23
| | 24g-23+1-g = 23g-22
| | 1-g
|-
|-
| | 2L23s
| | 2L23s
Line 1,959: Line 1,910:
| | g = 49\100
| | g = 49\100
| | ''g = 13\27, 14\29, 15\31''
| | ''g = 13\27, 14\29, 15\31''
| | 23g-11
| | 23g-11+1-2g = 21g-10
| | 1-2g
|-
|-
| | 3L22s
| | 3L22s
Line 1,966: Line 1,916:
| | g = 49\150
| | g = 49\150
| | g = ''9\28'', ''10\31'', 11\34
| | g = ''9\28'', ''10\31'', 11\34
| | 22g-7
| | 22g-7+1-3g = 19g-6
| | 1-3g
|-
|-
| | 4L21s
| | 4L21s
Line 1,973: Line 1,922:
| | g = 49\200
| | g = 49\200
| | g = ''7\29'', 8\33, 9\37
| | g = ''7\29'', 8\33, 9\37
| | 21g-5
| | 21g-5+1-4g = 17g-4
| | 1-4g
|-
|-
| | 5L20s
| | 5L20s
Line 1,980: Line 1,928:
| | g = 9\50
| | g = 9\50
| | g = ''5\30'', 6\35, 7\40
| | g = ''5\30'', 6\35, 7\40
| | 4g-3\5
| | 4g-3\5+1\5-g = 3g-2\5
| | 1\5-g
|-
|-
| | 6L19s
| | 6L19s
Line 1,987: Line 1,934:
| | g = 49\300
| | g = 49\300
| | g = ''5\31'', 6\37, 7\43
| | g = ''5\31'', 6\37, 7\43
| | 19g-3
| | 19g-3+1-6g = 13g-2
| | 1-6g
|-
|-
| | 7L18s
| | 7L18s
Line 1,994: Line 1,940:
| | g = 99\350
| | g = 99\350
| | g = 9\32, 11\39, 13\46
| | g = 9\32, 11\39, 13\46
| | 18g-5
| | 18g-5+2-7g = 11g-3
| | 2-7g
|-
|-
| | 8L17s
| | 8L17s
Line 2,001: Line 1,946:
| | g = 49\400
| | g = 49\400
| | g = 4\33, 5\41, 6\47
| | g = 4\33, 5\41, 6\47
| | <span style="line-height: 15.6000003814697px;">17g-2</span>
| | <span style="line-height: 15.6000003814697px;">17g-2+1-8g = 9g-1</span>
| | 1-8g
|-
|-
| | 9L16s
| | 9L16s
Line 2,008: Line 1,952:
| | g = 199\450
| | g = 199\450
| | g = 15\34, 19\43, 23\52
| | g = 15\34, 19\43, 23\52
| | 16g-7
| | 16g-7<span style="line-height: 15.6000003814697px;">+4-9g = 3-7g</span>
| | <span style="line-height: 15.6000003814697px;">-9g+4</span>
|-
|-
| | 10L15s
| | 10L15s
Line 2,015: Line 1,958:
| | g = 9\100
| | g = 9\100
| | g = 3\35, 4\45, 5\55
| | g = 3\35, 4\45, 5\55
| | 3g-1\5
| | 3g-1\5+1\5-2g = g
| | 1\5-2g
|-
|-
| | 11L14s
| | 11L14s
Line 2,022: Line 1,964:
| | g = 199\550
| | g = 199\550
| | g = 13\36, 17\47, 21\58
| | g = 13\36, 17\47, 21\58
| | 14g-5
| | 14g-5+4-11g = 3g-1
| | -11g+4
|-
|-
| | 12L13s
| | 12L13s
Line 2,029: Line 1,970:
| | g = 49\600
| | g = 49\600
| | g = 3\37, 4\49, 5\61
| | g = 3\37, 4\49, 5\61
| | 13g-1
| | 13g-1+1-12g = g
| | 1-12g
|-
|-
| | 13L12s
| | 13L12s
Line 2,036: Line 1,976:
| | g = 599\650
| | g = 599\650
| | g = 35\38, 47\51, 59\64
| | g = 35\38, 47\51, 59\64
| | 12g-11
| | 12g-11+12-13g = 1-g
| | 12-13g
|-
|-
| | 14L11s
| | 14L11s
Line 2,043: Line 1,982:
| | g = 449\700
| | g = 449\700
| | g = 25\39, 34\53, 43\67
| | g = 25\39, 34\53, 43\67
| | 11g-7
| | 11g-7+9-14g = 2-3g
| | -14g+9
|-
|-
| | 15L10s
| | 15L10s
Line 2,050: Line 1,988:
| | g = 19\150
| | g = 19\150
| | g = 5\40, 7\55, 9\70
| | g = 5\40, 7\55, 9\70
| | 2g-1\5
| | 2g-1\5+2\5-3g = 1\5-g
| | 2\5-3g
|-
|-
| | 16L9s
| | 16L9s
Line 2,057: Line 1,994:
| | g = 449\800
| | g = 449\800
| | g = 23\41, 32\57, 41\73
| | g = 23\41, 32\57, 41\73
| | 9g-5
| | 9g-5+9-16g = 4-7g
| | 9-16g
|-
|-
| | 17L8s
| | 17L8s
Line 2,064: Line 2,000:
| | g = 749\850
| | g = 749\850
| | g = 37\42, 52\59, 67\76
| | g = 37\42, 52\59, 67\76
| | 8g-7
| | 8g-7+15-17g = 8-9g
| | 15-17g
|-
|-
| | 18L7s
| | 18L7s
Line 2,071: Line 2,006:
| | g = 649\900
| | g = 649\900
| | g = 31\43, 44\61, 57\79
| | g = 31\43, 44\61, 57\79
| | 7g-5
| | 7g-5+13-18g = 8-11g
| | 13-18g
|-
|-
| | 19L6s
| | 19L6s
Line 2,078: Line 2,012:
| | g = 799\950
| | g = 799\950
| | g = 37\44, 53\63, 69\82
| | g = 37\44, 53\63, 69\82
| | 6g-5
| | 6g-5+16-19g = 11-13g
| | 16-19g
|-
|-
