User:Moremajorthanmajor/14edIX: Difference between revisions

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==Intervals==
==Intervals==
{| class="wikitable"
{| class="wikitable"
! rowspan="3" |Degrees
! rowspan="3" |Octatonic
! colspan="4" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
! colspan="9" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
! colspan="3" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
|-
|-
! rowspan="2" |Absolute Minimum
! rowspan="2" |Degrees
! rowspan="2" |Minimum
! rowspan="2" |Octatonic
! rowspan="2" |Median
! colspan="3" |Soft Phrygian
! rowspan="2" |Maximum
! colspan="4" |Phrygian
! colspan="3"|Intense Phrygian
|-
!Minimum
!Median
!Maximum
!Minimum
!Median
!15/7±13¢
!Maximum
|-
|1
|G#/Ab
|85.714
!89.61
! colspan="2" |89.796
!91.244
|93.317-95.1745
|94.286
|-
|2
|A
|171.429
!179.221
! colspan="2" |179.592
!182.4885
|186.635-190.349
|188.571
|-
|3
|A#/Bb
|257.143
!268.831
! colspan="2" |269.388
!273.733
|279.952-285.5235
|282.857
|-
|4
|B
|342.857
!358.442
! colspan="2" |359.184
!364.977
|373.269-380.698
|377.143
|-
|5
|B#/Cb
|428.571
!448.052
! colspan="2" |448.98
!456.221
|466.587-475.872
|471.429
|-
|6
|C
|514.286
!537.662
! colspan="2" |538.776
!547.465
|559.904-571.047
|565.714
|-
|7
|Q
|600
!627.273
! colspan="2" |628.571
!638.71
|653.224-666.221
|660
|-
|8
|Q#/Db
|685.714
!716.883
! colspan="2" |718.367
!729.954
|746.539-761.396
|754.286
|-
|9
|D
|771.429
!806.4935
! colspan="2" |808.163
!821.198
|839.856-856.57
|848.571
|-
|10
|D#/Eb
|857.143
!896.103
! colspan="2" |897.959
!912.442
|933.173-951.745
|942.857
|-
|11
|E
|942.857
!985.714
! colspan="2" |987.755
!1003.687
|1026.491-1046.919
|1037.143
|-
|12
|E#/Fb
|1028.571
!1075.325
! colspan="2" |1077.551
!1094.931
|1119.808-1142.094
|1131.429
|-
|13
|F
|1114.286
!1164.935
! colspan="2" |1167.735
!1186.175
|1213.1255-1237.268
|1225.714
|-
|14
|G
|1200
|1254.5455
| colspan="2" |1257.143
|1277.419
|1306.443-1332.443
|1320
|}
{| class="wikitable"
|-
! rowspan="2" |Degrees
! colspan="2" rowspan="2" |Octatonic
! colspan="3" |Intense Phrygian
! colspan="3" |Intense Phrygian-Soft Aeolian
! colspan="3" |Intense Phrygian-Soft Aeolian
! colspan="3" |Soft Aeolian
! colspan="4" |Soft Aeolian
! rowspan="2" |Minimum
! rowspan="2" |Median
! rowspan="2" |Maximum
|-
|-
!Minimum
!Minimum
Line 27: Line 158:
!Minimum
!Minimum
!Median
!Median
!11/5±13¢
!Maximum
!Maximum
|-
|-
| |1
|1
| |F#/Gb
|F#/Gb
|85.714
|G#/Ab
|89.143
|94.286
|91.429
| colspan="2" |94.286
|94.737
|94.737
| colspan="2" |95.238
| colspan="2" |95.238
Line 40: Line 170:
| colspan="2" |96.429
| colspan="2" |96.429
|97.143
|97.143
| colspan="2" |97.959
|96.572-98.429
|100
|97.959
|102.857
|-
|-
| |2
|2
| |G
|G
|171.429
|A
|178.286
|188.571
|182.857
| colspan="2" |188.571
|189.473
|189.473
| colspan="2" |190.476
| colspan="2" |190.476
Line 55: Line 182:
| colspan="2" |192.857
| colspan="2" |192.857
|194.286
|194.286
| colspan="2" |195.918
