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This scale occurs in 12edo, where it is the equal division of the major ninth. It has the Macroshrutis MOS with a 2:1 ratio of large against small.
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.
 
==Tuning spectrum==
==Tuning spectrum==
{| class="wikitable"
{| class="wikitable"
|+
! rowspan="2" |Degrees
! colspan="5" rowspan="2" |Period
! rowspan="2" |Octatonic
! colspan="6" |Octatonic (6L 2s)
! colspan="10" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
! rowspan="2" |Notes
|-
|-
!L
!Absolute Minimum
!s
!3ed(7/6)
! colspan="4" |Pentachord
! |Minimum
! |Golden
! |Median
! |Mean
!<nowiki><0 -11 0 11|/24</nowiki>
!5ed(21/16)
!ed(15/7)
! |Maximum
|-
|-
|1\1edo
| |1
|
| |F#/Gb
|
|
|
|171.429
|85.714
|85.714
|88.957
| |89.143
| |90.162
| |90.612
| |91.714
|92.286
|94.156
|94.246
| |94.286
|-
| |2
| |G
|171.429
|171.429
|342.857
|177.914
|514.286
| |178.286
|600
| |180.3245
|Phrygian Mode (aka Double) Neapolitan Temperament from here …
| |181.2245
| |183.429
|184.5715
|188.312
|188.492
| |188.571
|-
|-
|
| |3
|
| |G#/Ab
|
|257.143
|
|266.871
|15\14
| |267.429
|183.6735
| |270.487
|91.837
| |271.837
|183.6735
| |275.143
|367.347
|276.857
|551.02
|282.469
|642.857
|282.738
|
| |282.857
|-
|-
|
| |4
|
| |A
|
|342.857
|14\13
|355.828
|
| |356.571
|184.615
| |360.649
|92.308
| |362.449
|184.615
| |366.857
|369.231
|369.143
|553.846
|376.625
|646.154
|376.984
|
| |377.143
|-
|-
|
| |5
|
| |A#/Bb
|
|428.571
|
|444.785
|27\25
| |445.714
|185.143
| |450.811
|92.571
| |453.061
|185.143
| |458.571
|370.286
|461.429
|555.571
|470.781
|648
|471.23
|
| |471.429
|-
|-
|
| |6
|
| |B
|13\12
|514.286
|
|533.742
|
| |534.857
|185.714
| |540.973
|92.857
| |543.6735
|185.714
| |550.286
|371.429
|553.714
|557.143
|564.937
|650
|565.4755
|
| |565.714
|-
|-
|
| |7
|
| |H
|
|600
|
|622.698
|38\35
| |624
|186.122
| |631.136
|93.061
| |634.286
|186.122
| |642
|372.245
|646
|558.367
|659.093
|651.429
|659.721
|
| |660
|-
|-
|
| |8
|
| |H#/Cb
|
|685.714
|25\23
|711.656
|
| |713.143
|186.335
| |721.298
|93.168
| |724.898
|186.335
| |733.714
|372.671
|738.286
|559.006
|753.2495
|652.174
|753.967
|
| |754.286
|-
|-
|
| |9
|
| |C
|
|771.429
|
|800.612
|37\34
| |802.286
|186.555
| |811.46
|93.278
| |815.51
|186.555
| |825.429
|373.109
|830.572
|559.664
|847.406
|652.941
|848.213
|
| |848.571
|-
|-
|
| |10
|12\11
| |C#/Db
|
|857.143
|
|889.57
|
| |891.429
|187.013
| |901.622
|93.5065
| |906.122
|187.013
| |917.143
|374.026
|922.857
|561.039
|941.562
|654.5455
|942.459
|
| |942.857
