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Generator ranges of MOS: Difference between revisions

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m →8-tone: Denote 2L 6s as consisting of 2 periods.
 
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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 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.
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.


= 2, 3, and 4-tone =
== 2, 3, and 4-tone ==
'''Note 1: These sets are given for the sake of completeness as they are not really scales'''
'''Note 1: These sets are given for the sake of completeness as they are not really scales'''


'''Note 2: monosmall patterns are italicized from here below as the boundary of propriety does apply to them'''
'''Note 2: monosmall patterns are italicized from here below as the boundary of propriety does not apply to them'''


{| class="wikitable"
{| class="wikitable"
Line 13: Line 13:
! | Large step-Small step
! | Large step-Small step
|-
|-
| |[[1L 1s|''1L 1s'']]
| | [[1L 1s|''1L 1s'']]
| | ''1\2 < g < 1''
| | ''1\2 < g < 1''
| | ''g = 2\3, 3\4, 4\5-5\6''
| | ''g = 2\3, 3\4, 4\5-5\6''
| | ''g-(1-g) = 2g-1''
| | ''g-(1-g) = 2g-1''
|-
|-
| |[[1L 2s]]
| | [[1L 2s]]
| | 2\3 < g < 1
| | 2\3 < g < 1
| | g = 3\4, 4\5, 5\6-6\7
| | g = 3\4, 4\5, 5\6-6\7
| | 2g-1-(1-g) = 3g-2
| | 2g-1-(1-g) = 3g-2
|-
|-
| |[[2L 1s|''2L 1s'']]
| | [[2L 1s|''2L 1s'']]
| | ''1\3 < g < 1\2''
| | ''1\3 < g < 1\2''
| | ''g = 2\5, 3\7, 4\9-5\11''
| | ''g = 2\5, 3\7, 4\9-5\11''
| | ''g-(1-2g)= 3g-1''
| | ''g-(1-2g)= 3g-1''
|-
|-
| |[[1L 3s]]
| | [[1L 3s]]
| | 3\4 < g < 1
| | 3\4 < g < 1
| | g = 4\5, 5\6, 6\7-7\8
| | g = 4\5, 5\6, 6\7-7\8
| | 3g-2-(1-g) = 4g-3
| | 3g-2-(1-g) = 4g-3
|-
|-
| |[[2L 2s|''2L 2s'']] ''= 1L 1s (2)''
| | [[2L 2s|''2L 2s'']] ''= 1L 1s (2)''
| | ''1\4 < g < 1\2''
| | ''1\4 < g < 1\2''
| | ''g = 2\6, 3\8, 4\10-5\12''
| | ''g = 2\6, 3\8, 4\10-5\12''
| | ''g-(1\2-g) = 2g-1\2''
| | ''g-(1\2-g) = 2g-1\2''
|-
|-
| |[[3L 1s|''3L 1s'']]
| | [[3L 1s|''3L 1s'']]
| | ''1\4 < g < 1\3''
| | ''1\4 < g < 1\3''
| | ''g = 2\7, 3\10, 4\13-5\16''
| | ''g = 2\7, 3\10, 4\13-5\16''
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|}
|}


= 5-tone =
== 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"
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|}
|}


= 6-tone =
== 6-tone ==
{| class="wikitable"
{| class="wikitable"
|-
|-
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|}
|}


= 7-tone =
== 7-tone ==
{| class="wikitable"
{| class="wikitable"
|-
|-
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|}
|}


= 8-tone =
== 8-tone ==
{| class="wikitable"
{| class="wikitable"
|-
|-
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| | 7g-6-(1-g) = 8g-7
| | 7g-6-(1-g) = 8g-7
|-
|-
| | [[2L 6s]]
| | [[2L 6s|''2L 6s'']] ''= 1L 3s (2)''
| | 3\8 < g < 1\2
| | 3\8 < g < 1\2
| | g = ''4\10'', 5\12, 6\14-7\16
| | g = ''4\10'', 5\12, 6\14-7\16
Line 191: Line 191:
|}
|}


= 9-tone =
== 9-tone ==
{| class="wikitable"
{| class="wikitable"
|-
|-
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|}
|}


= 10-tone =
== 10-tone ==
{| class="wikitable"
{| class="wikitable"
|-
|-
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|}
|}


= 11-tone =
== 11-tone ==
{| class="wikitable"
{| class="wikitable"
|-
|-
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|}
|}


= 12-tone =
== 12-tone ==
{| class="wikitable"
{| class="wikitable"
|-
|-
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|}
|}


= 13-tone =
== 13-tone ==
{| class="wikitable"
{| class="wikitable"
|-
|-
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| | [[4L 9s]]
| | [[4L 9s]]
| | 3\13 < g < 1\4
| | 3\13 < g < 1\4
| | g = 4\17, 5\21, 6\25-7\28
| | g = 4\17, 5\21, 6\25-7\29
| | 9g-2-(1-4g) = 13g-3
| | 9g-2-(1-4g) = 13g-3
|-
|-
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|}
|}


= 14-tone =
== 14-tone ==
{| class="wikitable"
{| class="wikitable"
|-
|-
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|}
|}


= 15-tone =
== 15-tone ==
{| class="wikitable"
{| class="wikitable"
|-
|-
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|}
|}


= 16-tone =
== 16-tone ==
{| class="wikitable"
{| class="wikitable"
|-
|-
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|}
|}


= 17-tone =
== 17-tone ==
{| class="wikitable"
{| class="wikitable"
|-
|-
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|}
|}


= 18-tone =
== 18-tone ==
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 836: Line 836:
|-
|-
| | [[4L 14s]]
| | [[4L 14s]]
| | <span style="line-height: 15.6000003814697px;">4\18 &lt; g &lt; 1\4</span>
| | 4\18 &lt; g &lt; 1\4
| | <span style="line-height: 15.6000003814697px;">g = ''5\22'', 6\26,</span> 7\30-8\34
| | g = ''5\22'', 6\26, 7\30-8\34
| | 7g-3\2-(1\2-2g) = 9g-2
| | 7g-3\2-(1\2-2g) = 9g-2
|-
|-
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| | [[11L 7s]]
| | [[11L 7s]]
| | 13\18 &lt; g &lt; 8\11
| | 13\18 &lt; g &lt; 8\11
| | g = 21\29, 29\40, 37\51-41\62
| | g = 21\29, 29\40, 37\51-45\62
| | 7g-5-(8-11g) = 18g-13
| | 7g-5-(8-11g) = 18g-13
|-
|-
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|}
|}


= 19-tone =
== 19-tone ==
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 912: Line 912:
! | Generator range
! | Generator range
! | Boundaries of best, better, good behavior
! | Boundaries of best, better, good behavior
! |Large step-Small step
! | Large step-Small step
|-
|-
| | [[1L 18s]]
| | [[1L 18s]]
| | 18\19 &lt; g &lt; 1
| | 18\19 &lt; g &lt; 1
| | g = ''19\20, 20\21, 21\22-22\23''
| | g = ''19\20, 20\21, 21\22-22\23''
| |18g-17-(1-g) = 19g-18
| | 18g-17-(1-g) = 19g-18
|-
|-
| | [[2L 17s]]
| | [[2L 17s]]
| | 9\19 &lt; g &lt; 1\2
| | 9\19 &lt; g &lt; 1\2
| | g = ''10\21'', ''11\23'', 12\25-13\27
| | g = ''10\21'', ''11\23'', 12\25-13\27
| |17g-8-(1-2g) = 19g-9
| | 17g-8-(1-2g) = 19g-9
|-
|-
| | [[3L 16s]]
| | [[3L 16s]]
| | 6\19 &lt; g &lt; 1\3
| | 6\19 &lt; g &lt; 1\3
| | g = ''7\22'', 8\25, 9\28-10\31
| | g = ''7\22'', 8\25, 9\28-10\31
| |16g-5-(1-3g) = 19g-6
| | 16g-5-(1-3g) = 19g-6
|-
|-
| | [[4L 15s]]
| | [[4L 15s]]
| | 14\19 &lt; g &lt; 3\4
| | 14\19 &lt; g &lt; 3\4
| | g = ''17\23'', 20\27, 23\31-27\35
| | g = ''17\23'', 20\27, 23\31-27\35
| |15g-11-(3-4g) = 19g-14
| | 15g-11-(3-4g) = 19g-14
|-
|-
| | [[5L 14s]]
| | [[5L 14s]]
| | 15\19 &lt; g &lt; 4\5
| | 15\19 &lt; g &lt; 4\5
| | g = 19\24, 23\29, 27\34-31\39
| | g = 19\24, 23\29, 27\34-31\39
| |14g-11-(4-5g) = 19g-15
| | 14g-11-(4-5g) = 19g-15
|-
|-
| | [[6L 13s]]
| | [[6L 13s]]
| | 3\19 &lt; g &lt; 1\6
| | 3\19 &lt; g &lt; 1\6
| | g = 4\25, 5\31, 6\37-7\43
| | g = 4\25, 5\31, 6\37-7\43
| |13g-2-(1-6g) = 19g-3
| | 13g-2-(1-6g) = 19g-3
|-
|-
| | [[7L 12s]]
| | [[7L 12s]]
| | 8\19 &lt; g &lt; 3\7
| | 8\19 &lt; g &lt; 3\7
| | g = 11\26, 14\33, 17\40-20\47
| | g = 11\26, 14\33, 17\40-20\47
| |12g-5-(3-7g) = 19g-8
| | 12g-5-(3-7g) = 19g-8
|-
|-
| | [[8L 11s]]
| | [[8L 11s]]
| | 7\19 &lt; g &lt; 3\8
| | 7\19 &lt; g &lt; 3\8
| | g = 10\27, 13\35, 16\43-19\51
| | g = 10\27, 13\35, 16\43-19\51
| |11g-4-(3-8g) = 19g-7
| | 11g-4-(3-8g) = 19g-7
|-
|-
| | [[9L 10s]]
| | [[9L 10s]]
| | 2\19 &lt; g &lt; 1\9
| | 2\19 &lt; g &lt; 1\9
| | g = 3\28, 4\37, 5\46-6\55
| | g = 3\28, 4\37, 5\46-6\55
| |10g-1-(1-9g) = 19g-2
| | 10g-1-(1-9g) = 19g-2
|-
|-
| | [[10L 9s]]
| | [[10L 9s]]
| | 17\19 &lt; g &lt; 9\10
| | 17\19 &lt; g &lt; 9\10
| | g = 26\29, 35\39, 44\49-53\59
| | g = 26\29, 35\39, 44\49-53\59
| |9g-8-(9-10g) = 19g-17
| | 9g-8-(9-10g) = 19g-17
|-
|-
| | [[11L 8s]]
| | [[11L 8s]]
| | 12\19 &lt; g &lt; 7\11
| | 12\19 &lt; g &lt; 7\11
| | g = 19\30, 26\41, 33\52-40\63
| | g = 19\30, 26\41, 33\52-40\63
| |8g-5-(7-11g) = 19g-12
| | 8g-5-(7-11g) = 19g-12
|-
|-
| | [[12L 7s]]
| | [[12L 7s]]
| | 11\19 &lt; g &lt; 7\12
| | 11\19 &lt; g &lt; 7\12
| | g = 18\31, 25\43, 32\55-39\67
| | g = 18\31, 25\43, 32\55-39\67
| |7g-4-(7-12g) = 19g-11
| | 7g-4-(7-12g) = 19g-11
|-
|-
| | [[13L 6s]]
| | [[13L 6s]]
| | 16\19 &lt; g &lt; 11\13
| | 16\19 &lt; g &lt; 11\13
| | g = 27\32, 38\45, 49\58-60\71
| | g = 27\32, 38\45, 49\58-60\71
| |6g-5-(11-13g) = 19g-16
| | 6g-5-(11-13g) = 19g-16
|-
|-
| | [[14L 5s]]
| | [[14L 5s]]
| | 4\19 &lt; g &lt; 3\14
| | 4\19 &lt; g &lt; 3\14
| | g = 7\33, 10\47, 13\61-16\75
| | g = 7\33, 10\47, 13\61-16\75
| |5g-1-(3-14g) = 19g-4
| | 5g-1-(3-14g) = 19g-4
|-
|-
| | [[15L 4s]]
| | [[15L 4s]]
| | 5\19 &lt; g &lt; 4\15
| | 5\19 &lt; g &lt; 4\15
| | g = 9\34, 13\49, 17\64-21\79
| | g = 9\34, 13\49, 17\64-21\79
| |4g-1-(4-15g) = 19g-5
| | 4g-1-(4-15g) = 19g-5
|-
|-
| | [[16L 3s]]
| | [[16L 3s]]
| | 13\19 &lt; g &lt; 11\16
| | 13\19 &lt; g &lt; 11\16
| | g = 24\35, 35\51, 46\67-57\83
| | g = 24\35, 35\51, 46\67-57\83
| |3g-2-(11-16g) = 19g-13
| | 3g-2-(11-16g) = 19g-13
|-
|-
| | [[17L 2s]]
| | [[17L 2s]]
| | 10\19 &lt; g &lt; 9\17
| | 10\19 &lt; g &lt; 9\17
| | g = 19\36, 28\53, 37\70-46\87
| | g = 19\36, 28\53, 37\70-46\87
| |2g-1-(9-17g) = 19g-10
| | 2g-1-(9-17g) = 19g-10
|-
|-
| | [[18L 1s|''18L 1s'']]
| | [[18L 1s|''18L 1s'']]
| | ''1\19 &lt; g &lt; 1\18''
| | ''1\19 &lt; g &lt; 1\18''
| | ''g = 2\37, 3\55, 4\73-5\91''
| | ''g = 2\37, 3\55, 4\73-5\91''
| |''g-(1-18g) = 19g-1''
| | ''g-(1-18g) = 19g-1''
|}
|}


