16edX is the scale which occurs as the dominant reformed Mixolydian mode.
Intervals
| Degrees
|
Enneatonic
|
Intense Aeolian-Subpental Dorian
|
Dorian
|
| Subpental
|
Pental
|
Superpental
|
| Min-comma
|
Med
|
Max+comma~Min-comma
|
Med
|
Max+comma~Min-comma
|
Med
|
Max+comma~Min-comma
|
Med
|
Max+comma
|
| 1
|
1#/2b
|
G#/Jb
|
G#/Ab
|
87.5-90
|
91.071
|
89.167-94.167
|
92.308
|
91.25-96.25
|
95
|
92.9545-97.9545
|
95.833
|
96.429-98.929
|
| 2
|
2
|
J
|
A
|
175-180
|
182.143
|
178.333-188.333
|
184.615
|
182.5-192.5
|
190
|
185.909-195.909
|
191.667
|
192.857-197.857
|
| 3
|
2#/3b
|
J#/Ab
|
A#/Bb
|
262.5-270
|
273.214
|
267.5-282.5
|
276.923
|
273.75-288.75
|
285
|
278.864-293.864
|
287.5
|
289.286-296.786
|
| 4
|
3
|
A
|
B
|
350-360
|
364.286
|
356.667-376.667
|
369.231
|
365-385
|
380
|
371.818-391.818
|
383.333
|
385.714-395.714
|
| 5
|
3#/4b
|
A#/Bb
|
B#/Cb
|
437.5-450
|
455.357
|
445.833-470.833
|
461.5385
|
456.25-481.25
|
475
|
464.773-489.773
|
479.167
|
482.143-494.643
|
| 6
|
4
|
B
|
C
|
525-540
|
546-429
|
535-565
|
553.846
|
547.5-577.5
|
570
|
557.727-587.727
|
575
|
578.571-593.571
|
| 7
|
5
|
C
|
Q
|
612.5-630
|
637.5
|
624.167-659.167
|
646.154
|
638.75-673.75
|
665
|
650.682-685.682
|
670.833
|
675-692.5
|
| 8
|
5#/6b
|
C#/Qb
|
Q#/Db
|
700-720
|
728.571
|
713.333-753.333
|
738.4615
|
730-770
|
760
|
743.636-783.636
|
766.667
|
771.429-791.429
|
| 9
|
6
|
Q
|
D
|
787.5-810
|
819.642
|
802.5-847.5
|
830.769
|
821.25-856.25
|
855
|
836.591-875.591
|
862.5
|
867.857-890.357
|
| 10
|
6#/7b
|
Q#/Db
|
D#/Sb
|
875-900
|
910.714
|
891.667-941.667
|
923.071
|
912.5-962.5
|
950
|
929.5455-979.5455
|
958.333
|
964.286-989.286
|
| 11
|
7
|
D
|
S
|
962.5-990
|
1001.786
|
980.833-1035.833
|
1015.385
|
1003.75-1058.75
|
1045
|
1022.5-1077.5
|
1054.167
|
1060.714-1088.214
|
| 12
|
7#/8b
|
D#/Eb
|
S#/Eb
|
1050-1080
|
1092.857
|
1070-1130
|
1107.692
|
1095-1155
|
1140
|
1115.4545-1175.4545
|
1150
|
1157.143-1187.143
|
| 13
|
8
|
E
|
1137.5-1170
|
1183.929
|
1159.167-1224.167
|
1200
|
1186.25-1251.25
|
1235
|
1208.409-1273.409
|
1245.833
|
1253.571-1286.071
|
| 14
|
8#/9b
|
E#/Fb
|
1225-1260
|
1275
|
1248.333-1318.333
|
1292.308
|
1277.5-1347.5
|
1330
|
1301.364-1371.364
|
1341.667
|
1350-1385
|
| 15
|
9
|
F
|
1312.5-1350
|
1366.071
|
1337.5-1412.5
|
1384.615
|
1368.75-1443.75
|
1425
|
1394.318-1469.318
|
1437.5
|
1446.429-1483.929
