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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 4 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 or quintuple fourth (minor seventh, tenth, thirteenth or sixteenth), 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] or a minor sixteenth which is the Phrygian mode of Hyperionic. Since there are exactly 9 naturals in triple fourth notation, 12 in quadruple fourth and 15 in quintuple fourth notation, letters A-G plus J, Q or Q, S (GJABCQDEF or GABCQDSEF, flats written F molle) or dozenal or hex digits (0123456789XE0 or E1234567GABDE with flats written D molle or 123456789ABCDEF1 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<ref name=":05">Fractions repeating more than 4 digits written as continued fractions</ref>
|+Cents
!Notation
!Supersoft
!Soft
!Semisoft
!Basic
!Semihard
!Hard
!Superhard
|-
!Fourth
!~11ed4/3
!~8ed4/3
!~13ed4/3
!~5ed4/3
!~12ed4/3
!~7ed4\3
!~9ed4/3
|-
|F/C/G ut#
Do#, Sol#
 
د#,
 
ص#
|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
|-
| G/D/A reb
Reb, Lab
 
رb, لb
|3\11, 138.462
|2\8, 126.316
|3\13, 116.129
|2\12, 82.759
|1\7, 70.588
|1\9, 54.545
|-
|'''G/D/A re'''
'''Re, La'''
 
'''ر, ل'''
|'''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'''
|-
|G/D/A re#
Re#, La#
 
ر,# ل#
|5\11, 230.769
| 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
|-
|A/E/B mibb
Mibb, Sibb
 
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'''
|'''5\8,''' '''315.789'''
|'''8\13,''' '''309.677'''
|'''3\5,''' '''300'''
|'''7\12,''' '''289.655'''
|'''4\7,''' '''282.353'''
|'''5\9,''' '''272.727'''
|-
|A/E/B mi
Mi, Si
 
م, ت
|8\11, 369.231
|6\8, 378.947
|10\13, 387.097
|4\5, 400
|10\12, 413.793
|6\7, 423.529
|8\9, 436.364
|-
|A/E/B mi#
Mi#, Si#
 
م,#ت#
|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
|-
|F/C/G utb
Dob, Solb
 
دb,
 
صb
|10\11, 461.538
|11\13, 425.806
|4\5, 400
|9\12, 372.414
|5\7, 352.941
|6\9, 327.273
|-
!F/C/G ut
Do, Sol
 
د, 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'''
|}
 
{| class="wikitable"
|+Cents
! colspan="2" |Notation
! colspan="2" |Notation
!Supersoft
!Supersoft
Line 19: Line 161:
!Superhard
!Superhard
|-
|-
!Fourth
! colspan="2" |Seventh
!Seventh
!~11ed4/3
!~11ed4/3
!~8ed4/3
!~8ed4/3
Line 29: Line 170:
!~9ed4/3
!~9ed4/3
|-
|-
|Do#, Sol#
!Mixolydian
|Sol#
!Dorian
|1\11
!
46; 6.5
!
|1\8
!
63; 6.{{Overline|3}}
!
|2\13
!
77; 2, 2.6
!
| rowspan="2" |1\5
!
100
|3\12
124; 7.25
|2\7
141; 5.{{Overline|6}}
|3\9
163.{{Overline|63}}
|-
|-
|Reb, Lab
| F/C/G ut#
|Lab
Sol#
|3\11
 
138; 3.25
ص#
|2\8
|G/D/A re#
126; 3.1{{Overline|6}}
Re#
|3\13
 
116; 7.75
ر#
|2\12
|1\11, 46.154
82; 1.3{{Overline|18}}
|1\8, 63.158
|1\7
|2\13, 77.419
70; 1.7
| rowspan="2" |1\5, 100
|1\9
| 3\12, 124.138
54.{{Overline|54}}
|2\7, 141.176
|3\9, 163.636
|-
|-
|'''Re, La'''
|G/D/A reb
|'''La'''
Lab
|'''4\11'''
 
'''184; 1.625'''
لb
|'''3\8'''
|A/E/B mib
'''189; 2.{{Overline|1}}'''
Mib
|'''5\13'''
 
'''193; 1, 1, 4.{{Overline|6}}'''
مb
|'''2\5'''
|3\11, 138.462
'''200'''
|2\8, 126.316
|'''5\12'''
|3\13, 116.129
'''206; 1, 8.{{Overline|6}}'''
|2\12, 82.759
|'''3\7'''
|1\7, 70.588
'''211; 1, 3.25'''
|1\9, 54.545
|'''4\9'''
'''218.{{Overline|18}}'''
|-
|-
|Re#, La#
|'''G/D/A re'''
|La#
'''La'''
|5\11
 
230; 1.3
ل
|4\8
|'''A/E/B mi'''
252; 1.58{{Overline|3}}
'''Mi'''
|7\13
 
270; 1.0{{Overline|3}}
م
| rowspan="2" |'''3\5'''
|'''4\11,''' '''184.615'''
'''300'''
|'''3\8,''' '''189.474'''
|8\12
|'''5\13,''' '''193.548'''
331; 29
|'''2\5,''' '''200'''
|5\7
|'''5\12,''' '''206.897'''
352; 1.0625
|'''3\7,''' '''211.765'''
|7\9
|'''4\9,''' '''218.182'''
381.{{Overline|81}}
|-
|G/D/A re#
La#
 
ل#
| A/E/B mi#
Mi#
 
م#
|5\11, 230.769
| 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
|-
|A/E/B mibb
Sibb
 
تbb
|B/F/C fab
Fab
 
فb
|6\11, 276.923
|6\13, 232.258
|2\5, 200
|4\12, 165.517
|2\7, 141.176
|2\9, 109.091
|-
|-
|'''Mib, Sib'''
|'''A/E/B mib'''
|'''Sib'''
'''Sib'''
|'''7\11'''
 
'''323; 13'''
تb
|'''5\8'''
|'''B/F/C fa'''
'''315; 1.2{{Overline|6}}'''
'''Fa'''
|'''8\13'''
 
'''309; 1, 2.1'''
'''ف'''
|'''7\12'''
|'''7\11,''' '''323.077'''
'''289; 1, 1.9'''
|'''5\8,''' '''315.789'''
|'''4\7'''
|'''8\13,''' '''309.677'''
'''282; 2.8{{Overline|3}}'''
|'''3\5,''' '''300'''
|'''5\9'''
|'''7\12,''' '''289.655'''
'''272.{{Overline|72}}'''
|'''4\7,''' '''282.353'''
|'''5\9,''' '''272.727'''
|-
|-
|Mi, Si
|A/E/B mi
|Si
Si
|8\11
 
369; 4.{{Overline|3}}
ت
|6\8
|B/F/C fa#
378; 1.0{{Overline|5}}
Fa#
|10\13
 
387; 10.{{Overline|3}}
ف#
|4\5
| 8\11, 369.231
400
|6\8, 378.947
|10\12
|10\13, 387.097
413; 1, 3.8{{Overline|3}}
|4\5, 400
|6\7
|10\12, 413.793
423; 1.{{Overline|8}}
|6\7, 423.529
|8\9
|8\9, 436.364
436.{{Overline|36}}
|-
|-
|Mi#, Si#
|A/E/B mi#
|Si#
Si#
|9\11
 
415; 2.6
ت#
| rowspan="2" |7\8
|B/F/C fax
442; 9.5
Fax
|12\13
 
464; 1.9375
فx
|5\5
|9\11, 415.385
500
| rowspan="2" |7\8, 442.105
|13\12
|12\13, 464.516
537; 14.5
|5\5, 500
|8\7
|13\12, 537.069
564; 1.41{{Overline|6}}
|8\7, 564.705
|11\9
|11\9, 600
600
|-
|-
|Dob, Solb
| B/F/C fab
|Dob
Dob
|10\11
 
461; 1, 1.1{{Overline|6}}
دb
|11\13
|C/G/D solb
425; 1.24
Solb
|4\5
 
400
صb
|9\12
|10\11, 461.538
372; 2.41{{Overline|6}}
|11\13, 425.806
|5\7
|4\5, 400
352; 1.0625
|9\12, 372.414
|6\9
|5\7, 352.941
327.{{Overline|27}}
|6\9, 327.273
|-
|-
!Do, Sol
!B/F/C fa
!Do
Do
!'''11\11'''
 
