User:Moremajorthanmajor/16edX
This is the scale which occurs as the dominant major edX.
Intervals
| Degrees | Enneatonic | Minor mode Middletown temperament | Neutral mode Middletown temperament | Major mode Middletown temperament | |||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Intense Aeolian-Dorian | Dorian | Dorian-Mixolydian | Mixolydian | Mixolydian-Ionian | |||||||||||||||||||
| Subpental | Pental | Superpental | Subpental | Pental | Superpental | ||||||||||||||||||
| Soft | Intense | ||||||||||||||||||||||
| Min | Max | Min | Max | Min | Max | Min | Max | Min | Max | Min | Max | Min | Max | Min | Max | Min | Max | Min | Max | ||||
| 1 | 1#/2b | F#/Gb | 90 | 91.667 | 93.75 | 95.4545 | 96.429 | 97.5 | 98.4375 | 100 | 100.862 | 103.448 | 105 | ||||||||||
| 2 | 2 | G | 180 | 183.333 | 187.5 | 190.909 | 192.857 | 195 | 196.875 | 200 | 201.724 | 206.897 | 210 | ||||||||||
| 3 | 2#/3b | G#/Jb | G#/Ab | 270 | 275 | 281.25 | 286.364 | 289.286 | 292.5 | 295.3125 | 300 | 302.586 | 310.345 | 315 | |||||||||
| 4 | 3 | J | A | 360 | 366.667 | 375 | 381.818 | 385.714 | 390 | 393.75 | 400 | 403.448 | 413.793 | 420 | |||||||||
| 5 | 3#/4b | J#/Ab | A#/Bb | 450 | 458.333 | 468.75 | 477.273 | 482.143 | 487.5 | 492.1875 | 500 | 504.31 | 517.241 | 525 | |||||||||
| 6 | 4 | A | B | 540 | 550 | 562.5 | 572.727 | 578.571 | 585 | 590.625 | 600 | 605.172 | 620.69 | 630 | |||||||||
| 7 | 5 | B | H | 630 | 641.667 | 656.25 | 668.182 | 675 | 682.5 | 689.0625 | 700 | 706.0345 | 724.138 | 735 | |||||||||
| 8 | 5#/6b | B#/Hb | H#/Cb | 720 | 733.333 | 750 | 763.636 | 771.429 | 780 | 787.5 | 800 | 806.897 | 827.586 | 840 | |||||||||
| 9 | 6 | H | C | 810 | 825 | 843.75 | 859.091 | 867.857 | 877.5 | 885.9375 | 900 | 907.759 | 931.0345 | 945 | |||||||||
| 10 | 6#/7b | H#/Cb | C#/Db | 900 | 916.667 | 937.5 | 954.5455 | 964.286 | 975 | 984.375 | 1000 | 1008.621 | 1034.483 | 1050 | |||||||||
| 11 | 7 | C | D | 990 | 1018.333 | 1031.25 | 1050 | 1060.714 | 1072.5 | 1082.8125 | 1100 | 1109.483 | 1137.931 | 1155 | |||||||||
| 12 | 7#/8b | C#/Db | D#/Sb | 1080 | 1100 | 1125 | 1145.4545 | 1157.143 | 1170 | 1181.25 | 1200 | 1210.345 | 1241.379 | 1260 | |||||||||
| 13 | 8 | D | S | 1170 | 1191.667 | 1218.75 | 1240.909 | 1253.571 | 1267.5 | 1279.6875 | 1300 | 1311.207 | 1344.828 | 1365 | |||||||||
| 14 | 8#/9b | D#/Eb | S#/Eb | 1260 | 1283.333 | 1312.5 | 1336.364 | 1350 | 1365 | 1378.125 | 1400 | 1412.069 | 1448.276 | 1470 | |||||||||
| 15 | 9 | E | 1350 | 1375 | 1406.25 | 1431.818 | 1446.429 | 1462.5 | 1476.5625 | 1500 | 1512.931 | 1551.724 | 1575 | ||||||||||
| 16 | 1 | F | 1440 | 1466.667 | 1500 | 1527.273 | 1542.857 | 1560 | 1575 | 1600 | 1613.793 | 1655.172 | 1680 | ||||||||||
Most harmonic tunings
| Degrees | Enneatonic | Minor mode Middletown temperament | Neutral mode Middletown temperament | Major mode Middletown temperament | ||
|---|---|---|---|---|---|---|
| 7/3±13¢ | 22/9±13¢ | 5/2±13¢ | ||||
| 1 | 1#/2b | F#/Gb | 90.867-92.492 | 95.9005-97.5255 | 98.332-99.957 | |
| 2 | 2 | G | 181.734-184.984 | 191.801-195.051 | 196.664-199.914 | |
| 3 | 2#/3b | G#/Jb | G#/Ab | 272.601-277.476 | 287.7015-292.5765 | 294.996-299.871 |
| 4 | 3 | J | A | 363.468-369.968 | 383.602-390.102 | 393.328-399.828 |
| 5 | 3#/4b | J#/Ab | A#/Bb | 454.335-462.46 | 479.5025-487.6275 | 491.6605-499.7855 |
| 6 | 4 | A | B | 545.202-554.952 | 575.403-585.153 | 589.993-599.743 |
| 7 | 5 | B | H | 636.0685-647.4435 | 671.3035-382.6785 | 688.325-699.7 |
| 8 | 5#/6b | B#/Hb | H#/Cb | 726.9355-739.9355 | 767.204-780.204 | 786.657-799.657 |
| 9 | 6 | H | C | 817.802-832.427 | 863.1045-877.7295 | 884.989-899.614 |
| 10 | 6#/7b | H#/Cb | C#/Db | 908.669-924.919 | 959.005-975.255 | 983.321-999.571 |
| 11 | 7 | C | D | 999.536-1017.411 | 1054.9055-1072.7205 | 1081.653-1099.528 |
