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This is the scale which occurs as the dominant major edX.
'''16edX''' is the scale which occurs as the dominant reformed Mixolydian mode. It also gives the period of the 16th-decade Roccocavallo branch of the Carrera temperament family.
==Intervals==
== Intervals==
{| class="wikitable"
{| class="wikitable"
! rowspan="5" |Degrees
|+
! colspan="3" 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
|90.000
|Intense Aeolian-Subpental Dorian mode begins
|-
|17\14
| 91.071
|
|-
|-
! colspan="2" rowspan="3" |Aeolian-Dorian
|11\9
! colspan="6" |Dorian
|91.667
! colspan="2" rowspan="3" |Dorian-Mixolydian
| Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
! colspan="8" |Mixolydian
! colspan="2" rowspan="3" |Mixolydian-Ionian
|-
|-
! colspan="2" rowspan="2" |Subpental
|16\13
! colspan="2" rowspan="2" |Pental
| 92.308
! colspan="2" rowspan="2" |Superpental
|
! colspan="2" rowspan="2" |Subpental
! colspan="2" rowspan="2" |Pental
! colspan="4" |Superpental
|-
|-
! colspan="2" |Soft
|5\4
! colspan="2" |Intense
|93.750
|Subpental Dorian mode ends, Pental Dorian mode begins
|-
|-
! |Minimum
|24\19
! |Maximum
|94.737
!Minimum
|
!Maximum
!Minimum
!Maximum
!Minimum
!Maximum
!Minimum
! |Maximum
!Minimum
!Maximum
! |Minimum
!Maximum
!Minimum
!Maximum
!Minimum
!Maximum
!Minimum
! |Maximum
|-
|-
| |1
|19\15
|95.000
|
|-
|14\11
|95.455
|Pental Dorian mode ends, Superpental Dorian mode begins
|-
|23\18
|95.833
|
|-
|9\7
|96.429
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
|-
|31\24
|96.875
|
|-
|22\17
|97.059
|Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
|-
|35\27
|97.222
|
|-
| 13\10
|97.500
|Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
|-
|17\13
|98.077
|
|-
|21\16
|98.438
|Subpental Mixolydian mode ends, Pental Mixolydian mode begins
|-
|25\19
|98.684
|
|-
|29\22
|98.864
|
|-
|33\25
|99.000
|
|-
|4\3
|100.000
|Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
|-
|19\14
|101.786
|
|-
|15\11
|102.273
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
|-
|26\19
|102.632
|
|-
|11\8
|103.125
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
|-
|18\13
|103.846
|
|-
|25\18
|104.167
|
|-
|7\5
|105.000
|Mixolydian-Ionian mode ends
|}Relative cents
{| class="wikitable" style="text-align: center"
!Degrees
! colspan="3" |Enneatonic
!Intense Aeolian-Subpental Dorian
!Dorian
!Dorian-Mixolydian
|-
|1
|1#/2b
|1#/2b
| colspan="2" |F#/Gb
|G#/Jb
| |90
|''G#/Ab''
| colspan="2" |91.667
|''90.625''
| colspan="2" |93.75
|''93.75''
| colspan="2" |95.4545
|''96.875''
| colspan="2" |96.429
| colspan="2" |97.5
| colspan="2" |98.4375
| colspan="2" |100
| colspan="2" |100.862
| colspan="2" |103.448
| |105
|-
|-
| |2
|2
|2
| colspan="2" |G
| 2
| |180
|J
| colspan="2" |183.333
|''A''
| colspan="2" |187.5
|''181.25''
| colspan="2" |190.909
|''187.5''
| colspan="2" |192.857
|''193.75''
| colspan="2" |195
| colspan="2" |196.875
| colspan="2" |200
| colspan="2" |201.724
| colspan="2" |206.897
| |210
|-
|-
| |3
|3
|2#/3b
|2#/3b
|G#/Jb
|J#/Ab
|''G#/Ab''
|''A#/Bb''
| |270
|''271.875''
| colspan="2" |275
|''281.25''
| colspan="2" |281.25
|''290.625''
| colspan="2" |286.364
| colspan="2" |289.286
| colspan="2" |292.5
| colspan="2" |295.3125
| colspan="2" |300
| colspan="2" |302.586
| colspan="2" |310.345
| |315
|-
|-
| |4
|4
|3
|3
|J
|J
|''A''
|''B''
| |360
|''362.5''
| colspan="2" |366.667
|''375''
| colspan="2" |375
|''387.5''
| colspan="2" |381.818
