This is the scale which occurs as the dominant major edX.
Intervals
| Degrees
|
Enneatonic
|
Minor mode Middletown temperament
|
Neutral mode Middletown temperament
|
Major mode Middletown temperament
|
| Aeolian-Dorian
|
Dorian
|
Dorian-Mixolydian
|
Mixolydian
|
Mixolydian-Ionian
|
| Subpental
|
Pental
|
Superpental
|
Subpental
|
Pental
|
Superpental
|
| Soft
|
Intense
|
| Min
|
Max
|
Min
|
Max
|
Min
|
Max
|
Min
|
Max
|
Min
|
Max
|
Min
|
Max
|
Min
|
Max
|
Min
|
Max
|
Min
|
Max
|
Min
|
Max
|
| 1
|
1#/2b
|
F#/Gb
|
90
|
91.667
|
93.75
|
95.4545
|
96.429
|
97.5
|
98.4375
|
100
|
100.862
|
103.448
|
105
|
| 2
|
2
|
G
|
180
|
183.333
|
187.5
|
190.909
|
192.857
|
195
|
196.875
|
200
|
201.724
|
206.897
|
210
|
| 3
|
2#/3b
|
G#/Jb
|
G#/Ab
|
270
|
275
|
281.25
|
286.364
|
289.286
|
292.5
|
295.3125
|
300
|
302.586
|
310.345
|
315
|
| 4
|
3
|
J
|
A
|
360
|
366.667
|
375
|
381.818
|
385.714
|
390
|
393.75
|
400
|
403.448
|
413.793
|
420
|
| 5
|
3#/4b
|
J#/Ab
|
A#/Bb
|
450
|
458.333
|
468.75
|
477.273
|
482.143
|
487.5
|
492.1875
|
500
|
504.31
|
517.241
|
525
|
| 6
|
4
|
A
|
B
|
540
|
550
|
562.5
|
572.727
|
578.571
|
585
|
590.625
|
600
|
605.172
|
620.69
|
630
|
| 7
|
5
|
B
|
H
|
630
|
641.667
|
656.25
|
668.182
|
675
|
682.5
|
689.0625
|
700
|
706.0345
|
724.138
|
735
|
| 8
|
5#/6b
|
B#/Hb
|
H#/Cb
|
720
|
733.333
|
750
|
763.636
|
771.429
|
780
|
787.5
|
800
|
806.897
|
827.586
|
840
|
| 9
|
6
|
H
|
C
|
810
|
825
|
843.75
|
859.091
|
867.857
|
877.5
|
885.9375
|
900
|
907.759
|
931.0345
|
945
|
| 10
|
6#/7b
|
H#/Cb
|
C#/Db
|
900
|
916.667
|
937.5
|
954.5455
|
964.286
|
975
|
984.375
|
1000
|
1008.621
|
1034.483
|
1050
|
| 11
|
7
|
C
|
D
|
990
|
1018.333
|
1031.25
|
1050
|
1060.714
|
1072.5
|
1082.8125
|
1100
|
1109.483
|
1137.931
|
1155
|
| 12
|
7#/8b
|
C#/Db
|
D#/Sb
|
1080
|
1100
|
1125
|
1145.4545
|
1157.143
|
1170
|
1181.25
|
1200
|
1210.345
|
1241.379
|
1260
|
| 13
|
8
|
D
|
S
|
1170
|
1191.667
|
1218.75
|
1240.909
|
1253.571
|
1267.5
|
1279.6875
|
1300
|
1311.207
|
1344.828
|
1365
|
| 14
|
8#/9b
|
D#/Eb
|
S#/Eb
|
1260
|
1283.333
|
1312.5
|
1336.364
|
1350
|
1365
|
1378.125
|
1400
|
1412.069
|
1448.276
|
1470
|
| 15
|
9
|
E
|
1350
|
1375
|
1406.25
|
1431.818
|
1446.429
|
1462.5
|
1476.5625
|
1500
|
1512.931
|
1551.724
|
1575
|
| 16
|
1
|
F
|
1440
|
1466.667
|
1500
|
1527.273
|
1542.857
|
1560
|
1575
|
1600
|
1613.793
|
1655.172
|
1680
|
Most harmonic tunings
| Degrees
|
Enneatonic
|
Minor mode Middletown temperament
|
Neutral mode Middletown temperament
|
Major mode Middletown temperament
|
| 7/3±13¢
|
22/9±13¢
|
5/2±13¢
|
| 1
|
1#/2b
|
F#/Gb
|
90.867-92.492
|
95.9005-97.5255
|
98.332-99.957
|
| 2
|
2
|
G
|
181.734-184.984
|
191.801-195.051
|
196.664-199.914
|
| 3
|
2#/3b
|
G#/Jb
|
G#/Ab
|
272.601-277.476
|
287.7015-292.5765
|
294.996-299.871
|
| 4
|
3
|
J
|
A
|
363.468-369.968
|
383.602-390.102
|
393.328-399.828
