User:Moremajorthanmajor/15edX: Difference between revisions

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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]]

Revision as of 01:13, 23 October 2018

15edX is the scale which occurs as the dominant minor edX.

This is the neutral scale of the Middletown temperament family.

Intervals

Degrees Enneatonic Minor mode Middletown temperament Neutral mode Middletown temperament Major mode Middletown temperament
Aeolian-Dorian Dorian Dorian-Mixolydian Mixolydian Mixolydian-Ionian
Subpental Pental Superpental Subpental Pental Superpental
Soft Intense
Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum
1 F#/Gb 96 97.778 100 101.818 102.857 104 105 106.667 107.586 110.345 112
2 G 192 195.556 200 203.636 205.714 208 210 213.333 215.172 220.69 224
3 G#/Jb G#/Ab 288 293.333 300 305.4545 308.571 312 315 320 322.759 331.034 336
4 J A 384 391.111 400 407.273 411.429 416 420 426.667 430.345 441.379 448
5 A B 480 488.889 500 509.091 514.286 520 525 533.333 537.931 551.724 560
6 A#/Bb B#/Hb 576 586.667 600 610.909 617.143 624 630 640 645.517 662.069 672
7 B H 672 684.444 700 712.727 720 728 735 746.667 753.103 772.414 784
8 B#/Hb H#/Cb 768 782.822 800 814.5455 822.857 832 845 853.333 860.69 882.759 896
9 H C 864 880 900 916.364 925.714 936 940 960 968.276 993.103 1008
10 C D 960 977.778 1000 1018.182 1028.571 1040 1050 1066.667 1075.862 1103.448 1120
11 C#/Db D#/Sb 1056 1075.556 1100 1120 1131.429 1144 1155 1173.333 1183.448 1213.379 1232
12 D S 1152 1173.333 1200 1221.818 1234.286 1248 1260 1280 1291.034 1324.138 1344
13 D#/Eb S#/Eb 1248 1271.111 1300 1323.636 1337.143 1352 1365 1386.667 1398.621 1424.483 1456
14 E 1344 1368.889 1400 1425.4545 1440 1456 1470 1493.333 1506.207 1544.827 1568
15 F 1440 1466.667 1500 1527.273 1542.857 1560 1575 1600 1613.793 1655.172 1680

Golden tunings

Degrees Enneatonic Minor mode Middletown temperament Neutral mode Middletown temperament Major mode Middletown temperament
Aeolian-Dorian Dorian Dorian-Mixolydian Mixolydian Mixolydian-Ionian
Subpental Pental Superpental Subpental Pental Superpental
Soft Intense
1 F#/Gb 97.323 98.257 101.4845 102.1115 103.655 104.721 105.173 107.531 109.291 110.504
2 G 194.647 196.513 202.969 204.223 207.31 209.443 210.346 215.032 218.582 221.008
3 G#/Jb G#/Ab 291.97 294.77 304.454 306.334 310.965 314.164 315.519 322.593 327.873 331.613
4 J A 389.294 394.027 405.938 408.446 414.6195 418.885 420.639 430.124 437.1345 442.017
5 A B 486.617 491.283 507.423 510.557 518.274 523.607 525.865 537.655 546.456 552.521
6 A#/Bb B#/Hb 583.94 589.54 608.907 612.669 621.929 628.328 631.0385 645.186 655.747 663.025
7 B H 681.364 687.7965 710.392 714.78 725.584 733.0495 736.212 752.717 765.038 773.5235
8 B#/Hb H#/Cb 778.587 786.053 811.877 816.892 829.239 837.771 841.385 860.248 874.329 884.033
9 H C 875.9105 884.31 913.361 919.003 932.893 942.492 946.558 967.7785 983.62 994.538
10 C D 973.234 982.5665 1014.8455 1021.115 1036.549 1047.214 1051.731 1075.3095 1092.911 1105.042
11 C#/Db D#/Sb 1070.557 1080.823 1116.33 1123.226 1140.204 1151.935 1156.904 1182.84 1202.202 1215.546
12 D S 1167.881 1179.08 1217.8145 1225.3375 1243.859 1256.656 1262.077 1290.371 1311.4935 1326.051
13 D#/Eb S#/Eb 1265.204 1277.336 1319.299 1327.449 1347.513 1361.378 1367.25 1397.902 1420.785 1436.555
14 E 1362.527 1375.593 1420.783 1429.56 1451.168 1466.099 1472.423 1505.433 1530.076 1547.059
15 F 1459.851 1473.85 1522.268 1531.672 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.

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