15edX is the scale which occurs as the dominant minor edX (equal division of a tenth interval).
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
|
G#/Jb
|
G#/Ab
|
93.333-96
|
97.143
|
95.111-100.444
|
98.4615
|
97.333-102.667
|
101.333
|
99.1515-104.485
|
102.222
|
102.857-105.524
|
| 2
|
J
|
A
|
186.667-192
|
194.286
|
190.222-200.889
|
196.923
|
194.667-205.333
|
202.667
|
198.303-208.97
|
204.444
|
205.714-211.048
|
| 3
|
J#/Ab
|
A#/Bb
|
280-288
|
291.429
|
285.333-301.333
|
295.385
|
292-308
|
304
|
297.4545-313.4545
|
306.667
|
308.571-316.571
|
| 4
|
A
|
B
|
373.333-384
|
388.571
|
380.444-401.778
|
393.846
|
389.333-410.667
|
405.333
|
396.606-417.939
|
408.889
|
411.429-422.095
|
| 5
|
B
|
C
|
466.667-480
|
485.714
|
475.556-502.222
|
492.308
|
486.667-513.333
|
506.667
|
495.758-522.424
|
511.111
|
514.286-527.619
|
| 6
|
B#/Cb
|
C#/Qb
|
560-576
|
582.857
|
570.667-602.667
|
590.769
|
584-616
|
608
|
594.909-626.909
|
613.333
|
617.143-633.143
|
| 7
|
C
|
Q
|
653.333-672
|
680
|
665.778-703.111
|
689.231
|
681.333-718.667
|
709.333
|
694.061-731.394
|
715.556
|
720-738.667
|
| 8
|
C#/Qb
|
Q#/Db
|
746.667-768
|
757.143
|
760.889-803.556
|
787.692
|
778.667-821.333
|
810.667
|
793.212-835.879
|
817.778
|
822.857-844.1905
|
| 9
|
Q
|
D
|
840-864
|
874.286
|
856-904
|
886.154
|
876-924
|
912
|
892.364-940.364
|
920
|
925.714-949.714
|
| 10
|
D
|
S
|
933.333-960
|
971.429
|
951.111-1004.444
|
984.615
|
973.333-1026.667
|
1013.333
|
991.515-1044.8485
|
1022.222
|
1028.571-1055.238
|
| 11
|
D#/Eb
|
S#/Eb
|
1026.667-1056
|
1068.571
|
1046.222-1104.889
|
1083.077
|
1070.667-1129.333
|
1114.667
|
1090.667-1149.333
|
1124.444
|
1131.429-1160.761
|
| 12
|
E
|
1120-1152
|
1165.714
|
1141.333-1205.333
|
1181.5385
|
1168-1232
|
1216
|
1189.818-1253.818
|
1226.667
|
1234.286-1266.286
|
| 13
|
E#/Fb
|
1213.333-1248
|
1262.857
|
1236.444-1305.778
|
1280
|
1265.333-1334.667
|
1317.333
|
1288.97-1358.303
|
1328.889
|
1337.143-1371.8095
|
| 14
|
F
|
1306.667-1344
|
1360
|
1331.556-1406.222
|
1378.4615
|
1363.667-1437.333
|
1418.667
|
1388.121-1462.788
|
1431.111
|
1440-1477.333
|
| 15
|
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
|
F#/Gb
|
G#/Jb
|
G#/Ab
|
100.1905-102.857
|
103.333
|
100.863-106.196
|
103.704
|
104-106.667
|
| 2
|
G
|
J
|
A
|
200.381-205.714
|
206.667
|
201.7255-212.392
|
207.407
|
