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.
Tuning spectrum[edit]
Degrees | Octatonic | Phrygian Mode (aka Double) Neapolitan Temperament (natural minor) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Absolute Minimum | 3ed(7/6) | Minimum | Golden | Median | Mean | <0 -11 0 11|/24 | 5ed(21/16) | ed(15/7) | Maximum | ||
1 | F#/Gb | 85.714 | 88.957 | 89.143 | 90.162 | 90.612 | 91.714 | 92.286 | 94.156 | 94.246 | 94.286 |
2 | G | 171.429 | 177.914 | 178.286 | 180.3245 | 181.2245 | 183.429 | 184.5715 | 188.312 | 188.492 | 188.571 |
3 | G#/Ab | 257.143 | 266.871 | 267.429 | 270.487 | 271.837 | 275.143 | 276.857 | 282.469 | 282.738 | 282.857 |
4 | A | 342.857 | 355.828 | 356.571 | 360.649 | 362.449 | 366.857 | 369.143 | 376.625 | 376.984 | 377.143 |
5 | A#/Bb | 428.571 | 444.785 | 445.714 | 450.811 | 453.061 | 458.571 | 461.429 | 470.781 | 471.23 | 471.429 |
6 | B | 514.286 | 533.742 | 534.857 | 540.973 | 543.6735 | 550.286 | 553.714 | 564.937 | 565.4755 | 565.714 |
7 | H | 600 | 622.698 | 624 | 631.136 | 634.286 | 642 | 646 | 659.093 | 659.721 | 660 |
8 | H#/Cb | 685.714 | 711.656 | 713.143 | 721.298 | 724.898 | 733.714 | 738.286 | 753.2495 | 753.967 | 754.286 |
9 | C | 771.429 | 800.612 | 802.286 | 811.46 | 815.51 | 825.429 | 830.572 | 847.406 | 848.213 | 848.571 |
10 | C#/Db | 857.143 | 889.57 | 891.429 | 901.622 | 906.122 | 917.143 | 922.857 | 941.562 | 942.459 | 942.857 |
11 | D | 942.857 | 978.527 | 980.571 | 991.785 | 996.735 | 1008.857 | 1015.143 | 1035.718 | 1036.705 | 1037.143 |
12 | D#/Eb | 1028.571 | 1067.484 | 1069.714 | 1081.947 | 1087.247 | 1100.571 | 1107.429 | 1129.874 | 1130.951 | 1131.429 |
13 | E | 1114.286 | 1156.441 | 1158.857 | 1172.109 | 1177.959 | 1192.286 | 1199.7145 | 1224.03 | 1225.197 | 1225.714 |
14 | F | 1200 | 1245.397 | 1248 | 1262.271 | 1268.571 | 1284 | 1292 | 1318.1865 | 1319.443 | 1320 |
Degrees | Octatonic | Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor) | ||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Minimum | ed(28/13) | Golden | ed(13/6) | 8ed(14/9) | Mean | 3ed(13/11) | ed(24/11) | 4ed(5/4) | 10ed(7/4) | <… -3 0 8|/48 | Median | 7ed(40/27) | <-18 -4 13|\72 | ed(11/5) | 8ed(11/7) | Maximum | ||
1 | F#/Gb | 94.286 | 94.878 | 95.395 | 95.612 | 95.6145 | 96.122 | 96.403 | 96.474 | 96.578 | 96.883 | 97.107 | 97.143 | 97.207 | 97.42 | 97.5 | 97.8115 | 97.959 |
2 | G | 188.571 | 189.757 | 190.79 | 191.225 | 191.229 | 192.245 | 192.8065 | 192.948 | 193.157 | 193.765 | 194.213 | 194.286 | 194.414 | 194.8405 | 195.001 | 195.623 | 195.918 |
