User:Moremajorthanmajor/15edX: Difference between revisions

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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) (Intense Aeolian-Subpental 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) (Intense Aeolian-Subpental Dorian), [[9ed5/3|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 19:41, 3 June 2019

15edX is the scale which occurs as the dominant minor edX.

Intervals

Degrees Enneatonic Intense Aeolian-Subpental Dorian Dorian
Subpental Pental Superpental
Min-comma Med Max+comma Min-comma Med Max+comma Min-comma Med Max+comma Min-comma Med Max+comma
1 G#/Jb G#/Ab 94-96 97.143 95.778-99.778 98.4615 98-102 101.333 99.818-103.818 102.222 102.857-104.857
2 J A 188-192 194.286 191.556-199.556 196.923 196-204 202.667 199.636-207.636 204.444 205.714-209.714
3 J#/Ab A#/Bb 282-288 291.429 287.333-299.333 295.385 294-306 304 299.4545-311.4545 306.667 308.571-314.571
4 A B 376-384 388.571 383.111-399.111 393.846 392-408 405.333 399.273-415.273 408.889 411.429-419.429
5 B C 470-480 485.714 478.889-498.889 492.308 490-510 506.667 499.091-519.091 511.111 504.286-514.286
6 B#/Cb C#/Qb 564-576 582.857 574.889-598.889 590.769 588-612 608 598.909-622.909 613.333 617.143-629.143
7 C Q 658-672 680 670.444-698.444 689.231 686-714 709.333 698.727-726.727 715.556 720-734
8 C#/Qb Q#/Db 752-768 757.143 766.222-798.222 787.692 784-816 810.667 798.5455-830.5455 817.778 822.857-838.857
9 Q D 846-864 874.286 862-898 886.154 882-918 912 898.364-934.364 920 925.714-943.714
10 D S 940-960 971.429 957.778-997.778 984.615 980-1020 1013.333 998.182-1038.182 1022.222 1028.571-1048.571
11 D#/Eb S#/Eb 1034-1056 1068.571 1053.556-1097.778 1083.077 1078-1132 1114.667 1098-1142 1124.444 1131.429-1153.429
12 E 1128-1152 1165.714 1149.333-1197.333 1181.5385 1176-1224 1216 1197.818-1245.818 1226.667 1234.286-1258.286
13 E#/Fb 1222-1248 1362.857 1245.111-1297.111 1280 1274-1326 1317.333 1297.636-1349.636 1328.889 1337.143-1363.143
14 F 1316-1344 1360 1340.889-1396.889 1378.4615 1372-1428 1418.667 1397.4545-1453.4545 1431.111 1440-1468
15 G 1410-1440 1457.143 1436.667-1496.667 1476.923 1470-1530 1520 1497.273-1557.273 1533.333 1542.857-1572.857
Degrees Enneatonic Mohajira Beatles
Min-comma r¢ Med Max+comma Min-comma Med Max+comma
1 F#/Gb G#/Jb G#/Ab 100.857-102.857 103.333 101.529-105.529 103.704 104-106
2 G J A 201.714-205.714 206.667 203.059-211.059 207.407 208-212
3 G#/Jb G#/Ab J#/Ab A#/Bb 302.571-308.571 310 304.588-316.588 311.111 312-318
4 J A A B 403.429-411.429 413.333 406.118-422.118 414.815 416-424
5 A B B C 504.286-514.286 516.667 507.647-527.647 518.5185 520-530
6 A#/Bb B#/Hb B#/Cb C#/Qb 605.143-617.143 620 609.1765-633.1765 622.222 624-636
7 B H C Q 706-720 723.333 710.706-738.706 725.926 728-742
8 B#/Hb H#/Cb C#/Qb Q#/Db 806.857-822.857 826.667 812.235-844.235 829.63 832-848
9 H C Q D 908.714-925.714 930 913.765-949.765 933.333 936-954
10 C D D S 1028.571-1048.571 1033.333 1015.294-1055.294 1037.037 1040-1060
11 C#/Db D#/Sb D#/Eb S#/Eb 1109.429-1131.429 1136.667 1116.8235-1160.8235 1140.741 1144-1166
12 D S E 1210.286-1234.286 1240 1218.353-1266.353 1244.444 1248-1272
13 D#/Eb S#/Eb E#/Fb 1311.143-1337.143 1343.333 1345.882-1397.882 1348.148 1352-1378
14 E F 1412-1440 1446.667 1421.412-1477.412 1451.852 1456-1484
15 F G 1512.857-1542.857 1550 1522.941-1582.941 1555.556 1560-1590
Degrees Enneatonic Mixolydian Mixolydian-Ionian
Subpental Pental Superpental
Soft Intense
Min-comma Med Max+comma Min-comma Med Max+comma Min-comma Med Max+comma Min-comma Med Max+comma Min-comma Med Max+comma
1 F#/Gb 102-104 104.615 103-107 105.263 104.667-108.667 107.5 105.586-109.586 108.9655 108.345-112.345 110.588 112-114
2 G 204-208 209.231 206-214 210.526 209.333-217.333 215 211.172-219.172 217.931 216.69-224.69 221.1765 224-228
3 G#/Jb G#/Ab 306-312 313.846 309-321 315.7895 314-326 322.5 316.759-328.759 326.897 325.0345-337.0345 331.765 336-342
4 J A 408-416 418.4615 412-428 421.053 418.667-432.667 430 422.345-428.345 435.862 433.379-449.379 442.353 448-456
5 A B 510-520 523.077 515-535 526.316 523.333-543.333 537.5 527.931-547.931 544.828 541.724-561.724 552.941 560-570
6 A#/Bb B#/Hb 612-624 627.692 618-642 631.579 628-652 645 633.517-657.517 653.793 650.069-674.069 663.529 672-684
7 B H 714-728 732.308 721-749 736.842 732.667-760.667 752.5 739.103-767.103 762.759 758.414-796.414 774.118 784-798
8 B#/Hb H#/Cb 816-832 836.923 824-856 842.103 838.333-869.333 860 844.69-876.69 871.724 866.759-898.759 884.706 896-914
9 H C 918-936 941.5385 927-963 947.368 942-978 967.5 950.276-986.276 980.69 975.103-1001.103 995.294 1008-1026
10 C D 1020-1040 1046.154 1030-1070 1052.632 1046.667-1086.667 1075 1055.862-1095.862 1089.655 1083.448-1123.448 1105.882 1120-1140
11 C#/Db D#/Sb 1122-1144 1150.769 1133-1177 1157.895 1151.333-1195.333 1182.5 1161.448-1205.448 1198.621 1191.793-1335.793 1216.471 1232-1254
12 D S 1224-1248 1255.385 1236-1284 1263.158 1256-1304 1290 1267.0345-1315.0345 1307.586 1300.138-1348.138 1327.059 1344-1368
13 D#/Eb S#/Eb 1326-1352 1360 1339-1391 1368.421 1360.667-1412.667 1397.5 1372.621-1424.621 1416.552 1408.483-1460.483 1437.647 1456-1482
14 E 1428-1456 1464.615 1442-1498 1473.684 1465.333-1521.333 1505 1478.207-1534.207 1525.517 1516.828-1572.828 1548.235 1568-1596
15 F 1530-1560 1569.231 1545-1605 1578.947 1570-1630 1612.5 1583.793-1643.793. 1634.483 1625.172-1685.172 1658.8235 1680-1710

