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The generator range is 171.4 to 240 cents, placing it near the [[9/8|diatonic major second]], usually representing a major second of some type. The dark (chroma-negative) generator is, however, its fourth complement (240 to 342.9 cents).  
The generator range is 171.4 to 240 cents, placing it near the [[9/8|diatonic major second]], usually representing a major second of some type. The dark (chroma-negative) generator is, however, its fourth complement (240 to 342.9 cents).  


In the fourth-repeating version of the diatonic scale, each tone has a 4/3 perfect fourth above it. The scale has one major chord and two minor chords.  
In the fourth-repeating version of the diatonic scale, each tone has a perfect fourth above it. The scale has one major chord and two minor chords.  


[[Basic]] diatonic is in [[5ed4/3]], which is a very good fourth-based equal tuning similar to [[12edo]].
[[Basic]] diatonic is in [[5ed4/3]], which is a very good fourth-based equal tuning similar to [[12edo]].
==Notation==
==Notation==
There are 6 main ways to notate this scale. One method uses a simple fourth repeating notation consisting of 3 naturals (eg. Do Re Mi, Sol La Si). Given that 1-5/4-3/2 is fourth-equivalent to a tone cluster of 1-9/8-5/4, it may be more convenient to notate diatonic scales as repeating at the double, triple, quadruple, quintuple or sextuple fourth (minor seventh, tenth, thirteenth or sixteenth or diminished nineteenth), however it does make navigating the [[Generator|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 9/8. Notating this way produces a minor tenth which is the Dorian mode of Middletown[6L 3s], also known as the Mahur scale in Persian/Arabic music, a minor thirteenth which is the Aeolian mode of Bijou[8L 4s]; the bastonic chromatic scale, a minor sixteenth which is the Phrygian mode of Hyperionic[10L 5s] or a diminished nineteenth which is the Locrian mode of Subsextal[12L 6s]. Since there are exactly 9 naturals in triple fourth notation, 12 in quadruple fourth, 15 in quintuple fourth and 18 in sextuple fourth notation, letters A-G plus J, Q or Q, S (GJABCQDEF or GABCQDSEF, flats written F molle) or dozenal, hex or duohex digits (0123456789XE0 or E1234567GABDE with flats written D molle or 123456789ABCDEF1 or 0123456789XɜABCDEF0 with flats written F molle) may be used.
There are 6 main ways to notate this scale. One method uses a simple fourth repeating notation consisting of 3 naturals (eg. Do Re Mi, Sol La Si). Given that 1-5/4-3/2 is fourth-equivalent to a tone cluster of 1-9/8-5/4 and a fourth has too few notes for a structure analogous to the major scale, it may be more convenient to notate diatonic scales as repeating at the double, triple, quadruple, quintuple or sextuple fourth (minor seventh, tenth, thirteenth or sixteenth or diminished nineteenth), however it does make navigating the [[Generator|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 9/8. Notating this way produces a minor tenth which is the Dorian mode of Middletown[6L 3s], also known as the Mahur scale in Persian/Arabic music, a minor thirteenth which is the Aeolian mode of Bijou[8L 4s]; the bastonic chromatic scale, a minor sixteenth which is the Phrygian mode of Hyperionic[10L 5s] or a diminished nineteenth which is the Locrian mode of Subsextal[12L 6s]. Since there are exactly 9 naturals in triple fourth notation, 12 in quadruple fourth, 15 in quintuple fourth and 18 in sextuple fourth notation, letters A-G plus J, Q or Q, S (GJABCQDEF or GABCQDSEF, flats written F molle) or dozenal, hex or duohex digits (0123456789XE0 or E1234567GABDE with flats written D molle or 123456789ABCDEF1 or 0123456789XɜABCDEF0 with flats written F molle) may be used.
{| class="wikitable"
{| class="wikitable"
|+Cents
|+Cents
! colspan="3" |Notation
!Notation
!Supersoft
!Supersoft
!Soft
!Soft
Line 20: Line 20:
|-
|-
!Fourth
!Fourth
! colspan="2" |Seventh
!~11ed4/3
!~11ed4/3
!~8ed4/3
!~8ed4/3
Line 29: Line 28:
!~9ed4/3
!~9ed4/3
|-
|-
!
|F/C/G ut#
!Mixolydian
Do#, Sol#
!Dorian
 
!
د#,
!
 
!
ص#
!
!
!
!
|-
|Do#, Sol#
|Sol#
|Re#
|1\11, 46.154
|1\11, 46.154
|1\8, 63.158
|1\8, 63.158
Line 51: Line 42:
|3\9, 163.636
|3\9, 163.636
|-
|-
| Reb, Lab
| G/D/A reb
|Lab
Reb, Lab
|Mib
 
رb, لb
|3\11, 138.462
|3\11, 138.462
|2\8, 126.316
|2\8, 126.316
Line 61: Line 53:
|1\9, 54.545
|1\9, 54.545
|-
|-
|'''Re, La'''
|'''G/D/A re'''
|'''La'''
'''Re, La'''
|'''Mi'''
 
'''ر, ل'''
|'''4\11,''' '''184.615'''
|'''4\11,''' '''184.615'''
|'''3\8,''' '''189.474'''
|'''3\8,''' '''189.474'''
Line 72: Line 65:
|'''4\9,''' '''218.182'''
|'''4\9,''' '''218.182'''
|-
|-
|Re#, La#
|G/D/A re#
|La#
Re#, La#
|Mi#
 
ر,# ل#
|5\11, 230.769
|5\11, 230.769
|4\8, 252.632
| rowspan="2" |4\8, 252.632
|7\13, 270.967
|7\13, 270.967
| rowspan="2" |'''3\5,''' '''300'''
|3\5, 300
| 8\12, 331.034
| 8\12, 331.034
|5\7, 352.941
|5\7, 352.941
|7\9, 381.818
|7\9, 381.818
|-
|-
|'''Mib, Sib'''
|A/E/B mibb
|'''Sib'''
Mibb, Sibb
|'''Fa'''
 
مbb,تbb
|6\11, 276.923
|6\13, 232.258
|2\5, 200
|4\12, 165.517
|2\7, 141.176
|2\9, 109.091
|-
|'''A/E/B mib'''  
'''Mib, Sib'''
 
'''مb,تb'''
|'''7\11,''' '''323.077'''
|'''7\11,''' '''323.077'''
|'''5\8,''' '''315.789'''
|'''5\8,''' '''315.789'''
|'''8\13,''' '''309.677'''
|'''8\13,''' '''309.677'''
|'''3\5,''' '''300'''
|'''7\12,''' '''289.655'''
|'''7\12,''' '''289.655'''
|'''4\7,''' '''282.353'''
|'''4\7,''' '''282.353'''
|'''5\9,''' '''272.727'''
|'''5\9,''' '''272.727'''
|-
|-
|Mi, Si
|A/E/B mi
| Si
Mi, Si
|Fa#
 
م, ت
|8\11, 369.231
|8\11, 369.231
|6\8, 378.947
|6\8, 378.947
Line 104: Line 112:
|8\9, 436.364
|8\9, 436.364
|-
|-
|Mi#, Si#
|A/E/B mi#
|Si#
Mi#, Si#
|Fax
 
م,#ت#
|9\11, 415.385
|9\11, 415.385
| rowspan="2" |7\8, 442.105
| rowspan="2" |7\8, 442.105
Line 115: Line 124:
|11\9, 600
|11\9, 600
|-
|-
|Dob, Solb
|F/C/G utb
| Dob
Dob, Solb
|Solb
 
دb,
 
صb
|10\11, 461.538
|10\11, 461.538
|11\13, 425.806
|11\13, 425.806
Line 125: Line 137:
|6\9, 327.273
|6\9, 327.273
|-
|-
!Do, Sol
!F/C/G ut
!Do
Do, Sol
!Sol
 
د, ص
!'''11\11,''' '''507.692'''
!'''11\11,''' '''507.692'''
!'''8\8,''' '''505.263'''
!'''8\8,''' '''505.263'''
Line 135: Line 148:
!'''7\7,''' '''494.118'''
!'''7\7,''' '''494.118'''
!'''9\9,''' '''490.909'''
!'''9\9,''' '''490.909'''
|}
{| class="wikitable"
|+Cents
! colspan="2" |Notation
!Supersoft
!Soft
!Semisoft
!Basic
!Semihard
!Hard
!Superhard
|-
|-
|Do#, Sol#
! colspan="2" |Seventh
|Do#
!~11ed4/3
|Sol#
!~8ed4/3
|12\11, 553.846
!~13ed4/3
|9\8, 568.421
!~5ed4/3
|15\13, 580.645
!~12ed4/3
| rowspan="2" |6\5, 600
!~7ed4\3
|15\12, 620.690
!~9ed4/3
|9\7, 635.294
|12\9, 654.545
|-
|-
|Reb, Lab
!Mixolydian
|Reb
!Dorian
|Lab
!
|14\11, 646.154
!
|10\8, 631.579
!
|16\13, 619.355
!
|14\12, 579.310
!
|8\7, 564.706
!
|10\9, 545.455
!
|-
|-
|'''Re, La'''
| F/C/G ut#
|'''Re'''
Sol#
|'''La'''
 
|'''15\11,''' '''692.308'''
ص#
|'''11\8'''  '''694.737'''
|G/D/A re#
|'''18\13,''' '''696.774'''
Re#
|'''7\5,''' '''700'''
 
|'''17\12,''' '''703.448'''
ر#
|'''10\7,''' '''705.882'''
|1\11, 46.154
|'''13\9,''' '''709.091'''
|1\8, 63.158
|2\13, 77.419
| rowspan="2" |1\5, 100
| 3\12, 124.138
|2\7, 141.176
|3\9, 163.636
|-
|-
|Re#, La#
|G/D/A reb
|Re#
Lab
|La#
 
|16\11, 738.462
لb
|12\8, 757.895
|A/E/B mib
|20\13, 774.294
Mib
| rowspan="2" |'''8\5,''' '''800'''
 
|20\12, 827.586
مb
|12\7, 847.059
|3\11, 138.462
|16\9, 872.727
|2\8, 126.316
|3\13, 116.129
|2\12, 82.759
|1\7, 70.588
|1\9, 54.545
|-
|-
|'''Mib, Sib'''
|'''G/D/A re'''
|'''Mib'''
'''La'''
|'''Sib'''
 
|'''18\11,''' '''830.769'''
ل
|'''13\8,''' '''821.053'''
|'''A/E/B mi'''
|'''21\13,''' '''812.903'''
'''Mi'''
|'''19\12,''' '''786.207'''
 
|'''11\7,''' '''776.471'''
م
|'''14\9,''' '''763.636'''
|'''4\11,''' '''184.615'''
|'''3\8,''' '''189.474'''
|'''5\13,''' '''193.548'''
|'''2\5,''' '''200'''
|'''5\12,''' '''206.897'''
|'''3\7,''' '''211.765'''
|'''4\9,''' '''218.182'''
|-
|-
|Mi, Si
|G/D/A re#
|Mi
La#
|Si
 
|19\11, 876.923
ل#
|14\8, 884.211
| A/E/B mi#
|23\13, 890.323
Mi#
|9\5, 900
 
|22\12, 910.345
م#
|13\7, 917.647
|5\11, 230.769
|17\9, 927.727
| rowspan="2" |4\8, 252.632
| 7\13, 270.967
|3\5, 300
|8\12, 331.034
|5\7, 352.941
|7\9, 381.818
|-
|-
|Mi#, Si#
|A/E/B mibb
| Mi#
Sibb
|Si#
 
|20\11, 923.077
تbb
| rowspan="2" |15\8, 947.378
|B/F/C fab
|25\13, 967.742
Fab
|10\5, 1000
 
|25\12, 1034.483
فb
|15\7, 1058.824
|6\11, 276.923
|20\9, 1090.909
|6\13, 232.258
|2\5, 200
|4\12, 165.517
|2\7, 141.176
|2\9, 109.091
|-
|-
|Dob, Solb
|'''A/E/B mib'''
|Solb
'''Sib'''
|Reb
 
|21\11, 969.231
تb
|24\13, 929.033
|'''B/F/C fa'''
|9\5, 900
'''Fa'''
|21\12, 868.966
 
|11\7, 776.471
'''ف'''
|15\9, 818.182
|'''7\11,''' '''323.077'''
|'''5\8,''' '''315.789'''
|'''8\13,''' '''309.677'''
|'''3\5,''' '''300'''
|'''7\12,''' '''289.655'''
|'''4\7,''' '''282.353'''
|'''5\9,''' '''272.727'''
|-
|-
!Do, Sol
|A/E/B mi
!Sol
Si
!Re
 
