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{{Infobox MOS|Equalized=1|Equave=5/3|Name=|Collapsed=1|Pattern=LLLLs|nLargeSteps=4|nSmallSteps=1}}
{{Infobox MOS|Tuning=4L 1s<5/3>}}


'''4L 1s<5/3>''' (sometimes called '''diatonic'''), is a minor sixth-repeating MOS scale. The notation "<5/3>" means the period of the MOS is 5/3, disambiguating it from octave-repeating [[4L 1s]]. The name of the period interval is called the '''sextave''' (by analogy to the [[tritave]]).
{{MOS intro|Scale Signature=4L 1s<5/3>|Other names=diatonic}}The name of the period interval is called the '''sextave''' (by analogy to the [[tritave]]).


The generator range is 171.4 to 240  cents, placing it on the diatonic major second, usually representing a major second of some type (like [[8/7]]). The bright (chroma-positive) generator is, however, its major sixth complement (685.7 to 720 cents).  
Because this diatonic is a major sixth-repeating scale, each tone has a 5/3 major sixth above it. The scale has one augmented chord, two major chords, two minor chords. This diatonic also has two dominant 7th chords, making it a warped Neapolitan minor scale.


Because this diatonic is a major sixth-repeating scale, each tone has a 5/3 minor sixth above it. The scale has one augmented chord, two major chords, two minor chords. This diatonic also has two dominant 7th chords, making it a warped Neapolitan minor scale.
[[Basic]] diatonic is in [[9ed5/3]], which is a very good major sixth-based equal tuning similar to [[12edo]].
==Notation==