| | 20L5s
| | 20L5s
Line 2,085: Line 2,018:
| | g = 9\200
| | g = 9\200
| | g = 2\45, 3\65, 4\85
| | g = 2\45, 3\65, 4\85
| | g
| | g+1\5-4g = 1\5-3g
| | 1\5-4g
|-
|-
| | 21L4s
| | 21L4s
Line 2,092: Line 2,024:
| | g = 799\1050
| | g = 799\1050
| | g = 35\46, 51\67, 71\88
| | g = 35\46, 51\67, 71\88
| | 4g-3
| | 4g-3+16-21g = 13-17g
| | 16-21g
|-
|-
| | 22L3s
| | 22L3s
Line 2,099: Line 2,030:
| | g = 749\1100
| | g = 749\1100
| | g = 32\47, 47\69, 62\91
| | g = 32\47, 47\69, 62\91
| | 3g-2
| | 3g-2+15-22g = 13-19g
| | 15-22g
|-
|-
| | 23L2s
| | 23L2s
Line 2,106: Line 2,036:
| | g = 599\1150
| | g = 599\1150
| | g = 25\48, 37\71, 49\94
| | g = 25\48, 37\71, 49\94
| | 2g-1
| | 2g-1+11-23g = 10-21g
| | 11-23g
|-
|-
| | 24L1s
| | 24L1s
Line 2,113: Line 2,042:
| | g = 49\1200
| | g = 49\1200
| | g = 2\49, 3\73, 4\97
| | g = 2\49, 3\73, 4\97
| | g
| | g+1-24g = 1-23g
| | 1-24g
|}
|}


Line 2,125: Line 2,053:
! | <span style="background-color: #ffffff;">Midpoint</span>
! | <span style="background-color: #ffffff;">Midpoint</span>
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step
! | Large step+Small step
! | Small step
|-
|-
| | 1L25s
| | 1L25s
Line 2,132: Line 2,059:
| | g = 51\52
| | g = 51\52
| | ''g = 26\27, 27\28, 28\29''
| | ''g = 26\27, 27\28, 28\29''
| | 25g-24
| | 25g-24+1-g = 24g-23
| | 1-g
|-
|-
| | 2L24s
| | 2L24s
Line 2,139: Line 2,065:
| | g = 25\52
| | g = 25\52
| | ''g = 13\28, 14\30, 15\32''
| | ''g = 13\28, 14\30, 15\32''
| | 12g-11\2
| | 12g-11\2+1\2-g = 11g-5
| | 1\2-g
|-
|-
| | 3L23s
| | 3L23s
Line 2,146: Line 2,071:
| | g = 103\156
| | g = 103\156
| | g = ''19\29'', ''21\32'', 23\35
| | g = ''19\29'', ''21\32'', 23\35
| | 23g-15
| | 23g-15+2-3g = 20g-13
| | 2-3g
|-
|-
| | 4L22s
| | 4L22s
Line 2,153: Line 2,077:
| | g = 25\104
| | g = 25\104
| | g = ''7\30'', 8\34, 9\38
| | g = ''7\30'', 8\34, 9\38
| | 11g-5\2
| | 11g-5\2+<span style="line-height: 15.6000003814697px;">1\2-2g = 9g-2</span>
| | <span style="line-height: 15.6000003814697px;">1\2-2g</span>
|-
|-
| | 5L21s
| | 5L21s
Line 2,160: Line 2,083:
| | g = 51\260
| | g = 51\260
| | g = ''6\31'', 7\36, 8\41
| | g = ''6\31'', 7\36, 8\41
| | 21g-4
| | 21g-4+1-5g = 16g-3
| | 1-5g
|-
|-
| | 6L20s
| | 6L20s
Line 2,167: Line 2,089:
| | g = 25\156
| | g = 25\156
| | g = ''5\32'', 6\38, 7\44
| | g = ''5\32'', 6\38, 7\44
| | 10g-3\2
| | 10g-3\2+1\2-3g = 7g-1
| | 1\2-3g
|-
|-
| | 7L19s
| | 7L19s
Line 2,174: Line 2,095:
| | g = 155\364
| | g = 155\364
| | g = 14\33, 17\40, 20\47
| | g = 14\33, 17\40, 20\47
| | 19g-8
| | 19g-8+3-7g = 12g-5
| | 3-7g
|-
|-
| | 8L18s
| | 8L18s
Line 2,181: Line 2,101:
| | g = 25\208
| | g = 25\208
| | g = 4\34, 5\42, 6\50
| | g = 4\34, 5\42, 6\50
| | 9g-1
| | 9g-1+1\2-4g = 5g-1\2
| | 1\2-4g
|-
|-
| | 9L17s
| | 9L17s
Line 2,188: Line 2,107:
| | g = 415\468
| | g = 415\468
| | g = 31\35, 39\44, 47\53
| | g = 31\35, 39\44, 47\53
| | 17g-15
| | 17g-15+8-9g = 8g-7
| | 8-9g
|-
|-
| | 10L16s
| | 10L16s
Line 2,195: Line 2,113:
| | g = 51\260
| | g = 51\260
| | g = 7\36, 9\46, 11\56
| | g = 7\36, 9\46, 11\56
| | 8g-3\2
| | 8g-3\2+1-5g = 3g-1\2
| | 1-5g
|-
|-
| | 11L15s
| | 11L15s
Line 2,202: Line 2,119:
| | g = 155\572
| | g = 155\572
| | g = 10\37, 13\48, 16\59
| | g = 10\37, 13\48, 16\59
| | 15g-4
| | 15g-4+3-11g = 4g-1
| | 3-11g
|-
|-
| | 12L14s
| | 12L14s
Line 2,209: Line 2,125:
| | g = 25\312
| | g = 25\312
| | g = 3\38, 4\50, 5\62
| | g = 3\38, 4\50, 5\62
| | 7g-1\2
| | 7g-1\2+1\2-6g = g
| | 1\2-6g
|-
|-
| | 13L13s
| | 13L13s
Line 2,216: Line 2,131:
| | g = 3\52