!22\11, 1015.385
ت
!16\8, 1010.526
|B/F/C fa#
!26\13, 1006.452
Fa#
!10\5, 1000
 
!24\12, 993.103
ف#
!14\7, 988.235
| 8\11, 369.231
!18\9, 981.818
|6\8, 378.947
|}
|10\13, 387.097
{| class="wikitable"
|4\5, 400
! colspan="2" |Notation
|10\12, 413.793
!Supersoft
|6\7, 423.529
!Soft
|8\9, 436.364
!Semisoft
!Basic
!Semihard
!Hard
!Superhard
|-
|-
!Mahur
|A/E/B mi#
!Bijou
Si#
!~11ed4/3
 
! ~8ed4/3
ت#
!~13ed4/3
|B/F/C fax
!~5ed4/3
Fax
!~12ed4/3
 
!~7ed4\3
فx
!~9ed4/3
|9\11, 415.385
| rowspan="2" |7\8, 442.105
|12\13, 464.516
|5\5, 500
|13\12, 537.069
|8\7, 564.705
|11\9, 600
|-
|-
|G#
| B/F/C fab
|0#, E#
Dob
|1\11, 46.154
 
|1\8, 63.158
دb
|2\13, 77.419
|C/G/D solb
| rowspan="2" |1\5, 100
Solb
|3\12, 124.138
 
|2\7, 141.176
صb
|3\9, 163.636
|10\11, 461.538
|11\13, 425.806
|4\5, 400
|9\12, 372.414
|5\7, 352.941
|6\9, 327.273
|-
|-
|Jf, Af
!B/F/C fa
|1b, 1d
Do
|3\11, 138.462
 
|2\8, 126.316
د
| 3\13, 116.129
!C/G/D sol
|2\12, 82.759
Sol
|1\7, 70.588
 
|1\9, 54.545
ص
!'''11\11,''' '''507.692'''
!'''8\8,''' '''505.263'''
!'''13\13,''' '''503.226'''
!5\5, 500
!'''12\12,''' '''496.552'''
!'''7\7,''' '''494.118'''
!'''9\9,''' '''490.909'''
|-
|-
|'''J, A'''
|B/F/C fa#
|'''1'''
Do#
|'''4\11,''' '''184.615'''
 
|'''3\8,''' '''189.474'''
د#
|'''5\13,''' '''193.548'''
| C/G/D sol#
|'''2\5,''' '''200'''
Sol#
|'''5\12,''' '''206.897'''
 
|'''3\7,''' '''211.765'''
ص#
|'''4\9,''' '''218.182'''
|12\11, 553.846
|9\8, 568.421
|15\13, 580.645
| rowspan="2" |6\5, 600
|15\12, 620.690
|9\7, 635.294
|12\9, 654.545
|-
|-
|J#, A#
|C/G/D solb
|1#
Reb
|5\11, 230.769
 
|4\8, 252.632
رb
|7\13, 270.968
|D/A/E lab
| rowspan="2" |'''3\5,''' '''300'''
Lab
|8\12, 331.034
 
|5\7, 352.941
لb
|7\9, 381.818
|14\11, 646.154
|10\8, 631.579
|16\13, 619.355
|14\12, 579.310
|8\7, 564.706
|10\9, 545.455
|-
|-
|'''Af, Bf'''
|'''C/G/D sol'''
|'''2b, 2d'''
'''Re'''
|'''7\11,''' '''323.077'''
 
|'''5\8,''' '''315.789'''
ر
|'''8\13,''' '''309.677'''
|'''D/A/E la'''
|'''7\12,''' '''289.655'''
'''La'''
|'''4\7,''' '''282.353'''
 
|'''5\9,''' '''272.727'''
ل
|'''15\11,''' '''692.308'''
|'''11\8''' '''694.737'''
|'''18\13,''' '''696.774'''
|'''7\5,''' '''700'''
|'''17\12,''' '''703.448'''
|'''10\7,''' '''705.882'''
|'''13\9,''' '''709.091'''
|-
|-
|A, B
|C/G/D sol#
|2
Re#
|8\11, 369.231
 
|6\8, 378.947
د#
|10\13, 387.097
|D/A/E la#
|4\5, 400
La#
|10\12, 413.793
 
|6\7, 423.529
ل#
|8\9, 436.364
|16\11, 738.462
|12\8, 757.895
|20\13, 774.294
| rowspan="2" |'''8\5,''' '''800'''
|20\12, 827.586
|12\7, 847.059
|16\9, 872.727
|-
|-
|A#, B#
|'''D/A/E lab'''
|2#
'''Mib'''
|9\11, 415.385
 
| rowspan="2" |7\8, 442.105
مb
|12\13, 464.516
|'''E/B/F síb'''
|5\5, 500
'''Sib'''
|13\12, 537.069
 
|8\7, 564.705
تb
|11\9, 600
|'''18\11,''' '''830.769'''
|'''13\8,''' '''821.053'''
|'''21\13,''' '''812.903'''
|'''19\12,''' '''786.207'''
|'''11\7,''' '''776.471'''
|'''14\9,''' '''763.636'''
|-
|-
|Bb, Cf
|D/A/E la
|3b, 3d
Mi
|10\11, 461.538
 
|11\13, 425.806
م
| 4\5, 400
|E/B/F sí
|9\12, 372.414
Si
|5\7, 352.941
 
|6\9, 327.273
ت
|19\11, 876.923
|14\8, 884.211
|23\13, 890.323
|9\5, 900
|22\12, 910.345
|13\7, 917.647
|17\9, 927.727
|-
|-
!B, C
|D/A/E la#
!3
Mi#
!'''11\11,''' '''507.692'''
 
!'''8\8,''' '''505.263'''
م#
!'''13\13,''' '''503.226'''
|E/B/F sí#
!5\5, 500
Si#
!'''12\12,''' '''496.552'''
 
!'''7\7,''' '''494.118'''
ت#
!'''9\9,''' '''490.909'''
|20\11, 923.077
| rowspan="2" |15\8, 947.378
|25\13, 967.742
|10\5, 1000
|25\12, 1034.483
|15\7, 1058.824
|20\9, 1090.909
|-
|-
|B#, C#
|F/C/G utb
|3#
Solb
|12\11, 553.846
 
|9\8, 568.421
صb
|15\13, 580.645
|G/D/A reb
| rowspan="2" |6\5, 600
Reb
|15\12, 620.690
 
|9\7, 635.294
رb
|12\9, 654.545
|21\11, 969.231
|24\13, 929.033
|9\5, 900
|21\12, 868.966
|11\7, 776.471
|15\9, 818.182
|-
|-
|Cf, Qf
!F/C/G ut
|4b, 4d
Sol
|14\11, 646.154
 
