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This scale occurs in 12edo, where it is the equal division of the minor ninth.
This scale occurs in 12edo, where it is the equal division of the minor ninth. It has the Grandfather 5L 3s MOS with a 2:1 ratio of large against small.
 
==Tuning spectrum==
==Intervals==
 
Phrygian Mode (aka Double) Neapolitan Temperament
{| class="wikitable"
{| class="wikitable"
!Degrees
|+
!Octatonic
! colspan="5" rowspan="2" |Period
!Minimum
! colspan="5" |Octatonic (5L 3s)
!Mean
! rowspan="2" |Notes
!Median
!Golden
!Maximum
|-
|-
|1
!L
|F#/Gb
!s
| rowspan="13" |see [[13edo]]
! colspan="3" |Tetrachord
|96.923
|-
|1\1edo
|
|
|
|
|184.615
|92.308
|184.615
|369.231
|461.5385
|Phrygian Mode (aka Double) Neapolitan Temperament from here …
|-
|
|
|
|
|15\14
|197.802
|98.901
|197.802
|395.604
|494.5055
|
|-
|
|
|
|14\13
|
|198.817
|99.408
|198.817
|397.633
|497.041
|
|-
|
|
|
|
|27\25
|199.385
|99.692
|199.385
|398.769
|498.4615
|
|-
|
|
|13\12
|
|
|200
|100
|200
|400
|500
|
|-
|
|
|
|
|38\35
|200.44
|100.22
|200.44
|400.879
|501.099
|
|-
|
|
|
|25\23
|
|200.669
|100.334
|200.669
|401.338
|501.672
|
|-
|
|
|
|
|37\34
|200.905
|100.4525
|200.905
|401.81
|502.262
|
|-
|
|12\11
|
|
|
|201.399
|100.699
|100.699
|101.001
|201.399
|402.797
|503.4965
|
|-
|
|
|
|
|47\43
|201.789
|100.8945
|201.789
|403.578
|504.472
|
|-
|
|
|
|35\32
|
|201.923
|100.9615
|201.923
|403.846
|504.808
|
|-
|
|
|
|
|58\53
|202.032
|101.016
|202.032
|404.064
|505.08
|
|-
|
|
|23\21
|
|
|202.198
|101.099
|202.198
|404.396
|505.4945
|
|-
|
|
|
|
|57\52
|202.367
|101.183
|202.367
|404.734
|505.917
|
|-
|
|
|
|34\31
|
|202.481
|101.241
|202.481
|404.963
|506.2035
|
|-
|
|
|
|
|45\41
|202.627
|101.313
|202.627
|405.253
|506.567
|
|-
|11\10
|
|
|
|
|203.077
|101.5385
|101.5385
|203.077
|406.154
|507.692
|…to here
Phrygian-Aeolian Mode Neapolitan Temperament from here …
|-
|
|
|
|
|54\49
|203.454
|101.757
|203.454
|406.907
|508.634
|
|-
|
|
|
|43\39
|
|203.55
|101.775
|203.55
|407.101
|508.876
|
|-
|
|
|
|
|75\68
|203.62
|101.81
|203.62
|407.24
|509.05
|
|-
|
|
|32\29
|
|
|203.7135
|101.857
|203.7135
|407.427
|509.284
|
|-
|
|
|
|
|85\77
|203.796
|101.898
|203.796
|407.592
|509.4905
|
|-
|
|
|
|53\48
|
|203.846
|101.923
|203.846
|407.692
|509.615
|
|-
|
|
|
|
|74\67
|203.904
|101.952
|203.904
|407.807
|509.759
|Square root of 9/8 is near here
|-
|
|21\19
|
|
|
|204.049
|102.024
|204.049
|408.097
|510.1215
|
|-
|
|
|
|
|73\66
|204.196
|102.098
|204.196
|408.392
