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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"
|+
!Nonet
!Period
!Notes
|-
|-
! rowspan="2" |Degrees
|1/1
! rowspan="2" |Octatonic
|''85.714''
! colspan="3" |Soft Phrygian
|Soft Phrygian mode begins
! colspan="4" |Phrygian
|-
|-
!Minimum
|23\22
!Median
|89.610
!Maximum
|
!Minimum
!Median
!15/7±13¢
!Maximum
|-
|-
|1
|22\21
|G#/Ab
|89.796
|85.714
|Soft Phrygian mode ends, Thirdtone Phrygian mode begins
!89.61
! colspan="2" |89.796
!91.244
|93.317-95.1745
|94.286
|-
|-
|2
|21\20
|A
|90.000
|171.429
|
!179.221
! colspan="2" |179.592
!182.4885
|186.635-190.349
|188.571
|-
|-
|3
|20\19
|A#/Bb
|90.226
|257.143
|
!268.831
! colspan="2" |269.388
!273.733
|279.952-285.5235
|282.857
|-
|-
|4
|19\18
|B
|90.476
|342.857
|
!358.442
! colspan="2" |359.184
!364.977
|373.269-380.698
|377.143
|-
|-
|5
|37\35
|B#/Cb
|90.612
|428.571
|
!448.052
! colspan="2" |448.98
!456.221
|466.587-475.872
|471.429
|-
|-
|6
|18\17
|C
|90.756
|514.286
|
!537.662
! colspan="2" |538.776
!547.465
|559.904-571.047
|565.714
|-
|-
|7
|17\16
|Q
|91.071
|600
|
!627.273
! colspan="2" |628.571
!638.71
|653.224-666.221
|660
|-
|-
|8
|16\15
|Q#/Db
|91.429
|685.714
|Thirdtone Phrygian mode ends
!716.883
! colspan="2" |718.367
!729.954
|746.539-761.396
|754.286
|-
|-
|9
|15\14
|D
|91.837
|771.429
|Semitone Phrygian mode begins
!806.4935
! colspan="2" |808.163
!821.198
|839.856-856.57
|848.571
|-
|-
|10
|14\13
|D#/Eb
|92.308
|857.143
|
!896.103
! colspan="2" |897.959
!912.442
|933.173-951.745
|942.857
|-
|-
|11
|27\25
|E
|92.571
|942.857
|
!985.714
! colspan="2" |987.755
!1003.687
|1026.491-1046.919
|1037.143
|-
|-
|12
|13\12
|E#/Fb
|''92.857''
|1028.571
|
!1075.325
! colspan="2" |1077.551
!1094.931
|1119.808-1142.094
|1131.429
|-
|-
|13
|12\11
|F
|93.506
|1114.286
|
!1164.935
! colspan="2" |1167.735
!1186.175
|1213.1255-1237.268
|1225.714
|-
|-
|14
|11\10
|G
|94.286
|1200
|Semitone Phrygian mode ends, Intense Phrygian mode begins
|1254.5455
| colspan="2" |1257.143
|1277.419
|1306.443-1332.443
|1320
|}
{| class="wikitable"
|-
|-
! rowspan="2" |Degrees
|21\19
! colspan="2" rowspan="2" |Octatonic
|94.737
! colspan="3" |Intense Phrygian
|
! colspan="3" |Intense Phrygian-Soft Aeolian
! colspan="4" |Soft Aeolian
|-
|-
!Minimum
|10\9
!Median
|95.238
!Maximum
|Intense Phrygian mode ends, Intense Phrygian-Soft Aeolian mode begins
!Minimum
!Median
!Maximum
!Minimum
!Median
!11/5±13¢
!Maximum
|-
|-
|1
|19\17
|F#/Gb
|G#/Ab
|94.286
|94.737
| colspan="2" |95.238
|95.798
|95.798
| colspan="2" |96.429
|
|97.143
|96.572-98.429
|97.959
|-
|-
|2
|9\8
|G
|''96.429''
|A
|Intense Phrygian-Soft Aeolian mode ends, Soft Aeolian mode begins
|188.571
|189.473
| colspan="2" |190.476
|191.597
| colspan="2" |192.857
|194.286
|193.1435-196.858
|195.918
|-
|-
|3
|17\15
|G#/Ab
|97.143
|A#/Bb
|
|282.857
