Generator ranges of MOS: Difference between revisions

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Line 12: Line 12:
! | Midpoint
! | Midpoint
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step
! | Large step+Small step
! | Small step
|-
|-
| | 1L1s
| | 1L1s
Line 19: Line 18:
| | g = 3\4
| | g = 3\4
| | g = 2\3, 3\4, 4\5
| | g = 2\3, 3\4, 4\5
| | g
| | g+1-g = 1
| | 1-g
|-
|-
| | 1L2s
| | 1L2s
Line 26: Line 24:
| | g = 5\6
| | g = 5\6
| | g = 3\4, 4\5, 5\6
| | g = 3\4, 4\5, 5\6
| | 2g-1
| | 2g-1+1-g = g
| | 1-g
|-
|-
| | 2L1s
| | 2L1s
Line 33: Line 30:
| | g = 5\12
| | g = 5\12
| | g = 2\5, 3\7, 4\9
| | g = 2\5, 3\7, 4\9
| | g
| | g+1-2g = 1-g
| | 1-2g
|-
|-
| | 1L3s
| | 1L3s
Line 40: Line 36:
| | g = 7\8
| | g = 7\8
| | g = 4\5, 5\6, 6\7
| | g = 4\5, 5\6, 6\7
| | 3g-2
| | 3g-2+1-g = 2g-1
| | 1-g
|-
|-
| | 2L2s
| | 2L2s
Line 47: Line 42:
| | g = 3\8
| | g = 3\8
| | g = 2\6, 3\8, 4\10
| | g = 2\6, 3\8, 4\10
| | g
| | g+1\2-g = 1\2
| | 1\2-g
|-
|-
| | 3L1s
| | 3L1s
Line 54: Line 48:
| | g = 7\24
| | g = 7\24
| | g = 2\7, 3\10, 4\13
| | g = 2\7, 3\10, 4\13
| | g
| | g+1-3g = 1-2g
| | 1-3g
|}
|}


Line 66: Line 59:
! | Midpoint
! | Midpoint
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step
! | Large step+Small step
! | Small step
|-
|-
| | 1L4s
| | 1L4s
Line 73: Line 65:
| | g = 9\10
| | g = 9\10
| | g = ''5\6'', 6\7, 7\8
| | g = ''5\6'', 6\7, 7\8
| | 4g-3
| | 4g-3+1-g = 3g-2
| | 1-g
|-
|-
| | 2L3s
| | 2L3s
Line 80: Line 71:
| | g = 9\20
| | g = 9\20
| | g = 3\7, 4\9, 5\11
| | g = 3\7, 4\9, 5\11
| | 3g-1
| | 3g-1+1-2g = g
| | 1-2g
|-
|-
| | 3L2s
| | 3L2s
Line 87: Line 77:
| | g = 19\30
| | g = 19\30
| | g = 5\8, 7\11, 9\14
| | g = 5\8, 7\11, 9\14
| | 2g-1
| | 2g-1+2-3g = 1-g
| | 2-3g
|-
|-
| | 4L1s
| | 4L1s
Line 94: Line 83:
| | g = 9\40
| | g = 9\40
| | g = 2\9, 3\13, 4\17
| | g = 2\9, 3\13, 4\17
| | g
| | g+1-4g = 1-3g
| | 1-4g
|}
|}


Line 106: Line 94:
! | Midpoint
! | Midpoint
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step
! | Large step+Small step
! | Small step
|-
|-
| | 1L5s
| | 1L5s
Line 113: Line 100:
| | g = 11\12
| | g = 11\12
| | g = ''6\7'', 7\8, 8\9
| | g = ''6\7'', 7\8, 8\9
| | 5g-4
| | 5g-4+1-g = 4g-3
| | 1-g
|-
|-
| | 2L4s
| | 2L4s
Line 120: Line 106:
| | g = 5\12
| | g = 5\12
| | g = 3\8, 4\10, 5\12
| | g = 3\8, 4\10, 5\12
| | 2g-1\2
| | 2g-1\2+1\2-g = g
| | 1\2-g
|-
|-
| | 3L3s
| | 3L3s
Line 127: Line 112:
| | g = 3\12
| | g = 3\12
| | g = 2\9, 3\12, 4\15
| | g = 2\9, 3\12, 4\15
| | g
| | g+1\3-g = 1\3
| | 1\3-g
|-
|-
| | 4L2s
| | 4L2s
Line 134: Line 118:
| | g = 5\24
| | g = 5\24
| | g = 2\10, 3\14, 4\18
| | g = 2\10, 3\14, 4\18
| | g
| | g+1\2-2g = 1\2-g
| | 1\2-2g
|-
|-
| | 5L1s
| | 5L1s
Line 141: Line 124:
| | g = 11\60
| | g = 11\60
| | g = 2\11, 3\16, 4\21
| | g = 2\11, 3\16, 4\21
| | g
| | g+1-5g = 1-4g
| | 1-5g
|}
|}


Line 153: Line 135:
! | Midpoint
! | Midpoint
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step
! | Large step+Small step
! | Small step
|-
|-
| | 1L6s
| | 1L6s
Line 160: Line 141:
| | g = 13\14
| | g = 13\14
| | g = ''7\8'', 8\9, 9\10
| | g = ''7\8'', 8\9, 9\10
| | 6g-5
| | 6g-5+1-g = 5g-4
| | 1-g
|-
|-
| | 2L5s
| | 2L5s
Line 167: Line 147:
| | g = 13\28
| | g = 13\28
| | g = 4\9, 5\11, 6\13
| | g = 4\9, 5\11, 6\13
| | 5g-2
| | 5g-2+1-2g = 3g-1
| | 1-2g
|-
|-
| | 3L4s
| | 3L4s
Line 174: Line 153:
| | g = 13\42
| | g = 13\42
| | g = 3\10, 4\13, 5\16
| | g = 3\10, 4\13, 5\16
| | 4g-1
| | 4g-1+1-3g = g
| | 1-3g
|-
|-
| | 4L3s
| | 4L3s
Line 181: Line 159:
| | g = 41\56
| | g = 41\56
| | g = 8\11, 11\15, 14\19
| | g = 8\11, 11\15, 14\19
| | 3g-2
| | 3g-2+3-4g = 1-g
| | 3-4g
|-
|-
| | 5L2s
| | 5L2s
Line 188: Line 165:
| | g = 41\70
| | g = 41\70
| | g = 7\12, 10\17, 13\22
| | g = 7\12, 10\17, 13\22
| | 2g-1
| | 2g-1+3-5g = 2-3g
| | 3-5g
|-
|-
| | 6L1s
| | 6L1s
Line 195: Line 171:
| | g = 13\84
| | g = 13\84
| | g = 2\13, 3\19, 4\25
| | g = 2\13, 3\19, 4\25
| | g
| | g+1-6g = 1-5g
| | 1-6g
|}
|}


Line 207: Line 182:
! | Midpoint
! | Midpoint
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step
! | Large step+Small step
! | Small step
|-
|-
| | 1L7s
| | 1L7s
Line 214: Line 188:
| | g = 15\16
| | g = 15\16
| | g = I, 9\10, 10\11
| | g = I, 9\10, 10\11
| | 7g-6
| | 7g-6+1-g = 6g-5
| | 1-g
|-
|-
| | 2L6s
| | 2L6s
Line 221: Line 194:
| | g = 7\16
| | g = 7\16
| | g = 4\10, 5\12, 6\14
| | g = 4\10, 5\12, 6\14
| | 3g-1
| | 3g-1+1\2-g = 2g-1\2
| | 1\2-g
|-
|-
| | 3L5s
| | 3L5s
Line 228: Line 200:
| | g = 31\48
| | g = 31\48
| | g = 7\11, 9\14, 11\17
| | g = 7\11, 9\14, 11\17
| | 5g-3
| | 5g-3+2-3g = 2g-1
| | 2-3g
|-
|-
| | 4L4s
| | 4L4s
Line 235: Line 206:
| | g = 3\16
| | g = 3\16
| | g = 2\12, 3\16, 4\20
| | g = 2\12, 3\16, 4\20
| | g
| | g+1\4-g = 1\4
| | 1\4-g
|-
|-
| | 5L3s
| | 5L3s
Line 242: Line 212:
| | g = 31\80
| | g = 31\80
| | g = 5\13, 7\18, 9\23
| | g = 5\13, 7\18, 9\23
| | 3g-1
| | 3g-1+2-5g = 1-2g
| | 2-5g
|-
|-
| | 6L2s
| | 6L2s
Line 249: Line 218:
| | g = 7\48
| | g = 7\48
| | g = 2\14, 3\20, 4\26
| | g = 2\14, 3\20, 4\26
| | g
| | g+1\2-3g = 1\2-2g
| | 1\2-3g
|-
|-
| | 7L1s
| | 7L1s
Line 256: Line 224:
| | g = 15\112
| | g = 15\112
| | g = 2\15, 3\22, 4\29
| | g = 2\15, 3\22, 4\29
| | g
| | g+1-7g = 1-6g
| | 1-7g
|}
|}


Line 267: Line 234:
! | Midpoint
! | Midpoint
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step
! | Large step+Small step
! | Small step
|-
|-
| | 1L8s
| | 1L8s
Line 274: Line 240:
| | g = 17\18
| | g = 17\18
| | g = ''9\10'', ''10\11'', 11\12
| | g = ''9\10'', ''10\11'', 11\12
| | 8g-7
| | 8g-7+1-g = 7g-6
| | 1-g
|-
|-
| | 2L7s
| | 2L7s
Line 281: Line 246:
| | g = 17\36
| | g = 17\36
| | g = ''5\11'', 6\13, 7\15
| | g = ''5\11'', 6\13, 7\15
| | 7g-3
| | 7g-3+1-2g = 5g-2
| | 1-2g
|-
|-
| | 3L6s
| | 3L6s
Line 288: Line 252:
| | g = 5\18
| | g = 5\18
| | g = 3\12, 4\15, 5\18
| | g = 3\12, 4\15, 5\18
| | 2g-1\3
| | 2g-1\3+1\3-g = g
| | 1\3-g
|-
|-
| | 4L5s
| | 4L5s
Line 295: Line 258:
| | g = 17\72
| | g = 17\72
| | g = 3\13, 4\17, 5\21
| | g = 3\13, 4\17, 5\21
| | 5g-1
| | 5g-1+1-4g = g
| | 1-4g
|-
|-
| | 5L4s
| | 5L4s
Line 302: Line 264:
| | g = 71\90
| | g = 71\90
| | g = 11\14, 15\19, 18\23
| | g = 11\14, 15\19, 18\23
| | 4g-3
| | 4g-3+4-5g = 1-g
| | 4-5g
|-
|-
| | 6L3s
| | 6L3s
Line 309: Line 270:
| | g = 5\36
| | g = 5\36
| | g = 2\15, 3\21, 4\27
| | g = 2\15, 3\21, 4\27
| | g
| | g+1\3-2g = 1\3-g
| | 1\3-2g
|-
|-
| | 7L2s
| | 7L2s
Line 316: Line 276:
| | g = 71\126
| | g = 71\126
| | g = 9\16, 10\23, 17\30
| | g = 9\16, 10\23, 17\30
| | 2g-1
| | 2g-1+4-7g = 3-7g
| | 4-7g
|-
|-
| | 8L1s
| | 8L1s
Line 323: Line 282:
| | g = 17\144
| | g = 17\144
| | g = 2\17, 3\25, 4\33
| | g = 2\17, 3\25, 4\33
| | g
| | g+1-8g = 1-7g
| | 1-8g
|}
|}


