Xenharmonic Wiki

Generator ranges of MOS: Difference between revisions

← Older edit
VisualWikitext
Frostburn (talk | contribs)
autopatrolled, emailconfirmed
322 edits
m →8-tone: Denote 2L 6s as consisting of 2 periods.
 
(15 intermediate revisions by 3 users not shown)
Line 1: Line 1:
Below are ranges of generators for various L-s patterns of [[MOS scale]]s, 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.
Below are ranges of generators for various L-s patterns of [[MOS scale]]s, 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 bright generators in the second column, normalized so that the lower end of the range is where L/s = 1 (Nedo). The third column gives the boundaries of propriety, maximum expressiveness and diatonicity (i.e. best, better and good behavior). Finally, the fourth column gives the formula for the size of the chroma. We have normalized to the formula for the step size where the leading term is positive.


If the number of the [[Interval_class|generic interval]] to which the generator g belongs is C, and there are N scale steps to the interval of equivalence, then the average the size of an interval in class C is C/N. We have normalized so that C/N is the lower bound of the range of generators; since therefore g > C/N, g is larger than average and hence is the larger of the two sizes of intervals in its class, which means we have normalized to the [[Modal_UDP_Notation|chroma-positive]] generator. We have normalized to the formula for the step size where the leading term is positive.
== 2, 3, and 4-tone ==
'''Note 1: These sets are given for the sake of completeness as they are not really scales'''


=2, 3, 4=
'''Note 2: monosmall patterns are italicized from here below as the boundary of propriety does not apply to them'''
'''Note: These sets are given for the sake of completeness as they are not really scales'''


{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | Midpoint
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! | Large step+Small step
|-
|-
| | 1L1s
| | [[1L 1s|''1L 1s'']]
| | 1\2 < g < 1
| | ''1\2 < g < 1''
| | g = 3\4
| | ''g = 2\3, 3\4, 4\5-5\6''
| | g = 2\3, 3\4, 4\5
| | ''g-(1-g) = 2g-1''
| | g+1-g = 1
|-
|-
| | 1L2s
| | [[1L 2s]]
| | 2\3 < g < 1
| | 2\3 < g < 1
| | g = 5\6
| | g = 3\4, 4\5, 5\6-6\7
| | g = 3\4, 4\5, 5\6
| | 2g-1-(1-g) = 3g-2
| | 2g-1+1-g = g
|-
|-
| | 2L1s
| | [[2L 1s|''2L 1s'']]
| | 1\3 < g < 1\2
| | ''1\3 < g < 1\2''
| | g = 5\12
| | ''g = 2\5, 3\7, 4\9-5\11''
| | g = 2\5, 3\7, 4\9
| | ''g-(1-2g)= 3g-1''
| | g+1-2g = 1-g
|-
|-
| | 1L3s
| | [[1L 3s]]
| | 3\4 < g < 1
| | 3\4 < g < 1
| | g = 7\8
| | g = 4\5, 5\6, 6\7-7\8
| | g = 4\5, 5\6, 6\7
| | 3g-2-(1-g) = 4g-3
| | 3g-2+1-g = 2g-1
|-
|-
| | 2L2s
| | [[2L 2s|''2L 2s'']] ''= 1L 1s (2)''
| | 1\4 < g < 1\2
| | ''1\4 < g < 1\2''
| | g = 3\8
| | ''g = 2\6, 3\8, 4\10-5\12''
| | g = 2\6, 3\8, 4\10
| | ''g-(1\2-g) = 2g-1\2''
| | g+1\2-g = 1\2
|-
|-
| | 3L1s
| | [[3L 1s|''3L 1s'']]
| | 1\4 < g < 1\3
| | ''1\4 < g < 1\3''
| | g = 7\24
| | ''g = 2\7, 3\10, 4\13-5\16''
| | g = 2\7, 3\10, 4\13
| | ''g-(1-3g) = 4g-1''
| | g+1-3g = 1-2g
|}
|}


=5=
== 5-tone ==
'''Note: italicized generators from here below generate scales which are weakly tonal'''
'''Note: italicized generators from here below generate scales which are weakly tonal'''
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | Midpoint
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! | Large step+Small step
|-
|-
| | 1L4s
| | [[1L 4s]]
| | 4\5 < g < 1
| | 4\5 < g < 1
| | g = 9\10
| | g = 5\6, 6\7, 7\8-8\9
| | g = ''5\6'', 6\7, 7\8
| | 4g-3-(1-g) = 5g-4
| | 4g-3+1-g = 3g-2
|-
|-
| | 2L3s
| | [[2L 3s]]
| | 2\5 < g < 1\2
| | 2\5 < g < 1\2
| | g = 9\20
| | g = 3\7, 4\9, 5\11-6\13
| | g = 3\7, 4\9, 5\11
| | 3g-1-(1-2g) = 5g-2
| | 3g-1+1-2g = g
|-
|-
| | 3L2s
| | [[3L 2s]]
| | 3\5 < g < 2\3
| | 3\5 < g < 2\3
| | g = 19\30
| | g = 5\8, 7\11, 9\14-11\17
| | g = 5\8, 7\11, 9\14
| | 2g-1-(2-3g) = 5g-3
| | 2g-1+2-3g = 1-g
|-
|-
| | 4L1s
| | [[4L 1s|''4L 1s'']]
| | 1\5 < g < 1\4
| | ''1\5 < g < 1\4''
| | g = 9\40
| | ''g = 2\9, 3\13, 4\17-5\21''
| | g = 2\9, 3\13, 4\17
| | ''g-(1-4g) = 5g-1''
| | g+1-4g = 1-3g
|}
|}


=6=
== 6-tone ==
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | Midpoint
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! | Large step+Small step
|-
|-
| | 1L5s
| | [[1L 5s]]
| | 5\6 < g < 1
| | 5\6 < g < 1
| | g = 11\12
| | g = ''6\7'', 7\8, 8\9-9\10
| | g = ''6\7'', 7\8, 8\9
| | 5g-4-(1-g) = 6g-5
| | 5g-4+1-g = 4g-3
|-
|-
| | 2L4s
| | [[2L 4s]]
| | 2\6 < g < 1\2
| | 2\6 < g < 1\2
| | g = 5\12
| | g = 3\8, 4\10, 5\12-6\14
| | g = 3\8, 4\10, 5\12
| | 2g-1\2-(1\2-g) = 3g-1
| | 2g-1\2+1\2-g = g
|-
|-
| | 3L3s
| | [[3L 3s|''3L 3s'']] ''= 1L 1s (3)''
| | 1\6 < g < 1\3
| | ''1\6 < g < 1\3''
| | g = 3\12
| | ''g = 2\9, 3\12, 4\15-5\18''
| | g = 2\9, 3\12, 4\15
| | ''g-(1\3-g) = 2g-1\3''
| | g+1\3-g = 1\3
|-
|-
| | 4L2s
| | [[4L 2s|''4L 2s'']] ''= 2L 1s (2)''
| | 1\6 < g < 1\4
| | ''1\6 < g < 1\4''
| | g = 5\24
| | ''g = 2\10, 3\14, 4\18-5\22''
| | g = 2\10, 3\14, 4\18
| | ''g-(1\2-2g) = 3g-1\2''
| | g+1\2-2g = 1\2-g
|-
|-
| | 5L1s
| | [[5L 1s|''5L 1s'']]
| | 1\6 < g < 1\5
| | ''1\6 < g < 1\5''
| | g = 11\60
| | ''g = 2\11, 3\16, 4\21-5\26''
| | g = 2\11, 3\16, 4\21
| | ''g-(1-5g) = 6g-1''
| | g+1-5g = 1-4g
|}
|}


=7=
== 7-tone ==
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | Midpoint
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! | Large step+Small step
|-
|-
| | 1L6s
| | [[1L 6s]]
| | 6\7 < g < 1
| | 6\7 < g < 1
| | g = 13\14
| | g = ''7\8'', 8\9, 9\10-10\11
| | g = ''7\8'', 8\9, 9\10
| | 6g-5-(1-g) = 7g-6
| | 6g-5+1-g = 5g-4
|-
|-
| | 2L5s
| | [[2L 5s]]
| | 3\7 < g < 1\2
| | 3\7 < g < 1\2
| | g = 13\28
| | g = 4\9, 5\11, 6\13-7\15
| | g = 4\9, 5\11, 6\13
| | 5g-2-(1-2g) = 7g-3
| | 5g-2+1-2g = 3g-1
|-
|-
| | 3L4s
| | [[3L 4s]]
| | 2\7 < g < 1\3
| | 2\7 < g < 1\3
| | g = 13\42
| | g = 3\10, 4\13, 5\16-6\19
| | g = 3\10, 4\13, 5\16
| | 4g-1-(1-3g) = 7g-2
| | 4g-1+1-3g = g
|-
|-
| | 4L3s
| | [[4L 3s]]
| | 5\7 < g < 3\4
| | 5\7 < g < 3\4
| | g = 41\56
| | g = 8\11, 11\15, 14\19-17\23
| | g = 8\11, 11\15, 14\19
| | 3g-2-(3-4g) = 7g-5
| | 3g-2+3-4g = 1-g
|-
|-
| | 5L2s
| | [[5L 2s]]
| | 4\7 < g < 3\5
| | 4\7 < g < 3\5
| | g = 41\70
| | g = 7\12, 10\17, 13\22-16\27
| | g = 7\12, 10\17, 13\22
| | 2g-1-(3-5g) = 7g-4
| | 2g-1+3-5g = 2-3g
|-
|-
| | 6L1s
| | [[6L 1s|''6L 1s'']]
| | 1\7 < g < 1\6
| | ''1\7 < g < 1\6''
| | g = 13\84
| | ''g = 2\13, 3\19, 4\25-5\31''
| | g = 2\13, 3\19, 4\25
| | ''g-(1-6g) = 7g-1''
| | g+1-6g = 1-5g
|}
|}


=8=
== 8-tone ==
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | Midpoint
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! | Large step+Small step
|-
|-
| | 1L7s
| | [[1L 7s]]
| | 7\8 < g < 1
| | 7\8 < g < 1
| | g = 15\16
| | g = ''8\9, 9\10'', 10\11-11\12
| | g = I, 9\10, 10\11
| | 7g-6-(1-g) = 8g-7
| | 7g-6+1-g = 6g-5
|-
|-
| | 2L6s
| | [[2L 6s|''2L 6s'']] ''= 1L 3s (2)''
| | 3\8 < g < 1\2
| | 3\8 < g < 1\2
| | g = 7\16
| | g = ''4\10'', 5\12, 6\14-7\16
| | g = 4\10, 5\12, 6\14
| | 3g-1-(1\2-g) = 4g-3\2
| | 3g-1+1\2-g = 2g-1\2
|-
|-
| | 3L5s
| | [[3L 5s]]
| | 5\8 < g < 2\3
| | 5\8 < g < 2\3
| | g = 31\48
| | g = 7\11, 9\14, 11\17-13\20
| | g = 7\11, 9\14, 11\17
| | 5g-3-(2-3g) = 8g-5
| | 5g-3+2-3g = 2g-1
|-
|-
| | 4L4s
| | [[4L 4s|''4L 4s'']] ''= 1L 1s (4)''
| | 1\8 < g < 1\4
| | ''1\8 < g < 1\4''
| | g = 3\16
| | ''g = 2\12, 3\16, 4\20-5\24''
| | g = 2\12, 3\16, 4\20
| | ''g-(1\4-g) = 2g-1\4''
| | g+1\4-g = 1\4
|-
|-
| | 5L3s
| | [[5L 3s]]
| | 3\8 < g < 2\5
| | 3\8 < g < 2\5
| | g = 31\80
| | g = 5\13, 7\18, 9\23-11\28
| | g = 5\13, 7\18, 9\23
| | 3g-1-(2-5g) = 8g-3
| | 3g-1+2-5g = 1-2g
|-
|-
| | 6L2s
| | [[6L 2s|''6L 2s'']] ''= 3L 1s (2)''
| | 1\8 < g < 1\6
| | ''1\8 < g < 1\6''
| | g = 7\48
| | ''g = 2\14, 3\20, 4\26-5\32''
| | g = 2\14, 3\20, 4\26
| | ''g-(1\2-3g) = 4g-1\2''
| | g+1\2-3g = 1\2-2g
|-
|-
| | 7L1s
| | [[7L 1s|''7L 1s'']]
| | 1\8 < g < 1\7
| | ''1\8 < g < 1\7''
| | g = 15\112
| | ''g = 2\15, 3\22, 4\29-5\36''
| | g = 2\15, 3\22, 4\29
| | ''g-(1-7g) = 8g-1''
| | g+1-7g = 1-6g
|}
|}


=9=
== 9-tone ==
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | Midpoint
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! | Large step+Small step
|-
|-
| | 1L8s
| | [[1L 8s]]
| | 8\9 < g < 1
| | 8\9 < g < 1
| | g = 17\18
| | g = ''9\10'', ''10\11'', 11\12-12\13
| | g = ''9\10'', ''10\11'', 11\12
| | 8g-7-(1-g) = 9g-8
| | 8g-7+1-g = 7g-6
|-
|-
| | 2L7s
| | [[2L 7s]]
| | 4\9 < g < 1\2
| | 4\9 < g < 1\2
| | g = 17\36
| | g = ''5\11'', 6\13, 7\15-8\17
| | g = ''5\11'', 6\13, 7\15
| | 7g-3-(1-2g) = 9g-4
| | 7g-3+1-2g = 5g-2
|-
|-
| | 3L6s
| | [[3L 6s]]
| | 2\9 < g < 1\3
| | 2\9 < g < 1\3
| | g = 5\18
| | g = 3\12, 4\15, 5\18-6\21
| | g = 3\12, 4\15, 5\18
| | 2g-1\3-(1\3-g) = 3g-2\3
| | 2g-1\3+1\3-g = g
|-
|-
| | 4L5s
| | [[4L 5s]]
| | 2\9 < g < 1\4
| | 2\9 < g < 1\4
| | g = 17\72
| | g = 3\13, 4\17, 5\21-6\25
| | g = 3\13, 4\17, 5\21
| | 5g-1-(1-4g) = 9g-2
| | 5g-1+1-4g = g
|-
|-
| | 5L4s
| | [[5L 4s]]
| | 7\9 < g < 4\5
| | 7\9 < g < 4\5
| | g = 71\90
| | g = 11\14, 15\19, 19\24-23\29
| | g = 11\14, 15\19, 18\23
| | 4g-3-(4-5g) = 9g-7
| | 4g-3+4-5g = 1-g
|-
|-
| | 6L3s
| | [[6L 3s|''6L 3s'']] ''= 2L 1s (3)''
| | 1\9 < g < 1\6
| | ''1\9 < g < 1\6''
| | g = 5\36
| | ''g = 2\15, 3\21, 4\27-5\33''
| | g = 2\15, 3\21, 4\27
| | ''g-(1\3-2g) = 3g-1\3''
| | g+1\3-2g = 1\3-g
|-
|-
| | 7L2s
| | [[7L 2s]]
| | 5\9 < g < 4\7
| | 5\9 < g < 4\7
| | g = 71\126
| | g = 9\16, 13\23, 17\30-21\37
| | g = 9\16, 10\23, 17\30
| | 2g-1-(4-7g) = 9g-5
| | 2g-1+4-7g = 3-7g
|-
|-
| | 8L1s
| | [[8L 1s|''8L 1s'']]
| | 1\9 < g < 1\8
| | ''1\9 < g < 1\8''
| | g = 17\144
| | ''g = 2\17, 3\25, 4\33-5\41''
| | g = 2\17, 3\25, 4\33
| | ''g-(1-8g) = 9g-1''
| | g+1-8g = 1-7g
|}
|}


=10=
== 10-tone ==
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | Midpoint
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! | Large step+Small step
|-
|-
| | 1L9s
| | [[1L 9s]]
| | 9\10 < g < 1
| | 9\10 < g < 1
| | g = 19\20
| | g = ''10\11'', ''11\12'', 12\13-13\14
| | g = ''10\11'', ''11\12'', 12\13
| | 9g-8-(1-g) = 10g-9
| | 9g-8+1-g = 8g-7
|-
|-
| | 2L8s
| | [[2L 8s]]
| | 4\10 < g < 1\2
| | 4\10 < g < 1\2
| | g = 9\20
| | g = ''5\12'', 6\14, 7\16-8\18
| | g = ''5\12'', 6\14, 7\16
| | 4g-3\2-(1\2-g) = 5g-2
| | 4g-3\2+1\2-g = 3g-1
|-
|-
| | 3L7s
| | [[3L 7s]]
| | 3\10 < g < 1\3
| | 3\10 < g < 1\3
| | g = 19\60
| | g = 4\13, 5\16, 6\19-7\22
| | g = 4\13, 5\16, 6\19
| | 7g-2-(1-3g) = 10g-3
| | 7g-2+1-3g = 4g-1
|-
|-
| | 4L6s
| | [[4L 6s]]
| | 2\10 < g < 1\4
| | 2\10 < g < 1\4
| | g = 9\40
| | g = 3\14, 4\18, 5\22-6\26
| | g = 3\14, 4\18, 5\22
| | 3g-1\2-(1\2-2g) = 5g-1
| | 3g-1\2+1\2-2g = g
|-
|-
| | 5L5s
| | [[5L 5s|''5L 5s'']] ''= 1L 1s (5)''
| | 1\10 < g < 1\5
| | ''1\10 < g < 1\5''
| | g = 3\20
| | ''g = 2\15, 3\20, 4\25-5\30''
| | g = 2\15, 3\20, 4\25
| | ''g-(1\5-g) = 2g-1\5''
| | g+1\5-g = 1\5  
|-
|-
| | 6L4s
| | [[6L 4s]]
| | 3\10 < g < 2\6
| | 3\10 < g < 2\6
| | g = 19\60
| | g = 5\16, 7\22, 9\28-11\34
| | g = 5\16, 7\22, 9\28
| | 2g-1\2-(1-3g) = 5g-3\2
| | 2g-1\2+1-3g = 1\2-g
|-
|-
| | 7L3s
| | [[7L 3s]]
| | 7\10 < g < 5\7
| | 7\10 < g < 5\7
| | g = 99\140
| | g = 12\17, 17\24, 22\31-27\38
| | g = 12\17, 17\24, 22\31
| | 3g-2-(5-7g) = 10g-7
| | 3g-2+5-7g = 3-4g
|-
|-
| | 8L2s
| | [[8L 2s|''8L 2s'']] ''= 4L 1s (2)''
| | 1\10 < g < 1\8
| | ''1\10 < g < 1\8''
| | g = 9\80
| | ''g = 2\18, 3\26, 4\34-5\42''
| | g = 2\18, 3\26, 4\34
| | ''g-(1\2-4g) = 5g-1\2''
| | g+1\2-4g = 1\2-3g
|-
|-
| | 9L1s
| | [[9L 1s|''9L 1s'']]
| | 1\10 < g < 1\9
| | ''1\10 < g < 1\9''
| | g = 19\180
| | ''g = 2\19, 3\28, 4\37-5\46''
| | g = 2\19, 3\28, 4\37
| | ''g-(1-9g) = 10g-1''
| | g+1-9g = 1-8g
|}
|}


