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#REDIRECT [[3L 2s (8/5-equivalent)]]
'''3L 2s<minor sixth>''' (sometimes called '''diatonic'''), is a minor sixth-repeating MOS scale. The notation "<minor sixth>" means the period of the MOS is a minor sixth, disambiguating it from octave-repeating [[3L 2s]]. The name of the period interval is called the '''sextave''' (by analogy to the [[tritave]]).
 
The generator range is 240 to 342.9 cents, placing it on the [[6/5|diatonic minor third]], usually representing a minor third of some type (like [[6/5]]). The bright (chroma-positive) generator is, however, its minor sixth complement (480 to 514.3 cents).
 
Because this diatonic is a minor sixth-repeating scale, each tone has an 8/5 minor sixth above it. The scale has one major chord, one minor chord and three diminished chords. This diatonic also has two diminished 7th chords, making it a warped melodic minor scale.
 
[[Basic]] diatonic is in [[8ed8/5]], which is a very good minor sixth-based equal tuning similar to [[12edo]].
==Notation==
There are 2 main ways to notate the diatonic scale. One method uses a simple sextave (minor sixth) repeating notation consisting of 5 naturals (La, Si, Do, Re, Mi). Given that 1-7/6-3/2 is minor sixth-equivalent to a tone cluster of 1-16/15-7/6, it may be more convenient to notate these diatonic scales as repeating at the double sextave (diminished eleventh~tenth), however it does make navigating the [[Generator|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 16\15. Notating this way produces a tenth which is the Dorian mode of Annapolis[6L 4s] or Oriole[6L 4s]. Since there are exactly 10 naturals in double sextave notation, Greek numerals 1-10 may be used.
{| class="wikitable"
|+
Normalized
! colspan="2" |Notation
!Supersoft
!Soft
!Semisoft
!Basic
!Semihard
!Hard
!Superhard
|-
!Diatonic
!Oriole, Annapolis
!18eds
!13eds
!21eds
!8eds
!19eds
!11eds
!14eds
|-
|La#
|Α#
|1\18
46.154
|1\13
63.158
|2\21
77.419
| rowspan="2" |1\8
100
|3\19
124.138
|2\11
[[Tel:141.1765|141.1765]]
|3\14
163.{{Overline|63}}
|-
|Sib
|Βb
|3\18
138.4615
|2\13
126.316
|3\21
116.129
|2\19
82.759
|1\11
70.588
|1\14
54.{{Overline|54}}
|-
|Si
|Β
|4\18
184.615
|3\13
189.474
|5\21
193.548
|2\8
200
|5\19
206.897
|3\11
211.764
|4\14
218.{{Overline|18}}
|-
|Si#
|Β#
|5\18
230.769
| rowspan="2" |4\13
252.632
|7\21
270.968
|3\8
300
|8\19
331.0345
|5\11
352.941
|7\14
381.{{Overline|81}}
|-
|Dob
|Γb
|6\18
276.923
|6\21
232.258
|2\8
200
|4\19
165.517
|2\11
141.1765
|2\14
109.{{Overline|09}}
|-
|'''Do'''
|'''Γ'''
|'''7\18'''
'''323.076'''
|'''5\13'''
'''315.7895'''
|'''8\21'''
'''309.677'''
|'''3\8'''
'''300'''
|'''7\19'''
'''289.655'''
|'''4\11'''
'''282.353'''
|'''5\14'''
'''272.{{Overline|72}}'''
|-
|Do#
|Γ#
|8\18
369.231
|6\13
378.947
|10\21
387.0968
| rowspan="2" |4\8
400
|10\19
413.793
|6\11
423.529
|8\14
436.{{Overline|36}}
|-
|Reb
|Δb
|10\18
461.5385
|7\13
442.105
|11\21
425.8065
|9\19
372.413
|5\11
352.941
|6\14
327.{{Overline|27}}
|-
|'''Re'''
|'''Δ'''
|'''11\18'''
'''507.692'''
|'''8\13'''
'''505.263'''
|'''13\21'''
'''503.226'''
|'''5\8'''
'''500'''
|'''12\19'''
'''496.551'''
|'''7\11'''
'''494.118'''
|'''9\14'''
'''490.{{Overline|90}}'''
|-
|Re#
|Δ#
|12\18
553.846
|9\13
568.421
|15\21
580.645
| rowspan="2" |6\8
600
|15\19
620.689
|9\11
635.294
|12\14
654.{{Overline|54}}
|-
|Mib
|Εb
|14\18
646.154
|10\13
631.579
|16\21
619.355
|14\19
579.310
|8\11
564.706
|10\14
545.{{Overline|45}}
|-
|Mi
|Ε
|15\18
692.308
|11\13
694.737
|18\21
696.774
|7\8
700
|17\19
703.448
|10\11
705.88235
|13\14
709.{{Overline|09}}
|-
|Mi#
|Ε#
|16\18
738.4615
| rowspan="2" |12\13
757.895
|20\21
774.194
|8\8
800
|20\19
827.586
|12\11
847.059
|16\14
872.{{Overline|72}}
|-
|Lab
|Ϛb/Ϝb
|17\18
784.615
|19\21
735.484
|7\8
700
|16\19
662.069
|9\11
635.294
|11\14
600
|-
!La
!Ϛ/Ϝ
!18\18
830.769
!13\13
821.053
!21\21
812.903
!8\8
 
