User:Moremajorthanmajor/17edIX: Difference between revisions

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! rowspan="3" |Degrees
! rowspan="3" |Degrees
! colspan="2" rowspan="3" |Octatonic
! colspan="2" rowspan="3" |Octatonic
! colspan="4" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
! colspan="5" |Soft Phrygian
! colspan="9" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
! colspan="11" |Phrygian
! colspan="3" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
|-
|-
! rowspan="2" |Absolute 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" |Minimum
! rowspan="2" |Min-Med±13¢
! rowspan="2" |Median
! rowspan="2" |Median
! rowspan="2" |Min-Max/Med-Max±13¢
! rowspan="2" |Maximum
! rowspan="2" |Maximum
! colspan="5" |Thirdtone
! colspan="6" |Semitone
|-
|-
! |Minimum
!Median
!Maximum
!Minimum
!Minimum
!Min-Med/Min-Max±13¢
!Median
!Median
!Med-Max±13¢
!Maximum
!Maximum
!Minimum
!Minimum
!Min-Med/Min-Max±13¢
!Median
!Median
!Med-Max±13¢
!15/7±13¢
!Maximum
!Maximum
|-
|-
| |1
| |1
|G
|A
| |Gb
| |Ab
|70.588
|70.588
|74.622
|72.944-74.474
|75.294
|73.797
| colspan="2" |77.647
|73.089-74.618
|78.019
| colspan="2" |73.95
| colspan="2" |78.431
|73.379-75.205
|78.893
|74.51-74.622
| colspan="2" |79.412
|74.012-75.586
|80
| colspan="2" |75.294-75.63
| colspan="2" |80.672
|75.216-77.013
|82.353
|76.235-76.471
|84.706
|75.75-77.635
|76.85-78.379
|77.647
|-
|-
| |2
| |2
|A\\
|B\\
| |F#v/Gb^
| |G#v/Ab^
|141.1765
|141.1765
|149.244
|145.889-148.948
|150.588
|147.594
| colspan="2" |155.294
|146.178-149.236
|156.037
| colspan="2" |147.899
| colspan="2" |156.863
|146.758-150.409
|157.7855
|149.02-149.244
| colspan="2" |158.8235
|148.023-151.173
|160
| colspan="2" |150.588-151.2605
| colspan="2" |161.3445
|150.432-154.025
|164.706
|152.471-152.941
|169.412
|151.501-155.2705
|153.7-156.758
|155.294
|-
|-
| |3
| |3
|Gpv/A\\^
|Apv/B\\^
| |F#
| |G#
|211.765
|211.765
|213.8655
|218.833-223.4215
|225.882
|221.39
| colspan="2" |232.941
|219.266-223.855
|234.056
| colspan="2" |221.849
| colspan="2" |235.294
|220.137-225.614
|236.678
|223.529-213.8655
| colspan="2" |238.235
|222.035-226.759
|240
| colspan="2" |225.882-226.891
| colspan="2" |242.017
|225.648-230.037
|247.059
|228.706-229.1765
|254.118
|227.251-232.906
|230.549-235.137
|232.941
|-
|-
| |4
| |4
|Gp
|Ap
| |G
| |A
|282.353
|282.353
|298.487
|291.778-297.895
|301.1765
|295.187
| colspan="2" |310.588
|292.355-298.473
|312.074
| colspan="2" |295.798
| colspan="2" |313.7255
|293.5155-300.819
|315.571
|298.039-298.487
| colspan="2" |317.647
|296.047-302.346
|320
| colspan="2" |301.1765-302.521
| colspan="2" |322.689
|300.864-308.050
|329.412
|304.941-305.647
|338.8235
|303.002-301.541
|307.398-313.516
|310.588
|-
|-
| |5
| |5
| colspan="2" |A
| colspan="2" |B
|352.941
|352.941
|373.109
|364.722-372.369
|376.471
|368.984
| colspan="2" |387.235
|365.444-373.091
|390.093
| colspan="2" |369.748
| colspan="2" |392.156
|366.894-376.0235
|394.464
|372.549-373.109
| colspan="2" |397.058
|370.059-377.932
|400
| colspan="2" |376.471-378.151
| colspan="2" |403.361
|376.08-385.063
|411.765
|381.1765-382.118
|423.529
|378.752-388.176
|384.248-391.895
|387.235
|-
|-
| |6
| |6
| colspan="2" |B
| colspan="2" |C
|423.529
|423.529
|447.731
|437.6665-446.843
|451.765
|442.781
| colspan="2" |464.822
|438.533-447.709
|468.1115
| colspan="2" |443.698
| colspan="2" |470.588
|440.273-451.228
|473.356
|447.059-447.731
| colspan="2" |476.471
|444.070-453.519
|480
| colspan="2" |451.765-453.7815
| colspan="2" |484.034
|451.296-462.075
|494.118
|457.412-458.588
|508.235
|454.5025-465.811
|461.0975-470.274
|464.822
|-
|-
| |7
| |7
|H
|Q
| |Hb
| |Qb
|494.118
|494.118
|522.353
|510.611-521.317
|527.059
|516.5775
| colspan="2" |542.529
|511.621-522.327
|546.13
| colspan="2" |517.647
| colspan="2" |549.02