|284.2105
| colspan="2" |285.714
|287.395
| colspan="2" |289.286
|291.429
|289.715-295.287
|293.878
|-
|-
|4
|8\7
|A
|97.959
|B
|Soft Aeolian mode ends, Flattone Aeolian mode begins
|377.143
|378.947
| colspan="2" |380.952
|383.193
| colspan="2" |385.714
|388.571
|386.287-393.7155
|391.836
|-
|-
|5
|15\13
|A#/Bb
|98.901
|B#/Cb
|
|471.429
|473.684
| colspan="2" |476.1905
|478.992
| colspan="2" |482.143
|485.714
|482.859-492.144
|489.796
|-
|-
|6
|22\19
|B
|99.248
|C
|Flattone Aeolian mode ends, Meantone Aeolian mode begins
|565.714
|568.421
| colspan="2" |571.429
|574.79
| colspan="2" |578.571
|582.857
|579.43-590.573
|587.755
|-
|-
|7
|29\25
|H
| 99.429
|Q
|
|660
|663.158
| colspan="2" |666.667
|670.588
| colspan="2" |675
|680
|676.002-689.002
|685.714
|-
|-
|8
|7\6
|H#/Cb
|''100.000''
|Q#/Db
|Meantone Aeolian mode ends, Superpyth Intense Aeolian mode begins
|754.286
|757.894
| colspan="2" |761.905
|766.387
| colspan="2" |771.429
|777.143
|772.574-787.431
|783.6735
|-
|-
|9
|20\17
|C
|100.840
|D
|
|848.571
|853.632
| colspan="2" |857.143
|862.185
| colspan="2" |867.857
|874.286
|869.146-885.86
|881.633
|-
|-
|10
|13\11
|C#/Db
| 101.299
|D#/Eb
|Superpyth Intense Aeolian mode ends, Ultrapyth Intense Aeolian mode begins
|942.857
|947.368
| colspan="2" |952.381
|957.983
| colspan="2" |964.286
|971.429
|965.717-984.289
|979.592
|-
|-
|11
|19\16
|D
|101.786
|E
|
|1037.143
|1042.105
| colspan="2" |1047.619
|1053.7815
| colspan="2" |1060.714
|1068.571
|1062.289-1082.718
|1077.551
|-
|-
|12
|6\5
|D#/Eb
|102.857
|E#/Fb
|Ultrapyth Intense Aeolian mode ends
|1131.429
|}Golden/Pyrite Tunings±13¢
|1136.842
{| class="wikitable"
| colspan="2" |1142.857
|1149.58
| colspan="2" |1157.143
|1165.714
|1158.861-1181.1465
|1175.51
|-
|-
|13
! rowspan="3" |Degrees
|E
! rowspan="3" |Octatonic
|F
! colspan="2" |Soft Phrygian
|1225.714
! colspan="4" |Phrygian
|1231.579
| colspan="2" |1238.095
|1245.378
| colspan="2" |1253.571
|1262.857
|1255.4325-1279.575
|1273.469
|-
|-
|14
! rowspan="2" |Min-Med
|F
! rowspan="2" |Min-Max/Med-Max
|G
! colspan="2" |Thirdtone
|1320
! colspan="2" |Semitone
|1326.316
| colspan="2" |1333.333
|1341.1765
| colspan="2" |1350
|1360
|1352.004-1378.004
|1371.429
|}
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="2" |Octatonic
! colspan="3" |Aeolian
! colspan="4" |Intense Aeolian
|-
|-
!Minimum
!Min-Med/Min-Max
!Median
!Med-Max
!Maximum
!Min-Med/Min-Max
!Minimum
!Med-Max
!9/4±13¢
!Median
!Maximum
|-
|-
|1
|1
|F#/Gb
|97.959
|98.901
| colspan="2" |100
|99.351-101.208
!101.299
|102.857
|-
|2
|G
|195.918
|197.802
| colspan="2" |200
|198.701-202.416
!202.597
|205.714
|-
|3
|G#/Ab
|G#/Ab
|293.878
|296.703
| colspan="2" |300
|298.052-303.624
!303.896
|308.571
|-
|4
|A
|391.836
|395.604
| colspan="2" |400
|397.403-404.831
!405.195
|411.429
|-
|5
|A#/Bb
|489.796
|494.5055
| colspan="2" |500
