This scale, a Long Common Practice minor mode, occurs in 12edo; where it is the equal division of the minor ninth. It has the Grandfather 5L 3s MOS with a 2:1 ratio of large against small. It also gives the wide values for the period of the Greater Triskaidekic, tridecatonic, trideci and aluminium temperaments.
Intervals
| Nonet
|
Period
|
Notes
|
| 1/1
|
|
|
|
92.308
|
Soft Phrygian mode begins
|
|
|
23\22
|
|
|
96.5035
|
|
| 22\21
|
|
|
|
96.703
|
Soft Phrygian mode ends, Thirdtone Phrygian mode begins
|
| 21\20
|
|
|
|
96.923
|
|
| 20\19
|
|
|
|
97.166
|
|
| 19\18
|
|
|
|
97.436
|
|
|
|
37\35
|
|
|
97.582
|
|
| 18\17
|
|
|
|
97.738
|
|
| 17\16
|
|
|
|
98.077
|
|
| 16\15
|
|
|
|
98.4615
|
Thirdtone Phrygian mode ends
|
| 15\14
|
|
|
|
98.901
|
Semitone Phrygian mode begins
|
| 14\13
|
|
|
|
99.408
|
|
|
|
27\25
|
|
|
99.692
|
|
| 13\12
|
|
|
|
100
|
|
| 12\11
|
|
|
|
100.699
|
|
| 11\10
|
|
|
|
101.5385
|
Semitone Phrygian mode ends, Intense Phrygian mode begins
|
|
|
21\19
|
|
|
102.024
|
|
| 10\9
|
|
|
|
102.564
|
Intense Phrygian mode ends, Intense Phrygian-Soft Aeolian mode begins
|
|
|
19\17
|
|
|
103.167
|
|
| 9\8
|
|
|
|
103.846
|
Intense Phrygian-Soft Aeolian mode ends, Soft Aeolian mode begins
|
|
|
17\15
|
|
|
104.615
|
|
| 8\7
|
|
|
|
105.4945
|
Soft Aeolian mode ends, Flattone Aeolian mode begins
|
|
|
15\13
|
|
|
106.509
|
|
|
|
|
22\19
|
|
106.883
|
Flattone Aeolian mode ends, Meantone Aeolian mode begins
|
|
|
|
|
29\25
|
107.077
|
|
| 7\6
|
|
|
|
107.692
|
Meantone Aeolian mode ends, Superpyth Intense Aeolian mode begins
|
|
|
|
20\17
|
|
108.597
|
|
|
|
13\11
|
|
|
109.09
|
Superpyth Intense Aeolian mode ends, Ultrapyth Intense Aeolian mode begins
|
|
|
|
19\16
|
|
109.615
|
|
| 6\5
|
|
|
|
110.769
|
Ultrapyth Intense Aeolian mode ends
|
Golden/Pyrite Tunings±13¢
| Degrees
|
Octatonic
|
Soft Phrygian
|
Phrygian
|
| Min-Med
|
Min-Max/Med-Max
|
Thirdtone
|
Semitone
|
| Min-Med/Min-Max
|
Med-Max
|
Min-Med/Min-Max
|
Med-Max
|
| Natural
|
Subset of 26edn
|
| 1
|
G#/Ab
|
G#v/Ab^
|
95.389-97.389
|
95.578-97.578
|
95.957-98.345
|
96.785-98.844
|
98.359-100.709
|
99.058-101.523
|
| 2
|
A
|
190.778-194.778
|
191.155-195.155
|
191.914-196.689
|
193.569-197.688
|
196.719-201.417
|
198.1165-203.046
|
| 3
|
A#/Bb
|
A#v/Bb^
|
286.1665-292.1665
|
286.733-292.733
|
287.871-295.034
|
290.354-296.531
|
295.078-302.126
|
297.175-304.569
|
| 4
|
B
|
381.555-389.555
|
382.3105-390.3105
|
383.828-393.378
|
387.138-395.375
|
393.4375-402.835
|
396.233-406.092
|
| 5
|
C
|
B#v/Cb^
|
476.944-486.944
|
477.888-487.888
|
479.785-491.723
|
483.923-494.219
|
491.797-503.544
|
495.291-507.615