Line 335: Line 293:
! | Midpoint
! | Midpoint
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step
! | Large step+Small step
! | Small step
|-
|-
| | 1L9s
| | 1L9s
Line 342: Line 299:
| | g = 19\20
| | g = 19\20
| | g = ''10\11'', ''11\12'', 12\13
| | g = ''10\11'', ''11\12'', 12\13
| | 9g-8
| | 9g-8+1-g = 8g-7
| | 1-g
|-
|-
| | 2L8s
| | 2L8s
Line 349: Line 305:
| | g = 9\20
| | g = 9\20
| | g = ''5\12'', 6\14, 7\16
| | g = ''5\12'', 6\14, 7\16
| | 4g-3\2
| | 4g-3\2+1\2-g = 3g-1
| | 1\2-g
|-
|-
| | 3L7s
| | 3L7s
Line 356: Line 311:
| | g = 19\60
| | g = 19\60
| | g = 4\13, 5\16, 6\19
| | g = 4\13, 5\16, 6\19
| | 7g-2
| | 7g-2+1-3g = 4g-1
| | 1-3g
|-
|-
| | 4L6s
| | 4L6s
Line 363: Line 317:
| | g = 9\40
| | g = 9\40
| | g = 3\14, 4\18, 5\22
| | g = 3\14, 4\18, 5\22
| | 3g-1\2
| | 3g-1\2+1\2-2g = g
| | 1\2-2g
|-
|-
| | 5L5s
| | 5L5s
Line 370: Line 323:
| | g = 3\20
| | g = 3\20
| | g = 2\15, 3\20, 4\25
| | g = 2\15, 3\20, 4\25
| | g
| | g+1\5-g = 1\5
| | 1\5-g
|-
|-
| | 6L4s
| | 6L4s
Line 377: Line 329:
| | g = 19\60
| | g = 19\60
| | g = 5\16, 7\22, 9\28
| | g = 5\16, 7\22, 9\28
| | 2g-1\2
| | 2g-1\2+1-3g = 1\2-g
| | 1-3g
|-
|-
| | 7L3s
| | 7L3s
Line 384: Line 335:
| | g = 99\140
| | g = 99\140
| | g = 12\17, 17\24, 22\31
| | g = 12\17, 17\24, 22\31
| | 3g-2
| | 3g-2+5-7g = 3-4g
| | 5-7g
|-
|-
| | 8L2s
| | 8L2s
Line 391: Line 341:
| | g = 9\80
| | g = 9\80
| | g = 2\18, 3\26, 4\34
| | g = 2\18, 3\26, 4\34
| | g
| | g+1\2-4g = 1\2-3g
| | 1\2-4g
|-
|-
| | 9L1s
| | 9L1s
Line 398: Line 347:
| | g = 19\180
| | g = 19\180
| | g = 2\19, 3\28, 4\37
| | g = 2\19, 3\28, 4\37
| | g
| | g+1-9g = 1-8g
| | 1-9g
|}
|}


Line 410: Line 358:
! | Midpoint
! | Midpoint
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step
! | Large step+Small step
! | Small step
|-
|-
| | 1L10s
| | 1L10s
Line 417: Line 364:
| | g = 21\22
| | g = 21\22
| | g = ''11\12'', ''12\13'', 13\14
| | g = ''11\12'', ''12\13'', 13\14
| | 10g-9
| | 10g-9+1-g = 9g-8
| | 1-g
|-
|-
| | 2L9s
| | 2L9s
Line 424: Line 370:
| | g = 21\44
| | g = 21\44
| | g = ''6\13'', 7\15, 8\17
| | g = ''6\13'', 7\15, 8\17
| | 9g-4
| | 9g-4+1-2g = 7g-3
| | 1-2g
|-
|-
| | 3L8s
| | 3L8s
Line 431: Line 376:
| | g = 43\66
| | g = 43\66
| | g = 9\14, 11\17, 13\20
| | g = 9\14, 11\17, 13\20
| | 8g-5
| | 8g-5+2-3g = 5g-3
| | 2-3g
|-
|-
| | 4L7s
| | 4L7s
Line 438: Line 382:
| | g = 65\88
| | g = 65\88
| | g = 11\15, 14\19, 17\23
| | g = 11\15, 14\19, 17\23
| | 7g-5
| | 7g-5+3-4g = 3g-2
| | 3-4g
|-
|-
| | 5L6s
| | 5L6s
Line 445: Line 388:
| | g = 21\110
| | g = 21\110
| | g = 3\16, 4\21, 5\26
| | g = 3\16, 4\21, 5\26
| | 6g-1
| | 6g-1+1-5g = g
| | 1-5g
|-
|-
| | 6L5s
| | 6L5s
Line 452: Line 394:
| | g = 109\132
| | g = 109\132
| | g = 14\17, 19\23, 24\29
| | g = 14\17, 19\23, 24\29
| | 5g-4
| | 5g-4+5-6g = 1-g
| | 5-6g
|-
|-
| | 7L4s
| | 7L4s
Line 459: Line 400:
| | g = 43\154
| | g = 43\154
| | g = 5\18, 7\25, 9\32
| | g = 5\18, 7\25, 9\32
| | 4g-1
| | 4g-1+2-7g = 1-3g
| | 2-7g
|-
|-
| | 8L3s
| | 8L3s
Line 466: Line 406:
| | g = 65\176
| | g = 65\176
| | g = 7\19, 10\27, 13\35
| | g = 7\19, 10\27, 13\35
| | 3g-1
| | 3g-1+3-8g = 2-5g
| | 3-8g
|-
|-
| | 9L2s
| | 9L2s
Line 473: Line 412:
| | g = 109\198
| | g = 109\198
| | g = 11\20, 16\29, 21\38
| | g = 11\20, 16\29, 21\38
| | 2g-1
| | 2g-1+5-9g = 4-7g
| | 5-9g
|-
|-
| | 10L1s
| | 10L1s
Line 480: Line 418:
| | g = 21\220
| | g = 21\220
| | g = 2\21, 3\31, 4\41
| | g = 2\21, 3\31, 4\41
| | g
| | g+1-10g = 1-9g
| | 1-10g
|}
|}


Line 492: Line 429:
! | Midpoint
! | Midpoint
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step
! | Large step+Small step
! | Small step
|-
|-
| | 1L11s
| | 1L11s
Line 499: Line 435:
| | g = 23\24
| | g = 23\24
| | g = ''12\13,'' ''13\14'', 14\15
| | g = ''12\13,'' ''13\14'', 14\15
| | 11g-10
| | 11g-10+1-g = 10g-9
| | 1-g
|-
|-
| | 2L10s
| | 2L10s
Line 506: Line 441:
| | g = 11\24
| | g = 11\24
| | g = ''6\14'', 7\16, 8\18
| | g = ''6\14'', 7\16, 8\18
| | 5g-2
| | 5g-2+1\2-g = 4g-3\2
| | 1\2-g
|-
|-
| | 3L9s
| | 3L9s
Line 513: Line 447:
| | g = 7\24
| | g = 7\24
| | g = 4\15, 5\18, 6\21
| | g = 4\15, 5\18, 6\21
| | 3g-2\3
| | 3g-2\3+1\3-g = 2g-1\3
| | 1\3-g
|-
|-
| | 4L8s
| | 4L8s
Line 520: Line 453:
| | g = 5\24
| | g = 5\24
| | g = 3\16, 4\20, 5\24
| | g = 3\16, 4\20, 5\24
| | 2g-1\4
| | 2g-1\4+1\4-g = g
| | 1\4-g
|-
|-
| | 5L7s
| | 5L7s
Line 527: Line 459:
| | g = 71\120
| | g = 71\120
| | g = 10\17, 13\22, 16\27
| | g = 10\17, 13\22, 16\27
| | 7g-4
| | 7g-4+3-5g = 2g-1
| | 3-5g
|-
|-
| | 6L6s
| | 6L6s
Line 534: Line 465:
| | g = 3\24
| | g = 3\24
| | g = 2\18, 3\24, 4\30
| | g = 2\18, 3\24, 4\30
| | g
| | g+1\6-g = g
| | 1\6-g
|-
|-
| | 7L5s
| | 7L5s
Line 541: Line 471:
| | g = 71\168
| | g = 71\168
| | g = 8\19, 11\26, 14\33
| | g = 8\19, 11\26, 14\33
| | 5g-2
| | 5g-2+3-7g = 1-2g
| | 3-7g
|-
|-
| | 8L4s
| | 8L4s
Line 548: Line 477:
| | g = 5\48
| | g = 5\48
| | g = 2\20, 3\28, 4\36
| | g = 2\20, 3\28, 4\36
| | g
| | g+1\4-2g = 1\4-g
| | 1\4-2g
|-
|-
| | 9L3s
| | 9L3s
Line 555: Line 483:
| | g = 7\72
| | g = 7\72
| | g = 2\21, 3\30, 4\39
| | g = 2\21, 3\30, 4\39
| | g
| | g+1\3-3g = 1\3-2g
| | 1\3-3g
|-
|-
| | 10L2s
| | 10L2s
Line 562: Line 489:
| | g = 11\120
| | g = 11\120
| | g = 2\22, 3\32, 4\42
| | g = 2\22, 3\32, 4\42
| | g
| | g+1\2-5g = 1\2-4g
| | 1\2-5g
|-
|-
| | 11L1s
| | 11L1s
Line 569: Line 495:
| | g = 23\264
| | g = 23\264
| | g = 2\23, 3\34, 4\45
| | g = 2\23, 3\34, 4\45
| | g
| | g+1-11g = 1-10g
| | 1-11g
|}
|}