[[Basic]] diatonic is in [[9ed5/3]], which is a very good minor sixth-based equal tuning similar to [[12edo]].
There are 2 main ways to notate the diatonic scale. One method uses a simple sextave (major sixth) repeating notation consisting of 5 naturals (Do, Re, Mi, Fa, Sol or Sol, La, Si, Do, Re). Given that 1-5/4-3/2 is major sixth-equivalent to a tone cluster of 1-10/9-5/4, it may be more convenient to notate these diatonic scales as repeating at the double sextave (augmented eleventh~twelfth), however it does make navigating the [[Generator|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 10\9. Notating this way produces a twelfth which is the Scala Francisci[8L 2s]. Since there are exactly 10 naturals in double sextave notation, Greek numerals 1-10 may be used.
==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 (Do, Re, Mi, Fa, Sol or Sol, La, Si, Do, Re). Given that 1-5/4-3/2 is major sixth-equivalent to a tone cluster of 1-10/9-5/4, it may be more convenient to notate these diatonic scales as repeating at the double sextave (augmented eleventh~twelfth), however it does make navigating the [[Generator|genchain]] harder. This way, 3/2 is its own pitch class, distinct from 10\9. Notating this way produces a twelfth which is the Scala Francisci[8L 2s]. Since there are exactly 10 naturals in double sextave notation, Greek numerals 1-10 may be used.
{| class="wikitable"
{| class="wikitable"
|+
|+
Normalized
Normalized
! colspan="2" |Notation
!Notation
!Supersoft
!Supersoft
!Soft
!Soft
Line 23: Line 22:
|-
|-
!Diatonic
!Diatonic
!Scala Francisci
![[19ed5/3|19ed'''5/3''']]
!19eds
![[14ed5/3|14ed'''5/3''']]
!14eds
![[23ed5/3|23ed'''5/3''']]
!23eds
![[9ed5/3|9ed'''5/3''']]
!9eds
![[22ed5/3|22ed'''5/3''']]
!22eds
![[13ed5/3|13ed'''5/3''']]
!13eds
![[17ed5/3|17ed'''5/3''']]
!17eds
|-
|-
|Do#, Sol#
|Do#, Sol#
|Α#
|1\19, 46.545
|1\19
|1\14, 63.168
46.154
|2\23, 76.901
|1\14
| rowspan="2" |1\9, 98.262
63.158
|3\22, 120.594
|2\23
|2\13, 136.055
77.419
|3\17, 156.063
| rowspan="2" |1\9
100
|3\22
124.138
|2\13
141.1765
|3\17
163.{{Overline|63}}
|-
|-
|Reb, Lab
|Reb, Lab
|Βb
|3\19, 139.636
|3\19
|2\14, 126.337
138.4615
|3\23, 115.351
|2\14
|2\22, 80.396
126.316
|1\13, 68.028
|3\23
|1\17, 52.021
116.129
|2\22
82.759
|1\13
70.588
|1\17
54.{{Overline|54}}
|-
|-
|'''Re, La'''
|'''Re, La'''
|'''Β'''
|'''4\19,''' '''186.181'''
|'''4\19'''
|'''3\14,''' '''189.505'''
'''184.615'''
|'''5\23,''' '''192.252'''
|'''3\14'''
|'''2\9, 196.524'''
'''189.474'''
|'''5\22,''' '''200.991'''
|'''5\23'''
|'''3\13,''' '''204.083'''
'''193.548'''
|'''4\17, 208.084'''
|'''2\9'''
'''200'''
|'''5\22'''
'''206.897'''
|'''3\13'''
'''211.765'''
|'''4\17'''
'''218.{{Overline|18}}'''
|-
|-
|Re#, La#
|Re#, La#
|Β#
|5\19, 232.726
|5\19
|4\14, 252.673
230.769
|7\23, 269.153
|4\14
| rowspan="2" |3\9, 294.786
252.632
|8\22, 321.585
|7\23
|5\13, 340.138
270.968
|7\17, 364.148
| rowspan="2" |3\9
300
|8\22
331.0345
|5\13
352.941
|7\17
381.{{Overline|81}}
|-
|-
|Mib, Sib
|Mib, Sib
|Γb
|7\19, 325.816
|7\19
|5\14, 315.842
323.077
|8\23, 307.603
|5\14
|7\22, 281.387
315.7895
|4\13, 272.110
|8\23
|5\17, 260.106
309.677
|7\22
289.655
|4\13
282.353
|5\17
272.{{Overline|72}}
|-
|-
|Mi, Si
|Mi, Si
|Γ
|8\19, 372.362
|8\19
|6\14, 379.011
369.2301
|10\23, 384.504
|6\14
|4\9, 393.048
378.947
|10\22, 401.981
|10\23
|6\13, 408.166
387.097
|8\17, 416.169
|4\9
400
|10\22
413.793
|6\13
423.529
|8\17
436.{{Overline|36}}
|-
|-
|Mi#, Si#
|Mi#, Si#
|Γ#
|9\19, 418.906
|9\19
| rowspan="2" |7\14, 442.179
415.385
|12\23, 461.405
| rowspan="2" |7\14