=11=
== 11-tone ==
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | Midpoint
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! | Large step+Small step
|-
|-
| | 1L10s
| | [[1L 10s]]
| | 10\11 < g < 1
| | 10\11 < g < 1
| | g = 21\22
| | g = ''11\12'', ''12\13'', 13\14-14\15
| | g = ''11\12'', ''12\13'', 13\14
| | 10g-9-(1-g) = 11g-10
| | 10g-9+1-g = 9g-8
|-
|-
| | 2L9s
| | [[2L 9s]]
| | 5\11 < g < 1\2
| | 5\11 < g < 1\2
| | g = 21\44
| | g = ''6\13'', 7\15, 8\17-9\19
| | g = ''6\13'', 7\15, 8\17
| | 9g-4-(1-2g) = 11g-5
| | 9g-4+1-2g = 7g-3
|-
|-
| | 3L8s
| | [[3L 8s]]
| | 7\11 < g < 2\3
| | 7\11 < g < 2\3
| | g = 43\66
| | g = 9\14, 11\17, 13\20-15\23
| | g = 9\14, 11\17, 13\20
| | 8g-5-(2-3g) = 11g-7
| | 8g-5+2-3g = 5g-3
|-
|-
| | 4L7s
| | [[4L 7s]]
| | 8\11 < g < 3\4
| | 8\11 < g < 3\4
| | g = 65\88
| | g = 11\15, 14\19, 17\23-20\27
| | g = 11\15, 14\19, 17\23
| | 7g-5-(3-4g) = 11g-8
| | 7g-5+3-4g = 3g-2
|-
|-
| | 5L6s
| | [[5L 6s]]
| | 2\11 < g < 1\5
| | 2\11 < g < 1\5
| | g = 21\110
| | g = 3\16, 4\21, 5\26-6\31
| | g = 3\16, 4\21, 5\26
| | 6g-1-(1-5g) = 11g-2
| | 6g-1+1-5g = g
|-
|-
| | 6L5s
| | [[6L 5s]]
| | 9\11 < g < 5\6
| | 9\11 < g < 5\6
| | g = 109\132
| | g = 14\17, 19\23, 24\29-29\35
| | g = 14\17, 19\23, 24\29
| | 5g-4-(5-6g) = 11g-9
| | 5g-4+5-6g = 1-g
|-
|-
| | 7L4s
| | [[7L 4s]]
| | 3\11 < g < 2\7
| | 3\11 < g < 2\7
| | g = 43\154
| | g = 5\18, 7\25, 9\32-11\39
| | g = 5\18, 7\25, 9\32
| | 4g-1-(2-7g) = 11g-3
| | 4g-1+2-7g = 1-3g
|-
|-
| | 8L3s
| | [[8L 3s]]
| | 4\11 < g < 3\8
| | 4\11 < g < 3\8
| | g = 65\176
| | g = 7\19, 10\27, 13\35-16\43
| | g = 7\19, 10\27, 13\35
| | 3g-1-(3-8g) = 11g-4
| | 3g-1+3-8g = 2-5g
|-
|-
| | 9L2s
| | [[9L 2s]]
| | 6\11 < g < 5\9
| | 6\11 < g < 5\9
| | g = 109\198
| | g = 11\20, 16\29, 21\38-26\47
| | g = 11\20, 16\29, 21\38
| | 2g-1-(5-9g) = 11g-6
| | 2g-1+5-9g = 4-7g
|-
|-
| | 10L1s
| | [[10L 1s|''10L 1s'']]
| | 1\11 < g < 1\10
| | ''1\11 < g < 1\10''
| | g = 21\220
| | ''g = 2\21, 3\31, 4\41-5\51''
| | g = 2\21, 3\31, 4\41
| | ''g+1-10g = 11g-1''
| | g+1-10g = 1-9g
|}
|}


=12=
== 12-tone ==
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | Midpoint
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! | Large step+Small step
|-
|-
| | 1L11s
| | [[1L 11s]]
| | 11\12 < g < 1
| | 11\12 < g < 1
| | g = 23\24
| | g = ''12\13,'' ''13\14, 14\15''-15\16
| | g = ''12\13,'' ''13\14'', 14\15
| | 11g-10-(1-g) = 12g-11
| | 11g-10+1-g = 10g-9
|-
|-
| | 2L10s
| | [[2L 10s]]
| | 5\12 < g < 1\2
| | 5\12 < g < 1\2
| | g = 11\24
| | g = ''6\14'', 7\16, 8\18-9\20
| | g = ''6\14'', 7\16, 8\18
| | 5g-2-(1\2-g) = 6g-5\2
| | 5g-2+1\2-g = 4g-3\2
|-
|-
| | 3L9s
| | [[3L 9s]]
| | 3\12 < g < 1\3
| | 3\12 < g < 1\3
| | g = 7\24
| | g = ''4\15'', 5\18, 6\21-7\24
| | g = 4\15, 5\18, 6\21
| | 3g-2\3-(1\3-g) = 4g-1
| | 3g-2\3+1\3-g = 2g-1\3
|-
|-
| | 4L8s
| | [[4L 8s]]
| | 2\12 < g < 1\4
| | 2\12 < g < 1\4
| | g = 5\24
| | g = 3\16, 4\20, 5\24-6\28
| | g = 3\16, 4\20, 5\24
| | 2g-1\4-(1\4-g) = 3g-1\2
| | 2g-1\4+1\4-g = g
|-
|-
| | 5L7s
| | [[5L 7s]]
| | 7\12 < g < 3\5
| | 7\12 < g < 3\5
| | g = 71\120
| | g = 10\17, 13\22, 16\27-19\32
| | g = 10\17, 13\22, 16\27
| | 7g-4-(3-5g) = 12g-7
| | 7g-4+3-5g = 2g-1
|-
|-
| | 6L6s
| | [[6L 6s|''6L 6s'']] ''= 1L 1s (6)''
| | 1\12 < g < 1\6
| | ''1\12 < g < 1\6''
| | g = 3\24
| | ''g = 2\18, 3\24, 4\30-5\36''
| | g = 2\18, 3\24, 4\30
| | ''g-(1\6-g) = 2g-1\6''
| | g+1\6-g = g
|-
|-
| | 7L5s
| | [[7L 5s]]
| | 5\12 < g < 3\7
| | 5\12 < g < 3\7
| | g = 71\168
| | g = 8\19, 11\26, 14\33-17\40
| | g = 8\19, 11\26, 14\33
| | 5g-2-(3-7g) = 12g-5
| | 5g-2+3-7g = 1-2g
|-
|-
| | 8L4s
| | [[8L 4s|''8L 4s'']] ''= 2L 1s (4)''
| | 1\12 < g < 1\8
| | ''1\12 < g < 1\8''
| | g = 5\48
| | ''g = 2\20, 3\28, 4\36-5\44''
| | g = 2\20, 3\28, 4\36
| | ''g-(1\4-2g) = 3g-1\4''
| | g+1\4-2g = 1\4-g
|-
|-
| | 9L3s
| | [[9L 3s|''9L 3s'']] ''= 3L 1s (3)''
| | 1\12 < g < 1\9
| | ''1\12 < g < 1\9''
| | g = 7\72
| | ''g = 2\21, 3\30, 4\39-5\48''
| | g = 2\21, 3\30, 4\39
| | ''g-(1\3-3g) = 4g-1\3''
| | g+1\3-3g = 1\3-2g
|-
|-
| | 10L2s
| | [[10L 2s|''10L 2s'']] ''= 5L 1s (2)''
| | 1\12 < g < 1\10
| | ''1\12 < g < 1\10''
| | g = 11\120
| | ''g = 2\22, 3\32, 4\42-5\52''
| | g = 2\22, 3\32, 4\42
| | ''g-(1\2-5g) = 6g-1\2''
| | g+1\2-5g = 1\2-4g
|-
|-
| | 11L1s
| | [[11L 1s|''11L 1s'']]
| | 1\12 < g < 1\11
| | ''1\12 < g < 1\11''
| | g = 23\264
| | ''g = 2\23, 3\34, 4\45-5\56''
| | g = 2\23, 3\34, 4\45
| | ''g-(1-11g) = 12g-1''
| | g+1-11g = 1-10g
|}
|}


=13=
== 13-tone ==
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | Midpoint
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! | Large step+Small step
|-
|-
| | 1L12s
| | [[1L 12s]]
| | 12\13 < g < 1
| | 12\13 < g < 1
| | g = 25\26
| | g = ''13\14, 14\15, 15\16''-16\17
| | ''g = 13\14, 14\15, 15\16''
| | 12g-11-(1-g) = 13g-12
| | 12g-11+1-g = 11g-10
|-
|-
| | 2L11s
| | [[2L 11s]]
| | 6\13 < g < 1\2
| | 6\13 < g < 1\2
| | g = 25\52
| | g = ''7\15'', 8\17, 9\19-10\21
| | g = ''7\15'', 8\17, 9\19
| | 11g-5-(1-2g) = 13g-6
| | 11g-5-1-2g = 10g-6
|-
|-
| | 3L10s
| | [[3L 10s]]
| | 4\13 < g < 1\3
| | 4\13 < g < 1\3
| | g = 25\78
| | g = ''5\16'', 6\19, 7\22-8\25
| | g = ''5\16'', 6\19, 7/22
| | 10g-3-(1-3g) = 13g-4
| | 10g-3+1-3g = 7g-2
|-
|-
| | 4L9s
| | [[4L 9s]]
| | 3\13 < g < 1\4
| | 3\13 < g < 1\4
| | g = 25\104
| | g = 4\17, 5\21, 6\25-7\29
| | g = 4\17, 5\21, 6\25
| | 9g-2-(1-4g) = 13g-3
| | 9g-2+1-4g = 5g-1
|-
|-
| | 5L8s
| | [[5L 8s]]
| | 5\13 < g < 2\5
| | 5\13 < g < 2\5
| | g = 51\130
| | g = 7\18, 9\23, 11\28-13\33
| | g = 7\18, 9\23, 11\28
| | 8g-3-(2-5g) = 13g-5
| | 8g-3+2-5g = 3g-1
|-
|-
| | 6L7s
| | [[6L 7s]]
| | 2\13 < g < 1\6
| | 2\13 < g < 1\6
| | g = 25\156
| | g = 3\19, 4\25, 5\31-6\37
| | g = 3\19, 4\25, 5\31
| | 7g-1-(1-6g) = 13g-2
| | 7g-1+1-6g = g
|-
|-
| | 7L6s
| | [[7L 6s]]
| | 11\13 < g < 6\7
| | 11\13 < g < 6\7
| | g = 155\182
| | g = 17\20, 23\27, 29\34-35\41
| | g = 17\20, 23\27, 29\34
| | 6g-5-(6-7g) = 13g-11
| | 6g-5+6-7g = 1-g
|-
|-
| | 8L5s
| | [[8L 5s]]
| | 8\13 < g < 5\8
| | 8\13 < g < 5\8
| | g = 129\208
| | g = 13\21, 18\29, 23\37-28\45
| | g = 13\21, 18\29, 23\37
| | 5g-3-(5-8g) = 13g-8
| | 5g-3+5-8g = 2-3g
|-
|-
| | 9L4s
| | [[9L 4s]]
| | 10\13 < g < 7\9
| | 10\13 < g < 7\9
| | g = 181\234
| | g = 17\22, 24\31, 31\40-38\49
| | g = 17\22, 24\31, 31\40
| | 4g-3-(7-9g) = 13g-10
| | 4g-3+7-9g = 4-5g
|-
|-
| | 10L3s
| | [[10L 3s]]
| | 9\13 < g < 7\10
| | 9\13 < g < 7\10
| | g = 181\260
| | g = 16\23, 23\33, 30\43-37\53
| | g = 16\23, 23\33, 30\43
| | 3g-2-(7-10g) = 13g-9
| | 3g-2+7-10g = 5-7g
|-
|-
| | 11L2s
| | [[11L 2s]]
| | 7\13 < g < 6\11
| | 7\13 < g < 6\11
| | g = 155\286
| | g = 13\24, 19\35, 25\46-31\57
| | g = 13\24, 19\35, 25\46
| | 2g-1-(6-11g) = 13g-7
| | 2g-1+6-11g = 5-9g
|-
|-
| | 12L1s
| | [[12L 1s|''12L 1s'']]
| | 1\13 < g < 1\12
| | ''1\13 < g < 1\12''
| | g = 25\312
| | ''g = 2\25, 3\37, 4\49-5\61''
| | g = 2\25, 3\37, 4\49
| | ''g-(1-12g) = 13g-1''
| | g+1-12g = 1-11g
|}
|}


=14=
== 14-tone ==
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | Midpoint
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! | Large step+Small step
|-
|-
| | 1L13s
| | [[1L 13s]]
| | 13\14 < g < 1
| | 13\14 < g < 1
| | g = 27\28
| | g = ''14\15, 15\16, 16\17''-17\18
| | ''g = 14\15, 15\16, 16\17''
| | 13g-12-(1-g) = 14g-13
| | 13g-12+1-g = 12g-11
|-
|-
| | 2L12s
| | [[2L 12s]]
| | 6\14 < g < 1\2
| | 6\14 < g < 1\2
| | g = 13\28
| | g = ''7\16'', 8\18, 9\20-10\22
| | g = ''7\16'', 8\18, 9\20
| | 6g-5\2-(1\2-g) = 7g-3
| | 6g-5\2+1\2-g = 5g-2
|-
|-
| | 3L11s
| | [[3L 11s]]
| | 9\14 < g < 2\3
| | 9\14 < g < 2\3
| | g = 55\84
| | g = ''11\17'', 13\20, 15\23-17\26
| | g = ''11\17'', 13\20, 15\23
| | 11g-7-(2-3g) = 14g-9
| | 11g-7+2-3g = 9g-5
|-
|-
| | 4L10s
| | [[4L 10s]]
| | 3\14 < g < 1\4
| | 3\14 < g < 1\4
| | g = 13\56
| | g = 4\18, 5\22, 6\26-7\30
| | g = 4\18, 5\22, 6\26
| | 5g-1-(1\2-2g) = 7g-3\2
| | 5g-1+1\2-2g = 3g-1\2
|-
|-
| | 5L9s
| | [[5L 9s]]
| | 11\14 < g < 4\5
| | 11\14 < g < 4\5
| | g = 111\140
| | g = 15\19, 19\24, 23\29-27\34
| | g = 15\19, 19\24, 23\29
| | 9g-7-(4-5g) = 14g-11
| | 9g-7+4-5g = 4g-3
|-
|-
| | 6L8s
| | [[6L 8s]]
| | 2\14 < g < 1\6
| | 2\14 < g < 1\6
| | g = 13\84
| | g = 3\20, 4\26, 5\32-6\38
| | g = 3\20, 4\26, 5\32
| | 4g-1\2-(1\2-3g) = 7g-1
| | 4g-1\2-1\2-3g = g
|-
|-
| | 7L7s
| | [[7L 7s|''7L 7s'']] ''= 1L 1s (7)''
| | 1\14 < g < 1\7
| | ''1\14 < g < 1\7''
| | g = 3\28
| | ''g = 2\21, 3\28, 4\35-5\42''
| | g = 2\21, 3\28, 4\35
| | ''g-(1\7-g) = 2g-1\7''
| | g+1\7-g = 1\7
|-
|-
| | 8L6s
| | [[8L 6s]]
| | 5\14 < g < 3\8
| | 5\14 < g < 3\8
| | g = 41\112
| | g = 8\22, 11\30, 14\38-17\46
| | g = 8\22, 11\30, 14\38
| | 3g-1-(3\2-4g) = 7g-5\2
| | 3g-1+3\2-4g = 1\2-g
|-
|-
| | 9L5s
| | [[9L 5s]]
| | 3\14 < g < 2\9
| | 3\14 < g < 2\9
| | g = 55\252
| | g = 5\23, 7\32, 9\41-11\50
| | g = 5\23, 7\32, 9\41
| | 5g-1-(2-9g) = 14g-3
| | 5g-1+2-9g = 1-4g
|-
|-
| | 10L4s
| | [[10L 4s]]
| | 4\14 < g < 3\10
| | 4\14 < g < 3\10
| | g = 41\140
| | g = 7\24, 10\34, 13\44-16\54
| | g = 7\24, 10\34, 13\44
| | 2g-1\2-(3\2-5g) = 7g-2
| | 2g-1\2+3\2-5g = 1-3g
|-
|-
| | 11L3s
| | [[11L 3s]]
| | 5\14 < g < 4\11
| | 5\14 < g < 4\11
| | g = 111\308
| | g = 9\25, 13\36, 17\47-21\58
| | g = 9\25, 13\36, 17\47
| | 3g-1-(4-11g) = 14g-5
| | 3g-1+4-11g = 3-8g
|-
|-
| | 12L2s
| | [[12L 2s|''12L 2s'']] ''= 6L 1s (2)''
| | 1\14 < g < 1\12
| | ''1\14 < g < 1\12''
| | g = 13\168
| | ''g = 2\26, 3\38, 4\50-5\62''
| | g = 2\26, 3\38, 4\50
| | ''g-(1\2-6g) = 7g-1\2''
| | g+1\2-6g = 1\2-5g
|-
|-
| | 13L1s
| | [[13L 1s|''13L 1s'']]
| | 1\14 < g < 1\13
| | ''1\14 < g < 1\13''
| | g = 27\364
| | ''g = 2\27, 3\40, 4\53-5\66''
| | g = 2\27, 3\40, 4\53
| | ''g+1-13g = 14g-1''
| | g+1-13g = 1-12g
|}
|}


=15=
== 15-tone ==
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | Midpoint
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! | Large step+Small step
|-
|-
| | 1L14s
| | [[1L 14s]]
| | 14\15 < g < 1
| | 14\15 < g < 1
| | g = 29\30
| | g = ''15\16, 16\17, 17\18-''18\19
| | ''g = 15\16, 16\17, 17\18''
| | 14g-13-(1-g) = 15g-14
| | 14g-13+1-g = 13g-12
|-
|-
| | 2L13s
| | [[2L 13s]]
| | 7\15 < g < 1\2
| | 7\15 < g < 1\2
| | g = 29\60
| | g = ''8\17'', 9\19, 10\21-11\23
| | g = ''8\17'', 9\19, 10\21
| | 13g-6-(1-2g) = 15g-7
| | 13g-6+1-2g = 11g-5
|-
|-
| | 3L12s
| | [[3L 12s]]
| | 4\15 < g < 1\3
| | 4\15 < g < 1\3
| | g = 9\30
| | g = ''5\18'', 6\21, 7\24-8\27
| | g = ''5\18'', 6\21, 7\24
| | 4g-1-(1\3-g) = 5g-4\3
| | 4g-1+1\3-g = 3g-2\3
|-
|-
| | 4L11s
| | [[4L 11s]]
| | 11\15 < g < 3\4
| | 11\15 < g < 3\4
| | g = 89\120
| | g = 14\19, 17\23, 20\27-23\31
| | g = 14\19, 17\23, 20\27
| | 11g-8-(3-4g) = 15g-11
| | 11g-8+3-4g = 8g-4
|-
|-
| | 5L10s
| | [[5L 10s]]
| | 2\15 < g < 1\5
| | 2\15 < g < 1\5
| | g = 5\30
| | g = 3\20, 4\25, 5\30-6\35
| | g = 3\20, 4\25, 5\30
| | 2g-1\5-(1\5-g) = 3g-2\5
| | 2g-1\5+1\5-g = g
|-
|-
| | 6L9s
| | [[6L 9s]]
| | 2\15 < g < 1\6
| | 2\15 < g < 1\6
| | g = 9\60
| | g = 3\21, 4\27, 5\33-6\39
| | g = 3\21, 4\27, 5\33
| | 3g-1\3-(1\3-2g) = 5g-2\3
| | 3g-1\3+1\3-2g = g
|-
|-
| | 7L8s
| | [[7L 8s]]
| | 2\15 < g < 1\7
| | 2\15 < g < 1\7
| | g = 29\210
| | g = 3\22, 4\29, 5\36-6\43
| | g = 3\22, 4\29, 5\36
| | 8g-1-(1-7g) = 15g-2
| | 8g-1+1-7g = g
|-
|-
| | 8L7s
| | [[8L 7s]]
| | 13\15 < g < 7\8
| | 13\15 < g < 7\8
| | g = 209\240
| | g = 20\23, 27\31, 34\39-41\47
| | g = 20\23, 27\31, 34\39
| | 7g-6-(7-8g) = 15g-13
| | 7g-6+7-8g = 1-g
|-
|-
| | 9L6s
| | [[9L 6s]]
| | 3\15 < g < 2\9
| | 3\15 < g < 2\9
| | g = 19\90
| | g = 5\24, 7\33, 9\42-11\51
| | g = 5\24, 7\33, 9\42
| | 2g-1\3-(2\3-3g) = 5g-1
| | 2g-1\3+2\3-3g = 1\3-g
|-
|-
| | 10L5s
| | [[10L 5s|''10L 5s'']] ''= 2L 1s (5)''
| | 1\15 < g < 1\10
| | ''1\15 < g < 1\10''
| | g = 5\60
| | ''g = 2\25, 3\35, 4\45-5\55''
| | g = 2\25, 3\35, 4\45
| | ''g-(1\5-2g) = 3g-1\5''
| | g+1\5-2g = 1\5-g
|-
|-
| | 11L4s
| | [[11L 4s]]
| | 4\15 < g < 3\11
| | 4\15 < g < 3\11
| | g = 89\330
| | g = 7\26, 10\37, 13\48-16\59
| | g = 7\26, 10\37, 13\48
| | 4g-1-(3-11g) = 15g-4
| | 4g-1+3-11g = 2-7g
|-
|-
| | 12L3s
| | [[12L 3s|''12L 3s'']] ''= 4L 1s (3)''
| | 1\15 < g < 1\12
| | ''1\15 < g < 1\12''
| | g = 9\120
| | ''g = 2\27, 3\39, 4\51-5\63''
| | g = 2\27, 3\39, 4\51
| | ''g-(1\3-4g) = 5g-1\3''
| | g+1\3-4g = 1\3-3g
|-
|-
| | 13L2s
| | [[13L 2s]]
| | 8\15 < g < 7\13
| | 8\15 < g < 7\13
| | g = 209\390
| | g = 15\28, 22\41, 29\54-36\67
| | g = 15\28, 22\41, 29\54
| | 2g-1-(7-13g) = 15g-8
| | 2g-1+7-13g = 6-11g
|-
|-
| | 14L1s
| | [[14L 1s|''14L 1s'']]
| | 1\15 < g < 1\14
| | ''1\15 < g < 1\14''
| | g = 29\420
| | ''g = 2\29, 3\43, 4\57-5\71''
| | g = 2\29, 3\43, 4\57
| | ''g-(1-14g) = 15g-1''
| | g+1-14g = 1-13g
|}
|}