|10\8, 631.579
ص
|16\13, 619.355
!G/D/A re
|14\12, 579.310
Re
|8\7, 564.706
 
|10\9, 545.455
ر
!22\11, 1015.385
! 16\8, 1010.526
! 26\13, 1006.452
!10\5, 1000
!24\12, 993.103
!14\7, 988.235
!18\9, 981.818
|}
{| class="wikitable"
!Notation
!Supersoft
!Soft
!Semisoft
!Basic
!Semihard
!Hard
!Superhard
|-
|-
|'''C, Q'''
!Mahur
|'''4'''
!~11ed4/3
|'''15\11,''' '''692.308'''
!~8ed4/3
|'''11\8'''  '''694.737'''
!~13ed4/3
|'''18\13,''' '''696.774'''
!~5ed4/3
|'''7\5,''' '''700'''
!~12ed4/3
|'''17\12,''' '''703.448'''
!~7ed4\3
|'''10\7,''' '''705.882'''
! ~9ed4/3
|'''13\9,''' '''709.091'''
|-
|-
|C#, Q#
|G#
|4#
|1\11, 46.154
|16\11, 738.462
|1\8, 63.158
|12\8, 757.895
|2\13, 77.419
| 20\13, 774.194
| rowspan="2" |1\5, 100
| rowspan="2" |'''8\5,''' '''800'''
|3\12, 124.138
|20\12, 827.586
|2\7, 141.176
|12\7, 847.059
|3\9, 163.636
|16\9, 872.727
|-
|-
|'''Qf, Df'''
|Jf, Af
|'''5b, 5d'''
|3\11, 138.462
|'''18\11,''' '''830.769'''
|2\8, 126.316
|'''13\8,''' '''821.053'''
|3\13, 116.129
|'''21\13,''' '''812.903'''
|2\12, 82.759
|'''19\12,''' '''786.207'''
|1\7, 70.588
|'''11\7,''' '''776.471'''
|1\9, 54.545
|'''14\9,''' '''763.636'''
|-
|-
|Q, D
|'''J, A'''
|5
|'''4\11,''' '''184.615'''
|19\11, 876.923
|'''3\8,''' '''189.474'''
|14\8, 884.211
|'''5\13,''' '''193.548'''
|23\13, 890.323
|'''2\5,''' '''200'''
|9\5, 900
|'''5\12,''' '''206.897'''
|22\12, 910.345
|'''3\7,''' '''211.765'''
|13\7, 917.647
|'''4\9,''' '''218.182'''
|17\9, 927.727
|-
|-
|Q#, D#
| J#, A#
|5#
|5\11, 230.769
|20\11, 923.077
|4\8, 252.632
| rowspan="2" |15\8, 947.368
|7\13, 270.968
|25\13, 967.742
| rowspan="2" |'''3\5,''' '''300'''
|10\5, 1000
|8\12, 331.034
|25\12, 1034.483
|5\7, 352.941
|15\7, 1058.824
|7\9, 381.818
|20\9, 1090.909
|-
|-
|Df, Sf
|'''Af, Bf'''
|6b, 6d
|'''7\11,''' '''323.077'''
|21\11, 969.231
|'''5\8,''' '''315.789'''
|24\13, 929.033
|'''8\13,''' '''309.677'''
|9\5, 900
|'''7\12,''' '''289.655'''
|21\12, 868.966
|'''4\7,''' '''282.353'''
|11\7, 776.471
|'''5\9,''' '''272.727'''
|15\9, 818.182
|-
|-
!D, S
|A, B
!6
|8\11, 369.231
!22\11, 1015.385
|6\8, 378.947
!16\8, 1010.526
|10\13, 387.097
!26\13, 1006.452
|4\5, 400
!10\5, 1000
|10\12, 413.793
!24\12, 993.103
|6\7, 423.529
! 14\7, 988.235
|8\9, 436.364
!18\9, 981.818
|-
|-
|D#, S#
|A#, B#
|6#
|9\11, 415.385
|23\11, 1061.538
| rowspan="2" |7\8, 442.105
|17\8, 1073.684
|12\13, 464.516
|28\13, 1083.871
|5\5, 500
| rowspan="2" |11\5, 1100
|13\12, 537.069
|27\12, 1117.241
|8\7, 564.705
|16\7, 1129.412
|11\9, 600
|21\9, 1145.455
|-
|-
|Ef
|Bb, Cf
|7b, 7d
|10\11, 461.538
| 25\11, 1153.846
|11\13, 425.806
| 18\8, 1136.842
|4\5, 400
|29\13, 1122.581
|9\12, 372.414
|26\12, 1075.862
|5\7, 352.941
|15\7, 1058.824
|6\9, 327.273
|19\9, 1036.364
|-
|-
|'''E'''
!B, C
|'''7'''
!'''11\11,''' '''507.692'''
|'''26\11,''' '''1200'''
!'''8\8,''' '''505.263'''
|'''19\8,''' '''1200'''
!'''13\13,''' '''503.226'''
|'''31\13,''' '''1200'''
!5\5, 500
|'''12\5,''' '''1200'''
!'''12\12,''' '''496.552'''
|'''29\12,''' '''1200'''
!'''7\7,''' '''494.118'''
|'''17\7,''' '''1200'''
!'''9\9,''' '''490.909'''
|'''22\9,''' '''1200'''
|-
|B#, C#
|12\11, 553.846
|9\8, 568.421
|15\13, 580.645
| rowspan="2" |6\5, 600
|15\12, 620.690
| 9\7, 635.294
| 12\9, 654.545
|-
|-
|E#
|Cf, Qf
|7#
|14\11, 646.154
|27\11, 1246.154
|10\8, 631.579
|20\8, 1263.158
|16\13, 619.355
|33\13, 1277.419
|14\12, 579.310
| rowspan="2" |'''13\5,''' '''1300'''
|8\7, 564.706
|32\12, 1324.138
| 10\9, 545.455
|19\7, 1341.176
|25\9, 1363.636
|-
|-
|'''Ff'''
|'''C, Q'''
|'''8b, Gd'''
|'''15\11,''' '''692.308'''
|'''29\11,''' '''1338.462'''
|'''11\8''' '''694.737'''
|'''21\8,''' '''1326.316'''
|'''18\13,''' '''696.774'''
|'''34\13,''' '''1316.129'''
|'''7\5,''' '''700'''
|'''31\12,''' '''1282.759'''
|'''17\12,''' '''703.448'''
|'''18\7,''' '''1270.588'''
|'''10\7,''' '''705.882'''
|'''23\9,''' '''1254.545'''
|'''13\9,''' '''709.091'''
|-
|-
|F
|C#, Q#
|8, G
|16\11, 738.462
|30\11, 1384.615
|12\8, 757.895
|22\8, 1389.474
|20\13, 774.194
|36\13, 1393.548
| rowspan="2" |'''8\5,''' '''800'''
|14\5, 1400
|20\12, 827.586
|34\12, 1406.897
|12\7, 847.059
|20\7, 1411.765
|16\9, 872.727
|26\9, 1418.182
|-
|-
|F#
|'''Qf, Df'''
|8#, G#
|'''18\11,''' '''830.769'''
|31\11, 1430.769
|'''13\8,''' '''821.053'''
| rowspan="2" |23\8, 1452.632
|'''21\13,''' '''812.903'''
|38\13, 1470.968
|'''19\12,''' '''786.207'''
|15\5, 1500
|'''11\7,''' '''776.471'''
|37\12, 1531.034
|'''14\9,''' '''763.636'''
|22\7, 1552.941
|29\9, 1581.818
|-
|-
|Gf
|Q, D
|9b, Ad
|19\11, 876.923
|32\11, 1476.923
|14\8, 884.211
|37\13, 1432.258
|23\13, 890.323
|14\5, 1400
|9\5, 900
|33\12, 1365.517
|22\12, 910.345
|19\7, 1341.176
|13\7, 917.647
|24\9, 1309.091
| 17\9, 927.727
|-
|-
!G
|Q#, D#
!'''9, A'''
|20\11, 923.077
!33\11, 1523.077
| rowspan="2" |15\8, 947.368
!24\8, 1515.789
|25\13, 967.742
!39\13, 1509.677
| 10\5, 1000
!15\5, 1500
|25\12, 1034.483
!36\12, 1489.655
| 15\7, 1058.824
!21\7, 1482.353
| 20\9, 1090.909
!27\9, 1472.727
|-
|-
|G#
|Df, Sf
|9#, A#
| 21\11, 969.231
|34\11, 1569.231
|24\13, 929.033
| 25\8, 1578.947
|9\5, 900
|41\13, 1587.097
|21\12, 868.966
| rowspan="2" |16\5, 1600
|11\7, 776.471
|39\12, 1613.793
|15\9, 818.182
|23\7, 1623.529
|30\9, 1636.364
|-
|-
|Jf, Af
!D, S
|Xb, Bd
!22\11, 1015.385
|36\11, 1661.538
!16\8, 1010.526
|26\8, 1642.105
!26\13, 1006.452
|42\13, 1625.806
!10\5, 1000
|38\12, 1572.034
!24\12, 993.103
|22\7, 1552.941
!14\7, 988.235
|28\9, 1527.{{Overline|27}}
!18\9, 981.818
|-
|-
|'''J, A'''
|D#, S#
|'''X, B'''
|23\11, 1061.538
|'''37\11,''' '''1707.692'''
|17\8, 1073.684
|'''27\8,''' '''1705.263'''
|28\13, 1083.871
|'''44\13,''' '''1703.226'''
| rowspan="2" |11\5, 1100
|'''17\5,''' '''1700'''
|27\12, 1117.241
|'''41\12,''' '''1696.552'''
|16\7, 1129.412
|'''24\7,''' '''1694.118'''
|21\9, 1145.455
|'''31\9,''' '''1690.909'''
|-
|-
|J#, A#
|Ef
|X#, B#
|25\11, 1153.846
|38\11, 1753.846
|18\8, 1136.842
|28\8, 1768.421
|29\13, 1122.581
|46\13, 1780.645
|26\12, 1075.862
| rowspan="2" |'''18\5,''' '''1800'''
|15\7, 1058.824
|44\12, 1820.690
|19\9, 1036.364
|26\7, 1835.294
|34\9, 1854.545
|-
|-
|'''Af, Bf'''
|'''E'''
|'''Eb, Dd'''
|'''26\11,''' '''1200'''
|'''40\11,''' '''1846.154'''
|'''19\8,''' '''1200'''
|'''29\8,''' '''1831.579'''
|'''31\13,''' '''1200'''
|'''47\13,''' '''1819.355'''
|'''12\5,''' '''1200'''
|'''43\12,''' '''1779.310'''
|'''29\12,''' '''1200'''
|'''25\7,''' '''1764.706'''
|'''17\7,''' '''1200'''
|'''32\9,''' '''1745.455'''
|'''22\9,''' '''1200'''
|-
|-
|A, B
|E#
|E, D
|27\11, 1246.154
|41\11, 1892.308
|20\8, 1263.158
|30\8, 1894.737
|33\13, 1277.419
|49\13, 1896.774
| rowspan="2" |'''13\5,''' '''1300'''
|19\5, 1900
|32\12, 1324.138
|46\12, 1903.448
|19\7, 1341.176
|27\7, 1905.882
|25\9, 1363.636
|35\9, 1909.090
|-
|-
|A#, B#
|'''Ff'''
|E#, D#
|'''29\11,''' '''1338.462'''
|42\11, 1938.462
|'''21\8,''' '''1326.316'''
| rowspan="2" |31\8, 1957.895
|'''34\13,''' '''1316.129'''
|51\13, 1974.194
|'''31\12,''' '''1282.759'''
|20\5, 2000
|'''18\7,''' '''1270.588'''
|49\12, 2027.586
|'''23\9,''' '''1254.545'''
|29\7, 2047.059
|38\9, 2072.727
|-
|-
|Bb, Cf
|F
|0b, Ed
|30\11, 1384.615
| 43\11, 1984.615
|22\8, 1389.474
|50\13, 1935.484
|36\13, 1393.548
|19\5, 1900
|14\5, 1400
|45\12, 1862.069
|34\12, 1406.897
|26\7, 1835.294
|20\7, 1411.765
|33\9, 1800
| 26\9, 1418.182
|-
|-
!B, C
|F#
! 0, E
|31\11, 1430.769
!44\11, 2030.769
| rowspan="2" |23\8, 1452.632
!32\8, 2021.053
|38\13, 1470.968
!52\13, 2012.903
|15\5, 1500
!20\5, 2000
|37\12, 1531.034
!48\12, 1986.207
|22\7, 1552.941
!28\7, 1976.471
| 29\9, 1581.818
!36\9, 1963.636
|-
|Gf
|32\11, 1476.923
|37\13, 1432.258
|14\5, 1400
|33\12, 1365.517
|19\7, 1341.176
|24\9, 1309.091
|-
!G
!33\11, 1523.077
!24\8, 1515.789
!39\13, 1509.677
!15\5, 1500
!36\12, 1489.655
!21\7, 1482.353
!27\9, 1472.727
|}
|}
{| class="wikitable"
{| class="wikitable"
! colspan="2" |Notation
!Notation
!Supersoft
! Supersoft
!Soft
!Soft
!Semisoft
!Semisoft
! Basic
!Basic
