User:Moremajorthanmajor/15edX: Difference between revisions

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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.
By a surprising coincidence, the 15ed of the Pyrite tenth (7φ+6)\(5φ^2)edo is almost exactly every third degree of [[34edo]]. Additionally, those of the modal Golden and Pyrite 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.
[[Category:15-tone]]
[[Category:15-tone]]
[[Category:ed7/3]]
[[Category:ed7/3]]

Revision as of 22:16, 25 November 2018

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 Pyrite tenth (7φ+6)\(5φ^2)edo is almost exactly every third degree of 34edo. Additionally, those of the modal Golden and Pyrite 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.

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