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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.
This scale, a reformed minor mode,occurs in [[12edo]], where it is the equal division of the major ninth. It has the Long Common Practice Macroshrutis 6L 2s MOS with a 2:1 ratio of large against small. It also gives the wide values for the period of the Greater [[Silicon]] temperament.
==Intervals==
==Intervals==
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
|+
! rowspan="2" |Octatonic
!Nonet
! colspan="4" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
!Period
! colspan="3" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
!Notes
! colspan="3" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
|-
|-
!Absolute Minimum
|1/1
!Minimum
|''85.714''
!Median
|Soft Phrygian mode begins
!Maximum
! |Minimum
!Median
!Maximum
!Minimum
!Median
!Maximum
|-
|-
| |1
|23\22
| |F#/Gb
|89.610
|85.714
|
|89.143
|91.429
| colspan="2" |94.286
|95.798
| colspan="2" |97.959
|100
|102.857
|-
|-
| |2
|22\21
| |G
|89.796
|171.429
|Soft Phrygian mode ends, Thirdtone Phrygian mode begins
|178.286
|182.857
| colspan="2" |188.571
|191.597
| colspan="2" |195.918
|200
|205.714
|-
|-
| |3
|21\20
| |G#/Ab
|90.000
|257.143
|
|267.429
|274.286
| colspan="2" |282.857
|287.395
| colspan="2" |293.878
|300
|308.571
|-
|-
| |4
|20\19
| |A
|90.226
|342.857
|
|356.571
|365.714
| colspan="2" |377.143
|383.193
| colspan="2" |391.836
|400
|411.429
|-
|-
| |5
|19\18
| |A#/Bb
|90.476
|428.571
|
|445.714
|467.143
| colspan="2" |471.429
|478.992
| colspan="2" |489.796
|500
|514.286
|-
|-
| |6
|37\35
| |B
|90.612
|514.286
|
|534.857
|548.571
| colspan="2" |565.714
|574.79
| colspan="2" |587.755
|600
|617.143
|-
|-
| |7
|18\17
| |H
|90.756
|600
|
|624
|640
| colspan="2" |660
|670.588
| colspan="2" |685.714
|700
|720
|-
|-
| |8
|17\16
| |H#/Cb
|91.071
|685.714
|
|713.143
|731.429
| colspan="2" |754.286
|766.387
| colspan="2" |783.6735
|800
|822.857
|-
|-
| |9
|16\15
| |C
|91.429
|771.429
|Thirdtone Phrygian mode ends
|802.286
|822.857
| colspan="2" |848.571
|862.185
| colspan="2" |881.633
|900
|925.714
|-
|-
| |10
|15\14
| |C#/Db
|91.837
|857.143
|Semitone Phrygian mode begins
|891.429
|914.286
| colspan="2" |942.857
|957.983
| colspan="2" |979.592
|1000
|1028.571
|-
|-
| |11
|14\13
| |D
|92.308
|942.857
|
|980.571
|1005.714
| colspan="2" |1037.143
|1053.7815
| colspan="2" |1077.551
|1100
|1131.429
|-
|-
| |12
|27\25
| |D#/Eb
|92.571
|1028.571
|
|1069.714
|1097.143
| colspan="2" |1131.429
|1149.58
| colspan="2" |1175.51
|1200
|1234.286
|-
|-
| |13
|13\12
| |E
|''92.857''
|1114.286
|
|1158.857
|1188.571
| colspan="2" |1225.714
|1245.378
| colspan="2" |1273.469
|1300
|1337.143
|-
|-
|14
|12\11
|F
|93.506
|1200
|
|1268.571
|-
|1280
|11\10
| colspan="2" |1320
|94.286
|1341.1765
|Semitone Phrygian mode ends, Intense Phrygian mode begins
| colspan="2" |1371.429
|1400
|1440
|}Most harmonic tunings
{| class="wikitable"
|-
|-
! rowspan="2" |Degrees
|21\19
! rowspan="2" |Octatonic
|94.737
!Phrygian Mode (natural minor)
|
!Phrygian-Aeolian Mode (intermediate minor)