=16=
== 16-tone ==
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | Midpoint
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! | Large step+Small step
|-
|-
| | 1L15s
| | [[1L 15s]]
| | 15\16 < g < 1
| | 15\16 < g < 1
| | g = 31\32
| | g = ''16\17, 17\18, 18\19-19\20''
| | ''g = 16\17, 17\18, 18\19''
| | 15g-14-(1-g) = 16g-15
| | 15g-14+1-g = 14g-13
|-
|-
| | 2L14s
| | [[2L 14s]]
| | 7\16 < g < 1\2
| | 7\16 < g < 1\2
| | g = 15\32
| | g = ''8\18, 9\20'', 10\22-11\24
| | g = ''8\18'', 9\20, 10\22
| | 7g-3-(1\2-g) = 8g-7\2
| | 7g-3+1\2-g = 5\2-6g
|-
|-
| | 3L13s
| | [[3L 13s]]
| | 5\16 < g < 1\3
| | 5\16 < g < 1\3
| | g = 31\96
| | g = ''6\19'', 7\22, 8\25-9\28
| | g = ''6\19'', 7\22, 8\25
| | 13g-4-(1-3g) = 16g-5
| | 13g-4+1-3g = 10g-3
|-
|-
| | 4L12s
| | [[4L 12s]]
| | 3\16 < g < 1\4
| | 3\16 < g < 1\4
| | g = 7\32
| | g = ''4\20'', 5\24, 6\28-7\32
| | g = 4\20, 5\24, 6\28
| | 3g-1\2-(1\4-g) = 4g-3\4
| | 3g-1\2+1\4-g = 2g-1\4
|-
|-
| | 5L11s
| | [[5L 11s]]
| | 3\16 < g < 1\5
| | 3\16 < g < 1\5
| | g = 31\160
| | g = 4\21, 5\26, 6\31-7\36
| | g = 4\21, 5\26, 6\31
| | 11g-2-(1-5g) = 16g-3
| | 11g-2+1-5g = 6g-1
|-
|-
| | 6L10s
| | [[6L 10s]]
| | 5\16 < g < 2\6
| | 5\16 < g < 2\6
| | g = 31\96
| | g = 7\22, 9\28, 11\34-13\40
| | g = 7\22, 9\28, 11\34
| | 5g-3\2-(1-3g) = 8g-5\2
| | 5g-3\2+1-3g = 2g-1\2
|-
|-
| | 7L9s
| | [[7L 9s]]
| | 9\16 < g < 4\7
| | 9\16 < g < 4\7
| | g = 127\224
| | g = 13\23, 17\30, 21\37-25\44
| | g = 13\23, 17\30, 21\37
| | 9g-5-(4-7g) = 16g-9
| | 9g-5+4-7g = 2g-1
|-
|-
| | 8L8s
| | [[8L 8s|''8L 8s'']] = ''1L 1s (8)''
| | 1\16 < g < 1\8
| | ''1\16 < g < 1\8''
| | g = 3\32
| | ''g = 2\24, 3\32, 4\40-5\48''
| | g = 2\24, 3\32, 4\40
| | ''g-(1\8-g) = 2g-1\8''
| | g+1\8-g = 1\8
|-
|-
| | 9L7s
| | [[9L 7s]]
| | 7\16 < g < 4\9
| | 7\16 < g < 4\9
| | g = 127\286
| | g = 11\25, 15\34, 19\43-23\52
| | g = 11\25, 15\34, 19\43
| | 7g-3-(4-9g) = 16g-7
| | 7g-3+4-9g = 1-2g
|-
|-
| | 10L6s
| | [[10L 6s]]
| | 3\16 < g < 2\10
| | 3\16 < g < 2\10
| | g = 31\160
| | g = 5\26, 7\36, 9\46-11\56
| | g = 5\26, 7\36, 8\46
| | 3g-1\2-(1-5g) = 8g-3\2
| | 3g-1\2+1-5g = 1\2-2g
|-
|-
| | 11L5s
| | [[11L 5s]]
| | 13\16 < g < 9\11
| | 13\16 < g < 9\11
| | g = 287\352
| | g = 22\27, 31\38, 40\49-49\60
| | g = 22\27, 31\38, 40\49
| | 5g-4-(9-11g) = 16g-13
| | 5g-4+9-11g = 5-6g
|-
|-
| | 12L4s
| | [[12L 4s|''12L 4s'']] ''= 3L 1s (4)''
| | 1\16 < g < 1\12
| | ''1\16 < g < 1\12''
| | g = 7\48
| | ''g = 2\28, 3\40, 4\52-5\64''
| | g = 2\28, 3\40, 4\52
| | ''g-(1\4-3g) = 4g-1\4''
| | g+1\4-3g = 1\4-2g
|-
|-
| | 13L3s
| | [[13L 3s]]
| | 11\16 < g < 9\13
| | 11\16 < g < 9\13
| | g = 287\416
| | g = 20\29, 29\42, 38\55-47\68
| | g = 20\29, 29\42, 38\55
| | 3g-2-(9-13g) = 16g-11
| | 3g-2+9-13g = 7-10g
|-
|-
| | 14L2s
| | [[14L 2s|''14L 2s'']] ''= 7L 1s (2)''
| | 1\16 < g < 1\14
| | ''1\16 < g < 1\14''
| | g = 15\224
| | ''g = 2\30, 3\44, 4\58-5\72''
| | g = 2\30, 3\44, 4\58
| | ''g-(1\2-7g) = 8g-1\2''
| | g+1\2-7g = 1\2-6g
|-
|-
| | 15L1s
| | [[15L 1s|''15L 1s'']]
| | 1\16 < g < 1\15
| | ''1\16 < g < 1\15''
| | g = 31\480
| | ''g = 2\31, 3\46, 4\61-5\76''
| | g = 2\31, 3\46, 4\61
| | ''g-(1-15g) = 16g-1''
| | g+1-15g = 1-14g
|}
|}


=17=
== 17-tone ==
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | Midpoint
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! | Large step+Small step
|-
|-
| | 1L16s
| | [[1L 16s]]
| | 16\17 < g < 1
| | 16\17 < g < 1
| | g = 33\34
| | g = ''17\18, 18\19, 19\20-20\21''
| | ''g = 17\18, 18\19, 19\20''
| | 16g-15-(1-g) = 17g-16
| | 16g-15+1-g = 15g-14
|-
|-
| | 2L15s
| | [[2L 15s]]
| | 8\17 < g < 1\2
| | 8\17 < g < 1\2
| | g = 33\68
| | g = ''9\19'', ''10\21'', 11\23-13\25
| | g = ''9\19'', ''10\21'', 11\23
| | 15g-7-(1-2g) = 17g-8
| | 15g-7+1-2g = 13g-6
|-
|-
| | 3L14s
| | [[3L 14s]]
| | 11\17 < g < 2\3
| | 11\17 < g < 2\3
| | g = 67\102
| | g = ''13\20'', 15\23, 17\26-19\29
| | g = ''13\20'', 15\23, 17\26
| | 14g-9-(2-3g) = 17g-11
| | 14g-9+2-3g = 11g-7
|-
|-
| | 4L13s
| | [[4L 13s]]
| | 4\17 < g < 1\4
| | 4\17 < g < 1\4
| | g = 33\136
| | g = ''5\21'', 6\25, 7\29-8\33
| | g = ''5\21'', 6\25, 7\29
| | 13g-3-(1-4g) = 17g-4
| | 13g-3+1-4g = 9g-2
|-
|-
| | 5L12s
| | [[5L 12s]]
| | 10\17 < g < 3\5
| | 10\17 < g < 3\5
| | g = 101\170
| | g = 13\22, 16\27, 19\32-22\37
| | g = 13\22, 16\27, 19\32
| | 12g-7-(3-5g) = 17g-10
| | 12g-7+3-5g = 7g-4
|-
|-
| | 6L11s
| | [[6L 11s]]
| | 14\17 < g < 5\6
| | 14\17 < g < 5\6
| | g = 169\204
| | g = 19\23, 24\29, 29\35-34\41
| | g = 19\23, 24\29, 29\35
| | 11g-9-(5-6g) = 17g-14
| | 11g-9+5-6g = 5g-4
|-
|-
| | 7L10s
| | [[7L 10s]]
| | 12\17 < g < 5\7
| | 12\17 < g < 5\7
| | g = 169\238
| | g = 17\24, 22\31, 27\38-32\45
| | g = 17\24, 22\31, 27\38
| | 10g-7-(5-7g) = 17g-12
| | 10g-7+5-7g = 3g-2
|-
|-
| | 8L9s
| | [[8L 9s]]
| | 2\17 < g < 1\8
| | 2\17 < g < 1\8
| | g = 33\272
| | g = 3\25, 4\33, 5\41-6\49
| | g = 3\25, 4\33, 5\41
| | 9g-1-(1-8g) = 17g-2
| | 9g-1+1-8g = g
|-
|-
| | 9L8s
| | [[9L 8s]]
| | 15\17 < g < 8\9
| | 15\17 < g < 8\9
| | g = 271\306
| | g = 23\26, 31\35, 39\44-47\53
| | g = 23\26, 31\35, 39\44
| | 8g-7-(8-9g) = 17g-15
| | 8g-7+8-9g = 1-g
|-
|-
| | 10L7s
| | [[10L 7s]]
| | 5\17 < g < 3\10
| | 5\17 < g < 3\10
| | g = 101\340
| | g = 8\27, 11\37, 14\47-17\57
| | g = 8\27, 11\37, 14\47
| | 7g-2-(3-10g) = 17g-5
| | 7g-2+3-10g = 1-3g
|-
|-
| | 11L6s
| | [[11L 6s]]
| | 3\17 < g < 2\11
| | 3\17 < g < 2\11
| | g = 67\374
| | g = 5\28, 7\39, 9\50-11\61
| | g = 5\28, 7\39, 9\50
| | 6g-1-(2-11g) = 17g-3
| | 6g-1+2-11g = 1-5g
|-
|-
| | 12L5s
| | [[12L 5s]]
| | 7\17 < g < 5\12
| | 7\17 < g < 5\12
| | g = 169\408
| | g = 12\29, 17\41, 22\53-27\65
| | g = 12\29, 17\41, 22\53
| | 5g-2-(5-12g) = 17g-7
| | 5g-2+5-12g = 3-7g
|-
|-
| | 13L4s
| | [[13L 4s]]
| | 13\17 < g < 10\13
| | 13\17 < g < 10\13
| | g = 339\442
| | g = 23\30, 33\43, 43\56-53\69
| | g = 23\30, 33\43, 43\56
| | 4g-3-(10-13g) = 17g-13
| | 4g-3+10-13g = 7-9g
|-
|-
| | 14L3s
| | [[14L 3s]]
| | 6\17 < g < 5\14
| | 6\17 < g < 5\14
| | g = 169\476
| | g = 11\31, 16\45, 21\59-26\73
| | g = 11\31, 16\45, 21\59
| | 3g-1-(5-14g) = 17g-6
| | 3g-1+5-14g = 4-11g
|-
|-
| | 15L2s
| | [[15L 2s]]
| | 9\17 < g < 8\15
| | 9\17 < g < 8\15
| | g = 271\510
| | g = 17\32, 25\47, 33\62-41\77
| | g = 17\32, 25\47, 33\62
| | 2g-1-(8-15g) = 17g-9
| | 2g-1+8-15g = 7-13g
|-
|-
| | 16L1s
| | [[16L 1s|''16L 1s'']]
| | 1\17 < g < 1\16
| | ''1\17 < g < 1\16''
| | g = 33\544
| | ''g = 2\33, 3\49, 4\65-5\81''
| | g = 2\33, 3\49, 4\65
| | ''g-(1-16g) = 17g-1''
| | g+1-16g = 1-15g
|}
|}


=18=
== 18-tone ==
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | <span style="background-color: #ffffff;">Midpoint</span>
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! | Large step+Small step
|-
|-
| | 1L17s
| | [[1L 17s]]
| | 17\18 &lt; g &lt; 1
| | 17\18 &lt; g &lt; 1
| | g = 35\36
| | g = ''18\19, 19\20, 20\21-21\22''
| | ''g = 18\19, 19\20, 20\21''
| | 17g-16-(1-g) = 18g-17
| | 17g-16+1-g = 16g-15
|-
|-
| | 2L16s
| | [[2L 16s]]
| | 8\18 &lt; g &lt; 1\2
| | 8\18 &lt; g &lt; 1\2
| | g = 17\36
| | g = ''9\20'', ''10\22'', 11\24-12\26
| | g = ''9\20'', ''10\22'', 11\24
| | 8g-7\2-(1\2-g) = 9g-4
| | 8g-7\2+1\2-g = 7g-3
|-
|-
| | 3L15s
| | [[3L 15s]]
| | 5\18 &lt; g &lt; 1\3
| | 5\18 &lt; g &lt; 1\3
| | g = 11\36
| | g = ''6\21'', 7\24, 8\27-9\30
| | g = ''6\21'', 7\24, 8\27
| | 5g-4\3-(1\3-g) = 6g-5\3
| | 5g-4\3+1\3-g = 4g-3
|-
|-
| | 4L14s
| | [[4L 14s]]
| | <span style="line-height: 15.6000003814697px;">4\18 &lt; g &lt; 1\4</span>
| | 4\18 &lt; g &lt; 1\4
| | g = 17\72
| | g = ''5\22'', 6\26, 7\30-8\34
| | <span style="line-height: 15.6000003814697px;">g = ''5\22'', 6\26,</span> 7\30
| | 7g-3\2-(1\2-2g) = 9g-2
| | 7g-3\2+1\2-2g = 5g-2
|-
|-
| | 5L13s
| | [[5L 13s]]
| | 7\18 &lt; g &lt; 2\5
| | 7\18 &lt; g &lt; 2\5
| | g = 71\180
| | g = 9\23, 11\28, 13\33-15\38
| | g = 9\23, 11\28, 13\33
| | 13g-5-(2-5g) = 18g-7
| | 13g-5+2-5g = 8g-3
|-
|-
| | 6L12s
| | [[6L 12s]]
| | 2\18 &lt; g &lt; 1\6
| | 2\18 &lt; g &lt; 1\6
| | g = 5\36
| | g = 3\24, 4\30, 5\36-6\42
| | g = 3\24, 4\30, 5\36
| | 2g-1\6-(1\6-g) = 3g-1\3
| | 2g-1\6+1\6-g = g
|-
|-
| | 7L11s
| | [[7L 11s]]
| | 5\18 &lt; g &lt; 2\7
| | 5\18 &lt; g &lt; 2\7
| | g = 71\252
| | g = 7\25, 9\32, 11\39-13\46
| | g = 7\25, 9\32, 11\39
| | 11g-3-(2-7g) = 18g-5
| | 11g-3+2-7g = 4g-1
|-
|-
| | 8L10s
| | [[8L 10s]]
| | 2\18 &lt; g &lt; 1\8
| | 2\18 &lt; g &lt; 1\8
| | g = 17\144
| | g = 3\26, 4\34, 5\42-6\50
| | g = 3\26, 4\34, 5\42
| | 5g-1\2-(1\2-4g) = 9g-1
| | 5g-1\2+1\2-4g = g
|-
|-
| | 9L9s
| | [[9L 9s|''9L 9s'']] ''= 1L 1s (9)''
| | 1\18 &lt; g &lt; 1\9
| | ''1\18 &lt; g &lt; 1\9''
| | g = 3\36
| | ''g = 2\27, 3\36, 4\45-5\54''
| | g = 2\27, 3\36, 4\45
| | ''g-(1\9-g) = 2g-1\9''
| | g+1\9-g = 1\9
|-
|-
| | 10L8s
| | [[10L 8s]]
| | 7\18 &lt; g &lt; 4\10
| | 7\18 &lt; g &lt; 4\10
| | g = 71\180
| | g = 11\28, 15\38, 19\48-23\58
| | g = 11\28, 15\38, 19\48
| | 4g-3\2-(2-5g) = 9g-7\2
| | 4g-3\2+2-5g = 1\2-g
|-
|-
| | 11L7s
| | [[11L 7s]]
| | 13\18 &lt; g &lt; 8\11
| | 13\18 &lt; g &lt; 8\11
| | g = 287\396
| | g = 21\29, 29\40, 37\51-45\62
| | g = 21\29, 29\40, 37\51
| | 7g-5-(8-11g) = 18g-13
| | 7g-5+8-11g = 3-4g
|-
|-
| | 12L6s
| | [[12L 6s|''12L 6s'']] ''= 2L 1s (6)''
| | 1\18 &lt; g &lt; 1\12
| | ''1\18 &lt; g &lt; 1\12''
| | g = 5\72
| | ''g = 2\30, 3\42, 4\54-5\66''
| | g = 2\30, 3\42, 4\54
| | ''g-(1\6-2g) = 3g-1\6''
| | g+1\6-2g = 1\6-g
|-
|-
| | 13L5s
| | [[13L 5s]]
| | 11\18 &lt; g &lt; 8\13
| | 11\18 &lt; g &lt; 8\13
| | g = 287\468
| | g = 19\31, 27\44, 35\57-43\70
| | g = 19\31, 27\44, 35\57
| | 5g-3-(8-13g) = 18g-11
| | 5g-3+8-13g = 5-8g
|-
|-
| | 14L4s
| | [[14L 4s]]
| | 5\18 &lt; g &lt; 4\14
| | 5\18 &lt; g &lt; 4\14
| | g = 71\252
| | g = 9\32, 13\46, 17\60-21\74
| | g = 9\32, 13\46, 17\60
| | 2g-1\2-(2-7g) = 9g-5\2
| | 2g-1\2+2-7g = 3\2-5g
|-
|-
| | 15L3s
| | [[15L 3s|''15L 3s'']] ''= 5L 1s (3)''
| | 1\18 &lt; g &lt; 1\15
| | ''1\18 &lt; g &lt; 1\15''
| | g = 11\180
| | ''g = 2\33, 3\48, 4\63-5\78''
| | g = 2\33, 3\48, 4\63
| | ''g-(1\3-5g) = 6g-1\3''
| | g+1\3-5g = 1\3-4g
|-
|-
| | 16L2s
| | [[16L 2s|''16L 2s'']] ''= 8L 1s (2)''
| | 1\18 &lt; g &lt; 1\16
| | ''1\18 &lt; g &lt; 1\16''
| | g = 17\288
| | ''g = 2\34, 3\50, 4\66-5\82''
| | g = 2\34, 3\50, 4\66
| | ''g-(1\2-8g) = 9g-1\2''
| | g+1\2-8g = 1\2-7g
|-
|-
| | 17L1s
| | [[17L 1s|''17L 1s'']]
| | 1\18 &lt; g &lt; 1\17
| | ''1\18 &lt; g &lt; 1\17''
| | g = 35\618
| | ''g = 2\35, 3\52, 4\69-5\86''
| | g = 2\35, 3\52, 4\69
| | ''g-(1-17g) = 18g-1''
| | g+1-17g = 1-16g
|}
|}


