User:Moremajorthanmajor/16edX: Difference between revisions
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| Line 4: | Line 4: | ||
! rowspan="3" |Degrees | ! rowspan="3" |Degrees | ||
! colspan="3" rowspan="3" |Enneatonic | ! colspan="3" rowspan="3" |Enneatonic | ||
! colspan=" | ! colspan="3" rowspan="2" |Intense Aeolian-Subpental Dorian | ||
! colspan=" | ! colspan="10" |Dorian | ||
|- | |- | ||
! colspan=" | ! colspan="4" |Subpental | ||
! colspan="3" |Pental | |||
! colspan="3" |Superpental | |||
|- | |- | ||
!Min | !Min | ||
!Golden±13¢ | !Golden±13¢ | ||
!Max | !Max | ||
!Min | !Min | ||
!7/3±13¢ | |||
!Golden±13¢ | !Golden±13¢ | ||
!Max | !Max | ||
| Line 29: | Line 31: | ||
|90 | |90 | ||
|90.428-92.053 | |90.428-92.053 | ||
| colspan="2" |91.667 | |||
|90.867-92.492 | |90.867-92.492 | ||
|91.303-92.928 | |91.303-92.928 | ||
| colspan="2" |93.75 | | colspan="2" |93.75 | ||
| Line 44: | Line 46: | ||
|180 | |180 | ||
|180.856-184.106 | |180.856-184.106 | ||
| colspan="2" |183.333 | |||
|181.734-184.984 | |181.734-184.984 | ||
|182.606-185.856 | |182.606-185.856 | ||
| colspan="2" |187.5 | | colspan="2" |187.5 | ||
| Line 59: | Line 61: | ||
|270 | |270 | ||
|271.2845-276.159 | |271.2845-276.159 | ||
| colspan="2" |275 | |||
|272.601-277.476 | |272.601-277.476 | ||
|273.909-278.784 | |273.909-278.784 | ||
| colspan="2" |281.25 | | colspan="2" |281.25 | ||
| Line 74: | Line 76: | ||
|360 | |360 | ||
|361.712-368.213 | |361.712-368.213 | ||
| colspan="2" |366.667 | |||
|363.468-369.968 | |363.468-369.968 | ||
|365.212-371.712 | |365.212-371.712 | ||
| colspan="2" |375 | | colspan="2" |375 | ||
| Line 89: | Line 91: | ||
|450 | |450 | ||
|452.141-460.266 | |452.141-460.266 | ||
| colspan="2" |458.333 | |||
|454.335-462.46 | |454.335-462.46 | ||
|456.5155-464.6405 | |456.5155-464.6405 | ||
| colspan="2" |468.75 | | colspan="2" |468.75 | ||
| Line 104: | Line 106: | ||
|540 | |540 | ||
|542.569-552.319 | |542.569-552.319 | ||
| colspan="2" |550 | |||
|545.202-554.952 | |545.202-554.952 | ||
|547.819-557.569 | |547.819-557.569 | ||
| colspan="2" |562.5 | | colspan="2" |562.5 | ||
| Line 119: | Line 121: | ||
|630 | |630 | ||
|632.997-644.372 | |632.997-644.372 | ||
| colspan="2" |641.667 | |||
|636.0685-647.4435 | |636.0685-647.4435 | ||
|639.122-650.497 | |639.122-650.497 | ||
| colspan="2" |656.25 | | colspan="2" |656.25 | ||