Line 581: Line 506:
! | Midpoint
! | Midpoint
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step
! | Large step+Small step
! | Small step
|-
|-
| | 1L12s
| | 1L12s
Line 588: Line 512:
| | g = 25\26
| | g = 25\26
| | ''g = 13\14, 14\15, 15\16''
| | ''g = 13\14, 14\15, 15\16''
| | 12g-11
| | 12g-11+1-g = 11g-10
| | 1-g
|-
|-
| | 2L11s
| | 2L11s
Line 595: Line 518:
| | g = 25\52
| | g = 25\52
| | g = ''7\15'', 8\17, 9\19
| | g = ''7\15'', 8\17, 9\19
| | 11g-5
| | 11g-5-1-2g = 10g-6
| | 1-2g
|-
|-
| | 3L10s
| | 3L10s
Line 602: Line 524:
| | g = 25\78
| | g = 25\78
| | g = ''5\16'', 6\19, 7/22
| | g = ''5\16'', 6\19, 7/22
| | 10g-3
| | 10g-3+1-3g = 7g-2
| | 1-3g
|-
|-
| | 4L9s
| | 4L9s
Line 609: Line 530:
| | g = 25\104
| | g = 25\104
| | g = 4\17, 5\21, 6\25
| | g = 4\17, 5\21, 6\25
| | 9g-2
| | 9g-2+1-4g = 5g-1
| | 1-4g
|-
|-
| | 5L8s
| | 5L8s
Line 616: Line 536:
| | g = 51\130
| | g = 51\130
| | g = 7\18, 9\23, 11\28
| | g = 7\18, 9\23, 11\28
| | 8g-3
| | 8g-3+2-5g = 3g-1
| | 2-5g
|-
|-
| | 6L7s
| | 6L7s
Line 623: Line 542:
| | g = 25\156
| | g = 25\156
| | g = 3\19, 4\25, 5\31
| | g = 3\19, 4\25, 5\31
| | 7g-1
| | 7g-1+1-6g = g
| | 1-6g
|-
|-
| | 7L6s
| | 7L6s
Line 630: Line 548:
| | g = 155\182
| | g = 155\182
| | g = 17\20, 23\27, 29\34
| | g = 17\20, 23\27, 29\34
| | 6g-5
| | 6g-5+6-7g = 1-g
| | 6-7g
|-
|-
| | 8L5s
| | 8L5s
Line 637: Line 554:
| | g = 129\208
| | g = 129\208
| | g = 13\21, 18\29, 23\37
| | g = 13\21, 18\29, 23\37
| | 5g-3
| | 5g-3+5-8g = 2-3g
| | 5-8g
|-
|-
| | 9L4s
| | 9L4s
Line 644: Line 560:
| | g = 181\234
| | g = 181\234
| | g = 17\22, 24\31, 31\40
| | g = 17\22, 24\31, 31\40
| | 4g-3
| | 4g-3+7-9g = 4-5g
| | 7-9g
|-
|-
| | 10L3s
| | 10L3s
Line 651: Line 566:
| | g = 181\260
| | g = 181\260
| | g = 16\23, 23\33, 30\43
| | g = 16\23, 23\33, 30\43
| | 3g-2
| | 3g-2+7-10g = 5-7g
| | 7-10g
|-
|-
| | 11L2s
| | 11L2s
Line 658: Line 572:
| | g = 155\286
| | g = 155\286
| | g = 13\24, 19\35, 25\46
| | g = 13\24, 19\35, 25\46
| | 2g-1
| | 2g-1+6-11g = 5-9g
| | 6-11g
|-
|-
| | 12L1s
| | 12L1s
Line 665: Line 578:
| | g = 25\312
| | g = 25\312
| | g = 2\25, 3\37, 4\49
| | g = 2\25, 3\37, 4\49
| | g
| | g+1-12g = 1-11g
| | 1-12g
|}
|}


Line 677: Line 589:
! | Midpoint
! | Midpoint
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step
! | Large step+Small step
! | Small step
|-
|-
| | 1L13s
| | 1L13s
Line 684: Line 595:
| | g = 27\28
| | g = 27\28
| | ''g = 14\15, 15\16, 16\17''
| | ''g = 14\15, 15\16, 16\17''
| | 13g-12
| | 13g-12+1-g = 12g-11
| | 1-g
|-
|-
| | 2L12s
| | 2L12s
Line 691: Line 601:
| | g = 13\28
| | g = 13\28
| | g = ''7\16'', 8\18, 9\20
| | g = ''7\16'', 8\18, 9\20
| | 6g-5\2
| | 6g-5\2+1\2-g = 5g-2
| | 1\2-g
|-
|-
| | 3L11s
| | 3L11s
Line 698: Line 607:
| | g = 55\84
| | g = 55\84
| | g = ''11\17'', 13\20, 15\23
| | g = ''11\17'', 13\20, 15\23
| | 11g-7
| | 11g-7+2-3g = 9g-5
| | 2-3g
|-
|-
| | 4L10s
| | 4L10s
Line 705: Line 613:
| | g = 13\56
| | g = 13\56
| | g = 4\18, 5\22, 6\26
| | g = 4\18, 5\22, 6\26
| | 5g-1
| | 5g-1+1\2-2g = 3g-1\2
| | 1\2-2g
|-
|-
| | 5L9s
| | 5L9s
Line 712: Line 619:
| | g = 111\140
| | g = 111\140
| | g = 15\19, 19\24, 23\29
| | g = 15\19, 19\24, 23\29
| | 9g-7
| | 9g-7+4-5g = 4g-3
| | 4-5g
|-
|-
| | 6L8s
| | 6L8s
Line 719: Line 625:
| | g = 13\84
| | g = 13\84
| | g = 3\20, 4\26, 5\32
| | g = 3\20, 4\26, 5\32
| | 4g-1\2
| | 4g-1\2-1\2-3g = g
| | 1\2-3g
|-
|-
| | 7L7s
| | 7L7s
Line 726: Line 631:
| | g = 3\28
| | g = 3\28
| | g = 2\21, 3\28, 4\35
| | g = 2\21, 3\28, 4\35
| | g
| | g+1\7-g = 1\7
| | 1\7-g
|-
|-
| | 8L6s
| | 8L6s
Line 733: Line 637:
| | g = 41\112
| | g = 41\112
| | g = 8\22, 11\30, 14\38
| | g = 8\22, 11\30, 14\38
| | 3g-1
| | 3g-1+3\2-4g = 1\2-g
| | 3\2-4g
|-
|-
| | 9L5s
| | 9L5s
Line 740: Line 643:
| | g = 55\252
| | g = 55\252
| | g = 5\23, 7\32, 9\41
| | g = 5\23, 7\32, 9\41
| | 5g-1
| | 5g-1+2-9g = 1-4g
| | 2-9g
|-
|-
| | 10L4s
| | 10L4s
Line 747: Line 649:
| | g = 41\140
| | g = 41\140
| | g = 7\24, 10\34, 13\44
| | g = 7\24, 10\34, 13\44
| | 2g-1\2
| | 2g-1\2+3\2-5g = 1-3g
| | 3\2-5g
|-
|-
| | 11L3s
| | 11L3s
Line 754: Line 655:
| | g = 111\308
| | g = 111\308
| | g = 9\25, 13\36, 17\47
| | g = 9\25, 13\36, 17\47
| | 3g-1
| | 3g-1+4-11g = 3-8g
| | 4-11g
|-
|-
| | 12L2s
| | 12L2s
Line 761: Line 661:
| | g = 13\168
| | g = 13\168
| | g = 2\26, 3\38, 4\50
| | g = 2\26, 3\38, 4\50
| | g
| | g+1\2-6g = 1\2-5g
| | 1\2-6g
|-
|-
| | 13L1s
| | 13L1s
Line 768: Line 667:
| | g = 27\364
| | g = 27\364
| | g = 2\27, 3\40, 4\53
| | g = 2\27, 3\40, 4\53
| | g
| | g+1-13g = 1-12g
| | 1-13g
|}
|}


Line 780: Line 678:
! | Midpoint
! | Midpoint
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step
! | Large step+Small step
! | Small step
|-
|-
| | 1L14s
| | 1L14s
Line 787: Line 684:
| | g = 29\30
| | g = 29\30
| | ''g = 15\16, 16\17, 17\18''
| | ''g = 15\16, 16\17, 17\18''
| | 14g-13
| | 14g-13+1-g = 13g-12
| | 1-g
|-
|-
| | 2L13s
| | 2L13s
Line 794: Line 690:
| | g = 29\60
| | g = 29\60
| | g = ''8\17'', 9\19, 10\21
| | g = ''8\17'', 9\19, 10\21
| | 13g-6
| | 13g-6+1-2g = 11g-5
| | 1-2g
|-
|-
| | 3L12s
| | 3L12s
Line 801: Line 696:
| | g = 9\30
| | g = 9\30
| | g = ''5\18'', 6\21, 7\24
| | g = ''5\18'', 6\21, 7\24
| | 4g-1
| | 4g-1+1\3-g = 3g-2\3
| | 1\3-g
|-
|-
| | 4L11s
| | 4L11s
Line 808: Line 702:
| | g = 89\120
| | g = 89\120
| | g = 14\19, 17\23, 20\27
| | g = 14\19, 17\23, 20\27
| | 11g-8
| | 11g-8+3-4g = 8g-4
| | 3-4g
|-
|-
| | 5L10s
| | 5L10s
Line 815: Line 708:
| | g = 5\30
| | g = 5\30
| | g = 3\20, 4\25, 5\30
| | g = 3\20, 4\25, 5\30
| | 2g-1\5
| | 2g-1\5+1\5-g = g
| | 1\5-g
|-
|-
| | 6L9s
| | 6L9s
Line 822: Line 714:
| | g = 9\60
| | g = 9\60
| | g = 3\21, 4\27, 5\33
| | g = 3\21, 4\27, 5\33
| | 3g-1\3
| | 3g-1\3+1\3-2g = g
| | 1\3-2g
|-
|-
| | 7L8s
| | 7L8s
Line 829: Line 720:
| | g = 29\210
| | g = 29\210
| | g = 3\22, 4\29, 5\36
| | g = 3\22, 4\29, 5\36
| | 8g-1
| | 8g-1+1-7g = g
| | 1-7g
|-
|-
| | 8L7s
| | 8L7s
Line 836: Line 726:
| | g = 209\240
| | g = 209\240
| | g = 20\23, 27\31, 34\39
| | g = 20\23, 27\31, 34\39
| | 7g-6
| | 7g-6+7-8g = 1-g
| | 7-8g
|-
|-
| | 9L6s
| | 9L6s
Line 843: Line 732:
| | g = 19\90
| | g = 19\90
| | g = 5\24, 7\33, 9\42
| | g = 5\24, 7\33, 9\42
| | 2g-1\3
| | 2g-1\3+2\3-3g = 1\3-g
| | 2\3-3g
|-
|-
| | 10L5s
| | 10L5s
Line 850: Line 738:
| | g = 5\60
| | g = 5\60
| | g = 2\25, 3\35, 4\45
| | g = 2\25, 3\35, 4\45
| | g
| | g+1\5-2g = 1\5-g
| | 1\5-2g
|-
|-
| | 11L4s
| | 11L4s
Line 857: Line 744:
| | g = 89\330
| | g = 89\330
| | g = 7\26, 10\37, 13\48
| | g = 7\26, 10\37, 13\48
| | 4g-1
| | 4g-1+3-11g = 2-7g
| | 3-11g
|-
|-
| | 12L3s
| | 12L3s
Line 864: Line 750:
| | g = 9\120
| | g = 9\120
| | g = 2\27, 3\39, 4\51
| | g = 2\27, 3\39, 4\51
| | g
| | g+1\3-4g = 1\3-3g
| | 1\3-4g
|-
|-
| | 13L2s
| | 13L2s
Line 871: Line 756:
| | g = 209\390
| | g = 209\390
| | g = 15\28, 22\41, 29\54
| | g = 15\28, 22\41, 29\54
| | 2g-1
| | 2g-1+7-13g = 6-11g
| | 7-13g
|-
|-
| | 14L1s
| | 14L1s
Line 878: Line 762:
| | g = 29\420
| | g = 29\420
| | g = 2\29, 3\43, 4\57
| | g = 2\29, 3\43, 4\57
| | g
| | g+1-14g = 1-13g
| | 1-14g
|}
|}


