User:Moremajorthanmajor/9edX: Difference between revisions
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This is the neutral scale of the Middletown temperament family. | This is the neutral scale of the Middletown temperament family. | ||
==Intervals== | |||
== Intervals == | |||
{| class="wikitable" style="text-align: center" | {| class="wikitable" style="text-align: center" | ||
! rowspan="3" |Degrees | ! rowspan="3" |Degrees | ||
| Line 524: | Line 525: | ||
|1445.6595-1445.821 | |1445.6595-1445.821 | ||
|1461.834-1484.945 | |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|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. | |} | ||
By a surprising coincidence, the 9ed of the Pyrite tenth (7φ+6)\(5φ^2)edo is almost exactly every fifth degree of [[34edo|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. | |||
== See also == | |||
* [[9ed5/2]] - equal division of the classic major tenth | |||
* [[9ed7/3]] - equal division of the septimal minor tenth | |||
[[Category:EdX]] | [[Category:EdX]] | ||
Revision as of 13:04, 9 January 2022
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.