User:Moremajorthanmajor/16edX
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This is the scale which occurs as the dominant reformed Mixolydian mode.
Intervals
| Degrees | Enneatonic | Intense Aeolian-Subpental Dorian | Dorian | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Subpental | Pental | Superpental | |||||||||||||
| Min-comma | Med | Max+comma | Min-comma | Med | Max+comma | Min-comma | Med | Max+comma | Min-comma | Med | Max+comma | ||||
| 1 | 1#/2b | G#/Jb | G#/Ab | 88.125-90 | 91.071 | 89.792-93.542 | 92.308 | 91.875-95.625 | 95 | 93.5795-97.3295 | 95.833 | 96.429-98.304 | |||
| 2 | 2 | J | A | 176.25-180 | 182.143 | 179.583-187.083 | 184.615 | 183.75-191.25 | 190 | 187.159-194.659 | 191.667 | 192.857-196.607 | |||
| 3 | 2#/3b | J#/Ab | A#/Bb | 264.375-270 | 273.214 | 269.375-280.625 | 276.923 | 275.625-286.875 | 285 | 280.739-291.989 | 287.5 | 289.286-294.911 | |||
| 4 | 3 | J | B | 352.5-360 | 364.286 | 358.167-373.167 | 369.231 | 367.5-382.5 | 380 | 374.318-389.318 | 383.333 | 385.714-393.214 | |||
| 5 | 3#/4b | J#/Ab | B#/Cb | 440.625-450 | 455.357 | 448.958-467.708 | 461.5385 | 459.375-476.125 | 475 | 467.898-486.648 | 479.167 | 482.143-491.518 | |||
| 6 | 4 | A | C | 528.75-540 | 546-429 | 538.75-561.25 | 553.846 | 551.25-573.75 | 570 | 561.477-583.977 | 575 | 578.571-589.821 | |||
| 7 | 5 | A#/Bb | C#/Qb | 616.875-630 | 637.5 | 628.542-654.792 | 646.154 | 643.125-669.375 | 665 | 655.057-681.307 | 670.833 | 675-688.125 | |||
| 8 | 5#/6b | B | Q | 705-720 | 728.571 | 718.333-748.333 | 738.4615 | 735-765 | 760 | 748.636-778.636 | 766.667 | 771.429-786.429 | |||
| 9 | 6 | C | D | 793.125-810 | 819.642 | 808.125-841.875 | 830.769 | 826.875-860.625 | 855 | 842.216-875.966 | 862.5 | 867.857-884.732 | |||
| 10 | 6#/7b | C#/Db | D#/Sb | 881.25-900 | 910.714 | 897.917-935.417 | 923.071 | 918.75-956.25 | 950 | 935.7975-973.2975 | 958.333 | 964.286-983.036 | |||
| 11 | 7 | D | S | 969.375-990 | 1001.786 | 987.708-1028.958 | 1015.385 | 1010.625-1051.875 | 1045 | 1029.375-1070.605 | 1054.167 | 1060.714-1081.239 | |||
| 12 | 7#/8b | D#/Eb | S#/Eb | 1057.5-1080 | 1092.857 | 1077.5-1122.5 | 1107.692 | 1102.5-1147.5 | 1140 | 1122.9545-1167.9545 | 1150 | 1157.143-1179.643 | |||
| 13 | 8 | E | 1145.625-1170 | 1183.929 | 1167.292-1216.042 | 1200 | 1194.375-1241.125 | 1235 | 1216.534-1265.284 | 1245.833 | 1253.571-1277.946 | ||||
| 14 | 8#/9b | E#/Fb | 1233.75-1260 | 1275 | 1257.083-1309.583 | 1292.308 | 1286.25-1338.75 | 1330 | 1310.114-1362.614 | 1341.667 | 1350-1376.25 | ||||
