User:Moremajorthanmajor/17edIX: Difference between revisions

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Line 1: Line 1:
{| class="wikitable"
This scale, a Long Common Practice minor mode, has the Grandfather 3L 5s MOS with a 4:1 ratio of large against small.
! 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==
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="3" |Degrees
! colspan="2" rowspan="2" |Octatonic
! colspan="2" rowspan="3" |Octatonic
! colspan="4" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
! colspan="4" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
! colspan="3" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
! colspan="9" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
! colspan="3" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
! colspan="3" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
|-
|-
!Absolute Minimum
! rowspan="2" |Absolute Minimum
!Minimum
! rowspan="2" |Minimum
! rowspan="2" |Median
! rowspan="2" |Maximum
! colspan="3" |Intense Phrygian
! colspan="3" |Intense Phrygian-Soft Aeolian
! colspan="3" |Soft Aeolian
! rowspan="2" |Minimum
! rowspan="2" |Median
! rowspan="2" |Maximum
|-
! |Minimum
!Median
!Median
!Maximum
!Maximum
! |Minimum
!Minimum
!Median
!Median
!Maximum
!Maximum
Line 31: Line 37:
|75.294
|75.294
| colspan="2" |77.647
| colspan="2" |77.647
|78.019
| colspan="2" |78.431
|78.893
|78.893
| colspan="2" |79.412
|80
| colspan="2" |80.672
| colspan="2" |80.672
|82.353
|82.353
Line 43: Line 53:
|150.588
|150.588
| colspan="2" |155.294
| colspan="2" |155.294
|156.037
| colspan="2" |156.863
|157.7855
|157.7855
| colspan="2" |158.8235
|160
| colspan="2" |161.3445
| colspan="2" |161.3445
|164.706
|164.706
Line 55: Line 69:
|225.882
|225.882
| colspan="2" |232.941
| colspan="2" |232.941
|234.056
| colspan="2" |235.294
|236.678
|236.678
| colspan="2" |238.235
|240
| colspan="2" |242.017
| colspan="2" |242.017
|247.059
|247.059
Line 67: Line 85:
|301.1765
|301.1765
| colspan="2" |310.588
| colspan="2" |310.588
|312.074
| colspan="2" |313.7255
|315.571
|315.571
| colspan="2" |317.647
|320
| colspan="2" |322.689
| colspan="2" |322.689
|329.412
|329.412
Line 78: Line 100:
|376.471
|376.471
| colspan="2" |387.235
| colspan="2" |387.235
|390.093
| colspan="2" |392.156
|394.464
|394.464
| colspan="2" |397.058
|400
| colspan="2" |403.361
| colspan="2" |403.361
|411.765
|411.765
Line 89: Line 115:
|451.765
|451.765
| colspan="2" |464.822
| colspan="2" |464.822
|468.1115
| colspan="2" |470.588
|473.356
|473.356
| colspan="2" |476.471
|480
| colspan="2" |484.034
| colspan="2" |484.034