!Aeolian Mode (melodic/harmonic minor)
|-
|-
!15/7±13¢
|10\9
!11/5±13¢
|95.238
!9/4±13¢
|Intense Phrygian mode ends, Intense Phrygian-Soft Aeolian mode begins
|-
|-
| |1
|19\17
| |F#/Gb
|95.798
|93.317-95.1745
|
|96.572-98.429
|99.351-101.208
|-
|-
| |2
|9\8
| |G
|''96.429''
|186.635-190.349
|Intense Phrygian-Soft Aeolian mode ends, Soft Aeolian mode begins
|193.1435-196.858
|198.701-202.416
|-
|-
| |3
|17\15
| |G#/Ab
|97.143
|279.952-285.5235
|
|289.715-295.287
|298.052-303.624
|-
|-
| |4
|8\7
| |A
|97.959
|373.269-380.698
|Soft Aeolian mode ends, Flattone Aeolian mode begins
|386.287-393.7155
|397.403-404.831
|-
|-
| |5
|15\13
| |A#/Bb
|98.901
|466.587-475.872
|
|482.859-492.144
|496.754-506.039
|-
|-
| |6
|22\19
| |B
|99.248
|559.904-571.047
|Flattone Aeolian mode ends, Meantone Aeolian mode begins
|579.43-590.573
|596.104-607.247
|-
|-
| |7
|29\25
| |H
| 99.429
|653.224-666.221
|
|676.002-689.002
|695.455-708.455
|-
|-
| |8
|7\6
| |H#/Cb
|''100.000''
|746.539-761.396
|Meantone Aeolian mode ends, Superpyth Intense Aeolian mode begins
|772.574-787.431
|794.805-809.663
|-
|-
| |9
|20\17
| |C
|100.840
|839.856-856.57
|
|869.146-885.86
|894.156-910.871
|-
|-
| |10
|13\11
| |C#/Db
| 101.299
|933.173-951.745
|Superpyth Intense Aeolian mode ends, Ultrapyth Intense Aeolian mode begins
|965.717-984.289
|993.507-1012.079
|-
|-
| |11
|19\16
| |D
|101.786
|1026.491-1046.919
|
|1062.289-1082.718
|1092.858-1113.286
|-
|-
| |12
|6\5
| |D#/Eb
|102.857
|1119.808-1142.094
|Ultrapyth Intense Aeolian mode ends
|1158.861-1181.1465
|}Golden/Pyrite Tunings±13¢
|1192.209-1214.494
{| class="wikitable"
|-
|-
| |13
! rowspan="3" |Degrees
| |E
! rowspan="3" |Octatonic
|1213.1255-1237.268
! colspan="2" |Soft Phrygian
|1255.4325-1279.575
! colspan="4" |Phrygian
|1291.559-1315.702
|-
|-
|14
! rowspan="2" |Min-Med
|F
! rowspan="2" |Min-Max/Med-Max
|1306.443-1332.443
! colspan="2" |Thirdtone
|1352.004-1378.004
! colspan="2" |Semitone
|1390.91-1416.91
|}Golden Tunings
 
Phrygian Mode (natural minor)
{| class="wikitable"
|-
|-
!Degrees
!Min-Med/Min-Max
!Octatonic
!Med-Max
!Min-Med-13c
!Min-Med/Min-Max
!Min-Max-13c
!Med-Max
!Min-Med
!Min-Max
!Med-Max-13c
!Min-Med+13c
!Min-Max+13c
!Min-Max-13c
|-
|-
| |1
|1
| |F#/Gb
|G#/Ab
|89.855
|88.575-90.4325
|90.235
|88.751-90.608
|90.783
|89.103-91.32
|91.164
|89.871-91.7835
|91.334
|91.334-93.515
|91.712
|91.983-94.271
|92.092
|98.531
|-
|-
| |2
|2
| |G
|A
|179.709
|177.151-180.865
|180.47
|177.501-181.216
|181.566
|178.206-182.64
|182.327
|179.743-183.567
|182.667
|182.667-187.031
|183.4235
|183.965-188.543
|184.184
|197.061
|-
|-
| |3
|3
| |G#/Ab
|A#/Bb
|269.564
|265.756-271.2975
|270.705
|266.252-271.823
|272.35
|267.309-273.96
|273.491
|269.614-275.351
|274.001
|274.001-280.545
|275.135
|275.948-282.814
|276.276
|295.592
|-
|-
| |4
|4
| |A
|B
|359.4185
|354.301-361.73
|360.94
|355.003-362.431
|363.133
|356.412-365.28
|364.654
|359.4855-367.134
|365.335
|365.335-374.613
|366.847
|367.931-377.085
|368.3685
|394.123
|-
|-
| |5
|5
| |A#/Bb
|B#/Cb
|449.273
|442.877-452.1625
|451.175
