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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"
! rowspan="5" |Degrees
|+
! colspan="8" |Minor mode Vesuvius temperament
! Decade
! colspan="2" |Neutral mode Vesuvius temperament
!Period
! colspan="10" |Major mode Vesuvius temperament
!Notes
|-
|6\5
|180.000
|Intense Aeolian-Subpental Dorian mode begins
|-
|29\24
|''181.250''
|
|-
|-
! colspan="2" rowspan="3" |Aeolian-Dorian
|23\19
! colspan="6" |Dorian
|181.579
! colspan="2" rowspan="3" |Dorian-Mixolydian
|
! colspan="8" |Mixolydian
! colspan="2" rowspan="3" |Mixolydian-Ionian
|-
|-
! colspan="2" rowspan="2" |Subpental
|17\14
! colspan="2" rowspan="2" |Pental
|182.143
! colspan="2" rowspan="2" |Superpental
|
! colspan="2" rowspan="2" |Subpental
! colspan="2" rowspan="2" |Pental
! colspan="4" |Superpental
|-
|-
! colspan="2" |Soft
|11\9
! colspan="2" |Intense
|183.333
|Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
|-
|-
! | Minimum
|16\13
! | Maximum
|184.615
!Minimum
|
!Maximum
!Minimum
!Maximum
!Minimum
!Maximum
!Minimum
! | Maximum
!Minimum
!Maximum
! | Minimum
!Maximum
!Minimum
!Maximum
!Minimum
!Maximum
!Minimum
! | Maximum
|-
|-
| | 1
|21\17
| | 180
|185.294
| colspan="2" | 183.333
|
| colspan="2" |187.5
| colspan="2" |190.909
| colspan="2" |192.857
| colspan="2" | 195
| colspan="2" |196.875
| colspan="2" |200
| colspan="2" |201.724
| colspan="2" |206.897
| | 210
|-
|-
| | 2
|26\21
| | 360
|185.714
| colspan="2" | 366.667
|
| colspan="2" |375
| 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
|-
|-
| | 3
|31\25
| | 540
|186.000
| colspan="2" | 550
|
| colspan="2" |562.5
| 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
|-
|-
| | 4
|5\4
| | 720
|187.500
| colspan="2" | 733.333
| Subpental Dorian mode ends, Pental Dorian mode begins
| colspan="2" |750
| 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
|-
|-
| | 5
|34\27
| | 900
|188.889
| colspan="2" | 916.667
|
| colspan="2" |937.5
| 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
|-
|-
| | 6
|29\23
| | 1080
|189.130
| colspan="2" | 1100
|
| colspan="2" |1125
| 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
|-
|-
| | 7
|24\19
| | 1260
|189.474
| 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
|}
Most harmonic tunings
{| class="wikitable"
|-
|-
! rowspan="2" |Degrees
|19\15
!Minor mode Vesuvius temperament
|190.000
!Neutral mode Vesuvius temperament
|
!Major mode Vesuvius temperament
|-
|-
!7/3±13¢
|14\11
!22/9±13¢
|190.909
!5/2±13¢
|Pental Dorian mode ends, Superpental Dorian mode begins
|-
|-
| |1
|23\18
|181.734-184.984
|191.667
|191.801-195.051
|
|196.664-199.914
|-
|-
| |2
|9\7
|363.468-396.968
|192.857
|383.602-390.102
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
|393.328-399.828
|-
|-
| |3
|31\24
|545.202-554.952
|193.000
|575.403-585.153
|
|589.993-599.743
|-
|-
| |4
|22\17
|726.9355-739.9355
|194.118
|767.204-780.204
|Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
|786.657-799.657
|-
|-
| |5
|35\27
|908.669-922.919
|194.444
|959.005-973.255
|
|983.321-997.571
|-
|-
| |6
|13\10
|1090.403-1109.903
|195.000
|1150.806-1170.306
|Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
|1179.985-1199.485
|-
|-
| |7
|17\13
|1272.137-1294.387
|196.154
|1342.607-1365.357
|
|1376.6495-1399.3995
|}Golden tunings
 
