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 |