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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="5" |Degrees
{| class="wikitable"
! colspan="2" rowspan="5" |Enneatonic
|+
! colspan="8" |Minor mode Middletown temperament
!Decade
! colspan="2" |Neutral mode Middletown temperament
!Period
! colspan="10" |Major mode Middletown temperament
!Notes
|-
|-
! colspan="2" rowspan="3" |Aeolian-Dorian
|6\5
! colspan="6" |Dorian
|96.000
! colspan="2" rowspan="3" |Dorian-Mixolydian
|Intense Aeolian-Subpental Dorian mode begins
! colspan="8" |Mixolydian
! colspan="2" rowspan="3" |Mixolydian-Ionian
|-
|-
! colspan="2" rowspan="2" |Subpental
|17\14
! colspan="2" rowspan="2" |Pental
|97.143
! colspan="2" rowspan="2" |Superpental
|
! colspan="2" rowspan="2" |Subpental
! colspan="2" rowspan="2" |Pental
! colspan="4" |Superpental
|-
|-
! colspan="2" |Soft
|11\9
! colspan="2" |Intense
|97.778
|Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
|-
|-
! width="4%" | Min
|16\13
! width="4%" | Max
|98.462
! width="4%" | Min
|
! width="4%" | Max
! width="4%" | Min
! width="4%" | Max
! width="4%" | Min
! width="4%" | Max
! width="4%" | Min
! width="4%" | Max
! width="4%" | Min
! width="4%" | Max
! width="4%" | Min
! width="4%" | Max
! width="4%" | Min
! width="4%" | Max
! width="4%" | Min
! width="4%" | Max
! width="4%" | Min
! width="4%" | Max
|-
|-
| |1
|21\17
| colspan="2" |F#/Gb
|98.824
| |96
|
| colspan="2" |97.778
| colspan="2" |100
| colspan="2" |101.818
| colspan="2" |102.857
| colspan="2" |104
| colspan="2" |105
| colspan="2" |106.667
| colspan="2" |107.586
| colspan="2" |110.345
| |112
|-
|-
| |2
|26\21
| colspan="2" |G
|99.048
| |192
|
| colspan="2" |195.556
| colspan="2" |200
| colspan="2" |203.636
| colspan="2" |205.714
| colspan="2" |208
| colspan="2" |210
| colspan="2" |213.333
| colspan="2" |215.172
| colspan="2" |220.69
| |224
|-
|-
| |3
|5\4
|G#/Jb
|100.000
|''G#/Ab''
|Subpental Dorian mode ends, Pental Dorian mode begins
| |288
| colspan="2" |293.333
| colspan="2" |300
| colspan="2" |305.4545
| colspan="2" |308.571
| colspan="2" |312
| colspan="2" |315
| colspan="2" |320
| colspan="2" |322.759
| colspan="2" |331.034
| |336
|-
|-
| |4
|19\15
|J
|101.333
|''A''
|
| |384
| colspan="2" |391.111
| colspan="2" |400
| colspan="2" |407.273
| colspan="2" |411.429
| colspan="2" |416
| colspan="2" |420
| colspan="2" |426.667
| colspan="2" |430.345
| colspan="2" |441.379
| |448
|-
|-
| |5
|14\11
|A
|101.818
|''B''
|Pental Dorian mode ends, Superpental Dorian mode begins
| |480
| colspan="2" |488.889
| colspan="2" |500
| colspan="2" |509.091
| colspan="2" |514.286
| colspan="2" |520
| colspan="2" |525
| colspan="2" |533.333
| colspan="2" |537.931
| colspan="2" |551.724
| |560
|-
|-
| |6
|23\18
|A#/Bb
|102.222
|''B#/Hb''
|
| |576
| colspan="2" |586.667
| colspan="2" |600
| colspan="2" |610.909
| colspan="2" |617.143
| colspan="2" |624
| colspan="2" |630
| colspan="2" |640
| colspan="2" |645.517
| colspan="2" |662.069
| |672
|-
|-
| |7
|9\7
|B
|102.857
|''H''
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
| |672
| colspan="2" |684.444
| colspan="2" |700
| colspan="2" |712.727