Minor mode Vesuvius temperament
{| class="wikitable"
|+
! rowspan="3" |Degrees
! colspan="3" |Aeolian-Dorian
! colspan="9" |Dorian
|-
|-
! rowspan="2" |-13¢
|21\16
! rowspan="2" |Mean
|196.875
! rowspan="2" |-13¢ (s5D)
|Subpental Mixolydian mode ends, Pental Mixolydian mode begins
! colspan="3" |Subpental
! colspan="3" |Pental
! colspan="3" |Superpental
|-
|-
!+13¢ (A-D)
|25\19
!Mean
|197.368
!+13¢
|
!-13¢
!-13¢ (S5)
!Mean
!Mean
!+13¢ (5)
!-13¢ (D-M)
|-
|-
|1
|29\22
|180.856
|197.727
|182.481
|
|182.606
|184.106
|184.231
|185.856
|188.2585
|189.834
|190.2835
|191.459
|191.9085
|192.728
|-
|-
|2
|33\25
|361.712
|198.000
|364.962
|
|365.212
|367.213
|368.462
|371.712
|377.317
|379.668
|380.567
|382.918
|383.817
|385.456
|-
|-
|3
|37\28
|542.569
|198.214
|547.444
|
|547.819
|552.319
|552.694
|557.569
|565.974
|569.502
|570.851
|574.377
|575.726
|578.184
|-
|-
|4
|41\31
|723.425
|198.387
|729.925
|
|730.425
|736.425
|736.925
|743.425
|754.634
|759.336
|761.134
|765.836
|767.634
|770.912
|-
|-
|5
|45\34
|904.282
|198.529
|912.407
|
|913.031
|920.532
|921.156
|929.281
|943.293
|949.17
|951.418
|957.295
|959.543
|963.6935
|-
|-
|6
|49\37
|1085.138
|198.649
|1094.888
|
|1095.637
|1104.638
|1105.387
|1115.137
|1131.957
|1139.004
|1141.701
|1148.753
|1151.451
|1156.367
|-
|-
|7
|53\40
|1265.9945
|198.750
|1277.3695
|
|1278.2435
|1288.7445
|1289.6185
|1300.9935
|1320.61
|1328.838
|1331.985
|1340.213
|1343.36
|1349.095
|}
Neutral (Dorian-Mixolydian) mode Vesuvius temperament
{| class="wikitable"
|-
|-
!Degrees
|57\43
!+13¢ (S5D)
|198.837
!Mean
|
!-13¢ (s5M)
|-
|-
|1
|61\46
|193.084
|198.913
|194.353
|
|194.7275
|-
|-
|2
|65\49
|386.168
|198.980
|388.706
|
|389.455
|-
|-
|3
|69\52
|579.252
|199.038
|583.059
|
|584.183
|-
|-
|4
|4\3
|771.336
|200.000
|777.412
| Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
|779.41
|-
|-
|5
|35\26
|965.42
|201.923
|971.7645
|
|973.638
|-
|-
|6
|31\23
|1158.503
|202.174
|1166.117
|
|1168.365
|-
|-
|7
|27\20
|1351.588
|202.500
|1360.47
|
|1363.093
|}
Major mode Vesuvius temperament
{| class="wikitable"
|-
|-
! rowspan="4" |Degrees
|23\17
! colspan="13" |Mixolydian
|202.941
! colspan="2" |Mixolydian-Ionian
|
|-
|-
! colspan="3" |Subpental
|19\14
! colspan="4" |Pental
|203.571
! colspan="6" |Superpental
|
! rowspan="3" |Mean
! rowspan="3" |+13¢
|-
|-
! rowspan="2" |-13¢ (5)
|15\11
! rowspan="2" |+13¢ (D-M)
|204.545
! rowspan="2" |Mean
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
! rowspan="2" |Mean
! rowspan="2" |+13¢ (s5)
! rowspan="2" |+13¢
! rowspan="2" |-13¢ (Soft s5)
! rowspan="2" |Soft
! colspan="5" |Intense
|-
|-
!+13¢ (Soft s5)
|26\19
!-13¢
|205.263
!Mean
|
!-13¢ (M-I)
!+13¢ (Int S5M)
|-
|-
|1
|11\8
|195.5745
|206.250
|195.978
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
|196.3525
|197.1995
|197.9775
|198.8245
|199.9955
|201.6205
|203.2455
|203.296
|204.921
|205.57
|206.546
|207.195
|208.82
|-
|-
|2
|18\13
|391.149
|207.692
|391.956
|
|392.705
|394.399
|395.955
|397.649
|399.991
|403.241
|406.491
|406.592
|409.842
|411.141
|413.092
|414.391
|417.641
|-
|-
|3
|25\18
|586.724
|208.333
|587.934
|
|589.058
|591.599
|593.933
|596.474
|599.987
|604.862
|609.737
|609.888
|614.763
|616.711
|691.638
|621.586
|626.461
|-
|-
|4
|32\23
|782.298
|208.696
|783.912
|
|785.41
|788.798
|791.91
|795.298
|799.982
|806.482
|812.982
|813.1835
|819.6835
|822.282
|826.1835
|828.782
|835.282
|-
|-
|5
|39\28
|977.872
|208.929
|979.8895
|
|981.763
|985.998
|989.888
|994.123
|999.978
|1008.103
|1016.228
|1016.479
|1024.604
|1027.852
|1032.729
|1035.977
|1044.102
|-
|-
|6
|46\33
|1173.447
|209.091
|1175.867
|
|1178.115
|1183.197
|1189.865
|1192.947
|1199.973
|1209.723
|1219.473
|1219.775
|1229.525
|1233.422
|1239.275
|1243.172
|1252.922
|-
|-
|7
|7\5
|1369.022
|210.000
|1371.845
|Mixolydian-Ionian mode ends
|1374.468
|1380.397
|1385.843
|1391.772
|1399.968
|1411.344
|1422.719
|1423.071
|1434.446
|1438.993
|1445.821
|1450.368
|1461.743
|}
|}
 