|
| 16
|
1
|
G
|
1400-1440
|
1457.143
|
1426.667-1506.667
|
1476.923
|
1460-1540
|
1520
|
1487.273-1567.273
|
1533.333
|
1542.857-1582.857
|
| Degrees
|
Enneatonic
|
Mohajira
|
Beatles
|
| Min-comma
|
r¢
|
Med
|
Max+comma~Min-comma
|
Med
|
Max+comma
|
| 1
|
1#/2b
|
F#/Gb
|
G#/Jb
|
G#/Ab
|
93.929-96.429
|
96.875
|
94.559-99.559
|
97.222
|
97.5-100
|
| 2
|
2
|
G
|
J
|
A
|
187.857-192.857
|
193.75
|
189.118-199.118
|
194.444
|
195-200
|
| 3
|
2#/3b
|
G#/Jb
|
G#/Ab
|
J#/Ab
|
A#/Bb
|
281.786-289.286
|
290.625
|
283.6765-298.6765
|
291.667
|
292.5-300
|
| 4
|
3
|
J
|
A
|
J
|
B
|
375.714-385.714
|
387.5
|
378.235-398.235
|
388.889
|
390-400
|
| 5
|
3#/4b
|
J#/Ab
|
A#/Bb
|
J#/Ab
|
B#/Cb
|
469.643-482.143
|
484.375
|
472.794-497.794
|
486.111
|
487.5-500
|
| 6
|
4
|
A
|
B
|
A
|
C
|
563.571-578.571
|
581.25
|
567.353-597.353
|
583.333
|
585-600
|
| 7
|
5
|
B
|
H
|
A#/Bb
|
C#/Qb
|
657.5-675
|
678.125
|
661.912-696.912
|
680.556
|
682.5-700
|
| 8
|
5#/6b
|
B#/Hb
|
H#/Cb
|
B
|
Q
|
751.429-771.429
|
775
|
756.471-796.471
|
777.778
|
780-800
|
| 9
|
6
|
H
|
C
|
C
|
D
|
845.357-867.857
|
871.875
|
851.029-895.029
|
875
|
877.5-900
|
| 10
|
6#/7b
|
H#/Cb
|
C#/Db
|
C#/Db
|
D#/Sb
|
939.286-964.286
|
968.75
|
945.588-995.588
|
972.222
|
975-1000
|
| 11
|
7
|
C
|
D
|
D
|
S
|
1033.214-1060.714
|
1065.625
|
1040.147-1095.147
|
1069.444
|
1072.5-1100
|
| 12
|
7#/8b
|
C#/Db
|
D#/Sb
|
D#/Eb
|
S#/Eb
|
1127.143-1157.143
|
1162.5
|
1134.706-1194.706
|
1166.667
|
1170-1200
|
| 13
|
8
|
D
|
S
|
E
|
1223.071-1253.571
|
1259.375
|
1229.265-1294.265
|
1263.889
|
1267.5-1300
|
| 14
|
8#/9b
|
D#/Eb
|
S#/Eb
|
E#/Fb
|
1315-1350
|
1356.25
|
1323.8235-1393.8235
|
1361.111
|
1365-1400
|
| 15
|
9
|
E
|
F
|
1408.929-1446.429
|
1453.125
|
1418.382-1493.382
|
1458.333
|
1462.5-1500
|
| 16
|
1
|
F
|
G
|
1502.857-1542.857
|
1550
|
1512.941-1592.941
|
1555.556
|
1560-1600
|
| Degrees
|
Enneatonic
|
Mixolydian
|
Mixolydian-Ionian
|
| Subpental
|
Pental
|
Superpental
|
| Soft
|
Intense
|
| Min-comma
|
Med
|
Max+comma~Min-comma
|
Med
|
Max+comma~Min-comma
|
Med
|
Max+comma~~Min-comma
|
Med
|
Max+comma~~Min-comma
|
Med
|
Max+comma
|
| 1
|
1#/2b
|
F#/Gb
|
95-97.5
|
98.077
|
95.9375-100.9375
|
98.684
|
97.5-102.5
|
100.781
|
98.362-103.362
|
102.155
|
100.948-105.948
|
103.6765
|
105-107.5
|
| 2
|
2
|
G
|
190-195
|
196.154
|
191.875-201.875
|
197.368
|
195-205
|
201.5625
|
