User:Moremajorthanmajor/15edX: Difference between revisions

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Line 5: Line 5:
! colspan="2" rowspan="3" |Enneatonic
! colspan="2" rowspan="3" |Enneatonic
! colspan="4" rowspan="2" |Intense Aeolian-Subpental Dorian
! colspan="4" rowspan="2" |Intense Aeolian-Subpental Dorian
! colspan="10" |Dorian
! colspan="9" |Dorian
|-
|-
! colspan="10" |Subpental  
! colspan="9" |Subpental  
|-
|-
!Min
!Min
Line 14: Line 14:
!Max
!Max
!Min
!Min
!7/3±13¢
!Golden±13¢
!Golden±13¢
!Max
!Max
Line 31: Line 30:
|''96.667''
|''96.667''
| colspan="2" |97.778
| colspan="2" |97.778
|96.925-98.658
|97.39-99.123
|97.39-99.123
| colspan="2" |''100''
| colspan="2" |''100''
Line 46: Line 44:
|''193.333''
|''193.333''
| colspan="2" |195.556
| colspan="2" |195.556
|193.8495-197.316
|194.78-198.247
|194.78-198.247
| colspan="2" |''200''
| colspan="2" |''200''
Line 61: Line 58:
|''290''
|''290''
| colspan="2" |293.333
| colspan="2" |293.333
|290.774-295.974
|292.17-297.37
|292.17-297.37
| colspan="2" |''300''
| colspan="2" |''300''
Line 76: Line 72:
|''386.667''
|''386.667''
| colspan="2" |391.111
| colspan="2" |391.111
|387.699-394.632
|389.56-396.493
|389.56-396.493
| colspan="2" |''400''
| colspan="2" |''400''
Line 91: Line 86:
|''483.333''
|''483.333''
| colspan="2" |488.889
| colspan="2" |488.889
|484.624-493.29
|486.95-495.617
|486.95-495.617
| colspan="2" |''500''
| colspan="2" |''500''
Line 106: Line 100:
|''580''
|''580''
| colspan="2" |586.667
| colspan="2" |586.667
|581.548-591.948
|584.334-594.74
|584.334-594.74
| colspan="2" |''600''
| colspan="2" |''600''
Line 121: Line 114:
|''676.667''
|''676.667''
| colspan="2" |684.444
| colspan="2" |684.444
|678.473-690.606
|681.73-693.863
|681.73-693.863
| colspan="2" |''700''
| colspan="2" |''700''
Line 136: Line 128:
|''773.333''
|''773.333''
| colspan="2" |782.822
| colspan="2" |782.822
|775.398-789.2645
|779.12-792.9865
|779.12-792.9865
| colspan="2" |''800''
| colspan="2" |''800''
Line 151: Line 142:
|''870''
|''870''
| colspan="2" |880
| colspan="2" |880
|872.3225-887.9225
|876.51-892.11
|876.51-892.11
| colspan="2" |''900''
| colspan="2" |''900''
Line 166: Line 156:
|''966.667''
|''966.667''
| colspan="2" |977.778
| colspan="2" |977.778
|969.247-986.561
|973.9-991.233
|973.9-991.233
| colspan="2" |''1000''
| colspan="2" |''1000''
Line 181: Line 170:
|''1063.333''
|''1063.333''
| colspan="2" |1075.556
| colspan="2" |1075.556
|1066.172-1085.239
|1071.39-1090.356
|1071.39-1090.356
| colspan="2" |''1100''
| colspan="2" |''1100''
Line 195: Line 183:
|''1160''
|''1160''
| colspan="2" |1173.333
| colspan="2" |1173.333
|1163.097-1183.897
|1168.68-1189.48
|1168.68-1189.48
| colspan="2" |''1200''
| colspan="2" |''1200''
Line 209: Line 196:
|''1256.667''
|''1256.667''
| colspan="2" |1271.111
| colspan="2" |1271.111
|1260.0215-1282.555
