User:Moremajorthanmajor/2L 1s (perfect fourth-equivalent): Difference between revisions

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#REDIRECT [[2L 1s (4/3-equivalent)]]
'''2L 1s<fourth>''', is a fourth-repeating MOS scale. The notation "<fourth>" means the period of the MOS is a 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 4/3 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 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.
{| class="wikitable"
|+Cents<ref name=":05">Fractions repeating more than 4 digits written as continued fractions</ref>
! colspan="5" |Notation
!Supersoft
!Soft
!Semisoft
!Basic
!Semihard
!Hard
!Superhard
|-
! colspan="2" |Diatonic
! rowspan="2" |Mahur
! rowspan="2" |Bijou
! rowspan="2" |Hyperionic
! rowspan="2" |~11ed4/3
! rowspan="2" |~8ed4/3
! rowspan="2" |~13ed4/3
! rowspan="2" |~5ed4/3
! rowspan="2" |~12ed4/3
! rowspan="2" |~7ed4\3
! rowspan="2" |~9ed4/3
|-
!Fourth
!Seventh
|-
|Do#, Sol#
|Sol#
|G#
|0#, D#
|1#
|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
|Lab
|Jf, Af
|1b, 1d
|2f
|3\11
138; 3.25
|2\8
126; 3.1{{Overline|6}}
|3\13
116; 7.75
|2\12
82; 1.3{{Overline|18}}
|1\7
70; 1.7
|1\9
54.{{Overline|54}}
|-
|'''Re, La'''
|'''La'''
|'''J, A'''
|'''1'''
|'''2'''
|'''4\11'''
'''184; 1.625'''
|'''3\8'''
'''189; 2.{{Overline|1}}'''
|'''5\13'''
'''193; 1, 1, 4.{{Overline|6}}'''
|'''2\5'''
'''200'''
|'''5\12'''
'''206; 1, 8.{{Overline|6}}'''
|'''3\7'''
'''211; 1, 3.25'''
|'''4\9'''
'''218.{{Overline|18}}'''
|-
|Re#, La#
|La#
|J#, A#
|1#
|2#
|5\11
230; 1.3
|4\8
252; 1.58{{Overline|3}}
|7\13
270; 1.0{{Overline|3}}
| rowspan="2" |'''3\5'''
'''300'''
|8\12
331; 29
|5\7
352; 1.0625
|7\9
381.{{Overline|81}}
|-
|'''Mib, Sib'''
|'''Sib'''
|'''Af, Bf'''
|'''2b, 2d'''
|'''3f'''
|'''7\11'''
'''323; 13'''
|'''5\8'''
'''315; 1.2{{Overline|6}}'''
|'''8\13'''
'''309; 1, 2.1'''
|'''7\12'''
'''289; 1, 1.9'''
|'''4\7'''
'''282; 2.8{{Overline|3}}'''
|'''5\9'''
'''272.{{Overline|72}}'''
|-
|Mi, Si
|Si
|A, B
|2
|3
|8\11
369; 4.{{Overline|3}}
|6\8
378; 1.0{{Overline|5}}
|10\13
387; 10.{{Overline|3}}
|4\5
400
|10\12
413; 1, 3.8{{Overline|3}}
|6\7
423; 1.{{Overline|8}}
|8\9
436.{{Overline|36}}
|-
|Mi#, Si#
|Si#
|A#, B#
|2#
|3#
|9\11
415; 2.6
| rowspan="2" |7\8
442; 9.5
|12\13
464; 1.9375
|5\5
500
|13\12
537; 14.5
|8\7
564; 1.41{{Overline|6}}
|11\9
600
|-
|Dob, Solb
|Dob
|Bb, Cf
|3b, 3d
|4f
|10\11
461; 1, 1.1{{Overline|6}}
|11\13
425; 1.24
|4\5
400
|9\12
372; 2.41{{Overline|6}}
|5\7
352; 1.0625
|6\9
327.{{Overline|27}}
|-
!Do, Sol
!Do
!B, C
!3
!4
!'''11\11'''
'''507; 1.{{Overline|4}}'''
!'''8\8'''
'''505; 3.8'''
!'''13\13'''
'''503; 4, 2.{{Overline|3}}'''
!'''5\5'''
'''500'''
!'''12\12'''
'''496; 1.8125'''
!'''7\7'''
'''494; 8.5'''
!'''9\9'''
'''490.{{Overline|90}}'''
|-
|Do#, Sol#
|Do#
|B#, C#
|3#
|4#
|12\11
553; 1.{{Overline|18}}
|9\8
568; 2.375
|15\13
580; 1.55
| rowspan="2" |6\5
600
|15\12
620; 1.45
|9\7
635; 3.4
|12\9
654.{{Overline|54}}
|-
|Reb, Lab
|Reb
|Cf, Qf
|4b, 4d
|5f
|14\11
646; 6.5
|10\8
631; 1.{{Overline|72}}
|16\13
619; 2.{{Overline|81}}
|14\12
579; 3.{{Overline|2}}
|8\7
564; 1.41{{Overline|6}}
|10\9
545.{{Overline|45}}
|-
|'''Re, La'''
|'''Re'''
|'''C, Q'''
|'''4'''
|'''5'''
|'''15\11'''
'''692; 3.25'''
|'''11\8'''
'''694; 1, 2.8'''
|'''18\13'''
'''696; 1.291{{Overline|6}}'''
|'''7\5'''
'''700'''
|'''17\12'''
'''703; 2, 2.1{{Overline|6}}'''
|'''10\7'''
'''705; 1.1{{Overline|3}}'''
|'''13\9'''
'''709.{{Overline|09}}'''
|-
|Re#, La#
|Re#
|C#, Q#
|4#
|5#
|16\11