|513.652-526.433
|552.249
|521.569-522.353
| colspan="2" |555.882
|518.082-529.105
|560
| colspan="2" |527.059-529.412
| colspan="2" |564.706
|526.512-539.088
|576.471
|533.647-535.294
|592.941
|530.253-543.447
|537.947.548.653
|542.529
|-
|-
| |8
| |8
|C\\
|D\\
| |B#v/Hb^
| |C#v/Qb^
|564.706
|564.706
|596.975
|583.555-595.791
|602.353
|590.374
| colspan="2" |620.1765
|584.71-596.9455
|624.149
| colspan="2" |591.597
| colspan="2" |627.451
|587.031-601.638
|651.142
|596.078-596.975
| colspan="2" |635.294
|592.094-604.6915
|640
| colspan="2" |602.353-605.042
| colspan="2" |645.378
|601.728-616.101
|658.8235
|609.882-611.235
|677.647
|606.003-621.082
|614.797-627.032
|620.1765
|-
|-
| |9
| |9
|Hpv/C\\^
|Qpv/D\\^
| |B#
| |C#
|635.294
|635.294
|671.597
|656.5-670.264
|677.647
|664.171
| colspan="2" |697.8235
|657.799-671.564
|702.167
| colspan="2" |665.546
| colspan="2" |705.882
|660.41-676.842
|710.035
|670.588-671.597
| colspan="2" |714.706
|661.1055-680.278
|720
| colspan="2" |677.647-680.672
| colspan="2" |726.05
|676.944-693.1135
|741.1765
|686.118-688.765
|762.653
|681.754-698.717
|691.646-705.411
|697.8235
|-
|-
| |10
| |10
|Hp
|Qp
| |H
| |Q
|705.882
|705.882
|746.2185
|729.444-744.738
|752.941
|737.97
| colspan="2" |777.471
|730.888-746.182
|780.186
| colspan="2" |739.496
| colspan="2" |784.314
|733.789-752.047
|788.927
|745.098-746.2185
| colspan="2" |794.118
|740.117-755.864
|800
| colspan="2" |752.941-756.3025
| colspan="2" |806.723
|752.16-770.126
|823.529
|762.353-764.706
|847.059
|757.504-776.352
|768.496-783.79
|777.471
|-
|-
| |11
| |11
| colspan="2" |C
| colspan="2" |D
|776.471
|776.471
|820.84
|802.3885-819.212
|828.235
|811.765
| colspan="2" |855.118
|803.9765-820.8
|858.204
| colspan="2" |813.445
| colspan="2" |862.745
|807.468-827.252
|867.82
|819.608-820.84
| colspan="2" |873.529
|814.129-831.451
|880
| colspan="2" |828.235-831.932
| colspan="2" |887.395
|827.376-847.139
|905.882
|838.588-841.412
|931.765
|833.255-853.988
|845.345-862.169
|855.118
|-
|-
| |12
| |12
| colspan="2" |D
| colspan="2" |E
|847.059
|847.059
|895.462
|875.333-893.686
|903.529
|885.5616
| colspan="2" |932.765
|877.065-895.418
|936.223
| colspan="2" |887.395
| colspan="2" |941.1765
|880.5465-902.456
|946.713
|894.118-895.462
| colspan="2" |952.941
|888.141-907.037
|960
| colspan="2" |903.529-907.563
| colspan="2" |968.067
|902.592-924.151
|988.235
|914.8235-917.882
|1016.471
|909.005-931.622
|922.195-940.548
|932.765
|-
|-
| |13
| |13
|E
|F
| |Eb
| |Fb
|917.647
|917.647
|970.084
|948.277-968.16
|978.8235
|959.358
| colspan="2" |1010.412
|950.154-970.0365
|1014.2415
| colspan="2" |961.3445
| colspan="2" |1019.607
|953.925-977.661
|1025.6055
|968.6275-970.084
| colspan="2" |1032.353
|962.152-982.624
|1040
| colspan="2" |978.8235-983.193
| colspan="2" |1048.7395
|977.808-1001.164
|1070.588
|991.059-994.353
|1101.1765
|984.755-1009.258
|999.0445-1018.927
|1010.412
|-
|-
|14
|14
|F\\
|F\\
|D#v/Eb^
|E#v/Fb^
|988.235
|988.235
|1044.706
|1021.222-1042.6335
|1054.118
|1033.155
| colspan="2" |1088.059
|1023.243-1044.655
|1092.26
| colspan="2" |1035.294
| colspan="2" |1098.039
|1027.304-1052.866
|1104.598
|1043.137-1044.706
| colspan="2" |1111.765
|1036.164-1058.21
|1120
| colspan="2" |1054.118-1058.8235
| colspan="2" |1129.412
|1053.024-1078.177
|1152.941
|1067.294-1080.8235
|1185.882
|1060.506-1086.893
|1075.894-1097.306
|1088.059
|-
|-
|15
|15
|Epv/F\\^
|Fpv/G\\^
|D#
|E#
|1058.8235
|1058.8235
|1119.328
|1094.166-1117.107
|1129.412
|1106.952
| colspan="2" |1164.706
|1096.332-1119.273
|1170.028
| colspan="2" |1109.244
| colspan="2" |1176.471
|1100.683-1128.0705
|1183.391
|1117.647-1119.328
| colspan="2" |1191.1765
|1110.176-1133.7965
|1200
| colspan="2" |1129.412-1134.454
| colspan="2" |1210.084
|1128.24-1155.189
|1233.294
|1143.529-1147.059
|1270.588
