User:Moremajorthanmajor/17edX
Intervals
| Degrees | Enneatonic | 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 | G | Gb | 84.706 | 86.2745 | 88.235 | 89.84 | 90.756 | 91.765 | 92.647 | 94.118 | 94.929 | 97.363 | 98.8235 | |||||||||||
| 2 | J\\ | A\\ | F# | 169.412 | 172.549 | 176.471 | 179.679 | 181.513 | 183.528 | 185.294 | 188.235 | 189.858 | 194.726 | 197.647 | ||||||||||
| 3 | Gp | G | 254.118 | 258.8235 | 264.706 | 269.519 | 272.268 | 275.294 | 277.941 | 282.353 | 284.787 | 292.089 | 296.471 | |||||||||||
| 4 | J | A | J | A | 338.8235 | 345.098 | 352.941 | 359.358 | 363.025 | 367.059 | 370.588 | 376.471 | 379.716 | 389.452 | 395.294 | |||||||||
| 5 | A | B | Ab | Bb | 423.529 | 431.3725 | 441.1765 | 449.198 | 453.7815 | 458.8235 | 463.235 | 470.588 | 474.645 | 486.815 | 494.118 | |||||||||
| 6 | B\\ | H\\ | J# | A# | 508.235 | 517.647 | 529.412 | 539.037 | 544.538 | 550.588 | 555.882 | 564.706 | 569.574 | 584.1785 | 592.941 | |||||||||
| 7 | Ap | Bp | A | B | 592.941 | 603.921 | 617.647 | 628.877 | 635.394 | 642.353 | 648.529 | 658.8235 | 664.503 | 681.542 | 691.765 | |||||||||
| 8 | B | H | B | H | 677.647 | 690.169 | 705.882 | 718.717 | 726.05 | 734.118 | 741.1765 | 752.941 | 759.432 | 778.905 | 790.588 | |||||||||
| 9 | H | C | Hb | Cb | 762.653 | 776.471 | 794.118 | 808.556 | 816.806 | 825.882 | 833.8235 | 847.059 | 854.361 | 876.268 | 889.412 | |||||||||
| 10 | C\\ | D\\ | B# | H# | 847.059 | 862.745 | 882.353 | 898.396 | 907.563 | 917.647 | 926.471 | 941.1765 | 949.29 | 973.631 | 988.235 | |||||||||
| 11 | Hp | Cp | H | C | 931.765 | 949.02 | 970.588 | 988.235 | 998.319 | 1009.412 | 1019.118 | 1035.294 | 1044.219 | 1070.994 | 1087.059 | |||||||||
| 12 | C | D | C | D | 1016.471 | 1035.294 | 1058.8235 | 1078.075 | 1089.076 | 1101.1765 | 1111.765 | 1129.412 | 1139.148 | 1168.357 | 1185.882 | |||||||||
| 13 | D | S | Db | Sb | 1101.1765 | 1121.569 | 1147.059 | 1167.914 | 1179.832 | 1192.941 | 1204.412 | 1223.529 | 1234.077 | 1265.72 | 1284.706 | |||||||||
| 14 | E | C# | D# | 1185.882 | 1027.843 | 1235.294 | 1257.754 | 1270.588 | 1284.706 | 1297.059 | 1317.647 | 1329.006 | 1363.083 | 1383.529 | ||||||||||
| 15 | F\\ | D | S | 1270.588 | 1294.118 | 1323.529 | 1347.594 | 1361.3445 | 1376.471 | 1389.706 | 1411.765 | 1423.935 | 1460.446 | 1482.352 | ||||||||||
| 16 | Ep | E | 1355.294 | 1380.392 | 1411.765 | 1437.433 | 1452.101 | 1468.235 | 1482.353 | 1505.882 | 1518.864 | 1557.809 | 1581.1765 | |||||||||||
| 17 | F | F | 1440 | 1466.667 | 1500 | 1527.273 | 1542.857 | 1560 | 1575 | 1600 | 1613.793 | 1655.172 | 1680 | |||||||||||
Most harmonic tunings
| Degrees | Enneatonic | Minor mode Middletown temperament | Neutral mode Middletown temperament | Major mode Middletown temperament | |||
|---|---|---|---|---|---|---|---|
| 7/3±13¢ | 22/9±13¢ | 5/2±13¢ | |||||
| 1 | G | Gb | 85.522-87.051 | 90.259-91.789 | 92.548-94.077 | ||