| Line 134: | Line 136: | ||
|720 | |720 | ||
|723.425-736.425 | |723.425-736.425 | ||
| colspan="2" |733.333 | |||
|726.9355-739.9355 | |726.9355-739.9355 | ||
|730.425-743.425 | |730.425-743.425 | ||
| colspan="2" |750 | | colspan="2" |750 | ||
| Line 149: | Line 151: | ||
|810 | |810 | ||
|813.854-828.479 | |813.854-828.479 | ||
| colspan="2" |825 | |||
|817.802-832.427 | |817.802-832.427 | ||
|821.728-836.353 | |821.728-836.353 | ||
| colspan="2" |843.75 | | colspan="2" |843.75 | ||
| Line 164: | Line 166: | ||
|900 | |900 | ||
|904.282-920.532 | |904.282-920.532 | ||
| colspan="2" |916.667 | |||
|908.669-924.919 | |908.669-924.919 | ||
|913.031-920.281 | |913.031-920.281 | ||
| colspan="2" |937.5 | | colspan="2" |937.5 | ||
| Line 179: | Line 181: | ||
|990 | |990 | ||
|994.71-1012.585 | |994.71-1012.585 | ||
| colspan="2" |1018.333 | |||
|999.536-1017.411 | |999.536-1017.411 | ||
|1004.334-1022.209 | |1004.334-1022.209 | ||
| colspan="2" |1031.25 | | colspan="2" |1031.25 | ||
| Line 194: | Line 196: | ||
|1080 | |1080 | ||
|1085.138-1104.638 | |1085.138-1104.638 | ||
| colspan="2" |1100 | |||
|1090.403-1109.903 | |1090.403-1109.903 | ||
|1095.637-1115.137 | |1095.637-1115.137 | ||
| colspan="2" |1125 | | colspan="2" |1125 | ||
| Line 208: | Line 210: | ||
|1170 | |1170 | ||
|1175.566-1106.691 | |1175.566-1106.691 | ||
| colspan="2" |1191.667 | |||
|1181.27-1202.395 | |1181.27-1202.395 | ||
|1186.94-1208.065 | |1186.94-1208.065 | ||
| colspan="2" |1218.75 | | colspan="2" |1218.75 | ||
| Line 222: | Line 224: | ||
|1260 | |1260 | ||
|1265.9945-1288.7445 | |1265.9945-1288.7445 | ||
| colspan="2" |1283.333 | |||
|1272.137-1294.887 | |1272.137-1294.887 | ||
|1278.2435-1300.9935 | |1278.2435-1300.9935 | ||
| colspan="2" |1312.5 | | colspan="2" |1312.5 | ||
| Line 236: | Line 238: | ||
|1350 | |1350 | ||
|1356.423-1380.798 | |1356.423-1380.798 | ||
| colspan="2" |1375 | |||
|1363.004-1387.378 | |1363.004-1387.378 | ||
|1369.547-1393.922 | |1369.547-1393.922 | ||
| colspan="2" |1406.25 | | colspan="2" |1406.25 | ||
| Line 250: | Line 252: | ||
|1440 | |1440 | ||
|1446.851-1472.851 | |1446.851-1472.851 | ||
| colspan="2" |1466.667 | |||
|1453.871-1479.871 | |1453.871-1479.871 | ||
|1460.85-1486.85 | |1460.85-1486.85 | ||
| colspan="2" |1500 | | colspan="2" |1500 | ||
Revision as of 22:15, 22 December 2018
This is the scale which occurs as the dominant major edX.