|1136.256-1164.5285
|1152.744-1175.685
|1164.706
|-
|-
|16
|16
|Ep
|Fp
|E
|F
|1129.412
|1129.412
|1193.95
|1167.111-1191.581
|1204.706
|1180.749
| colspan="2" |1242.353
|1169.42-1193.891
|1248.297
| colspan="2" |1183.193
| colspan="2" |1254.902
|1174.062-1203.275
|1262.284
|1192.156-1193.95
| colspan="2" |1270.588
|1184.188-1209.382
|1280
| colspan="2" |1204.706-1210.084
| colspan="2" |1290.756
|1203.456-1232.202
|1317.647
|1219.765-1223.529
|1355.294
|1212.007-1242.164
|1229.593-1254.064
|1242.353
|-
|-
|17
|17
| colspan="2" |F
| colspan="2" |G
|1200
|1200
|1268.571
|1240.055-1266.055
|1280
|1254.5455
| colspan="2" |1320
|1242.506-1268.509
|1326.316
| colspan="2" |1257.143
| colspan="2" |1333.333
|1247.441-1278.48
|1341.1765
|1266.667-1268.571
| colspan="2" |1350
|1258.199-1284.969
|1360
| colspan="2" |1280-1285.714
| colspan="2" |1371.429
|1278.672-1309.2145
|1400
|1296-1300
|1440
|1287.757-1319.799
|}Most harmonic tunings
{| class="wikitable"
|+
! rowspan="2" |Degrees
! colspan="2" rowspan="2" |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
| 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
|1306.443-1332.443
|1352.004-1378.004
|1320
|1390.91-1416.91
|}
|}
Golden Tunings
Phrygian Mode (natural minor)
{| class="wikitable"
{| class="wikitable"
|-
|-
!Degrees
! colspan="2" |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
| colspan="2" |A
|369.99-377.637
|371.556-379.203
|376.08-383.727
|-
| |6
| colspan="2" |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
| colspan="2" |C
|813.977-830.801
|817.423-834.246
|827.376-844.166
|-
| |12
| colspan="2" |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
| colspan="2" |F
|1257.965-1283.965
|1263.29-1289.29
|1278.672-1304.672
|}
Phrygian-Aeolian Mode (intermediate minor)
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="2" |Degrees
! colspan="2" rowspan="2" |Octatonic
! colspan="4" rowspan="2" |Octatonic
! colspan="2" |Intense Phrygian
! colspan="5" |Intense Phrygian
! colspan="2" |Intense Phrygian-Soft Aeolian
! colspan="5" |Intense Phrygian-Soft Aeolian
! colspan="2" |Soft Aeolian
! colspan="6" |Soft Aeolian
|-
|-
!Minimum
!Min-Med/Min-Max±13¢
!Min-Med/Min-Max±13¢
!Median
!Med-Max±13¢
!Med-Max±13¢
!Maximum
!Minimum
!Min-Med/Min-Max±13¢
!Min-Med/Min-Max±13¢
!Median
!Med-Max±13¢
!Med-Max±13¢
!Maximum
!Minimum
!Min-Med/Min-Max±13¢
!Min-Med/Min-Max±13¢
!Median
!Med-Max±13¢
!Med-Max±13¢
!11/5±13¢
!Maximum
|-
|-
| |1
|1
|G
|G
| |Gb
|Gb
|A
|Ab
|77.647
|77.163-78.692
|77.163-78.692
|78.019
|77.347-78.877
|77.347-78.877
| colspan="2" |78.431
|78.014-79.544
|78.014-79.544
|78.893
|78.245-79.774
|78.245-79.774
| colspan="2" |79.412
|79.0895-80.618
|79.0895-80.618
|80
|79.385-80.915
|79.385-80.915
|79.53-81.059
|80.672
|-
|-
| |2
|2
|A\\
|A\\
| |F#v/Gb^
|F#v/Gb^
|B\\
|G#v/Ab^
|155.294
|155.325-157.384
|155.325-157.384
|156.037
|155.695-157.7535
|155.695-157.7535
| colspan="2" |156.863
|156.029-159.087
|156.029-159.087
|157.7855
|156.49-159.549
|156.49-159.549
| colspan="2" |158.8235
|158.179-161.238
|158.179-161.238
|160
|158.772-161.83
|158.772-161.83
|159.059-162.118
|161.3445
|-
|-
| |3
|3
|Gpv/A\\^
|Gpv/A\\^
| |F#
|F#
|Apv/B\\^
|G#
|232.941
|231.488-236.076
|231.488-236.076
|234.056
|232.042-236.63
|232.042-236.63
| colspan="2" |235.294
|234.043-238.631
|234.043-238.631
|236.678
|234.735-239.323
|234.735-239.323
| colspan="2" |238.235
|237.268-241.857
|237.268-241.857
|240
|238.157-242.746
|238.157-242.746
|238.589-243.177
|242.017
|-
|-
| |4
|4
|Gp
|Gp
| |G
|G
|Ap
|A
|310.588
|308.651-314.768
|308.651-314.768
|312.074
|309.389-315.507
|309.389-315.507
| colspan="2" |313.7255
|312.057-318.175
|312.057-318.175
|315.571
|312.98-319.098
|312.98-319.098
| colspan="2" |317.647
|316.358-322.4755
|316.358-322.4755
|320
|317.543-323.661
|317.543-323.661
|318.119-324.236
|322.689