800
!19\19
786.207
!11\11
776.471
!14\14
 
763.{{Overline|63}}
|-
|La#
|Ϛ#/Ϝ#
|19\18
876.923
|14\13
884.2105
|23\21
890.323
| rowspan="2" |9\8
900
|22\19
910.345
|13\11
917.647
|17\14
927.{{Overline|27}}
|-
|Sib
|Ζb
|21\18
969.231
|15\13
947.368
|24\21
929.032
|21\19
868.9655
|12\11
847.059
|15\14
818.{{Overline|18}}
|-
|Si
|Ζ
|22\18
1015.385
|16\13
1010.526
|26\21
1006.452
|10\8
1000
|24\19
993.1035
|14\11
988.235
|18\14
981.{{Overline|81}}
|-
|Si#
|Ζ#
|23\18
1061.5385
| rowspan="2" |17\13
1071.684
|28\21
1083.871
|11\8
1100
|27\19
1117.241
|16\11
1129.412
|21\14
1145.{{Overline|45}}
|-
|Dob
|Ηb
|24\18
1107.692
|27\21
1045.161
|10\8
1000
|23\19
951.724
|13\11
917.647
|16\14
872.{{Overline|72}}
|-
|'''Do'''
|'''Η'''
|'''25\18'''
'''1153.846'''
|'''18\13'''
'''1136.842'''
|'''29\21'''
'''1122.581'''
|'''11\8'''
'''1100'''
|'''26\19'''
'''1075.862'''
|'''15\11'''
'''1052.8235'''
|'''19\14'''
'''1036.{{Overline|36}}'''
|-
|Do#
|Η#
|26\18
1200
|19\13
1200
|31\21
1200
| rowspan="2" |12\8
1200
|29\19
1200
|17\11
1200
|22\14
1200
|-
|Reb
|Θb
|28\18
1292.308
|20\13
1263.158
|32\21
1238.710
|28\19
1158.621
|16\11
1129.412
|20\14
1090.{{Overline|90}}
|-
|'''Re'''
|'''Θ'''
|'''29\18'''
'''1338.4615'''
|'''21\13'''
'''1326.316'''
|'''34\21'''
'''1316.129'''
|'''13\8'''
'''1300'''
|'''31\19'''
'''1282.759'''
|'''18\11'''
'''1270.588'''
|'''23\14'''
'''1254.{{Overline|54}}'''
|-
|Re#
|Θ#
|30\18
1384.615
|22\13
1389.474
|36\21
1393.548
| rowspan="2" |14\8
1400
|34\19
1406.897
|20\11
1411.765
|26\14
1418.{{Overline|18}}
|-
|Mib
|Ιb
|32\18
1476.923
|23\13
1452.632
|37\21
1432.258
|33\19
1365.517
|19\11
1341.1765
|24\14
1309.{{Overline|09}}
|-
|Mi
|Ι
|33\18
1523.077
|24\13
1515.7895
|39\21
1509.677
|15\8
1500
|36\19
1489.655
|21\11
1482.352
|27\14
1472.{{Overline|72}}
|-
|Mi#
|Ι#
|34\18
1569.231
| rowspan="2" |25\13
1578.947
|41\21
1587.097
|16\8
1600
|39\19
1613.793
|23\11
1623.529
|30\14
1636.{{Overline|36}}
|-
|Lab
|Αb
|35\18
1615.385
|40\21
1548.387
|15\8
1500
|35\19
1448.286
|20\11
1411.765
|25\14
1363.{{Overline|63}}
|-
!La
!Α
!36\18
1661.5385
!26\13
1642.105
!42\21
1625.8065
!16\8
 
