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