= 20-tone =
== 20-tone ==
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 1,015: Line 1,015:
| | [[1L 19s]]
| | [[1L 19s]]
| | 19\20 &lt; g &lt; 1
| | 19\20 &lt; g &lt; 1
| | ''g = 20\21, 21\22, 22\23-23\24''
| | g = ''20\21, 21\22, 22\23-23\24''
| | 19g-18-(1-g) = 20g-19
| | 19g-18-(1-g) = 20g-19
|-
|-
Line 1,080: Line 1,080:
| | [[14L 6s]]
| | [[14L 6s]]
| | 7\20 &lt; g &lt; 5\14
| | 7\20 &lt; g &lt; 5\14
| | g = 12\34, 17\48, 22\62-32\76
| | g = 12\34, 17\48, 22\62-27\76
| | 3g-1-(5\2-7g) = 10g-7\2
| | 3g-1-(5\2-7g) = 10g-7\2
|-
|-
Line 1,109: Line 1,109:
|}
|}


= 21-tone =
== 21-tone ==
'''Note: bolded generators from here below generate scales which are well temperaments'''
'''Note: bolded generators from here below generate scales which are well temperaments'''
{| class="wikitable"
{| class="wikitable"
Line 1,118: Line 1,118:
! | Large step-Small step
! | Large step-Small step
|-
|-
| |[[1L 20s]]
| | [[1L 20s]]
| | 20\21 &lt; g &lt; 1
| | 20\21 &lt; g &lt; 1
| |''g = 21\22, 22\23, 23\24-24\25''
| | g = ''21\22, 22\23, 23\24-24\25''
| | 20g-19-(1-g) = 21g-20
| | 20g-19-(1-g) = 21g-20
|-
|-
| |[[2L 19s]]
| | [[2L 19s]]
| | 10\21 &lt; g &lt; 1\2
| | 10\21 &lt; g &lt; 1\2
| | g = ''11\23, 12\25'', 13\27-13\29
| | g = ''11\23, 12\25'', 13\27-13\29
| | 19g-9-(1-2g) = 21g-10
| | 19g-9-(1-2g) = 21g-10
|-
|-
| |[[3L 18s]]
| | [[3L 18s]]
| | 6\21 &lt; g &lt; 1\3
| | 6\21 &lt; g &lt; 1\3
| | g = ''7\24'', 8\27, 9\30-10\33
| | g = ''7\24'', 8\27, 9\30-10\33
| | 6g-5\3-(1\3-g) = 7g-2
| | 6g-5\3-(1\3-g) = 7g-2
|-
|-
| |[[4L 17s]]
| | [[4L 17s]]
| | 5\21 &lt; g &lt; 1\4
| | 5\21 &lt; g &lt; 1\4
| | g = ''6\25'', 7\29, 8\33-9\37
| | g = ''6\25'', 7\29, 8\33-9\37
| | 17g-4-(1-4g) = 21g-5
| | 17g-4-(1-4g) = 21g-5
|-
|-
| |[[5L 16s]]
| | [[5L 16s]]
| | 4\21 &lt; g &lt; 1\5
| | 4\21 &lt; g &lt; 1\5
| | g = ''5\26'', 6\31, 7\36-8\41
| | g = ''5\26'', 6\31, 7\36-8\41
| | 16g-3-(1-5g) = 21g-4
| | 16g-3-(1-5g) = 21g-4
|-
|-
| |[[6L 15s]]
| | [[6L 15s]]
| | 3\21 &lt; g &lt; 1\6
| | 3\21 &lt; g &lt; 1\6
| | g = 4\27, 5\33, 6\39-7\45
| | g = 4\27, 5\33, 6\39-7\45
| | 5g-2\3-(1\3-2g) = 7g-1
| | 5g-2\3-(1\3-2g) = 7g-1
|-
|-
| |[[7L 14s]]
| | [[7L 14s]]
| | 2\21 &lt; g &lt; 1\7
| | 2\21 &lt; g &lt; 1\7
| | g = 3\28, 4\35, 5\42-6\49
| | g = 3\28, 4\35, 5\42-6\49
| | 2g-1\7-(1\7-g) = 3g-2\7
| | 2g-1\7-(1\7-g) = 3g-2\7
|-
|-
| |[[8L 13s]]
| | [[8L 13s]]
| | 13\21 &lt; g &lt; 5\8
| | 13\21 &lt; g &lt; 5\8
| | g = 18\29, 23\37, 28\45-33\53
| | g = 18\29, 23\37, 28\45-33\53
| | 13g-8-(5-8g) = 21g-13
| | 13g-8-(5-8g) = 21g-13
|-
|-
| |[[9L 12s]]
| | [[9L 12s]]
| | 2\21 &lt; g &lt; 1\9
| | 2\21 &lt; g &lt; 1\9
| | g = 3\30, 4\39, 5\48-6\57
| | g = 3\30, 4\39, 5\48-6\57
| | 4g-1\3-(1\3-3g) = 7g-2\3
| | 4g-1\3-(1\3-3g) = 7g-2\3
|-
|-
| |[[10L 11s]]
| | [[10L 11s]]
| | 2\21 &lt; g &lt; 1\10
| | 2\21 &lt; g &lt; 1\10
| | g = 3\31, 4\41, 5\51-6\61
| | g = 3\31, 4\41, 5\51-6\61
| | 11g-1-(1-10g) = 21g-2
| | 11g-1-(1-10g) = 21g-2
|-
|-
| |[[11L 10s]]
| | [[11L 10s]]
| | 19\21 &lt; g &lt; 10\11
| | 19\21 &lt; g &lt; 10\11
| | g = 29\32, 39\43, 49\54-59\65
| | g = 29\32, 39\43, 49\54-59\65
| | 10g-9-(10-11g) = 21g-19
| | 10g-9-(10-11g) = 21g-19
|-
|-
| |[[12L 9s]]
| | [[12L 9s]]
| | 5\21 &lt; g &lt; 3\12
| | 5\21 &lt; g &lt; 3\12
| | g = 8\33, 11\45, 14\57-17\69
| | g = 8\33, 11\45, 14\57-17\69
| | 3g-2\3-(1-4g) = 7g-1\3
| | 3g-2\3-(1-4g) = 7g-1\3
|-
|-
| |[[13L 8s]]
| | [[13L 8s]]
| | 8\21 &lt; g &lt; 5\13
| | 8\21 &lt; g &lt; 5\13
| | g = 13\34, 18\47, 23\60-28\73
| | g = 13\34, 18\47, 23\60-28\73
| | 8g-3-(5-13g) = 21g-8
| | 8g-3-(5-13g) = 21g-8
|-
|-
| |[[14L 7s|''14L 7s'']] ''= 2L 1s (7)''
| | [[14L 7s|''14L 7s'']] ''= 2L 1s (7)''
| | ''1\21 &lt; g &lt; 1\14''
| | ''1\21 &lt; g &lt; 1\14''
| | ''g = 2\35, 3\49, 4\63-5\77''
| | ''g = 2\35, 3\49, 4\63-5\77''
| | ''g-(1\7-2g) = 3g-1\7''
| | ''g-(1\7-2g) = 3g-1\7''
|-
|-
| |[[15L 6s]]
| | [[15L 6s]]
| | 4\21 &lt; g &lt; 3\15
| | 4\21 &lt; g &lt; 3\15
| | g = 7\36, 10\51, 13\66-16\81
| | g = 7\36, 10\51, 13\66-16\81
| | 2g-1\3-(1-5g) = 7g-4\3
| | 2g-1\3-(1-5g) = 7g-4\3
|-
|-
| |[[16L 5s]]
| | [[16L 5s]]
| | 17\21 &lt; g &lt; 13\16
| | 17\21 &lt; g &lt; 13\16
| | g = 30\37, 43\53, 56\69-69\85
| | g = 30\37, 43\53, 56\69-69\85
| | 5g-4-(13-16g) = 21g-17
| | 5g-4-(13-16g) = 21g-17
|-
|-
| |[[17L 4s]]
| | [[17L 4s]]
| | 16\21 &lt; g &lt; 13\17
| | 16\21 &lt; g &lt; 13\17
| | g = 29\38, 42\55, 55\72-68\89
| | g = 29\38, 42\55, 55\72-68\89
| | 4g-3-(13-17g) = 21g-16
| | 4g-3-(13-17g) = 21g-16
|-
|-
| |[[18L 3s|''18L 3s'']] ''= 6L 1s (3)''
| | [[18L 3s|''18L 3s'']] ''= 6L 1s (3)''
| | ''1\21 &lt; g &lt; 1\18''
| | ''1\21 &lt; g &lt; 1\18''
| | ''g = 2\39, 3\57, 4\75-5\93''
| | ''g = 2\39, 3\57, 4\75-5\93''
| | ''g-(1\3-6g) = 7g-1\3''
| | ''g-(1\3-6g) = 7g-1\3''
|-
|-
| |[[19L 2s]]
| | [[19L 2s]]
| | 11\21 &lt; g &lt; 10\19
| | 11\21 &lt; g &lt; 10\19
| | g = '''21\40''', 31\59, 41\78-51\97
| | g = '''21\40''', 31\59, 41\78-51\97
| | 2g-1-(10-19g) = 21g-11
| | 2g-1-(10-19g) = 21g-11
|-
|-
| |[[20L 1s|''20L 1s'']]
| | [[20L 1s|''20L 1s'']]
| | ''1\21 &lt; g &lt; 1\20''
| | ''1\21 &lt; g &lt; 1\20''
| | ''g = '''2\41''', 3\61, 4\81-5\101''
| | ''g = '''2\41''', 3\61, 4\81-5\101''
Line 1,219: Line 1,219:
|}
|}


