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 | 840 | 853.333 | 860.69 | 882.759 | 896 | |||||||||
| 9 | H | C | 864 | 880 | 900 | 916.364 | 925.714 | 936 | 945 | 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±13¢
| 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 | ||||||||||||
| 1 | F#/Gb | 96.457-98.19 | 97.39-99.123 | 100.618-102.351 | 101.245-102.978 | 102.788-104.5215 | 103.855-105.788 | 104.306-106.04 | 106.664-108.398 | 108.4245-110.158 | 109.6375-111.371 | ||
| 2 | G | 192.913-196.38 | 194.78-198.247 | 201.236-204.702 | 202.49-205.956 | 205.576-209.043 | 207.709-211.576 | 208.613-212.08 | 213.329-216.795 | 216.849-220.316 | 219.275-222.742 | ||
| 3 | G#/Jb | G#/Ab | 289.37-294.57 | 292.17-297.37 | 301.854-204.702 | 303.734-308.934 | 308.365-313.565 | 311.564-317.364 | 312.919-318.119 | 319.993-325.193 | 325.273-330.473 | 328.913-334.113 | |
| 4 | J | A | 385.829-392.76 | 389.56-396.493 | 402.4715-307.054 | 404.979-411.9215 | 411.153-418.086 | 415.419-423.152 | 417.226-424.159 | 426.657-433.5905 | 433.698-440.631 | 438.55-445.4835 | |
| 5 | A | B | 482.284-490.95 | 486.95-495.617 | 503.089-511.756 | 509.502-514.891 | 513.941-526.308 | 519.2735-528.94 | 521.532-530.199 | 533.321-541.988 | 542.122-550.789 | 548.188-556.854 | |
| 6 | A#/Bb | B#/Hb | 578.74-589.14 | 584.334-594.74 | 603.707-614.107 | 607.469-617.869 | 616.729-627.129 | 623.128-634.728 | 625.8385-636.238 | 639.987-650.386 | 650.547-660.947 | 657.825-668.225 | |
| 7 | B | H | 675.197-687.33 | 681.73-693.863 | 704.325-716.4585 | 708.7135-720.847 | 719.5175-731.651 | 726.983-740.516 | 730.145-742.278 | 746.65-758.783 | 758.971-771.105 | 767.463-779.596 | |
| 8 | B#/Hb | H#/Cb | 771.654-785.52 | 779.12-792.9865 | 804.943-818.81 | 809.958-823.825 | 822.306-836.172 | 830.8375-844.704 | 834.451-848.318 | 853.314-867.181 | 867.396-881.262 | 877.1-890.967 | |
| 9 | H | C | 868.1105-883.7105 | 876.51-892.11 | 905.561-921.161 | 911.203-926.823 | 925.094-940.694 | 934.693-952.092 | 938.758-954.358 | 959.9785-975.5785 | 975.82-991.42 | 986.738-1002.338 | |
| 10 | C | D | 964.567-981.901 | 973.9-991.233 | 1006.179-1023.512 | 1012.448-1029.781 | 1027.882-1045.2155 | 1038.547-1057.88 | 1043.064-1060.3975 | 1066.643-1083.976 | 1084.245-1101.578 | 1096.3755-1113.709 | |
| 11 | C#/Db | D#/Sb | 1061.024-1080.091 | 1071.39-1090.356 | 1106.797-1125.863 | 1113.693-1132.759 | 1130.67-1149.737 | 1142.402-1163.668 | 1147.3705-1166.437 | 1173.307-1192.374 | 1192.669-1211.736 | 1206.013-1225.08 | |
| 12 | D | S | 1157.481-1178.281 | 1168.68-1189.48 | 1207.4145-1228.2145 | 1214.9375-1235.7375 | 1233.459-1254.259 | 1246.256-1269.456 | 1251.677-1272.477 | 1279.971-1300.771 | 1301.0395-1321.8935 | 1315.651-1336.451 | |
| 13 | D#/Eb | S#/Eb | 1253.937-1276.471 | 1266.07-1288.603 | 1308.032-1330.566 | 1316.182-1338.716 | 1336.247-1358.78 | 1353.111-1275.244 | 1355.983-1378.517 | 1386.636-1409.169 | 1409.518-1425.288 | 1438.993-1447.8215 | |
| 14 | E | 1350.394-1374.661 | 1363.46-1387.726 | 1408.65-1432.917 | 1417.427-1441.694 | 1439.035-1463.302 | 1453.966-1481.032 | 1460.29-1484.556 | 1493.3-1517.567 | 1517.9425-1534.926 | 1541.778-1559.192 | ||
| 15 | F | 1446.851-1472.851 | 1460.85-1486.85 | 1509.268-1535.268 | 1518.672-1544.672 | 1541.823-1567.823 | 1557.82-1583.82 | 1564.596-1590.596 | 1599.964-1625.964 | 1626.366-1652.366 | 1644.563-1670.563 | ||
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.