|1266.07-1288.603
|1266.07-1288.603
| colspan="2" |''1300''
| colspan="2" |''1300''
Line 223: Line 209:
|''1353.333''
|''1353.333''
| colspan="2" |1368.889
| colspan="2" |1368.889
|1356.946-1381.213
|1363.46-1387.726
|1363.46-1387.726
| colspan="2" |''1400''
| colspan="2" |''1400''
Line 237: Line 222:
|''1450''
|''1450''
| colspan="2" |1466.667
| colspan="2" |1466.667
|1453.871-1479.871
|1460.85-1486.85
|1460.85-1486.85
| colspan="2" |''1500''
| colspan="2" |''1500''
Line 250: Line 234:
! colspan="4" |Enneatonic
! colspan="4" |Enneatonic
!Min
!Min
!22/9±13¢
!Golden±13¢
!Golden±13¢
!''r¢''
!''r¢''
Line 260: Line 243:
|''G#/Ab''
|''G#/Ab''
|102.857
|102.857
|102.294-104.027
|102.788-104.5215
|102.788-104.5215
|''103.333''
|''103.333''
Line 270: Line 252:
|''A''
|''A''
|205.714
|205.714
|204.588-208.054
|205.576-209.043
|205.576-209.043
|''206.667''
|''206.667''
Line 281: Line 262:
|''A#/Bb''
|''A#/Bb''
|308.571
|308.571
|306.8815-312.0815
|308.365-313.565
|308.365-313.565
|''310''
|''310''
Line 292: Line 272:
|''B''
|''B''
|411.429
|411.429
|409.1755-416.109
|411.153-418.086
|411.153-418.086
|''413.333''
|''413.333''
Line 303: Line 282:
|''C''
|''C''
|514.286
|514.286
|511.469-520.136
|513.941-526.308
|513.941-526.308
|''516.667''
|''516.667''
Line 314: Line 292:
|''C#/Qb''
|''C#/Qb''
|617.143
|617.143
|613.763-624.163
|616.729-627.129
|616.729-627.129
|''620''
|''620''
Line 325: Line 302:
|''Q''
|''Q''
|720
|720
|716.057-728.19
|719.5175-731.651
|719.5175-731.651
|''723.333''
|''723.333''
Line 336: Line 312:
|''Q#/Db''
|''Q#/Db''
|822.857
|822.857
|818.351-832.218
|822.306-836.172
|822.306-836.172
|''826.667''
|''826.667''
Line 347: Line 322:
|''D''
|''D''
|925.714
|925.714
|920.645-936.245
|925.094-940.694
|925.094-940.694
|''930''
|''930''
Line 358: Line 332:
|''S''
|''S''
|1028.571
|1028.571
|1022.939-1040.272
|1027.882-1045.2155
|1027.882-1045.2155
|''1033.333''
|''1033.333''
Line 369: Line 342:
|''S#/Eb''
|''S#/Eb''
|1131.429
|1131.429
|1125.2325-1144.299
|1130.67-1149.737
|1130.67-1149.737
|''1136.667''
|''1136.667''
Line 379: Line 351:
| colspan="2" |E
| colspan="2" |E
|1234.286
|1234.286
|1227.526-1248.326
|1233.459-1254.259
|1233.459-1254.259
|''1240''
|''1240''
Line 389: Line 360:
| colspan="2" |E#/Fb
| colspan="2" |E#/Fb
|1337.143
|1337.143
|1329.82-1352.3535
|1336.247-1358.78
|1336.247-1358.78
|''1343.333''
|''1343.333''
Line 398: Line 368:
| colspan="2" |F
| colspan="2" |F
|1440
|1440
|1432.114-1456.381
|1439.035-1463.302
|1439.035-1463.302
|''1446.667''
|''1446.667''
Line 407: Line 376:
| colspan="2" |G
| colspan="2" |G
|1542.857
|1542.857
|1534.408-1560.408
|1541.823-1567.823
|1541.823-1567.823
|''1550''
|''1550''
Line 417: Line 385:
! rowspan="4" |Degrees
! rowspan="4" |Degrees
! colspan="2" rowspan="4" |Enneatonic
! colspan="2" rowspan="4" |Enneatonic
! colspan="14" |Mixolydian