|494.118
|494.118
Line 101: Line 131:
|527.059
|527.059
| colspan="2" |542.529
| colspan="2" |542.529
|546.13
| colspan="2" |549.02
|552.249
|552.249
| colspan="2" |555.882
|560
| colspan="2" |564.706
| colspan="2" |564.706
|576.471
|576.471
Line 113: Line 147:
|602.353
|602.353
| colspan="2" |620.1765
| colspan="2" |620.1765
|624.149
| colspan="2" |627.451
|651.142
|651.142
| colspan="2" |635.294
|640
| colspan="2" |645.378
| colspan="2" |645.378
|658.8235
|658.8235
Line 125: Line 163:
|677.647
|677.647
| colspan="2" |697.8235
| colspan="2" |697.8235
|702.167
| colspan="2" |705.882
|710.035
|710.035
| colspan="2" |714.706
|720
| colspan="2" |726.05
| colspan="2" |726.05
|741.1765
|741.1765
Line 137: Line 179:
|752.941
|752.941
| colspan="2" |777.471
| colspan="2" |777.471
|780.186
| colspan="2" |784.314
|788.927
|788.927
| colspan="2" |794.118
|800
| colspan="2" |806.723
| colspan="2" |806.723
|823.529
|823.529
Line 148: Line 194:
|828.235
|828.235
| colspan="2" |855.118
| colspan="2" |855.118
|858.204
| colspan="2" |862.745
|867.82
|867.82
| colspan="2" |873.529
|880
| colspan="2" |887.395
| colspan="2" |887.395
|905.882
|905.882
Line 159: Line 209:
|903.529
|903.529
| colspan="2" |932.765
| colspan="2" |932.765
|956.713
|936.223
| colspan="2" |941.1765
|946.713
| colspan="2" |952.941
|960
| colspan="2" |968.067
| colspan="2" |968.067
|988.235
|988.235
Line 171: Line 225:
|978.8235
|978.8235
| colspan="2" |1010.412
| colspan="2" |1010.412
|1014.2415
| colspan="2" |1019.607
|1025.6055
|1025.6055
| colspan="2" |1032.353
|1040
| colspan="2" |1048.7395
| colspan="2" |1048.7395
|1070.588
|1070.588
Line 183: Line 241:
|1054.118
|1054.118
| colspan="2" |1088.059
| colspan="2" |1088.059
|1092.26
| colspan="2" |1098.039
|1104.598
|1104.598
| colspan="2" |1111.765
|1120
| colspan="2" |1129.412
| colspan="2" |1129.412
|1152.941
|1152.941
Line 195: Line 257:
|1129.412
|1129.412
| colspan="2" |1164.706
| colspan="2" |1164.706
|1170.028
| colspan="2" |1176.471
|1183.391
|1183.391
| colspan="2" |1191.1765
|1200
| colspan="2" |1210.084
| colspan="2" |1210.084
|1233.294
|1233.294
Line 207: Line 273:
|1204.706
|1204.706
| colspan="2" |1242.353
| colspan="2" |1242.353
|1248.297
| colspan="2" |1254.902
|1262.284
|1262.284
| colspan="2" |1270.588
|1280
| colspan="2" |1290.756
| colspan="2" |1290.756
|1317.647
|1317.647
Line 218: Line 288:
|1280
|1280
| colspan="2" |1320
| colspan="2" |1320
|1326.316
| colspan="2" |1333.333
|1341.1765
|1341.1765
| colspan="2" |1350
|1360
| colspan="2" |1371.429
| colspan="2" |1371.429
|1400
|1400
Line 356: Line 430:
!Degrees
!Degrees