|5\9, 491.310
442.105
|13\22, 522.576
|12\23
|8\13, 544.221
464.516
|11\17, 572.232
|5\9
500
|13\22
537.931
|8\13
564.706
|11\17
600
|-
|-
|Fab, Dob
|Fab, Dob
|Δb
|10\19, 465.452
|10\19
|11\23, 422.954
461.5385
|4\9, 393.048
|11\23
|9\22, 361.783
425.8065
|5\13, 340.138
|4\9
|6\17, 312.127
400
|9\22
372.414
|5\13
352.941
|6\17
327.{{Overline|27}}
|-
|-
|Fa, Do
|Fa, Do
|Δ
|11\19, 511.997
|11\19
|8\14, 505.348
507.692
|13\23, 499.855
|8\14
|5\9, 491.310
505.263
|12\22, 482.377
|13\23
|7\13, 476.193
503.226
|9\17, 468.190
|5\9
500
|12\22
496.552
|7\13
494.118
|9\17
490.{{Overline|90}}
|-
|-
|Fa#, Do#
|Fa#, Do#
|Δ#
|12\19, 558.542
|12\19
|9\14, 568.516
553.846
|15\23, 576.756
|9\14
| rowspan="2" |6\9, 589.572
568.421
|15\22, 602.972
|15\23
|9\13, 612.248
580.645
|12\17, 624.253
| rowspan="2" |6\9
600
|15\22
620.690
|9\13
635.294
|12\17
654.{{Overline|54}}
|-
|-
|Solb, Reb
|Solb, Reb
|Εb
|14\19, 651.632
|14\19
|10\14, 631.685
646.154
|16\23, 615.206
|10\14
|14\22, 562.773
631.579
|8\13, 544.221
|16\23
|10\17, 520.211
619.355
|14\22
579.310
|8\13
564.706
|10\17
545.{{Overline|45}}
|-
|-
|'''Sol, Re'''
|'''Sol, Re'''
|'''Ε'''
|'''15\19,''' '''698.178'''
|'''15\19'''
|'''11\14,''' '''694.853'''
'''692.308'''
|'''18\23,''' '''692.107'''
|'''11\14'''
|'''7\9, 687.835'''
'''694.737'''
|'''17\22, 683.368'''
|'''18\23'''
|'''10\13, 680.276'''
'''696.774'''
|'''13\17, 676.274'''
|'''7\9'''
'''700'''
|'''17\22'''
'''703.448'''
|'''10\13'''
'''705.882'''
|'''13\17'''
'''709.{{Overline|09}}'''
|-
|-
|Sol#, Re#
|Sol#, Re#
|Ε#
|16\19, 744.723
|16\19
|12\14, 758.022
738.4615
|20\23, 769.008
|12\14
| rowspan="2" |8\9, 786.096
757.8947
|20\22, 803.962
|20\23
|12\13, 816.331
774.194
|16\14, 832.338
| rowspan="2" |8\9
800
|20\22
827.586
|12\13
847.059
|16\14
872.{{Overline|72}}
|-
|-
|Dob, Solb
|Dob, Solb
|Ϛb/Ϝb
|18\19, 837.814
|18\19
|13\14, 821.190
830.769
|21\23, 809.458
|13\14
|19\22, 763.764
821.053
|11\13, 748.304
|21\23
|14\17, 728.295
812.903
|19\22
786.207
|11\13
776.647
|14\17
763.{{Overline|63}}
|-
!Do, Sol
!Ϛ/Ϝ
!19\19
876.923
!14\14
884.2105
!23\23
890.323
!9\9
900
!22\22
910.345
!13\13
917.647
!17\17
927.{{Overline|27}}
|-
|Do#, Sol#
|Ϛ#/Ϝ#
|20\19
923.077
|15\14
947.368
|24\23
929.032
| rowspan="2" |10\9
1000
|25\22
1034.483
|15\13
1052.8235
|20\17
1090.{{Overline|90}}
|-
|Reb, Lab
|Ζb
|22\19
1015.385
|16\14
1010.526
|26\23
1006.452
|24\22
993.103
|14\13
988.235
|18\17
981.{{Overline|81}}
|-
|'''Re, La'''
|'''Ζ'''
|'''23\19'''
'''1061.5385'''
|'''17\14'''
'''1071.684'''
|'''28\23'''
'''1083.871'''
|'''11\9'''
'''1100'''
|'''27\22'''
'''1117.241'''
|'''16\13'''
'''1129.412'''
|'''21\17'''
'''1145.{{Overline|45}}'''
|-
|Re#, La#
|Ζ#
|24\19
1107.692
|18\14
1136.842
|30\23
1161.290
| rowspan="2" |12\9
1200
|30\22
1241.379
|18\13
1270.588
|24\14
1309.{{Overline|09}}
|-
|Mib, Sib
|Ηb
|26\19
1200
|19\14
1200
|31\23
1200
|29\22
1200
|17\13
1200
|22\17
1200
|-
|Mi, Si
|Η
|27\19
1246.154
|20\14
1263.158
|33\23
1277.419
|13\9
1300
|32\22
1324.138
|19\13
1341.1765
|25\17
1363.{{Overline|63}}
|-
|Mi#, Si#
|Η#
|28\19
1292.308
| rowspan="2" |21\14
1326.316
|35\23
1354.839
|14\9
1400
|35\22
1448.276
|21\13
1482.353
|28\17
1527.{{Overline|27}}
|-
|Fab, Dob
|Θb
|29\19
1338.4615
|34\23
1316.129
|13\9
1300
|31\22
1282.759
|18\13
1270.588
|23\17
1254.{{Overline|54}}
|-
|Fa, Do
|Θ
|30\19
1384.615
|22\14
1389.474
|36\23
1393.548
|14\9
1400
|34\22
1406.897
|20\13
1411.765
|26\17
1418.{{Overline|18}}
|-
|Fa#, Do#
|Θ#
|31\19
1430.769
|23\14
1452.632
|38\23
1470.968
| rowspan="2" |15\9
1500
|37\22
1531.0345
|22\13
1552.941
|29\17