|-
|-
| |5
|5
| colspan="2" |A
| colspan="2" |A
| colspan="2" |B
|387.235
|385.814-393.4605
|385.814-393.4605
|390.093
|386.737-394.384
|386.737-394.384
| colspan="2" |392.156
|390.071-397.7185
|390.071-397.7185
|394.464
|391.225-398.872
|391.225-398.872
| colspan="2" |397.058
|395.447-403.094
|395.447-403.094
|400
|396.929-404.576
|396.929-404.576
|394.648-405.295
|403.361
|-
|-
| |6
|6
| colspan="2" |B
| colspan="2" |B
| colspan="2" |C
|464.822
|462.976-472.1525
|462.976-472.1525
|468.1115
|464.084-473.261
|464.084-473.261
| colspan="2" |470.588
|468.086-477.262
|468.086-477.262
|473.356
|469.469-478.646
|469.469-478.646
| colspan="2" |476.471
|474.537-483.713
|474.537-483.713
|480
|476.315-485.4913
|476.315-485.4913
|477.178-486.354
|484.034
|-
|-
| |7
|7
|H
|H
| |Hb
|Hb
|Q
|Qb
|542.529
|540.139-550.845
|540.139-550.845
|546.13
|541.4315-549.423
|541.4315-549.423
| colspan="2" |549.02
|546.1-556.806
|546.1-556.806
|552.249
|547.715-558.421
|547.715-558.421
| colspan="2" |555.882
|553.627-564.332
|553.627-564.332
|560
|555.7005-566.406
|555.7005-566.406
|556.707-567.4135
|564.706
|-
|-
| |8
|8
|C\\
|C\\
| |B#v/Hb^
|B#v/Hb^
|D\\
|C#v/Qb^
|620.1765
|617.3015-629.537
|617.3015-629.537
|624.149
|618.779-631.014
|618.779-631.014
| colspan="2" |627.451
|624.114-636.35
|624.114-636.35
|651.142
|625.96-638.195
|625.96-638.195
| colspan="2" |635.294
|632.716-644.951
|632.716-644.951
|640
|635.086-647.322
|635.086-647.322
|636.237-648.473
|645.378
|-
|-
| |9
|9
|Hpv/C\\^
|Hpv/C\\^
| |B#
|B#
|Qpv/D\\^
|C#
|697.8235
|694.464-708.229
|694.464-708.229
|702.167
|696.126-709.891
|696.126-709.891
| colspan="2" |705.882
|702.129-715.893
|702.129-715.893
|710.035
|704.205-717.969
|704.205-717.969
| colspan="2" |714.706
|711.805-725.57
|711.805-725.57
|720
|714.805-728.237
|714.805-728.237
|715.767-729.532
|726.05
|-
|-
| |10
|10
|Hp
|Hp
| |H
|H
|Qp
|Q
|777.471
|771.629-786.921
|771.629-786.921
|780.186
|773.4735-788.768
|773.4735-788.768
| colspan="2" |784.314
|780.143-795.437
|780.143-795.437
|788.927
|782.45-797.744
|782.45-797.744
| colspan="2" |794.118
|790.895-806.189
|790.895-806.189
|800
|793.858-809.152
|793.858-809.152
|795.297-810.591
|806.723
|-
|-
| |11
|11
| colspan="2" |C
| colspan="2" |C
| colspan="2" |D
|855.118
|848.79-865.613
|848.79-865.613
|858.204
|865.821-867.644
|865.821-867.644
| colspan="2" |862.745
|858.157-874.981
|858.157-874.981
|867.82
|860.695-877.518
|860.695-877.518
| colspan="2" |873.529
|869.984-886.808
|869.984-886.808
|880
|873.243-890.067
|873.243-890.067
|874.826-891.65
|887.395
|-
|-
| |12
|12
| colspan="2" |D
| colspan="2" |D
| colspan="2" |E
|932.765
|925.952-944.305
|925.952-944.305
|936.223
|928.168-946.521
|928.168-946.521
| colspan="2" |941.1765
|936.171-954.527
|936.171-954.527
|946.713
|938.94-957.293
|938.94-957.293
| colspan="2" |952.941
|949.074-967.427
|949.074-967.427
|960
|952.692-970.982
|952.692-970.982
|954.356-972.709
|968.067
|-
|-
| |13
|13
|E
|E
| |Eb
|Eb
|F
|Fb
|1010.412
|1003.115-1022.997
|1003.115-1022.997
|1014.2415
|1005.516-1025.398
|1005.516-1025.398
| colspan="2" |1019.607
|1014.186-1034.0668
|1014.186-1034.0668
|1025.6055
|1017.185-1037.067
|1017.185-1037.067
| colspan="2" |1032.353
|1028.163-1048.045
|1028.163-1048.045
|1040
|1032.015-1051.8975
|1032.015-1051.8975
|1033.886-1053.768
|1048.7395
|-
|-
|14
|14
|F\\
|F\\
|D#v/Eb^
|D#v/Eb^
|F\\
|E#v/Fb^
|1088.059
|1080.278-1101.689
|1080.278-1101.689
|1092.26
|1082.863-1104.275
|1082.863-1104.275
| colspan="2" |1098.039
|1092.2-1113.612
|1092.2-1113.612
|1104.598
|1095.43-1116.841
|1095.43-1116.841
| colspan="2" |1111.765
|1107.253-1128.664
|1107.253-1128.664
|1120
|1111.401-1132.813
|1111.401-1132.813
|1113.415-1134.827
|1129.412
|-
|-
|15
|15
|Epv/F\\^
|Epv/F\\^
|D#
|D#
|Fpv/G\\^
|E#
|1164.706
|1157.44-1180.381
|1157.44-1180.381