'''507; 1.{{Overline|4}}'''
د
!'''8\8'''
!C/G/D sol
'''505; 3.8'''
Sol
!'''13\13'''
 
'''503; 4, 2.{{Overline|3}}'''
ص
!'''5\5'''
!'''11\11,''' '''507.692'''
'''500'''
!'''8\8,''' '''505.263'''
!'''12\12'''
!'''13\13,''' '''503.226'''
'''496; 1.8125'''
!5\5, 500
!'''7\7'''
!'''12\12,''' '''496.552'''
'''494; 8.5'''
!'''7\7,''' '''494.118'''
!'''9\9'''
!'''9\9,''' '''490.909'''
'''490.{{Overline|90}}'''
|-
|-
|Do#, Sol#
|B/F/C fa#
|Do#
Do#
|12\11
 
553; 1.{{Overline|18}}
د#
|9\8
| C/G/D sol#
568; 2.375
Sol#
|15\13
 
580; 1.55
ص#
| rowspan="2" |6\5
|12\11, 553.846
600
|9\8, 568.421
|15\12
|15\13, 580.645
620; 1.45
| rowspan="2" |6\5, 600
|9\7
|15\12, 620.690
635; 3.4
|9\7, 635.294
|12\9
|12\9, 654.545
654.{{Overline|54}}
|-
|-
|Reb, Lab
|C/G/D solb
|Reb
Reb
|14\11
 
646; 6.5
رb
|10\8
|D/A/E lab
631; 1.{{Overline|72}}
Lab
|16\13
 
619; 2.{{Overline|81}}
لb
|14\12
|14\11, 646.154
579; 3.{{Overline|2}}
|10\8, 631.579
|8\7
|16\13, 619.355
564; 1.41{{Overline|6}}
|14\12, 579.310
|10\9
|8\7, 564.706
545.{{Overline|45}}
|10\9, 545.455
|-
|-
|'''Re, La'''
|'''C/G/D sol'''
|'''Re'''
'''Re'''
|'''15\11'''
 
'''692; 3.25'''
ر
|'''11\8'''
|'''D/A/E la'''
'''694; 1, 2.8'''
'''La'''
|'''18\13'''
 
'''696; 1.291{{Overline|6}}'''
ل
|'''7\5'''
|'''15\11,''' '''692.308'''
'''700'''
|'''11\8''' '''694.737'''
|'''17\12'''
|'''18\13,''' '''696.774'''
'''703; 2, 2.1{{Overline|6}}'''
|'''7\5,''' '''700'''
|'''10\7'''
|'''17\12,''' '''703.448'''
'''705; 1.1{{Overline|3}}'''
|'''10\7,''' '''705.882'''
|'''13\9'''
|'''13\9,''' '''709.091'''
'''709.{{Overline|09}}'''
|-
|-
|Re#, La#
|C/G/D sol#
|Re#
Re#
|16\11
 
738; 2.1{{Overline|6}}
د#
|12\8
|D/A/E la#
757; 1, 8.5
La#
|20\13
 
774; 5.1{{Overline|6}}
ل#
| rowspan="2" |'''8\5'''
|16\11, 738.462
'''800'''
|12\8, 757.895
|20\12
|20\13, 774.294
827; 1, 1.41{{Overline|6}}
| rowspan="2" |'''8\5,''' '''800'''
|12\7
|20\12, 827.586
847; 17
|12\7, 847.059
|16\9
|16\9, 872.727
872.{{Overline|72}}
|-
|-
|'''Mib, Sib'''
|'''D/A/E lab'''
|'''Mib'''
'''Mib'''
|'''18\11'''
 
'''830; 1.3'''
مb
|'''13\8'''
|'''E/B/F síb'''
'''821; 19'''
'''Sib'''
|'''21\13'''
 
'''812; 1, 9.{{Overline|3}}'''
تb
|'''19\12'''
|'''18\11,''' '''830.769'''
'''786; 4.8{{Overline|3}}'''
|'''13\8,''' '''821.053'''
|'''11\7'''
|'''21\13,''' '''812.903'''
'''776; 2.125'''
|'''19\12,''' '''786.207'''
|'''14\9'''
|'''11\7,''' '''776.471'''
'''763.{{Overline|63}}'''
|'''14\9,''' '''763.636'''
|-
|-
|Mi, Si
|D/A/E la
|Mi
Mi
|19\11
 
876; 1.08{{Overline|3}}
م
|14\8
|E/B/F sí
884; 4.75
Si
|23\13
 
890; 3.1
ت
|9\5
|19\11, 876.923
900
|14\8, 884.211
|22\12
|23\13, 890.323
910; 2.9
|9\5, 900
|13\7
|22\12, 910.345
917; 1.{{Overline|54}}
|13\7, 917.647
|17\9
|17\9, 927.727
927.{{Overline|27}}
|-
|-
|Mi#, Si#
|D/A/E la#
|Mi#
Mi#
|20\11
 
923: 13
م#
| rowspan="2" |15\8
|E/B/F sí#
947; 2, 1.4
Si#
|25\13
 
967; 1, 2.875
ت#
|10\5
|20\11, 923.077
1000
| rowspan="2" |15\8, 947.378
|25\12
|25\13, 967.742
1034; 2, 14
|10\5, 1000
|15\7
|25\12, 1034.483
1058; 1, 4.{{Overline|6}}
|15\7, 1058.824
|20\9
|20\9, 1090.909
1090.{{Overline|90}}
|-
|-
|Dob, Solb
|F/C/G utb
|Solb
Solb
|21\11
 
969; 4.{{Overline|3}}
صb
|24\13
|G/D/A reb
929; 31
Reb
|9\5
 
900
رb
|21\12
|21\11, 969.231
868; 1, 28
|24\13, 929.033
|11\7
|9\5, 900
776; 2.125
|21\12, 868.966
|15\9
|11\7, 776.471
818.{{Overline|18}}
|15\9, 818.182
|-
|-
!Do, Sol
!F/C/G ut
!Sol
Sol
!22\11
 
