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This is the neutral scale of the Vesuvius temperament family.
This is the neutral scale of the Vesuvius temperament family. It also gives every other period of the 16th-decade Roccocavallo branch of the Carrera temperament family.
 
==Intervals==
== Intervals ==
{| class="wikitable"
{| class="wikitable" style="text-align: center"
|+
! rowspan="3" |Degrees
! colspan="5" | Decade
! colspan="3" rowspan="2" |Intense Aeolian-Subpental Dorian
!Period
! colspan="9" |Dorian
!Notes
|-
|6\5
|
|
|
|
|180
|Intense Aeolian-Subpental Dorian mode begins
|-
|-
! colspan="3" |Subpental
|
! colspan="3" |Pental
|17\14
! colspan="3" |Superpental
|
|
|
|182.143
|
|-
|-
!Min-comma
|11\9
!Med
|
! colspan="2" |Max+comma~Min-comma
|
!Med
|
! colspan="2" |Max+comma~Min-comma
|
!Med
|183.{{Overline|3}}
! colspan="2" |Max+comma~Min-comma
|Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
!Med
!Max+comma
|-
|-
|1
|
|175-180
|16\13
|182.143
|
| colspan="2" |178.333-188.333
|
|
|184.615
|184.615
| colspan="2" |182.5-192.5
|
|190
|-
| colspan="2" |185.909-195.909
|
|191.667
|
|192.857-197.857
|21\17
|
|
|185.294
|
|-
|
|
|
|26\21
|
|185.714
|
|-
|
|
|
|
|31\25
|186
|
|-
|5\4
|
|
|
|
|187,5
| Subpental Dorian mode ends, Pental Dorian mode begins
|-
|-
|2
|
|350-360
|
|364.286
|
| colspan="2" |356.667-376.667
|
|369.231
|34\27
| colspan="2" |365-385
|188.{{Overline|8}}
|380
|
| colspan="2" |371.818-391.818
|383.333
|385.714-395.714
|-
|-
|3
|
|525-540
|
|546-429
|
| colspan="2" |535-565
|29\23
|553.846
|
| colspan="2" |547.5-577.5
|189.13
|570
|
| colspan="2" |557.727-587.727
|575
|578.571-593.571
|-
|-
|4
|
|700-720
|
|728.571
|24\19
| colspan="2" |713.333-753.333
|
|738.4615
|
| colspan="2" |730-770
|189.474
|760
|
| colspan="2" |743.636-783.636
|766.667
|771.429-791.429
|-
|-
|5
|
|875-900
|19\15
|910.714
|
| colspan="2" |891.667-941.667
|
|923.071
|
| colspan="2" |912.5-962.5
|190
|950
|
| colspan="2" |929.5455-979.5455
|958.333
|964.286-989.286
|-
|-
|6
|14\11
|1050-1080
|
|1092.857
|
| colspan="2" |1070-1130
|
|1107.692
|
| colspan="2" |1095-1155
|190.{{Overline|90}}
|1140
|Pental Dorian mode ends, Superpental Dorian mode begins
| colspan="2" |1115.4545-1175.4545
|1150
|1157.143-1187.143
|-
|-
|7
|
|1225-1260
|23\18
|1275
|
| colspan="2" |1248.333-1318.333
|
|1292.308
|
| colspan="2" |1277.5-1347.5
|191.{{Overline|6}}
|1330
|
| colspan="2" |1301.364-1371.364
|1341.667
|1350-1385
|}
{| class="wikitable" style="text-align: center"
! rowspan="2" |Degrees
! colspan="4" |Mohajira
! colspan="3" |Beatles
|-
|-
!Min-comma
|9\7
!''r¢''
|
!Med
|
! colspan="2" |Max+comma~Min-comma
|
!Med
|
!Max+comma
|192.857
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
|-
|-
|1
|
|187.857-192.857
|31\24
| colspan="2" |''193.75''
|