| colspan="2" |385.714
| colspan="2" |390
| colspan="2" |393.75
| colspan="2" |400
| colspan="2" |403.448
| colspan="2" |413.793
| |420
|-
|-
| |5
|5
|3#/4b
|3#/4b
|J#/Ab
|J#/Ab
|''A#/Bb''
|B#/Cb
| |450
|''453.125''
| colspan="2" |458.333
|''468.75''
| colspan="2" |468.75
|''484.375''
| colspan="2" |477.273
| colspan="2" |482.143
| colspan="2" |487.5
| colspan="2" |492.1875
| colspan="2" |500
| colspan="2" |504.31
| colspan="2" |517.241
| |525
|-
|-
| |6
|6
|4
|4
|A
|A
|''B''
|''C''
| |540
|''543.75''
| colspan="2" |550
|''562.5''
| colspan="2" |562.5
|''581.25''
| colspan="2" |572.727
| colspan="2" |578.571
| colspan="2" |585
| colspan="2" |590.625
| colspan="2" |600
| colspan="2" |605.172
| colspan="2" |620.69
| |630
|-
|-
| |7
|7
|5
|5
|B
|A#/Bb
|''H''
|''C#/Qb''
| |630
|''633.375''
| colspan="2" |641.667
|''656.25''
| colspan="2" |656.25
|''678.125''
| colspan="2" |668.182
| colspan="2" |675
| colspan="2" |682.5
| colspan="2" |689.0625
| colspan="2" |700
| colspan="2" |706.0345
| colspan="2" |724.138
| |735
|-
|-
|8
|8
|5#/6b
|5#/6b
|B#/Hb
|B
|''H#/Cb''
|''Q''
|720
|''725''
| colspan="2" |733.333
|''750''
| colspan="2" |750
|''775''
| colspan="2" |763.636
| colspan="2" |771.429
| colspan="2" |780
| colspan="2" |787.5
| colspan="2" |800
| colspan="2" |806.897
| colspan="2" |827.586
|840
|-
|-
|9
|9
|6
|6
|H
|C
|''C''
|''D''
|810
|''815.625''
| colspan="2" |825
|''843.75''
| colspan="2" |843.75
|''871.875''
| colspan="2" |859.091
| colspan="2" |867.857
| colspan="2" |877.5
| colspan="2" |885.9375
| colspan="2" |900
| colspan="2" |907.759
| colspan="2" |931.0345
|945
|-
|-
|10
|10
|6#/7b
|6#/7b
|H#/Cb
| C#/Db
|''C#/Db''
|D#/Sb
|900
|''906.25''
| colspan="2" |916.667
|''937.5''
| colspan="2" |937.5
|''968.75''
| colspan="2" |954.5455
| colspan="2" |964.286
| colspan="2" |975
| colspan="2" |984.375
| colspan="2" |1000
| colspan="2" |1008.621
| colspan="2" |1034.483
|1050
|-
|-
|11
|11
|7
|7
|C
|D
|''D''
|''S''
|990
|''996.875''
| colspan="2" |1018.333
|''1031.25''
| colspan="2" |1031.25
|''1065.625''
| colspan="2" |1050
| colspan="2" |1060.714
| colspan="2" |1072.5
| colspan="2" |1082.8125
| colspan="2" |1100
| colspan="2" |1109.483
| colspan="2" |1137.931
|1155
|-
|-
|12
|12
|7#/8b
| 7#/8b
|C#/Db
|D#/Eb
|''D#/Sb''
|''S#/Eb''
|1080
|''1087.5''
| colspan="2" |1100
|''1125''
| colspan="2" |1125
|''1162.5''
| colspan="2" |1145.4545
| colspan="2" |1157.143
| colspan="2" |1170
| colspan="2" |1181.25
| colspan="2" |1200
| colspan="2" |1210.345
| colspan="2" |1241.379
|1260
|-
|-
|13
|13
|8
|8
|D
| colspan="2" | E
|''S''
|''1178.125''
|1170
|''1218.75''
| colspan="2" |1191.667
|''1259.375''
| colspan="2" |1218.75
| colspan="2" |1240.909
| 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
|14
|8#/9b
|8#/9b
|D#/Eb
| colspan="2" |E#/Fb
|''S#/Eb''
|''1268.75''
|1260
|''1312.5''
| colspan="2" |1283.333
|''1356.25''
| 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
|15
|9
|9
| colspan="2" |E
| colspan="2" |F
|1350
|''1359.375''
| colspan="2" |1375
|''1406.25''
| colspan="2" |1406.25
|''1453.125''
| 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
|16
|1
|1
| colspan="2" |F
| colspan="2" |G
|1440
|''1450''
| colspan="2" |1466.667
|''1500''
| colspan="2" |1500
|''1550''
| colspan="2" |1527.273
|}
| colspan="2" |1542.857
{| class="wikitable" style="text-align: center"
| colspan="2" |1560
!Degrees
| colspan="2" |1575
! colspan="3" |Enneatonic
| colspan="2" |1600
!Subpental-Soft Superpental Mixolydian
