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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="3" |Degrees
|+
! rowspan="3" |Octatonic
!Nonet
! colspan="4" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
!Period
! colspan="9" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
!Notes
! colspan="3" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
|-
|-
! rowspan="2" |Absolute Minimum
|1/1
! rowspan="2" |Minimum
|''85.714''
! rowspan="2" |Median
|Soft Phrygian mode begins
! 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
|23\22
!Median
|89.610
!Maximum
|
!Minimum
!Median
!Maximum
!Minimum
!Median
!Maximum
|-
|-
| |1
|22\21
| |F#/Gb
|89.796
|85.714
|Soft Phrygian mode ends, Thirdtone Phrygian mode begins
|89.143
|91.429
| colspan="2" |94.286
|94.737
| colspan="2" |95.238
|95.798
| colspan="2" |96.429
|97.143
| colspan="2" |97.959
|100
|102.857
|-
|-
| |2
|21\20
| |G
|90.000
|171.429
|
|178.286
|182.857
| colspan="2" |188.571
|189.473
| colspan="2" |190.476
|191.597
| colspan="2" |192.857
|194.286
| colspan="2" |195.918
|200
|205.714
|-
|-
| |3
|20\19
| |G#/Ab
|90.226
|257.143
|
|267.429
|274.286
| colspan="2" |282.857
|284.2105
| colspan="2" |285.714
|287.395
| colspan="2" |289.286
|291.429
| colspan="2" |293.878
|300
|308.571
|-
|-
| |4
|19\18
| |A
|90.476
|342.857
|
|356.571
|365.714
| colspan="2" |377.143
|378.947
| colspan="2" |380.952
|383.193
| colspan="2" |385.714
|388.571
| colspan="2" |391.836
|400
|411.429
|-
|-
| |5
|37\35
| |A#/Bb
|90.612
|428.571
|
|445.714
|467.143
| colspan="2" |471.429
|473.684
| colspan="2" |476.1905
|478.992
| colspan="2" |482.143
|485.714
| colspan="2" |489.796
|500
|514.286
|-
|-
| |6
|18\17
| |B
|90.756
|514.286
|
|534.857
|548.571
| colspan="2" |565.714
|568.421
| colspan="2" |571.429
|574.79
| colspan="2" |578.571
|582.857
| colspan="2" |587.755
|600
|617.143
|-
|-
| |7
|17\16
| |H
|91.071
|600
|
|624
|640
| colspan="2" |660
|663.158
| colspan="2" |666.667
|670.588
| colspan="2" |675
|680
| colspan="2" |685.714
|700
|720
|-
|-
| |8
|16\15
| |H#/Cb
|91.429
|685.714
|Thirdtone Phrygian mode ends
|713.143
|731.429
| colspan="2" |754.286
|757.894
| colspan="2" |761.905
|766.387
| colspan="2" |771.429
|777.143
| colspan="2" |783.6735
|800
|822.857
|-
|-
| |9
|15\14
| |C
|91.837
|771.429
|Semitone Phrygian mode begins
|802.286
|822.857
| colspan="2" |848.571
|853.632
| colspan="2" |857.143
|862.185
| colspan="2" |867.857
|874.286
| colspan="2" |881.633
|900
|925.714
|-
|-
| |10
|14\13
| |C#/Db
|92.308
|857.143
|
|891.429
|914.286
| colspan="2" |942.857
|947.368
| colspan="2" |952.381
|957.983
| colspan="2" |964.286
|971.429
| colspan="2" |979.592
|1000
|1028.571
|-
|-
| |11
|27\25
| |D
|92.571
|942.857
|
|980.571
|1005.714
| colspan="2" |1037.143
|1042.105
| colspan="2" |1047.619
|1053.7815
| colspan="2" |1060.714
|1068.571
| colspan="2" |1077.551
|1100
|1131.429
|-
|-
| |12
|13\12
| |D#/Eb
|''92.857''
|1028.571
|
|1069.714
|1097.143
| colspan="2" |1131.429
|1136.842
| colspan="2" |1142.857
|1149.58
| colspan="2" |1157.143
|1165.714
| colspan="2" |1175.51
|1200
|1234.286
|-
|-
| |13
|12\11
| |E
|93.506
|1114.286
|
|1158.857
|1188.571
| colspan="2" |1225.714
|1231.579
| colspan="2" |1238.095
|1245.378
| colspan="2" |1253.571
|1262.857
| colspan="2" |1273.469
|1300
|1337.143
|-
|-
|14
|11\10
|F
|94.286
|1200