196.724-206.724
|
204.31
|
201.897-211.897
|
207.353
|
210-215
|
| 3
|
2#/3b
|
G#/Jb
|
G#/Ab
|
285-292.5
|
294.231
|
287.8125-302.8125
|
296.053
|
292.5-307.5
|
302.344
|
295.086-310.086
|
306.4655
|
302.845-316.845
|
311.029
|
315-322.5
|
| 4
|
3
|
J
|
A
|
380-390
|
392.308
|
383.75-403.75
|
394.737
|
390-410
|
403.125
|
393.448-413.448
|
408.621
|
403.793-423.793
|
414.706
|
420-430
|
| 5
|
3#/4b
|
J#/Ab
|
A#/Bb
|
475-487.5
|
490.385
|
479.6875-504.6875
|
493.421
|
487.5-512.5
|
503.906
|
491.81-516.81
|
510.776
|
504.741-529.741
|
518.382
|
525-537.5
|
| 6
|
4
|
A
|
B
|
570-585
|
588.4615
|
575.625-605.625
|
592.105
|
585-615
|
604.6875
|
590.172-620.172
|
612.931
|
605.69-635.69
|
622.059
|
630-645
|
| 7
|
5
|
B
|
H
|
665-682.5
|
686.5385
|
671.5625-706.5625
|
690.7895
|
682.5-717.5
|
705.469
|
688.5345-723.5345
|
715.086
|
706.638-741.638
|
725.735
|
735-752.5
|
| 8
|
5#/6b
|
B#/Hb
|
H#/Cb
|
760-780
|
784.615
|
767.5-807.5
|
789.474
|
780-820
|
806.25
|
786.897-826.897
|
817.241
|
807.586-847.586
|
829.412
|
840-860
|
| 9
|
6
|
H
|
C
|
855-877.5
|
882.962
|
863.4375-908.4375
|
888.158
|
877.5-922.5
|
907.031
|
885.259-930.259
|
919.397
|
908.5345-953.5345
|
933.088
|
945-967.5
|
| 10
|
6#/7b
|
H#/Cb
|
C#/Db
|
950-975
|
980.769
|
959.375-1009.375
|
986.842
|
975-1025
|
1007.8125
|
983.621-1033.621
|
1021.552
|
1009.483-1059.483
|
1036.765
|
1050-1075
|
| 11
|
7
|
C
|
D
|
1045-1072.5
|
1078.846
|
1055.3125-1110.3125
|
1085.526
|
1072.5-1127.5
|
1108.594
|
1081.983-1136.983
|
1123.707
|
1110.431-1165.431
|
1140.441
|
1155-1182.5
|
| 12
|
7#/8b
|
C#/Db
|
D#/Sb
|
1140-1170
|
1176.923
|
1151.25-1211.25
|
1184.2105
|
1170-1230
|
1209.375
|
1180.345-1240.345
|
1225.862
|
1211.379-1271.379
|
1244.118
|
1260-1290
|
| 13
|
8
|
D
|
S
|
1235-1267.5
|
1275
|
1247.1875-1312.1875
|
1282.895
|
1267.5-1332.5
|
1310.156
|
1278.707-1343.707
|
1328.017
|
1312.328-1377.328
|
1347.794
|
1365-1397.5
|
| 14
|
8#/9b
|
D#/Eb
|
S#/Eb
|
1330-1365
|
1373.077
|
1343.125-1413.125
|
1381.579
|
1365-1435
|
1410.9375
|
1377.069-1447.069
|
1430.172
|
1413.276-1483.276
|
1451.471
|
1470-1505
|
| 15
|
9
|
E
|
1425-1462.5
|
1471.154
|
1439.0625-1514.0625
|
1480.263
|
1462.5-1537.5
|
1511.719
|
1475.431-1550.431
|
1532.328
|
1514.224-1589.224
|
1555.147
|
1575-1612.5
|
| 16
|
1
|
F
|
1520-1560
|
1569.231
|
1535-1615
|
1578.947
|
1560-1640
|
1612.5
|
1573.793-1653.793.