1600
!38\19
1572.414
!22\11
1552.941
!28\14
1527.{{Overline|27}}
|}
{| class="wikitable"
|+''ed8\12 (→ed2\3)''
! colspan="2" |Notation
!Supersoft
!Soft
!Semisoft
!Basic
!Semihard
!Hard
!Superhard
|-
!Diatonic
!Oriole, Annapolis
!18eds
!13eds
!21eds
!8eds
!19eds
!11eds
!14eds
|-
|La#
|Α#
|''1\18''
''44.{{Overline|4}}''
|''1\13''
''61.5385''
|''2\21''
''76.1905''
| rowspan="2" |''1\8''
''100''
|''3\19''
''126.316''
|''2\11''
''145.{{Overline|45}}''
|''3\14''
''171.429''
|-
|Sib
|Βb
|''3\18''
''133.{{Overline|3}}''
|''2\13''
''123.077''
|''3\21''
''114.286''
|''2\19''
''84.2105''
|''1\11''
''72.{{Overline|72}}''
|''1\14''
''57.143''
|-
|Si
|Β
|''4\18''
''177.{{Overline|7}}''
|''3\13''
''184.615''
|''5\21''
''190.476''
|''2\8''
''200''
|''5\19''
''210.526''
|''3\11''
''218.{{Overline|18}}''
|''4\14''
''228.571''
|-
|Si#
|Β#
|''5\18''
''222.{{Overline|2}}''
| rowspan="2" |''4\13''
''246.154''
|''7\21''
''266.{{Overline|6}}''
|''3\8''
''300''
|''8\19''
''336.842''
|''5\11''
''363.{{Overline|63}}''
|''7\14''
''400''
|-
|Dob
|Γb
|''6\18''
''266.{{Overline|6}}''
|''6\21''
''228.571''
|''2\8''
''200''
|''4\19''
''168.421''
|''2\11''
''145.{{Overline|45}}''
|''2\14''
''114.28''
|-
|'''Do'''
|'''Γ'''
|'''''7\18'''''
'''''311.{{Overline|1}}'''''
|'''''5\13'''''
'''''307.692'''''
|'''''8\21'''''
'''''304.762'''''
|'''''3\8'''''
'''''300'''''
|'''''7\19'''''
'''''294.737'''''
|'''''4\11'''''
'''''290.{{Overline|90}}'''''
|'''''5\14'''''
'''''285.714'''''
|-
|Do#
|Γ#
|''8\18''
''355.{{Overline|5}}''
|''6\13''
''369.231''
|''10\21''
''380.952''
| rowspan="2" |''4\8''
''400''
|''10\19''
''421.053''
|''6\11''
''436.{{Overline|36}}''
|''8\14''
''457.143''
|-
|Reb
|Δb
|''10\18''
''444.{{Overline|4}}''
|''7\13''
''430.769''
|''11\21''
''419.048''
|''9\19''
''378.947''
|''5\11''
''363.{{Overline|63}}''
|''6\14''
''342.857''
|-
|'''Re'''
|'''Δ'''
|'''''11\18'''''
'''''488.{{Overline|8}}'''''
|'''''8\13'''''
'''''492.308'''''
|'''''13\21'''''
'''''495.238'''''
|'''''5\8'''''
'''''500'''''
|'''''12\19'''''
'''''505.263'''''
|'''''7\11'''''
'''''509.{{Overline|09}}'''''
|'''''9\14'''''
'''''514.286'''''
|-
|Re#
|Δ#
|''12\18''
''533.{{Overline|3}}''
|''9\13''
''553.846''
|''15\21''
''571.429''
| rowspan="2" |''6\8''
''600''
|''15\19''
''631.421''
|''9\11''
''654.{{Overline|54}}''
|''12\14''
''685.714''
|-
|Mib
|Εb
|''14\18''
''622.{{Overline|2}}''
|''10\13''
''615.385''
|''16\21''
''609.524''
|''14\19''
''589.474''
|''8\11''
''581.{{Overline|81}}''
|''10\14''
''571.424''
|-
|Mi
|Ε
|''15\18''
''666.{{Overline|6}}''
|''11\13''
''676.9231''
|''18\21''
''685.7143''
|''7\8''
''700''
|''17\19''
''715.7895''
|''10\11''
''727.{{Overline|27}}''
|''13\14''
''742.857''
|-
|Mi#
|Ε#
|''16\18''
''711.{{Overline|1}}''
| rowspan="2" |''12\13''
''738.4615''
|''20\21''
''761.905''
|''8\8''
''800''
|''20\19''
''842.105''
|''12\11''
''872.{{Overline|72}}''
|''16\14''
''914.286''
|-
|Lab
|Ϛb/Ϝb
|''17\18''
''755.{{Overline|5}}''
|''19\21''
''723.8095''
|''7\8''
''700''
|''16\19''
''673.684''
|''8\11''
''581.{{Overline|81}}''