738; 2.1{{Overline|6}}
|12\8
757; 1, 8.5
|20\13
774; 5.1{{Overline|6}}
| rowspan="2" |'''8\5'''
'''800'''
|20\12
827; 1, 1.41{{Overline|6}}
|12\7
847; 17
|16\9
872.{{Overline|72}}
|-
|'''Mib, Sib'''
|'''Mib'''
|'''Qf, Df'''
|'''5b, 5d'''
|'''6f'''
|'''18\11'''
'''830; 1.3'''
|'''13\8'''
'''821; 19'''
|'''21\13'''
'''812; 1, 9.{{Overline|3}}'''
|'''19\12'''
'''786; 4.8{{Overline|3}}'''
|'''11\7'''
'''776; 2.125'''
|'''14\9'''
'''763.{{Overline|63}}'''
|-
|Mi, Si
|Mi
|Q, D
|5
|6
|19\11
876; 1.08{{Overline|3}}
|14\8
884; 4.75
|23\13
890; 3.1
|9\5
900
|22\12
910; 2.9
|13\7
917; 1.{{Overline|54}}
|17\9
927.{{Overline|27}}
|-
|Mi#, Si#
|Mi#
|Q#, D#
|5#
|6#
|20\11
923: 13
| rowspan="2" |15\8
947; 2, 1.4
|25\13
967; 1, 2.875
|10\5
1000
|25\12
1034; 2, 14
|15\7
1058; 1, 4.{{Overline|6}}
|20\9
1090.{{Overline|90}}
|-
|Dob, Solb
|Solb
|Df, Sf
|6b, 6d
|7f
|21\11
969; 4.{{Overline|3}}
|24\13
929; 31
|9\5
900
|21\12
868; 1, 28
|11\7
776; 2.125
|15\9
818.{{Overline|18}}
|-
!Do, Sol
!Sol
!D, S
!6
!7
!22\11
1015; 2.6
!16\8
1010; 1.9
!26\13
1006; 2, 4.{{Overline|6}}
!10\5
1000
!24\12
993; 9.{{Overline|6}}
!14\7
988; 4.25
!18\9
981.{{Overline|81}}
|-
|Do#, Sol#
|Sol#
|D#, S#
|6#
|7#
|23\11
1061; 1, 1.1{{Overline|6}}
|17\8
1073; 1, 2.1{{Overline|6}}
|28\13
1083; 1.{{Overline|148}}
| rowspan="2" |11\5
1100
|27\12
1117; 4, 7
|16\7
1129; 2, 2.{{Overline|3}}
|24\9
1309.{{Overline|09}}
|-
|Reb, Lab
|Lab
|Ef
|7b, 7d
|8f
|25\11
1153; 1.{{Overline|18}}
|18\8
1136; 1.1875
|29\13
1122; 1.7{{Overline|2}}
|26\12
1075; 1.16
|15\7
1058; 1, 4.{{Overline|6}}
|19\9
1036.{{Overline|36}}
|-
|'''Re, La'''
|'''La'''
|'''E'''
|'''7'''
|'''8'''
|'''26\11'''
'''1200'''
|'''19\8'''
'''1200'''
|'''31\13'''
'''1200'''
|'''12\5'''
'''1200'''
|'''29\12'''
'''1200'''
|'''17\7'''
'''1200'''
|'''22\9'''
'''1200'''
|-
|Re#, La#
|La#
|E#
|7#
|8#
|27\11
1246; 6,5
|20\8
1263; 6.{{Overline|3}}
|33\13
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}}
|-
|'''Mib, Sib'''
|'''Sib'''
|'''Ff'''
|'''8b, Fd'''
|'''9f'''
|'''29\11'''
'''1338; 3.25'''
|'''21\8'''
'''1326; 3.16̄'''
|'''34\13'''
'''1316; 7.75'''
|'''31\12'''
'''1282; 1.3{{Overline|18}}'''
|'''18\7'''
'''1270; 1.7'''
|'''23\9'''
'''1254.{{Overline|54}}'''
|-
|Mi, Si
|Si
|F
|8, F
|9
|30\11
1384; 1.625
|22\8
1389; 2.1̄
|36\13
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}}
|-
|Mi#, Si#
|Si#
|F#
|8#, F#
|9#
|31\11
1430; 1.3
| rowspan="2" |23\8
1452; 1.58{{Overline|3}}
|38\13
1470; 1.0{{Overline|3}}
|15\5
1500
|37\12
1531; 29
|22\7
1552; 1.0625
|29\9
1581.{{Overline|81}}
|-
|Dob, Solb
|Dob
|Gf
|9b, Gd
|Af
|32\11
1476; 1.08{{Overline|3}}
|37\13
1432: 3.875
|14\5
1400
|33\12
1365; 1.9{{Overline|3}}
|19\7
1341; 5.{{Overline|3}}
|24\9
1309.{{Overline|09}}
|-
!Do, Sol
!Do
!G
!'''9, G'''
!A
!33\11
1523; 13
!24\8
1515; 1.2{{Overline|6}}
!39\13
1509; 1, 2.1
!15\5
1500
!36\12
1489; 1, 1.9
!21\7
1482; 2.8{{Overline|3}}
!27\9
1472.{{Overline|72}}
|-
|Do#, Sol#
|Do#
|G#
|9#, G#
|A#
|34\11
1569; 4.{{Overline|3}}
|25\8
1578; 1.05̄
|41\13
1587; 10.{{Overline|3}}
| rowspan="2" |16\5
1600
|39\12
1613; 1, 3.8{{Overline|3}}
|23\7
1623; 1.{{Overline|8}}
|30\9
1636.{{Overline|36}}
|-
|Reb, Lab
|Reb
|Jf, Af
|Xb, Ad
|Bf
|36\11
1661; 1, 1.1{{Overline|6}}
|26\8
1642; 9.5
|42\13
1625; 1.24
|38\12
1572; 29
|22\7
1552; 1.0625
|28\9
1527.{{Overline|27}}
|-
|'''Re, La'''
|'''Re'''
|'''J, A'''
|'''X, A'''
|'''B'''
|'''37\11'''
'''1707; 1.{{Overline|4}}'''
|'''27\8'''
'''1705; 3.8'''
|'''44\13'''
'''1703; 4, 2.3̄'''
|'''17\5'''
 