! colspan="2" |Octatonic
! colspan="2" |Octatonic
!Min-Med-13c
!Min-Med±13¢
!Min-Max-13c
!Min-Max±13¢
!Min-Med
!Med-Max±13¢
!Min-Max
!Med-Max-13c
!Min-Med+13c
!Min-Max+13c
!Med-Max
!Med-Max+13c
|-
|-
| |1
| |1
|G
|G
| |Gb
| |Gb
|73.998
|73.998-75.527
|74.311
|74.311-75.841
|74.763
|75.216-76.745
|75.076
|75.216
|75.527
|75.841
|75.981
|76.745
|-
|-
| |2
| |2
|A\\
|A\\
| |F#v/Gb^
| |F#v/Gb^
|147.996
|147.996-151.055
|148.622
|148.622-151.681
|149.525
|150.432-153.491
|150.152
|150.432
|151.055
|151.681
|151.961
|153.491
|-
|-
| |3
| |3
|Gpv/A\\^
|Gpv/A\\^
| |F#
| |F#
|221.994
|221.994-226.582
|222.9335
|222.9335-227.522
|224.288
|225.648-230.236
|225.228
|225.648
|226.582
|227.522
|227.942
|230.236
|-
|-
| |4
| |4
|Gp
|Gp
| |G
| |G
|295.992
|295.992-302.109
|297.245
|297.245-303.362
|299.0505
|300.864-306.982
|300.3035
|300.864
|302.109
|303.362
|303.923
|306.982
|-
|-
| |5
| |5
| colspan="2" |A
| colspan="2" |A
|369.99
|369.99-377.637
|371.556
|371.556-379.203
|373.813
|376.08-383.727
|375.379
|376.08
|377.637
|379.203
|379.9035
|383.727
|-
|-
| |6
| |6
| colspan="2" |B
| colspan="2" |B
|443.9875
|443.9875-453.164
|445.867
|445.867-455.0435
|448.576
|451.296-460.472
|450.455
|451.296
|453.164
|455.0435
|455.884
|460.472
|-
|-
| |7
| |7
|H
|H
| |Hb
| |Hb
|517.985
|517.985-528.691
|520.178
|520.178-530.884
|523.338
|526.512-537.218
|525.531
|526.512
|528.691
|530.884
|531.865
|537.218
|-
|-
| |8
| |8
|C\\
|C\\
| |B#v/Hb^
| |B#v/Hb^
|591.983
|591.983-604.219
|594.489
|594.489-606.725
|598.101
|601.728-612.963
|600.607
|601.728
|604.219
|606.725
|607.846
|612.963
|-
|-
| |9
| |9
|Hpv/C\\^
|Hpv/C\\^
| |B#
| |B#
|665.981
|665.981-679.746
|668.8005
|668.8005-682.565
|672.864
|676.944-690.709
|675.683
|676.944
|679.746
|682.565
|683.826
|690.709
|-
|-
| |10
| |10
|Hp
|Hp
| |H
| |H
|739.979
|739.979-755.273
|743.112
|743.112-758.406
|747.626
|752.16-767.454
|750.759
|752.16
|755.273
|758.406
|759.807
|767.454
|-
|-
| |11
| |11
| colspan="2" |C
| colspan="2" |C
|813.977
|813.977-830.801
|817.423
|817.423-834.246
|822.389
|827.376-844.166
|825.835
|827.376
|830.801
|834.246
|835.788
|844.166
|-
|-
| |12
| |12
| colspan="2" |D
| colspan="2" |D
|887.975
|887.975-906.328
|891.734
|891.734-910.087
|897.1515
|902.592-920.945
|900.9105
|902.592
|906.328
|910.087
|911.768
|920.945
|-
|-
| |13
| |13
|E
|E
| |Eb
| |Eb
|961.972
|961.972-981.855
|966.045
|966.045-985.9275
|971.914
|977.808-997.69
|975.986
|977.808
|981.855
|985.9275
|987.749
|997.69
|-
|-
|14
|14
|F\\
|F\\
|D#v/Eb^
|D#v/Eb^
|1035.971
|1035.971-1057.383
|1040.356
|1040.356-1061.768
|1046.877
|1053.024-1074.436
