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-comma Median Maximum+comma Thirdtone Semitone
Minimum-comma Median Maximum+comma Minimum-comma Median Maximum+comma
1 G#/Ab 89.231-92.308 96.5035 93.626-99.78 97.436-97.582 95.385-101.978 99.692-100 101.5385-104.615
2 A 178.4615-184.615 193.007 187.253-199.56 194.872-195.165 190.769-203.956 199.385-200 203.077-209.231
3 A#/Bb 267.692-276.923 289.5105 280.879-299.341 292.308-292.747 286.154-305.934 299.077-300 304.615-313.846
4 B 356.923-369.231 386.014 374.5055-399.121 389.735-390.33 381.5385-407.912 398.769-400 406.154-418.4615
5 C 446.154-461.5385 482.5175 468.132-498.901 487.1795-487.912 476.923-509.89 498.4615-500 507.692-523.077
6 C#/Qb 535.385-553.846 579.021 561.758-598.681 584.615-585.4945 572.308-611.868 598.154-600 609.231-627.692
7 Q 624.615-646.154 675.5245 655.385-698.4615 682.051-683.077 667.692-713.846 697.846-700 710.769-732.308
8 D 713.846-738.4615 772.0228 749.011-798.242 779.487-780.659 763.077-815.824 797.5385-800 812.308-836.932
9 D#/Eb 802.077-830.769 868.5315 842.637-898.022 876.923-878.242 858.4615-917.802 897.231-900 913.846-941.5385
10 E 892.308-923.077 965.035 936.264-997.802 974.359-975.824 953.846-1019.78 996.923-1000 1015.385-1046.154
11 E#/Fb 981.5385-1015.385 1061.5385 1029.89-1097.582 1071.795-1073.407 1049.231-1121.758 1096.615-1100 1116.923-1150.769
12 F 1070.769-1107.692 1158.042 1123.363-1197.363 1169.231-1170.989 1144.615-1223.736 1196.308-1200 1218.4615-1255.385
13 G 1160-1200 1254.5455 1217.143-1297.143 1266.667-1268.571 1240-1325.714 1296-1300 1320-1360
Degrees Octatonic Intense Phrygian Intense Phrygian-Soft Aeolian Soft Aeolian
Minimum-comma Median Maximum+comma Minimum-comma Median Maximum+comma Minimum-comma Median Maximum+comma
1 F#/Gb G#/Ab 98.4615-101.5385 102.024 99.487-105.641 103.167 100.769-106.923 103.846 104.615 105.4945-108.571
2 G A 196.923-203.077 204.0485 198.974-211.282 206.335 201.5385-213.846 207.692 209.231 210.989-217.143
3 G#/Ab A#/Bb 295.385-304.615 306.073 298.4615-316.923 309.502 302.308-320.769 311.5385 313.846 316.4835-325.714
4 A B 393.846-406.154 408.097 397.949-422.564 412.67 403.077-427.692 415.385 418.4615 421.978-434.286
5 B C 492.308-507.692 510.1215 497.436-528.205 515.837 503.846-534.615 519.231 523.077 527.4725-542.857
6 B#/Hb C#/Qb 590.769-609.231 612.146 596.923-633.846 619.0045 604.615-641.5385 623.077 627.692 632.967-651.429
7 H Q 689.231-710.769 714.17 696.41-739.487 722.172 705.385-748.465 726.923 732.308 738.4615-760
8 C D 787.692-812.308 816.194 795.897-845.128 825.339 806.154-855.385 830.769 836.923 843.856-868.571
9 C#/Db D#/Eb 886.154-913.846 918.219 895.385-948.769 929.507 906.923-962.308 934.615 941.5385 949.4505-977.143
10 D E 984.615-1015.385 1020.243 994.872-1056.41 1031.674 1007.692-1069.231 1038.4615 1046.154 1054.945-1085.714
11 D#/Eb E#/Fb 1083.077-1116.923 1123.267 1094.359-1162.051 1134.842 1108.4615-1176.154 1142.308 1150.769 1160.44-1194.286
12 E F 1181.5385-1218.4615 1224.291 1193.846-1267.692 1238.009 1209.231-1283.077 1246.154 1255.385 1265.935-1302.857
13 F G 1280-1320 1326.316 1293.333-1373.333 1341.1765 1310-1390 1350 1360 1371.429-1411.429
Degrees Octatonic Aeolian Intense Aeolian
Flattone Meantone Superpyth Ultrapyth
Minimum-comma Median Maximum+comma Minimum-comma Median Maximum+comma Minimum-comma Median Maximum+comma Minimum-comma Median Maximum+comma
1 F#/Gb 102.418-105.4945 106.509 103.806-109.9595 107.077 104.615-110.769 107.692 108.597 106.014-112.168 109.615 110.769-113.846
2 G 204.835-210.989 213.018 207.611-219.919 214.154 209.231-221.5385 215.385 217.1945 212.028-224.336 219.231 221.5385-227.692
3 G#/Ab 307.253-316.4835 319.527 311.417-329.8785 321.231 313.846-332.308 323.077 325.792 318.042-336.5035 328.846 332.308-341.5385
4 A 409.67-421.978 426.036 415.223-439.838 428.308 418.4615-443.077 430.769 434.389 424.056-448.671 438.4615 443.077-455.385
5 B 512.088-527.4725 532.544 519.028-549.798 535.385 523.077-553.846 538.4615 542.986 530.07-560.839 548.077 553.846-569.231
6 B#/Hb 614.5055-632.967 639.053 622.834-659.757 642.4615 627.692-664.615 646.154 651.584 636.084-673.007 657.692 664.615-683.077
