User:Moremajorthanmajor/15edX
15edX is the scale which occurs as the dominant minor edX.
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 | |||||||||||||||||||||
| Min | Max | Min | Max | Min | Max | Min | Max | Min | Max | Min | Max | Min | Max | Min | Max | Min | Max | Min | Max | |||
| 1 | F#/Gb | 96 | 97.778 | 100 | 101.818 | 102.857 | 104 | 105 | 106.667 | 107.586 | 110.345 | 112 | ||||||||||
| 2 | G | 192 | 195.556 | 200 | 203.636 | 205.714 | 208 | 210 | 213.333 | 215.172 | 220.69 | 224 | ||||||||||
| 3 | G#/Jb | G#/Ab | 288 | 293.333 | 300 | 305.4545 | 308.571 | 312 | 315 | 320 | 322.759 | 331.034 | 336 | |||||||||
| 4 | J | A | 384 | 391.111 | 400 | 407.273 | 411.429 | 416 | 420 | 426.667 | 430.345 | 441.379 | 448 | |||||||||
| 5 | A | B | 480 | 488.889 | 500 | 509.091 | 514.286 | 520 | 525 | 533.333 | 537.931 | 551.724 | 560 | |||||||||
| 6 | A#/Bb | B#/Hb | 576 | 586.667 | 600 | 610.909 | 617.143 | 624 | 630 | 640 | 645.517 | 662.069 | 672 | |||||||||
| 7 | B | H | 672 | 684.444 | 700 | 712.727 | 720 | 728 | 735 | 746.667 | 753.103 | 772.414 | 784 | |||||||||
| 8 | B#/Hb | H#/Cb | 768 | 782.822 | 800 | 814.5455 | 822.857 | 832 | 845 | 853.333 | 860.69 | 882.759 | 896 | |||||||||
| 9 | H | C | 864 | 880 | 900 | 916.364 | 925.714 | 936 | 940 | 960 | 968.276 | 993.103 | 1008 | |||||||||
| 10 | C | D | 960 | 977.778 | 1000 | 1018.182 | 1028.571 | 1040 | 1050 | 1066.667 | 1075.862 | 1103.448 | 1120 | |||||||||
| 11 | C#/Db | D#/Sb | 1056 | 1075.556 | 1100 | 1120 | 1131.429 | 1144 | 1155 | 1173.333 | 1183.448 | 1213.379 | 1232 | |||||||||
| 12 | D | S | 1152 | 1173.333 | 1200 | 1221.818 | 1234.286 | 1248 | 1260 | 1280 | 1291.034 | 1324.138 | 1344 | |||||||||
| 13 | D#/Eb | S#/Eb | 1248 | 1271.111 | 1300 | 1323.636 | 1337.143 | 1352 | 1365 | 1386.667 | 1398.621 | 1424.483 | 1456 | |||||||||
| 14 | E | 1344 | 1368.889 | 1400 | 1425.4545 | 1440 | 1456 | 1470 | 1493.333 | 1506.207 | 1544.827 | 1568 | ||||||||||
| 15 | 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 | F#/Gb | 96.925-98.658 | 102.294-104.027 | 104.888-106.621 | |
| 2 | G | 193.8495-197.316 | 204.588-208.054 | 209.77-213.242 | |
| 3 | G#/Jb | G#/Ab | 290.774-295.974 | 306.8815-312.0815 | 314.663-319.863 |
| 4 | J | A | 387.699-394.632 | 409.1755-416.109 | 419.559-426.484 |
| 5 | A | B | 484.624-493.29 | 511.469-520.136 | 524.438-533.105 |
| 6 | A#/Bb | B#/Hb | 581.548-591.948 | 613.763-624.163 | 629.3255-639.7255 |
| 7 | B | H | 678.473-690.606 | 716.057-728.19 | 734.213-746.346 |
| 8 | B#/Hb | H#/Cb | 775.398-789.2645 | 818.351-832.218 | 839.101-852.967 |
| 9 | H | C | 872.3225-887.9225 | 920.645-936.245 | 943.988-959.588 |
| 10 | C | D | 969.247-986.561 | 1022.939-1040.272 | 1048.876-1066.209 |
| 11 | C#/Db | D#/Sb | 1066.172-1085.239 | 1125.2325-1144.299 | 1153.763-1172.83 |
| 12 | D | S | 1163.097-1183.897 | 1227.526-1248.326 | 1258.651-1279.451 |
| 13 | D#/Eb | S#/Eb | 1260.0215-1282.555 | 1329.82-1352.3535 | 1363.539-1386.072 |
| 14 | E | 1356.946-1381.213 | 1432.114-1456.381 | 1468.426-1492.693 | |