|
1634.483
|
1615.172-1695.172
|
1658.8235
|
1680-1720
|
Relative cents
| Degrees
|
Enneatonic
|
Intense Aeolian-Subpental Dorian
|
Dorian
|
| 1
|
1#/2b
|
G#/Jb
|
G#/Ab
|
90.625
|
93.75
|
| 2
|
2
|
J
|
A
|
181.25
|
187.5
|
| 3
|
2#/3b
|
J#/Ab
|
A#/Bb
|
271.875
|
281.25
|
| 4
|
3
|
J
|
B
|
362.5
|
375
|
| 5
|
3#/4b
|
J#/Ab
|
B#/Cb
|
453.125
|
468.75
|
| 6
|
4
|
A
|
C
|
543.75
|
562.5
|
| 7
|
5
|
A#/Bb
|
C#/Qb
|
633.375
|
656.25
|
| 8
|
5#/6b
|
B
|
Q
|
725
|
750
|
| 9
|
6
|
C
|
D
|
815.625
|
843.75
|
| 10
|
6#/7b
|
C#/Db
|
D#/Sb
|
906.25
|
937.5
|
| 11
|
7
|
D
|
S
|
996.875
|
1031.25
|
| 12
|
7#/8b
|
D#/Eb
|
S#/Eb
|
1087.5
|
1125
|
| 13
|
8
|
E
|
1178.125
|
1218.75
|
| 14
|
8#/9b
|
E#/Fb
|
1268.75
|
1312.5
|
| 15
|
9
|
F
|
1359.375
|
1406.25
|
| 16
|
1
|
G
|
1450
|
1500
|
| Degrees
|
Enneatonic
|
Subpental-Soft Superpental Mixolydian
|
Intense Superpental Mixolydian ~ Mixolydian-Ionian
|
| 1
|
1#/2b
|
F#/Gb
|
100
|
103.125
|
| 2
|
2
|
G
|
200
|
206.25
|
| 3
|
2#/3b
|
G#/Jb
|
G#/Ab
|
300
|
309.375
|
| 4
|
3
|
J
|
A
|
400
|
412.5
|
| 5
|
3#/4b
|
J#/Ab
|
A#/Bb
|
500
|
515.625
|
| 6
|
4
|
A
|
B
|
600
|
618.75
|
| 7
|
5
|
B
|
H
|
700
|
721.875
|
| 8
|
5#/6b
|
B#/Hb
|
H#/Cb
|
800
|
825
|
| 9
|
6
|
H
|
C
|
900
|
928.125
|
| 10
|
6#/7b
|
H#/Cb
|
C#/Db
|
1000
|
1031.25
|
| 11
|
7
|
C
|
D
|
1100
|
1134.375
|
| 12
|
7#/8b
|
C#/Db
|
D#/Sb
|
1200
|
1237.5
|
| 13
|
8
|
D
|
S
|
1300
|
1340.625
|
| 14
|
8#/9b
|
D#/Eb
|
S#/Eb
|
1400
|
1443.75
|
| 15
|
9
|
E
|
1500
|
1546.875
|
| 16
|
1
|
F
|
1600
|
1650
|
Golden/Pyrite Tunings±13¢
| Degrees
|
Enneatonic
|
Intense Aeolian-Subpental Dorian
|
Dorian
|
| Subpental
|
Pental
|
Superpental
|
| 1
|
1#/2b
|
G#/Jb
|
G#/Ab
|
90.428-92.053
|
91.303-92.928
|
94.329-95.943
|
94.917-96.542
|
| 2
|
2
|
J
|
A
|
180.856-184.106
|
182.606-185.856
|
188.2585-191.9085
|
189.834-193.084
|
| 3
|
2#/3b
|
J#/Ab
|
A#/Bb
|
271.2845-276.159
|
273.909-278.784
|
282.988-287.863
|
284.751-289.626
|
| 4
|
3
|
J
|
B
|
361.712-368.213
|
365.212-371.712
|
377.317-383.817
|
379.668-386.168
|
| 5
|
3#/4b
|
J#/Ab
|
B#/Cb
|
452.141-460.266
|
456.5155-464.6405
|
471.646-479.771
|
474.585-482.71
|
| 6
|
4
|
A
|
C
|
542.569-552.319
|
547.819-557.569
|
565.974-575.726
|
569.502-579.252
|
| 7
|
5
|
A#/Bb
|
C#/Qb
|
632.997-644.372
|
639.122-650.497
|
660.305-671.68
|
664.419-675.794
|
| 8
|
5#/6b
|
B
|
Q
|
723.425-736.425
|
730.425-743.425
|
754.634-767.634
|
759.336-771.336
|
| 9
|
6
|
C
|
D
|
813.854-828.479
|
821.728-836.353
|
848.963-863.588
|
854.253-868.878
|
| 10
|
6#/7b
|
C#/Db
|
D#/Sb
|
904.282-920.532
|
913.031-920.281
|
943.293-959.543
|
949.17-965.42
|
| 11
|
7
|
D
|
S
|
994.71-1012.585
|
1004.334-1022.209
|
1037.622-1055.497
|
1044.087-1061.962
|
| 12
|
7#/8b
|
D#/Eb
|
S#/Eb
|
1085.138-1104.638
|
1095.637-1115.137
|
1131.951-1151.451
|
1139.004-1158.503
|
| 13
|
8
|
E
|
1175.566-1106.691
|
1186.94-1208.065
|
1226.38-1247.405
|
1233.921-1255.046
|
| 14
|
8#/9b
|
E#/Fb
|
1265.9945-1288.7445
|
1278.2435-1300.9935
|
1320.61-1343.36
|
1328.838-1351.588
|
| 15
|
9
|
F
|
1356.423-1380.798