Intervals
| Degrees | Enneatonic | Intense Aeolian-Subpental Dorian | Dorian | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Subpental | Pental | Superpental | ||||||||||||||
| Min | Golden±13¢ | Max | Min | 7/3±13¢ | Golden±13¢ | Max | Min | Golden±13¢ | Max | Min | Golden±13¢ | Max | ||||
| 1 | 1#/2b | G#/Jb | G#/Ab | 90 | 90.428-92.053 | 91.667 | 90.867-92.492 | 91.303-92.928 | 93.75 | 94.329-95.943 | 95.4545 | 94.917-96.542 | 96.429 | |||
| 2 | 2 | J | A | 180 | 180.856-184.106 | 183.333 | 181.734-184.984 | 182.606-185.856 | 187.5 | 188.2585-191.9085 | 190.909 | 189.834-193.084 | 192.857 | |||
| 3 | 2#/3b | J#/Ab | A#/Bb | 270 | 271.2845-276.159 | 275 | 272.601-277.476 | 273.909-278.784 | 281.25 | 282.988-287.863 | 286.364 | 284.751-289.626 | 289.286 | |||
| 4 | 3 | J | B | 360 | 361.712-368.213 | 366.667 | 363.468-369.968 | 365.212-371.712 | 375 | 377.317-383.817 | 381.818 | 379.668-386.168 | 385.714 | |||
| 5 | 3#/4b | J#/Ab | B#/Cb | 450 | 452.141-460.266 | 458.333 | 454.335-462.46 | 456.5155-464.6405 | 468.75 | 471.646-479.771 | 477.273 | 474.585-482.71 | 482.143 | |||
| 6 | 4 | A | C | 540 | 542.569-552.319 | 550 | 545.202-554.952 | 547.819-557.569 | 562.5 | 565.974-575.726 | 572.727 | 569.502-579.252 | 578.571 | |||
| 7 | 5 | A#/Bb | C#/Qb | 630 | 632.997-644.372 | 641.667 | 636.0685-647.4435 | 639.122-650.497 | 656.25 | 660.305-671.68 | 668.182 | 664.419-675.794 | 675 | |||
| 8 | 5#/6b | B | Q | 720 | 723.425-736.425 | 733.333 | 726.9355-739.9355 | 730.425-743.425 | 750 | 754.634-767.634 | 763.636 | 759.336-771.336 | 771.429 | |||
| 9 | 6 | C | D | 810 | 813.854-828.479 | 825 | 817.802-832.427 | 821.728-836.353 | 843.75 | 848.963-863.588 | 859.091 | 854.253-868.878 | 867.857 | |||
| 10 | 6#/7b | C#/Db | D#/Sb | 900 | 904.282-920.532 | 916.667 | 908.669-924.919 | 913.031-920.281 | 937.5 | 943.293-959.543 | 954.5455 | 949.17-965.42 | 964.286 | |||
| 11 | 7 | D | S | 990 | 994.71-1012.585 | 1018.333 | 999.536-1017.411 | 1004.334-1022.209 | 1031.25 | 1037.622-1055.497 | 1050 | 1044.087-1061.962 | 1060.714 | |||
| 12 | 7#/8b | D#/Eb | S#/Eb | 1080 | 1085.138-1104.638 | 1100 | 1090.403-1109.903 | 1095.637-1115.137 | 1125 | 1131.951-1151.451 | 1145.4545 | 1139.004-1158.503 | 1157.143 | |||
| 13 | 8 | E | 1170 | 1175.566-1106.691 | 1191.667 | 1181.27-1202.395 | 1186.94-1208.065 | 1218.75 | 1226.38-1247.405 | 1240.909 | 1233.921-1255.046 | 1253.571 | ||||
| 14 | 8#/9b | E#/Fb | 1260 | 1265.9945-1288.7445 | 1283.333 | 1272.137-1294.887 | 1278.2435-1300.9935 | 1312.5 | 1320.61-1343.36 | 1336.364 | 1328.838-1351.588 | 1350 | ||||