| 15 | 9 | F | 1321.875-1350 | 1366.071 | 1346.875-1403.125 | 1384.615 | 1378.125-1434.375 | 1425 | 1403.693-1459.943 | 1437.5 | 1446.429-1474.554 | ||||
| 16 | 1 | G | 1410-1440 | 1457.143 | 1436.667-1496.667 | 1476.923 | 1470-1530 | 1520 | 1497.273-1557.273 | 1533.333 | 1542.857-1572.857 | ||||
| Degrees | Enneatonic | Mohajira | Beatles | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Min-comma | r¢ | Med | Max+comma | Min-comma | Med | Max+comma | ||||||
| 1 | 1#/2b | F#/Gb | G#/Jb | G#/Ab | 94.554-96.429 | 96.875 | 95.184-98.934 | 97.222 | 97.5-99.375 | |||
| 2 | 2 | G | J | A | 189.107-192.857 | 193.75 | 190.368-197.868 | 194.444 | 195-198.75 | |||
| 3 | 2#/3b | G#/Jb | G#/Ab | J#/Ab | A#/Bb | 283.661-289.286 | 290.625 | 285.5515-296.8015 | 291.667 | 292.5-298.125 | ||
| 4 | 3 | J | A | J | B | 378.214-385.714 | 387.5 | 380.735-395.735 | 388.889 | 390-397.5 | ||
| 5 | 3#/4b | J#/Ab | A#/Bb | J#/Ab | B#/Cb | 472.767-482.143 | 484.375 | 475.919-494.669 | 486.111 | 487.5-496.875 | ||
| 6 | 4 | A | B | A | C | 567.321-578.571 | 581.25 | 571.103-593.603 | 583.333 | 585-596.25 | ||
| 7 | 5 | B | H | A#/Bb | C#/Qb | 661.875-675 | 678.125 | 666.287-692.537 | 680.556 | 682.5-695.625 | ||
| 8 | 5#/6b | B#/Hb | H#/Cb | B | Q | 756.429-771.429 | 775 | 761.471-791.471 | 777.778 | 780-795 | ||
| 9 | 6 | H | C | C | D | 850.982-867.857 | 871.875 | 856.654-890.404 | 875 | 877.5-894.375 | ||
| 10 | 6#/7b | H#/Cb | C#/Db | C#/Db | D#/Sb | 945.536-964.286 | 968.75 | 951.738-989.238 | 972.222 | 975-993.75 | ||
| 11 | 7 | C | D | D | S | 1040.089-1060.714 | 1065.625 | 1047.022-1088.252 | 1069.444 | 1072.5-1093.125 | ||
| 12 | 7#/8b | C#/Db | D#/Sb | D#/Eb | S#/Eb | 1134.643-1157.143 | 1162.5 | 1142.203-1187.206 | 1166.667 | 1170-1192.5 | ||
| 13 | 8 | D | S | E | 1229.196-1253.571 | 1259.375 | 1237.39-1286.14 | 1263.889 | 1267.5-1291.875 | |||
| 14 | 8#/9b | D#/Eb | S#/Eb | E#/Fb | 1323.75-1350 | 1356.25 | 1332.5735-1385.0735 | 1361.111 | 1365-1391.25 | |||
| 15 | 9 | E | F | 1418.304-1446.429 | 1453.125 | 1427.757-1484.007 | 1458.333 | 1462.5-1490.625 | ||||
| 16 | 1 | F | G | 1512.857-1542.857 | 1550 | 1522.941-1582.941 | 1555.556 | 1560-1590 | ||||
| Degrees | Enneatonic | Mixolydian | Mixolydian-Ionian | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Subpental | Pental | Superpental | ||||||||||||||||
| Soft | Intense | |||||||||||||||||
| Min-comma | Med | Max+comma | Min-comma | Med | Max+comma | Min-comma | Med | Max+comma | Min-comma | Med | Max+comma | Min-comma | Med | Max+comma | ||||