|-
|-
|
| |11
|
| |D
|
|942.857
|
|978.527
|46\43
| |980.571
|187.375
| |991.785
|93.688
| |996.735
|187.375
| |1008.857
|374.751
|1015.143
|562.126
|1035.718
|655.813
|1036.705
|
| |1037.143
|-
|-
|
| |12
|
| |D#/Eb
|
|1028.571
|35\32
|1067.484
|
| |1069.714
|187.5
| |1081.947
|93.75
| |1087.247
|187.5
| |1100.571
|375
|1107.429
|562.5
|1129.874
|656.25
|1130.951
|
| |1131.429
|-
|-
|
| |13
|
| |E
|
|1114.286
|
|1156.441
|58\53
| |1158.857
|187.601
| |1172.109
|93.8005
| |1177.959
|187.601
| |1192.286
|375.202
|1199.7145
|562.803
|1224.03
|656.604
|1225.197
|
| |1225.714
|-
|-
|
|14
|
|F
|23\21
|1200
|
|1245.397
|
|1248
|187.755
|1262.271
|93.878
|1268.571
|187.755
|1284
|375.51
|1292
|563.265
|1318.1865
|657.143
|1319.443
|
|1320
|}
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="2" |Octatonic
! colspan="17" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
|-
|-
|
! |Minimum
|
!ed(28/13)
|
! |Golden
|
!ed(13/6)
|57\52
!8ed(14/9)
|187.912
! |Mean
|93.956
!3ed(13/11)
|187.912
!ed(24/11)
|375.824
!4ed(5/4)
|563.736
!10ed(7/4)
|658.242
!<nowiki><… -3 0 8|/48</nowiki>
|
! |Median
!7ed(40/27)
!<nowiki><-18 -4 13|\72</nowiki>
!ed(11/5)
!8ed(11/7)
! |Maximum
|-
|-
|
| |1
|
| |F#/Gb
|
| |94.286
|34\31
|94.878
|
| |95.395
|188.018
|95.612
|94.009
|95.6145
|188.018
| |96.122
|376.037
|96.403
|564.055
|96.474
|658.0645
|96.578
|
|96.883
|97.107
| |97.143
|97.207
|97.42
|97.5
|97.8115
| |97.959
|-
|-
|
| |2
|
| |G
|
| |188.571
|
|189.757
|45\41
| |190.79
|188.153
|191.225
|94.077
|191.229
|188.153
| |192.245
|376.307
|192.8065
|564.46
|192.948
|658.537
|193.157
|
|193.765
|194.213
| |194.286
|194.414
|194.8405
|195.001
|195.623
| |195.918
|-
|-
|11\10
| |3
|
| |G#/Ab
|
| |282.857
|
|284.635
|
| |286.185
|188.571
|286.837
|94.286
|286.843
|188.571
| |288.367
|377.143
|289.21
|565.714
|289.422
|660
|289.735
|…to here
|290.648
Phrygian-Aeolian Mode Neapolitan Temperament from here …
|291.322
| |291.429
|291.621
|292.261
|292.501
|293.4345
| |293.878
|-
|-
|
| |4
|
| |A
|
| |377.143
|
|379.512
|54\49
| |381.58
|188.921
|382.449
|94.461
|382.458
|188.921
| |384.488
|377.842
|385.613
|566.764
|385.896
|661.2245
|386.314
|
|387.53
|388.429
| |388.571
|338.828
|389.681
|390.001
|391.246
| |391.836
|-
|-
|
| |5
|
| |A#/Bb
|
| |471.429
|43\39
|474.392
|
| |476.975
|189.011
|478.062
|94.5055
|478.072
|189.011
| |480.612
|378.022
|482.016
|567.033
|482.37
|661.5385
|482.892
|
|484.413
|485.537
| |485.714
|486.035
|487.101
|487.5015
|489.0575
| |489.796
|-
|-
|
| |6
|
| |B
|
| |565.714
|
|569.271
|75\68
| |572.37