Line 890: Line 773:
! | Midpoint
! | Midpoint
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step
! | Large step+Small step
! | Small step
|-
|-
| | 1L15s
| | 1L15s
Line 897: Line 779:
| | g = 31\32
| | g = 31\32
| | ''g = 16\17, 17\18, 18\19''
| | ''g = 16\17, 17\18, 18\19''
| | 15g-14
| | 15g-14+1-g = 14g-13
| | 1-g
|-
|-
| | 2L14s
| | 2L14s
Line 904: Line 785:
| | g = 15\32
| | g = 15\32
| | g = ''8\18'', 9\20, 10\22
| | g = ''8\18'', 9\20, 10\22
| | 7g-3
| | 7g-3+1\2-g = 5\2-6g
| | 1\2-g
|-
|-
| | 3L13s
| | 3L13s
Line 911: Line 791:
| | g = 31\96
| | g = 31\96
| | g = ''6\19'', 7\22, 8\25
| | g = ''6\19'', 7\22, 8\25
| | 13g-4
| | 13g-4+1-3g = 10g-3
| | 1-3g
|-
|-
| | 4L12s
| | 4L12s
Line 918: Line 797:
| | g = 7\32
| | g = 7\32
| | g = 4\20, 5\24, 6\28
| | g = 4\20, 5\24, 6\28
| | 3g-1\2
| | 3g-1\2+1\4-g = 2g-1\4
| | 1\4-g
|-
|-
| | 5L11s
| | 5L11s
Line 925: Line 803:
| | g = 31\160
| | g = 31\160
| | g = 4\21, 5\26, 6\31
| | g = 4\21, 5\26, 6\31
| | 11g-2
| | 11g-2+1-5g = 6g-1
| | 1-5g
|-
|-
| | 6L10s
| | 6L10s
Line 932: Line 809:
| | g = 31\96
| | g = 31\96
| | g = 7\22, 9\28, 11\34
| | g = 7\22, 9\28, 11\34
| | 5g-3\2
| | 5g-3\2+1-3g = 2g-1\2
| | 1-3g
|-
|-
| | 7L9s
| | 7L9s
Line 939: Line 815:
| | g = 127\224
| | g = 127\224
| | g = 13\23, 17\30, 21\37
| | g = 13\23, 17\30, 21\37
| | 9g-5
| | 9g-5+4-7g = 2g-1
| | 4-7g
|-
|-
| | 8L8s
| | 8L8s
Line 946: Line 821:
| | g = 3\32
| | g = 3\32
| | g = 2\24, 3\32, 4\40
| | g = 2\24, 3\32, 4\40
| | g
| | g+1\8-g = 1\8
| | 1\8-g
|-
|-
| | 9L7s
| | 9L7s
Line 953: Line 827:
| | g = 127\286
| | g = 127\286
| | g = 11\25, 15\34, 19\43
| | g = 11\25, 15\34, 19\43
| | 7g-3
| | 7g-3+4-9g = 1-2g
| | 4-9g
|-
|-
| | 10L6s
| | 10L6s
Line 960: Line 833:
| | g = 31\160
| | g = 31\160
| | g = 5\26, 7\36, 8\46
| | g = 5\26, 7\36, 8\46
| | 3g-1\2
| | 3g-1\2+1-5g = 1\2-2g
| | 1-5g
|-
|-
| | 11L5s
| | 11L5s
Line 967: Line 839:
| | g = 287\352
| | g = 287\352
| | g = 22\27, 31\38, 40\49
| | g = 22\27, 31\38, 40\49
| | 5g-4
| | 5g-4+9-11g = 5-6g
| | 9-11g
|-
|-
| | 12L4s
| | 12L4s
Line 974: Line 845:
| | g = 7\48
| | g = 7\48
| | g = 2\28, 3\40, 4\52
| | g = 2\28, 3\40, 4\52
| | g
| | g+1\4-3g = 1\4-2g
| | 1\4-3g
|-
|-
| | 13L3s
| | 13L3s
Line 981: Line 851:
| | g = 287\416
| | g = 287\416
| | g = 20\29, 29\42, 38\55
| | g = 20\29, 29\42, 38\55
| | 3g-2
| | 3g-2+9-13g = 7-10g
| | 9-13g
|-
|-
| | 14L2s
| | 14L2s
Line 988: Line 857:
| | g = 15\224
| | g = 15\224
| | g = 2\30, 3\44, 4\58
| | g = 2\30, 3\44, 4\58
| | g
| | g+1\2-7g = 1\2-6g
| | 1\2-7g
|-
|-
| | 15L1s
| | 15L1s
Line 995: Line 863:
| | g = 31\480
| | g = 31\480
| | g = 2\31, 3\46, 4\61
| | g = 2\31, 3\46, 4\61
| | g
| | g+1-15g = 1-14g
| | 1-15g
|}
|}


Line 1,007: Line 874:
! | Midpoint
! | Midpoint
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step
! | Large step+Small step
! | Small step
|-
|-
| | 1L16s
| | 1L16s
Line 1,014: Line 880:
| | g = 33\34
| | g = 33\34
| | ''g = 17\18, 18\19, 19\20''
| | ''g = 17\18, 18\19, 19\20''
| | 16g-15
| | 16g-15+1-g = 15g-14
| | 1-g
|-
|-
| | 2L15s
| | 2L15s
Line 1,021: Line 886:
| | g = 33\68
| | g = 33\68
| | g = ''9\19'', ''10\21'', 11\23
| | g = ''9\19'', ''10\21'', 11\23
| | 15g-7
| | 15g-7+1-2g = 13g-6
| | 1-2g
|-
|-
| | 3L14s
| | 3L14s
Line 1,028: Line 892:
| | g = 67\102
| | g = 67\102
| | g = ''13\20'', 15\23, 17\26
| | g = ''13\20'', 15\23, 17\26
| | 14g-9
| | 14g-9+2-3g = 11g-7
| | 2-3g
|-
|-
| | 4L13s
| | 4L13s
Line 1,035: Line 898:
| | g = 33\136
| | g = 33\136
| | g = ''5\21'', 6\25, 7\29
| | g = ''5\21'', 6\25, 7\29
| | 13g-3
| | 13g-3+1-4g = 9g-2
| | 1-4g
|-
|-
| | 5L12s
| | 5L12s
Line 1,042: Line 904:
| | g = 101\170
| | g = 101\170
| | g = 13\22, 16\27, 19\32
| | g = 13\22, 16\27, 19\32
| | 12g-7
| | 12g-7+3-5g = 7g-4
| | 3-5g
|-
|-
| | 6L11s
| | 6L11s
Line 1,049: Line 910:
| | g = 169\204
| | g = 169\204
| | g = 19\23, 24\29, 29\35
| | g = 19\23, 24\29, 29\35
| | 11g-9
| | 11g-9+5-6g = 5g-4
| | 5-6g
|-
|-
| | 7L10s
| | 7L10s
Line 1,056: Line 916:
| | g = 169\238
| | g = 169\238
| | g = 17\24, 22\31, 27\38
| | g = 17\24, 22\31, 27\38
| | 10g-7
| | 10g-7+5-7g = 3g-2
| | 5-7g
|-
|-
| | 8L9s
| | 8L9s
Line 1,063: Line 922:
| | g = 33\272
| | g = 33\272
| | g = 3\25, 4\33, 5\41
| | g = 3\25, 4\33, 5\41
| | 9g-1
| | 9g-1+1-8g = g
| | 1-8g
|-
|-
| | 9L8s
| | 9L8s
Line 1,070: Line 928:
| | g = 271\306
| | g = 271\306
| | g = 23\26, 31\35, 39\44
| | g = 23\26, 31\35, 39\44
| | 8g-7
| | 8g-7+8-9g = 1-g
| | 8-9g
|-
|-
| | 10L7s
| | 10L7s
Line 1,077: Line 934:
| | g = 101\340
| | g = 101\340
| | g = 8\27, 11\37, 14\47
| | g = 8\27, 11\37, 14\47
| | 7g-2
| | 7g-2+3-10g = 1-3g
| | 3-10g
|-
|-
| | 11L6s
| | 11L6s
Line 1,084: Line 940:
| | g = 67\374
| | g = 67\374
| | g = 5\28, 7\39, 9\50
| | g = 5\28, 7\39, 9\50
| | 6g-1
| | 6g-1+2-11g = 1-5g
| | 2-11g
|-
|-
| | 12L5s
| | 12L5s
Line 1,091: Line 946:
| | g = 169\408
| | g = 169\408
| | g = 12\29, 17\41, 22\53
| | g = 12\29, 17\41, 22\53
| | 5g-2
| | 5g-2+5-12g = 3-7g
| | 5-12g
|-
|-
| | 13L4s
| | 13L4s
Line 1,098: Line 952:
| | g = 339\442
| | g = 339\442
| | g = 23\30, 33\43, 43\56
| | g = 23\30, 33\43, 43\56
| | 4g-3
| | 4g-3+10-13g = 7-9g
| | 10-13g
|-
|-
| | 14L3s
| | 14L3s
Line 1,105: Line 958:
| | g = 169\476
| | g = 169\476
| | g = 11\31, 16\45, 21\59
| | g = 11\31, 16\45, 21\59
| | 3g-1
| | 3g-1+5-14g = 4-11g
| | 5-14g
|-
|-
| | 15L2s
| | 15L2s
Line 1,112: Line 964:
| | g = 271\510
| | g = 271\510
| | g = 17\32, 25\47, 33\62
| | g = 17\32, 25\47, 33\62
| | 2g-1
| | 2g-1+8-15g = 7-13g
| | 8-15g
|-
|-
| | 16L1s
| | 16L1s
Line 1,119: Line 970:
| | g = 33\544
| | g = 33\544
| | g = 2\33, 3\49, 4\65
| | g = 2\33, 3\49, 4\65
| | g
| | g+1-16g = 1-15g
| | 1-16g
|}
|}