1581.{{Overline|81}}
|-
|Solb, Reb
|Ιb
|33\19
1523.077
|24\14
1515.7895
|39\23
1509.677
|36\22
1489.655
|21\13
1482.353
|27\17
1472.{{Overline|72}}
|-
|'''Sol, Re'''
|'''Ι'''
|'''34\19'''
'''1569.231'''
|'''25\14'''
'''1578.947'''
|'''41\23'''
'''1587.097'''
|'''16\9'''
'''1600'''
|'''39\22'''
'''1613.793'''
|'''23\13'''
'''1623.529'''
|'''30\17'''
'''1636.{{Overline|36}}'''
|-
|Sol#, Re#
|Ι#
|35\19
1615.385
|26\14
1642.105
|43\23
1664.516
| rowspan="2" |17\9
1700
|42\22
1737.931
|25\13
1764.706
|33\17
1800
|-
|Dob, Solb
|Αb
|37\19
1707.692
|27\14
1705.263
|44\23
1703.226
|41\22
1696.552
|20\13
1694.118
|31\17
1490.{{Overline|90}}
|-
|-
!Do, Sol
!Do, Sol
!Α
!19\19, 884.359
!38\19
!14\14, 884.359
1753.846
!23\23, 884.359
!28\14
!9\9, 884.359
1768.421
!22\22, 884.359
!46\23
!13\13, 884.359
1780.645
!17\17, 884.359
!18\9
1800
!44\22
1820.690
!26\13
1835.2941
!34\17
1854.{{Overline|54}}
|}
|}
{| class="wikitable"
{| class="wikitable"
|+''ed3\4''
|+
! colspan="2" |Notation
Normalized
!Notation
!Supersoft
!Supersoft
!Soft
!Soft
Line 531: Line 170:
!Semihard
!Semihard
!Hard
!Hard
!Superhard
! Superhard
|-
|-
!Diatonic
!Scala Francisci
!Scala Francisci
!19eds
![[19ed5/3|19ed'''5/3''']]
!14eds
![[14ed5/3|14ed'''5/3''']]
!23eds
![[23ed5/3|23ed'''5/3''']]
!9eds
![[9ed5/3|9ed'''5/3''']]
!22eds
![[22ed5/3|22ed'''5/3''']]
!13eds
![[13ed5/3|13ed'''5/3''']]
!17eds
![[17ed5/3|17ed'''5/3''']]
|-
|-
|Do#, Sol#
|Α#
|Α#
|''1\19''
|1\19, 46.545
''47.3684''
|1\14, 63.168
|''1\14''
| 2\23, 76.901
''64.2857''
| rowspan="2" |1\9, 98.262
|''2\23''
|3\22, 120.594
''78.2609''
|2\13, 136.055
| rowspan="2" |''1\9''
|3\17, 156.063
''100''
|''3\22''
''122.{{Overline|72}}''
|''2\13''
''[[Tel:138.4615|138.4615]]''
|''3\17''
''[[Tel:158.8235|158.8235]]''
|-
|-
|Reb, Lab
|Βb
|Βb
|''3\19''
|3\19, 139.636
''[[Tel:142.1053|142.1053]]''
|2\14, 126.337
|''2\14''
|3\23, 115.351
''[[Tel:128.5714|128.5714]]''
|2\22, 80.396
|''3\23''
|1\13, 68.028
''[[Tel:117.3913|117.3913]]''
|1\17, 52.021
|''2\22''
''81.{{Overline|81}}''
|''1\13''
''69.2308''
|''1\17''
''52.9412''
|-
|-
|'''Re, La'''
|'''Β'''
|Β
|'''4\19,''' '''186.181'''
|'''''4\19'''''
|'''3\14,''' '''189.505'''
'''''[[Tel:189.4737|189.4737]]'''''
|'''5\23,''' '''192.252'''
|'''''3\14'''''
|'''2\9, 196.524'''
'''''[[Tel:192.8571|192.8571]]'''''
|'''5\22,''' '''200.991'''
|'''''5\23'''''
|'''3\13,''' '''204.083'''
'''''[[Tel:195.6522|195.6522]]'''''
|'''4\17, 208.084'''
|'''''2\9'''''
'''''200'''''
|'''''5\22'''''
'''''204.{{Overline|54}}'''''
|'''''3\13'''''
'''''[[Tel:207.6923|207.6923]]'''''
|'''''4\17'''''
'''''[[Tel:211.7647|211.7647]]'''''
|-
|-
|Re#, La#
| Β#
|Β#
|5\19, 232.726
|''5\19''
|4\14, 252.673
''[[Tel:236.8421|236.8421]]''
|7\23, 269.153
|''4\14''
| rowspan="2" |3\9, 294.786
''[[Tel:257.1429|257.1429]]''
|8\22, 321.585
|''7\23''
|5\13, 340.138
''273.913''
|7\17, 364.148
| rowspan="2" |''3\9''
''300''
|''8\22''
''327.{{Overline|27}}''
|''5\13''
''346.15385''
|''7\17''
''[[Tel:370.5882|370.5882]]''
|-
|-
|Mib, Sib
|Γb
|Γb
|''7\19''
|7\19, 325.816
''331.57895''
|5\14, 315.842
|''5\14''
|8\23, 307.603
''[[Tel:321.4286|321.4286]]''
| 7\22, 281.387
|''8\23''
| 4\13, 272.110
''[[Tel:313.0345|313.0345]]''
|5\17, 260.106
|''7\22''
''286.{{Overline|36}}''
|''4\13''
''[[Tel:276.9231|276.9231]]''
|''5\17''
''[[Tel:264.7059|264.7059]]''
|-
|-
|Mi, Si
|Γ
|Γ
|''8\19''
|8\19, 372.362
''[[Tel:378.9474|378.9474]]''
|6\14, 379.011
|''6\14''
|10\23, 384.504
''[[Tel:385.7143|385.7143]]''
|4\9, 393.048
|''10\23''
|10\22, 401.981
''391.304''
|6\13, 408.166
|''4\9''
|8\17, 416.169
 