Relative cents

Degrees Enneatonic Intense Aeolian-Subpental Dorian Dorian
1 G#/Jb G#/Ab 96.667 100
2 J A 193.333 200
3 J#/Ab A#/Bb 290 300
4 A B 386.667 400
5 B C 483.333 500
6 B#/Cb C#/Qb 580 600
7 C Q 676.667 700
8 C#/Qb Q#/Db 773.333 800
9 Q D 870 900
10 D S 966.667 1000
11 D#/Eb S#/Eb 1063.333 1100
12 E 1160 1200
13 E#/Fb 1256.667 1300
14 F 1353.333 1400
15 G 1450 1500
Degrees Enneatonic Subpental-Soft Superpental Mixolydian Intense Superpental Mixolydian ~ Mixolydian-Ionian
1 F#/Gb 106.667 110
2 G 213.333 220
3 G#/Jb G#/Ab 320 330
4 J A 426.667 440
5 A B 533.333 550
6 A#/Bb B#/Hb 640 660
7 B H 746.667 770
8 B#/Hb H#/Cb 853.333 880
9 H C 960 990
10 C D 1066.667 1100
11 C#/Db D#/Sb 1173.333 1210
12 D S 1280 1320
13 D#/Eb S#/Eb 1386.667 1430
14 E 1493.333 1540
15 F 1600 1650

