User:Moremajorthanmajor/19edX
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Explanation needed for what this is. See edX maybe?
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 | Gb | 75.7895 | 77.193 | 78.947 | 80.383 | 81.203 | 82.105 | 82.895 | 84.2105 | 84.9365 | 87.114 | 88.421 | ||||||||||
| 2 | F# | 151.579 | 154.386 | 157.895 | 160.766 | 162.406 | 164.2105 | 165.7896 | 168.421 | 169.873 | 174.229 | 176.842 | ||||||||||
| 3 | G | 227.368 | 231.579 | 236.842 | 241.148 | 243.609 | 246.316 | 248.684 | 252.632 | 254.809 | 261.343 | 265.263 | ||||||||||
| 4 | J | A | 303.158 | 308.772 | 315.7895 | 321.531 | 324.812 | 328.421 | 331.579 | 336.842 | 339.746 | 348.457 | 353.684 | |||||||||
| 5 | Ab | Bb | 378.947 | 385.965 | 394.737 | 401.914 | 406.015 | 410.526 | 414.474 | 421.053 | 424.682 | 435.527 | 442.105 | |||||||||
| 6 | J# | A# | 454.737 | 463.158 | 473.684 | 482.297 | 487.218 | 492.632 | 497.368 | 505.263 | 509.619 | 522.686 | 530.526 | |||||||||
| 7 | A | B | 530.526 | 540.351 | 552.632 | 592.679 | 568.421 | 574.737 | 580.263 | 589.474 | 594.555 | 609.8 | 618.947 | |||||||||
| 8 | B | H | 606.316 | 617.544 | 631.579 | 643.062 | 647.624 | 656.842 | 663.158 | 673.684 | 679.491 | 696.915 | 707.368 | |||||||||
| 9 | Hb | Cb | 682.105 | 694.737 | 710.526 | 723.445 | 730.827 | 738.947 | 746.053 | 757.895 | 764.418 | 784.029 | 795.7895 | |||||||||
| 10 | B# | H# | 757.895 | 771.93 | 789.474 | 803.828 | 812.03 | 821.053 | 828.947 | 842.105 | 849.365 | 871.143 | 884.2105 | |||||||||
| 11 | H | C | 833.654 | 849.123 | 868.421 | 884.2105 | 893.233 | 903.158 | 911.843 | 926.316 | 934.302 | 958.258 | 972.632 | |||||||||
| 12 | C | D | 909.474 | 926.326 | 947.378 | 964.593 | 974.436 | 985.263 | 994.737 | 1010.526 | 1019.238 | 1045.372 | 1061.053 | |||||||||
| 13 | Db | Sb | 985.263 | 1003.509 | 1026.316 | 1044.976 | 1055.639 | 1067.368 | 1077.612 | 1094.737 | 1104.172 | 1132.486 | 1149.474 | |||||||||
| 14 | C# | D# | 1061.053 | 1080.702 | 1105.263 | 1125.359 | 1136.842 | 1149.474 | 1160.526 | 1178.947 | 1189.111 | 1220.601 | 1237.895 | |||||||||
| 15 | D | S | 1136.842 | 1107.895 | 1184.2105 | 1205.742 | 1218.045 | 1231.579 | 1243.421 | 1263.158 | 1274.047 | 1306.715 | 1326.316 | |||||||||
| 16 | Eb | 1212.632 | 1235.088 | 1363.156 | 1286.124 | 1299.248 | 1313.684 | 1326.316 | 1347.378 | 1359.984 | 1393.829 | 1414.737 | ||||||||||
| 17 | D# | S# | 1288.421 | 1312.181 | 1042.105 | 1366.507 | 1380.451 | 1395.7895 | 1408.2105 | 1431.579 | 1443.98 | 1480.944 | 1503.158 | |||||||||
| 18 | E | 1364.2105 | 1389.474 | 1421.053 | 1446.89 | 1461.654 | 1477.895 | 1491.105 | 1515.7895 | 1526.8275 | 1568.058 | 1591.579 | ||||||||||