|193.1435-196.858
|200
|195.918
|205.714
|-
|-
| |3
|3
| |G#/Ab
|G#/Ab
|257.143
|A#/Bb
|267.429
|282.857
|274.286
| colspan="2" |282.857
|284.2105
|284.2105
| colspan="2" |285.714
| colspan="2" |285.714
Line 70: Line 194:
| colspan="2" |289.286
| colspan="2" |289.286
|291.429
|291.429
| colspan="2" |293.878
|289.715-295.287
|300
|293.878
|308.571
|-
|-
| |4
|4
| |A
|A
|342.857
|B
|356.571
|377.143
|365.714
| colspan="2" |377.143
|378.947
|378.947
| colspan="2" |380.952
| colspan="2" |380.952
Line 85: Line 206:
| colspan="2" |385.714
| colspan="2" |385.714
|388.571
|388.571
| colspan="2" |391.836
|386.287-393.7155
|400
|391.836
|411.429
|-
|-
| |5
|5
| |A#/Bb
|A#/Bb
|428.571
|B#/Cb
|445.714
|471.429
|467.143
| colspan="2" |471.429
|473.684
|473.684
| colspan="2" |476.1905
| colspan="2" |476.1905
Line 100: Line 218:
| colspan="2" |482.143
| colspan="2" |482.143
|485.714
|485.714
| colspan="2" |489.796
|482.859-492.144
|500
|489.796
|514.286
|-
|-
| |6
|6
| |B
|B
|514.286
|C
|534.857
|565.714
|548.571
| colspan="2" |565.714
|568.421
|568.421
| colspan="2" |571.429
| colspan="2" |571.429
Line 115: Line 230:
| colspan="2" |578.571
| colspan="2" |578.571
|582.857
|582.857
| colspan="2" |587.755
|579.43-590.573
|600
|587.755
|617.143
|-
|-
| |7
|7
| |H
|H
|600
|Q
|624
|660
|640
| colspan="2" |660
|663.158
|663.158
| colspan="2" |666.667
| colspan="2" |666.667
Line 130: Line 242:
| colspan="2" |675
| colspan="2" |675
|680
|680
| colspan="2" |685.714
|676.002-689.002
|700
|685.714
|720
|-
|-
| |8
|8
| |H#/Cb
|H#/Cb
|685.714
|Q#/Db
|713.143
|754.286
|731.429
| colspan="2" |754.286
|757.894
|757.894
| colspan="2" |761.905
| colspan="2" |761.905
Line 145: Line 254:
| colspan="2" |771.429
| colspan="2" |771.429
|777.143
|777.143
| colspan="2" |783.6735
|772.574-787.431
|800
|783.6735
|822.857
|-
|-
| |9
|9
| |C
|C
|771.429
|D
|802.286
|848.571
|822.857
| colspan="2" |848.571
|853.632
|853.632
| colspan="2" |857.143
| colspan="2" |857.143
Line 160: Line 266:
| colspan="2" |867.857
| colspan="2" |867.857
|874.286
|874.286
| colspan="2" |881.633
|869.146-885.86
|900
|881.633
|925.714
|-
|-
| |10
|10
| |C#/Db
|C#/Db
|857.143
|D#/Eb
|891.429
|942.857
|914.286
| colspan="2" |942.857
|947.368
|947.368
| colspan="2" |952.381
| colspan="2" |952.381
Line 175: Line 278:
| colspan="2" |964.286
| colspan="2" |964.286
|971.429
|971.429
| colspan="2" |979.592
|965.717-984.289
|1000
|979.592
|1028.571
|-
|-
| |11
|11
| |D
|D
|942.857
|E
|980.571
|1037.143
|1005.714
| colspan="2" |1037.143
|1042.105
|1042.105
| colspan="2" |1047.619
| colspan="2" |1047.619
Line 190: Line 290:
| colspan="2" |1060.714
| colspan="2" |1060.714
|1068.571
|1068.571
| colspan="2" |1077.551
|1062.289-1082.718
|1100
|1077.551
|-
|12
|D#/Eb
|E#/Fb
|1131.429
|1131.429
|-
| |12
| |D#/Eb
|1028.571
|1069.714
|1097.143
| colspan="2" |1131.429
|1136.842
|1136.842
| colspan="2" |1142.857
| colspan="2" |1142.857
Line 205: Line 302:
| colspan="2" |1157.143
| colspan="2" |1157.143
|1165.714
|1165.714
| colspan="2" |1175.51
|1158.861-1181.1465
|1200
|1175.51
|1234.286
|-
|-
| |13
|13
| |E
|E
|1114.286
|F
|1158.857
|1225.714
|1188.571
| colspan="2" |1225.714
|1231.579
|1231.579
| colspan="2" |1238.095
| colspan="2" |1238.095
Line 220: Line 314:
| colspan="2" |1253.571
| colspan="2" |1253.571
|1262.857
|1262.857
| colspan="2" |1273.469
|1255.4325-1279.575
|1300
|1273.469
|1337.143
|-
|-
|14
|14
|F
|F
|1200
|G
|1268.571
|1320
|1280
| colspan="2" |1320
|1326.316
|1326.316
| colspan="2" |1333.333
| colspan="2" |1333.333
Line 235: Line 326:
| colspan="2" |1350
| colspan="2" |1350
|1360
|1360
| colspan="2" |1371.429
|1352.004-1378.004
|1400
|1371.429
|1440
|}
|}Most harmonic tunings
{| class="wikitable"
{| class="wikitable"
|-
! rowspan="2" |Degrees
! rowspan="2" |Degrees
! rowspan="2" |Octatonic
! rowspan="2" |Octatonic
!Phrygian Mode (natural minor)
! colspan="3" |Aeolian
!Phrygian-Aeolian Mode (intermediate minor)
! colspan="4" |Intense Aeolian
!Aeolian Mode (melodic/harmonic minor)
|-
|-
!15/7±13¢
!Minimum
!11/5±13¢
!Median
!Maximum
!Minimum
!9/4±13¢
!9/4±13¢
!Median
!Maximum
|-
|-
| |1
|1
| |F#/Gb
|F#/Gb
|93.317-95.1745
|97.959
|96.572-98.429
|98.901
| colspan="2" |100
|99.351-101.208
|99.351-101.208
!101.299
|102.857
|-
|-
| |2
|2
| |G
|G
|186.635-190.349
|195.918
|193.1435-196.858
|197.802
| colspan="2" |200
|198.701-202.416
|198.701-202.416
!202.597
|205.714
|-
|-
| |3
|3
| |G#/Ab
|G#/Ab
|279.952-285.5235
|293.878
|289.715-295.287
|296.703
| colspan="2" |300
|298.052-303.624
|298.052-303.624
!303.896
|308.571
|-
|-
| |4
|4
| |A
|A
|373.269-380.698
|391.836
|386.287-393.7155
|395.604
| colspan="2" |400
|397.403-404.831
|397.403-404.831
!405.195
|411.429
|-
|-
| |5
|5
| |A#/Bb
|A#/Bb
|466.587-475.872
|489.796
|482.859-492.144
|494.5055
| colspan="2" |500
|496.754-506.039
|496.754-506.039
!506.4935
|514.286
|-
|-
| |6
|6
| |B
|B
|559.904-571.047
|587.755
|579.43-590.573
|593.407
| colspan="2" |600
|596.104-607.247
|596.104-607.247
!607.792
|617.143
|-
|-
| |7
|7
| |H
|H
|653.224-666.221
|685.714
|676.002-689.002
|692.308
| colspan="2" |700
|695.455-708.455
|695.455-708.455
!709.091
|720
|-
|-
| |8
|8
| |H#/Cb
|H#/Cb
|746.539-761.396
|783.6735
|772.574-787.431
|791.209
| colspan="2" |800
|794.805-809.663
|794.805-809.663
!810.39
|822.857
|-
|-
| |9
|9
| |C
|C
|839.856-856.57
|881.633
|869.146-885.86
|890.11
| colspan="2" |900
|894.156-910.871
|894.156-910.871
!911.688
|925.714
|-
|-
| |10
|10
| |C#/Db
|C#/Db
|933.173-951.745
|979.592
|965.717-984.289
|989.011
| colspan="2" |1000
|993.507-1012.079
|993.507-1012.079
!1012.987
|1028.571
|-
|-
| |11
|11
| |D
|D
|1026.491-1046.919
|1077.551
|1062.289-1082.718
|1087.912
| colspan="2" |1100
|1092.858-1113.286
|1092.858-1113.286
!1114.286
|1131.429
|-
|-
| |12
|12
| |D#/Eb
|D#/Eb
|1119.808-1142.094
|1175.51
|1158.861-1181.1465
|1186.813
| colspan="2" |1200
|1192.209-1214.494