| colspan="2" |720
| colspan="2" |728
| colspan="2" |735
| colspan="2" |746.667
| colspan="2" |753.103
| colspan="2" |772.414
| |784
|-
|-
|8
|31\24
|B#/Hb
|103.333
|''H#/Cb''
|
|768
| colspan="2" |782.822
| colspan="2" |800
| colspan="2" |814.5455
| colspan="2" |822.857
| colspan="2" |832
| colspan="2" |840
| colspan="2" |853.333
| colspan="2" |860.69
| colspan="2" |882.759
|896
|-
|-
|9
|22\17
|H
|103.529
|''C''
|Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
|864
| colspan="2" |880
| colspan="2" |900
| colspan="2" |916.364
| colspan="2" |925.714
| colspan="2" |936
| colspan="2" |945
| colspan="2" |960
| colspan="2" |968.276
| colspan="2" |993.103
|1008
|-
|-
|10
|35\27
|C
|103.704
|''D''
|
|960
| colspan="2" |977.778
| colspan="2" |1000
| colspan="2" |1018.182
| colspan="2" |1028.571
| colspan="2" |1040
| colspan="2" |1050
| colspan="2" |1066.667
| colspan="2" |1075.862
| colspan="2" |1103.448
|1120
|-
|-
|11
|13\10
|C#/Db
|104.000
|''D#/Sb''
|Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
|1056
| colspan="2" |1075.556
| colspan="2" |1100
| colspan="2" |1120
| colspan="2" |1131.429
| colspan="2" |1144
| colspan="2" |1155
| colspan="2" |1173.333
| colspan="2" |1183.448
| colspan="2" |1213.379
|1232
|-
|-
|12
|17\13
|D
|104.615
|''S''
|
|1152
| colspan="2" |1173.333
| colspan="2" |1200
| colspan="2" |1221.818
| colspan="2" |1234.286
| colspan="2" |1248
| colspan="2" |1260
| colspan="2" |1280
| colspan="2" |1291.034
| colspan="2" |1324.138
|1344
|-
|-
|13
|21\16
|D#/Eb
|105.000
|''S#/Eb''
|Subpental Mixolydian mode ends, Pental Mixolydian mode begins
|1248
| colspan="2" |1271.111
| colspan="2" |1300
| colspan="2" |1323.636
| colspan="2" |1337.143
| colspan="2" |1352
| colspan="2" |1365
| colspan="2" |1386.667
| colspan="2" |1398.621
| colspan="2" |1424.483
|1456
|-
|14
| colspan="2" |E
|1344
| colspan="2" |1368.889
| colspan="2" |1400
| colspan="2" |1425.4545
| colspan="2" |1440
| colspan="2" |1456
| colspan="2" |1470
| colspan="2" |1493.333
| colspan="2" |1506.207
| colspan="2" |1544.827
|1568
|-
|15
| colspan="2" |F
|1440
| colspan="2" |1466.667
| colspan="2" |1500
| colspan="2" |1527.273
| colspan="2" |1542.857
| colspan="2" |1560
| colspan="2" |1575
| colspan="2" |1600
| colspan="2" |1613.793
| colspan="2" |1655.172
|1680
|}
 
Most harmonic tunings
{| class="wikitable"
|-
|-
! rowspan="2" |Degrees
|25\19
! colspan="2" rowspan="2" |Enneatonic
|105.263
!Minor mode Middletown temperament
|
!Neutral mode Middletown temperament
!Major mode Middletown temperament
|-
|-
!7/3±13¢
|4\3
!22/9±13¢
|106.667
!5/2±13¢
|Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
|-
|-
|1
|31\23
| colspan="2" |F#/Gb
|107.826
|96.925-98.658
|
|102.294-104.027
|104.888-106.621
|-
|-
| |2
|27\20
| colspan="2" |G
|108.000
|193.8495-197.316
|
|204.588-208.054
|209.77-213.242
|-
|-
|3
|23\17
|G#/Jb
|108.235
|''G#/Ab''
|
|290.774-295.974
|306.8815-312.0815
|314.663-319.863
|-
|-
| |4
|19\14
|J
|108.571
|''A''
|
|387.699-394.632
|409.1755-416.109
|419.559-426.484
|-
|-
| |5
|15\11
|A
|109.091
|''B''
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
|484.624-493.29