| | g = 3\52
| | g = 2\39, 3\52, 4\65
| | g = 2\39, 3\52, 4\65
| | g
| | g+1\13-g = 1\13
| | 1\13-g
|-
|-
| | <span style="line-height: 15.6000003814697px;">14L12s</span>
| | <span style="line-height: 15.6000003814697px;">14L12s</span>
Line 2,223: Line 2,137:
| | g = 155\364
| | g = 155\364
| | g = 17\40, 23\54, 29\68
| | g = 17\40, 23\54, 29\68
| | 6g-5\2
| | 6g-5\2+3-7g = 1\2-g
| | 3-7g
|-
|-
| | <span style="line-height: 15.6000003814697px;">15L11s</span>
| | <span style="line-height: 15.6000003814697px;">15L11s</span>
Line 2,230: Line 2,143:
| | g = 571\780
| | g = 571\780
| | g = 30\41, 41\56, 52\71
| | g = 30\41, 41\56, 52\71
| | 11g-8
| | 11g-8+11-15g = 3-4g
| | 11-15g
|-
|-
| | <span style="line-height: 15.6000003814697px;">16L10s</span>
| | <span style="line-height: 15.6000003814697px;">16L10s</span>
Line 2,237: Line 2,149:
| | g = 129\416
| | g = 129\416
| | g = 13\42, 18\58, 23\74
| | g = 13\42, 18\58, 23\74
| | 13\2-8g
| | 5g-3\2+5\2-8g = 1-3g
| | 5g-4
|-
|-
| | <span style="line-height: 15.6000003814697px;">17L9s</span>
| | <span style="line-height: 15.6000003814697px;">17L9s</span>
Line 2,244: Line 2,155:
| | g = 103\884
| | g = 103\884
| | g = 5\43, 7\60, 9\77
| | g = 5\43, 7\60, 9\77
| | 9g-1
| | 9g-1+2-17g = 1-8g
| | 2-17g
|-
|-
| | <span style="line-height: 15.6000003814697px;">18L</span>8s
| | <span style="line-height: 15.6000003814697px;">18L</span>8s
Line 2,251: Line 2,161:
| | g = 181\468
| | g = 181\468
| | g = 17\44, 24\62, 31\80
| | g = 17\44, 24\62, 31\80
| | 4g-7\2
| | 4g-7\2+7-9g = 7\2-5g
| | 7-9g
|-
|-
| | <span style="line-height: 15.6000003814697px;">19L</span>7s
| | <span style="line-height: 15.6000003814697px;">19L</span>7s
Line 2,258: Line 2,167:
| | g = 571\988
| | g = 571\988
| | g = 26\45, 37\64, 48\83
| | g = 26\45, 37\64, 48\83
| | 7g-4
| | 7g-4+11-19g = 7-12g
| | 11-19g
|-
|-
| | <span style="line-height: 15.6000003814697px;">20L</span>6s
| | <span style="line-height: 15.6000003814697px;">20L</span>6s
Line 2,265: Line 2,173:
| | g = 181\520
| | g = 181\520
| | g = 16\46, 23\66, 30\86
| | g = 16\46, 23\66, 30\86
| | 3g-1
| | 3g-1+7\2-10g = 5\2-7g
| | 7\2-10g
|-
|-
| | <span style="line-height: 15.6000003814697px;">21L</span>5s
| | <span style="line-height: 15.6000003814697px;">21L</span>5s
Line 2,272: Line 2,179:
| | g = 883\1092
| | g = 883\1092
| | g = 38\47, 55\68, 72\89
| | g = 38\47, 55\68, 72\89
| | 5g-4
| | 5g-4+16-21g = 12-16g
| | 16-21g
|-
|-
| | <span style="line-height: 15.6000003814697px;">22L</span>4s
| | <span style="line-height: 15.6000003814697px;">22L</span>4s
Line 2,279: Line 2,185:
| | g = 155\572
| | g = 155\572
| | g = 13\48, 19\70, 25\92
| | g = 13\48, 19\70, 25\92
| | 2g-1\2
| | 2g-1\2+3-11g = 5\2-9g
| | 3-11g
|-
|-
| | <span style="line-height: 15.6000003814697px;">23L</span>3s
| | <span style="line-height: 15.6000003814697px;">23L</span>3s
Line 2,286: Line 2,191:
| | g = 415\1196
| | g = 415\1196
| | g = 17\49, 25\72, 33/95
| | g = 17\49, 25\72, 33/95
| | 3g-1
| | 3g-1+8-23g = 7-20g
| | 8-23g
|-
|-
| | <span style="line-height: 15.6000003814697px;">24L</span>2s
| | <span style="line-height: 15.6000003814697px;">24L</span>2s
Line 2,293: Line 2,197:
| | g = 25\312
| | g = 25\312
| | g = 2\50, 3\74, 4\98
| | g = 2\50, 3\74, 4\98
| | g
| | g+1\2-12g = 1\2-11g
| | 1\2-12g
|-
|-
| | 25L1s
| | 25L1s
Line 2,300: Line 2,203:
| | g = 51\1300
| | g = 51\1300
| | g = 2\51, 3\76, 4\101
| | g = 2\51, 3\76, 4\101
| | g
| | g+1-25g = 1-24g
| | 1-25g
|}
|}


Line 2,312: Line 2,214:
! | <span style="background-color: #ffffff;">Midpoint</span>
! | <span style="background-color: #ffffff;">Midpoint</span>
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step
! | Large step+Small step
! | Small step
|-
|-
| | 1L26s
| | 1L26s
Line 2,319: Line 2,220:
| | g = 53\54
| | g = 53\54
| | <span style="line-height: 15.6000003814697px;">''g = 27\28,''</span> ''28\29, 29\30''
| | <span style="line-height: 15.6000003814697px;">''g = 27\28,''</span> ''28\29, 29\30''
| | 26g-25
| | 26g-25+1-g = 25g-24
| | 1-g
|-
|-
| | 2L25s
| | 2L25s
Line 2,326: Line 2,226:
| | g = 53\108
| | g = 53\108
| | ''g = 14\29, 15\31, 16\33''
| | ''g = 14\29, 15\31, 16\33''
| | 25g-12
| | 25g-12+1-2g = 23g-11
| | 1-2g
|-
|-
| | 3L24s
| | 3L24s
Line 2,333: Line 2,232:
| | g = 17\54
| | g = 17\54
| | g = ''9\30'', ''10\33'', 11\36
| | g = ''9\30'', ''10\33'', 11\36
| | 8g-7\3
| | 8g-7\3+1-3g = 5g-2
| | 1-3g
|-
|-
| | 4L23s
| | 4L23s
Line 2,340: Line 2,238:
| | g = 161\216
| | g = 161\216
| | g = ''23\31'', 26\35, 29\39
| | g = ''23\31'', 26\35, 29\39
| | 23g-17
| | 23g-17+3-4g = 19g-14
| | 3-4g
|-
|-
| | 5L22s
| | 5L22s
Line 2,347: Line 2,244:
| | g = 161\270
| | g = 161\270
| | g = ''19\32'', 22\37, 25\42
| | g = ''19\32'', 22\37, 25\42
| | 22g-13
| | 22g-13+3-5g = 17g-10
| | 3-5g
|-
|-
| | 6L21s
| | 6L21s
Line 2,354: Line 2,250:
| | g = 17\108
| | g = 17\108
| | g = ''5\33'', 6\39, 7\45
| | g = ''5\33'', 6\39, 7\45
| | 7g-1
| | 7g-1+1\3-2g = 5g-2\3
| | 1\3-2g
|-
|-
| | 7L20s
| | 7L20s
Line 2,361: Line 2,256:
| | g = 323\378
| | g = 323\378
| | g = 29\34, 35\41, 41\48
| | g = 29\34, 35\41, 41\48
| | 20g-17
| | 20g-17+6-7g = 13g-11
| | 6-7g
|-
|-
| | 8L19s
| | 8L19s
Line 2,368: Line 2,262:
| | g = 161\432
| | g = 161\432
| | g = 13\35, 16\43, 19\51
| | g = 13\35, 16\43, 19\51
| | 19g-7
| | 19g-7+3-8g = 11g-4
| | 3-8g
|-
|-
| | 9L18s
| | 9L18s
Line 2,375: Line 2,268:
| | g = 5\54
| | g = 5\54
| | g = 3\36, 4\45, 5\54
| | g = 3\36, 4\45, 5\54
| | 2g-1\9
| | 2g-1\9+1\9-g = g
| | 1\9-g
|-
|-
| | 10L17s
| | 10L17s
Line 2,382: Line 2,274:
| | g = 161\540
| | g = 161\540
| | g = 11\37, 14\47, 17\57
| | g = 11\37, 14\47, 17\57
| | 17g-5
| | 17g-5+3-10g = 7g-2
| | 3-10g
|-
|-
| | 11L16s
| | 11L16s
Line 2,389: Line 2,280:
| | g = 485\594
| | g = 485\594
| | g = 31\38, 40\49, 49\60
| | g = 31\38, 40\49, 49\60
| | 16g-13
| | 16g-13+9-11g = 5g-4
| | 9-11g
|-
|-
| | 12L15s
| | 12L15s
Line 2,396: Line 2,286:
| | g = 17\216
| | g = 17\216
| | g = 3\39, 4\51, 5\63
| | g = 3\39, 4\51, 5\63
| | 5g-1\3
| | 5g-1\3+1\3-4g = g
| | 1\3-4g
|-
|-
| | 13L14s
| | 13L14s
Line 2,403: Line 2,292:
| | g = 53\702
| | g = 53\702
| | g = 3\40, 4\53, 5\66
| | g = 3\40, 4\53, 5\66
| | 14g-1
| | 14g-1+1-13g = g
| | 1-13g
|-
|-
| | 14L13s
| | 14L13s
Line 2,410: Line 2,298:
| | g = 701\756
| | g = 701\756
| | g = 38\41, 51\55, 64\69
| | g = 38\41, 51\55, 64\69
| | 13g-12
| | 13g-12+13-14g = 1-g
| | 13-14g
|-
|-
| | 15L12s
| | 15L12s
Line 2,417: Line 2,304:
| | g = 71\270
| | g = 71\270
| | g = 11\42, 15\57, 19\72
| | g = 11\42, 15\57, 19\72
| | 4g-4
| | 4g-1+4\3-5g = 1\3-g
| | 14\3-5g
|-
|-
| | 16L11s
| | 16L11s
Line 2,424: Line 2,310:
| | g = 161\864
| | g = 161\864
| | g = 8\43, 11\59, 14\75
| | g = 8\43, 11\59, 14\75
| | 11g-2
| | 11g-2+3-16g = 1-5g
| | 3-16g
|-
|-
| | 17L10s
| | 17L10s
Line 2,431: Line 2,316:
| | g = 647\918
| | g = 647\918
| | g = 31\44, 43\61, 55\78
| | g = 31\44, 43\61, 55\78
| | 10g-7
| | 10g-7+12-17g = 5-7g
| | 12-17g
|-
|-
| | 18L9s
| | 18L9s
Line 2,438: Line 2,322:
| | g = 5\108
| | g = 5\108