'''1700'''
|'''41\12'''
'''1696; 1.8125'''
|'''24\7'''
'''1694; 8.5'''
|'''31\9'''
'''1690.{{Overline|90}}'''
|-
|Re#, La#
|Re#
|J#, A#
|X#, A#
|B#
|38\11
1753; 1.{{Overline|18}}
|28\8
1768; 2.375
|46\13
1780; 1.55
| rowspan="2" |'''18\5'''
'''1800'''
|44\12
1820; 1.45
|26\7
1835; 3,4
|34\9
1854.{{Overline|54}}
|-
|'''Mib, Sib'''
|'''Mib'''
|'''Af, Bf'''
|'''Eb, Bd'''
|'''Cf'''
|'''40\11'''
'''1846; 6.5'''
|'''29\8'''
 
'''1831; 1.{{Overline|72}}'''
|'''47\13'''
'''1819; 2.{{Overline|81}}'''
|'''43\12'''
'''1779; 3.{{Overline|2}}'''
|'''25\7'''
'''1764; 1, 3.25'''
|'''32\9'''
'''1745.{{Overline|45}}'''
|-
|Mi, Si
|Mi
|A, B
|E, B
|C
|41\11
1892; 3.25
|30\8
1894; 1, 2.8
|49\13
1896; 1.291{{Overline|6}}
|19\5
1900
|46\12
1903; 2, 2.1{{Overline|6}}
|27\7
1905; 1, 7.5
|35\9
1909.{{Overline|09}}
|-
|Mi#, Si#
|Mi#
|A#, B#
|E#, B#
|C#
|42\11
1938; 2.1{{Overline|6}}
| rowspan="2" |31\8
1957; 1, 8.5
|51\13
1974; 5.1{{Overline|6}}
|20\5
2000
|49\12
2027; 1, 1.41{{Overline|6}}
|29\7
2047; 17
|38\9
2072.{{Overline|72}}
|-
|Dob, Solb
|Solb
|Bb, Cf
|0b, Dd
|Df
|43\15
1984; 1.625
|50\13
1935; 2.0{{Overline|6}}
|19\5
1900
|45\12
1862; 14.5
|26\7
1835; 3,4
|33\9
1800
|-
!Do, Sol
!Sol
!B, C
!0, D
!D
!44\11
2030; 1.3
!32\8
 