= 22-tone =
== 22-tone ==
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 1,225: Line 1,225:
! | Generator range
! | Generator range
! | Boundaries of best, better, good behavior
! | Boundaries of best, better, good behavior
! |Large step-Small step
! | Large step-Small step
|-
|-
| | [[1L 21s]]
| | [[1L 21s]]
| | 21\22 &lt; g &lt; 1
| | 21\22 &lt; g &lt; 1
| | ''g = 22\23, 23\24, 24/25-25\26''
| | g = ''22\23, 23\24, 24/25-25\26''
| |21g-20-(1-g) = 22g-21
| | 21g-20-(1-g) = 22g-21
|-
|-
| | [[2L 20s]]
| | [[2L 20s]]
| | 10\22 &lt; g &lt; 1\2
| | 10\22 &lt; g &lt; 1\2
| | g = ''11\24,'' ''12\26'', 13\28-14\30
| | g = ''11\24,'' ''12\26'', 13\28-14\30
| |10g-9\2-(1\2-g) = 11g-5
| | 10g-9\2-(1\2-g) = 11g-5
|-
|-
| | [[3L 19s]]
| | [[3L 19s]]
| | 7\22 &lt; g &lt; 1\3
| | 7\22 &lt; g &lt; 1\3
| | g = ''8\25'', 9\28, 10\31-11\34
| | g = ''8\25'', 9\28, 10\31-11\34
| |19g-6-(1-3g) = 22g-7
| | 19g-6-(1-3g) = 22g-7
|-
|-
| | [[4L 18s]]
| | [[4L 18s]]
| | 5\22 &lt; g &lt; 1\4
| | 5\22 &lt; g &lt; 1\4
| | g = ''6\26'', 7\30, 8\34-9\38
| | g = ''6\26'', 7\30, 8\34-9\38
| |9g-2-(1\2-2g) = 11g-5\2
| | 9g-2-(1\2-2g) = 11g-5\2
|-
|-
| | [[5L 17s]]
| | [[5L 17s]]
| | 13\22 &lt; g &lt; 3\5
| | 13\22 &lt; g &lt; 3\5
| | g = ''16\27'', 19\32, 22\37-25\42
| | g = ''16\27'', 19\32, 22\37-25\42
| |17g-10-(3-5g) = 22g-13
| | 17g-10-(3-5g) = 22g-13
|-
|-
| | [[6L 16s]]
| | [[6L 16s]]
| | 7\22 &lt; g &lt; 2\6
| | 7\22 &lt; g &lt; 2\6
| | g = 9\28, 11\34, 13\40-15\44
| | g = 9\28, 11\34, 13\40-15\46
| |8g-5\2-(1-3g) = 11g-7\2
| | 8g-5\2-(1-3g) = 11g-7\2
|-
|-
| | [[7L 15s]]
| | [[7L 15s]]
| | 3\22 &lt; g &lt; 1\7
| | 3\22 &lt; g &lt; 1\7
| | g = 4\29, 5\36, 6\43-7\50
| | g = 4\29, 5\36, 6\43-7\50
| |15g-2-(1-7g) = 22g-3
| | 15g-2-(1-7g) = 22g-3
|-
|-
| | [[8L 14s]]
| | [[8L 14s]]
| | 8\22 &lt; g &lt; 3\8
| | 8\22 &lt; g &lt; 3\8
| | g = 11\30, 14\38, 17\46-20\54
| | g = 11\30, 14\38, 17\46-20\54
| |7g-5\2-(3\2-4g) = 11g-4
| | 7g-5\2-(3\2-4g) = 11g-4
|-
|-
| | [[9L 13s]]
| | [[9L 13s]]
| | 17\22 &lt; g &lt; 7\9
| | 17\22 &lt; g &lt; 7\9
| | g = 24\31, 31\40, 38\49-45\58
| | g = 24\31, 31\40, 38\49-45\58
| |13g-10-(7-9g) = 22g-17
| | 13g-10-(7-9g) = 22g-17
|-
|-
| | [[10L 12s]]
| | [[10L 12s]]
| | 2\22 &lt; g &lt; 1\10
| | 2\22 &lt; g &lt; 1\10
| | g = 3\32, 4\42, 5\52-6\62
| | g = 3\32, 4\42, 5\52-6\62
| |6g-1\2-(1\2-5g) = 11g-1
| | 6g-1\2-(1\2-5g) = 11g-1
|-
|-
| | ''[[11L 11s]] = 1L 1s (11)''
| | ''[[11L 11s]] = 1L 1s (11)''
| | ''1\22 &lt; g &lt; 1\11''
| | ''1\22 &lt; g &lt; 1\11''
| | ''g = 2\33, 3\44, 4\55-5\66''
| | ''g = 2\33, 3\44, 4\55-5\66''
| |''g-(1\11-g) = 2g-1\11''
| | ''g-(1\11-g) = 2g-1\11''
|-
|-
| | [[12L 10s]]
| | [[12L 10s]]
| | 9\22 &lt; g &lt; 5\12
| | 9\22 &lt; g &lt; 5\12
| | g = 14\34, 19\46, 24\58-29\70
| | g = 14\34, 19\46, 24\58-29\70
| |5g-2-(5\2-6g) = 11g-7\2
| | 5g-2-(5\2-6g) = 11g-7\2
|-
|-
| | [[13L 9s]]
| | [[13L 9s]]
| | 5\22 &lt; g &lt; 3\13
| | 5\22 &lt; g &lt; 3\13
| | g = 8\35, 11\48, 14\61-17\74
| | g = 8\35, 11\48, 14\61-17\74
| |9g-2-(3-13g) = 22g-5
| | 9g-2-(3-13g) = 22g-5
|-
|-
| | [[14L 8s]]
| | [[14L 8s]]
| | 3\22 &lt; g &lt; 2\14
| | 3\22 &lt; g &lt; 2\14
| | g = 5\36, 7\50, 9\64-11\78
| | g = 5\36, 7\50, 9\64-11\78
| |4g-1\2-(1-7g) = 11g-3\2
| | 4g-1\2-(1-7g) = 11g-3\2
|-
|-
| | [[15L 7s]]
| | [[15L 7s]]
| | 19\22 &lt; g &lt; 13\15
| | 19\22 &lt; g &lt; 13\15
| | g = 32\37, 45\52, 58\67-71\82
| | g = 32\37, 45\52, 58\67-71\82
| |7g-6-(13-15g) = 22g-13
| | 7g-6-(13-15g) = 22g-13
|-
|-
| | [[16L 6s]]
| | [[16L 6s]]
| | 4\22 &lt; g &lt; 3\16
| | 4\22 &lt; g &lt; 3\16
| | g = 7\38, 10\54, 13\70-16\86
| | g = 7\38, 10\54, 13\70-16\86
| |3g-1\2-(3\2-8g) = 11g-2
| | 3g-1\2-(3\2-8g) = 11g-2
|-
|-
| | [[17L 5s]]
| | [[17L 5s]]
| | 9\22 &lt; g &lt; 7\17
| | 9\22 &lt; g &lt; 7\17
| | g = 16\39, 23\56, 30\73-37\90
| | g = 16\39, 23\56, 30\73-37\90
| |5g-2-(7-17g) = 22g-9
| | 5g-2-(7-17g) = 22g-9
|-
|-
| | [[18L 4s]]
| | [[18L 4s]]
| | 6\22 &lt; g &lt; 5\18
| | 6\22 &lt; g &lt; 5\18
| | g = '''11\40''', 16\58, 21\76-26\94
| | g = '''11\40''', 16\58, 21\76-26\94
| |2g-1\2-(5\2-9g) = 11g-3
| | 2g-1\2-(5\2-9g) = 11g-3
|-
|-
| | [[19L 3s]]
| | [[19L 3s]]
| | 15\22 &lt; g &lt; 13\19
| | 15\22 &lt; g &lt; 13\19
| | g = '''28\41''', 41\60, 54\79-67\98
| | g = '''28\41''', 41\60, 54\79-67\98
| |3g-2-(13-19g) = 22g-15
| | 3g-2-(13-19g) = 22g-15
|-
|-
| | ''[[20L 2s]] = 10L 1s (2)''
| | ''[[20L 2s]] = 10L 1s (2)''
| | ''1\22 &lt; g &lt; 1\20''
| | ''1\22 &lt; g &lt; 1\20''
| | ''g = '''2\42''', 3\62, 4\82-5\102''
| | ''g = '''2\42''', 3\62, 4\82-5\102''
| |''g-(1\2-10g) = 11g-1\2''
| | ''g-(1\2-10g) = 11g-1\2''
|-
|-
| | [[21L 1s|''21L 1s'']]
| | [[21L 1s|''21L 1s'']]
| | ''1\22 &lt; g &lt; 1\21''
| | ''1\22 &lt; g &lt; 1\21''
| | ''g = '''2\43''', 3\64, 4\85-5\106''
| | ''g = '''2\43''', 3\64, 4\85-5\106''
| |''g-(1-21g) = 22g-1''
| | ''g-(1-21g) = 22g-1''
|}
|}


= 23-tone =
== 23-tone ==
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 1,343: Line 1,343:
| | [[1L 22s]]
| | [[1L 22s]]
| | 22\23 &lt; g &lt; 1
| | 22\23 &lt; g &lt; 1
| | ''g = 23\24, 24\25, 25\26-26\27''
| | g = ''23\24, 24\25, 25\26-26\27''
| | 22g-21-(1-g) = 23g-22
| | 22g-21-(1-g) = 23g-22
|-
|-
Line 1,368: Line 1,368:
| | [[6L 17s]]
| | [[6L 17s]]
| | 19\23 &lt; g &lt; 5\6
| | 19\23 &lt; g &lt; 5\6
| | g = 24\29, 29\35, 34\41-39\46
| | g = 24\29, 29\35, 34\41-39\47
| | 17g-15-(1-6g) = 23g-16
| | 17g-15-(1-6g) = 23g-16
|-
|-
| | [[7L 16s]]
| | [[7L 16s]]
| | 13\23 &lt; g &lt; 4\7
| | 13\23 &lt; g &lt; 4\7
| | g = 17\30, 21\37, 25\44-29\60
| | g = 17\30, 21\37, 25\44-29\51
| | 16g-9-(4-7g) = 23g-13
| | 16g-9-(4-7g) = 23g-13
|-
|-
Line 1,398: Line 1,398:
| | [[12L 11s]]
| | [[12L 11s]]
| | 21\23 &lt; g &lt; 11\12
| | 21\23 &lt; g &lt; 11\12
| | g = 32\35, 43\47, 54\59-65\73
| | g = 32\35, 43\47, 54\59-65\71
| | 11g-10-(11-12g) = 23g-21
| | 11g-10-(11-12g) = 23g-21
|-
|-
| | [[13L 10s]]
| | [[13L 10s]]
| | 7\23 &lt; g &lt; 4\13
| | 7\23 &lt; g &lt; 4\13
| | g = 11\36, 15\49, 19\62-22\75
| | g = 11\36, 15\49, 19\62-23\75
| | 10g-3-(4-13g) = 23g-7
| | 10g-3-(4-13g) = 23g-7
|-
|-
Line 1,433: Line 1,433:
| | [[19L 4s]]
| | [[19L 4s]]
| | 6\23 &lt; g &lt; 5\19
| | 6\23 &lt; g &lt; 5\19
| | g = '''11\42''', 16\61, 21\80-27\99
| | g = '''11\42''', 16\61, 21\80-26\99
| | 4g-1-(5-19g) = 23g-6
| | 4g-1-(5-19g) = 23g-6
|-
|-
Line 1,452: Line 1,452:
|}
|}