=19=
== 19-tone ==
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | <span style="background-color: #ffffff;">Midpoint</span>
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! |Large step+Small step
|-
|-
| | 1L18s
| | [[1L 18s]]
| | 18\19 &lt; g &lt; 1
| | 18\19 &lt; g &lt; 1
| | g = 37\38
| | g = ''19\20, 20\21, 21\22-22\23''
| | ''g = 19\20, 20\21, 21\22''
| | 18g-17-(1-g) = 19g-18
| |18g-17+1-g = 17g-16
|-
|-
| | 2L17s
| | [[2L 17s]]
| | 9\19 &lt; g &lt; 1\2
| | 9\19 &lt; g &lt; 1\2
| | g = 37\76
| | g = ''10\21'', ''11\23'', 12\25-13\27
| | g = ''10\21'', ''11\23'', 12\25
| | 17g-8-(1-2g) = 19g-9
| |17g-8+1-2g = 15g-7
|-
|-
| | 3L16s
| | [[3L 16s]]
| | 6\19 &lt; g &lt; 1\3
| | 6\19 &lt; g &lt; 1\3
| | g = 37\114
| | g = ''7\22'', 8\25, 9\28-10\31
| | g = ''7\22'', 8\25, 10\31
| | 16g-5-(1-3g) = 19g-6
| |16g-5+1-3g = 13g-4
|-
|-
| | 4L15s
| | [[4L 15s]]
| | 14\19 &lt; g &lt; 3\4
| | 14\19 &lt; g &lt; 3\4
| | g = 113\152
| | g = ''17\23'', 20\27, 23\31-27\35
| | g = ''17\23'', 20\27, 23\31
| | 15g-11-(3-4g) = 19g-14
| |15g-11+3-4g = 11g-8
|-
|-
| | 5L14s
| | [[5L 14s]]
| | 15\19 &lt; g &lt; 4\5
| | 15\19 &lt; g &lt; 4\5
| | g = 151\190
| | g = 19\24, 23\29, 27\34-31\39
| | g = 19\24, 23\29, 27\34
| | 14g-11-(4-5g) = 19g-15
| |14g-11+4-5g = 9g-7
|-
|-
| | 6L13s
| | [[6L 13s]]
| | 3\19 &lt; g &lt; 1\6
| | 3\19 &lt; g &lt; 1\6
| | g = 37\228
| | g = 4\25, 5\31, 6\37-7\43
| | g = 4\25, 5\31, 6/37
| | 13g-2-(1-6g) = 19g-3
| |13g-2+1-6g = 7g-1
|-
|-
| | 7L12s
| | [[7L 12s]]
| | 8\19 &lt; g &lt; 3\7
| | 8\19 &lt; g &lt; 3\7
| | g = 113\266
| | g = 11\26, 14\33, 17\40-20\47
| | g = 11\26, 14\33, 17\40
| | 12g-5-(3-7g) = 19g-8
| |12g-5+3-7g = 5g-2
|-
|-
| | 8L11s
| | [[8L 11s]]
| | 7\19 &lt; g &lt; 3\8
| | 7\19 &lt; g &lt; 3\8
| | g = 113\304
| | g = 10\27, 13\35, 16\43-19\51
| | g = 10\27, 13\35, 16\43
| | 11g-4-(3-8g) = 19g-7
| |11g-4+3-8g = 3g-1
|-
|-
| | 9L10s
| | [[9L 10s]]
| | 2\19 &lt; g &lt; 1\9
| | 2\19 &lt; g &lt; 1\9
| | g = 37\342
| | g = 3\28, 4\37, 5\46-6\55
| | g = 3\28, 4\37, 5\46
| | 10g-1-(1-9g) = 19g-2
| |10g-1+1-9g = g
|-
|-
| | 10L9s
| | [[10L 9s]]
| | 17\19 &lt; g &lt; 9\10
| | 17\19 &lt; g &lt; 9\10
| | g = 341\380
| | g = 26\29, 35\39, 44\49-53\59
| | g = 26\29, 35\39, 44\49
| | 9g-8-(9-10g) = 19g-17
| |9g-8+9-10g = 1-g
|-
|-
| | 11L8s
| | [[11L 8s]]
| | 12\19 &lt; g &lt; 7\11
| | 12\19 &lt; g &lt; 7\11
| | g = 265\418
| | g = 19\30, 26\41, 33\52-40\63
| | g = 19\30, 26\41, 33\52
| | 8g-5-(7-11g) = 19g-12
| |8g-5+7-11g = 2-3g
|-
|-
| | 12L7s
| | [[12L 7s]]
| | 11\19 &lt; g &lt; 7\12
| | 11\19 &lt; g &lt; 7\12
| | g = 265\456
| | g = 18\31, 25\43, 32\55-39\67
| | g = 18\31, 25\43, 32\55
| | 7g-4-(7-12g) = 19g-11
| |7g-4+7-12g = 3-5g
|-
|-
| | 13L6s
| | [[13L 6s]]
| | 16\19 &lt; g &lt; 11\13
| | 16\19 &lt; g &lt; 11\13
| | g = 417\494
| | g = 27\32, 38\45, 49\58-60\71
| | g = 27\32, 38\45, 49\58
| | 6g-5-(11-13g) = 19g-16
| |6g-5+11-13g = 6-7g
|-
|-
| | 14L5s
| | [[14L 5s]]
| | 4\19 &lt; g &lt; 3\14
| | 4\19 &lt; g &lt; 3\14
| | g = 113\532
| | g = 7\33, 10\47, 13\61-16\75
| | g = 7\33, 10\47, 13\61
| | 5g-1-(3-14g) = 19g-4
| |5g-1+3-14g = 2-9g
|-
|-
| | 15L4s
| | [[15L 4s]]
| | 5\19 &lt; g &lt; 4\15
| | 5\19 &lt; g &lt; 4\15
| | g = 151\570
| | g = 9\34, 13\49, 17\64-21\79
| | g = 9\34, 13\49, 17\64
| | 4g-1-(4-15g) = 19g-5
| |4g-1+4-15g = 3-11g
|-
|-
| | 16L3s
| | [[16L 3s]]
| | 13\19 &lt; g &lt; 11\16
| | 13\19 &lt; g &lt; 11\16
| | g = 417\608
| | g = 24\35, 35\51, 46\67-57\83
| | g = 24\35, 35\51, 46\67
| | 3g-2-(11-16g) = 19g-13
| |3g-2+11-16g = 9-13g
|-
|-
| | 17L2s
| | [[17L 2s]]
| | 10\19 &lt; g &lt; 9\17
| | 10\19 &lt; g &lt; 9\17
| | g = 341\646
| | g = 19\36, 28\53, 37\70-46\87
| | g = 19\36, 28\53, 37\70
| | 2g-1-(9-17g) = 19g-10
| |2g-1+9-17g = 8-15g
|-
|-
| | 18L1s
| | [[18L 1s|''18L 1s'']]
| | 1\19 &lt; g &lt; 1\18
| | ''1\19 &lt; g &lt; 1\18''
| | g = 37\684
| | ''g = 2\37, 3\55, 4\73-5\91''
| | g = 2\37, 3\55, 4\73
| | ''g-(1-18g) = 19g-1''
| |g+1-18g = 1-17g
|}
|}


=20=
== 20-tone ==
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | <span style="background-color: #ffffff;">Midpoint</span>
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! | Large step+Small step
|-
|-
| | 1L19s
| | [[1L 19s]]
| | 19\20 &lt; g &lt; 1
| | 19\20 &lt; g &lt; 1
| | g = 39\40
| | g = ''20\21, 21\22, 22\23-23\24''
| | ''g = 20\21, 21\22, 22\23''
| | 19g-18-(1-g) = 20g-19
| | 19g-18+1-g = 18g-17
|-
|-
| | 2L18s
| | [[2L 18s]]
| | 9\20 &lt; g &lt; 1\2
| | 9\20 &lt; g &lt; 1\2
| | g = 19\40
| | g = ''10\22'', ''11\24'', 12\26-13\28
| | g = ''10\22'', ''11\24'', 12\26
| | 9g-4-(1\2-g) = 10g-9\2
| | 9g-4+1\2-g = 8g-7\2
|-
|-
| | 3L17s
| | [[3L 17s]]
| | 13\20 &lt; g &lt; 2\3
| | 13\20 &lt; g &lt; 2\3
| | g = 79\120
| | g = ''15\23'', 17\26, 19\29-21\32
| | g = ''15\23'', 17\26, 20\29
| | 17g-11-(2-3g) = 20g-13
| | 17g-11+2-3g = 14g-9
|-
|-
| | 4L16s
| | [[4L 16s]]
| | 4\20 &lt; g &lt; 1\4
| | 4\20 &lt; g &lt; 1\4
| | g = 9\40
| | g = ''5\24'', 6\28, 7\32-8\36
| | g = ''5\24'', 6\28, 7\32
| | 4g-3\4-(1\4-g) = 5g-1
| | 4g-3\4+1\4-g = 3g-1\4
|-
|-
| | 5L15s
| | [[5L 15s]]
| | 3\20 &lt; g &lt; 1\5
| | 3\20 &lt; g &lt; 1\5
| | g = 7\40
| | g = ''4\25'', 5\30, 6\35-7\40
| | g = 4\25, 5\30, 6\35
| | 3g-2\5-(1\5-g) = 4g-3\5
| | 3g-2\5+1\5-g = 2g-1\5
|-
|-
| | 6L14s
| | [[6L 14s]]
| | 3\20 &lt; g &lt; 1\6
| | 3\20 &lt; g &lt; 1\6
| | g = 19\120
| | g = 4\26, 5\32, 6\38-7\44
| | g = 4\26, 5\32, 6\38
| | 7g-1-(1\2-3g) = 10g-3\2
| | 7g-1+1\2-3g = 4g-1\2
|-
|-
| | 7L13s
| | [[7L 13s]]
| | 17\20 &lt; g &lt; 6\7
| | 17\20 &lt; g &lt; 6\7
| | g = 239\280
| | g = 23\27, 29\34, 35\41-41\48
| | g = 23\27, 29\34, 35\41
| | 13g-11-(6-7g) = 20g-17
| | 13g-11+6-7g = 6g-5
|-
|-
| | 8L12s
| | [[8L 12s]]
| | 2\20 &lt; g &lt; 1\8
| | 2\20 &lt; g &lt; 1\8
| | g = 9\80
| | g = 3\28, 4\36, 5\44-6\52
| | g = 3\28, 4\36, 5\44
| | 3g-1\4-(1\4-2g) = 5g-1\2
| | 3g-1\4+1\4-2g = g
|-
|-
| | 9L11s
| | [[9L 11s]]
| | 11\20 &lt; g &lt; 5\9
| | 11\20 &lt; g &lt; 5\9
| | g = 199\360
| | g = 16\29, 21\38, 26\47-31\56
| | g = 16\29, 21\38, 26\47
| | 11g-6-(5-9g) = 20g-11
| | 11g-6+5-9g =2g-1
|-
|-
| | 10L10s
| | [[10L 10s|''10L 10s'']] ''= 1L 1s (10)''
| | 1\20 &lt; g &lt; 1\10
| | ''1\20 &lt; g &lt; 1\10''
| | g = 3\40
| | ''g = 2\30, 3\40, 4\50-5\60''
| | g = 2\30, 3\40, 4\50
| | ''g-(1\10-g) = 2g-1\10''
| | g+1\10-g = 1\10
|-
|-
| | 11L9s
| | [[11L 9s]]
| | 9\20 &lt; g &lt; 5\11
| | 9\20 &lt; g &lt; 5\11
| | g = 199\440
| | g = 14\31, 19\42, 24\53-29\64
| | g = 14\31, 19\42, 24\53
| | 9g-4-(5-11g) = 20g-9
| | 9g-4+5-11g = 1-2g
|-
|-
| | 12L8s
| | [[12L 8s]]
| | 3\20 &lt; g &lt; 2\12
| | 3\20 &lt; g &lt; 2\12
| | g = 19\120
| | g = 5\32, 7\44, 9\56-11\68
| | g = 5\32, 7\44, 9\56
| | 2g-1\4-(1\2-3g) = 5g-3\4
| | 2g-1\4+1\2-3g = 1\4-g
|-
|-
| | 13L7s
| | [[13L 7s]]
| | 3\20 &lt; g &lt; 2\13
| | 3\20 &lt; g &lt; 2\13
| | g = 79\520
| | g = 5\33, 7\46, 9\59-11\72
| | g = 5\33, 7\46, 9\59
| | 7g-1-(2-13g) = 20g-3
| | 7g-1+2-13g = 1-6g
|-
|-
| | 14L6s
| | [[14L 6s]]
| | 7\20 &lt; g &lt; 5\14
| | 7\20 &lt; g &lt; 5\14
| | g = 99\280
| | g = 12\34, 17\48, 22\62-27\76
| | g = 12\34, 17\48, 22\62
| | 3g-1-(5\2-7g) = 10g-7\2
| | 3g-1+5\2-7g = 2-4g
|-
|-
| | 15L5s
| | [[15L 5s|''15L 5s'']] ''= 3L 1s (5)''
| | 1\20 &lt; g &lt; 1\15
| | ''1\20 &lt; g &lt; 1\15''
| | g = 7\120
| | ''g = 2\35, 3\50, 4\65-5\80''
| | g = 2\35, 3\50, 4\65
| | ''g-(1\5-3g) = 4g-1\5''
| | g+1\5-3g = 1\5-2g
|-
|-
| | 16L4s
| | [[16L 4s|''16L 4s'']] ''= 4L 1s (4)''
| | 1\20 &lt; g &lt; 1\16
| | ''1\20 &lt; g &lt; 1\16''
| | g = 9\160
| | ''g = 2\36, 3\52, 4\68-5\84''
| | g = 2\36, 3\52, 4\68
| | ''g-(1\4-4g) = 5g-1\4''
| | g+1\4-4g = 1\4-3g
|-
|-
| | 17L3s
| | [[17L 3s]]
| | 7\20 &lt; g &lt; 6\17
| | 7\20 &lt; g &lt; 6\17
| | g = 239\680
| | g = 13\37, 19\54, 25\71-31\88
| | g = 13\37, 19\54, 25\71
| | 3g-1-(6-17g) = 5-14g
| | 3g-1+6-17g = 5-14g
|-
|-
| | 18L2s
| | [[18L 2s|''18L 2s'']] ''= 9L 1s (2)''
| | 1\20 &lt; g &lt; 1\18
| | ''1\20 &lt; g &lt; 1\18''
| | g = 19\360
| | ''g = 2\38, 3\56, 4\74-5\92''
| | g = 2\38, 3\56, 4\74
| | ''g-(1\2-9g) = 10g-1\2''
| | g+1\2-9g = 1\2-8g
|-
|-
| | 19L1s
| | [[19L 1s|''19L 1s'']]
| | 1\20 &lt; g &lt; 1\19
| | ''1\20 &lt; g &lt; 1\19''
| | g = 39\760
| | ''g = 2\39, 3\58, 4\77-5\96''
| | g = 2\39, 3\58, 4\77
| | ''g-(1-19g) = 20g-1''
| | g+1-19g = 1-18g
|}
|}


=21=
== 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
! | <span style="background-color: #ffffff;">Midpoint</span>
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! | Large step+Small step
|-
|-
| | 1L20s
| | [[1L 20s]]
| | 20\21 &lt; g &lt; 1
| | 20\21 &lt; g &lt; 1
| | g = 41\42
| | g = ''21\22, 22\23, 23\24-24\25''
| | ''g = 21\22, 22\23, 23\24''
| | 20g-19-(1-g) = 21g-20
| | 20g-19+1-g = 19g-18
|-
|-
| | 2L19s
| | [[2L 19s]]
| | 10\21 &lt; g &lt; 1\2
| | 10\21 &lt; g &lt; 1\2
| | g = 41\84
| | g = ''11\23, 12\25'', 13\27-13\29
| | g = ''11\23, 12\25'', 13\27
| | 19g-9-(1-2g) = 21g-10
| | 19g-9+1-2g = 17g-8
|-
|-
| | 3L18s
| | [[3L 18s]]
| | 6\21 &lt; g &lt; 1\3
| | 6\21 &lt; g &lt; 1\3
| | g = 13\42
| | g = ''7\24'', 8\27, 9\30-10\33
| | g = ''7\24'', 8\27, 9\30
| | 6g-5\3-(1\3-g) = 7g-2
| | 6g-5\3+1\3-g = 5g-4\3
|-
|-
| | 4L17s
| | [[4L 17s]]
| | 5\21 &lt; g &lt; 1\4
| | 5\21 &lt; g &lt; 1\4
| | g = 41\168
| | g = ''6\25'', 7\29, 8\33-9\37
| | g = ''6\25'', 7\29, 8\33
| | 17g-4-(1-4g) = 21g-5
| | 17g-2+1-4g = 13g-1
|-
|-
| | 5L16s
| | [[5L 16s]]
| | 4\21 &lt; g &lt; 1\5
| | 4\21 &lt; g &lt; 1\5
| | g = 41\210
| | g = ''5\26'', 6\31, 7\36-8\41
| | g = ''5\26'', 6\31, 7\36
| | 16g-3-(1-5g) = 21g-4
| | 16g-3+1-5g = 11g-2
|-
|-
| | 6L15s
| | [[6L 15s]]
| | 3\21 &lt; g &lt; 1\6
| | 3\21 &lt; g &lt; 1\6
| | g = 13\84
| | g = 4\27, 5\33, 6\39-7\45
| | g = 4\27, 5\33, 6\39
| | 5g-2\3-(1\3-2g) = 7g-1
| | 5g-2\3+1\3-2g = 3g-1\3
|-
|-
| | 7L14s
| | [[7L 14s]]
| | 2\21 &lt; g &lt; 1\7
| | 2\21 &lt; g &lt; 1\7
| | g = 5\42
| | g = 3\28, 4\35, 5\42-6\49
| | g = 3\28, 4\35, 5\42
| | 2g-1\7-(1\7-g) = 3g-2\7
| | 2g-1\7+1\7-g = g
|-
|-
| | 8L13s
| | [[8L 13s]]
| | 13\21 &lt; g &lt; 5\8
| | 13\21 &lt; g &lt; 5\8
| | g = 209\336
| | g = 18\29, 23\37, 28\45-33\53
| | g = 18\29, 23\37, 28\45
| | 13g-8-(5-8g) = 21g-13
| | 13g-8+5-8g = 5g-3
|-
|-
| | 9L12s
| | [[9L 12s]]
| | 2\21 &lt; g &lt; 1\9
| | 2\21 &lt; g &lt; 1\9
| | g = 13\126
| | g = 3\30, 4\39, 5\48-6\57
| | g = 3\30, 4\39, 5\48
| | 4g-1\3-(1\3-3g) = 7g-2\3
| | 4g-1\3+1\3-3g = g
|-
|-
| | 10L11s
| | [[10L 11s]]
| | 2\21 &lt; g &lt; 1\10
| | 2\21 &lt; g &lt; 1\10
| | g = 41\420
| | g = 3\31, 4\41, 5\51-6\61
| | g = 3\31, 4\41, 5\51
| | 11g-1-(1-10g) = 21g-2
| | 11g-1+1-10g = g
|-
|-
| | 11L10s
| | [[11L 10s]]
| | 19\21 &lt; g &lt; 10\11
| | 19\21 &lt; g &lt; 10\11
| | g = 419\462
| | g = 29\32, 39\43, 49\54-59\65
| | g = 29\32, 39\43, 49\54
| | 10g-9-(10-11g) = 21g-19
| | 10g-9+10-11g = 1-g
|-
|-
| | 12L9s
| | [[12L 9s]]
| | 5\21 &lt; g &lt; 3\12
| | 5\21 &lt; g &lt; 3\12
| | g = 41\168
| | g = 8\33, 11\45, 14\57-17\69
| | g = 8\33, 11\45, 14\57
| | 3g-2\3-(1-4g) = 7g-1\3
| | 3g-2\3+1-4g = 1\3-3g
|-
|-
| | 13L8s
| | [[13L 8s]]
| | 8\21 &lt; g &lt; 5\13
| | 8\21 &lt; g &lt; 5\13
| | g = 209\546
| | g = 13\34, 18\47, 23\60-28\73
| | g = 13\34, 18\47, 23\70
| | 8g-3-(5-13g) = 21g-8
| | 8g-3+5-13g = 2-5g
|-
|-
| | 14L7s
| | [[14L 7s|''14L 7s'']] ''= 2L 1s (7)''
| | 1\21 &lt; g &lt; 1\14
| | ''1\21 &lt; g &lt; 1\14''
| | g = 5\84
| | ''g = 2\35, 3\49, 4\63-5\77''
| | g = 2\35, 3\49, 4\63
| | ''g-(1\7-2g) = 3g-1\7''
| | g+1\7-2g = 1\7-g
|-
|-
| | 15L6s
| | [[15L 6s]]
| | 4\21 &lt; g &lt; 3\15
| | 4\21 &lt; g &lt; 3\15
| | g = 41\210
| | g = 7\36, 10\51, 13\66-16\81
| | g = 7\36, 10\51, 13\66
| | 2g-1\3-(1-5g) = 7g-4\3
| | 2g-1\3+1-5g = 2\3-3g
|-
|-
| | 16L5s
| | [[16L 5s]]
| | 17\21 &lt; g &lt; 13\16
| | 17\21 &lt; g &lt; 13\16
| | g = 545\672
| | g = 30\37, 43\53, 56\69-69\85
| | g = 30\37, 43\53, 56\69
| | 5g-4-(13-16g) = 21g-17
| | 5g-4+13-16g = 9-11g
|-
|-
| | 17L4s
| | [[17L 4s]]
| | 16\21 &lt; g &lt; 13\17
| | 16\21 &lt; g &lt; 13\17
| | g = 545\714
| | g = 29\38, 42\55, 55\72-68\89
| | g = 29\38, 42\55, 55\72
| | 4g-3-(13-17g) = 21g-16
| | 4g-3+13-17g = 10-13g
|-
|-
| | 18L3s
| | [[18L 3s|''18L 3s'']] ''= 6L 1s (3)''
| | 1\21 &lt; g &lt; 1\18
| | ''1\21 &lt; g &lt; 1\18''
| | g = 13\252
| | ''g = 2\39, 3\57, 4\75-5\93''
| | g = 2\39, 3\57, 4\75
| | ''g-(1\3-6g) = 7g-1\3''
| | g+1\3-6g = 1\3-5g
|-
|-
| | 19L2s
| | [[19L 2s]]
| | 11\21 &lt; g &lt; 10\19
| | 11\21 &lt; g &lt; 10\19
| | g = 419\798
| | g = '''21\40''', 31\59, 41\78-51\97
| | g = 21\40, 31\59, 41\78
| | 2g-1-(10-19g) = 21g-11
| | 2g-1+10-19g = 9-17g
|-
|-
| | 20L1s
| | [[20L 1s|''20L 1s'']]
| | 1\21 &lt; g &lt; 1\20
| | ''1\21 &lt; g &lt; 1\20''
| | g = 41\840
| | ''g = '''2\41''', 3\61, 4\81-5\101''
| | g = 2\41, 3\61, 4/81
| | ''g-(1-20g) = 21g-1''
| | g+1-20g = 1-19g
|}
|}