|
| 5
|
3#/4b
|
J#/Ab
|
A#/Bb
|
454.335-462.46
|
479.5025-487.6275
|
491.6605-499.7855
|
| 6
|
4
|
A
|
B
|
545.202-554.952
|
575.403-585.153
|
589.993-599.743
|
| 7
|
5
|
B
|
H
|
636.0685-647.4435
|
671.3035-382.6785
|
688.325-699.7
|
| 8
|
5#/6b
|
B#/Hb
|
H#/Cb
|
726.9355-739.9355
|
767.204-780.204
|
786.657-799.657
|
| 9
|
6
|
H
|
C
|
817.802-832.427
|
863.1045-877.7295
|
884.989-899.614
|
| 10
|
6#/7b
|
H#/Cb
|
C#/Db
|
908.669-924.919
|
959.005-975.255
|
983.321-999.571
|
| 11
|
7
|
C
|
D
|
999.536-1017.411
|
1054.9055-1072.7205
|
1081.653-1099.528
|
| 12
|
7#/8b
|
C#/Db
|
D#/Sb
|
1090.403-1109.903
|
1150.806-1170.306
|
1179.985-1199.485
|
| 13
|
8
|
D
|
S
|
1181.27-1202.395
|
1246.7065-1267.8315
|
1278.317-1299.442
|
| 14
|
8#/9b
|
D#/Eb
|
S#/Eb
|
1272.137-1294.887
|
1342.607-1365.357
|
1376.6495-1399.3995
|
| 15
|
9
|
E
|
1363.004-1387.378
|
1438.507-1462.882
|
1474.982-1499.366
|
| 16
|
1
|
F
|
1453.871-1479.871
|
1534.408-1560.408
|
1573.314-1599.314
|
Golden tunings±13¢
| Degrees
|
Enneatonic
|
Minor mode Middletown temperament
|
Neutral mode Middletown temperament
|
Major mode Middletown temperament
|
| Aeolian-Dorian
|
Dorian
|
Dorian-Mixolydian
|
Mixolydian
|
Mixolydian-Ionian
|
| Subpental
|
Pental
|
Superpental
|
Subpental
|
Pental
|
Superpental
|
| Soft
|
Intense
|
| 1
|
1#/2b
|
F#/Gb
|
90.428-92.053
|
91.303-92.928
|
94.329-95.943
|
94.917-96.542
|
96.369-97.989
|
97.364-98.989
|
97.787-99.412
|
99.998-101.623
|
101.648-103.273
|
102.785-104.41
|
| 2
|
2
|
G
|
180.856-184.106
|
182.606-185.856
|
188.2585-191.9085
|
189.834-193.084
|
192.728-195.978
|
194.7275-197.9775
|
195.5745-198.8245
|
199.9955-203.2455
|
203.296-206.546
|
205.57-208.82
|
| 3
|
2#/3b
|
G#/Jb
|
G#/Ab
|
271.2845-276.159
|
273.909-278.784
|
282.988-287.863
|
284.751-289.626
|
289.092-293.967
|
292.091-296.966
|
293.362-298.237
|
299.993-304.868
|
304.944-309.819
|
308.356-313.231
|
| 4
|
3
|
J
|
A
|
361.712-368.213
|
365.212-371.712
|
377.317-383.817
|
379.668-386.168
|
385.456-391.956
|
389.455-395.955
|
391.149-397.649
|
399.991-406.491
|
406.592-413.092
|
411.141-417.641
|
| 5
|
3#/4b
|
J#/Ab
|
A#/Bb
|
452.141-460.266
|
456.5155-464.6405
|
471.646-479.771
|
474.585-482.71
|
481.82-489.945
|
486.819-494.944
|
488.936-497.061
|
499.989-508.114
|
508.24-516.365
|
513.926-522.051
|
| 6
|
4
|
A
|
B
|
542.569-552.319
|
547.819-557.569
|
565.974-575.726
|
569.502-579.252
|
578.184-587.934
|
584.183-593.933
|
586.724-596.474
|
599.987-609.737
|
609.888-619.638
|
616.711-626.461
|
| 7
|
5
|
B
|
H
|
632.997-644.372
|
639.122-650.497
|
660.305-671.68
|
664.419-675.794
|
674.548-685.923
|
681.546-692.921
|
684.571-695.886
|
699.984-711.359
|
711.5355-722.9105
|
719.496-730.871
|
| 8
|
5#/6b
|
B#/Hb
|
H#/Cb
|
723.425-736.425
|
730.425-743.425
|
754.634-767.634
|
759.336-771.336
|
770.912-783.912
|
778.91-791.91
|
782.298-795.298.
