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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.


This is the neutral scale of the Middletown temperament family.
== Intervals ==
==Intervals==
{| class="wikitable"
{| class="wikitable"
! rowspan="5" |Degrees
|+
! colspan="2" rowspan="5" |Enneatonic
!Decade
! colspan="8" |Minor mode Middletown temperament
!Period
! colspan="2" |Neutral mode Middletown temperament
!Notes
! colspan="10" |Major mode Middletown temperament
|-
|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
|
|-
|-
! colspan="2" rowspan="3" |Aeolian-Dorian
|26\21
! colspan="6" |Dorian
|99.048
! colspan="2" rowspan="3" |Dorian-Mixolydian
|
! colspan="8" |Mixolydian
! colspan="2" rowspan="3" |Mixolydian-Ionian
|-
|-
! colspan="2" rowspan="2" |Subpental
|5\4
! colspan="2" rowspan="2" |Pental
|100.000
! colspan="2" rowspan="2" |Superpental
|Subpental Dorian mode ends, Pental Dorian mode begins
! colspan="2" rowspan="2" |Subpental
! colspan="2" rowspan="2" |Pental
! colspan="4" |Superpental
|-
|-
! colspan="2" |Soft
|19\15
! colspan="2" |Intense
|101.333
|
|-
|-
! |Minimum
|14\11
! |Maximum
|101.818
!Minimum
|Pental Dorian mode ends, Superpental Dorian mode begins
!Maximum
!Minimum
!Maximum
!Minimum
!Maximum
!Minimum
! |Maximum
!Minimum
!Maximum
! |Minimum
!Maximum
!Minimum
!Maximum
!Minimum
!Maximum
!Minimum
! |Maximum
|-
|-
| |1
|23\18
| colspan="2" |F#/Gb
|102.222
| |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
|9\7
| colspan="2" |G
|102.857
| |192
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
| 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
|31\24
|G#/Jb
|103.333
|''G#/Ab''
|
| |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
|22\17
|J
|103.529
|''A''
|Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
| |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
|35\27
|A
|103.704
|''B''
|
| |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
|13\10
|A#/Bb
|104.000
|''B#/Hb''
|Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
| |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
|17\13
|B
|104.615
|''H''
|
| |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
|21\16
|B#/Hb
|105.000
|''H#/Cb''
|Subpental Mixolydian mode ends, Pental Mixolydian mode begins
|768
| colspan="2" |782.822
| colspan="2" |800
| colspan="2" |814.5455
| colspan="2" |822.857
| colspan="2" |832
| colspan="2" |845
| colspan="2" |853.333
| colspan="2" |860.69
| colspan="2" |882.759
|896
|-
|-
|9
|25\19
|H
|105.263
|''C''
|
|864
| colspan="2" |880
| colspan="2" |900
| colspan="2" |916.364
| colspan="2" |925.714
| colspan="2" |936
| colspan="2" |940
| colspan="2" |960
| colspan="2" |968.276
| colspan="2" |993.103
|1008
|-
|-
|10
|4\3
|C
|106.667
|''D''
|Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
|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
|31\23
|C#/Db
|107.826
|''D#/Sb''
|
|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
|27\20
|D
|108.000
|''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
|23\17
|D#/Eb
|108.235
|''S#/Eb''
|
|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
|19\14
| colspan="2" |E
|108.571
|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
|15\11
| colspan="2" |F
|109.091
|1440
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
| 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
|}Golden tunings
{| class="wikitable"
|+
! rowspan="4" |Degrees
! colspan="2" rowspan="4" |Enneatonic
! colspan="4" |Minor mode Middletown temperament
!Neutral mode Middletown temperament
! colspan="5" |Major mode Middletown temperament
|-
|-
! rowspan="3" |Aeolian-Dorian
|26\19
! colspan="3" |Dorian
|109.474
! rowspan="3" |Dorian-Mixolydian
|
! colspan="4" |Mixolydian
! rowspan="3" |Mixolydian-Ionian
|-
|-
! rowspan="2" |Subpental
|11\8
! rowspan="2" |Pental
|110.000
! rowspan="2" |Superpental
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
! rowspan="2" |Subpental
! rowspan="2" |Pental