| colspan="2" |189.118-199.118
|
|194.444
|
|195-200
|193
|
|-
|-
|2
|22\17
|375.714-385.714
|
| colspan="2" |''387.5''
|
| colspan="2" |378.235-398.235
|
|388.889
|
|390-400
|194.118
|Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
|-
|-
|3
|
|563.571-578.571
|35\27
| colspan="2" |''581.25''
|
| colspan="2" |567.353-597.353
|
|583.333
|
|585-600
|194.{{Overline|4}}
|
|-
|-
|4
|13\10
|751.429-771.429
|
| colspan="2" |''775''
|
| colspan="2" |756.471-796.471
|
|777.778
|
|780-800
|195
|Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
|-
|-
|5
|17\13
|939.286-964.286
|
| colspan="2" |''968.75''
|
| colspan="2" |945.588-995.588
|
|972.222
|
|975-1000
|196.154
|
|-
|-
|6
|21\16
|1127.143-1157.143
|
| colspan="2" |''1162.5''
|
| colspan="2" |1134.706-1194.706
|
|1166.667
|
|1170-1200
|196.875
|Subpental Mixolydian mode ends, Pental Mixolydian mode begins
|-
|-
|7
|
|1315-1350
|25\19
| colspan="2" |''1356.25''
|
| colspan="2" |1323.8235-1393.8235
|
|1361.111
|
|1365-1400
|197.37
|}
|
{| class="wikitable" style="text-align: center"
|-
|-
! rowspan="4" |Degrees
|
! colspan="12" |Mixolydian
|
! colspan="3" rowspan="3" |Mixolydian-Ionian
|29\22
|
|
|197.{{Overline|72}}
|
|-
|-
! colspan="3" rowspan="2" |Subpental
|
! colspan="3" rowspan="2" |Pental
|
! colspan="6" |Superpental
|
|33\25
|
|198
|
|-
|-
! colspan="3" |Soft
|
! colspan="3" |Intense
|
|
|
|37\28
|
|
|-
|-
! width="4%" |Min-comma
|4\3
!Med
|
! colspan="2" width="4%" |Max+comma~Min-comma
|
!Med
|
! colspan="2" width="4%" |Max+comma~Min-comma
|
!Med
|100
! colspan="2" width="4%" |Max+comma~Min-comma
| Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
!Med
! colspan="2" width="4%" |Max+comma~Min-comma
!Med
!Max+comma
|-
|-
| |1
|
|190-195
|19\14
|196.154
|
| colspan="2" |191.875-201.875
|
|197.368
|
| colspan="2" |195-205
|101.786
|201.5625
|
| colspan="2" |196.724-206.724
|204.31
| colspan="2" |201.897-211.897
|207.353
|210-215
|-
|-
| |2
|15\11
|380-390
|
|392.308
|
| colspan="2" |383.75-403.75
|
|394.737
|
| colspan="2" |390-410
|102.{{Overline|27}}
|403.125
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
| colspan="2" |393.448-413.448
|408.621
| colspan="2" |403.793-423.793
|414.706
|420-430
|-
|-
| |3
|
|570-585
|26\19
|588.4615
|
| colspan="2" |575.625-605.625
|
|592.105
|
| colspan="2" |585-615
|102.632
|604.6875
|
| colspan="2" |590.172-620.172
|612.931
| colspan="2" |605.69-635.69
|622.059
|630-645
|-
|-
|4
|11\8
|760-780
|
|784.615
|
| colspan="2" |767.5-807.5
|
|789.474
|
| colspan="2" |780-820
|103.125
|806.25
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
| colspan="2" |786.897-826.897
|817.241
| colspan="2" |807.586-847.586
|829.412
|840-860
|-
|-
|5
|
|950-975
|18\13
|980.769
|
| colspan="2" |959.375-1008.375
|
|986.842
|
| colspan="2" |975-1025
|103.846
|1007.8125
|