! colspan="13" |Mixolydian
! colspan="3" rowspan="3" |Mixolydian-Ionian
! colspan="3" rowspan="3" |Mixolydian-Ionian
|-
|-
! colspan="3" rowspan="2" |Subpental
! colspan="3" rowspan="2" |Subpental
! colspan="4" rowspan="2" |Pental
! colspan="3" rowspan="2" |Pental
! colspan="7" |Superpental
! colspan="7" |Superpental
|-
|-
Line 432: Line 400:
! width="4%" | Min
! width="4%" | Min
!Golden±13¢
!Golden±13¢
!5/2±13¢
! width="4%" | Max
! width="4%" | Max
! width="4%" | Min
! width="4%" | Min
Line 451: Line 418:
| colspan="2" |105
| colspan="2" |105
|104.306-106.04
|104.306-106.04
|104.888-106.621
| colspan="2" |''106.667''
| colspan="2" |''106.667''
|106.664-108.398
|106.664-108.398
Line 467: Line 433:
| colspan="2" |210
| colspan="2" |210
|208.613-212.08
|208.613-212.08
|209.77-213.242
| colspan="2" |''213.333''
| colspan="2" |''213.333''
|213.329-216.795
|213.329-216.795
Line 484: Line 449:
| colspan="2" |315
| colspan="2" |315
|312.919-318.119
|312.919-318.119
|314.663-319.863
| colspan="2" |''320''
| colspan="2" |''320''
|319.993-325.193
|319.993-325.193
Line 501: Line 465:
| colspan="2" |420
| colspan="2" |420
|417.226-424.159
|417.226-424.159
|419.559-426.484
| colspan="2" |''426.667''
| colspan="2" |''426.667''
|426.657-433.5905
|426.657-433.5905
Line 518: Line 481:
| colspan="2" |525
| colspan="2" |525
|521.532-530.199
|521.532-530.199
|524.438-533.105
| colspan="2" |''533.333''
| colspan="2" |''533.333''
|533.321-541.988
|533.321-541.988
Line 535: Line 497:
| colspan="2" |630
| colspan="2" |630
|625.8385-636.238
|625.8385-636.238
|629.3255-639.7255
| colspan="2" |''640''
| colspan="2" |''640''
|639.987-650.386
|639.987-650.386
Line 552: Line 513:
| colspan="2" |735
| colspan="2" |735
|730.145-742.278
|730.145-742.278
|734.213-746.346
| colspan="2" |''746.667''
| colspan="2" |''746.667''
|746.65-758.783
|746.65-758.783
Line 569: Line 529:
| colspan="2" |840
| colspan="2" |840
|834.451-848.318
|834.451-848.318
|839.101-852.967
| colspan="2" |''853.333''
| colspan="2" |''853.333''
|853.314-867.181
|853.314-867.181
Line 586: Line 545:
| colspan="2" |945
| colspan="2" |945
|938.758-954.358
|938.758-954.358
|943.988-959.588
| colspan="2" |''960''
| colspan="2" |''960''
|959.9785-975.5785
|959.9785-975.5785
Line 603: Line 561:
| colspan="2" |1050
| colspan="2" |1050
|1043.064-1060.3975
|1043.064-1060.3975
|1048.876-1066.209
| colspan="2" |''1066.667''
| colspan="2" |''1066.667''
|1066.643-1083.976
|1066.643-1083.976
Line 620: Line 577:
| colspan="2" |1155
| colspan="2" |1155
|1147.3705-1166.437
|1147.3705-1166.437
|1153.763-1172.83
| colspan="2" |''1173.333''
| colspan="2" |''1173.333''
|1173.307-1192.374
|1173.307-1192.374
Line 637: Line 593:
| colspan="2" |1260
| colspan="2" |1260
|1251.677-1272.477
|1251.677-1272.477
|1258.651-1279.451
| colspan="2" |''1280''
| colspan="2" |''1280''
|1279.971-1300.771
|1279.971-1300.771
