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Generator ranges of MOS: Difference between revisions

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= 21-tone =
= 21-tone =
'''Note: bolded generators from here below generate scales which are well temperaments'''
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of best, better, good behavior
! | Large step+Small step
! | Large step-Small step
|-
|-
| | [[1L 20s]]
| |[[1L 20s]]
| | 20\21 < g < 1
| | 20\21 < g < 1
| | ''g = 21\22, 22\23, 23\24''
| |''g = 21\22, 22\23, 23\24-24\25''
| | 20g-19+1-g = 19g-18
| | 20g-19-(1-g) = 21g-20
|-
|-
| | [[2L 19s]]
| |[[2L 19s]]
| | 10\21 < g < 1\2
| | 10\21 < g < 1\2
| | g = ''11\23, 12\25'', 13\27
| | g = ''11\23, 12\25'', 13\27-13\29
| | 19g-9+1-2g = 17g-8
| | 19g-9-(1-2g) = 21g-10
|-
|-
| | [[3L 18s]]
| |[[3L 18s]]
| | 6\21 < g < 1\3
| | 6\21 < g < 1\3
| | g = ''7\24'', 8\27, 9\30
| | g = ''7\24'', 8\27, 9\30-10\33
| | 6g-5\3+1\3-g = 5g-4\3
| | 6g-5\3-(1\3-g) = 7g-2
|-
|-
| | [[4L 17s]]
| |[[4L 17s]]
| | 5\21 < g < 1\4
| | 5\21 < g < 1\4
| | g = ''6\25'', 7\29, 8\33
| | g = ''6\25'', 7\29, 8\33-9\37
| | 17g-2+1-4g = 13g-1
| | 17g-4-(1-4g) = 21g-5
|-
|-
| | [[5L 16s]]
| |[[5L 16s]]
| | 4\21 < g < 1\5
| | 4\21 < g < 1\5
| | g = ''5\26'', 6\31, 7\36
| | g = ''5\26'', 6\31, 7\36-8\41
| | 16g-3+1-5g = 11g-2
| | 16g-3-(1-5g) = 21g-4
|-
|-
| | [[6L 15s]]
| |[[6L 15s]]
| | 3\21 < g < 1\6
| | 3\21 < g < 1\6
| | g = 4\27, 5\33, 6\39
| | g = 4\27, 5\33, 6\39-7\45
| | 5g-2\3+1\3-2g = 3g-1\3
| | 5g-2\3-(1\3-2g) = 7g-1
|-
|-
| | [[7L 14s]]
| |[[7L 14s]]
| | 2\21 < g < 1\7
| | 2\21 < g < 1\7
| | g = 3\28, 4\35, 5\42
| | g = 3\28, 4\35, 5\42-6\49
| | 2g-1\7+1\7-g = g
| | 2g-1\7-(1\7-g) = 3g-2\7
|-
|-
| | [[8L 13s]]
| |[[8L 13s]]
| | 13\21 < g < 5\8
| | 13\21 < g < 5\8
| | g = 18\29, 23\37, 28\45
| | g = 18\29, 23\37, 28\45-33\53
| | 13g-8+5-8g = 5g-3
| | 13g-8-(5-8g) = 21g-13
|-
|-
| | [[9L 12s]]
| |[[9L 12s]]
| | 2\21 < g < 1\9
| | 2\21 < g < 1\9
| | g = 3\30, 4\39, 5\48
| | g = 3\30, 4\39, 5\48-6\57
| | 4g-1\3+1\3-3g = g
| | 4g-1\3-(1\3-3g) = 7g-2\3
|-
|-
| | [[10L 11s]]
| |[[10L 11s]]
| | 2\21 < g < 1\10
| | 2\21 < g < 1\10
| | g = 3\31, 4\41, 5\51
| | g = 3\31, 4\41, 5\51-6\61
| | 11g-1+1-10g = g
| | 11g-1-(1-10g) = 21g-2
|-
|-
| | [[11L 10s]]
| |[[11L 10s]]
| | 19\21 < g < 10\11
| | 19\21 < g < 10\11