| colspan="2" |983.621-1033.621
|1021.552
| colspan="2" |1009.483-1059.483
|1036.765
|1050-1075
|-
|-
|6
|
|1140-1170
|
|1176.923
| 25\18
| colspan="2" |1151.25-1211.25
|
|1184.2105
|
| colspan="2" |1170-1230
|104.1{{Overline|6}}
|1209.375
|
| colspan="2" |1180.345-1240.345
|1225.862
| colspan="2" |1211.379-1271.379
|1244.118
|1260-1290
|-
|-
|7
|7\5
|1330-1365
|
|1373.077
|
| colspan="2" |1343.125-1413.125
|
|1381.579
|
| colspan="2" |1365-1435
|105
|1410.9375
|Mixolydian-Ionian mode ends
| colspan="2" |1377.069-1447.069
|}Relative cents
|1430.172
| colspan="2" |1413.276-1483.276
|1451.471
|1470-1505
|}
Relative cents
 
{| class="wikitable" style="text-align: center"
{| class="wikitable" style="text-align: center"
!Degrees
!Degrees
! colspan="3" |Enneatonic
!Intense Aeolian-Subpental Dorian
!Intense Aeolian-Subpental Dorian
!Dorian
!Dorian
!Subpental-Soft Superpental Mixolydian  
!Dorian-Mixolydian
!Intense Superpental Mixolydian ~ Mixolydian-Ionian
|-
|-
|-
|1
|1
|181.25
|1#/2b
|187.5
|G#/Jb
|200
|''G#/Ab''
|206.25
|''90.625''
|''93.75''
|''96.875''
|-
|-
|2
|2
|362.5
|2
|375
|J
|400
|''A''
|412.5
|''181.25''
|''187.5''
|''193.75''
|-
|-
|3
|3
|543.75
|2#/3b
|562.5
|J#/Ab
|600
|''A#/Bb''
|618.75
|''271.875''
|''281.25''
|''290.625''
|-
|-
|4
|4
|543.75
|3
|750
|J
|800
|''B''
|825
|''362.5''
|''375''
|''387.5''
|-
|-
|5
|5
|906.25
|3#/4b
|937.5
|J#/Ab
|1000
|B#/Cb
|1031.25
|''453.125''
|''468.75''
|''484.375''
|-
|-
|6
|6
|1087.5
|4
|1125
|A
|1200
|''C''
|1237.5
|''543.75''
|''562.5''
|''581.25''
|-
|-
|7
|7
|1268.75
|5
|1312.5
|A#/Bb
|1400
|''C#/Qb''
|1443.75
|''633.375''
|}
|''656.25''
Golden/Pyrite Tunings±13¢
|''678.125''
{| class="wikitable" style="text-align: center"
|-
! rowspan="2" |Degrees
|8
! rowspan="2" |Intense Aeolian-Subpental Dorian
|5#/6b
! colspan="3" |Dorian
|B
|''Q''
|''725''
|''750''
|''775''
|-
|-
!Subpental
|9
!Pental
|6
!Superpental
|C
|''D''
|''815.625''
|''843.75''
|''871.875''
|-
|-
|1
|10
|180.856-184.106
|6#/7b
|182.606-185.856
|C#/Db
|188.2585-191.9085
|D#/Sb
|189.834-193.084
|''906.25''
|''937.5''
|''968.75''
|-
|-
|2
|11
|361.712-368.213
|7
|365.212-371.712
|D
|377.317-383.817
|''S''
|379.668-386.168
|''996.875''
|''1031.25''
|''1065.625''
|-
|-
|3
|12
|542.569-552.319
|7#/8b
|547.819-557.569
|D#/Eb
|565.974-575.726
|''S#/Eb''
|569.502-579.252
|''1087.5''
|''1125''
|''1162.5''
|-
|-
|4
| 13
|723.425-736.425
|8
|730.425-743.425
| colspan="2" |E
|754.634-767.634
|''1178.125''
|759.336-771.336
|''1218.75''
|''1259.375''
|-
|-
|5
|14
|904.282-920.532
|8#/9b
|913.031-920.281
| colspan="2" |E#/Fb
|943.293-959.543
|''1268.75''
|949.17-965.42
|''1312.5''
|''1356.25''
|-
|-
|6
|15
|1085.138-1104.638
|9
|1095.637-1115.137
| colspan="2" |F
|1131.951-1151.451
|''1359.375''
|1139.004-1158.503
|''1406.25''
|''1453.125''
|-
|-
|7
|16
