User:Moremajorthanmajor/14edIX
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This scale, a Long Common Practice minor mode,occurs in 12edo, where it is the equal division of the major ninth. It has the Macroshrutis 6L 2s MOS with a 2:1 ratio of large against small.
Intervals
| Degrees | Octatonic | 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 | F#/Gb | 85.714 | 89.143 | 91.429 | 94.286 | 95.798 | 97.959 | 100 | 102.857 | ||
| 2 | G | 171.429 | 178.286 | 182.857 | 188.571 | 191.597 | 195.918 | 200 | 205.714 | ||
| 3 | G#/Ab | 257.143 | 267.429 | 274.286 | 282.857 | 287.395 | 293.878 | 300 | 308.571 | ||
| 4 | A | 342.857 | 356.571 | 365.714 | 377.143 | 383.193 | 391.836 | 400 | 411.429 | ||
| 5 | A#/Bb | 428.571 | 445.714 | 467.143 | 471.429 | 478.992 | 489.796 | 500 | 514.286 | ||
| 6 | B | 514.286 | 534.857 | 548.571 | 565.714 | 574.79 | 587.755 | 600 | 617.143 | ||
| 7 | H | 600 | 624 | 640 | 660 | 670.588 | 685.714 | 700 | 720 | ||
| 8 | H#/Cb | 685.714 | 713.143 | 731.429 | 754.286 | 766.387 | 783.6735 | 800 | 822.857 | ||
| 9 | C | 771.429 | 802.286 | 822.857 | 848.571 | 862.185 | 881.633 | 900 | 925.714 | ||
| 10 | C#/Db | 857.143 | 891.429 | 914.286 | 942.857 | 957.983 | 979.592 | 1000 | 1028.571 | ||
| 11 | D | 942.857 | 980.571 | 1005.714 | 1037.143 | 1053.7815 | 1077.551 | 1100 | 1131.429 | ||
| 12 | D#/Eb | 1028.571 | 1069.714 | 1097.143 | 1131.429 | 1149.58 | 1175.51 | 1200 | 1234.286 | ||
| 13 | E | 1114.286 | 1158.857 | 1188.571 | 1225.714 | 1245.378 | 1273.469 | 1300 | 1337.143 | ||
| 14 | F | 1200 | 1268.571 | 1280 | 1320 | 1341.1765 | 1371.429 | 1400 | 1440 | ||
Most harmonic tunings
| Degrees | Octatonic | Phrygian Mode (natural minor) | Phrygian-Aeolian Mode (intermediate minor) | Aeolian Mode (melodic/harmonic minor) |
|---|---|---|---|---|
| 15/7±13¢ | 11/5±13¢ | 9/4±13¢ | ||
| 1 | F#/Gb | 93.317-95.1745 | 96.572-98.429 | 99.351-101.208 |
| 2 | G | 186.635-190.349 | 193.1435-196.858 | 198.701-202.416 |
| 3 | G#/Ab | 279.952-285.5235 | 289.715-295.287 | 298.052-303.624 |
| 4 | A | 373.269-380.698 | 386.287-393.7155 | 397.403-404.831 |
| 5 | A#/Bb | 466.587-475.872 | 482.859-492.144 | 496.754-506.039 |
| 6 | B | 559.904-571.047 | 579.43-590.573 | 596.104-607.247 |
| 7 | H | 653.224-666.221 | 676.002-689.002 | 695.455-708.455 |
| 8 | H#/Cb | 746.539-761.396 | 772.574-787.431 | 794.805-809.663 |
| 9 | C | 839.856-856.57 | 869.146-885.86 | 894.156-910.871 |
| 10 | C#/Db | 933.173-951.745 | 965.717-984.289 | 993.507-1012.079 |
| 11 | D | 1026.491-1046.919 | 1062.289-1082.718 | 1092.858-1113.286 |
| 12 | D#/Eb | 1119.808-1142.094 | 1158.861-1181.1465 | 1192.209-1214.494 |
| 13 | E | 1213.1255-1237.268 | 1255.4325-1279.575 | 1291.559-1315.702 |
| 14 | F | 1306.443-1332.443 | 1352.004-1378.004 | 1390.91-1416.91 |
Golden Tunings
Phrygian Mode (natural minor)
| Degrees | Octatonic | Min-Med-13c | Min-Max-13c | Min-Med | Min-Max | Med-Max-13c | Min-Med+13c | Min-Max+13c | Min-Max-13c |
|---|---|---|---|---|---|---|---|---|---|
| 1 | F#/Gb | 89.855 | 90.235 | 90.783 | 91.164 | 91.334 | 91.712 | 92.092 | 98.531 |
| 2 | G | 179.709 | 180.47 | 181.566 | 182.327 | 182.667 | 183.4235 | 184.184 | 197.061 |
| 3 | G#/Ab | 269.564 | 270.705 | 272.35 | 273.491 | 274.001 | 275.135 | 276.276 | 295.592 |
| 4 | A | 359.4185 | 360.94 | 363.133 | 364.654 | 365.335 | 366.847 | 368.3685 | 394.123 |
| 5 | A#/Bb | 449.273 | 451.175 | 453.916 | 455.818 | 456.6685 | 458.559 | 460.461 | 492.653 |
| 6 | B | 539.128 | 541.41 | 544.699 | 546.981 | 548.002 | 550.271 | 552.553 | 591.184 |
