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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)
|-
|1/1
|''85.714''
|Soft Phrygian mode begins
|-
|23\22
|89.610
|
|-
|22\21
|89.796
|Soft Phrygian mode ends, Thirdtone Phrygian mode begins
|-
|21\20
|90.000
|
|-
|20\19
|90.226
|
|-
|19\18
|90.476
|
|-
|37\35
|90.612
|
|-
|18\17
|90.756
|
|-
|-
!Absolute Minimum
|17\16
!Minimum
|91.071
!Median
|
!Maximum
! |Minimum
!Median
!Maximum
!Minimum
!Median
!Maximum
|-
|-
| |1
|16\15
| |F#/Gb
|85.714
|89.143
|91.429
|91.429
| colspan="2" |94.286
|Thirdtone Phrygian mode ends
|-
|15\14
|91.837
|Semitone Phrygian mode begins
|-
|14\13
|92.308
|
|-
|27\25
|92.571
|
|-
|13\12
|''92.857''
|
|-
|12\11
|93.506
|
|-
|11\10
|94.286
|Semitone Phrygian mode ends, Intense Phrygian mode begins
|-
|21\19
|94.737
|
|-
|10\9
|95.238
|Intense Phrygian mode ends, Intense Phrygian-Soft Aeolian mode begins
|-
|19\17
|95.798
|95.798
| colspan="2" |97.959
|
|100
|-
|9\8
|''96.429''
|Intense Phrygian-Soft Aeolian mode ends, Soft Aeolian mode begins
|-
|17\15
|97.143
|
|-
|8\7
|97.959
|Soft Aeolian mode ends, Flattone Aeolian mode begins
|-
|15\13
|98.901
|
|-
|22\19
|99.248
|Flattone Aeolian mode ends, Meantone Aeolian mode begins
|-
|29\25
| 99.429
|
|-
|7\6
|''100.000''
|Meantone Aeolian mode ends, Superpyth Intense Aeolian mode begins
|-
|20\17
|100.840
|
|-
|13\11
| 101.299
|Superpyth Intense Aeolian mode ends, Ultrapyth Intense Aeolian mode begins
|-
|19\16
|101.786
|
|-
|6\5
|102.857
|102.857
|Ultrapyth Intense Aeolian mode ends
|}Golden/Pyrite Tunings±13¢
{| class="wikitable"
|-
! rowspan="3" |Degrees
! rowspan="3" |Octatonic
! colspan="2" |Soft Phrygian
! colspan="4" |Phrygian
|-
! rowspan="2" |Min-Med
! rowspan="2" |Min-Max/Med-Max
! colspan="2" |Thirdtone
! colspan="2" |Semitone
|-
!Min-Med/Min-Max
!Med-Max
!Min-Med/Min-Max
!Med-Max
|-
|-
| |2
|1
| |G
|G#/Ab
|171.429
|88.575-90.4325
|178.286
|88.751-90.608
|182.857
|89.103-91.32
| colspan="2" |188.571
|89.871-91.7835
|191.597
|91.334-93.515
| colspan="2" |195.918
|91.983-94.271
|200
|205.714
|-
|-
| |3
|2
| |G#/Ab
|A
|257.143
|177.151-180.865
|267.429
|177.501-181.216
|274.286
|178.206-182.64
| colspan="2" |282.857
|179.743-183.567
|287.395
|182.667-187.031
| colspan="2" |293.878
|183.965-188.543
|300
|308.571
|-
|-
| |4
|3
| |A
|A#/Bb
|342.857
|265.756-271.2975
|356.571
|266.252-271.823
|365.714
|267.309-273.96
| colspan="2" |377.143
|269.614-275.351
|383.193
|274.001-280.545
| colspan="2" |391.836
|275.948-282.814
|400
|411.429
|-
|-
| |5
|4
| |A#/Bb
|B
|428.571
|354.301-361.73
|445.714
|355.003-362.431
|467.143
|356.412-365.28
| colspan="2" |471.429
|359.4855-367.134
|478.992
|365.335-374.613
| colspan="2" |489.796
|367.931-377.085
|500
|514.286
|-
|-
| |6
|5
| |B
|B#/Cb
|514.286
|442.877-452.1625
|534.857
|443.753-453.039
|548.571
|445.515-456.6
| colspan="2" |565.714
|449.357-458.918
|574.79
|456.6685-467.577
| colspan="2" |587.755
|459.913-471.357
|600
|617.143
|-
|-
| |7
|6
| |H
|C
|600
|531.452-542.595
|624
|532.504-543.647
|640
|534.6175-547.92
| colspan="2" |660
|539.228-550.701
|670.588
|548.002-561.092