|189.076
|573.674
|94.538
|573.687
|189.076
| |576.735
|378.151
|875.419
|567.227
|578.8445
|661.765
|579.471
|
|581.2955
|582.644
| |582.857
|583.242
|584.5215
|585.002
|586.869
| |587.755
|-
|-
|
| |7
|
| |H
|32\29
| |660
|
|664.149
|
| |667.765
|189.163
|669.286
|94.581
|669.301
|189.163
| |672.857
|378.325
|674.823
|567.488
|975.3185
|662.069
|676.049
|
|678.178
|679.752
| |680
|680.448
|681.942
|682.002
|684.6805
| |685.714
|-
|-
|
| |8
|
| |H#/Cb
|
| |754.286
|
|759.028
|85\77
| |763.16
|189.239
|764.899
|94.62
|764.916
|189.239
| |768.98
|378.478
|771.226
|567.717
|771.793
|662.338
|772.627
|
|775.06
|776.859
| |777.143
|777.656
|779.362
|780.002
|782.492
| |783.6735
|-
|-
|
| |9
|
| |C
|
| |848.571
|53\48
|853.906
|
| |858.555
|189.286
|860.511
|94.643
|860.53
|189.286
| |865.102
|378.571
|867.629
|567.857
|868.267
|662.5
|869.206
|
|871.943
|873.966
| |874.286
|874.862
|876.782
|877.503
|880.3035
| |881.633
|-
|-
|
| |10
|
| |C#/Db
|
| |942.857
|
|948.7845
|74\67
| |953.95
|189.339
|956.123
|94.6695
|956.145
|189.339
| |961.2245
|378.678
|964.032
|568.017
|964.741
|662.687
|965.784
|
|968.826
|971.073
| |971.429
|972.07
|974.2025
|975.003
|978.115
| |979.592
|-
|-
|
| |11
|21\19
| |D
|
| |1037.143
|
|1043.663
|
| |1049.345
|189.474
|1051.736
|94.736
|1051.759
|189.474
| |1057.347
|378.947
|1060.436
|568.421
|1061.215
|663.158
|1062.363
|
|1065.7085
|1068.181
| |1068.579
|1069.277
|1071.623
|1072.503
|1075.9265
| |1077.551
|-
|-
|
| |12
|
| |D#/Eb
|
| |1131.429
|
|1138.541
|73\66
| |1144.74
|189.61
|1147.348
|94.805
|1147.374
|189.61
| |1153.469
|379.221
|1156.839
|568.831
|1157.689
|663.636
|1158.941
|
|1162.591
|1165.2885
| |1165.714
|1166.4835
|1169.043
|1170.004
|1173.738
| |1175.51
|-
|-
|
| |13
|
| |E
|
| |1225.714
|52\47
|1233.42
|
| |1240.435
|189.666
|1242.96
|94.833
|1242.988
|189.666
| |1249.592
|379.331
|1253.242
|568.997
|1254.163
|663.83
|1255.52
|
|1259.474
|1262.396
| |1262.857
|1263.6905
|1266.463
|1267.504
|1271.55
| |1273.469
|-
|-
|
|14
|
|F
|
|1320
|
|1328.298
|83\75
|1335.53
|189.714
|1338.573
|94.857
|1338.603
|189.714
|1345.714
|379.429
|1349.645
|569.143
|1350.637
|664
|1352.089
|
|1356.356
|-
|1359.503
|
|1360
|
|1360.897
|31\28
|1363.884
|
|1365.004
|
|1369.361
|189.796
|1371.429
|94.898
|}
|189.796
{| class="wikitable"
|379.591
! rowspan="2" |Degrees
|569.388
! rowspan="2" |Octatonic
|664.286
! colspan="17" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
|
|-
|
|
|
|
|72\65
|189.89
|94.945
|189.89
|379.78
|569.67
|664.615
|
|-
|
|
|
|41\37
|
|189.961
|94.981
|189.961