|1051.062
|1053.024
|1057.383
|1061.768
|1063.728
|1074.436
|-
|-
|15
|15
|Epv/F\\^
|Epv/F\\^
|D#
|D#
|1109.969
|1109.969-1132.91
|1114.6675
|1114.6675-1137.609
|1121.439
|1128.24-1151.181
|1126.138
|1128.24
|1132.91
|1137.609
|1139.71
|1151.181
|-
|-
|16
|16
|Ep
|Ep
|E
|E
|1183.967
|1183.967-1208.437
|1188.979
|1188.979-1213.449
|1196.202
|1203.456-1227.926
|1201.214
|1203.456
|1208.437
|1213.449
|1215.69
|1227.926
|-
|-
|17
|17
| colspan="2" |F
| colspan="2" |F
|1257.965
|1257.965-1283.965
|1263.29
|1263.29-1289.29
|1270.965
|1278.672-1304.672
|1276.29
|1278.672
|1283.965
|1289.29
|1291.672
|1304.672
|}
|}
Phrygian-Aeolian Mode (intermediate minor)
Phrygian-Aeolian Mode (intermediate minor)
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! colspan="2" rowspan="2" |Octatonic
! colspan="2" |Intense Phrygian
! colspan="2" |Intense Phrygian-Soft Aeolian
! colspan="2" |Soft Aeolian
|-
|-
!Degrees
!Min-Med/Min-Max±13¢
! colspan="2" |Octatonic
!Med-Max±13¢
!Min-Med/Min-Max-13c
!Min-Med/Min-Max±13¢
!Med-Max-13c
!Med-Max±13¢
!Min-Med/Min-Max
!Min-Med/Min-Max±13¢
!Med-Max
!Med-Max±13¢
!Min-Med/Min-Max+13c
!Med-Max+13c
!Min-Med-13c (Aeolian)
|-
|-
| |1
| |1
|G
|G
| |Gb
| |Gb
|77.796
|77.163-78.692
|78.489
|77.347-78.877
|78.561
|78.014-79.544
|79.254
|78.245-79.774
|79.325
|79.0895-80.618
|80.018
|79.385-80.915
|80.49
|-
|-
| |2
| |2
|A\\
|A\\
| |F#v/Gb^
| |F#v/Gb^
|155.592
|155.325-157.384
|156.976
|155.695-157.7535
|157.121
|156.029-159.087
|158.5075
|156.49-159.549
|158.651
|158.179-161.238
|160.037
|158.772-161.83
|160.979
|-
|-
| |3
| |3
|Gpv/A\\^
|Gpv/A\\^
| |F#
| |F#
|233.388
|231.488-236.076
|235.467
|232.042-236.63
|235.982
|234.043-238.631
|237.761
|234.735-239.323
|237.976
|237.268-241.857
|240.055
|238.157-242.746
|241.469
|-
|-
| |4
| |4
|Gp
|Gp
| |G
| |G
|311.184
|308.651-314.768
|313.956
|309.389-315.507
|314.242
|312.057-318.175
|317.015
|312.98-319.098
|317.301
|316.358-322.4755
|320.074
|317.543-323.661
|321.958
|-
|-
| |5
| |5
| colspan="2" |A
| colspan="2" |A
|388.9795
|385.814-393.4605
|392.445
|386.737-394.384
|392.803
|390.071-397.7185
|396.269
|391.225-398.872
|396.627
|395.447-403.094
|400.092
|396.929-404.576
|402.448
|-
|-
| |6
| |6
| colspan="2" |B
| colspan="2" |B
|466.775
|462.976-472.1525
|470.934
|464.084-473.261
|471.264
|468.086-477.262
|475.522
|469.469-478.646
|475.952
|474.537-483.713
|480.111
|476.315-485.4913
|482.937
|-
|-
| |7
| |7
|H
|H
| |Hb
| |Hb
|544.571
|540.139-550.845
|549.423
|541.4315-549.423
|549.924
|546.1-556.806
|554.776
|547.715-558.421
|555.277
|553.627-564.332
|560.129
|555.7005-566.406
|563.427
|-
|-
| |8
