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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.
==Tuning spectrum==
==Intervals==
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
|+
! rowspan="2" |Octatonic
!Nonet
! colspan="10" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
!Period
!Notes
|-
|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
|
|-
|17\16
|91.071
|
|-
|16\15
|91.429
|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
|
|-
|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
|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
|-
|-
!Absolute Minimum
!Min-Med/Min-Max
!3ed(7/6)
!Med-Max
! |Minimum
!Min-Med/Min-Max
! |Golden
!Med-Max
! |Median
! |Mean
!<nowiki><0 -11 0 11|/24</nowiki>
!5ed(21/16)
!ed(15/7)
! |Maximum
|-
|-
| |1
|1
| |F#/Gb
|G#/Ab
|85.714
|88.575-90.4325
|88.957
|88.751-90.608
| |89.143
|89.103-91.32
| |90.162
|89.871-91.7835
| |90.612
|91.334-93.515
| |91.714
|91.983-94.271
|92.286
|94.156
|94.246
| |94.286
|-
|-
| |2
|2
| |G
|A
|171.429
|177.151-180.865
|177.914
|177.501-181.216
| |178.286
|178.206-182.64
| |180.3245
|179.743-183.567
| |181.2245
|182.667-187.031
| |183.429
|183.965-188.543
|184.5715
|188.312
|188.492
| |188.571
|-
|-
| |3
|3
| |G#/Ab
|A#/Bb
|257.143
|265.756-271.2975
|266.871
|266.252-271.823
| |267.429
|267.309-273.96
| |270.487
|269.614-275.351
| |271.837
|274.001-280.545
| |275.143
|275.948-282.814
|276.857
|282.469
|282.738
| |282.857
|-
|-
| |4
|4
| |A
|B
|342.857
|354.301-361.73
|355.828
|355.003-362.431
| |356.571
|356.412-365.28
| |360.649
|359.4855-367.134
| |362.449
|365.335-374.613
| |366.857
|367.931-377.085
|369.143
|376.625
|376.984
| |377.143
|-
|-
| |5
|5
| |A#/Bb
|B#/Cb
|428.571
|442.877-452.1625
|444.785
|443.753-453.039
| |445.714
|445.515-456.6
| |450.811
|449.357-458.918
| |453.061
|456.6685-467.577
| |458.571
|459.913-471.357
|461.429
|470.781
|471.23
| |471.429
|-
|-
| |6
|6
| |B
|C
|514.286
|531.452-542.595
|533.742
|532.504-543.647
| |534.857
|534.6175-547.92
| |540.973
|539.228-550.701
| |543.6735
|548.002-561.092
| |550.286
|551.896-565.628
|553.714
|564.937
|565.4755
| |565.714
|-
|-
| |7
|7
| |H
|Q
|600
|620.0275-633.0275
|622.698
|621.253-634.253
| |624
|623.7205-639.24
| |631.136
|629.1-642.485
| |634.286
|639.335-654.335
| |642
|643.879-659.8995
|646
|659.093
|659.721
| |660
|-
|-
| |8
|8
| |H#/Cb
|Q#/Db
|685.714
|708.603-723.46
|711.656
|710.005-724.862
| |713.143
|712.823-730.56
| |721.298
|718.971-734
| |724.898
|730.67-748.123
| |733.714
|735.861-754.171
|738.286
|753.2495
|753.967
| |754.286
|-
|-
| |9
|9
| |C
|D
|771.429
|797.178-813.8925
|800.612
|798.756-815.47
| |802.286
|801.926-821.88
| |811.46
|808.842-826.032
| |815.51
|822.003-841.78
| |825.429
|827.844848.442
|830.572
|847.406
|848.213
| |848.571
|-
|-
| |10
|10
| |C#/Db
|D#/Eb
|857.143
|885.754-904.325
|889.57
|887.507-906.078
| |891.429
|891.029-913.2
| |901.622
|898.714-917.835
| |906.122
|913.337-935.153
| |917.143
|919.8265-942.7135
|922.857
|941.562
|942.459
| |942.857
|-
|-
| |11
|11
| |D
|E
|942.857