| 1 | 1#/2b | F#/Gb | 95.625-97.5 | 98.077 | 96.5625-100.3125 | 98.684 | 98.125-101.875 | 100.781 | 98.987-102.737 | 102.155 | 101.573-105.323 | 103.6765 | 105-106.875 | |||||
| 2 | 2 | G | 191.25-195 | 196.154 | 193.125-200.625 | 197.368 | 196.25-203.75 | 201.5625 | 197.974-205.474 | 204.31 | 203.147-210.647 | 207.353 | 210-213.75 | |||||
| 3 | 2#/3b | G#/Jb | G#/Ab | 286.875-292.5 | 294.231 | 289.6875-300.9375 | 296.053 | 294.375-305.625 | 302.344 | 296.961-308.211 | 306.4655 | 304.72-315.97 | 311.029 | 315-320.625 | ||||
| 4 | 3 | J | A | 382.5-390 | 392.308 | 386.25-401.25 | 394.737 | 392.5-407.5 | 403.125 | 395.948-410.948 | 408.621 | 406.293-421.293 | 414.706 | 420-427.5 | ||||
| 5 | 3#/4b | J#/Ab | A#/Bb | 478.125-487.5 | 490.385 | 482.8125-501.5625 | 493.421 | 490.625-509.375 | 503.906 | 494.935-513.685 | 510.776 | 507.866-526.616 | 518.382 | 525-534.375 | ||||
| 6 | 4 | A | B | 573.75-585 | 588.4615 | 579.375-601.875 | 592.105 | 588.75-611.25 | 604.6875 | 593.922-616.422 | 612.931 | 609.44-631.94 | 622.059 | 630-641.25 | ||||
| 7 | 5 | B | H | 669.375-682.5 | 686.5385 | 675.9375-702.1875 | 690.7895 | 687.875-713.125 | 705.469 | 692.9095-719.1595 | 715.086 | 711.012-737.262 | 725.735 | 735-748.125 | ||||
| 8 | 5#/6b | B#/Hb | H#/Cb | 765-780 | 784.615 | 772.5-802.5 | 789.474 | 785-815 | 806.25 | 791.897-821.897 | 817.241 | 812.586-842.586 | 829.412 | 840-855 | ||||
| 9 | 6 | H | C | 860.625-877.5 | 882.962 | 869.0625-903.8125 | 888.158 | 883.125-916.875 | 907.031 | 890.884-924.624 | 919.397 | 914.1595-947.9095 | 933.088 | 945-961.875 | ||||
| 10 | 6#/7b | H#/Cb | C#/Db | 956.25-975 | 980.769 | 965.625-1003.125 | 986.842 | 981.25-1018.75 | 1007.8125 | 989.871-1027.371 | 1021.552 | 1015.733-1053.233 | 1036.765 | 1050-1068.75 | ||||
| 11 | 7 | C | D | 1051.875-1072.5 | 1078.846 | 1062.1875-1103.4375 | 1085.526 | 1079.375-1120.625 | 1108.594 | 1088.858-1130.108 | 1123.707 | 117.306-1158.556 | 1140.441 | 1155-1175.625 | ||||
| 12 | 7#/8b | C#/Db | D#/Sb | 1147.5-1170 | 1176.923 | 1158.75-1203.75 | 1184.2105 | 1177.5-1222.5 | 1209.375 | 1187.845-1232.845 | 1225.862 | 1218.879-1263.879 | 1244.118 | 1260-1282.5 | ||||
| 13 | 8 | D | S | 1243.125-1267.5 | 1275 | 1255.3125-1304.0625 | 1282.895 | 1275.625-1324.325 | 1310.156 | 1286.832-1335.585 | 1328.017 | 1320.453-1369.203 | 1347.794 | 1365-1389.375 | ||||