| |8
|C\\
|C\\
| |B#v/Hb^
| |B#v/Hb^
|622.367
|617.3015-629.537
|627.912
|618.779-631.014
|628.485
|624.114-636.35
|634.03
|625.96-638.195
|634.6025
|632.716-644.951
|640.1475
|635.086-647.322
|643.917
|-
|-
| |9
| |9
|Hpv/C\\^
|Hpv/C\\^
| |B#
| |B#
|700.163
|694.464-708.229
|706.401
|696.126-709.891
|707.0455
|702.129-715.893
|713.284
|704.205-717.969
|713.928
|711.805-725.57
|720.166
|714.805-728.237
|724.406
|-
|-
| |10
| |10
|Hp
|Hp
| |H
| |H
|777.959
|771.629-786.921
|784.89
|773.4735-788.768
|785.606
|780.143-795.437
|792.537
|782.45-797.744
|793.253
|790.895-806.189
|800.184
|793.858-809.152
|804.896
|-
|-
| |11
| |11
| colspan="2" |C
| colspan="2" |C
|855.755
|848.79-865.613
|893.379
|865.821-867.644
|864.168
|858.157-874.981
|871.791
|860.695-877.518
|872.5785
|869.984-886.808
|880.203
|873.243-890.067
|885.385
|-
|-
| |12
| |12
| colspan="2" |D
| colspan="2" |D
|933.551
|925.952-944.305
|941.868
|928.168-946.521
|942.727
|936.171-954.527
|951.045
|938.94-957.293
|951.903
|949.074-967.427
|960.221
|952.692-970.982
|965.875
|-
|-
| |13
| |13
|E
|E
| |Eb
| |Eb
|1011.347
|1003.115-1022.997
|1020.357
|1005.516-1025.398
|1021.288
|1014.186-1034.0668
|1030.2985
|1017.185-1037.067
|1031.229
|1028.163-1048.045
|1040.24
|1032.015-1051.8975
|1046.364
|-
|-
|14
|14
|F\\
|F\\
|D#v/Eb^
|D#v/Eb^
|1089.143
|1080.278-1101.689
|1098.846
|1082.863-1104.275
|1099.849
|1092.2-1113.612
|1109.552
|1095.43-1116.841
|1110.554
|1107.253-1128.664
|1120.258
|1111.401-1132.813
|1126.854
|-
|-
|15
|15
|Epv/F\\^
|Epv/F\\^
|D#
|D#
|1166.939
|1157.44-1180.381
|1177.335
|1160.21-1183.151
|1178.409
|1170.214-1193.1555
|1188.806
|1173.675-1196.616
|1189.878
|1186.3425-1209.283
|1200.2765
|1190.788-1213.728
|1207.344
|-
|-
|16
|16
|Ep
|Ep
|E
|E
|1244.734
|1234.603-1259.0735
|1255.834
|1237.558-1262.028
|1256.97
|1248.229-1272.699
|1268.06
|1251.9195-1276.39
|1269.205
|1265.4315-1289.902
|1280.295
|1270.173-1294.643
|1287.833
|-
|-
|17
|17
| colspan="2" |F
| colspan="2" |F
|1322.53
|1311.767-1337.767
|1334.313
|1314.905-1340.905
|1335.53
|1326.243-1352.243
|1347.313
|1330.1645-1356.1645
|1348.53
|1344.521-1370.521
|1360.313
|1349.558-1375.558
|1368.322
|}
|}
Aeolian Mode (melodic/harmonic minor)
Aeolian Mode (melodic/harmonic minor)
Line 782: Line 733:
!Degrees
!Degrees
! colspan="2" |Octatonic
! colspan="2" |Octatonic
!Min-Max-13c
!Min-Med±13¢
!Min-Med
!Min-Max±13¢
!Min-Max
!Med-Max±13¢
!Min-Med+13c
!Med-Max-13c
!Min-Max+13c
!Med-Max
!Med-Max+13c
|-
|-
|1
|1
|G
|G
|Gb
|Gb
|81.143
|80.49-82.019
|81.254
|81.143-82.672
|81.908
|82.388-83.9175
|82.019
|82.388
|82.672
|83.153
|83.9175
