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This scale, a Long Common Practice minor mode, has the Grandfather 3L 5s MOS with a 4:1 ratio of large against small.
This scale, a Long Common Practice minor mode, has the Grandfather 3L 5s MOS with a 4:1 ratio of large against small.


Revision as of 01:01, 14 January 2022

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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 Soft Phrygian Phrygian
Minimum-comma Median Maximum+comma Thirdtone Semitone
Minimum-comma Median Maximum+comma~Minimum-comma Median Maximum+comma
Natural Subset of 34edn
1 A Ab Ab 68.235-70.588 73.797 71.597-76.3025 74.51-74.622 72.941-77.983 76.235-76.471 77.647-80
2 B\\ G#v/Ab^ G#^ 136.471-141.1765 147.594 143.193-152.605 149.02-149.244 145.882-155.966 152.471-152.941 155.294-160
3 Apv/B\\^ G# Bbv 204.706-211.765 221.39 214.79-228.908 223.529-213.8655 218.8235-233.95 228.706-229.1765 232.941-240
4 Ap A Bb 272.941-282.353 295.187 286.386-305.21 298.039-298.487 291.765-311.933 304.941-305.647 310.588-320
5 B 341.1765-352.941 368.984 357.983-381.513 372.549-373.109 364.706-389.916 381.1765-382.118 387.235-400
6 C Cb 409.412-423.529 442.781 429.58-457.815 447.059-447.731 437.647-467.899 457.412-458.588 464.882-480
7 Q Qb B#^ 477.647-494.118 516.5775 501.1765-534.118 521.569-522.353 510.588-545.882 533.647-535.294 542.529-560
8 D\\ C#v/Qb^ C^ 545.882-564.706 590.374 572.773-610.42 596.078-596.975 583.529-623.8655 609.882-611.235 620.1765-640
9 Qpv/D\\^ C# Q^ 614.118-635.294 664.171 644.37-686.723 670.588-671.597 656.471-701.849 686.118-688.765 697.8235-720
10 Qp Q Db 682.353-705.882 737.97 715.966-763.025 745.098-746.2185 729.412-779.832 762.353-764.706 777.471-800
11 D 750.588-776.471 811.765 787.563-839.328 819.608-820.84 802.353-857.815 838.588-841.412 855.118-880
12 E Eb 818.8235-847.059 885.5616 859.16-915.63 894.118-895.462 875.294-935.798 914.8235-917.882 932.765-960
13 F Fb D#^ 887.059-917.647 959.358 930.756-991.933 968.6275-970.084 948.235-1013.7815 991.059-994.353 1010.412-1040
14 F\\ E#v/Fb^ Fbv 955.294-988.235 1033.155 1002.353-1068.235 1043.137-1044.706 1021.1765-1091.765 1067.294-1080.8235 1088.059-1120
15 Fpv/G\\^ E# Fb 1023.529-1058.8235 1106.952 1073.95-1144.538 1117.647-1119.328 1094.118-1169.747 1143.529-1147.059 1164.706-1200
16 Fp F 1091.765-1129.412 1180.749 1145.546-1220.84 1192.156-1193.95 1167.059-1247.731 1219.765-1223.529 1242.353-1280
17 G 1160-1200 1254.5455 1217.143-1297.143 1266.667-1268.571 1240-1325.714 1296-1300 1320-1360
Degrees Octatonic Intense Phrygian Intense Phrygian-Soft Aeolian Soft Aeolian
Minimum-comma Median Maximum+comma~Minimum-comma Median Maximum+comma~Minimum-comma r¢ Median Maximum+comma
Natural Subset of 34edn
1 G Gb A Ab Gb Ab 75.294-77.647 78.019 76.078-80.784 78.893 77.059-81.765 79.412 80 80.672-83.025
2 A\\ F#v/Gb^ B\\ G#v/Ab^ F#^ G#^ 150.588-155.294 156.037 152.157-161.567 157.7855 154.118-163.529 158.8235 160 161.3445-166.05
3 Gpv/A\\^ F# Apv/B\\^ G# Abv Bbv 225.882-232.941 234.056 228.235-242.353 236.678 231.1765-245.294 238.235 240 242.017-249.076
4 Gp G Ap A Ab Bb 301.1765-310.588 312.074 304.314-323.137 315.571 308.235-327.059 317.647 320 322.689-332.101