| 14 | 8#/9b | D#/Eb | S#/Eb | 1338.25-1365 | 1373.077 | 1351.875-1404.375 | 1381.579 | 1373.75-1426.25 | 1410.9375 | 1385.819-1438.319 | 1430.172 | 1422.026-1474.526 | 1451.471 | 1470-1496.25 | ||||
| 15 | 9 | E | 1434.375-1462.5 | 1471.154 | 1448.4375-1504.6875 | 1480.263 | 1471.875-1528.125 | 1511.719 | 1484.806-1541.056 | 1532.328 | 1523.599-1579.849 | 1555.147 | 1575-1603.125 | |||||
| 16 | 1 | F | 1530-1560 | 1569.231 | 1545-1605 | 1578.947 | 1570-1630 | 1612.5 | 1583.793-1643.793. | 1634.483 | 1625.172-1685.172 | 1658.8235 | 1680-1710 | |||||
Relative cents
| Degrees | Enneatonic | Intense Aeolian-Subpental Dorian | Dorian | ||
|---|---|---|---|---|---|
| 1 | 1#/2b | G#/Jb | G#/Ab | 90.625 | 93.75 |
| 2 | 2 | J | A | 181.25 | 187.5 |
| 3 | 2#/3b | J#/Ab | A#/Bb | 271.875 | 281.25 |
| 4 | 3 | J | B | 362.5 | 375 |
| 5 | 3#/4b | J#/Ab | B#/Cb | 453.125 | 468.75 |
| 6 | 4 | A | C | 543.75 | 562.5 |
| 7 | 5 | A#/Bb | C#/Qb | 633.375 | 656.25 |
| 8 | 5#/6b | B | Q | 725 | 750 |
| 9 | 6 | C | D | 815.625 | 843.75 |
| 10 | 6#/7b | C#/Db | D#/Sb | 906.25 | 937.5 |
| 11 | 7 | D | S | 996.875 | 1031.25 |
| 12 | 7#/8b | D#/Eb | S#/Eb | 1087.5 | 1125 |
| 13 | 8 | E | 1178.125 | 1218.75 | |
| 14 | 8#/9b | E#/Fb | 1268.75 | 1312.5 | |
| 15 | 9 | F | 1359.375 | 1406.25 | |
| 16 | 1 | G | 1450 | 1500 | |
| Degrees | Enneatonic | Subpental-Soft Superpental Mixolydian | Intense Superpental Mixolydian ~ Mixolydian-Ionian | ||
|---|---|---|---|---|---|
| 1 | 1#/2b | F#/Gb | 100 | 103.125 | |
| 2 | 2 | G | 200 | 206.25 | |
| 3 | 2#/3b | G#/Jb | G#/Ab | 300 | 309.375 |
| 4 | 3 | J | A | 400 | 412.5 |
| 5 | 3#/4b | J#/Ab | A#/Bb | 500 | 515.625 |
| 6 | 4 | A | B | 600 | 618.75 |
| 7 | 5 | B | H | 700 | 721.875 |
| 8 | 5#/6b | B#/Hb | H#/Cb | 800 | 825 |
| 9 | 6 | H | C | 900 | 928.125 |
| 10 | 6#/7b | H#/Cb | C#/Db | 1000 | 1031.25 |
| 11 | 7 | C | D | 1100 | 1134.375 |
| 12 | 7#/8b | C#/Db | D#/Sb | 1200 | 1237.5 |
| 13 | 8 | D | S | 1300 | 1340.625 |
| 14 | 8#/9b | D#/Eb | S#/Eb | 1400 | 1443.75 |
| 15 | 9 | E | 1500 | 1546.875 | |
| 16 | 1 | F | 1600 | 1650 | |
Golden/Pyrite Tunings±13¢
| Degrees | Enneatonic | Intense Aeolian-Subpental Dorian | Dorian | ||||
|---|---|---|---|---|---|---|---|
| Subpental | Pental | Superpental | |||||
| 1 | 1#/2b | G#/Jb | G#/Ab | 90.428-92.053 | 91.303-92.928 | 94.329-95.943 | 94.917-96.542 |
| 2 | 2 | J | A | 180.856-184.106 | 182.606-185.856 | 188.2585-191.9085 | 189.834-193.084 |
| 3 | 2#/3b | J#/Ab | A#/Bb | 271.2845-276.159 | 273.909-278.784 | 282.988-287.863 | 284.751-289.626 |
| 4 | 3 | J | B | 361.712-368.213 | 365.212-371.712 | 377.317-383.817 | 379.668-386.168 |