| | g = 2\45, 3\63, 4\81
| | g = 2\45, 3\63, 4\81
| | g
| | g+1\9-2g = 1\9-g
| | 1\9-2g
|-
|-
| | 19L8s
| | 19L8s
Line 2,445: Line 2,328:
| | g = 647\1026
| | g = 647\1026
| | g = 29\46, 41\65, 53\84
| | g = 29\46, 41\65, 53\84
| | 8g-5
| | 8g-5+12-19g = 7-11g
| | 12-19g
|-
|-
| | 20L7s
| | 20L7s
Line 2,452: Line 2,334:
| | g = 161\1080
| | g = 161\1080
| | g = 7\47, 10\67, 13\87
| | g = 7\47, 10\67, 13\87
| | 7g-1
| | 7g-1+3-20g = 2-13g
| | 3-20g
|-
|-
| | 21L6s
| | 21L6s
Line 2,459: Line 2,340:
| | g = 71\378
| | g = 71\378
| | g = 9\48, 13\69, 17\90
| | g = 9\48, 13\69, 17\90
| | 2g-1\3
| | 2g-1\3+4\3-7g = 1-5g
| | 4-7g
|-
|-
| | 22L5s
| | 22L5s
Line 2,466: Line 2,346:
| | g = 485\1188
| | g = 485\1188
| | g = 20\49, 29\71, 38\93
| | g = 20\49, 29\71, 38\93
| | 5g-2
| | 5g-2+9-22g = 7-17g
| | 9-22g
|-
|-
| | 23L4s
| | 23L4s
Line 2,473: Line 2,352:
| | g = 323\1242
| | g = 323\1242
| | g = 13\50, 19\73, 25\96
| | g = 13\50, 19\73, 25\96
| | 4g-1
| | 4g-1+6-23g = 5-19g
| | 6-23g
|-
|-
| | 24L3s
| | 24L3s
Line 2,480: Line 2,358:
| | g = 17\432
| | g = 17\432
| | g = 2\51, 3\75, 4\99
| | g = 2\51, 3\75, 4\99
| | g
| | g+1\3-8g = 1\3-7g
| | 1\3-8g
|-
|-
| | 25L2s
| | 25L2s
Line 2,487: Line 2,364:
| | g = 701\1350
| | g = 701\1350
| | g = 27\52, 40\77, 53\102
| | g = 27\52, 40\77, 53\102
| | 2g-1
| | 2g-1+13-25g = 12-23g
| | 13-25g
|-
|-
| | 26L1s
| | 26L1s
Line 2,494: Line 2,370:
| | g = 53\1404
| | g = 53\1404
| | g = 2\53, 3\79, 4\105
| | g = 2\53, 3\79, 4\105
| | g
| | g+1-26g = 1-25g
| | 1-26g
|}
|}


Line 2,506: Line 2,381:
! | <span style="background-color: #ffffff;">Midpoint</span>
! | <span style="background-color: #ffffff;">Midpoint</span>
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step
! | Large step+Small step
! | Small step
|-
|-
| | 1L27s
| | 1L27s
Line 2,513: Line 2,387:
| | g = 55\56
| | g = 55\56
| | ''g = 28\29, 29\30, 30\31''
| | ''g = 28\29, 29\30, 30\31''
| | 27g-26
| | 27g-26+1-g = 26g-25
| | 1-g
|-
|-
| | 2L26s
| | 2L26s
Line 2,520: Line 2,393:
| | g = 27\56
| | g = 27\56
| | ''g = 14\30, 15\32, 16\34''
| | ''g = 14\30, 15\32, 16\34''
| | 13g-6
| | 13g-6+1\2-g = 12g-11\2
| | 1\2-g
|-
|-
| | 3L25s
| | 3L25s
Line 2,527: Line 2,399:
| | g = 55\168
| | g = 55\168
| | g = ''10\31'',<span style="line-height: 15.6000003814697px;"> ''11\34'',</span> 12\37
| | g = ''10\31'',<span style="line-height: 15.6000003814697px;"> ''11\34'',</span> 12\37
| | 25g-8
| | 25g-8+1-3g = 22g-7
| | 1-3g
|-
|-
| | 4L24s
| | 4L24s
Line 2,534: Line 2,405:
| | g = 13\56
| | g = 13\56
| | g = ''7\32'', 8\36, 9\40
| | g = ''7\32'', 8\36, 9\40
| | 6g-5\4
| | 6g-5\4+1\4-g = 5g-1
| | 1\4-g
|-
|-
| | 5L23s
| | 5L23s
Line 2,541: Line 2,411:
| | g = 111\280
| | g = 111\280
| | g = ''13\33'', 15\38, 17\43
| | g = ''13\33'', 15\38, 17\43
| | 23g-9
| | 23g-9+2-5g = 18g-7
| | 2-5g
|-
|-
| | 6L22s
| | 6L22s
Line 2,548: Line 2,417:
| | g = 55\168
| | g = 55\168
| | g = ''11\34'', 13\40, 15\46
| | g = ''11\34'', 13\40, 15\46
| | 11g-7\2
| | 11g-7\2+1-3g = 8g-3
| | 1-3g
|-
|-
| | 7L21s
| | 7L21s
Line 2,555: Line 2,423:
| | g = 7\56
| | g = 7\56
| | g = 4\35, 5\42, 6\49
| | g = 4\35, 5\42, 6\49
| | 3g-2\7
| | 3g-2\7+1\7-g = 2g-1\7
| | 1\7-g
|-
|-
| | 8L20s
| | 8L20s
Line 2,562: Line 2,429:
| | g = 13\112
| | g = 13\112
| | g = 4\36, 5\44, 6\52
| | g = 4\36, 5\44, 6\52
| | 5g-1\2
| | 5g-1\2+1\4-2g = 3g-1\4
| | 1\4-2g
|-
|-
| | 9L19s
| | 9L19s
Line 2,569: Line 2,435:
| | g = 55\504
| | g = 55\504
| | g = 4\37, 5\46, 6\55
| | g = 4\37, 5\46, 6\55
| | 19g-2
| | 19g-2+1-9g = 10g-1