|''11\14''
''628.571''
|-
!La
!Ϛ/Ϝ
! colspan="7" |''800''
|-
|La#
|Ϛ#/Ϝ#
|''19\18''
''844.{{Overline|4}}''
|''14\13''
''861.5385''
|''23\21''
''876.1905''
| rowspan="2" |''9\8''
''900''
|''22\19''
''926.316''
|''13\11''
''945.{{Overline|45}}''
|''17\14''
''971.429''
|-
|Sib
|Ζb
|''21\18''
''933.{{Overline|3}}''
|''15\13''
''923.077''
|''24\21''
''914.286''
|''21\19''
''884.2105''
|''12\11''
''872.{{Overline|72}}''
|''15\14''
''857.143''
|-
|Si
|Ζ
|''22\18''
''977.{{Overline|7}}''
|''16\13''
''984.615''
|''26\21''
''990.476''
|''10\8''
''1000''
|''24\19''
''1010.526''
|''14\11''
''1018.{{Overline|18}}''
|''18\14''
''1028.571''
|-
|Si#
|Ζ#
|''23\18''
''1022.{{Overline|2}}''
| rowspan="2" |''17\13''
''1046.154''
|''28\21''
''1066.{{Overline|6}}''
|''11\8''
''1100''
|''27\19''
''1136.8421''
|''16\11''
''1163.{{Overline|63}}''
|''21\14''
''1200''
|-
|Dob
|Ηb
|''24\18''
''1066.{{Overline|6}}''
|''27\21''
''1028.571''
|''10\8''
''1000''
|''23\19''
''968.421''
|''13\11''
''945.{{Overline|45}}''
|''16\14''
''914.286''
|-
|'''Do'''
|'''Η'''
|'''''25\18'''''
'''''1111.{{Overline|1}}'''''
|'''''18\13'''''
'''''1107.692'''''
|'''''29\21'''''
'''''1104.762'''''
|'''''11\8'''''
'''''1100'''''
|'''''26\19'''''
'''''1094.737'''''
|'''''15\11'''''
'''''1090.{{Overline|90}}'''''
|'''''19\14'''''
'''''1085.714'''''
|-
|Do#
|Η#
|''26\18''
''1155.{{Overline|5}}''
|''19\13''
''1169.237''
|''31\21''
''1180.952''
| rowspan="2" |''12\8''
''1200''
|''29\19''
''1221.053''
|''17\11''
''1236.{{Overline|36}}''
|''22\14''
''1257.143''
|-
|Reb
|Θb
|''28\18''
''1244.{{Overline|4}}''
|''20\13''
''1230.769''
|''32\21''
''1219.048''
|''28\19''
''1178.947''
|''16\11''
''1163.{{Overline|63}}''
|''20\14''
''1142.857''
|-
|'''Re'''
|'''Θ'''
|'''''29\18'''''
'''''1288.{{Overline|8}}'''''
|'''''21\13'''''
'''''1292.308'''''
|'''''34\21'''''
'''''1295.238'''''
|'''''13\8'''''
'''''1300'''''
|'''''31\19'''''
'''''1305.263'''''
|'''''18\11'''''
'''''1309.{{Overline|09}}'''''
|'''''23\14'''''
'''''1314.286'''''
|-
|Re#
|Θ#
|''30\18''
''1333.{{Overline|3}}''
|''22\13''
''1187.924''
|''36\21''
''1371.429''
| rowspan="2" |''14\8''
''1400''
|''34\19''
''1431.421''
|''20\11''
''1454.{{Overline|54}}''
|''26\14''
''1485.714''
|-
|Mib
|Ιb
|''32\18''
''1422.{{Overline|2}}''
|''23\13''
''1415.385''
|''37\21''
''1409.524''
|''33\19''
''1389.474''
|''19\11''
''1381.{{Overline|81}}''
|''24\14''
''1371.429''
|-
|Mi
|Ι
|''33\18''
''1466.{{Overline|6}}''
|''24\13''
''1476.923''
|''39\21''
''1485.714''
|''15\8''
''1500''
|''36\19''
''1515.7895''
|''21\11''
''1527.{{Overline|27}}''
|''27\14''
''1542.857''
|-
|Mi#
|Ι#
|''34\18''
''1511.{{Overline|1}}''
| rowspan="2" |''25\13''
''1538.4615''
|''41\21''
''1561.905''
|''16\8''
''1600''
|''39\19''
''1642.105''
|''23\11''
''1672.{{Overline|72}}''
|''30\14''
''1714.286''
|-
|Lab
|Αb
|''35\18''
''1555.{{Overline|5}}''
|''40\21''
''1523.8095''
|''15\8''
''1500''
|''35\19''
''1473.684''
|''20\11''
''1454.{{Overline|54}}''
|''25\14''
''1428.571''
|-
!La
!Α
! colspan="7" |''1600''
|}
 