|443.753-453.039
|453.916
|445.515-456.6
|455.818
|449.357-458.918
|456.6685
|456.6685-467.577
|458.559
|459.913-471.357
|460.461
|492.653
|-
|-
| |6
|6
| |B
|C
|539.128
|531.452-542.595
|541.41
|532.504-543.647
|544.699
|534.6175-547.92
|546.981
|539.228-550.701
|548.002
|548.002-561.092
|550.271
|551.896-565.628
|552.553
|591.184
|-
|-
| |7
|7
| |H
|Q
|628.982
|620.0275-633.0275
|631.645
|621.253-634.253
|635.482
|623.7205-639.24
|638.145
|629.1-642.485
|639.336
|639.335-654.335
|641.982
|643.879-659.8995
|644.645
|689.7145
|-
|-
| |8
|8
| |H#/Cb
|Q#/Db
|718.837
|708.603-723.46
|721.88
|710.005-724.862
|726.2655
|712.823-730.56
|729.3085
|718.971-734
|730.67
|730.67-748.123
|733.694
|735.861-754.171
|736.737
|788.245
|-
|-
| |9
|9
| |C
|D
|808.692
|797.178-813.8925
|812.115
|798.756-815.47
|817.049
|801.926-821.88
|820.472
|808.842-826.032
|822.003
|822.003-841.78
|825.406
|827.844848.442
|828.829
|886.776
|-
|-
| |10
|10
| |C#/Db
|D#/Eb
|898.546
|885.754-904.325
|902.35
|887.507-906.078
|907.832
|891.029-913.2
|911.636
|898.714-917.835
|913.337
|913.337-935.153
|917.118
|919.8265-942.7135
|920.921
|985.306
|-
|-
| |11
|11
| |D
|E
|988.401
|974.329-994.7575
|992.585
|976.257-996.686
|998.615
|980.132-1004.52
|1002.799
|988.585-1009.619
|1007.671
|1007.671-1028.6685
|1008.829
|1011.809-1036.985
|1013.013
|1083.837
|-
|-
| |12
|12
| |D#/Eb
|E#/Fb
|1078.255
|1062.904-1085.19
|1082.82
|1065.008-1087.294
|1089.398
|1069.235-1095.84
|1093.963
|1078.4565-1101.023
|1096.004
|1096.004-1121.1894
|1100.541
|1103.792-1131.256
|1105.106
|1182.368
|-
|-
| |13
|13
| |E
|F
|1168.11
|1151.48-1175.6225
|1173.055
|1153.759-1177.901
|1180.1815
|1158.338-1187.16
|1185.126
|1168.328-1193.186
|1187.338
|1187.338-1215.699
|1192.253
|1195.7745-1225.528
|1197.198
|1280.898
|-
|-
|14
|14
|F
|G
|1257.965
|1240.055-1266.055
|1263.29
|1242.506-1268.506
|1270.965
|1247.441-1278.48
|1276.29
|1258.199-1284.969
|1278.672
|1278.672-1309.2145
|1283.965
|1287.757-1319.799
|1289.29
|1379.429
|}
|}
Phrygian-Aeolian Mode (intermediate minor)
{| class="wikitable"
{| class="wikitable"
|-
|-
!Degrees
! rowspan="2" |Degrees
!Octatonic
! colspan="2" rowspan="2" |Octatonic
!Min-Med/Min-Max-13c
! colspan="2" |Intense Phrygian
!Med-Max-13c
! colspan="2" |Intense Phrygian-Soft Aeolian
! colspan="2" |Soft Aeolian
|-
!Min-Med/Min-Max
!Med-Max
!Min-Med/Min-Max
!Med-Max
!Min-Med/Min-Max
!Min-Med/Min-Max
!Med-Max
!Med-Max
!Min-Med/Min-Max+13c
!Med-Max+13c
!Min-Med-13c (Aeolian)
|-
|-
|1
|1
|F#/Gb
|F#/Gb
|94.4665
|G#/Ab
|95.308
|93.6975-95.555
|95.395
|93.922-95.779
|96.237
|94.732-96.589
|96.324
|95.012-96.869
|97.165
|96.037-97.894
|97.737
|96.397-98.254
|-
|-
|2
|2
|G
|G
|188.933
|A
|190.616
|187.395-191.109
|190.79
|187.844-191.558
|192.473
|189.463-193.178
|192.647
|190.0235-193.738
|194.3305
|192.074-195.789
|195.475
|192.794-196.508
|-
|-
|3
|3
|G#/Ab
|G#/Ab
|283.399
|A#/Bb
|285.924
|281.093-286.664
|286.185
|281.765-287.337
|288.71
|284.195-289.766
|288.971
|285.035-290.607
|291.496
|288.112-293.683
|293.212
|289.191-294.7625
|-
|-
|4
|4
|A
|A
|377.866
|B
|381.228