2021; 19
!52\13
2012; 1, 9.{{Overline|3}}
!20\5
2000
!48\12
1986; 4.8{{Overline|3}}
!28\7
1976; 2.125
!36\9
1963.{{Overline|63}}
|-
|Do#, Sol#
|Sol#
|B#, C#
|0#, D#
|D#
|45\11
2076; 1.08{{Overline|3}}
|33\8
2084; 4.75
|54\13
2090; 3.1
| rowspan="2" |21\5
2100
|51\12
2110; 2.9
|30\7
2117; 1.{{Overline|54}}
|39\9
2127.{{Overline|27}}
|-
|Reb, Lab
|Lab
|Cf, Qf
|1b, 1d
|Ef
|47\11
2169; 4.{{Overline|3}}
|34\8
2147; 2, 1.4
|55\13
2129; 31
|50\12
2068; 1, 28
|29\7
2047; 17
|37\9
2018.{{Overline|18}}
|-
|'''Re, La'''
|'''La'''
|'''C, Q'''
|'''1'''
|'''E'''
|'''48\11'''
'''2215; 2.6'''
|'''35\8'''
'''2210; 1.9'''
|'''57\13'''
'''2206; 2, 4.{{Overline|6}}'''
|'''22\5'''
'''2200'''
|'''53\12'''
'''2193; 9.{{Overline|6}}'''
|'''31\7'''
'''2188; 4.25'''
|'''40\9'''
'''2181.{{Overline|81}}'''
|-
|Re#, La#
|La#
|C#, Q#
|1#
|E#
|49\11
2261; 1, 1.1{{Overline|6}}
|36\8
2273; 1, 2.1{{Overline|6}}
|59\13
2083; 1.{{Overline|148}}
| rowspan="2" |'''23\5'''
'''2300'''
|56\12
2327; 4, 7
|33\7
2329; 2, 2.{{Overline|3}}
|43\9
2345.{{Overline|45}}
|-
|'''Mib, Sib'''
|'''Sib'''
|'''Qf, Df'''
|'''2b, 2d'''
|'''Ff'''
|'''51\11'''
'''2353; 1.{{Overline|18}}'''
|'''37\8'''
'''2336; 1.1875'''
|'''61\13'''
'''2322; 1.7{{Overline|2}}'''
|'''55\12'''
'''2275; 1.16'''
|'''32\7'''
'''2258; 1, 4.{{Overline|6}}'''
|'''41\9'''
'''2236.{{Overline|36}}'''
|-
|Mi, Si
|Si
|Q, D
|2
|F
|52\11
2400
|38\8
2400
|62\13
2400
|24\5
2400
|58\12
2400
|34\7
2400
|44\9
2400
|-
|Mi#, Si#
|Si#
|Q#, D#
|2#
|F#
|53\11
2446; 6.5
| rowspan="2" |39\8
2463; 6.{{Overline|3}}
|64\13
2477; 2, 2.6
|25\5
2500
|61\12
2524; 7.25
|36\7
2541; 5.{{Overline|6}}
|47/9
2563.{{Overline|63}}
|-
|Dob, Solb
|Dob
|Df, Sf
|3b, 3d
|1f
|54\11
2492; 3.25
|63\13
2438; 1.1{{Overline|36}}
|24\5
2400
|57\12
2358; 1.61̄
|33\7
2329; 2, 2.{{Overline|3}}
|42\9
2390.{{Overline|90}}
|-
!Do, Sol
!Do
!D, S
!3
!1
!55\11
2538; 2.1{{Overline|6}}
!40\8
2526; 3.1{{Overline|6}}
!65\13
2516; 7.75
!25\5
2500
!60\12
2482; '''1.3{{Overline|18}}'''
!35\7
2470; 1.7
!45\9
2454.{{Overline|54}}
|}
{| class="wikitable"
|+Relative cents<ref name=":05" />
! colspan="5" |Notation
!Supersoft
!Soft
!Semisoft
!Basic
!Semihard
!Hard
!Superhard
|-
! colspan="2" |Diatonic
! rowspan="2" |Mahur
! rowspan="2" |Bijou
! rowspan="2" |Hyperionic
! rowspan="2" |~11ed4/3
! rowspan="2" |~8ed4/3
! rowspan="2" |~13ed4/3
! rowspan="2" |~5ed4/3
! rowspan="2" |~12ed4/3
! rowspan="2" |~7ed4\3
! rowspan="2" |~9ed4/3
|-
!Fourth
!Seventh
|-
|Do#, Sol#
|Sol#
|G#
|0#, D#
|1#
|1\11
''45.{{Overline|45}}''
|1\8
''62.5''
|2\13
''76; 1.08{{Overline|3}}''
| rowspan="2" |1\5
''100''
|3\12
''125''
|2\7
''142; 1.1{{Overline|6}}''
|3\9
''166.{{Overline|6}}''
|-
|Reb, Lab
|Lab
|Jf, Af
|1b, 1d
|2f
|3\11
''136.{{Overline|36}}''
|2\8
''125''
|3\13
''115; 2.6''
|2\12
''83.{{Overline|3}}''
|1\7
''71; 2.{{Overline|3}}''
|1\9
''55.5̄''
|-
|'''Re, La'''
|'''La'''
|'''J, A'''
|'''1'''
|'''2'''
|'''4\11'''
'''''181.{{Overline|81}}'''''
|'''3\8'''
'''''187.5'''''
|'''5\13'''
'''''192; 3.25'''''
|'''2\5'''
'''''200'''''
|'''5\12'''
'''''208.{{Overline|3}}'''''
|'''3\7'''
'''''214; 3.5'''''
|'''4\9'''
'''''222.{{Overline|2}}'''''
|-
|Re#, La#
|La#
|J#, A#
|1#
|2#
|5\11
''227.{{Overline|27}}''
|4\8
''250''
|7\13
''269; 4.{{Overline|3}}''
| rowspan="2" |'''3\5'''
'''''300'''''
|8\12
''333.{{Overline|3}}''
|5\7
''357; 7''
|7\9
''388.{{Overline|8}}''
|-
|'''Mib, Sib'''
|'''Sib'''
|'''Af, Bf'''
|'''2b, 2d'''
|'''3f'''
|'''7\11'''
'''''318.{{Overline|18}}'''''
|'''5\8'''
'''''312.5'''''
|'''8\13'''
'''''307; 1.{{Overline|4}}'''''
|'''7\12'''
'''''291.6̄'''''
|'''4\7'''
'''''285; 1.4'''''
|'''5\9'''
'''''277.{{Overline|7}}'''''
|-
|Mi, Si
|Si
|A, B
|2
|3
|8\11
''363.{{Overline|63}}''
|6\8
''375''
|10\13
''384; 1.625''
|4\5
''400''
|10\12
''416.{{Overline|6}}''
|6\7
''428; 1.75''
|8\9
''444.{{Overline|4}}''
|-
|Mi#, Si#
|Si#
|A#, B#
|2#
|3#
|9\11
''409.{{Overline|09}}''
| rowspan="2" |7\8
''437.5''
|12\13
''461; 1, 1.1{{Overline|6}}''
|5\5
''500''
|13\12
''541.{{Overline|6}}''
|8\7
''571; 2.{{Overline|3}}''
|11\9
''611.1̄''
|-
|Dob, Solb
|Dob
|Bb, Cf
|3b, 3d
|4f
|10\11
''454.{{Overline|54}}''
|11\13
''423; 13''
|4\5
''400''
|9\12
''375''
|5\7
''357; 7''
|6\9
''333.{{Overline|3}}''
|-
!Do, Sol
!Do
!B, C
!3
!4
! colspan="7" |''500''
|-
|Do#, Sol#
|Do#
|B#, C#
|3#
|4#
|12\11
''545.{{Overline|45}}''