Line 1,131: Line 981:
! | <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
|-
|-
| | 1L17s
| | 1L17s
Line 1,138: Line 987:
| | g = 35\36
| | g = 35\36
| | ''g = 18\19, 19\20, 20\21''
| | ''g = 18\19, 19\20, 20\21''
| | 17g-16
| | 17g-16+1-g = 16g-15
| | 1-g
|-
|-
| | 2L16s
| | 2L16s
Line 1,145: Line 993:
| | g = 17\36
| | g = 17\36
| | g = ''9\20'', ''10\22'', 11\24
| | g = ''9\20'', ''10\22'', 11\24
| | 8g-7\2
| | 8g-7\2+1\2-g = 7g-3
| | 1\2-g
|-
|-
| | 3L15s
| | 3L15s
Line 1,152: Line 999:
| | g = 11\36
| | g = 11\36
| | g = ''6\21'', 7\24, 8\27
| | g = ''6\21'', 7\24, 8\27
| | 5g-4\3
| | 5g-4\3+1\3-g = 4g-3
| | 1\3-g
|-
|-
| | 4L14s
| | 4L14s
Line 1,159: Line 1,005:
| | g = 17\72
| | g = 17\72
| | <span style="line-height: 15.6000003814697px;">g = ''5\22'', 6\26,</span> 7\30
| | <span style="line-height: 15.6000003814697px;">g = ''5\22'', 6\26,</span> 7\30
| | 7g-3\2
| | 7g-3\2+1\2-2g = 5g-2
| | 1\2-2g
|-
|-
| | 5L13s
| | 5L13s
Line 1,166: Line 1,011:
| | g = 71\180
| | g = 71\180
| | g = 9\23, 11\28, 13\33
| | g = 9\23, 11\28, 13\33
| | 13g-5
| | 13g-5+2-5g = 8g-3
| | 2-5g
|-
|-
| | 6L12s
| | 6L12s
Line 1,173: Line 1,017:
| | g = 5\36
| | g = 5\36
| | g = 3\24, 4\30, 5\36
| | g = 3\24, 4\30, 5\36
| | 2g-1\6
| | 2g-1\6+1\6-g = g
| | 1\6-g
|-
|-
| | 7L11s
| | 7L11s
Line 1,180: Line 1,023:
| | g = 71\252
| | g = 71\252
| | g = 7\25, 9\32, 11\39
| | g = 7\25, 9\32, 11\39
| | 11g-3
| | 11g-3+2-7g = 4g-1
| | 2-7g
|-
|-
| | 8L10s
| | 8L10s
Line 1,187: Line 1,029:
| | g = 17\144
| | g = 17\144
| | g = 3\26, 4\34, 5\42
| | g = 3\26, 4\34, 5\42
| | 5g-1\2
| | 5g-1\2+1\2-4g = g
| | 1\2-4g
|-
|-
| | 9L9s
| | 9L9s
Line 1,194: Line 1,035:
| | g = 3\36
| | g = 3\36
| | g = 2\27, 3\36, 4\45
| | g = 2\27, 3\36, 4\45
| | g
| | g+1\9-g = 1\9
| | 1\9-g
|-
|-
| | 10L8s
| | 10L8s
Line 1,201: Line 1,041:
| | g = 71\180
| | g = 71\180
| | g = 11\28, 15\38, 19\48
| | g = 11\28, 15\38, 19\48
| | 4g-3\2
| | 4g-3\2+2-5g = 1\2-g
| | 2-5g
|-
|-
| | 11L7s
| | 11L7s
Line 1,208: Line 1,047:
| | g = 287\396
| | g = 287\396
| | g = 21\29, 29\40, 37\51
| | g = 21\29, 29\40, 37\51
| | 7g-5
| | 7g-5+8-11g = 3-4g
| | 8-11g
|-
|-
| | 12L6s
| | 12L6s
Line 1,215: Line 1,053:
| | g = 5\72
| | g = 5\72
| | g = 2\30, 3\42, 4\54
| | g = 2\30, 3\42, 4\54
| | g
| | g+1\6-2g = 1\6-g
| | 1\6-2g
|-
|-
| | 13L5s
| | 13L5s
Line 1,222: Line 1,059:
| | g = 287\468
| | g = 287\468
| | g = 19\31, 27\44, 35\57
| | g = 19\31, 27\44, 35\57
| | 5g-3
| | 5g-3+8-13g = 5-8g
| | 8-13g
|-
|-
| | 14L4s
| | 14L4s
Line 1,229: Line 1,065:
| | g = 71\252
| | g = 71\252
| | g = 9\32, 13\46, 17\60
| | g = 9\32, 13\46, 17\60
| | 2g-1\2
| | 2g-1\2+2-7g = 3\2-5g
| | 2-7g
|-
|-
| | 15L3s
| | 15L3s
Line 1,236: Line 1,071:
| | g = 11\180
| | g = 11\180
| | g = 2\33, 3\48, 4\63
| | g = 2\33, 3\48, 4\63
| | g
| | g+1\3-5g = 1\3-4g
| | 1\3-5g
|-
|-
| | 16L2s
| | 16L2s
Line 1,243: Line 1,077:
| | g = 17\288
| | g = 17\288
| | g = 2\34, 3\50, 4\66
| | g = 2\34, 3\50, 4\66
| | g
| | g+1\2-8g = 1\2-7g
| | 1\2-8g
|-
|-
| | 17L1s
| | 17L1s
Line 1,250: Line 1,083:
| | g = 35\618
| | g = 35\618
| | g = 2\35, 3\52, 4\69
| | g = 2\35, 3\52, 4\69
| | g
| | g+1-17g = 1-16g
| | 1-17g
|}
|}


Line 1,381: Line 1,213:
! | <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
|-
|-
| | 1L19s
| | 1L19s
Line 1,388: Line 1,219:
| | g = 39\40
| | g = 39\40
| | ''g = 20\21, 21\22, 22\23''
| | ''g = 20\21, 21\22, 22\23''
| | 19g-18
| | 19g-18+1-g = 18g-17
| | 1-g
|-
|-
| | 2L18s
| | 2L18s
Line 1,395: Line 1,225:
| | g = 19\40
| | g = 19\40
| | g = ''10\22'', ''11\24'', 12\26
| | g = ''10\22'', ''11\24'', 12\26
| | 9g-4
| | 9g-4+1\2-g = 8g-7\2
| | 1\2-g
|-
|-
| | 3L17s
| | 3L17s
Line 1,402: Line 1,231:
| | g = 79\120
| | g = 79\120
| | g = ''15\23'', 17\26, 20\29
| | g = ''15\23'', 17\26, 20\29
| | 17g-11
| | 17g-11+2-3g = 14g-9
| | 2-3g
|-
|-
| | 4L16s
| | 4L16s
Line 1,409: Line 1,237:
| | g = 9\40
| | g = 9\40
| | g = ''5\24'', 6\28, 7\32
| | g = ''5\24'', 6\28, 7\32
| | 4g-3\4
| | 4g-3\4+1\4-g = 3g-1\4
| | 1\4-g
|-
|-
| | 5L15s
| | 5L15s
Line 1,416: Line 1,243:
| | g = 7\40
| | g = 7\40
| | g = 4\25, 5\30, 6\35
| | g = 4\25, 5\30, 6\35
| | 3g-2\5
| | 3g-2\5+1\5-g = 2g-1\5
| | 1\5-g
|-
|-
| | 6L14s
| | 6L14s
Line 1,423: Line 1,249:
| | g = 19\120
| | g = 19\120
| | g = 4\26, 5\32, 6\38
| | g = 4\26, 5\32, 6\38
| | 7g-1
| | 7g-1+1\2-3g = 4g-1\2
| | 1\2-3g
|-
|-
| | 7L13s
| | 7L13s
Line 1,430: Line 1,255:
| | g = 239\280
| | g = 239\280
| | g = 23\27, 29\34, 35\41
| | g = 23\27, 29\34, 35\41
| | 13g-11
| | 13g-11+6-7g = 6g-5
| | 6-7g
|-
|-
| | 8L12s
| | 8L12s
Line 1,437: Line 1,261:
| | g = 9\80
| | g = 9\80
| | g = 3\28, 4\36, 5\44
| | g = 3\28, 4\36, 5\44
| | 3g-1\4
| | 3g-1\4+1\4-2g = g
| | 1\4-2g
|-
|-
| | 9L11s
| | 9L11s
Line 1,444: Line 1,267:
| | g = 199\360
| | g = 199\360
| | g = 16\29, 21\38, 26\47
| | g = 16\29, 21\38, 26\47
| | 11g-6
| | 11g-6+5-9g =2g-1
| | 5-9g
|-
|-
| | 10L10s
| | 10L10s
Line 1,451: Line 1,273:
| | g = 3\40
| | g = 3\40
| | g = 2\30, 3\40, 4\50
| | g = 2\30, 3\40, 4\50
| | g
| | g+1\10-g = 1\10
| | 1\10-g
|-
|-
| | 11L9s
| | 11L9s
Line 1,458: Line 1,279:
| | g = 199\440
| | g = 199\440
| | g = 14\31, 19\42, 24\53
| | g = 14\31, 19\42, 24\53
| | 9g-4
| | 9g-4+5-11g = 1-2g
| | 5-11g
|-
|-
| | 12L8s
| | 12L8s
Line 1,465: Line 1,285:
| | g = 19\120
| | g = 19\120
| | g = 5\32, 7\44, 9\56
| | g = 5\32, 7\44, 9\56
| | 2g-1\4
| | 2g-1\4+1\2-3g = 1\4-g
| | 1\2-3g
|-
|-
| | 13L7s
| | 13L7s
Line 1,472: Line 1,291:
| | g = 79\520
| | g = 79\520
| | g = 5\33, 7\46, 9\59
| | g = 5\33, 7\46, 9\59
| | 7g-1
| | 7g-1+2-13g = 1-6g
| | 2-13g
|-
|-
| | 14L6s
| | 14L6s
Line 1,479: Line 1,297:
| | g = 99\280
| | g = 99\280
| | g = 12\34, 17\48, 22\62
| | g = 12\34, 17\48, 22\62
| | 3g-1
| | 3g-1+5\2-7g = 2-4g
| | 5\2-7g
|-
|-
| | 15L5s
| | 15L5s
Line 1,486: Line 1,303:
| | g = 7\120
| | g = 7\120
| | g = 2\35, 3\50, 4\65
| | g = 2\35, 3\50, 4\65
| | g
| | g+1\5-3g = 1\5-2g
| | 1\5-3g
|-
|-
| | 16L4s
| | 16L4s
Line 1,493: Line 1,309:
| | g = 9\160
| | g = 9\160
| | g = 2\36, 3\52, 4\68
| | g = 2\36, 3\52, 4\68
| | g
| | g+1\4-4g = 1\4-3g
| | 1\4-4g
|-
|-
| | 17L3s
| | 17L3s
Line 1,500: Line 1,315:
| | g = 239\680
| | g = 239\680
| | g = 13\37, 19\54, 25\71
| | g = 13\37, 19\54, 25\71
| | 3g-1
| | 3g-1+6-17g = 5-14g
| | 6-17g
|-
|-
| | 18L2s
| | 18L2s
Line 1,507: Line 1,321:
| | g = 19\360
| | g = 19\360
| | g = 2\38, 3\56, 4\74
| | g = 2\38, 3\56, 4\74
| | g
| | g+1\2-9g = 1\2-8g
| | 1\2-9g
|-
|-
| | 19L1s
| | 19L1s
Line 1,514: Line 1,327:
| | g = 39\760
| | g = 39\760
| | g = 2\39, 3\58, 4\77
| | g = 2\39, 3\58, 4\77
| | g
| | g+1-19g = 1-18g
| | -19g+1
|}
|}