= 24-tone =
== 24-tone ==
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 1,462: Line 1,462:
| | [[1L 23s]]
| | [[1L 23s]]
| | 23\24 &lt; g &lt; 1
| | 23\24 &lt; g &lt; 1
| | ''g = 24\25, 25\26, 26\27''
| | g = ''24\25, 25\26, 26\27-27\28''
| | 23g-22+1-g = 22g-21
| | 23g-22-(1-g) = 24g-23
|-
|-
| | [[2L 22s]]
| | [[2L 22s]]
| | 11\24 &lt; g &lt; 1\2
| | 11\24 &lt; g &lt; 1\2
| | g = ''12\26, 13\28, 14\30''
| | g = ''12\26, 13\28, 14\30''-15\32
| | 11g-5+1/2-g = 10g-9/2
| | 11g-5-(1/2-g) = 12g-11/2
|-
|-
| | [[3L 21s]]
| | [[3L 21s]]
| | 7\24 &lt; g &lt; 1\3
| | 7\24 &lt; g &lt; 1\3
| | g = ''8\27, 9\30'', 10\33
| | g = ''8\27, 9\30'', 10\33-11\36
| | 7g-2+1/3-g = 6g-5/3
| | 7g-2-(1/3-g) = 8g-7/3
|-
|-
| | [[4L 20s]]
| | [[4L 20s]]
| | 5\24 &lt; g &lt; 1\4
| | 5\24 &lt; g &lt; 1\4
| | g = ''6\28'', 7\32, 8\36
| | g = ''6\28'', 7\32, 8\36-9\40
| | 5g-1+1/4-g = 4g-3/4
| | 5g-1-(1/4-g) = 6g-5/4
|-
|-
| | [[5L 19s]]
| | [[5L 19s]]
| | 19\24 &lt; g &lt; 4\5
| | 19\24 &lt; g &lt; 4\5
| | g = ''23\29'', 27\34, 31\39
| | g = ''23\29'', 27\34, 31\39-35\44
| | 19g-15+4-5g = 14g-11
| | 19g-15-(4-5g) = 24g-19
|-
|-
| | [[6L 18s]]
| | [[6L 18s]]
| | 3\24 &lt; g &lt; 1\6
| | 3\24 &lt; g &lt; 1\6
| | g = ''4\30'', 5\36, 6\42
| | g = ''4\30'', 5\36, 6\42-7\48
| | 3g-1\3+1\6-g = 2g-1\6
| | 3g-1\3-(1\6-g) = 4g-1\2
|-
|-
| | [[7L 17s]]
| | [[7L 17s]]
| | 17\24 &lt; g &lt; 5\7
| | 17\24 &lt; g &lt; 5\7
| | g = 22\31, 27\38, 32\45
| | g = 22\31, 27\38, 32\45-37\52
| | 17g-12+5-7g = 10g-7
| | 17g-12-(5-7g) = 24g-17
|-
|-
| | [[8L 16s]]
| | [[8L 16s]]
| | 2\24 &lt; g &lt; 1\8
| | 2\24 &lt; g &lt; 1\8
| | g = 3\32, 4\40, 5\48
| | g = 3\32, 4\40, 5\48-6\56
| | 2g-1\8+1\8-g = g
| | 2g-1\8-(1\8-g) = 3g-1\4
|-
|-
| | [[9L 15s]]
| | [[9L 15s]]
| | 5\24 &lt; g &lt; 2\9
| | 5\24 &lt; g &lt; 2\9
| | g = 7\33, 9\42, 11\51
| | g = 7\33, 9\42, 11\51-13\60
| | 5g-1+2\3-3g = 2g-1\3
| | 5g-1-(2\3-3g) = 8g-5\3
|-
|-
| | [[10L 14s]]
| | [[10L 14s]]
| | 7\24 &lt; g &lt; 3\10
| | 7\24 &lt; g &lt; 3\10
| | g = 10\34, 13\44, 16\54
| | g = 10\34, 13\44, 16\54-19\64
| | 7g-2+3\2-5g = 2g-1\2
| | 7g-2-(3\2-5g) = 12g-7\2
|-
|-
| | [[11L 13s]]
| | [[11L 13s]]
| | 13\24 &lt; g &lt; 6\11
| | 13\24 &lt; g &lt; 6\11
| | g = 19\35, 25\46, 31\57
| | g = 19\35, 25\46, 31\57-37\68
| | 13g-7+6-11g = 2g-1
| | 13g-7-(6-11g) = 24g-12
|-
|-
| | ''[[12L 12s]] = 1L 1s (12)''
| | ''[[12L 12s]] = 1L 1s (12)''
| | ''1\24 &lt; g &lt; 1\12''
| | ''1\24 &lt; g &lt; 1\12''
| | ''g = 2\36, 3\48, 4\60''
| | ''g = 2\36, 3\48, 4\60-5\72''
| | ''g+1\12-g = 1\12''
| | ''g-(1\12-g) = 2g-1\12''
|-
|-
| | [[13L 11s]]
| | [[13L 11s]]
| | 11\24 &lt; g &lt; 6\13
| | 11\24 &lt; g &lt; 6\13
| | g = 17\37, 23\50, 29\63
| | g = 17\37, 23\50, 29\63-35\76
| | 11g-5+6-13g = 1-2g
| | 11g-5-(6-13g) = 24g-11
|-
|-
| | [[14L 10s]]
| | [[14L 10s]]
| | 17\24 &lt; g &lt; 10\14
| | 17\24 &lt; g &lt; 10\14
| | g = 27\38, 37\52, 47\66
| | g = 27\38, 37\52, 47\66-57\80
| | 5g-7\2+5-7g = 3\2-2g
| | 5g-7\2-(5-7g) = 12g-17\2
|-
|-
| | [[15L 9s]]
| | [[15L 9s]]
| | 3\24 &lt; g &lt; 2\15
| | 3\24 &lt; g &lt; 2\15
| | g = 5\39, 7\54, 9\69
| | g = 5\39, 7\54, 9\69-11\84
| | 3g-1\3+2\3-5g = 1\3-2g
| | 3g-1\3-(2\3-5g) = 8g-1
|-
|-
| | ''[[16L 8s]] = 2L 1s (8)''
| | ''[[16L 8s]] = 2L 1s (8)''
| | ''1\24 &lt; g &lt; 1\16''
| | ''1\24 &lt; g &lt; 1\16''
| | ''g = '''2\40''', 3\56, 4\72''
| | ''g = '''2\40''', 3\56, 4\72-5\88''
| | ''g+1\8-2g = 1\8-g''
| | ''g-(1\8-2g) = 3g-1\8''
|-
|-
| | [[17L 7s]]
| | [[17L 7s]]
| | 7\24 &lt; g &lt; 5\17
| | 7\24 &lt; g &lt; 5\17
| | g = '''12\41''', 17\58, 22\75
| | g = '''12\41''', 17\58, 22\75-27\92
| | 7g-2+5-17g = 3-10g
| | 7g-2-(5-17g) = 24g-7
|-
|-
| | ''[[18L 6s]] = 3L 1s (6)''
| | ''[[18L 6s]] = 3L 1s (6)''
| | ''1\24 &lt; g &lt; 1\18''
| | ''1\24 &lt; g &lt; 1\18''
| | ''g = '''2\42''', 3\60, 4\78''
| | ''g = '''2\42''', 3\60, 4\78-5\96''
| | ''g+1\6-3g = 1\6-2g''
| | ''g-(1\6-3g) = 4g-1\6''
|-
|-
| | [[19L 5s]]
| | [[19L 5s]]
| | 5\24 &lt; g &lt; 4\19
| | 5\24 &lt; g &lt; 4\19
| | g = '''9\43''', 13\62, 17\81
| | g = '''9\43''', 13\62, 17\81-21\100
| | 5g-5+4-19g = 1-18g
| | 5g-1-(4-19g) = 24g-5
|-
|-
| | ''[[20L 4s]] = 5L 1s (4)''
| | ''[[20L 4s]] = 5L 1s (4)''
| | ''1\24 &lt; g &lt; 1\20''
| | ''1\24 &lt; g &lt; 1\20''
| | ''g = '''2\44''', 3\64, 4\84''
| | ''g = '''2\44''', 3\64, 4\84-5\104''
| | ''g+1\4-5g = 1\4-4g''
| | ''g-(1\4-5g) = 6g-1\4''
|-
|-
| | ''[[21L 3s]] = 7L 1s (3)''
| | ''[[21L 3s]] = 7L 1s (3)''
| | ''1\24 &lt; g &lt; 1\21''
| | ''1\24 &lt; g &lt; 1\21''
| | ''g = '''2\45''', 3\66, 4\87''
| | ''g = '''2\45''', 3\66, 4\87-5\108''
| | ''g+1\3-7g = 1\3-6g''
| | ''g-(1\3-7g) = 8g-1\3''
|-
|-
| | ''[[22L 2s]] = 11L 1s (2)''
| | ''[[22L 2s]] = 11L 1s (2)''
| | ''1\24 &lt; g &lt; 1\22''
| | ''1\24 &lt; g &lt; 1\22''
| | ''g = '''2\46''', 3\68, 4\90''
| | ''g = '''2\46''', 3\68, 4\90-5\112''
| | ''g+1\2-11g = 1\2-10g''
| | ''g-(1\2-11g) = 12g-1\2''
|-
|-
| | [[23L 1s|''23L 1s'']]
| | [[23L 1s|''23L 1s'']]
| | ''1\24 &lt; g &lt; 1\23''
| | ''1\24 &lt; g &lt; 1\23''
| | ''g = '''2\47''', 3\70, 4\93''
| | ''g = '''2\47''', 3\70, 4\93-5\116''
| | ''g+1-23g = 1-22g''
| | ''g+1-23g = 24g-1''
|}
|}