=22=
== 22-tone ==
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | <span style="background-color: #ffffff; color: #000000;">Midpoint</span>
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! |Large step+Small step
|-
|-
| | 1L21s
| | [[1L 21s]]
| | 21\22 &lt; g &lt; 1
| | 21\22 &lt; g &lt; 1
| | g = 43\44
| | g = ''22\23, 23\24, 24/25-25\26''
| | ''g = 22\23, 23\24, 24/25''
| | 21g-20-(1-g) = 22g-21
| |21g-20+1-g = 20g-19
|-
|-
| | 2L20s
| | [[2L 20s]]
| | 10\22 &lt; g &lt; 1\2
| | 10\22 &lt; g &lt; 1\2
| | g = 21\44
| | g = ''11\24,'' ''12\26'', 13\28-14\30
| | g = ''11\24,'' ''12\26'', 13\28
| | 10g-9\2-(1\2-g) = 11g-5
| |10g-9\2+1\2-g = 9g-4
|-
|-
| | 3L19s
| | [[3L 19s]]
| | 7\22 &lt; g &lt; 1\3
| | 7\22 &lt; g &lt; 1\3
| | g = 43\132
| | g = ''8\25'', 9\28, 10\31-11\34
| | g = ''8\25'', 9\28, 10\31
| | 19g-6-(1-3g) = 22g-7
| |19g-6+1-3g = 16g-5
|-
|-
| | 4L18s
| | [[4L 18s]]
| | 5\22 &lt; g &lt; 1\4
| | 5\22 &lt; g &lt; 1\4
| | g = 21\88
| | g = ''6\26'', 7\30, 8\34-9\38
| | g = ''6\26'', 7\30, 8\34
| | 9g-2-(1\2-2g) = 11g-5\2
| |9g-2+1\2-2g = 7g-3\2
|-
|-
| | 5L17s
| | [[5L 17s]]
| | 13\22 &lt; g &lt; 3\5
| | 13\22 &lt; g &lt; 3\5
| | g = 131\220
| | g = ''16\27'', 19\32, 22\37-25\42
| | g = ''16\27'', 19\32, 22\37
| | 17g-10-(3-5g) = 22g-13
| |17g-10+3-5g = 12g-7
|-
|-
| | 6L16s
| | [[6L 16s]]
| | 7\22 &lt; g &lt; 2\6
| | 7\22 &lt; g &lt; 2\6
| | g = 43\132
| | g = 9\28, 11\34, 13\40-15\46
| | g = 9\28, 11\34, 13\40
| | 8g-5\2-(1-3g) = 11g-7\2
| |8g-5\2+1-3g = 5g-2
|-
|-
| | 7L15s
| | [[7L 15s]]
| | 3\22 &lt; g &lt; 1\7
| | 3\22 &lt; g &lt; 1\7
| | g = 43\308
| | g = 4\29, 5\36, 6\43-7\50
| | g = 4\29, 5\36, 6\43
| | 15g-2-(1-7g) = 22g-3
| |15g-2+1-7g = 8g-1
|-
|-
| | 8L14s
| | [[8L 14s]]
| | 8\22 &lt; g &lt; 3\8
| | 8\22 &lt; g &lt; 3\8
| | g = 65\176
| | g = 11\30, 14\38, 17\46-20\54
| | g = 11\30, 14\38, 17\46
| | 7g-5\2-(3\2-4g) = 11g-4
| |7g-5\2+3\2-4g = 3g-2
|-
|-
| | 9L13s
| | [[9L 13s]]
| | 17\22 &lt; g &lt; 7\9
| | 17\22 &lt; g &lt; 7\9
| | g = 307\396
| | g = 24\31, 31\40, 38\49-45\58
| | g = 24\31, 31\40, 38\49
| | 13g-10-(7-9g) = 22g-17
| |13g-10+7-9g = 4g-3
|-
|-
| | 10L12s
| | [[10L 12s]]
| | 2\22 &lt; g &lt; 1\10
| | 2\22 &lt; g &lt; 1\10
| | g = 21\220
| | g = 3\32, 4\42, 5\52-6\62
| | g = 3\32, 4\42, 5\52
| | 6g-1\2-(1\2-5g) = 11g-1
| |6g-1\2+1\2-5g = g
|-
|-
| | 11L11s
| | ''[[11L 11s]] = 1L 1s (11)''
| | 1\22 &lt; g &lt; 1\11
| | ''1\22 &lt; g &lt; 1\11''
| | g = 3\44
| | ''g = 2\33, 3\44, 4\55-5\66''
| | g = 2\33, 3\44, 4\55
| | ''g-(1\11-g) = 2g-1\11''
| |g + 1\11-g = 1\11
|-
|-
| | 12L10s
| | [[12L 10s]]
| | 9\22 &lt; g &lt; 5\12
| | 9\22 &lt; g &lt; 5\12
| | g = 109\264
| | g = 14\34, 19\46, 24\58-29\70
| | g = 14\34, 19\46, 24\58
| | 5g-2-(5\2-6g) = 11g-7\2
| |5g-2+5\2-6g = 1\2-g
|-
|-
| | 13L9s
| | [[13L 9s]]
| | 5\22 &lt; g &lt; 3\13
| | 5\22 &lt; g &lt; 3\13
| | g = 131\572
| | g = 8\35, 11\48, 14\61-17\74
| | g = 8\35, 11\48, 14\61
| | 9g-2-(3-13g) = 22g-5
| |9g-2+3-13g = 1-4g
|-
|-
| | 14L8s
| | [[14L 8s]]
| | 3\22 &lt; g &lt; 2\14
| | 3\22 &lt; g &lt; 2\14
| | g = 43\308
| | g = 5\36, 7\50, 9\64-11\78
| | g = 5\36, 7\50, 9\64
| | 4g-1\2-(1-7g) = 11g-3\2
| |4g-1\2+1-7g = 1\2-3g
|-
|-
| | 15L7s
| | [[15L 7s]]
| | 19\22 &lt; g &lt; 13\15
| | 19\22 &lt; g &lt; 13\15
| | g = 571\660
| | g = 32\37, 45\52, 58\67-71\82
| | g = 32\37, 45\52, 58\67
| | 7g-6-(13-15g) = 22g-13
| |7g-6+13-15g = 7-8g
|-
|-
| | 16L6s
| | [[16L 6s]]
| | 4\22 &lt; g &lt; 3\16
| | 4\22 &lt; g &lt; 3\16
| | g = 65\352
| | g = 7\38, 10\54, 13\70-16\86
| | g = 7\38, 10\54, 13\70
| | 3g-1\2-(3\2-8g) = 11g-2
| |3g-1\2+3\2-8g = 1-5g
|-
|-
| | 17L5s
| | [[17L 5s]]
| | 9\22 &lt; g &lt; 7\17
| | 9\22 &lt; g &lt; 7\17
| | g = 207\748
| | g = 16\39, 23\56, 30\73-37\90
| | g = 16\39, 23\56, 30\73
| | 5g-2-(7-17g) = 22g-9
| |5g-2+7-17g = 5-12g
|-
|-
| | 18L4s
| | [[18L 4s]]
| | 6\22 &lt; g &lt; 5\18
| | 6\22 &lt; g &lt; 5\18
| | g = 109\396
| | g = '''11\40''', 16\58, 21\76-26\94
| | g = 11\40, 16\58, 21\76
| | 2g-1\2-(5\2-9g) = 11g-3
| |2g-1\2+5\2-9g = 2-7g
|-
|-
| | 19L3s
| | [[19L 3s]]
| | 15\22 &lt; g &lt; 13\19
| | 15\22 &lt; g &lt; 13\19
| | g = 571\836
| | g = '''28\41''', 41\60, 54\79-67\98
| | g = 28\41, 41\60, 54\79
| | 3g-2-(13-19g) = 22g-15
| |3g-2+13-19g = 11-16g
|-
|-
| | 20L2s
| | ''[[20L 2s]] = 10L 1s (2)''
| | 1\22 &lt; g &lt; 1\20
| | ''1\22 &lt; g &lt; 1\20''
| | g = 21\440
| | ''g = '''2\42''', 3\62, 4\82-5\102''
| | g = 2\42, 3\62, 4\72
| | ''g-(1\2-10g) = 11g-1\2''
| |g+1\2-10g = 1\2-9g
|-
|-
| | 21L1s
| | [[21L 1s|''21L 1s'']]
| | 1\22 &lt; g &lt; 1\21
| | ''1\22 &lt; g &lt; 1\21''
| | g = 43\924
| | ''g = '''2\43''', 3\64, 4\85-5\106''
| | g = 2\43, 3\64, 4\85
| | ''g-(1-21g) = 22g-1''
| |g+1-21g = 1-20g
|}
|}


=23=
== 23-tone ==
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | <span style="background-color: #ffffff;">Midpoint</span>
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! | Large step+Small step
|-
|-
| | 1L22s
| | [[1L 22s]]
| | <span style="line-height: 15.6000003814697px;">22\23 &lt; g &lt; 1</span>
| | 22\23 &lt; g &lt; 1
| | g = 45\46
| | g = ''23\24, 24\25, 25\26-26\27''
| | ''g = 23\24, 24\25, 25\26''
| | 22g-21-(1-g) = 23g-22
| | 22g-21+1-g = 21g-20
|-
|-
| | 2L21s
| | [[2L 21s]]
| | 11\23 &lt; g &lt; 1\2
| | 11\23 &lt; g &lt; 1\2
| | g = 45\92
| | g = ''12\25, 13\27'', 14\29-15\31
| | g = ''12\25, 13\27'', 14\29
| | 21g-10-(1-2g) = 23g-11
| | 21g-10+1-2g = 19g-9
|-
|-
| | 3L20s
| | [[3L 20s]]
| | 15\23 &lt; g &lt; 2\3
| | 15\23 &lt; g &lt; 2\3
| | g = 91\138
| | g = ''17\26'', 19\29, 21\32-23\35
| | g = ''17\26'', 19\29, 21\32
| | 20g-13-(1-3g) = 23g-14
| | 20g-13+1-3g = 17g-12
|-
|-
| | 4L19s
| | [[4L 19s]]
| | 17\23 &lt; g &lt; 3\4
| | 17\23 &lt; g &lt; 3\4
| | g = 137\184
| | g = ''20\27'', 23\31, 26\35-29\39
| | g = ''20\27'', 23\31, 26\35
| | 19g-14-(3-4g) = 23g-17
| | 19g-14+3-4g = 15g-11
|-
|-
| | 5L18s
| | [[5L 18s]]
| | 9\23 &lt; g &lt; 2\5
| | 9\23 &lt; g &lt; 2\5
| | g = 91\230
| | g = ''11\28'', 13\33, 15\38-17\43
| | g = ''11\28'', 13\33, 15\38
| | 18g-7-(2-5g) = 13g-9
| | 18g-7+2-5g = 13g-5
|-
|-
| | 6L17s
| | [[6L 17s]]
| | 19\23 &lt; g &lt; 5\6
| | 19\23 &lt; g &lt; 5\6
| | g = 229\276
| | g = 24\29, 29\35, 34\41-39\47
| | g = 24\29, 29\35, 34\41
| | 17g-15-(1-6g) = 23g-16
| | 17g-15+1-6g = 11g-14
|-
|-
| | 7L16s
| | [[7L 16s]]
| | 13\23 &lt; g &lt; 4\7
| | 13\23 &lt; g &lt; 4\7
| | g = 183\322
| | g = 17\30, 21\37, 25\44-29\51
| | g = 17\30,<span style="line-height: 15.6000003814697px;"> 21\37,</span> 25\44
| | 16g-9-(4-7g) = 23g-13
| | 16g-9+4-7g = 9g-5
|-
|-
| | 8L15s
| | [[8L 15s]]
| | 20\23 &lt; g &lt; 7\8
| | 20\23 &lt; g &lt; 7\8
| | g = 321\368
| | g = 27\31, 34\39, 41\47-48\55
| | g = 27\31, 34\39, 41\47
| | 15g-13-(7-8g) = 23g-20
| | 15g-13+7-8g = 7g-6
|-
|-
| | 9L14s
| | [[9L 14s]]
| | 5\23 &lt; g &lt; 2\9
| | 5\23 &lt; g &lt; 2\9
| | g = 91\414
| | g = 7\32, 9\41, 11\50-13\59
| | g = 7\32, 9\41, 11\50
| | 14g-3-(2-9g) = 23g-5
| | 14g-7+<span style="line-height: 15.6000003814697px;">2-9g = 5g-5</span>
|-
|-
| | 10L13s
| | [[10L 13s]]
| | 16\23 &lt; g &lt; 7\10
| | 16\23 &lt; g &lt; 7\10
| | g = 321\460
| | g = 23\33, 30\43, 37\53-44\63
| | g = 23\33, 30\43, 37\53
| | 13g-9-(7-10g) = 23g-16
| | 13g-9+7-10g = 3g-2
|-
|-
| | 11L12s
| | [[11L 12s]]
| | 2\23 &lt; g &lt; 1\11
| | 2\23 &lt; g &lt; 1\11
| | g = 45\506
| | g = 3\34, 4\45, 5\56-6\67
| | g = 3\34, 4\45, 5\56
| | 12g-1-(1-11g) = 23g-2
| | 12g-1+1-11g = g
|-
|-
| | 12L11s
| | [[12L 11s]]
| | 21\23 &lt; g &lt; 11\12
| | 21\23 &lt; g &lt; 11\12
| | g = 505\552
| | g = 32\35, 43\47, 54\59-65\71
| | g = 32\35, 43\47, 54\59
| | 11g-10-(11-12g) = 23g-21
| | <span style="line-height: 15.6000003814697px;">11g-10+11-12g = 1-g</span>
|-
|-
| | 13L10s
| | [[13L 10s]]
| | 7\23 &lt; g &lt; 4\13
| | 7\23 &lt; g &lt; 4\13
| | g = 183\598
| | g = 11\36, 15\49, 19\62-23\75
| | g = 11\36, 15\49, 19\62
| | 10g-3-(4-13g) = 23g-7
| | 10g-3+4-13g =1-3g
|-
|-
| | 14L9s
| | [[14L 9s]]
| | 18\23 &lt; g &lt; 11\14
| | 18\23 &lt; g &lt; 11\14
| | g = 505\644
| | g = 29\37, 40\51, 51\65-62\79
| | g = 29\37, 40\51, 51\65
| | 9g-7-(11-14g) = 23g-18
| | 9g-7+11-14g = 4-5g
|-
|-
| | 15L8s
| | [[15L 8s]]
| | 3\23 &lt; g &lt; 2\15
| | 3\23 &lt; g &lt; 2\15
| | g = 91\690
| | g = 5\38, 7\53, 9\68-11\83
| | g = 5\38, 7\53, 9\68
| | 8g-1-(2-15g) = 23g-3
| | 8g-1+2-15g = 1-7g
|-
|-
| | 16L7s
| | [[16L 7s]]
| | 10\23 &lt; g &lt; 7\16
| | 10\23 &lt; g &lt; 7\16
| | g = 321\736
| | g = 17\39, 24\55, 31\71-38\87
| | g = 17\39, 24\55, 31\71
| | 7g-3-(7-16g) = 23g-10
| | 7g-3+<span style="line-height: 15.6000003814697px;">7-16g = 4-9g</span>
|-
|-
| | 17L6s
| | [[17L 6s]]
| | 4\23 &lt; g &lt; 3\17
| | 4\23 &lt; g &lt; 3\17
| | g = 137\782
| | g = '''7\40''', 10\57, 13\74-16\91
| | g = 7\40, 10\57, 13\74
| | 6g-1-(3-17g) = 23g-4
| | 6g-1+3-17g = 2-11g
|-
|-
| | 18L5s
| | [[18L 5s]]
| | 14\23 &lt; g &lt; 11\18
| | 14\23 &lt; g &lt; 11\18
| | g = 505\828
| | g = '''25\41''', 36\59, 47\77-58\95
| | g = 25\41, 36\59, 47\77
| | 5g-4-(11-18g) = 23g-15
| | 5g-4+11-18g = 7-13g
|-
|-
| | 19L4s
| | [[19L 4s]]
| | 6\23 &lt; g &lt; 5\19
| | 6\23 &lt; g &lt; 5\19
| | g = 229\874
| | g = '''11\42''', 16\61, 21\80-26\99
| | g = 11\42, 16\61, 21\80
| | 4g-1-(5-19g) = 23g-6
| | 4g-1+5-19g = 4-15g
|-
|-
| | 20L3s
| | [[20L 3s]]
| | 8\23 &lt; g &lt; 7\20
| | 8\23 &lt; g &lt; 7\20
| | g = 321\920
| | g = '''15\43''', 22\63, 29\83-36\103
| | g = 15\43, 22\63, 29\83
| | 3g-1-(13-20g) = 23g-14
| | 3g-1+13-20g = 12-17g
|-
|-
| | 21L2s
| | [[21L 2s]]
| | 12\23 &lt; g &lt; 11\21
| | 12\23 &lt; g &lt; 11\21
| | g = 505\966
| | g = '''23\44''', 34\65, 45\86-56\107
| | g = 23\44, 34\65, 45\86
| | 2g-1-(11-21g) = 23g-12
| | 2g-1+11-21g = 10-19g
|-
|-
| | 22L1s
| | [[22L 1s|''22L 1s'']]
| | 1\23 &lt; g &lt; 1\22
| | ''1\23 &lt; g &lt; 1\22''
| | g = 45\1012
| | ''g = '''2\45''', 3\67, 4\89-5\111''
| | g = 2\45, 3\67, 4\89
| | ''g-(1-22g) = 23g-1''
| | g+1-22g = 1-221
|}
|}


