15edX is the scale which occurs as the dominant minor edX.
Intervals
| Degrees
|
Enneatonic
|
Minor mode Middletown temperament
|
Neutral mode Middletown temperament
|
Major mode Middletown temperament
|
| Intense 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
|
F#/Gb
|
96
|
97.778
|
100
|
101.818
|
102.857
|
104
|
105
|
106.667
|
107.586
|
110.345
|
112
|
| 2
|
G
|
192
|
195.556
|
200
|
203.636
|
205.714
|
208
|
210
|
213.333
|
215.172
|
220.69
|
224
|
| 3
|
G#/Jb
|
G#/Ab
|
288
|
293.333
|
300
|
305.4545
|
308.571
|
312
|
315
|
320
|
322.759
|
331.034
|
336
|
| 4
|
J
|
A
|
384
|
391.111
|
400
|
407.273
|
411.429
|
416
|
420
|
426.667
|
430.345
|
441.379
|
448
|
| 5
|
A
|
B
|
480
|
488.889
|
500
|
509.091
|
514.286
|
520
|
525
|
533.333
|
537.931
|
551.724
|
560
|
| 6
|
A#/Bb
|
B#/Hb
|
576
|
586.667
|
600
|
610.909
|
617.143
|
624
|
630
|
640
|
645.517
|
662.069
|
672
|
| 7
|
B
|
H
|
672
|
684.444
|
700
|
712.727
|
720
|
728
|
735
|
746.667
|
753.103
|
772.414
|
784
|
| 8
|
B#/Hb
|
H#/Cb
|
768
|
782.822
|
800
|
814.5455
|
822.857
|
832
|
840
|
853.333
|
860.69
|
882.759
|
896
|
| 9
|
H
|
C
|
864
|
880
|
900
|
916.364
|
925.714
|
936
|
945
|
960
|
968.276
|
993.103
|
1008
|
| 10
|
C
|
D
|
960
|
977.778
|
1000
|
1018.182
|
1028.571
|
1040
|
1050
|
1066.667
|
1075.862
|
1103.448
|
1120
|
| 11
|
C#/Db
|
D#/Sb
|
1056
|
1075.556
|
1100
|
1120
|
1131.429
|
1144
|
1155
|
1173.333
|
1183.448
|
1213.379
|
1232
|
| 12
|
D
|
S
|
1152
|
1173.333
|
1200
|
1221.818
|
1234.286
|
1248
|
1260
|
1280
|
1291.034
|
1324.138
|
1344
|
| 13
|
D#/Eb
|
S#/Eb
|
1248
|
1271.111
|
1300
|
1323.636
|
1337.143
|
1352
|
1365
|
1386.667
|
1398.621
|
1424.483
|
1456
|
| 14
|
E
|
1344
|
1368.889
|
1400
|
1425.4545
|
1440
|
1456
|
1470
|
1493.333
|
1506.207
|
1544.827
|
1568
|
| 15
|
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
|
F#/Gb
|
96.925-98.658
|
102.294-104.027
|
104.888-106.621
|
| 2
|
G
|
193.8495-197.316
|
204.588-208.054
|
209.77-213.242
|
| 3
|
G#/Jb
|
G#/Ab
|
290.774-295.974
|
306.8815-312.0815
|
314.663-319.863
|
| 4
|
J
|
A
|
387.699-394.632
|
409.1755-416.109
|
419.559-426.484
|
| 5
|
A
|
B
|
484.624-493.29
|
511.469-520.136
|
524.438-533.105
|
| 6
|
A#/Bb
|
B#/Hb
|
581.548-591.948
|
613.763-624.163
|
629.3255-639.7255
|
| 7
|
B
|
H
|
678.473-690.606
|
716.057-728.19
|
734.213-746.346
|
| 8
|
B#/Hb
|
H#/Cb
|
775.398-789.2645
|
818.351-832.218
|
839.101-852.967
|
| 9
|
H
|
C
|
872.3225-887.9225
|
920.645-936.245
|
943.988-959.588
|
| 10
|
C
|
D
|
969.247-986.561
|
1022.939-1040.272
|
1048.876-1066.209
|
| 11
|
C#/Db
|
D#/Sb
|
1066.172-1085.239
|
1125.2325-1144.299
|
1153.763-1172.83
|
| 12
|
D
|
S
|
1163.097-1183.897
|
1227.526-1248.326
|
1258.651-1279.451
|
| 13
|
D#/Eb
|
S#/Eb
|
1260.0215-1282.555
|
1329.82-1352.3535
|
1363.539-1386.072
|
| 14
|
E
|
1356.946-1381.213
|
1432.114-1456.381
|
1468.426-1492.693
|
| 15
|
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
