User:Moremajorthanmajor/16edX
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16edX 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 | 87.5-90 | 91.071 | 89.167-94.167 | 92.308 | 91.25-96.25 | 95 | 92.9545-97.9545 | 95.833 | 96.429-98.929 | |||
2 | 2 | J | A | 175-180 | 182.143 | 178.333-188.333 | 184.615 | 182.5-192.5 | 190 | 185.909-195.909 | 191.667 | 192.857-197.857 | |||
3 | 2#/3b | J#/Ab | A#/Bb | 262.5-270 | 273.214 | 267.5-282.5 | 276.923 | 273.75-288.75 | 285 | 278.864-293.864 | 287.5 | 289.286-296.786 | |||
4 | 3 | A | B | 350-360 | 364.286 | 356.667-376.667 | 369.231 | 365-385 | 380 | 371.818-391.818 | 383.333 | 385.714-395.714 | |||
5 | 3#/4b | A#/Bb | B#/Cb | 437.5-450 | 455.357 | 445.833-470.833 | 461.5385 | 456.25-481.25 | 475 | 464.773-489.773 | 479.167 | 482.143-494.643 | |||
6 | 4 | B | C | 525-540 | 546-429 | 535-565 | 553.846 | 547.5-577.5 | 570 | 557.727-587.727 | 575 | 578.571-593.571 | |||
7 | 5 | C | Q | 612.5-630 | 637.5 | 624.167-659.167 | 646.154 | 638.75-673.75 | 665 | 650.682-685.682 | 670.833 | 675-692.5 | |||
8 | 5#/6b | C#/Qb | Q#/Db | 700-720 | 728.571 | 713.333-753.333 | 738.4615 | 730-770 | 760 | 743.636-783.636 | 766.667 | 771.429-791.429 | |||
9 | 6 | Q | D | 787.5-810 | 819.642 | 802.5-847.5 | 830.769 | 821.25-856.25 | 855 | 836.591-875.591 | 862.5 | 867.857-890.357 | |||
10 | 6#/7b | Q#/Db | D#/Sb | 875-900 | 910.714 | 891.667-941.667 | 923.071 | 912.5-962.5 | 950 | 929.5455-979.5455 | 958.333 | 964.286-989.286 | |||
11 | 7 | D | S | 962.5-990 | 1001.786 | 980.833-1035.833 | 1015.385 | 1003.75-1058.75 | 1045 | 1022.5-1077.5 | 1054.167 | 1060.714-1088.214 | |||
12 | 7#/8b | D#/Eb | S#/Eb | 1050-1080 | 1092.857 | 1070-1130 | 1107.692 | 1095-1155 | 1140 | 1115.4545-1175.4545 | 1150 | 1157.143-1187.143 | |||
13 | 8 | E | 1137.5-1170 | 1183.929 | 1159.167-1224.167 | 1200 | 1186.25-1251.25 | 1235 | 1208.409-1273.409 | 1245.833 | 1253.571-1286.071 | ||||
14 | 8#/9b | E#/Fb | 1225-1260 | 1275 | 1248.333-1318.333 | 1292.308 | 1277.5-1347.5 | 1330 | 1301.364-1371.364 | 1341.667 | 1350-1385 | ||||
15 | 9 | F | 1312.5-1350 | 1366.071 | 1337.5-1412.5 | 1384.615 | 1368.75-1443.75 | 1425 | 1394.318-1469.318 | 1437.5 | 1446.429-1483.929 | ||||
16 | 1 | G | 1400-1440 | 1457.143 | 1426.667-1506.667 | 1476.923 | 1460-1540 | 1520 | 1487.273-1567.273 | 1533.333 | 1542.857-1582.857 |
Degrees | Enneatonic | Mohajira | Beatles | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Min-comma | r¢ | Med | Max+comma~Min-comma | Med | Max+comma | |||||||
1 | 1#/2b | F#/Gb | G#/Jb | G#/Ab | 93.929-96.429 | 96.875 | 94.559-99.559 | 97.222 | 97.5-100 | |||
2 | 2 | G | J | A | 187.857-192.857 | 193.75 | 189.118-199.118 | 194.444 | 195-200 | |||
3 | 2#/3b | G#/Jb | G#/Ab | J#/Ab | A#/Bb | 281.786-289.286 | 290.625 | 283.6765-298.6765 | 291.667 | 292.5-300 | ||
4 | 3 | J | A | J | B | 375.714-385.714 | 387.5 | 378.235-398.235 | 388.889 | 390-400 | ||
5 | 3#/4b | J#/Ab | A#/Bb | J#/Ab | B#/Cb | 469.643-482.143 | 484.375 | 472.794-497.794 | 486.111 | 487.5-500 | ||
6 | 4 | A | B | A | C | 563.571-578.571 | 581.25 | 567.353-597.353 | 583.333 | 585-600 | ||
7 | 5 | B | H | A#/Bb | C#/Qb | 657.5-675 | 678.125 | 661.912-696.912 | 680.556 | 682.5-700 | ||
8 | 5#/6b | B#/Hb | H#/Cb | B | Q | 751.429-771.429 | 775 | 756.471-796.471 | 777.778 | 780-800 | ||
9 | 6 | H | C | C | D | 845.357-867.857 | 871.875 | 851.029-895.029 | 875 | 877.5-900 | ||
10 | 6#/7b | H#/Cb | C#/Db | C#/Db | D#/Sb | 939.286-964.286 | 968.75 | 945.588-995.588 | 972.222 | 975-1000 | ||
