User:Moremajorthanmajor/15edX: Difference between revisions

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! rowspan="3" |Degrees
! rowspan="3" |Degrees
! colspan="2" rowspan="3" |Enneatonic
! colspan="2" rowspan="3" |Enneatonic
! colspan="4" rowspan="2" |Intense Aeolian-Subpental Dorian
! colspan="3" rowspan="2" |Intense Aeolian-Subpental Dorian
! colspan="9" |Dorian
! colspan="10" |Dorian
|-
|-
! colspan="9" |Subpental  
! colspan="10" |Subpental  
|-
|-
!Min
!Min
!Golden±13¢
!Golden±13¢
!7/3±13¢
!Max
!Max
!Min
!Min
!7/3±13¢
!Golden±13¢
!Golden±13¢
!Max
!Max
Line 28: Line 28:
| |96
| |96
|96.457-98.19
|96.457-98.19
| colspan="2" |97.778
|96.925-98.658
|96.925-98.658
| colspan="2" |97.778
|97.39-99.123
|97.39-99.123
| colspan="2" |100
| colspan="2" |100
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| |192
| |192
|192.913-196.38
|192.913-196.38
| colspan="2" |195.556
|193.8495-197.316
|193.8495-197.316
| colspan="2" |195.556
|194.78-198.247
|194.78-198.247
| colspan="2" |200
| colspan="2" |200
Line 56: Line 56:
| |288
| |288
|289.37-294.57
|289.37-294.57
| colspan="2" |293.333
|290.774-295.974
|290.774-295.974
| colspan="2" |293.333
|292.17-297.37
|292.17-297.37
| colspan="2" |300
| colspan="2" |300
Line 70: Line 70:
| |384
| |384
|385.829-392.76
|385.829-392.76
| colspan="2" |391.111
|387.699-394.632
|387.699-394.632
| colspan="2" |391.111
|389.56-396.493
|389.56-396.493
| colspan="2" |400
| colspan="2" |400
Line 84: Line 84:
| |480
| |480
|482.284-490.95
|482.284-490.95
| colspan="2" |488.889
|484.624-493.29
|484.624-493.29
| colspan="2" |488.889
|486.95-495.617
|486.95-495.617
| colspan="2" |500
| colspan="2" |500
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| |576
| |576
|578.74-589.14
|578.74-589.14
| colspan="2" |586.667
|581.548-591.948
|581.548-591.948
| colspan="2" |586.667
|584.334-594.74
|584.334-594.74
| colspan="2" |600
| colspan="2" |600
Line 112: Line 112:
| |672
| |672
|675.197-687.33
|675.197-687.33
| colspan="2" |684.444
|678.473-690.606
|678.473-690.606
| colspan="2" |684.444
|681.73-693.863
|681.73-693.863
| colspan="2" |700
| colspan="2" |700
Line 126: Line 126:
|768
|768
|771.654-785.52
|771.654-785.52
| colspan="2" |782.822
|775.398-789.2645
|775.398-789.2645
| colspan="2" |782.822
|779.12-792.9865
|779.12-792.9865
| colspan="2" |800
| colspan="2" |800
Line 140: Line 140:
|864
|864
|868.1105-883.7105
|868.1105-883.7105
| colspan="2" |880
|872.3225-887.9225
|872.3225-887.9225
| colspan="2" |880
|876.51-892.11
|876.51-892.11
| colspan="2" |900
| colspan="2" |900
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|960
|960
|964.567-981.901
|964.567-981.901
| colspan="2" |977.778
|969.247-986.561
|969.247-986.561
| colspan="2" |977.778
|973.9-991.233
|973.9-991.233
| colspan="2" |1000
| colspan="2" |1000
Line 168: Line 168:
|1056
|1056
|1061.024-1080.091
|1061.024-1080.091
| colspan="2" |1075.556
|1066.172-1085.239
|1066.172-1085.239
| colspan="2" |1075.556
|1071.39-1090.356
|1071.39-1090.356
| colspan="2" |1100
| colspan="2" |1100
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|1152
|1152
|1157.481-1178.281
|1157.481-1178.281
| colspan="2" |1173.333
|1163.097-1183.897
|1163.097-1183.897
| colspan="2" |1173.333
|1168.68-1189.48
|1168.68-1189.48
| colspan="2" |1200
| colspan="2" |1200
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|1248
|1248
|1253.937-1276.471
|1253.937-1276.471
| colspan="2" |1271.111
|1260.0215-1282.555
|1260.0215-1282.555
| colspan="2" |1271.111
|1266.07-1288.603
|1266.07-1288.603
| colspan="2" |1300
| colspan="2" |1300
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|1344
|1344
|1350.394-1374.661
|1350.394-1374.661
| colspan="2" |1368.889
|1356.946-1381.213
|1356.946-1381.213
| colspan="2" |1368.889
|1363.46-1387.726
|1363.46-1387.726
| colspan="2" |1400
| colspan="2" |1400
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|1440
|1440
|1446.851-1472.851
|1446.851-1472.851
| colspan="2" |1466.667
|1453.871-1479.871
|1453.871-1479.871
| colspan="2" |1466.667
|1460.85-1486.85
|1460.85-1486.85
| colspan="2" |1500
| colspan="2" |1500