|374.79-382.219
|381.58
|375.687-383.116
|384.947
|378.9265-386.219
|385.294
|380.047-387.476
|388.661
|384.149-391.577
|390.949
|385.588-393.017
|-
|-
|5
|5
|A#/Bb
|A#/Bb
|472.332
|B#/Cb
|476.5405
|468.488-477.773
|476.975
|469.609-478.895
|481.183
|473.658-482.944
|481.618
|475.059-484.3445
|485.826
|480.186-489.472
|488.687
|481.985-491.271
|-
|-
|6
|6
|B
|B
|566.799
|C
|571.849
|562.185-573.328
|572.37
|563.531-574.674
|577.42
|568.39-579.533
|577.942
|570.0705-581.213
|582.9915
|576.223-587.366
|586.424
|578.382-589.525
|-
|-
|7
|7
|H
|H
|661.265
|Q
|667.157
|655.883-668.883
|667.765
|657.4525-670.4525
|673.658
|663.121-676.121
|674.265
|665.082-678.082
|680.157
|672.2605-685.2605
|684.161
|674.779-687.779
|-
|-
|8
|8
|H#/Cb
|H#/Cb
|755.732
|Q#/Db
|762.465
|749.58-764.4375
|763.16
|751.374-766.231
|769.893
|757.853-772.71
|770.589
|760.094-774.951
|777.322
|768.298-783.155
|781.899
|771.176-786.033
|-
|-
|9
|9
|C
|C
|850.198
|D
|857.773
|843.278-859.992
|858.555
|845.296-862.01
|866.13
|852.585-869.299
|866.912
|855.105-871.82
|874.487
|864.335-881.049
|879.636
|867.573-884.2875
|-
|-
|10
|10
|C#/Db
|C#/Db
|944.665
|D#/Eb
|953.081
|936.975-955.5546
|953.95
|939.218-957.789
|962.367
|947.316-965.887
|963.236
|950.1175-968.689
|971.652
|960.372-978.9435
|977.373
|963.97-982.542
|-
|-
|11
|11
|D
|D
|1039.131
|E
|1048.298
|1030.672-1051.101
|1049.345
|1033.101-1053.568
|1058.603
|1042.048-1062.477
|1059.56
|1045.129-1065.558
|1068.818
|1056.409-1076.838
|1075.111
|1060.367-1080.796
|-
|-
|12
|12
|D#/Eb
|D#/Eb
|1113.5975
|E#/Fb
|1143.697
|1124.3705-1146.656
|1144.74
|1127.061-1149.347
|1154.84
|1136.78-1159.065
|1155.883
|1140.141-1162.427
|1165.983
|1152.4465-1174.732
|1172.848
|1156.764-1179.05
|-
|-
|13
|13
|E
|E
|1228.064
|F
|1239.005
|1218.068-1242.211
|1240.435
|1220.983-1245.126
|1251.077
|1231.511-1255.654
|1252.207
|1235.153-1259.295
|1263.148
|1248.484-1272.626
|1270.585
|1253.161-1227.304
|-
|-
|14
|14
|F
|F
|1322.53
|G
|1334.313
|1311.767-1337.767
|1335.53
|1314.905-1340.905
|1347.313
|1326.243-1352.243
|1348.53
|1330.1645-1356.1645
|1360.313
|1344.521-1370.521
|1368.322
|1349.558-1375.558
|}
|}
Aeolian Mode (melodic/harmonic minor)
{| class="wikitable"
{| class="wikitable"
! rowspan="3" |Degrees
! rowspan="3" |Octatonic
! colspan="4" |Aeolian
! colspan="4" |Intense Aeolian
|-
! colspan="2" |Flattone
! colspan="2" |Meantone
! colspan="2" |Superpyth
! colspan="2" |Ultrapyth
|-
|-
!Degrees
!Octatonic
!Min-Max-13c
!Min-Med
!Min-Med
!Min-Max
!Med-Max~Min-Max
!Min-Med+13c
!Min-Med/Min-Max
!Med-Max-13c
!Med-Max
!Min-Max+13c
!Min-Med
!Min-Max/Med-Max
!Min-Med/Min-Max
!Med-Max
!Med-Max
!Med-Max+13c
|-
|-
|1
|1
|F#/Gb
|F#/Gb
|98.531
|97.737-99.5945
|98.666
| colspan="2" |98.0805-100.2995
|99.459
|98.574-100.431
|99.5945
|99.761-101.618
|100.043
|100.043-101.9
|100.388
|100.712-102.569
|100.971
|101.031-102.888
|101.9
|-
|-
|2
|2
|G
|G
|197.061
|195.475-199.189
|197.332
| colspan="2" |196.161-200.599
|198.918
|197.148-200.862
|199.189
|199.523-203.237
|200.085
|200.085-203.8
|200.776
|201.424-205.138
|201.943