| 12 | 7#/8b | C#/Db | D#/Sb | 1090.403-1109.903 | 1150.806-1170.306 | 1179.985-1199.485 |
| 13 | 8 | D | S | 1181.27-1202.395 | 1246.7065-1267.8315 | 1278.317-1299.442 |
| 14 | 8#/9b | D#/Eb | S#/Eb | 1272.137-1294.887 | 1342.607-1365.357 | 1376.6495-1399.3995 |
| 15 | 9 | E | 1363.004-1387.378 | 1438.507-1462.882 | 1474.982-1499.366 | |
| 16 | 1 | F | 1453.871-1479.871 | 1534.408-1560.408 | 1573.314-1599.314 | |
Golden tunings±13¢
| Degrees | Enneatonic | Minor mode Middletown temperament | Neutral mode Middletown temperament | Major mode Middletown temperament | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Intense Aeolian-Dorian | Dorian | Dorian-Mixolydian | Mixolydian | Mixolydian-Ionian | |||||||||
| Subpental | Pental | Superpental | Subpental | Pental | Superpental | ||||||||
| Soft | Intense | ||||||||||||
| 1 | 1#/2b | F#/Gb | 90.428-92.053 | 91.303-92.928 | 94.329-95.943 | 94.917-96.542 | 96.369-97.989 | 97.364-98.989 | 97.787-99.412 | 99.998-101.623 | 101.648-103.273 | 102.785-104.41 | |
| 2 | 2 | G | 180.856-184.106 | 182.606-185.856 | 188.2585-191.9085 | 189.834-193.084 | 192.728-195.978 | 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 | 271.2845-276.159 | 273.909-278.784 | 282.988-287.863 | 284.751-289.626 | 289.092-293.967 | 292.091-296.966 | 293.362-298.237 | 299.993-304.868 | 304.944-309.819 | 308.356-313.231 |
| 4 | 3 | J | A | 361.712-368.213 | 365.212-371.712 | 377.317-383.817 | 379.668-386.168 | 385.456-391.956 | 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 | 452.141-460.266 | 456.5155-464.6405 | 471.646-479.771 | 474.585-482.71 | 481.82-489.945 | 486.819-494.944 | 488.936-497.061 | 499.989-508.114 | 508.24-516.365 | 513.926-522.051 |
| 6 | 4 | A | B | 542.569-552.319 | 547.819-557.569 | 565.974-575.726 | 569.502-579.252 | 578.184-587.934 | 584.183-593.933 | 586.724-596.474 | 599.987-609.737 | 609.888-619.638 | 616.711-626.461 |
| 7 | 5 | B | H | 632.997-644.372 | 639.122-650.497 | 660.305-671.68 | 664.419-675.794 | 674.548-685.923 | 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 | 723.425-736.425 | 730.425-743.425 | 754.634-767.634 | 759.336-771.336 | 770.912-783.912 | 778.91-791.91 | 782.298-795.298. | 799.982-812.982 | 813.1835-826.1835 | 822.282-835.282 |
| 9 | 6 | H | C | 813.854-828.479 | 821.728-836.353 | 848.963-863.588 | 854.253-868.878 | 867.2755-881.9005 | 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 | 904.282-920.532 | 913.031-920.281 | 943.293-959.543 | 949.17-965.42 | 963.6935-979.8895 | 973.638-989.888 | 977.873-994.123 | 999.978-1016.238 | 1016.479-1032.729 | 1027.852-1044.102 |
| 11 | 7 | C | D | 994.71-1012.585 | 1004.334-1022.209 | 1037.622-1055.497 | 1044.087-1061.962 | 1060.0035-1087.8785 | 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 | 1085.138-1104.638 | 1095.637-1115.137 | 1131.951-1151.451 | 1139.004-1158.503 | 1156.367-1175.867 | 1168.365-1187.865 | 1173.447-1192.947 | 1199.973-1219.473 | 1219.775-1239.275 | 1233.422-1252.922 |
| 13 | 8 | D | S | 1175.566-1106.691 | 1186.94-1208.065 | 1226.38-1247.405 | 1233.921-1255.046 | 1252.731-1273.856 | 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 | 1265.9945-1288.7445 | 1278.2435-1300.9935 | 1320.61-1343.36 | 1328.838-1351.588 | 1349.095-1371.845 | 1363.093-1385.843 | 1369.022-1391.772 | 1399.968-1422.719 | 1423.071-1445.821 | 1438.993-1461.743 |
| 15 | 9 | E | 1356.423-1380.798 | 1369.547-1393.922 | 1414.939-1439.314 | 1423.755-1448.13 | 1445.459-1469.834 | 1460.457-1484.832 | 1455.809-1491.184 | 1499.9665-1524.3415 | 1524.719-1549.094 | 1541.778-1566.153 | |
| 16 | 1 | F | 1446.851-1472.851 | 1460.85-1486.85 | 1509.268-1535.268 | 1518.672-1544.672 | 1541.823-1567.823 | 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 3.596 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.