|
| 6
|
C#/Qb
|
C
|
572.333-584.333
|
573.466-585.466
|
575.742-590.068
|
580.707-593.063
|
590.156-604.253
|
594.349-609.138
|
| 7
|
Q
|
Db
|
667.722-681.722
|
669.043-683.043
|
671.699-688.412
|
677.492-691.907
|
688.516-704.962
|
693.408-710.661
|
| 8
|
D
|
Q#
|
763.111-781.111
|
764.621-780.621
|
767.656-786.757
|
774.2765-790.75
|
786.875-805.67
|
792.466-812.184
|
| 9
|
D#/Eb
|
Eb
|
858.5-876.5
|
860.199-878.199
|
863.613-885.1015
|
871.061-889.594
|
885.234-906.379
|
891.524-913.707
|
| 10
|
E
|
D#
|
953.8885-973.8885
|
955.776-975.776
|
959.57-983.446
|
967.846-988.438
|
983.594-1007.088
|
990.582-1015.23
|
| 11
|
E#/Fb
|
Fb
|
1049.277-1071.277
|
1051.354-1073.354
|
1055.527-1081.791
|
1064.63-1087.282
|
1081.953-1107.797
|
1089.641-1116.75
|
| 12
|
F
|
E#
|
1144.666-1168.666
|
1146.932-1170.932
|
1151.484-1180.135
|
1161.415-1186.126
|
1180.312-1208.506
|
1188.699-1218.276
|
| 13
|
G
|
1240.055-1266.055
|
1242.506-1268.509
|
1247.441-1278.48
|
1258.199-1284.969
|
1278.672-1309.2145
|
1287.757-1319.799
|
| Degrees
|
Octatonic
|
Intense Phrygian
|
Intense Phrygian-Soft Aeolian
|
Soft Aeolian
|
| Min-Med/Min-Max
|
Med-Max
|
Min-Med/Min-Max
|
Med-Max
|
Min-Med/Min-Max
|
Med-Max
|
| Natural
|
Subset of 26edn
|
| 1
|
F#/Gb
|
G#/Ab
|
F#v/Gb^
|
G#v/Ab^
|
100.905-102.905
|
101.1465-103.1465
|
102.019-104.019
|
102.32-104.32
|
103.425-105.425
|
103.812-105.812
|
| 2
|
G
|
A
|
G
|
A
|
201.81-205.81
|
202.293-206.293
|
204.037-208.037
|
204.641-208.641
|
206.849-210.849
|
207.624-211.624
|
| 3
|
G#/Ab
|
A#/Bb
|
G#v/Ab^
|
A#v/Bb^
|
302.715-308.715
|
303.44-309.44
|
306.056-312.056
|
306.961-312.961
|
310.274-316.274
|
311.4365-317.4365
|
| 4
|
A
|
B
|
A
|
B
|
403.62-411.62
|
404.586-412.586
|
408.075-416.075
|
409.281-417.281
|
413.699-421.699
|
415.249-423.249
|
| 5
|
B
|
C
|
A#v/Bb^
|
B#v/Cb^
|
504.525-514.525
|
505.733-515.733
|
510.093-520.093
|
511.602-521.602
|
517.123-527.123
|
519.061-529.061
|
| 6
|
B#/Hb
|
C#/Qb
|
B
|
C
|
605.43-617.43
|
606.879-618.879
|
612.112-624.112
|
613.922-625.922
|
620.548-632.548
|
622.873-634.873
|
| 7
|
H
|
Q
|
Cb
|
Db
|
706.335-720.335
|
708.026-722.026
|
714.131-728.131
|
716.242-730.242
|
723.973-737.973
|
726.685-740.685
|
| 8
|
C
|
D
|
H#
|
Q#
|
807.24-823.24
|
809.172-825.172
|
816.1495-832.1495
|
818.563-834.563
|
827.3975-843.3975
|
830.497-846.497
|
| 9
|
C#/Db
|
D#/Eb
|
Db
|
Eb
|
908.145-926.145
|
910.319-928.319
|
918.168-936.168
|
920.883-938.883
|
930.822-948.822
|
934.309-952.309
|
| 10
|
D
|
E
|
C#
|
D#
|
1009.0505-1029.0505
|
1011.465-1031.465
|
1020.186-1040.186
|
1023.2035-1043.2035
|
1034.247-1054.2547
|