|1192.209-1214.494
!1215.584
|1234.286
|-
|-
| |13
|13
| |E
|E
|1213.1255-1237.268
|1273.469
|1255.4325-1279.575
|1285.714
| colspan="2" |1300
|1291.559-1315.702
|1291.559-1315.702
!1316.883
|1337.143
|-
|-
|14
|14
|F
|F
|1306.443-1332.443
|1371.429
|1352.004-1378.004
|1384.615
| colspan="2" |1400
|1390.91-1416.91
|1390.91-1416.91
|}Golden Tunings
|1418.182
 
|1440
Phrygian Mode (natural minor)
|}Phrygian Mode (Neapolitan minor/"major")
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="2" |Octatonic
! colspan="2" |Soft Phrygian
! colspan="3" |Phrygian
|-
|-
!Degrees
!Min-Med±13¢
!Octatonic
!Min-Max/Med-Max±13¢
!Min-Med±13¢
!Min-Med±13¢
!Min-Max±13¢
!Min-Max±13¢
Line 346: Line 482:
|-
|-
| |1
| |1
| |F#/Gb
| |G#/Ab
|88.575-90.4325
|88.751-90.608
|89.855-91.712
|89.855-91.712
|90.235-92.092
|90.235-92.092
Line 352: Line 490:
|-
|-
| |2
| |2
| |G
| |A
|177.151-180.865
|177.501-181.216
|179.709-183.4235
|179.709-183.4235
|180.47-184.184
|180.47-184.184
Line 358: Line 498:
|-
|-
| |3
| |3
| |G#/Ab
| |A#/Bb
|265.756-271.2975
|266.252-271.823
|269.564-275.135
|269.564-275.135
|270.705-276.276
|270.705-276.276
Line 364: Line 506:
|-
|-
| |4
| |4
| |A
| |B
|354.301-361.73
|355.003-362.431
|359.4185-366.847
|359.4185-366.847
|360.94-368.3685
|360.94-368.3685
Line 370: Line 514:
|-
|-
| |5
| |5
| |A#/Bb
| |B#/Cb
|442.877-452.1625
|443.753-453.039
|449.273-458.559
|449.273-458.559
|451.175-460.461
|451.175-460.461
Line 376: Line 522:
|-
|-
| |6
| |6
| |B
| |C
|531.452-542.595
|532.504-543.647
|539.128-550.271
|539.128-550.271
|541.41-552.553
|541.41-552.553
Line 382: Line 530:
|-
|-
| |7
| |7
| |H
| |Q
|620.0275-633.0275
|621.253-634.253
|628.982-641.982
|628.982-641.982
|631.645-644.645
|631.645-644.645
Line 388: Line 538:
|-
|-
| |8
| |8
| |H#/Cb
| |Q#/Db
|708.603-723.46
|710.005-724.862
|718.837-733.694
|718.837-733.694
|721.88-736.737
|721.88-736.737
Line 394: Line 546:
|-
|-
| |9
| |9
| |C
| |D
|797.178-813.8925
|798.756-815.47
|808.692-825.406
|808.692-825.406
|812.115-828.829
|812.115-828.829
Line 400: Line 554:
|-
|-
| |10
| |10
| |C#/Db
| |D#/Eb
|885.754-904.325
|887.507-906.078
|898.546-917.118
|898.546-917.118
|902.35-920.921
|902.35-920.921
Line 406: Line 562:
|-
|-
| |11
| |11
| |D
| |E
|974.329-994.7575
|976.257-996.686
|988.401-1008.829
|988.401-1008.829
|992.585-1013.013
|992.585-1013.013
Line 412: Line 570:
|-
|-
| |12
| |12
| |D#/Eb
| |E#/Fb
|1062.904-1085.19
|1065.008-1087.294
|1078.255-1100.541
|1078.255-1100.541
|1082.82-1105.106
|1082.82-1105.106
Line 418: Line 578:
|-
|-
| |13
| |13
| |E
| |F
|1151.48-1175.6225
|1153.759-1177.901
|1168.11-1192.253
|1168.11-1192.253
|1173.055-1197.198
|1173.055-1197.198
Line 424: Line 586:
|-
|-
|14
|14
|F
|G
|1240.055-1266.055
|1242.506-1268.506
|1257.965-1283.965
|1257.965-1283.965
|1263.29-1289.29
|1263.29-1289.29
Line 432: Line 596:
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="2" |Degrees
! rowspan="2" |Octatonic