=24=
== 24-tone ==
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | <span style="background-color: #ffffff;">Midpoint</span>
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! | Large step+Small step
|-
|-
| | 1L23s
| | [[1L 23s]]
| | 23\24 &lt; g &lt; 1
| | 23\24 &lt; g &lt; 1
| | g = 47\48
| | g = ''24\25, 25\26, 26\27-27\28''
| | ''g = 24\25, 25\26, 26\27''
| | 23g-22-(1-g) = 24g-23
| | 23g-22+1-g = 22g-21
|-
|-
| | 2L22s
| | [[2L 22s]]
| | 11\24 &lt; g &lt; 1\2
| | 11\24 &lt; g &lt; 1\2
| | g = 23\48
| | g = ''12\26, 13\28, 14\30''-15\32
| | g = ''12\26, 13\28'', 14\30
| | 11g-5-(1/2-g) = 12g-11/2
| | 11g-5+1/2-g = 10g-9/2
|-
|-
| | 3L21s
| | [[3L 21s]]
| | 7\24 &lt; g &lt; 1\3
| | 7\24 &lt; g &lt; 1\3
| | g = 15\48
| | g = ''8\27, 9\30'', 10\33-11\36
| | g = ''8\27'', 9\30, 10\33
| | 7g-2-(1/3-g) = 8g-7/3
| | 7g-2+1/3-g = 6g-5/3
|-
|-
| | 4L20s
| | [[4L 20s]]
| | 5\24 &lt; g &lt; 1\4
| | 5\24 &lt; g &lt; 1\4
| | g = 11\48
| | g = ''6\28'', 7\32, 8\36-9\40
| | g = ''6\28'', 7\32, 8\36
| | 5g-1-(1/4-g) = 6g-5/4
| | 5g-1+1/4-g = 4g-3/4
|-
|-
| | 5L19s
| | [[5L 19s]]
| | 19\24 &lt; g &lt; 4\5
| | 19\24 &lt; g &lt; 4\5
| | g = 191\240
| | g = ''23\29'', 27\34, 31\39-35\44
| | g = ''23\29'', 27\34, 31\39
| | 19g-15-(4-5g) = 24g-19
| | 19g-15+4-5g = 14g-11
|-
|-
| | 6L18s
| | [[6L 18s]]
| | 3\24 &lt; g &lt; 1\6
| | 3\24 &lt; g &lt; 1\6
| | g = 7\48
| | g = ''4\30'', 5\36, 6\42-7\48
| | g = 4\30, 5\36, 6\42
| | 3g-1\3-(1\6-g) = 4g-1\2
| | 3g-1\3+1\6-g = 2g-1\6
|-
|-
| | 7L17s
| | [[7L 17s]]
| | 17\24 &lt; g &lt; 5\7
| | 17\24 &lt; g &lt; 5\7
| | g = 239\336
| | g = 22\31, 27\38, 32\45-37\52
| | g = 22\31, 27\38, 32\45
| | 17g-12-(5-7g) = 24g-17
| | 17g-12+5-7g = 10g-7
|-
|-
| | 8L16s
| | [[8L 16s]]
| | 2\24 &lt; g &lt; 1\8
| | 2\24 &lt; g &lt; 1\8
| | g = 5\48
| | g = 3\32, 4\40, 5\48-6\56
| | g = 3\32, 4\40, 5\48
| | 2g-1\8-(1\8-g) = 3g-1\4
| | 2g-1\8+1\8-g = g
|-
|-
| | 9L15s
| | [[9L 15s]]
| | 5\24 &lt; g &lt; 2\9
| | 5\24 &lt; g &lt; 2\9
| | g = 31\144
| | g = 7\33, 9\42, 11\51-13\60
| | g = 7\33, 9\42, 11\51
| | 5g-1-(2\3-3g) = 8g-5\3
| | 5g-1+2\3-3g = 2g-1\3
|-
|-
| | 10L14s
| | [[10L 14s]]
| | 7\24 &lt; g &lt; 3\10
| | 7\24 &lt; g &lt; 3\10
| | g = 71\240
| | g = 10\34, 13\44, 16\54-19\64
| | g = 10\34, 13\44, 16\54
| | 7g-2-(3\2-5g) = 12g-7\2
| | 7g-2+3\2-5g = 2g-1\2
|-
|-
| | 11L13s
| | [[11L 13s]]
| | 13\24 &lt; g &lt; 6\11
| | 13\24 &lt; g &lt; 6\11
| | g = 287\528
| | g = 19\35, 25\46, 31\57-37\68
| | g = 19\35, 25\46, 31\57
| | 13g-7-(6-11g) = 24g-12
| | 13g-7+6-11g = 2g-1
|-
|-
| | 12L12s
| | ''[[12L 12s]] = 1L 1s (12)''
| | 1\24 &lt; g &lt; 1\12
| | ''1\24 &lt; g &lt; 1\12''
| | g = 3\48
| | ''g = 2\36, 3\48, 4\60-5\72''
| | g = 2\36, 3\48, 4\60
| | ''g-(1\12-g) = 2g-1\12''
| | g+1\12-g = 1\12
|-
|-
| | 13L11s
| | [[13L 11s]]
| | 11\24 &lt; g &lt; 6\13
| | 11\24 &lt; g &lt; 6\13
| | g = 287\624
| | g = 17\37, 23\50, 29\63-35\76
| | g = 17\37, 23\50, 29\63
| | 11g-5-(6-13g) = 24g-11
| | 11g-5+6-13g = 1-2g
|-
|-
| | 14L10s
| | [[14L 10s]]
| | 17\24 &lt; g &lt; 10\14
| | 17\24 &lt; g &lt; 10\14
| | g = 239\336
| | g = 27\38, 37\52, 47\66-57\80
| | g = 27\38, 37\52, 47\66
| | 5g-7\2-(5-7g) = 12g-17\2
| | 5g-7\2+5-7g = 3\2-2g
|-
|-
| | 15L9s
| | [[15L 9s]]
| | 3\24 &lt; g &lt; 2\15
| | 3\24 &lt; g &lt; 2\15
| | g = 31\240
| | g = 5\39, 7\54, 9\69-11\84
| | g = 5\39, 7\54, 9\69
| | 3g-1\3-(2\3-5g) = 8g-1
| | 3g-1\3+2\3-5g = 1\3-2g
|-
|-
| | 16L8s
| | ''[[16L 8s]] = 2L 1s (8)''
| | 1\24 &lt; g &lt; 1\16
| | ''1\24 &lt; g &lt; 1\16''
| | g = 5\96
| | ''g = '''2\40''', 3\56, 4\72-5\88''
| | g = 2\40, 3\56, 4\72
| | ''g-(1\8-2g) = 3g-1\8''
| | g+1\8-2g = 1\8-g
|-
|-
| | 17L7s
| | [[17L 7s]]
| | 7\24 &lt; g &lt; 5\17
| | 7\24 &lt; g &lt; 5\17
| | g = 239\816
| | g = '''12\41''', 17\58, 22\75-27\92
| | g = 12\41, 17\58, 22\75
| | 7g-2-(5-17g) = 24g-7
| | 7g-2+5-17g = 3-10g
|-
|-
| | 18L6s
| | ''[[18L 6s]] = 3L 1s (6)''
| | 1\24 &lt; g &lt; 1\18
| | ''1\24 &lt; g &lt; 1\18''
| | g = 7\144
| | ''g = '''2\42''', 3\60, 4\78-5\96''
| | g = 2\42, 3\60, 4\78
| | ''g-(1\6-3g) = 4g-1\6''
| | g+1\6-3g = 1\6-2g
|-
|-
| | 19L5s
| | [[19L 5s]]
| | 5\24 &lt; g &lt; 4\19
| | 5\24 &lt; g &lt; 4\19
| | g = 191\912
| | g = '''9\43''', 13\62, 17\81-21\100
| | g = 9\43, 13\62, 17\81
| | 5g-1-(4-19g) = 24g-5
| | 5g-5+4-19g = 1-18g
|-
|-
| | 20L4s
| | ''[[20L 4s]] = 5L 1s (4)''
| | 1\24 &lt; g &lt; 1\20
| | ''1\24 &lt; g &lt; 1\20''
| | g = 11\240
| | ''g = '''2\44''', 3\64, 4\84-5\104''
| | g = 2\44, 3\64, 4\84
| | ''g-(1\4-5g) = 6g-1\4''
| | g+1\4-5g = 1\4-4g
|-
|-
| | 21L3s
| | ''[[21L 3s]] = 7L 1s (3)''
| | 1\24 &lt; g &lt; 1\21
| | ''1\24 &lt; g &lt; 1\21''
| | g = 15\336
| | ''g = '''2\45''', 3\66, 4\87-5\108''
| | g = 2\45, 3\66, 4\87
| | ''g-(1\3-7g) = 8g-1\3''
| | g+1\3-7g = 1\3-6g
|-
|-
| | 22L2s
| | ''[[22L 2s]] = 11L 1s (2)''
| | 1\24 &lt; g &lt; 1\22
| | ''1\24 &lt; g &lt; 1\22''
| | g = 23\264
| | ''g = '''2\46''', 3\68, 4\90-5\112''
| | g = 2\46, 3\68, 4\90
| | ''g-(1\2-11g) = 12g-1\2''
| | g+1\2-11g = 1\2-10g
|-
|-
| | 23L1s
| | [[23L 1s|''23L 1s'']]
| | 1\24 &lt; g &lt; 1\23
| | ''1\24 &lt; g &lt; 1\23''
| | g = 47\1104
| | ''g = '''2\47''', 3\70, 4\93-5\116''
| | g = 2\47, 3\70, 4\93
| | ''g+1-23g = 24g-1''
| | g+1-23g = 1-22g
|}
|}


=25=
== 25-tone ==
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | <span style="background-color: #ffffff;">Midpoint</span>
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! | Large step+Small step
|-
|-
| | 1L24s
| | [[1L 24s]]
| | 24\25 &lt; g &lt; 1
| | 24\25 &lt; g &lt; 1
| | g = 49\50
| | g = ''25\26, 26\27, 27\28-28\29''
| | ''g = 25\26, 26\27, 27\28''
| | 24g-23-(1-g) = 25g-24
| | 24g-23+1-g = 23g-22
|-
|-
| | 2L23s
| | [[2L 23s]]
| | 12\25 &lt; g &lt; 1\2
| | 12\25 &lt; g &lt; 1\2
| | g = 49\100
| | g = ''13\27, 14\29, 15\31''-16\33
| | ''g = 13\27, 14\29, 15\31''
| | 23g-11-(1-2g) = 25g-13
| | 23g-11+1-2g = 21g-10
|-
|-
| | 3L22s
| | [[3L 22s]]
| | 8\25 &lt; g &lt; 1\3
| | 8\25 &lt; g &lt; 1\3
| | g = 49\150
| | g = ''9\28'', ''10\31'', 11\34-12\37
| | g = ''9\28'', ''10\31'', 11\34
| | 22g-7-(1-3g) = 25g-8
| | 22g-7+1-3g = 19g-6
|-
|-
| | 4L21s
| | [[4L 21s]]
| | 6\25 &lt; g &lt; 1\4
| | 6\25 &lt; g &lt; 1\4
| | g = 49\200
| | g = ''7\29'', 8\33, 9\37-10\41
| | g = ''7\29'', 8\33, 9\37
| | 21g-5-(1-4g) = 25g-6
| | 21g-5+1-4g = 17g-4
|-
|-
| | 5L20s
| | [[5L 20s]]
| | 4\25 &lt; g &lt; 1\5
| | 4\25 &lt; g &lt; 1\5
| | g = 9\50
| | g = ''5\30'', 6\35, 7\40-8\45
| | g = ''5\30'', 6\35, 7\40
| | 4g-3\5-(1\5-g) = 5g-4\5
| | 4g-3\5+1\5-g = 3g-2\5
|-
|-
| | 6L19s
| | [[6L 19s]]
| | 4\25 &lt; g &lt; 1\6
| | 4\25 &lt; g &lt; 1\6
| | g = 49\300
| | g = ''5\31'', 6\37, 7\43-8\49
| | g = ''5\31'', 6\37, 7\43
| | 19g-3-(1-6g) = 25g-4
| | 19g-3+1-6g = 13g-2
|-
|-
| | 7L18s
| | [[7L 18s]]
| | 7\25 &lt; g &lt; 2\7
| | 7\25 &lt; g &lt; 2\7
| | g = 99\350
| | g = 9\32, 11\39, 13\46-15\53
| | g = 9\32, 11\39, 13\46
| | 18g-5-(2-7g) = 25g-7
| | 18g-5+2-7g = 11g-3
|-
|-
| | 8L17s
| | [[8L 17s]]
| | 3\25 &lt; g &lt; 1\8
| | 3\25 &lt; g &lt; 1\8
| | g = 49\400
| | g = 4\33, 5\41, 6\49-7\57
| | g = 4\33, 5\41, 6\47
| | 17g-2-(1-8g) = 25g-3
| | <span style="line-height: 15.6000003814697px;">17g-2+1-8g = 9g-1</span>
|-
|-
| | 9L16s
| | [[9L 16s]]
| | 11\25 &lt; g &lt; 4\9
| | 11\25 &lt; g &lt; 4\9
| | g = 199\450
| | g = 15\34, 19\43, 23\52-27\61
| | g = 15\34, 19\43, 23\52
| | 16g-7-(4-9g) = 25g-11
| | 16g-7<span style="line-height: 15.6000003814697px;">+4-9g = 3-7g</span>
|-
|-
| | 10L15s
| | [[10L 15s]]
| | 2\25 &lt; g &lt; 1\10
| | 2\25 &lt; g &lt; 1\10
| | g = 9\100
| | g = 3\35, 4\45, 5\55-6\65
| | g = 3\35, 4\45, 5\55
| | 3g-1\5-(1\5-2g) = 5g-2\5
| | 3g-1\5+1\5-2g = g
|-
|-
| | 11L14s
| | [[11L 14s]]
| | 9\25 &lt; g &lt; 4\11
| | 9\25 &lt; g &lt; 4\11
| | g = 199\550
| | g = 13\36, 17\47, 21\58-25\69
| | g = 13\36, 17\47, 21\58
| | 14g-5-(4-11g) = 25g-9
| | 14g-5+4-11g = 3g-1
|-
|-
| | 12L13s
| | [[12L 13s]]
| | 2\25 &lt; g &lt; 1\12
| | 2\25 &lt; g &lt; 1\12
| | g = 49\600
| | g = 3\37, 4\49, 5\61-6\73
| | g = 3\37, 4\49, 5\61
| | 13g-1-(1-12g) = 25g-2
| | 13g-1+1-12g = g
|-
|-
| | 13L12s
| | [[13L 12s]]
| | 23\25 &lt; g &lt; 12\13
| | 23\25 &lt; g &lt; 12\13
| | g = 599\650
| | g = 35\38, 47\51, 59\64-71\77
| | g = 35\38, 47\51, 59\64
| | 12g-11-(12-13g) = 25g-23
| | 12g-11+12-13g = 1-g
|-
|-
| | 14L11s
| | [[14L 11s]]
| | 16\25 &lt; g &lt; 9\14
| | 16\25 &lt; g &lt; 9\14
| | g = 449\700
| | g = 25\39, 34\53, 43\67-52\81
| | g = 25\39, 34\53, 43\67
| | 11g-7-(9-14g) = 25g-16
| | 11g-7+9-14g = 2-3g
|-
|-
| | 15L10s
| | [[15L 10s]]
| | 3\25 &lt; g &lt; 2\15
| | 3\25 &lt; g &lt; 2\15
| | g = 19\150
| | g = '''5\40''', 7\55, 9\70-11\85
| | g = 5\40, 7\55, 9\70
| | 2g-1\5-(2\5-3g) = 5g-1\5
| | 2g-1\5+2\5-3g = 1\5-g
|-
|-
| | 16L9s
| | [[16L 9s]]
| | 14\25 &lt; g &lt; 9\16
| | 14\25 &lt; g &lt; 9\16
| | g = 449\800
| | g = '''23\41''', 32\57, 41\73-50\89
| | g = 23\41, 32\57, 41\73
| | 9g-5-(9-16g) = 25g-14
| | 9g-5+9-16g = 4-7g
|-
|-
| | 17L8s
| | [[17L 8s]]
| | 22\25 &lt; g &lt; 15\17
| | 22\25 &lt; g &lt; 15\17
| | g = 749\850
| | g = '''37\42''', 52\59, 67\76-82\93
| | g = 37\42, 52\59, 67\76
| | 8g-7-(15-17g) = 25g-22
| | 8g-7+15-17g = 8-9g
|-
|-
| | 18L7s
| | [[18L 7s]]
| | 18\25 &lt; g &lt; 13\18
| | 18\25 &lt; g &lt; 13\18
| | g = 649\900
| | g = '''31\43''', 44\61, 57\79-80\97
| | g = 31\43, 44\61, 57\79
| | 7g-5-(13-18g) = 25g-18
| | 7g-5+13-18g = 8-11g
|-
|-
| | 19L6s
| | [[19L 6s]]
| | 21\25 &lt; g &lt; 16\19
| | 21\25 &lt; g &lt; 16\19
| | g = 799\950
| | g = '''37\44''', 53\63, 69\82-85\101
| | g = 37\44, 53\63, 69\82
| | 6g-5+16-19g = 25g-21
| | 6g-5+16-19g = 11-13g
|-
|-
| | 20L5s
| | ''[[20L 5s]] = 4L 1s (5)''
| | 1\25 &lt; g &lt; 1\20
| | ''1\25 &lt; g &lt; 1\20''
| | g = 9\200
| | ''g = '''2\45''', 3\65, 4\85-5\105''
| | g = 2\45, 3\65, 4\85
| | ''g-(1\5-4g) = 5g-1\5''
| | g+1\5-4g = 1\5-3g
|-
|-
| | 21L4s
| | [[21L 4s]]
| | 16\21 &lt; g &lt; 19\25
| | 19\25 &lt; g &lt; 16\21
| | g = 799\1050
| | g = '''35\46''', 51\67, 67\88-83\109
| | g = 35\46, 51\67, 71\88
| | 4g-3-(16-21g) = 25g-19
| | 4g-3+16-21g = 13-17g
|-
|-
| | 22L3s
| | [[22L 3s]]
| | 17\25 &lt; g &lt; 15\22
| | 17\25 &lt; g &lt; 15\22
| | g = 749\1100
| | g = '''32\47''', 47\69, 62\91-77\113
| | g = 32\47, 47\69, 62\91
| | 3g-2-(15-22g) = 25g-17
| | 3g-2+15-22g = 13-19g
|-
|-
| | 23L2s
| | [[23L 2s]]
| | 13\25 &lt; g &lt; 12\23
| | 13\25 &lt; g &lt; 12\23
| | g = 599\1150
| | g = '''25\48''', 37\71, 49\94-61\117
| | g = 25\48, 37\71, 49\94
| | 2g-1-(11-23g) = 25g-13
| | 2g-1+11-23g = 10-21g
|-
|-
| | 24L1s
| | [[24L 1s|''24L 1s'']]
| | 1\25 &lt; g &lt; 1\24
| | ''1\25 &lt; g &lt; 1\24''
| | g = 49\1200
| | ''g = '''2\49''', 3\73, 4\97-5\121''
| | g = 2\49, 3\73, 4\97
| | ''g-(1-24g) = 25g-1''
| | g+1-24g = 1-23g
|}
|}