|
1369.547-1393.922
|
1414.939-1439.314
|
1423.755-1448.13
|
| 16
|
1
|
G
|
1446.851-1472.851
|
1460.85-1486.85
|
1509.268-1535.268
|
1518.672-1544.672
|
| Degrees
|
Enneatonic
|
Mohajira
|
Beatles
|
| 1
|
1#/2b
|
F#/Gb
|
G#/Jb
|
G#/Ab
|
96.1185-97.7435
|
96.364-97.989
|
| 2
|
2
|
G
|
J
|
A
|
192.237-195.487
|
192.728-195.978
|
| 3
|
2#/3b
|
G#/Jb
|
G#/Ab
|
J#/Ab
|
A#/Bb
|
288.355-293.23
|
289.092-293.965
|
| 4
|
3
|
J
|
A
|
J
|
B
|
384.474-390.974
|
385.456-391.956
|
| 5
|
3#/4b
|
J#/Ab
|
A#/Bb
|
J#/Ab
|
B#/Cb
|
480.592-488.717
|
481.82-489.945
|
| 6
|
4
|
A
|
B
|
A
|
C
|
576.711-585.961
|
578.184-587.934
|
| 7
|
5
|
B
|
H
|
A#/Bb
|
C#/Qb
|
672.829-684.454
|
674.548-685.923
|
| 8
|
5#/6b
|
B#/Hb
|
H#/Cb
|
B
|
Q
|
768.948-781.948
|
770.912-783.912
|
| 9
|
6
|
H
|
C
|
C
|
D
|
865.066-879.691
|
867.276-881.901
|
| 10
|
6#/7b
|
H#/Cb
|
C#/Db
|
C#/Db
|
D#/Sb
|
961.185-977.435
|
963.6395-979.8895
|
| 11
|
7
|
C
|
D
|
D
|
S
|
1057.303-1075.178
|
1060.0035-1077.8785
|
| 12
|
7#/8b
|
C#/Db
|
D#/Sb
|
D#/Eb
|
S#/Eb
|
1153.422-1172.921
|
1156.367-1175.867
|
| 13
|
8
|
D
|
S
|
E
|
1249.54-1270.665
|
1252.731-1273.856
|
| 14
|
8#/9b
|
D#/Eb
|
S#/Eb
|
E#/Fb
|
1345.659-1368.409
|
1349.095-1372.345
|
| 15
|
9
|
E
|
F
|
1441.777-1366.152
|
1445.459-1469.834
|
| 16
|
1
|
F
|
G
|
1537.8955-1563.8955
|
1541.823-1577.823
|
| Degrees
|
Enneatonic
|
Mixolydian
|
Mixolydian-Ionian
|
| Subpental
|
Pental
|
Superpental
|
| Soft
|
Intense
|
| 1
|
1#/2b
|
F#/Gb
|
97.364-98.989
|
97.787-99.412
|
99.998-101.623
|
101.648-103.273
|
102.785-104.41
|
| 2
|
2
|
G
|
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
|
292.091-296.966
|
293.362-298.237
|
299.993-304.868
|
304.944-309.819
|
308.356-313.231
|
| 4
|
3
|
J
|
A
|
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
|
486.819-494.944
|
488.936-497.061
|
499.989-508.114
|
508.24-516.365
|
513.926-522.051
|
| 6
|
4
|
A
|
B
|
584.183-593.933
|
586.724-596.474
|
599.987-609.737
|
609.888-619.638
|
616.711-626.461
|
| 7
|
5
|
B
|
H
|
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
|
778.91-791.91
|
782.298-795.298.
|
799.982-812.982
|
813.1835-826.1835
|
822.282-835.282
|
| 9
|
6
|
H
|
C
|
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
|
973.638-989.888
|
977.873-994.123
|
999.978-1016.238
|
1016.479-1032.729
|
1027.852-1044.102
|
| 11
|
7
|
C
|
D
|
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
|
1168.365-1187.865
|
1173.447-1192.947
|
1199.973-1219.473
|
1219.775-1239.275
|
1233.422-1252.922
|
| 13
|
8
|
D
|
S
|
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
|
1363.093-1385.843
|
1369.022-1391.772
|
1399.968-1422.719
|
1423.071-1445.821
|
1438.993-1461.743
|
| 15
|
9
|
E
|
1460.457-1484.832
|
1455.809-1491.184
|
1499.9665-1524.3415
|
1524.719-1549.094
|
1541.778-1566.153
|
| 16
|
1
|
F
|
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 3.686 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.
See also
- 16ed5/2 - equal division of the classic major tenth
- 16ed7/3 - equal division of the septimal minor tenth