! colspan="2" |Superpental
|-
|-
!Soft
|18\13
!Intense
|110.769
|
|-
|-
|1
|25\18
| colspan="2" |F#/Gb
|111.111
|97.323
|
|98.257
|101.4845
|102.1115
|103.655
|104.721
|105.173
|107.531
|109.291
|110.504
|-
|-
|2
|7\5
| colspan="2" |G
|112.500
|194.647
|Mixolydian-Ionian mode ends
|196.513
|}
|202.969
Relative cents
|204.223
{| class="wikitable" style="text-align: center"
|207.31
!Degrees
|209.443
! colspan="2" |Enneatonic
|210.346
!Intense Aeolian-Subpental Dorian
|215.032
!Dorian
|218.582
!Dorian-Mixolydian
|221.008
!Subpental-Soft Superpental Mixolydian
!Intense Superpental Mixolydian ~ Mixolydian-Ionian
|-
|-
|3
| |1
|G#/Jb
|G#/Jb
|''G#/Ab''
|''G#/Ab''
|291.97
|96.{{Overline|6}}
|294.77
|100
|304.454
|103.{{Overline|3}}
|306.334
|106.{{Overline|6}}
|310.965
|110
|314.164
|315.519
|322.593
|327.873
|331.613
|-
|-
|4
| |2
|J
|J
|''A''
|''A''
|389.294
|193.{{Overline|3}}
|394.027
|200
|405.938
|206.{{Overline|6}}
|408.446
|213.{{Overline|3}}
|414.6195
|220
|418.885
|420.639
|430.124
|437.1345
|442.017
|-
|-
|5
| |3
|J#/Ab
|''A#/Bb''
|290
|300
|310
|320
|330
|-
| |4
|A
|A
|''B''
|''B''
|486.617
|386.{{Overline|6}}
|491.283
|400
|507.423
|413.{{Overline|3}}
|510.557
|426.{{Overline|6}}
|518.274
|440
|523.607
|525.865
|537.655
|546.456
|552.521
|-
|-
|6
| |5
|A#/Bb
|B
|''B#/Hb''
|''C''
|583.94
|483.{{Overline|3}}
|589.54
|500
|608.907
|516.{{Overline|6}}
|612.669
|533.{{Overline|3}}
|621.929
|550
|628.328
|631.0385
|645.186
|655.747
|663.025
|-
|-
|7
| |6
|B
|B#/Cb
|''H''
|''C#/Qb''
|681.364
|580
|687.7965
|600
|710.392
|620
|714.78
|640
|725.584
|660
|733.0495
|-
|736.212
| |7
|752.717
|C
|765.038
|''Q''
|773.5235
|676.{{Overline|6}}
|700
|723.{{Overline|3}}
|746.{{Overline|6}}
|770
|-
|-
|8
|8
|B#/Hb
|C#/Qb
|''H#/Cb''
|''Q#/Db''
|778.587
|773.{{Overline|3}}
|786.053
|800
|811.877
|826.{{Overline|6}}
|816.892
|853.{{Overline|3}}
|829.239
|880
|837.771
|841.385
|860.248
|874.329
|884.033
|-
|-
|9
|9
|H
|Q
|''C''
|''D''
|875.9105
|870
|884.31
|900
|913.361
|930
|919.003
|960
|932.893
|990
|942.492
|946.558
|967.7785
|983.62
|994.538
|-
|-
|10
|10
|C
|D
|''D''
|''S''
|973.234
|966.{{Overline|6}}
|982.5665
|1000
|1014.8455
|1033.{{Overline|3}}
|1021.115
|1066.{{Overline|6}}
|1036.549
|1100
|1047.214
|1051.731
|1075.3095
|1092.911
|1105.042
|-
|-
|11
|11
|C#/Db
|D#/Eb
|''D#/Sb''
|''S#/Eb''
|1070.557
|1063.{{Overline|3}}
|1080.823
|1100
|1116.33
|1136.{{Overline|6}}
|1123.226
|1173.{{Overline|3}}
|1140.204
|1210
|1151.935
|1156.904
|1182.84
|1202.202
|1215.546
|-
|-
|12
|12
|D
| colspan="2" |E
|''S''
|1160
|1167.881
|1200
|1179.08
|1240
|1217.8145
|1280
|1225.3375
|1320
|1243.859
|1256.656
|1262.077
|1290.371
|1311.4935
|1326.051
|-
|-
|13
|13
|D#/Eb
| colspan="2" |E#/Fb
|''S#/Eb''
|1256.{{Overline|6}}
|1265.204
|1300
|1277.336
|1343.{{Overline|3}}
|1319.299
|1386.{{Overline|6}}
|1327.449
|1430
|1347.513
|1361.378
|1367.25
|1397.902
|1420.785
|1436.555
|-
|-
|14
|14
| colspan="2" |E
| colspan="2" |F
|1362.527
|1353.{{Overline|3}}
|1375.593
|1400
|1420.783
|1446.{{Overline|6}}
|1429.56
|1493.{{Overline|3}}
|1451.168
|1540
|1466.099
|1472.423
|1505.433
|1530.076
|1547.059
|-
|-
|15
|15
| colspan="2" |F
| colspan="2" |G
|1459.851
|1450
|1473.85
|1500
|1522.268
|1550
|1531.672
|1600
|1554.823
|1650
|1570.82
|}
|1577.596
 
|1612.964
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.
|1639.366
== See also ==
|1657.563
* [[15ed5/2]] - equal division of the classic major tenth
|}By a surprising coincidence, the 15ed of the Golden tenth (7φ+6)\(5φ^2)edo is almost exactly every third degree of [[34edo]]. Additionally, those of the modal Golden 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.
* [[15ed7/3]] - equal division of the septimal minor tenth


[[Category:15-tone]]
[[Category:15-tone scales]]
[[Category:ed7/3]]
[[Category:EdX]]
[[Category:edX]]
[[Category:todo:add_definition]]
[[Category:todo:unify_precision]]
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