View source for User:Moremajorthanmajor/2L 1s (perfect fourth-equivalent)

'''2L 1s<perfect fourth>''', is a perfect fourth-repeating MOS scale. The notation "<perfect fourth>" means the period of the MOS is a perfect fourth, disambiguating it from octave-repeating [[2L 1s]].

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 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]].
==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 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"
|+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
!Supersoft
!Soft
!Semisoft
!Basic
!Semihard
!Hard
!Superhard
|-
! colspan="2" |Seventh
!~11ed4/3
!~8ed4/3
!~13ed4/3
!~5ed4/3
!~12ed4/3
!~7ed4\3
!~9ed4/3
|-
!Mixolydian
!Dorian
!
!
!
!
!
!
!
|-
| F/C/G ut#
Sol#

ص#
|G/D/A re#
Re#

ر#
|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
Lab

لb
|A/E/B mib
Mib

مb
|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'''
'''La'''

ل
|'''A/E/B mi'''
'''Mi'''

م
|'''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#
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
|-
|'''A/E/B mib'''
'''Sib'''

تb
|'''B/F/C fa'''
'''Fa'''

'''ف'''
|'''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
Si

ت
|B/F/C fa#
Fa#

ف#
| 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#
Si#

ت#
|B/F/C fax
Fax

فx
|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
|-
| B/F/C fab
Dob

دb
|C/G/D solb
Solb

صb
|10\11, 461.538
|11\13, 425.806
|4\5, 400
|9\12, 372.414
|5\7, 352.941
|6\9, 327.273
|-
!B/F/C fa
Do

د
!C/G/D sol
Sol

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'''
|-
|B/F/C fa#
Do#

د#
| C/G/D sol#
Sol#

ص#
|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
|-
|C/G/D solb
Reb

رb
|D/A/E lab
Lab

لb
|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/G/D sol'''
'''Re'''

ر
|'''D/A/E la'''
'''La'''

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'''
|-
|C/G/D sol#
Re#

د#
|D/A/E la#
La#

ل#
|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
|-
|'''D/A/E lab'''
'''Mib'''

مb
|'''E/B/F síb'''
'''Sib'''

تb
|'''18\11,''' '''830.769'''
|'''13\8,''' '''821.053'''
|'''21\13,''' '''812.903'''
|'''19\12,''' '''786.207'''
|'''11\7,''' '''776.471'''
|'''14\9,''' '''763.636'''
|-
|D/A/E la
Mi

م
|E/B/F sí
Si

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
|-
|D/A/E la#
Mi#

م#
|E/B/F sí#
Si#

ت#
|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
|-
|F/C/G utb
Solb

صb
|G/D/A reb
Reb

رb
|21\11, 969.231
|24\13, 929.033
|9\5, 900
|21\12, 868.966
|11\7, 776.471
|15\9, 818.182
|-
!F/C/G ut
Sol

