User:Moremajorthanmajor/8edX

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This is the neutral scale of the Vesuvius temperament family.

Intervals

Degrees Minor mode Vesuvius temperament Neutral mode Vesuvius temperament Major mode Vesuvius 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
1 180 183.333 187.5 190.909 192.857 195 196.875 200 201.724 206.897 210
2 360 366.667 375 381.818 385.714 390 393.75 400 403.448 413.793 420
3 540 550 562.5 572.727 578.571 585 590.625 600 605.172 620.69 630
4 720 733.333 750 763.636 771.429 780 787.5 800 806.897 827.586 840
5 900 916.667 937.5 954.5455 964.286 975 984.375 1000 1008.621 1034.483 1050
6 1080 1100 1125 1145.4545 1157.143 1170 1181.25 1200 1210.345 1241.379 1260
7 1260 1283.333 1312.5 1336.364 1350 1365 1378.125 1400 1412.069 1448.276 1470

Most harmonic tunings

Degrees Minor mode Vesuvius temperament Neutral mode Vesuvius temperament Major mode Vesuvius temperament
7/3±13¢ 22/9±13¢ 5/2±13¢
1 181.734-184.984 191.801-195.051 196.664-199.914
2 363.468-396.968 383.602-390.102 393.328-399.828
3 545.202-554.952 575.403-585.153 589.993-599.743
4 726.9355-739.9355 767.204-780.204 786.657-799.657
5 908.669-922.919 959.005-973.255 983.321-997.571
6 1090.403-1109.903 1150.806-1170.306 1179.985-1199.485
7 1272.137-1294.387 1342.607-1365.357 1376.6495-1399.3995

Golden tunings

Minor mode Vesuvius temperament

Degrees 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)
1 180.856 182.481 182.606 184.106 184.231 185.856 188.2585 189.834 190.2835 191.459 191.9085 192.728
2 361.712 364.962 365.212 367.213 368.462 371.712 377.317 379.668 380.567 382.918 383.817 385.456
3 542.569 547.444 547.819 552.319 552.694 557.569 565.974 569.502 570.851 574.377 575.726 578.184
4 723.425 729.925 730.425 736.425 736.925 743.425 754.634 759.336 761.134 765.836 767.634 770.912
5 904.282 912.407 913.031 920.532 921.156 929.281 943.293 949.17 951.418 957.295 959.543 963.6935
6 1085.138 1094.888 1095.637 1104.638 1105.387 1115.137 1131.957 1139.004 1141.701 1148.753 1151.451 1156.367
7 1265.9945 1277.3695 1278.2435 1288.7445 1289.6185 1300.9935 1320.61 1328.838 1331.985 1340.213 1343.36 1349.095

Neutral (Dorian-Mixolydian) mode Vesuvius temperament

Degrees +13¢ (S5D) Mean -13¢ (s5M)
1 193.084 194.353 194.7275
2 386.168 388.706 389.455
3 579.252 583.059 584.183
4 771.336 777.412 779.41
5 965.42 971.7645 973.638
6 1158.503 1166.117 1168.365
7 1351.588 1360.47 1363.093

Major mode Vesuvius temperament

Degrees 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¢ (Int S5M)
1 195.5745 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
2 391.149 391.956 392.705 394.399 395.955 397.649 399.991 403.241 406.491 406.592 409.842 411.141 413.092 414.391 417.641
3 586.724 587.934 589.058 591.599 593.933 596.474 599.987 604.862 609.737 609.888 614.763 616.711 691.638 621.586 626.461
4 782.298 783.912 785.41 788.798 791.91 795.298 799.982 806.482 812.982 813.1835 819.6835 822.282 826.1835 828.782 835.282
5 977.872 979.8895 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
6 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
7 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
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