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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.


This is the neutral scale of the Middletown temperament family.
==Intervals==
==Intervals==
{| class="wikitable"
{| class="wikitable"
! rowspan="5" |Degrees
! colspan="2" rowspan="5" |Enneatonic
! colspan="8" |Minor mode Middletown temperament
! colspan="2" |Neutral mode Middletown temperament
! colspan="10" |Major mode Middletown temperament
|-
! colspan="2" rowspan="3" |Aeolian-Dorian
! colspan="6" |Dorian
! colspan="2" rowspan="3" |Dorian-Mixolydian
! colspan="8" |Mixolydian
! colspan="2" rowspan="3" |Mixolydian-Ionian
|-
! colspan="2" rowspan="2" |Subpental
! colspan="2" rowspan="2" |Pental
! colspan="2" rowspan="2" |Superpental
! colspan="2" rowspan="2" |Subpental
! colspan="2" rowspan="2" |Pental
! colspan="4" |Superpental
|-
! colspan="2" |Soft
! colspan="2" |Intense
|-
! |Minimum
! |Maximum
!Minimum
!Maximum
!Minimum
!Maximum
!Minimum
!Maximum
!Minimum
! |Maximum
!Minimum
!Maximum
! |Minimum
!Maximum
!Minimum
!Maximum
!Minimum
!Maximum
!Minimum
! |Maximum
|-
| |1
| colspan="2" |F#/Gb
| |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
| colspan="2" |G
| |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
|G#/Jb
|''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
|J
|''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
|A
|''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
|A#/Bb
|''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
|B
|''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
|B#/Hb
|''H#/Cb''
|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
|H
|''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
|C
|''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
|C#/Db
|''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
|D
|''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
|D#/Eb
|''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
| 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
|}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
! colspan="3" |Dorian
! 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
|-
|-
! | Degrees
!Soft
! | Enneatonic
!Intense
! | Minimum
! | ed(7/3)
! | Mean/Median
! | Golden
! | Maximum
|-
|-
| | 1
|1
| | E#/Fb
| colspan="2" |F#/Gb
| | 96
|97.323
| | 97.791
|98.257
| | 104
|101.4845
| | 105.888'5
|102.1115
| | 112
|103.655
|104.721
|105.173
|107.531
|109.291
|110.504
|-
|-
| | 2
|2
| | F
| colspan="2" |G
| | 192
|194.647
| | 195.582
|196.513
| | 208
|202.969
| | 211.777
|204.223
| | 224
|207.31
|209.443
|210.346
|215.032
|218.582
|221.008
|-
|-
| | 3
|3
| | F#/Gb
|G#/Jb
| | 288
|''G#/Ab''
| | 293.374
|291.97
| | 312
|294.77
| | 317.666
|304.454
| | 336
|306.334
|310.965
|314.164
|315.519
|322.593
|327.873
|331.613
|-
|-
| | 4
|4
| | G
|J
| | 384
|''A''
| | 391.166
|389.294
| | 416
|394.027
| | 423.554
|405.938
| | 448
|408.446
|414.6195
|418.885
|420.639
|430.124
|437.1345
|442.017
|-
|-
| | 5
|5
| | H
|A
| | 480
|''B''
| | 488.957
|486.617
| | 520
|491.283
| | 529.443
|507.423
| | 560
|510.557
|518.274
|523.607
|525.865
|537.655
|546.456
|552.521
|-
|-
| | 6
|6
| | H#/Jb
|A#/Bb
| | 576
|''B#/Hb''
| | 586.748
|583.94
| | 624
|589.54
| | 635.331
|608.907
| | 672
|612.669
|621.929
|628.328
|631.0385
|645.186
|655.747
|663.025
|-
|-
| | 7
|7
| | J
|B
| | 672
|''H''
| | 684.54
|681.364
| | 728
|687.7965
| | 741.22
|710.392
| | 784
|714.78
|725.584
|733.0495
|736.212
|752.717
|765.038
|773.5235
|-
|-
| | 8
|8
| | J#/Ab
|B#/Hb
| | 768
|''H#/Cb''
| | 782.331
|778.587
| | 832
|786.053
| | 847.108
|811.877
| | 896
|816.892
|829.239
|837.771
|841.385
|860.248
|874.329
|884.033
|-
|-
| | 9
|9
| | A
|H
| | 864
|''C''
| | 880.122'5
|875.9105
| | 936
|884.31
| | 952.997
|913.361
| | 1008
|919.003
|932.893
|942.492
|946.558
|967.7785
|983.62
|994.538
|-
|-
| | 10
|10
| | B
|C
| | 960
|''D''
| | 977.913
|973.234
| | 1040
|982.5665
| | 1058.885
|1014.8455
| | 1120
|1021.115
|1036.549
|1047.214
|1051.731
|1075.3095
|1092.911
|1105.042
|-
|-
| | 11
|11
| | B#/Cb
|C#/Db
| | 1056
|''D#/Sb''
| | 1075.705
|1070.557
| | 1144
|1080.823
| | 1164.774
|1116.33
| | 1232
|1123.226
|1140.204
|1151.935
|1156.904
|1182.84
|1202.202
|1215.546
|-
|-
| | 12
|12
| | C
|D
| | 1152
|''S''
| | 1173.497
|1167.881
| | 1248
|1179.08
| | 1270.6625
|1217.8145
| | 1344
|1225.3375
|1243.859
|1256.656
|1262.077
|1290.371
|1311.4935
|1326.051
|-
|-
| | 13
|13
| | C#/Db
|D#/Eb
| | 1248
|''S#/Eb''
| | 1271.288
|1265.204
| | 1352
|1277.336
| | 1376.551
|1319.299
| | 1456
|1327.449
|1347.513
|1361.378
|1367.25
|1397.902
|1420.785
|1436.555
|-
|-
| | 14
|14
| | D
| colspan="2" |E
| | 1344
|1362.527
| | 1369.0795
|1375.593
| | 1456
|1420.783
| | 1482.44
|1429.56
| | 1568
|1451.168
|1466.099
|1472.423
|1505.433
|1530.076
|1547.059
|-
|-
| | 15
|15
| | E
| colspan="2" |F
| | 1440
|1459.851
| | 1466.871
|1473.85
| | 1560
|1522.268
| | 1588.328
|1531.672
| | 1680
|1554.823
|}
|1570.82
|1577.596
|1612.964
|1639.366
|1657.563
|}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.


By a surprising coincidence, the Golden tuning of this [[edX|edX]] is almost exactly every third degree of [[34edo|34edo]].
[[Category:15-tone]]
[[Category:15-tone]]
[[Category:ed7/3]]
[[Category:ed7/3]]
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/15edX"