User:Moremajorthanmajor/13edIX

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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.

Intervals

Degrees Octatonic Phrygian Mode (aka Double) Neapolitan Temperament (natural minor) Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor) Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
Absolute Minimum Minimum Median Maximum Intense Phrygian Intense Phrygian-Soft Aeolian Soft Aeolian Minimum Median Maximum
Minimum Median Maximum Minimum Median Maximum Minimum Median Maximum
1 F#/Gb 92.308 97.582 98.4615 101.5385 102.024 102.564 103.167 103.846 104.615 105.4945 107.692 110.769
2 G 184.615 195.165 196.923 203.077 204.0485 205.128 206.335 207.692 209.231 210.989 215.385 221.5385
3 G#/Ab 276.923 292.747 295.385 304.615 306.073 307.692 309.502 311.5385 313.846 316.4835 323.077 332.308
4 A 369.231 390.33 393.846 406.154 408.097 410.256 412.67 415.385 418.4615 421.978 430.769 443.076
5 B 461.5385 487.912 491.308 507.692 510.1215 512.8205 515.837 519.231 523.077 527.4725 538.4615 553.846
6 B#/Hb 553.846 585.4945 589.769 609.231 612.146 615.384 619.0045 623.077 627.692 632.967 646.154 664.615
7 H 646.154 683.077 690.231 710.769 714.17 717.945 722.172 736.923 732.308 738.4615 754.846 775.385
8 C 738.4615 780.66 788.692 812.308 816.194 820.513 825.339 830.769 836.923 843.856 861.5385 886.154
9 C#/Db 830.769 878.242 896.154 913.846 918.219 923.077 929.507 934.615 941.5385 949.4505 969.231 996.923
10 D 923.077 975.824 984.615 1015.385 1020.243 1025.641 1031.674 1038.4165 1046.154 1054.945 1076.923 1107.692
11 D#/Eb 1015.385 1073.407 1083.077 1116.923 1123.267 1128.205 1134.842 1142.308 1150.769 1160.44 1184.615 1218.4615
12 E 1107.692 1170.99 1181.5385 1218.4615 1224.291 1230.769 1238.009 1246.154 1255.385 1265.9348 1292.308 1329.231
13 F 1200 1268.571 1280 1320 1326.316 1333.333 1341.1765 1350 1360 1371.429 1400 1440

Most harmonic tunings

Degrees Octatonic Phrygian Mode (natural minor) Phrygian-Aeolian Mode (intermediate minor) Aeolian Mode (melodic/harmonic minor)
15/7±13¢ 11/5±13¢ 9/4±13¢
1 F#/Gb 100.496-102.496 104-106 106.993-108.993
2 G 200.991-204.912 208.001-212.001 213.986-217.986
3 G#/Ab 301.487-307.487 312.001-318.001 320.979-326.979
4 A 401.982-409.982 416.001-424.001 427.972-435.972
5 B 502.478-512.478 520.002-530.002 534.965-544.965
6 B#/Hb 602.974-614.974 624.002-636.002 641.9585-653.9585
7 H 703.469-717.469 728.002-742.0022 748.9515-762.9515
8 C 803.965-819.965 832.003-848.002 855.945-871.945
9 C#/Db 904.46-922.46 936.003-924.003 962.938-980.938
10 D 1004.956-1024.956 1040.003-1060.003 1069.931-1089.931
11 D#/Eb 1105.452-1127.452 1144.004-1166.004 1177-924-1199.924
12 E 1205.947-1299.947 1248.004-1272.004 1283.917-1307.917
13 F 1306.443-1332.443 1352.004-1378.004 1390.91-1416.91

Golden Tunings

Phrygian Mode (natural minor)

Degrees Octatonic Min-Med±13¢ Min-Max±13¢ Med-Max±13¢
1 F#/Gb 96.7665-98.7665 97.176-99.176 98.359-100.359
2 G 193.533-197.533 194.352-198.352 196.719-200.719
3 G#/Ab 290.2995-296.2995 291.528-297.528 295.078-301.078
4 A 387.063-395.063 388.705-396.705 393.4375-401.4375
5 B 483.833-493.833 485.881-495.881 491.797-501.797
6 B#/Hb 580.299-592.299 583.057-595.057 590.156-602.156
7 H 677.366-691.366 680.233-694.233 688.516-702.516
8 C 774.132-790.132 777.409-793.409 786.875-802.875
9 C#/Db 870.899-888.899 874.585-892.585 885.234-903.234
10 D 967.665-987.665 971.761-991.761 983.594-1003.594
11 D#/Eb 1064.432-1086.432 1068.9375-1090.9375 1081.953-1103.953
12 E 1161.198-1185.198 1166.114-1190.114 1180.312-1204.312
13 F 1257.965-1283.965 1263.29-1289.29 1278.672-1304.672

Phrygian-Aeolian Mode (intermediate minor)

Degrees Octatonic Intense Phrygian Intense Phrygian-Soft Aeolian Soft Aeolian
Min-Med/Min-Max±13¢ Med-Max±13¢ Min-Med/Min-Max±13¢ Med-Max±13¢ Min-Med/Min-Max±13¢ Med-Max±13¢
1 F#/Gb 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 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 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 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 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 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 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 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 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 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 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 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 1311.767-1337.767 1314.905-1340.905 1326.243-1352.243 1343.1645-1396.1645 1344.521-1370.521 1349.558-1375.558

Aeolian Mode (melodic/harmonic minor)

Degrees Octatonic Min-Med±13¢ Min-Max±13¢ Med-Max-13c
1 F#/Gb 105.256-107.256 106.11-108.11 107.738-109.738
2 G 210.511-214.511 212.22-216.22 215.477-219.477
3 G#/Ab 315.767-321.767 318.33-324.33 323.215-329.215
4 A 421.022-429.022 424.44-432.44 430.953-438.953
5 B 526.278-536.278 530.55-540.55 538.6915-548.6915
6 B#/Hb 631.534-643.534 636.6595-648.6595 646.43-658.43
7 H 736.789-750.789 742.769-756.769 754.168-768.168
8 C 842.045-858.045 848.879-864.879 861.906-877.906
9 C#/Db 947.3-965.3 954.989-972.989 969.645-986.645
10 D 1052.556-1072.556 1061.099-1081.099 1077.383-1077.383
11 D#/Eb 1157.8115-1179.8115 1167.209-1189.209 1185.121-1207.121
12 E 1264.067-1287.067 1273.319-1297.319 1292.86-1316.86
13 F 1368.322-1394.322 1379.429-1405.429 1400.598-1426.598