==Intervals==
{| class="wikitable"
!Generators
!Sextave notation
!Interval category name
!Generators
!Notation of sixth inverse
!Interval category name
|-
| colspan="6" |The 5-note MOS has the following intervals (from some root):
|-
|0
|La
|sextave (minor sixth)
|0
|La
|perfect unison
|-
|1
|Re
|perfect fourth
| -1
|Do
|minor third
|-
|2
|Si
|major second
| -2
|Mib
|diminished fifth
|-
|3
|Mi
|perfect fifth
| -3
|Sib
|minor second
|-
|4
|Do#
|major third
| -4
|Reb
|diminished fourth
|-
| colspan="6" |The chromatic 8-note MOS also has the following intervals (from some root):
|-
|5
|La#
|augmented unison (chroma)
| -5
|Lab
|diminished sextave
|-
|6
|Re#
|augmented fourth
| -6
|Dob
|diminished third
|-
|7
|Si#
|augmented second
| -7
|Mibb
|doubly diminished fifth
|}
==Genchain==
The generator chain for this scale is as follows:
{| class="wikitable"
|Sibb
|Mibb
|Dob
|Lab
|Reb
|Sib
|Mib
|Do
|La
|Re
|Si
|Mi
|Do#
|La#
|Re#
|Si#
|Mi#
|-
|d2
|dd5
|d3
|d6
|d4
|m2
|d5
|m3
|P1
|P4
|M2
|P5
|M3
|A1
|A4
|A2
|A5
|}
==Modes==
The mode names are based on the modes of the diatonic scale , in order of size:
{| class="wikitable"
!Mode
!Scale
![[Modal UDP Notation|UDP]]
! colspan="4" |Interval type
|-
!name
!pattern
!notation
!2nd
!3rd
!4th
!5th
|-
|Hindu
|LLsLs
|<nowiki>4|0</nowiki>
|M
|M
|P
|P
|-
|Minor
|LsLLs
|<nowiki>3|1</nowiki>
|M
|m
|P
|P
|-
|Half diminished
|LsLsL
|<nowiki>2|2</nowiki>
|M
|m
|P
|d
|-
|Diminished
|sLLsL
|<nowiki>1|3</nowiki>
|m
|m
|P
|d
|-
|Altered
|sLsLL
|<nowiki>0|4</nowiki>
|m
|m
|d
|d
|}
 
