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'''15edX''' is the scale which occurs as the dominant minor edX.
'''15edX''' is the scale which occurs as the dominant minor edX (equal division of a tenth interval). It also gives the period of the 15th-decade Alfincavallo branch of the Carrera temperament family.
==Intervals==
 
{| class="wikitable" style="text-align: center"
== Intervals ==
! rowspan="3" |Degrees
{| class="wikitable"
! colspan="2" rowspan="3" |Enneatonic
|+
! colspan="4" rowspan="2" |Intense Aeolian-Subpental Dorian
!Decade
! colspan="9" |Dorian
!Period
!Notes
|-
|6\5
|96.000
|Intense Aeolian-Subpental Dorian mode begins
|-
|17\14
|97.143
|
|-
|11\9
|97.778
|Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
|-
|16\13
|98.462
|
|-
|21\17
|98.824
|
|-
|26\21
|99.048
|
|-
|5\4
|100.000
|Subpental Dorian mode ends, Pental Dorian mode begins
|-
|19\15
|101.333
|
|-
|-
! colspan="9" |Subpental
|14\11
|101.818
|Pental Dorian mode ends, Superpental Dorian mode begins
|-
|-
!Min
|23\18
!Golden±13¢
|102.222
!''r¢''
|
!Max
!Min
!Golden±13¢
!Max
!Min
!Golden±13¢
!Max
!Min
!Golden±13¢
!Max
|-
|-
| |1
|9\7
|G#/Jb
|''G#/Ab''
| |96
|96.457-98.19
|''96.667''
| colspan="2" |97.778
|97.39-99.123
| colspan="2" |''100''
|100.618-102.351
| colspan="2" |101.818
|101.245-102.978
|102.857
|102.857
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
|-
|-
| |2
|31\24
|J
|103.333
|''A''
|
| |192
|-
|192.913-196.38
|22\17
|''193.333''
|103.529
| colspan="2" |195.556
|Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
|194.78-198.247
|-
| colspan="2" |''200''
|35\27
|201.236-204.702
|103.704
| colspan="2" |203.636
|
|202.49-205.956
|-
|205.714
|13\10
|104.000
|Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
|-
|17\13
|104.615
|
|-
|-
| |3
|21\16
|J#/Ab
|105.000
|''A#/Bb''
|Subpental Mixolydian mode ends, Pental Mixolydian mode begins
| |288
|289.37-294.57
|''290''
| colspan="2" |293.333
|292.17-297.37
| colspan="2" |''300''
|301.854-204.702
| colspan="2" |305.4545
|303.734-308.934
|308.571
|-
|-
| |4
|25\19
|J
|105.263
|''B''
|
| |384
|385.829-392.76
|''386.667''
| colspan="2" |391.111
|389.56-396.493
| colspan="2" |''400''
|402.4715-307.054
| colspan="2" |407.273
|404.979-411.9215
|411.429
|-
|-
| |5
|4\3
|A
|106.667
|''C''
|Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
| |480
|482.284-490.95
|''483.333''
| colspan="2" |488.889
|486.95-495.617
| colspan="2" |''500''
|503.089-511.756
| colspan="2" |509.091
|509.502-514.891
|514.286
|-
|-
| |6
|31\23
|A#/Bb
|107.826
|''C#/Qb''
|
| |576
|578.74-589.14
|''580''
| colspan="2" |586.667
|584.334-594.74
| colspan="2" |''600''
|603.707-614.107
| colspan="2" |610.909
|607.469-617.869
|617.143
|-
|-
| |7
|27\20
|B
|108.000
|''Q''
|
| |672
|675.197-687.33
|''676.667''
| colspan="2" |684.444
|681.73-693.863
| colspan="2" |''700''
|704.325-716.4585
| colspan="2" |712.727
|708.7135-720.847
|720
|-
|-
|8
|23\17
|B#/Cb
|108.235
|''Q#/Db''
|
|768
|771.654-785.52
|''773.333''
| colspan="2" |782.822