|202.061.205.7755
|203.8
|-
|-
|3
|3
|G#/Ab
|G#/Ab
|295.592
|293.212-298.783
|295.998
| colspan="2" |294.2415-300.8985
|298.377
|295.721-301.293
|298.783
|299.284-304.885
|300.128
|300.128-305.6995
|301.163
|302.135-307.707
|302.913
|303.092-308.663
|305.6995
|-
|-
|4
|4
|A
|A
|394.123
|390.949-398.378
|394.664
| colspan="2" |392.322-401.198
|397.839
|394.295-401.724
|398.378
|399.045-406.474
|400.171
|400.171-407.599
|401.551
|402.848-410.276
|403.885
|404.122-411.551
|407.599
|-
|-
|5
|5
|A#/Bb
|A#/Bb
|492.653
|488.687-497.972
|493.3295
| colspan="2" |490.4025-501.497
|497.296
|492.869-502.155
|497.972
|498.806-508.092
|500.2135
|500.2135-509.499
|501.939
|503.56-512.845
|504.856
|505.153-514.439
|509.499
|-
|-
|6
|6
|B
|B
|591.184
|586.424-597.567
|591.9955
| colspan="2" |588.483-601.797
|597.755
|591.443-602.586
|597.567
|598.568-609.711
|600.256
|600.256-611.399
|602.327
|604.2715-615.414
|605.828
|606.1835-617.326
|611.399
|-
|-
|7
|7
|H
|H
|689.7145
|684.161-697.161
|690.661
| colspan="2" |686.5635-702.096
|696.2145
|690.017-703.017
|697.161
|698.329-711.329
|700.299
|700.299-713.299
|702.7145
|704.983-717.983
|706.799
|707.214-720.214
|713.299
|-
|-
|8
|8
|H#/Cb
|H#/Cb
|788.245
|781.899-796.756
|789.327
| colspan="2" |784.644-802.3955
|795.674
|788.5905-803.448
|796.756
|798.09-812.947
|800.342
|800.342-815.199
|803.102
|805.695-820.5525
|807.77
|808.245-823.102
|815.199
|-
|-
|9
|9
|C
|C
|886.776
|879.636-896.35
|887.993
| colspan="2" |882.724-902.695
|895.133
|887.164-903.879
|896.35
|897.8582-914.566.
|900.384
|900.384-917.099
|903.49
|906.407-923.1215
|908.7415
|909.275-925.9895
|917.099
|-
|-
|10
|10
|C#/Db
|C#/Db
|985.306
|977.373-995.945
|986.659
| colspan="2" |980.805-1002.995
|994.592
|985.738-1004.3095
|995.945
|997.613-1016.184
|1000.427
|1000.427-1018.9985
|1003.878
|1007.119-1025.691
|1009.713
|1010.306-1028.877
|1018.9985
|-
|-
|11
|11
|D
|D
|1083.837
|1075.111-1095.539
|1085.325
| colspan="2" |1078.885-1003.294
|1094.051
|1084.312-1104.7405
|1095.539
|1097.374-1117.803
|1100.47
|1100.47-1120.898
|1104.266
|1107.831-1128.26
|1110.684
|1111.134-1131.765
|1120.898
|-
|-
|12
|12
|D#/Eb
|D#/Eb
|1182.368
|1172.848-1195.134
|1183.991
| colspan="2" |1176.966-1203.594
|1193.5105
|1182.886-1205.171
|1195.134
|1197.135-1219.421
|1200.512
|1200.512-1222.798
|1204.653
|1208.543-1230.829
|1211.655
|1212.367-1234.653
|1222.798
|-
|-
|13
|13
|E
|E
|1280.898
|1270.585-1294.728
|1282.657
| colspan="2" |1275.046-1303.893
|1292.97
|1281.4956-1305.603
|1294.728
|1296.867-1321.04
|1300.555
|1300.555-1324.698
|1305.041
|1309.255-1333.398
|1312.627
|1313.3975-1337.54
|1324.698
|-
|-
|14
|14
|F
|F
|1379.429
|1368.323-1394.324
|1381.322
| colspan="2" |1373.127-1404.193
|1392.429
|1380.033-1406.033
|1394.322
|1396.658-1422.658
|1400.598
|1400.598-1426.598
|1405.429
|1409.967-1435.967
|1413.598
|1414.428-1440.428
|1426.598
|}
|}
[[Category:14-tone]]
[[Category:ed9/4]]
[[Category:edIX]]
[[Category:todo:add_definition]]
[[Category:todo:unify_precision]]
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/14edIX"