1015; 2.6
ص
!16\8
!G/D/A re
1010; 1.9
Re
!26\13
 
1006; 2, 4.{{Overline|6}}
ر
!10\5
!22\11, 1015.385
1000
! 16\8, 1010.526
!24\12
! 26\13, 1006.452
993; 9.{{Overline|6}}
!10\5, 1000
!14\7
!24\12, 993.103
988; 4.25
!14\7, 988.235
!18\9
!18\9, 981.818
981.{{Overline|81}}
|}
|}
{| class="wikitable"
{| class="wikitable"
! colspan="3" |Notation
!Notation
!Supersoft
!Supersoft
!Soft
!Soft
Line 333: Line 488:
!Superhard
!Superhard
|-
|-
! rowspan="2" |Mahur
!Mahur
! rowspan="2" |Bijou
!~11ed4/3
! rowspan="2" |Hyperionic
!~8ed4/3
! rowspan="2" |~11ed4/3
!~13ed4/3
! rowspan="2" |~8ed4/3
!~5ed4/3
! rowspan="2" |~13ed4/3
!~12ed4/3
! rowspan="2" |~5ed4/3
!~7ed4\3
! rowspan="2" |~12ed4/3
! ~9ed4/3
! rowspan="2" |~7ed4\3
|-
! rowspan="2" |~9ed4/3
|G#
|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
|-
|Jf, Af
|3\11, 138.462
|2\8, 126.316
|3\13, 116.129
|2\12, 82.759
|1\7, 70.588
|1\9, 54.545
|-
|'''J, A'''
|'''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'''
|-
| J#, A#
|5\11, 230.769
|4\8, 252.632
|7\13, 270.968
| rowspan="2" |'''3\5,''' '''300'''
|8\12, 331.034
|5\7, 352.941
|7\9, 381.818
|-
|'''Af, Bf'''
|'''7\11,''' '''323.077'''
|'''5\8,''' '''315.789'''
|'''8\13,''' '''309.677'''
|'''7\12,''' '''289.655'''
|'''4\7,''' '''282.353'''
|'''5\9,''' '''272.727'''
|-
|A, B
|8\11, 369.231
|6\8, 378.947
|10\13, 387.097
|4\5, 400
|10\12, 413.793
|6\7, 423.529
|8\9, 436.364
|-
|A#, B#
|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
|-
|Bb, Cf
|10\11, 461.538
|11\13, 425.806
|4\5, 400
|9\12, 372.414
|5\7, 352.941
|6\9, 327.273
|-
!B, C
!'''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'''
|-
|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
|-
|Cf, Qf
|14\11, 646.154
|10\8, 631.579
|16\13, 619.355
|14\12, 579.310
|8\7, 564.706
| 10\9, 545.455
|-
|'''C, Q'''
|'''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'''
|-
|C#, Q#
|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
|-
|'''Qf, Df'''
|'''18\11,''' '''830.769'''
|'''13\8,''' '''821.053'''
|'''21\13,''' '''812.903'''
|'''19\12,''' '''786.207'''
|'''11\7,''' '''776.471'''
|'''14\9,''' '''763.636'''
|-
|Q, D
|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
|-
|Q#, D#
|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
|-
|-
|Df, Sf
| 21\11, 969.231
|24\13, 929.033
|9\5, 900
|21\12, 868.966
|11\7, 776.471
|15\9, 818.182
|-
!D, S
!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
|-
|D#, S#
|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
|-
|Ef
|25\11, 1153.846
|18\8, 1136.842
|29\13, 1122.581
|26\12, 1075.862
|15\7, 1058.824
|19\9, 1036.364
|-
|'''E'''
|'''26\11,''' '''1200'''
|'''19\8,''' '''1200'''
|'''31\13,''' '''1200'''
|'''12\5,''' '''1200'''
|'''29\12,''' '''1200'''
|'''17\7,''' '''1200'''
|'''22\9,''' '''1200'''
|-
|E#
|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
|-
|'''Ff'''
|'''29\11,''' '''1338.462'''
|'''21\8,''' '''1326.316'''
|'''34\13,''' '''1316.129'''
|'''31\12,''' '''1282.759'''
|'''18\7,''' '''1270.588'''
|'''23\9,''' '''1254.545'''
|-
|F
|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
|-
|F#
|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
|-
|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"
!Notation
! Supersoft
!Soft
!Semisoft
!Basic
!Semihard
!Hard
!Superhard
|-
!Bijou
!~11ed4/3
! ~8ed4/3
!~13ed4/3
!~5ed4/3
!~12ed4/3
!~7ed4\3
!~9ed4/3
|-
|-
|G#
|0#, E#
|0#, D#
|1\11, 46.154
|1#
|1\8, 63.158
|1\11
|2\13, 77.419
46; 6.5
| rowspan="2" |1\5, 100
|1\8
|3\12, 124.138
63; 6.{{Overline|3}}
|2\7, 141.176
|2\13
| 3\9, 163.636
77; 2, 2.6
| rowspan="2" |1\5
100
|3\12
124; 7.25
|2\7
141; 5.{{Overline|6}}
|3\9
163.{{Overline|63}}
|-
|-
|Jf, Af
|1b, 1d
|1b, 1d
|2f
|3\11, 138.462
|3\11
|2\8, 126.316
138; 3.25
|3\13, 116.129
|2\8
| 2\12, 82.759
126; 3.1{{Overline|6}}
|1\7, 70.588
|3\13
|1\9, 54.545
116; 7.75
|2\12
82; 1.3{{Overline|18}}
|1\7
70; 1.7
|1\9
54.{{Overline|54}}
|-
|-
|'''J, A'''
|'''1'''
|'''1'''
|'''2'''
|'''4\11,''' '''184.615'''
|'''4\11'''
|'''3\8,''' '''189.474'''
'''184; 1.625'''
|'''5\13,''' '''193.548'''
|'''3\8'''
|'''2\5,''' '''200'''
'''189; 2.{{Overline|1}}'''
|'''5\12,''' '''206.897'''
|'''5\13'''
|'''3\7,''' '''211.765'''
'''193; 1, 1, 4.{{Overline|6}}'''
|'''4\9,''' '''218.182'''
|'''2\5'''
'''200'''
|'''5\12'''
'''206; 1, 8.{{Overline|6}}'''
|'''3\7'''
'''211; 1, 3.25'''
|'''4\9'''
'''218.{{Overline|18}}'''
|-
|-
|J#, A#
|1#
|1#
|2#
|5\11, 230.769
|5\11
|4\8, 252.632
230; 1.3
|7\13, 270.968
|4\8
| rowspan="2" |'''3\5,''' '''300'''
252; 1.58{{Overline|3}}
|8\12, 331.034
|7\13
|5\7, 352.941
270; 1.0{{Overline|3}}
|7\9, 381.818
| rowspan="2" |'''3\5'''
'''300'''
|8\12
331; 29
|5\7
352; 1.0625
|7\9
381.{{Overline|81}}
|-
|-
|'''Af, Bf'''
|'''2b, 2d'''
|'''2b, 2d'''
|'''3f'''
|'''7\11,''' '''323.077'''
|'''7\11'''
|'''5\8,''' '''315.789'''
'''323; 13'''
|'''8\13,''' '''309.677'''
|'''5\8'''
|'''7\12,''' '''289.655'''
'''315; 1.2{{Overline|6}}'''
|'''4\7,''' '''282.353'''
|'''8\13'''
|'''5\9,''' '''272.727'''
'''309; 1, 2.1'''
|'''7\12'''
'''289; 1, 1.9'''
|'''4\7'''
'''282; 2.8{{Overline|3}}'''
|'''5\9'''
'''272.{{Overline|72}}'''
|-
|-
|A, B
|2
|2
|3
|8\11, 369.231
|8\11
|6\8, 378.947
369; 4.{{Overline|3}}
|10\13, 387.097
|6\8
|4\5, 400
378; 1.0{{Overline|5}}
|10\12, 413.793
|10\13
|6\7, 423.529
387; 10.{{Overline|3}}
|8\9, 436.364
|4\5
400
|10\12
413; 1, 3.8{{Overline|3}}
|6\7
423; 1.{{Overline|8}}
|8\9
436.{{Overline|36}}
|-
|-
|A#, B#
|2#
|2#
|3#
|9\11, 415.385
|9\11
| rowspan="2" |7\8, 442.105
415; 2.6
|12\13, 464.516
| rowspan="2" |7\8
|5\5, 500
442; 9.5
|13\12, 537.069
|12\13
|8\7, 564.705
464; 1.9375
|11\9, 600
|5\5
500
|13\12
537; 14.5
|8\7
564; 1.41{{Overline|6}}
|11\9
600
|-
|-
|Bb, Cf
|3b, 3d
|3b, 3d
|4f
|10\11, 461.538
|10\11
|11\13, 425.806
461; 1, 1.1{{Overline|6}}
|4\5, 400
|11\13
|9\12, 372.414
425; 1.24
|5\7, 352.941
|4\5
|6\9, 327.273
400
|9\12
372; 2.41{{Overline|6}}
|5\7
352; 1.0625
|6\9
327.{{Overline|27}}
|-
|-
!B, C
!3
!3
!4
!'''11\11,''' '''507.692'''
!'''11\11'''
!'''8\8,''' '''505.263'''
'''507; 1.{{Overline|4}}'''
!'''13\13,''' '''503.226'''
!'''8\8'''
!5\5, 500
'''505; 3.8'''
!'''12\12,''' '''496.552'''
!'''13\13'''
!'''7\7,''' '''494.118'''
'''503; 4, 2.{{Overline|3}}'''
!'''9\9,''' '''490.909'''
!'''5\5'''
'''500'''
!'''12\12'''
'''496; 1.8125'''
!'''7\7'''
'''494; 8.5'''
!'''9\9'''
'''490.{{Overline|90}}'''
|-
|-
|B#, C#
|3#
|3#
|4#
|12\11, 553.846
|12\11
|9\8, 568.421
553; 1.{{Overline|18}}
|15\13, 580.645
|9\8
| rowspan="2" |6\5, 600
568; 2.375
|15\12, 620.690
|15\13
|9\7, 635.294
580; 1.55
|12\9, 654.545
| rowspan="2" |6\5
600
|15\12
620; 1.45
|9\7
635; 3.4
|12\9
654.{{Overline|54}}
|-
|-
|Cf, Qf
|4b, 4d
|4b, 4d
|5f
|14\11, 646.154
|14\11
|10\8, 631.579
646; 6.5
|16\13, 619.355
|10\8
|14\12, 579.310
631; 1.{{Overline|72}}
|8\7, 564.706
|16\13
|10\9, 545.455
619; 2.{{Overline|81}}
|14\12
579; 3.{{Overline|2}}
|8\7
564; 1.41{{Overline|6}}
|10\9
545.{{Overline|45}}
|-
|-
|'''C, Q'''
|'''4'''
|'''4'''
|'''5'''
|'''15\11,''' '''692.308'''
|'''15\11'''
|'''11\8''' '''694.737'''
'''692; 3.25'''
|'''18\13,''' '''696.774'''
|'''11\8'''
|'''7\5,''' '''700'''
'''694; 1, 2.8'''
|'''17\12,''' '''703.448'''
|'''18\13'''
|'''10\7,''' '''705.882'''
'''696; 1.291{{Overline|6}}'''
|'''13\9,''' '''709.091'''
|'''7\5'''
'''700'''
|'''17\12'''
'''703; 2, 2.1{{Overline|6}}'''
|'''10\7'''
'''705; 1.1{{Overline|3}}'''
|'''13\9'''
'''709.{{Overline|09}}'''
|-
|-
|C#, Q#
|4#
|4#
|5#
|16\11, 738.462
|16\11
|12\8, 757.895
738; 2.1{{Overline|6}}
|20\13, 774.194
|12\8
| rowspan="2" |'''8\5,''' '''800'''
757; 1, 8.5
|20\12, 827.586
|20\13
|12\7, 847.059
774; 5.1{{Overline|6}}
|16\9, 872.727
| rowspan="2" |'''8\5'''
'''800'''
|20\12
827; 1, 1.41{{Overline|6}}
|12\7
847; 17
|16\9
872.{{Overline|72}}
|-
|-
|'''Qf, Df'''
|'''5b, 5d'''
|'''5b, 5d'''
|'''6f'''
|'''18\11,''' '''830.769'''
|'''18\11'''
|'''13\8,''' '''821.053'''
'''830; 1.3'''
|'''21\13,''' '''812.903'''
|'''13\8'''
|'''19\12,''' '''786.207'''
'''821; 19'''
|'''11\7,''' '''776.471'''
|'''21\13'''
|'''14\9,''' '''763.636'''
'''812; 1, 9.{{Overline|3}}'''
|'''19\12'''
'''786; 4.8{{Overline|3}}'''
|'''11\7'''
'''776; 2.125'''
|'''14\9'''
'''763.{{Overline|63}}'''
|-
|-
|Q, D
|5
|5
|6
|19\11, 876.923
|19\11
|14\8, 884.211
876; 1.08{{Overline|3}}