| | g = 29\32, 39\43, 49\54
| | g = 29\32, 39\43, 49\54-59\65
| | 10g-9+10-11g = 1-g
| | 10g-9-(10-11g) = 21g-19
|-
|-
| | [[12L 9s]]
| |[[12L 9s]]
| | 5\21 < g < 3\12
| | 5\21 < g < 3\12
| | g = 8\33, 11\45, 14\57
| | g = 8\33, 11\45, 14\57-17\69
| | 3g-2\3+1-4g = 1\3-3g
| | 3g-2\3-(1-4g) = 7g-1\3
|-
|-
| | [[13L 8s]]
| |[[13L 8s]]
| | 8\21 < g < 5\13
| | 8\21 < g < 5\13
| | g = 13\34, 18\47, 23\70
| | g = 13\34, 18\47, 23\60-28\73
| | 8g-3+5-13g = 2-5g
| | 8g-3-(5-13g) = 21g-8
|-
|-
| | [[14L 7s]]
| |[[14L 7s|''14L 7s'']] ''= 2L 1s (7)''
| | 1\21 < g < 1\14
| | ''1\21 < g < 1\14''
| | g = 2\35, 3\49, 4\63
| | ''g = 2\35, 3\49, 4\63-5\77''
| | g+1\7-2g = 1\7-g
| | ''g-(1\7-2g) = 3g-1\7''
|-
|-
| | [[15L 6s]]
| |[[15L 6s]]
| | 4\21 < g < 3\15
| | 4\21 < g < 3\15
| | g = 7\36, 10\51, 13\66
| | g = 7\36, 10\51, 13\66-16\81
| | 2g-1\3+1-5g = 2\3-3g
| | 2g-1\3-(1-5g) = 7g-4\3
|-
|-
| | [[16L 5s]]
| |[[16L 5s]]
| | 17\21 < g < 13\16
| | 17\21 < g < 13\16
| | g = 30\37, 43\53, 56\69
| | g = 30\37, 43\53, 56\69-69\85
| | 5g-4+13-16g = 9-11g
| | 5g-4-(13-16g) = 21g-17
|-
|-
| | [[17L 4s]]
| |[[17L 4s]]
| | 16\21 < g < 13\17
| | 16\21 < g < 13\17
| | g = 29\38, 42\55, 55\72
| | g = 29\38, 42\55, 55\72-68\89
| | 4g-3+13-17g = 10-13g
| | 4g-3-(13-17g) = 21g-16
|-
|-
| | [[18L 3s]]
| |[[18L 3s|''18L 3s'']] ''= 6L 1s (3)''
| | 1\21 < g < 1\18
| | ''1\21 < g < 1\18''
| | g = 2\39, 3\57, 4\75
| | ''g = 2\39, 3\57, 4\75-5\93''
| | g+1\3-6g = 1\3-5g
| | ''g-(1\3-6g) = 7g-1\3''
|-
|-
| | [[19L 2s]]
| |[[19L 2s]]
| | 11\21 < g < 10\19
| | 11\21 < g < 10\19
| | g = 21\40, 31\59, 41\78
| | g = '''21\40''', 31\59, 41\78-51\97
| | 2g-1+10-19g = 9-17g
| | 2g-1-(10-19g) = 21g-11
|-
|-
| | [[20L 1s]]
| |[[20L 1s|''20L 1s'']]
| | 1\21 < g < 1\20
| | ''1\21 < g < 1\20''
| | g = 2\41, 3\61, 4/81
| | ''g = '''2\41''', 3\61, 4\81-5\101''
| | g+1-20g = 1-19g
| | ''g-(1-20g) = 21g-1''
|}
|}


Line 1,221: Line 1,222:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of best, better, good behavior
! |Large step+Small step
! |Large step-Small step
|-
|-
| | [[1L 21s]]
| | [[1L 21s]]
Line 1,335: Line 1,336:
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Boundaries of best, better, good behavior
! | Large step+Small step
! | Large step-Small step
|-
|-
| | [[1L 22s]]
| | [[1L 22s]]
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