==Temperaments==
The most basic rank-2 temperament interpretation of this diatonic is '''Aeolianic''', which has septimal 6:7:9 or pental 10:12:15 chords spelled <code>root-(p-1g)-(3g)</code> (p = the minor sixth, g = the approximate 4/3). The name "Aeolianic" comes from the Aeolian minor mode having the minor sixth as its characteristic interval.
==='''Aeolianic-Meantone'''===
[[Subgroup]]: 8/5.4/3.3/2
 
[[Comma]] list: [[81/80]]
 
[[POL2]] generator: ~6/5 = 308.3057
 
[[Mapping]]: [{{val|1 1 2}}, {{val|0 -1 -3}}]
 
[[Optimal ET sequence]]: 5ed8/5, 8ed8/5, 13ed8/5
==='''Aeolianic-Superpyth'''===
[[Subgroup]]: 14/9.4/3.3/2
 
[[Comma]] list: [[64/63]]
 
[[POL2]] generator: ~7/6 = 276.0795
 
[[Mapping]]:  [{{val|1 1 2}}, {{val|0 -1 -3}}]
 
[[Optimal ET sequence]]: 3ed14/9, 11ed14/9, 14ed14/9
 
==Scale tree==
The spectrum looks like this:
{| class="wikitable"
! colspan="3" rowspan="2" |Generator
(bright)
! colspan="2" |Normalised
! colspan="2" |''ed8\12 (→ed2\3)''
! rowspan="2" |L
! rowspan="2" |s
! rowspan="2" |L/s
! rowspan="2" |Comments
|-
!Chroma-positive
!Chroma-negative
!Chroma-positive
!Chroma-negative
|-
|3\5
|
|
|514.286
|342.857
|''480''
|''320''
|1
|1
|1.000
|Equalised
|-
|17\28
|
|
|510
|330
|''485.714''
|''314.286''
|6
|5
|1.200
|
|-
|
|48\79
|
|509.7345
|329.2035
|''486.076''
|''313.924''
|17
|14
|1.214
|
|-
|
|31\51
|
|509.589
|328.767
|''486.2745''
|''313.7255''
|11
|9
|1.222
|
|-
|14\23
|
|
|509.{{Overline|09}}
|327.{{Overline|27}}
|''486.9565''
|''313.0435''
|5
|4
|1.250
|
|-
|
|39\64
|
|508.966
|326.087
|''487.5''
|''312.5''
|14
|11
|1.273
|
|-
|
|25\41
|
|508.475
|325.424
|''487.805''
|''312.195''
|9
|7
|1.286
|
|-
|
|36\59
|
|508.235
|324.706
|''488.136''
|''311.864''
|13
|10
|1.300
|
|-
|11\18
|
|
|507.692
|323.077
|''488.{{Overline|8}}''
|''311.{{Overline|1}}''
|4
|3
|1.333
|
|-
|
|63\103
|
|507.383
|322.148
|''489.32''
|''310.68''
|23
|17
|1.353
|
|-
|
|52\85
|
|507.317
|321.951
|''489.412''
|''310.588''
|19
|14
|1.357
|
|-
|
|41\67
|
|507.2165
|321.6495
|''489.552''
|''310.448''
|15
|11
|1.364
|
|-
|
|30\49
|
|507.062
|321.127
|''489.796''
|''310.204''
|11
|8
|1.375
|
|-
|
|19\31
|
|506.{{Overline|6}}
|320
|''490.323''
|''309.678''
|7
|5
|1.400
|
|-
|
|
|46\75
|506.422
|319.266
|''490.{{Overline|6}}''
|''309.{{Overline|3}}''
|17
|12
|1.417
|
|-
|
|27\44
|
|506.25
|318.75
|''490.{{Overline|90}}''
|''309.{{Overline|09}}''
|10
|7
|1.429
|
|-
|
|35\57
|
|506.024
|318.072
|''491.228''
|''308.712''
|13
|9
|1.444
|
|-
|
|43\70
|
|505.882
|317.647
|''491.429''
|''308.571''
|16
|11
|1.4545
|
|-
|
|51\83
|
|505.785
|317.355
|''491.566''
|''308.434''
|19
|13
|1.4615
|
|-
|8\13
|
|
|505.263
|315.79
|''492.308''
|''307.692''
|3
|2
|1.500
