User:Moremajorthanmajor/17edIX
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 | Intense Phrygian | Intense Phrygian-Soft Aeolian | Soft Aeolian | Minimum | Median | Maximum | |||||||||
| Minimum | Median | Maximum | Minimum | Median | Maximum | Minimum | Median | Maximum | ||||||||||
| 1 | G | Gb | 70.588 | 74.622 | 75.294 | 77.647 | 78.019 | 78.431 | 78.893 | 79.412 | 80 | 80.672 | 82.353 | 84.706 | ||||
| 2 | A\\ | F#v/Gb^ | 141.1765 | 149.244 | 150.588 | 155.294 | 156.037 | 156.863 | 157.7855 | 158.8235 | 160 | 161.3445 | 164.706 | 169.412 | ||||
| 3 | Gpv/A\\^ | F# | 211.765 | 213.8655 | 225.882 | 232.941 | 234.056 | 235.294 | 236.678 | 238.235 | 240 | 242.017 | 247.059 | 254.118 | ||||
| 4 | Gp | G | 282.353 | 298.487 | 301.1765 | 310.588 | 312.074 | 313.7255 | 315.571 | 317.647 | 320 | 322.689 | 329.412 | 338.8235 | ||||
| 5 | A | 352.941 | 373.109 | 376.471 | 387.235 | 390.093 | 392.156 | 394.464 | 397.058 | 400 | 403.361 | 411.765 | 423.529 | |||||
| 6 | B | 423.529 | 447.731 | 451.765 | 464.822 | 468.1115 | 470.588 | 473.356 | 476.471 | 480 | 484.034 | 494.118 | 508.235 | |||||
| 7 | H | Hb | 494.118 | 522.353 | 527.059 | 542.529 | 546.13 | 549.02 | 552.249 | 555.882 | 560 | 564.706 | 576.471 | 592.941 | ||||
| 8 | C\\ | B#v/Hb^ | 564.706 | 596.975 | 602.353 | 620.1765 | 624.149 | 627.451 | 651.142 | 635.294 | 640 | 645.378 | 658.8235 | 677.647 | ||||
| 9 | Hpv/C\\^ | B# | 635.294 | 671.597 | 677.647 | 697.8235 | 702.167 | 705.882 | 710.035 | 714.706 | 720 | 726.05 | 741.1765 | 762.653 | ||||
| 10 | Hp | H | 705.882 | 746.2185 | 752.941 | 777.471 | 780.186 | 784.314 | 788.927 | 794.118 | 800 | 806.723 | 823.529 | 847.059 | ||||
| 11 | C | 776.471 | 820.84 | 828.235 | 855.118 | 858.204 | 862.745 | 867.82 | 873.529 | 880 | 887.395 | 905.882 | 931.765 | |||||
| 12 | D | 847.059 | 895.462 | 903.529 | 932.765 | 936.223 | 941.1765 | 946.713 | 952.941 | 960 | 968.067 | 988.235 | 1016.471 | |||||
| 13 | E | Eb | 917.647 | 970.084 | 978.8235 | 1010.412 | 1014.2415 | 1019.607 | 1025.6055 | 1032.353 | 1040 | 1048.7395 | 1070.588 | 1101.1765 | ||||
| 14 | F\\ | D#v/Eb^ | 988.235 | 1044.706 | 1054.118 | 1088.059 | 1092.26 | 1098.039 | 1104.598 | 1111.765 | 1120 | 1129.412 | 1152.941 | 1185.882 | ||||
| 15 | Epv/F\\^ | D# | 1058.8235 | 1119.328 | 1129.412 | 1164.706 | 1170.028 | 1176.471 | 1183.391 | 1191.1765 | 1200 | 1210.084 | 1233.294 | 1270.588 | ||||
| 16 | Ep | E | 1129.412 | 1193.95 | 1204.706 | 1242.353 | 1248.297 | 1254.902 | 1262.284 | 1270.588 | 1280 | 1290.756 | 1317.647 | 1355.294 | ||||