''400''
|''10\22''
''409.{{Overline|09}}''
|''6\13''
''[[Tel:415.3846|415.3846]]''
|''8\17''
''[[Tel:423.5294|423.5294]]''
|-
|-
|Mi#, Si#
|Γ#
|Γ#
|''9\19''
|9\19, 418.906
''[[Tel:426.3158|426.3158]]''
| rowspan="2" |7\14, 442.179
| rowspan="2" |''7\14''
|12\23, 461.405
''450''
|5\9, 491.310
|''12\23''
|13\22, 522.576
''[[Tel:469.5652|469.5652]]''
| 8\13, 544.221
|''5\9''
| 11\17, 572.232
''500''
|''13\22''
''531.{{Overline|81}}''
|''8\13''
''553.84615''
|''11\17''
''[[Tel:582.3529|582.3529]]''
|-
|-
|Fab, Dob
|Δb
|Δb
|''10\19''
|10\19, 465.452
''[[Tel:473.6842|473.6842]]''
|11\23, 422.954
|''11\23''
|4\9, 393.048
''[[Tel:430.7692|430.7692]]''
|9\22, 361.783
|''4\9''
|5\13, 340.138
''400''
|6\17, 312.127
|''9\22''
''368.''{{Overline|18}}
|''5\13''
''346.15385''
|''6\17''
''[[Tel:317.6471|317.6471]]''
|-
|-
|Fa, Do
|Δ
|Δ
|''11\19''
|11\19, 511.997
''[[Tel:521.0526|521.0526]]''
|8\14, 505.348
|''8\14''
|13\23, 499.855
''[[Tel:514.2857|514.2857]]''
|5\9, 491.310
|''13\23''
|12\22, 482.377
''508.696''
|7\13, 476.193
|''5\9''
|9\17, 468.190
''500''
|''12\22''
''490.{{Overline|90}}''
|''7\13''
''[[Tel:484.6154|484.6154]]''
|''9\17''
''[[Tel:476.4706|476.4706]]''
|-
|-
|Fa#, Do#
|Δ#
|Δ#
|''12\19''
|12\19, 558.542
''568.42105''
|9\14, 568.516
|''9\14''
|15\23, 576.756
''[[Tel:578.5714|578.5714]]''
| rowspan="2" |6\9, 589.572
|''15\23''
|15\22, 602.972
''[[Tel:587.9655|587.9655]]''
|9\13, 612.248
| rowspan="2" |''6\9''
|12\17, 624.253
''600''
|''15\22''
''613.{{Overline|63}}''
|''9\13''
''[[Tel:623.0769|623.0769]]''
|''12\17''
''[[Tel:635.2931|635.2931]]''
|-
|-
|Solb, Reb
|Εb
|Εb
|''14\19''
|14\19, 651.632
''[[Tel:663.1579|663.1579]]''
|10\14, 631.685
|''10\14''
|16\23, 615.206
''[[Tel:642.8571|642.8571]]''
|14\22, 562.773
|''16\23''
|8\13, 544.221
''626.087''
|10\17, 520.211
|''14\22''
''572.''{{Overline|72}}
|''8\13''
''553.84615''
|''10\17''
''[[Tel:529.4118|529.4118]]''
|-
|-
|'''Sol, Re'''
|'''Ε'''
|'''Ε'''
|'''''15\19'''''
|'''15\19,''' '''698.178'''
'''''[[Tel:710.5263|710.5263]]'''''
|'''11\14,''' '''694.853'''
|'''''11\14'''''
|'''18\23,''' '''692.107'''
'''''[[Tel:707.1429|707.1429]]'''''
|'''7\9, 687.835'''
|'''''18\23'''''
|'''17\22, 683.368'''
'''''[[Tel:704.3478|704.3478]]'''''
|'''10\13, 680.276'''
|'''''7\8'''''
|'''13\17, 676.274'''
'''''700'''''
|'''''17\22'''''
'''''695.{{Overline|45}}'''''
|'''''10\13'''''
'''''[[Tel:692.3077|692.3077]]'''''
|'''''13\17'''''
'''''[[Tel:688.2353|688.2353]]'''''
|-
|-
|Sol#, Re#
|Ε#
|Ε#
|''16\19''
|16\19, 744.723
''[[Tel:757.8947|757.8947]]''
|12\14, 758.022
|''12\14''
|20\23, 769.008
''[[Tel:771.4286|771.4286]]''
| rowspan="2" |8\9, 786.096
|''20\23''
|20\22, 803.962
''[[Tel:782.6087|782.6087]]''
|12\13, 816.331
| rowspan="2" |''8\8''
|16\14, 832.338
''800''
|''20\22''
''818.{{Overline|18}}''
|''12\13''
''[[Tel:830.7692|830.7692]]''
|''16\14''
''[[Tel:847.0588|847.0588]]''
|-
|-
|Dob, Solb
|Ϛb/Ϝb
|Ϛb/Ϝb
|''18\19''
|18\19, 837.814
''[[Tel:852.6316|852.6316]]''
|13\14, 821.190
|''13\14''
|21\23, 809.458
''[[Tel:835.7143|835.7143]]''
|19\22, 763.764
|''21\23''
|11\13, 748.304
''[[Tel:821.7391|821.7391]]''
|14\17, 728.295
|''19\22''
''777.{{Overline|27}}''
|''11\13''
''[[Tel:761.5385|761.5385]]''
|''14\17''
''[[Tel:741.1765|741.1765]]''
|-
|-
!Do, Sol
!Ϛ/Ϝ
!Ϛ/Ϝ
! colspan="7" |''900''
!19\19, 884.359
!14\14, 884.359
!23\23, 884.359
!9\9, 884.359
!22\22, 884.359
!13\13, 884.359
!17\17, 884.359
|-
|-
|Do#, Sol#
|Ϛ#/Ϝ#
|Ϛ#/Ϝ#
|''20\19''
|20\19, 930.903
''[[Tel:947.3684|947.3684]]''
|15\14, 947.527
|''15\14''
|24\23, 922.806
''[[Tel:964.2857|964.2857]]''
| rowspan="2" |10\9, 982.621
|''25\23''
|25\22, 1004.953
''[[Tel:978.2609|978.2609]]''
|15\13, 1020.413
| rowspan="2" |''10\9''
|20\17, 1040.422
''1000''
|''25\22''
''1022.{{Overline|72}}''
|''15\13''
''1038.4615''
|''20\17''
''1058.8235''
|-
|-
|Reb, Lab
|Ζb
|Ζb
|''22\19''
|22\19, 1023.994
''1042.1053''
|16\14, 1010.696
|''16\14''
|26\23, 999.710
''1028.5714''
|24\22, 964.755
|''26\23''
|14\13, 952.386
''1017.3913''
|18\17, 936.380
|''24\22''
''981.{{Overline|81}}''
|''14\13''
''[[Tel:969.2308|969.2308]]''
|''18\17''
''[[Tel:952.9412|952.9412]]''
|-
|-
|'''Re, La'''
|'''Ζ'''
|'''Ζ'''
|'''''23\19'''''
|'''23\19,''' '''1070.539'''
'''''1089.4737'''''
|'''17\14,''' '''1073.864'''
|'''''17\14'''''
|'''28\23,''' '''1076.611'''
'''''1092.8571'''''
|'''11\9,''' '''1080.882'''
|'''''28\23'''''
|'''27\22,''' '''1085.349'''
'''''1095.6522'''''
|'''16\13,''' '''1088.441'''
|'''''11\9'''''
|'''21\17,''' '''1092.442'''
'''''1100'''''
|'''''27\22'''''
'''''1104.{{Overline|54}}'''''
|'''''16\13'''''
'''''1107.6923'''''
|'''''21\17'''''
'''''1111.7647'''''
|-
|-
|Re#, La#
|Ζ#
|Ζ#
|''24\19''
|24\19, 1117.085
''1136.8421''
|18\14, 1137.033
|''18\14''
|30\23, 1153.511
''1157.1429''
| rowspan="2" |12\9, 1179.145
|''30\23''
|30\22, 1205.944
''1173.913''
|18\13, 1224.497
| rowspan="2" |''12\9''
|24\14, 1248.506
 