Revision as of 23:02, 22 December 2018

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

Intervals

Degrees Enneatonic Intense Aeolian-Subpental Dorian Dorian
Subpental
Min Golden±13¢ Max Min 7/3±13¢ Golden±13¢ Max Min Golden±13¢ Max Min Golden±13¢ Max
1 G#/Jb G#/Ab 96 96.457-98.19 97.778 96.925-98.658 97.39-99.123 100 100.618-102.351 101.818 101.245-102.978 102.857
2 J A 192 192.913-196.38 195.556 193.8495-197.316 194.78-198.247 200 201.236-204.702 203.636 202.49-205.956 205.714
3 J#/Ab A#/Bb 288 289.37-294.57 293.333 290.774-295.974 292.17-297.37 300 301.854-204.702 305.4545 303.734-308.934 308.571
4 J B 384 385.829-392.76 391.111 387.699-394.632 389.56-396.493 400 402.4715-307.054 407.273 404.979-411.9215 411.429
5 A C 480 482.284-490.95 488.889 484.624-493.29 486.95-495.617 500 503.089-511.756 509.091 509.502-514.891 514.286
6 A#/Bb C#/Qb 576 578.74-589.14 586.667 581.548-591.948 584.334-594.74 600 603.707-614.107 610.909 607.469-617.869 617.143
7 B Q 672 675.197-687.33 684.444 678.473-690.606 681.73-693.863 700 704.325-716.4585 712.727 708.7135-720.847 720
8 B#/Cb Q#/Db 768 771.654-785.52 782.822 775.398-789.2645 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 880 872.3225-887.9225 876.51-892.11 900 905.561-921.161 916.364 911.203-926.823 925.714
10 D S 960 964.567-981.901 977.778 969.247-986.561 973.9-991.233 1000 1006.179-1023.512 1018.182 1012.448-1029.781 1028.571
11 D#/Eb S#/Eb 1056 1061.024-1080.091 1075.556 1066.172-1085.239 1071.39-1090.356 1100 1106.797-1125.863 1120 1113.693-1132.759 1131.429
12 E 1152 1157.481-1178.281 1173.333 1163.097-1183.897 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 1271.111 1260.0215-1282.555 1266.07-1288.603 1300 1308.032-1330.566 1323.636 1316.182-1338.716 1337.143
14 F 1344 1350.394-1374.661 1368.889 1356.946-1381.213 1363.46-1387.726 1400 1408.65-1432.917 1425.4545 1417.427-1441.694 1440
15 G 1440 1446.851-1472.851 1466.667 1453.871-1479.871 1460.85-1486.85 1500 1509.268-1535.268 1527.273 1518.672-1544.672 1542.857
Degrees Enneatonic Min 22/9±13¢ Golden±13¢ Max
1 F#/Gb G#/Jb G#/Ab 102.857 102.294-104.027 102.788-104.5215 104
2 G J A 205.714 204.588-208.054 205.576-209.043 208
3 G#/Jb G#/Ab J#/Ab A#/Bb 308.571 306.8815-312.0815 308.365-313.565 312
4 J A J B 411.429 409.1755-416.109 411.153-418.086 416
5 A B A C 514.286 511.469-520.136 513.941-526.308 520
6 A#/Bb B#/Hb A#/Bb C#/Qb 617.143 613.763-624.163 616.729-627.129 624
7 B H B Q 720 716.057-728.19 719.5175-731.651 728
8 B#/Hb H#/Cb B#/Cb Q#/Db 822.857 818.351-832.218 822.306-836.172 832
9 H C C D 925.714 920.645-936.245 925.094-940.694 936
10 C D D S 1028.571 1022.939-1040.272 1027.882-1045.2155 1040
11 C#/Db D#/Sb D#/Eb S#/Eb 1131.429 1125.2325-1144.299 1130.67-1149.737 1144
