User:Moremajorthanmajor/9edX
This is the neutral scale of the Middletown temperament family.
Intervals
| Degrees | Minor mode Middletown temperament | Neutral mode Middletown temperament | Major mode Middletown temperament | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Aeolian-Dorian | Dorian | Dorian-Mixolydian | Mixolydian | Mixolydian-Ionian | ||||||||||||||||
| Subpental | Pental | Superpental | Subpental | Pental | Superpental | |||||||||||||||
| Soft | Intense | |||||||||||||||||||
| Minimum | Maximum | Minimum | Maximum | Minimum | Maximum | Minimum | Maximum | Minimum | Maximum | Minimum | Maximum | Minimum | Maximum | Minimum | Maximum | Minimum | Maximum | Minimum | Maximum | |
| 1 | 160 | 162.963 | 166.667 | 169.697 | 171.429 | 173.333 | 175 | 177.778 | 179.31 | 183.908 | 186.667 | |||||||||
| 2 | 320 | 325.926 | 333.333 | 339.394 | 342.857 | 246.667 | 350 | 355.556 | 358.621 | 367.816 | 373.333 | |||||||||
| 3 | 480 | 488.889 | 500 | 509.091 | 514.286 | 520 | 525 | 533.333 | 537.931 | 551.724 | 560 | |||||||||
| 4 | 640 | 651.852 | 666.667 | 678.788 | 685.714 | 693.333 | 700 | 711.111 | 717.241 | 735.632 | 746.667 | |||||||||
| 5 | 800 | 814.815 | 833.333 | 848.485 | 857.143 | 866.667 | 875 | 888.889 | 896.552 | 919.54 | 1033.333 | |||||||||
| 6 | 960 | 977.778 | 1000 | 1018.182 | 1028.571 | 1040 | 1050 | 1066.667 | 1075.862 | 1103.448 | 1120 | |||||||||
| 7 | 1120 | 1140.741 | 1166.666 | 1187.879 | 1200 | 1213.333 | 1225 | 1244.444 | 1255.172 | 1287.356 | 1306.667 | |||||||||
| 8 | 1280 | 1303.704 | 1333.333 | 1357.576 | 1371.429 | 1386.667 | 1400 | 1422.222 | 1434.483 | 1471.264 | 1493.333 | |||||||||
Most harmonic tunings
| Degrees | Minor mode Middletown temperament | Neutral mode Middletown temperament | Major mode Middletown temperament |
|---|---|---|---|
| 7/3±13¢ | 22/9±13¢ | 5/2±13¢ | |
| 1 | 161.541-164.43 | 170.49-173.379 | 174.813-177.7015 |
| 2 | 323.082-328.86 | 340.9795-346.757 | 349.625-355.403 |
| 3 | 484.624-493.29 | 511.469-520.136 | 524.438-533.105 |
| 4 | 646.165-657.72 | 681.959-693.515 | 699.2505-710.806 |
| 5 | 807.706-822.1505 | 852.489-866.893 | 874.063-888.508 |
| 6 | 969.247-986.581 | 1022.939-1040.272 | 1048.876-1066.5425 |
| 7 | 1130.7885-1151.011 | 1193.428-1215.651 | 1223.688-1244.466 |
| 8 | 1292.33-1315.441 | 1363.918-1387.293 | 1398.4501-1422.391 |
Golden tunings±13¢
| Degrees | Minor mode Middletown temperament | Neutral mode Middletown temperament | Major mode Middletown temperament | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Aeolian-Dorian | Dorian | Dorian-Mixolydian | Mixolydian | Mixolydian-Ionian | ||||||
| Subpental | Pental | Superpental | Subpental | Pental | Superpental | |||||
| Soft | Intense | |||||||||
| 1 | 160.761-163.65 | 162.317-165.2055 | 167.6965-170.585 | 168.741-171.63 | 171.314-174.203 | 173.091-175.98 | 173.844-176.733 | 177.774-180.663 | 180.707-183.596 | 182.729-185.618 |
| 2 | 321.522-327.3 | 364.633-330.411 | 335.393-341.171 | 337.483-343.36 | 342.617-348.405 | 346.182-351.96 | 347.688-353.466 | 355.548-361.325 | 361.415-367.193 | 365.4585-371.236 |
| 3 | 482.284-490.95 | 486.95-495.617 | 503.089-511.756 | 506.224-514.891 | 513.941-522.608 | 519.2735-527.94 | 521.532-530.199 | 533.321-541.988 | 542.122-550.789 | 548.188-556.854 |
| 4 | 643.045-654.6 | 649.2665-660.822 | 670.786-682.341 | 674.965-686.521 | 685.255-696.81 | 692.365-703.92 | 695.376-706.932 | 711.095-722.651 | 722.83-734.385 | 730.917-742.4725 |
| 5 | 803.806-818.25 | 811.583-826.028 | 838.482-852.927 | 843.707-858.151 | 856.568-871.012 | 865.456-879.9 | 869.22-883.6645 | 888.896-903.3135 | 903.537-917.982 | 913.646-928.091 |
| 6 | 964.567-981.9 | 973.9-991.233 | 1006.179-1023.512 | 1012.448-1029.781 | 1027.882-1045.2155 | 1038.547-1055.88 | 1043.064-1060.3975 | 1033.634-1083.976 | 1084.245-1101.578 | 1096.3755-1113.709 |
| 7 | 1125.328-1145.55 | 1136.216-1156.439 | 1173.875-1194.0975 | 1181.189-1201.411 | 1199.196-1219.418 | 1211.638-1231.86 | 1216.908-1237.13 | 1244.417-1264.639 | 1264.952-1285.174 | 1279.105-1299.327 |
| 8 | 1286.09-1309.2 | 1278.2435-1321.644 | 1341.572-1343.36 | 1349.9305-1373.042 | 1370.5095-1393.621 | 1384.729-1407.84 | 1390.752-1413.863 | 1422.19-1445.3015 | 1445.6595-1445.821 | 1461.834-1484.945 |
Minor mode Middletown temperament
Neutral (Dorian-Mixolydian) mode Middletown temperament
Major mode Middletown temperament
By a surprising coincidence, the 9ed of the Pyrite tenth (7*phi+6)\(5*phi^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.