''1200''
|''30\22''
''1227.{{Overline|27}}''
|''18\13''
''1246.15385''
|''24\14''
''1270.5882''
|-
|-
|Mib, Sib
|Ηb
|Ηb
|''26\19''
|26\19, 1210.175
''1231.57895''
|19\14, 1200.201
|''19\14''
|31\23, 1191.952
''1221.4286''
|29\22, 1165.745
|''31\23''
|17\13, 1156.469
''1213.0345''
|22\17, 1144.464
|''29\22''
''1186.{{Overline|36}}''
|''17\13''
''1176.9231''
|''22\17''
''1164.7059''
|-
|-
|Mi, Si
|Η
|Η
|''27\19''
|27\19, 1256.720
''1278.9474''
|20\14, 1263.370
|''20\14''
|33\23, 1268.863
''1285.7143''
|13\9, 1277.407
|''33\23''
|32\22, 1286.340
''1291.304''
|19\13, 1292.524
|''13\9''
|25\17, 1300.528
''1300''
|''32\22''
''1309.{{Overline|09}}''
|''19\13''
''1315.3846''
|''25\17''
''1323.5294''
|-
|-
|Mi#, Si#
|Η#
|Η#
|''28\19''
|28\19, 1303.265
''1326.3158''
| rowspan="2" |21\14, 1326.538
| rowspan="2" |''21\14''
|35\23, 1345.763
''1350''
|14\9, 1375.669
|''35\23''
|35\22, 1406.934
''1369.5652''
|21\13, 1428.579
|''14\9''
|28\17, 1456.591
''1400''
|''35\22''
''1431.{{Overline|81}}''
|''21\13''
''1453.15385''
|''28\17''
''1482.3529''
|-
|-
|Fab, Dob
|Θb
|Θb
|''29\19''
|29\19, 1349.811
''1373.6842''
|34\23, 1307.313
|''34\23''
|13\9, 1277.407
''1330.7692''
|31\22, 1246.142
|''13\9''
|18\13, 1224.497
''1300''
|23\17, 1196.485
|''31\22''
''1368.{{Overline|18}}''
|''18\13''
''1346.84615''
|''23\17''
''1317.6471''
|-
|-
|Fa, Do
|Θ
|Θ
|''30\19''
|30\19, 1396.356
''1421.0526''
|22\14, 1389.707
|''22\14''
|36\23, 1384.214
''1414.2857''
|14\9, 1375.669
|''36\23''
|34\22, 1366.736
''1408.696''
|20\13, 1360.552
|''14\9''
|26\17, 1352.549
''1400''
|''34\22''
''1390.{{Overline|90}}''
|''20\13''
''1384.6154''
|''26\17''
''1376.4706''
|-
|-
|Fa#, Do#
|Θ#
|Θ#
|''31\19''
|31\19, 1442.901
''1468.42105''
|23\14, 1452.875
|''23\14''
|38\23, 1461.114
''1478.7143''
| rowspan="2" |15\9, 1473.931
|''38\23''
|37\22, 1487.331
''1487.9655''
|22\13, 1496.606
| rowspan="2" |''15\9''
|29\17, 1508.612
''1500''
|''37\22''
''1513.{{Overline|63}}''
|''22\13''
''1523.0769''
|''29\17''
''1581.{{Overline|81}}''
|-
|-
|Solb, Reb
|Ιb
|Ιb
|''33\19''
|33\19, 1535.991
''1563.1579''
|24\14, 1516.044
|''24\14''
|39\23, 1499.565
''1542.8571''
|36\22, 1447.132
|''39\23''
|21\13, 1428.579
''1526.087''
|27\17, 1404.570
|''36\22''
''1472.{{Overline|72}}''
|''21\13''
''1453.15385''
|''27\17''
''1429.4118''
|-
|-
|'''Sol, Re'''
|'''Ι'''
|'''Ι'''
|'''''34\19'''''
|'''34\19,''' '''1582.537'''
'''''1610.5263'''''
|'''25\14,''' '''1579.212'''
|'''''25\14'''''
|'''41\23,''' '''1576.466'''
'''''1607.1429'''''
|'''16\9, 1572.193'''
|'''''41\23'''''
|'''39\22,''' '''1567.723'''
'''''1604.3478'''''
|'''23\13,''' '''1564.635'''
|'''''16\9'''''
|'''30\17,''' '''1560.633'''
'''''1600'''''
|'''''39\22'''''
'''''1595.{{Overline|45}}'''''
|'''''23\13'''''
'''''1592.3077'''''
|'''''30\17'''''
'''''1588.2353'''''
|-
|-
|Sol#, Re#
|Ι#
|Ι#
|''35\19''
|35\19, 1629.081
''1657.8947''
|26\14, 1642.380
|''26\14''
|43\23, 1653.366
''1671.4286''
| rowspan="2" |17\9, 1670.455
|''43\23''
|42\22, 1688.321
''1682.6087''
|25\13, 1700.690
| rowspan="2" |''17\9''
|33\17, 1664.675
''1700''
|''42\22''
''1718.''{{Overline|18}}
|''25\13''
''1730.7692''
|''33\17''
''1747.0588''
|-
|-
|Dob, Solb
|Αb
|Αb
|''37\19''
|37\19, 1722.172
''1752.6316''
|27\14, 1705.549
|''27\14''
|44\23, 1691.817
''1735.7143''
|41\22, 1648.123
|''44\23''
|24\13, 1632.662
''1721.7391''
|31\17, 1612.654
|''41\22''
''1677.{{Overline|27}}''
|''20\13''
''1661.5385''
|''31\17''
''1641.1761''
|-
|-
!Do, Sol
!Α
!Α
! colspan="7" |''1800''
!38\19, 1768.717
!28\14, 1768.717
!46\23, 1768.717
!18\9, 1768.717
!44\22, 1768.717
!26\13, 1768.717
!34\17, 1768.717
|}
|}