7 H 716.923-738.4615 745.562 726.64-769.717 749.5385 732.308-775.385 754.846 760.181 742.098-785.175 767.308 775.385-796.923
8 C 819.341-843.856 853.071 830.445-879.676 856.615 836.923-886.154 861.5385 868.778 848.112-897.343 876.923 886.154-910.769
9 C#/Db 921.758-949.4505 958.58 934.251-989.636 963.692 941.5385-996.923 969.231 977.376 954.126-1009.5105 986.5385 996.923-1024.615
10 D 1024.176-1054.945 1065.089 1038.057-1099.595 1070.769 1046.154-1107.692 1076.923 1085.973 1060.14-1121.678 1096.154 1107.692-1138.4615
11 D#/Eb 1126.593-1160.44 1171.598 1141.862-1209.555 1177.846 1150.769-1218.4685 1184.615 1194.57 1166.154-1233.846 1205.769 1218.4615-1252.308
12 E 1229.011-1265.934 1278.1065 1245.668-1319.514 1284.923 1255.385-1329.231 1292.308 1303.167 1272.168-1346.014 1315.385 1329.231-1366.154
13 F 1331.429-1371.429 1384.615 1349.474-1429.474 1392 1360-1440 1400 1411.765 1378.182-1458.182 1425 1440-1480

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
1 G#/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 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 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 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 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 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 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 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 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 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±13¢ Median Med-Max±13¢ Maximum Minimum Min-Med/Min-Max±13¢ Median Med-Max±13¢ Maximum
1 F#/Gb G#/Ab 100.905-102.905 101.1465-103.1465 102.019-104.019 103.167 102.32-104.32 103.846 103.425-105.425 104.615 103.812-105.812 105.4945
2 G A 201.81-205.81 202.293-206.293 204.037-208.037 206.335 204.641-208.641 207.692 206.849-210.849 209.231 207.624-211.624 210.989
3 G#/Ab A#/Bb 302.715-308.715 303.44-309.44 306.056-312.056 309.502 306.961-312.961 311.5385 310.274-316.274 313.846 311.4365-317.4365 316.4835
4 A B 403.62-411.62 404.586-412.586 408.075-416.075 412.67 409.281-417.281 415.385 413.699-421.699 418.4615 415.249-423.249 421.978
5 B C 504.525-514.525 505.733-515.733 510.093-520.093 515.837 511.602-521.602 519.231 517.123-527.123 523.077 519.061-529.061 527.4725
6 B#/Hb C#/Qb 605.43-617.43 606.879-618.879 612.112-624.112 619.0045 613.922-625.922 623.077 620.548-632.548 627.692 622.873-634.873 632.967
7 H Q 706.335-720.335 708.026-722.026 714.131-728.131 722.172 716.242-730.242 736.923 723.973-737.973 732.308 726.685-740.685 738.4615
8 C D 807.24-823.24 809.172-825.172 816.1495-832.1495 825.339 818.563-834.563 830.769 827.3975-843.3975 836.923 830.497-846.497 843.856
9 C#/Db D#/Eb 908.145-926.145 910.319-928.319 918.168-936.168 929.507 920.883-938.883 934.615 930.822-948.822 941.5385 934.309-952.309 949.4505
10 D E 1009.0505-1029.0505 1011.465-1031.465 1020.186-1040.186 1031.674 1023.2035-1043.2035 1038.4165 1034.247-1054.2547 1046.154 1038.122-1058.122 1054.945
11 D#/Eb E#/Fb 1109.9555-1131.9555 1112.61-1134.612 1122.2055-1143.2055 1134.842 1125.524-1147.524 1142.308 1137.672-1159.672 1150.769 1141.934-1163.934 1160.44
12 E F 1210.861-1234.861 1213.758-1227.758 1224.224-1248.224 1238.009 1225.844-1249.884 1246.154 1241.096-1265.096 1255.385 1245.746-1269.746 1265.935
13 F G 1311.767-1337.767 1314.905-1340.905 1326.243-1352.243 1341.1765 1343.1645-1396.1645 1350 1344.521-1370.521 1360 1349.558-1375.558 1371.429
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
1 F#/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 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 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 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 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 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 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 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 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 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