Line 1,526: Line 1,338:
! | <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
|-
|-
| | 1L20s
| | 1L20s
Line 1,533: Line 1,344:
| | g = 41\42
| | g = 41\42
| | ''g = 21\22, 22\23, 23\24''
| | ''g = 21\22, 22\23, 23\24''
| | 20g-19
| | 20g-19+1-g = 19g-18
| | 1-g
|-
|-
| | 2L19s
| | 2L19s
Line 1,540: Line 1,350:
| | g = 41\84
| | g = 41\84
| | g = ''11\23, 12\25'', 13\27
| | g = ''11\23, 12\25'', 13\27
| | 19g-9
| | 19g-9+1-2g = 17g-8
| | 1-2g
|-
|-
| | 3L18s
| | 3L18s
Line 1,547: Line 1,356:
| | g = 13\42
| | g = 13\42
| | g = ''7\24'', 8\27, 9\30
| | g = ''7\24'', 8\27, 9\30
| | 6g-5\3
| | 6g-5\3+1\3-g = 5g-4\3
| | 1\3-g
|-
|-
| | 4L17s
| | 4L17s
Line 1,554: Line 1,362:
| | g = 41\168
| | g = 41\168
| | g = ''6\25'', 7\29, 8\33
| | g = ''6\25'', 7\29, 8\33
| | 17g-2
| | 17g-2+1-4g = 13g-1
| | 1-4g
|-
|-
| | 5L16s
| | 5L16s
Line 1,561: Line 1,368:
| | g = 41\210
| | g = 41\210
| | g = ''5\26'', 6\31, 7\36
| | g = ''5\26'', 6\31, 7\36
| | 16g-3
| | 16g-3+1-5g = 11g-2
| | 1-5g
|-
|-
| | 6L15s
| | 6L15s
Line 1,568: Line 1,374:
| | g = 13\84
| | g = 13\84
| | g = 4\27, 5\33, 6\39
| | g = 4\27, 5\33, 6\39
| | 5g-2\3
| | 5g-2\3+1\3-2g = 3g-1\3
| | 1\3-2g
|-
|-
| | 7L14s
| | 7L14s
Line 1,575: Line 1,380:
| | g = 5\42
| | g = 5\42
| | g = 3\28, 4\35, 5\42
| | g = 3\28, 4\35, 5\42
| | 2g-1\7
| | 2g-1\7+1\7-g = g
| | 1\7-g
|-
|-
| | 8L13s
| | 8L13s
Line 1,582: Line 1,386:
| | g = 209\336
| | g = 209\336
| | g = 18\29, 23\37, 28\45
| | g = 18\29, 23\37, 28\45
| | 13g-8
| | 13g-8+5-8g = 5g-3
| | 5-8g
|-
|-
| | 9L12s
| | 9L12s
Line 1,589: Line 1,392:
| | g = 13\126
| | g = 13\126
| | g = 3\30, 4\39, 5\48
| | g = 3\30, 4\39, 5\48
| | 4g-1\3
| | 4g-1\3+1\3-3g = g
| | 1\3-3g
|-
|-
| | 10L11s
| | 10L11s
Line 1,596: Line 1,398:
| | g = 41\420
| | g = 41\420
| | g = 3\31, 4\41, 5\51
| | g = 3\31, 4\41, 5\51
| | 11g-1
| | 11g-1+1-10g = g
| | 1-10g
|-
|-
| | 11L10s
| | 11L10s
Line 1,603: Line 1,404:
| | g = 419\462
| | g = 419\462
| | g = 29\32, 39\43, 49\54
| | g = 29\32, 39\43, 49\54
| | 10g-9
| | 10g-9+10-11g = 1-g
| | 10-11g
|-
|-
| | 12L9s
| | 12L9s
Line 1,610: Line 1,410:
| | g = 41\168
| | g = 41\168
| | g = 8\33, 11\45, 14\57
| | g = 8\33, 11\45, 14\57
| | 3g-2\3
| | 3g-2\3+1-4g = 1\3-3g
| | 1-4g
|-
|-
| | 13L8s
| | 13L8s
Line 1,617: Line 1,416:
| | g = 209\546
| | g = 209\546
| | g = 13\34, 18\47, 23\70
| | g = 13\34, 18\47, 23\70
| | 8g-3
| | 8g-3+5-13g = 2-5g
| | 5-13g
|-
|-
| | 14L7s
| | 14L7s
Line 1,624: Line 1,422:
| | g = 5\84
| | g = 5\84
| | g = 2\35, 3\49, 4\63
| | g = 2\35, 3\49, 4\63
| | g
| | g+1\7-2g = 1\7-g
| | 1\7-2g
|-
|-
| | 15L6s
| | 15L6s
Line 1,631: Line 1,428:
| | g = 41\210
| | g = 41\210
| | g = 7\36, 10\51, 13\66
| | g = 7\36, 10\51, 13\66
| | 2g-1\3
| | 2g-1\3+1-5g = 2\3-3g
| | 1-5g
|-
|-
| | 16L5s
| | 16L5s
Line 1,638: Line 1,434:
| | g = 545\672
| | g = 545\672
| | g = 30\37, 43\53, 56\69
| | g = 30\37, 43\53, 56\69
| | 5g-4
| | 5g-4+13-16g = 9-11g
| | 13-16g
|-
|-
| | 17L4s
| | 17L4s
Line 1,645: Line 1,440:
| | g = 545\714
| | g = 545\714
| | g = 29\38, 42\55, 55\72
| | g = 29\38, 42\55, 55\72
| | 4g-3
| | 4g-3+13-17g = 10-13g
| | 13-17g
|-
|-
| | 18L3s
| | 18L3s
Line 1,652: Line 1,446:
| | g = 13\252
| | g = 13\252
| | g = 2\39, 3\57, 4\75
| | g = 2\39, 3\57, 4\75
| | g
| | g+1\3-6g = 1\3-5g
| | 1\3-6g
|-
|-
| | 19L2s
| | 19L2s
Line 1,659: Line 1,452:
| | g = 419\798
| | g = 419\798
| | g = 21\40, 31\59, 41\78
| | g = 21\40, 31\59, 41\78
| | 2g-1
| | 2g-1+10-19g = 9-17g
| | 10-19g
|-
|-
| | 20L1s
| | 20L1s
Line 1,666: Line 1,458:
| | g = 41\840
| | g = 41\840
| | g = 2\41, 3\61, 4/81
| | g = 2\41, 3\61, 4/81
| | g
| | g+1-20g = 1-19g
| | 1-20g
|}
|}


Revision as of 04:20, 24 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
2L21s 11\23 < g < 1\2 g = 45\92 g = 12\25, 13\27, 14\29 21g-10 1-2g
3L20s 15\23 < g < 2\3 g = 91\138 g = 17\26, 19\29, 21\32 20g-13 1-3g
4L19s 17\23 < g < 3\4 g = 137\184 g = 20\27, 23\31, 26\35 19g-14 3-4g
5L18s 9\23 < g < 2\5 g = 91\230 g = 11\28, 13\33, 15\38 18g-7 2-5g
6L17s 19\23 < g < 5\6 g = 229\276 g = 24\29, 29\35, 34\41 17g-15 1-6g
7L16s 13\23 < g < 4\7 g = 183\322 g = 17\30, 21\37, 25\44 16g-9 4-7g
8L15s 20\23 < g < 7\8 g = 321\368 g = 27\31, 34\39, 41\47 15g-13 7-8g
9L14s 5\23 < g < 2\9 g = 91\414 g = 7\32, 9\41, 11\50 14g-7 11-9g
10L13s 16\23 < g < 7\10 g = 321\460 g = 23\33, 30\43, 37\53 13g-9 7-10g
11L12s 2\23 < g < 1\11 g = 45\506 g = 3\34, 4\45, 5\56 12g-1 1-11g
12L11s 21\23 < g < 11\12 g = 505\552 g = 32\35, 43\47, 54\59 11g-10 11-12g
13L10s 7\23 < g < 4\13 g = 183\598 g = 11\36, 15\49, 19\62 10g-3 4-13g
14L9s 18\23 < g < 11\14 g = 505\644 g = 29\37, 40\51, 51\65 9g-7 11-14g
15L8s 3\23 < g < 2\15 g = 91\690 g = 5\38, 7\53, 9\68 8g-1 2-15g
16L7s 10\23 < g < 7\16 g = 321\736 g = 17\39, 24\55, 31\71 7g-3 7-16g
17L6s 4\23 < g < 3\17 g = 137\782 g = 7\40, 10\57, 13\74 6g-1 3-17g
18L5s 14\23 < g < 11\18 g = 505\828 g = 25\41, 36\59, 47\77 5g-4 11-18g
19L4s 6\23 < g < 5\19 g = 229\874 g = 11\42, 16\61, 21\80 4g-1 5-19g
20L3s 8\23 < g < 7\20 g = 321\920 g = 15\43, 22\63, 29\83 3g-1 13-20g
21L2s 12\23 < g < 11\21 g = 505\966 g = 23\44, 34\65, 45\86 2g-1 1-21g
22L1s 1\23 < g < 1\22 g = 45\1012 g = 2\45, 3\67, 4\89 g 1-22g