|379.923
|569.884
|644.865
|
|-
|
|
|
|
|51\46
|190.062
|95.031
|190.062
|380.124
|570.186
|665.217
|
|-
|10\9
|
|
|
|
|190.476
|95.238
|190.476
|380.952
|571.429
|666.667
|
|-
|
|
|
|
|49\44
|190.909
|95.4545
|190.909
|381.818
|572.727
|668.182
|
|-
|
|
|
|39\35
|
|191.02
|95.51
|191.02
|382.041
|573.061
|668.571
|
|-
|
|
|
|
|68\61
|191.101
|95.55
|191.101
|382.201
|573.302
|668.8525
|
|-
|
|
|29\26
|
|
|191.209
|95.604
|191.209
|382.418
|573.626
|669.231
|
|-
|
|
|
|
|77\69
|191.304
|95.652
|191.304
|382.609
|573.913
|669.567
|
|-
|
|
|
|48\43
|
|191.362
|95.681
|191.362
|382.724
|574.086
|669.767
|
|-
|
|
|
|
|67\60
|191.429
|95.714
|191.429
|382.857
|574.286
|670
|
|-
|
|19\17
|
|
|
|191.597
|95.798
|191.597
|383.193
|574.79
|670.588
|
|-
|
|
|
|
|66\59
|191.768
|95.884
|191.768
|383.535
|575.303
|671.187
|
|-
|
|
|
|47\42
|
|191.837
|95.918
|191.837
|383.675
|575.51
|671.429
|
|-
|
|
|
|
|75\67
|191.898
|95.949
|191.898
|383.795
|575.693
|671.642
|
|-
|
|
|28\25
|
|
|192
|96
|192
|384
|576
|672
|
|-
|
|
|
|
|65\58
|192.118
|96.059
|192.118
|384.236
|576.355
|672.414
|
|-
|
|
|
|37\33
|
|192.208
|96.104
|192.208
|384.416
|576.623
|672.727
|
|-
|
|
|
|
|46\41
|192.334
|96.167
|192.334
|384.669
|577.0035
|673.171
|
|-
|9\8
|
|
|
|
|192.857
|96.429
|192.857
|385.714
|578.571
|675
|
|-
|
|
|
|
|44\39
|193.407
|96.703
|193.407
|386.813
|580.22
|676.923
|
|-
|
|
|
|35\31
|
|193.548
|96.774
|193.548
|387.097
|580.645
|677.419
|
|-
|
|
|
|
|61\54
|193.651
|96.825
|193.651
|387.302
|580.952
|677.778
|
|-
|
|
|26\23
|
|
|193.789
|96.894
|193.789
|387.578
|581.3665
|678.261
|
|-
|
|
|
|
|69\61
|193.911
|96.9555
|193.911
|387.822
|581.733
|678.6885
|
|-
|
|
|
|43\38
|
|193.985
|96.9925
|193.985
|387.97
|581.955
|678.947
|
|-
|
|
|
|
|60\53
|194.07
|97.035
|194.07
|388.14
|582.21
|679.245
|
|-
|
|17\15
|
|
|
|194.286
|97.143
|194.286
|388.571
|582.857
|680
|
|-
|
|
|
|
|59\52
|194.5055
|97.253
|194.5055
|389.011
|583.5165
|680.769
|
|-
|
|
|
|42\37
|
|194.595
|94.297
|194.595
|389.189
|583.784
|681.081
|
|-
|
|
|
|
|67\59
|194.673
|97.337
|194.673
|389.346
|584.019
|681.356
|
|-
|
|
|25\22
|
|
|194.805
|97.403
|194.805
|389.61
|584.416
|681.818
|
|-
|
|
|
|
|58\51
|194.958
|97.479
|194.958
|389.916
|584.874
|682.353
|
|-
|
|
|
|33\29
|
|195.074
|97.537
|195.074
|390.148
|585.222
|682.759
|
|-
|
|
|
|
|41\36
|195.238
|97.619
|195.238
|390.476
|585.714
|683.333
|
|-
|8\7
|
|
|
|
|195.918
|97.959
|195.918
|391.836
|587.755
|685.714
|…to here
Aeolian Mode Neapolitan Temperament from here …
|-
|
|
|
|
|39\34