= 25-tone =
== 25-tone ==
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 1,586: Line 1,586:
| | [[1L 24s]]
| | [[1L 24s]]
| | 24\25 &lt; g &lt; 1
| | 24\25 &lt; g &lt; 1
| | ''g = 25\26, 26\27, 27\28''
| | g = ''25\26, 26\27, 27\28-28\29''
| | 24g-23+1-g = 23g-22
| | 24g-23-(1-g) = 25g-24
|-
|-
| | [[2L 23s]]
| | [[2L 23s]]
| | 12\25 &lt; g &lt; 1\2
| | 12\25 &lt; g &lt; 1\2
| | ''g = 13\27, 14\29, 15\31''
| | g = ''13\27, 14\29, 15\31''-16\33
| | 23g-11+1-2g = 21g-10
| | 23g-11-(1-2g) = 25g-13
|-
|-
| | [[3L 22s]]
| | [[3L 22s]]
| | 8\25 &lt; g &lt; 1\3
| | 8\25 &lt; g &lt; 1\3
| | g = ''9\28'', ''10\31'', 11\34
| | g = ''9\28'', ''10\31'', 11\34-12\37
| | 22g-7+1-3g = 19g-6
| | 22g-7-(1-3g) = 25g-8
|-
|-
| | [[4L 21s]]
| | [[4L 21s]]
| | 6\25 &lt; g &lt; 1\4
| | 6\25 &lt; g &lt; 1\4
| | g = ''7\29'', 8\33, 9\37
| | g = ''7\29'', 8\33, 9\37-10\41
| | 21g-5+1-4g = 17g-4
| | 21g-5-(1-4g) = 25g-6
|-
|-
| | [[5L 20s]]
| | [[5L 20s]]
| | 4\25 &lt; g &lt; 1\5
| | 4\25 &lt; g &lt; 1\5
| | g = ''5\30'', 6\35, 7\40
| | g = ''5\30'', 6\35, 7\40-8\45
| | 4g-3\5+1\5-g = 3g-2\5
| | 4g-3\5-(1\5-g) = 5g-4\5
|-
|-
| | [[6L 19s]]
| | [[6L 19s]]
| | 4\25 &lt; g &lt; 1\6
| | 4\25 &lt; g &lt; 1\6
| | g = ''5\31'', 6\37, 7\43
| | g = ''5\31'', 6\37, 7\43-8\49
| | 19g-3+1-6g = 13g-2
| | 19g-3-(1-6g) = 25g-4
|-
|-
| | [[7L 18s]]
| | [[7L 18s]]
| | 7\25 &lt; g &lt; 2\7
| | 7\25 &lt; g &lt; 2\7
| | g = 9\32, 11\39, 13\46
| | g = 9\32, 11\39, 13\46-15\53
| | 18g-5+2-7g = 11g-3
| | 18g-5-(2-7g) = 25g-7
|-
|-
| | [[8L 17s]]
| | [[8L 17s]]
| | 3\25 &lt; g &lt; 1\8
| | 3\25 &lt; g &lt; 1\8
| | g = 4\33, 5\41, 6\47
| | g = 4\33, 5\41, 6\49-7\57
| | 17g-2+1-8g = 9g-1
| | 17g-2-(1-8g) = 25g-3
|-
|-
| | [[9L 16s]]
| | [[9L 16s]]
| | 11\25 &lt; g &lt; 4\9
| | 11\25 &lt; g &lt; 4\9
| | g = 15\34, 19\43, 23\52
| | g = 15\34, 19\43, 23\52-27\61
| | 16g-7+4-9g = 3-7g
| | 16g-7-(4-9g) = 25g-11
|-
|-
| | [[10L 15s]]
| | [[10L 15s]]
| | 2\25 &lt; g &lt; 1\10
| | 2\25 &lt; g &lt; 1\10
| | g = 3\35, 4\45, 5\55
| | g = 3\35, 4\45, 5\55-6\65
| | 3g-1\5+1\5-2g = g
| | 3g-1\5-(1\5-2g) = 5g-2\5
|-
|-
| | [[11L 14s]]
| | [[11L 14s]]
| | 9\25 &lt; g &lt; 4\11
| | 9\25 &lt; g &lt; 4\11
| | g = 13\36, 17\47, 21\58
| | g = 13\36, 17\47, 21\58-25\69
| | 14g-5+4-11g = 3g-1
| | 14g-5-(4-11g) = 25g-9
|-
|-
| | [[12L 13s]]
| | [[12L 13s]]
| | 2\25 &lt; g &lt; 1\12
| | 2\25 &lt; g &lt; 1\12
| | g = 3\37, 4\49, 5\61
| | g = 3\37, 4\49, 5\61-6\73
| | 13g-1+1-12g = g
| | 13g-1-(1-12g) = 25g-2
|-
|-
| | [[13L 12s]]
| | [[13L 12s]]
| | 23\25 &lt; g &lt; 12\13
| | 23\25 &lt; g &lt; 12\13
| | g = 35\38, 47\51, 59\64
| | g = 35\38, 47\51, 59\64-71\77
| | 12g-11+12-13g = 1-g
| | 12g-11-(12-13g) = 25g-23
|-
|-
| | [[14L 11s]]
| | [[14L 11s]]
| | 16\25 &lt; g &lt; 9\14
| | 16\25 &lt; g &lt; 9\14
| | g = 25\39, 34\53, 43\67
| | g = 25\39, 34\53, 43\67-52\81
| | 11g-7+9-14g = 2-3g
| | 11g-7-(9-14g) = 25g-16
|-
|-
| | [[15L 10s]]
| | [[15L 10s]]
| | 3\25 &lt; g &lt; 2\15
| | 3\25 &lt; g &lt; 2\15
| | g = '''5\40''', 7\55, 9\70
| | g = '''5\40''', 7\55, 9\70-11\85
| | 2g-1\5+2\5-3g = 1\5-g
| | 2g-1\5-(2\5-3g) = 5g-1\5
|-
|-
| | [[16L 9s]]
| | [[16L 9s]]
| | 14\25 &lt; g &lt; 9\16
| | 14\25 &lt; g &lt; 9\16
| | g = '''23\41''', 32\57, 41\73
| | g = '''23\41''', 32\57, 41\73-50\89
| | 9g-5+9-16g = 4-7g
| | 9g-5-(9-16g) = 25g-14
|-
|-
| | [[17L 8s]]
| | [[17L 8s]]
| | 22\25 &lt; g &lt; 15\17
| | 22\25 &lt; g &lt; 15\17
| | g = '''37\42''', 52\59, 67\76
| | g = '''37\42''', 52\59, 67\76-82\93
| | 8g-7+15-17g = 8-9g
| | 8g-7-(15-17g) = 25g-22
|-
|-
| | [[18L 7s]]
| | [[18L 7s]]
| | 18\25 &lt; g &lt; 13\18
| | 18\25 &lt; g &lt; 13\18
| | g = '''31\43''', 44\61, 57\79
| | g = '''31\43''', 44\61, 57\79-80\97
| | 7g-5+13-18g = 8-11g
| | 7g-5-(13-18g) = 25g-18
|-
|-
| | [[19L 6s]]
| | [[19L 6s]]
| | 21\25 &lt; g &lt; 16\19
| | 21\25 &lt; g &lt; 16\19
| | g = '''37\44''', 53\63, 69\82
| | g = '''37\44''', 53\63, 69\82-85\101
| | 6g-5+16-19g = 11-13g
| | 6g-5+16-19g = 25g-21
|-
|-
| | ''[[20L 5s]] = 4L 1s (5)''
| | ''[[20L 5s]] = 4L 1s (5)''
| | ''1\25 &lt; g &lt; 1\20''
| | ''1\25 &lt; g &lt; 1\20''
| | ''g = '''2\45''', 3\65, 4\85''
| | ''g = '''2\45''', 3\65, 4\85-5\105''
| | ''g+1\5-4g = 1\5-3g''
| | ''g-(1\5-4g) = 5g-1\5''
|-
|-
| | [[21L 4s]]
| | [[21L 4s]]
| | 16\21 &lt; g &lt; 19\25
| | 19\25 &lt; g &lt; 16\21
| | g = '''35\46''', 51\67, 71\88
| | g = '''35\46''', 51\67, 67\88-83\109
| | 4g-3+16-21g = 13-17g
| | 4g-3-(16-21g) = 25g-19
|-
|-
| | [[22L 3s]]
| | [[22L 3s]]
| | 17\25 &lt; g &lt; 15\22
| | 17\25 &lt; g &lt; 15\22
| | g = '''32\47''', 47\69, 62\91
| | g = '''32\47''', 47\69, 62\91-77\113
| | 3g-2+15-22g = 13-19g
| | 3g-2-(15-22g) = 25g-17
|-
|-
| | [[23L 2s]]
| | [[23L 2s]]
| | 13\25 &lt; g &lt; 12\23
| | 13\25 &lt; g &lt; 12\23
| | g = '''25\48''', 37\71, 49\94
| | g = '''25\48''', 37\71, 49\94-61\117
| | 2g-1+11-23g = 10-21g
| | 2g-1-(11-23g) = 25g-13
|-
|-
| | [[24L 1s|''24L 1s'']]
| | [[24L 1s|''24L 1s'']]
| | ''1\25 &lt; g &lt; 1\24''
| | ''1\25 &lt; g &lt; 1\24''
| | ''g = '''2\49''', 3\73, 4\97''
| | ''g = '''2\49''', 3\73, 4\97-5\121''
| | ''g+1-24g = 1-23g''
| | ''g-(1-24g) = 25g-1''
|}
|}


= 26-tone =
== 26-tone ==
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 1,715: Line 1,715:
| | [[1L 25s]]
| | [[1L 25s]]
| | 25\26 &lt; g &lt; 1
| | 25\26 &lt; g &lt; 1
| | ''g = 26\27, 27\28, 28\29''
| | g = ''26\27, 27\28, 28\29-29\30''
| | 25g-24+1-g = 24g-23
| | 25g-24-(1-g) = 25g-24
|-
|-
| | [[2L 24s]]
| | [[2L 24s]]
| | 12\26 &lt; g &lt; 1\2
| | 12\26 &lt; g &lt; 1\2
| | ''g = 13\28, 14\30, 15\32''
| | g = ''13\28, 14\30, 15\32''-16\34
| | 12g-11\2+1\2-g = 11g-5
| | 12g-11\2-(1\2-g) = 13g-6
|-
|-
| | [[3L 23s]]
| | [[3L 23s]]
| | 17\26 &lt; g &lt; 2\3
| | 17\26 &lt; g &lt; 2\3
| | g = ''19\29'', ''21\32'', 23\35
| | g = ''19\29'', ''21\32'', 23\35-25\38
| | 23g-15+2-3g = 20g-13
| | 23g-15-(2-3g) = 26g-17
|-
|-
| | [[4L 22s]]
| | [[4L 22s]]
| | 6\26 &lt; g &lt; 1\4
| | 6\26 &lt; g &lt; 1\4
| | g = ''7\30'', 8\34, 9\38
| | g = ''7\30'', 8\34, 9\38-10\42
| | 11g-5\2+1\2-2g = 9g-2
| | 11g-5\2-(1\2-2g) = 13g-3
|-
|-
| | [[5L 21s]]
| | [[5L 21s]]
| | 5\26 &lt; g &lt; 1\5
| | 5\26 &lt; g &lt; 1\5
| | g = ''6\31'', 7\36, 8\41
| | g = ''6\31'', 7\36, 8\41-9\46
| | 21g-4+1-5g = 16g-3
| | 21g-4-(1-5g) = 26g-5
|-
|-
| | [[6L 20s]]
| | [[6L 20s]]
| | 4\26 &lt; g &lt; 1\6
| | 4\26 &lt; g &lt; 1\6
| | g = ''5\32'', 6\38, 7\44
| | g = ''5\32'', 6\38, 7\44-8\50
| | 10g-3\2+1\2-3g = 7g-1
| | 10g-3\2-(1\2-3g) = 13g-2
|-
|-
| | [[7L 19s]]
| | [[7L 19s]]
| | 11\26 &lt; g &lt; 3\7
| | 11\26 &lt; g &lt; 3\7
| | g = 14\33, 17\40, 20\47
| | g = 14\33, 17\40, 20\47-23\54
| | 19g-8+3-7g = 12g-5
| | 19g-8-(3-7g) = 26g-11
|-
|-
| | [[8L 18s]]
| | [[8L 18s]]
| | 3\26 &lt; g &lt; 1\8
| | 3\26 &lt; g &lt; 1\8
| | g = 4\34, 5\42, 6\50
| | g = 4\34, 5\42, 6\50-7\58
| | 9g-1+1\2-4g = 5g-1\2
| | 9g-1-(1\2-4g) = 13g-3\2
|-
|-
| | [[9L 17s]]
| | [[9L 17s]]
| | 23\26 &lt; g &lt; 8\9
| | 23\26 &lt; g &lt; 8\9
| | g = 31\35, 39\44, 47\53
| | g = 31\35, 39\44, 47\53-55\62
| | 17g-15+8-9g = 8g-7
| | 17g-15-(8-9g) = 26g-23
|-
|-
| | [[10L 16s]]
| | [[10L 16s]]
| | 5\26 &lt; g &lt; 2\10
| | 5\26 &lt; g &lt; 2\10
| | g = 7\36, 9\46, 11\56
| | g = 7\36, 9\46, 11\56-13\66
| | 8g-3\2+1-5g = 3g-1\2
| | 8g-3\2-(1-5g) = 13g-5\2
|-
|-
| | [[11L 15s]]
| | [[11L 15s]]
| | 7\26 &lt; g &lt; 3\11
| | 7\26 &lt; g &lt; 3\11
| | g = 10\37, 13\48, 16\59
| | g = 10\37, 13\48, 16\59-19\70
| | 15g-4+3-11g = 4g-1
| | 15g-4-(3-11g) = 26g-7
|-
|-
| | [[12L 14s]]
| | [[12L 14s]]
| | 2\26 &lt; g &lt; 1\12
| | 2\26 &lt; g &lt; 1\12
| | g = 3\38, 4\50, 5\62
| | g = 3\38, 4\50, 5\62-6\74
| | 7g-1\2+1\2-6g = g
| | 7g-1\2-(1\2-6g) = 13g-1
|-
|-
| | ''[[13L 13s]] = 1L 1s (13)''
| | ''[[13L 13s]] = 1L 1s (13)''
| | ''1\26 &lt; g &lt; 1\13''
| | ''1\26 &lt; g &lt; 1\13''
| | ''g = 2\39, 3\52, 4\65''
| | ''g = 2\39, 3\52, 4\65-5\78''
| | ''g+1\13-g = 1\13''
| | ''g-(1\13-g) = 2g-1\13''
|-
|-
| | [[14L 12s]]
| | [[14L 12s]]
| | 11\26 &lt; g &lt; 6\14
| | 11\26 &lt; g &lt; 6\14
| | g = '''17\40''', 23\54, 29\68
| | g = '''17\40''', 23\54, 29\68-35\82
| | 6g-5\2+3-7g = 1\2-g
| | 6g-5\2-(3-7g) = 13g-11\2
|-
|-
| | [[15L 11s]]
| | [[15L 11s]]
| | 19\26 &lt; g &lt; 11\15
| | 19\26 &lt; g &lt; 11\15
| | g = '''30\41''', 41\56, 52\71
| | g = '''30\41''', 41\56, 52\71-63\86
| | 11g-8+11-15g = 3-4g
| | 11g-8-(11-15g) = 26g-19
|-
|-
| | [[16L 10s]]
| | [[16L 10s]]
| | 8\26 &lt; g &lt; 5\16
| | 8\26 &lt; g &lt; 5\16
| | g = '''13\42''', 18\58, 23\74
| | g = '''13\42''', 18\58, 23\74-28\90
| | 5g-3\2+5\2-8g = 1-3g
| | 5g-3\2-(5\2-8g) = 13g-4
|-
|-
| | [[17L 9s]]
| | [[17L 9s]]
| | 3\26 &lt; g &lt; 2\17
| | 3\26 &lt; g &lt; 2\17
| | g = '''5\43''', 7\60, 9\77
| | g = '''5\43''', 7\60, 9\77-11\94
| | 9g-1+2-17g = 1-8g
| | 9g-1-(2-17g) = 26g-3
|-
|-
| | [[18L 8s]]
| | [[18L 8s]]
| | 10\26 &lt; g &lt; 7\18
| | 10\26 &lt; g &lt; 7\18
| | g = '''17\44''', 24\62, 31\80
| | g = '''17\44''', 24\62, 31\80-38\98
| | 4g-7\2+7-9g = 7\2-5g
| | 4g-3\2-(7\2-9g) = 13g-5
|-
|-
| | [[19L 7s]]
| | [[19L 7s]]
| | 15\26 &lt; g &lt; 11\19
| | 15\26 &lt; g &lt; 11\19
| | g = '''26\45''', 37\64, 48\83
| | g = '''26\45''', 37\64, 48\83-59\102
| | 7g-4+11-19g = 7-12g
| | 7g-4-(11-19g) = 26g-15
|-
|-
| | [[20L 6s]]
| | [[20L 6s]]
| | 9\26 &lt; g &lt; 7\20
| | 9\26 &lt; g &lt; 7\20
| | g = '''16\46''', 23\66, 30\86
| | g = '''16\46''', 23\66, 30\86-37\106
| | 3g-1+7\2-10g = 5\2-7g
| | 3g-1-(7\2-10g) = 13g-9\2
|-
|-
| | [[21L 5s]]
| | [[21L 5s]]
| | 21\26 &lt; g &lt; 17\21
| | 21\26 &lt; g &lt; 17\21
| | g = '''38\47''', 55\68, 72\89
| | g = '''38\47''', 55\68, 72\89-89\110
| | 5g-4+16-21g = 12-16g
| | 5g-4-(17-21g) = 26g-21
|-
|-
| | [[22L 4s]]
| | [[22L 4s]]
| | 7\26 &lt; g &lt; 6\22
| | 7\26 &lt; g &lt; 6\22
| | g = '''13\48''', 19\70, 25\92
| | g = '''13\48''', 19\70, 25\92-31\114
| | 2g-1\2+3-11g = 5\2-9g
| | 2g-1\2-(3-11g) = 13g-7\2
|-
|-
| | [[23L 3s]]
| | [[23L 3s]]
| | 9\26 &lt; g &lt; 8\23
| | 9\26 &lt; g &lt; 8\23
| | g = '''17\49''', 25\72, 33/95
| | g = '''17\49''', 25\72, 33\95-41\118
| | 3g-1+8-23g = 7-20g
| | 3g-1-(8-23g) = 26g-9
|-
|-
| | ''[[24L 2s]] = 12L 1s (2)''
| | ''[[24L 2s]] = 12L 1s (2)''
| | ''1\26 &lt; g &lt; 1\24''
| | ''1\26 &lt; g &lt; 1\24''
| | ''g = '''2\50''', 3\74, 4\98''
| | ''g = '''2\50''', 3\74, 4\98-5\122''
| | ''g+1\2-12g = 1\2-11g''
| | ''g-(1\2-12g) = 13g-1\2''
|-
|-
| | [[25L 1s|''25L 1s'']]
| | [[25L 1s|''25L 1s'']]
| | ''1\26 &lt; g &lt; 1\25''
| | ''1\26 &lt; g &lt; 1\25''
| | ''g = '''2\51''', 3\76, 4\101''
| | ''g = '''2\51''', 3\76, 4\101-5\126''
| | ''g+1-25g = 1-24g''
| | ''g-(1-25g) = 26g-1''
|}
|}