=26=
== 26-tone ==
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | <span style="background-color: #ffffff;">Midpoint</span>
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! | Large step+Small step
|-
|-
| | 1L25s
| | [[1L 25s]]
| | 25\26 &lt; g &lt; 1
| | 25\26 &lt; g &lt; 1
| | g = 51\52
| | g = ''26\27, 27\28, 28\29-29\30''
| | ''g = 26\27, 27\28, 28\29''
| | 25g-24-(1-g) = 25g-24
| | 25g-24+1-g = 24g-23
|-
|-
| | 2L24s
| | [[2L 24s]]
| | 12\26 &lt; g &lt; 1\2
| | 12\26 &lt; g &lt; 1\2
| | g = 25\52
| | g = ''13\28, 14\30, 15\32''-16\34
| | ''g = 13\28, 14\30, 15\32''
| | 12g-11\2-(1\2-g) = 13g-6
| | 12g-11\2+1\2-g = 11g-5
|-
|-
| | 3L23s
| | [[3L 23s]]
| | 17\26 &lt; g &lt; 2\3
| | 17\26 &lt; g &lt; 2\3
| | g = 103\156
| | g = ''19\29'', ''21\32'', 23\35-25\38
| | g = ''19\29'', ''21\32'', 23\35
| | 23g-15-(2-3g) = 26g-17
| | 23g-15+2-3g = 20g-13
|-
|-
| | 4L22s
| | [[4L 22s]]
| | 6\26 &lt; g &lt; 1\4
| | 6\26 &lt; g &lt; 1\4
| | g = 25\104
| | g = ''7\30'', 8\34, 9\38-10\42
| | g = ''7\30'', 8\34, 9\38
| | 11g-5\2-(1\2-2g) = 13g-3
| | 11g-5\2+<span style="line-height: 15.6000003814697px;">1\2-2g = 9g-2</span>
|-
|-
| | 5L21s
| | [[5L 21s]]
| | 5\26 &lt; g &lt; 1\5
| | 5\26 &lt; g &lt; 1\5
| | g = 51\260
| | g = ''6\31'', 7\36, 8\41-9\46
| | g = ''6\31'', 7\36, 8\41
| | 21g-4-(1-5g) = 26g-5
| | 21g-4+1-5g = 16g-3
|-
|-
| | 6L20s
| | [[6L 20s]]
| | 4\26 &lt; g &lt; 1\6
| | 4\26 &lt; g &lt; 1\6
| | g = 25\156
| | g = ''5\32'', 6\38, 7\44-8\50
| | g = ''5\32'', 6\38, 7\44
| | 10g-3\2-(1\2-3g) = 13g-2
| | 10g-3\2+1\2-3g = 7g-1
|-
|-
| | 7L19s
| | [[7L 19s]]
| | 11\26 &lt; g &lt; 3\7
| | 11\26 &lt; g &lt; 3\7
| | g = 155\364
| | g = 14\33, 17\40, 20\47-23\54
| | g = 14\33, 17\40, 20\47
| | 19g-8-(3-7g) = 26g-11
| | 19g-8+3-7g = 12g-5
|-
|-
| | 8L18s
| | [[8L 18s]]
| | 3\26 &lt; g &lt; 1\8
| | 3\26 &lt; g &lt; 1\8
| | g = 25\208
| | g = 4\34, 5\42, 6\50-7\58
| | g = 4\34, 5\42, 6\50
| | 9g-1-(1\2-4g) = 13g-3\2
| | 9g-1+1\2-4g = 5g-1\2
|-
|-
| | 9L17s
| | [[9L 17s]]
| | 23\26 &lt; g &lt; 8\9
| | 23\26 &lt; g &lt; 8\9
| | g = 415\468
| | g = 31\35, 39\44, 47\53-55\62
| | g = 31\35, 39\44, 47\53
| | 17g-15-(8-9g) = 26g-23
| | 17g-15+8-9g = 8g-7
|-
|-
| | 10L16s
| | [[10L 16s]]
| | 5\26 &lt; g &lt; 2\10
| | 5\26 &lt; g &lt; 2\10
| | g = 51\260
| | g = 7\36, 9\46, 11\56-13\66
| | g = 7\36, 9\46, 11\56
| | 8g-3\2-(1-5g) = 13g-5\2
| | 8g-3\2+1-5g = 3g-1\2
|-
|-
| | 11L15s
| | [[11L 15s]]
| | 7\26 &lt; g &lt; 3\11
| | 7\26 &lt; g &lt; 3\11
| | g = 155\572
| | g = 10\37, 13\48, 16\59-19\70
| | g = 10\37, 13\48, 16\59
| | 15g-4-(3-11g) = 26g-7
| | 15g-4+3-11g = 4g-1
|-
|-
| | 12L14s
| | [[12L 14s]]
| | 2\26 &lt; g &lt; 1\12
| | 2\26 &lt; g &lt; 1\12
| | g = 25\312
| | g = 3\38, 4\50, 5\62-6\74
| | g = 3\38, 4\50, 5\62
| | 7g-1\2-(1\2-6g) = 13g-1
| | 7g-1\2+1\2-6g = g
|-
|-
| | 13L13s
| | ''[[13L 13s]] = 1L 1s (13)''
| | 1\26 &lt; g &lt; 1\13
| | ''1\26 &lt; g &lt; 1\13''
| | g = 3\52
| | ''g = 2\39, 3\52, 4\65-5\78''
| | g = 2\39, 3\52, 4\65
| | ''g-(1\13-g) = 2g-1\13''
| | g+1\13-g = 1\13
|-
|-
| | <span style="line-height: 15.6000003814697px;">14L12s</span>
| | [[14L 12s]]
| | 11\26 &lt; g &lt; 6\14
| | 11\26 &lt; g &lt; 6\14
| | g = 155\364
| | g = '''17\40''', 23\54, 29\68-35\82
| | g = 17\40, 23\54, 29\68
| | 6g-5\2-(3-7g) = 13g-11\2
| | 6g-5\2+3-7g = 1\2-g
|-
|-
| | <span style="line-height: 15.6000003814697px;">15L11s</span>
| | [[15L 11s]]
| | 19\26 &lt; g &lt; 11\15
| | 19\26 &lt; g &lt; 11\15
| | g = 571\780
| | g = '''30\41''', 41\56, 52\71-63\86
| | g = 30\41, 41\56, 52\71
| | 11g-8-(11-15g) = 26g-19
| | 11g-8+11-15g = 3-4g
|-
|-
| | <span style="line-height: 15.6000003814697px;">16L10s</span>
| | [[16L 10s]]
| | 8\26 &lt; g &lt; 5\16
| | 8\26 &lt; g &lt; 5\16
| | g = 129\416
| | g = '''13\42''', 18\58, 23\74-28\90
| | g = 13\42, 18\58, 23\74
| | 5g-3\2-(5\2-8g) = 13g-4
| | 5g-3\2+5\2-8g = 1-3g
|-
|-
| | <span style="line-height: 15.6000003814697px;">17L9s</span>
| | [[17L 9s]]
| | 3\26 &lt; g &lt; 2\17
| | 3\26 &lt; g &lt; 2\17
| | g = 103\884
| | g = '''5\43''', 7\60, 9\77-11\94
| | g = 5\43, 7\60, 9\77
| | 9g-1-(2-17g) = 26g-3
| | 9g-1+2-17g = 1-8g
|-
|-
| | <span style="line-height: 15.6000003814697px;">18L</span>8s
| | [[18L 8s]]
| | 10\26 &lt; g &lt; 7\18
| | 10\26 &lt; g &lt; 7\18
| | g = 181\468
| | g = '''17\44''', 24\62, 31\80-38\98
| | g = 17\44, 24\62, 31\80
| | 4g-3\2-(7\2-9g) = 13g-5
| | 4g-7\2+7-9g = 7\2-5g
|-
|-
| | <span style="line-height: 15.6000003814697px;">19L</span>7s
| | [[19L 7s]]
| | 15\26 &lt; g &lt; 11\19
| | 15\26 &lt; g &lt; 11\19
| | g = 571\988
| | g = '''26\45''', 37\64, 48\83-59\102
| | g = 26\45, 37\64, 48\83
| | 7g-4-(11-19g) = 26g-15
| | 7g-4+11-19g = 7-12g
|-
|-
| | <span style="line-height: 15.6000003814697px;">20L</span>6s
| | [[20L 6s]]
| | 9\26 &lt; g &lt; 7\20
| | 9\26 &lt; g &lt; 7\20
| | g = 181\520
| | g = '''16\46''', 23\66, 30\86-37\106
| | g = 16\46, 23\66, 30\86
| | 3g-1-(7\2-10g) = 13g-9\2
| | 3g-1+7\2-10g = 5\2-7g
|-
|-
| | <span style="line-height: 15.6000003814697px;">21L</span>5s
| | [[21L 5s]]
| | 21\26 &lt; g &lt; 17\21
| | 21\26 &lt; g &lt; 17\21
| | g = 883\1092
| | g = '''38\47''', 55\68, 72\89-89\110
| | g = 38\47, 55\68, 72\89
| | 5g-4-(17-21g) = 26g-21
| | 5g-4+16-21g = 12-16g
|-
|-
| | <span style="line-height: 15.6000003814697px;">22L</span>4s
| | [[22L 4s]]
| | 7\26 &lt; g &lt; 6\22
| | 7\26 &lt; g &lt; 6\22
| | g = 155\572
| | g = '''13\48''', 19\70, 25\92-31\114
| | g = 13\48, 19\70, 25\92
| | 2g-1\2-(3-11g) = 13g-7\2
| | 2g-1\2+3-11g = 5\2-9g
|-
|-
| | <span style="line-height: 15.6000003814697px;">23L</span>3s
| | [[23L 3s]]
| | 9\26 &lt; g &lt; 8\23
| | 9\26 &lt; g &lt; 8\23
| | g = 415\1196
| | g = '''17\49''', 25\72, 33\95-41\118
| | g = 17\49, 25\72, 33/95
| | 3g-1-(8-23g) = 26g-9
| | 3g-1+8-23g = 7-20g
|-
|-
| | <span style="line-height: 15.6000003814697px;">24L</span>2s
| | ''[[24L 2s]] = 12L 1s (2)''
| | 1\26 &lt; g &lt; 1\24
| | ''1\26 &lt; g &lt; 1\24''
| | g = 25\312
| | ''g = '''2\50''', 3\74, 4\98-5\122''
| | g = 2\50, 3\74, 4\98
| | ''g-(1\2-12g) = 13g-1\2''
| | g+1\2-12g = 1\2-11g
|-
|-
| | 25L1s
| | [[25L 1s|''25L 1s'']]
| | 1\26 &lt; g &lt; 1\25
| | ''1\26 &lt; g &lt; 1\25''
| | g = 51\1300
| | ''g = '''2\51''', 3\76, 4\101-5\126''
| | g = 2\51, 3\76, 4\101
| | ''g-(1-25g) = 26g-1''
| | g+1-25g = 1-24g
|}
|}


=27=
== 27-tone ==
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | <span style="background-color: #ffffff;">Midpoint</span>
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! | Large step+Small step
|-
|-
| | 1L26s
| | [[1L 26s]]
| | 26\27 &lt; g &lt; 1
| | 26\27 &lt; g &lt; 1
| | g = 53\54
| | g = ''27\28, 28\29, 29\30-30\31''
| | <span style="line-height: 15.6000003814697px;">''g = 27\28,''</span> ''28\29, 29\30''
| | 26g-25-(1-g) = 27g-26
| | 26g-25+1-g = 25g-24
|-
|-
| | 2L25s
| | [[2L 25s]]
| | 13\27 &lt; g &lt; 1\2
| | 13\27 &lt; g &lt; 1\2
| | g = 53\108
| | g = ''14\29, 15\31, 16\33''-17\35
| | ''g = 14\29, 15\31, 16\33''
| | 25g-12-(1-2g) = 27g-12
| | 25g-12+1-2g = 23g-11
|-
|-
| | 3L24s
| | [[3L 24s]]
| | 8\27 &lt; g &lt; 1\3
| | 8\27 &lt; g &lt; 1\3
| | g = 17\54
| | g = ''9\30'', ''10\33'', 11\36-12\39
| | g = ''9\30'', ''10\33'', 11\36
| | 8g-7\3-(1\3-3g) = 9g-8\3
| | 8g-7\3+1-3g = 5g-2
|-
|-
| | 4L23s
| | [[4L 23s]]
| | 20\27 &lt; g &lt; 3\4
| | 20\27 &lt; g &lt; 3\4
| | g = 161\216
| | g = ''23\31'', 26\35, 29\39-32\43
| | g = ''23\31'', 26\35, 29\39
| | 23g-17-(3-4g) = 19g-14
| | 23g-17+3-4g = 19g-14
|-
|-
| | 5L22s
| | [[5L 22s]]
| | 16\27 &lt; g &lt; 3\5
| | 16\27 &lt; g &lt; 3\5
| | g = 161\270
| | g = ''19\32'', 22\37, 25\42-28\47
| | g = ''19\32'', 22\37, 25\42
| | 22g-13-(3-5g) = 27g-16
| | 22g-13+3-5g = 17g-10
|-
|-
| | 6L21s
| | [[6L 21s]]
| | 4\27 &lt; g &lt; 1\6
| | 4\27 &lt; g &lt; 1\6
| | g = 17\108
| | g = ''5\33'', 6\39, 7\45-8\51
| | g = ''5\33'', 6\39, 7\45
| | 7g-1-(1\3-2g) = 9g-4\3
| | 7g-1+1\3-2g = 5g-2\3
|-
|-
| | 7L20s
| | [[7L 20s]]
| | 23\27 &lt; g &lt; 6\7
| | 23\27 &lt; g &lt; 6\7
| | g = 323\378
| | g = 29\34, 35\41, 41\48-47\55
| | g = 29\34, 35\41, 41\48
| | 20g-17-(6-7g) = 27g-23
| | 20g-17+6-7g = 13g-11
|-
|-
| | 8L19s
| | [[8L 19s]]
| | 10\27 &lt; g &lt; 3\8
| | 10\27 &lt; g &lt; 3\8
| | g = 161\432
| | g = 13\35, 16\43, 19\51-22\59
| | g = 13\35, 16\43, 19\51
| | 19g-7-(3-8g) = 27g-10
| | 19g-7+3-8g = 11g-4
|-
|-
| | 9L18s
| | [[9L 18s]]
| | 2\27 &lt; g &lt; 1\9
| | 2\27 &lt; g &lt; 1\9
| | g = 5\54
| | g = 3\36, 4\45, 5\54-6\63
| | g = 3\36, 4\45, 5\54
| | 2g-1\9-(1\9-g) = 3g-1\9
| | 2g-1\9+1\9-g = g
|-
|-
| | 10L17s
| | [[10L 17s]]
| | 8\27 &lt; g &lt; 3\10
| | 8\27 &lt; g &lt; 3\10
| | g = 161\540
| | g = 11\37, 14\47, 17\57–20\67
| | g = 11\37, 14\47, 17\57
| | 17g-5-(3-10g) = 27g-8
| | 17g-5+3-10g = 7g-2
|-
|-
| | 11L16s
| | [[11L 16s]]
| | 22\27 &lt; g &lt; 9\11
| | 22\27 &lt; g &lt; 9\11
| | g = 485\594
| | g = 31\38, 40\49, 49\60-58\71
| | g = 31\38, 40\49, 49\60
| | 16g-13-(9-11g) = 27g-22
| | 16g-13+9-11g = 5g-4
|-
|-
| | 12L15s
| | [[12L 15s]]
| | 2\27 &lt; g &lt; 1\12
| | 2\27 &lt; g &lt; 1\12
| | g = 17\216
| | g = 3\39, 4\51, 5\63-6\75
| | g = 3\39, 4\51, 5\63
| | 5g-1\3-(1\3-4g) = 9g-2\3
| | 5g-1\3+1\3-4g = g
|-
|-
| | 13L14s
| | [[13L 14s]]
| | 2\27 &lt; g &lt; 1\13
| | 2\27 &lt; g &lt; 1\13
| | g = 53\702
| | g = '''3\40''', 4\53, 5\66-6\79
| | g = 3\40, 4\53, 5\66
| | 14g-1-(1-13g) = 27g-2
| | 14g-1+1-13g = g
|-
|-
| | 14L13s
| | [[14L 13s]]
| | 25\27 &lt; g &lt; 13\14
| | 25\27 &lt; g &lt; 13\14
| | g = 701\756
| | g = '''38\41''', 51\55, 64\69-77\83
| | g = 38\41, 51\55, 64\69
| | 13g-12-(13-14g) = 27g-25
| | 13g-12+13-14g = 1-g
|-
|-
| | 15L12s
| | [[15L 12s]]
| | 7\27 &lt; g &lt; 4\15
| | 7\27 &lt; g &lt; 4\15
| | g = 71\270
| | g = '''11\42''', 15\57, 19\72-23\87
| | g = 11\42, 15\57, 19\72
| | 4g-1-(4\3-5g) = 9g-4\3
| | 4g-1+4\3-5g = 1\3-g
|-
|-
| | 16L11s
| | [[16L 11s]]
| | 5\27 &lt; g &lt; 3\16
| | 5\27 &lt; g &lt; 3\16
| | g = 161\864
| | g = '''8\43''', 11\59, 14\75-17\91
| | g = 8\43, 11\59, 14\75
| | 11g-2-(3-16g) = 27g-5
| | 11g-2+3-16g = 1-5g
|-
|-
| | 17L10s
| | [[17L 10s]]
| | 19\27 &lt; g &lt; 12\17
| | 19\27 &lt; g &lt; 12\17
| | g = 647\918
| | g = '''31\44''', 43\61, 55\78-67\95
| | g = 31\44, 43\61, 55\78
| | 10g-7-(12-17g) = 27g-19
| | 10g-7+12-17g = 5-7g
|-
|-
| | 18L9s
| | ''[[18L 9s]] = 2L 1s (9)''
| | 1\27 &lt; g &lt; 1\18
| | ''1\27 &lt; g &lt; 1\18''
| | g = 5\108
| | ''g = '''2\45''', 3\63, 4\81-5\99''
| | g = 2\45, 3\63, 4\81
| | ''g-(1\9-2g) = 3g-1\9''
| | g+1\9-2g = 1\9-g
|-
|-
| | 19L8s
| | [[19L 8s]]
| | 17\27 &lt; g &lt; 12\19
| | 17\27 &lt; g &lt; 12\19
| | g = 647\1026
| | g = '''29\46''', 41\65, 53\84-65\103
| | g = 29\46, 41\65, 53\84
| | 8g-5-(12-19g) = 27g-17
| | 8g-5+12-19g = 7-11g
|-
|-
| | 20L7s
| | [[20L 7s]]
| | 4\27 &lt; g &lt; 3\20
| | 4\27 &lt; g &lt; 3\20
| | g = 161\1080
| | g = '''7\47''', 10\67, 13\87-16\107
| | g = 7\47, 10\67, 13\87
| | 7g-1-(3-20g) = 27g-4
| | 7g-1+3-20g = 2-13g
|-
|-
| | 21L6s
| | [[21L 6s]]
| | 5\27 &lt; g &lt; 4\21
| | 5\27 &lt; g &lt; 4\21
| | g = 71\378
| | g = '''9\48''', 13\69, 17\90-17\111
| | g = 9\48, 13\69, 17\90
| | 2g-1\3-(4\3-7g) = 9g-5\3
| | 2g-1\3+4\3-7g = 1-5g
|-
|-
| | 22L5s
| | [[22L 5s]]
| | <span style="line-height: 15.6000003814697px;">11</span>\27 &lt; g &lt; 9\22
| | 11\27 &lt; g &lt; 9\22
| | g = 485\1188
| | g = '''20\49''', 29\71, 38\93-47\115
| | g = 20\49, 29\71, 38\93
| | 5g-2-(9-22g) = 27g-11
| | 5g-2+9-22g = 7-17g
|-
|-
| | 23L4s
| | [[23L 4s]]
| | 7\27 &lt; g &lt; 6\23
| | 7\27 &lt; g &lt; 6\23
| | g = 323\1242
| | g = '''13\50''', 19\73, 25\96-31\119
| | g = 13\50, 19\73, 25\96
| | 4g-1-(6-23g) = 27g-7
| | 4g-1+6-23g = 5-19g
|-
|-
| | 24L3s
| | ''[[24L 3s]] = 8L 1s (3)''
| | 1\27 &lt; g &lt; 1\24
| | ''1\27 &lt; g &lt; 1\24''
| | g = 17\432
| | ''g = '''2\51''', 3\75, 4\99-5\123''
| | g = 2\51, 3\75, 4\99
| | ''g-(1\3-8g) = 9g-1\3''
| | g+1\3-8g = 1\3-7g
|-
|-
| | 25L2s
| | [[25L 2s]]
| | 14\27 &lt; g &lt; 13\25
| | 14\27 &lt; g &lt; 13\25
| | g = 701\1350
| | g = '''27\52''', 40\77, 53\102-66\127
| | g = 27\52, 40\77, 53\102
| | 2g-1-(13-25g) = 24g-14
| | 2g-1+13-25g = 12-23g
|-
|-
| | 26L1s
| | [[26L 1s|''26L 1s'']]
| | 1\27 &lt; g &lt; 1\26
| | ''1\27 &lt; g &lt; 1\26''
| | g = 53\1404
| | ''g = '''2\53''', 3\79, 4\105-5\131''
| | g = 2\53, 3\79, 4\105
| | ''g-(1-26g) = 27g-1''
| | g+1-26g = 1-25g
|}
|}