!Semihard
!Semihard
!Hard
!Hard
!Superhard
!Superhard
|-
|-
!Hyperionic
!Bijou
!Subsextal
!~11ed4/3
!~11ed4/3
!~8ed4/3
! ~8ed4/3
!~13ed4/3
!~13ed4/3
!~5ed4/3
!~5ed4/3
!~12ed4/3
!~12ed4/3
! ~7ed4\3
!~7ed4\3
!~9ed4/3
!~9ed4/3
|-
|-
|1#
|0#, E#
|0#
|1\11, 46.154
|1\11, 46.154
|1\8, 63.158
|1\8, 63.158
Line 628: Line 758:
|3\12, 124.138
|3\12, 124.138
|2\7, 141.176
|2\7, 141.176
|3\9, 163.636
| 3\9, 163.636
|-
|-
|2f
|1b, 1d
|1f
|3\11, 138.462
| 3\11, 138.462
|2\8, 126.316
|2\8, 126.316
|3\13, 116.129
|3\13, 116.129
|2\12, 82.759
| 2\12, 82.759
|1\7, 70.588
|1\7, 70.588
|1\9, 54.545
|1\9, 54.545
|-
|-
|'''2'''
|'''1'''
|'''1'''
|'''4\11,''' '''184.615'''
|'''4\11,''' '''184.615'''
Line 649: Line 777:
|'''4\9,''' '''218.182'''
|'''4\9,''' '''218.182'''
|-
|-
|2#
|1#
|1#
| 5\11, 230.769
|5\11, 230.769
| 4\8, 252.632
|4\8, 252.632
|7\13, 270.967
|7\13, 270.968
| rowspan="2" |'''3\5,''' '''300'''
| rowspan="2" |'''3\5,''' '''300'''
|8\12, 331.034
|8\12, 331.034
|5\7, 352.941
|5\7, 352.941
| 7\9, 381.818
|7\9, 381.818
|-
|-
|'''3f'''
|'''2b, 2d'''
|2f
|'''7\11,''' '''323.077'''
|'''7\11,''' '''323.077'''
|'''5\8,''' '''315.789'''
|'''5\8,''' '''315.789'''
Line 668: Line 794:
|'''5\9,''' '''272.727'''
|'''5\9,''' '''272.727'''
|-
|-
|3
|2
|'''2'''
|8\11, 369.231
| 8\11, 369.231
|6\8, 378.947
|6\8, 378.947
|10\13, 387.098
|10\13, 387.097
|4\5, 400
|4\5, 400
|10\12, 413.793
|10\12, 413.793
Line 678: Line 803:
|8\9, 436.364
|8\9, 436.364
|-
|-
|3#
|2#
| 2#
|9\11, 415.385
| 9\11, 415.385
| rowspan="2" |7\8, 442.105
| rowspan="2" | 7\8, 442.105
|12\13, 464.516
| 12\13, 464.516
|5\5, 500
|5\5, 500
|13\12, 537.069
|13\12, 537.069
Line 688: Line 812:
|11\9, 600
|11\9, 600
|-
|-
|4f
|3b, 3d
|'''3f'''
|10\11, 461.538
|10\11, 461.538
|11\13, 425.806
|11\13, 425.806
|4\5, 400
|4\5, 400
|9\12, 372.414
|9\12, 372.414
| 5\7, 352.941
|5\7, 352.941
|6\9, 327.273
|6\9, 327.273
|-
|-
!4
!3
!3
!'''11\11,''' '''507.692'''
!'''11\11,''' '''507.692'''
!'''8\8,''' '''505.263'''
!'''8\8,''' '''505.263'''
!'''13\13,''' '''503.226'''
!'''13\13,''' '''503.226'''
! 5\5, 500
!5\5, 500
!'''12\12,''' '''496.552'''
!'''12\12,''' '''496.552'''
!'''7\7,''' '''494.118'''
!'''7\7,''' '''494.118'''
!'''9\9,''' '''490.909'''
!'''9\9,''' '''490.909'''
|-
|-
|4#
|3#
| 3#
|12\11, 553.846
|12\11, 553.846
| 9\8, 568.421
|9\8, 568.421
|15\13, 580.645
|15\13, 580.645
| rowspan="2" | 6\5, 600
| rowspan="2" |6\5, 600
| 15\12, 620.690
|15\12, 620.690
|9\7, 635.294
|9\7, 635.294
|12\9, 654.545
|12\9, 654.545
|-
|-
|5f
|4b, 4d
|4f
|14\11, 646.154
|14\11, 646.154
|10\8, 631.579
|10\8, 631.579
Line 726: Line 846:
|10\9, 545.455
|10\9, 545.455
|-
|-
|'''5'''
|'''4'''
|'''4'''
|'''15\11,''' '''692.308'''
|'''15\11,''' '''692.308'''
Line 736: Line 855:
|'''13\9,''' '''709.091'''
|'''13\9,''' '''709.091'''
|-
|-
|5#
|4#
|4#
|16\11, 738.462
|16\11, 738.462
Line 743: Line 861:
| rowspan="2" |'''8\5,''' '''800'''
| rowspan="2" |'''8\5,''' '''800'''
|20\12, 827.586
|20\12, 827.586
| 12\7, 847.059
|12\7, 847.059
|16\9, 872.727
|16\9, 872.727
|-
|-
|'''6f'''
|'''5b, 5d'''
|5f
|'''18\11,''' '''830.769'''
|'''18\11,''' '''830.769'''
|'''13\8,''' '''821.053'''
|'''13\8,''' '''821.053'''
Line 755: Line 872:
|'''14\9,''' '''763.636'''
|'''14\9,''' '''763.636'''
|-
|-
|6
|5
|'''5'''
|19\11, 876.923
|19\11, 876.923
|14\8, 884.211
|14\8, 884.211
Line 765: Line 881:
|17\9, 927.727
|17\9, 927.727
|-
|-
|6#
|5#
|5#
|20\11, 923.077
|20\11, 923.077
| rowspan="2" | 15\8, 947.368
| rowspan="2" |15\8, 947.368
|25\13, 967.742
|25\13, 967.742
|10\5, 1000
|10\5, 1000
Line 775: Line 890:
|20\9, 1090.909
|20\9, 1090.909
|-
|-
|7f
|6b, 6d
|'''6f'''
|21\11, 969.231
|21\11, 969.231
|24\13, 929.032
|24\13, 929.033
|9\5, 900
| 9\5, 900
|21\12, 868.966
|21\12, 868.966
|11\7, 776.471
|11\7, 776.471
|15\9, 818.182
|15\9, 818.182
|-
|-
!7
!6
!6
!22\11, 1015.385
!22\11, 1015.385
Line 794: Line 907:
!18\9, 981.818
!18\9, 981.818
|-
|-
|7#
|6#
|6#
|23\11, 1061.538
|23\11, 1061.538
Line 804: Line 916:
|21\9, 1145.455
|21\9, 1145.455
|-
|-
|8f
|7b, 7d
| 7f
| 25\11, 1153.846
|25\11, 1153.846
|18\8, 1136.842
|18\8, 1136.842
|29\13, 1122.581
|29\13, 1122.581
| 26\12, 1075.862
|26\12, 1075.862
|15\7, 1058.824
|15\7, 1058.824
|19\9, 1036.364
|19\9, 1036.364
|-
|-
|'''8'''
|'''7'''
|7
|'''26\11,''' '''1200'''
|'''26\11,''' '''1200'''
|'''19\8,''' '''1200'''
|'''19\8,''' '''1200'''
Line 823: Line 933:
|'''22\9,''' '''1200'''
|'''22\9,''' '''1200'''
|-
|-
|8#
|7#
|7#
|27\11, 1246.154
|27\11, 1246.154
Line 833: Line 942:
|25\9, 1363.636
|25\9, 1363.636
|-
|-
|'''9f'''
|'''8b, Gd'''
|8f
|'''29\11,''' '''1338.462'''
|'''29\11,''' '''1338.462'''
|'''21\8,''' '''1326.316'''
|'''21\8,''' '''1326.316'''
Line 842: Line 950:
|'''23\9,''' '''1254.545'''
|'''23\9,''' '''1254.545'''
|-
|-
|9
|8, G
|'''8'''
|30\11, 1384.615
|30\11, 1384.615
|22\8, 1389.474
|22\8, 1389.474
Line 852: Line 959:
|26\9, 1418.182
|26\9, 1418.182
|-
|-
|9#
|8#, G#
|8#
|31\11, 1430.769
| 31\11, 1430.769
| rowspan="2" |23\8, 1452.632
| rowspan="2" | 23\8, 1452.632
|38\13, 1470.968
|38\13, 1470.968
|15\5, 1500
|15\5, 1500
|37\12, 1531.034
|37\12, 1531.034
|22\7, 1552.941
|22\7, 1552.941
|29\9, 1581.818
| 29\9, 1581.818
|-
|-
|Af
|9b, Ad
|9f
|32\11, 1476.923
|32\11, 1476.923
| 37\13, 1432.258
|37\13, 1432.258
|14\5, 1400
|14\5, 1400
|33\12, 1365.517
|33\12, 1365.517
Line 871: Line 976:
|24\9, 1309.091
|24\9, 1309.091
|-
|-
!A
!'''9, A'''
!9
!33\11, 1523.077
!33\11, 1523.077
!24\8, 1515.789
!24\8, 1515.789
Line 881: Line 985:
!27\9, 1472.727
!27\9, 1472.727
|-
|-
|A#
|9#, A#
|9#
|34\11, 1569.231
|34\11, 1569.231
|25\8, 1578.947
| 25\8, 1578.947
|41\13, 1587.097
|41\13, 1587.097
| rowspan="2" |16\5, 1600
| rowspan="2" |16\5, 1600
Line 891: Line 994:
|30\9, 1636.364
|30\9, 1636.364
|-
|-
|Bf
|Xb, Bd
|Xb
|36\11, 1661.538
|36\11, 1661.538
|26\8, 1642.105
|26\8, 1642.105
|42\13, 1625.806
|42\13, 1625.806
|38\12, 1572.034
|38\12, 1572.034
|22\7, 1552.941
| 22\7, 1552.941
|28\9, 1527.{{Overline|27}}
|28\9, 1527.{{Overline|27}}
|-
|-
|'''B'''
|'''X, B'''
|'''X'''
|'''37\11,''' '''1707.692'''
|'''37\11,''' '''1707.692'''
|'''27\8,''' '''1705.263'''
|'''27\8,''' '''1705.263'''
Line 910: Line 1,011:
|'''31\9,''' '''1690.909'''
|'''31\9,''' '''1690.909'''
|-
|-
|B#
|X#, B#
|X#
|38\11, 1753.846
|38\11, 1753.846
|28\8, 1768.421
|28\8, 1768.421
Line 920: Line 1,020:
|34\9, 1854.545
|34\9, 1854.545
|-
|-
|'''Cf'''
|'''Eb, Dd'''
|'''ɛf'''
|'''40\11,''' '''1846.154'''
|'''40\11,''' '''1846.154'''
|'''29\8,''' '''1831.579'''
|'''29\8,''' '''1831.579'''
Line 929: Line 1,028:
|'''32\9,''' '''1745.455'''
|'''32\9,''' '''1745.455'''
|-
|-
|C
|E, D
|ɛ
|41\11, 1892.308
|41\11, 1892.308
|30\8, 1894.737
|30\8, 1894.737
Line 939: Line 1,037:
|35\9, 1909.090
|35\9, 1909.090
|-
|-
|C#
|E#, D#
|ɛ#
|42\11, 1938.462
|42\11, 1938.462
| rowspan="2" |31\8, 1957.895
| rowspan="2" |31\8, 1957.895
Line 949: Line 1,046:
|38\9, 2072.727
|38\9, 2072.727
|-
|-
|Df
|0b, Ed
|Af
|43\11, 1984.615
|43\11, 1984.615
|50\13, 1935.484
|50\13, 1935.484
Line 958: Line 1,054:
|33\9, 1800
|33\9, 1800
|-
|-
!D
!0, E
!A
!44\11, 2030.769
!44\11, 2030.769
!32\8, 2021.053
!32\8, 2021.053
Line 967: Line 1,062:
!28\7, 1976.471
!28\7, 1976.471
!36\9, 1963.636
!36\9, 1963.636
|}
{| class="wikitable"
! Notation
!Supersoft
! Soft
!Semisoft
!Basic
!Semihard
!Hard
!Superhard
|-
|-
|D#
!Hyperionic
|A#
!~11ed4/3
|45\11, 2076.923
!~8ed4/3
|33\8, 2084.211
!~13ed4/3
| 54\13, 2090.323
!~5ed4/3
| rowspan="2" |21\5, 2100
!~12ed4/3
|51\12, 2110.345
!~7ed4\3
|30\7, 2117.647
!~9ed4/3
|39\9, 2127.273
|-
|-
|Ef
|1#
|Bf
|1\11, 46.154
|47\11, 2169.231
|1\8, 63.158
|34\8, 2147.368
|2\13, 77.419
|55\13, 2129.032
| rowspan="2" |1\5, 100
|50\12, 2068.966
|3\12, 124.138
|29\7, 2047.059
|2\7, 141.176
|37\9, 2018.182
|3\9, 163.636
|-
|-
|'''E'''
|2f
|'''B'''
|3\11, 138.462
|'''48\11,''' '''2215.385'''
|2\8, 126.316
|'''35\8,''' '''2210.526'''
|3\13, 116.129
|'''57\13,''' '''2206.452'''