= 27-tone =
== 27-tone ==
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 1,849: Line 1,849:
| | [[1L 26s]]
| | [[1L 26s]]
| | 26\27 &lt; g &lt; 1
| | 26\27 &lt; g &lt; 1
| | ''g = 27\28,'' ''28\29, 29\30''
| | g = ''27\28, 28\29, 29\30-30\31''
| | 26g-25+1-g = 25g-24
| | 26g-25-(1-g) = 27g-26
|-
|-
| | [[2L 25s]]
| | [[2L 25s]]
| | 13\27 &lt; g &lt; 1\2
| | 13\27 &lt; g &lt; 1\2
| | ''g = 14\29, 15\31, 16\33''
| | g = ''14\29, 15\31, 16\33''-17\35
| | 25g-12+1-2g = 23g-11
| | 25g-12-(1-2g) = 27g-12
|-
|-
| | [[3L 24s]]
| | [[3L 24s]]
| | 8\27 &lt; g &lt; 1\3
| | 8\27 &lt; g &lt; 1\3
| | g = ''9\30'', ''10\33'', 11\36
| | g = ''9\30'', ''10\33'', 11\36-12\39
| | 8g-7\3+1-3g = 5g-2
| | 8g-7\3-(1\3-3g) = 9g-8\3
|-
|-
| | [[4L 23s]]
| | [[4L 23s]]
| | 20\27 &lt; g &lt; 3\4
| | 20\27 &lt; g &lt; 3\4
| | g = ''23\31'', 26\35, 29\39
| | g = ''23\31'', 26\35, 29\39-32\43
| | 23g-17+3-4g = 19g-14
| | 23g-17-(3-4g) = 19g-14
|-
|-
| | [[5L 22s]]
| | [[5L 22s]]
| | 16\27 &lt; g &lt; 3\5
| | 16\27 &lt; g &lt; 3\5
| | g = ''19\32'', 22\37, 25\42
| | g = ''19\32'', 22\37, 25\42-28\47
| | 22g-13+3-5g = 17g-10
| | 22g-13-(3-5g) = 27g-16
|-
|-
| | [[6L 21s]]
| | [[6L 21s]]
| | 4\27 &lt; g &lt; 1\6
| | 4\27 &lt; g &lt; 1\6
| | g = ''5\33'', 6\39, 7\45
| | g = ''5\33'', 6\39, 7\45-8\51
| | 7g-1+1\3-2g = 5g-2\3
| | 7g-1-(1\3-2g) = 9g-4\3
|-
|-
| | [[7L 20s]]
| | [[7L 20s]]
| | 23\27 &lt; g &lt; 6\7
| | 23\27 &lt; g &lt; 6\7
| | g = 29\34, 35\41, 41\48
| | g = 29\34, 35\41, 41\48-47\55
| | 20g-17+6-7g = 13g-11
| | 20g-17-(6-7g) = 27g-23
|-
|-
| | [[8L 19s]]
| | [[8L 19s]]
| | 10\27 &lt; g &lt; 3\8
| | 10\27 &lt; g &lt; 3\8
| | g = 13\35, 16\43, 19\51
| | g = 13\35, 16\43, 19\51-22\59
| | 19g-7+3-8g = 11g-4
| | 19g-7-(3-8g) = 27g-10
|-
|-
| | [[9L 18s]]
| | [[9L 18s]]
| | 2\27 &lt; g &lt; 1\9
| | 2\27 &lt; g &lt; 1\9
| | g = 3\36, 4\45, 5\54
| | g = 3\36, 4\45, 5\54-6\63
| | 2g-1\9+1\9-g = g
| | 2g-1\9-(1\9-g) = 3g-1\9
|-
|-
| | [[10L 17s]]
| | [[10L 17s]]
| | 8\27 &lt; g &lt; 3\10
| | 8\27 &lt; g &lt; 3\10
| | g = 11\37, 14\47, 17\57
| | g = 11\37, 14\47, 17\57–20\67
| | 17g-5+3-10g = 7g-2
| | 17g-5-(3-10g) = 27g-8
|-
|-
| | [[11L 16s]]
| | [[11L 16s]]
| | 22\27 &lt; g &lt; 9\11
| | 22\27 &lt; g &lt; 9\11
| | g = 31\38, 40\49, 49\60
| | g = 31\38, 40\49, 49\60-58\71
| | 16g-13+9-11g = 5g-4
| | 16g-13-(9-11g) = 27g-22
|-
|-
| | [[12L 15s]]
| | [[12L 15s]]
| | 2\27 &lt; g &lt; 1\12
| | 2\27 &lt; g &lt; 1\12
| | g = 3\39, 4\51, 5\63
| | g = 3\39, 4\51, 5\63-6\75
| | 5g-1\3+1\3-4g = g
| | 5g-1\3-(1\3-4g) = 9g-2\3
|-
|-
| | [[13L 14s]]
| | [[13L 14s]]
| | 2\27 &lt; g &lt; 1\13
| | 2\27 &lt; g &lt; 1\13
| | g = '''3\40''', 4\53, 5\66
| | g = '''3\40''', 4\53, 5\66-6\79
| | 14g-1+1-13g = g
| | 14g-1-(1-13g) = 27g-2
|-
|-
| | [[14L 13s]]
| | [[14L 13s]]
| | 25\27 &lt; g &lt; 13\14
| | 25\27 &lt; g &lt; 13\14
| | g = '''38\41''', 51\55, 64\69
| | g = '''38\41''', 51\55, 64\69-77\83
| | 13g-12+13-14g = 1-g
| | 13g-12-(13-14g) = 27g-25
|-
|-
| | [[15L 12s]]
| | [[15L 12s]]
| | 7\27 &lt; g &lt; 4\15
| | 7\27 &lt; g &lt; 4\15
| | g = '''11\42''', 15\57, 19\72
| | g = '''11\42''', 15\57, 19\72-23\87
| | 4g-1+4\3-5g = 1\3-g
| | 4g-1-(4\3-5g) = 9g-4\3
|-
|-
| | [[16L 11s]]
| | [[16L 11s]]
| | 5\27 &lt; g &lt; 3\16
| | 5\27 &lt; g &lt; 3\16
| | g = '''8\43''', 11\59, 14\75
| | g = '''8\43''', 11\59, 14\75-17\91
| | 11g-2+3-16g = 1-5g
| | 11g-2-(3-16g) = 27g-5
|-
|-
| | [[17L 10s]]
| | [[17L 10s]]
| | 19\27 &lt; g &lt; 12\17
| | 19\27 &lt; g &lt; 12\17
| | g = '''31\44''', 43\61, 55\78
| | g = '''31\44''', 43\61, 55\78-67\95
| | 10g-7+12-17g = 5-7g
| | 10g-7-(12-17g) = 27g-19
|-
|-
| | ''[[18L 9s]] = 2L 1s (9)''
| | ''[[18L 9s]] = 2L 1s (9)''
| | ''1\27 &lt; g &lt; 1\18''
| | ''1\27 &lt; g &lt; 1\18''
| | ''g = '''2\45''', 3\63, 4\81''
| | ''g = '''2\45''', 3\63, 4\81-5\99''
| | ''g+1\9-2g = 1\9-g''
| | ''g-(1\9-2g) = 3g-1\9''
|-
|-
| | [[19L 8s]]
| | [[19L 8s]]
| | 17\27 &lt; g &lt; 12\19
| | 17\27 &lt; g &lt; 12\19
| | g = '''29\46''', 41\65, 53\84
| | g = '''29\46''', 41\65, 53\84-65\103
| | 8g-5+12-19g = 7-11g
| | 8g-5-(12-19g) = 27g-17
|-
|-
| | [[20L 7s]]
| | [[20L 7s]]
| | 4\27 &lt; g &lt; 3\20
| | 4\27 &lt; g &lt; 3\20
| | g = '''7\47''', 10\67, 13\87
| | g = '''7\47''', 10\67, 13\87-16\107
| | 7g-1+3-20g = 2-13g
| | 7g-1-(3-20g) = 27g-4
|-
|-
| | [[21L 6s]]
| | [[21L 6s]]
| | 5\27 &lt; g &lt; 4\21
| | 5\27 &lt; g &lt; 4\21
| | g = '''9\48''', 13\69, 17\90
| | g = '''9\48''', 13\69, 17\90-17\111
| | 2g-1\3+4\3-7g = 1-5g
| | 2g-1\3-(4\3-7g) = 9g-5\3
|-
|-
| | [[22L 5s]]
| | [[22L 5s]]
| | 11\27 &lt; g &lt; 9\22
| | 11\27 &lt; g &lt; 9\22
| | g = '''20\49''', 29\71, 38\93
| | g = '''20\49''', 29\71, 38\93-47\115
| | 5g-2+9-22g = 7-17g
| | 5g-2-(9-22g) = 27g-11
|-
|-
| | [[23L 4s]]
| | [[23L 4s]]
| | 7\27 &lt; g &lt; 6\23
| | 7\27 &lt; g &lt; 6\23
| | g = '''13\50''', 19\73, 25\96
| | g = '''13\50''', 19\73, 25\96-31\119
| | 4g-1+6-23g = 5-19g
| | 4g-1-(6-23g) = 27g-7
|-
|-
| | ''[[24L 3s]] = 8L 1s (3)''
| | ''[[24L 3s]] = 8L 1s (3)''
| | ''1\27 &lt; g &lt; 1\24''
| | ''1\27 &lt; g &lt; 1\24''
| | ''g = '''2\51''', 3\75, 4\99''
| | ''g = '''2\51''', 3\75, 4\99-5\123''
| | ''g+1\3-8g = 1\3-7g''
| | ''g-(1\3-8g) = 9g-1\3''
|-
|-
| | [[25L 2s]]
| | [[25L 2s]]
| | 14\27 &lt; g &lt; 13\25
| | 14\27 &lt; g &lt; 13\25
| | g = '''27\52''', 40\77, 53\102
| | g = '''27\52''', 40\77, 53\102-66\127
| | 2g-1+13-25g = 12-23g
| | 2g-1-(13-25g) = 24g-14
|-
|-
| | [[26L 1s|''26L 1s'']]
| | [[26L 1s|''26L 1s'']]
| | ''1\27 &lt; g &lt; 1\26''
| | ''1\27 &lt; g &lt; 1\26''
| | ''g = '''2\53''', 3\79, 4\105''
| | ''g = '''2\53''', 3\79, 4\105-5\131''
| | ''g+1-26g = 1-25g''
| | ''g-(1-26g) = 27g-1''
|}
|}