|9\8
''562.5''
|15\13
''576; 1.08{{Overline|3}}''
| rowspan="2" |6\5
''600''
|15\12
''625''
|9\7
''642; 1.1{{Overline|6}}''
|12\9
''666.{{Overline|6}}''
|-
|Reb, Lab
|Reb
|Cf, Qf
|4b, 4d
|5f
|14\11
''636.{{Overline|36}}''
|10\8
''625''
|16\13
''615; 2.6''
|14\12
''583.{{Overline|3}}''
|8\7
''571; 2.{{Overline|3}}''
|10\9
''555.5̄''
|-
|'''Re, La'''
|'''Re'''
|'''C, Q'''
|'''4'''
|'''5'''
|'''15\11'''
'''''681.{{Overline|81}}'''''
|'''11\8'''
'''''687.5'''''
|'''18\13'''
'''''692; 3.25'''''
|'''7\5'''
'''''700'''''
|'''17\12'''
'''''708.{{Overline|3}}'''''
|'''10\7'''
'''''714; 3.5'''''
|'''13\9'''
'''''722.{{Overline|2}}'''''
|-
|Re#, La#
|Re#
|C#, Q#
|4#
|5#
|16\11
''727.{{Overline|27}}''
|12\8
''750''
|20\13
''769; 4.{{Overline|3}}''
| rowspan="2" |'''8\5'''
'''''800'''''
|20\12
''833.{{Overline|3}}''
|12\7
''857; 7''
|16\9
''888.{{Overline|8}}''
|-
|'''Mib, Sib'''
|'''Sib'''
|'''Qf, Df'''
|'''5b, 5d'''
|'''6f'''
|'''18\11'''
'''''818.{{Overline|18}}'''''
|'''13\8'''
'''''812.5'''''
|'''21\13'''
'''''807; 1.{{Overline|4}}'''''
|'''19\12'''
'''''791.{{Overline|6}}'''''
|'''11\7'''
'''''785; 1.4'''''
|'''14\9'''
'''''777.{{Overline|7}}'''''
|-
|Mi, Si
|Si
|Q, D
|5
|6
|19\11
''863.{{Overline|63}}''
|14\8
''875''
|23\13
''884; 1.625''
|9\5
''900''
|22\12
''916.{{Overline|6}}''
|13\7
''928; 1.75''
|17\9
''944.{{Overline|4}}''
|-
|Mi#, Si#
|Si#
|Q#, D#
|5#
|6#
|20\11
''909.{{Overline|09}}''
| rowspan="2" |15\8
''937.5''
|25\13
''961; 1, 1.1{{Overline|6}}''
|10\5
''1000''
|25\12
''1041.{{Overline|6}}''
|15\7
''1071; 2.{{Overline|3}}''
|20\9
''1111.1̄''
|-
|Dob, Solb
|Solb
|Df, Sf
|6b, 6d
|7f
|21\11
''954.{{Overline|54}}''
|24\13
''923; 13''
|9\5
''900''
|21\12
''875''
|12\7
''857; 7''
|15\9
''833.{{Overline|3}}''
|-
!Do, Sol
!Sol
!D, S
!6
!7
! colspan="7" |''1000''
|-
|Do#, Sol#
|Sol#
|D#, S#
|6#
|7#
|23\11
''1045.{{Overline|45}}''
|17\8
''1062.5''
|28\13
''1076; 1.08{{Overline|3}}''
| rowspan="2" |11\5
''1100''
|27\12
''1125''
|16\7
''1142; 1.1{{Overline|6}}''
|21\9
''1166.{{Overline|6}}''
|-
|Reb, Lab
|Lab
|Ef
|7b, 7d
|8f
|25\11
''1136.{{Overline|36}}''
|18\8
''1125''
|29\13
''1115; 2.6''
|26\12
''1083.{{Overline|3}}''
|22\7
''1571; 2.{{Overline|3}}''
|19\9
''1055.5̄''
|-
|'''Re, La'''
|'''La'''
|'''E'''
|'''7'''
|'''8'''
|'''26\11'''
'''''1181.{{Overline|81}}'''''
|'''19\8'''
'''''1187.5'''''
|'''31\13'''
'''''1192; 3.25'''''
|'''12\5'''
'''''1200'''''
|'''29\12'''
'''''1208.{{Overline|3}}'''''
|'''17\7'''
'''''1214; 3.5'''''
|'''22\9'''
'''''1222.{{Overline|2}}'''''
|-
|Re#, La#
|La#
|E#
|7#
|8#
|27\11
''1227.{{Overline|27}}''
|20\8
''1250''
|33\13
''1269; 4.{{Overline|3}}''
| rowspan="2" |'''13\5'''
'''''1300'''''
|32\12
''1333.{{Overline|3}}''
|19\7
''1357; 7''
|25\9
''1388.{{Overline|8}}''
|-
|'''Mib, Sib'''
|'''Sib'''
|'''Ff'''
|'''8b, Fd'''
|'''9f'''
|'''29\11'''
'''''1318.{{Overline|18}}'''''
|'''21\8'''
'''''1312.5'''''
|'''34\13'''
'''''1307; 1.{{Overline|4}}'''''
|'''31\12'''
'''''1291.{{Overline|6}}'''''
|'''18\7'''
'''''1285; 1.4'''''
|'''23\9'''
'''''1277.{{Overline|7}}'''''
|-
|Mi, Si
|Si
|F
|8, F
|9
|30\11
''1363.{{Overline|63}}''
|22\8
''1375''
|36\13
''1384; 1.625''
|14\5
''1400''
|34\12
''1416.{{Overline|6}}''
|20\7
''1428; 1.75''
|26\9
''1444.{{Overline|4}}''
|-
|Mi#, Si#
|Si#
|F#
|8#, F#
|9#
|31\11
''1409.{{Overline|09}}''
| rowspan="2" |23\8
''1437.5''
|38\13
''1461; 1, 1.1{{Overline|6}}''
|15\5
''1500''
|37\12
''1541.{{Overline|6}}''
|22\7
''1571; 2.{{Overline|3}}''
|29\9
''1611.1̄''
|-
|Dob, Solb
|Dob
|Gf
|9b, Gd
|Af
|32\11
''1454.{{Overline|54}}''
|37\13
''1423; 13''
|14\5
''1400''
|33\12
''1375''
|19\7
''1357; 7''
|24\9
''1333.{{Overline|3}}''
|-
!Do, Sol
!Do
!G
!'''9, G'''
!A
! colspan="7" |''1500''
|-
|Do#, Sol#
|Sol#
|G#
|9#, G#
|A#
|34\11
''1545.{{Overline|45}}''
|25\8
''1562.5''
|41\13
''1576; 1.08{{Overline|3}}''
| rowspan="2" |16\5
''1600''
|39\12
''1625''
|23\7
''1642; 1.1{{Overline|6}}''
|30\9
''1666.{{Overline|6}}''
|-
|Reb, Lab
|Lab
|Jf, Af
|Xb, Ad
|Bf
|36\11
''1636.{{Overline|36}}''
|26\8
''1625''
|42\13
''1615; 2.6''
|38\12
''1583.{{Overline|3}}''
|22\7
''1571; 2.{{Overline|3}}''
|28\9
''1555.5̄''
|-
|'''Re, La'''
|'''La'''
|'''J, A'''
|'''X, A'''
|'''B'''
|'''37\11'''
'''''1681.{{Overline|81}}'''''
|'''27\8'''
'''''1687.5'''''
|'''44\13'''
'''''1692; 3.25'''''
|'''17\5'''
 
