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User:Moremajorthanmajor/17edIX: Difference between revisions

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This scale, a Long Common Practice minor mode, has the Grandfather 3L 5s MOS with a 4:1 ratio of large against small.
{| class="wikitable"
! colspan="4" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
! colspan="3" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
! colspan="3" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
|}This scale, a Long Common Practice minor mode, has the Grandfather 3L 5s MOS with a 4:1 ratio of large against small.


==Intervals==
==Intervals==
Line 69: Line 73:
|-
|-
| |5
| |5
|A
| colspan="2" |A
| |A
|352.941
|352.941
|373.109
|373.109
Line 81: Line 84:
|-
|-
| |6
| |6
|B
| colspan="2" |B
| |B
|423.529
|423.529
|447.731
|447.731
Line 141: Line 143:
|-
|-
| |11
| |11
|C
| colspan="2" |C
| |C
|776.471
|776.471
|820.84
|820.84
Line 153: Line 154:
|-
|-
| |12
| |12
|D
| colspan="2" |D
| |D
|847.059
|847.059
|895.462
|895.462
Line 222: Line 222:
|1400
|1400
|1440
|1440
|}Golden Tunings
|}Most harmonic tunings
{| class="wikitable"
{| class="wikitable"
|-
|+
! rowspan="2" |Degrees
! rowspan="2" |Degrees
! colspan="2" rowspan="2" |Octatonic
! colspan="2" rowspan="2" |Octatonic
! colspan="3" |Phrygian Mode (natural minor)
!Phrygian Mode (natural minor)
! colspan="2" |Phrygian-Aeolian Mode (intermediate minor)
!Phrygian-Aeolian Mode (intermediate minor)
! colspan="3" |Aeolian Mode (melodic/harmonic minor)
!Aeolian Mode (melodic/harmonic minor)
|-
!15/7±13¢
!11/5±13¢
!9/4±13¢
|-
|1
|G
|Gb
|76.85-78.379
|79.53-81.059
|81.818-83.348
|-
|2
|A\\
|F#v/Gb^
|153.7-156.758
|159.059-162.118
|163.6365-166.695
|-
|3
|Gpv/A\\^
|F#
|230.549-235.137
|238.589-243.177
|245.455-250.043
|-
|4
|Gp
|G
|307.398-313.516
|318.119-324.236
|327.272-333.391
|-
|5
| colspan="2" |A
|384.248-391.895
|394.648-405.295
|409.091-416.738
|-
|6
| colspan="2" |B
|461.0975-470.274
|477.178-486.354
|490.909-500.086
|-
|7
|H
|Hb
|537.947.548.653
|556.707-567.4135
|572.728-583.4335
|-
|8
|C\\
|B#v/Hb^
|614.797-627.032
|636.237-648.473
|654.546-666.781
|-
|9
|Hpv/C\\^
|B#
|691.646-705.411
|715.767-729.532
|736.364-753.087
|-
|10
|Hp
|H
|768.496-783.79
|795.297-810.591
|818.182-833.4765
|-
|11
| colspan="2" |C
|845.345-862.169
|874.826-891.65
|900.001-916.824
|-
|12
| colspan="2" |D
|922.195-940.548
|954.356-972.709
|981.819-100.172
|-
|13
|E
|Eb
|999.0445-1018.927
|1033.886-1053.768
|1063.637-1083.519
|-
|14
|F\\
|D#v/Eb^
|1075.894-1097.306
|1113.415-1134.827
|1145.455-1166.867
|-
|15
|Epv/F\\^
|D#
|1152.744-1175.685
|1189.945-1215.876
|1227.2735-1250.215
|-
|16
|Ep
|E
|1229.593-1254.064
|1272.474-1296.945
|1309.092-1333.562
|-
|-
|17
| colspan="2" |F
|1306.443-1332.443
|1352.004-1378.004
|1390.91-1416.91
|}
Golden Tunings
Phrygian Mode (natural minor)
{| class="wikitable"
|-
!Degrees
! colspan="2" |Octatonic
!Min-Med-13c
!Min-Max-13c
!Min-Med
!Min-Med
!Min-Max
!Min-Max
!Med-Max-13c
!Min-Med+13c
!Min-Max+13c
!Med-Max
!Med-Max
!Min-Med/Min-Max
!Med-Max+13c
!Med-Max
!Min-Med
!Min-Max
!Med-Max
|-
|-
| |1
| |1
|G
|G
| |Gb
| |Gb
|73.998
|74.311
|74.763
|74.763
|75.076
|75.076
|75.216
|75.527
|75.841
|75.981
|75.981
|78.561
|76.745
|79.254
|81.254
|81.908
|83.153
|-
|-
| |2
| |2
|A\\
|A\\
| |F#v/Gb^