| colspan="2" |685.714
|551.896-565.628
|700
|720
|-
|-
| |8
|7
| |H#/Cb
|Q
|685.714
|620.0275-633.0275
|713.143
|621.253-634.253
|731.429
|623.7205-639.24
| colspan="2" |754.286
|629.1-642.485
|766.387
|639.335-654.335
| colspan="2" |783.6735
|643.879-659.8995
|800
|822.857
|-
|-
| |9
|8
| |C
|Q#/Db
|771.429
|708.603-723.46
|802.286
|710.005-724.862
|822.857
|712.823-730.56
| colspan="2" |848.571
|718.971-734
|862.185
|730.67-748.123
| colspan="2" |881.633
|735.861-754.171
|900
|925.714
|-
|-
| |10
|9
| |C#/Db
|D
|857.143
|797.178-813.8925
|891.429
|798.756-815.47
|914.286
|801.926-821.88
| colspan="2" |942.857
|808.842-826.032
|957.983
|822.003-841.78
| colspan="2" |979.592
|827.844848.442
|1000
|1028.571
|-
|-
| |11
|10
| |D
|D#/Eb
|942.857
|885.754-904.325
|980.571
|887.507-906.078
|1005.714
|891.029-913.2
| colspan="2" |1037.143
|898.714-917.835
|1053.7815
|913.337-935.153
| colspan="2" |1077.551
|919.8265-942.7135
|1100
|1131.429
|-
|-
| |12
|11
| |D#/Eb
|E
|1028.571
|974.329-994.7575
|1069.714
|976.257-996.686
|1097.143
|980.132-1004.52
| colspan="2" |1131.429
|988.585-1009.619
|1149.58
|1007.671-1028.6685
| colspan="2" |1175.51
|1011.809-1036.985
|1200
|1234.286
|-
|-
| |13
|12
| |E
|E#/Fb
|1114.286
|1062.904-1085.19
|1158.857
|1065.008-1087.294
|1188.571
|1069.235-1095.84
| colspan="2" |1225.714
|1078.4565-1101.023
|1245.378
|1096.004-1121.1894
| colspan="2" |1273.469
|1103.792-1131.256
|1300
|-
|1337.143
|13
|F
|1151.48-1175.6225
|1153.759-1177.901
|1158.338-1187.16
|1168.328-1193.186
|1187.338-1215.699
|1195.7745-1225.528
|-
|14
|G
|1240.055-1266.055
|1242.506-1268.506
|1247.441-1278.48
|1258.199-1284.969
|1278.672-1309.2145
|1287.757-1319.799
|}
{| class="wikitable"
|-
! rowspan="2" |Degrees
! colspan="2" rowspan="2" |Octatonic
! colspan="2" |Intense Phrygian
! 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
!Med-Max
|-
|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
|14
|F
|F
|1200
|G
|1268.571
|1311.767-1337.767
|1280
|1314.905-1340.905
| colspan="2" |1320
|1326.243-1352.243
|1341.1765
|1330.1645-1356.1645
| colspan="2" |1371.429
|1344.521-1370.521
|1400
|1349.558-1375.558
|1440
|}
|}Golden Tunings
{| class="wikitable"
{| class="wikitable"
! rowspan="3" |Degrees
! rowspan="3" |Octatonic
! colspan="4" |Aeolian
! colspan="4" |Intense Aeolian
|-
|-
! rowspan="2" |Degrees
! colspan="2" |Flattone
! rowspan="2" |Octatonic
! colspan="2" |Meantone
! colspan="3" |Phrygian Mode (natural minor)
! colspan="2" |Superpyth
! colspan="2" |Phrygian-Aeolian Mode (intermediate minor)
! colspan="2" |Ultrapyth
! colspan="3" |Aeolian Mode (melodic/harmonic minor)
|-
|-
!Min-Med
!Min-Med
!Min-Max
!Med-Max~Min-Max
!Med-Max
!Min-Med/Min-Max
!Min-Med/Min-Max
!Med-Max
!Med-Max
!Min-Med
!Min-Med
!Min-Max
!Min-Max/Med-Max
!Min-Med/Min-Max
!Med-Max
!Med-Max
|-
|-
| |1
|1
| |F#/Gb
|F#/Gb
|90.783
|97.737-99.5945
|91.164
| colspan="2" |98.0805-100.2995
|92.262
|98.574-100.431
|95.395
|99.761-101.618
|96.237
|100.043-101.9
|98.666
|100.712-102.569
|99.459
|101.031-102.888
|100.971
|-
|-
| |2
|2
| |G
|G
|181.566
|195.475-199.189
|182.327