==See also==
[[Category:EdX]]
*[[8ed5/2]] - equal division of the classic major tenth
*[[8ed7/3]] - equal division of the septimal minor tenth

Latest revision as of 13:40, 6 March 2026

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

Decade Period Notes
6\5 180.000 Intense Aeolian-Subpental Dorian mode begins
29\24 181.250
23\19 181.579
17\14 182.143
11\9 183.333 Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
16\13 184.615
21\17 185.294
26\21 185.714
31\25 186.000
5\4 187.500 Subpental Dorian mode ends, Pental Dorian mode begins
34\27 188.889
29\23 189.130
24\19 189.474
19\15 190.000
14\11 190.909 Pental Dorian mode ends, Superpental Dorian mode begins
23\18 191.667
9\7 192.857 Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
31\24 193.000
22\17 194.118 Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
35\27 194.444
13\10 195.000 Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
17\13 196.154
21\16 196.875 Subpental Mixolydian mode ends, Pental Mixolydian mode begins
25\19 197.368
29\22 197.727
33\25 198.000
37\28 198.214
41\31 198.387
45\34 198.529
49\37 198.649
53\40 198.750
57\43 198.837
61\46 198.913
65\49 198.980
69\52 199.038
4\3 200.000 Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
35\26 201.923
31\23 202.174
27\20 202.500
23\17 202.941
19\14 203.571
15\11 204.545 Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
26\19 205.263
11\8 206.250 Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
18\13 207.692
25\18 208.333
32\23 208.696
39\28 208.929
46\33 209.091
7\5 210.000 Mixolydian-Ionian mode ends

See also

  • 8ed5/2 - equal division of the classic major tenth
  • 8ed7/3 - equal division of the septimal minor tenth
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