|510.4895
|
|-
|
|
|
|52\47
|
|204.255
|102.128
|204.255
|408.511
|510.638
|
|-
|
|
|
|
|83\75
|204.308
|102.154
|204.308
|409.615
|510.769
|
|-
|
|
|31\28
|
|
|204.396
|102.198
|204.396
|408.792
|510.989
|
|-
|
|
|
|
|72\65
|204.497
|102.248
|204.497
|408.994
|511.242
|
|-
|
|
|
|41\37
|
|204.574
|102.287
|204.574
|409.148
|511.4345
|
|-
|
|
|
|
|51\46
|204.682
|102.341
|204.682
|409.3645
|511.706
|
|-
|10\9
|
|
|
|
|205.128
|102.564
|205.128
|410.256
|512.8205
|
|-
|
|
|
|
|49\44
|205.594
|102.797
|205.594
|411.189
|513.986
|
|-
|
|
|
|39\35
|
|205.714
|102.857
|205.714
|411.429
|514.286
|
|-
|
|
|
|
|68\61
|205.801
|102.9
|205.801
|411.6015
|514.502
|
|-
|
|
|29\26
|
|
|205.917
|102.959
|205.917
|411.824
|514.799
|
|-
|
|
|
|
|77\69
|206.02
|103.01
|206.02
|412.04
|515.05
|
|-
|
|
|
|48\43
|
|206.082
|103.041
|206.082
|412.165
|515.205
|
|-
|
|
|
|
|67\60
|206.154
|103.077
|206.154
|412.308
|515.385
|
|-
|
|19\17
|
|
|
|206.335
|103.167
|206.335
|412.67
|515.837
|
|-
|
|
|
|
|66\59
|206.519
|103.2595
|206.519
|413.038
|516.297
|
|-
|
|
|
|47\42
|
|206.593
|103.297
|206.593
|413.187
|516.4835
|
|-
|
|
|
|
|75\67
|206.659
|103.3295
|206.659
|413.318
|516.6475
|
|-
|-
|2
|
|G
|
|193.846
|28\25
|201.399
|
|202.002
|
|203.077
|206.769
|103.385
|206.769
|413.5385
|516.923
|
|-
|-
|3
|
|A
|
|290.769
|
|302.098
|
|303.0035
|65\58
|304.615
|206.897
|103.443
|206.897
|413.793
|517.241
|
|-
|-
|4
|
|A#/Bb
|
|387.692
|
|402.797
|37\33
|404.005
|
|406.154
|206.993
|103.4965
|206.993
|413.986
|517.4825
|
|-
|-
|5
|
|B
|
|484.615
|
|503.4965
|
|505.006
|46\41
|507.692
|207.1295
|103.565
|207.1295
|414.259
|517.824
|
|-
|-
|6
|9\8
|B#/Hb
|
|581.5385
|
|604.196
|
|606.007
|
|609.231
|207.692
|103.846
|207.692
|415.385
|519.231
|
|-
|-
|7
|
|H
|
|678.4615
|
|704.895
|
|707.008
|44\39
|710.769
|208.284
|104.142
|208.284
|416.568
|520.71
|
|-
|-
|8
|
|C
|
|775.385
|
|805.594
|35\31
|808.009
|
|812.308
|208.437
|104.218
|208.437
|416.873
|521.092
|
|-
|-
|9
|
|C#/Db
|
|872.318
|
|906.294
|
|909.011
|61\54
|913.846
|208.547
|104.2735
|208.547
|417.094
|521.3675
|
|-
|-
|10
|
|D
|
|969.231
|26\23
|1006.993
|
|1010.012
|
|1015.385
|208.696
|104.348
|208.696
|417.391
|521.739
|
|-
|-
|11
|
|D#/Eb
|
|1066.154
|
|1107.692
|
|1111.013
|69\61
|1116.923
|208.827
|104.414
|208.827
|417.6545
|522.068
|
|-
|-
|12
|
|E
|
|1163.077
|
|1208.392
|43\38
|1212.014
|
|1218.4615
|208.907
|104.453
|208.907
|417.814
|522.267
|
|-
|-
|13
|
|F
|
|1260
|
|1309.091
|
|1313.015
|60\53
|1320