= 28-tone =
== 28-tone ==
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 1,988: Line 1,988:
| | [[1L 27s]]
| | [[1L 27s]]
| | 27\28 &lt; g &lt; 1
| | 27\28 &lt; g &lt; 1
| | ''g = 28\29, 29\30, 30\31''
| | g = ''28\29, 29\30, 30\31-30\32''
| | 27g-26+1-g = 26g-25
| | 27g-26-(1-g) = 28g-27
|-
|-
| | [[2L 26s]]
| | [[2L 26s]]
| | 13\28 &lt; g &lt; 1\2
| | 13\28 &lt; g &lt; 1\2
| | ''g = 14\30, 15\32, 16\34''
| | g = ''14\30, 15\32, 16\34''-17\36
| | 13g-6+1\2-g = 12g-11\2
| | 13g-6-(1\2-g) = 14g-13\2
|-
|-
| | [[3L 25s]]
| | [[3L 25s]]
| | 9\28 &lt; g &lt; 1\3
| | 9\28 &lt; g &lt; 1\3
| | g = ''10\31'', ''11\34'', 12\37
| | g = ''10\31'', ''11\34'', 12\37-13\40
| | 25g-8+1-3g = 22g-7
| | 25g-8-(1-3g) = 28g-9
|-
|-
| | [[4L 24s]]
| | [[4L 24s]]
| | 6\28 &lt; g &lt; 1\4
| | 6\28 &lt; g &lt; 1\4
| | g = ''7\32'', 8\36, 9\40
| | g = ''7\32'', 8\36, 9\40-10\44
| | 6g-5\4+1\4-g = 5g-1
| | 6g-5\4-(1\4-g) = 7g-3\2
|-
|-
| | [[5L 23s]]
| | [[5L 23s]]
| | 11\28 &lt; g &lt; 2\5
| | 11\28 &lt; g &lt; 2\5
| | g = ''13\33'', 15\38, 17\43
| | g = ''13\33'', 15\38, 17\43-19\48
| | 23g-9+2-5g = 18g-7
| | 23g-9-(2-5g) = 28g-11
|-
|-
| | [[6L 22s]]
| | [[6L 22s]]
| | 9\28 &lt; g &lt; 2\6
| | 9\28 &lt; g &lt; 2\6
| | g = ''11\34'', 13\40, 15\46
| | g = ''11\34'', 13\40, 15\46-17\52
| | 11g-7\2+1-3g = 8g-3
| | 11g-7\2-(1-3g) = 14g-9\2
|-
|-
| | [[7L 21s]]
| | [[7L 21s]]
| | 3\28 &lt; g &lt; 1\7
| | 3\28 &lt; g &lt; 1\7
| | g = 4\35, 5\42, 6\49
| | g = 4\35, 5\42, 6\49-7\56
| | 3g-2\7+1\7-g = 2g-1\7
| | 3g-2\7-(1\7-g) = 4g-3\7
|-
|-
| | [[8L 20s]]
| | [[8L 20s]]
| | 3\28 &lt; g &lt; 1\8
| | 3\28 &lt; g &lt; 1\8
| | g = 4\36, 5\44, 6\52
| | g = 4\36, 5\44, 6\52-7\60
| | 5g-1\2+1\4-2g = 3g-1\4
| | 5g-1\2-(1\4-2g) = 7g-3\4
|-
|-
| | [[9L 19s]]
| | [[9L 19s]]
| | 3\28 &lt; g &lt; 1\9
| | 3\28 &lt; g &lt; 1\9
| | g = 4\37, 5\46, 6\55
| | g = 4\37, 5\46, 6\55-7\64
| | 19g-2+1-9g = 10g-1
| | 19g-2-(1-9g) = 28g-3
|-
|-
| | [[10L 18s]]
| | [[10L 18s]]
| | 11\28 &lt; g &lt; 4\10
| | 11\28 &lt; g &lt; 4\10
| | g = 15\38, 19\48, 23\58
| | g = 15\38, 19\48, 23\58-27\68
| | 9g-7\2+2-5g = 4g-3\2
| | 9g-7\2-(2-5g) = 14g-11\2
|-
|-
| | [[11L 17s]]
| | [[11L 17s]]
| | 5\28 &lt; g &lt; 2\11
| | 5\28 &lt; g &lt; 2\11
| | g = 7\39, 9\50, 11\61
| | g = 7\39, 9\50, 11\61-13\72
| | 17g-3+2-11g = 6g-1
| | 17g-3-(2-11g) = 28g-5
|-
|-
| | [[12L 16s]]
| | [[12L 16s]]
| | 2\28 &lt; g &lt; 1\12
| | 2\28 &lt; g &lt; 1\12
| | g = '''3\40''', 4\52, 5\64
| | g = '''3\40''', 4\52, 5\64-6\76
| | 4g-1\4+1\4-3g = g
| | 4g-1\4-(1\4-3g) = 7g-1\2
|-
|-
| | [[13L 15s]]
| | [[13L 15s]]
| | 15\28 &lt; g &lt; 7\13
| | 15\28 &lt; g &lt; 7\13
| | g = '''22\41''', 29\54, 36\67
| | g = '''22\41''', 29\54, 36\67-43\80
| | 15g-8+7-13g = 2g-1
| | 15g-8-(7-13g) = 28g-15
|-
|-
| | ''[[14L 14s]] = 1L 1s (14)''
| | ''[[14L 14s]] = 1L 1s (14)''
| | ''1\28 &lt; g &lt; 1\14''
| | ''1\28 &lt; g &lt; 1\14''
| | ''g = '''2\42''', 3\56, 4\70''
| | ''g = '''2\42''', 3\56, 4\70-5\84''
| | ''g+1\14-g = 1\14''
| | ''g-(1\14-g) = 2g-1\14''
|-
|-
| | [[15L 13s]]
| | [[15L 13s]]
| | 13\28 &lt; g &lt; 7\15
| | 13\28 &lt; g &lt; 7\15
| | g = '''20\43''', 27\58, 34\73
| | g = '''20\43''', 27\58, 34\73-41\88
| | 13g-6+7-15g = 1-2g
| | 13g-6-(7-15g) = 28g-13
|-
|-
| | [[16L 12s]]
| | [[16L 12s]]
| | 5\28 &lt; g &lt; 3\16
| | 5\28 &lt; g &lt; 3\16
| | g = '''8\44''', 11\60, 14\76
| | g = '''8\44''', 11\60, 14\76-17\92
| | 3g-1\2+3\4-4g = 1\4-g
| | 3g-1\2-(3\4-4g) = 7g-7\4
|-
|-
| | [[17L 11s]]
| | [[17L 11s]]
| | 23\28 &lt; g &lt; 14\17
| | 23\28 &lt; g &lt; 14\17
| | g = '''37\45''', 51\62, 65\79
| | g = '''37\45''', 51\62, 65\79-79\96
| | 11g-9+13-17g = 4-6g
| | 11g-9-(14-17g) = 28g-23
|-
|-
| | [[18L 10s]]
| | [[18L 10s]]
| | 3\28 &lt; g &lt; 2\18
| | 3\28 &lt; g &lt; 2\18
| | g = '''5\46''', 7\64, 9\82
| | g = '''5\46''', 7\64, 9\82-11\100
| | 5g-1\2+1-9g = 1\2-4g
| | 5g-1\2-(1-9g) = 14g-3\2
|-
|-
| | [[19L 9s]]
| | [[19L 9s]]
| | 25\28 &lt; g &lt; 17\19
| | 25\28 &lt; g &lt; 17\19
| | g = '''42\47''', 59\66, 76\85
| | g = '''42\47''', 59\66, 76\85-93\104
| | 9g-8+17-19g = 9-10g
| | 9g-8-(17-19g) = 28g-25
|-
|-
| | [[20L 8s]]
| | [[20L 8s]]
| | 4\28 &lt; g &lt; 3\20
| | 4\28 &lt; g &lt; 3\20
| | g = '''7\48''', 10\68, 13\88
| | g = '''7\48''', 10\68, 13\88-16\108
| | 2g-1\4+3\4-5g = 1\2-3g
| | 2g-1\4-(3\4-5g) = 7g-1
|-
|-
| | ''[[21L 7s]] = 3L 1s (7)''
| | ''[[21L 7s]] = 3L 1s (7)''
| | ''1\28 &lt; g &lt; 1\21''
| | ''1\28 &lt; g &lt; 1\21''
| | ''g = '''2\49''', 3\70, 4\91''
| | ''g = '''2\49''', 3\70, 4\91-5\112''
| | ''g+1\7-2g = 1\7-g''
| | ''g-(1\7-3g) = 4g-1\7''
|-
|-
| | [[22L 6s]]
| | [[22L 6s]]
| | 5\28 &lt; g &lt; 4\22
| | 5\28 &lt; g &lt; 4\22
| | g = '''9\50''', 13\72, 17\94
| | g = '''9\50''', 13\72, 17\94-21\116
| | 3g-1\2+2-11g = 3\2-8g
| | 3g-1\2-(2-11g) = 14g-5\2
|-
|-
| | [[23L 5s]]
| | [[23L 5s]]
| | 17\28 &lt; g &lt; 14\23
| | 17\28 &lt; g &lt; 14\23
| | g = '''31\51''', 45\74, 59\97
| | g = '''31\51''', 45\74, 59\97-73\120
| | 5g-3+14-23g = 11-18g
| | 5g-3-(14-23g) = 28g-17
|-
|-
| | ''[[24L 4s]] = 6L 1s (4)''
| | ''[[24L 4s]] = 6L 1s (4)''
| | ''1\28 &lt; g &lt; 1\24''
| | ''1\28 &lt; g &lt; 1\24''
| | ''g = '''2\52''', 3\76, 4\100''
| | ''g = '''2\52''', 3\76, 4\100-5\124''
| | ''g+1\4-6g = 1\4-5g''
| | ''g-(1\4-6g) = 7g-1\4''
|-
|-
| | [[25L 3s]]
| | [[25L 3s]]
| | 19\28 &lt; g &lt; 17\25
| | 19\28 &lt; g &lt; 17\25
| | g = '''36\53''', 53\78, 70\103
| | g = '''36\53''', 53\78, 70\103-87\128
| | 3g-2+17-25g = 15+22g
| | 3g-2-(17-25g) = 28g-19
|-
|-
| | ''[[26L 2s]] = 13L 1s (2)''
| | ''[[26L 2s]] = 13L 1s (2)''
| | ''15\28 &lt; g &lt; 14\26''
| | ''15\28 &lt; g &lt; 14\26''
| | ''g = '''29\54''', 43\80, 57\106''
| | ''g = '''29\54''', 43\80, 57\106-71\132''
| | ''g-1\2+7-13g = 13\2-12g''
| | ''g-1\2-(7-13g) = 14g-15\2''
|-
|-
| | [[27L 1s|''27L 1s'']]
| | [[27L 1s|''27L 1s'']]
| | ''1\28 &lt; g &lt; 1\27''
| | ''1\28 &lt; g &lt; 1\27''
| | ''g = '''2\55''', 3\82, 4\109''
| | ''g = '''2\55''', 3\82, 4\109-5\136''
| | ''g+1-27g = 1-26g''
| | ''g-(1-27g) = 28g-1''
|}
|}