Golden/Pyrite Tunings±13¢

Degrees Enneatonic Intense Aeolian-Subpental Dorian Dorian
Subpental Pental Superpental
1 G#/Jb G#/Ab 96.457-98.19 97.39-99.123 100.618-102.351 101.245-102.978
2 J A 192.913-196.38 194.78-198.247 201.236-204.702 202.49-205.956
3 J#/Ab A#/Bb 289.37-294.57 292.17-297.37 301.854-204.702 303.734-308.934
4 A B 385.829-392.76 389.56-396.493 402.4715-307.054 404.979-411.9215
5 B C 482.284-490.95 486.95-495.617 503.089-511.756 509.502-514.891
6 B#/Cb C#/Qb 578.74-589.14 584.334-594.74 603.707-614.107 607.469-617.869
7 C Q 675.197-687.33 681.73-693.863 704.325-716.4585 708.7135-720.847
8 C#/Qb Q#/Db 771.654-785.52 779.12-792.9865 804.943-818.81 809.958-823.825
9 Q D 868.1105-883.7105 876.51-892.11 905.561-921.161 911.203-926.823
10 D S 964.567-981.901 973.9-991.233 1006.179-1023.512 1012.448-1029.781
11 D#/Eb S#/Eb 1061.024-1080.091 1071.39-1090.356 1106.797-1125.863 1113.693-1132.759
12 E 1157.481-1178.281 1168.68-1189.48 1207.4145-1228.2145 1214.9375-1235.7375
13 E#/Fb 1253.937-1276.471 1266.07-1288.603 1308.032-1330.566 1316.182-1338.716
14 F 1350.394-1374.661 1363.46-1387.726 1408.65-1432.917 1417.427-1441.694
15 G 1446.851-1472.851 1460.85-1486.85 1509.268-1535.268 1518.672-1544.672
Degrees Enneatonic Mohajira Beatles
1 F#/Gb G#/Jb G#/Ab 102.526-104.26 102.788-104.5215
2 G J A 205.053-208.519 205.576-209.431
3 G#/Jb G#/Ab J#/Ab A#/Bb 307.579-312.779. 308.365-313.565
4 J A A B 410.1055-417.099 411.153-418.086
5 A B B C 512.632-521.2985 513.941-522.607
6 A#/Bb B#/Hb B#/Cb C#/Qb 615.158-625.558 616.729-627.129
7 B H C Q 717.685-729.818 719.5175-731.651
8 B#/Hb H#/Cb C#/Qb Q#/Db 820.211-834.078 822.306-836.172
9 H C Q D 922.737-938.337 925.094-940.694
10 C D D S 1025.264-1042.597 1027.882-1045.215
11 C#/Db D#/Sb D#/Eb S#/Eb 1127.79-1146.857 1130.67-1149.737
12 D S E 1230.316-1251.116 1233.459-1254.259
13 D#/Eb S#/Eb E#/Fb 1332.843-1355.376 1336.247-1358.78
14 E F 1435.369-1459.666 1439.035-1463.302
15 F G 1537.8955-1563.8955 1541.823-1577.823
Degrees Enneatonic Mixolydian Mixolydian-Ionian
Subpental Pental Superpental
Soft Intense
1 F#/Gb 103.855-105.788 104.306-106.04 106.664-108.398 108.4245-110.158 109.6375-111.371
2 G 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 311.564-317.364 312.919-318.119 319.993-325.193 325.273-330.473 328.913-334.113
4 J A 415.419-423.152 417.226-424.159 426.657-433.5905 433.698-440.631 438.55-445.4835
5 A B 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 623.128-634.728 625.8385-636.238 639.987-650.386 650.547-660.947 657.825-668.225
7 B H 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 830.8375-844.704 834.451-848.318 853.314-867.181 867.396-881.262 877.1-890.967
9 H C 934.693-952.092 938.758-954.358 959.9785-975.5785 975.82-991.42 986.738-1002.338
10 C D 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 1142.402-1163.668 1147.3705-1166.437 1173.307-1192.374 1192.669-1211.736 1206.013-1225.08
12 D S 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 1353.111-1275.244 1355.983-1378.517 1386.636-1409.169 1409.518-1425.288 1438.993-1447.8215
14 E 1453.966-1481.032 1460.29-1484.556 1493.3-1517.567 1517.9425-1534.926 1541.778-1559.192
15 F 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) (Intense Aeolian-Subpental 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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