| 17 | F | 1200 | 1268.571 | 1280 | 1320 | 1326.316 | 1333.333 | 1341.1765 | 1350 | 1360 | 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±13¢ | Min-Max±13¢ | Med-Max±13¢ | |
|---|---|---|---|---|---|
| 1 | G | Gb | 73.998-75.527 | 74.311-75.841 | 75.216-76.745 |
| 2 | A\\ | F#v/Gb^ | 147.996-151.055 | 148.622-151.681 | 150.432-153.491 |
| 3 | Gpv/A\\^ | F# | 221.994-226.582 | 222.9335-227.522 | 225.648-230.236 |
| 4 | Gp | G | 295.992-302.109 | 297.245-303.362 | 300.864-306.982 |
| 5 | A | 369.99-377.637 | 371.556-379.203 | 376.08-383.727 | |
| 6 | B | 443.9875-453.164 | 445.867-455.0435 | 451.296-460.472 | |
| 7 | H | Hb | 517.985-528.691 | 520.178-530.884 | 526.512-537.218 |
| 8 | C\\ | B#v/Hb^ | 591.983-604.219 | 594.489-606.725 | 601.728-612.963 |
| 9 | Hpv/C\\^ | B# | 665.981-679.746 | 668.8005-682.565 | 676.944-690.709 |
| 10 | Hp | H | 739.979-755.273 | 743.112-758.406 | 752.16-767.454 |
| 11 | C | 813.977-830.801 | 817.423-834.246 | 827.376-844.166 | |
| 12 | D | 887.975-906.328 | 891.734-910.087 | 902.592-920.945 | |
| 13 | E | Eb | 961.972-981.855 | 966.045-985.9275 | 977.808-997.69 |
| 14 | F\\ | D#v/Eb^ | 1035.971-1057.383 | 1040.356-1061.768 | 1053.024-1074.436 |
| 15 | Epv/F\\^ | D# | 1109.969-1132.91 | 1114.6675-1137.609 | 1128.24-1151.181 |
| 16 | Ep | E | 1183.967-1208.437 | 1188.979-1213.449 | 1203.456-1227.926 |
| 17 | F | 1257.965-1283.965 | 1263.29-1289.29 | 1278.672-1304.672 | |
Phrygian-Aeolian Mode (intermediate minor)
| Degrees | Octatonic | Intense Phrygian | Intense Phrygian-Soft Aeolian | Soft Aeolian | ||||
|---|---|---|---|---|---|---|---|---|
| Min-Med/Min-Max±13¢ | Med-Max±13¢ | Min-Med/Min-Max±13¢ | Med-Max±13¢ | Min-Med/Min-Max±13¢ | Med-Max±13¢ | |||
| 1 | G | Gb | 77.163-78.692 | 77.347-78.877 | 78.014-79.544 | 78.245-79.774 | 79.0895-80.618 | 79.385-80.915 |
| 2 | A\\ | F#v/Gb^ | 155.325-157.384 | 155.695-157.7535 | 156.029-159.087 | 156.49-159.549 | 158.179-161.238 | 158.772-161.83 |
| 3 | Gpv/A\\^ | F# | 231.488-236.076 | 232.042-236.63 | 234.043-238.631 | 234.735-239.323 | 237.268-241.857 | 238.157-242.746 |
| 4 | Gp | G | 308.651-314.768 | 309.389-315.507 | 312.057-318.175 | 312.98-319.098 | 316.358-322.4755 | 317.543-323.661 |
| 5 | A | 385.814-393.4605 | 386.737-394.384 | 390.071-397.7185 | 391.225-398.872 | 395.447-403.094 | 396.929-404.576 | |
| 6 | B | 462.976-472.1525 | 464.084-473.261 | 468.086-477.262 | 469.469-478.646 | 474.537-483.713 | 476.315-485.4913 | |
| 7 | H | Hb | 540.139-550.845 | 541.4315-549.423 | 546.1-556.806 | 547.715-558.421 | 553.627-564.332 | 555.7005-566.406 |
| 8 | C\\ | B#v/Hb^ | 617.3015-629.537 | 618.779-631.014 | 624.114-636.35 | 625.96-638.195 | 632.716-644.951 | 635.086-647.322 |