==Intervals==
== Intervals ==
{| class="wikitable"
{| class="wikitable"
!Generators
!Generators
Line 1,040: Line 472:
| -2
| -2
|Mi, Si
|Mi, Si
|major third  
|major third
|-
|-
|3
|3
|Mib, Sib
|Mib, Sib
|minor third  
|minor third
| -3
| -3
|Fa#, Do#
|Fa#, Do#
Line 1,063: Line 495:
| -5
| -5
|Do#, Sol#
|Do#, Sol#
|augmented unison (chroma)  
|augmented unison (chroma)
|-
|-
|6
|6
Line 1,070: Line 502:
| -6
| -6
|Re#, La#
|Re#, La#
|augmented second  
|augmented second
|-
|-
|7
|7
Line 1,077: Line 509:
| -7
| -7
|Mi#, Si#
|Mi#, Si#
|augmented third  
|augmented third
|-
|-
|8
|8
Line 1,144: Line 576:
|}
|}
==Modes==
==Modes==
The mode names are based on the major satellites of Uranus, in order of size:
The mode names are based on the classical modes:
{| class="wikitable"
{| class="wikitable"
!Mode
!Mode
Line 1,200: Line 632:
|}
|}
==Temperaments==
==Temperaments==
The most basic rank-2 temperament interpretation of this diatonic is '''Dorianic''', which has pental 4:5:6 or septimal 14:18:21 chords spelled <code>root-(2g)-(p-1g)</code> (p = the major sixth, g = the whole tone). The name "Dorianic" comes from the Dorian major mode having the minor sixth as its characteristic interval.
The most basic rank-2 temperament interpretation of this diatonic is '''Dorianic''', which has pental 4:5:6 or septimal 14:18:21 chords spelled <code>root-(2g)-(p-1g)</code> (p = the major sixth, g = the whole tone). The name "Dorianic" comes from the Dorian mode having the major sixth as its characteristic interval.
==='''Dorianic-Meantone'''===
==='''Dorianic-Meantone'''===
[[Subgroup]]: 5/3.4/3.3/2
[[Subgroup]]: 5/3.4/3.3/2
Line 1,206: Line 638:
[[Comma]] list: [[81/80]]
[[Comma]] list: [[81/80]]