| 19 | 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 | Gb | 76.5195-77.888 | 80.758-82.127 | 82.806-84.174 | |
| 2 | F# | 153.039-155.776 | 161.517-164.2535 | 165.612-168.349 | |
| 3 | G | 229.559-233.664 | 242.275-246.38 | 248.418-252.523 | |
| 4 | J | A | 306.078-311.552 | 323.033-328.507 | 331.224-336.698 |
| 5 | Ab | Bb | 382.598-389.44 | 403.792-410.634 | 414.03-420.872 |
| 6 | J# | A# | 459.117-467.328 | 484.55-492.76 | 496.835-505.046 |
| 7 | A | B | 535.637-545.216 | 565.308-574.887 | 579.342-589.221 |
| 8 | B | H | 612.156-623.1035 | 646.0665-657.014 | 662.448-673.395 |
| 9 | Hb | Cb | 688.676-700.9915 | 726.825-739.141 | 745.254-757.57 |
| 10 | B# | H# | 765.195-778.879 | 807.583-821.267 | 828.06-841.744 |
| 11 | H | C | 841.715-856.767. | 888.341-903.394 | 910.866-925.9185 |
| 12 | C | D | 918.234-934.655 | 969.1-985.52 | 993.672-1010.093 |
| 13 | Db | Sb | 994.754-1012.543 | 1049.858-1067.6475 | 1076.478-1094.267 |
| 14 | C# | D# | 1071.273-1090.431 | 1130.616-1149.774 | 1159.284-1178.442 |
| 15 | D | S | 1147.793-1168.319 | 1211.375-1231.901 | 1242.09-1262.616 |
| 16 | Eb | 1224.312-1266.207 | 1292.133-1314.028 | 1324.896-1346.7905 | |
| 17 | D# | S# | 1300.832--1324.095 | 1372.891-1396.1545 | 1407.702-1430.965 |
| 18 | E | 1377.351-1401.983 | 1453.65-1478.281 | 1490.507-1515.139 | |
| 19 | 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 | Gb | 76.15 | 76.834 | 76.887 | 77.5185 | 77.571 | 78.255 | 79.435 | 79.93 | 80.119 | 80.614 | 80.804 | 81.149 | |
| 2 | F# | 152.3 | 153.6685 | 153.774 | 155.037 | 155.142 | 156.5105 | 158.87 | 159.86 | 160.239 | 161.229 | 161.607 | 162.297 | |
| 3 | G | 228.45 | 230.503 | 230.6605 | 232.555 | 232.713 | 234.766 | 238.3055 | 239.79 | 240.358 | 241.843 | 242.411 | 243.446 | |
| 4 | J | A | 304.6 | 307.337 | 307.547 | 310.074 | 310.284 | 313.021 | 317.741 | 319.72 | 320.4775 | 322.457 | 323.214 | 324.594 |
| 5 | Ab | Bb | 380.75 | 384.171 | 384.434 | 387.592 | 387.855 | 391.276 | 397.176 | 399.6505 | 400.597 | 403.3715 | 404.018 | 405.743 |
| 6 | J# | A# | 456.9 | 461.055 | 461.321 | 465.111 | 465.426 | 469.5315 | 476.611 | 479.581 | 480.716 | 483.686 | 484.8215 | 486.8915 |
| 7 | A | B | 533.05 | 537.84 | 538.208 | 542.926 | 542.997 | 547.787 | 556.046 | 559.511 | 560.836 | 564.3 | 565.625 | 568.04 |
| 8 | B | H | 609.2 | 614.074 | 615.095 | 620.148 | 620.568 | 626.042 | 635.481 | 639.441 | 640.955 | 644.9145 | 648.429 | 649.189 |
| 9 | Hb | Cb | 685.35 | 691.508 | 691.981 | 697.666 | 698.139 | 704.297 | 714.9165 | 719.371 | 721.074 | 725.529 | 727.232 | 730.337 |