|
| Intense Aeolian-Dorian
|
Dorian
|
Dorian-Mixolydian
|
Mixolydian
|
Mixolydian-Ionian
|
| Subpental
|
Pental
|
Superpental
|
Subpental
|
Pental
|
Superpental
|
| Soft
|
Intense
|
| 1
|
F#/Gb
|
96.457-98.19
|
97.39-99.123
|
100.618-102.351
|
101.245-102.978
|
102.788-104.5215
|
103.855-105.788
|
104.306-106.04
|
106.664-108.398
|
108.4245-110.158
|
109.6375-111.371
|
| 2
|
G
|
192.913-196.38
|
194.78-198.247
|
201.236-204.702
|
202.49-205.956
|
205.576-209.043
|
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
|
289.37-294.57
|
292.17-297.37
|
301.854-204.702
|
303.734-308.934
|
308.365-313.565
|
311.564-317.364
|
312.919-318.119
|
319.993-325.193
|
325.273-330.473
|
328.913-334.113
|
| 4
|
J
|
A
|
385.829-392.76
|
389.56-396.493
|
402.4715-307.054
|
404.979-411.9215
|
411.153-418.086
|
415.419-423.152
|
417.226-424.159
|
426.657-433.5905
|
433.698-440.631
|
438.55-445.4835
|
| 5
|
A
|
B
|
482.284-490.95
|
486.95-495.617
|
503.089-511.756
|
509.502-514.891
|
513.941-526.308
|
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
|
578.74-589.14
|
584.334-594.74
|
603.707-614.107
|
607.469-617.869
|
616.729-627.129
|
623.128-634.728
|
625.8385-636.238
|
639.987-650.386
|
650.547-660.947
|
657.825-668.225
|
| 7
|
B
|
H
|
675.197-687.33
|
681.73-693.863
|
704.325-716.4585
|
708.7135-720.847
|
719.5175-731.651
|
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
|
771.654-785.52
|
779.12-792.9865
|
804.943-818.81
|
809.958-823.825
|
822.306-836.172
|
830.8375-844.704
|
834.451-848.318
|
853.314-867.181
|
867.396-881.262
|
877.1-890.967
|
| 9
|
H
|
C
|
868.1105-883.7105
|
876.51-892.11
|
905.561-921.161
|
911.203-926.823
|
925.094-940.694
|
934.693-952.092
|
938.758-954.358
|
959.9785-975.5785
|
975.82-991.42
|
986.738-1002.338
|
| 10
|
C
|
D
|
964.567-981.901
|
973.9-991.233
|
1006.179-1023.512
|
1012.448-1029.781
|
1027.882-1045.2155
|
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
|
1061.024-1080.091
|
1071.39-1090.356
|
1106.797-1125.863
|
1113.693-1132.759
|
1130.67-1149.737
|
1142.402-1163.668
|
1147.3705-1166.437
|
1173.307-1192.374
|
1192.669-1211.736
|
1206.013-1225.08
|
| 12
|
D
|
S
|
1157.481-1178.281
|
1168.68-1189.48
|
1207.4145-1228.2145
|
1214.9375-1235.7375
|
1233.459-1254.259
|
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
|
1253.937-1276.471
|
1266.07-1288.603
|
1308.032-1330.566
|
1316.182-1338.716
|
1336.247-1358.78
|
1353.111-1275.244
|
1355.983-1378.517
|
1386.636-1409.169
|
1409.518-1425.288
|
1438.993-1447.8215
|
| 14
|
E
|
1350.394-1374.661
|
1363.46-1387.726
|
1408.65-1432.917
|
1417.427-1441.694
|
1439.035-1463.302
|
1453.966-1481.032
|
1460.29-1484.556
|
1493.3-1517.567
|
1517.9425-1534.926
|
1541.778-1559.192
|
| 15
|
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, 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-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.