User:Moremajorthanmajor/16edX: Difference between revisions

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This is the scale which occurs as the dominant major edX.
This is the scale which occurs as the dominant major edX.
==Intervals==
==Intervals==
{| class="wikitable"
{| class="wikitable"
! rowspan="5" |Degrees
! colspan="3" rowspan="5" |Enneatonic
! colspan="8" |Minor mode Middletown temperament
! colspan="2" |Neutral mode Middletown temperament
! colspan="10" |Major mode Middletown temperament
|-
|-
! | Degrees
! colspan="2" rowspan="3" |Aeolian-Dorian
! | Enneatonic
! colspan="6" |Dorian
! | Minimum
! colspan="2" rowspan="3" |Dorian-Mixolydian
! | ed(7/3)
! colspan="8" |Mixolydian
! | Mean/Median
! colspan="2" rowspan="3" |Mixolydian-Ionian
! | Golden
! | Maximum
|-
|-
| | 1
! colspan="2" rowspan="2" |Subpental
| | 1#/2b
! colspan="2" rowspan="2" |Pental
 
! colspan="2" rowspan="2" |Superpental
D#/Eb
! colspan="2" rowspan="2" |Subpental
| | 90
! colspan="2" rowspan="2" |Pental
| | 91.679
! colspan="4" |Superpental
| | 97.5
| | 99.2705
| | 105
|-
|-
| | 2
! colspan="2" |Soft
| | 2
! colspan="2" |Intense
 
E
| | 180
| | 183.358
| | 195
| | 198.541
| | 210
|-
|-
| | 3
! |Minimum
| | 2#/3b
! |Maximum
 
!Minimum
E#/Fb
!Maximum
| | 270
!Minimum
| | 275.038
!Maximum
| | 292.5
!Minimum
| | 297.811'5
!Maximum
| | 315
!Minimum
! |Maximum
!Minimum
!Maximum
! |Minimum
!Maximum
!Minimum
!Maximum
!Minimum
!Maximum
!Minimum
! |Maximum
|-
|-
| | 4
| |1
| | 3
|1#/2b
 
| colspan="2" |F#/Gb
F
| |90
| | 360
| colspan="2" |91.667
| | 366.718
| colspan="2" |93.75
| | 390
| colspan="2" |95.4545
| | 397.082
| colspan="2" |96.429
| | 420
| colspan="2" |97.5
| colspan="2" |98.4375
| colspan="2" |100
| colspan="2" |100.862
| colspan="2" |103.448
| |105
|-
|-
| | 5
| |2
| | 3#/4b
|2
 
| colspan="2" |G
F#/Gb
| |180
| | 450
| colspan="2" |183.333
| | 458.397
| colspan="2" |187.5
| | 487.5
| colspan="2" |190.909
| | 496.352'5
| colspan="2" |192.857
| | 525
| colspan="2" |195
| colspan="2" |196.875
| colspan="2" |200
| colspan="2" |201.724
| colspan="2" |206.897
| |210
|-
|-
| | 6
| |3
| | 4
|2#/3b
 
|G#/Jb
G
|''G#/Ab''
| | 540
| |270
| | 550.077
| colspan="2" |275
| | 585
| colspan="2" |281.25
| | 595.623
| colspan="2" |286.364
| | 630
| colspan="2" |289.286
| colspan="2" |292.5
| colspan="2" |295.3125
| colspan="2" |300
| colspan="2" |302.586
| colspan="2" |310.345
| |315
|-
|-
| | 7
| |4
| | 5
|3
 
|J
H
|''A''
| | 630
| |360
| | 641.756
| colspan="2" |366.667
| | 682.5
| colspan="2" |375
| | 694.893
| colspan="2" |381.818
| | 735
| colspan="2" |385.714
| colspan="2" |390
| colspan="2" |393.75
| colspan="2" |400
| colspan="2" |403.448
| colspan="2" |413.793
| |420
|-
|-
| | 8
| |5
| | 5#/6b
|3#/4b
 
|J#/Ab
H#/Jb
|''A#/Bb''
| | 720
| |450
| | 733.435'5
| colspan="2" |458.333
| | 780
| colspan="2" |468.75
| | 794.154
| colspan="2" |477.273
| | 840
| colspan="2" |482.143
| colspan="2" |487.5
| colspan="2" |492.1875
| colspan="2" |500
| colspan="2" |504.31
| colspan="2" |517.241
| |525
|-
|-
| | 9
| |6
| | 6
|4
 