|-
|-
|2
|2
|A\\
|A\\
|F#v/Gb^
|F#v/Gb^
|162.286
|160.979-164.038
|162.509
|162.286-165.345
|163.815
|164.776-167.835
|164.038
|164.776
|165.345
|166.306
|167.835
|-
|-
|3
|3
|Gpv/A\\^
|Gpv/A\\^
|F#
|F#
|243.429
|241.469-246.057
|243.763
|243.429-248.017
|245.723
|247.164-251.753
|246.057
|247.164
|248.017
|249.458
|251.753
|-
|-
|4
|4
|Gp
|Gp
|G
|G
|324.5715
|321.958-328.076
|325.017
|324.5715-330.689
|327.63
|329.552-335.67
|328.076
|329.552
|330.689
|332.611
|335.67
|-
|-
|5
|5
| colspan="2" |A
| colspan="2" |A
|405.714
|402.448-410.095
|406.271
|405.714-413.3615
|409.538
|411.9405-419.588
|410.095
|411.9405
|413.3615
|415.764
|419.588
|-
|-
|6
|6
| colspan="2" |B
| colspan="2" |B
|486.857
|482.937-492.114
|487.526
|486.857-496.034
|491.4455
|494.329-503.505
|492.114
|494.329
|496.034
|498.917
|503.505
|-
|-
|7
|7
|H
|H
|Hb
|Hb
|568
|563.427-574.133
|568.78
|568-578.716
|573.353
|576.717-587.423
|574.133
|576.717
|578.716
|582.07
|587.423
|-
|-
|8
|8
|C\\
|C\\
|B#v/Hb^
|B#v/Hb^
|649.143
|643.917-656.152
|650.034
|649.143-661.378
|655.261
|659.105-671.34
|656.152
|659.105
|661.378
|665.2225
|671.34
|-
|-
|9
|9
|Hpv/C\\^
|Hpv/C\\^
|B#
|B#
|730.286
|724.406-738.171
|731.2885
|730.286-744.051
|737.168
|741.493-755.258
|738.171
|741.493
|744.051
|748.375
|755.258
|-
|-
|10
|10
|Hp
|Hp
|H
|H
|811.429
|804.896-820.19
|812.543
|811.429-826.723
|819.076
|823.881-839.175
|820.19
|823.881
|826.723
|831.528
|839.175
|-
|-
|11
|11
|C
|C
|C
|C
|892.572
|885.385-902.209
|893.797
|892.572-909.395
|900.983
|906.269-923.093
|902.209
|906.269
|909.395
|914.681
|923.093
|-
|-
|12
|12
|D
|D
|D
|D
|973.715
|965.875-984.228
|975.051
|973.715-992.0675
|982.891
|988.657-1007.01
|984.228
|988.657
|992.0675
|997.833
|1007.01
|-
|-
|13
|13
|E
|E
|Eb
|Eb
|1054.857
|1046.364-1066.247
|1056.306
|1054.857-1074.74
|1064.799
|1071.045-1090.928
|1066.247
|1071.045
|1074.74
|1080.986
|1090.928
|-
|-
|14
|14
|F\\
|F\\
|D#v/Eb^
|D#v/Eb^
|1136
|1126.854-1148.266
|1137.56
|1136-1157.412
|1146.706
|1153.4335-1174.845
|1148.266
|1153.4335
|1157.412
|1164.139
|1174.845
|-
|-
|15
|15
|Epv/F\\^
|Epv/F\\^
|D#
|D#
|1217.143
|1207.344-1230.285
|1218.814
|1217.143-1240.084
|1228.614
|1235.822-1258.762
|1230.285
|1235.822
|1240.084
|1247.292
|1258.762
|-
|-
|16
|16
|Ep
|Ep
|E
|E
|1298.286
|1287.833-1312.304
|1300.0685
|1298.286-1332.757
|1310.521
|1318.21-1342.68
|1312.304
|1318.21
|1332.757
|1330.445
|1342.68
|-
|-
|17
|17
| colspan="2" |F
| colspan="2" |F
|1379.429
|1368.322-1394.322
|1381.322
|1379.429-1405.429
|1392.429
|1400.598-1426.598
|1394.322
|1400.598
|1405.429
|1413.598
|1426.598
|}
|}