|2\12, 82.759
|'''22\5,''' '''2200'''
| 1\7, 70.588
|'''53\12,''' '''2193.103'''
|1\9, 54.545
|'''31\7,''' '''2188.235'''
|'''40\9,''' '''2181.818'''
|-
|-
|E#
|'''2'''
|B#
|'''4\11,''' '''184.615'''
|49\11, 2261.538
|'''3\8,''' '''189.474'''
|36\8, 2273.684
|'''5\13,''' '''193.548'''
|59\13, 2283.871
|'''2\5,''' '''200'''
| rowspan="2" |'''23\5,''' '''2300'''
|'''5\12,''' '''206.897'''
|56\12, 2317.241
|'''3\7,''' '''211.765'''
|33\7, 2329.412
|'''4\9,''' '''218.182'''
|43\9, 2345.455
|-
|-
|'''Ff'''
|2#
|'''Cf'''
| 5\11, 230.769
|'''51\11,''' '''2353.846'''
|4\8, 252.632
|'''37\8,''' '''2336.842'''
|7\13, 270.967
|'''61\13,''' '''2322.581'''
| rowspan="2" |'''3\5,''' '''300'''
|'''55\12,''' '''2275.864'''
| 8\12, 331.034
|'''32\7,''' '''2258.824'''
|5\7, 352.941
|'''41\9,''' '''2236.364'''
|7\9, 381.818
|-
|-
|F
|'''3f'''
|C
|'''7\11,''' '''323.077'''
| 52\11, 2400
|'''5\8,''' '''315.789'''
|38\8, 2400
|'''8\13,''' '''309.677'''
|62\13, 2400
|'''7\12,''' '''289.655'''
|24\5, 2400
|'''4\7,''' '''282.353'''
| 58\12, 2400
|'''5\9,''' '''272.727'''
|34\7, 2400
| 44\9, 2400
|-
|-
|F#
|3
|C#
|8\11, 369.231
|53\11, 2446.154
|6\8, 378.947
| rowspan="2" |39\8, 2463.158
|10\13, 387.098
|64\13, 2477.419
|4\5, 400
|25\5, 2500
|10\12, 413.793
|61\12, 2524.138
|6\7, 423.529
|36\7, 2541.176
|8\9, 436.364
|47/9, 2563.636
|-
|-
|1f
|3#
|Df
|9\11, 415.385
|54\11, 2492.308
| rowspan="2" |7\8, 442.105
|63\13, 2438.710
|12\13, 464.516
|24\5, 2400
|5\5, 500
|57\12, 2358.621
|13\12, 537.069
|33\7, 2329.412
|8\7, 564.705
|42\9, 2390.909
|11\9, 600
|-
|-
! 1
|4f
!D
|10\11, 461.538
!55\11, 2538.462
|11\13, 425.806
!40\8, 2526.316
|4\5, 400
! 65\13, 2516.129
|9\12, 372.414
!25\5, 2500
|5\7, 352.941
!60\12, 2482.759
|6\9, 327.273
!35\7, 2470.588
!45\9, 2454.545
|-
|-
|1#
!4
|D#
!'''11\11,''' '''507.692'''
|56\11, 2584.615
!'''8\8,''' '''505.263'''
|41\8, 2589.474
!'''13\13,''' '''503.226'''
|67\13, 2593.548
!5\5, 500
| rowspan="2" |26\5, 2600
!'''12\12,''' '''496.552'''
|63\12, 2606.897
!'''7\7,''' '''494.118'''
|37\7, 2611.765
!'''9\9,''' '''490.909'''
|48\9, 2618.182
|-
|-
|2f
|4#
|Ef
|12\11, 553.846
|58\11, 2676.923
|9\8, 568.421
| 42\8, 2652.632
|15\13, 580.645
|69\13, 2670.968
| rowspan="2" |6\5, 600
|62\12, 2565.517
|15\12, 620.690
|36\7, 2541.176
|9\7, 635.294
|46\9, 2509.091
|12\9, 654.545
|-
|-
|'''2'''
|5f
|'''E'''
|14\11, 646.154
|'''59\11,''' '''2723.077'''
|10\8, 631.579
|'''43\8,''' '''2715.789'''
|16\13, 619.355
|'''70\13,''' '''2709.677'''
|14\12, 579.310
|'''27\5,''' '''2700'''
|8\7, 564.706
|'''65\12,''' '''2689.655'''
|10\9, 545.455
|'''38\7,''' '''2682.353'''
|'''49\9,''' '''2672.727'''
|-
|-
|2#
|'''5'''
|E#
|'''15\11,''' '''692.308'''
|60\11, 2769.231
|'''11\8'''  '''694.737'''
|44\8, 2778.947
|'''18\13,''' '''696.774'''
|72\13, 2787.097
|'''7\5,''' '''700'''
| rowspan="2" |'''28\5,''' '''2800'''
|'''17\12,''' '''703.448'''
|68\12, 2813.793
|'''10\7,''' '''705.882'''
|40\7, 2823.529
|'''13\9,''' '''709.091'''
|52\9, 2836.364
|-
|-
|'''3f'''
|5#
|'''Ff'''
|16\11, 738.462
|'''62\11,''' '''2861.538'''
|12\8, 757.895
|'''45\8,''' '''2842.105'''
|20\13, 774.194
|'''73\13,''' '''2825.806'''
| rowspan="2" |'''8\5,''' '''800'''
|'''67\12,''' '''2772.034'''
|20\12, 827.586
|'''39\7,''' '''2752.941'''
|12\7, 847.059
|'''50\9,''' '''2727.273'''
|16\9, 872.727
|-
|-
| 3
|'''6f'''
|F
|'''18\11,''' '''830.769'''
|63\11, 2907.692
|'''13\8,''' '''821.053'''
|46\8, 2905.263
|'''21\13,''' '''812.903'''
|75\13, 2903.226
|'''19\12,''' '''786.207'''
|29\5, 2900
|'''11\7,''' '''776.471'''
|70\12, 2896.552
|'''14\9,''' '''763.636'''
|41\7, 2894.118
|53\9, 2890.909
|-
|-
|3#
|6
|F#
|19\11, 876.923
|64\11, 2953.846
|14\8, 884.211
| rowspan="2" |47\8, 2968.421
|23\13, 890.323
|77\13, 2980.645
|9\5, 900
|30\5, 3000
|22\12, 910.345
|73\12, 3020.690
|13\7, 917.647
|43\7, 3035.294
|17\9, 927.727
|55\9, 3000
|-
|-
|4f
|6#
|0f
|20\11, 923.077
|65\11, 3000
| rowspan="2" |15\8, 947.368
|76\13, 2941.935
|25\13, 967.742
|29\5, 2900
|10\5, 1000
|69\29, 2855.172
| 25\12, 1034.483
|40\7, 2823.529
|15\7, 1058.824
|52\9, 2836.364
|20\9, 1090.909
|-
|7f
|21\11, 969.231
|24\13, 929.032
|9\5, 900
|21\12, 868.966
| 11\7, 776.471
|15\9, 818.182
|-
|-
!4
!7
!0
!22\11, 1015.385
!66\11, 3046.154
!16\8, 1010.526
!48\8, 30'''31.579'''
!26\13, 1006.452
!78\13, 30'''19.355'''
!10\5, 1000
!30\5, 3000
!24\12, 993.103
!72\12, 29'''79.310'''
!14\7, 988.235
!42\7, 2964.706
! 18\9, 981.818
!54\9, 2945.455
|-
|}
| 7#
==Intervals==
|23\11, 1061.538
{| class="wikitable"
|17\8, 1073.684
!Generators
|28\13, 1083.871
!Fourth notation
| rowspan="2" |11\5, 1100
!Interval category name
|27\12, 1117.241
!Generators
|16\7, 1129.412
!Notation of 4/3 inverse
|21\9, 1145.455
!Interval category name
|-
|8f
|25\11, 1153.846
|18\8, 1136.842
|29\13, 1122.581
|26\12, 1075.862
|15\7, 1058.824
|19\9, 1036.364
|-
|'''8'''
|'''26\11,''' '''1200'''
|'''19\8,''' '''1200'''
|'''31\13,''' '''1200'''
|'''12\5,''' '''1200'''
|'''29\12,''' '''1200'''
|'''17\7,''' '''1200'''
|'''22\9,''' '''1200'''
|-
|8#
|27\11, 1246.154
|20\8, 1263.158
|33\13, 1277.419
| rowspan="2" |'''13\5,''' '''1300'''
|32\12, 1324.138
|19\7, 1341.176
|25\9, 1363.636
|-
|'''9f'''
|'''29\11,''' '''1338.462'''
|'''21\8,''' '''1326.316'''
|'''34\13,''' '''1316.129'''
|'''31\12,''' '''1282.759'''
|'''18\7,''' '''1270.588'''
|'''23\9,''' '''1254.545'''
|-
|9
|30\11, 1384.615
|22\8, 1389.474
| 36\13, 1393.548
|14\5, 1400
|34\12, 1406.897
|20\7, 1411.765
|26\9, 1418.182
|-
|9#
|31\11, 1430.769
| rowspan="2" |23\8, 1452.632
|38\13, 1470.968
|15\5, 1500
|37\12, 1531.034
|22\7, 1552.941
| 29\9, 1581.818
|-
|Af
|32\11, 1476.923
|37\13, 1432.258
|14\5, 1400
|33\12, 1365.517
|19\7, 1341.176
|24\9, 1309.091
|-
!A
!33\11, 1523.077
!24\8, 1515.789
!39\13, 1509.677
!15\5, 1500
!36\12, 1489.655
!21\7, 1482.353
!27\9, 1472.727
|-
|A#
|34\11, 1569.231
|25\8, 1578.947
|41\13, 1587.097
| rowspan="2" |16\5, 1600
|39\12, 1613.793
|23\7, 1623.529
|30\9, 1636.364
|-
|Bf
|36\11, 1661.538
|26\8, 1642.105
|42\13, 1625.806
|38\12, 1572.034
|22\7, 1552.941
|28\9, 1527.{{Overline|27}}
|-
|'''B'''
|'''37\11,''' '''1707.692'''
|'''27\8,''' '''1705.263'''
|'''44\13,''' '''1703.226'''
|'''17\5,''' '''1700'''
|'''41\12,''' '''1696.552'''
|'''24\7,''' '''1694.118'''
|'''31\9,''' '''1690.909'''
|-
|B#
| 38\11, 1753.846
|28\8, 1768.421
|46\13, 1780.645
| rowspan="2" |'''18\5,''' '''1800'''
|44\12, 1820.690
|26\7, 1835.294
| 34\9, 1854.545
|-
|'''Cf'''
|'''40\11,''' '''1846.154'''
|'''29\8,''' '''1831.579'''
|'''47\13,''' '''1819.355'''
|'''43\12,''' '''1779.310'''
|'''25\7,''' '''1764.706'''
|'''32\9,''' '''1745.455'''
|-
|C
| 41\11, 1892.308
|30\8, 1894.737
|49\13, 1896.774
|19\5, 1900
|46\12, 1903.448
|27\7, 1905.882
|35\9, 1909.090
|-
|C#
|42\11, 1938.462
| rowspan="2" |31\8, 1957.895
|51\13, 1974.194
|20\5, 2000
|49\12, 2027.586
|29\7, 2047.059
| 38\9, 2072.727
|-
|Df
|43\11, 1984.615
|50\13, 1935.484
|19\5, 1900
|45\12, 1862.069
|26\7, 1835.294
|33\9, 1800
|-
!D
!44\11, 2030.769
!32\8, 2021.053
! 52\13, 2012.903
!20\5, 2000
!48\12, 1986.207
!28\7, 1976.471
!36\9, 1963.636
|-
| D#
|45\11, 2076.923
|33\8, 2084.211
|54\13, 2090.323
| rowspan="2" |21\5, 2100
|51\12, 2110.345
|30\7, 2117.647
|39\9, 2127.273
|-
|Ef
|47\11, 2169.231
|34\8, 2147.368
|55\13, 2129.032
|50\12, 2068.966
|29\7, 2047.059
|37\9, 2018.182
|-
|'''E'''
|'''48\11,''' '''2215.385'''
|'''35\8,''' '''2210.526'''
|'''57\13,''' '''2206.452'''
|'''22\5,''' '''2200'''
|'''53\12,''' '''2193.103'''
|'''31\7,''' '''2188.235'''
|'''40\9,''' '''2181.818'''
|-
|E#
|49\11, 2261.538
|36\8, 2273.684
|59\13, 2283.871
| rowspan="2" |'''23\5,''' '''2300'''
|56\12, 2317.241
|33\7, 2329.412
|43\9, 2345.455
|-
|'''Ff'''
|'''51\11,''' '''2353.846'''
|'''37\8,''' '''2336.842'''
|'''61\13,''' '''2322.581'''
|'''55\12,''' '''2275.864'''
|'''32\7,''' '''2258.824'''
|'''41\9,''' '''2236.364'''
|-
|F
|52\11, 2400
|38\8, 2400
|62\13, 2400
|24\5, 2400