[[POL2]] generator: ~9/8 = 193.8419
[[POL2]] generator: ~9/8 = 193.8419¢


[[Mapping]]: [{{val|1 1 1}}, {{val|0 -2 -1}}]
[[Mapping]]: [{{val|1 1 1}}, {{val|0 -2 -1}}]


[[Vals]]: {{val list|5ed5/3, 9ed5/3, 14ed5/3}}
[[Optimal ET sequence]]: [[5ed5/3]], [[9ed5/3]], [[14ed5/3]]
===='''Dorianic-Superpyth'''====
[[Subgroup]]: 12/7.4/3.3/2
 
[[Comma]] list: [[64/63]]
 
[[POL2]] generator: ~9/8 = 216.5781
 
[[Mapping]]: [{{val|1 1 1}}, {{val|0 -2 -1}}]
 
[[Vals]]: {{val list|4ed14/9, 13ed14/9, 17ed14/9}}
==Scale tree==
==Scale tree==
The spectrum looks like this:
The spectrum looks like this:
{| class="wikitable"
{{MOS tuning spectrum|Scale Signature=4L 1s<5/3>}}
! colspan="3" rowspan="2" |Generator
 
(bright)
== See also ==
! colspan="2" |Normalised
[[8L 2s (72/25-equivalent)]] - 8/1 complement of Scala Francisci
! colspan="2" |''ed3\4''
! rowspan="2" |L
! rowspan="2" |s
! rowspan="2" |L/s
! rowspan="2" |Comments
|-
!Chroma-positive
!Chroma-negative
!Chroma-positive
!Chroma-negative
|-
|1\5
|
|
|171.429
|685.714
|''180''
|''720''
|1
|1
|1.000
|Equalised
|-
|6\29
|
|
|180
|690
|''186.207''
|''713.793''
|6
|5
|1.200
|
|-
|5\24
|
|
|181.{{Overline|81}}
|490.{{Overline|90}}
|''187.5''
|''712.5''
|5
|4
|1.250
|
|-
|
|14\67
|
|182.609
|691.304
|''188.06''
|''711.94''
|14
|11
|1.273
|
|-
|
|9\43
|
|183.051
|691.525
|''188.372''
|''711.628''
|9
|7
|1.286
|
|-
|4\19
|
|
|184.615
|692.308
|''189.474''
|''710.526''
|4
|3
|1.333
|
|-
|
|11\52
|
|185.915
|692.958
|''190.385''
|''709.615''
|11
|8
|1.375
|
|-
|
|7\33
|
|186.{{Overline|6}}
|693.{{Overline|3}}
|''190.{{Overline|90}}''
|''709.{{Overline|09}}''
|7
|5
|1.400
|
|-
|
|10\47
|
|187.5
|693.75
|''191.498''
|''708.519''
|10
|7
|1.429
|
|-
|3\14
|
|
|189.474
|694.737
|''192.857''
|''707.143''
|3
|2
|1.500
|Dorianic-Meantone starts here
|-
|
|14\65
|
|190.{{Overline|90}}
|695.{{Overline|45}}
|''193.846''
|''706.154''
|14
|9
|1.556
|
|-
|
|11\51
|
|191.304
|695.652
|''194.118''
|''705.882''
|11
|7
|1.571
|
|-
|
|8\37
|
|192
|696
|''194.{{Overline|594}}''
|''705.{{Overline|495}}''
|8
|5
|1.600
|
|-
|
|
|13\60
|192.{{Overline|692}}
|696.{{Overline|296}}
|''195''
|''705''
|13
|8
|1.625
|
|-
|
|5\23
|
|193.548
|696.774
|''195.652''
|''704.348''
|5
|3
|1.667
|
|-
|
|
|12\55
|194.{{Overline|594}}
|697.{{Overline|297}}
|''196.{{Overline|36}}''
|''703.{{Overline|63}}''
|12
|7
|1.714
|
|-
|
|7\32
|
|195.349
|697.674
|''196.875''
|''703.125''
|7
|4
|1.750
|
|-
|
|9\41
|
|196.{{Overline|36}}
|698.{{Overline|18}}
|''197.561''
|''702.439''
|9
|5
|1.800
|
|-
|
|11\50
|
|197.015
|698.507
|''198''
|''702''
|11
|6
|1.833
|
|-
|
|13\59
|
|197.468
|698.734
|''198.305''
|''701.695''
|13
|7
|1.857
|
|-
|
|15\68
|
|197.802
|698.901
|''198.529''
|''701.471''
|15
|8
|1.875
|
|-
|
|17\77
|
|198.058
|699.029
|''198.701''
|''701.299''
|17
|9
|1.889
|
|-
|
|19\86
|
|198.261
|699.13
|''198.837''
|''701.163''
|19
|10
|1.900
|
|-
|
|21\95
|
|198.425
|699.213
|''198.947''
|''701.053''
|21
|11
|1.909
|
|-
|
|23\104
|
|198.561
|699.281
|''199.039''
|''700.961''
|23
|12
|1.917
|
|-
|2\9
|
|
|200
|700
|''200''
|''700''
|2
|1
|2.000
|Dorianic-Meantone ends, Dorianic-Pythagorean begins
|-
|
|23\103
|
|201.46
|700.73
|''200.971''
|''699.029''
|23
|11
|2.091
|
|-
|
|21\94
|
|201.6
|700.8
|''201.064''
|''698.936''
|21
|10
|2.100
|
|-
|
|19\85
|
|201.77
|700.885
|''[[Tel:201.1765|201.1765]]''
|''[[Tel:698.8235|698.8235]]''
|19
|9
|2.111
|
|-
|
|17\76
|
|201.98
|700.99
|''201.316''
|''698.684''
|17
|8
|2.125
|
|-
|
|15\67
|
|202.247
|701.123
|''[[Tel:201.4925|201.4925]]''
|''[[Tel:698.5075|698.5075]]''
|15
|7
|2.143
|
|-
|
|13\58
|
|202.597
|701.299
|''201.724''
|''698.276''
|13
|6
|2.167
|
|-
|
|11\49
|
|203.076
|701.538
|''202.041''
|''697.959''
|11
|5
|2.200
|
|-
|
|9\40
|
|203.774
|701.887
|''202.5''
|''697.5''
|9
|4
|2.250
|
|-
|
|7\31
|
|204.838
|702.439
|''203.226''
|''696.774''
|7
|3
|2.333
|
|-
|
|
|12\53
|205.714
|702.858
|''203.774''
|''696.226''
|12
|5
|2.400
|
|-
|
|5\22
|
|206.897
|703.448
|''204.{{Overline|54}}''
|''695.{{Overline|45}}''
|5
|2
|2.500
|
|-
|
|
|18\79
|207.692
|703.847
|''205.063''
|''694.937''
|18
|7
|2.571
|
|-
|
|8\35
|
|208.696
|704.348
|''205.714''
|''694.286''
|8
|3
|2.667
|
|-
|
|11\48
|
|209.524
|704.762
|''206.25''
|''693.75''
|11
|4
|2.750
|
|-
|
|14\61
|
|210
|705
|''206.557''
|''693.443''
|14
|5
|2.800
|
|-
|3\13
|
|
|211.765
|705.882
|''207.692''
|''692.308''
|3
|1
|3.000
|Dorianic-Pythagorean ends, Dorianic-Superpyth begins
|-
|
|22\95
|
|212.903
|706.452
|''208.421''
|''691.579''
|22
|7
|3.143
|
|-
|
|19\82
|
|213.084
|706.542
|''[[Tel:208.5365|208.5365]]''
|''[[Tel:691.4635|691.4635]]''
|19
|6
|3.167
|
|-
|
|16\69
|
|213.{{Overline|3}}
|706.{{Overline|6}}
|''208.696''
|''691.304''
|16
|5
|3.200
|
|-
|
|13\56
|
|213.699
|706.849
|''208.929''
|''691.071''
|13
|4
|3.250
|
|-
|
|10\43
|
|214.286
|707.143
|''209.322''
|''690.678''
|10
|3
|3.333
|
|-
|
|7\30
|
|215.385
|707.692
|''210''
|''690''
|7
|2
|3.500
|
|-
|
|11\47
|
|216.393
|708.192
|''210.638''
|''689.362''
|11
|3
|3.667
|
|-
|
|15\64
|
|216.867
|708.434
|''[[Tel:210.9375|210.9375]]''
|''[[Tel:689.0625|689.0625]]''
|15
|4
|3.750
|
|-
|
|19\81
|
|217.143
|708.571
|''211.{{Overline|1}}''
|''688.{{Overline|8}}''
|19
|5
|3.800
|
|-
|4\17
|
|
|218.{{Overline|18}}
|709.{{Overline|09}}
|''211.765''
|''688.235''
|4
|1
|4.000
|
|-
|
|21\89
|
|219.13
|709.565
|''212.36''
|''687.64''
|21
|5
|R.200
|
|-
|
|17\72
|
|219.355
|709.677
|''212.5''
|''687.5''
|17
|4
|4.250
|
|-
|
|13\55
|
|219.718
|709.859
|''212.{{Overline|72}}''
|''687.{{Overline|27}}''
|13
|3
|4.333
|
|-
|
|9\38
|
|220.408
|710.204
|''213.158''
|''686.842''
|9
|2
|4.500
|
|-
|
|14\59
|
|221.053
|710.526
|''213.559''
|''686.441''
|14
|3
|4.667
|
|-
|5\21
|
|
|222.{{Overline|2}}
|711.{{Overline|1}}
|''214.286''
|''685.714''
|5
|1
|5.000
|Dorianic-Superpyth ends
|-
|
|16\67
|
|223.256
|711.628
|''214.925''
|''685.075''
|16
|3
|5.333
|
|-
|
|11\46
|
|223.729
|711.864
|''215.217''
|''684.783''
|11
|2
|5.500
|
|-
|
|17\71
|
|224.176
|712.088
|''215.492''
|''215.508''
|17
|3
|5.667
|
|-
|6\25
|
|
|225
|712.5
|''216''
|''684''
|6
|1
|6.000
|
|-
|1\4
|
|
|240
|720
|''225''
|''675''
|1
|0
|→ inf
|Paucitonic
|}
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/4L_1s_(5/3-equivalent)"