[[Category:edIX]]
[[Category:edIX]]

Revision as of 03:09, 25 November 2018

This scale, a Long Common Practice minor mode, has the Grandfather 3L 5s MOS with a 4:1 ratio of large against small.

Intervals

Degrees Octatonic Phrygian Mode (aka Double) Neapolitan Temperament (natural minor) Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor) Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
Absolute Minimum Minimum Median Maximum Intense Phrygian Intense Phrygian-Soft Aeolian Soft Aeolian Minimum Median Maximum
Minimum Median Maximum Minimum Median Maximum Minimum Median Maximum
1 G Gb 70.588 74.622 75.294 77.647 78.019 78.431 78.893 79.412 80 80.672 82.353 84.706
2 A\\ F#v/Gb^ 141.1765 149.244 150.588 155.294 156.037 156.863 157.7855 158.8235 160 161.3445 164.706 169.412
3 Gpv/A\\^ F# 211.765 213.8655 225.882 232.941 234.056 235.294 236.678 238.235 240 242.017 247.059 254.118
4 Gp G 282.353 298.487 301.1765 310.588 312.074 313.7255 315.571 317.647 320 322.689 329.412 338.8235
5 A 352.941 373.109 376.471 387.235 390.093 392.156 394.464 397.058 400 403.361 411.765 423.529
6 B 423.529 447.731 451.765 464.822 468.1115 470.588 473.356 476.471 480 484.034 494.118 508.235
7 H Hb 494.118 522.353 527.059 542.529 546.13 549.02 552.249 555.882 560 564.706 576.471 592.941
8 C\\ B#v/Hb^ 564.706 596.975 602.353 620.1765 624.149 627.451 651.142 635.294 640 645.378 658.8235 677.647
9 Hpv/C\\^ B# 635.294 671.597 677.647 697.8235 702.167 705.882 710.035 714.706 720 726.05 741.1765 762.653
10 Hp H 705.882 746.2185 752.941 777.471 780.186 784.314 788.927 794.118 800 806.723 823.529 847.059
11 C 776.471 820.84 828.235 855.118 858.204 862.745 867.82 873.529 880 887.395 905.882 931.765
12 D 847.059 895.462 903.529 932.765 936.223 941.1765 946.713 952.941 960 968.067 988.235 1016.471
13 E Eb 917.647 970.084 978.8235 1010.412 1014.2415 1019.607 1025.6055 1032.353 1040 1048.7395 1070.588 1101.1765
14 F\\ D#v/Eb^ 988.235 1044.706 1054.118 1088.059 1092.26 1098.039 1104.598 1111.765 1120 1129.412 1152.941 1185.882
15 Epv/F\\^ D# 1058.8235 1119.328 1129.412 1164.706 1170.028 1176.471 1183.391 1191.1765 1200 1210.084 1233.294 1270.588
16 Ep E 1129.412 1193.95 1204.706 1242.353 1248.297 1254.902 1262.284 1270.588 1280 1290.756 1317.647 1355.294
17 F 1200 1268.571 1280 1320 1326.316 1333.333 1341.1765 1350 1360 1371.429 1400 1440

Most harmonic tunings

Degrees Octatonic Phrygian Mode (natural minor) Phrygian-Aeolian Mode (intermediate 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 A 384.248-391.895 394.648-405.295 409.091-416.738
6 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 C 845.345-862.169 874.826-891.65 900.001-916.824
12 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 F 1306.443-1332.443 1352.004-1378.004 1390.91-1416.91

Golden Tunings

Phrygian Mode (natural minor)

Degrees Octatonic Min-Med±13¢ Min-Max±13¢ Med-Max±13¢
1 G Gb 73.998-75.527 74.311-75.841 75.216-76.745
2 A\\ F#v/Gb^ 147.996-151.055 148.622-151.681 150.432-153.491
3 Gpv/A\\^ F# 221.994-226.582 222.9335-227.522 225.648-230.236
4 Gp G 295.992-302.109 297.245-303.362 300.864-306.982
5 A 369.99-377.637 371.556-379.203 376.08-383.727
6 B 443.9875-453.164 445.867-455.0435 451.296-460.472
7 H Hb 517.985-528.691 520.178-530.884 526.512-537.218
8 C\\ B#v/Hb^ 591.983-604.219 594.489-606.725 601.728-612.963
9 Hpv/C\\^ B# 665.981-679.746 668.8005-682.565 676.944-690.709
10 Hp H 739.979-755.273 743.112-758.406 752.16-767.454
11 C 813.977-830.801 817.423-834.246 827.376-844.166
12 D 887.975-906.328 891.734-910.087 902.592-920.945
13 E Eb 961.972-981.855 966.045-985.9275 977.808-997.69
14 F\\ D#v/Eb^ 1035.971-1057.383 1040.356-1061.768 1053.024-1074.436
15 Epv/F\\^ D# 1109.969-1132.91 1114.6675-1137.609 1128.24-1151.181
16 Ep E 1183.967-1208.437 1188.979-1213.449 1203.456-1227.926
17 F 1257.965-1283.965 1263.29-1289.29 1278.672-1304.672

Phrygian-Aeolian Mode (intermediate minor)