|974.329-994.7575
|978.527
|976.257-996.686
| |980.571
|980.132-1004.52
| |991.785
|988.585-1009.619
| |996.735
|1007.671-1028.6685
| |1008.857
|1011.809-1036.985
|1015.143
|1035.718
|1036.705
| |1037.143
|-
|-
| |12
|12
| |D#/Eb
|E#/Fb
|1028.571
|1062.904-1085.19
|1067.484
|1065.008-1087.294
| |1069.714
|1069.235-1095.84
| |1081.947
|1078.4565-1101.023
| |1087.247
|1096.004-1121.1894
| |1100.571
|1103.792-1131.256
|1107.429
|1129.874
|1130.951
| |1131.429
|-
|-
| |13
|13
| |E
|F
|1114.286
|1151.48-1175.6225
|1156.441
|1153.759-1177.901
| |1158.857
|1158.338-1187.16
| |1172.109
|1168.328-1193.186
| |1177.959
|1187.338-1215.699
| |1192.286
|1195.7745-1225.528
|1199.7145
|1224.03
|1225.197
| |1225.714
|-
|-
|14
|14
|F
|G
|1200
|1240.055-1266.055
|1245.397
|1242.506-1268.506
|1248
|1247.441-1278.48
|1262.271
|1258.199-1284.969
|1268.571
|1278.672-1309.2145
|1284
|1287.757-1319.799
|1292
|1318.1865
|1319.443
|1320
|}
|}
{| class="wikitable"
{| class="wikitable"
|-
! rowspan="2" |Degrees
! rowspan="2" |Degrees
! rowspan="2" |Octatonic
! colspan="2" rowspan="2" |Octatonic
! colspan="17" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
! colspan="2" |Intense Phrygian
! colspan="2" |Intense Phrygian-Soft Aeolian
! colspan="2" |Soft Aeolian
|-
|-
! |Minimum
!Min-Med/Min-Max
!ed(28/13)
!Med-Max
! |Golden
!Min-Med/Min-Max
!ed(13/6)
!Med-Max
!8ed(14/9)
!Min-Med/Min-Max
! |Mean
!Med-Max
!3ed(13/11)
!ed(24/11)
!4ed(5/4)
!10ed(7/4)
!<nowiki><… -3 0 8|/48</nowiki>
! |Median
!7ed(40/27)
!<nowiki><-18 -4 13|\72</nowiki>
!ed(11/5)
!8ed(11/7)
! |Maximum
|-
|-
| |1
|1
| |F#/Gb
|F#/Gb
| |94.286
|G#/Ab
|94.878
|93.6975-95.555
| |95.395
|93.922-95.779
|95.612
|94.732-96.589
|95.6145
|95.012-96.869
| |96.122
|96.037-97.894
|96.403
|96.397-98.254
|96.474
|96.578
|96.883
|97.107
| |97.143
|97.207
|97.42
|97.5
|97.8115
| |97.959
|-
|-
| |2
|2
| |G
|G
| |188.571
|A
|189.757
|187.395-191.109
| |190.79
|187.844-191.558
|191.225
|189.463-193.178
|191.229
|190.0235-193.738
| |192.245
|192.074-195.789
|192.8065
|192.794-196.508
|192.948
|193.157
|193.765
|194.213
| |194.286
|194.414
|194.8405
|195.001
|195.623
| |195.918
|-
|-
| |3
|3
| |G#/Ab
|G#/Ab
| |282.857
|A#/Bb
|284.635
|281.093-286.664
| |286.185
|281.765-287.337
|286.837
|284.195-289.766
|286.843
|285.035-290.607
| |288.367
|288.112-293.683
|289.21
|289.191-294.7625
|289.422
|289.735
|290.648
|291.322
| |291.429
|291.621
|292.261
|292.501
|293.4345
| |293.878
|-
|-
| |4
|4
| |A
|A
| |377.143
|B
|379.512
|374.79-382.219
| |381.58
|375.687-383.116
|382.449
|378.9265-386.219
|382.458
|380.047-387.476
| |384.488
|384.149-391.577
|385.613
|385.588-393.017
|385.896
|386.314
|387.53
|388.429
| |388.571
|338.828
|389.681
|390.001
|391.246
| |391.836
|-
|-
| |5
|5
| |A#/Bb
|A#/Bb
| |471.429
|B#/Cb
|474.392
|468.488-477.773
| |476.975
|469.609-478.895
|478.062
|473.658-482.944
|478.072
|475.059-484.3445
| |480.612
|480.186-489.472
|482.016
|481.985-491.271
|482.37
|482.892
|484.413
|485.537
| |485.714
|486.035
|487.101
|487.5015
|489.0575
| |489.796
|-
|-