|58\12, 2400
|34\7, 2400
|44\9, 2400
|-
|F#
|53\11, 2446.154
| rowspan="2" |39\8, 2463.158
|64\13, 2477.419
|25\5, 2500
|61\12, 2524.138
|36\7, 2541.176
|47/9, 2563.636
|-
|1f
|54\11, 2492.308
|63\13, 2438.710
|24\5, 2400
|57\12, 2358.621
|33\7, 2329.412
|42\9, 2390.909
|-
!1
!55\11, 2538.462
!40\8, 2526.316
!65\13, 2516.129
!25\5, 2500
!60\12, 2482.759
!35\7, 2470.588
!45\9, 2454.545
|}
{| class="wikitable"
!Notation
!Supersoft
!Soft
!Semisoft
!Basic
!Semihard
!Hard
!Superhard
|-
!Subsextal
!~11ed4/3
!~8ed4/3
!~13ed4/3
!~5ed4/3
!~12ed4/3
!~7ed4\3
!~9ed4/3
|-
|0#
|1\11, 46.154
|1\8, 63.158
|2\13, 77.419
| rowspan="2" |1\5, 100
|3\12, 124.138
|2\7, 141.176
|3\9, 163.636
|-
|1f
|3\11, 138.462
|2\8, 126.316
|3\13, 116.129
|2\12, 82.759
|1\7, 70.588
|1\9, 54.545
|-
|'''1'''
|'''4\11,''' '''184.615'''
|'''3\8,''' '''189.474'''
|'''5\13,''' '''193.548'''
|'''2\5,''' '''200'''
|'''5\12,''' '''206.897'''
|'''3\7,''' '''211.765'''
|'''4\9,''' '''218.182'''
|-
|1#
|5\11, 230.769
|4\8, 252.632
|7\13, 270.967
| rowspan="2" |'''3\5,''' '''300'''
|8\12, 331.034
|5\7, 352.941
|7\9, 381.818
|-
|2f
|'''7\11,''' '''323.077'''
|'''5\8,''' '''315.789'''
|'''8\13,''' '''309.677'''
|'''7\12,''' '''289.655'''
|'''4\7,''' '''282.353'''
|'''5\9,''' '''272.727'''
|-
|'''2'''
|8\11, 369.231
|6\8, 378.947
|10\13, 387.098
|4\5, 400
|10\12, 413.793
|6\7, 423.529
|8\9, 436.364
|-
|2#
|9\11, 415.385
| rowspan="2" |7\8, 442.105
|12\13, 464.516
|5\5, 500
|13\12, 537.069
|8\7, 564.705
|11\9, 600
|-
|'''3f'''
|10\11, 461.538
|11\13, 425.806
|4\5, 400
|9\12, 372.414
|5\7, 352.941
|6\9, 327.273
|-
!3
!'''11\11,''' '''507.692'''
!'''8\8,''' '''505.263'''
!'''13\13,''' '''503.226'''
!5\5, 500
!'''12\12,''' '''496.552'''
!'''7\7,''' '''494.118'''
!'''9\9,''' '''490.909'''
|-
|3#
|12\11, 553.846
|9\8, 568.421
|15\13, 580.645
| rowspan="2" |6\5, 600
|15\12, 620.690
|9\7, 635.294
|12\9, 654.545
|-
|4f
|14\11, 646.154
|10\8, 631.579
|16\13, 619.355
|14\12, 579.310
|8\7, 564.706
|10\9, 545.455
|-
|'''4'''
|'''15\11,''' '''692.308'''
|'''11\8'''  '''694.737'''
|'''18\13,''' '''696.774'''
|'''7\5,''' '''700'''
|'''17\12,''' '''703.448'''
|'''10\7,''' '''705.882'''
|'''13\9,''' '''709.091'''
|-
|4#
|16\11, 738.462
|12\8, 757.895
|20\13, 774.194
| rowspan="2" |'''8\5,''' '''800'''
|20\12, 827.586
|12\7, 847.059
|16\9, 872.727
|-
|5f
|'''18\11,''' '''830.769'''
|'''13\8,''' '''821.053'''
|'''21\13,''' '''812.903'''
|'''19\12,''' '''786.207'''
|'''11\7,''' '''776.471'''
|'''14\9,''' '''763.636'''
|-
|'''5'''
|19\11, 876.923
|14\8, 884.211
|23\13, 890.323
|9\5, 900
|22\12, 910.345
|13\7, 917.647
|17\9, 927.727
|-
|5#
|20\11, 923.077
| rowspan="2" |15\8, 947.368
|25\13, 967.742
|10\5, 1000
|25\12, 1034.483
|15\7, 1058.824
|20\9, 1090.909
|-
|'''6f'''
|21\11, 969.231
|24\13, 929.032
|9\5, 900
|21\12, 868.966
|11\7, 776.471
|15\9, 818.182
|-
!6
!22\11, 1015.385
!16\8, 1010.526
!26\13, 1006.452
!10\5, 1000
!24\12, 993.103
!14\7, 988.235
!18\9, 981.818
|-
|6#
|23\11, 1061.538
|17\8, 1073.684
|28\13, 1083.871
| rowspan="2" |11\5, 1100
|27\12, 1117.241
|16\7, 1129.412
|21\9, 1145.455
|-
|7f
|25\11, 1153.846
|18\8, 1136.842
|29\13, 1122.581
|26\12, 1075.862
|15\7, 1058.824
|19\9, 1036.364
|-
|7
|'''26\11,''' '''1200'''
|'''19\8,''' '''1200'''
|'''31\13,''' '''1200'''
|'''12\5,''' '''1200'''
|'''29\12,''' '''1200'''
|'''17\7,''' '''1200'''
|'''22\9,''' '''1200'''
|-
|7#
|27\11, 1246.154
|20\8, 1263.158
|33\13, 1277.419
| rowspan="2" |'''13\5,''' '''1300'''
|32\12, 1324.138
|19\7, 1341.176
|25\9, 1363.636
|-
|8f
|'''29\11,''' '''1338.462'''
|'''21\8,''' '''1326.316'''
|'''34\13,''' '''1316.129'''
|'''31\12,''' '''1282.759'''
|'''18\7,''' '''1270.588'''
|'''23\9,''' '''1254.545'''
|-
|'''8'''
|30\11, 1384.615
|22\8, 1389.474
|36\13, 1393.548
|14\5, 1400
|34\12, 1406.897
|20\7, 1411.765
|26\9, 1418.182
|-
|8#
|31\11, 1430.769
| rowspan="2" |23\8, 1452.632
|38\13, 1470.968
|15\5, 1500
|37\12, 1531.034
|22\7, 1552.941
|29\9, 1581.818
|-
|9f
|32\11, 1476.923
|37\13, 1432.258
|14\5, 1400
|33\12, 1365.517
|19\7, 1341.176
|24\9, 1309.091
|-
!9
!33\11, 1523.077
!24\8, 1515.789
!39\13, 1509.677
!15\5, 1500
!36\12, 1489.655
!21\7, 1482.353
!27\9, 1472.727
|-
|9#
|34\11, 1569.231
|25\8, 1578.947
|41\13, 1587.097
| rowspan="2" |16\5, 1600
|39\12, 1613.793
|23\7, 1623.529
|30\9, 1636.364
|-
|Xb
|36\11, 1661.538
|26\8, 1642.105
|42\13, 1625.806
|38\12, 1572.034
|22\7, 1552.941
|28\9, 1527.{{Overline|27}}
|-
|'''X'''
|'''37\11,''' '''1707.692'''
|'''27\8,''' '''1705.263'''
|'''44\13,''' '''1703.226'''
|'''17\5,''' '''1700'''
|'''41\12,''' '''1696.552'''
|'''24\7,''' '''1694.118'''
|'''31\9,''' '''1690.909'''
|-
|X#
|38\11, 1753.846
|28\8, 1768.421
|46\13, 1780.645
| rowspan="2" |'''18\5,''' '''1800'''
|44\12, 1820.690
|26\7, 1835.294
|34\9, 1854.545
|-
|'''ɛf'''
|'''40\11,''' '''1846.154'''
|'''29\8,''' '''1831.579'''
|'''47\13,''' '''1819.355'''
|'''43\12,''' '''1779.310'''
|'''25\7,''' '''1764.706'''
|'''32\9,''' '''1745.455'''
|-
|ɛ
|41\11, 1892.308
|30\8, 1894.737
|49\13, 1896.774
|19\5, 1900
|46\12, 1903.448
|27\7, 1905.882
|35\9, 1909.090
|-
|ɛ#
|42\11, 1938.462
| rowspan="2" |31\8, 1957.895
|51\13, 1974.194
|20\5, 2000
|49\12, 2027.586
|29\7, 2047.059
|38\9, 2072.727
|-
|Af
|43\11, 1984.615
|50\13, 1935.484
|19\5, 1900
|45\12, 1862.069
|26\7, 1835.294
|33\9, 1800
|-
!A
!44\11, 2030.769
!32\8, 2021.053
!52\13, 2012.903
!20\5, 2000
!48\12, 1986.207
!28\7, 1976.471
!36\9, 1963.636
|-
|A#
|45\11, 2076.923
|33\8, 2084.211
|54\13, 2090.323
| rowspan="2" |21\5, 2100
|51\12, 2110.345
|30\7, 2117.647
|39\9, 2127.273
|-
|Bf
|47\11, 2169.231
|34\8, 2147.368
|55\13, 2129.032
|50\12, 2068.966
|29\7, 2047.059
|37\9, 2018.182
|-
|'''B'''
|'''48\11,''' '''2215.385'''
|'''35\8,''' '''2210.526'''
|'''57\13,''' '''2206.452'''
|'''22\5,''' '''2200'''
|'''53\12,''' '''2193.103'''
|'''31\7,''' '''2188.235'''
|'''40\9,''' '''2181.818'''
|-
|B#
|49\11, 2261.538
|36\8, 2273.684
|59\13, 2283.871
| rowspan="2" |'''23\5,''' '''2300'''
|56\12, 2317.241
|33\7, 2329.412
|43\9, 2345.455
|-
|'''Cf'''
|'''51\11,''' '''2353.846'''
|'''37\8,''' '''2336.842'''
|'''61\13,''' '''2322.581'''
|'''55\12,''' '''2275.864'''
|'''32\7,''' '''2258.824'''
|'''41\9,''' '''2236.364'''
|-
|C
|52\11, 2400
|38\8, 2400
|62\13, 2400
|24\5, 2400
|58\12, 2400
|34\7, 2400
|44\9, 2400
|-
|C#
|53\11, 2446.154
| rowspan="2" |39\8, 2463.158
|64\13, 2477.419
|25\5, 2500
|61\12, 2524.138
|36\7, 2541.176
|47/9, 2563.636
|-
|Df
|54\11, 2492.308
|63\13, 2438.710
|24\5, 2400
|57\12, 2358.621
|33\7, 2329.412
|42\9, 2390.909
|-
!D
!55\11, 2538.462
!40\8, 2526.316
!65\13, 2516.129
!25\5, 2500
!60\12, 2482.759
!35\7, 2470.588
!45\9, 2454.545
|-
|D#
|56\11, 2584.615
|41\8, 2589.474
|67\13, 2593.548
| rowspan="2" |26\5, 2600
|63\12, 2606.897
|37\7, 2611.765
|48\9, 2618.182
|-
|Ef
|58\11, 2676.923
|42\8, 2652.632
|69\13, 2670.968
|62\12, 2565.517
|36\7, 2541.176
|46\9, 2509.091
|-
|'''E'''
|'''59\11,''' '''2723.077'''
|'''43\8,''' '''2715.789'''
|'''70\13,''' '''2709.677'''
|'''27\5,''' '''2700'''
|'''65\12,''' '''2689.655'''
|'''38\7,''' '''2682.353'''
|'''49\9,''' '''2672.727'''
|-
|E#
|60\11, 2769.231
|44\8, 2778.947
|72\13, 2787.097
| rowspan="2" |'''28\5,''' '''2800'''
|68\12, 2813.793
|40\7, 2823.529
|52\9, 2836.364
|-
|'''Ff'''
|'''62\11,''' '''2861.538'''
|'''45\8,''' '''2842.105'''
|'''73\13,''' '''2825.806'''
|'''67\12,''' '''2772.034'''
|'''39\7,''' '''2752.941'''
|'''50\9,''' '''2727.273'''
|-
|F
|63\11, 2907.692
|46\8, 2905.263
|75\13, 2903.226
|29\5, 2900
|70\12, 2896.552
|41\7, 2894.118
|53\9, 2890.909
|-
|F#
|64\11, 2953.846
| rowspan="2" |47\8, 2968.421
|77\13, 2980.645
|30\5, 3000
|73\12, 3020.690
|43\7, 3035.294
|55\9, 3000
|-
|0f
|65\11, 3000
|76\13, 2941.935
|29\5, 2900
|69\29, 2855.172
|40\7, 2823.529
|52\9, 2836.364
|-
!0
!66\11, 3046.154
!48\8, 30'''31.579'''
!78\13, 30'''19.355'''
!30\5, 3000
!72\12, 29'''79.310'''
!42\7, 2964.706
!54\9, 2945.455
|}
 
