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 Soft Phrygian Phrygian
Minimum Median Maximum Minimum Median 15/7±13¢ Maximum
1 G#/Ab 92.308 96.5035 96.703 98.263 100.496-102.496 101.5385
2 A 184.615 193.007 193.407 196.526 200.991-204.912 203.077
3 A#/Bb 276.923 289.5105 290.11 294.789 301.487-307.487 304.615
4 B 369.231 386.014 386.813 393.052 401.982-409.982 406.154
5 C 461.5385 482.5175 483.5165 491.315 502.478-512.478 507.692
6 C#/Qb 553.846 579.021 580.22 589.578 602.974-614.974 609.231
7 Q 646.154 675.5245 676.923 687.841 703.469-717.469 710.769
8 D 738.4615 772.0228 773.626 786.104 803.965-819.965 812.308
9 D#/Eb 830.769 868.5315 870.33 884.367 904.46-922.46 913.846
10 E 923.077 965.035 967.033 982.63 1004.956-1024.956 1015.385
11 E#/Fb 1015.385 1061.5385 1063.736 1080.893 1105.452-1127.452 1116.923
12 F 1107.692 1158.042 1160.4395 1179.156 1205.947-1299.947 1218.4615
13 G 1200 1254.5455 1257.143 1277.419 1306.443-1332.443 1320
Degrees Octatonic Intense Phrygian Intense Phrygian-Soft Aeolian Soft Aeolian
Minimum Median Maximum Minimum Median Maximum Minimum Median 11/5±13¢ Maximum
1 F#/Gb G#/Ab 101.5385 102.024 102.564 103.167 103.846 104.615 104-106 105.4945
2 G A 203.077 204.0485 205.128 206.335 207.692 209.231 208.001-212.001 210.989
3 G#/Ab A#/Bb 304.615 306.073 307.692 309.502 311.5385 313.846 312.001-318.001 316.4835
4 A B 406.154 408.097 410.256 412.67 415.385 418.4615 416.001-424.001 421.978
5 B C 507.692 510.1215 512.8205 515.837 519.231 523.077 520.002-530.002 527.4725
6 B#/Hb C#/Qb 609.231 612.146 615.384 619.0045 623.077 627.692 624.002-636.002 632.967
7 H Q 710.769 714.17 717.945 722.172 736.923 732.308 728.002-742.0022 738.4615
8 C D 812.308 816.194 820.513 825.339 830.769 836.923 832.003-848.002 843.856
9 C#/Db D#/Eb 913.846 918.219 923.077 929.507 934.615 941.5385 936.003-924.003 949.4505
10 D E 1015.385 1020.243 1025.641 1031.674 1038.4165 1046.154 1040.003-1060.003 1054.945
11 D#/Eb E#/Fb 1116.923 1123.267 1128.205 1134.842 1142.308 1150.769 1144.004-1166.004 1160.44
12 E F 1218.4615 1224.291 1230.769 1238.009 1246.154 1255.385 1248.004-1272.004 1265.935
13 F G 1320 1326.316 1333.333 1341.1765 1350 1360 1352.004-1378.004 1371.429
Degrees Octatonic Aeolian Intense Aeolian
Minimum Median Maximum Minimum 9/4±13¢ Median Maximum
1 F#/Gb 105.4945 106.509 107.692 106.993-108.993 109.091 110.769
2 G 210.989 213.018 215.385 213.986-217.986 218.182 221.5385
3 G#/Ab 316.4835 319.527 323.077 320.979-326.979 327.273 332.308
4 A 421.978 426.036 430.769 427.972-435.972 436.364 443.076
5 B 527.4725 532.544 538.4615 534.965-544.965 545.4545 553.846
6 B#/Hb 632.967 639.053 646.154 641.9585-653.9585 654.5455 664.615
7 H 738.4615 745.562 754.846 748.9515-762.9515 763.636 775.385
8 C 843.856 853.071 861.5385 855.945-871.945 872.727 886.154
9 C#/Db 949.4505 958.58 969.231 962.938-980.938 981.818 996.923
10 D 1054.945 1065.089 1076.923 1069.931-1089.931 1090.909 1107.692
11 D#/Eb 1160.44 1171.598 1184.615 1177-924-1199.924 1200 1218.4615
12 E 1265.9344 1278.1065 1292.308 1283.917-1307.917 1309.094 1329.231
13 F 1371.429 1384.615 1400 1390.91-1416.91 1418.182 1440