|A
J
|''B''
| | 810
| |540
| | 825.115
| colspan="2" |550
| | 877.5
| colspan="2" |562.5
| | 893.435
| colspan="2" |572.727
| | 945
| colspan="2" |578.571
| colspan="2" |585
| colspan="2" |590.625
| colspan="2" |600
| colspan="2" |605.172
| colspan="2" |620.69
| |630
|-
|-
| | 10
| |7
| | 6#/7b
|5
 
|B
J#/Ab
|''H''
| | 900
| |630
| | 916.794
| colspan="2" |641.667
| | 975
| colspan="2" |656.25
| | 992.705
| colspan="2" |668.182
| | 1050
| colspan="2" |675
| colspan="2" |682.5
| colspan="2" |689.0625
| colspan="2" |700
| colspan="2" |706.0345
| colspan="2" |724.138
| |735
|-
|-
| | 11
|8
| | 7
|5#/6b
 
|B#/Hb
A
|''H#/Cb''
| | 990
|720
| | 1008.473
| colspan="2" |733.333
| | 1072.5
| colspan="2" |750
| | 1091.976
| colspan="2" |763.636
| | 1155
| colspan="2" |771.429
| colspan="2" |780
| colspan="2" |787.5
| colspan="2" |800
| colspan="2" |806.897
| colspan="2" |827.586
|840
|-
|-
| | 12
|9
| | 7#/8b
|6
 
|H
A#/Bb
|''C''
| | 1080
|810
| | 1100.153
| colspan="2" |825
| | 1170
| colspan="2" |843.75
| | 1191.246
| colspan="2" |859.091
| | 1260
| colspan="2" |867.857
| colspan="2" |877.5
| colspan="2" |885.9375
| colspan="2" |900
| colspan="2" |907.759
| colspan="2" |931.0345
|945
|-
|-
| | 13
|10
| | 8
|6#/7b
 
|H#/Cb
B
|''C#/Db''
| | 1170
|900
| | 1191.833
| colspan="2" |916.667
| | 1267.5
| colspan="2" |937.5
| | 1290.517
| colspan="2" |954.5455
| | 1365
| colspan="2" |964.286
| colspan="2" |975
| colspan="2" |984.375
| colspan="2" |1000
| colspan="2" |1008.621
| colspan="2" |1034.483
|1050
|-
|-
| | 14
|11
| | 8#/9b
|7
 
|C
B#/Cb
|''D''
| | 1260
|990
| | 1283.512
| colspan="2" |1018.333
| | 1365
| colspan="2" |1031.25
| | 1389.787
| colspan="2" |1050
| | 1470
| colspan="2" |1060.714
| colspan="2" |1072.5
| colspan="2" |1082.8125
| colspan="2" |1100
| colspan="2" |1109.483
| colspan="2" |1137.931
|1155
|-
|-
| | 15
|12
| | 9
|7#/8b
 
|C#/Db
C
|''D#/Sb''
| | 1350
|1080
| | 1375.1915
| colspan="2" |1100
| | 1462.5
| colspan="2" |1125
| | 1489.058
| colspan="2" |1145.4545
| | 1575
| colspan="2" |1157.143
| colspan="2" |1170
| colspan="2" |1181.25
| colspan="2" |1200
| colspan="2" |1210.345
| colspan="2" |1241.379
|1260
|-
|-
| | 16
|13
| | 1
|8
 