3 | G#/Ab | 282.857 | 284.635 | 286.185 | 286.837 | 286.843 | 288.367 | 289.21 | 289.422 | 289.735 | 290.648 | 291.322 | 291.429 | 291.621 | 292.261 | 292.501 | 293.4345 | 293.878 |
4 | A | 377.143 | 379.512 | 381.58 | 382.449 | 382.458 | 384.488 | 385.613 | 385.896 | 386.314 | 387.53 | 388.429 | 388.571 | 338.828 | 389.681 | 390.001 | 391.246 | 391.836 |
5 | A#/Bb | 471.429 | 474.392 | 476.975 | 478.062 | 478.072 | 480.612 | 482.016 | 482.37 | 482.892 | 484.413 | 485.537 | 485.714 | 486.035 | 487.101 | 487.5015 | 489.0575 | 489.796 |
6 | B | 565.714 | 569.271 | 572.37 | 573.674 | 573.687 | 576.735 | 875.419 | 578.8445 | 579.471 | 581.2955 | 582.644 | 582.857 | 583.242 | 584.5215 | 585.002 | 586.869 | 587.755 |
7 | H | 660 | 664.149 | 667.765 | 669.286 | 669.301 | 672.857 | 674.823 | 975.3185 | 676.049 | 678.178 | 679.752 | 680 | 680.448 | 681.942 | 682.002 | 684.6805 | 685.714 |
8 | H#/Cb | 754.286 | 759.028 | 763.16 | 764.899 | 764.916 | 768.98 | 771.226 | 771.793 | 772.627 | 775.06 | 776.859 | 777.143 | 777.656 | 779.362 | 780.002 | 782.492 | 783.6735 |
9 | C | 848.571 | 853.906 | 858.555 | 860.511 | 860.53 | 865.102 | 867.629 | 868.267 | 869.206 | 871.943 | 873.966 | 874.286 | 874.862 | 876.782 | 877.503 | 880.3035 | 881.633 |
10 | C#/Db | 942.857 | 948.7845 | 953.95 | 956.123 | 956.145 | 961.2245 | 964.032 | 964.741 | 965.784 | 968.826 | 971.073 | 971.429 | 972.07 | 974.2025 | 975.003 | 978.115 | 979.592 |
11 | D | 1037.143 | 1043.663 | 1049.345 | 1051.736 | 1051.759 | 1057.347 | 1060.436 | 1061.215 | 1062.363 | 1065.7085 | 1068.181 | 1068.579 | 1069.277 | 1071.623 | 1072.503 | 1075.9265 | 1077.551 |
12 | D#/Eb | 1131.429 | 1138.541 | 1144.74 | 1147.348 | 1147.374 | 1153.469 | 1156.839 | 1157.689 | 1158.941 | 1162.591 | 1165.2885 | 1165.714 | 1166.4835 | 1169.043 | 1170.004 | 1173.738 | 1175.51 |
13 | E | 1225.714 | 1233.42 | 1240.435 | 1242.96 | 1242.988 | 1249.592 | 1253.242 | 1254.163 | 1255.52 | 1259.474 | 1262.396 | 1262.857 | 1263.6905 | 1266.463 | 1267.504 | 1271.55 | 1273.469 |
14 | F | 1320 | 1328.298 | 1335.53 | 1338.573 | 1338.603 | 1345.714 | 1349.645 | 1350.637 | 1352.089 | 1356.356 | 1359.503 | 1360 | 1360.897 | 1363.884 | 1365.004 | 1369.361 | 1371.429 |
Degrees | Octatonic | Aeolian Mode Neapolitan Temperament (melodic/harmonic minor) | ||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Minimum | 9ed(5/3) | ed(20/9) | Golden | 28ed5 | 5ed(4/3) | Median | 7edf | 56ed(180/7) | Mean | 28ed(36/7) | 8ed(8/5) | 10ed(9/5) | 2ed(9/8) | 9ed(17/10) | ed(16/7) | Maximum | ||