! colspan="2" rowspan="2" |Octatonic
! colspan="2" |Intense Phrygian
! colspan="2" |Intense Phrygian
! colspan="2" |Intense Phrygian-Soft Aeolian
! colspan="2" |Intense Phrygian-Soft Aeolian
Line 446: Line 610:
|1
|1
|F#/Gb
|F#/Gb
|G#/Ab
|93.6975-95.555
|93.6975-95.555
|93.922-95.779
|93.922-95.779
Line 455: Line 620:
|2
|2
|G
|G
|A
|187.395-191.109
|187.395-191.109
|187.844-191.558
|187.844-191.558
Line 464: Line 630:
|3
|3
|G#/Ab
|G#/Ab
|A#/Bb
|281.093-286.664
|281.093-286.664
|281.765-287.337
|281.765-287.337
Line 473: Line 640:
|4
|4
|A
|A
|B
|374.79-382.219
|374.79-382.219
|375.687-383.116
|375.687-383.116
Line 482: Line 650:
|5
|5
|A#/Bb
|A#/Bb
|B#/Cb
|468.488-477.773
|468.488-477.773
|469.609-478.895
|469.609-478.895
Line 491: Line 660:
|6
|6
|B
|B
|C
|562.185-573.328
|562.185-573.328
|563.531-574.674
|563.531-574.674
Line 500: Line 670:
|7
|7
|H
|H
|Q
|655.883-668.883
|655.883-668.883
|657.4525-670.4525
|657.4525-670.4525
Line 509: Line 680:
|8
|8
|H#/Cb
|H#/Cb
|Q#/Db
|749.58-764.4375
|749.58-764.4375
|751.374-766.231
|751.374-766.231
Line 518: Line 690:
|9
|9
|C
|C
|D
|843.278-859.992
|843.278-859.992
|845.296-862.01
|845.296-862.01
Line 527: Line 700:
|10
|10
|C#/Db
|C#/Db
|D#/Eb
|936.975-955.5546
|936.975-955.5546
|939.218-957.789
|939.218-957.789
Line 536: Line 710:
|11
|11
|D
|D
|E
|1030.672-1051.101
|1030.672-1051.101
|1033.101-1053.568
|1033.101-1053.568
Line 545: Line 720:
|12
|12
|D#/Eb
|D#/Eb
|E#/Fb
|1124.3705-1146.656
|1124.3705-1146.656
|1127.061-1149.347
|1127.061-1149.347
Line 554: Line 730:
|13
|13
|E
|E
|F
|1218.068-1242.211
|1218.068-1242.211
|1220.983-1245.126
|1220.983-1245.126
Line 563: Line 740:
|14
|14
|F
|F
|G
|1311.767-1337.767
|1311.767-1337.767
|1314.905-1340.905
|1314.905-1340.905
Line 570: Line 748:
|1349.558-1375.558
|1349.558-1375.558
|}
|}
Aeolian Mode (melodic/harmonic minor)
Aeolian Mode (natural/harmonic minor)
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="2" |Octatonic
! colspan="2" |Aeolian
! colspan="2" |Intense Aeolian
|-
|-
!Degrees
!Min-Med/Min-Max±13¢
!Octatonic
!Med-Max-13c
!Min-Med±13¢
!Min-Med/Min-Max±13¢
!Min-Max±13¢
!Med-Max-13c
!Med-Max±13¢
|-
|-
|1
|1
|F#/Gb
|F#/Gb
|97.737-99.5945
|97.737-99.5945
|98.531-100.388
|98.216-100.074
|100.043-101.9
|100.043-101.9
|100.712-102.569
|-
|-
|2
|2
|G
|G
|195.475-199.189
|195.475-199.189
|197.061-200.776
|196.433-200.147
|200.085-203.8
|200.085-203.8
|201.424-205.138
|-
|-
|3
|3
|G#/Ab
|G#/Ab
|293.212-298.783
|293.212-298.783
|295.592-301.163
|294.649-300.221
|300.128-305.6995
|300.128-305.6995
|302.236-307.707
|-
|-
|4
|4
|A
|A
|390.949-398.378
|390.949-398.378
|394.123-401.551
|392.866-400.294
|400.171-407.599
|400.171-407.599
|402.848-410.276
|-
|-
|5
|5
|A#/Bb
|A#/Bb
|488.687-497.972
|488.687-497.972
|492.653-501.939
|491.082-500.368
|500.2135-509.499
|500.2135-509.499
|503.56-512.845
|-
|-
|6
|6
|B
|B
|586.424-597.567
|586.424-597.567
|591.184-602.327
|589.2985-600.441