|D
D
|''S''
| | 1440
|1170
| | 1466.871
| colspan="2" |1191.667
| | 1560
| colspan="2" |1218.75
| | 1588.328
| colspan="2" |1240.909
| | 1680
| colspan="2" |1253.571
|}
| colspan="2" |1267.5
| colspan="2" |1279.6875
| colspan="2" |1300
| colspan="2" |1311.207
| colspan="2" |1344.828
|1365
|-
|14
|8#/9b
|D#/Eb
|''S#/Eb''
|1260
| colspan="2" |1283.333
| colspan="2" |1312.5
| colspan="2" |1336.364
| colspan="2" |1350
| colspan="2" |1365
| colspan="2" |1378.125
| colspan="2" |1400
| colspan="2" |1412.069
| colspan="2" |1448.276
|1470
|-
|15
|9
| colspan="2" |E
|1350
| colspan="2" |1375
| colspan="2" |1406.25
| colspan="2" |1431.818
| colspan="2" |1446.429
| colspan="2" |1462.5
| colspan="2" |1476.5625
| colspan="2" |1500
| colspan="2" |1512.931
| colspan="2" |1551.724
|1575
|-
|16
|1
| 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="3" 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
|-
!Soft
!Intense
|-
|1
|1#/2b
| colspan="2" |F#/Gb
|91.241
|92.116
|95.142
|95.7295
|97.176
|98.176
|98.6
|100.81
|102.46
|103.598
|-
|2
|2
| colspan="2" |G
|182.481
|184.231
|190.2835
|191.459
|194.353
|196.3525
|197.1995
|201.6205
|204.921
|207.195
|-
|3
|2#/3b
|G#/Jb
|''G#/Ab''
|273.722
|276.347
|285.425
|287.1885
|291.529
|294.529
|295.799
|302.431
|307.381
|310.793
|-
|4
|3
|J
|''A''
|364.962
|368.462
|380.567
|382.918
|388.706
|392.705
|394.399
|403.241
|409.842
|414.391
|-
|5
|3#/4b
|J#/Ab
|''A#/Bb''
|456.203
|460.578
|475.709
|478.6475
|485.882
|490.881
|492.999
|504.051
|512.302
|517.9885
|-
|6
|4
|A
|''B''
|547.444
|552.694
|570.851
|574.377
|680.235
|589.058
|591.599
|604.862
|614.763
|621.586
|-
|7
|5
|B
|''H''
|638.685
|644.809
|665.992
|670.106
|725.584
|687.234
|690.198
|705.672
|717.223
|725.184
|-
|8
|5#/6b
|B#/Hb
|''H#/Cb''
|729.925
|736.925
|761.134
|765.836
|777.412
|785.41
|788.798
|806.482
|819.6835
|828.781
|-
|9
|6
|H
|''C''
|821.166
|829.04
|856.276
|861.565
|874.588
|883.5865
|887.398
|907.292
|922.144
|932.379
|-
|10
|6#/7b
|H#/Cb
|''C#/Db''
|912.407
|921.156
|951.418
|957.295
|971.7645
|981.763
|985.998
|1008.103
|1024.604
|1035.977
|-
|11
|7
|C
|''D''
|1003.6475
|1013.272
|1046.559
|1053.024
|1068.941
|1079.939
|1084.597
|1108.913
|1127.065
|1139.575
|-
|12
|7#/8b
|C#/Db
|''D#/Sb''
|1094.888
|1105.387
|1141.701
|1148.753
|1166.117
|1178.115
|1183.197
|1209.723
|1229.525
|1243.172
|-
|13
|8
|D
|''S''
|1186.129
|1197.502
|1236.843
|1244.483
|1263.293
|1276.292
|1281.797
|1310.533
|1331.986
|1346.77
|-
|14
|8#/9b
|D#/Eb
|''S#/Eb''
|1277.3965
|1289.6185
|1331.985
|1340.213
|1360.47
|1374.468
|1380.397
|1411.344
|1434.446
|1450.368
|-
|15
|9
| colspan="2" |E
|1368.61
|1381.734
|1427.126
|1435.942
|1457.645
|1472.644
|1478.996
|1512.154
|1536.9065
|1553.9655
|-
|16
|1
| colspan="2" |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, neutral 16edX turns out to be a false Pelogic temperament with a very pure 5:4 (mistuned by no more than 3.596 cents), and tuning 5:3 pure creates a tenth almost exactly equal to 38/29edo or almost exactly the Golden Subpental Mixolydian step or every ninth step of [[110edo]], and tuning 4:3 pure creates an almost exact 43/74edo fifth. Also, the Golden Soft Superpental Mixolydian step is almost exactly (25/24)^(10/7) and tuning 12:7 pure creates almost exactly the Golden Mixolydian-Ionian step.


By a surprising coincidence, neutral 16edX turns out to be a false Pelogic temperament with a very pure 5:4 (mistuned by no more than 3.596 cents), and tuning 5:3 pure creates a tenth almost exactly equal to 38/29edo, and tuning 4:3 pure creates an almost exact 43/74edo fifth.
By a surprising coincidence, neutral 16edX turns out to be a false Pelogic temperament with a very pure 5:4 (mistuned by no more than 3.596 cents), and tuning 5:3 pure creates a tenth almost exactly equal to 38/29edo, and tuning 4:3 pure creates an almost exact 43/74edo fifth.

Revision as of 23:49, 23 October 2018

This is the scale which occurs as the dominant major edX.

