User:Moremajorthanmajor/9edX: Difference between revisions
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!Min-comma | !Min-comma | ||
!Med | !Med | ||
!Max+comma | ! colspan="2" |Max+comma~Min-comma | ||
!Med | !Med | ||
!Max+comma | ! colspan="2" |Max+comma~Min-comma | ||
!Med | !Med | ||
!Max+comma | ! colspan="2" |Max+comma~Min-comma | ||
!Med | !Med | ||
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!''r¢'' | !''r¢'' | ||
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!Max+comma | ! colspan="2" |Max+comma~Min-comma | ||
!Med | !Med | ||
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!Min-comma | !Min-comma | ||
!Med | !Med | ||
!Max+comma | ! colspan="2" |Max+comma~Min-comma | ||
!Med | !Med | ||
!Max+comma | ! colspan="2" |Max+comma~Min-comma | ||
!Med | !Med | ||
!Max+comma | ! colspan="2" |Max+comma~Min-comma | ||
!Med | !Med | ||
!Max+comma | ! colspan="2" |Max+comma~Min-comma | ||
!Med | !Med | ||
! |Max+comma | ! |Max+comma | ||
Revision as of 15:33, 2 January 2020
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 | 155.556-160 | 161.905 | 158.5185-167.407 | 164.103 | 162.222-171.111 | 168.889 | 165.2525-174.141 | 170.37 | 171.429-175.873 | |||
| 2 | 311.111-320 | 323.8095 | 317.037-334.814 | 328.205 | 324.444-342.222 | 337.778 | 330.505-348.283 | 340.741 | 342.857-351.746 | |||
| 3 | 466.667-480 | 485.714 | 475.556-502.222 | 492.308 | 486.667-513.333 | 506.667 | 495.758-522.424 | 511.111 | 514.286-527.619 | |||
| 4 | 622.222-640 | 647.619 | 634.074-669.63 | 656.41 | 648.889-684.444 | 675.556 | 661.01-696.566 | 681.4815 | 685.714-703.492 | |||
| 5 | 777.778-800 | 809.524 | 792.593-837.037 | 820.512 | 811.111-855.556 | 844.444 | 826.263-870.707 | 851.852 | 857.143-878.365 | |||
| 6 | 943.333-960 | 971.429 | 951.111-1004.444 | 984.615 | 973.333-1026.667 | 1013.333 | 988.515-1044.848 | 1022.222 | 1028.571-1055.238 | |||
| 7 | 1088.889-1120 | 1133.333 | 1109.63-1171.852 | 1148.718 | 1135.556-1197.778 | 1182.222 | 1156.768-1218.99 | 1192.593 | 1200-1231.111 | |||
| 8 | 1244.444-1280 | 1295.238 | 1238.148-1339.259 | 1312.8205 | 1297.778-1368.889 | 1351.111 | 1321.02-1392.131 | 1362.963 | 1371.429-1406.984 | |||
| Degrees | Mohajira | Beatles | |||||
|---|---|---|---|---|---|---|---|
| Min-comma | r¢ | Med | Max+comma~Min-comma | Med | Max+comma | ||
| 1 | 166.984-171.429 | 172.222 | 168.105-176.9935 | 172.8395 | 173.333-177.778 | ||
| 2 | 333.968-342.857 | 344.444 | 336.209-353.987 | 345.679 | 346.667-355.556 | ||
| 3 | 500.952-514.286 | 516.667 | 504.314-530.98 | 518.5185 | 520-533.333 | ||
| 4 | 667.9365-685.714 | 688.889 | 672.418-707.974 | 691.358 | 693.333-711.111 | ||
| 5 | 834.921-857.143 | 861.111 | 840.523-885.967 | 864.1975 | 866.667-888.889 | ||
| 6 | 1001.904-1028.571 | 1033.333 | 1008.6275-1062.961 | 1037.037 | 1040-1066.667 | ||
| 7 | 1168.889-1200 | 1205.556 | 1176.732-1239.954 | 1209.8765 | 1213.333-1244.444 | ||
| 8 | 1335.873-1371.429 | 1377.778 | 1344.837-1416.948 | 1382.716 | 1386.667-1422.222 | ||
| 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 | 168.889-173.333 | 174.359 | 170.556-179.444 | 175.439 | 173.333-182.222 | 179.167 | 174.866-183.755 | 181.609 | 179.464-188.3525 | 184.314 | 186.667-191.111 | ||||
| 2 | 337.778-346.667 | 348.718 | 341.111-358.889 | 350.877 | 346.667-364.444 | 358.333 | 349.732-367.51 | 363.218 | 368.927-376.705 | 368.6275 | 373.333-382.222 | ||||
| 3 | 506.667-520 | 523.077 | 511.667-538.333 | 526.316 | 520-546.667 | 537.5 | 524.598-551.264 | 544.828 | 538.391-565.0575 | 552.941 | 560-573.333 | ||||
| 4 | 675.556-693.333 | 697.436 | 682.222-717.778 | 701.754 | 693.333-728.889 | 716.667 | 699.464-735.019 | 726.437 | 717.854-753.41 | 737.255 | 746.667-764.444 | ||||
| 5 | 844.444-866.667 | 871.795 | 852.778-897.222 | 877.193 | 866.667-911.111 | 895.833 | 874.3295-918.774 | 908.046 | 897.318-942.7625 | 921.569 | 933.333-955.556 | ||||
| 6 | 1013.333-1040 | 1046.154 | 1023.333-1076.667 | 1052.632 | 1040-1093.333 | 1075 | 1049.195-1102.529 | 1089.655 | 1076.782-1130.115 | 1105.882 | 1120-1146.667 | ||||
| 7 | 1182.222-1213.333 | 1220.513 | 1193.889-1256.111 | 1228.07 | 1213.333-1275.556 | 1254.167 | 1224.061-1286.2835 | 1271.264 | 1256.245-1318.457 | 1290.196 | 1306.667-1337.778 | ||||
| 8 | 1351.111-1386.667 | 1394.872 | 1364.444-1435.556 | 1403.509 | 1386.667-1457.778 | 1433.333 | 1398.927-1470.038 | 1452.874 | 1438.709-1506.82 | 1474.51 | 1493.333-1528.889 | ||||
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 | 1025.264-1042.597 | 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.