| 15 | 9 | F | 1350 | 1356.423-1380.798 | 1375 | 1363.004-1387.378 | 1369.547-1393.922 | 1406.25 | 1414.939-1439.314 | 1431.818 | 1423.755-1448.13 | 1446.429 | ||||
| 16 | 1 | G | 1440 | 1446.851-1472.851 | 1466.667 | 1453.871-1479.871 | 1460.85-1486.85 | 1500 | 1509.268-1535.268 | 1527.273 | 1518.672-1544.672 | 1542.857 | ||||
| Degrees | Enneatonic | Min | 22/9±13¢ | Golden±13¢ | Max | ||||
|---|---|---|---|---|---|---|---|---|---|
| 1 | 1#/2b | F#/Gb | G#/Jb | G#/Ab | 96.429 | 95.9005-97.5255 | 96.369-97.989 | 97.5 | |
| 2 | 2 | G | J | A | 192.857 | 191.801-195.051 | 192.728-195.978 | 195 | |
| 3 | 2#/3b | G#/Jb | G#/Ab | J#/Ab | A#/Bb | 289.286 | 287.7015-292.5765 | 289.092-293.967 | 292.5 |
| 4 | 3 | J | A | J | B | 385.714 | 383.602-390.102 | 385.456-391.956 | 390 |
| 5 | 3#/4b | J#/Ab | A#/Bb | J#/Ab | B#/Cb | 482.143 | 479.5025-487.6275 | 481.82-489.945 | 487.5 |
| 6 | 4 | A | B | A | C | 578.571 | 575.403-585.153 | 578.184-587.934 | 585 |
| 7 | 5 | B | H | A#/Bb | C#/Qb | 675 | 671.3035-382.6785 | 674.548-685.923 | 682.5 |
| 8 | 5#/6b | B#/Hb | H#/Cb | B | Q | 771.429 | 767.204-780.204 | 770.912-783.912 | 780 |
| 9 | 6 | H | C | C | D | 867.857 | 863.1045-877.7295 | 867.2755-881.9005 | 877.5 |
| 10 | 6#/7b | H#/Cb | C#/Db | C#/Db | D#/Sb | 964.286 | 959.005-975.255 | 963.6935-979.8895 | 975 |
| 11 | 7 | C | D | D | S | 1060.714 | 1054.9055-1072.7205 | 1060.0035-1087.8785 | 1072.5 |
| 12 | 7#/8b | C#/Db | D#/Sb | D#/Eb | S#/Eb | 1157.143 | 1150.806-1170.306 | 1156.367-1175.867 | 1170 |
| 13 | 8 | D | S | E | 1253.571 | 1246.7065-1267.8315 | 1252.731-1273.856 | 1267.5 | |
| 14 | 8#/9b | D#/Eb | S#/Eb | E#/Fb | 1350 | 1342.607-1365.357 | 1349.095-1371.845 | 1365 | |
| 15 | 9 | E | F | 1446.429 | 1438.507-1462.882 | 1445.459-1469.834 | 1462.5 | ||
| 16 | 1 | F | G | 1542.857 | 1534.408-1560.408 | 1541.823-1567.823 | 1560 | ||
| Degrees | Enneatonic | Mixolydian | Mixolydian-Ionian | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Subpental | Pental | Superpental | |||||||||||||||||
| Soft | Intense | ||||||||||||||||||
| Min | Golden±13¢ | Max | Min | Golden±13¢ | 5/2±13¢ | Max | Min | Golden±13¢ | Max | Min | Golden±13¢ | Max | Min | Golden±13¢ | Max | ||||
| 1 | 1#/2b | F#/Gb | 97.5 | 97.364-98.989 | 98.4375 | 97.787-99.412 | 98.332-99.957 | 100 | 99.998-101.623 | 100.862 | 101.648-103.273 | 103.448 | 102.785-104.41 | 105 | |||||
| 2 | 2 | G | 195 | 194.7275-197.9775 | 196.875 | 195.5745-198.8245 | 196.664-199.914 | 200 | 199.9955-203.2455 | 201.724 | 203.296-206.546 | 206.897 | 205.57-208.82 | 210 | |||||
| 3 | 2#/3b | G#/Jb | G#/Ab | 292.5 | 292.091-296.966 | 295.3125 | 293.362-298.237 | 294.996-299.871 | 300 | 299.993-304.868 | 302.586 | 304.944-309.819 | 310.345 | 308.356-313.231 | 315 | ||||