208-213.333
|
| 3
|
G#/Jb
|
G#/Ab
|
J#/Ab
|
A#/Bb
|
300.571-308.571
|
310
|
302.588-318.588
|
311.111
|
312-320
|
| 4
|
J
|
A
|
A
|
B
|
400.702-411.429
|
413.333
|
403.451-424.784
|
414.815
|
416-426.667
|
| 5
|
A
|
B
|
B
|
C
|
500.952-514.286
|
516.667
|
504.314-530.98
|
518.5185
|
520-533.33
|
| 6
|
A#/Bb
|
B#/Hb
|
B#/Cb
|
C#/Qb
|
601.143-617.143
|
620
|
605.1765-637.1765
|
622.222
|
624-640
|
| 7
|
B
|
H
|
C
|
Q
|
701.333-720
|
723.333
|
706.04-743.3725
|
725.926
|
728-746.667
|
| 8
|
B#/Hb
|
H#/Cb
|
C#/Qb
|
Q#/Db
|
801.524-822.857
|
826.667
|
806.902-849.569
|
829.63
|
832-853.333
|
| 9
|
H
|
C
|
Q
|
D
|
901.714-925.714
|
930
|
907.765-955.765
|
933.333
|
936-960
|
| 10
|
C
|
D
|
D
|
S
|
1001.905-1048.571
|
1033.333
|
1008.6275-1061.961
|
1037.037
|
1040-1066.667
|
| 11
|
C#/Db
|
D#/Sb
|
D#/Eb
|
S#/Eb
|
1102.095-1131.429
|
1136.667
|
1109.49-1168.157
|
1140.741
|
1144-1173.333
|
| 12
|
D
|
S
|
E
|
1202.286-1234.286
|
1240
|
1210.353-1274.353
|
1244.444
|
1248-1280
|
| 13
|
D#/Eb
|
S#/Eb
|
E#/Fb
|
1302.476-1337.143
|
1343.333
|
1311.216-1380.549
|
1348.148
|
1352-1386.667
|
| 14
|
E
|
F
|
1402.667-1440
|
1446.667
|
1412.078-1486.745
|
1451.852
|
1456-1493.333
|
| 15
|
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
|
F#/Gb
|
101.333-104
|
104.615
|
102.333-107.667
|
105.263
|
104-109.333
|
107.5
|
104.9195-110.253
|
108.9655
|
107.678-113.0115
|
110.588
|
112-114.667
|
| 2
|
G
|
202.667-208
|
209.231
|
204.667-215.333
|
210.526
|
208-218.667
|
215
|
209.809-220.506
|
217.931
|
215.356-226.023
|
221.1765
|
224-229.333
|
| 3
|
G#/Jb
|
G#/Ab
|
304-312
|
313.846
|
307-323
|
315.7895
|
312-328
|
322.5
|
314.759-330.759
|
326.897
|
323.0345-339.0345
|
331.765
|
336-344
|
| 4
|
J
|
A
|
405.333-416
|
418.4615
|
409.333-435.667
|
421.053
|
416-437.333
|
430
|
419.678-441.0115
|
435.862
|
430.713-452.046
|
442.353
|
448-458.667
|
| 5
|
A
|
B
|
516.667-520
|
523.077
|
511.667-538.333
|
526.316
|
520-546.667
|
537.5
|
524.598-541.264
|
544.828
|
538.391-565.0575
|
552.941
|
560-573.333
|
| 6
|
A#/Bb
|
B#/Hb
|
608-624
|
627.692
|
614-646
|
631.579
|
624-656
|
645
|
629.517-661.517
|
653.793
|
646.069-678.069
|
663.529
|
672-688
|
| 7
|
B
|
H
|
709.333-728
|
732.308
|
716.333-753.667
|
736.842
|
728-765.333
|
752.5
|
734.437-771.77
|
762.759
|
753.747-791.0805
|
774.118
|
784-802.667
|
| 8
|
B#/Hb
|
H#/Cb
|
810.666-832