|23\13, 890.323
|14\8
|9\5, 900
884; 4.75
|22\12, 910.345
|23\13
|13\7, 917.647
890; 3.1
|17\9, 927.727
|9\5
900
|22\12
910; 2.9
|13\7
917; 1.{{Overline|54}}
|17\9
927.{{Overline|27}}
|-
|-
|Q#, D#
|5#
|5#
|6#
|20\11, 923.077
|20\11
| rowspan="2" |15\8, 947.368
923: 13
|25\13, 967.742
| rowspan="2" |15\8
|10\5, 1000
947; 2, 1.4
|25\12, 1034.483
|25\13
|15\7, 1058.824
967; 1, 2.875
|20\9, 1090.909
|10\5
1000
|25\12
1034; 2, 14
|15\7
1058; 1, 4.{{Overline|6}}
|20\9
1090.{{Overline|90}}
|-
|-
|Df, Sf
|6b, 6d
|6b, 6d
|7f
|21\11, 969.231
|21\11
|24\13, 929.033
969; 4.{{Overline|3}}
| 9\5, 900
|24\13
|21\12, 868.966
929; 31
|11\7, 776.471
|9\5
|15\9, 818.182
900
|21\12
868; 1, 28
|11\7
776; 2.125
|15\9
818.{{Overline|18}}
|-
|-
!D, S
!6
!6
!7
!22\11, 1015.385
!22\11
!16\8, 1010.526
1015; 2.6
!26\13, 1006.452
!16\8
!10\5, 1000
1010; 1.9
!24\12, 993.103
!26\13
!14\7, 988.235
1006; 2, 4.{{Overline|6}}
!18\9, 981.818
!10\5
1000
!24\12
993; 9.{{Overline|6}}
!14\7
988; 4.25
!18\9
981.{{Overline|81}}
|-
|-
|D#, S#
|6#
|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
|-
|7b, 7d
| 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#
|7#
|23\11
|27\11, 1246.154
1061; 1, 1.1{{Overline|6}}
|20\8, 1263.158
|17\8
|33\13, 1277.419
1073; 1, 2.1{{Overline|6}}
| rowspan="2" |'''13\5,''' '''1300'''
|28\13
|32\12, 1324.138
1083; 1.{{Overline|148}}
|19\7, 1341.176
| rowspan="2" |11\5
|25\9, 1363.636
1100
|-
|27\12
|'''8b, Gd'''
1117; 4, 7
|'''29\11,''' '''1338.462'''
|16\7
|'''21\8,''' '''1326.316'''
1129; 2, 2.{{Overline|3}}
|'''34\13,''' '''1316.129'''
|24\9
|'''31\12,''' '''1282.759'''
1309.{{Overline|09}}
|'''18\7,''' '''1270.588'''
|'''23\9,''' '''1254.545'''
|-
|8, G
|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#, G#
|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
|-
|9b, Ad
|32\11, 1476.923
|37\13, 1432.258
|14\5, 1400
|33\12, 1365.517
|19\7, 1341.176
|24\9, 1309.091
|-
!'''9, 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
|-
|9#, 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
|-
|Xb, Bd
|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, 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'''
|-
|X#, 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
|-
|'''Eb, Dd'''
|'''40\11,''' '''1846.154'''
|'''29\8,''' '''1831.579'''
|'''47\13,''' '''1819.355'''
|'''43\12,''' '''1779.310'''
|'''25\7,''' '''1764.706'''
|'''32\9,''' '''1745.455'''
|-
|E, D
|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
|-
|E#, D#
|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
|-
|0b, Ed
|43\11, 1984.615
|50\13, 1935.484
|19\5, 1900
|45\12, 1862.069
|26\7, 1835.294
|33\9, 1800
|-
!0, E
!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
|}
{| class="wikitable"
! Notation
!Supersoft
! Soft
!Semisoft
!Basic
!Semihard
!Hard
!Superhard
|-
!Hyperionic
!~11ed4/3
!~8ed4/3
!~13ed4/3
!~5ed4/3
!~12ed4/3
!~7ed4\3
!~9ed4/3
|-
|1#
|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
|-
|2f
|3\11, 138.462
|2\8, 126.316
|3\13, 116.129
|2\12, 82.759
| 1\7, 70.588
|1\9, 54.545
|-
|'''2'''
|'''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'''
|-
|2#
| 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
|-
|'''3f'''
|'''7\11,''' '''323.077'''
|'''5\8,''' '''315.789'''
|'''8\13,''' '''309.677'''
|'''7\12,''' '''289.655'''
|'''4\7,''' '''282.353'''
|'''5\9,''' '''272.727'''
|-
|3
|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
|-
|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
|-
|4f
|10\11, 461.538
|11\13, 425.806
|4\5, 400
|9\12, 372.414
|5\7, 352.941
|6\9, 327.273
|-
!4
!'''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'''
|-
|4#
|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
|-
|5f
|14\11, 646.154
|10\8, 631.579
|16\13, 619.355
|14\12, 579.310
|8\7, 564.706
|10\9, 545.455
|-
|'''5'''
|'''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'''
|-
|5#
|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
|-
|'''6f'''
|'''18\11,''' '''830.769'''
|'''13\8,''' '''821.053'''
|'''21\13,''' '''812.903'''
|'''19\12,''' '''786.207'''
|'''11\7,''' '''776.471'''
|'''14\9,''' '''763.636'''
|-
|6
|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
|-
|6#
|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
|-
|7f
|21\11, 969.231
|24\13, 929.032
|9\5, 900
|21\12, 868.966
| 11\7, 776.471
|15\9, 818.182
|-
!7
!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
|-
| 7#
|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
|-
|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
|Ef
|7b, 7d
|47\11, 2169.231
|8f
|34\8, 2147.368
|25\11
|55\13, 2129.032
1153; 1.{{Overline|18}}
|50\12, 2068.966
|18\8
|29\7, 2047.059
1136; 1.1875
|37\9, 2018.182
|29\13
1122; 1.7{{Overline|2}}
|26\12
1075; 1.16
|15\7
1058; 1, 4.{{Overline|6}}
|19\9
1036.{{Overline|36}}
|-
|-
|'''E'''
|'''E'''
|'''7'''
|'''48\11,''' '''2215.385'''
|'''8'''
|'''35\8,''' '''2210.526'''
|'''26\11'''
|'''57\13,''' '''2206.452'''
'''1200'''
|'''22\5,''' '''2200'''
|'''19\8'''
|'''53\12,''' '''2193.103'''
'''1200'''
|'''31\7,''' '''2188.235'''
|'''31\13'''
|'''40\9,''' '''2181.818'''
'''1200'''
|'''12\5'''
'''1200'''
|'''29\12'''
'''1200'''
|'''17\7'''
'''1200'''
|'''22\9'''
'''1200'''
|-
|-
|E#
|E#
|7#
|49\11, 2261.538
|8#
|36\8, 2273.684
|27\11
|59\13, 2283.871
1246; 6,5
| rowspan="2" |'''23\5,''' '''2300'''
|20\8
|56\12, 2317.241
1263; 6.{{Overline|3}}
|33\7, 2329.412
|33\13
|43\9, 2345.455
1277; 2, 2.6
| rowspan="2" |'''13\5'''
'''1300'''
|32\12
1324; 7.25
|19\7
1341; 5.{{Overline|6}}
|25\9
1363.{{Overline|63}}
|-
|-
|'''Ff'''
|'''Ff'''
|'''8b, Fd'''
|'''51\11,''' '''2353.846'''
|'''9f'''
|'''37\8,''' '''2336.842'''
|'''29\11'''
|'''61\13,''' '''2322.581'''
'''1338; 3.25'''
|'''55\12,''' '''2275.864'''
|'''21\8'''
|'''32\7,''' '''2258.824'''
'''1326; 3.16̄'''
|'''41\9,''' '''2236.364'''
|'''34\13'''
'''1316; 7.75'''
|'''31\12'''
'''1282; 1.3{{Overline|18}}'''
|'''18\7'''
'''1270; 1.7'''
|'''23\9'''
'''1254.{{Overline|54}}'''
|-
|-
|F
|F
|8, F
|52\11, 2400
|9
|38\8, 2400
|30\11
|62\13, 2400
1384; 1.625
|24\5, 2400
|22\8
|58\12, 2400
1389; 2.1̄
|34\7, 2400
|36\13
|44\9, 2400
1393; 1, 1, 4.{{Overline|6}}
|14\5
1400
|34\12
1406; 1, 8.{{Overline|6}}
|20\7
1411; 1, 3.25
|26\9
1418.{{Overline|18}}
|-
|-
|F#
|F#
|8#, 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#
|9#
|31\11
|34\11, 1569.231
1430; 1.3
|25\8, 1578.947
| rowspan="2" |23\8
|41\13, 1587.097
1452; 1.58{{Overline|3}}
| rowspan="2" |16\5, 1600
|38\13
|39\12, 1613.793
1470; 1.0{{Overline|3}}
|23\7, 1623.529
|15\5
|30\9, 1636.364
1500
|-
|37\12
|Xb
1531; 29
|36\11, 1661.538
|22\7
|26\8, 1642.105
1552; 1.0625
|42\13, 1625.806
|29\9
|38\12, 1572.034
1581.{{Overline|81}}
|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
|-
|-
|Gf
|9b, Gd
|Af
|Af
|32\11
|43\11, 1984.615
1476; 1.08{{Overline|3}}
|50\13, 1935.484
|37\13
|19\5, 1900
1432: 3.875
|45\12, 1862.069
|14\5
|26\7, 1835.294
1400
|33\9, 1800
|33\12
1365; 1.9{{Overline|3}}
|19\7
1341; 5.{{Overline|3}}
|24\9
1309.{{Overline|09}}
|-
|-
!G
!'''9, G'''
!A
!A
!33\11
!44\11, 2030.769
1523; 13
!32\8, 2021.053
!24\8
!52\13, 2012.903
1515; 1.2{{Overline|6}}
!20\5, 2000
!39\13
!48\12, 1986.207
1509; 1, 2.1
!28\7, 1976.471
!15\5
!36\9, 1963.636
1500
!36\12
1489; 1, 1.9
!21\7
1482; 2.8{{Overline|3}}
!27\9
1472.{{Overline|72}}
|-
|-
|G#
|9#, G#
|A#
|A#
|34\11
|45\11, 2076.923
1569; 4.{{Overline|3}}
|33\8, 2084.211
|25\8
|54\13, 2090.323
1578; 1.05̄
| rowspan="2" |21\5, 2100
|41\13
|51\12, 2110.345
1587; 10.{{Overline|3}}
|30\7, 2117.647
| rowspan="2" |16\5
|39\9, 2127.273
1600
|39\12
1613; 1, 3.8{{Overline|3}}
|23\7
1623; 1.{{Overline|8}}
|30\9
1636.{{Overline|36}}
|-
|-
|Jf, Af
|Xb, Ad
|Bf
|Bf
|36\11
|47\11, 2169.231
1661; 1, 1.1{{Overline|6}}
|34\8, 2147.368
|26\8
|55\13, 2129.032
1642; 9.5
|50\12, 2068.966
|42\13
|29\7, 2047.059
1625; 1.24
|37\9, 2018.182
|38\12
1572; 29
|22\7
1552; 1.0625
|28\9
1527.{{Overline|27}}
|-
|-
|'''J, A'''
|'''X, A'''
|'''B'''
|'''B'''
|'''37\11'''
|'''48\11,''' '''2215.385'''
'''1707; 1.{{Overline|4}}'''
|'''35\8,''' '''2210.526'''
|'''27\8'''
|'''57\13,''' '''2206.452'''
'''1705; 3.8'''
|'''22\5,''' '''2200'''
|'''44\13'''
|'''53\12,''' '''2193.103'''
'''1703; 4, 2.3̄'''
|'''31\7,''' '''2188.235'''
|'''17\5'''
|'''40\9,''' '''2181.818'''
 