| 5 | 3#/4b | J#/Ab | B#/Cb | 452.141-460.266 | 456.5155-464.6405 | 471.646-479.771 | 474.585-482.71 |
| 6 | 4 | A | C | 542.569-552.319 | 547.819-557.569 | 565.974-575.726 | 569.502-579.252 |
| 7 | 5 | A#/Bb | C#/Qb | 632.997-644.372 | 639.122-650.497 | 660.305-671.68 | 664.419-675.794 |
| 8 | 5#/6b | B | Q | 723.425-736.425 | 730.425-743.425 | 754.634-767.634 | 759.336-771.336 |
| 9 | 6 | C | D | 813.854-828.479 | 821.728-836.353 | 848.963-863.588 | 854.253-868.878 |
| 10 | 6#/7b | C#/Db | D#/Sb | 904.282-920.532 | 913.031-920.281 | 943.293-959.543 | 949.17-965.42 |
| 11 | 7 | D | S | 994.71-1012.585 | 1004.334-1022.209 | 1037.622-1055.497 | 1044.087-1061.962 |
| 12 | 7#/8b | D#/Eb | S#/Eb | 1085.138-1104.638 | 1095.637-1115.137 | 1131.951-1151.451 | 1139.004-1158.503 |
| 13 | 8 | E | 1175.566-1106.691 | 1186.94-1208.065 | 1226.38-1247.405 | 1233.921-1255.046 | |
| 14 | 8#/9b | E#/Fb | 1265.9945-1288.7445 | 1278.2435-1300.9935 | 1320.61-1343.36 | 1328.838-1351.588 | |
| 15 | 9 | F | 1356.423-1380.798 | 1369.547-1393.922 | 1414.939-1439.314 | 1423.755-1448.13 | |
| 16 | 1 | G | 1446.851-1472.851 | 1460.85-1486.85 | 1509.268-1535.268 | 1518.672-1544.672 | |
| Degrees | Enneatonic | Mohajira | Beatles | ||||
|---|---|---|---|---|---|---|---|
| 1 | 1#/2b | F#/Gb | G#/Jb | G#/Ab | 96.1185-97.7435 | 96.364-97.989 | |
| 2 | 2 | G | J | A | 192.237-195.487 | 192.728-195.978 | |
| 3 | 2#/3b | G#/Jb | G#/Ab | J#/Ab | A#/Bb | 288.355-293.23 | 289.092-293.965 |
| 4 | 3 | J | A | J | B | 384.474-390.974 | 385.456-391.956 |
| 5 | 3#/4b | J#/Ab | A#/Bb | J#/Ab | B#/Cb | 480.592-488.717 | 481.82-489.945 |
| 6 | 4 | A | B | A | C | 576.711-585.961 | 578.184-587.934 |
| 7 | 5 | B | H | A#/Bb | C#/Qb | 672.829-684.454 | 674.548-685.923 |
| 8 | 5#/6b | B#/Hb | H#/Cb | B | Q | 768.948-781.948 | 770.912-783.912 |
| 9 | 6 | H | C | C | D | 865.066-879.691 | 867.276-881.901 |
| 10 | 6#/7b | H#/Cb | C#/Db | C#/Db | D#/Sb | 961.185-977.435 | 963.6395-979.8895 |
| 11 | 7 | C | D | D | S | 1057.303-1075.178 | 1060.0035-1077.8785 |
| 12 | 7#/8b | C#/Db | D#/Sb | D#/Eb | S#/Eb | 1153.422-1172.921 | 1156.367-1175.867 |
| 13 | 8 | D | S | E | 1249.54-1270.665 | 1252.731-1273.856 | |
| 14 | 8#/9b | D#/Eb | S#/Eb | E#/Fb | 1345.659-1368.409 | 1349.095-1372.345 | |
| 15 | 9 | E | F | 1441.777-1366.152 | 1445.459-1469.834 | ||
| 16 | 1 | F | G | 1537.8955-1563.8955 | 1541.823-1577.823 | ||
| Degrees | Enneatonic | Mixolydian | Mixolydian-Ionian | |||||
