User:Moremajorthanmajor/17edIX
| Phrygian Mode (aka Double) Neapolitan Temperament (natural minor) | Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor) | Aeolian Mode Neapolitan Temperament (melodic/harmonic minor) | |||||||
|---|---|---|---|---|---|---|---|---|---|
This scale, a Long Common Practice minor mode, has the Grandfather 3L 5s MOS with a 4:1 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 | G | Gb | 70.588 | 74.622 | 75.294 | 77.647 | 78.893 | 80.672 | 82.353 | 84.706 | ||
| 2 | A\\ | F#v/Gb^ | 141.1765 | 149.244 | 150.588 | 155.294 | 157.7855 | 161.3445 | 164.706 | 169.412 | ||
| 3 | Gpv/A\\^ | F# | 211.765 | 213.8655 | 225.882 | 232.941 | 236.678 | 242.017 | 247.059 | 254.118 | ||
| 4 | Gp | G | 282.353 | 298.487 | 301.1765 | 310.588 | 315.571 | 322.689 | 329.412 | 338.8235 | ||
| 5 | A | 352.941 | 373.109 | 376.471 | 387.235 | 394.464 | 403.361 | 411.765 | 423.529 | |||
| 6 | B | 423.529 | 447.731 | 451.765 | 464.822 | 473.356 | 484.034 | 494.118 | 508.235 | |||
| 7 | H | Hb | 494.118 | 522.353 | 527.059 | 542.529 | 552.249 | 564.706 | 576.471 | 592.941 | ||
| 8 | C\\ | B#v/Hb^ | 564.706 | 596.975 | 602.353 | 620.1765 | 651.142 | 645.378 | 658.8235 | 677.647 | ||
| 9 | Hpv/C\\^ | B# | 635.294 | 671.597 | 677.647 | 697.8235 | 710.035 | 726.05 | 741.1765 | 762.653 | ||
| 10 | Hp | H | 705.882 | 746.2185 | 752.941 | 777.471 | 788.927 | 806.723 | 823.529 | 847.059 | ||
| 11 | C | 776.471 | 820.84 | 828.235 | 855.118 | 867.82 | 887.395 | 905.882 | 931.765 | |||
| 12 | D | 847.059 | 895.462 | 903.529 | 932.765 | 956.713 | 968.067 | 988.235 | 1016.471 | |||
| 13 | E | Eb | 917.647 | 970.084 | 978.8235 | 1010.412 | 1025.6055 | 1048.7395 | 1070.588 | 1101.1765 | ||
| 14 | F\\ | D#v/Eb^ | 988.235 | 1044.706 | 1054.118 | 1088.059 | 1104.598 | 1129.412 | 1152.941 | 1185.882 | ||
| 15 | Epv/F\\^ | D# | 1058.8235 | 1119.328 | 1129.412 | 1164.706 | 1183.391 | 1210.084 | 1233.294 | 1270.588 | ||
| 16 | Ep | E | 1129.412 | 1193.95 | 1204.706 | 1242.353 | 1262.284 | 1290.756 | 1317.647 | 1355.294 | ||
| 17 | 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 | G | Gb | 76.85-78.379 | 79.53-81.059 | 81.818-83.348 |
| 2 | A\\ | F#v/Gb^ | 153.7-156.758 | 159.059-162.118 | 163.6365-166.695 |
| 3 | Gpv/A\\^ | F# | 230.549-235.137 | 238.589-243.177 | 245.455-250.043 |
| 4 | Gp | G | 307.398-313.516 | 318.119-324.236 | 327.272-333.391 |
| 5 | A | 384.248-391.895 | 394.648-405.295 | 409.091-416.738 | |
| 6 | B | 461.0975-470.274 | 477.178-486.354 | 490.909-500.086 | |
| 7 | H | Hb | 537.947.548.653 | 556.707-567.4135 | 572.728-583.4335 |
| 8 | C\\ | B#v/Hb^ | 614.797-627.032 | 636.237-648.473 | 654.546-666.781 |
| 9 | Hpv/C\\^ | B# | 691.646-705.411 | 715.767-729.532 | 736.364-753.087 |
| 10 | Hp | H | 768.496-783.79 | 795.297-810.591 | 818.182-833.4765 |