| |6
|6
| |B
|B
| |565.714
|C
|569.271
|562.185-573.328
| |572.37
|563.531-574.674
|573.674
|568.39-579.533
|573.687
|570.0705-581.213
| |576.735
|576.223-587.366
|875.419
|578.382-589.525
|578.8445
|579.471
|581.2955
|582.644
| |582.857
|583.242
|584.5215
|585.002
|586.869
| |587.755
|-
|-
| |7
|7
| |H
|H
| |660
|Q
|664.149
|655.883-668.883
| |667.765
|657.4525-670.4525
|669.286
|663.121-676.121
|669.301
|665.082-678.082
| |672.857
|672.2605-685.2605
|674.823
|674.779-687.779
|975.3185
|676.049
|678.178
|679.752
| |680
|680.448
|681.942
|682.002
|684.6805
| |685.714
|-
|-
| |8
|8
| |H#/Cb
|H#/Cb
| |754.286
|Q#/Db
|759.028
|749.58-764.4375
| |763.16
|751.374-766.231
|764.899
|757.853-772.71
|764.916
|760.094-774.951
| |768.98
|768.298-783.155
|771.226
|771.176-786.033
|771.793
|772.627
|775.06
|776.859
| |777.143
|777.656
|779.362
|780.002
|782.492
| |783.6735
|-
|-
| |9
|9
| |C
|C
| |848.571
|D
|853.906
|843.278-859.992
| |858.555
|845.296-862.01
|860.511
|852.585-869.299
|860.53
|855.105-871.82
| |865.102
|864.335-881.049
|867.629
|867.573-884.2875
|868.267
|869.206
|871.943
|873.966
| |874.286
|874.862
|876.782
|877.503
|880.3035
| |881.633
|-
|-
| |10
|10
| |C#/Db
|C#/Db
| |942.857
|D#/Eb
|948.7845
|936.975-955.5546
| |953.95
|939.218-957.789
|956.123
|947.316-965.887
|956.145
|950.1175-968.689
| |961.2245
|960.372-978.9435
|964.032
|963.97-982.542
|964.741
|965.784
|968.826
|971.073
| |971.429
|972.07
|974.2025
|975.003
|978.115
| |979.592
|-
|-
| |11
|11
| |D
|D
| |1037.143
|E
|1043.663
|1030.672-1051.101
| |1049.345
|1033.101-1053.568
|1051.736
|1042.048-1062.477
|1051.759
|1045.129-1065.558
| |1057.347
|1056.409-1076.838
|1060.436
|1060.367-1080.796
|1061.215
|1062.363
|1065.7085
|1068.181
| |1068.579
|1069.277
|1071.623
|1072.503
|1075.9265
| |1077.551
|-
|-
| |12
|12
| |D#/Eb
|D#/Eb
| |1131.429
|E#/Fb
|1138.541
|1124.3705-1146.656
| |1144.74
|1127.061-1149.347
|1147.348
|1136.78-1159.065
|1147.374
|1140.141-1162.427
| |1153.469
|1152.4465-1174.732
|1156.839
|1156.764-1179.05
|1157.689
|1158.941
|1162.591
|1165.2885
| |1165.714
|1166.4835
|1169.043
|1170.004
|1173.738
| |1175.51
|-
|-
| |13
|13
| |E
|E
| |1225.714
|F
|1233.42
|1218.068-1242.211
| |1240.435
|1220.983-1245.126
|1242.96
|1231.511-1255.654
|1242.988
|1235.153-1259.295
| |1249.592
|1248.484-1272.626
|1253.242
|1253.161-1227.304
|1254.163
|1255.52
|1259.474
|1262.396
| |1262.857
|1263.6905
|1266.463
|1267.504
|1271.55
| |1273.469
|-
|-
|14
|14
|F
|F
|1320
|G
|1328.298
|1311.767-1337.767
|1335.53
|1314.905-1340.905
|1338.573
|1326.243-1352.243
|1338.603
|1330.1645-1356.1645
|1345.714
|1344.521-1370.521
|1349.645
|1349.558-1375.558
|1350.637
|1352.089
|1356.356
|1359.503
|1360
|1360.897
|1363.884
|1365.004
|1369.361
|1371.429
|}
|}
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="3" |Degrees
! rowspan="2" |Octatonic
! rowspan="3" |Octatonic
! colspan="17" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
! colspan="4" |Aeolian
! colspan="4" |Intense Aeolian
|-
! colspan="2" |Flattone
! colspan="2" |Meantone