Line 654: Line 609:
| colspan="2" |1365
| colspan="2" |1365
|1355.983-1378.517
|1355.983-1378.517
|1363.539-1386.072
| colspan="2" |''1386.667''
| colspan="2" |''1386.667''
|1386.636-1409.169
|1386.636-1409.169
Line 670: Line 624:
| colspan="2" |1470
| colspan="2" |1470
|1460.29-1484.556
|1460.29-1484.556
|1468.426-1492.693
| colspan="2" |''1493.333''
| colspan="2" |''1493.333''
|1493.3-1517.567
|1493.3-1517.567
Line 686: Line 639:
| colspan="2" |1575
| colspan="2" |1575
|1564.596-1590.596
|1564.596-1590.596
|1573.314-1599.314
| colspan="2" |''1600''
| colspan="2" |''1600''
|1599.964-1625.964
|1599.964-1625.964

Revision as of 14:19, 7 March 2019

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

Intervals

Degrees Enneatonic Intense Aeolian-Subpental Dorian Dorian
Subpental
Min Golden±13¢ r¢ Max Min Golden±13¢ Max Min Golden±13¢ Max Min Golden±13¢ Max
1 G#/Jb G#/Ab 96 96.457-98.19 96.667 97.778 97.39-99.123 100 100.618-102.351 101.818 101.245-102.978 102.857
2 J A 192 192.913-196.38 193.333 195.556 194.78-198.247 200 201.236-204.702 203.636 202.49-205.956 205.714
3 J#/Ab A#/Bb 288 289.37-294.57 290 293.333 292.17-297.37 300 301.854-204.702 305.4545 303.734-308.934 308.571
4 J B 384 385.829-392.76 386.667 391.111 389.56-396.493 400 402.4715-307.054 407.273 404.979-411.9215 411.429
5 A C 480 482.284-490.95 483.333 488.889 486.95-495.617 500 503.089-511.756 509.091 509.502-514.891 514.286
6 A#/Bb C#/Qb 576 578.74-589.14 580 586.667 584.334-594.74 600 603.707-614.107 610.909 607.469-617.869 617.143
7 B Q 672 675.197-687.33 676.667 684.444 681.73-693.863 700 704.325-716.4585 712.727 708.7135-720.847 720
8 B#/Cb Q#/Db 768 771.654-785.52 773.333 782.822 779.12-792.9865 800 804.943-818.81 814.5455 809.958-823.825 822.857
9 C D 864 868.1105-883.7105 870 880 876.51-892.11 900 905.561-921.161 916.364 911.203-926.823 925.714
10 D S 960 964.567-981.901 966.667 977.778 973.9-991.233 1000 1006.179-1023.512 1018.182 1012.448-1029.781 1028.571
11 D#/Eb S#/Eb 1056 1061.024-1080.091 1063.333 1075.556 1071.39-1090.356 1100 1106.797-1125.863 1120 1113.693-1132.759 1131.429
12 E 1152 1157.481-1178.281 1160 1173.333 1168.68-1189.48 1200 1207.4145-1228.2145 1221.818 1214.9375-1235.7375 1234.286
13 E#/Fb 1248 1253.937-1276.471 1256.667 1271.111 1266.07-1288.603 1300 1308.032-1330.566 1323.636 1316.182-1338.716 1337.143
14 F 1344 1350.394-1374.661 1353.333 1368.889 1363.46-1387.726 1400 1408.65-1432.917 1425.4545 1417.427-1441.694 1440
15 G 1440 1446.851-1472.851 1450 1466.667 1460.85-1486.85 1500 1509.268-1535.268 1527.273 1518.672-1544.672 1542.857
Degrees Enneatonic Min Golden±13¢ r¢ Max
1 F#/Gb G#/Jb G#/Ab 102.857 102.788-104.5215 103.333 104
2 G J A 205.714 205.576-209.043 206.667 208
3 G#/Jb G#/Ab J#/Ab A#/Bb 308.571 308.365-313.565 310 312
4 J A J B 411.429 411.153-418.086 413.333 416