|496.754-506.039
!506.4935
|514.286
|-
|6
|B
|587.755
|593.407
| colspan="2" |600
|596.104-607.247
!607.792
|617.143
|-
|7
|H
|685.714
|692.308
| colspan="2" |700
|695.455-708.455
!709.091
|720
|-
|8
|H#/Cb
|783.6735
|791.209
| colspan="2" |800
|794.805-809.663
!810.39
|822.857
|-
|9
|C
|881.633
|890.11
| colspan="2" |900
|894.156-910.871
!911.688
|925.714
|-
|10
|C#/Db
|979.592
|989.011
| colspan="2" |1000
|993.507-1012.079
!1012.987
|1028.571
|-
|11
|D
|1077.551
|1087.912
| colspan="2" |1100
|1092.858-1113.286
!1114.286
|1131.429
|-
|12
|D#/Eb
|1175.51
|1186.813
| colspan="2" |1200
|1192.209-1214.494
!1215.584
|1234.286
|-
|13
|E
|1273.469
|1285.714
| colspan="2" |1300
|1291.559-1315.702
!1316.883
|1337.143
|-
|14
|F
|1371.429
|1384.615
| colspan="2" |1400
|1390.91-1416.91
|1418.182
|1440
|}Phrygian Mode (Neapolitan minor/"major")
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="2" |Octatonic
! colspan="2" |Soft Phrygian
! colspan="3" |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
|88.575-90.4325
|88.751-90.608
|88.751-90.608
|89.855-91.712
|89.103-91.32
|90.235-92.092
|89.871-91.7835
|91.234-93.191
|91.334-93.515
|91.983-94.271
|-
|-
| |2
|2
| |A
|A
|177.151-180.865
|177.151-180.865
|177.501-181.216
|177.501-181.216
|179.709-183.4235
|178.206-182.64
|180.47-184.184
|179.743-183.567
|182.667-186.382
|182.667-187.031
|183.965-188.543
|-
|-
| |3
|3
| |A#/Bb
|A#/Bb
|265.756-271.2975
|265.756-271.2975
|266.252-271.823
|266.252-271.823
|269.564-275.135
|267.309-273.96
|270.705-276.276
|269.614-275.351
|274.001-279.5725
|274.001-280.545
|275.948-282.814
|-
|-
| |4
|4
| |B
|B
|354.301-361.73
|354.301-361.73
|355.003-362.431
|355.003-362.431
|359.4185-366.847
|356.412-365.28
|360.94-368.3685
|359.4855-367.134
|365.335-372.763
|365.335-374.613
|367.931-377.085
|-
|-
| |5
|5
| |B#/Cb
|B#/Cb
|442.877-452.1625
|442.877-452.1625
|443.753-453.039
|443.753-453.039
|449.273-458.559
|445.515-456.6
|451.175-460.461
|449.357-458.918
|456.6685-465.954
|456.6685-467.577
|459.913-471.357
|-
|-
| |6
|6
| |C
|C
|531.452-542.595
|531.452-542.595
|532.504-543.647
|532.504-543.647
|539.128-550.271
|534.6175-547.92
|541.41-552.553
|539.228-550.701
|548.002-559.145
|548.002-561.092
|551.896-565.628
|-
|-
| |7
|7
| |Q
|Q
|620.0275-633.0275
|620.0275-633.0275
|621.253-634.253
|621.253-634.253
|628.982-641.982
|623.7205-639.24
|631.645-644.645
|629.1-642.485
|639.335-652.335
|639.335-654.335
|643.879-659.8995
|-
|-
| |8
|8
| |Q#/Db
|Q#/Db
|708.603-723.46
|708.603-723.46
|710.005-724.862
|710.005-724.862
|718.837-733.694
|712.823-730.56
|721.88-736.737
|718.971-734
|730.67-745.257
|730.67-748.123
|735.861-754.171
|-
|-
| |9
|9
| |D
|D
|797.178-813.8925
|797.178-813.8925
|798.756-815.47
|798.756-815.47
|808.692-825.406
|801.926-821.88
|812.115-828.829
|808.842-826.032
|822.003-838.718
|822.003-841.78