| 15 | 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 | F#/Gb | 96.457 | 97.323 | 97.39 | 98.19 | 98.257 | 99.123 | 100.618 | 101.245 | 101.4845 | 102.1115 | 102.351 | 102.788 | |
| 2 | G | 192.913 | 194.647 | 194.78 | 196.38 | 196.513 | 198.247 | 201.236 | 202.49 | 202.969 | 204.223 | 204.702 | 205.576 | |
| 3 | G#/Jb | G#/Ab | 289.37 | 291.97 | 292.17 | 294.57 | 294.77 | 297.37 | 301.854 | 303.734 | 304.454 | 306.334 | 307.054 | 308.365 |
| 4 | J | A | 385.829 | 389.294 | 389.56 | 392.76 | 394.027 | 396.493 | 402.4715 | 404.979 | 405.938 | 408.446 | 409.405 | 411.153 |
| 5 | A | B | 482.284 | 486.617 | 486.95 | 490.95 | 491.283 | 495.617 | 503.089 | 569.502 | 507.423 | 510.557 | 511.756 | 513.941 |
| 6 | A#/Bb | B#/Hb | 578.74 | 583.94 | 584.334 | 589.14 | 589.54 | 594.74 | 603.707 | 607.469 | 608.907 | 612.669 | 614.107 | 616.729 |
| 7 | B | H | 675.197 | 681.364 | 681.73 | 687.33 | 687.7965 | 693.863 | 704.325 | 708.7135 | 710.392 | 714.78 | 716.4585 | 719.5175 |
| 8 | B#/Hb | H#/Cb | 771.654 | 778.587 | 779.12 | 785.52 | 786.053 | 792.9865 | 804.943 | 809.958 | 811.877 | 816.892 | 818.81 | 822.306 |
| 9 | H | C | 868.1105 | 875.9105 | 876.51 | 883.7105 | 884.31 | 892.11 | 905.561 | 911.203 | 913.361 | 919.003 | 921.161 | 925.094 |
| 10 | C | D | 964.567 | 973.234 | 973.9 | 981.901 | 982.5665 | 991.233 | 1006.179 | 1012.448 | 1014.8455 | 1021.115 | 1023.512 | 1027.882 |
| 11 | C#/Db | D#/Sb | 1061.024 | 1070.557 | 1071.39 | 1080.091 | 1080.823 | 1090.356 | 1106.797 | 1113.693 | 1116.33 | 1123.226 | 1125.863 | 1130.67 |
| 12 | D | S | 1157.481 | 1167.881 | 1168.68 | 1178.281 | 1179.08 | 1189.48 | 1207.4145 | 1214.9375 | 1217.8145 | 1225.3375 | 1228.2145 | 1233.459 |
| 13 | D#/Eb | S#/Eb | 1253.937 | 1265.204 | 1266.07 | 1176.471 | 1277.336 | 1288.603 | 1308.032 | 1316.182 | 1319.299 | 1327.449 | 1330.566 | 1336.247 |
| 14 | E | 1350.394 | 1362.527 | 1363.46 | 1374.661 | 1375.593 | 1387.726 | 1408.65 | 1417.427 | 1420.783 | 1429.56 | 1432.917 | 1439.035 | |
| 15 | 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 | F#/Gb | 102.978 | 103.655 | 103.855 | |
| 2 | G | 205.956 | 207.31 | 207.709 | |
| 3 | G#/Jb | G#/Ab | 308.934 | 310.965 | 311.564 |
| 4 | J | A | 411.9215 | 414.6195 | 415.419 |
| 5 | A | B | 514.891 | 518.274 | 519.2735 |
| 6 | A#/Bb | B#/Hb | 617.869 | 621.929 | 623.128 |
| 7 | B | H | 720.847 | 725.584 | 726.983 |
| 8 | B#/Hb | H#/Cb | 823.825 | 829.239 | 830.8375 |
| 9 | H | C | 926.823 | 932.893 | 934.693 |
| 10 | C | D | 1029.781 | 1036.549 | 1038.547 |
| 11 | C#/Db | D#/Sb | 1132.759 | 1140.204 | 1142.402 |
| 12 | D | S | 1235.7375 | 1243.859 | 1246.256 |
| 13 | D#/Eb | S#/Eb | 1338.716 | 1347.513 | 1353.111 |
| 14 | E | 1441.694 | 1451.168 | 1453.966 | |
| 15 | 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 | F#/Gb | 104.306 | 104.5215 | 104.721 | 105.173 | 105.788 | 106.04 | 106.664 | 107.531 | 108.398 | 108.4245 | 109.291 | 109.6375 | 110.158 | 110.504 | 111.371 | |