|
836.923
|
818.667-861.333
|
842.103
|
832-874.667
|
860
|
839.356-882.023
|
871.724
|
861.425-904.092
|
884.706
|
896-917.333
|
| 9
|
H
|
C
|
912-936
|
941.5385
|
921-969
|
947.368
|
936-984
|
967.5
|
944.276-992.276
|
980.69
|
969.103-1007.103
|
995.294
|
1008-1032
|
| 10
|
C
|
D
|
1013.333-1040
|
1046.154
|
1023.333-1076.667
|
1052.632
|
1040-1093.333
|
1075
|
1049.195-1102.529
|
1089.655
|
1076.782-1130.115
|
1105.882
|
1120-1146.667
|
| 11
|
C#/Db
|
D#/Sb
|
1114.667-1144
|
1150.769
|
1125.667-1184.333
|
1157.895
|
1144-1202.667
|
1182.5
|
1154.115-1212.782
|
1198.621
|
1184.46-1243.126
|
1216.471
|
1232-1261.333
|
| 12
|
D
|
S
|
1216-1248
|
1255.385
|
1228-1292
|
1263.158
|
1248-1312
|
1290
|
1259.0345-1323.0345
|
1307.586
|
1292.138-1356.138
|
1327.059
|
1344-1376
|
| 13
|
D#/Eb
|
S#/Eb
|
1317.333-1352
|
1360
|
1330.333-1399.667
|
1368.421
|
1352-1421.333
|
1397.5
|
1363.954-1433.287
|
1416.552
|
1399.816-1469.149
|
1437.647
|
1456-1490.667
|
| 14
|
E
|
1418.667-1456
|
1464.615
|
1432.667-1506.333
|
1473.684
|
1456-1530.337
|
1505
|
1468.874-1534.54
|
1525.517
|
1507.494-1582.161
|
1548.235
|
1568-1605.333
|
| 15
|
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
|
Subpental-Soft Superpental Mixolydian
|
Intense Superpental Mixolydian ~ Mixolydian-Ionian
|
| 1
|
G#/Jb
|
G#/Ab
|
96.667
|
100
|
106.667
|
110
|
| 2
|
J
|
A
|
193.333
|
200
|
213.333
|
220
|
| 3
|
J#/Ab
|
A#/Bb
|
290
|
300
|
320
|
330
|
| 4
|
A
|
B
|
386.667
|
400
|
426.667
|
440
|
| 5
|
B
|
C
|
483.333
|
500
|
533.333
|
550
|
| 6
|
B#/Cb
|
C#/Qb
|
580
|
600
|
640
|
660
|
| 7
|
C
|
Q
|
676.667
|
700
|
746.667
|
770
|
| 8
|
C#/Qb
|
Q#/Db
|
773.333
|
800
|
853.333
|
880
|
| 9
|
Q
|
D
|
870
|
900
|
960
|
990
|
| 10
|
D
|
S
|
966.667
|
1000
|
1066.667
|
1100
|
| 11
|
D#/Eb
|
S#/Eb
|
1063.333
|
1100
|
1173.333
|
1210
|
| 12
|
E
|
1160
|
1200
|
1280
|
1320
|
| 13
|
E#/Fb
|
1256.667
|
1300
|
1386.667
|
1430
|
| 14
|
F
|
1353.333
|
1400
|
1493.333
|
1540
|
| 15
|
G
|
1450
|
1500
|
1600
|
1650
|
Golden/Pyrite Tunings±13¢
| Degrees
|
Enneatonic
|
Intense Aeolian-Subpental Dorian
|
Dorian
|
| Subpental
|
Pental
|
Superpental
|
| 1
|
G#/Jb
|
G#/Ab
|
96.457-98.19
|
97.39-99.123
|
100.618-102.351
|
101.245-102.978
|
| 2
|
J
|
A
|
192.913-196.38
|
194.78-198.247
|
201.236-204.702
|
202.49-205.956
|
| 3
|
J#/Ab
|
A#/Bb
|
289.37-294.57
|
292.17-297.37