|208.9985
|}
|104.499
Phrygian-Aeolian Mode Neapolitan Temperament
|208.9985
{| class="wikitable"
|417.997
!Degrees
|522.496
!Octatonic
|
!Minimum
!Golden
!Mean
!Median
!Maximum
|-
|-
|1
|
|F#/Gb
|17\15
|101.5385
|
|102.733
|
|103.5165
|
|209.231
|104.615
|104.615
|209.231
|418.4615
|523.077
|
|-
|
|
|
|
|59\52
|209.4675
|104.734
|209.4675
|418.935
|523.669
|
|-
|
|
|
|42\37
|
|209.563
|104.782
|209.563
|419.127
|523.9085
|
|-
|
|
|
|
|67\59
|209.648
|104.824
|209.648
|419.296
|524.12
|
|-
|
|
|25\22
|
|
|209.79
|104.895
|209.79
|419.58
|524.4755
|
|-
|
|
|
|
|58\51
|209.955
|104.977
|209.955
|419.91
|524.887
|
|-
|
|
|
|33\29
|
|210.08
|105.04
|210.08
|420.159
|525.199
|
|-
|
|
|
|
|41\36
|210.256
|105.128
|210.256
|420.513
|525.641
|
|-
|8\7
|
|
|
|
|210.989
|105.4945
|105.4945
|210.989
|421.978
|527.4725
|…to here
Aeolian Mode Neapolitan Temperament from here …
|-
|
|
|
|
|39\34
|211.765
|105.882
|211.765
|423.529
|529.412
|
|-
|
|
|
|31\27
|
|211.966
|105.983
|211.966
|423.932
|529.9145
|
|-
|
|
|
|
|54\47
|212.111
|106.056
|212.111
|424.223
|530.278
|
|-
|-
|2
|
|G
|
|203.077
|23\20
|205.466
|
|207.033
|
|209.231
|212.308
|210.989
|106.154
|212.308
|424.615
|530.769
|
|-
|
|
|
|
|61\53
|212.482
|106.241
|212.482
|424.964
|531.205
|
|-
|
|
|
|38\33
|
|212.587
|106.294
|212.587
|425.175
|531.4685
|
|-
|
|
|
|
|53\46
|212.709
|106.3595
|212.709
|425.418
|531.773
|
|-
|-
|3
|
|A
|15\13
|304.615
|
|308.199
|
|310.5465
|
|313.846
|213.018
|316.4835
|106.509
|213.018
|426.0355
|532.544
|
|-
|-
|4
|
|A#/Bb
|
|406.154
|
|410.932
|
|414.066
|52\45
|418.4615
|213.333
|421.978
|106.667
|213.333
|426.667
|533.333
|
|-
|-
|5
|
|B
|
|507.692
|
|513.6655
|37\32
|517.582
|
|523.077
|213.4615
|527.4725
|106.731
|213.4615
|426.923
|533.654
|
|-
|-
|6
|
|B#/Hb
|
|609.231
|
|616.399
|
|621.099
|59\51
|627.692
|213.575
|632.967
|106.787
|213.575
|427.149
|533.937
|
|-
|-
|7
|
|H
|
|710.769
|22\19
|719.132
|
|724.615
|
|732.318
|213.765
|738.4615
|106.883
|213.765
|427.52
|534.413
|
|-
|-
|8
|
|C
|
|812.308
|
|821.865
|
|828.132
|51\44
|836.923
|213.986
|843.856
|106.993
|213.986
|427.972
|534.965
|
|-
|-
|9
|
|C#/Db
|
|913.846
|
|924.598
|29\25
|931.648
|
|941.5385
|214.154
|949.4505
|107.077
|214.154
|428.308
|535.385
|
|-
|-
|10
|
|D
|
|1015.385
|
|1027.331
|
|1035.165
|36\31
|1046.154
|214.392
|1054.945
|107.196
|214.392
|428.784
|535.98
|
|-
|-
|11
|7\6
|D#/Eb
|
|1116.923
|
|1130.064
|
|1138.681
|
|1150.769
|215.385
|1160.44
|107.692
|215.385
|430.769
|538.4615
|
|-
|-
