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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==


== Intervals ==
{| class="wikitable"
{| class="wikitable"
|+
!Decade
!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
|
|-
|14\11
|101.818
|Pental Dorian mode ends, Superpental Dorian mode begins
|-
|23\18
|102.222
|
|-
|9\7
|102.857
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
|-
|31\24
|103.333
|
|-
|22\17
|103.529
|Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
|-
|-
! | Degrees
|35\27
! | Enneatonic
|103.704
! | Minimum
|
! | ed(7/3)
! | Mean/Median
! | Golden
! | Maximum
|-
|-
| | 1
|13\10
| | E#/Fb
|104.000
| | 96
|Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
| | 97.791
| | 104
| | 105.888'5
| | 112
|-
|-
| | 2
|17\13
| | F
|104.615
| | 192
|
| | 195.582
| | 208
| | 211.777
| | 224
|-
|-
| | 3
|21\16
| | F#/Gb
|105.000
| | 288
|Subpental Mixolydian mode ends, Pental Mixolydian mode begins
| | 293.374
| | 312
| | 317.666
| | 336
|-
|-
| | 4
|25\19
| | G
|105.263
| | 384
|
| | 391.166
| | 416
| | 423.554
| | 448
|-
|-
| | 5
|4\3
| | H
|106.667
| | 480
|Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
| | 488.957
| | 520
| | 529.443
| | 560
|-
|-
| | 6
|31\23
| | H#/Jb
|107.826
| | 576
|
| | 586.748
| | 624
| | 635.331
| | 672
|-
|-
| | 7
|27\20
| | J
|108.000
| | 672
|
| | 684.54
| | 728
| | 741.22
| | 784
|-
|-
| | 8
|23\17
| | J#/Ab
|108.235
| | 768
|
| | 782.331
| | 832
| | 847.108
| | 896
|-
|-
| | 9
|19\14
| | A
|108.571
| | 864
|
| | 880.122'5
| | 936
| | 952.997
| | 1008
|-
|-
| | 10
|15\11
| | B
|109.091
| | 960
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
| | 977.913
| | 1040
| | 1058.885
| | 1120
|-
|-
| | 11
|26\19
| | B#/Cb
|109.474
| | 1056
|
| | 1075.705
| | 1144
| | 1164.774
| | 1232
|-
|-
| | 12
|11\8
| | C
|110.000
| | 1152
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
| | 1173.497
| | 1248
| | 1270.6625
| | 1344
|-
|-
| | 13
|18\13
| | C#/Db
|110.769
| | 1248
|
| | 1271.288
| | 1352
| | 1376.551
| | 1456
|-
|-
| | 14
|25\18
| | D
|111.111
| | 1344
|
| | 1369.0795
| | 1456
| | 1482.44
| | 1568
|-
|-
| | 15
|7\5
| | E
|112.500
| | 1440
|Mixolydian-Ionian mode ends
| | 1466.871
| | 1560
| | 1588.328
| | 1680
|}
|}
Relative cents
{| class="wikitable" style="text-align: center"
!Degrees
! colspan="2" |Enneatonic
!Intense Aeolian-Subpental Dorian
!Dorian
!Dorian-Mixolydian
!Subpental-Soft Superpental Mixolydian
!Intense Superpental Mixolydian ~ Mixolydian-Ionian
|-
| |1
|G#/Jb
|''G#/Ab''
|96.{{Overline|6}}
|100
|103.{{Overline|3}}
|106.{{Overline|6}}
|110
|-
| |2
|J
|''A''
|193.{{Overline|3}}
|200
|206.{{Overline|6}}
|213.{{Overline|3}}
|220
|-
| |3
|J#/Ab
|''A#/Bb''
|290
|300
|310
|320
|330
|-
| |4
|A
|''B''
|386.{{Overline|6}}
|400
|413.{{Overline|3}}
|426.{{Overline|6}}
|440
|-
| |5
|B
|''C''
|483.{{Overline|3}}
|500
|516.{{Overline|6}}
|533.{{Overline|3}}
|550
|-
| |6
|B#/Cb
|''C#/Qb''
|580
|600
|620
|640
|660
|-
| |7
|C
|''Q''
|676.{{Overline|6}}
|700
|723.{{Overline|3}}
|746.{{Overline|6}}
|770
|-
|8
|C#/Qb
|''Q#/Db''
|773.{{Overline|3}}
|800
|826.{{Overline|6}}
|853.{{Overline|3}}
|880
|-
|9
|Q
|''D''
|870
|900
|930
|960
|990
|-
|10
|D
|''S''
|966.{{Overline|6}}
|1000
|1033.{{Overline|3}}
|1066.{{Overline|6}}
|1100
|-
|11
|D#/Eb
|''S#/Eb''
|1063.{{Overline|3}}
|1100
|1136.{{Overline|6}}
|1173.{{Overline|3}}
|1210
|-
|12
| colspan="2" |E
|1160
|1200
|1240
|1280
|1320
|-
|13
| colspan="2" |E#/Fb
|1256.{{Overline|6}}
|1300
|1343.{{Overline|3}}
|1386.{{Overline|6}}
|1430
|-
|14
| colspan="2" |F
|1353.{{Overline|3}}
|1400
|1446.{{Overline|6}}
|1493.{{Overline|3}}
|1540
|-
|15
| colspan="2" |G
|1450
|1500
|1550
|1600
|1650
|}
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 ==
* [[15ed5/2]] - equal division of the classic major tenth
* [[15ed7/3]] - equal division of the septimal minor tenth


By a surprising coincidence, the Golden tuning of this [[edX|edX]] is almost exactly every third degree of [[34edo|34edo]].
[[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"