|---|---|---|---|---|---|---|---|---|
| Subpental | Pental | Superpental | ||||||
| Soft | Intense | |||||||
| 1 | 1#/2b | F#/Gb | 97.364-98.989 | 97.787-99.412 | 99.998-101.623 | 101.648-103.273 | 102.785-104.41 | |
| 2 | 2 | G | 194.7275-197.9775 | 195.5745-198.8245 | 199.9955-203.2455 | 203.296-206.546 | 205.57-208.82 | |
| 3 | 2#/3b | G#/Jb | G#/Ab | 292.091-296.966 | 293.362-298.237 | 299.993-304.868 | 304.944-309.819 | 308.356-313.231 |
| 4 | 3 | J | A | 389.455-395.955 | 391.149-397.649 | 399.991-406.491 | 406.592-413.092 | 411.141-417.641 |
| 5 | 3#/4b | J#/Ab | A#/Bb | 486.819-494.944 | 488.936-497.061 | 499.989-508.114 | 508.24-516.365 | 513.926-522.051 |
| 6 | 4 | A | B | 584.183-593.933 | 586.724-596.474 | 599.987-609.737 | 609.888-619.638 | 616.711-626.461 |
| 7 | 5 | B | H | 681.546-692.921 | 684.571-695.886 | 699.984-711.359 | 711.5355-722.9105 | 719.496-730.871 |
| 8 | 5#/6b | B#/Hb | H#/Cb | 778.91-791.91 | 782.298-795.298. | 799.982-812.982 | 813.1835-826.1835 | 822.282-835.282 |
| 9 | 6 | H | C | 876.274-890.899 | 880.085-894.71 | 899.98-914.605 | 914.831-929.456 | 925.067-939.692 |
| 10 | 6#/7b | H#/Cb | C#/Db | 973.638-989.888 | 977.873-994.123 | 999.978-1016.238 | 1016.479-1032.729 | 1027.852-1044.102 |
| 11 | 7 | C | D | 1071.0015-1088.8765 | 1075.66-1093.535 | 1099.975-1117.85 | 1118.127-1136.002 | 1130.637-1148.512 |
| 12 | 7#/8b | C#/Db | D#/Sb | 1168.365-1187.865 | 1173.447-1192.947 | 1199.973-1219.473 | 1219.775-1239.275 | 1233.422-1252.922 |
| 13 | 8 | D | S | 1265.729-1286.854 | 1271.234-1292.359 | 1299.971-1321.096 | 1321.423-1342.548 | 1336.208-1357.333 |
| 14 | 8#/9b | D#/Eb | S#/Eb | 1363.093-1385.843 | 1369.022-1391.772 | 1399.968-1422.719 | 1423.071-1445.821 | 1438.993-1461.743 |
| 15 | 9 | E | 1460.457-1484.832 | 1455.809-1491.184 | 1499.9665-1524.3415 | 1524.719-1549.094 | 1541.778-1566.153 | |
| 16 | 1 | F | 1557.82-1583.82 | 1564.596-1590.596 | 1599.964-1625.964 | 1626.366-1652.366 | 1644.563-1670.563 | |
By a surprising coincidence, neutral 16edX turns out to be a false Pelogic temperament with a very pure 5:4 (mistuned by no more than 3.686 cents), and tuning 5:3 pure creates a tenth almost exactly equal to 38/29edo or almost exactly the Golden Subpental Mixolydian step or every ninth step of 110edo, and tuning 4:3 pure creates an almost exact 43/74edo fifth. Also, the Golden Soft Superpental Mixolydian step is almost exactly (25/24)^(10/7) and tuning 12:7 pure creates almost exactly the Golden Mixolydian-Ionian step.