|600.256-611.399
|600.256-611.399
|604.2715-615.414
|-
|-
|7
|7
|H
|H
|684.161-697.161
|684.161-697.161
|689.7145-702.7145
|687.515-700.515
|700.299-713.299
|700.299-713.299
|704.983-717.983
|-
|-
|8
|8
|H#/Cb
|H#/Cb
|781.899-796.756
|781.899-796.756
|788.245-803.102
|785.731-800.5885
|800.342-815.199
|800.342-815.199
|805.695-820.5525
|-
|-
|9
|9
|C
|C
|879.636-896.35
|879.636-896.35
|886.776-903.49
|883.948-900.662
|900.384-917.099
|900.384-917.099
|906.407-923.1215
|-
|-
|10
|10
|C#/Db
|C#/Db
|977.373-995.945
|977.373-995.945
|985.306-1003.878
|982.164-1000.7436
|1000.427-1018.9985
|1000.427-1018.9985
|1007.119-1025.691
|-
|-
|11
|11
|D
|D
|1075.111-1095.539
|1075.111-1095.539
|1083.837-1104.266
|1080.381-1100.809
|1100.47-1120.898
|1100.47-1120.898
|1107.831-1128.26
|-
|-
|12
|12
|D#/Eb
|D#/Eb
|1172.848-1195.134
|1172.848-1195.134
|1182.368-1204.653
|1178.597-1200.883
|1200.512-1222.798
|1200.512-1222.798
|1208.543-1230.829
|-
|-
|13
|13
|E
|E
|1270.585-1294.728
|1270.585-1294.728
|1280.898-1305.041
|1276.813-1300.956
|1300.555-1324.698
|1300.555-1324.698
|1309.255-1333.398
|-
|-
|14
|14
|F
|F
|1368.322-1394.322
|1368.322-1394.322
|1379.429-1405.429
|1375.03-1401.03
|1400.598-1426.598
|1400.598-1426.598
|1409.967-1435.967
|}
|}
[[Category:14-tone]]
[[Category:14-tone]]

Revision as of 03:01, 12 December 2018

This scale, a Long Common Practice minor mode,occurs in 12edo, where it is the equal division of the major ninth. It has the Macroshrutis 6L 2s MOS with a 2:1 ratio of large against small.

Intervals

Degrees Octatonic Soft Phrygian Phrygian
Minimum Median Maximum Minimum Median 15/7±13¢ Maximum
1 G#/Ab 85.714 89.61 89.796 91.244 93.317-95.1745 94.286
2 A 171.429 179.221 179.592 182.4885 186.635-190.349 188.571
3 A#/Bb 257.143 268.831 269.388 273.733 279.952-285.5235 282.857
4 B 342.857 358.442 359.184 364.977 373.269-380.698 377.143
5 B#/Cb 428.571 448.052 448.98 456.221 466.587-475.872 471.429
6 C 514.286 537.662 538.776 547.465 559.904-571.047 565.714
7 Q 600 627.273 628.571 638.71 653.224-666.221 660
8 Q#/Db 685.714 716.883 718.367 729.954 746.539-761.396 754.286
9 D 771.429 806.4935 808.163 821.198 839.856-856.57 848.571
10 D#/Eb 857.143 896.103 897.959 912.442 933.173-951.745 942.857
11 E 942.857 985.714 987.755 1003.687 1026.491-1046.919 1037.143
12 E#/Fb 1028.571 1075.325 1077.551 1094.931 1119.808-1142.094 1131.429
13 F 1114.286 1164.935 1167.735 1186.175 1213.1255-1237.268 1225.714
14 G 1200 1254.5455 1257.143 1277.419 1306.443-1332.443 1320
Degrees Octatonic Intense Phrygian Intense Phrygian-Soft Aeolian Soft Aeolian
Minimum Median Maximum Minimum Median Maximum Minimum Median 11/5±13¢ Maximum
1 F#/Gb G#/Ab 94.286 94.737 95.238 95.798 96.429 97.143 96.572-98.429 97.959
2 G A 188.571 189.473 190.476 191.597 192.857 194.286 193.1435-196.858 195.918
3 G#/Ab A#/Bb 282.857 284.2105 285.714 287.395 289.286 291.429 289.715-295.287 293.878