| 2 | J\\ | A\\ | F# | 171-044-174.1025 | 180.5185-183.577 | 185.096-188.155 | |
| 3 | Gp | G | 256.5655-261.154 | 270.778-275.366 | 277.644-282.232 | ||
| 4 | J | A | J | A | 342.087-348.205 | 361.037-367.155 | 370.1915-376.309 |
| 5 | A | B | Ab | Bb | 427.609-435.256 | 451.2965-458.9435 | 462.739-470.386 |
| 6 | B\\ | H\\ | J# | A# | 513.131-522.307 | 541.556-550.732 | 555.287-564.464 |
| 7 | Ap | Bp | A | B | 598.653-609.359 | 631.815-642.521 | 647.835-658.541 |
| 8 | B | H | B | H | 684.1745-696.41. | 722.074-734.31 | 740.383-752.618 |
| 9 | H | C | Hb | Cb | 769.696-783.461 | 812.334-826.098 | 832.931-846.6955 |
| 10 | C\\ | D\\ | B# | H# | 855.218-870.512 | 902.593-917.887 | 925.479-940.773 |
| 11 | Hp | Cp | H | C | 940.74-957.5635 | 992.852.1009.676 | 1018.0265-1034.85 |
| 12 | C | D | C | D | 1026.262-1044.615 | 1083.1115-1101.464 | 1110.574-1128.927 |
| 13 | D | S | Db | Sb | 1111.7847-1131.666 | 1173.371-1193.253 | 1203.122-1223.005 |
| 14 | E | C# | D# | 1197.3055-1218.717 | 1353.889-1375.042 | 1295.67-1317.082 | |
| 15 | F\\ | D | S | 1282.827-1305.768 | 1444.149-1466.83 | 1388.218-1411.159 | |
| 16 | Ep | E | 1368.249-1392.82 | 1534.408-1558.619 | 1480.766-1505.236 | ||
| 17 | F | F | 1453.871-1479.871 | 1534.408-1560.408 | 1573.314-1599.314 | ||
Golden tunings
Minor mode Middletown temperament
| Degrees | Enneatonic | Aeolian-Dorian | Dorian | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| -13¢ | Mean | -13¢ (s5D) | Subpental | Pental | Superpental | |||||||||||
| +13¢ (A-D) | Mean | +13¢ | -13¢ | -13¢ (S5) | Mean | Mean | +13¢ (5) | -13¢ (D-M) | ||||||||
| 1 | G | Gb | 85.109 | 85.874 | 85.932 | 86.638 | 86.697 | 87.462 | 88.7805 | 89.334 | 89.545 | 90.098 | 90.31 | 90.6955 | ||
| 2 | J\\ | A\\ | F# | 170.218 | 171.747 | 171.865 | 173.277 | 173.394 | 174.9235 | 177.561 | 178.667 | 179.09 | 180.197 | 180.62 | 181.391 | |
| 3 | Gp | G | 255.327 | 257.621 | 257.797 | 259.915 | 260.091 | 262.385 | 266.341 | 268.001 | 268.636 | 270.295 | 270.93 | 272.086 | ||
| 4 | J | A | J | A | 340.4355 | 343.494 | 343.729 | 346.553 | 346.788 | 349.847 | 355.122 | 357.335 | 358.181 | 360.393 | 361.2395 | 362.782 |
| 5 | A | B | Ab | Bb | 425.544 | 429.368 | 429.662 | 433.1915 | 433.485 | 437.309 | 442.902 | 446.668 | 447.726 | 450.492 | 451.5495 | 453.477 |
| 6 | B\\ | H\\ | J# | A# | 510.653 | 515.2415 | 515.594 | 519.83 | 520.182 | 524.7705 | 532.683 | 536.002 | 537.271 | 540.59 | 541.859 | 544.173 |
| 7 | Ap | Bp | A | B | 595.762 | 601.115 | 601.526 | 606.468 | 606.879 | 612.232 | 621.463 | 625.3355 | 626.516 | 630.688 | 632.169 | 634.868 |
| 8 | B | H | B | H | 680.871 | 686.989 | 687.459 | 693.106 | 693.576 | 699.694 | 710.244 | 714.996 | 716.3615 | 720.787 | 722.479 | 725.563 |
| 9 | H | C | Hb | Cb | 765.98 | 772.862 | 773.391 | 779.745 | 780.273 | 787.156 | 799.024 | 804.003 | 805.907 | 810.885 | 812.789 | 816.259 |