|
301.854-204.702
|
303.734-308.934
|
| 4
|
A
|
B
|
385.829-392.76
|
389.56-396.493
|
402.4715-307.054
|
404.979-411.9215
|
| 5
|
B
|
C
|
482.284-490.95
|
486.95-495.617
|
503.089-511.756
|
509.502-514.891
|
| 6
|
B#/Cb
|
C#/Qb
|
578.74-589.14
|
584.334-594.74
|
603.707-614.107
|
607.469-617.869
|
| 7
|
C
|
Q
|
675.197-687.33
|
681.73-693.863
|
704.325-716.4585
|
708.7135-720.847
|
| 8
|
C#/Qb
|
Q#/Db
|
771.654-785.52
|
779.12-792.9865
|
804.943-818.81
|
809.958-823.825
|
| 9
|
Q
|
D
|
868.1105-883.7105
|
876.51-892.11
|
905.561-921.161
|
911.203-926.823
|
| 10
|
D
|
S
|
964.567-981.901
|
973.9-991.233
|
1006.179-1023.512
|
1012.448-1029.781
|
| 11
|
D#/Eb
|
S#/Eb
|
1061.024-1080.091
|
1071.39-1090.356
|
1106.797-1125.863
|
1113.693-1132.759
|
| 12
|
E
|
1157.481-1178.281
|
1168.68-1189.48
|
1207.4145-1228.2145
|
1214.9375-1235.7375
|
| 13
|
E#/Fb
|
1253.937-1276.471
|
1266.07-1288.603
|
1308.032-1330.566
|
1316.182-1338.716
|
| 14
|
F
|
1350.394-1374.661
|
1363.46-1387.726
|
1408.65-1432.917
|
1417.427-1441.694
|
| 15
|
G
|
1446.851-1472.851
|
1460.85-1486.85
|
1509.268-1535.268
|
1518.672-1544.672
|
| Degrees
|
Enneatonic
|
Mohajira
|
Beatles
|
| 1
|
F#/Gb
|
G#/Jb
|
G#/Ab
|
102.526-104.26
|
102.788-104.5215
|
| 2
|
G
|
J
|
A
|
205.053-208.519
|
205.576-209.431
|
| 3
|
G#/Jb
|
G#/Ab
|
J#/Ab
|
A#/Bb
|
307.579-312.779.
|
308.365-313.565
|
| 4
|
J
|
A
|
A
|
B
|
410.1055-417.099
|
411.153-418.086
|
| 5
|
A
|
B
|
B
|
C
|
512.632-521.2985
|
513.941-522.607
|
| 6
|
A#/Bb
|
B#/Hb
|
B#/Cb
|
C#/Qb
|
615.158-625.558
|
616.729-627.129
|
| 7
|
B
|
H
|
C
|
Q
|
717.685-729.818
|
719.5175-731.651
|
| 8
|
B#/Hb
|
H#/Cb
|
C#/Qb
|
Q#/Db
|
820.211-834.078
|
822.306-836.172
|
| 9
|
H
|
C
|
Q
|
D
|
922.737-938.337
|
925.094-940.694
|
| 10
|
C
|
D
|
D
|
S
|
1025.264-1042.597
|
1027.882-1045.215
|
| 11
|
C#/Db
|
D#/Sb
|
D#/Eb
|
S#/Eb
|
1127.79-1146.857
|
1130.67-1149.737
|
| 12
|
D
|
S
|
E
|
1230.316-1251.116
|
1233.459-1254.259
|
| 13
|
D#/Eb
|
S#/Eb
|
E#/Fb
|
1332.843-1355.376
|
1336.247-1358.78
|
| 14
|
E
|
F
|
1435.369-1459.666
|
1439.035-1463.302
|
| 15
|
F
|
G
|
1537.8955-1563.8955
|
1541.823-1577.823
|
| Degrees
|
Enneatonic
|
Mixolydian
|
Mixolydian-Ionian
|
| Subpental
|
Pental
|
Superpental
|
| Soft
|
Intense
|
| 1
|
F#/Gb
|
103.855-105.788
|
104.306-106.04
|
106.664-108.398
|
108.4245-110.158
|
109.6375-111.371
|
| 2
