User:Moremajorthanmajor/16edX

From Xenharmonic Wiki
Jump to navigation Jump to search

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 1414.939 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.

Retrieved from "https://en.xen.wiki/index.php?title=User:Moremajorthanmajor/16edX&oldid=38378"