'''1700'''
|'''41\12'''
'''1696; 1.8125'''
|'''24\7'''
'''1694; 8.5'''
|'''31\9'''
'''1690.{{Overline|90}}'''
|-
|-
|J#, A#
|X#, A#
|B#
|B#
|38\11
|49\11, 2261.538
1753; 1.{{Overline|18}}
|36\8, 2273.684
|28\8
|59\13, 2283.871
1768; 2.375
| rowspan="2" |'''23\5,''' '''2300'''
|46\13
|56\12, 2317.241
1780; 1.55
|33\7, 2329.412
| rowspan="2" |'''18\5'''
|43\9, 2345.455
'''1800'''
|44\12
1820; 1.45
|26\7
1835; 3,4
|34\9
1854.{{Overline|54}}
|-
|-
|'''Af, Bf'''
|'''Eb, Bd'''
|'''Cf'''
|'''Cf'''
|'''40\11'''
|'''51\11,''' '''2353.846'''
'''1846; 6.5'''
|'''37\8,''' '''2336.842'''
|'''29\8'''
|'''61\13,''' '''2322.581'''
 
|'''55\12,''' '''2275.864'''
'''1831; 1.{{Overline|72}}'''
|'''32\7,''' '''2258.824'''
|'''47\13'''
|'''41\9,''' '''2236.364'''
'''1819; 2.{{Overline|81}}'''
|'''43\12'''
'''1779; 3.{{Overline|2}}'''
|'''25\7'''
'''1764; 1, 3.25'''
|'''32\9'''
'''1745.{{Overline|45}}'''
|-
|-
|A, B
|E, B
|C
|C
|41\11
|52\11, 2400
1892; 3.25
|38\8, 2400
|30\8
|62\13, 2400
1894; 1, 2.8
|24\5, 2400
|49\13
|58\12, 2400
1896; 1.291{{Overline|6}}
|34\7, 2400
|19\5
|44\9, 2400
1900
|46\12
1903; 2, 2.1{{Overline|6}}
|27\7
1905; 1, 7.5
|35\9
1909.{{Overline|09}}
|-
|-
|A#, B#
|E#, B#
|C#
|C#
|42\11
|53\11, 2446.154
1938; 2.1{{Overline|6}}
| rowspan="2" |39\8, 2463.158
| rowspan="2" |31\8
|64\13, 2477.419
1957; 1, 8.5
|25\5, 2500
|51\13
|61\12, 2524.138
1974; 5.1{{Overline|6}}
|36\7, 2541.176
|20\5
|47/9, 2563.636
2000
|49\12
2027; 1, 1.41{{Overline|6}}
|29\7
2047; 17
|38\9
2072.{{Overline|72}}
|-
|-
|Bb, Cf
|0b, Dd
|Df
|Df
|43\15
|54\11, 2492.308
1984; 1.625
|63\13, 2438.710
|50\13
|24\5, 2400
1935; 2.0{{Overline|6}}
|57\12, 2358.621
|19\5
|33\7, 2329.412
1900
|42\9, 2390.909
|45\12
1862; 14.5
|26\7
1835; 3,4
|33\9
1800
|-
|-
!B, C
!0, D
!D
!D
!44\11
!55\11, 2538.462
2030; 1.3
!40\8, 2526.316
!32\8
!65\13, 2516.129
 