Degrees Octatonic Intense Phrygian Intense Phrygian-Soft Aeolian Soft Aeolian
Min-Med/Min-Max±13¢ Med-Max±13¢ Min-Med/Min-Max±13¢ Med-Max±13¢ Min-Med/Min-Max±13¢ Med-Max±13¢
1 G Gb 77.163-78.692 77.347-78.877 78.014-79.544 78.245-79.774 79.0895-80.618 79.385-80.915
2 A\\ F#v/Gb^ 155.325-157.384 155.695-157.7535 156.029-159.087 156.49-159.549 158.179-161.238 158.772-161.83
3 Gpv/A\\^ F# 231.488-236.076 232.042-236.63 234.043-238.631 234.735-239.323 237.268-241.857 238.157-242.746
4 Gp G 308.651-314.768 309.389-315.507 312.057-318.175 312.98-319.098 316.358-322.4755 317.543-323.661
5 A 385.814-393.4605 386.737-394.384 390.071-397.7185 391.225-398.872 395.447-403.094 396.929-404.576
6 B 462.976-472.1525 464.084-473.261 468.086-477.262 469.469-478.646 474.537-483.713 476.315-485.4913
7 H Hb 540.139-550.845 541.4315-549.423 546.1-556.806 547.715-558.421 553.627-564.332 555.7005-566.406
8 C\\ B#v/Hb^ 617.3015-629.537 618.779-631.014 624.114-636.35 625.96-638.195 632.716-644.951 635.086-647.322
9 Hpv/C\\^ B# 694.464-708.229 696.126-709.891 702.129-715.893 704.205-717.969 711.805-725.57 714.805-728.237
10 Hp H 771.629-786.921 773.4735-788.768 780.143-795.437 782.45-797.744 790.895-806.189 793.858-809.152
11 C 848.79-865.613 865.821-867.644 858.157-874.981 860.695-877.518 869.984-886.808 873.243-890.067
12 D 925.952-944.305 928.168-946.521 936.171-954.527 938.94-957.293 949.074-967.427 952.692-970.982
13 E Eb 1003.115-1022.997 1005.516-1025.398 1014.186-1034.0668 1017.185-1037.067 1028.163-1048.045 1032.015-1051.8975
14 F\\ D#v/Eb^ 1080.278-1101.689 1082.863-1104.275 1092.2-1113.612 1095.43-1116.841 1107.253-1128.664 1111.401-1132.813
15 Epv/F\\^ D# 1157.44-1180.381 1160.21-1183.151 1170.214-1193.1555 1173.675-1196.616 1186.3425-1209.283 1190.788-1213.728
16 Ep E 1234.603-1259.0735 1237.558-1262.028 1248.229-1272.699 1251.9195-1276.39 1265.4315-1289.902 1270.173-1294.643
17 F 1311.767-1337.767 1314.905-1340.905 1326.243-1352.243 1330.1645-1356.1645 1344.521-1370.521 1349.558-1375.558

Aeolian Mode (melodic/harmonic minor)

Degrees Octatonic Min-Med±13¢ Min-Max±13¢ Med-Max±13¢
1 G Gb 80.49-82.019 81.143-82.672 82.388-83.9175
2 A\\ F#v/Gb^ 160.979-164.038 162.286-165.345 164.776-167.835
3 Gpv/A\\^ F# 241.469-246.057 243.429-248.017 247.164-251.753
4 Gp G 321.958-328.076 324.5715-330.689 329.552-335.67
5 A 402.448-410.095 405.714-413.3615 411.9405-419.588
6 B 482.937-492.114 486.857-496.034 494.329-503.505
7 H Hb 563.427-574.133 568-578.716 576.717-587.423
8 C\\ B#v/Hb^ 643.917-656.152 649.143-661.378 659.105-671.34
9 Hpv/C\\^ B# 724.406-738.171 730.286-744.051 741.493-755.258
10 Hp H 804.896-820.19 811.429-826.723 823.881-839.175
11 C C 885.385-902.209 892.572-909.395 906.269-923.093
12 D D 965.875-984.228 973.715-992.0675 988.657-1007.01
13 E Eb 1046.364-1066.247 1054.857-1074.74 1071.045-1090.928
14 F\\ D#v/Eb^ 1126.854-1148.266 1136-1157.412 1153.4335-1174.845
15 Epv/F\\^ D# 1207.344-1230.285 1217.143-1240.084 1235.822-1258.762
16 Ep E 1287.833-1312.304 1298.286-1332.757 1318.21-1342.68
17 F 1368.322-1394.322 1379.429-1405.429 1400.598-1426.598
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