|1170.028
|1160.21-1183.151
|1160.21-1183.151
| colspan="2" |1176.471
|1170.214-1193.1555
|1170.214-1193.1555
|1183.391
|1173.675-1196.616
|1173.675-1196.616
| colspan="2" |1191.1765
|1186.3425-1209.283
|1186.3425-1209.283
|1200
|1190.788-1213.728
|1190.788-1213.728
|1189.945-1215.876
|1210.084
|-
|-
|16
|16
|Ep
|Ep
|E
|E
|Fp
|F
|1242.353
|1234.603-1259.0735
|1234.603-1259.0735
|1248.297
|1237.558-1262.028
|1237.558-1262.028
| colspan="2" |1254.902
|1248.229-1272.699
|1248.229-1272.699
|1262.284
|1251.9195-1276.39
|1251.9195-1276.39
| colspan="2" |1270.588
|1265.4315-1289.902
|1265.4315-1289.902
|1280
|1270.173-1294.643
|1270.173-1294.643
|1272.474-1296.945
|1290.756
|-
|-
|17
|17
| colspan="2" |F
| colspan="2" |F
| colspan="2" |G
|1320
|1311.767-1337.767
|1311.767-1337.767
|1326.316
|1314.905-1340.905
|1314.905-1340.905
| colspan="2" |1333.333
|1326.243-1352.243
|1326.243-1352.243
|1341.1765
|1330.1645-1356.1645
|1330.1645-1356.1645
| colspan="2" |1350
|1344.521-1370.521
|1344.521-1370.521
|1360
|1349.558-1375.558
|1349.558-1375.558
|1352.004-1378.004
|1371.429
|}
|}
Aeolian Mode (melodic/harmonic minor)
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! colspan="2" rowspan="2" |Octatonic
! colspan="5" |Aeolian
! colspan="6" |Intense Aeolian
|-
|-
!Degrees
!Minimum
! colspan="2" |Octatonic
!Min-Med/Min-Max±13¢
!Min-Med±13¢
!Median
!Min-Max±13¢
!Med-Max-13¢
!Med-Max±13¢
!Maximum
!Minimum
!9/4±13¢
!Min-Med/Min-Max±13¢
!Median
!Med-Max-13¢
!Maximum
|-
|-
|1
|1
|G
|G
|Gb
|Gb
|80.672
|80.49-82.019
|80.49-82.019
|81.143-82.672
!81.448
!80.884-82.4135
| colspan="2" |82.353
|81.818-83.348
|82.388-83.9175
|82.388-83.9175
!83.422
|82.939-84.469
|84.706
|-
|-
|2
|2
|A\\
|A\\
|F#v/Gb^
|F#v/Gb^
|161.3445
|160.979-164.038
|160.979-164.038
|162.286-165.345
!162.896
!161.768-164.827
| colspan="2" |164.706
|163.6365-166.695
|164.776-167.835
|164.776-167.835
!166.845
|165.8785-168.937
|169.412
|-
|-
|3
|3
|Gpv/A\\^
|Gpv/A\\^
|F#
|F#
|242.017
|241.469-246.057
|241.469-246.057
|243.429-248.017
!244.344
!343.652-247.241
| colspan="2" |247.059
|245.455-250.043
|247.164-251.753
|247.164-251.753
!250.267
|248.818-253.405
|254.118
|-
|-
|4
|4
|Gp
|Gp
|G
|G
|322.689
|321.958-328.076
|321.958-328.076
|324.5715-330.689
!325.792
!323.536-329.654
| colspan="2" |329.412
|327.272-333.391
|329.552-335.67
|329.552-335.67
!333.69
|331.757-337.875
|338.8235
|-
|-
|5
|5
| colspan="2" |A
| colspan="2" |A
|403.361
|402.448-410.095
|402.448-410.095
|405.714-413.3615
!407.24
!404.4205-412.068
| colspan="2" |411.765
|409.091-416.738
|411.9405-419.588
|411.9405-419.588
!417.112
|414.696-422.343
|423.529
|-
|-
|6
|6
| colspan="2" |B
| colspan="2" |B
|484.034
|482.937-492.114
|482.937-492.114
|486.857-496.034
!488.688
!485.305-494.481
| colspan="2" |494.118
|490.909-500.086
|494.329-503.505
|494.329-503.505
!500.535
|497.635-506.812
|508.235
|-
|-
|7
|7
|H
|H
|Hb
|Hb
|564.706
|563.427-574.133
|563.427-574.133
|568-578.716
!570.136
!566.189-576.895
| colspan="2" |576.471
|572.728-583.4335
|576.717-587.423
|576.717-587.423
!583.957
|580.575-591.2805
|592.941
|-
|-
|8
|8
|C\\
|C\\
|B#v/Hb^
|B#v/Hb^
|645.378
|643.917-656.152
|643.917-656.152
|649.143-661.378
!651.584
!647.073-359.308
| colspan="2" |658.8235
|654.546-666.781
|659.105-671.34
|659.105-671.34
!667.38
|663.514-675.749
|677.647
|-
|-
|9
|9
|Hpv/C\\^
|Hpv/C\\^
|B#
|B#
|726.05
|724.406-738.171
|724.406-738.171
|730.286-744.051
!733.032
!727.957-741.723
| colspan="2" |741.1765
|736.364-753.087
|741.493-755.258
|741.493-755.258
!750.802
|746.453-760.218
|762.653
|-
|-
|10
|10
|Hp
|Hp
|H
|H
|806.723
|804.896-820.19
|804.896-820.19
|811.429-826.723
!814.48
!808.841-824.135
| colspan="2" |823.529
|818.182-833.4765
|823.881-839.175
|823.881-839.175
!834.225
|829.392-844.686
|847.059
|-
|-
|11
|11
|C
| colspan="2" |C
|C