'''''1700'''''
|'''41\12'''
'''''1708.{{Overline|3}}'''''
|'''24\7'''
'''''1714; 3.5'''''
|'''31\9'''
'''''1722.{{Overline|2}}'''''
|-
|Re#, La#
|La#
|J#, A#
|X#, A#
|B#
|38\11
''1727.{{Overline|27}}''
|28\8
''1750''
|46\13
''1769; 4.{{Overline|3}}''
| rowspan="2" |'''18\5'''
'''''1800'''''
|44\12
''1833.{{Overline|3}}''
|26\7
''1857; 7''
|34\9
''1888.{{Overline|8}}''
|-
|'''Mib, Sib'''
|'''Sib'''
|'''Af, Bf'''
|'''Eb, Bd'''
|'''Cf'''
|'''40\11'''
'''''1818.{{Overline|18}}'''''
|'''29\8'''
 
'''''1812.5'''''
|'''47\13'''
'''''1807; 1.{{Overline|4}}'''''
|'''43\12'''
'''''1791.{{Overline|6}}'''''
|'''25\7'''
'''''1785; 1.4'''''
|'''32\9'''
'''''1777.{{Overline|7}}'''''
|-
|Mi, Si
|Si
|A, B
|E, B
|C
|41\11
''1863.{{Overline|63}}''
|30\8
''1875''
|49\13
''1884; 1.625''
|19\5
''1900''
|46\12
''1916.{{Overline|6}}''
|27\7
''1928; 1.75''
|35\9
''1944.{{Overline|4}}''
|-
|Mi#, Si#
|Si#
|A#, B#
|E#, B#
|C#
|42\11
''1909.{{Overline|09}}''
| rowspan="2" |31\8
''1937.5''
|51\13
''1961; 1, 1.1{{Overline|6}}''
|20\5
''2000''
|49\12
''2041.{{Overline|6}}''
|29\7
''2071; 2.{{Overline|3}}''
|38\9
''2111.1̄''
|-
|Dob, Solb
|Dob
|Bb, Cf
|0b, Dd
|Df
|43\11
''1954.{{Overline|54}}''
|50\13
''1923; 13''
|19\5
''1900''
|45\12
''1875''
|26\7
''1857; 7''
|33\9
''1833.{{Overline|3}}''
|-
!Do, Sol
!Sol
!B, C
!0, D
!D
! colspan="7" |''2000''
|-
|Do#, Sol#
|Sol#
|B#, C#
|0#, D#
|D#
|45\11
''2045.{{Overline|45}}''
|33\8
''2062.5''
|54\13
''2076; 1.08{{Overline|3}}''
| rowspan="2" |21\5
''2100''
|51\12
''2125''
|30\7
''2142; 1.1{{Overline|6}}''
|39\9
 
''2166.{{Overline|6}}''
|-
|Reb, Lab
|Lab
|Cf, Qf
|1b, 1d
|Ef
|47\11
''2136.{{Overline|36}}''
|34\8
''2125''
|55\13
''2115; 2.6''
|50\12
''2083.{{Overline|3}}''
|29\7
''2071; 2.{{Overline|3}}''
|37\9
''2055.5̄''
|-
|'''Re, La'''
|'''La'''
|'''C, Q'''
|'''1'''
|'''E'''
|'''48\11'''
'''''2181.{{Overline|81}}'''''
|'''35\8'''
'''''2187.5'''''
|'''57\13'''
'''''2192; 3.25'''''
|'''22\5'''
'''''2200'''''
|'''53\12'''
'''''2208.{{Overline|3}}'''''
|'''31\7'''
'''''2214; 3.5'''''
|'''40\9'''
'''''2222.{{Overline|2}}'''''
|-
|Re#, La#
|La#
|C#, Q#
|1#
|E#
|49\11
''2227.{{Overline|27}}''
|36\8
''2250''
|59\13
''2269; 4.{{Overline|3}}''
| rowspan="2" |'''23\5'''
'''''2300'''''
|56\12
''2333.{{Overline|3}}''
|33\7
''2357; 7''
|43\9
''2388.{{Overline|8}}''
|-
|'''Mib, Sib'''
|'''Sib'''
|'''Qf, Df'''
|'''2b, 2d'''
|'''Ff'''
|'''51\11'''
'''''2318.{{Overline|18}}'''''
|'''37\8'''
 
'''''2312.5'''''
|'''60\13'''
'''''2307; 1.{{Overline|4}}'''''
|'''55\12'''
'''''2291.{{Overline|6}}'''''
|'''32\7'''
'''''2285; 1.4'''''
|'''41\9'''
'''''2277.{{Overline|7}}'''''
|-
|Mi, Si
|Si
|Q, D
|2
|F
|52\11
''2363.{{Overline|63}}''
|38\8
''2375''
|62\13
''2384; 1.625''
|24\5
''2400''
|58\12
''2416.{{Overline|6}}''
|34\7
''2428; 1.75''
|44\9
''2444.{{Overline|4}}''
|-
|Mi#, Si#
|Si#
|Q#, D#
|2#
|F#
|53\11
''2409.{{Overline|09}}''
| rowspan="2" |39\8
 
''2437.5''
|64\13
''2461; 1, 1.1{{Overline|6}}''
|25\5
''2500''
|61\12
''2541.{{Overline|6}}''
|36\7
''2571; 2.3̄''
|47\9
''2611.1̄''
|-
|Dob, Solb
|Dob
|Df, Sf
|3b, 3d
|1f
|54\11
''2454.{{Overline|54}}''
|63\13
''2423; 13''
|24\5
''2400''
|57\12
''2375''
|33\7
''2357; 7''
|42\9
''2333.{{Overline|3}}''
|-
!Do, Sol
!Do
!D, S
!3
!1
! colspan="7" |''2500''
|}
 