11 | 7 | C | D | D | S | 1033.214-1060.714 | 1065.625 | 1040.147-1095.147 | 1069.444 | 1072.5-1100 | ||
12 | 7#/8b | C#/Db | D#/Sb | D#/Eb | S#/Eb | 1127.143-1157.143 | 1162.5 | 1134.706-1194.706 | 1166.667 | 1170-1200 | ||
13 | 8 | D | S | E | 1223.071-1253.571 | 1259.375 | 1229.265-1294.265 | 1263.889 | 1267.5-1300 | |||
14 | 8#/9b | D#/Eb | S#/Eb | E#/Fb | 1315-1350 | 1356.25 | 1323.8235-1393.8235 | 1361.111 | 1365-1400 | |||
15 | 9 | E | F | 1408.929-1446.429 | 1453.125 | 1418.382-1493.382 | 1458.333 | 1462.5-1500 | ||||
16 | 1 | F | G | 1502.857-1542.857 | 1550 | 1512.941-1592.941 | 1555.556 | 1560-1600 |
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 | 95-97.5 | 98.077 | 95.9375-100.9375 | 98.684 | 97.5-102.5 | 100.781 | 98.362-103.362 | 102.155 | 100.948-105.948 | 103.6765 | 105-107.5 | |||||
2 | 2 | G | 190-195 | 196.154 | 191.875-201.875 | 197.368 | 195-205 | 201.5625 | 196.724-206.724 | 204.31 | 201.897-211.897 | 207.353 | 210-215 | |||||
3 | 2#/3b | G#/Jb | G#/Ab | 285-292.5 | 294.231 | 287.8125-302.8125 | 296.053 | 292.5-307.5 | 302.344 | 295.086-310.086 | 306.4655 | 302.845-316.845 | 311.029 | 315-322.5 | ||||
4 | 3 | J | A | 380-390 | 392.308 | 383.75-403.75 | 394.737 | 390-410 | 403.125 | 393.448-413.448 | 408.621 | 403.793-423.793 | 414.706 | 420-430 | ||||
5 | 3#/4b | J#/Ab | A#/Bb | 475-487.5 | 490.385 | 479.6875-504.6875 | 493.421 | 487.5-512.5 | 503.906 | 491.81-516.81 | 510.776 | 504.741-529.741 | 518.382 | 525-537.5 | ||||
6 | 4 | A | B | 570-585 | 588.4615 | 575.625-605.625 | 592.105 | 585-615 | 604.6875 | 590.172-620.172 | 612.931 | 605.69-635.69 | 622.059 | 630-645 | ||||
7 | 5 | B | H | 665-682.5 | 686.5385 | 671.5625-706.5625 | 690.7895 | 682.5-717.5 | 705.469 | 688.5345-723.5345 | 715.086 | 706.638-741.638 | 725.735 | 735-752.5 | ||||
8 | 5#/6b | B#/Hb | H#/Cb | 760-780 | 784.615 | 767.5-807.5 | 789.474 | 780-820 | 806.25 | 786.897-826.897 | 817.241 | 807.586-847.586 | 829.412 | 840-860 | ||||
9 | 6 | H | C | 855-877.5 | 882.962 | 863.4375-908.4375 | 888.158 | 877.5-922.5 | 907.031 | 885.259-930.259 | 919.397 | 908.5345-953.5345 | 933.088 | 945-967.5 | ||||
10 | 6#/7b | H#/Cb | C#/Db | 950-975 | 980.769 | 959.375-1009.375 | 986.842 | 975-1025 | 1007.8125 | 983.621-1033.621 | 1021.552 | 1009.483-1059.483 | 1036.765 | 1050-1075 | ||||
11 | 7 | C | D | 1045-1072.5 | 1078.846 | 1055.3125-1110.3125 | 1085.526 | 1072.5-1127.5 | 1108.594 | 1081.983-1136.983 | 1123.707 | 1110.431-1165.431 | 1140.441 | 1155-1182.5 | ||||
12 | 7#/8b | C#/Db | D#/Sb | 1140-1170 | 1176.923 | 1151.25-1211.25 | 1184.2105 | 1170-1230 | 1209.375 | 1180.345-1240.345 | 1225.862 | 1211.379-1271.379 | 1244.118 | 1260-1290 | ||||
13 | 8 | D | S | 1235-1267.5 | 1275 | 1247.1875-1312.1875 | 1282.895 | 1267.5-1332.5 | 1310.156 | 1278.707-1343.707 | 1328.017 | 1312.328-1377.328 | 1347.794 | 1365-1397.5 | ||||
14 | 8#/9b | D#/Eb | S#/Eb | 1330-1365 | 1373.077 | 1343.125-1413.125 | 1381.579 | 1365-1435 | 1410.9375 | 1377.069-1447.069 | 1430.172 | 1413.276-1483.276 | 1451.471 | 1470-1505 | ||||
15 | 9 | E | 1425-1462.5 | 1471.154 | 1439.0625-1514.0625 | 1480.263 | 1462.5-1537.5 | 1511.719 | 1475.431-1550.431 | 1532.328 | 1514.224-1589.224 | 1555.147 | 1575-1612.5 | |||||
16 | 1 | F | 1520-1560 | 1569.231 | 1535-1615 | 1578.947 | 1560-1640 | 1612.5 | 1573.793-1653.793. | 1634.483 | 1615.172-1695.172 | 1658.8235 | 1680-1720 |
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.