 
==Intervals==
{| class="wikitable"
!Generators
!Fourth notation
!Interval category name
!Generators
!Notation of 4/3 inverse
!Interval category name
|-
| colspan="6" |The 3-note MOS has the following intervals (from some root):
|-
|0
|F/C/G ut
Do, Sol
 
د, ص
|perfect unison
|0
|F/C/G ut
Do, Sol
 
د, ص
|perfect fourth
|-
|1
|A/E/B mib
Mib, Sib
 
صb, مb
|diminished third
| -1
|G/D/A re
Re, La
 
ر, ل
|perfect second
|-
|2
|G/D/A reb
Reb, Lab
 
رb, لb
|diminished second
| -2
|A/E/B mi
Mi, Si
 
ص, م
|perfect third
|-
| colspan="6" |The chromatic 5-note MOS also has the following intervals (from some root):
|-
|3
|F/C/G utb
Dob, Solb
 
دb, صb
|diminished fourth
| -3
|F/C/G ut#
Do#, Sol#
 
د, #ص#
|augmented unison (chroma)
|-
|4
|A/E/B mibb
Mibb, Sibb
 
مbb, صbb
|doubly diminished third
| -4
|G/D/A re#
Re#, La#
 
ر ,# ل#
|augmented second
|}
==Genchain==
The generator chain for this scale is as follows:
{| class="wikitable"
|A/E/B mibb
|F/C/G utb
|G/D/A reb
|A/E/B mib
|F/C/G ut
|G/D/A re
|A/E/B mi
|F/C/G ut#
|G/D/A re#
|A/E/B mi#
|-
|Mibb
Sibb
|Dob
Solb
|Reb
Lab
|Mib
Sib
|Do
Sol
|Re
La
|Mi
Si
|Do#
Sol#
|Re#
La#
|Mi#
Si#
|-
|-
| colspan="6" |The 3-note MOS has the following intervals (from some root):
|مbb
تbb
|دb
صb
|رb
لb
|مb
تb
|د
ص
|ر
ل
|م
ت
|د#
ص#
|ر#
ل#
|م#
ت#
|-
|-
|0
|dd3
|Do, Sol
|d4
|perfect unison
|d2
|0
|d3
|Do, Sol
|P1
|perfect fourth
|P2
|-
|P3
| 1
|A1
|Mib, Sib
|A2
|diminished third
|A3
| -1
|}
|Re, La
==Modes==
|perfect second
The mode names are based on the species of fourth:
{| class="wikitable"
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="2" |Interval type
|-
|-
|2
!name
|Reb, Lab
!pattern
|diminished second
!notation
| -2
!2nd
|Mi, Si
!3rd
|perfect third
|-
|-
| colspan="6" |The chromatic 5-note MOS also has the following intervals (from some root):
|Major
|LLs
|<nowiki>2|0</nowiki>
|P
|P
|-
|-
|3
|Minor
|Dob, Solb
|LsL
| diminished fourth
|<nowiki>1|1</nowiki>
| -3
|P
|Do#, Sol#
|d
|augmented unison (chroma)
|-
|-
|4
|Phrygian
|Mibb, Sibb
|sLL
|doubly diminished third
|<nowiki>0|2</nowiki>
| -4
|d
|Re#, La#
|d
|augmented second
|}
|}
==Genchain==
==Temperaments==
The generator chain for this scale is as follows:
The most basic rank-2 temperament interpretation of diatonic is '''Mahuric'''. The name "Mahuric" comes from the “Mahur” scale in Persian and Arabic music. The major triad is spelled <code>root-2g-(p+g)</code> (p = 4/3, g = the whole tone) and approximates 4:5:6 in pental interpretations or 14:18:21 in septimal ones. Basic ~5ed4/3 fits both interpretations.
{| class="wikitable"
==='''Mahuric-Meantone'''===
|Mibb
[[Subgroup]]: 4/3.5/4.3/2
Sibb
 
|Dob
[[Comma]] list: [[81/80]]
Solb
 
|Reb
[[POL2]] generator: ~9/8 = 193.6725¢
Lab
 
|Mib
[[Mapping]]: [{{val|1 0 1}}, {{val|0 2 1}}]
Sib
 
|Do
[[Optimal ET sequence]]: [[15ed12/5]], [[24ed12/5]], [[39ed12/5]] ≈ [[5ed4/3]], [[8ed4/3]], [[13ed4/3]]
Sol
==='''Mahuric-Superpyth'''===
|Re
[[Subgroup]]: 4/3.9/7.3/2
La
 
|Mi
[[Comma]] list: [[64/63]]
Si
 
|Do#
[[POL2]] generator: ~8/7 = 216.7325¢
Sol#
 
|Re#
[[Mapping]]: [{{val|1 0 1}}, {{val|0 2 1}}]
La#
 
|Mi#
[[Optimal ET sequence]]: [[15ed7/3]], [[21ed7/3]], [[27ed7/3]], [[33ed7/3]] ≈ [[5ed4/3]], [[7ed4/3]], [[9ed4/3]], [[11ed4/3]]
Si#
====Scale tree====
The spectrum looks like this:
{| class="wikitable"
!Generator
(bright)
!Cents
!L
!s
!L/s
!Comments
|-
|1\3
|171.429
|1
|1
|1.000
|Equalised
|-
|-
|dd3
|6\17
|d4
|180.000
|d2
|6
|d3
|5
|P1
|1.200
|P2
|
|P3
|A1
|A2
|A3
|}
==Modes==
The mode names are based on the species of fourth:
{| class="wikitable"
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="2" |Interval type
|-
|-
!name
|5\14
!pattern
|181.818
!notation
|5
! 2nd
|4
!3rd
|1.250
|
|-
|-
|Major
|14\39
|LLs
|182.609
|<nowiki>2|0</nowiki>
|14
|P
|11
|P
|1.273
|
|-
|-
|Minor
|9\25
|LsL
|183.051
|<nowiki>1|1</nowiki>
|9
|P
|7
|d
|1.286
|
|-
|4\11
|184.615
|4
|3
|1.333
|
|-
|-
|Phrygian
|11\30
|sLL
|185.915
|<nowiki>0|2</nowiki>
|11
|d
|8
|d
|1.375
|}
|
==Temperaments==
The most basic rank-2 temperament interpretation of diatonic is '''Mahuric'''. The name "Mahuric" comes from the “Mahur” scale in Persian and Arabic music. The major triad is spelled <code>root-2g-(p+g)</code> (p = 4/3, g = the whole tone) and approximates 4:5:6 in pental interpretations or 14:18:21 in septimal ones. Basic ~5ed4/3 fits both interpretations.
==='''Mahuric-Meantone'''===
[[Subgroup]]: 4/3.5/4.3/2
 
[[Comma]] list: [[81/80]]
 
[[POL2]] generator: ~9/8 = 193.6725¢
 
[[Mapping]]: [{{val|1 0 1}}, {{val|0 2 1}}]
 
[[Optimal ET sequence]]: ~(5ed4/3, 8ed4/3, 13ed4/3)
==='''Mahuric-Superpyth'''===
[[Subgroup]]: 4/3.9/7.3/2
 
[[Comma]] list: [[64/63]]
 
[[POL2]] generator: ~8/7 = 216.7325¢
 
[[Mapping]]: [{{val|1 0 1}}, {{val|0 2 1}}]
 