| 7 | H | 628.982 | 631.645 | 635.482 | 638.145 | 639.336 | 641.982 | 644.645 | 689.7145 |
| 8 | H#/Cb | 718.837 | 721.88 | 726.2655 | 729.3085 | 730.67 | 733.694 | 736.737 | 788.245 |
| 9 | C | 808.692 | 812.115 | 817.049 | 820.472 | 822.003 | 825.406 | 828.829 | 886.776 |
| 10 | C#/Db | 898.546 | 902.35 | 907.832 | 911.636 | 913.337 | 917.118 | 920.921 | 985.306 |
| 11 | D | 988.401 | 992.585 | 998.615 | 1002.799 | 1007.671 | 1008.829 | 1013.013 | 1083.837 |
| 12 | D#/Eb | 1078.255 | 1082.82 | 1089.398 | 1093.963 | 1096.004 | 1100.541 | 1105.106 | 1182.368 |
| 13 | E | 1168.11 | 1173.055 | 1180.1815 | 1185.126 | 1187.338 | 1192.253 | 1197.198 | 1280.898 |
| 14 | F | 1257.965 | 1263.29 | 1270.965 | 1276.29 | 1278.672 | 1283.965 | 1289.29 | 1379.429 |
Phrygian-Aeolian Mode (intermediate minor)
| Degrees | Octatonic | 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 | F#/Gb | 94.4665 | 95.308 | 95.395 | 96.237 | 96.324 | 97.165 | 97.737 |
| 2 | G | 188.933 | 190.616 | 190.79 | 192.473 | 192.647 | 194.3305 | 195.475 |
| 3 | G#/Ab | 283.399 | 285.924 | 286.185 | 288.71 | 288.971 | 291.496 | 293.212 |
| 4 | A | 377.866 | 381.228 | 381.58 | 384.947 | 385.294 | 388.661 | 390.949 |
| 5 | A#/Bb | 472.332 | 476.5405 | 476.975 | 481.183 | 481.618 | 485.826 | 488.687 |
| 6 | B | 566.799 | 571.849 | 572.37 | 577.42 | 577.942 | 582.9915 | 586.424 |
| 7 | H | 661.265 | 667.157 | 667.765 | 673.658 | 674.265 | 680.157 | 684.161 |
| 8 | H#/Cb | 755.732 | 762.465 | 763.16 | 769.893 | 770.589 | 777.322 | 781.899 |
| 9 | C | 850.198 | 857.773 | 858.555 | 866.13 | 866.912 | 874.487 | 879.636 |
| 10 | C#/Db | 944.665 | 953.081 | 953.95 | 962.367 | 963.236 | 971.652 | 977.373 |
| 11 | D | 1039.131 | 1048.298 | 1049.345 | 1058.603 | 1059.56 | 1068.818 | 1075.111 |
| 12 | D#/Eb | 1113.5975 | 1143.697 | 1144.74 | 1154.84 | 1155.883 | 1165.983 | 1172.848 |
| 13 | E | 1228.064 | 1239.005 | 1240.435 | 1251.077 | 1252.207 | 1263.148 | 1270.585 |
| 14 | F | 1322.53 | 1334.313 | 1335.53 | 1347.313 | 1348.53 | 1360.313 | 1368.322 |
Aeolian Mode (melodic/harmonic minor)
| Degrees | Octatonic | Min-Max-13c | Min-Med | Min-Max | Min-Med+13c | Med-Max-13c | Min-Max+13c | Med-Max | Med-Max+13c |
|---|---|---|---|---|---|---|---|---|---|
| 1 | F#/Gb | 98.531 | 98.666 | 99.459 | 99.5945 | 100.043 | 100.388 | 100.971 | 101.9 |
| 2 | G | 197.061 | 197.332 | 198.918 | 199.189 | 200.085 | 200.776 | 201.943 | 203.8 |
| 3 | G#/Ab | 295.592 | 295.998 | 298.377 | 298.783 | 300.128 | 301.163 | 302.913 | 305.6995 |
| 4 | A | 394.123 | 394.664 | 397.839 | 398.378 | 400.171 | 401.551 | 403.885 | 407.599 |
| 5 | A#/Bb | 492.653 | 493.3295 | 497.296 | 497.972 | 500.2135 | 501.939 | 504.856 | 509.499 |
| 6 | B | 591.184 | 591.9955 | 597.755 | 597.567 | 600.256 | 602.327 | 605.828 | 611.399 |
| 7 | H | 689.7145 | 690.661 | 696.2145 | 697.161 | 700.299 | 702.7145 | 706.799 | 713.299 |
| 8 | H#/Cb | 788.245 | 789.327 | 795.674 | 796.756 | 800.342 | 803.102 | 807.77 | 815.199 |
| 9 | C | 886.776 | 887.993 | 895.133 | 896.35 | 900.384 | 903.49 | 908.7415 | 917.099 |
| 10 | C#/Db | 985.306 | 986.659 | 994.592 | 995.945 | 1000.427 | 1003.878 | 1009.713 | 1018.9985 |
| 11 | D | 1083.837 | 1085.325 | 1094.051 | 1095.539 | 1100.47 | 1104.266 | 1110.684 | 1120.898 |
| 12 | D#/Eb | 1182.368 | 1183.991 | 1193.5105 | 1195.134 | 1200.512 | 1204.653 | 1211.655 | 1222.798 |
| 13 | E | 1280.898 | 1282.657 | 1292.97 | 1294.728 | 1300.555 | 1305.041 | 1312.627 | 1324.698 |
| 14 | F | 1379.429 | 1381.322 | 1392.429 | 1394.322 | 1400.598 | 1405.429 | 1413.598 | 1426.598 |