|827.844848.442
|-
|-
| |10
|10
| |D#/Eb
|D#/Eb
|885.754-904.325
|885.754-904.325
|887.507-906.078
|887.507-906.078
|898.546-917.118
|891.029-913.2
|902.35-920.921
|898.714-917.835
|913.337-931.908
|913.337-935.153
|919.8265-942.7135
|-
|-
| |11
|11
| |E
|E
|974.329-994.7575
|974.329-994.7575
|976.257-996.686
|976.257-996.686
|988.401-1008.829
|980.132-1004.52
|992.585-1013.013
|988.585-1009.619
|1007.671-1025.099
|1007.671-1028.6685
|1011.809-1036.985
|-
|-
| |12
|12
| |E#/Fb
|E#/Fb
|1062.904-1085.19
|1062.904-1085.19
|1065.008-1087.294
|1065.008-1087.294
|1078.255-1100.541
|1069.235-1095.84
|1082.82-1105.106
|1078.4565-1101.023
|1096.004-1118.29
|1096.004-1121.1894
|1103.792-1131.256
|-
|-
| |13
|13
| |F
|F
|1151.48-1175.6225
|1151.48-1175.6225
|1153.759-1177.901
|1153.759-1177.901
|1168.11-1192.253
|1158.338-1187.16
|1173.055-1197.198
|1168.328-1193.186
|1187.338-1211.481
|1187.338-1215.699
|1195.7745-1225.528
|-
|-
|14
|14
Line 589: Line 265:
|1240.055-1266.055
|1240.055-1266.055
|1242.506-1268.506
|1242.506-1268.506
|1257.965-1283.965
|1247.441-1278.48
|1263.29-1289.29
|1258.199-1284.969
|1278.672-1304.672
|1278.672-1309.2145
|1287.757-1319.799
|}
|}
Phrygian-Aeolian Mode (intermediate minor)
{| class="wikitable"
{| class="wikitable"
|-
! rowspan="2" |Degrees
! rowspan="2" |Degrees
! colspan="2" rowspan="2" |Octatonic
! colspan="2" rowspan="2" |Octatonic
Line 601: Line 278:
! colspan="2" |Soft Aeolian
! colspan="2" |Soft Aeolian
|-
|-
!Min-Med/Min-Max±13¢
!Min-Med/Min-Max
!Med-Max±13¢
!Med-Max
!Min-Med/Min-Max±13¢
!Min-Med/Min-Max
!Med-Max±13¢
!Med-Max
!Min-Med/Min-Max±13¢
!Min-Med/Min-Max
!Med-Max±13¢
!Med-Max
|-
|-
|1
|1
Line 748: Line 425:
|1349.558-1375.558
|1349.558-1375.558
|}
|}
Aeolian Mode (natural/harmonic minor)
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="3" |Degrees
! rowspan="2" |Octatonic
! rowspan="3" |Octatonic
! colspan="2" |Aeolian
! colspan="4" |Aeolian
! colspan="2" |Intense Aeolian
! colspan="4" |Intense Aeolian
|-
! colspan="2" |Flattone
! colspan="2" |Meantone
! colspan="2" |Superpyth
! colspan="2" |Ultrapyth
|-
|-
!Min-Med/Min-Max±13¢
!Min-Med
!Med-Max-13c
!Med-Max~Min-Max
!Min-Med/Min-Max±13¢
!Min-Med/Min-Max
!Med-Max-13c
!Med-Max
!Min-Med
!Min-Max/Med-Max
!Min-Med/Min-Max
!Med-Max
|-
|-
|1
|1
|F#/Gb
|F#/Gb
|97.737-99.5945
|97.737-99.5945
|98.216-100.074
| colspan="2" |98.0805-100.2995
|98.574-100.431
|99.761-101.618
|100.043-101.9
|100.043-101.9
|100.712-102.569
|100.712-102.569
|101.031-102.888
|-
|-
|2
|2
|G
|G
|195.475-199.189
|195.475-199.189
|196.433-200.147
| colspan="2" |196.161-200.599
|197.148-200.862
|199.523-203.237
|200.085-203.8
|200.085-203.8
|201.424-205.138
|201.424-205.138
|202.061.205.7755
|-
|-
|3
|3
|G#/Ab
|G#/Ab
|293.212-298.783
|293.212-298.783
|294.649-300.221
| colspan="2" |294.2415-300.8985
|295.721-301.293
|299.284-304.885