= 29-tone =
== 29-tone ==
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 2,132: Line 2,132:
| | [[1L 28s]]
| | [[1L 28s]]
| | 28\29 &lt; g &lt; 1
| | 28\29 &lt; g &lt; 1
| | ''g = 29\30, 30\31, 31\32''
| | g = ''29\30, 30\31, 31\32-32\33''
| | 28g-27+1-g = 27g-26
| | 28g-27-(1-g) = 29g-28
|-
|-
| | [[2L 27s]]
| | [[2L 27s]]
| | 14\29 &lt; g &lt; 1\2
| | 14\29 &lt; g &lt; 1\2
| | ''g = 15\31, 16\33, 17\35''
| | g = ''15\31, 16\33, 17\35''-18\37
| | 27g-13+1-2g = 25g-12
| | 27g-13-(1-2g) = 29g-15
|-
|-
| | [[3L 26s]]
| | [[3L 26s]]
| | 19\29 &lt; g &lt; 2\3
| | 19\29 &lt; g &lt; 2\3
| | g = ''21\32'', ''23\35'', 25\38
| | g = ''21\32'', ''23\35'', 25\38-27\41
| | 26g-17+2-3g = 23g-15
| | 26g-17-(2-3g) = 29g-19
|-
|-
| | [[4L 25s]]
| | [[4L 25s]]
| | 7\29 &lt; g &lt; 1\4
| | 7\29 &lt; g &lt; 1\4
| | g = ''8\33'', 9\37, 10\41
| | g = ''8\33'', 9\37, 10\41-11\45
| | 25g-6+1-4g = 21g-5
| | 25g-6-(1-4g) = 29g-7
|-
|-
| | [[5L 24s]]
| | [[5L 24s]]
| | 23\29 &lt; g &lt; 4\5
| | 23\29 &lt; g &lt; 4\5
| | g = ''27\34'', 31\39, 35\44
| | g = ''27\34'', 31\39, 35\44-39\49
| | 24g-19+4-5g = 19g-15
| | 24g-19-(4-5g) = 29g-23
|-
|-
| | [[6L 23s]]
| | [[6L 23s]]
| | 24\29 &lt; g &lt; 5\6
| | 24\29 &lt; g &lt; 5\6
| | g = ''29\35'', 34\41, 39\47
| | g = ''29\35'', 34\41, 39\47-44\53
| | 23g-19+5-6g = 17g-14
| | 23g-19-(5-6g) = 29g-24
|-
|-
| | [[7L 22s]]
| | [[7L 22s]]
| | 4\29 &lt; g &lt; 1\7
| | 4\29 &lt; g &lt; 1\7
| | g = ''5\36'', 6\43, 7\50
| | g = ''5\36'', 6\43, 7\50-8\57
| | 22g-3+1-7g = 15g-2
| | 22g-3-(1-7g) = 29g-4
|-
|-
| | [[8L 21s]]
| | [[8L 21s]]
| | 18\29 &lt; g &lt; 5\8
| | 18\29 &lt; g &lt; 5\8
| | g = 23\37, 28\45, 33\53
| | g = 23\37, 28\45, 33\53-38\61
| | 21g-13+5-8g = 13g-8
| | 21g-13-(5-8g) = 29g-18
|-
|-
| | [[9L 20s]]
| | [[9L 20s]]
| | 16\29 &lt; g &lt; 5\9
| | 16\29 &lt; g &lt; 5\9
| | g = 21\38, 26\47, 31\56
| | g = 21\38, 26\47, 31\56-36\65
| | 20g-11+5-9g = 11g-6
| | 20g-11-(5-9g) = 29g-16
|-
|-
| | [[10L 19s]]
| | [[10L 19s]]
| | 26\29 &lt; g &lt; 9\10
| | 26\29 &lt; g &lt; 9\10
| | g = 35\39, 44\49, 53\59
| | g = 35\39, 44\49, 53\59-62\69
| | 19g-17+9-10g = 9g-8
| | 19g-17-(9-10g) = 29g-26
|-
|-
| | [[11L 18s]]
| | [[11L 18s]]
| | 21\29 &lt; g &lt; 8\11
| | 21\29 &lt; g &lt; 8\11
| | g = '''29\40''', 37\51, 45\62
| | g = '''29\40''', 37\51, 45\62-53\73
| | 18g-13+8-11g = 7g-2
| | 18g-13-(8-11g) = 29g-21
|-
|-
| | [[12L 17s]]
| | [[12L 17s]]
| | 12\29 &lt; g &lt; 5\12
| | 12\29 &lt; g &lt; 5\12
| | g = '''17\41''', 22\53, 27\65
| | g = '''17\41''', 22\53, 27\65-32\77
| | 17g-7+5-12g = 5g-2
| | 17g-7-(5-12g) = 29g-12
|-
|-
| | [[13L 16s]]
| | [[13L 16s]]
| | 20\29 &lt; g &lt; 9\13
| | 20\29 &lt; g &lt; 9\13
| | g = '''29\42''', 38\55, 47\68
| | g = '''29\42''', 38\55, 47\68-56\81
| | 16g+11+9-13g = 3g-2
| | 16g+11-(9-13g) = 29g-20
|-
|-
| | [[14L 15s]]
| | [[14L 15s]]
| | 2\29 &lt; g &lt; 1\14
| | 2\29 &lt; g &lt; 1\14
| | g = '''3\43''', 4\57, 5\71
| | g = '''3\43''', 4\57, 5\71-6\85
| | 15g-1+1-14g = g
| | 15g-1-(1-14g) = 29g-2
|-
|-
| | [[15L 14s]]
| | [[15L 14s]]
| | 27\29 &lt; g &lt; 14\15
| | 27\29 &lt; g &lt; 14\15
| | g = '''41\44''', 55\59, 69\74
| | g = '''41\44''', 55\59, 69\74-83\89
| | 14g-13+14-15g = 1-g
| | 14g-13-(14-15g) = 29g-27
|-
|-
| | [[16L 13s]]
| | [[16L 13s]]
| | 9\29 &lt; g &lt; 5\16
| | 9\29 &lt; g &lt; 5\16
| | g = '''14\45''', 19\61, 24\77
| | g = '''14\45''', 19\61, 24\77-29\93
| | 13g-4+5-16g = 1-3g
| | 13g-4-(5-16g) = 29g-9
|-
|-
| | [[17L 12s]]
| | [[17L 12s]]
| | 17\29 &lt; g &lt; 10\17
| | 17\29 &lt; g &lt; 10\17
| | g = '''27\46''', 37\63, 47\80
| | g = '''27\46''', 37\63, 47\80-57\97
| | 12g-5+7-17g = 2-5g
| | 12g-5-(7-17g) = 29g-12
|-
|-
| | [[18L 11s]]
| | [[18L 11s]]
| | 8\29 &lt; g &lt; 5\18
| | 8\29 &lt; g &lt; 5\18
| | g = '''13\47''', 18\65, 23\83
| | g = '''13\47''', 18\65, 23\83-28\101
| | 11g-3+5-18g = 2-7g
| | 11g-3-(5-18g) = 29g-8
|-
|-
| | [[19L 10s]]
| | [[19L 10s]]
| | 3\29 &lt; g &lt; 2\19
| | 3\29 &lt; g &lt; 2\19
| | g = '''5\48''', 7\67, 9\86
| | g = '''5\48''', 7\67, 9\86-11\105
| | 10g-1+2-19g = 1-9g
| | 10g-1-(2-19g) = 29g-1
|-
|-
| | [[20L 9s]]
| | [[20L 9s]]
| | 13\29 &lt; g &lt; 9\20
| | 13\29 &lt; g &lt; 9\20
| | g = '''22\49''', 31\69, 40\89
| | g = '''22\49''', 31\69, 40\89-49\109
| | 9g-5+9-20g = 4-11g
| | 9g-4-(9-20g) = 29g-13
|-
|-
| | [[21L 8s]]
| | [[21L 8s]]
| | 11\29 &lt; g &lt; 8\21
| | 11\29 &lt; g &lt; 8\21
| | g = '''19\50''', 27\71, 35\92
| | g = '''19\50''', 27\71, 35\92-43\113
| | 8g-3+8-21g = 5-13g
| | 8g-3-(8-21g) = 29g-11
|-
|-
| | [[22L 7s]]
| | [[22L 7s]]
| | 25\29 &lt; g &lt; 19\22
| | 25\29 &lt; g &lt; 19\22
| | g = '''44\51''', 63\73, 82\95
| | g = '''44\51''', 63\73, 82\95-101\117
| | 7g-6+9-22g = 3-16g
| | 7g-6-(9-22g) = 29g-15
|-
|-
| | [[23L 6s]]
| | [[23L 6s]]
| | 5\29 &lt; g &lt; 4\23
| | 5\29 &lt; g &lt; 4\23
| | g = '''9\52''', 13\75, 17\98
| | g = '''9\52''', 13\75, 17\98-21\121
| | 6g-1+4-23g = 3-17g
| | 6g-1-(4-23g) = 29g-5
|-
|-
| | [[24L 5s]]
| | [[24L 5s]]
| | 6\29 &lt; g &lt; 5\24
| | 6\29 &lt; g &lt; 5\24
| | g = '''11\53''', 16\77, 21\101
| | g = '''11\53''', 16\77, 21\101-26\125
| | 5g-9+5-24g = 4-19g
| | 5g-9-(5-24g) = 29g-14
|-
|-
| | [[25L 4s]]
| | [[25L 4s]]
| | 22\29 &lt; g &lt; 19\25
| | 22\29 &lt; g &lt; 19\25
| | g = '''41\54''', 60\79, 79\104
| | g = '''41\54''', 60\79, 79\104-98\129
| | 4g-3+19-25g = 16-21g
| | 4g-3-(19-25g) = 29g-22
|-
|-
| | [[26L 3s]]
| | [[26L 3s]]
| | 10\29 &lt; g &lt; 9\26
| | 10\29 &lt; g &lt; 9\26
| | g = '''19\55''', 28\81, 37\107
| | g = '''19\55''', 28\81, 37\107-46\133
| | 3g-1+9-26g = 8-23g
| | 3g-1-(9-26g) = 29g-10
|-
|-
| | [[27L 2s]]
| | [[27L 2s]]
| | 15\29 &lt; g &lt; 14\27
| | 15\29 &lt; g &lt; 14\27
| | g = '''29\56''', 43\83, 57\110
| | g = '''29\56''', 43\83, 57\110-71\137
| | 2g-1+17-27g = 16-25g
| | 2g-1-(17-27g) = 29g-18
|-
|-
| | [[28L 1s|''28L 1s'']]
| | [[28L 1s|''28L 1s'']]
| | ''1\29 &lt; g &lt; 1\28''
| | ''1\29 &lt; g &lt; 1\28''
| | ''g = '''2\57''', 3\85, 4\113''
| | ''g = '''2\57''', 3\85, 4\113-5\141''
| | ''g+1-28g = 1-27g''
| | ''g-(1-28g) = 29g-28''
|}
|}


[[Category:MOS scale]]
[[Category:MOS scale]]
[[Category:Lists of scales]]
[[Category:Lists of scales]]
Retrieved from "https://en.xen.wiki/w/Generator_ranges_of_MOS"