|12
|
|E
|
|1218.4615
|
|1232.797
|
|1242.198
|34\29
|1255.385
|216.446
|1265.9348
|108.223
|216.446
|432.891
|541.114
|
|-
|-
|13
|
|F
|
|1320
|
|1335.53
|27\23
|1345.714
|
|1360
|216.722
|1371.429
|108.361
|}
|216.722
Aeolian Mode Neapolitan Temperament
|433.445
{| class="wikitable"
|541.806
|
|-
|-
! |Degrees
|
! |Octatonic
|
! |Minimum
|
! |Golden
|
! |Median
|47\40
! |ed(9/4)
|216.923
! |Mean
|108.4615
! |Maximum
|216.923
|433.846
|542.308
|
|-
|-
| |1
|
| |F#/Gb
|
| |105.4945
|20\17
| |107.11
|
| |107.692
|
| |107.993
|217.195
| |108.132
|108.597
| |110.769
|217.195
|434.389
|542.986
|
|-
|-
| |2
|
| |G
|
| |210.989
|
| |214.22
|
| |214.385
|53\45
| |215.986
|217.436
| |216.264
|108.718
| |221.5385
|217.436
|434.872
|543.59
|
|-
|-
| |3
|
| |A
|
| |316.4835
|
| |321.33
|33\28
| |322.077
|
| |323.979
|217.582
| |324.396
|108.791
| |332.308
|217.582
|435.165
|543.956
|
|-
|-
| |4
|
| |A#/Bb
|
| |421.978
|
| |428.44
|
| |429.769
|46\39
| |431.972
|217.7515
| |432.5275
|108.876
| |443.076
|217.7515
|435.503
|544.679
|
|-
|-
| |5
|
| |B
|13\11
| |527.4725
|
| |535.55
|
| |583.4615
|
| |539.965
|218.182
| |540.659
|109.091
| |553.846
|218.182
|436.364
|545.4545
|
|-
|-
| |6
|
| |B#/Hb
|
| |632.967
|
| |642.6595
|
| |646.154
|45\38
| |647.9585
|218.6235
| |648.791
|109.312
| |664.615
|218.6235
|437.247
|546.5559
|
|-
|-
| |7
|
| |H
|
| |738.4615
|
| |749.769
|32\27
| |753.846
|
| |755.9515
|218.803
| |756.923
|109.402
| |775.385
|218.803
|437.606
|547.0085
|
|-
|-
| |8
|
| |C
|
| |843.856
|
| |856.879
|
| |861.5385
|51\43
| |863.945
|218.962
| |865.055
|109.461
| |886.154
|218.962
|406.6445
|547.406
|
|-
|-
| |9
|
| |C#/Db
|
| |949.4505
|19\16
| |963.989
|
| |969.231
|
| |971.938
|219.231
| |973.187
|109.615
| |996.923
|219.231
|438.4615
|548.077
|
|-
|-
| |10
|
| |D
|
| |1054.945
|
| |1071.099
|
| |1076.923
|44\37
| |1079.931
|219.543
| |1081.319
|109.771
| |1107.692
|219.543
|439.085
|548.8565
|
|-
|-
| |11
|
| |D#/Eb
|
| |1160.44
|
| |1178.209
|25\21
| |1184.615
|
| |1187.924
|219.78
| |1189.4505
|109.89
| |1218.4615
|219.78
|439.56
|549.4505
|
|-
|-
| |12
|
| |E
|
| |1265.9348
|
| |1285.319
|
| |1292.308
|31\26
| |1295.917
|220.118
| |1297.582
|110.059
| |1329.231
|220.118
|440.237
|550.296
|
|-
|-
| |13
|6\5
| |F
|
| |1371.429
|
| |1392.429
|
| |1400
|
| |1403.91
|221.5385
| |1405.714
|110.769
| |1440
|221.5385
|443.077
|553.846
|…to here
|}
|}
[[Category:13-tone]]
[[Category:13-tone]]
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/13edIX"