|
G
|
207.709-211.576
|
208.613-212.08
|
213.329-216.795
|
216.849-220.316
|
219.275-222.742
|
| 3
|
G#/Jb
|
G#/Ab
|
311.564-317.364
|
312.919-318.119
|
319.993-325.193
|
325.273-330.473
|
328.913-334.113
|
| 4
|
J
|
A
|
415.419-423.152
|
417.226-424.159
|
426.657-433.5905
|
433.698-440.631
|
438.55-445.4835
|
| 5
|
A
|
B
|
519.2735-528.94
|
521.532-530.199
|
533.321-541.988
|
542.122-550.789
|
548.188-556.854
|
| 6
|
A#/Bb
|
B#/Hb
|
623.128-634.728
|
625.8385-636.238
|
639.987-650.386
|
650.547-660.947
|
657.825-668.225
|
| 7
|
B
|
H
|
726.983-740.516
|
730.145-742.278
|
746.65-758.783
|
758.971-771.105
|
767.463-779.596
|
| 8
|
B#/Hb
|
H#/Cb
|
830.8375-844.704
|
834.451-848.318
|
853.314-867.181
|
867.396-881.262
|
877.1-890.967
|
| 9
|
H
|
C
|
934.693-952.092
|
938.758-954.358
|
959.9785-975.5785
|
975.82-991.42
|
986.738-1002.338
|
| 10
|
C
|
D
|
1038.547-1057.88
|
1043.064-1060.3975
|
1066.643-1083.976
|
1084.245-1101.578
|
1096.3755-1113.709
|
| 11
|
C#/Db
|
D#/Sb
|
1142.402-1163.668
|
1147.3705-1166.437
|
1173.307-1192.374
|
1192.669-1211.736
|
1206.013-1225.08
|
| 12
|
D
|
S
|
1246.256-1269.456
|
1251.677-1272.477
|
1279.971-1300.771
|
1301.0395-1321.8935
|
1315.651-1336.451
|
| 13
|
D#/Eb
|
S#/Eb
|
1353.111-1275.244
|
1355.983-1378.517
|
1386.636-1409.169
|
1409.518-1425.288
|
1438.993-1447.8215
|
| 14
|
E
|
1453.966-1481.032
|
1460.29-1484.556
|
1493.3-1517.567
|
1517.9425-1534.926
|
1541.778-1559.192
|
| 15
|
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, the 15ed of the Pyrite tenth (7φ+6)\(5φ^2)edo is almost exactly every third degree of 34edo. Additionally, those of the modal Golden and Pyrite tenths are almost exactly +1/28-syntonic comma 4ed(5/4) (Intense Aeolian-Subpental Dorian), 9ed(5/3)/equal multiples of 18/17 (Subpental Dorian), 13ed(15/7) (Pental Dorian), 2ed(9/8) (Superpental Dorian), -1/12-syntonic comma 3ed(6/5) (Dorian-Mixolydian), 14ed(7/3)/equal multiples of 17/16/100π\3 cents (Subpental Mixolydian), 3ed(6/5) (Pental Mixolydian), -1/20-septimal comma 4ed(9/7)/-1/28-syntonic comma 14ed(12/5)/9ed(7/4) (Soft Superpental Mixolydian), 12ed(32/15) (Intense Superpental Mixolydian) and 8ed(5/3)/-1/9 schismic 9ed(16/9)/14ed(22/9) (Mixolydian-Ionian) respectively.
See also
- 15ed5/2 - equal division of the classic major tenth
- 15ed7/3 - equal division of the septimal minor tenth