5 A B A B 376.471-387.235 390.093 380.392-403.922 394.464 385.294-408.8235 397.058 400 403.361-415.126
6 B C Bb Cb 451.765-464.822 468.1115 456.471-484.706 473.356 462.353-490.588 476.471 480 484.034-498.151
7 H Hb Q Qb A#^ B#^ 527.059-542.529 546.13 532.549-565.49 552.249 539.412-572.353 555.882 560 564.706-581.1765
8 C\\ B#v/Hb^ D\\ C#v/Qb^ B^ C^ 602.353-620.1765 624.149 608.6275-646.2745 651.142 616.471-654.118 635.294 640 645.378-664.202
9 Hpv/C\\^ B# Qpv/D\\^ C# H^ Q^ 677.647-697.8235 702.167 684.706-727.059 710.035 693.529-735.882 714.706 720 726.05-747.227
10 Hp H Qp Q Cb Db 752.353-777.471 780.186 760.784-807.843 788.927 770.588-817.647 794.118 800 806.723-830.252
11 C D C D 828.235-855.118 858.204 836.862-888.6275 867.82 847.647-899.412 873.529 880 887.395-913.277
12 D E Db Eb 903.529-932.765 936.223 912.941-968.412 946.713 924.706-981.1765 952.941 960 968.067-996.3025
13 E Eb F Fb C#^ D#^ 978.8235-1010.412 1014.2415 989.02-1050.196 1025.6055 1001.765-1062.941 1032.353 1040 1048.7395-1079.328
14 F\\ D#v/Eb^ F\\ E#v/Fb^ Ebv Fbv 1055.118-1088.059 1092.26 1065.098-1130.98 1104.598 1078.8235-1144.706 1111.765 1120 1129.412-1162.353
15 Epv/F\\^ D# Fpv/G\\^ E# Eb Fb 1129.412-1164.706 1170.028 1141.1765-1210.765 1183.391 1155.882-1226.471 1191.1765 1200 1210.084-1245.378
16 Ep E Fp F E F 1204.706-1242.353 1248.297 1217.255-1292.549 1262.284 1232.941-1308.235 1270.588 1280 1290.756-1328.403
17 F G F G 1280-1320 1326.316 1293.333-1373.333 1341.1765 1310-1390 1350 1360 1371.429-1411.429
Degrees Octatonic Aeolian Intense Aeolian
Flattone Meantone Superpyth Ultrapyth
Minimum-comma Median Maximum+comma~Minimum-comma Median Maximum+comma~Minimum-comma r¢ Median Maximum+comma~Minimum-comma Median Maximum+comma
Natural Subset of 34edn
1 G Gb Gb 78.319-80.672 81.448 79.381-84.087 81.882 80-84.706 82.353 83.045 81.0695-85.775 83.8235 84.706-87.059
2 A\\ F#v/Gb^ F#^ 156.637-161.3445 162.896 158.761-169.173 163.765 160-169.412 164.706 166.09 162.139-171.551 167.647 169.412-174.118
3 Gpv/A\\^ F# Abv 234.958-242.017 244.344 238.142-252.26 245.647 240-254.118 247.059 249.135 243.209-257.326 251.471 254.118-261.1765
4 Gp G Ab 313.277-322.689 325.792 317.523-336.347 327.529 320-338.8235 329.412 332.18 324.278-343.102 335.294 338.8235-348.235
5 A 391.597-403.361 407.24 396.904-420.433 409.412 400-423.529 411.765 415.225 405.348-428.877 419.118 423.529-435.294
6 B Bb 469.916-484.034 488.688 476.285-504.52 491.294 480-508.235 494.118 498.27 486.417-514.652 502.941 508.235-522.353
7 H Hb A#^ 548.235-564.706 570.136 555.666-588.607 573.1765 560-592.941 576.471 581.315 567.487-600.428 586.768 592.941-609.412
8 C\\ B#v/Hb^ B^ 626.555-645.378 651.584 635.046-672.6935 655.059 640-677.647 658.8235 664.36 648.556-686.203 670.588 677.647-696.471
9 Hpv/C\\^ B# H^ 704.874-726.05 733.032 714.427-756.78 736.941 720-762.353 741.1765 747.405 729.626-771.979 754.412 762.653-783.529
10 Hp H Cb 783.193-806.723 814.48 793.808-840.867 818.8235 800-847.059 823.529 830.45 810.695-857.754 838.235 847.059-870.588
11 C 861.513-887.395 895.928 873.189-924.954 900.706 880-931.765 905.882 913.495 891.765-943.529 922.059 931.765-957.647