24

Large-small numbers Generator range Midpoint Boundaries of propriety, maximum expressiveness, diatonicity Large step Small step
1L23s 23\24 < g < 1 g = 47\48 g = 24\25, 25\26, 26\27 23g-22 1-g
2L22s 11\24 < g < 1\2 g = 23\48 g = 12\26, 13\28, 14\30 1/2-g 11g-5
3L21s 7\24 < g < 1\3 g = 15\48 g = 8\27, 9\30, 10\33 2/3-2g g-1/3
4L20s 5\24 < g < 1\4 g = 11\48 g = 6\28, 7\32, 8\36 5g-1 1/4-g
5L19s 19\24 < g < 4\5 g = 191\240 g = 23\29, 27\34, 31\39 19g-15 4-5g
6L18s 3\24 < g < 1\6 g = 7\48 g = 4\30, 5\36, 6\42 3g-1\3 1\6-g
7L17s 17\24 < g < 5\7 g = 239\336 g = 22\31, 27\38, 32\45 5-17g 7g-2
8L16s 2\24 < g < 1\8 g = 5\48 g = 3\32, 4\40, 5\48 2g-1\8 1\8-g
9L15s 5\24 < g < 2\9 g = 31\144 g = 7\33, 9\42, 11\51 5g-1 2\3-3g
10L14s 7\24 < g < 3\10 g = 71\240 g = 10\34, 13\44, 16\54 7g-2 3\2-5g
11L13s 13\24 < g < 6\11 g = 287\528 g = 19\35, 25\46, 31\57 13g-7 6-11g
12L12s 1\24 < g < 1\12 g = 3\48 g = 2\36, 3\48, 4\60 g 1\12-g
13L11s 11\24 < g < 6\13 g = 287\624 g = 17\37, 23\50, 29\63 11g-5 6-13g
14L10s 17\24 < g < 10\14 g = 239\336 g = 27\38, 37\52, 47\66 3\2-5g 7g-2
15L9s 3\24 < g < 2\15 g = 31\240 g = 5\39, 7\54, 9\69 3g-1\3 2\3-5g
16L8s 1\24 < g < 1\16 g = 5\96 g = 2\40, 3\56, 4\72 g 1\8-2g
17L7s 7\24 < g < 5\17 g = 239\816 g = 12\41, 17\58, 22\75 4-7g 17g-12
18L6s 1\24 < g < 1\18 g = 7\144 g = 2\42, 3\60, 4\78 g 1\6-3g
19L5s 5\24 < g < 4\19 g = 191\912 g = 9\43, 13\62, 17\81 5g-5 4-19g
20L4s 1\24 < g < 1\20 g = 11\240 g = 2\44, 3\64, 4\84 g 1\4-5g
21L3s 1\24 < g < 1\21 g = 15\336 g = 2\45, 3\66, 4\87 g 1\3-7g
22L2s 1\24 < g < 1\22 g = 23\264 g = 2\46, 3\68, 4\90 g 1\2-11g
23L1s 1\24 < g < 1\23 g = 47\1104 g = 2\47, 3\70, 4\93 g 1-23g

25

Large-small numbers Generator range Midpoint Boundaries of propriety, maximum expressiveness, diatonicity Large step Small step
1L24s 24\25 < g < 1 g = 49\50 g = 25\26, 26\27, 27\28 24g-23 1-g
2L23s 12\25 < g < 1\2 g = 49\100 g = 13\27, 14\29, 15\31 23g-11 1-2g
3L22s 8\25 < g < 1\3 g = 49\150 g = 9\28, 10\31, 11\34 22g-7 1-3g
4L21s 6\25 < g < 1\4 g = 49\200 g = 7\29, 8\33, 9\37 21g-5 1-4g
5L20s 4\25 < g < 1\5 g = 9\50 g = 5\30, 6\35, 7\40 4g-3\5 1\5-g
6L19s 4\25 < g < 1\6 g = 49\300 g = 5\31, 6\37, 7\43 19g-3 1-6g
7L18s 7\25 < g < 2\7 g = 99\350 g = 9\32, 11\39, 13\46 18g-5 2-7g
8L17s 3\25 < g < 1\8 g = 49\400 g = 4\33, 5\41, 6\47 17g-2 1-8g
9L16s 11\25 < g < 4\9 g = 199\450 g = 15\34, 19\43, 23\52 16g-7 -9g+4
10L15s 2\25 < g < 1\10 g = 9\100 g = 3\35, 4\45, 5\55 3g-1\5 1\5-2g
11L14s 9\25 < g < 4\11 g = 199\550 g = 13\36, 17\47, 21\58 14g-5 -11g+4
12L13s 2\25 < g < 1\12 g = 49\600 g = 3\37, 4\49, 5\61 13g-1 1-12g
13L12s 23\25 < g < 12\13 g = 599\650 g = 35\38, 47\51, 59\64 12g-11 12-13g
14L11s 16\25 < g < 9\14 g = 449\700 g = 25\39, 34\53, 43\67 11g-7 -14g+9
15L10s 3\25 < g < 2\15 g = 19\150 g = 5\40, 7\55, 9\70 2g-1\5 2\5-3g
16L9s 14\25 < g < 9\16 g = 449\800 g = 23\41, 32\57, 41\73 9g-5 9-16g
17L8s 22\25 < g < 15\17 g = 749\850 g = 37\42, 52\59, 67\76 8g-7 15-17g
18L7s 18\25 < g < 13\18 g = 649\900 g = 31\43, 44\61, 57\79 7g-5 13-18g
19L6s 21\25 < g < 16\19 g = 799\950 g = 37\44, 53\63, 69\82 6g-5 16-19g
20L5s 1\25 < g < 1\20 g = 9\200 g = 2\45, 3\65, 4\85 g 1\5-4g
21L4s 16\21 < g < 19\25 g = 799\1050 g = 35\46, 51\67, 71\88 4g-3 16-21g
22L3s 17\25 < g < 15\22 g = 749\1100 g = 32\47, 47\69, 62\91 3g-2 15-22g
23L2s 13\25 < g < 12\23 g = 599\1150 g = 25\48, 37\71, 49\94 2g-1 11-23g
24L1s 1\25 < g < 1\24 g = 49\1200 g = 2\49, 3\73, 4\97 g 1-24g

26

Large-small numbers Generator range Midpoint Boundaries of propriety, maximum expressiveness, diatonicity Large step Small step
1L25s 25\26 < g < 1 g = 51\52 g = 26\27, 27\28, 28\29 25g-24 1-g
2L24s 12\26 < g < 1\2 g = 25\52 g = 13\28, 14\30, 15\32 12g-11\2 1\2-g
3L23s 17\26 < g < 2\3 g = 103\156 g = 19\29, 21\32, 23\35 23g-15 2-3g
4L22s 6\26 < g < 1\4 g = 25\104 g = 7\30, 8\34, 9\38 11g-5\2 1\2-2g
5L21s 5\26 < g < 1\5 g = 51\260 g = 6\31, 7\36, 8\41 21g-4 1-5g
6L20s 4\26 < g < 1\6 g = 25\156 g = 5\32, 6\38, 7\44 10g-3\2 1\2-3g
7L19s 11\26 < g < 3\7 g = 155\364 g = 14\33, 17\40, 20\47 19g-8 3-7g
8L18s 3\26 < g < 1\8 g = 25\208 g = 4\34, 5\42, 6\50 9g-1 1\2-4g
9L17s 23\26 < g < 8\9 g = 415\468 g = 31\35, 39\44, 47\53 17g-15 8-9g
10L16s 5\26 < g < 2\10 g = 51\260 g = 7\36, 9\46, 11\56 8g-3\2 1-5g
11L15s 7\26 < g < 3\11 g = 155\572 g = 10\37, 13\48, 16\59 15g-4 3-11g
12L14s 2\26 < g < 1\12 g = 25\312 g = 3\38, 4\50, 5\62 7g-1\2 1\2-6g
13L13s 1\26 < g < 1\13 g = 3\52 g = 2\39, 3\52, 4\65 g 1\13-g
14L12s 11\26 < g < 6\14 g = 155\364 g = 17\40, 23\54, 29\68 6g-5\2 3-7g
15L11s 19\26 < g < 11\15 g = 571\780 g = 30\41, 41\56, 52\71 11g-8 11-15g
16L10s 8\26 < g < 5\16 g = 129\416 g = 13\42, 18\58, 23\74 13\2-8g 5g-4
17L9s 3\26 < g < 2\17 g = 103\884 g = 5\43, 7\60, 9\77 9g-1 2-17g
18L8s 10\26 < g < 7\18 g = 181\468 g = 17\44, 24\62, 31\80 4g-7\2 7-9g
19L7s 15\26 < g < 11\19 g = 571\988 g = 26\45, 37\64, 48\83 7g-4 11-19g
20L6s 9\26 < g < 7\20 g = 181\520 g = 16\46, 23\66, 30\86 3g-1 7\2-10g
21L5s 21\26 < g < 17\21 g = 883\1092 g = 38\47, 55\68, 72\89 5g-4 16-21g
22L4s 7\26 < g < 6\22 g = 155\572 g = 13\48, 19\70, 25\92 2g-1\2 3-11g
23L3s 9\26 < g < 8\23 g = 415\1196 g = 17\49, 25\72, 33/95 3g-1 8-23g
24L2s 1\26 < g < 1\24 g = 25\312 g = 2\50, 3\74, 4\98 g 1\2-12g
25L1s 1\26 < g < 1\25 g = 51\1300 g = 2\51, 3\76, 4\101 g 1-25g