| 10 | C\\ | D\\ | B# | H# | 851.089 | 858.736 | 859.323 | 866.383 | 866.97 | 874.6175 | 887.805 | 893.336 | 895.452 | 900.983 | 903.099 | 906.955 |
| 11 | Hp | Cp | H | C | 936.198 | 944.609 | 945.256 | 953.021 | 953.667 | 962.079 | 976.585 | 982.67 | 984.997 | 991.082 | 993.409 | 997.65 |
| 12 | C | D | C | D | 1021.3065 | 1030.483 | 1031.188 | 1039.66 | 1040.3645 | 1049.541 | 1065.366 | 1072.004 | 1074.542 | 1081.18 | 1083.719 | 1088.346 |
| 13 | D | S | Db | Sb | 1106.415 | 1116.3565 | 1117.12 | 1186.94 | 1127.0615 | 1137.003 | 1154.146 | 1161.337 | 1164.087 | 1171.2785 | 1174.029. | 1179.041 |
| 14 | E | C# | D# | 1191.524 | 1202.23 | 1203.052 | 1212.936 | 1213.759 | 1224.464 | 1242.927 | 1250.671 | 1253.633 | 1261.377 | 1264.3385 | 1269.737 | |
| 15 | F\\ | D | S | 1276.633 | 1288.104 | 1288.985 | 1299.5745 | 1300.456 | 1311.926 | 1331.707 | 1340.005 | 1343.178 | 1351.475 | 1354.648 | 1360.432 | |
| 16 | Ep | E | 1361.741 | 1373.977 | 1374.917 | 1386.213 | 1387.153 | 1399.388 | 1420.488 | 1426.338 | 1432.723 | 1441.5735 | 1424.958 | 1451.128 | ||
| 17 | F | F | 1446.851 | 1459.851 | 1460.85 | 1472.851 | 1473.85 | 1486.85 | 1509.268 | 1518.672 | 1522.268 | 1531.672 | 1535.268 | 1541.823 | ||
Neutral (Dorian-Mixolydian) mode Middletown temperament
| Degrees | Enneatonic | +13¢ (S5D) | Mean | -13¢ (s5M) | |||
|---|---|---|---|---|---|---|---|
| 1 | G | Gb | 90.863 | 91.46 | 92.019 | ||
| 2 | J\\ | A\\ | F# | 181.726 | 182.92 | 184.038 | |
| 3 | Gp | G | 272.589 | 274.381 | 276.0565 | ||
| 4 | J | A | J | A | 363.452 | 365.841 | 368.075 |
| 5 | A | B | Ab | Bb | 454.315 | 457.301 | 460.094 |
| 6 | B\\ | H\\ | J# | A# | 545.178 | 548.761 | 552.113 |
| 7 | Ap | Bp | A | B | 636.041 | 640.221 | 664.132 |
| 8 | B | H | B | H | 726.904 | 731.6815 | 736.151 |
| 9 | H | C | Hb | Cb | 817.767 | 823.142 | 828.17 |
| 10 | C\\ | D\\ | B# | H# | 908.6305 | 914.602 | 920.1885 |
| 11 | Hp | Cp | H | C | 999.4935 | 1006.062 | 1012.207 |
| 12 | C | D | C | D | 1090.357 | 1097.522 | 1104.226 |
| 13 | D | S | Db | Sb | 1181.22 | 1188.982 | 1196.245 |
| 14 | E | C# | D# | 1272.083 | 1280.443 | 1288.234 | |
| 15 | F\\ | D | S | 1362.946 | 1371.903 | 1380.283 | |
| 16 | Ep | E | 1453.809 | 1463.363 | 1472.3015 | ||
| 17 | F | F | 1544.672 | 1554.823 | 1557.82 | ||
Major mode Middletown temperament
| Degrees | Enneatonic | Mixolydian | Mixolydian-Ionian | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Subpental | Pental | Superpental | Mean | +13¢ | |||||||||||||||
| -13¢ (5) | +13¢ (D-M) | Mean | Mean | +13¢ (s5) | +13¢ | -13¢ (Soft s5) | Soft | Intense | |||||||||||
| +13¢ (Soft s5) | -13¢ | Mean | -13¢ (M-I) | +13¢ | |||||||||||||||
| 1 | G | Gb | 92.035 | 92.225 | 92.401 | 92.8 | 93.548 | 93.5645 | 94.1155 | 94.88 | 95.645 | 95.669 | 96.433 | 96.739 | 97.198 | 97.504 | 98.268 | ||