12 D Db 939.831-968.067 977.376 952.57-1009.04 982.588 960-1016.471 988.235 996.54 972.834-1029.305 1005.882 1016.471-1044.706
13 E Eb C#^ 1018.151-1048.7395 1058.8235 1031.9505-1093.127 1064.471 1040-1101.1765 1070.588 1079.585 1053.904-1115.08 1089.706 1101.1765-1131.765
14 F\\ D#v/Eb^ Ebv 1096.471-1129.412 1140.2715 1111.331-1177.214 1146.353 1120-1185.882 1152.941 1162.63 1134.973-1200.856 1173.529 1185.882-1218.8235
15 Epv/F\\^ D# Eb 1174.79-1210.084 1221.7195 1190.712-1261.3 1228.235 1200-1270.588 1233.294 1245.675 1216.043-1286.631 1257.353 1270.588-1305.882
16 Ep E 1253.109-1290.756 1303.167 1270.093-1345.39 1310.118 1280-1355.294 1317.647 1328.72 1297.112-1372.406 1341.1765 1355.294-1392.941
17 F 1331.429-1371.429 1384.615 1349.474-1429.474 1392 1360-1440 1400 1411.765 1378.182-1458.182 1425 1440-1480

Golden/Pyrite Tunings±13¢

Degrees Octatonic Soft Phrygian Phrygian
Min-Med Min-Max/Med-Max Thirdtone Semitone
Min-Med/Min-Max Med-Max Min-Med/Min-Max Med-Max
1 A Ab 72.944-74.474 73.089-74.618 73.379-75.205 74.012-75.586 75.216-77.013 75.75-77.635
2 B\\ G#v/Ab^ 145.889-148.948 146.178-149.236 146.758-150.409 148.023-151.173 150.432-154.025 151.501-155.2705
3 Apv/B\\^ G# 218.833-223.4215 219.266-223.855 220.137-225.614 222.035-226.759 225.648-230.037 227.251-232.906
4 Ap A 291.778-297.895 292.355-298.473 293.5155-300.819 296.047-302.346 300.864-308.050 303.002-301.541
5 B 364.722-372.369 365.444-373.091 366.894-376.0235 370.059-377.932 376.08-385.063 378.752-388.176
6 C 437.6665-446.843 438.533-447.709 440.273-451.228 444.070-453.519 451.296-462.075 454.5025-465.811
7 Q Qb 510.611-521.317 511.621-522.327 513.652-526.433 518.082-529.105 526.512-539.088 530.253-543.447
8 D\\ C#v/Qb^ 583.555-595.791 584.71-596.9455 587.031-601.638 592.094-604.6915 601.728-616.101 606.003-621.082
9 Qpv/D\\^ C# 656.5-670.264 657.799-671.564 660.41-676.842 661.1055-680.278 676.944-693.1135 681.754-698.717
10 Qp Q 729.444-744.738 730.888-746.182 733.789-752.047 740.117-755.864 752.16-770.126 757.504-776.352
11 D 802.3885-819.212 803.9765-820.8 807.468-827.252 814.129-831.451 827.376-847.139 833.255-853.988
12 E 875.333-893.686 877.065-895.418 880.5465-902.456 888.141-907.037 902.592-924.151 909.005-931.622
13 F Fb 948.277-968.16 950.154-970.0365 953.925-977.661 962.152-982.624 977.808-1001.164 984.755-1009.258
14 F\\ E#v/Fb^ 1021.222-1042.6335 1023.243-1044.655 1027.304-1052.866 1036.164-1058.21 1053.024-1078.177 1060.506-1086.893
15 Fpv/G\\^ E# 1094.166-1117.107 1096.332-1119.273 1100.683-1128.0705 1110.176-1133.7965 1128.24-1155.189 1136.256-1164.5285
16 Fp F 1167.111-1191.581 1169.42-1193.891 1174.062-1203.275 1184.188-1209.382 1203.456-1232.202 1212.007-1242.164
17 G 1240.055-1266.055 1242.506-1268.509 1247.441-1278.48 1258.199-1284.969 1278.672-1309.2145 1287.757-1319.799
Degrees Octatonic Intense Phrygian Intense Phrygian-Soft Aeolian Soft Aeolian
Min-Med/Min-Max Med-Max Min-Med/Min-Max Med-Max Min-Med/Min-Max Med-Max
