User:Moremajorthanmajor/16edX

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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
Aeolian-Dorian Dorian Dorian-Mixolydian Mixolydian Mixolydian-Ionian
Subpental Pental Superpental Subpental Pental Superpental
Soft Intense
Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum
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

Minor mode Middletown temperament

Degrees Enneatonic Aeolian-Dorian Dorian
-13¢ Mean -13¢ (s5D) Subpental Pental Superpental
+13¢ (A-D) Mean +13¢ -13¢ -13¢ (S5) Mean Mean +13¢ (5) -13¢ (D-M)
1 1#/2b F#/Gb 90.428 91.241 91.303 92.053 92.116 92.928 94.329 94.917 95.142 95.7295 95.943 96.369
2 2 G 180.856 182.481 182.606 184.106 184.231 185.856 188.2585 189.834 190.2835 191.459 191.9085 192.728
3 2#/3b G#/Jb G#/Ab 271.2845 273.722 273.909 276.159 276.347 278.784 282.988 284.751 285.425 287.1885 287.863 289.092
4 3 J A 361.712 364.962 365.212 368.213 368.462 371.712 377.317 379.668 380.567 382.918 383.817 385.456
5 3#/4b J#/Ab A#/Bb 452.141 456.203 456.5155 460.266 460.578 464.6405 471.646 474.585. 475.709 478.6475 479.771 481.82
6 4 A B 542.569 547.444 547.819 552.319 552.694 557.569 565.974 569.502 570.851 574.377 575.726 578.184
7 5 B H 632.997 638.685 639.122 644.372 644.809 650.497 660.305 664.419 665.992 670.106 671.68 674.548
8 5#/6b B#/Hb H#/Cb 723.425 729.925 730.425 736.425 736.925 743.425 754.634 759.336 761.134 765.836 767.634 770.912
9 6 H C 813.854 821.166 821.728 828.479 829.04 836.353 848.963 854.253 856.276 861.565 863.588 867.2755
10 6#/7b H#/Cb C#/Db 904.282 912.407 913.031 920.532 921.156 920.281 943.293 949.17 951.418 957.295 959.543 963.6935
11 7 C D 994.71 1003.6475 1004.334 1012.585 1013.272 1022.209 1037.622 1044.087 1046.559 1053.024 1055.497 1060.0035
12 7#/8b C#/Db D#/Sb 1085.138 1094.888 1095.637 1104.638 1105.387 1115.137 1131.951 1139.004 1141.701 1148.753 1151.451 1156.367
13 8 D S 1175.566 1186.129 1186.94 1106.691 1197.502 1208.065 1226.38 1233.921 1236.843 1244.483 1247.405 1252.731
14 8#/9b D#/Eb S#/Eb 1265.9945 1277.3965 1278.2435 1288.7445 1289.6185 1300.9935 1320.61 1328.838 1331.985 1340.213 1343.36 1349.095
15 9 E 1356.423 1368.61 1369.547 1380.798 1381.734 1393.922 141.939 1423.755 1427.126 1435.942 1439.314 1445.459
16 1 F 1446.851 1459.851 1460.85 1472.851 1473.85 1486.85 1509.268 1518.672 1522.268 1531.672 1535.268 1541.823

Neutral (Dorian-Mixolydian) mode Middletown temperament

Degrees Enneatonic +13¢ (S5D) Mean -13¢ (s5M)
1 1#/2b F#/Gb 96.542 97.176 97.364
2 2 G 193.084 194.353 194.7275
3 2#/3b G#/Jb G#/Ab 289.626 291.529 292.091
4 3 J A 386.168 388.706 389.455
5 3#/4b J#/Ab A#/Bb 482.71 485.882 486.819
6 4 A B 579.252 580.235 584.183
7 5 B H 675.794 725.584 681.546
8 5#/6b B#/Hb H#/Cb 771.336 777.412 779.41
9 6 H C 868.878 874.588 876.274
10 6#/7b H#/Cb C#/Db 965.42 971.7645 973.638
11 7 C D 1061.962 1068.941 1071.0015
12 7#/8b C#/Db D#/Sb 1158.503 1166.117 1168.365
13 8 D S 1255.046 1263.293 1265.729
14 8#/9b D#/Eb S#/Eb 1351.588 1360.47 1363.093
15 9 E 1448.13 1457.645 1460.457
16 1 F 1544.672 1554.823 1557.82