| 2 | J\\ | A\\ | F# | 184.07 | 184.45 | 184.802 | 185.6 | 187.139 | 198.8245 | 188.231 | 189.7605 | 191.29 | 191.337 | 192.867 | 193.478 | 194.396 | 195.007 | 196.537 | |
| 3 | Gp | G | 276.105 | 276.675 | 277.204 | 278.399 | 280.645 | 280.693 | 282.347 | 284.641 | 286.935 | 287.006 | 289.3 | 290.217 | 291.594 | 292.511 | 294.805 | ||
| 4 | J | A | J | A | 368.14 | 368.9 | 369.605 | 371.199 | 374.193 | 374.258 | 376.462 | 379.521 | 382.58 | 382.675 | 385.733 | 386.956 | 388.792 | 390.015 | 393.074 |
| 5 | A | B | Ab | Bb | 460.175 | 461.1245 | 462.006 | 463.999 | 467.741 | 467.822 | 470.578 | 474.401 | 478.225 | 478.343 | 482.167 | 483.695 | 485.99 | 487.519 | 491.342 |
| 6 | B\\ | H\\ | J# | A# | 552.21 | 553.349 | 554.407 | 556.799 | 561.29 | 561.387 | 564.693 | 569.2815 | 573.87 | 574.012 | 578.6 | 580.434 | 583.188 | 585.022 | 589.6105 |
| 7 | Ap | Bp | A | B | 644.2455 | 645.574 | 646.808 | 649.598 | 654.838 | 654.951 | 658.809 | 664.162 | 669.515 | 669.6805 | 675.033 | 677.173 | 680.386 | 682.526 | 687.879 |
| 8 | B | H | B | H | 736.281 | 737.8 | 739.21 | 742.398 | 748.386 | 748.516 | 752.924 | 759.042 | 765.16 | 765.349 | 771.467 | 773.912 | 777.584 | 780.03 | 783.147 |
| 9 | H | C | Hb | Cb | 828.316 | 830.024 | 831.611 | 835.198 | 841.934 | 842.08 | 847.04 | 853.922 | 860.805 | 861.018 | 867.9 | 870.416 | 874.7852 | 877.5335 | 884.416 |
| 10 | C\\ | D\\ | B# | H# | 920.351 | 922.249 | 924.012 | 927.998 | 935.483 | 935.645 | 941.155 | 948.8025 | 956.45 | 956.6865 | 964.3335 | 967.39 | 971.9805 | 975.037 | 982.684 |
| 11 | Hp | Cp | H | C | 1012.386 | 1014.474 | 1016.413 | 1020.7975 | 1029.031 | 1029.209 | 1035.271 | 1043.683 | 1052.0945 | 1052.355 | 1060.767 | 1064.129 | 1069.179 | 1072.541 | 1080.953 |
| 12 | C | D | C | D | 1104.421 | 1106.699 | 1108.814 | 1113.567 | 1122.579 | 1122.774 | 1129.3865 | 1138.563 | 1147.7395 | 1148.024 | 1157.2 | 1160.868 | 1166.377 | 1170.045 | 1179.221 |
| 13 | D | S | Db | Sb | 1196.456 | 1198.924 | 1201.216 | 1206.397 | 1216.127 | 1216.338 | 1223.502 | 1233.443 | 1243.384 | 1243.692 | 1253.6335 | 1257.607 | 1263.575 | 1267.548 | 1277.4895 |
| 14 | E | C# | D# | 1288.491 | 1291.1485 | 1293.617 | 1299.197 | 1309.676 | 1309.903 | 1317.618 | 1328.3235 | 1339.026 | 1339.361 | 1350.067 | 1354.346 | 1360.773 | 1365.052 | 1375.758 | |
| 15 | F\\ | D | S | 1380.526 | 1383.373 | 1386.018 | 1391.997 | 1403.224 | 1403.467 | 1411.733 | 1423.204 | 1434.674 | 1435.03 | 1446.5 | 1451.085 | 1457.97 | 1462.556 | 1474.026 | |
| 16 | Ep | E | 1472.561 | 1475.598 | 1478.419 | 1484.796 | 1496.772 | 1497.032 | 1505.849 | 1518.083 | 1530.319 | 1530.698 | 1542.934 | 1547.824 | 1555.169 | 1560.0595 | 1572.295 | ||
| 17 | F | F | 1564.596 | 1567.96 | 1570.82 | 1577.596 | 1583.82 | 1590.596 | 1599.964 | 1612.964 | 1625.964 | 1626.366 | 1639.366 | 1644.563 | 1652.366 | 1657.563 | 1670.563 | ||