Golden Tunings

Phrygian Mode (Neapolitan minor/"major")

Degrees Octatonic Soft Phrygian Phrygian
Min-Med±13¢ Min-Max/Med-Max±13¢ Min-Med±13¢ Min-Max±13¢ Med-Max±13¢
1 G#/Ab 95.389-97.389 95.578-97.578 96.7665-98.7665 97.176-99.176 98.359-100.359
2 A 190.778-194.778 191.155-195.155 193.533-197.533 194.352-198.352 196.719-200.719
3 A#/Bb 286.1665-292.1665 286.733-292.733 290.2995-296.2995 291.528-297.528 295.078-301.078
4 B 381.555-389.555 382.3105-390.3105 387.063-395.063 388.705-396.705 393.4375-401.4375
5 C 476.944-486.944 477.888-487.888 483.833-493.833 485.881-495.881 491.797-501.797
6 C#/Qb 572.333-584.333 573.466-585.466 580.299-592.299 583.057-595.057 590.156-602.156
7 Q 667.722-681.722 669.043-683.043 677.366-691.366 680.233-694.233 688.516-702.516
8 D 763.111-781.111 764.621-780.621 774.132-790.132 777.409-793.409 786.875-802.875
9 D#/Eb 858.5-876.5 860.199-878.199 870.899-888.899 874.585-892.585 885.234-903.234
10 E 953.8885-973.8885 955.776-975.776 967.665-987.665 971.761-991.761 983.594-1003.594
11 E#/Fb 1049.277-1071.277 1051.354-1073.354 1064.432-1086.432 1068.9375-1090.9375 1081.953-1103.953
12 F 1144.666-1168.666 1146.932-1170.932 1161.198-1185.198 1166.114-1190.114 1180.312-1204.312
13 G 1240.055-1266.055 1242.506-1268.509 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 G#/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 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 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 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 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 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 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 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 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 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 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 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 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 (natural/harmonic minor)

Degrees Octatonic Aeolian Intense Aeolian
Min-Med/Min-Max±13¢ Med-Max-13c Min-Med/Min-Max±13¢ Med-Max-13c
1 F#/Gb 105.256-107.256 105.7715-107.7715 107.738-109.738 108.459-110.459
2 G 210.511-214.511 211.543-215.543 215.477-219.477 216.918-220.918
3 G#/Ab 315.767-321.767 317.315-323.315 323.215-329.215 325.377-331.377
4 A 421.022-429.022 423.086-431.086 430.953-438.953 433.836-437.836
5 B 526.278-536.278 528.858-538.858 538.6915-548.6915 542.295-552.295
6 B#/Hb 631.534-643.534 634.629-646.629 646.43-658.43 650.754-666.754
7 H 736.789-750.789 740.401-754.401 754.168-768.168 759.213-773.213
8 C 842.045-858.045 846.172-862.172 861.906-877.906 867.672-883.672
9 C#/Db 947.3-965.3 951.944-969.944 969.645-986.645 976.131-994.131
10 D 1052.556-1072.556 1057.715-1077.715 1077.383-1077.383 1084.59-1104.59
11 D#/Eb 1157.8115-1179.8115 1163.487-1187.487 1185.121-1207.121 1193.049-1215.049
12 E 1264.067-1287.067 1269.258-1293.258 1292.86-1316.86 1301.508-1325.508
13 F 1368.322-1394.322 1375.03-1401.03 1400.598-1426.598 1409.967-1435.967
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