4 A B 377.143 378.947 380.952 383.193 385.714 388.571 386.287-393.7155 391.836
5 A#/Bb B#/Cb 471.429 473.684 476.1905 478.992 482.143 485.714 482.859-492.144 489.796
6 B C 565.714 568.421 571.429 574.79 578.571 582.857 579.43-590.573 587.755
7 H Q 660 663.158 666.667 670.588 675 680 676.002-689.002 685.714
8 H#/Cb Q#/Db 754.286 757.894 761.905 766.387 771.429 777.143 772.574-787.431 783.6735
9 C D 848.571 853.632 857.143 862.185 867.857 874.286 869.146-885.86 881.633
10 C#/Db D#/Eb 942.857 947.368 952.381 957.983 964.286 971.429 965.717-984.289 979.592
11 D E 1037.143 1042.105 1047.619 1053.7815 1060.714 1068.571 1062.289-1082.718 1077.551
12 D#/Eb E#/Fb 1131.429 1136.842 1142.857 1149.58 1157.143 1165.714 1158.861-1181.1465 1175.51
13 E F 1225.714 1231.579 1238.095 1245.378 1253.571 1262.857 1255.4325-1279.575 1273.469
14 F G 1320 1326.316 1333.333 1341.1765 1350 1360 1352.004-1378.004 1371.429
Degrees Octatonic Aeolian Intense Aeolian
Minimum Median Maximum Minimum 9/4±13¢ Median Maximum
1 F#/Gb 97.959 98.901 100 99.351-101.208 101.299 102.857
2 G 195.918 197.802 200 198.701-202.416 202.597 205.714
3 G#/Ab 293.878 296.703 300 298.052-303.624 303.896 308.571
4 A 391.836 395.604 400 397.403-404.831 405.195 411.429
5 A#/Bb 489.796 494.5055 500 496.754-506.039 506.4935 514.286
6 B 587.755 593.407 600 596.104-607.247 607.792 617.143
7 H 685.714 692.308 700 695.455-708.455 709.091 720
8 H#/Cb 783.6735 791.209 800 794.805-809.663 810.39 822.857
9 C 881.633 890.11 900 894.156-910.871 911.688 925.714
10 C#/Db 979.592 989.011 1000 993.507-1012.079 1012.987 1028.571
11 D 1077.551 1087.912 1100 1092.858-1113.286 1114.286 1131.429
12 D#/Eb 1175.51 1186.813 1200 1192.209-1214.494 1215.584 1234.286
13 E 1273.469 1285.714 1300 1291.559-1315.702 1316.883 1337.143
14 F 1371.429 1384.615 1400 1390.91-1416.91 1418.182 1440

Phrygian Mode (Neapolitan minor/"major")

Degrees Octatonic Soft Phrygian Phrygian
Min-Med±13¢ Min-Max/Med-Max±13¢ Min-Med±13¢ Min-Max±13¢ Med-Max±13¢
1 G#/Ab 88.575-90.4325 88.751-90.608 89.855-91.712 90.235-92.092 91.234-93.191
2 A 177.151-180.865 177.501-181.216 179.709-183.4235 180.47-184.184 182.667-186.382
3 A#/Bb 265.756-271.2975 266.252-271.823 269.564-275.135 270.705-276.276 274.001-279.5725
4 B 354.301-361.73 355.003-362.431 359.4185-366.847 360.94-368.3685 365.335-372.763
5 B#/Cb 442.877-452.1625 443.753-453.039 449.273-458.559 451.175-460.461 456.6685-465.954
6 C 531.452-542.595 532.504-543.647 539.128-550.271 541.41-552.553 548.002-559.145
7 Q 620.0275-633.0275 621.253-634.253 628.982-641.982 631.645-644.645 639.335-652.335
8 Q#/Db 708.603-723.46 710.005-724.862 718.837-733.694 721.88-736.737 730.67-745.257
9 D 797.178-813.8925 798.756-815.47 808.692-825.406 812.115-828.829 822.003-838.718
10 D#/Eb 885.754-904.325 887.507-906.078 898.546-917.118 902.35-920.921 913.337-931.908
11 E 974.329-994.7575 976.257-996.686 988.401-1008.829 992.585-1013.013 1007.671-1025.099