| 9 | Hpv/C\\^ | B# | 694.464-708.229 | 696.126-709.891 | 702.129-715.893 | 704.205-717.969 | 711.805-725.57 | 714.805-728.237 |
| 10 | Hp | H | 771.629-786.921 | 773.4735-788.768 | 780.143-795.437 | 782.45-797.744 | 790.895-806.189 | 793.858-809.152 |
| 11 | C | 848.79-865.613 | 865.821-867.644 | 858.157-874.981 | 860.695-877.518 | 869.984-886.808 | 873.243-890.067 | |
| 12 | D | 925.952-944.305 | 928.168-946.521 | 936.171-954.527 | 938.94-957.293 | 949.074-967.427 | 952.692-970.982 | |
| 13 | E | Eb | 1003.115-1022.997 | 1005.516-1025.398 | 1014.186-1034.0668 | 1017.185-1037.067 | 1028.163-1048.045 | 1032.015-1051.8975 |
| 14 | F\\ | D#v/Eb^ | 1080.278-1101.689 | 1082.863-1104.275 | 1092.2-1113.612 | 1095.43-1116.841 | 1107.253-1128.664 | 1111.401-1132.813 |
| 15 | Epv/F\\^ | D# | 1157.44-1180.381 | 1160.21-1183.151 | 1170.214-1193.1555 | 1173.675-1196.616 | 1186.3425-1209.283 | 1190.788-1213.728 |
| 16 | Ep | E | 1234.603-1259.0735 | 1237.558-1262.028 | 1248.229-1272.699 | 1251.9195-1276.39 | 1265.4315-1289.902 | 1270.173-1294.643 |
| 17 | F | 1311.767-1337.767 | 1314.905-1340.905 | 1326.243-1352.243 | 1330.1645-1356.1645 | 1344.521-1370.521 | 1349.558-1375.558 | |
Aeolian Mode (melodic/harmonic minor)
| Degrees | Octatonic | Min-Med±13¢ | Min-Max±13¢ | Med-Max±13¢ | |
|---|---|---|---|---|---|
| 1 | G | Gb | 80.49-82.019 | 81.143-82.672 | 82.388-83.9175 |
| 2 | A\\ | F#v/Gb^ | 160.979-164.038 | 162.286-165.345 | 164.776-167.835 |
| 3 | Gpv/A\\^ | F# | 241.469-246.057 | 243.429-248.017 | 247.164-251.753 |
| 4 | Gp | G | 321.958-328.076 | 324.5715-330.689 | 329.552-335.67 |
| 5 | A | 402.448-410.095 | 405.714-413.3615 | 411.9405-419.588 | |
| 6 | B | 482.937-492.114 | 486.857-496.034 | 494.329-503.505 | |
| 7 | H | Hb | 563.427-574.133 | 568-578.716 | 576.717-587.423 |
| 8 | C\\ | B#v/Hb^ | 643.917-656.152 | 649.143-661.378 | 659.105-671.34 |
| 9 | Hpv/C\\^ | B# | 724.406-738.171 | 730.286-744.051 | 741.493-755.258 |
| 10 | Hp | H | 804.896-820.19 | 811.429-826.723 | 823.881-839.175 |
| 11 | C | C | 885.385-902.209 | 892.572-909.395 | 906.269-923.093 |
| 12 | D | D | 965.875-984.228 | 973.715-992.0675 | 988.657-1007.01 |
| 13 | E | Eb | 1046.364-1066.247 | 1054.857-1074.74 | 1071.045-1090.928 |
| 14 | F\\ | D#v/Eb^ | 1126.854-1148.266 | 1136-1157.412 | 1153.4335-1174.845 |
| 15 | Epv/F\\^ | D# | 1207.344-1230.285 | 1217.143-1240.084 | 1235.822-1258.762 |
| 16 | Ep | E | 1287.833-1312.304 | 1298.286-1332.757 | 1318.21-1342.68 |
| 17 | F | 1368.322-1394.322 | 1379.429-1405.429 | 1400.598-1426.598 | |