| | 1-9g
|-
|-
| | 10L18s
| | 10L18s
Line 2,576: Line 2,441:
| | g = 111\280
| | g = 111\280
| | g = 15\38, 19\48, 23\58
| | g = 15\38, 19\48, 23\58
| | 4g-7\2
| | 9g-7\2+2-5g = 4g-3\2
| | 2-5g
|-
|-
| | 11L17s
| | 11L17s
Line 2,583: Line 2,447:
| | g = 111\616
| | g = 111\616
| | g = 7\39, 9\50, 11\61
| | g = 7\39, 9\50, 11\61
| | 17g-3
| | 17g-3+2-11g = 6g-1
| | 2-11g
|-
|-
| | 12L16s
| | 12L16s
Line 2,590: Line 2,453:
| | g = 13\168
| | g = 13\168
| | g = 3\40, 4\52, 5\64
| | g = 3\40, 4\52, 5\64
| | 4g-1\4
| | 4g-1\4+1\4-3g = g
| | 1\4-3g
|-
|-
| | 13L15s
| | 13L15s
Line 2,597: Line 2,459:
| | g = 391\728
| | g = 391\728
| | g = 22\41, 29\54, 36\67
| | g = 22\41, 29\54, 36\67
| | 15g-8
| | 15g-8+7-13g = 2g-1
| | 7-13g
|-
|-
| | 14L14s
| | 14L14s
Line 2,604: Line 2,465:
| | g = 3\56
| | g = 3\56
| | g = 2\42, 3\56, 4\70
| | g = 2\42, 3\56, 4\70
| | g
| | g+1\14-g = 1\14
| | 1\14-g
|-
|-
| | <span style="line-height: 15.6000003814697px;">15L13s</span>
| | <span style="line-height: 15.6000003814697px;">15L13s</span>
Line 2,611: Line 2,471:
| | g = 391\840
| | g = 391\840
| | g = 20\43, 27\58, 34\73
| | g = 20\43, 27\58, 34\73
| | 13g-6
| | 13g-6+7-15g = 1-2g
| | 7-15g
|-
|-
| | <span style="line-height: 15.6000003814697px;">16L12s</span>
| | <span style="line-height: 15.6000003814697px;">16L12s</span>
Line 2,618: Line 2,477:
| | g = 41\224
| | g = 41\224
| | g = 8\44, 11\60, 14\76
| | g = 8\44, 11\60, 14\76
| | 3g-1\2
| | 3g-1\2+3\4-4g = 1\4-g
| | 3\4-4g
|-
|-
| | <span style="line-height: 15.6000003814697px;">17L11s</span>
| | <span style="line-height: 15.6000003814697px;">17L11s</span>
Line 2,625: Line 2,483:
| | g = 783\952
| | g = 783\952
| | g = 37\45, 51\62, 65\79
| | g = 37\45, 51\62, 65\79
| | 11g-9
| | 11g-9+13-17g = 4-6g
| | 13-17g
|-
|-
| | <span style="line-height: 15.6000003814697px;">18L10s</span>
| | <span style="line-height: 15.6000003814697px;">18L10s</span>
Line 2,632: Line 2,489:
| | g = 55\504
| | g = 55\504
| | g = 5\46, 7\64, 9\82
| | g = 5\46, 7\64, 9\82
| | 5g-1\2
| | 5g-1\2+1-9g = 1\2-4g
| | 1-9g
|-
|-
| | <span style="line-height: 15.6000003814697px;">19L9s</span>
| | <span style="line-height: 15.6000003814697px;">19L9s</span>
Line 2,639: Line 2,495:
| | g = 951\1064
| | g = 951\1064
| | g = 42\47, 59\66, 76\85
| | g = 42\47, 59\66, 76\85
| | 9g-8
| | 9g-8+17-19g = 9-10g
| | 17-19g
|-
|-
| | <span style="line-height: 15.6000003814697px;">20L</span>8s
| | <span style="line-height: 15.6000003814697px;">20L</span>8s
Line 2,646: Line 2,501:
| | g = 41\280
| | g = 41\280
| | g = 7\48, 10\68, 13\88
| | g = 7\48, 10\68, 13\88
| | 2g-1\4
| | 2g-1\4+3\4-5g = 1\2-3g
| | 3\4-5g
|-
|-
| | <span style="line-height: 15.6000003814697px;">21L7s</span>
| | <span style="line-height: 15.6000003814697px;">21L7s</span>
Line 2,653: Line 2,507:
| | g = 7\168
| | g = 7\168
| | g = 2\49, 3\70, 4\91
| | g = 2\49, 3\70, 4\91
| | g
| | g+<span style="line-height: 15.6000003814697px;">1\7-2g = 1\7-g</span>
| | <span style="line-height: 15.6000003814697px;">1\7-3g</span>
|-
|-
| | <span style="line-height: 15.6000003814697px;">22L</span>6s
| | <span style="line-height: 15.6000003814697px;">22L</span>6s
Line 2,660: Line 2,513:
| | g = 111\616
| | g = 111\616
| | g = 9\50, 13\72, 17\94
| | g = 9\50, 13\72, 17\94
| | 3g-1\2
| | 3g-1\2+2-11g = 3\2-8g
| | 2-11g
|-
|-
| | <span style="line-height: 15.6000003814697px;">23L</span>5s
| | <span style="line-height: 15.6000003814697px;">23L</span>5s
Line 2,667: Line 2,519:
| | g = 783\1288
| | g = 783\1288