|Aeolianic-Meantone starts here
|-
|
|45\73
|
|504.673
|314.019
|''493.151''
|''306.849''
|17
|11
|1.5455
|
|-
|
|37\60
|
|504.{{Overline|54}}
|313.{{Overline|63}}
|''493.{{Overline|3}}''
|''306.{{Overline|6}}''
|14
|9
|1.556
|
|-
|
|29\47
|
|504.348
|313.043
|''493.617''
|''306.383''
|11
|7
|1.571
|
|-
|
|21\34
|
|504
|312
|''494.118''
|''305.882''
|8
|5
|1.600
|
|-
|
|
|34\55
|503.{{Overline|703}}
|311.{{Overline|1}}
|''494.{{Overline|54}}''
|''305.{{Overline|45}}''
|13
|8
|1.625
|
|-
|
|
|47\76
|503.571
|310.714
|''494.737''
|''305.263''
|18
|11
|1.636
|
|-
|
|13\21
|
|503.226
|309.678
|''495.238''
|''304.762''
|5
|3
|1.667
|
|-
|
|
|31\50
|502.{{Overline|702}}
|308.{{Overline|108}}
|''496''
|''304''
|12
|7
|1.714
|
|-
|
|
|49\79
|502.564
|307.692
|''496.2025''
|''303.7975''
|19
|11
|1.727
|
|-
|
|18\29
|
|502.326
|306.977
|''496.552''
|''303.448''
|7
|4
|1.750
|
|-
|
|23\37
|
|501.{{Overline|81}}
|305.{{Overline|45}}
|''497.{{Overline|297}}''
|''302.{{Overline|702}}''
|9
|5
|1.800
|
|-
|
|28\45
|
|501.492
|304.478
|''497.{{Overline|7}}''
|''302.{{Overline|2}}''
|11
|6
|1.833
|
|-
|
|33\53
|
|501.265
|303.797
|''498.113''
|''301.887''
|13
|7
|1.857
|
|-
|
|38\61
|
|501.09
|303.297
|''498.361''
|''301.639''
|15
|8
|1.875
|
|-
|
|43\69
|
|500.971
|302.913
|''498.551''
|''301.449''
|17
|9
|1.889
|
|-
|5\8
|
|
|500
|300
|''500''
|''300''
|2
|1
|2.000
|Aeolianic-Meantone ends, Aeolianic-Pythagorean begins
|-
|
|42\67
|
|499.01
|297.03
|''501.4925''
|''298.5075''
|17
|8
|2.125
|
|-
|
|37\59
|
|498.876
|296.629
|''501.695''
|''298.305''
|15
|7
|2.143
|
|-
|
|32\51
|
|498.701
|296.104
|''501.961''
|''298.039''
|13
|6
|2.167
|
|-
|
|27\43
|
|498.461
|295.385
|''502.326''
|''297.674''
|11
|5
|2.200
|
|-
|
|22\35
|
|498.113
|294.34
|''502.857''
|''297.143''
|9
|4
|2.250
|
|-
|
|
|39\62
|497.872
|293.617
|''503.226''
|''296.774''
|16
|7
|2.286
|
|-
|
|17\27
|
|497.561
|292.683
|''503.{{Overline|703}}''
|''296.{{Overline|296}}''
|7
|3
|2.333
|
|-
|
|
|29\46
|497.143
|291.429
|''504.348''
|''295.652''
|12
|5
|2.400
|
|-
|
|
|41\65
|496.{{Overline|96}}
|290.{{Overline|90}}
|''504.615''
|''295.385''
|17
|7
|2.429
|
|-
|
|12\19
|
|496.552
|289.655
|''505.263''
|''294.737''
|5
|2
|2.500
|
|-
|
|
|31\49
|496
|288
|''506.122''
|''293.878''
|13
|5
|2.600
|
|-
|
|
|50\79
|495.868
|287.633
|''506.329''
|''293.671''
|21
|8
|2.625
|
|-
|
|19\30
|
|495.652
|286.957
|''506.{{Overline|6}}''
|''293.{{Overline|3}}''
|8
|3
|2.667
|
|-
|
|26\41
|
|495.238
|285.714
|''507.317''
|''292.683''
|11
|4
|2.750
|
|-
|
|33\52
|
|495
|285
|''507.692''
|''292.308''
|14
|5
|2.800
|
|-
|
|40\63
|
|494.536
|284.536
|''507.9365''
|''292.0635''
|17
|6
|2.833
|
|-
|
|47\74
|
|494.737
|284.211
|''508.{{Overline|108}}''