| 10 | B# | H# | 761.5 | 768.3425 | 768.868 | 775.185 | 775.71 | 782.5525 | 794.352 | 799.301 | 801.194 | 806.143 | 808.036 | 811.486 |
| 11 | H | C | 837.6505 | 845.177 | 845.755 | 852.703 | 853.281 | 860.808 | 873.787 | 879.231 | 881.313 | 886.757 | 888.8395 | 892.6345 |
| 12 | C | D | 913.8005 | 922.011 | 922.642 | 930.222 | 930.852 | 939.063 | 953.222 | 959.161 | 964.4325 | 967.372 | 969.643 | 973.783 |
| 13 | Db | Sb | 989.951 | 998.845 | 999.529 | 1007.74 | 1008.4235 | 1017.318 | 1032.657 | 1039.091 | 1041.552 | 1047.986 | 1050.447 | 1054.932 |
| 14 | C# | D# | 1066.101 | 1075.68 | 1076.416 | 1085.2585 | 1085.9945 | 1095.5735 | 1112.092 | 1119.021 | 1121.671 | 1128.6 | 1131.25 | 1136.08 |
| 15 | D | S | 1142.251 | 1152.514 | 1153.302 | 1162.777 | 1163.566 | 1173.829 | 1191.5275 | 1198.9515 | 1201.791 | 1209.215 | 1212.054 | 1217.229 |
| 16 | Eb | 1218.401 | 1229.348 | 1230.159 | 1240.295 | 1241.137 | 1525.054 | 1270.963 | 1279.882 | 1281.91 | 1289.829 | 1292.857 | 1298.377 | |
| 17 | D# | S# | 1294.551 | 1306.182 | 1307.0769 | 1317.814 | 1318.708 | 1330.339 | 1350.298 | 1358.612 | 1362.029 | 1370.443 | 1373.661 | 1379.526 |
| 18 | E | 1370.701 | 1383.017 | 1383.963 | 1395.332 | 1396.279 | 1408.594 | 1429.833 | 1438.742 | 1442.149 | 1451.0575 | 1454.465 | 1460.675 | |
| 19 | 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 | Gb | 81.2985 | 81.833 | 81.9905 | |
| 2 | F# | 162.597 | 163.666 | 163.984 | |
| 3 | G | 243.896 | 245.498 | 245.972 | |
| 4 | J | A | 325.164 | 327.331 | 327.962 |
| 5 | Ab | Bb | 406.493 | 409.164 | 409.953 |
| 6 | J# | A# | 487.791 | 490.997 | 491.943 |
| 7 | A | B | 569.09 | 572.83 | 573.934 |
| 8 | B | H | 650.388 | 654.662 | 655.924 |
| 9 | Hb | Cb | 731.687 | 736.495 | 737.915 |
| 10 | B# | H# | 812.985 | 818.327 | 819.9055 |
| 11 | H | C | 894.284 | 900.161 | 901.896 |
| 12 | C | D | 975.582. | 981.994 | 983.887 |
| 13 | Db | Sb | 1056.881 | 1063.826 | 1065.877 |
| 14 | C# | D# | 1138.179 | 1145.659 | 1147.868 |
| 15 | D | S | 1219.478 | 1227.492 | 1229.858 |
| 16 | Eb | 1300.776 | 1309.325 | 1311.849 | |
| 17 | D# | S# | 1382.075 | 1391.158 | 1393.839 |
| 18 | E | 1463.373 | 1472.99 | 1475.83 | |
| 19 | 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 | Gb | 82.347 | 82.517 | 82.675 | 83.031 | 83.359 | 83.716 | 84.209 | 84.893 | 85.557 | 85.598 | 86.2825 | 86.556 | 86.967 | 87.24 | 87.924 | |
| 2 | F# | 164.695 | 165.034 | 165.3495 | 166.063 | 166.718 | 167.431 | 168.417 | 169.786 | 171.154 | 171.1965 | 172.565 | 173.112 | 173.933 | 174.48 | 175.849 | |
| 3 | G | 247.0415 | 247.551 | 248.024 | 249.094 | 250.077 | 251.147 | 252.626 | 254.679 | 256.731 | 256.795 | 258.847 | 259.668 | 260.9 | 261.7205 | 263.773 | |