[[Optimal ET sequence]]: ~(5ed4/3, 7ed4/3, 9ed4/3, 11ed4/3)
====Scale tree ====
The spectrum looks like this:
{| class="wikitable"
!Generator
(bright)
!Cents
!L
!s
!L/s
!Comments
|-
|-
|1\3
|7\19
|171.429
|186.667
| 1
|7
|1
|1.000
|Equalised
|-
|6\17
|180.000
|6
|5
|5
|1.200
|1.400
|
|
|-
|-
|5\14
|10\27
|181.818
|187.500
|5
|10
|4
|7
|1.250
|1.429
|
|
|-
|-
|14\39
|13\35
|182.609
|187.952
|14
|13
|11
|9
|1.273
|1.444
|
|
|-
|-
|9\25
|16\43
|183.051
|188.253
|9
|16
|7
|11
|1.286
|1.4545
|
|
|-
|-
|4\11
|3\8
|184.615
|189.474
|4
|3
|3
|1.333
|2
|1.500
|Mahuric-Meantone starts here
|-
|14\37
|190.909
|14
|9
|1.556
|
|
|-
|-
|11\30
|11\29
|185.915
|191.304
|11
|11
| 8
|7
|1.375
|1.571
|
|
|-
|-
|7\19
|8\21
| 186.667
|192.000
|7
|8
|5
|5
| 1.400
|1.600
|
|
|-
|-
|10\27
|5\13
|187.500
|193.548
|10
|5
|7
|3
|1.429
|1.667
|
|
|-
|-
|13\35
|12\31
|187.952
|194.595
|13
|12
|9
|7
|1.444
|1.714
|
|
|-
|-
|16\43
|7\18
|188.253
|195.348
|16
|7
|11
|4
|1.4545
|1.750
|
|
|-
|-
|3\8
|9\23
|189.474
|196.364
| 3
|2
|1.500
| Mahuric-Meantone starts here
|-
|14\37
|190.909
| 14
|9
|9
|1.556
|5
|1.800
|
|
|-
|-
|11\29
|11\28
|191.304
|197.015
|11
|11
| 7
|6
|1.571
|1.833
|
|
|-
|-
|8\21
|13\33
|192.000
|197.468
|13
|7
|1.857
|
|-
|15\38
|197.802
|15
|8
|8
|5
|1.875
|1.600
|
|
|-
|-
|5\13
|17\43
| 193.548
|198.058
|5
|17
|3
|9
|1.667
|1.889
|
|
|-
|-
|12\31
|19\48
|194.595
|198.261
|12
|19
|7
|10
|1.714
|1.900
|
|
|-
|-
|7\18
|21\53
|195.348
|198.425
|7
|21
|4
|11
|1.750
|1.909
|
|
|-
|-
|9\23
|23\58
|196.364
|198.561
|9
|23
|5
|12
|1.800
|1.917
|
|
|-
|-
|11\28
|25\63
|197.015
|198.675
| 11
|25
|6
|13
|1.833
|1.923
|
|
|-
|-
|13\33
|27\68
|197.468
|198.773
|13
|27
|7
|14
|1.857
|1.929
|
|
|-
|-
|15\38
|29\73
|197.802
|198.857
| 15
|29
|8
|15
|1.875
|1.933
|
|
|-
|-
|17\43
|31\78
|198.058
|198.930
|17
|31
|9
|16
|1.889
|1.9375
|
|
|-
|-
|19\48
|33\83
|198.261
|198.995
|19
|33
|10
|17
|1.900
|1.941
|
|
|-
|-
|21\53
|35\88
|198.425
|199.052
|21
|35
|11
|18
|1.909
|1.944
|
|
|-
|-
|23\58
|2\5
|198.561
|200.000
|23
|2
|12
|1
|1.917
|2.000
|
|Mahuric-Meantone ends, Mahuric-Pythagorean begins
|-
|-
|25\63
|17\42
|198.675
|201.980
|25
|17
|13
|8
|1.923
|2.125
|
|
|-
|-
|27\68
|15\37
|198.773
|202.247
|27
|15
|14
|7
|1.929
|2.143
|
|
|-
|-
|29\73
|13\32
|198.857
|202.597
|29
|13
|15
|6
|1.933
|2.167
|
|
|-
|-
|31\78
|11\27
|198.930
|203.077
|31
|11
|16
|5
|1.9375
|2.200
|
|
|-
|-
|33\83
|9\22
| 198.995
|203.774
|33
|9
|17
|4
|1.941
|2.250
|
|
|-
|-
|35\88
|7\17
| 199.052
|204.878
|35
|7
|18
|3
|1.944
|2.333
|
|
|-
|-
|2\5
|12\29
|200.000
|205.714
|12
|5
|2.400
|
|-
|5\12
|206.897
|5
|2
|2
|1
|2.500
|2.000
|Mahuric-Neogothic heartland is from here…
|Mahuric-Meantone ends, Mahuric-Pythagorean begins
|-
|-
|17\42
|18\43
|201.980
|207.693
|17
|18
|8
|2.125
|
|-
|15\37
|202.247
|15
|7
|7
|2.143
|2.571
|
|
|-
|-
|13\32
|13\31
|202.597
|208.000
|13
|13
|6
|5
|2.167
|2.600
|
|
|-
|-
|11\27
|8\19
|203.077
|208.696
|8
|3
|2.667
|…to here
|-
|11\26
|209.524
|11
|11
|4
|2.750
|
|-
|14\33
|210.000
|14
|5
|5
|2.200
|2.800
|
|
|-
|-
|9\22
|3\7
|203.774
|211.755
|9
|3
|4
|1
|2.250
|3.000
|Mahuric-Pythagorean ends, Mahuric-Superpyth begins
|-
|22\51
|212.903
|22
|7
|3.143
|
|
|-
|-
|7\17
|19\44
|204.878
|213.084
|7
|19
|3
|6
|2.333
|3.167
|
|
|-
|-
|12\29
|16\37
|205.714
|213.333
| 12
|16
|5
|5
|2.400
|3.200
|
|
|-
|-
|5\12
|13\30
|206.897
|213.699
|5
|13
|2
|4
|2.500
|3.250
|Mahuric-Neogothic heartland is from here…
|-
|18\43
|207.693
|18
|7
|2.571
|
|
|-
|-
|13\31
|10\23
|208.000
|214.286
|13
|10
|5
|3
|2.600
|3.333
|
|
|-
|-
|8\19
|7\16
|208.696
|215.385
|8
|7
|2
|3.500
|
|-
|11\25
|216.393
|11
|3
|3
|2.667
|3.667
|…to here
|
|-
|-
|11\26
|15\34
|209.524
|216.867
|11
|15
|4
|4
|2.750
|3.750
|
|
|-
|-
|14\33
|19\43
|210.000
|217.143
|14
|19
|5
|5
|2.800
|3.800
|
|
|-
|-
|3\7
|4\9
|211.755
|218.182
|3
|4
|1
|1
|3.000
|4.000
|Mahuric-Pythagorean ends, Mahuric-Superpyth begins
|
|-
|-
|22\51
|13\29
|212.903
|219.718
|22
|13
|7
|3
|3.143
|4.333
|
|
|-
|-
|19\44
|9\20
|213.084
|220.408
| 19
|9
|6
|2
|3.167
|4.500
|
|
|-
|-
|16\37
|14\31
|213.333
|221.053
|16
|14
|3
|4.667
|
|-
|5\11
|222.222
|5
|5
|3.200
|1
|5.000
|Mahuric-Superpyth ends
|-
|11\24
|223.728
|11
|2
|5.500
|
|
|-
|-
|13\30
|17\37
|213.699
|224.176
|13
|17
|4
|3
|3.250
|5.667
|
|
|-
|-
|10\23
|6\13
|214.286
|225.000
|10
|6
|3
|1
|3.333
|6.000
|
|
|-
|-
|7\16
|1\2
|215.385
|240.000
|7
|1
|2
|0
|3.500
|→ inf
|
|Paucitonic
|-
|}
|11\25
 
|216.393
==See also==
|11
[[2L 1s (4/3-equivalent)]] - idealized tuning
|3
 
|3.667
[[4L 2s (7/4-equivalent)]] - Mixolydian and Dorian hexatonic Archytas temperament
|
 
|-
[[4L 2s (39/22-equivalent)]] - Mixolydian and Dorian hexatonic Neogothic temperament
|15\34
 
|216.867
[[4L 2s (Komornik–Loreti constant-equivalent)]] - Mixolydian and Dorian hexatonic Komornik–Loreti temperament
|15
 
|4
[[4L 2s (9/5-equivalent)]] - Mixolydian and Dorian hexatonic Meantone temperament
|3.750
 
|
[[6L 3s (7/3-equivalent)]] - Mahuric-Archytas temperament
|-
 
|19\43
[[6L 3s (26/11-equivalent)]] - Mahuric-Neogothic temperament
|217.143
 
|19
[[6L 3s (12/5-equivalent)]] - Mahuric-Meantone temperament
|5
 
|3.800
[[8L 4s (28/9-equivalent)]] - Bijou Archytas temperament
|
 
|-
[[8L 4s (22/7-equivalent)]] and [[8L 4s (π-equivalent)|8L 4s ([math]π[/math]-equivalent)]] - Bijou Neogothic temperament
|4\9
 
|218.{{Overline|18}}
[[8L 4s (16/5-equivalent)]] - Bijou Meantone temperament
|4
 
|1
[[10L 5s (112/27-equivalent)]] - Hyperionic Archytas temperament
|4.000
 
|
[[10L 5s (88/21-equivalent)]] - Hyperionic Neogothic temperament
|-
 
|13\29
[[10L 5s (64/15-equivalent)]] - Hyperionic Meantone temperament
|219.718
 
|13
[[10L 5s (30/7-equivalent)]] - Hyperionic septimal Meantone temperament
|3
 
|4.333
[[12L 6s (16/3-equivalent)]] - Warped Pythagorean Subsextal temperament
|
 
|-
[[12L 6s (343/64-equivalent)]] - 1/2 comma Archytas Subsextal temperament]
|9\20
 
|220.408
[[12L 6s (11/2-equivalent)]] - Low undecimal Subsextal temperament
|9
 
|2
[[12L 6s (448/81-equivalent)]] - 1/6 comma Archytas Subsextal temperament
|4.500
 
|
[[12L 6s (4096/729-equivalent)]] - Pythagorean Subsextal temperament
|-
 
|14\31
[[12L 6s (28/5-equivalent)]] - Low septimal (meantone) Subsextal temperament
|221.053
 
|14
[[12L 6s (45/16-equivalent)|12L 6s (256/45-equivalent)]] - 1/6 comma meantone Subsextal temperament
|3
|4.667
|
|-
|5\11
|222.222
|5
|1
|5.000
|Mahuric-Superpyth ends
|-
|11\24
|223.728
|11
|2
|5.500
|
|-
|17\37
|224.176
|17
|3
|5.667
|
|-
|6\13
|225.000
|6
|1
|6.000
|
|-
| 1\3
|240.000
|1
|0
|→ inf
|Paucitonic
|}


==See also==
[[12L 6s (40/7-equivalent)]] - High septimal Subsextal temperament  
[[2L 1s (4/3-equivalent)]] - idealized tuning
 
[[4L 2s (7/4-equivalent)]] - Mixolydian and Dorian hexatonic Archytas temperament
 
[[4L 2s (39/22-equivalent)]] - Mixolydian and Dorian hexatonic Neogothic temperament
 
[[4L 2s (Komornik–Loreti constant-equivalent)]] - Mixolydian and Dorian hexatonic Komornik–Loreti temperament
 
[[4L 2s (9/5-equivalent)]] - Mixolydian and Dorian hexatonic Meantone temperament
 
[[6L 3s (7/3-equivalent)]] - Mahuric-Archytas temperament
 
[[6L 3s (26/11-equivalent)]] - Mahuric-Neogothic temperament
 
[[6L 3s (12/5-equivalent)]] - Mahuric-Meantone temperament
 
[[8L 4s (28/9-equivalent)]] - Bijou Archytas temperament
 
[[8L 4s (22/7-equivalent)]] and [[8L 4s (π-equivalent)|8L 4s ([math]π[/math]-equivalent)]] - Bijou Neogothic temperament
 
[[8L 4s (16/5-equivalent)]] - Bijou Meantone temperament
 
[[10L 5s (112/27-equivalent)]] - Hyperionic Archytas temperament


[[10L 5s (88/21-equivalent)]] - Hyperionic Neogothic temperament
[[12L 6s (64/11-equivalent)]] - High undecimal Subsextal temperament  
 
[[10L 5s (30/7-equivalent)]] - Hyperionic Meantone temperament
 
[[12L 6s (11/2-equivalent)]] - Low undecimal Subsextal temperament
 
[[12L 6s (28/5-equivalent)]] - Low septimal Subsextal temperament
 
[[12L 6s (40/7-equivalent)]] - High septimal Subsextal temperament  


[[12L 6s (64/11-equivalent)]] - High undecimal Subsextal temperament <references />
[[12L 6s (729/125-equivalent)]] - 1/2 comma meantone Subsextal temperament <references />
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