|779.12-792.9865
| colspan="2" |''800''
|804.943-818.81
| colspan="2" |814.5455
|809.958-823.825
|822.857
|-
|-
|9
|19\14
|C
|108.571
|''D''
|
|864
|868.1105-883.7105
|''870''
| colspan="2" |880
|876.51-892.11
| colspan="2" |''900''
|905.561-921.161
| colspan="2" |916.364
|911.203-926.823
|925.714
|-
|-
|10
|15\11
|D
|109.091
|''S''
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
|960
|964.567-981.901
|''966.667''
| colspan="2" |977.778
|973.9-991.233
| colspan="2" |''1000''
|1006.179-1023.512
| colspan="2" |1018.182
|1012.448-1029.781
|1028.571
|-
|-
|11
|26\19
|D#/Eb
|109.474
|''S#/Eb''
|
|1056
|1061.024-1080.091
|''1063.333''
| colspan="2" |1075.556
|1071.39-1090.356
| colspan="2" |''1100''
|1106.797-1125.863
| colspan="2" |1120
|1113.693-1132.759
|1131.429
|-
|-
|12
|11\8
| colspan="2" |E
|110.000
|1152
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
|1157.481-1178.281
|''1160''
| colspan="2" |1173.333
|1168.68-1189.48
| colspan="2" |''1200''
|1207.4145-1228.2145
| colspan="2" |1221.818
|1214.9375-1235.7375
|1234.286
|-
|-
|13
|18\13
| colspan="2" |E#/Fb
|110.769
|1248
|
|1253.937-1276.471
|''1256.667''
| colspan="2" |1271.111
|1266.07-1288.603
| colspan="2" |''1300''
|1308.032-1330.566
| colspan="2" |1323.636
|1316.182-1338.716
|1337.143
|-
|-
|14
|25\18
| colspan="2" |F
|111.111
|1344
|
|1350.394-1374.661
|''1353.333''
| colspan="2" |1368.889
|1363.46-1387.726
| colspan="2" |''1400''
|1408.65-1432.917
| colspan="2" |1425.4545
|1417.427-1441.694
|1440
|-
|-
|15
|7\5
| colspan="2" |G
|112.500
|1440
|Mixolydian-Ionian mode ends
|1446.851-1472.851
|''1450''
| colspan="2" |1466.667
|1460.85-1486.85
| colspan="2" |''1500''
|1509.268-1535.268
| colspan="2" |1527.273
|1518.672-1544.672
|1542.857
|}
|}
 
Relative cents
{| class="wikitable" style="text-align: center"
{| class="wikitable" style="text-align: center"
!Degrees
!Degrees
! colspan="4" |Enneatonic
! colspan="2" |Enneatonic
!Min
!Intense Aeolian-Subpental Dorian
!Golden±13¢
!Dorian
!''r¢''
!Dorian-Mixolydian
!Max
!Subpental-Soft Superpental Mixolydian
!Intense Superpental Mixolydian ~ Mixolydian-Ionian
|-
|-
| |1
| |1
| colspan="2" |F#/Gb
|G#/Jb
|G#/Jb
|''G#/Ab''
|''G#/Ab''
|102.857
|96.{{Overline|6}}
|102.788-104.5215
|100
|''103.333''
|103.{{Overline|3}}
|104
|106.{{Overline|6}}
|110
|-
|-
| |2
| |2
| colspan="2" |G
|J
|J
|''A''
|''A''
|205.714
|193.{{Overline|3}}
|205.576-209.043
|200
|''206.667''
|206.{{Overline|6}}
|208
|213.{{Overline|3}}
|220
|-
|-
| |3
| |3
|G#/Jb
|''G#/Ab''
|J#/Ab
|J#/Ab
|''A#/Bb''
|''A#/Bb''
|308.571
|290
|308.365-313.565
|300
|''310''
|310
|312
|320
|330
|-
|-
| |4
| |4
|J
|A
|''A''
|J
|''B''
|''B''
|411.429
|386.{{Overline|6}}
|411.153-418.086
|400
|''413.333''
|413.{{Overline|3}}
|416
|426.{{Overline|6}}
|440
|-
|-
| |5
| |5
|A
|B
|''B''
|A
|''C''
|''C''
|514.286
|483.{{Overline|3}}
|513.941-526.308
|500
|''516.667''
|516.{{Overline|6}}
|520
|533.{{Overline|3}}
|550
|-
|-
| |6
| |6
|A#/Bb
|B#/Cb
|''B#/Hb''
|A#/Bb
|''C#/Qb''
|''C#/Qb''