| |F#v/Gb^
|147.996
|148.622
|149.525
|149.525
|150.152
|150.152
|150.432
|151.055
|151.681
|151.961
|151.961
|157.121
|153.491
|158.5075
|162.509
|163.815
|166.306
|-
|-
| |3
| |3
|Gpv/A\\^
|Gpv/A\\^
| |F#
| |F#
|221.994
|222.9335
|224.288
|224.288
|225.228
|225.228
|225.648
|226.582
|227.522
|227.942
|227.942
|235.982
|230.236
|237.761
|243.763
|245.723
|249.458
|-
|-
| |4
| |4
|Gp
|Gp
| |G
| |G
|295.992
|297.245
|299.0505
|299.0505
|300.3035
|300.3035
|300.864
|302.109
|303.362
|303.923
|303.923
|314.242
|306.982
|317.015
|325.017
|327.63
|332.611
|-
|-
| |5
| |5
|A
| colspan="2" |A
| |A
|369.99
|371.556
|373.813
|373.813
|375.379
|375.379
|376.08
|377.637
|379.203
|379.9035
|379.9035
|392.803
|383.727
|396.269
|406.271
|409.538
|415.764
|-
|-
| |6
| |6
|B
| colspan="2" |B
| |B
|443.9875
|445.867
|448.576
|448.576
|450.455
|450.455
|451.296
|453.164
|455.0435
|455.884
|455.884
|471.264
|460.472
|475.522
|487.526
|491.4455
|498.917
|-
|-
| |7
| |7
|H
|H
| |Hb
| |Hb
|517.985
|520.178
|523.338
|523.338
|525.531
|525.531
|526.512
|528.691
|530.884
|531.865
|531.865
|549.924
|537.218
|554.776
|568.78
|573.353
|582.07
|-
|-
| |8
| |8
|C\\
|C\\
| |B#v/Hb^
| |B#v/Hb^
|591.983
|594.489
|598.101
|598.101
|600.607
|600.607
|601.728
|604.219
|606.725
|607.846
|607.846
|628.485
|612.963
|634.03
|650.034
|655.261
|665.2225
|-
|-
| |9
| |9
|Hpv/C\\^
|Hpv/C\\^
| |B#
| |B#
|665.981
|668.8005
|672.864
|672.864
|675.683
|675.683
|676.944
|679.746
|682.565
|683.826
|683.826
|707.0455
|690.709
|713.284
|731.2885
|737.168
|748.375
|-
|-
| |10
| |10
|Hp
|Hp
| |H
| |H
|739.979
|743.112
|747.626
|747.626
|750.759
|750.759
|752.16
|755.273
|758.406
|759.807
|759.807
|785.606
|767.454
|792.537
|812.543
|819.076
|831.528
|-
|-
| |11
| |11
|C
| colspan="2" |C
| |C
|813.977
|817.423
|822.389
|822.389
|825.835
|825.835
|827.376
|830.801
|834.246
|835.788
|835.788
|864.168
|844.166
|871.791
|893.797
|900.983
|914.681
|-
|-
| |12
| |12
|D
| colspan="2" |D
| |D
|887.975
|891.734
|897.1515
|897.1515
|900.9105
|900.9105
|902.592
|906.328
|910.087
|911.768
|911.768
|942.727
|920.945
|951.045
|975.051
|982.891
|997.833
|-
|-
| |13
| |13
|E
|E
| |Eb
| |Eb
|961.972
|966.045
|971.914
|971.914
|975.986
|975.986
|977.808
|981.855
|985.9275
|987.749
|987.749
|997.69
|-
|14
|F\\
|D#v/Eb^
|1035.971
|1040.356
|1046.877
|1051.062
|1053.024
|1057.383
|1061.768
|1063.728
|1074.436
|-
|15
|Epv/F\\^
|D#
|1109.969
|1114.6675
|1121.439
|1126.138
|1128.24
|1132.91
|1137.609
|1139.71
|1151.181
|-
|16
|Ep
|E
|1183.967
|1188.979
|1196.202
|1201.214
|1203.456
|1208.437
|1213.449
|1215.69
|1227.926
|-
|17
| colspan="2" |F
|1257.965
|1263.29
|1270.965
|1276.29
|1278.672
|1283.965
|1289.29
|1291.672
|1304.672
|}
Phrygian-Aeolian Mode (intermediate minor)
{| class="wikitable"
|-
!Degrees
! colspan="2" |Octatonic
!Min-Med/Min-Max-13c
!Med-Max-13c
!Min-Med/Min-Max
!Med-Max
!Min-Med/Min-Max+13c
!Med-Max+13c
!Min-Med-13c (Aeolian)
|-
| |1
|G
| |Gb
|77.796
|78.489
|78.561
|79.254
|79.325
|80.018
|80.49
|-
| |2
|A\\
| |F#v/Gb^
|155.592
|156.976
|157.121
|158.5075
|158.651
|160.037
|160.979
|-
| |3
|Gpv/A\\^
| |F#
|233.388
|235.467
|235.982
|237.761
|237.976
|240.055
|241.469
|-
| |4
|Gp
| |G
|311.184
|313.956
|314.242
|317.015
|317.301
|320.074
|321.958
|-
| |5
| colspan="2" |A
|388.9795
|392.445
|392.803
|396.269