| 4 | 3 | J | A | 390 | 389.455-395.955 | 393.75 | 391.149-397.649 | 393.328-399.828 | 400 | 399.991-406.491 | 403.448 | 406.592-413.092 | 413.793 | 411.141-417.641 | 420 | ||||
| 5 | 3#/4b | J#/Ab | A#/Bb | 487.5 | 486.819-494.944 | 492.1875 | 488.936-497.061 | 491.6605-499.7855 | 500 | 499.989-508.114 | 504.31 | 508.24-516.365 | 517.241 | 513.926-522.051 | 525 | ||||
| 6 | 4 | A | B | 585 | 584.183-593.933 | 590.625 | 586.724-596.474 | 589.993-599.743 | 600 | 599.987-609.737 | 605.172 | 609.888-619.638 | 620.69 | 616.711-626.461 | 630 | ||||
| 7 | 5 | B | H | 682.5 | 681.546-692.921 | 689.0625 | 684.571-695.886 | 688.325-699.7 | 700 | 699.984-711.359 | 706.0345 | 711.5355-722.9105 | 724.138 | 719.496-730.871 | 735 | ||||
| 8 | 5#/6b | B#/Hb | H#/Cb | 780 | 778.91-791.91 | 787.5 | 782.298-795.298. | 786.657-799.657 | 800 | 799.982-812.982 | 806.897 | 813.1835-826.1835 | 827.586 | 822.282-835.282 | 840 | ||||
| 9 | 6 | H | C | 877.5 | 876.274-890.899 | 885.9375 | 880.085-894.71 | 884.989-899.614 | 900 | 899.98-914.605 | 907.759 | 914.831-929.456 | 931.0345 | 925.067-939.692 | 945 | ||||
| 10 | 6#/7b | H#/Cb | C#/Db | 975 | 973.638-989.888 | 984.375 | 977.873-994.123 | 983.321-999.571 | 1000 | 999.978-1016.238 | 1008.621 | 1016.479-1032.729 | 1034.483 | 1027.852-1044.102 | 1050 | ||||
| 11 | 7 | C | D | 1072.5 | 1071.0015-1088.8765 | 1082.8125 | 1075.66-1093.535 | 1081.653-1099.528 | 1100 | 1099.975-1117.85 | 1109.483 | 1118.127-1136.002 | 1137.931 | 1130.637-1148.512 | 1155 | ||||
| 12 | 7#/8b | C#/Db | D#/Sb | 1170 | 1168.365-1187.865 | 1181.25 | 1173.447-1192.947 | 1179.985-1199.485 | 1200 | 1199.973-1219.473 | 1210.345 | 1219.775-1239.275 | 1241.379 | 1233.422-1252.922 | 1260 | ||||
| 13 | 8 | D | S | 1267.5 | 1265.729-1286.854 | 1279.6875 | 1271.234-1292.359 | 1278.317-1299.442 | 1300 | 1299.971-1321.096 | 1311.207 | 1321.423-1342.548 | 1344.828 | 1336.208-1357.333 | 1365 | ||||
| 14 | 8#/9b | D#/Eb | S#/Eb | 1365 | 1363.093-1385.843 | 1378.125 | 1369.022-1391.772 | 1376.6495-1399.3995 | 1400 | 1399.968-1422.719 | 1412.069 | 1423.071-1445.821 | 1448.276 | 1438.993-1461.743 | 1470 | ||||
| 15 | 9 | E | 1462.5 | 1460.457-1484.832 | 1476.5625 | 1455.809-1491.184 | 1474.982-1499.366 | 1500 | 1499.9665-1524.3415 | 1512.931 | 1524.719-1549.094 | 1551.724 | 1541.778-1566.153 | 1575 | |||||
| 16 | 1 | F | 1560 | 1557.82-1583.82 | 1575 | 1564.596-1590.596 | 1573.314-1599.314 | 1600 | 1599.964-1625.964 | 1613.793 | 1626.366-1652.366 | 1655.172 | 1644.563-1670.563 | 1680 | |||||
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.