1 G Gb A Ab 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^ B\\ G#v/Ab^ 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# Apv/B\\^ G# 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 Ap A 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 B 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 C 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 Q Qb 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^ D\\ C#v/Qb^ 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# Qpv/D\\^ C# 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 Qp Q 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 D 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 E 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 F Fb 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^ F\\ E#v/Fb^ 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# Fpv/G\\^ E# 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 Fp F 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 G 1311.767-1337.767 1314.905-1340.905 1326.243-1352.243 1330.1645-1356.1645 1344.521-1370.521 1349.558-1375.558
Degrees Octatonic Aeolian Intense Aeolian
Flattone Meantone Superpyth Ultrapyth
Min-Med Med-Max~Min-Max Min-Med/Min-Max Med-Max Min-Med Min-Max/Med-Max Min-Med/Min-Max Med-Max
1 G Gb 80.49-82.019 80.772-82.6 81.178-82.707 82.156-83.686 82.388-83.9175 82.939-84.469 83.202-84.731
2 A\\ F#v/Gb^ 160.979-164.038 161.544-165.199 162.356-165.416 164.127-167.31715 164.776-167.835 165.8785-168.937 166.403-169.462
3 Gpv/A\\^ F# 241.469-246.057 242.316-247.799 243.535-248.1235 246.469-251.057 247.164-251.753 248.818-253.405 249.605-254.193
4 Gp G 321.958-328.076 323.089-330.398 324.714-330.831 328.625-334.743 329.552-335.67 331.757-337.875 332.807-338.324
5 A 402.448-410.095 403.861-412.998 405.892-413.539 410.782-418.429 411.9405-419.588 414.696-422.343 416.008-423.655
6 B 482.937-492.114 484.633-495.597 487.071-496.247 492.938-502-115 494.329-503.505 497.635-506.812 499.21-508.386
7 H Hb 563.427-574.133 565.405-578.197 568.249-578.955 575.0945-585.8 576.717-587.423 580.575-591.2805 582.416-593.117
8 C\\ B#v/Hb^ 643.917-656.152 647.177-660.797 649.4275-661.663 657.251-669.486 659.105-671.34 663.514-675.749 665.613-677.8485
9 Hpv/C\\^ B# 724.406-738.171 726.9495-743.396 730.606-744.371 739.407-753.172 741.493-755.258 746.453-760.218 748.815-762.58
10 Hp H 804.896-820.19 807.722-825.996 811.784-827.0785 821.5635-836.858 823.881-839.175 829.392-844.686 832.0165-847.311
11 C 885.385-902.209 888.494-908.595 892.963-909.7886 903.72-920.543 906.269-923.093 912.331-929.155 915.218-932.041
12 D 965.875-984.228 969.266-991.195 974.141-992.494 985.876-1004.229 988.657-1007.01 995.271-1013.624 998.419-1016.773
13 E Eb 1046.364-1066.247 1050.004-1073.794 1055.32-1075.202 1068.033-1087.915 1071.045-1090.928 1078.21-1098.092 1081.6215-1101.504-
14 F\\ D#v/Eb^ 1126.854-1148.266 1130.81-1156.394 1136.498-1157.91 1150.189-1171.601 1153.4335-1174.845 1161.149-1182.561 1164.823-1186.235
15 Epv/F\\^ D# 1207.344-1230.285 1211.583-1238.9935 1217.6765-1240.617 1232.345-1255.2865 1235.822-1258.762 1244.088-1267.03 1248.025-1270.966
16 Ep E 1287.833-1312.304 1292.3545-1321.593 1298.855-1323.3255 1314.502-1338.972 1318.21-1342.68 1327.028-1351.498 1331.226-1355.697
17 F 1368.322-1394.322 1373.127-1404.193 1380.033-1406.033 1396.658-1422.658 1400.598-1426.598 1409.967-1435.967 1414.428-1440.428
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