| 11 | C | 845.345-862.169 | 874.826-891.65 | 900.001-916.824 | |
| 12 | D | 922.195-940.548 | 954.356-972.709 | 981.819-100.172 | |
| 13 | E | Eb | 999.0445-1018.927 | 1033.886-1053.768 | 1063.637-1083.519 |
| 14 | F\\ | D#v/Eb^ | 1075.894-1097.306 | 1113.415-1134.827 | 1145.455-1166.867 |
| 15 | Epv/F\\^ | D# | 1152.744-1175.685 | 1189.945-1215.876 | 1227.2735-1250.215 |
| 16 | Ep | E | 1229.593-1254.064 | 1272.474-1296.945 | 1309.092-1333.562 |
| 17 | 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 | Med-Max | Med-Max+13c | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | G | Gb | 73.998 | 74.311 | 74.763 | 75.076 | 75.216 | 75.527 | 75.841 | 75.981 | 76.745 |
| 2 | A\\ | F#v/Gb^ | 147.996 | 148.622 | 149.525 | 150.152 | 150.432 | 151.055 | 151.681 | 151.961 | 153.491 |
| 3 | Gpv/A\\^ | F# | 221.994 | 222.9335 | 224.288 | 225.228 | 225.648 | 226.582 | 227.522 | 227.942 | 230.236 |
| 4 | Gp | G | 295.992 | 297.245 | 299.0505 | 300.3035 | 300.864 | 302.109 | 303.362 | 303.923 | 306.982 |
| 5 | A | 369.99 | 371.556 | 373.813 | 375.379 | 376.08 | 377.637 | 379.203 | 379.9035 | 383.727 | |
| 6 | B | 443.9875 | 445.867 | 448.576 | 450.455 | 451.296 | 453.164 | 455.0435 | 455.884 | 460.472 | |
| 7 | H | Hb | 517.985 | 520.178 | 523.338 | 525.531 | 526.512 | 528.691 | 530.884 | 531.865 | 537.218 |
| 8 | C\\ | B#v/Hb^ | 591.983 | 594.489 | 598.101 | 600.607 | 601.728 | 604.219 | 606.725 | 607.846 | 612.963 |
| 9 | Hpv/C\\^ | B# | 665.981 | 668.8005 | 672.864 | 675.683 | 676.944 | 679.746 | 682.565 | 683.826 | 690.709 |
| 10 | Hp | H | 739.979 | 743.112 | 747.626 | 750.759 | 752.16 | 755.273 | 758.406 | 759.807 | 767.454 |
| 11 | C | 813.977 | 817.423 | 822.389 | 825.835 | 827.376 | 830.801 | 834.246 | 835.788 | 844.166 | |
| 12 | D | 887.975 | 891.734 | 897.1515 | 900.9105 | 902.592 | 906.328 | 910.087 | 911.768 | 920.945 | |
| 13 | E | Eb | 961.972 | 966.045 | 971.914 | 975.986 | 977.808 | 981.855 | 985.9275 | 987.749 | 997.69 |
| 14 | F\\ | D#v/Eb^ | 1035.971 | 1040.356 | 1046.877 | 1051.062 | 1053.024 | 1057.383 | 1061.768 | 1063.728 | 1074.436 |
| 15 | Epv/F\\^ | D# | 1109.969 | 1114.6675 | 1121.439 | 1126.138 | 1128.24 | 1132.91 | 1137.609 | 1139.71 | 1151.181 |
| 16 | Ep | E | 1183.967 | 1188.979 | 1196.202 | 1201.214 | 1203.456 | 1208.437 | 1213.449 | 1215.69 | 1227.926 |
| 17 | F | 1257.965 | 1263.29 | 1270.965 | 1276.29 | 1278.672 | 1283.965 | 1289.29 | 1291.672 | 1304.672 | |
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 | G | Gb | 77.796 | 78.489 | 78.561 | 79.254 | 79.325 | 80.018 | 80.49 |
| 2 | A\\ | F#v/Gb^ | 155.592 | 156.976 | 157.121 | 158.5075 | 158.651 | 160.037 | 160.979 |
| 3 | Gpv/A\\^ | F# | 233.388 | 235.467 | 235.982 | 237.761 | 237.976 | 240.055 | 241.469 |
| 4 | Gp | G | 311.184 | 313.956 | 314.242 | 317.015 | 317.301 | 320.074 | 321.958 |