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 1#/2b F#/Gb 90 91.667 93.75 95.4545 96.429 97.5 98.4375 100 100.862 103.448 105
2 2 G 180 183.333 187.5 190.909 192.857 195 196.875 200 201.724 206.897 210
3 2#/3b G#/Jb G#/Ab 270 275 281.25 286.364 289.286 292.5 295.3125 300 302.586 310.345 315
4 3 J A 360 366.667 375 381.818 385.714 390 393.75 400 403.448 413.793 420
5 3#/4b J#/Ab A#/Bb 450 458.333 468.75 477.273 482.143 487.5 492.1875 500 504.31 517.241 525
6 4 A B 540 550 562.5 572.727 578.571 585 590.625 600 605.172 620.69 630
7 5 B H 630 641.667 656.25 668.182 675 682.5 689.0625 700 706.0345 724.138 735
8 5#/6b B#/Hb H#/Cb 720 733.333 750 763.636 771.429 780 787.5 800 806.897 827.586 840
9 6 H C 810 825 843.75 859.091 867.857 877.5 885.9375 900 907.759 931.0345 945
10 6#/7b H#/Cb C#/Db 900 916.667 937.5 954.5455 964.286 975 984.375 1000 1008.621 1034.483 1050
11 7 C D 990 1018.333 1031.25 1050 1060.714 1072.5 1082.8125 1100 1109.483 1137.931 1155
12 7#/8b C#/Db D#/Sb 1080 1100 1125 1145.4545 1157.143 1170 1181.25 1200 1210.345 1241.379 1260
13 8 D S 1170 1191.667 1218.75 1240.909 1253.571 1267.5 1279.6875 1300 1311.207 1344.828 1365
14 8#/9b D#/Eb S#/Eb 1260 1283.333 1312.5 1336.364 1350 1365 1378.125 1400 1412.069 1448.276 1470
15 9 E 1350 1375 1406.25 1431.818 1446.429 1462.5 1476.5625 1500 1512.931 1551.724 1575
16 1 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 1#/2b F#/Gb 91.241 92.116 95.142 95.7295 97.176 98.176 98.6 100.81 102.46 103.598
2 2 G 182.481 184.231 190.2835 191.459 194.353 196.3525 197.1995 201.6205 204.921 207.195
3 2#/3b G#/Jb G#/Ab 273.722 276.347 285.425 287.1885 291.529 294.529 295.799 302.431 307.381 310.793
4 3 J A 364.962 368.462 380.567 382.918 388.706 392.705 394.399 403.241 409.842 414.391
5 3#/4b J#/Ab A#/Bb 456.203 460.578 475.709 478.6475 485.882 490.881 492.999 504.051 512.302 517.9885
6 4 A B 547.444 552.694 570.851 574.377 680.235 589.058 591.599 604.862 614.763 621.586
7 5 B H 638.685 644.809 665.992 670.106 725.584 687.234 690.198 705.672 717.223 725.184
8 5#/6b B#/Hb H#/Cb 729.925 736.925 761.134 765.836 777.412 785.41 788.798 806.482 819.6835 828.781
9 6 H C 821.166 829.04 856.276 861.565 874.588 883.5865 887.398 907.292 922.144 932.379
10 6#/7b H#/Cb C#/Db 912.407 921.156 951.418 957.295 971.7645 981.763 985.998 1008.103 1024.604 1035.977
11 7 C D 1003.6475 1013.272 1046.559 1053.024 1068.941 1079.939 1084.597 1108.913 1127.065 1139.575
12 7#/8b C#/Db D#/Sb 1094.888 1105.387 1141.701 1148.753 1166.117 1178.115 1183.197 1209.723 1229.525 1243.172
13 8 D S 1186.129 1197.502 1236.843 1244.483 1263.293 1276.292 1281.797 1310.533 1331.986 1346.77
14 8#/9b D#/Eb S#/Eb 1277.3965 1289.6185 1331.985 1340.213 1360.47 1374.468 1380.397 1411.344 1434.446 1450.368
15 9 E 1368.61 1381.734 1427.126 1435.942 1457.645 1472.644 1478.996 1512.154 1536.9065 1553.9655
16 1 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, neutral 16edX turns out to be a false Pelogic temperament with a very pure 5:4 (mistuned by no more than 3.596 cents), and tuning 5:3 pure creates a tenth almost exactly equal to 38/29edo or almost exactly the Golden Subpental Mixolydian step or every ninth step of 110edo, and tuning 4:3 pure creates an almost exact 43/74edo fifth. Also, the Golden Soft Superpental Mixolydian step is almost exactly (25/24)^(10/7) and tuning 12:7 pure creates almost exactly the Golden Mixolydian-Ionian step.

By a surprising coincidence, neutral 16edX turns out to be a false Pelogic temperament with a very pure 5:4 (mistuned by no more than 3.596 cents), and tuning 5:3 pure creates a tenth almost exactly equal to 38/29edo, and tuning 4:3 pure creates an almost exact 43/74edo fifth.

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