1 | F#/Gb | 97.959 | 98.262 | 98.743 | 99.459 | 99.511 | 99.609 | 100 | 100.279 | 100.382 | 100.408 | 101.253 | 101.711 | 101.76 | 101.955 | 102.071 | 102.227 | 102.857 |
2 | G | 195.918 | 196.524 | 197.486 | 198.918 | 199.022 | 199.218 | 200 | 200.559 | 200.764 | 200.816 | 202.506 | 203.422 | 203.519 | 203.91 | 204.143 | 204.453 | 205.714 |
3 | G#/Ab | 293.878 | 294.786 | 286.229 | 298.377 | 298.534 | 298.827 | 300 | 300.837 | 301.146 | 301.2245 | 303.759 | 305.132 | 305.279 | 305.865 | 306.214 | 306.68 | 308.571 |
4 | A | 391.836 | 393.048 | 394.9725 | 397.839 | 398.045 | 398.436 | 400 | 401.117 | 401.528 | 401.633 | 405.012 | 406.843 | 407.0385 | 407.82 | 408.285 | 408.907 | 411.429 |
5 | A#/Bb | 489.796 | 491.31 | 493.716 | 497.296 | 497.556 | 498.045 | 500 | 501.396 | 501.9105 | 502.041 | 506.265 | 508.554 | 508.798 | 509.775 | 510.3565 | 511.134 | 514.286 |
6 | B | 587.755 | 589.5725 | 592.459 | 597.755 | 597.067 | 597.654 | 600 | 601.676 | 602.293 | 602.449 | 607.518 | 610.265 | 610.558 | 611.73 | 612.428 | 613.36 | 617.143 |
7 | H | 685.714 | 687.835 | 691.202 | 696.2145 | 696.578 | 697.263 | 700 | 701.955 | 702.675 | 702.857 | 708.771 | 711.976 | 712.317 | 713.685 | 714.499 | 715.587 | 720 |
8 | H#/Cb | 783.6735 | 786.097 | 789.945 | 795.674 | 796.099 | 796.872 | 800 | 802.234 | 803.057 | 803.265 | 810.024 | 813.686 | 814.077 | 815.64 | 816.57 | 817.814 | 822.857 |
9 | C | 881.633 | 884.359 | 888.688 | 895.133 | 895.301 | 896.481 | 900 | 902.514 | 903.439 | 903.6735 | 911.277 | 915.397 | 915.837 | 917.595 | 918.462 | 920.041 | 925.714 |
10 | C#/Db | 979.592 | 982.621 | 987.431 | 994.592 | 995.112 | 996.09 | 1000 | 1002.793 | 1003.821 | 1004.4082 | 1012.53 | 1017.108 | 1017.596 | 1019.55 | 1020.712 | 1022.267 | 1028.571 |
11 | D | 1077.551 | 1080.882 | 1086.174 | 1094..051 | 1094.623 | 1095.699 | 1100 | 1103.072 | 1104.203 | 1104.49 | 1113.783 | 1118.819 | 1119.356 | 1121.505 | 1122.784 | 1124.494 | 1131.429 |
12 | D#/Eb | 1175.51 | 1179.145 | 1184.9175 | 1193.5105 | 1194.134 | 1195.308 | 1200 | 1203.3514 | 1204.585 | 1204.898 | 1215.036 | 1220.529 | 1221.1155 | 1223.46 | 1224.856 | 1226.721 | 1234.286 |
13 | E | 1273.469 | 1277.407 | 1283.661 | 1292.97 | 1293.646 | 1294.916 | 1300 | 1303.631 | 1304.967 | 1305.306 | 1316.289 | 1322.24 | 1322.875 | 1325.415 | 1326.927 | 1238.947 | 1337.143 |
14 | F | 1371.429 | 1375.669 | 1382.403 | 1392.429 | 1393.157 | 1394.526 | 1400 | 1403.91 | 1405.3495 | 1405.714 | 1417.524 | 1423.951 | 1424.635 | 1427.37 | 1428.998 | 1431.174 | 1440 |