! colspan="2" |Superpyth
! colspan="2" |Ultrapyth
|-
|-
! |Minimum
!Min-Med
!9ed(5/3)
!Med-Max~Min-Max
!ed(20/9)
!Min-Med/Min-Max
! |Golden
!Med-Max
!28ed5
!Min-Med
!5ed(4/3)
!Min-Max/Med-Max
! |Median
!Min-Med/Min-Max
! |7edf
!Med-Max
!56ed(180/7)
! |Mean
!28ed(36/7)
!8ed(8/5)
!10ed(9/5)
!2ed(9/8)
!9ed(17/10)
!ed(16/7)
! |Maximum
|-
|-
| |1
|1
| |F#/Gb
|F#/Gb
| |97.959
|97.737-99.5945
|98.262
| colspan="2" |98.0805-100.2995
|98.743
|98.574-100.431
| |99.459
|99.761-101.618
|99.511
|100.043-101.9
|99.609
|100.712-102.569
| |100
|101.031-102.888
| |100.279
|100.382
| |100.408
|101.253
|101.711
|101.76
|101.955
|102.071
|102.227
| |102.857
|-
|-
| |2
|2
| |G
|G
| |195.918
|195.475-199.189
|196.524
| colspan="2" |196.161-200.599
|197.486
|197.148-200.862
| |198.918
|199.523-203.237
|199.022
|200.085-203.8
|199.218
|201.424-205.138
| |200
|202.061.205.7755
| |200.559
|200.764
| |200.816
|202.506
|203.422
|203.519
|203.91
|204.143
|204.453
| |205.714
|-
|-
| |3
|3
| |G#/Ab
|G#/Ab
| |293.878
|293.212-298.783
|294.786
| colspan="2" |294.2415-300.8985
|286.229
|295.721-301.293
| |298.377
|299.284-304.885
|298.534
|300.128-305.6995
|298.827
|302.135-307.707
| |300
|303.092-308.663
| |300.837
|301.146
| |301.2245
|303.759
|305.132
|305.279
|305.865
|306.214
|306.68
| |308.571
|-
|-
| |4
|4
| |A
|A
| |391.836
|390.949-398.378
|393.048
| colspan="2" |392.322-401.198
|394.9725
|394.295-401.724
| |397.839
|399.045-406.474
|398.045
|400.171-407.599
|398.436
|402.848-410.276
| |400
|404.122-411.551
| |401.117
|401.528
| |401.633
|405.012
|406.843
|407.0385
|407.82
|408.285
|408.907
| |411.429
|-
|-
| |5
|5
| |A#/Bb
|A#/Bb
| |489.796
|488.687-497.972
|491.31
| colspan="2" |490.4025-501.497
|493.716
|492.869-502.155
| |497.296
|498.806-508.092
|497.556
|500.2135-509.499
|498.045
|503.56-512.845
| |500
|505.153-514.439
| |501.396
|501.9105
| |502.041
|506.265
|508.554
|508.798
|509.775
|510.3565
|511.134
| |514.286
|-
|-
| |6
|6
| |B
|B
| |587.755
|586.424-597.567
|589.5725
| colspan="2" |588.483-601.797
|592.459
|591.443-602.586
| |597.755
|598.568-609.711
|597.067
|600.256-611.399
|597.654
|604.2715-615.414
| |600
|606.1835-617.326
| |601.676
|602.293
| |602.449
|607.518
|610.265
|610.558
|611.73
|612.428
|613.36
| |617.143
|-
|-
| |7
|7
| |H
|H
| |685.714
|684.161-697.161
|687.835
| colspan="2" |686.5635-702.096
|691.202
|690.017-703.017
| |696.2145
|698.329-711.329
|696.578
|700.299-713.299
|697.263
|704.983-717.983
| |700
|707.214-720.214
| |701.955
|702.675
| |702.857
|708.771
|711.976
|712.317
|713.685
|714.499
|715.587
| |720
|-
|-
| |8
|8
| |H#/Cb
|H#/Cb
| |783.6735
|781.899-796.756
|786.097
| colspan="2" |784.644-802.3955
|789.945
|788.5905-803.448
| |795.674
|798.09-812.947
|796.099
|800.342-815.199
|796.872
|805.695-820.5525
| |800
|808.245-823.102
| |802.234
|803.057
| |803.265
|810.024
|813.686
|814.077
|815.64
|816.57
|817.814
| |822.857
|-
|-
| |9
|9
| |C
|C
| |881.633
|879.636-896.35
|884.359
| colspan="2" |882.724-902.695
|888.688
|887.164-903.879
| |895.133
|897.8582-914.566.