|887.395
|885.385-902.209
|885.385-902.209
|892.572-909.395
!895.928
!889.725-906.549
| colspan="2" |905.882
|900.001-916.824
|906.269-923.093
|906.269-923.093
!917.647
|912.331-929.155
|931.765
|-
|-
|12
|12
|D
| colspan="2" |D
|D
|968.067
|965.875-984.228
|965.875-984.228
|973.715-992.0675
!977.376
!970.609-988.962
| colspan="2" |988.235
|981.819-100.172
|988.657-1007.01
|988.657-1007.01
!1001.0695
|995.271-1013.624
|1016.471
|-
|-
|13
|13
|E
|E
|Eb
|Eb
|1048.7395
|1046.364-1066.247
|1046.364-1066.247
|1054.857-1074.74
!1058.8235
!1051.493-1071.376
| colspan="2" |1070.588
|1063.637-1083.519
|1071.045-1090.928
|1071.045-1090.928
!1084.492
|1078.21-1098.092
|1101.1765
|-
|-
|14
|14
|F\\
|F\\
|D#v/Eb^
|D#v/Eb^
|1129.412
|1126.854-1148.266
|1126.854-1148.266
|1136-1157.412
!1140.2715
!1132.3775-1153.789
| colspan="2" |1152.941
|1145.455-1166.867
|1153.4335-1174.845
|1153.4335-1174.845
!1167.914
|1161.149-1182.561
|1185.882
|-
|-
|15
|15
|Epv/F\\^
|Epv/F\\^
|D#
|D#
|1210.084
|1207.344-1230.285
|1207.344-1230.285
|1217.143-1240.084
!1221.7195
!1213.262-1236.203
| colspan="2" |1233.294
|1227.2735-1250.215
|1235.822-1258.762
|1235.822-1258.762
!1251.337
|1244.088-1267.03
|1270.588
|-
|-
|16
|16
|Ep
|Ep
|E
|E
|1290.756
|1287.833-1312.304
|1287.833-1312.304
|1298.286-1332.757
!1303.167
!1294.146-1318.616
| colspan="2" |1317.647
|1309.092-1333.562
|1318.21-1342.68
|1318.21-1342.68
!1334.759
|1327.028-1351.498
|1355.294
|-
|-
|17
|17
| colspan="2" |F
| colspan="2" |F
|1371.429
|1368.322-1394.322
|1368.322-1394.322
|1379.429-1405.429
|1384.615
|1375.03-1401.03
| colspan="2" |1400
|1390.91-1416.91
|1400.598-1426.598
|1400.598-1426.598
|1418.182
|1409.967-1435.967
|1440
|}
|}


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

Revision as of 02:58, 20 December 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 Soft Phrygian Phrygian
Minimum Min-Med±13¢ Median Min-Max/Med-Max±13¢ Maximum Thirdtone Semitone
Minimum Min-Med/Min-Max±13¢ Median Med-Max±13¢ Maximum Minimum Min-Med/Min-Max±13¢ Median Med-Max±13¢ 15/7±13¢ Maximum
1 A Ab 70.588 72.944-74.474 73.797 73.089-74.618 73.95 73.379-75.205 74.51-74.622 74.012-75.586 75.294-75.63 75.216-77.013 76.235-76.471 75.75-77.635 76.85-78.379 77.647
2 B\\ G#v/Ab^ 141.1765 145.889-148.948 147.594 146.178-149.236 147.899 146.758-150.409 149.02-149.244 148.023-151.173 150.588-151.2605 150.432-154.025 152.471-152.941 151.501-155.2705 153.7-156.758 155.294
3 Apv/B\\^ G# 211.765 218.833-223.4215 221.39 219.266-223.855 221.849 220.137-225.614 223.529-213.8655 222.035-226.759 225.882-226.891 225.648-230.037 228.706-229.1765 227.251-232.906 230.549-235.137 232.941
4 Ap A 282.353 291.778-297.895 295.187 292.355-298.473 295.798 293.5155-300.819 298.039-298.487 296.047-302.346 301.1765-302.521 300.864-308.050 304.941-305.647 303.002-301.541 307.398-313.516 310.588
5 B 352.941 364.722-372.369 368.984 365.444-373.091 369.748 366.894-376.0235 372.549-373.109 370.059-377.932 376.471-378.151 376.08-385.063 381.1765-382.118 378.752-388.176 384.248-391.895 387.235
6 C 423.529 437.6665-446.843 442.781 438.533-447.709 443.698 440.273-451.228 447.059-447.731 444.070-453.519 451.765-453.7815 451.296-462.075 457.412-458.588 454.5025-465.811 461.0975-470.274 464.822
7 Q Qb 494.118 510.611-521.317 516.5775 511.621-522.327 517.647 513.652-526.433 521.569-522.353 518.082-529.105 527.059-529.412 526.512-539.088 533.647-535.294 530.253-543.447 537.947.548.653 542.529
8 D\\ C#v/Qb^ 564.706 583.555-595.791 590.374 584.71-596.9455 591.597 587.031-601.638 596.078-596.975 592.094-604.6915 602.353-605.042 601.728-616.101 609.882-611.235 606.003-621.082 614.797-627.032 620.1765
9 Qpv/D\\^ C# 635.294 656.5-670.264 664.171 657.799-671.564 665.546 660.41-676.842 670.588-671.597 661.1055-680.278 677.647-680.672 676.944-693.1135 686.118-688.765 681.754-698.717 691.646-705.411 697.8235