1038.122-1058.122
|
| 11
|
D#/Eb
|
E#/Fb
|
Eb
|
Fb
|
1109.9555-1131.9555
|
1112.61-1134.612
|
1122.2055-1143.2055
|
1125.524-1147.524
|
1137.672-1159.672
|
1141.934-1163.934
|
| 12
|
E
|
F
|
D#
|
E#
|
1210.861-1234.861
|
1213.758-1227.758
|
1224.224-1248.224
|
1225.844-1249.884
|
1241.096-1265.096
|
1245.746-1269.746
|
| 13
|
F
|
G
|
F
|
G
|
1311.767-1337.767
|
1314.905-1340.905
|
1326.243-1352.243
|
1343.1645-1396.1645
|
1344.521-1370.521
|
1349.558-1375.558
|
| Degrees
|
Octatonic
|
Aeolian
|
Intense Aeolian
|
| Flattone
|
Meantone
|
Superpyth
|
Ultrapyth
|
| Min-Med
|
Med-Max~Min-Max
|
Min-Med/Min-Max
|
Med-Max
|
Min-Med
|
Min-Max/Med-Max
|
Min-Med/Min-Max
|
Med-Max
|
| Natural
|
Subset of 26edn
|
| 1
|
F#/Gb
|
F#v/Gb^
|
105.256-107.256
|
105.625-108.015
|
106.156-108.156
|
107.435-109.435
|
107.738-109.738
|
108.459-110.459
|
108.802-110.802
|
| 2
|
G
|
210.511-214.511
|
211.25-216.03
|
212.313-216.313
|
214.8705-218.8705
|
215.4765-219.4765
|
216.918-220.918
|
217.604-221.604
|
| 3
|
G#/Ab
|
G#v/Ab^
|
315.767-321.767
|
316.875-324.044
|
318.469-324.469
|
321.306-329.306
|
322.215-330.215
|
325.377-331.377
|
326.4065-332.4065
|
| 4
|
A
|
421.022-429.022
|
422.501-432.059
|
424.626-432.626
|
429.741-437.741
|
430.953-438.953
|
433.836-437.836
|
435.209-443.209
|
| 5
|
B
|
A#v/Bb^
|
526.278-536.278
|
528.126-540.074
|
530.782-540.782
|
547.176-547.176
|
538.6915-548.6915
|
542.295-552.295
|
544.011-554.011
|
| 6
|
B#/Hb
|
B
|
631.534-643.534
|
633.751-648.089
|
636.9385-648.9385
|
644.611-656.611
|
646.43-658.43
|
650.754-666.754
|
652.813-664.813
|
| 7
|
H
|
Cb
|
736.789-750.789
|
739.376-756.104
|
743.095-757.095
|
752.047-766.047
|
754.168-768.168
|
759.213-773.213
|
761.615-775.615
|
| 8
|
C
|
H#
|
842.045-858.045
|
845.001-864.1185
|
849.251-865.521
|
859.482-875.482
|
861.906-877.906
|
867.672-883.672
|
870.417-886.417
|
| 9
|
C#/Db
|
Db
|
947.3-965.3
|
950.626-972.133
|
958.408-976.408
|
966.917-984.917
|
969.645-986.645
|
976.131-994.131
|
979.219-997.219
|
| 10
|
D
|
C#
|
1052.556-1072.556
|
1056.2515-1080.148
|
1061.564-1081.564
|
1074.352-1094.352
|
1077.383-1077.383
|
1084.59-1104.59
|
1088.022-1108.022
|
| 11
|
D#/Eb
|
Eb
|
1157.8115-1179.8115
|
1161.877-1188.163
|
1167.7205-1189.7205
|
1181.7875-1203.7875
|
1185.121-1207.121
|
1193.049-1215.049
|
1196.824-1218.824
|
| 12
|
E
|
D#
|
1264.067-1287.067
|
1267.502-1296.178
|
1273.877-1298.877
|
1288.223-1312.223
|
1292.86-1316.86
|
1301.508-1325.508
|
1304.626-1328-626
|
| 13
|
F
|
1368.323-1394.323
|
1373.127-1404.193
|
1380.033-1406.033
|
1396.658-1422.658
|
1400.598-1426.598
|
1409.967-1435.967
|
1414.428-1440.428
|