!25\5, 2500
2021; 19
!60\12, 2482.759
!52\13
!35\7, 2470.588
2012; 1, 9.{{Overline|3}}
!45\9, 2454.545
!20\5
2000
!48\12
1986; 4.8{{Overline|3}}
!28\7
1976; 2.125
!36\9
1963.{{Overline|63}}
|-
|-
|B#, C#
|0#, D#
|D#
|D#
|45\11
|56\11, 2584.615
2076; 1.08{{Overline|3}}
|41\8, 2589.474
|33\8
|67\13, 2593.548
2084; 4.75
| rowspan="2" |26\5, 2600
|54\13
|63\12, 2606.897
2090; 3.1
|37\7, 2611.765
| rowspan="2" |21\5
|48\9, 2618.182
2100
|51\12
2110; 2.9
|30\7
2117; 1.{{Overline|54}}
|39\9
2127.{{Overline|27}}
|-
|-
|Cf, Qf
|1b, 1d
|Ef
|Ef
|47\11
|58\11, 2676.923
2169; 4.{{Overline|3}}
|42\8, 2652.632
|34\8
|69\13, 2670.968
2147; 2, 1.4
|62\12, 2565.517
|55\13
|36\7, 2541.176
2129; 31
|46\9, 2509.091
|50\12
2068; 1, 28
|29\7
2047; 17
|37\9
2018.{{Overline|18}}
|-
|-
|'''C, Q'''
|'''1'''
|'''E'''
|'''E'''
|'''48\11'''
|'''59\11,''' '''2723.077'''
'''2215; 2.6'''
|'''43\8,''' '''2715.789'''
|'''35\8'''
|'''70\13,''' '''2709.677'''
'''2210; 1.9'''
|'''27\5,''' '''2700'''
|'''57\13'''
|'''65\12,''' '''2689.655'''
'''2206; 2, 4.{{Overline|6}}'''
|'''38\7,''' '''2682.353'''
|'''22\5'''
|'''49\9,''' '''2672.727'''
'''2200'''
|'''53\12'''
'''2193; 9.{{Overline|6}}'''
|'''31\7'''
'''2188; 4.25'''
|'''40\9'''
'''2181.{{Overline|81}}'''
|-
|-
|C#, Q#
|1#
|E#
|E#
|49\11
|60\11, 2769.231
2261; 1, 1.1{{Overline|6}}
|44\8, 2778.947
|36\8
|72\13, 2787.097
2273; 1, 2.1{{Overline|6}}
| rowspan="2" |'''28\5,''' '''2800'''
|59\13
|68\12, 2813.793
2083; 1.{{Overline|148}}
|40\7, 2823.529
| rowspan="2" |'''23\5'''
|52\9, 2836.364
'''2300'''
|56\12
2327; 4, 7
|33\7
2329; 2, 2.{{Overline|3}}
|43\9
2345.{{Overline|45}}
|-
|-
|'''Qf, Df'''
|'''2b, 2d'''
|'''Ff'''
|'''Ff'''
|'''51\11'''
|'''62\11,''' '''2861.538'''
'''2353; 1.{{Overline|18}}'''
|'''45\8,''' '''2842.105'''
|'''37\8'''
|'''73\13,''' '''2825.806'''
'''2336; 1.1875'''
|'''67\12,''' '''2772.034'''
|'''61\13'''
|'''39\7,''' '''2752.941'''
'''2322; 1.7{{Overline|2}}'''
|'''50\9,''' '''2727.273'''
|'''55\12'''
'''2275; 1.16'''
|'''32\7'''
'''2258; 1, 4.{{Overline|6}}'''
|'''41\9'''
'''2236.{{Overline|36}}'''
|-
|-
|Q, D
|2
|F
|F
|52\11
|63\11, 2907.692
2400
|46\8, 2905.263
|38\8
|75\13, 2903.226
2400
|29\5, 2900
|62\13
|70\12, 2896.552
2400
|41\7, 2894.118
|24\5
|53\9, 2890.909
2400
|58\12
2400
|34\7
2400
|44\9
2400
|-
|-
|Q#, D#
|2#
|F#
|F#
|53\11
|64\11, 2953.846
2446; 6.5
| rowspan="2" |47\8, 2968.421
| rowspan="2" |39\8
|77\13, 2980.645
2463; 6.{{Overline|3}}
|30\5, 3000
|64\13
|73\12, 3020.690
2477; 2, 2.6
|43\7, 3035.294
|25\5
|55\9, 3000
2500
|61\12
2524; 7.25
|36\7
2541; 5.{{Overline|6}}
|47/9
2563.{{Overline|63}}
|-
|-
|Df, Sf
|0f
|3b, 3d
|65\11, 3000
|1f
|76\13, 2941.935
|54\11
|29\5, 2900
2492; 3.25
|69\29, 2855.172
|63\13
|40\7, 2823.529
2438; 1.1{{Overline|36}}
|52\9, 2836.364
|24\5
2400
|57\12
2358; 1.61̄
|33\7
2329; 2, 2.{{Overline|3}}
|42\9
2390.{{Overline|90}}
|-
|-
!D, S
!0
!3
!66\11, 3046.154
!1
!48\8, 30'''31.579'''
!55\11
!78\13, 30'''19.355'''
2538; 2.1{{Overline|6}}
!30\5, 3000
!40\8
!72\12, 29'''79.310'''
2526; 3.1{{Overline|6}}
!42\7, 2964.706
!65\13
!54\9, 2945.455
2516; 7.75
!25\5
2500
!60\12
2482; '''1.3{{Overline|18}}'''
!35\7
2470; 1.7
!45\9
2454.{{Overline|54}}
|}
|}
==Intervals==
==Intervals==
{| class="wikitable"
{| class="wikitable"
Line 1,141: Line 1,973:
|-
|-
|0
|0
|Do, Sol
|F/C/G ut
Do, Sol
 
د, ص
|perfect unison
|perfect unison
|0
|0
|Do, Sol
|F/C/G ut
Do, Sol
 
د, ص
|perfect fourth
|perfect fourth
|-
|-
|1
|1
|Mib, Sib
|A/E/B mib
Mib, Sib
 
صb, مb
|diminished third
|diminished third
| -1
| -1
|Re, La
|G/D/A re
Re, La
 
ر, ل
|perfect second
|perfect second
|-
|-
|2
|2
|Reb, Lab
|G/D/A reb
Reb, Lab
 
رb, لb
|diminished second
|diminished second
| -2
| -2
|Mi, Si
|A/E/B mi
Mi, Si
 
ص, م
|perfect third
|perfect third
|-
|-
Line 1,164: Line 2,014:
|-
|-
|3
|3
|Dob, Solb
|F/C/G utb
Dob, Solb
 
دb, صb
|diminished fourth
|diminished fourth
| -3
| -3
|Do#, Sol#
|F/C/G ut#
Do#, Sol#
 
د, #ص#
|augmented unison (chroma)
|augmented unison (chroma)
|-
|-
|4
|4
|Mibb, Sibb
|A/E/B mibb
Mibb, Sibb
 
مbb, صbb
|doubly diminished third
|doubly diminished third
| -4
| -4
|Re#, La#
|G/D/A re#
Re#, La#
 