|''291.{{Overline|891}}''
|20
|7
|2.857
|
|-
|
|54\85
|
|494.6565
|283.9695
|''508.235''
|''291.765''
|23
|8
|2.875
|
|-
|
|61\96
|
|494.{{Overline|594}}
|283.{{Overline|783}}
|''508.{{Overline|3}}''
|''291.{{Overline|6}}''
|26
|9
|2.889
|
|-
|7\11
|
|
|494.118
|282.353
|''509.{{Overline|09}}''
|''290.{{Overline|90}}''
|3
|1
|3.000
|Aeolianic-Pythagorean ends, Aeolianic-Superpyth begins
|-
|
|65\102
|
|493.671
|281.013
|''509.804''
|''290.196''
|28
|9
|3.111
|
|-
|
|58\91
|
|493.617
|280.851
|''509.89''
|''290.11''
|25
|8
|3.125
|
|-
|
|51\80
|
|493.548
|280.645
|''510''
|''290''
|22
|7
|3.143
|
|-
|
|44\69
|
|493.458
|280.374
|''510.145''
|''289.855''
|19
|6
|3.167
|
|-
|
|37\58
|
|493.{{Overline|3}}
|280
|''510.345''
|''289.655''
|16
|5
|3.200
|
|-
|
|30\47
|
|493.151
|279.452
|''510.638''
|''289.362''
|13
|4
|3.250
|
|-
|
|23\36
|
|492.857
|278.571
|''511.{{Overline|1}}''
|''288.{{Overline|8}}''
|10
|3
|3.333
|
|-
|
|16\25
|
|492.308
|276.923
|''512''
|''288''
|7
|2
|3.500
|
|-
|
|25\39
|
|491.803
|275.41
|''512.8205''
|''287.1795''
|11
|3
|3.667
|
|-
|
|34\53
|
|491.566
|274.699
|''513.2075''
|''286.7925''
|15
|4
|3.750
|
|-
|
|43\67
|
|491.429
|274.286
|''513.433''
|''286.567''
|19
|5
|3.800
|
|-
|
|52\81
|
|491.339
|274.016
|''513.58''
|''286.42''
|23
|6
|3.833
|
|-
|
|61\95
|
|491.275
|273.825
|''513.684''
|''286.316''
|27
|7
|3.857
|
|-
|9\14
|
|
|490.{{Overline|90}}
|272.{{Overline|72}}
|''514.286''
|''285.714''
|4
|1
|4.000
|
|-
|
|47\73
|
|490.435
|271.304
|''515.0685''
|''284.3315''
|21
|5
|4.200
|
|-
|
|38\59
|
|490.323
|270.968
|''515.254''
|''284.746''
|17
|4
|4.250
|
|-
|
|29\45
|
|490.141
|270.422
|''515.{{Overline|5}}''
|''284.{{Overline|4}}''
|13
|3
|4.333
|
|-
|
|20\31
|
|489.795
|269.388
|''516.129''
|''283.871''
|9
|2
|4.500
|
|-
|
|31\48
|
|489.474
|268.421
|''516.{{Overline|6}}''
|''283.{{Overline|3}}''
|14
|3
|4.667
|
|-
|
|42\65
|
|489.32
|267.961
|''516.923''
|''283.077''
|19
|4
|4.750
|
|-
|11\17
|
|
|488.{{Overline|8}}
|266.{{Overline|6}}
|''517.647''
|''282.353''
|5
|1
|5.000
|Aeolianic-Superpyth ends
|-
|
|35\54
|
|488.372
|265.116
|''518.{{Overline|518}}''
|''281.{{Overline|481}}''
|16
|3
|5.333
|
|-
|
|24\37
|
|488.136
|264.407
|''518.{{Overline|918}}''
|''281.{{Overline|081}}''
|11
|2
|5.500
|
|-
|
|37\57
|
|487.912
|263.736
|''519.298''
|''280.702''
|17
|3
|5.667
|
|-
|13\20
|
|
|487.5
|262.2
|''520''
|''280''
|6
|1
|6.000
|
|-
|2\3
|
|
|480
|240
|''533.{{Overline|3}}''
|''266.{{Overline|6}}''
|1
|0
|→ inf
|Paucitonic
|}
==See also==
[[3L 2s (14/9-equivalent)]] - idealized Archytas tuning
 
[[3L 2s (8/5-equivalent)]] - idealized Meantone tuning
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/3L_2s_(minor_sixth-equivalent)"