==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
|Do, Sol
|perfect unison
|0
|Do, Sol
|perfect fourth
|-
|1
|Mib, Sib
|diminished third
| -1
|Re, La
|perfect second
|-
|2
|Reb, Lab
|diminished second
| -2
|Mi, Si
|perfect third
|-
| colspan="6" |The chromatic 5-note MOS also has the following intervals (from some root):
|-
|3
|Dob, Solb
|diminished fourth
| -3
|Do#, Sol#
|augmented unison (chroma)
|-
|4
|Mibb, Sibb
|doubly diminished third
| -4
|Re#, La#
|augmented second
|}
==Genchain==
The generator chain for this scale is as follows:
{| class="wikitable"
|Mibb
Sibb
|Dob
Solb
|Reb
Lab
|Mib
Sib
|Do
Sol
|Re
La
|Mi
Si
|Do#
Sol#
|Re#
La#
|Mi#
Si#
|-
|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
|LsLL
|<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]]: ~(5ed4/3, 8ed4/3, 13ed4/3)
==='''Mahuric-Superpyth'''===
[[Subgroup]]: 4/3.9/7.3/2
 
[[Comma]] list: [[64/63]]
 
[[POL2]] generator: ~8/7 = 216.7325
 
[[Mapping]]: [{{val|1 0 1}}, {{val|0 2 1}}]
 