|Semitone Phrygian mode ends, Intense Phrygian mode begins
|1268.571
|1280
| colspan="2" |1320
|1326.316
| colspan="2" |1333.333
|1341.1765
| colspan="2" |1350
|1360
| 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±13¢
!Min-Med/Min-Max
!Min-Max±13¢
!Med-Max
!Med-Max±13¢
|-
|-
| |1
|1
| |F#/Gb
|G#/Ab
|89.855-91.712
|88.575-90.4325
|90.235-92.092
|88.751-90.608
|91.234-93.191
|89.103-91.32
|89.871-91.7835
|91.334-93.515
|91.983-94.271
|-
|-
| |2
|2
| |G
|A
|179.709-183.4235
|177.151-180.865
|180.47-184.184
|177.501-181.216
|182.667-186.382
|178.206-182.64
|179.743-183.567
|182.667-187.031
|183.965-188.543
|-
|-
| |3
|3
| |G#/Ab
|A#/Bb
|269.564-275.135
|265.756-271.2975
|270.705-276.276
|266.252-271.823
|274.001-279.5725
|267.309-273.96
|269.614-275.351
|274.001-280.545
|275.948-282.814
|-
|-
| |4
|4
| |A
|B
|359.4185-366.847
|354.301-361.73
|360.94-368.3685
|355.003-362.431
|365.335-372.763
|356.412-365.28
|359.4855-367.134
|365.335-374.613
|367.931-377.085
|-
|-
| |5
|5
| |A#/Bb
|B#/Cb
|449.273-458.559
|442.877-452.1625
|451.175-460.461
|443.753-453.039
|456.6685-465.954
|445.515-456.6
|449.357-458.918
|456.6685-467.577
|459.913-471.357
|-
|-
| |6
|6
| |B
|C
|539.128-550.271
|531.452-542.595
|541.41-552.553
|532.504-543.647
|548.002-559.145
|534.6175-547.92
|539.228-550.701
|548.002-561.092
|551.896-565.628
|-
|-
| |7
|7
| |H
|Q
|628.982-641.982
|620.0275-633.0275
|631.645-644.645
|621.253-634.253
|639.335-652.335
|623.7205-639.24
|629.1-642.485
|639.335-654.335
|643.879-659.8995
|-
|-
| |8
|8
| |H#/Cb
|Q#/Db
|718.837-733.694
|708.603-723.46
|721.88-736.737
|710.005-724.862
|730.67-745.257
|712.823-730.56
|718.971-734
|730.67-748.123
|735.861-754.171
|-
|-
| |9
|9
| |C
|D
|808.692-825.406
|797.178-813.8925
|812.115-828.829
|798.756-815.47
|822.003-838.718
|801.926-821.88
|808.842-826.032
|822.003-841.78
|827.844848.442
|-
|-
| |10
|10
| |C#/Db
|D#/Eb
|898.546-917.118
|885.754-904.325
|902.35-920.921
|887.507-906.078
|913.337-931.908
|891.029-913.2
|898.714-917.835
|913.337-935.153
|919.8265-942.7135
|-
|-
| |11
|11
| |D
|E
|988.401-1008.829
|974.329-994.7575
|992.585-1013.013
|976.257-996.686
|1007.671-1025.099
|980.132-1004.52
|988.585-1009.619
|1007.671-1028.6685
|1011.809-1036.985
|-
|-
| |12
|12
| |D#/Eb
|E#/Fb
|1078.255-1100.541
|1062.904-1085.19
|1082.82-1105.106
|1065.008-1087.294
|1096.004-1118.29
|1069.235-1095.84
|1078.4565-1101.023
|1096.004-1121.1894
|1103.792-1131.256
|-
|-
| |13
|13
| |E
|F
|1168.11-1192.253
|1151.48-1175.6225
|1173.055-1197.198
|1153.759-1177.901
|1187.338-1211.481
|1158.338-1187.16
|1168.328-1193.186
|1187.338-1215.699
|1195.7745-1225.528
|-
|-
|14
|14
|F
|G
|1257.965-1283.965
|1240.055-1266.055
|1263.29-1289.29
|1242.506-1268.506
|1278.672-1304.672
|1247.441-1278.48
|1258.199-1284.969
|1278.672-1309.2145
|1287.757-1319.799
|}
|}
Phrygian-Aeolian Mode (intermediate minor)
{| 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
! 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
|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 297:
|2
|2
|G
|G
|A
|187.395-191.109
|187.395-191.109
|187.844-191.558
|187.844-191.558
Line 464: Line 307:
|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 317:
|4
|4
|A
|A
|B
|374.79-382.219
|374.79-382.219
|375.687-383.116
|375.687-383.116
Line 482: Line 327:
|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 337:
|6
|6
|B
|B
|C
|562.185-573.328
|562.185-573.328
|563.531-574.674
|563.531-574.674
Line 500: Line 347:
|7
|7
|H
|H
|Q
|655.883-668.883
|655.883-668.883
|657.4525-670.4525
|657.4525-670.4525
Line 509: Line 357:
|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 367:
|9
|9
|C
|C
|D
|843.278-859.992
|843.278-859.992
|845.296-862.01
|845.296-862.01
Line 527: Line 377:
|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 387:
|11
|11
|D
|D
|E
|1030.672-1051.101
|1030.672-1051.101
|1033.101-1053.568
|1033.101-1053.568
Line 545: Line 397:
|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 407:
|13
|13
|E
|E
|F
|1218.068-1242.211
|1218.068-1242.211
|1220.983-1245.126
|1220.983-1245.126
Line 563: Line 417:
|14
|14
|F
|F
|G
|1311.767-1337.767
|1311.767-1337.767
|1314.905-1340.905
|1314.905-1340.905
Line 570: Line 425:
|1349.558-1375.558
|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
!Min-Med
!Octatonic
!Med-Max~Min-Max
!Min-Med±13¢
!Min-Med/Min-Max
!Min-Max±13¢
!Med-Max
!Med-Max±13¢
!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
|98.531-100.388
| 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
|101.031-102.888
|-
|-
|2
|2
|G
|G
|195.475-199.189
|195.475-199.189
|197.061-200.776
| 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
|202.061.205.7755
|-
|-
|3
|3
|G#/Ab
|G#/Ab
|293.212-298.783
|293.212-298.783
|295.592-301.163
| colspan="2" |294.2415-300.8985
|295.721-301.293
|299.284-304.885
|300.128-305.6995
|300.128-305.6995
|302.135-307.707
|303.092-308.663
|-
|-
|4
|4
|A
|A
|390.949-398.378
|390.949-398.378
|394.123-401.551
| 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
|404.122-411.551
|-
|-
|5
|5
|A#/Bb
|A#/Bb
|488.687-497.972
|488.687-497.972
|492.653-501.939
| 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
|505.153-514.439
|-
|-
|6
|6
|B
|B
|586.424-597.567
|586.424-597.567
|591.184-602.327
| 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
|606.1835-617.326
|-
|-
|7
|7
|H
|H
|684.161-697.161
|684.161-697.161
|689.7145-702.7145
| 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
|707.214-720.214
|-
|-
|8
|8
|H#/Cb
|H#/Cb
|781.899-796.756
|781.899-796.756
|788.245-803.102
| 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
|808.245-823.102
|-
|-
|9
|9
|C
|C
|879.636-896.35
|879.636-896.35
|886.776-903.49
| 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
|909.275-925.9895
|-
|-
|10
|10
|C#/Db
|C#/Db
|977.373-995.945
|977.373-995.945
|985.306-1003.878
| 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
|1010.306-1028.877
|-
|-
|11
|11
|D
|D
|1075.111-1095.539
|1075.111-1095.539
|1083.837-1104.266
| 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
|1111.134-1131.765
|-
|-
|12
|12
|D#/Eb
|D#/Eb
|1172.848-1195.134
|1172.848-1195.134
|1182.368-1204.653
| 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
|1212.367-1234.653
|-
|-
|13
|13
|E
|E
|1270.585-1294.728
|1270.585-1294.728
|1280.898-1305.041
| 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
|1313.3975-1337.54
|-
|-
|14
|14
|F
|F
|1368.322-1394.322
|1368.323-1394.324
|1379.429-1405.429
| 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
|1414.428-1440.428
|}
|}
[[Category:14-tone]]
[[Category:ed9/4]]
[[Category:edIX]]
[[Category:todo:add_definition]]
[[Category:todo:unify_precision]]
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