27

Large-small numbers Generator range Midpoint Boundaries of propriety, maximum expressiveness, diatonicity Large step Small step
1L26s 26\27 < g < 1 g = 53\54 g = 27\28, 28\29, 29\30 26g-25 1-g
2L25s 13\27 < g < 1\2 g = 53\108 g = 14\29, 15\31, 16\33 25g-12 1-2g
3L24s 8\27 < g < 1\3 g = 17\54 g = 9\30, 10\33, 11\36 8g-7\3 1-3g
4L23s 20\27 < g < 3\4 g = 161\216 g = 23\31, 26\35, 29\39 23g-17 3-4g
5L22s 16\27 < g < 3\5 g = 161\270 g = 19\32, 22\37, 25\42 22g-13 3-5g
6L21s 4\27 < g < 1\6 g = 17\108 g = 5\33, 6\39, 7\45 7g-1 1\3-2g
7L20s 23\27 < g < 6\7 g = 323\378 g = 29\34, 35\41, 41\48 20g-17 6-7g
8L19s 10\27 < g < 3\8 g = 161\432 g = 13\35, 16\43, 19\51 19g-7 3-8g
9L18s 2\27 < g < 1\9 g = 5\54 g = 3\36, 4\45, 5\54 2g-1\9 1\9-g
10L17s 8\27 < g < 3\10 g = 161\540 g = 11\37, 14\47, 17\57 17g-5 3-10g
11L16s 22\27 < g < 9\11 g = 485\594 g = 31\38, 40\49, 49\60 16g-13 9-11g
12L15s 2\27 < g < 1\12 g = 17\216 g = 3\39, 4\51, 5\63 5g-1\3 1\3-4g
13L14s 2\27 < g < 1\13 g = 53\702 g = 3\40, 4\53, 5\66 14g-1 1-13g
14L13s 25\27 < g < 13\14 g = 701\756 g = 38\41, 51\55, 64\69 13g-12 13-14g
15L12s 7\27 < g < 4\15 g = 71\270 g = 11\42, 15\57, 19\72 4g-4 14\3-5g
16L11s 5\27 < g < 3\16 g = 161\864 g = 8\43, 11\59, 14\75 11g-2 3-16g
17L10s 19\27 < g < 12\17 g = 647\918 g = 31\44, 43\61, 55\78 10g-7 12-17g
18L9s 1\27 < g < 1\18 g = 5\108 g = 2\45, 3\63, 4\81 g 1\9-2g
19L8s 17\27 < g < 12\19 g = 647\1026 g = 29\46, 41\65, 53\84 8g-5 12-19g
20L7s 4\27 < g < 3\20 g = 161\1080 g = 7\47, 10\67, 13\87 7g-1 3-20g
21L6s 5\27 < g < 4\21 g = 71\378 g = 9\48, 13\69, 17\90 2g-1\3 4-7g
22L5s 11\27 < g < 9\22 g = 485\1188 g = 20\49, 29\71, 38\93 5g-2 9-22g
23L4s 7\27 < g < 6\23 g = 323\1242 g = 13\50, 19\73, 25\96 4g-1 6-23g
24L3s 1\27 < g < 1\24 g = 17\432 g = 2\51, 3\75, 4\99 g 1\3-8g
25L2s 14\27 < g < 13\25 g = 701\1350 g = 27\52, 40\77, 53\102 2g-1 13-25g
26L1s 1\27 < g < 1\26 g = 53\1404 g = 2\53, 3\79, 4\105 g 1-26g

28

Large-small numbers Generator range Midpoint Boundaries of propriety, maximum expressiveness, diatonicity Large step Small step
1L27s 27\28 < g < 1 g = 55\56 g = 28\29, 29\30, 30\31 27g-26 1-g
2L26s 13\28 < g < 1\2 g = 27\56 g = 14\30, 15\32, 16\34 13g-6 1\2-g
3L25s 9\28 < g < 1\3 g = 55\168 g = 10\31, 11\34, 12\37 25g-8 1-3g
4L24s 6\28 < g < 1\4 g = 13\56 g = 7\32, 8\36, 9\40 6g-5\4 1\4-g
5L23s 11\28 < g < 2\5 g = 111\280 g = 13\33, 15\38, 17\43 23g-9 2-5g
6L22s 9\28 < g < 2\6 g = 55\168 g = 11\34, 13\40, 15\46 11g-7\2 1-3g
7L21s 3\28 < g < 1\7 g = 7\56 g = 4\35, 5\42, 6\49 3g-2\7 1\7-g
8L20s 3\28 < g < 1\8 g = 13\112 g = 4\36, 5\44, 6\52 5g-1\2 1\4-2g
9L19s 3\28 < g < 1\9 g = 55\504 g = 4\37, 5\46, 6\55 19g-2 1-9g
10L18s 11\28 < g < 4\10 g = 111\280 g = 15\38, 19\48, 23\58 4g-7\2 2-5g
11L17s 5\28 < g < 2\11 g = 111\616 g = 7\39, 9\50, 11\61 17g-3 2-11g
12L16s 2\28 < g < 1\12 g = 13\168 g = 3\40, 4\52, 5\64 4g-1\4 1\4-3g
13L15s 15\28 < g < 7\13 g = 391\728 g = 22\41, 29\54, 36\67 15g-8 7-13g
14L14s 1\28 < g < 1\14 g = 3\56 g = 2\42, 3\56, 4\70 g 1\14-g
15L13s 13\28 < g < 7\15 g = 391\840 g = 20\43, 27\58, 34\73 13g-6 7-15g
16L12s 5\28 < g < 3\16 g = 41\224 g = 8\44, 11\60, 14\76 3g-1\2 3\4-4g
17L11s 23\28 < g < 14\17 g = 783\952 g = 37\45, 51\62, 65\79 11g-9 13-17g
18L10s 3\28 < g < 2\18 g = 55\504 g = 5\46, 7\64, 9\82 5g-1\2 1-9g
19L9s 25\28 < g < 17\19 g = 951\1064 g = 42\47, 59\66, 76\85 9g-8 17-19g
20L8s 4\28 < g < 3\20 g = 41\280 g = 7\48, 10\68, 13\88 2g-1\4 3\4-5g
21L7s 1\28 < g < 1\21 g = 7\168 g = 2\49, 3\70, 4\91 g 1\7-3g
22L6s 5\28 < g < 4\22 g = 111\616 g = 9\50, 13\72, 17\94 3g-1\2 2-11g
23L5s 17\28 < g < 14\23 g = 783\1288 g = 31\51, 45\74, 59\97 5g-3 14-23g
24L4s 1\28 < g < 1\24 g = 13\336 g = 2\52, 3\76, 4\100 g 1\4-6g
25L3s 19\28 < g < 17\25 g = 951\1400 g = 36\53, 53\78, 70\103 3g-2 17-25g
26L2s 15\28 < g < 14\26 g = 391\728 g = 29\54, 43\80, 57\106 g-1\2 19\2-13g
27L1s 1\28 < g < 1\27 g = 55\1512 g = 2\55, 3\82, 4\109 g 1-27g

29

Large-small numbers Generator range Midpoint Boundaries of propriety, maximum expressiveness, diatonicity Large step Small step
1L28s 28\29 < g < 1 g = 57\58 g = 29\30, 30\31, 31\32 28g-27 1-g
2L27s 14\29 < g < 1\2 g = 57\116 g = 15\31, 16\33, 17\35 27g-13 1-2g
3L26s 19\29 < g < 2\3 g = 115\174 g = 21\32, 23\35, 25\38 26g-17 2-3g
4L25s 7\29 < g < 1\4 g = 57\232 g = 8\33, 9\37, 10\41 25g-6 1-4g
5L24s 23\29 < g < 4\5 g = 231\290 g = 27\34, 31\39, 35\44 24g-19 4-5g
6L23s 24\29 < g < 5\6 g = 289\348 g = 29\35, 34\41, 39\47 23g-19 5-6g
7L22s 4\29 < g < 1\7 g = 57\406 g = 5\36, 6\43, 7\50 22g-3 1-7g
8L21s 18\29 < g < 5\8 g = 289\464 g = 23\37, 28\45, 33\53 21g-13 5-8g
9L20s 16\29 < g < 5\9 g = 289\522 g = 21\38, 26\47, 31\56 20g-11 5-9g
10L19s 26\29 < g < 9\10 g = 521\580 g = 35\39, 44\49, 53\59 19g-17 9-10g
11L18s 21\29 < g < 8\11 g = 463\638 g = 29\40, 37\51, 45\62 18g-13 8-11g
12L17s 12\29 < g < 5\12 g = 289\696 g = 17\41, 22\53, 27\65 17g-7 5-12g
13L16s 20\29 < g < 9\13 g = 521\754 g = 29\42, 38\55, 47\68 16g+11 9-13g
14L15s 2\29 < g < 1\14 g = 57\812 g = 3\43, 4\57, 5\71 15g-1 1-14g
15L14s 27\29 < g < 14\15 g = 811\870 g = 41\44, 55\59, 69\74 14g-13 14-15g
16L13s 9\29 < g < 5\16 g = 289\928 g = 14\45, 19\61, 24\77 13g-4 5-16g
17L12s 17\29 < g < 10\17 g = 579\986 g = 27\46, 37\63, 47\80 12g-5 7-17g
18L11s 8\29 < g < 5\18 g = 289\1044 g = 13\47, 18\65, 23\83 11g-3 5-18g
19L10s 3\29 < g < 2\19 g = 115\1102 g = 5\48, 7\67, 9\86 10g-1 2-19g
20L9s 13\29 < g < 9\20 g = 521\1160 g = 22\49, 31\69, 40\89 9g-5 9-20g
21L8s 11\29 < g < 8\21 g = 463\1216 g = 19\50, 27\71, 35\92 8g-3 8-21g
22L7s 25\29 < g < 19\22 g = 1001\1274 g = 44\51, 63\73, 82\95 7g-6 9-22g
23L6s 5\29 < g < 4\23 g = 231\1332 g = 9\52, 13\75, 17\98 6g-1 4-23g
24L5s 6\29 < g < 5\24 g = 289\1392 g = 11\53, 16\77, 21\101 5g-9 5-24g
25L4s 22\29 < g < 19\25 g = 1001\1450 g = 41\54, 60\79, 79\104 4g-3 19-25g
26L3s 10\29 < g < 9\26 g = 521\1508 g = 19\55, 28\81, 37\107 3g-1 19\2-26g
27L2s 15\29 < g < 14\27 g = 811\1564 g = 29\56, 43\83, 57\110 2g-1 17-27g
28L1s 1\29 < g < 1\28 g = 57\1622 g = 2\57, 3\85, 4\113 g 1-28g
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