|196.639
|98.314
|196.639
|393.277
|589.916
|688.235
|
|-
|
|
|
|31\27
|
|196.825
|98.413
|196.825
|393.651
|590.476
|688.889
|
|-
|
|
|
|
|54\47
|196.9605
|98.48
|196.9605
|393.921
|590.8815
|689.362
|
|-
|
|
|23\20
|
|
|197.143
|98.571
|197.143
|394.286
|591.429
|690
|
|-
|
|
|
|
|61\53
|197.305
|98.602
|197.305
|394.609
|591.914
|690.566
|
|-
|
|
|
|38\33
|
|197.403
|98.701
|197.403
|394.805
|592.208
|690.909
|
|-
|
|
|
|
|53\46
|197.5155
|98.758
|197.5155
|395.031
|592.547
|691.304
|
|-
|
|15\13
|
|
|
|197.802
|98.901
|197.802
|395.604
|593.407
|692.308
|
|-
|
|
|
|
|52\45
|198.095
|99.048
|198.095
|396.1905
|594.286
|693.333
|
|-
|
|
|
|37\32
|
|198.214
|99.107
|198.214
|396.429
|594.643
|693.75
|
|-
|
|
|
|
|59\51
|198.319
|99.16
|198.319
|396.639
|594.958
|694.118
|
|-
|
|
|22\19
|
|
|198.496
|99.248
|198.496
|396.9925
|595.489
|694.737
|
|-
|
|
|
|
|51\44
|198.701
|99.351
|198.701
|397.403
|596.104
|695.4545
|
|-
|
|
|
|29\25
|
|198.857
|99.429
|198.857
|397.714
|596.571
|696
|
|-
|
|
|
|
|36\31
|199.078
|99.539
|199.078
|398.157
|597.235
|696.774
|
|-
|7\6
|
|
|
|
|200
|100
|200
|400
|600
|700
|
|-
|
|
|
|
|34\29
|200.985
|100.493
|200.985
|400.97
|602.956
|703.448
|
|-
|-
|
! |Minimum
|
!9ed(5/3)
|
!ed(20/9)
|27\23
! |Golden
|
!28ed5
|201.242
!5ed(4/3)
|101.621
! |Median
|201.242
! |7edf
|402.4845
!56ed(180/7)
|603.727
! |Mean
|704.348
!28ed(36/7)
|
!8ed(8/5)
!10ed(9/5)
!2ed(9/8)
!9ed(17/10)
!ed(16/7)
! |Maximum
|-
|-
|
| |1
|
| |F#/Gb
|
| |97.959
|
|98.262
|47\40
|98.743
|201.429
| |99.459
|100.714
|99.511
|201.429
|99.609
|403.857
| |100
|603.286
| |100.279
|705
|100.382
|
| |100.408
|101.253
|101.711
|101.76
|101.955
|102.071
|102.227
| |102.857
|-
|-
|
| |2
|
| |G
|20\17
| |195.918
|
|196.524
|
|197.486
|201.681
| |198.918
|100.84
|199.022
|201.681
|199.218
|403.361
| |200
|605.045
| |200.559
|705.882
|200.764
|
| |200.816
|202.506
|203.422
|203.519
|203.91
|204.143
|204.453
| |205.714
|-
|-
|
| |3
|
| |G#/Ab
|
| |293.878
|
|294.786
|53\45
|286.229
|201.905
| |298.377
|100.952
|298.534
|201.905
|298.827
|403.8095
| |300
|605.714
| |300.837
|706.667
|301.146
|
| |301.2245
|303.759
|305.132
|305.279
|305.865
|306.214
|306.68
| |308.571
|-
|-
|
| |4
|
| |A
|
| |391.836
|33\28
|393.048
|
|394.9725
|202.041
| |397.839
|101.02
|398.045
|202.041
|398.436
|404.082
| |400
|606.122
| |401.117
|707.143
|401.528
|
| |401.633
|405.012
|406.843
|407.0385
|407.82
|408.285
|408.907
| |411.429
|-
|-
|
| |5
|
| |A#/Bb
|
| |489.796
|
|491.31
|46\39
|493.716
|202.198
| |497.296
|101.099
|497.556
|202.198
|498.045