| colspan="2" |196.161-200.599
|184.5245
|197.148-200.862
|190.79
|199.523-203.237
|192.473
|200.085-203.8
|197.332
|201.424-205.138
|198.918
|202.061.205.7755
|201.943
|-
|-
| |3
|3
| |G#/Ab
|G#/Ab
|272.35
|293.212-298.783
|273.491
| colspan="2" |294.2415-300.8985
|276.787
|295.721-301.293
|286.185
|299.284-304.885
|288.71
|300.128-305.6995
|295.998
|302.135-307.707
|298.377
|303.092-308.663
|302.913
|-
|-
| |4
|4
| |A
|A
|363.133
|390.949-398.378
|364.654
| colspan="2" |392.322-401.198
|396.049
|394.295-401.724
|381.58
|399.045-406.474
|384.947
|400.171-407.599
|394.664
|402.848-410.276
|397.839
|404.122-411.551
|403.885
|-
|-
| |5
|5
| |A#/Bb
|A#/Bb
|453.916
|488.687-497.972
|455.818
| colspan="2" |490.4025-501.497
|461.311
|492.869-502.155
|476.975
|498.806-508.092
|481.183
|500.2135-509.499
|493.3295
|503.56-512.845
|497.296
|505.153-514.439
|504.856
|-
|-
| |6
|6
| |B
|B
|544.699
|586.424-597.567
|546.981
| colspan="2" |588.483-601.797
|553.574
|591.443-602.586
|572.37
|598.568-609.711
|577.42
|600.256-611.399
|591.9955
|604.2715-615.414
|597.755
|606.1835-617.326
|605.828
|-
|-
| |7
|7
| |H
|H
|635.482
|684.161-697.161
|638.145
| colspan="2" |686.5635-702.096
|645.836
|690.017-703.017
|667.765
|698.329-711.329
|673.658
|700.299-713.299
|690.661
|704.983-717.983
|696.2145
|707.214-720.214
|706.799
|-
|-
| |8
|8
| |H#/Cb
|H#/Cb
|726.2655
|781.899-796.756
|729.3085
| colspan="2" |784.644-802.3955
|738.098
|788.5905-803.448
|763.16
|798.09-812.947
|769.893
|800.342-815.199
|789.327
|805.695-820.5525
|795.674
|808.245-823.102
|807.77
|-
|-
| |9
|9
| |C
|C
|817.049
|879.636-896.35
|820.472
| colspan="2" |882.724-902.695
|830.3605
|887.164-903.879
|858.555
|897.8582-914.566.
|866.13
|900.384-917.099
|887.993
|906.407-923.1215
|895.133
|909.275-925.9895
|908.7415
|-
|-
| |10
|10
| |C#/Db
|C#/Db
|907.832
|977.373-995.945
|911.636
| colspan="2" |980.805-1002.995
|922.623
|985.738-1004.3095
|953.95
|997.613-1016.184
|962.367
|1000.427-1018.9985
|986.659
|1007.119-1025.691
|994.592
|1010.306-1028.877
|1009.713
|-
|-
| |11
|11
| |D
|D
|998.615
|1075.111-1095.539
|1002.799
| colspan="2" |1078.885-1003.294
|1014.885
|1084.312-1104.7405
|1049.345
|1097.374-1117.803
|1058.603
|1100.47-1120.898
|1085.325
|1107.831-1128.26
|1094.051
|1111.134-1131.765
|1110.684
|-
|-
| |12
|12
| |D#/Eb
|D#/Eb
|1089.398
|1172.848-1195.134
|1093.963
| colspan="2" |1176.966-1203.594
|1107.147
|1182.886-1205.171
|1144.74
|1197.135-1219.421
|1154.84
|1200.512-1222.798
|1183.991
|1208.543-1230.829
|1193.5105
|1212.367-1234.653
|1211.655
|-
|-
| |13
|13
| |E
|E
|1180.1815
|1270.585-1294.728
|1185.126
| colspan="2" |1275.046-1303.893
|1199.41
|1281.4956-1305.603
|1240.435
|1296.867-1321.04
|1251.077
|1300.555-1324.698
|1282.657
|1309.255-1333.398
|1292.97
|1313.3975-1337.54
|1312.627
|-
|-
|14
|14
|F
|F
|1270.965
|1368.323-1394.324
|1276.29
| colspan="2" |1373.127-1404.193
|1291.672
|1380.033-1406.033
|1335.53
|1396.658-1422.658
|1347.313
|1400.598-1426.598
|1381.322
|1409.967-1435.967
|1392.429
|1414.428-1440.428
|1413.598
|}
|}
[[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"