ص
!G/D/A re
Re

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
|-
!Mahur
!~11ed4/3
!~8ed4/3
!~13ed4/3
!~5ed4/3
!~12ed4/3
!~7ed4\3
! ~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
|-
|0#, E#
|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
|-
|1b, 1d
|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, 270.968
| rowspan="2" |'''3\5,''' '''300'''
|8\12, 331.034
|5\7, 352.941
|7\9, 381.818
|-
|'''2b, 2d'''
|'''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, 387.097
|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
|-
|3b, 3d
|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
|-
|4b, 4d
|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
|-
|'''5b, 5d'''
|'''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
|-
|6b, 6d
|21\11, 969.231
|24\13, 929.033
| 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
|-
|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#
|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
|-
|'''8b, Gd'''
|'''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, 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
|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#
|-
|مbb
تbb
|دb
صb
|رb
لb
|مb
تb
|د
ص
|ر
ل
|م
ت
|د#
ص#
|ر#
ل#
|م#
ت#
|-
|dd3
|d4
|d2
|d3
|P1
|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
!pattern
!notation
!2nd
!3rd
|-
|Major
|LLs
|<nowiki>2|0</nowiki>
|P
|P
|-
|Minor
|LsL
|<nowiki>1|1</nowiki>
|P
|d
|-
|Phrygian
|sLL
|<nowiki>0|2</nowiki>
|d
|d
|}
==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]]: [[15ed12/5]], [[24ed12/5]], [[39ed12/5]] ≈ [[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]]: [[15ed7/3]], [[21ed7/3]], [[27ed7/3]], [[33ed7/3]] ≈ [[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
|171.429
|1
|1
|1.000
|Equalised
|-
|6\17
|180.000
|6
|5
|1.200
|
|-
|5\14
|181.818
|5
|4
|1.250
|
|-
|14\39
|182.609
|14
|11
|1.273
|
|-
|9\25
|183.051
|9
|7
|1.286
|
|-
|4\11
|184.615
|4
|3
|1.333
|
|-
|11\30
|185.915
|11
|8
|1.375
|
|-
|7\19
|186.667
|7
|5
|1.400
|
|-
|10\27
|187.500
|10
|7
|1.429
|
|-
|13\35
|187.952
|13
|9
|1.444
|
|-
|16\43
|188.253
|16
|11
|1.4545
|
|-
|3\8
|189.474
|3
|2
|1.500
|Mahuric-Meantone starts here
|-
|14\37
|190.909
|14
|9
|1.556
|
|-
|11\29
|191.304
|11
|7
|1.571
|
|-
|8\21
|192.000
|8
|5
|1.600
|
|-
|5\13
|193.548
|5
|3
|1.667
|
|-
|12\31
|194.595
|12
|7
|1.714
|
|-
|7\18
|195.348
|7
|4
|1.750
|
|-
|9\23
|196.364
|9
|5
|1.800
|
|-
|11\28
|197.015
|11
|6
|1.833
|
|-
|13\33
|197.468
|13
|7
|1.857
|
|-
|15\38
|197.802
|15
|8
|1.875
|
|-
|17\43
|198.058
|17
|9
|1.889
|
|-
|19\48
|198.261
|19
|10
|1.900
|
|-
|21\53
|198.425
|21
|11
|1.909
|
|-
|23\58
|198.561
|23
|12
|1.917
|
|-
|25\63
|198.675
|25
|13
|1.923
|
|-
|27\68
|198.773
|27
|14
|1.929
|
|-
|29\73
|198.857
|29
|15
|1.933
|
|-
|31\78
|198.930
|31
|16
|1.9375
|
|-
|33\83
|198.995
|33
|17
|1.941
|
|-
|35\88
|199.052
|35
|18
|1.944
|
|-
|2\5
|200.000
|2
|1
|2.000
|Mahuric-Meantone ends, Mahuric-Pythagorean begins
|-
|17\42
|201.980
|17
|8
|2.125
|
|-
|15\37
|202.247
|15
|7
|2.143
|
|-
|13\32
|202.597
|13
|6
|2.167
|
|-
|11\27
|203.077
|11
|5
|2.200
|
|-
|9\22
|203.774
|9
|4
|2.250
|
|-
|7\17
|204.878
|7
|3
|2.333
|
|-
|12\29
|205.714
|12
|5
|2.400
|
|-
|5\12
|206.897
|5
|2
|2.500
|Mahuric-Neogothic heartland is from here…
|-
|18\43
|207.693
|18
|7
|2.571
|
|-
|13\31
|208.000
|13
|5
|2.600
|
|-
|8\19
|208.696
|8
|3
|2.667
|…to here
|-
|11\26
|209.524
|11
|4
|2.750
|
|-
|14\33
|210.000
|14
|5
|2.800
|
|-
|3\7
|211.755
|3
|1
|3.000
|Mahuric-Pythagorean ends, Mahuric-Superpyth begins
|-
|22\51
|212.903
|22
|7
|3.143
|
|-
|19\44
|213.084
|19
|6
|3.167
|
|-
|16\37
|213.333
|16
|5
|3.200
|
|-
|13\30
|213.699
|13
|4
|3.250
|
|-
|10\23
|214.286
|10
|3
|3.333
|
|-
|7\16
|215.385
|7
|2
|3.500
|
|-
|11\25
|216.393
|11
|3
|3.667
|
|-
|15\34
|216.867
|15
|4
|3.750
|
|-
|19\43
|217.143
|19
|5
|3.800
|
|-
|4\9
|218.182
|4
|1
|4.000
|
|-
|13\29
|219.718
|13
|3
|4.333
|
|-
|9\20
|220.408
|9
|2
|4.500
|
|-
|14\31
|221.053
|14
|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\2
|240.000
|1
|0
|→ inf
|Paucitonic
|}

==See also==
[[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

[[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 />