16edX

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This 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.

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