|895.301
|900.384-917.099
|896.481
|906.407-923.1215
| |900
|909.275-925.9895
| |902.514
|903.439
| |903.6735
|911.277
|915.397
|915.837
|917.595
|918.462
|920.041
| |925.714
|-
|-
| |10
|10
| |C#/Db
|C#/Db
| |979.592
|977.373-995.945
|982.621
| colspan="2" |980.805-1002.995
|987.431
|985.738-1004.3095
| |994.592
|997.613-1016.184
|995.112
|1000.427-1018.9985
|996.09
|1007.119-1025.691
| |1000
|1010.306-1028.877
| |1002.793
|1003.821
| |1004.4082
|1012.53
|1017.108
|1017.596
|1019.55
|1020.712
|1022.267
| |1028.571
|-
|-
| |11
|11
| |D
|D
| |1077.551
|1075.111-1095.539
|1080.882
| colspan="2" |1078.885-1003.294
|1086.174
|1084.312-1104.7405
| |1094..051
|1097.374-1117.803
|1094.623
|1100.47-1120.898
|1095.699
|1107.831-1128.26
| |1100
|1111.134-1131.765
| |1103.072
|1104.203
| |1104.49
|1113.783
|1118.819
|1119.356
|1121.505
|1122.784
|1124.494
| |1131.429
|-
|-
| |12
|12
| |D#/Eb
|D#/Eb
| |1175.51
|1172.848-1195.134
|1179.145
| colspan="2" |1176.966-1203.594
|1184.9175
|1182.886-1205.171
| |1193.5105
|1197.135-1219.421
|1194.134
|1200.512-1222.798
|1195.308
|1208.543-1230.829
| |1200
|1212.367-1234.653
| |1203.3514
|1204.585
| |1204.898
|1215.036
|1220.529
|1221.1155
|1223.46
|1224.856
|1226.721
| |1234.286
|-
|-
| |13
|13
| |E
|E
| |1273.469
|1270.585-1294.728
|1277.407
| colspan="2" |1275.046-1303.893
|1283.661
|1281.4956-1305.603
| |1292.97
|1296.867-1321.04
|1293.646
|1300.555-1324.698
|1294.916
|1309.255-1333.398
| |1300
|1313.3975-1337.54
| |1303.631
|1304.967
| |1305.306
|1316.289
|1322.24
|1322.875
|1325.415
|1326.927
|1238.947
| |1337.143
|-
|-
|14
|14
|F
|F
|1371.429
|1368.323-1394.324
|1375.669
| colspan="2" |1373.127-1404.193
|1382.403
|1380.033-1406.033
|1392.429
|1396.658-1422.658
|1393.157
|1400.598-1426.598
|1394.526
|1409.967-1435.967
|1400
|1414.428-1440.428
|1403.91
|1405.3495
|1405.714
|1417.524
|1423.951
|1424.635
|1427.37
|1428.998
|1431.174
|1440
|}
|}
[[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"