|396.627
|400.092
|402.448
|-
| |6
| colspan="2" |B
|466.775
|470.934
|471.264
|475.522
|475.952
|480.111
|482.937
|-
| |7
|H
| |Hb
|544.571
|549.423
|549.924
|554.776
|555.277
|560.129
|563.427
|-
| |8
|C\\
| |B#v/Hb^
|622.367
|627.912
|628.485
|634.03
|634.6025
|640.1475
|643.917
|-
| |9
|Hpv/C\\^
| |B#
|700.163
|706.401
|707.0455
|713.284
|713.928
|720.166
|724.406
|-
| |10
|Hp
| |H
|777.959
|784.89
|785.606
|792.537
|793.253
|800.184
|804.896
|-
| |11
| colspan="2" |C
|855.755
|893.379
|864.168
|871.791
|872.5785
|880.203
|885.385
|-
| |12
| colspan="2" |D
|933.551
|941.868
|942.727
|951.045
|951.903
|960.221
|965.875
|-
| |13
|E
| |Eb
|1011.347
|1020.357
|1021.288
|1021.288
|1030.2985
|1030.2985
|1031.229
|1040.24
|1046.364
|-
|14
|F\\
|D#v/Eb^
|1089.143
|1098.846
|1099.849
|1109.552
|1110.554
|1120.258
|1126.854
|-
|15
|Epv/F\\^
|D#
|1166.939
|1177.335
|1178.409
|1188.806
|1189.878
|1200.2765
|1207.344
|-
|16
|Ep
|E
|1244.734
|1255.834
|1256.97
|1268.06
|1269.205
|1280.295
|1287.833
|-
|17
| colspan="2" |F
|1322.53
|1334.313
|1335.53
|1347.313
|1348.53
|1360.313
|1368.322
|}
Aeolian Mode (melodic/harmonic minor)
{| class="wikitable"
|-
!Degrees
! colspan="2" |Octatonic
!Min-Max-13c
!Min-Med
!Min-Max
!Min-Med+13c
!Med-Max-13c
!Min-Max+13c
!Med-Max
!Med-Max+13c
|-
|1
|G
|Gb
|81.143
|81.254
|81.908
|82.019
|82.388
|82.672
|83.153
|83.9175
|-
|2
|A\\
|F#v/Gb^
|162.286
|162.509
|163.815
|164.038
|164.776
|165.345
|166.306
|167.835
|-
|3
|Gpv/A\\^
|F#
|243.429
|243.763
|245.723
|246.057
|247.164
|248.017
|249.458
|251.753
|-
|4
|Gp
|G
|324.5715
|325.017
|327.63
|328.076
|329.552
|330.689
|332.611
|335.67
|-
|5
| colspan="2" |A
|405.714
|406.271
|409.538
|410.095
|411.9405
|413.3615
|415.764
|419.588
|-
|6
| colspan="2" |B
|486.857
|487.526
|491.4455
|492.114
|494.329
|496.034
|498.917
|503.505
|-
|7
|H
|Hb
|568
|568.78
|573.353
|574.133
|576.717
|578.716
|582.07
|587.423
|-
|8
|C\\
|B#v/Hb^
|649.143
|650.034
|655.261
|656.152
|659.105
|661.378
|665.2225
|671.34
|-
|9
|Hpv/C\\^
|B#
|730.286
|731.2885
|737.168
|738.171
|741.493
|744.051
|748.375
|755.258
|-
|10
|Hp
|H
|811.429
|812.543
|819.076
|820.19
|823.881
|826.723
|831.528
|839.175
|-
|11
|C
|C
|892.572
|893.797
|900.983
|902.209
|906.269
|909.395
|914.681
|923.093
|-
|12
|D
|D
|973.715
|975.051
|982.891
|984.228
|988.657
|992.0675
|997.833
|1007.01
|-
|13
|E
|Eb
|1054.857
|1056.306
|1056.306
|1064.799
|1064.799
|1066.247
|1071.045
|1074.74
|1080.986
|1080.986
|1090.928
|-
|-
|14
|14
|F\\
|F\\
|D#v/Eb^
|D#v/Eb^
|1046.877
|1136
|1051.062
|1063.728
|1099.849
|1109.552
|1137.56
|1137.56
|1146.706
|1146.706
|1148.266
|1153.4335
|1157.412
|1164.139
|1164.139
|1174.845
|-
|-
|15
|15
|Epv/F\\^
|Epv/F\\^
|D#
|D#
|1121.439
|1217.143
|1126.138
|1139.71
|1178.409
|1188.806
|1218.814
|1218.814
|1228.614
|1228.614
|1230.285
|1235.822
|1240.084
|1247.292
|1247.292
|1258.762
|-
|-
|16
|16
|Ep
|Ep
|E
|E
|1196.202
|1298.286
|1201.214
|1215.69
|1256.97
|1268.06
|1300.0685
|1300.0685
|1310.521
|1310.521
|1312.304
|1318.21
|1332.757
|1330.445
|1330.445
|1342.68
|-
|-
|17
|17
| colspan="2" |F
| colspan="2" |F
|1270.965
|1379.429
|1276.29
|1291.672
|1335.53
|1347.313
|1381.322
|1381.322
|1392.429
|1392.429
|1394.322
|1400.598
|1405.429
|1413.598
|1413.598
|1426.598
|}
|}
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