[[Optimal ET sequence]]: ~(5ed4/3, 7ed4/3, 9ed4/3, 11ed4/3)
====Scale tree====
The spectrum looks like this:
{| class="wikitable"
! colspan="3" rowspan="2" |Generator
(bright)
! colspan="2" |Cents
! rowspan="2" |L
! rowspan="2" |s
! rowspan="2" |L/s
! rowspan="2" |Comments
|-
!Normalised<ref name=":05" />
!''ed5\12<ref name=":05" />''
|-
|1\3
|
|
|171; 2.{{Overline|3}}
|''166.{{Overline|6}}''
|1
|1
|1.000
|Equalised
|-
|6\17
|
|
|180
|''176; 2.125''
|6
|5
|1.200
|
|-
|
|11\31
|
|180; 1.21{{Overline|6}}
|''177; 2, 2.6''
|11
|9
|1.222
|
|-
|5\14
|
|
|181.{{Overline|81}}
|''178; 1.75''
|5
|4
|1.250
|
|-
|
|14\39
|
|182; 1, 1.5
|''179; 2, 19''
|14
|11
|1.273
|
|-
|
|9\25
|
|183; 19.{{Overline|6}}
|''180''
|9
|7
|1.286
|
|-
|4\11
|
|
|184; 1.625
|''181.{{Overline|81}}''
|4
|3
|1.333
|
|-
|
|15\41
|
|185; 1.7{{Overline|63}}
|''182; 1, 12.{{Overline|6}}''
|15
|11
|1.364
|
|-
|
|11\30
|
|185, 1, 10.8{{Overline|3}}
|''183.{{Overline|3}}''
|11
|8
|1.375
|
|-
|
|7\19
|
|186.{{Overline|6}}
|''184; 4.75''
|7
|5
|1.400
|
|-
|
|10\27
|
|187.5
|''185.{{Overline|185}}''
|10
|7
|1.429
|
|-
|
|13\35
|
|187; 1, 19.75
|''185; 1.4''
|13
|9
|1.444
|
|-
|
|16\43
|
|188; 4.25
|''186; 21.5''
|16
|11
|1.4545
|
|-
|3\8
|
|
|189; 2.{{Overline|1}}
|''187.5''
|3
|2
|1.500
|Mahuric-Meantone starts here
|-
|
|17\45
|
|190; 1, 1.{{Overline|12}}
|''188.{{Overline|8}}''
|17
|11
|1.5455
|
|-
|
|14\37
|
|190.{{Overline|90}}
|''189.{{Overline|189}}''
|14
|9
|1.556
|
|-
|
|11\29
|
|191; 3, 2.{{Overline|3}}
|''189; 1, 1.9''
|11
|7
|1.571
|
|-
|
|8\21
|
|192
|''190; 2.1''
|8
|5
|1.600
|
|-
|
|
|13\34
|192.{{Overline|592}}
|''191; 5.{{Overline|6}}''
|13
|8
|1.625
|
|-
|
|5\13
|
|193; 1, 1, 4.{{Overline|6}}
|''192; 4.{{Overline|3}}''
|5
|3
|1.667
|
|-
|
|
|12\31
|194.{{Overline|594}}
|''193; 1, 1, 4.{{Overline|6}}''
|12
|7
|1.714
|
|-
|
|7\18
|
|195; 2.8{{Overline|6}}
|''194.{{Overline|4}}''
|7
|4
|1.750
|
|-
|
|9\23
|
|196.{{Overline|36}}
|''195; 1.5{{Overline|3}}''
|9
|5
|1.800
|
|-
|
|11\28
|
|197; 67
|''196; 2.{{Overline|3}}''
|11
|6
|1.833
|
|-
|
|13\33
|
|197; 2.{{Overline|135}}
|''196.{{Overline|96}}''
|13
|7
|1.857
|
|-
|
|15\38
|
|197; 1, 2, 1, 1.{{Overline|54}}
|''197; 2, 1.4''
|15
|8
|1.875
|
|-
|
|17\43
|
|198; 17.1{{Overline|6}}
|''197; 1, 2, 14''
|17
|9
|1.889
|
|-
|
|19\48
|
|198: 3, 1, 28
|''197.91{{Overline|6}}''
|19
|10
|1.900
|
|-
|
|21\53
|
|198; 2.3{{Overline|518}}
|''198; 8.8{{Overline|3}}''
|21
|11
|1.909
|
|-
|
|23\58
|
|198; 1, 3, 1.7
|''198; 3.625''
|23
|12
|1.917
|
|-
|
|25\63
|
|198; 1, 2, 12.25
|''198; 2, 2.{{Overline|36}}''
|25
|13
|1.923
|
|-
|
|27\68
|
|198; 1, 3.{{Overline|405}}
|''198; 1.{{Overline|8}}''
|27
|14
|1.929
|
|-
|
|29\73
|
|198; 1, 1.1{{Overline|6}}
|''198; 1, 1.{{Overline|703}}''
|29
|15
|1.933
|
|-
|
|31\78
|
|198; 1, 12, 2.8
|''198; 1, 2.{{Overline|54}}''
|31
|16
|1.9375
|
|-
|
|33\83
|
|198; 1.{{Overline|005}}
|''198; 1.2{{Overline|57}}''
|33
|17
|1.941
|
|-
|
|35\88
|
|199; 19.{{Overline|18}}
|''198.8{{Overline|63}}''
|35
|18
|1.944
|
|-
|2\5
|
|
|200
|''200''
|2
|1
|2.000
|Mahuric-Meantone ends, Mahuric-Pythagorean begins
|-
|
|17\42
|
|201.{{Overline|9801}}
|''202; 2.625''
|17
|8
|2.125
|
|-
|
|15\37
|
|202; 4.0{{Overline|45}}
|''202.{{Overline|702}}''
|15
|7
|2.143
|
|-
|
|13\32
|
|202; 1, 1, 2.0{{Overline|6}}
|''203.125''
|13
|6
|2.167
|
|-
|
|11\27
|
|203; 13
|''203.{{Overline|703}}''
|11
|5
|2.200
|
|-
|
|9\22
|
|203; 1, 3.41{{Overline|6}}
|''204.{{Overline|54}}''
|9
|4
|2.250
|
|-
|
|7\17
|
|204; 1. 7.2
|''205; 1.1{{Overline|3}}''
|7
|3
|2.333
|
|-
|
|
|12\29
|205; 1.4
|''206; 1, 8.{{Overline|6}}''
|12
|5
|2.400
|
|-
|
|
|17\41
|206.{{Overline|06}}
|''207; 3, 6.5''
|17
|7
|2.429
|
|-
|
|5\12
|
|206; 1, 8.{{Overline|6}}
|''208.{{Overline|3}}''
|5
|2
|2.500
|Mahuric-Neogothic heartland is from here…
|-
|
|
|18\43
|207; 1.{{Overline|4}}
|''209; 3, 4.{{Overline|3}}''
|18
|7
|2.571
|
|-
|
|
|13\31
|208
|''209; 1, 2.1''
|13
|5
|2.600
|
|-
|
|8\19
|
|208; 1.4375
|''210; 1.9''
|8
|3
|2.667
|…to here
|-
|
|11\26
|
|209; 1.{{Overline|90}}
|''211; 1, 1.1{{Overline|6}}''
|11
|4
|2.750
|
|-
|
|14\33
|
|210
|''212.{{Overline|12}}''
|14
|5
|2.800
|
|-
|
|17\40
|
|210; 3.2{{Overline|3}}
|''212.5''
|17
|6
|2.833
|
|-
|
|20\47
|
|210; 1.9
|''212; 1.{{Overline|30}}''
|20
|7
|2.857
|
|-
|
|23\54
|
|210; 1.4{{Overline|5}}
|''212.{{Overline|962}}''
|23
|8
|2.875
|
|-
|
|26\61
|
|210.{{Overline|810}}
|''213; 8, 1.4''
|26
|9
|2.889
|
|-
|3\7
|
|
|211; 1, 3.25
|''214; 3.5''
|3
|1
|3.000
|Mahuric-Pythagorean ends, Mahuric-Superpyth begins
|-
|
|22\51
|
|212; 1, 9.{{Overline|3}}
|''215; 1, 2,1875''
|22
|7
|3.143
|
|-
|
|19\44
|
|213; 11.{{Overline|8}}
|''215.{{Overline|90}}''
|19
|6
|3.167
|
|-
|
|16\37
|
|213.3̄
|''216.{{Overline|216}}''
|16
|5
|3.200
|
|-
|
|13\30
|
|213; 1, 2.3{{Overline|18}}
|''216.{{Overline|6}}''
|13
|4
|3.250
|
|-
|
|10\23
|
|214; 3.5
|''217; 5.75''
|10
|3
|3.333
|
|-
|
|7\16
|
|215; 2.6
|''218.75''
|7
|2
|3.500
|
|-
|
|
|18\41
|216
|''219; 1, 1.05''
|18
|5
|3.600
|
|-
|
|11\25
|
|216; 2.541{{Overline|6}}
|''220''
|11
|3
|3.667
|
|-
|
|15\34
|
|216; 1.152{{Overline|7}}
|''220; 1.7''
|15
|4
|3.750
|
|-
|
|19\43
|
|217; 7
|''220; 1, 7.6''
|19
|5
|3.800
|
|-
|
|23\52
|
|217; 3, 10.25
|''221; 6.5''
|23
|6
|3.833
|
|-
|4\9
|
|
|218.{{Overline|18}}
|''222.{{Overline|2}}''
|4
|1
|4.000
|
|-
|
|17\38
|
|219; 1, 2.{{Overline|90}}
|''223; 1.58{{Overline|3}}''
|17
|4
|4.250
|
|-
|
|13\29
|
|219; 1, 2.55
|''224; 7.25''
|13
|3
|4.333
|
|-
|
|9\20
|
|220; 2.45
|''225''
|9
|2
|4.500
|
|-
|
|14\31
|
|221; 19
|''225; 1.24''
|14
|3
|4.667
|
|-
|
|19\42
|
|221; 2.{{Overline|783}}
|''226; 4.2''
|19
|4
|4.750
|
|-
|5\11
|
|
|222.{{Overline|2}}
|''227.{{Overline|27}}''
|5
|1
|5.000
|Mahuric-Superpyth ends
|-
|
|16\35
|
|223; 3.{{Overline|90}}
|''228; 1.75''
|16
|3
|5.333
|
|-
|
|11\24
|
|223; 1, 2.6875
|''229.1{{Overline|6}}''
|11
|2
|5.500
|
|-
|
|17\37
|
|224; 5.7{{Overline|2}}
|''229.{{Overline|729}}''
|17
|3
|5.667
|
|-
|6\13
|
|
|225
|''230; 1.3''
|6
|1
|6.000
|
|-
|1\3
|
|
|240
|''250''
|1
|0
|→ inf
|Paucitonic
|}
 
== See also ==
[[2L 1s (4/3-equivalent)]] - idealized tuning<references />