User:Moremajorthanmajor/9edIX

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This Long Common Practice minor mode is the neutral scale of the Fujiyama temperament family.

Intervals

Degrees Phrygian Mode (aka Double) Neapolitan Temperament (natural minor) Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor) Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
Absolute Minimum Minimum Median Maximum Minimum Median Maximum Minimum Median Maximum
1 133.333 138.667 142.222 146.667 149.02 152.381 155.556 160
2 266.667 277.333 284.444 293.333 288.039 304.762 311.111 320
3 400 416 426.667 440 447.059 457.143 466.667 480
4 533.333 554.667 568.889 586.667 596.078 609.524 622.222 640
5 666.667 693.333 711.111 733.333 745.098 761.905 777.778 800
6 800 832 853.333 880 894.118 914.286 933.333 960
7 933.333 970.667 995.556 1026.667 1043.137 1066.667 1088.889 1120
8 1066.667 1109.333 1137.778 1177.333 1192.157 1219.048 1244.444 1280

Most harmonic tunings

Degrees Phrygian Mode (natural minor) Phrygian-Aeolian Mode (intermediate minor) Aeolian Mode (melodic/harmonic minor)
15/7±13¢ 11/5±13¢ 9/4±13¢
1 145.16-148.049 150.223-153.112 154.546-157.434
2 290.321-296.098 300.445-306.223 309.091-314.869
3 435.481-444.148 450.668459.335 463.637-473.303
4 580.641-592.197 600.891-612.446 618.182-629.738
5 725.802-740.246 751.1135-765.558 772.728-787.172
6 870.962*888.295 901.336-918.6695 927.273-944.607
7 1016.122-1036.344 1051.559-1071.781 1081.819-1102.041
8 1161.2825-1184.395 1201.7815-1224.893 1236.364-1259.476

Golden Tunings

Phrygian Mode (natural minor)

Degrees Min-Med-13c Min-Max-13c Min-Med Min-Max Med-Max-13c Min-Med+13c Min-Max+13c Med-Max Med-Max+13c
1 139.774 140.366 141.218 141.81 142.075 142.663 143.254 143.519 144.9635
2 279.548 280.731 282.437 283.62 284.149 285.3255 286.509 287.038 289.927
3 419.3215 421.097 423.655 424.43 426.224 427.988 429.763 430.557 434.891
4 559.095 561.462 564.876 566.24 568.3 570.650 573.018 574.076 579.854
5 698.869 701.828 706.0915 709.05 710.373 713.314 716.272 717.5955 724.818
6 838.643 842.193 847.308 850.86 852.448 855.976 859.5265 861.115 869.781
7 978.417 982.559 988.528 992.67 994.5225 998.639 1002.781 1004.634 1014.745
8 1118.191 1122.924 1129.746 1134.48 1136.597 1141.302 1146.035 1148.153 1159.708

Phrygian-Aeolian Mode (intermediate minor)

Degrees Min-Med/Min-Max-13c Med-Max-13c Min-Med/Min-Max Med-Max Min-Med/Min-Max+13c Med-Max+13c Min-Med-13c (Aeolian)
1 146.948 148.257 148.392 149.7015 149.836 151.146 152.036
2 293.896 296.514 296.7845 299.403 299.673 302.292 304.072
3 440.8435 444.771 445.177 449.1045 449.51 453.438 456.408
4 587.791 593.028 593.5695 598.806 599.347 604.584 608.143
5 734.739 741.285 741.961 748.507 749.184 755.73 760.179
6 881.687 889.542 890.354 898.209 899.02 906.876 912.215
7 1028.635 1037.799 1038.746 1047.91 1048.857 1058.0215 1064.251
8 1175.583 1186.056 1187.138 1197.612 1198.694 1209.1675 1216.387

Aeolian Mode (melodic/harmonic minor)

Degrees Min-Med-13c Min-Med Min-Max Min-Med+13c Med-Max-13c Min-Max+13c Med-Max Med-Max+13c
1 153.27 153.48 154.714 154.925 155.622 156.159 157.066 158.511
2 306.54 306.961 308.429 309.8495 311.244 312.3175 314.133 317.022
3 459.81 460.441 464.143 464.774 466.866 468.476 471.199 475.533
4 613.0795 613.921 618.857 619.699 622.488 624.635 628.266 634.0435
5 766.349 767.4015 773.572 774.624 778.11 780.794 785.332 792.554
6 919.619 920.882 928.286 929.5845 933.732 936.953 942.399 951.065
7 1072.889 1074.362 1083 1084.473 1089.354 1093.111 1099.465 1109.576
8 1226.159 1227.842 1237.715 1239.398 1244.976 1249.27 1256.531 1268.087

By coincidence, using an equivalence wider than 1350 cents is identical to repeating a Phrygian mode Napoli scale one tone later.