|1265.9945-1288.7445
|1
|1278.2435-1300.9935
| colspan="2" |G
|1320.61-1343.36
|''1450''
|1328.838-1351.588
|''1500''
|''1550''
|}
|}
{| class="wikitable" style="text-align: center"
{| class="wikitable" style="text-align: center"
!Degrees
!Degrees
!Mohajira
! colspan="3" |Enneatonic
!Beatles
!Subpental-Soft Superpental Mixolydian
!Intense Superpental Mixolydian ~ Mixolydian-Ionian
|-
|-
|1
| | 1
|192.237-195.487
|1#/2b
|192.728-195.978
| colspan="2" |F#/Gb
|''100''
|''103.125''
|-
|-
| |2
|2
|2
|384.474-390.974
| colspan="2" |G
|385.456-391.956
|''200''
|''206.25''
|-
|-
| |3
|2#/3b
|G#/Jb
|''G#/Ab''
|''300''
|''309.375''
|-
| |4
|3
|3
|576.711-585.961
|J
|578.184-587.934
|''A''
|''400''
|''412.5''
|-
|-
| |5
|3#/4b
|J#/Ab
|''A#/Bb''
|''500''
|''515.625''
|-
| |6
|4
|4
|768.948-781.948
|A
|770.912-783.912
|''B''
|''600''
|''618.75''
|-
|-
| | 7
|5
|5
|961.185-977.435
|B
|963.6395-979.8895
|''H''
|''700''
|''721.875''
|-
|-
|8
| 5#/6b
|B#/Hb
|''H#/Cb''
|''800''
|''825''
|-
|9
|6
|6
|1153.422-1172.921
|H
|1156.367-1175.867
|''C''
|''900''
|''928.125''
|-
|-
|10
|6#/7b
|H#/Cb
|''C#/Db''
|''1000''
|''1031.25''
|-
|11
|7
|7
|1345.659-1368.409
|C
|1349.095-1372.345
|''D''
|}
|''1100''
{| class="wikitable" style="text-align: center"
|''1134.375''
|-
|-
! rowspan="3" |Degrees
|12
! colspan="4" |Mixolydian
|7#/8b
! rowspan="3" |Mixolydian-Ionian
|C#/Db
|''D#/Sb''
|''1200''
|''1237.5''
|-
|-
! rowspan="2" |Subpental
|13
! rowspan="2" |Pental
|8
! colspan="2" |Superpental
|D
|''S''
|''1300''
|''1340.625''
|-
|-
!Soft
|14
!Intense
|8#/9b
|D#/Eb
|''S#/Eb''
|''1400''
|''1443.75''
|-
|-
| |1
|15
|194.7275-197.9775
|9
|195.5745-198.8245
| colspan="2" |E
|199.9955-203.2455
|''1500''
|203.296-206.546
|''1546.875''
|205.57-208.82
|-
|-
| |2
|16
|389.455-395.955
|1
|391.149-397.649
| colspan="2" |F
|399.991-406.491
|''1600''
|406.592-413.092
|''1650''
|411.141-417.641
|}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.
|-
==See also==
| |3
*[[16ed5/2]] - equal division of the classic major tenth
|584.183-593.933
*[[16ed7/3]] - equal division of the septimal minor tenth
|586.724-596.474
|599.987-609.737
|609.888-619.638
|616.711-626.461
|-
|4
|778.91-791.91
|782.298-795.298
|799.982-812.982
|813.1835-826.1835
|822.282-835.282
|-
|5
|973.638-989.888
|977.873-994.123
|999.978-1016.238
|1016.479-1032.729
|1027.852-1044.102
|-
|6
|1168.365-1187.865
|1173.447-1192.947
|1199.973-1219.473
|1219.775-1239.275
|1233.422-1252.922
|-
|7
|1363.093-1385.843
|1369.022-1391.772
|1399.968-1422.719
|1423.071-1445.821
|1438.993-1461.743
|}
 
== See also ==
* [[8ed5/2]] - equal division of the classic major tenth
* [[8ed7/3]] - equal division of the septimal minor tenth


[[Category:16-tone scales]]
[[Category:EdX]]
[[Category:EdX]]
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/8edX"