ر ,# ل#
|augmented second
|augmented second
|}
|}
Line 1,180: Line 2,042:
The generator chain for this scale is as follows:
The generator chain for this scale is as follows:
{| class="wikitable"
{| 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
|Mibb
Sibb
Sibb
Line 1,200: Line 2,073:
|Mi#
|Mi#
Si#
Si#
|-
|مbb
تbb
|دb
صb
|رb
لb
|مb
تb
|د
ص
|ر
ل
|م
ت
|د#
ص#
|ر#
ل#
|م#
ت#
|-
|-
|dd3
|dd3
Line 1,239: Line 2,133:
|-
|-
|Phrygian
|Phrygian
|LsLL
|sLL
|<nowiki>0|2</nowiki>
|<nowiki>0|2</nowiki>
|d
|d
Line 1,255: Line 2,149:
[[Mapping]]: [{{val|1 0 1}}, {{val|0 2 1}}]
[[Mapping]]: [{{val|1 0 1}}, {{val|0 2 1}}]


[[Optimal ET sequence]]: ~(5ed4/3, 8ed4/3, 13ed4/3)
[[Optimal ET sequence]]: [[15ed12/5]], [[24ed12/5]], [[39ed12/5]] ≈ [[5ed4/3]], [[8ed4/3]], [[13ed4/3]]
==='''Mahuric-Superpyth'''===
==='''Mahuric-Superpyth'''===
[[Subgroup]]: 4/3.9/7.3/2
[[Subgroup]]: 4/3.9/7.3/2
Line 1,265: Line 2,159:
[[Mapping]]: [{{val|1 0 1}}, {{val|0 2 1}}]
[[Mapping]]: [{{val|1 0 1}}, {{val|0 2 1}}]


[[Optimal ET sequence]]: ~(5ed4/3, 7ed4/3, 9ed4/3, 11ed4/3)
[[Optimal ET sequence]]: [[15ed7/3]], [[21ed7/3]], [[27ed7/3]], [[33ed7/3]] ≈ [[5ed4/3]], [[7ed4/3]], [[9ed4/3]], [[11ed4/3]]
====Scale tree====
====Scale tree====
The spectrum looks like this:
The spectrum looks like this:
{| class="wikitable"
{| class="wikitable"
! colspan="3" |Generator
!Generator
(bright)
(bright)
!Cents<ref name=":05" />
!Cents
!L
!L
!s
!s
Line 1,278: Line 2,172:
|-
|-
|1\3
|1\3
|
|171.429
|
|171; 2.{{Overline|3}}
|1
|1
|1
|1
Line 1,287: Line 2,179:
|-
|-
|6\17
|6\17
|
|180.000
|
|180
|6
|6
|5
|5
|1.200
|1.200
|
|-
|
|11\31
|
|180; 1.21{{Overline|6}}
|11
|9
|1.222
|
|
|-
|-
|5\14
|5\14
|
|181.818
|
|181.{{Overline|81}}
|5
|5
|4
|4
Line 1,313: Line 2,192:
|
|
|-
|-
|
|14\39
|14\39
|
|182.609
|182; 1, 1.5
|14
|14
|11
|11
Line 1,322: Line 2,199:
|
|
|-
|-
|
|9\25
|9\25
|
|183.051
|183; 19.{{Overline|6}}
|9
|9
|7
|7
Line 1,332: Line 2,207:
|-
|-
|4\11
|4\11
|
|184.615
|
|184; 1.625
|4
|4
|3
|3
Line 1,340: Line 2,213:
|
|
|-
|-
|
|15\41
|
|185; 1.7{{Overline|63}}
|15
|11
|1.364
|
|-
|
|11\30
|11\30
|
|185.915
|185, 1, 10.8{{Overline|3}}
|11
|11
|8
|8
Line 1,358: Line 2,220:
|
|
|-
|-
|
|7\19
|7\19
|
|186.667
|186.{{Overline|6}}
|7
|7
|5
|5
Line 1,367: Line 2,227:
|
|
|-
|-
|
|10\27
|10\27
|
|187.500
|187.5
|10
|10
|7
|7
Line 1,376: Line 2,234:
|
|
|-
|-
|
|13\35
|13\35
|
|187.952
|187; 1, 19.75
|13
|13
|9
|9
Line 1,385: Line 2,241:
|
|
|-
|-
|
|16\43
|16\43
|
|188.253
|188; 4.25
|16
|16
|11
|11
Line 1,395: Line 2,249:
|-
|-
|3\8
|3\8
|
|189.474
|
|189; 2.{{Overline|1}}
|3
|3
|2
|2
Line 1,403: Line 2,255:
|Mahuric-Meantone starts here
|Mahuric-Meantone starts here
|-
|-
|
|14\37
|14\37
|
|190.909
|190.{{Overline|90}}
|14
|14
|9
|9
Line 1,412: Line 2,262:
|
|
|-
|-
|
|11\29
|11\29
|
|191.304
|191; 3, 2.{{Overline|3}}
|11
|11
|7
|7
Line 1,421: Line 2,269:
|
|
|-
|-
|
|8\21
|8\21
|
|192.000
|192
|8
|8
|5
|5
Line 1,430: Line 2,276:
|
|
|-
|-
|
|5\13
|5\13
|
|193.548
|193; 1, 1, 4.{{Overline|6}}
|5
|5
|3
|3
Line 1,439: Line 2,283:
|
|
|-
|-
|
|
|12\31
|12\31
|194.{{Overline|594}}
|194.595
|12
|12
|7
|7
Line 1,448: Line 2,290:
|
|
|-
|-
|
|7\18
|7\18
|
|195.348
|195; 2.8{{Overline|6}}
|7
|7
|4
|4
Line 1,457: Line 2,297:
|
|
|-
|-
|
|9\23
|9\23
|
|196.364
|196.{{Overline|36}}
|9
|9
|5
|5
Line 1,466: Line 2,304:
|
|
|-
|-
|
|11\28
|11\28
|
|197.015
|197; 67
|11
|11
|6
|6
Line 1,475: Line 2,311:
|
|
|-
|-
|
|13\33
|13\33
|
|197.468
|197; 2.{{Overline|135}}
|13
|13
|7
|7
Line 1,484: Line 2,318:
|
|
|-
|-
|
|15\38
|15\38
|
|197.802
|197; 1, 2, 1, 1.{{Overline|54}}
|15
|15
|8
|8
Line 1,493: Line 2,325:
|
|
|-
|-
|
|17\43
|17\43
|
|198.058
|198; 17.1{{Overline|6}}
|17
|17
|9
|9
Line 1,502: Line 2,332:
|
|
|-
|-
|
|19\48
|19\48
|
|198.261
|198: 3, 1, 28
|19
|19
|10
|10
Line 1,511: Line 2,339:
|
|
|-
|-
|
|21\53
|21\53
|
|198.425
|198; 2.3{{Overline|518}}
|21
|21
|11
|11
Line 1,520: Line 2,346:
|
|
|-
|-
|
|23\58
|23\58
|
|198.561
|198; 1, 3, 1.7
|23
|23
|12
|12
Line 1,529: Line 2,353:
|
|
|-
|-
|
|25\63
|25\63
|
|198.675
|198; 1, 2, 12.25
|25
|25
|13
|13
Line 1,538: Line 2,360:
|
|
|-
|-
|
|27\68
|27\68
|
|198.773
|198; 1, 3.{{Overline|405}}
|27
|27
|14
|14
Line 1,547: Line 2,367:
|
|
|-
|-
|
|29\73
|29\73
|
|198.857
|198; 1, 1.1{{Overline|6}}
|29
|29
|15
|15
Line 1,556: Line 2,374:
|
|
|-
|-
|
|31\78
|31\78
|
|198.930
|198; 1, 12, 2.8
|31
|31
|16
|16
Line 1,565: Line 2,381:
|
|
|-
|-
|
|33\83
|33\83
|
|198.995
|198; 1.{{Overline|005}}
|33
|33
|17
|17
Line 1,574: Line 2,388:
|
|
|-
|-
|
|35\88
|35\88
|
|199.052
|199; 19.{{Overline|18}}
|35
|35
|18
|18
Line 1,584: Line 2,396:
|-
|-
|2\5
|2\5
|
|200.000
|
|200
|2
|2
|1
|1
Line 1,592: Line 2,402:
|Mahuric-Meantone ends, Mahuric-Pythagorean begins
|Mahuric-Meantone ends, Mahuric-Pythagorean begins
|-
|-
|
|17\42
|17\42
|
|201.980
|201.{{Overline|9801}}
|17
|17
|8
|8
Line 1,601: Line 2,409:
|
|
|-
|-
|
|15\37
|15\37
|
|202.247
|202; 4.0{{Overline|45}}
|15
|15
|7
|7
Line 1,610: Line 2,416:
|
|
|-
|-
|
|13\32
|13\32
|
|202.597
|202; 1, 1, 2.0{{Overline|6}}
|13
|13
|6
|6
Line 1,619: Line 2,423:
|
|
|-
|-
|
|11\27
|11\27
|
|203.077
|203; 13
|11
|11
|5
|5
Line 1,628: Line 2,430:
|
|
|-
|-
|
|9\22
|9\22
|
|203.774
|203; 1, 3.41{{Overline|6}}
|9
|9
|4
|4
Line 1,637: Line 2,437:
|
|
|-
|-
|
|7\17
|7\17
|
|204.878
|204; 1. 7.2
|7
|7
|3
|3
Line 1,646: Line 2,444:
|
|
|-
|-
|
|
|12\29
|12\29
|205; 1.4
|205.714
|12
|12
|5
|5
Line 1,655: Line 2,451:
|
|
|-
|-
|
|5\12
|5\12
|
|206.897
|206; 1, 8.{{Overline|6}}
|5
|5
|2
|2
Line 1,664: Line 2,458:
|Mahuric-Neogothic heartland is from here…
|Mahuric-Neogothic heartland is from here…
|-
|-
|
|
|18\43
|18\43
|207; 1.{{Overline|4}}
|207.693
|18
|18
|7
|7
Line 1,673: Line 2,465:
|
|
|-
|-
|
|
|13\31
|13\31
|208
|208.000
|13
|13
|5
|5
Line 1,682: Line 2,472:
|
|
|-
|-
|
|8\19
|8\19
|
|208.696
|208; 1.4375
|8
|8
|3
|3
Line 1,691: Line 2,479:
|…to here
|…to here
|-
|-
|
|11\26
|11\26
|
|209.524
|209; 1.{{Overline|90}}
|11
|11
|4
|4
Line 1,700: Line 2,486:
|
|
|-
|-
|
|14\33
|14\33
|
|210.000
|210
|14
|14
|5
|5
Line 1,710: Line 2,494:
|-
|-
|3\7
|3\7
|
|211.755
|
|211; 1, 3.25
|3
|3
|1
|1
Line 1,718: Line 2,500:
|Mahuric-Pythagorean ends, Mahuric-Superpyth begins
|Mahuric-Pythagorean ends, Mahuric-Superpyth begins
|-
|-
|
|22\51
|22\51
|
|212.903
|212; 1, 9.{{Overline|3}}
|22
|22
|7
|7
Line 1,727: Line 2,507:
|
|
|-
|-
|
|19\44
|19\44
|
|213.084
|213; 11.{{Overline|8}}
|19
|19
|6
|6
Line 1,736: Line 2,514:
|
|
|-
|-
|
|16\37
|16\37
|
|213.333
|213.3̄
|16
|16
|5
|5
Line 1,745: Line 2,521:
|
|
|-
|-
|
|13\30
|13\30
|
|213.699
|213; 1, 2.3{{Overline|18}}
|13
|13
|4
|4
Line 1,754: Line 2,528:
|
|
|-
|-
|
|10\23
|10\23
|
|214.286
|214; 3.5
|10
|10
|3
|3
Line 1,763: Line 2,535:
|
|
|-
|-
|
|7\16
|7\16
|
|215.385
|215; 2.6
|7
|7
|2
|2
Line 1,772: Line 2,542:
|
|
|-
|-
|
|11\25
|11\25
|
|216.393
|216; 2.541{{Overline|6}}
|11
|11
|3
|3
Line 1,781: Line 2,549:
|
|
|-
|-
|
|15\34
|15\34
|
|216.867
|216; 1.152{{Overline|7}}
|15
|15
|4
|4
Line 1,790: Line 2,556:
|
|
|-
|-
|
|19\43
|19\43
|
|217.143
|217; 7
|19
|19
|5
|5
Line 1,800: Line 2,564:
|-
|-
|4\9
|4\9
|
|218.182
|
|218.{{Overline|18}}
|4
|4
|1
|1
Line 1,808: Line 2,570:
|
|
|-
|-
|
|13\29
|13\29
|
|219.718
|219; 1, 2.55
|13
|13
|3
|3
Line 1,817: Line 2,577:
|
|
|-
|-
|
|9\20
|9\20
|
|220.408
|220; 2.45
|9
|9
|2
|2
Line 1,826: Line 2,584:
|
|
|-
|-
|
|14\31
|14\31
|
|221.053
|221; 19
|14
|14
|3
|3
Line 1,836: Line 2,592:
|-
|-
|5\11
|5\11
|
|222.222
|
|222.{{Overline|2}}
|5
|5
|1
|1
Line 1,844: Line 2,598:
|Mahuric-Superpyth ends
|Mahuric-Superpyth ends
|-
|-
|
|11\24
|11\24
|
|223.728
|223; 1, 2.6875
|11
|11
|2
|2
Line 1,853: Line 2,605:
|
|
|-
|-
|
|17\37
|17\37
|
|224.176
|224; 5.7{{Overline|2}}
|17
|17
|3
|3
Line 1,863: Line 2,613:
|-
|-
|6\13
|6\13
|
|225.000
|
|225
|6
|6
|1
|1
Line 1,871: Line 2,619:
|
|
|-
|-
|1\3
|1\2
|
|240.000
|
|240
|1
|1
|0
|0
Line 1,881: Line 2,627:
|}
|}