12 E#/Fb 1062.904-1085.19 1065.008-1087.294 1078.255-1100.541 1082.82-1105.106 1096.004-1118.29
13 F 1151.48-1175.6225 1153.759-1177.901 1168.11-1192.253 1173.055-1197.198 1187.338-1211.481
14 G 1240.055-1266.055 1242.506-1268.506 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 F#/Gb G#/Ab 93.6975-95.555 93.922-95.779 94.732-96.589 95.012-96.869 96.037-97.894 96.397-98.254
2 G A 187.395-191.109 187.844-191.558 189.463-193.178 190.0235-193.738 192.074-195.789 192.794-196.508
3 G#/Ab A#/Bb 281.093-286.664 281.765-287.337 284.195-289.766 285.035-290.607 288.112-293.683 289.191-294.7625
4 A B 374.79-382.219 375.687-383.116 378.9265-386.219 380.047-387.476 384.149-391.577 385.588-393.017
5 A#/Bb B#/Cb 468.488-477.773 469.609-478.895 473.658-482.944 475.059-484.3445 480.186-489.472 481.985-491.271
6 B C 562.185-573.328 563.531-574.674 568.39-579.533 570.0705-581.213 576.223-587.366 578.382-589.525
7 H Q 655.883-668.883 657.4525-670.4525 663.121-676.121 665.082-678.082 672.2605-685.2605 674.779-687.779
8 H#/Cb Q#/Db 749.58-764.4375 751.374-766.231 757.853-772.71 760.094-774.951 768.298-783.155 771.176-786.033
9 C D 843.278-859.992 845.296-862.01 852.585-869.299 855.105-871.82 864.335-881.049 867.573-884.2875
10 C#/Db D#/Eb 936.975-955.5546 939.218-957.789 947.316-965.887 950.1175-968.689 960.372-978.9435 963.97-982.542
11 D E 1030.672-1051.101 1033.101-1053.568 1042.048-1062.477 1045.129-1065.558 1056.409-1076.838 1060.367-1080.796
12 D#/Eb E#/Fb 1124.3705-1146.656 1127.061-1149.347 1136.78-1159.065 1140.141-1162.427 1152.4465-1174.732 1156.764-1179.05
13 E F 1218.068-1242.211 1220.983-1245.126 1231.511-1255.654 1235.153-1259.295 1248.484-1272.626 1253.161-1227.304
14 F G 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 (natural/harmonic minor)

Degrees Octatonic Aeolian Intense Aeolian
Min-Med/Min-Max±13¢ Med-Max-13c Min-Med/Min-Max±13¢ Med-Max-13c
1 F#/Gb 97.737-99.5945 98.216-100.074 100.043-101.9 100.712-102.569
2 G 195.475-199.189 196.433-200.147 200.085-203.8 201.424-205.138
3 G#/Ab 293.212-298.783 294.649-300.221 300.128-305.6995 302.236-307.707
4 A 390.949-398.378 392.866-400.294 400.171-407.599 402.848-410.276
5 A#/Bb 488.687-497.972 491.082-500.368 500.2135-509.499 503.56-512.845
6 B 586.424-597.567 589.2985-600.441 600.256-611.399 604.2715-615.414
7 H 684.161-697.161 687.515-700.515 700.299-713.299 704.983-717.983
8 H#/Cb 781.899-796.756 785.731-800.5885 800.342-815.199 805.695-820.5525
9 C 879.636-896.35 883.948-900.662 900.384-917.099 906.407-923.1215
10 C#/Db 977.373-995.945 982.164-1000.7436 1000.427-1018.9985 1007.119-1025.691
11 D 1075.111-1095.539 1080.381-1100.809 1100.47-1120.898 1107.831-1128.26
12 D#/Eb 1172.848-1195.134 1178.597-1200.883 1200.512-1222.798 1208.543-1230.829
13 E 1270.585-1294.728 1276.813-1300.956 1300.555-1324.698 1309.255-1333.398
14 F 1368.322-1394.322 1375.03-1401.03 1400.598-1426.598 1409.967-1435.967
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