|300.128-305.6995
|300.128-305.6995
|302.236-307.707
|302.135-307.707
|303.092-308.663
|-
|-
|4
|4
|A
|A
|390.949-398.378
|390.949-398.378
|392.866-400.294
| colspan="2" |392.322-401.198
|394.295-401.724
|399.045-406.474
|400.171-407.599
|400.171-407.599
|402.848-410.276
|402.848-410.276
|404.122-411.551
|-
|-
|5
|5
|A#/Bb
|A#/Bb
|488.687-497.972
|488.687-497.972
|491.082-500.368
| colspan="2" |490.4025-501.497
|492.869-502.155
|498.806-508.092
|500.2135-509.499
|500.2135-509.499
|503.56-512.845
|503.56-512.845
|505.153-514.439
|-
|-
|6
|6
|B
|B
|586.424-597.567
|586.424-597.567
|589.2985-600.441
| colspan="2" |588.483-601.797
|591.443-602.586
|598.568-609.711
|600.256-611.399
|600.256-611.399
|604.2715-615.414
|604.2715-615.414
|606.1835-617.326
|-
|-
|7
|7
|H
|H
|684.161-697.161
|684.161-697.161
|687.515-700.515
| colspan="2" |686.5635-702.096
|690.017-703.017
|698.329-711.329
|700.299-713.299
|700.299-713.299
|704.983-717.983
|704.983-717.983
|707.214-720.214
|-
|-
|8
|8
|H#/Cb
|H#/Cb
|781.899-796.756
|781.899-796.756
|785.731-800.5885
| colspan="2" |784.644-802.3955
|788.5905-803.448
|798.09-812.947
|800.342-815.199
|800.342-815.199
|805.695-820.5525
|805.695-820.5525
|808.245-823.102
|-
|-
|9
|9
|C
|C
|879.636-896.35
|879.636-896.35
|883.948-900.662
| colspan="2" |882.724-902.695
|887.164-903.879
|897.8582-914.566.
|900.384-917.099
|900.384-917.099
|906.407-923.1215
|906.407-923.1215
|909.275-925.9895
|-
|-
|10
|10
|C#/Db
|C#/Db
|977.373-995.945
|977.373-995.945
|982.164-1000.7436
| colspan="2" |980.805-1002.995
|985.738-1004.3095
|997.613-1016.184
|1000.427-1018.9985
|1000.427-1018.9985
|1007.119-1025.691
|1007.119-1025.691
|1010.306-1028.877
|-
|-
|11
|11
|D
|D
|1075.111-1095.539
|1075.111-1095.539
|1080.381-1100.809
| colspan="2" |1078.885-1003.294
|1084.312-1104.7405
|1097.374-1117.803
|1100.47-1120.898
|1100.47-1120.898
|1107.831-1128.26
|1107.831-1128.26
|1111.134-1131.765
|-
|-
|12
|12
|D#/Eb
|D#/Eb
|1172.848-1195.134
|1172.848-1195.134
|1178.597-1200.883
| colspan="2" |1176.966-1203.594
|1182.886-1205.171
|1197.135-1219.421
|1200.512-1222.798
|1200.512-1222.798
|1208.543-1230.829
|1208.543-1230.829
|1212.367-1234.653
|-
|-
|13
|13
|E
|E
|1270.585-1294.728
|1270.585-1294.728
|1276.813-1300.956
| colspan="2" |1275.046-1303.893
|1281.4956-1305.603
|1296.867-1321.04
|1300.555-1324.698
|1300.555-1324.698
|1309.255-1333.398
|1309.255-1333.398
|1313.3975-1337.54
|-
|-
|14
|14
|F
|F
|1368.322-1394.322
|1368.323-1394.324
|1375.03-1401.03
| colspan="2" |1373.127-1404.193
|1380.033-1406.033
|1396.658-1422.658
|1400.598-1426.598
|1400.598-1426.598
|1409.967-1435.967
|1409.967-1435.967
|1414.428-1440.428
|}
|}
[[Category:14-tone]]
[[Category:ed9/4]]
[[Category:edIX]]
[[Category:todo:add_definition]]
[[Category:todo:unify_precision]]
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