=28=
== 28-tone ==
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | <span style="background-color: #ffffff;">Midpoint</span>
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! | Large step+Small step
|-
|-
| | 1L27s
| | [[1L 27s]]
| | 27\28 &lt; g &lt; 1
| | 27\28 &lt; g &lt; 1
| | g = 55\56
| | g = ''28\29, 29\30, 30\31-30\32''
| | ''g = 28\29, 29\30, 30\31''
| | 27g-26-(1-g) = 28g-27
| | 27g-26+1-g = 26g-25
|-
|-
| | 2L26s
| | [[2L 26s]]
| | 13\28 &lt; g &lt; 1\2
| | 13\28 &lt; g &lt; 1\2
| | g = 27\56
| | g = ''14\30, 15\32, 16\34''-17\36
| | ''g = 14\30, 15\32, 16\34''
| | 13g-6-(1\2-g) = 14g-13\2
| | 13g-6+1\2-g = 12g-11\2
|-
|-
| | 3L25s
| | [[3L 25s]]
| | 9\28 &lt; g &lt; 1\3
| | 9\28 &lt; g &lt; 1\3
| | g = 55\168
| | g = ''10\31'', ''11\34'', 12\37-13\40
| | g = ''10\31'',<span style="line-height: 15.6000003814697px;"> ''11\34'',</span> 12\37
| | 25g-8-(1-3g) = 28g-9
| | 25g-8+1-3g = 22g-7
|-
|-
| | 4L24s
| | [[4L 24s]]
| | 6\28 &lt; g &lt; 1\4
| | 6\28 &lt; g &lt; 1\4
| | g = 13\56
| | g = ''7\32'', 8\36, 9\40-10\44
| | g = ''7\32'', 8\36, 9\40
| | 6g-5\4-(1\4-g) = 7g-3\2
| | 6g-5\4+1\4-g = 5g-1
|-
|-
| | 5L23s
| | [[5L 23s]]
| | 11\28 &lt; g &lt; 2\5
| | 11\28 &lt; g &lt; 2\5
| | g = 111\280
| | g = ''13\33'', 15\38, 17\43-19\48
| | g = ''13\33'', 15\38, 17\43
| | 23g-9-(2-5g) = 28g-11
| | 23g-9+2-5g = 18g-7
|-
|-
| | 6L22s
| | [[6L 22s]]
| | 9\28 &lt; g &lt; 2\6
| | 9\28 &lt; g &lt; 2\6
| | g = 55\168
| | g = ''11\34'', 13\40, 15\46-17\52
| | g = ''11\34'', 13\40, 15\46
| | 11g-7\2-(1-3g) = 14g-9\2
| | 11g-7\2+1-3g = 8g-3
|-
|-
| | 7L21s
| | [[7L 21s]]
| | 3\28 &lt; g &lt; 1\7
| | 3\28 &lt; g &lt; 1\7
| | g = 7\56
| | g = 4\35, 5\42, 6\49-7\56
| | g = 4\35, 5\42, 6\49
| | 3g-2\7-(1\7-g) = 4g-3\7
| | 3g-2\7+1\7-g = 2g-1\7
|-
|-
| | 8L20s
| | [[8L 20s]]
| | 3\28 &lt; g &lt; 1\8
| | 3\28 &lt; g &lt; 1\8
| | g = 13\112
| | g = 4\36, 5\44, 6\52-7\60
| | g = 4\36, 5\44, 6\52
| | 5g-1\2-(1\4-2g) = 7g-3\4
| | 5g-1\2+1\4-2g = 3g-1\4
|-
|-
| | 9L19s
| | [[9L 19s]]
| | 3\28 &lt; g &lt; 1\9
| | 3\28 &lt; g &lt; 1\9
| | g = 55\504
| | g = 4\37, 5\46, 6\55-7\64
| | g = 4\37, 5\46, 6\55
| | 19g-2-(1-9g) = 28g-3
| | 19g-2+1-9g = 10g-1
|-
|-
| | 10L18s
| | [[10L 18s]]
| | 11\28 &lt; g &lt; 4\10
| | 11\28 &lt; g &lt; 4\10
| | g = 111\280
| | g = 15\38, 19\48, 23\58-27\68
| | g = 15\38, 19\48, 23\58
| | 9g-7\2-(2-5g) = 14g-11\2
| | 9g-7\2+2-5g = 4g-3\2
|-
|-
| | 11L17s
| | [[11L 17s]]
| | 5\28 &lt; g &lt; 2\11
| | 5\28 &lt; g &lt; 2\11
| | g = 111\616
| | g = 7\39, 9\50, 11\61-13\72
| | g = 7\39, 9\50, 11\61
| | 17g-3-(2-11g) = 28g-5
| | 17g-3+2-11g = 6g-1
|-
|-
| | 12L16s
| | [[12L 16s]]
| | 2\28 &lt; g &lt; 1\12
| | 2\28 &lt; g &lt; 1\12
| | g = 13\168
| | g = '''3\40''', 4\52, 5\64-6\76
| | g = 3\40, 4\52, 5\64
| | 4g-1\4-(1\4-3g) = 7g-1\2
| | 4g-1\4+1\4-3g = g
|-
|-
| | 13L15s
| | [[13L 15s]]
| | 15\28 &lt; g &lt; 7\13
| | 15\28 &lt; g &lt; 7\13
| | g = 391\728
| | g = '''22\41''', 29\54, 36\67-43\80
| | g = 22\41, 29\54, 36\67
| | 15g-8-(7-13g) = 28g-15
| | 15g-8+7-13g = 2g-1
|-
|-
| | 14L14s
| | ''[[14L 14s]] = 1L 1s (14)''
| | 1\28 &lt; g &lt; 1\14
| | ''1\28 &lt; g &lt; 1\14''
| | g = 3\56
| | ''g = '''2\42''', 3\56, 4\70-5\84''
| | g = 2\42, 3\56, 4\70
| | ''g-(1\14-g) = 2g-1\14''
| | g+1\14-g = 1\14
|-
|-
| | <span style="line-height: 15.6000003814697px;">15L13s</span>
| | [[15L 13s]]
| | 13\28 &lt; g &lt; 7\15
| | 13\28 &lt; g &lt; 7\15
| | g = 391\840
| | g = '''20\43''', 27\58, 34\73-41\88
| | g = 20\43, 27\58, 34\73
| | 13g-6-(7-15g) = 28g-13
| | 13g-6+7-15g = 1-2g
|-
|-
| | <span style="line-height: 15.6000003814697px;">16L12s</span>
| | [[16L 12s]]
| | 5\28 &lt; g &lt; 3\16
| | 5\28 &lt; g &lt; 3\16
| | g = 41\224
| | g = '''8\44''', 11\60, 14\76-17\92
| | g = 8\44, 11\60, 14\76
| | 3g-1\2-(3\4-4g) = 7g-7\4
| | 3g-1\2+3\4-4g = 1\4-g
|-
|-
| | <span style="line-height: 15.6000003814697px;">17L11s</span>
| | [[17L 11s]]
| | 23\28 &lt; g &lt; 14\17
| | 23\28 &lt; g &lt; 14\17
| | g = 783\952
| | g = '''37\45''', 51\62, 65\79-79\96
| | g = 37\45, 51\62, 65\79
| | 11g-9-(14-17g) = 28g-23
| | 11g-9+13-17g = 4-6g
|-
|-
| | <span style="line-height: 15.6000003814697px;">18L10s</span>
| | [[18L 10s]]
| | 3\28 &lt; g &lt; 2\18
| | 3\28 &lt; g &lt; 2\18
| | g = 55\504
| | g = '''5\46''', 7\64, 9\82-11\100
| | g = 5\46, 7\64, 9\82
| | 5g-1\2-(1-9g) = 14g-3\2
| | 5g-1\2+1-9g = 1\2-4g
|-
|-
| | <span style="line-height: 15.6000003814697px;">19L9s</span>
| | [[19L 9s]]
| | 25\28 &lt; g &lt; 17\19
| | 25\28 &lt; g &lt; 17\19
| | g = 951\1064
| | g = '''42\47''', 59\66, 76\85-93\104
| | g = 42\47, 59\66, 76\85
| | 9g-8-(17-19g) = 28g-25
| | 9g-8+17-19g = 9-10g
|-
|-
| | <span style="line-height: 15.6000003814697px;">20L</span>8s
| | [[20L 8s]]
| | 4\28 &lt; g &lt; 3\20
| | 4\28 &lt; g &lt; 3\20
| | g = 41\280
| | g = '''7\48''', 10\68, 13\88-16\108
| | g = 7\48, 10\68, 13\88
| | 2g-1\4-(3\4-5g) = 7g-1
| | 2g-1\4+3\4-5g = 1\2-3g
|-
|-
| | <span style="line-height: 15.6000003814697px;">21L7s</span>
| | ''[[21L 7s]] = 3L 1s (7)''
| | 1\28 &lt; g &lt; 1\21
| | ''1\28 &lt; g &lt; 1\21''
| | g = 7\168
| | ''g = '''2\49''', 3\70, 4\91-5\112''
| | g = 2\49, 3\70, 4\91
| | ''g-(1\7-3g) = 4g-1\7''
| | g+<span style="line-height: 15.6000003814697px;">1\7-2g = 1\7-g</span>
|-
|-
| | <span style="line-height: 15.6000003814697px;">22L</span>6s
| | [[22L 6s]]
| | 5\28 &lt; g &lt; 4\22
| | 5\28 &lt; g &lt; 4\22
| | g = 111\616
| | g = '''9\50''', 13\72, 17\94-21\116
| | g = 9\50, 13\72, 17\94
| | 3g-1\2-(2-11g) = 14g-5\2
| | 3g-1\2+2-11g = 3\2-8g
|-
|-
| | <span style="line-height: 15.6000003814697px;">23L</span>5s
| | [[23L 5s]]
| | 17\28 &lt; g &lt; 14\23
| | 17\28 &lt; g &lt; 14\23
| | g = 783\1288
| | g = '''31\51''', 45\74, 59\97-73\120
| | g = 31\51, 45\74, 59\97
| | 5g-3-(14-23g) = 28g-17
| | 5g-3+14-23g = 11-18g
|-
|-
| | <span style="line-height: 15.6000003814697px;">24L</span>4s
| | ''[[24L 4s]] = 6L 1s (4)''
| | 1\28 &lt; g &lt; 1\24
| | ''1\28 &lt; g &lt; 1\24''
| | g = 13\336
| | ''g = '''2\52''', 3\76, 4\100-5\124''
| | g = 2\52, 3\76, 4\100
| | ''g-(1\4-6g) = 7g-1\4''
| | g+1\4-6g = 1\4-5g
|-
|-
| | <span style="line-height: 15.6000003814697px;">25L</span>3s
| | [[25L 3s]]
| | 19\28 &lt; g &lt; 17\25
| | 19\28 &lt; g &lt; 17\25
| | g = 951\1400
| | g = '''36\53''', 53\78, 70\103-87\128
| | g = 36\53, 53\78, 70\103
| | 3g-2-(17-25g) = 28g-19
| | 3g-2+17-25g = 15+22g
|-
|-
| | <span style="line-height: 15.6000003814697px;">26L</span>2s
| | ''[[26L 2s]] = 13L 1s (2)''
| | 15\28 &lt; g &lt; 14\26
| | ''15\28 &lt; g &lt; 14\26''
| | g = 391\728
| | ''g = '''29\54''', 43\80, 57\106-71\132''
| | g = 29\54, 43\80, 57\106
| | ''g-1\2-(7-13g) = 14g-15\2''
| | g-1\2+7-13g = 13\2-12g
|-
|-
| | 27L1s
| | [[27L 1s|''27L 1s'']]
| | 1\28 &lt; g &lt; 1\27
| | ''1\28 &lt; g &lt; 1\27''
| | g = 55\1512
| | ''g = '''2\55''', 3\82, 4\109-5\136''
| | g = 2\55, 3\82, 4\109
| | ''g-(1-27g) = 28g-1''
| | g+1-27g = 1-26g
|}
|}


=29=
== 29-tone ==
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! | Large-small numbers
! | L-s pattern
! | Generator range
! | Generator range
! | <span style="background-color: #ffffff;">Midpoint</span>
! | Boundaries of best, better, good behavior
! | Boundaries of propriety, maximum expressiveness, diatonicity
! | Large step-Small step
! | Large step+Small step
|-
|-
| | 1L28s
| | [[1L 28s]]
| | 28\29 &lt; g &lt; 1
| | 28\29 &lt; g &lt; 1
| | g = 57\58
| | g = ''29\30, 30\31, 31\32-32\33''
| | ''g = 29\30, 30\31, 31\32''
| | 28g-27-(1-g) = 29g-28
| | 28g-27+1-g = 27g-26
|-
|-
| | 2L27s
| | [[2L 27s]]
| | 14\29 &lt; g &lt; 1\2
| | 14\29 &lt; g &lt; 1\2
| | g = 57\116
| | g = ''15\31, 16\33, 17\35''-18\37
| | ''g = 15\31, 16\33, 17\35''
| | 27g-13-(1-2g) = 29g-15
| | 27g-13+1-2g = 25g-12
|-
|-
| | 3L26s
| | [[3L 26s]]
| | 19\29 &lt; g &lt; 2\3
| | 19\29 &lt; g &lt; 2\3
| | g = 115\174
| | g = ''21\32'', ''23\35'', 25\38-27\41
| | g = ''21\32'', ''23\35'', 25\38
| | 26g-17-(2-3g) = 29g-19
| | 26g-17+2-3g = 23g-15
|-
|-
| | 4L25s
| | [[4L 25s]]
| | 7\29 &lt; g &lt; 1\4
| | 7\29 &lt; g &lt; 1\4
| | g = 57\232
| | g = ''8\33'', 9\37, 10\41-11\45
| | g = ''8\33'', 9\37, 10\41
| | 25g-6-(1-4g) = 29g-7
| | 25g-6+1-4g = 21g-5
|-
|-
| | 5L24s
| | [[5L 24s]]
| | 23\29 &lt; g &lt; 4\5
| | 23\29 &lt; g &lt; 4\5
| | g = 231\290
| | g = ''27\34'', 31\39, 35\44-39\49
| | g = ''27\34'', 31\39, 35\44
| | 24g-19-(4-5g) = 29g-23
| | 24g-19+4-5g = 19g-15
|-
|-
| | 6L23s
| | [[6L 23s]]
| | 24\29 &lt; g &lt; 5\6
| | 24\29 &lt; g &lt; 5\6
| | g = 289\348
| | g = ''29\35'', 34\41, 39\47-44\53
| | g = ''29\35'', 34\41, 39\47
| | 23g-19-(5-6g) = 29g-24
| | 23g-19+5-6g = 17g-14
|-
|-
| | 7L22s
| | [[7L 22s]]
| | 4\29 &lt; g &lt; 1\7
| | 4\29 &lt; g &lt; 1\7
| | g = 57\406
| | g = ''5\36'', 6\43, 7\50-8\57
| | g = ''5\36'', 6\43, 7\50
| | 22g-3-(1-7g) = 29g-4
| | 22g-3+1-7g = 15g-2
|-
|-
| | 8L21s
| | [[8L 21s]]
| | 18\29 &lt; g &lt; 5\8
| | 18\29 &lt; g &lt; 5\8
| | g = 289\464
| | g = 23\37, 28\45, 33\53-38\61
| | g = 23\37, 28\45, 33\53
| | 21g-13-(5-8g) = 29g-18
| | <span style="line-height: 15.6000003814697px;">21g-13+5-8g = 13g-8</span>
|-
|-
| | 9L20s
| | [[9L 20s]]
| | 16\29 &lt; g &lt; 5\9
| | 16\29 &lt; g &lt; 5\9
| | g = 289\522
| | g = 21\38, 26\47, 31\56-36\65
| | g = 21\38, 26\47, 31\56
| | 20g-11-(5-9g) = 29g-16
| | 20g-11+5-9g = 11g-6
|-
|-
| | 10L19s
| | [[10L 19s]]
| | 26\29 &lt; g &lt; 9\10
| | 26\29 &lt; g &lt; 9\10
| | g = 521\580
| | g = 35\39, 44\49, 53\59-62\69
| | g = 35\39, 44\49, 53\59
| | 19g-17-(9-10g) = 29g-26
| | 19g-17+9-10g = 9g-8
|-
|-
| | 11L18s
| | [[11L 18s]]
| | 21\29 &lt; g &lt; 8\11
| | 21\29 &lt; g &lt; 8\11
| | g = 463\638
| | g = '''29\40''', 37\51, 45\62-53\73
| | g = 29\40, 37\51, 45\62
| | 18g-13-(8-11g) = 29g-21
| | 18g-13+8-11g = 7g-2
|-
|-
| | 12L17s
| | [[12L 17s]]
| | 12\29 &lt; g &lt; 5\12
| | 12\29 &lt; g &lt; 5\12
| | g = 289\696
| | g = '''17\41''', 22\53, 27\65-32\77
| | g = 17\41, 22\53, 27\65
| | 17g-7-(5-12g) = 29g-12
| | 17g-7+5-12g = 5g-2
|-
|-
| | 13L16s
| | [[13L 16s]]
| | 20\29 &lt; g &lt; 9\13
| | 20\29 &lt; g &lt; 9\13
| | g = 521\754
| | g = '''29\42''', 38\55, 47\68-56\81
| | g = 29\42, 38\55, 47\68
| | 16g+11-(9-13g) = 29g-20
| | 16g+11+9-13g = 3g-2
|-
|-
| | 14L15s
| | [[14L 15s]]
| | 2\29 &lt; g &lt; 1\14
| | 2\29 &lt; g &lt; 1\14
| | g = 57\812
| | g = '''3\43''', 4\57, 5\71-6\85
| | g = 3\43, 4\57, 5\71
| | 15g-1-(1-14g) = 29g-2
| | 15g-1+1-14g = g
|-
|-
| | 15L14s
| | [[15L 14s]]
| | 27\29 &lt; g &lt; 14\15
| | 27\29 &lt; g &lt; 14\15
| | g = 811\870
| | g = '''41\44''', 55\59, 69\74-83\89
| | g = 41\44, 55\59, 69\74
| | 14g-13-(14-15g) = 29g-27
| | 14g-13+14-15g = 1-g
|-
|-
| | 16L13s
| | [[16L 13s]]
| | 9\29 &lt; g &lt; 5\16
| | 9\29 &lt; g &lt; 5\16
| | g = 289\928
| | g = '''14\45''', 19\61, 24\77-29\93
| | g = 14\45, 19\61, 24\77
| | 13g-4-(5-16g) = 29g-9
| | 13g-4+5-16g = 1-3g
|-
|-
| | 17L12s
| | [[17L 12s]]
| | 17\29 &lt; g &lt; 10\17
| | 17\29 &lt; g &lt; 10\17
| | g = 579\986
| | g = '''27\46''', 37\63, 47\80-57\97
| | g = 27\46, 37\63, 47\80
| | 12g-5-(7-17g) = 29g-12
| | 12g-5+7-17g = 2-5g
|-
|-
| | 18L11s
| | [[18L 11s]]
| | 8\29 &lt; g &lt; 5\18
| | 8\29 &lt; g &lt; 5\18
| | g = 289\1044
| | g = '''13\47''', 18\65, 23\83-28\101
| | g = 13\47, 18\65, 23\83
| | 11g-3-(5-18g) = 29g-8
| | 11g-3+5-18g = 2-7g
|-
|-
| | 19L10s
| | [[19L 10s]]
| | 3\29 &lt; g &lt; 2\19
| | 3\29 &lt; g &lt; 2\19
| | g = 115\1102
| | g = '''5\48''', 7\67, 9\86-11\105
| | g = 5\48, 7\67, 9\86
| | 10g-1-(2-19g) = 29g-1
| | 10g-1+2-19g = 1-9g
|-
|-
| | 20L9s
| | [[20L 9s]]
| | 13\29 &lt; g &lt; 9\20
| | 13\29 &lt; g &lt; 9\20
| | g = 521\1160
| | g = '''22\49''', 31\69, 40\89-49\109
| | g = 22\49, 31\69, 40\89
| | 9g-4-(9-20g) = 29g-13
| | 9g-5+9-20g = 4-11g
|-
|-
| | 21L8s
| | [[21L 8s]]
| | 11\29 &lt; g &lt; 8\21
| | 11\29 &lt; g &lt; 8\21
| | g = 463\1216
| | g = '''19\50''', 27\71, 35\92-43\113
| | g = 19\50, 27\71, 35\92
| | 8g-3-(8-21g) = 29g-11
| | 8g-3+8-21g = 5-13g
|-
|-
| | 22L7s
| | [[22L 7s]]
| | 25\29 &lt; g &lt; 19\22
| | 25\29 &lt; g &lt; 19\22
| | g = 1001\1274
| | g = '''44\51''', 63\73, 82\95-101\117
| | g = 44\51, 63\73, 82\95
| | 7g-6-(9-22g) = 29g-15
| | 7g-6+9-22g = 3-16g
|-
|-
| | 23L6s
| | [[23L 6s]]
| | 5\29 &lt; g &lt; 4\23
| | 5\29 &lt; g &lt; 4\23
| | g = 231\1332
| | g = '''9\52''', 13\75, 17\98-21\121
| | g = 9\52, 13\75, 17\98
| | 6g-1-(4-23g) = 29g-5
| | 6g-1+4-23g = 3-17g
|-
|-
| | 24L5s
| | [[24L 5s]]
| | 6\29 &lt; g &lt; 5\24
| | 6\29 &lt; g &lt; 5\24
| | g = 289\1392
| | g = '''11\53''', 16\77, 21\101-26\125
| | g = 11\53, 16\77, 21\101
| | 5g-9-(5-24g) = 29g-14
| | 5g-9+5-24g = 4-19g
|-
|-
| | 25L4s
| | [[25L 4s]]
| | 22\29 &lt; g &lt; 19\25
| | 22\29 &lt; g &lt; 19\25
| | g = 1001\1450
| | g = '''41\54''', 60\79, 79\104-98\129
| | g = 41\54, 60\79, 79\104
| | 4g-3-(19-25g) = 29g-22
| | 4g-3+19-25g = 16-21g
|-
|-
| | 26L3s
| | [[26L 3s]]
| | 10\29 &lt; g &lt; 9\26
| | 10\29 &lt; g &lt; 9\26
| | g = 521\1508
| | g = '''19\55''', 28\81, 37\107-46\133
| | g = 19\55, 28\81, 37\107
| | 3g-1-(9-26g) = 29g-10
| | 3g-1+9-26g = 8-23g
|-
|-
| | 27L2s
| | [[27L 2s]]
| | 15\29 &lt; g &lt; 14\27
| | 15\29 &lt; g &lt; 14\27
| | g = 811\1564
| | g = '''29\56''', 43\83, 57\110-71\137
| | g = 29\56, 43\83, 57\110
| | 2g-1-(17-27g) = 29g-18
| | 2g-1+17-27g = 16-25g
|-
|-
| | 28L1s
| | [[28L 1s|''28L 1s'']]
| | 1\29 &lt; g &lt; 1\28
| | ''1\29 &lt; g &lt; 1\28''
| | g = 57\1622
| | ''g = '''2\57''', 3\85, 4\113-5\141''
| | g = 2\57,<span style="line-height: 15.6000003814697px;"> 3\85,</span> 4\113
| | ''g-(1-28g) = 29g-28''
| | g+1-28g = 1-27g
|}
|}
[[Category:MOS scale]]
[[Category:Lists of scales]]
Retrieved from "https://en.xen.wiki/w/Generator_ranges_of_MOS"