User:Moremajorthanmajor/9edX

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This is the neutral scale of the Middletown temperament family.

Intervals

Degrees Intense Aeolian-Subpental Dorian Dorian
Subpental Pental Superpental
Min-comma Med Max+comma Min-comma Med Max+comma Min-comma Med Max+comma Min-comma Med Max+comma
1 156.667-160 161.905 159.63-166.297 164.103 163.333-170 168.889 166.364-173.03 170.37 168.095-171.429
2 313.333-320 323.8095 319.26-333.593 328.205 326.667-340 337.778 332.727-346.06 340.741 336.19-342.857
3 470-480 485.714 478.889-498.889 492.308 490-510 506.667 499.091-519.091 511.111 504.286-514.286
4 626.666-640 647.619 638.5185-665.185 656.41 653.333-680 675.556 665.4545-682.121 681.4815 672.381-685.714
5 783.333-800 809.524 798.148-831.4815 820.512 816.667-850 844.444 831.818-851.1515 851.852 843.476-857.143
6 940-960 971.429 957.778-997.778 984.615 980-1020 1013.333 998.182-1038.182 1022.222 1008.571-1028.571
7 1096.667-1120 1133.333 1117.407-1164.074 1148.718 1143.333-1190 1182.222 1164.5455-1211.212 1192.593 1176.667-1200
8 1253.333-1280 1295.238 1277.037-1310.33 1312.8205 1306.667-1360 1351.111 1330.909-1384.242 1362.963 1334.762-1371.429
Degrees Mohajira Beatles
Min-comma r¢ Med Max+comma Min-comma Med Max+comma
1 171.429-174.762 172.222 169.216-175.883 172.8395 173.333-176.667
2 342.857-349.524 344.444 338.431-351.765 345.679 346.667-353.333
3 514.286-524.286 516.667 507.647-527.647 518.5185 520-530
4 685.714-699.048 688.889 676.863-703.529 691.358 693.333-706.667
5 857.143-873.81 861.111 846.078-879.412 864.1975 866.667-883.333
6 1028.571-1048.571 1033.333 1015.294-1055.294 1037.037 1040-1060
7 1200-1223.333 1205.556 1184.51-1231.1765 1209.8765 1213.333-1236.667
8 1371.429-1398.095 1377.778 1353.7255-1407.059 1382.716 1386.667-1413.333
Degrees Mixolydian Mixolydian-Ionian
Subpental Pental Superpental
Soft Intense
Min-comma Med Max+comma Min-comma Med Max+comma Min-comma Med Max+comma Min-comma Med Max+comma Min-comma Med Max+comma
1 170-173.333 174.359 171.667-178.333 175.439 174.444-181.111 179.167 157.977-182.644 181.609 180.575-187.241 184.314 186.667-190
2 340-346.667 348.718 343.333-356.667 350.877 348.889-362.222 358.333 355.954-365.287 363.218 361.149-374.483 368.6275 373.333-380
3 510-520 523.077 515-535 526.316 523.333-543.333 537.5 527.931-547.931 544.828 541.724-561.724 552.941 560-570
4 680-693.333 697.436 686.667-713.333 701.754 697.778-724.444 716.667 703.908-730.576 726.437 722.299-748.9655 737.255 746.667-760
5 850-866.667 871.795 858.333-891.667 877.193 872.222-905.556 895.833 879.885-912.218 908.046 903.207-936.8735 921.569 933.333-950
6 1020-1040 1046.154 1030-1070 1052.632 1046.667-1086.667 1075 1055.862-1095.862 1089.655 1083.448-1123.448 1105.882 1120-1140
7 1190-1213.333 1220.513 1201.667-1248.333 1228.07 1221.111-1267.778 1254.167 1221.839-1268.506 1271.264 1264.023-1330.69 1290.196 1306.667-1330
8 1360-1386.667 1394.872 1373.333-1426.667 1403.509 1395.556-1448.889 1433.333 1407.816-1462.419 1452.874 1444.598-1496.931 1474.51 1493.333-1520

Relative cents

Degrees Intense Aeolian-Subpental Dorian Dorian Subpental-Soft Superpental Mixolydian Intense Superpental Mixolydian ~ Mixolydian-Ionian
1 161.111 166.667 177.778 183.333
2 322.222 333.333 355.556 366.667
3 483.333 500 533.333 550
4 644.444 666.667 711.111 733.333
5 805.556 833.333 888.889 916.667
6 966.667 1000 1066.667 1100
7 1127.778 1166.666 1244.444 1283.333
8 1288.889 1333.333 1422.222 1466.667

Golden/Pyrite Tunings±13¢

Degrees Intense Aeolian-Subpental Dorian Dorian
Subpental Pental Superpental
1 160.761-163.65 162.317-165.2055 167.6965-170.585 168.741-171.63
2 321.522-327.3 364.633-330.411 335.393-341.171 337.483-343.36
3 482.284-490.95 486.95-495.617 503.089-511.756 506.224-514.891
4 643.045-654.6 649.2665-660.822 670.786-682.341 674.965-686.521
5 803.806-818.25 811.583-826.028 838.482-852.927 843.707-858.151
6 964.567-981.9 973.9-991.233 1006.179-1023.512 1012.448-1029.781
7 1125.328-1145.55 1136.216-1156.439 1173.875-1194.0975 1181.189-1201.411
8 1286.09-1309.2 1278.2435-1321.644 1341.572-1343.36 1349.9305-1373.042
Degrees Mohajira Beatles
1 170.877-173.776 171.314-174.203
2 341.755-347.513 342.627-348.405
3 512.632-521.2985 513.941-522.607
4 683.509-695.065 685.255-696.81
5 854.386-868.831 856.568-870.112
6 1025.264-1042.997 1027.882-1045.215
7 1196.141-1216.363 1199.196-1219.418
8 1367.018-1389.119 1370.5095-1393.621
Degrees Mixolydian Mixolydian-Ionian
Subpental Pental Superpental
Soft Intense
1 173.091-175.98 173.844-176.733 177.774-180.663 180.707-183.596 182.729-185.618
2 346.182-351.96 347.688-353.466 355.548-361.325 361.415-367.193 365.4585-371.236
3 519.2735-527.94 521.532-530.199 533.321-541.988 542.122-550.789 548.188-556.854
4 692.365-703.92 695.376-706.932 711.095-722.651 722.83-734.385 730.917-742.4725
5 865.456-879.9 869.22-883.6645 888.896-903.3135 903.537-917.982 913.646-928.091
6 1038.547-1055.88 1043.064-1060.3975 1033.634-1083.976 1084.245-1101.578 1096.3755-1113.709
7 1211.638-1231.86 1216.908-1237.13 1244.417-1264.639 1264.952-1285.174 1279.105-1299.327
8 1384.729-1407.84 1390.752-1413.863 1422.19-1445.3015 1445.6595-1445.821 1461.834-1484.945

By a surprising coincidence, the 9ed of the Pyrite tenth (7φ+6)\(5φ^2)edo is almost exactly every fifth degree of 34edo. Additionally, those of the Golden Subpental Dorian and Pental and Intense Superpental Mixolydian tenths are almost exactly every third step of 22edo, 4edf and equal multiples of 10/9 respectively.

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