10 Qp Q 705.882 729.444-744.738 737.97 730.888-746.182 739.496 733.789-752.047 745.098-746.2185 740.117-755.864 752.941-756.3025 752.16-770.126 762.353-764.706 757.504-776.352 768.496-783.79 777.471
11 D 776.471 802.3885-819.212 811.765 803.9765-820.8 813.445 807.468-827.252 819.608-820.84 814.129-831.451 828.235-831.932 827.376-847.139 838.588-841.412 833.255-853.988 845.345-862.169 855.118
12 E 847.059 875.333-893.686 885.5616 877.065-895.418 887.395 880.5465-902.456 894.118-895.462 888.141-907.037 903.529-907.563 902.592-924.151 914.8235-917.882 909.005-931.622 922.195-940.548 932.765
13 F Fb 917.647 948.277-968.16 959.358 950.154-970.0365 961.3445 953.925-977.661 968.6275-970.084 962.152-982.624 978.8235-983.193 977.808-1001.164 991.059-994.353 984.755-1009.258 999.0445-1018.927 1010.412
14 F\\ E#v/Fb^ 988.235 1021.222-1042.6335 1033.155 1023.243-1044.655 1035.294 1027.304-1052.866 1043.137-1044.706 1036.164-1058.21 1054.118-1058.8235 1053.024-1078.177 1067.294-1080.8235 1060.506-1086.893 1075.894-1097.306 1088.059
15 Fpv/G\\^ E# 1058.8235 1094.166-1117.107 1106.952 1096.332-1119.273 1109.244 1100.683-1128.0705 1117.647-1119.328 1110.176-1133.7965 1129.412-1134.454 1128.24-1155.189 1143.529-1147.059 1136.256-1164.5285 1152.744-1175.685 1164.706
16 Fp F 1129.412 1167.111-1191.581 1180.749 1169.42-1193.891 1183.193 1174.062-1203.275 1192.156-1193.95 1184.188-1209.382 1204.706-1210.084 1203.456-1232.202 1219.765-1223.529 1212.007-1242.164 1229.593-1254.064 1242.353
17 G 1200 1240.055-1266.055 1254.5455 1242.506-1268.509 1257.143 1247.441-1278.48 1266.667-1268.571 1258.199-1284.969 1280-1285.714 1278.672-1309.2145 1296-1300 1287.757-1319.799 1306.443-1332.443 1320
Degrees Octatonic Intense Phrygian Intense Phrygian-Soft Aeolian Soft Aeolian
Minimum Min-Med/Min-Max±13¢ Median Med-Max±13¢ Maximum Minimum Min-Med/Min-Max±13¢ Median Med-Max±13¢ Maximum Minimum Min-Med/Min-Max±13¢ Median Med-Max±13¢ 11/5±13¢ Maximum
1 G Gb A Ab 77.647 77.163-78.692 78.019 77.347-78.877 78.431 78.014-79.544 78.893 78.245-79.774 79.412 79.0895-80.618 80 79.385-80.915 79.53-81.059 80.672
2 A\\ F#v/Gb^ B\\ G#v/Ab^ 155.294 155.325-157.384 156.037 155.695-157.7535 156.863 156.029-159.087 157.7855 156.49-159.549 158.8235 158.179-161.238 160 158.772-161.83 159.059-162.118 161.3445
3 Gpv/A\\^ F# Apv/B\\^ G# 232.941 231.488-236.076 234.056 232.042-236.63 235.294 234.043-238.631 236.678 234.735-239.323 238.235 237.268-241.857 240 238.157-242.746 238.589-243.177 242.017
4 Gp G Ap A 310.588 308.651-314.768 312.074 309.389-315.507 313.7255 312.057-318.175 315.571 312.98-319.098 317.647 316.358-322.4755 320 317.543-323.661 318.119-324.236 322.689
5 A B 387.235 385.814-393.4605 390.093 386.737-394.384 392.156 390.071-397.7185 394.464 391.225-398.872 397.058 395.447-403.094 400 396.929-404.576 394.648-405.295 403.361
6 B C 464.822 462.976-472.1525 468.1115 464.084-473.261 470.588 468.086-477.262 473.356 469.469-478.646 476.471 474.537-483.713 480 476.315-485.4913 477.178-486.354 484.034
7 H Hb Q Qb 542.529 540.139-550.845 546.13 541.4315-549.423 549.02 546.1-556.806 552.249 547.715-558.421 555.882 553.627-564.332 560 555.7005-566.406 556.707-567.4135 564.706
8 C\\ B#v/Hb^ D\\ C#v/Qb^ 620.1765 617.3015-629.537 624.149 618.779-631.014 627.451 624.114-636.35 651.142 625.96-638.195 635.294 632.716-644.951 640 635.086-647.322 636.237-648.473 645.378
9 Hpv/C\\^ B# Qpv/D\\^ C# 697.8235 694.464-708.229 702.167 696.126-709.891 705.882 702.129-715.893 710.035 704.205-717.969 714.706 711.805-725.57 720 714.805-728.237 715.767-729.532 726.05
10 Hp H Qp Q 777.471 771.629-786.921 780.186 773.4735-788.768 784.314 780.143-795.437 788.927 782.45-797.744 794.118 790.895-806.189 800 793.858-809.152 795.297-810.591 806.723