|404.396
| |500
|606.593
| |501.396
|707.692
|501.9105
|
| |502.041
|506.265
|508.554
|508.798
|509.775
|510.3565
|511.134
| |514.286
|-
|-
|
| |6
|13\11
| |B
|
| |587.755
|
|589.5725
|
|592.459
|202.597
| |597.755
|101.299
|597.067
|202.597
|597.654
|405.195
| |600
|607.792
| |601.676
|709.091
|602.293
|
| |602.449
|607.518
|610.265
|610.558
|611.73
|612.428
|613.36
| |617.143
|-
|-
|
| |7
|
| |H
|
| |685.714
|
|687.835
|45\38
|691.202
|203.0075
| |696.2145
|101.504
|696.578
|203.0075
|697.263
|406.015
| |700
|609.023
| |701.955
|710.526
|702.675
|
| |702.857
|708.771
|711.976
|712.317
|713.685
|714.499
|715.587
| |720
|-
|-
|
| |8
|
| |H#/Cb
|
| |783.6735
|32\27
|786.097
|
|789.945
|203.175
| |795.674
|101.587
|796.099
|203.175
|796.872
|406.349
| |800
|609.524
| |802.234
|711.111
|803.057
|
| |803.265
|810.024
|813.686
|814.077
|815.64
|816.57
|817.814
| |822.857
|-
|-
|
| |9
|
| |C
|
| |881.633
|
|884.359
|51\43
|888.688
|203.322
| |895.133
|101.661
|895.301
|203.322
|896.481
|406.6445
| |900
|609.967
| |902.514
|711.629
|903.439
|
| |903.6735
|911.277
|915.397
|915.837
|917.595
|918.462
|920.041
| |925.714
|-
|-
|
| |10
|
| |C#/Db
|19\16
| |979.592
|
|982.621
|
|987.431
|203.571
| |994.592
|101.786
|995.112
|203.571
|996.09
|407.143
| |1000
|610.714
| |1002.793
|712.5
|1003.821
|
| |1004.4082
|1012.53
|1017.108
|1017.596
|1019.55
|1020.712
|1022.267
| |1028.571
|-
|-
|
| |11
|
| |D
|
| |1077.551
|
|1080.882
|44\37
|1086.174
|203.861
| |1094..051
|101.9305
|1094.623
|203.861
|1095.699
|407.722
| |1100
|611.583
| |1103.072
|713.5135
|1104.203
|
| |1104.49
|1113.783
|1118.819
|1119.356
|1121.505
|1122.784
|1124.494
| |1131.429
|-
|-
|
| |12
|
| |D#/Eb
|
| |1175.51
|25\21
|1179.145
|
|1184.9175
|204.082
| |1193.5105
|102.041
|1194.134
|204.082
|1195.308
|408.163
| |1200
|612.245
| |1203.3514
|714.286
|1204.585
|
| |1204.898
|1215.036
|1220.529
|1221.1155
|1223.46
|1224.856
|1226.721
| |1234.286
|-
|-
|
| |13
|
| |E
|
| |1273.469
|
|1277.407
|31\26
|1283.661
|204.396
| |1292.97
|102.198
|1293.646
|204.396
|1294.916
|408.791
| |1300
|613.187
| |1303.631
|715.384
|1304.967
|
| |1305.306
|1316.289
|1322.24
|1322.875
|1325.415
|1326.927
|1238.947
| |1337.143
|-
|-
|6\5
|14
|
|F
|
|1371.429
|
|1375.669
|
|1382.403
|205.714
|1392.429
|102.857
|1393.157
|205.714
|1394.526
|411.429
|1400
|617.143
|1403.91
|720
|1405.3495
|…to here
|1405.714
|1417.524
|1423.951
|1424.635
|1427.37
|1428.998
|1431.174
|1440
|}
|}
[[Category:14-tone]]
[[Category:14-tone]]
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/14edIX"