Major mode Middletown temperament

Degrees Enneatonic Mixolydian Mixolydian-Ionian
Subpental Pental Superpental Mean +13¢
-13¢ (5) +13¢ (D-M) Mean Mean +13¢ (s5) +13¢ -13¢ (Soft s5) Soft Intense
+13¢ (Soft s5) -13¢ Mean -13¢ (M-I) +13¢
1 1#/2b F#/Gb 97.787 97.989 98.176 98.6 98.989 99.412 99.998 100.81 101.623 101.648 102.46 102.785 103.273 103.598 104.41
2 2 G 195.5745 195.978 196.3525 197.1995 197.9775 198.8245 199.9955 201.6205 203.2455 203.296 204.921 205.57 206.546 207.195 208.82
3 2#/3b G#/Jb G#/Ab 293.362 293.967 294.529 295.799 296.966 298.237 299.993 302.431 304.868 304.944 307.381 308.356 309.819 310.793 313.231
4 3 J A 391.149 391.956 392.705 394.399 395.955 397.649 399.991 403.241 406.491 406.592 409.842 411.141 413.092 414.391 417.641
5 3#/4b J#/Ab A#/Bb 488.936 489.945 490.881 492.999 494.944 497.061 499.989 504.051 508.114 508.24 512.302 513.926 516.365 517.9885 522.051
6 4 A B 586.724 587.934 589.058 591.599 593.933 596.474 599.987 599.987 609.737 609.888 614.763 616.711 619.638 621.586 626.461
7 5 B H 684.511 685.923 687.234 690.198 692.921 695.886 699.984 705.672 711.359 711.5355 717.223 719.496 722.9105 725.184 730.871
8 5#/6b B#/Hb H#/Cb 782.298 783.912 785.41 788.798 791.91 795.298 799.982 799.982 812.982 813.1835 819.6835 822.282 826.1835 828.781 835.282
9 6 H C 880.085 881.9005 883.5865 887.398 890.899 894.71 899.98 907.292 914.605 914.831 922.144 925.067 929.456 932.379 939.692
10 6#/7b H#/Cb C#/Db 977.872 979.8895 981.763 985.998 989.888 994.123 999.978 1008.103 1016.228 1016.479 1024.604 1027.852 1032.729 1035.977 1044.102
11 7 C D 1075.66 1087.8785 1079.939 1084.597 1088.8765 1093.535 1099.975 1108.913 1117.85 1118.127 1127.065 1130.637 1136.002 1139.575 1148.512
12 7#/8b C#/Db D#/Sb 1173.447 1175.867 1178.115 1183.197 1189.865 1192.947 1199.973 1209.723 1219.473 1219.775 1229.525 1233.422 1239.275 1243.172 1252.922
13 8 D S 1271.234 1273.856 1276.292 1281.797 1286.854 1292.359 1299.971 1310.533 1321.096 1321.423 1331.986 1336.208 1342.548 1346.77 1357.333
14 8#/9b D#/Eb S#/Eb 1369.022 1371.845 1374.468 1380.397 1385.843 1391.772 1399.968 1411.344 1422.719 1423.071 1434.446 1438.993 1445.821 1450.368 1461.743
15 9 E 1455.809 1469.834 1472.644 1478.996 1484.832 1491.184 1499.9665 1512.154 1524.3415 1524.719 1536.9065 1541.778 1549.094 1553.9655 1566.153
16 1 F 1564.596 1567.96 1570.82 1577.596 1583.82 1590.596 1599.964 1612.964 1625.964 1626.366 1639.366 1644.563 1652.366 1657.563 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.

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