|511.469-520.136
|524.438-533.105
|-
|-
|6
|26\19
|A#/Bb
|109.474
|''B#/Hb''
|
|581.548-591.948
|613.763-624.163
|629.3255-639.7255
|-
|-
| |7
|11\8
|B
|110.000
|''H''
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
|678.473-690.606
|716.057-728.19
|734.213-746.346
|-
|-
|8
|18\13
|B#/Hb
|110.769
|''H#/Cb''
|
|775.398-789.2645
|818.351-832.218
|839.101-852.967
|-
|-
|9
|25\18
|H
|111.111
|''C''
|
|872.3225-887.9225
|920.645-936.245
|943.988-959.588
|-
|-
|10
|7\5
|C
|112.500
|''D''
|Mixolydian-Ionian mode ends
|969.247-986.561
|}
|1022.939-1040.272
Relative cents
|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
| colspan="2" |E
|1356.946-1381.213
|1432.114-1456.381
|1468.426-1492.693
|-
|15
| colspan="2" |F
|1453.871-1479.871
|1534.408-1560.408
|1573.314-1599.314
|}Golden tunings±13¢
{| class="wikitable" style="text-align: center"
{| class="wikitable" style="text-align: center"
! rowspan="4" |Degrees
!Degrees
! colspan="2" rowspan="4" |Enneatonic
! colspan="2" |Enneatonic
! colspan="4" |Minor mode Middletown temperament
!Intense Aeolian-Subpental Dorian
!Neutral mode Middletown temperament
!Dorian
! colspan="6" |Major mode Middletown temperament
!Dorian-Mixolydian
|-
!Subpental-Soft Superpental Mixolydian
! rowspan="3" |Aeolian-Dorian
!Intense Superpental Mixolydian ~ Mixolydian-Ionian
! colspan="3" |Dorian
! colspan="2" rowspan="3" |Dorian-Mixolydian
! colspan="4" |Mixolydian
! rowspan="3" |Mixolydian-Ionian
|-
! rowspan="2" |Subpental
! rowspan="2" |Pental
! rowspan="2" |Superpental
! rowspan="2" |Subpental
! rowspan="2" |Pental
! colspan="2" |Superpental
|-
!Soft
!Intense
|-
|-
| |1
| |1
| colspan="2" |F#/Gb
|G#/Jb
| |96.457-98.19
|''G#/Ab''
|97.39-99.123
|96.{{Overline|6}}
|100.618-102.351
|100
|101.245-102.978
|103.{{Overline|3}}
| colspan="2" |102.788-104.5215
|106.{{Overline|6}}
|103.855-105.788
|110
|104.306-106.04
|106.664-108.398
|108.4245-110.158
|109.6375-111.371
|-
|-
| |2
| |2
| colspan="2" |G
|J
| |192.913-196.38
|''A''
|194.78-198.247
|193.{{Overline|3}}
|201.236-204.702
|200
|202.49-205.956
|206.{{Overline|6}}
| colspan="2" |205.576-209.043
|213.{{Overline|3}}
|207.709-211.576
|220
|208.613-212.08
|213.329-216.795
|216.849-220.316
|219.275-222.742
|-
|-
| |3
| |3
|G#/Jb
|J#/Ab
|''G#/Ab''
|''A#/Bb''
| |289.37-294.57
|290
|292.17-297.37
|300
|301.854-204.702
|310
|303.734-308.934
|320
| colspan="2" |308.365-313.565
|330
|311.564-317.364
|312.919-318.119
|319.993-325.193
|325.273-330.473
|328.913-334.113
|-
|-
| |4
| |4
|J
|A
|''A''
|''B''
| |385.829-392.76
|386.{{Overline|6}}
|389.56-396.493
|400
|402.4715-307.054
|413.{{Overline|3}}
|404.979-411.9215
|426.{{Overline|6}}
| colspan="2" |411.153-418.086
|440
|415.419-423.152
|417.226-424.159
|426.657-433.5905
|433.698-440.631
|438.55-445.4835
|-
|-
| |5
| |5
|A
|B
|''B''
|''C''
| |482.284-490.95
|483.{{Overline|3}}
|486.95-495.617
|500
|503.089-511.756
|516.{{Overline|6}}
|509.502-514.891
|533.{{Overline|3}}
| colspan="2" |513.941-526.308
|550
|519.2735-528.94
|521.532-530.199
|533.321-541.988
|542.122-550.789
|548.188-556.854
|-
|-
| |6
| |6
|A#/Bb
|B#/Cb
|''B#/Hb''
|''C#/Qb''