12 D S E 1234.286 1227.526-1248.326 1233.459-1254.259 1248
13 D#/Eb S#/Eb E#/Fb 1337.143 1329.82-1352.3535 1336.247-1358.78 1352
14 E F 1440 1432.114-1456.381 1439.035-1463.302 1456
15 F G 1542.857 1534.408-1560.408 1541.823-1567.823 1560
Degrees Enneatonic Mixolydian Mixolydian-Ionian
Subpental Pental Superpental
Soft Intense
Min Golden±13¢ Max Min Golden±13¢ 5/2±13¢ Max Min Golden±13¢ Max Min Golden±13¢ Max Min Golden±13¢ Max
1 F#/Gb 104 103.855-105.788 105 104.306-106.04 104.888-106.621 106.667 106.664-108.398 107.586 108.4245-110.158 110.345 109.6375-111.371 112
2 G 208 207.709-211.576 210 208.613-212.08 209.77-213.242 213.333 213.329-216.795 215.172 216.849-220.316 220.69 219.275-222.742 224
3 G#/Jb G#/Ab 312 311.564-317.364 315 312.919-318.119 314.663-319.863 320 319.993-325.193 322.759 325.273-330.473 331.034 328.913-334.113 336
4 J A 416 415.419-423.152 420 417.226-424.159 419.559-426.484 426.667 426.657-433.5905 430.345 433.698-440.631 441.379 438.55-445.4835 448
5 A B 520 519.2735-528.94 525 521.532-530.199 524.438-533.105 533.333 533.321-541.988 537.931 542.122-550.789 551.724 548.188-556.854 560
6 A#/Bb B#/Hb 624 623.128-634.728 630 625.8385-636.238 629.3255-639.7255 640 639.987-650.386 645.517 650.547-660.947 662.069 657.825-668.225 672
7 B H 728 726.983-740.516 735 730.145-742.278 734.213-746.346 746.667 746.65-758.783 753.103 758.971-771.105 772.414 767.463-779.596 784
8 B#/Hb H#/Cb 832 830.8375-844.704 840 834.451-848.318 839.101-852.967 853.333 853.314-867.181 860.69 867.396-881.262 882.759 877.1-890.967 896
9 H C 936 934.693-952.092 945 938.758-954.358 943.988-959.588 960 959.9785-975.5785 968.276 975.82-991.42 993.103 986.738-1002.338 1008
10 C D 1040 1038.547-1057.88 1050 1043.064-1060.3975 1048.876-1066.209 1066.667 1066.643-1083.976 1075.862 1084.245-1101.578 1103.448 1096.3755-1113.709 1120
11 C#/Db D#/Sb 1144 1142.402-1163.668 1155 1147.3705-1166.437 1153.763-1172.83 1173.333 1173.307-1192.374 1183.448 1192.669-1211.736 1213.379 1206.013-1225.08 1232
12 D S 1248 1246.256-1269.456 1260 1251.677-1272.477 1258.651-1279.451 1280 1279.971-1300.771 1291.034 1301.0395-1321.8935 1324.138 1315.651-1336.451 1344
13 D#/Eb S#/Eb 1352 1353.111-1275.244 1365 1355.983-1378.517 1363.539-1386.072 1386.667 1386.636-1409.169 1398.621 1409.518-1425.288 1424.483 1438.993-1447.8215 1456
14 E 1456 1453.966-1481.032 1470 1460.29-1484.556 1468.426-1492.693 1493.333 1493.3-1517.567 1506.207 1517.9425-1534.926 1544.827 1541.778-1559.192 1568
15 F 1560 1557.82-1583.82 1575 1564.596-1590.596 1573.314-1599.314 1600 1599.964-1625.964 1613.793 1626.366-1652.366 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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