| 2 | G | 208.613 | 209.043 | 209.443 | 210.346 | 211.576 | 212.08 | 213.329 | 215.032 | 216.795 | 216.849 | 218.582 | 219.275 | 220.316 | 221.008 | 222.742 | |
| 3 | G#/Jb | G#/Ab | 312.919 | 313.565 | 314.164 | 315.519 | 317.364 | 318.119 | 319.993 | 322.593 | 325.193 | 325.273 | 327.873 | 328.913 | 330.473 | 331.613 | 334.113 |
| 4 | J | A | 417.226 | 418.086 | 418.885 | 420.639 | 423.152 | 424.159 | 426.657 | 430.124 | 433.5905 | 433.698 | 437.1345 | 438.55 | 440.631 | 442.017 | 445.4835 |
| 5 | A | B | 521.532 | 526.308 | 523.607 | 525.865 | 528.94 | 530.199 | 533.321 | 537.655 | 541.988 | 542.122 | 546.456 | 548.188 | 550.789 | 552.521 | 556.854 |
| 6 | A#/Bb | B#/Hb | 625.8385 | 627.129 | 628.328 | 631.0385 | 634.728 | 636.238 | 639.987 | 645.186 | 650.386 | 650.547 | 655.747 | 657.825 | 660.947 | 663.025 | 668.225 |
| 7 | B | H | 730.145 | 731.651 | 733.0495 | 736.212 | 740.516 | 742.278 | 746.65 | 752.717 | 758.783 | 758.971 | 765.038 | 767.463 | 771.105 | 773.5235 | 779.596 |
| 8 | B#/Hb | H#/Cb | 834.451 | 836.172 | 837.771 | 841.385 | 846.304 | 853.314 | 899.98 | 867.181 | 914.605 | 867.396 | 874.329 | 877.1 | 881.262 | 884.033 | 890.967 |
| 9 | H | C | 938.758 | 940.694 | 942.492 | 946.558 | 952.092 | 954.358 | 999.978 | 967.7785 | 1016.228 | 975.82 | 983.62 | 986.738 | 991.42 | 994.538 | 1002.338 |
| 10 | C | D | 1043.064 | 1045.2155 | 1047.214 | 1051.731 | 1057.88 | 1060.3975 | 1066.643 | 1075.3095 | 1083.976 | 1084.245 | 1092.911 | 1096.3755 | 1101.578 | 1105.042 | 1113.709 |
| 11 | C#/Db | D#/Sb | 1147.3705 | 1149.737 | 1151.935 | 1156.904 | 1163.668 | 1166.437 | 1173.307 | 1182.84 | 1192.374 | 1192.669 | 1202.202 | 1206.013 | 1211.736 | 1215.546 | 1225.08 |
| 12 | D | S | 1251.677 | 1254.259 | 1256.656 | 1262.077 | 1269.456 | 1272.477 | 1279.971 | 1290.371 | 1300.771 | 1301.0395 | 1311.4935 | 1315.651 | 1321.8935 | 1326.051 | 1336.451 |
| 13 | D#/Eb | S#/Eb | 1355.983 | 1358.78 | 1361.378 | 1367.25 | 1275.244 | 1378.517 | 1386.636 | 1397.902 | 1409.169 | 1409.518 | 1420.785 | 1438.993 | 1425.288 | 1436.555 | 1447.8215 |
| 14 | E | 1460.29 | 1463.302 | 1466.099 | 1472.423 | 1481.032 | 1484.556 | 1493.3 | 1505.433 | 1517.567 | 1517.9425 | 1530.076 | 1541.778 | 1534.926 | 1547.059 | 1559.192 | |
| 15 | 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 | |
By a surprising coincidence, the 15ed of the Golden tenth (7φ+6)\(5φ^2)edo is almost exactly every third degree of 34edo. Additionally, those of the modal Golden tenths are almost exactly +1/28-syntonic comma 4ed(5/4) (Aeolian-Dorian), 9ed(5/3)/equal multiples of 18/17 (Subpental Dorian), 13ed(15/7) (Pental Dorian), 2ed(9/8) (Superpental Dorian), -1/12-syntonic comma 3ed(6/5) (Dorian-Mixolydian), 14ed(7/3)/equal multiples of 17/16/100π\3 cents (Subpental Mixolydian), 3ed(6/5) (Pental Mixolydian), -1/20-septimal comma 4ed(9/7)/-1/28-syntonic comma 14ed(12/5)/9ed(7/4) (Soft Superpental Mixolydian), 12ed(32/15) (Intense Superpental Mixolydian) and 8ed(5/3)/-1/9 schismic 9ed(16/9)/14ed(22/9) (Mixolydian-Ionian) respectively.