11 C D 855.118 848.79-865.613 858.204 865.821-867.644 862.745 858.157-874.981 867.82 860.695-877.518 873.529 869.984-886.808 880 873.243-890.067 874.826-891.65 887.395
12 D E 932.765 925.952-944.305 936.223 928.168-946.521 941.1765 936.171-954.527 946.713 938.94-957.293 952.941 949.074-967.427 960 952.692-970.982 954.356-972.709 968.067
13 E Eb F Fb 1010.412 1003.115-1022.997 1014.2415 1005.516-1025.398 1019.607 1014.186-1034.0668 1025.6055 1017.185-1037.067 1032.353 1028.163-1048.045 1040 1032.015-1051.8975 1033.886-1053.768 1048.7395
14 F\\ D#v/Eb^ F\\ E#v/Fb^ 1088.059 1080.278-1101.689 1092.26 1082.863-1104.275 1098.039 1092.2-1113.612 1104.598 1095.43-1116.841 1111.765 1107.253-1128.664 1120 1111.401-1132.813 1113.415-1134.827 1129.412
15 Epv/F\\^ D# Fpv/G\\^ E# 1164.706 1157.44-1180.381 1170.028 1160.21-1183.151 1176.471 1170.214-1193.1555 1183.391 1173.675-1196.616 1191.1765 1186.3425-1209.283 1200 1190.788-1213.728 1189.945-1215.876 1210.084
16 Ep E Fp F 1242.353 1234.603-1259.0735 1248.297 1237.558-1262.028 1254.902 1248.229-1272.699 1262.284 1251.9195-1276.39 1270.588 1265.4315-1289.902 1280 1270.173-1294.643 1272.474-1296.945 1290.756
17 F G 1320 1311.767-1337.767 1326.316 1314.905-1340.905 1333.333 1326.243-1352.243 1341.1765 1330.1645-1356.1645 1350 1344.521-1370.521 1360 1349.558-1375.558 1352.004-1378.004 1371.429
Degrees Octatonic Aeolian Intense Aeolian
Minimum Min-Med/Min-Max±13¢ Median Med-Max-13¢ Maximum Minimum 9/4±13¢ Min-Med/Min-Max±13¢ Median Med-Max-13¢ Maximum
1 G Gb 80.672 80.49-82.019 81.448 80.884-82.4135 82.353 81.818-83.348 82.388-83.9175 83.422 82.939-84.469 84.706
2 A\\ F#v/Gb^ 161.3445 160.979-164.038 162.896 161.768-164.827 164.706 163.6365-166.695 164.776-167.835 166.845 165.8785-168.937 169.412
3 Gpv/A\\^ F# 242.017 241.469-246.057 244.344 343.652-247.241 247.059 245.455-250.043 247.164-251.753 250.267 248.818-253.405 254.118
4 Gp G 322.689 321.958-328.076 325.792 323.536-329.654 329.412 327.272-333.391 329.552-335.67 333.69 331.757-337.875 338.8235
5 A 403.361 402.448-410.095 407.24 404.4205-412.068 411.765 409.091-416.738 411.9405-419.588 417.112 414.696-422.343 423.529
6 B 484.034 482.937-492.114 488.688 485.305-494.481 494.118 490.909-500.086 494.329-503.505 500.535 497.635-506.812 508.235
7 H Hb 564.706 563.427-574.133 570.136 566.189-576.895 576.471 572.728-583.4335 576.717-587.423 583.957 580.575-591.2805 592.941
8 C\\ B#v/Hb^ 645.378 643.917-656.152 651.584 647.073-359.308 658.8235 654.546-666.781 659.105-671.34 667.38 663.514-675.749 677.647
9 Hpv/C\\^ B# 726.05 724.406-738.171 733.032 727.957-741.723 741.1765 736.364-753.087 741.493-755.258 750.802 746.453-760.218 762.653
10 Hp H 806.723 804.896-820.19 814.48 808.841-824.135 823.529 818.182-833.4765 823.881-839.175 834.225 829.392-844.686 847.059
11 C 887.395 885.385-902.209 895.928 889.725-906.549 905.882 900.001-916.824 906.269-923.093 917.647 912.331-929.155 931.765
12 D 968.067 965.875-984.228 977.376 970.609-988.962 988.235 981.819-100.172 988.657-1007.01 1001.0695 995.271-1013.624 1016.471
13 E Eb 1048.7395 1046.364-1066.247 1058.8235 1051.493-1071.376 1070.588 1063.637-1083.519 1071.045-1090.928 1084.492 1078.21-1098.092 1101.1765
14 F\\ D#v/Eb^ 1129.412 1126.854-1148.266 1140.2715 1132.3775-1153.789 1152.941 1145.455-1166.867 1153.4335-1174.845 1167.914 1161.149-1182.561 1185.882
15 Epv/F\\^ D# 1210.084 1207.344-1230.285 1221.7195 1213.262-1236.203 1233.294 1227.2735-1250.215 1235.822-1258.762 1251.337 1244.088-1267.03 1270.588
16 Ep E 1290.756 1287.833-1312.304 1303.167 1294.146-1318.616 1317.647 1309.092-1333.562 1318.21-1342.68 1334.759 1327.028-1351.498 1355.294
17 F 1371.429 1368.322-1394.322 1384.615 1375.03-1401.03 1400 1390.91-1416.91 1400.598-1426.598 1418.182 1409.967-1435.967 1440
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