|617.143
|580
|616.729-627.129
|600
|''620''
|620
|624
|640
|660
|-
|-
| |7
| |7
|B
|C
|''H''
|B
|''Q''
|''Q''
|720
|676.{{Overline|6}}
|719.5175-731.651
|700
|''723.333''
|723.{{Overline|3}}
|728
|746.{{Overline|6}}
|770
|-
|-
|8
|8
|B#/Hb
|C#/Qb
|''H#/Cb''
|B#/Cb
|''Q#/Db''
|''Q#/Db''
|822.857
|773.{{Overline|3}}
|822.306-836.172
|800
|''826.667''
|826.{{Overline|6}}
|832
|853.{{Overline|3}}
|880
|-
|-
|9
|9
|H
|Q
|''C''
|C
|''D''
|''D''
|925.714
|870
|925.094-940.694
|900
|''930''
|930
|936
|960
|990
|-
|-
|10
|10
|C
|''D''
|D
|D
|''S''
|''S''
|1028.571
|966.{{Overline|6}}
|1027.882-1045.2155
|1000
|''1033.333''
|1033.{{Overline|3}}
|1040
|1066.{{Overline|6}}
|1100
|-
|-
|11
|11
|C#/Db
|''D#/Sb''
|D#/Eb
|D#/Eb
|''S#/Eb''
|''S#/Eb''
|1131.429
|1063.{{Overline|3}}
|1130.67-1149.737
|1100
|''1136.667''
|1136.{{Overline|6}}
|1144
|1173.{{Overline|3}}
|1210
|-
|-
|12
|12
|D
|''S''
| colspan="2" |E
| colspan="2" |E
|1234.286
|1160
|1233.459-1254.259
|1200
|''1240''
|1240
|1248
|1280
|1320
|-
|-
|13
|13
|D#/Eb
|''S#/Eb''
| colspan="2" |E#/Fb
| colspan="2" |E#/Fb
|1337.143
|1256.{{Overline|6}}
|1336.247-1358.78
|1300
|''1343.333''
|1343.{{Overline|3}}
|1352
|1386.{{Overline|6}}
|1430
|-
|-
|14
|14
| colspan="2" |E
| colspan="2" |F
| colspan="2" |F
|1440
|1353.{{Overline|3}}
|1439.035-1463.302
|1400
|''1446.667''
|1446.{{Overline|6}}
|1456
|1493.{{Overline|3}}
|1540
|-
|-
|15
|15
| colspan="2" |F
| colspan="2" |G
| colspan="2" |G
|1542.857
|1450
|1541.823-1567.823
|1500
|''1550''
|1550
|1560
|1600
|1650
|}
|}


{| class="wikitable" style="text-align: center"
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), 4ed(9/7)/+1/36-syntonic comma 14ed(12/5) (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.
|-
== See also ==
! rowspan="4" |Degrees
* [[15ed5/2]] - equal division of the classic major tenth
! colspan="2" rowspan="4" |Enneatonic
* [[15ed7/3]] - equal division of the septimal minor tenth
! colspan="13" |Mixolydian
! colspan="3" rowspan="3" |Mixolydian-Ionian
|-
! colspan="3" rowspan="2" |Subpental
! colspan="3" rowspan="2" |Pental
! colspan="7" |Superpental
|-
! colspan="3" |Soft
! colspan="4" |Intense
|-
! width="4%" | Min
!Golden±13¢
! width="4%" | Max
! width="4%" | Min
!Golden±13¢
! width="4%" | Max
! width="4%" | Min
!Golden±13¢
! width="4%" | Max
! width="4%" | Min
!Golden±13¢
!''r¢''
! width="4%" | Max
!Min
!Golden±13¢
!Max
|-
| |1
| colspan="2" |F#/Gb
|104
|103.855-105.788
| colspan="2" |105
|104.306-106.04
| colspan="2" |''106.667''
|106.664-108.398
| colspan="2" |107.586
|108.4245-110.158
|''110''
| colspan="2" |110.345
|109.6375-111.371
|112
|-
| |2
| colspan="2" |G
|208
|207.709-211.576
| colspan="2" |210
|208.613-212.08
| colspan="2" |''213.333''
|213.329-216.795
| colspan="2" |215.172
|216.849-220.316
|''220''
| colspan="2" |220.69
|219.275-222.742
|224
|-
| |3
|G#/Jb
|''G#/Ab''
|312
|311.564-317.364
| colspan="2" |315
|312.919-318.119
| colspan="2" |''320''
|319.993-325.193
| colspan="2" |322.759
|325.273-330.473