| | g = 31\51, 45\74, 59\97
| | g = 31\51, 45\74, 59\97
| | 5g-3
| | 5g-3+14-23g = 11-18g
| | 14-23g
|-
|-
| | <span style="line-height: 15.6000003814697px;">24L</span>4s
| | <span style="line-height: 15.6000003814697px;">24L</span>4s
Line 2,674: Line 2,525:
| | g = 13\336
| | g = 13\336
| | g = 2\52, 3\76, 4\100
| | g = 2\52, 3\76, 4\100
| | g
| | g+1\4-6g = 1\4-5g
| | 1\4-6g
|-
|-
| | <span style="line-height: 15.6000003814697px;">25L</span>3s
| | <span style="line-height: 15.6000003814697px;">25L</span>3s
Line 2,681: Line 2,531:
| | g = 951\1400
| | g = 951\1400
| | g = 36\53, 53\78, 70\103
| | g = 36\53, 53\78, 70\103
| | 3g-2
| | 3g-2+17-25g = 15+22g
| | 17-25g
|-
|-
| | <span style="line-height: 15.6000003814697px;">26L</span>2s
| | <span style="line-height: 15.6000003814697px;">26L</span>2s
Line 2,688: Line 2,537:
| | g = 391\728
| | g = 391\728
| | g = 29\54, 43\80, 57\106
| | g = 29\54, 43\80, 57\106
| | g-1\2
| | g-1\2+7-13g = 13\2-12g
| | 19\2-13g
|-
|-
| | 27L1s
| | 27L1s
Line 2,695: Line 2,543:
| | g = 55\1512
| | g = 55\1512
| | g = 2\55, 3\82, 4\109
| | g = 2\55, 3\82, 4\109
| | g
| | g+1-27g = 1-26g
| | 1-27g
|}
|}


Line 2,707: Line 2,554:
! | <span style="background-color: #ffffff;">Midpoint</span>
! | <span style="background-color: #ffffff;">Midpoint</span>
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step
! | Large step+Small step
! | Small step
|-
|-
| | 1L28s
| | 1L28s
Line 2,714: Line 2,560:
| | g = 57\58
| | g = 57\58
| | ''g = 29\30, 30\31, 31\32''
| | ''g = 29\30, 30\31, 31\32''
| | 28g-27
| | 28g-27+1-g = 27g-26
| | 1-g
|-
|-
| | 2L27s
| | 2L27s
Line 2,721: Line 2,566:
| | g = 57\116
| | g = 57\116
| | ''g = 15\31, 16\33, 17\35''
| | ''g = 15\31, 16\33, 17\35''
| | 27g-13
| | 27g-13+1-2g = 25g-12
| | 1-2g
|-
|-
| | 3L26s
| | 3L26s
Line 2,728: Line 2,572:
| | g = 115\174
| | g = 115\174
| | g = ''21\32'', ''23\35'', 25\38
| | g = ''21\32'', ''23\35'', 25\38
| | 26g-17
| | 26g-17+2-3g = 23g-15
| | 2-3g
|-
|-
| | 4L25s
| | 4L25s
Line 2,735: Line 2,578:
| | g = 57\232
| | g = 57\232
| | g = ''8\33'', 9\37, 10\41
| | g = ''8\33'', 9\37, 10\41
| | 25g-6
| | 25g-6+1-4g = 21g-5
| | 1-4g
|-
|-
| | 5L24s
| | 5L24s
Line 2,742: Line 2,584:
| | g = 231\290
| | g = 231\290
| | g = ''27\34'', 31\39, 35\44
| | g = ''27\34'', 31\39, 35\44
| | 24g-19
| | 24g-19+4-5g = 19g-15
| | 4-5g
|-
|-
| | 6L23s
| | 6L23s
Line 2,749: Line 2,590:
| | g = 289\348
| | g = 289\348
| | g = ''29\35'', 34\41, 39\47
| | g = ''29\35'', 34\41, 39\47
| | 23g-19
| | 23g-19+5-6g = 17g-14
| | 5-6g
|-
|-
| | 7L22s
| | 7L22s
Line 2,756: Line 2,596:
| | g = 57\406
| | g = 57\406
| | g = ''5\36'', 6\43, 7\50
| | g = ''5\36'', 6\43, 7\50
| | 22g-3
| | 22g-3+1-7g = 15g-2
| | 1-7g
|-
|-
| | 8L21s
| | 8L21s
Line 2,763: Line 2,602:
| | g = 289\464
| | g = 289\464
| | g = 23\37, 28\45, 33\53
| | g = 23\37, 28\45, 33\53
| | <span style="line-height: 15.6000003814697px;">21g-13</span>
| | <span style="line-height: 15.6000003814697px;">21g-13+5-8g = 13g-8</span>
| | <span style="line-height: 15.6000003814697px;">5-8g</span>
|-
|-
| | 9L20s
| | 9L20s
Line 2,770: Line 2,608:
| | g = 289\522
| | g = 289\522
| | g = 21\38, 26\47, 31\56
| | g = 21\38, 26\47, 31\56
| | 20g-11
| | 20g-11+5-9g = 11g-6
| | 5-9g
|-
|-
| | 10L19s
| | 10L19s
Line 2,777: Line 2,614:
| | g = 521\580
| | g = 521\580
| | g = 35\39, 44\49, 53\59
| | g = 35\39, 44\49, 53\59
| | 19g-17
| | 19g-17+9-10g = 9g-8
| | 9-10g
|-
|-
| | 11L18s
| | 11L18s
Line 2,784: Line 2,620:
| | g = 463\638
| | g = 463\638