== See also ==
==See also==
[[2L 1s (4/3-equivalent)]] - idealized tuning
[[2L 1s (4/3-equivalent)]] - idealized tuning


[[4L 2s (7/4-equivalent)]] - Mixolydian Archytas temperament  
[[4L 2s (7/4-equivalent)]] - Mixolydian and Dorian hexatonic Archytas temperament  


[[4L 2s (39/22-equivalent)]] - Mixolydian Neogothic temperament  
[[4L 2s (39/22-equivalent)]] - Mixolydian and Dorian hexatonic Neogothic temperament  


[[4L 2s (9/5-equivalent)]] - Mixolydian Meantone 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 (7/3-equivalent)]] - Mahuric-Archytas temperament
Line 1,898: Line 2,646:
[[8L 4s (28/9-equivalent)]] - Bijou Archytas temperament
[[8L 4s (28/9-equivalent)]] - Bijou Archytas temperament


[[8L 4s (22/7-equivalent)]] - Bijou Neogothic 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
[[8L 4s (16/5-equivalent)]] - Bijou Meantone temperament
Line 1,906: Line 2,654:
[[10L 5s (88/21-equivalent)]] - Hyperionic Neogothic temperament
[[10L 5s (88/21-equivalent)]] - Hyperionic Neogothic temperament


[[10L 5s (30/7-equivalent)]] - Hyperionic Meantone temperament<references />
[[10L 5s (64/15-equivalent)]] - Hyperionic Meantone temperament
 
[[10L 5s (30/7-equivalent)]] - Hyperionic septimal Meantone temperament
 
[[12L 6s (16/3-equivalent)]] - Warped Pythagorean Subsextal temperament
 
[[12L 6s (343/64-equivalent)]] - 1/2 comma Archytas Subsextal temperament]
 
[[12L 6s (11/2-equivalent)]] - Low undecimal Subsextal temperament
 
[[12L 6s (448/81-equivalent)]] - 1/6 comma Archytas Subsextal temperament
 
[[12L 6s (4096/729-equivalent)]] - Pythagorean Subsextal temperament
 
[[12L 6s (28/5-equivalent)]] - Low septimal (meantone) Subsextal temperament
 
[[12L 6s (45/16-equivalent)|12L 6s (256/45-equivalent)]] - 1/6 comma meantone Subsextal temperament
 
[[12L 6s (40/7-equivalent)]] - High septimal Subsextal temperament
 
[[12L 6s (64/11-equivalent)]] - High undecimal Subsextal temperament
 
[[12L 6s (729/125-equivalent)]] - 1/2 comma meantone Subsextal temperament <references />
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