| 4 | J | A | 329.389 | 330.068 | 330.7 | 332.1255 | 333.436 | 334.862 | 336.835 | 339.571 | 342.308 | 342.393 | 345.13 | 346.224 | 347.867 | 348.961 | 351.6975 |
| 5 | Ab | Bb | 411.736 | 412.585 | 413.374 | 415.157 | 416.795 | 418.578 | 421.043 | 424.464 | 427.885 | 427.991 | 431.412 | 432.78 | 434.833 | 436.201 | 439.622 |
| 6 | J# | A# | 494.083 | 495.102 | 496.0485 | 498.188 | 500.154 | 502.2935 | 505.252 | 509.357 | 513.462 | 513.59 | 517.695 | 519.336 | 521.8 | 523.441 | 527.546 |
| 7 | A | B | 576.43 | 577.619 | 578.723 | 581.22 | 583.513 | 586.001 | 589.4602 | 594.25 | 599.0395 | 599.188 | 603.977 | 605.892 | 608.767 | 610.681 | 615.471 |
| 8 | B | H | 658.777 | 660.136 | 661.398 | 664.251 | 666.872 | 669.725 | 673.669 | 679.143 | 684.6165 | 684.786 | 690.26 | 692.448 | 694.733 | 697.921 | 703.395 |
| 9 | Hb | Cb | 741.1245 | 742.653 | 744.073 | 747.282 | 750.231 | 752.44 | 757.878 | 764.036 | 770.194 | 770.384 | 776.542 | 779.004 | 782.7 | 785.1615 | 791.319 |
| 10 | B# | H# | 834.451 | 825.17 | 826.748 | 830.314 | 833.59 | 837.156 | 842.086 | 848.9285 | 855.771 | 855.983 | 862.825 | 865.56 | 881.262 | 872.402 | 879.244 |
| 11 | H | C | 905.819 | 907.687 | 909.422 | 913.345 | 916.949 | 917.156 | 926.295 | 933.821 | 941.348 | 941.581 | 949.107 | 952.1155 | 956.6335 | 959.642 | 967.168 |
| 12 | C | D | 988.166 | 990.304 | 992.097 | 996.3765 | 1000.308 | 1000.8715 | 1010.503 | 1018.714 | 1026.925 | 1027.179 | 1035.39 | 1038.6715 | 1043.6 | 1046.882 | 1055.093 |
| 13 | Db | Sb | 1070.513 | 1072.721 | 1074.772 | 1079.408 | 1083.667 | 1084.587 | 1094.712 | 1103.607 | 1112.502 | 1112.777 | 1121.672 | 1125.2275 | 1130.567 | 1134.122 | 1143.017 |
| 14 | C# | D# | 1152.86 | 1152.238 | 1157.44 | 1162.439 | 1167.026 | 1168.303 | 1178.921 | 1188.5 | 1198.079 | 1198.376 | 1207.955 | 1211.783 | 1217.5335 | 1221.362 | 1230.941 |
| 15 | D | S | 1235.2075 | 1237.755 | 1240.121 | 1245.471 | 1250.3845 | 1252.018 | 1263.13 | 1273.392 | 1283.656 | 1283.974 | 1294.237 | 1298.339 | 1304.5 | 1308.6025 | 1318.451 |
| 16 | Eb | 1317.555 | 1320.272 | 1322.796 | 1328.502 | 1333.743 | 1335.734 | 1347.338 | 1358.286 | 1369.233 | 1369.572 | 1380.5195 | 1384.895 | 1389.467 | 1395.843 | 1406.79 | |
| 17 | D# | S# | 1355.983 | 1402.789 | 1405.471 | 1411.533 | 1417.1025 | 1378.517 | 1431.547 | 1443.1785 | 1454.81 | 1455.17 | 1466.802 | 1471.451 | 1478.434 | 1483.083 | 1494.7145 |
| 18 | E | 1399.902 | 1485.306 | 1488.149 | 1494.565 | 1500.461 | 1499.446 | 1515.756 | 1528.071 | 1540.387 | 1540.769 | 1553.0845 | 1558.007 | 1565.4 | 1570.323 | 1582.639 | |
| 19 | 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 | |