|''330''
| colspan="2" |331.034
|328.913-334.113
|336
|-
| |4
|J
|''A''
|416
|415.419-423.152
| colspan="2" |420
|417.226-424.159
| colspan="2" |''426.667''
|426.657-433.5905
| colspan="2" |430.345
|433.698-440.631
|''440''
| colspan="2" |441.379
|438.55-445.4835
|448
|-
| |5
|A
|''B''
|520
|519.2735-528.94
| colspan="2" |525
|521.532-530.199
| colspan="2" |''533.333''
|533.321-541.988
| colspan="2" |537.931
|542.122-550.789
|''550''
| colspan="2" |551.724
|548.188-556.854
|560
|-
| |6
|A#/Bb
|''B#/Hb''
|624
|623.128-634.728
| colspan="2" |630
|625.8385-636.238
| colspan="2" |''640''
|639.987-650.386
| colspan="2" |645.517
|650.547-660.947
|''660''
| colspan="2" |662.069
|657.825-668.225
|672
|-
| |7
|B
|''H''
|728
|726.983-740.516
| colspan="2" |735
|730.145-742.278
| colspan="2" |''746.667''
|746.65-758.783
| colspan="2" |753.103
|758.971-771.105
|''770''
| colspan="2" |772.414
|767.463-779.596
|784
|-
|8
|B#/Hb
|''H#/Cb''
|832
|830.8375-844.704
| colspan="2" |840
|834.451-848.318
| colspan="2" |''853.333''
|853.314-867.181
| colspan="2" |860.69
|867.396-881.262
|''880''
| colspan="2" |882.759
|877.1-890.967
|896
|-
|9
|H
|''C''
|936
|934.693-952.092
| colspan="2" |945
|938.758-954.358
| colspan="2" |''960''
|959.9785-975.5785
| colspan="2" |968.276
|975.82-991.42
|''990''
| colspan="2" |993.103
|986.738-1002.338
|1008
|-
|10
|C
|''D''
|1040
|1038.547-1057.88
| colspan="2" |1050
|1043.064-1060.3975
| colspan="2" |''1066.667''
|1066.643-1083.976
| colspan="2" |1075.862
|1084.245-1101.578
|''1100''
| colspan="2" |1103.448
|1096.3755-1113.709
|1120
|-
|11
|C#/Db
|''D#/Sb''
|1144
|1142.402-1163.668
| colspan="2" |1155
|1147.3705-1166.437
| colspan="2" |''1173.333''
|1173.307-1192.374
| colspan="2" |1183.448
|1192.669-1211.736
|''1210''
| colspan="2" |1213.379
|1206.013-1225.08
|1232
|-
|12
|D
|''S''
|1248
|1246.256-1269.456
| colspan="2" |1260
|1251.677-1272.477
| colspan="2" |''1280''
|1279.971-1300.771
| colspan="2" |1291.034
|1301.0395-1321.8935
|''1320''
| colspan="2" |1324.138
|1315.651-1336.451
|1344
|-
|13
|D#/Eb
|''S#/Eb''
|1352
|1353.111-1275.244
| colspan="2" |1365
|1355.983-1378.517
| colspan="2" |''1386.667''
|1386.636-1409.169
| colspan="2" |1398.621
|1409.518-1425.288
|''1430''
| colspan="2" |1424.483
|1438.993-1447.8215
|1456
|-
|14
| colspan="2" |E
|1456
|1453.966-1481.032
| colspan="2" |1470
|1460.29-1484.556
| colspan="2" |''1493.333''
|1493.3-1517.567
| colspan="2" |1506.207
|1517.9425-1534.926
|''1540''
| colspan="2" |1544.827
|1541.778-1559.192
|1568
|-
|15
| colspan="2" |F
|1560
|1557.82-1583.82
| colspan="2" |1575
|1564.596-1590.596
| colspan="2" |''1600''
|1599.964-1625.964
| colspan="2" |1613.793
|1626.366-1652.366
|''1650''
| colspan="2" |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.
[[Category:15-tone scales]]
[[Category:15-tone]]
[[Category:EdX]]
[[Category:ed7/3]]
[[Category:edX]]
[[Category:todo:add_definition]]
[[Category:todo:unify_precision]]
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/15edX"