| |578.74-589.14
|580
|584.334-594.74
|600
|603.707-614.107
|620
|607.469-617.869
|640
| colspan="2" |616.729-627.129
|660
|623.128-634.728
|625.8385-636.238
|639.987-650.386
|650.547-660.947
|657.825-668.225
|-
|-
| |7
| |7
|B
|C
|''H''
|''Q''
| |675.197-687.33
|676.{{Overline|6}}
|681.73-693.863
|700
|704.325-716.4585
|723.{{Overline|3}}
|708.7135-720.847
|746.{{Overline|6}}
| colspan="2" |719.5175-731.651
|770
|726.983-740.516
|730.145-742.278
|746.65-758.783
|758.971-771.105
|767.463-779.596
|-
|-
|8
|8
|B#/Hb
|C#/Qb
|''H#/Cb''
|''Q#/Db''
|771.654-785.52
|773.{{Overline|3}}
|779.12-792.9865
|800
|804.943-818.81
|826.{{Overline|6}}
|809.958-823.825
|853.{{Overline|3}}
| colspan="2" |822.306-836.172
|880
|830.8375-844.704
|834.451-848.318
|853.314-867.181
|867.396-881.262
|877.1-890.967
|-
|-
|9
|9
|H
|Q
|''C''
|''D''
|868.1105-883.7105
|870
|876.51-892.11
|900
|905.561-921.161
|930
|911.203-926.823
|960
| colspan="2" |925.094-940.694
|990
|934.693-952.092
|938.758-954.358
|959.9785-975.5785
|975.82-991.42
|986.738-1002.338
|-
|-
|10
|10
|C
|D
|''D''
|''S''
|964.567-981.901
|966.{{Overline|6}}
|973.9-991.233
|1000
|1006.179-1023.512
|1033.{{Overline|3}}
|1012.448-1029.781
|1066.{{Overline|6}}
| colspan="2" |1027.882-1045.2155
|1100
|1038.547-1057.88
|1043.064-1060.3975
|1066.643-1083.976
|1084.245-1101.578
|1096.3755-1113.709
|-
|-
|11
|11
|C#/Db
|D#/Eb
|''D#/Sb''
|''S#/Eb''
|1061.024-1080.091
|1063.{{Overline|3}}
|1071.39-1090.356
|1100
|1106.797-1125.863
|1136.{{Overline|6}}
|1113.693-1132.759
|1173.{{Overline|3}}
| colspan="2" |1130.67-1149.737
|1210
|1142.402-1163.668
|1147.3705-1166.437
|1173.307-1192.374
|1192.669-1211.736
|1206.013-1225.08
|-
|-
|12
|12
|D
| colspan="2" |E
|''S''
|1160
|1157.481-1178.281
|1200
|1168.68-1189.48
|1240
|1207.4145-1228.2145
|1280
|1214.9375-1235.7375
|1320
| colspan="2" |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
|13
|D#/Eb
| colspan="2" |E#/Fb
|''S#/Eb''
|1256.{{Overline|6}}
|1253.937-1276.471
|1300
|1266.07-1288.603
|1343.{{Overline|3}}
|1308.032-1330.566
|1386.{{Overline|6}}
|1316.182-1338.716
|1430
| colspan="2" |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
|14
| colspan="2" |E
| colspan="2" |F
|1350.394-1374.661
|1353.{{Overline|3}}
|1363.46-1387.726
|1400
|1408.65-1432.917
|1446.{{Overline|6}}
|1417.427-1441.694
|1493.{{Overline|3}}
| colspan="2" |1439.035-1463.302
|1540
|1453.966-1481.032
|1460.29-1484.556
|1493.3-1517.567
|1517.9425-1534.926
|1541.778-1559.192
|-
|-
|15
|15
| colspan="2" |F
| colspan="2" |G
|1446.851-1472.851
|1450
|1460.85-1486.85
|1500
|1509.268-1535.268
|1550
|1518.672-1544.672
|1600
| colspan="2" |1541.823-1567.823
|1650
|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.
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.
[[Category:15-tone]]
== See also ==
[[Category:ed7/3]]
* [[15ed5/2]] - equal division of the classic major tenth
[[Category:edX]]
* [[15ed7/3]] - equal division of the septimal minor tenth
[[Category:todo:add_definition]]
 
[[Category:todo:unify_precision]]
[[Category:15-tone scales]]
[[Category:EdX]]
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