|
799.982-812.982
|
813.1835-826.1835
|
822.282-835.282
|
| 9
|
6
|
H
|
C
|
813.854-828.479
|
821.728-836.353
|
848.963-863.588
|
854.253-868.878
|
867.2755-881.9005
|
876.274-890.899
|
880.085-894.71
|
899.98-914.605
|
914.831-929.456
|
925.067-939.692
|
| 10
|
6#/7b
|
H#/Cb
|
C#/Db
|
904.282-920.532
|
913.031-920.281
|
943.293-959.543
|
949.17-965.42
|
963.6935-979.8895
|
973.638-989.888
|
977.873-994.123
|
999.978-1016.238
|
1016.479-1032.729
|
1027.852-1044.102
|
| 11
|
7
|
C
|
D
|
994.71-1012.585
|
1004.334-1022.209
|
1037.622-1055.497
|
1044.087-1061.962
|
1060.0035-1087.8785
|
1071.0015-1088.8765
|
1075.66-1093.535
|
1099.975-1117.85
|
1118.127-1136.002
|
1130.637-1148.512
|
| 12
|
7#/8b
|
C#/Db
|
D#/Sb
|
1085.138-1104.638
|
1095.637-1115.137
|
1131.951-1151.451
|
1139.004-1158.503
|
1156.367-1175.867
|
1168.365-1187.865
|
1173.447-1192.947
|
1199.973-1219.473
|
1219.775-1239.275
|
1233.422-1252.922
|
| 13
|
8
|
D
|
S
|
1175.566-1106.691
|
1186.94-1208.065
|
1226.38-1247.405
|
1233.921-1255.046
|
1252.731-1273.856
|
1265.729-1286.854
|
1271.234-1292.359
|
1299.971-1321.096
|
1321.423-1342.548
|
1336.208-1357.333
|
| 14
|
8#/9b
|
D#/Eb
|
S#/Eb
|
1265.9945-1288.7445
|
1278.2435-1300.9935
|
1320.61-1343.36
|
1328.838-1351.588
|
1349.095-1371.845
|
1363.093-1385.843
|
1369.022-1391.772
|
1399.968-1422.719
|
1423.071-1445.821
|
1438.993-1461.743
|
| 15
|
9
|
E
|
1356.423-1380.798
|
1369.547-1393.922
|
1414.939-1439.314
|
1423.755-1448.13
|
1445.459-1469.834
|
1460.457-1484.832
|
1455.809-1491.184
|
1499.9665-1524.3415
|
1524.719-1549.094
|
1541.778-1566.153
|
| 16
|
1
|
F
|
1446.851-1472.851
|
1460.85-1486.85
|
1509.268-1535.268
|
1518.672-1544.672
|
1541.823-1567.823
|
1557.82-1583.82
|
1564.596-1590.596
|
1599.964-1625.964
|
1626.366-1652.366
|
1644.563-1670.563
|
By a surprising coincidence, neutral 16edX turns out to be a false Pelogic temperament with a very pure 5:4 (mistuned by no more than 3.596 cents), and tuning 5:3 pure creates a tenth almost exactly equal to 38/29edo or almost exactly the Golden Subpental Mixolydian step or every ninth step of 110edo, and tuning 4:3 pure creates an almost exact 43/74edo fifth. Also, the Golden Soft Superpental Mixolydian step is almost exactly (25/24)^(10/7) and tuning 12:7 pure creates almost exactly the Golden Mixolydian-Ionian step.