| | g = 29\40, 37\51, 45\62
| | g = 29\40, 37\51, 45\62
| | 18g-13
| | 18g-13+8-11g = 7g-2
| | 8-11g
|-
|-
| | 12L17s
| | 12L17s
Line 2,791: Line 2,626:
| | g = 289\696
| | g = 289\696
| | g = 17\41, 22\53, 27\65
| | g = 17\41, 22\53, 27\65
| | 17g-7
| | 17g-7+5-12g = 5g-2
| | 5-12g
|-
|-
| | 13L16s
| | 13L16s
Line 2,798: Line 2,632:
| | g = 521\754
| | g = 521\754
| | g = 29\42, 38\55, 47\68
| | g = 29\42, 38\55, 47\68
| | 16g+11
| | 16g+11+9-13g = 3g-2
| | 9-13g
|-
|-
| | 14L15s
| | 14L15s
Line 2,805: Line 2,638:
| | g = 57\812
| | g = 57\812
| | g = 3\43, 4\57, 5\71
| | g = 3\43, 4\57, 5\71
| | 15g-1
| | 15g-1+1-14g = g
| | 1-14g
|-
|-
| | 15L14s
| | 15L14s
Line 2,812: Line 2,644:
| | g = 811\870
| | g = 811\870
| | g = 41\44, 55\59, 69\74
| | g = 41\44, 55\59, 69\74
| | 14g-13
| | 14g-13+14-15g = 1-g
| | 14-15g
|-
|-
| | 16L13s
| | 16L13s
Line 2,819: Line 2,650:
| | g = 289\928
| | g = 289\928
| | g = 14\45, 19\61, 24\77
| | g = 14\45, 19\61, 24\77
| | 13g-4
| | 13g-4+5-16g = 1-3g
| | 5-16g
|-
|-
| | 17L12s
| | 17L12s
Line 2,826: Line 2,656:
| | g = 579\986
| | g = 579\986
| | g = 27\46, 37\63, 47\80
| | g = 27\46, 37\63, 47\80
| | 12g-5
| | 12g-5+7-17g = 2-5g
| | 7-17g
|-
|-
| | 18L11s
| | 18L11s
Line 2,833: Line 2,662:
| | g = 289\1044
| | g = 289\1044
| | g = 13\47, 18\65, 23\83
| | g = 13\47, 18\65, 23\83
| | 11g-3
| | 11g-3+5-18g = 2-7g
| | 5-18g
|-
|-
| | 19L10s
| | 19L10s
Line 2,840: Line 2,668:
| | g = 115\1102
| | g = 115\1102
| | g = 5\48, 7\67, 9\86
| | g = 5\48, 7\67, 9\86
| | 10g-1
| | 10g-1+2-19g = 1-9g
| | 2-19g
|-
|-
| | 20L9s
| | 20L9s
Line 2,847: Line 2,674:
| | g = 521\1160
| | g = 521\1160
| | g = 22\49, 31\69, 40\89
| | g = 22\49, 31\69, 40\89
| | 9g-5
| | 9g-5+9-20g = 4-11g
| | 9-20g
|-
|-
| | 21L8s
| | 21L8s
Line 2,854: Line 2,680:
| | g = 463\1216
| | g = 463\1216
| | g = 19\50, 27\71, 35\92
| | g = 19\50, 27\71, 35\92
| | 8g-3
| | 8g-3+8-21g = 5-13g
| | 8-21g
|-
|-
| | 22L7s
| | 22L7s
Line 2,861: Line 2,686:
| | g = 1001\1274
| | g = 1001\1274
| | g = 44\51, 63\73, 82\95
| | g = 44\51, 63\73, 82\95
| | 7g-6
| | 7g-6+9-22g = 3-16g
| | 9-22g
|-
|-
| | 23L6s
| | 23L6s
Line 2,868: Line 2,692:
| | g = 231\1332
| | g = 231\1332
| | g = 9\52, 13\75, 17\98
| | g = 9\52, 13\75, 17\98
| | 6g-1
| | 6g-1+4-23g = 3-17g
| | 4-23g
|-
|-
| | 24L5s
| | 24L5s
Line 2,875: Line 2,698:
| | g = 289\1392
| | g = 289\1392
| | g = 11\53, 16\77, 21\101
| | g = 11\53, 16\77, 21\101
| | 5g-9
| | 5g-9+5-24g = 4-19g
| | 5-24g
|-
|-
| | 25L4s
| | 25L4s
Line 2,882: Line 2,704:
| | g = 1001\1450
| | g = 1001\1450
| | g = 41\54, 60\79, 79\104
| | g = 41\54, 60\79, 79\104
| | 4g-3
| | 4g-3+19-25g = 16-21g
| | 19-25g
|-
|-
| | 26L3s
| | 26L3s
Line 2,889: Line 2,710:
| | g = 521\1508
| | g = 521\1508
| | g = 19\55, 28\81, 37\107
| | g = 19\55, 28\81, 37\107
| | 3g-1
| | 3g-1+9-26g = 8-23g
| | 19\2-26g
|-
|-
| | 27L2s
| | 27L2s
Line 2,896: Line 2,716:
| | g = 811\1564
| | g = 811\1564
| | g = 29\56, 43\83, 57\110
| | g = 29\56, 43\83, 57\110
| | 2g-1
| | 2g-1+17-27g = 16-25g
| | 17-27g
|-
|-
| | 28L1s
| | 28L1s
Line 2,903: Line 2,722:
| | g = 57\1622
| | g = 57\1622
| | g = 2\57,<span style="line-height: 15.6000003814697px;"> 3\85,</span> 4\113
| | g = 2\57,<span style="line-height: 15.6000003814697px;"> 3\85,</span> 4\113
| | g
| | g+1-28g = 1-27g
| | 1-28g
|}
|}

Revision as of 23:47, 25 June 2019

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 = I, 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
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