| colspan="2" |1613.793
!Intense Superpental Mixolydian ~ Mixolydian-Ionian
| 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
| |1
! 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
|1#/2b
| colspan="2" |F#/Gb
| colspan="2" |F#/Gb
|91.241
|''100''
|92.116
|''103.125''
|95.142
|95.7295
|97.176
|98.176
|98.6
|100.81
|102.46
|103.598
|-
|-
|2
| |2
|2
|2
| colspan="2" |G
| colspan="2" |G
|182.481
|''200''
|184.231
|''206.25''
|190.2835
|191.459
|194.353
|196.3525
|197.1995
|201.6205
|204.921
|207.195
|-
|-
|3
| |3
|2#/3b
|2#/3b
|G#/Jb
|G#/Jb
|''G#/Ab''
|''G#/Ab''
|273.722
|''300''
|276.347
|''309.375''
|285.425
|287.1885
|291.529
|294.529
|295.799
|302.431
|307.381
|310.793
|-
|-
|4
| |4
|3
|3
|J
|J
|''A''
|''A''
|364.962
|''400''
|368.462
|''412.5''
|380.567
|382.918
|388.706
|392.705
|394.399
|403.241
|409.842
|414.391
|-
|-
|5
| | 5
|3#/4b
|3#/4b
|J#/Ab
|J#/Ab
|''A#/Bb''
|''A#/Bb''
|456.203
|''500''
|460.578
|''515.625''
|475.709
|478.6475
|485.882
|490.881
|492.999
|504.051
|512.302
|517.9885
|-
|-
|6
| |6
|4
|4
|A
|A
|''B''
|''B''
|547.444
|''600''
|552.694
|''618.75''
|570.851
|574.377
|680.235
|589.058
|591.599
|604.862
|614.763
|621.586
|-
|-
|7
| | 7
|5
|5
|B
|B
|''H''
|''H''
|638.685
|''700''
|644.809
|''721.875''
|665.992
|670.106
|725.584
|687.234
|690.198
|705.672
|717.223
|725.184
|-
|-
|8
|8
Line 428: Line 303:
|B#/Hb
|B#/Hb
|''H#/Cb''
|''H#/Cb''
|729.925
|''800''
|736.925
|''825''
|761.134
|765.836
|777.412
|785.41
|788.798
|806.482
|819.6835
|828.781
|-
|-
|9
|9
Line 443: Line 310:
|H
|H
|''C''
|''C''
|821.166
|''900''
|829.04
|''928.125''
|856.276
|861.565
|874.588
|883.5865
|887.398
|907.292
|922.144
|932.379
|-
|-
|10
|10
Line 458: Line 317:
|H#/Cb
|H#/Cb
|''C#/Db''
|''C#/Db''
|912.407
|''1000''
|921.156
|''1031.25''
|951.418
|957.295
|971.7645
|981.763
|985.998
|1008.103
|1024.604
|1035.977
|-
|-
|11
|11
Line 473: Line 324:
|C
|C
|''D''
|''D''
|1003.6475
|''1100''
|1013.272
|''1134.375''
|1046.559
|1053.024
|1068.941
|1079.939
|1084.597
|1108.913
|1127.065
|1139.575
|-
|-
|12
|12
Line 488: Line 331:
|C#/Db
|C#/Db
|''D#/Sb''
|''D#/Sb''
|1094.888
|''1200''
|1105.387
|''1237.5''
|1141.701
|1148.753
|1166.117
|1178.115
|1183.197
|1209.723
|1229.525
|1243.172
|-
|-
|13
|13
Line 503: Line 338:
|D
|D
|''S''
|''S''
|1186.129
|''1300''
|1197.502
|''1340.625''
|1236.843
|1244.483
|1263.293
|1276.292
|1281.797
|1310.533
|1331.986
|1346.77
|-
|-
|14
|14
|8#/9b
|8#/9b
|D#/Eb
| D#/Eb
|''S#/Eb''
|''S#/Eb''
|1277.3965
|''1400''
|1289.6185
|''1443.75''
|1331.985
|1340.213
|1360.47
|1374.468
|1380.397
|1411.344
|1434.446
|1450.368
|-
|-
|15
| 15
|9
|9
| colspan="2" |E
| colspan="2" |E
|1368.61
|''1500''
|1381.734
|''1546.875''
|1427.126
|1435.942
|1457.645
|1472.644
|1478.996
|1512.154
|1536.9065
|1553.9655
|-
|-
|16
|16
|1
|1
| colspan="2" |F
| colspan="2" |F
|1459.851
|''1600''
|1473.85
|''1650''
|1522.268
|}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 3.686 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.
|1531.672
==See also==
|1554.823
*[[16ed5/2]] - equal division of the classic major tenth
|1570.82
*[[16ed7/3]] - equal division of the septimal minor tenth
|1577.596
 
|1612.964
[[Category:16-tone scales]]
|1639.366
[[Category:EdX]]
|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.
[[Category:16-tone]]
[[Category:ed7/3]]
[[Category:edX]]
[[Category:todo:add_definition]]
[[Category:todo:unify_precision]]
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/16edX"