| 5 | A | 388.9795 | 392.445 | 392.803 | 396.269 | 396.627 | 400.092 | 402.448 | |
| 6 | B | 466.775 | 470.934 | 471.264 | 475.522 | 475.952 | 480.111 | 482.937 | |
| 7 | H | Hb | 544.571 | 549.423 | 549.924 | 554.776 | 555.277 | 560.129 | 563.427 |
| 8 | C\\ | B#v/Hb^ | 622.367 | 627.912 | 628.485 | 634.03 | 634.6025 | 640.1475 | 643.917 |
| 9 | Hpv/C\\^ | B# | 700.163 | 706.401 | 707.0455 | 713.284 | 713.928 | 720.166 | 724.406 |
| 10 | Hp | H | 777.959 | 784.89 | 785.606 | 792.537 | 793.253 | 800.184 | 804.896 |
| 11 | C | 855.755 | 893.379 | 864.168 | 871.791 | 872.5785 | 880.203 | 885.385 | |
| 12 | D | 933.551 | 941.868 | 942.727 | 951.045 | 951.903 | 960.221 | 965.875 | |
| 13 | E | Eb | 1011.347 | 1020.357 | 1021.288 | 1030.2985 | 1031.229 | 1040.24 | 1046.364 |
| 14 | F\\ | D#v/Eb^ | 1089.143 | 1098.846 | 1099.849 | 1109.552 | 1110.554 | 1120.258 | 1126.854 |
| 15 | Epv/F\\^ | D# | 1166.939 | 1177.335 | 1178.409 | 1188.806 | 1189.878 | 1200.2765 | 1207.344 |
| 16 | Ep | E | 1244.734 | 1255.834 | 1256.97 | 1268.06 | 1269.205 | 1280.295 | 1287.833 |
| 17 | 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 | G | Gb | 81.143 | 81.254 | 81.908 | 82.019 | 82.388 | 82.672 | 83.153 | 83.9175 |
| 2 | A\\ | F#v/Gb^ | 162.286 | 162.509 | 163.815 | 164.038 | 164.776 | 165.345 | 166.306 | 167.835 |
| 3 | Gpv/A\\^ | F# | 243.429 | 243.763 | 245.723 | 246.057 | 247.164 | 248.017 | 249.458 | 251.753 |
| 4 | Gp | G | 324.5715 | 325.017 | 327.63 | 328.076 | 329.552 | 330.689 | 332.611 | 335.67 |
| 5 | A | 405.714 | 406.271 | 409.538 | 410.095 | 411.9405 | 413.3615 | 415.764 | 419.588 | |
| 6 | B | 486.857 | 487.526 | 491.4455 | 492.114 | 494.329 | 496.034 | 498.917 | 503.505 | |
| 7 | H | Hb | 568 | 568.78 | 573.353 | 574.133 | 576.717 | 578.716 | 582.07 | 587.423 |
| 8 | C\\ | B#v/Hb^ | 649.143 | 650.034 | 655.261 | 656.152 | 659.105 | 661.378 | 665.2225 | 671.34 |
| 9 | Hpv/C\\^ | B# | 730.286 | 731.2885 | 737.168 | 738.171 | 741.493 | 744.051 | 748.375 | 755.258 |
| 10 | Hp | H | 811.429 | 812.543 | 819.076 | 820.19 | 823.881 | 826.723 | 831.528 | 839.175 |
| 11 | C | C | 892.572 | 893.797 | 900.983 | 902.209 | 906.269 | 909.395 | 914.681 | 923.093 |
| 12 | D | D | 973.715 | 975.051 | 982.891 | 984.228 | 988.657 | 992.0675 | 997.833 | 1007.01 |
| 13 | E | Eb | 1054.857 | 1056.306 | 1064.799 | 1066.247 | 1071.045 | 1074.74 | 1080.986 | 1090.928 |
| 14 | F\\ | D#v/Eb^ | 1136 | 1137.56 | 1146.706 | 1148.266 | 1153.4335 | 1157.412 | 1164.139 | 1174.845 |
| 15 | Epv/F\\^ | D# | 1217.143 | 1218.814 | 1228.614 | 1230.285 | 1235.822 | 1240.084 | 1247.292 | 1258.762 |
| 16 | Ep | E | 1298.286 | 1300.0685 | 1310.521 | 1312.304 | 1318.21 | 1332.757 | 1330.445 | 1342.68 |
| 17 | F | 1379.429 | 1381.322 | 1392.429 | 1394.322 | 1400.598 | 1405.429 | 1413.598 | 1426.598 | |