5 A B A C 514.286 513.941-526.308 516.667 520
6 A#/Bb B#/Hb A#/Bb C#/Qb 617.143 616.729-627.129 620 624
7 B H B Q 720 719.5175-731.651 723.333 728
8 B#/Hb H#/Cb B#/Cb Q#/Db 822.857 822.306-836.172 826.667 832
9 H C C D 925.714 925.094-940.694 930 936
10 C D D S 1028.571 1027.882-1045.2155 1033.333 1040
11 C#/Db D#/Sb D#/Eb S#/Eb 1131.429 1130.67-1149.737 1136.667 1144
12 D S E 1234.286 1233.459-1254.259 1240 1248
13 D#/Eb S#/Eb E#/Fb 1337.143 1336.247-1358.78 1343.333 1352
14 E F 1440 1439.035-1463.302 1446.667 1456
15 F G 1542.857 1541.823-1567.823 1550 1560
Degrees Enneatonic Mixolydian Mixolydian-Ionian
Subpental Pental Superpental
Soft Intense
Min Golden±13¢ Max Min Golden±13¢ Max Min Golden±13¢ Max Min Golden±13¢ r¢ Max Min Golden±13¢ Max
1 F#/Gb 104 103.855-105.788 105 104.306-106.04 106.667 106.664-108.398 107.586 108.4245-110.158 110 110.345 109.6375-111.371 112
2 G 208 207.709-211.576 210 208.613-212.08 213.333 213.329-216.795 215.172 216.849-220.316 220 220.69 219.275-222.742 224
3 G#/Jb G#/Ab 312 311.564-317.364 315 312.919-318.119 320 319.993-325.193 322.759 325.273-330.473 330 331.034 328.913-334.113 336
4 J A 416 415.419-423.152 420 417.226-424.159 426.667 426.657-433.5905 430.345 433.698-440.631 440 441.379 438.55-445.4835 448
5 A B 520 519.2735-528.94 525 521.532-530.199 533.333 533.321-541.988 537.931 542.122-550.789 550 551.724 548.188-556.854 560
6 A#/Bb B#/Hb 624 623.128-634.728 630 625.8385-636.238 640 639.987-650.386 645.517 650.547-660.947 660 662.069 657.825-668.225 672
7 B H 728 726.983-740.516 735 730.145-742.278 746.667 746.65-758.783 753.103 758.971-771.105 770 772.414 767.463-779.596 784
8 B#/Hb H#/Cb 832 830.8375-844.704 840 834.451-848.318 853.333 853.314-867.181 860.69 867.396-881.262 880 882.759 877.1-890.967 896
9 H C 936 934.693-952.092 945 938.758-954.358 960 959.9785-975.5785 968.276 975.82-991.42 990 993.103 986.738-1002.338 1008
10 C D 1040 1038.547-1057.88 1050 1043.064-1060.3975 1066.667 1066.643-1083.976 1075.862 1084.245-1101.578 1100 1103.448 1096.3755-1113.709 1120
11 C#/Db D#/Sb 1144 1142.402-1163.668 1155 1147.3705-1166.437 1173.333 1173.307-1192.374 1183.448 1192.669-1211.736 1210 1213.379 1206.013-1225.08 1232
12 D S 1248 1246.256-1269.456 1260 1251.677-1272.477 1280 1279.971-1300.771 1291.034 1301.0395-1321.8935 1320 1324.138 1315.651-1336.451 1344
13 D#/Eb S#/Eb 1352 1353.111-1275.244 1365 1355.983-1378.517 1386.667 1386.636-1409.169 1398.621 1409.518-1425.288 1430 1424.483 1438.993-1447.8215 1456
14 E 1456 1453.966-1481.032 1470 1460.29-1484.556 1493.333 1493.3-1517.567 1506.207 1517.9425-1534.926 1540 1544.827 1541.778-1559.192 1568
15 F 1560 1557.82-1583.82 1575 1564.596-1590.596 1600 1599.964-1625.964 1613.793 1626.366-1652.366 1650 1655.172 1644.563-1670.563 1680

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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