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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.
This scale, a Long Common Practice minor mode, 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. It also gives the wide values for the period of the Greater [[Orwellismic temperaments #Triskaidekic|Triskaidekic]], [[Octagar temperaments #Tridecatonic|tridecatonic]], [[Ragismic microtemperaments #Trideci|trideci]] and [[aluminium]] temperaments.
==Tuning spectrum==
==Intervals==
{| class="wikitable"
{| class="wikitable"
|+
|+
! colspan="5" rowspan="2" |Period
!Nonet
! colspan="5" |Octatonic (5L 3s)
!Period
! rowspan="2" |Notes
!Notes
|-
|-
!L
|1/1
!s
|''92.308''
! colspan="3" |Tetrachord
|Soft Phrygian mode begins
|-
|-
|1\1edo
|25\24
|''96.154''
|
|
|
|
|
|184.615
|92.308
|184.615
|369.231
|461.5385
|Phrygian Mode (aka Double) Neapolitan Temperament from here …
|-
|-
|
|24\23
|
|96.321
|
|
|15\14
|197.802
|98.901
|197.802
|395.604
|494.5055
|
|
|-
|-
|
|23\22
|
|96.503
|
|14\13
|
|198.817
|99.408
|198.817
|397.633
|497.041
|
|
|-
|-
|
|22\21
|
|96.703
|
|Soft Phrygian mode ends, Thirdtone Phrygian mode begins
|
|27\25
|199.385
|99.692
|199.385
|398.769
|498.4615
|
|-
|-
|
|21\20
|
|96.923
|13\12
|
|
|200
|100
|200
|400
|500
|
|
|-
|-
|
|20\19
|
|97.166
|
|
|38\35
|200.44
|100.22
|200.44
|400.879
|501.099
|
|
|-
|-
|
|19\18
|
|97.436
|
|25\23
|
|200.669
|100.334
|200.669
|401.338
|501.672
|
|
|-
|-
|
|37\35
|
|97.582
|
|
|37\34
|200.905
|100.4525
|200.905
|401.81
|502.262
|
|
|-
|-
|
|18\17
|12\11
|97.738
|
|
|
|201.399
|100.699
|201.399
|402.797
|503.4965
|
|
|-
|-
|
|17\16
|
|98.077
|
|
|47\43
|201.789
|100.8945
|201.789
|403.578
|504.472
|
|
|-
|-
|
|16\15
|
|98.462
|
|Thirdtone Phrygian mode ends
|35\32
|
|201.923
|100.9615
|201.923
|403.846
|504.808
|
|-
|-
|
|15\14
|
|98.901
|
|Semitone Phrygian mode begins
|
|58\53
|202.032
|101.016
|202.032
|404.064
|505.08
|
|-
|-
|
|14\13
|
|99.408
|23\21
|
|
|202.198
|101.099
|202.198
|404.396
|505.4945
|
|
|-
|-
|
|27\25
|
|99.692
|
|
|57\52
|202.367
|101.183
|202.367
|404.734
|505.917
|
|
|-
|-
|
|13\12
|
|''100.000''
|
|34\31
|
|202.481
|101.241
|202.481
|404.963
|506.2035
|
|
|-
|-
|
|12\11
|
|100.699
|
|
|45\41
|202.627
|101.313
|202.627
|405.253
|506.567
|
|
|-
|-
|11\10
|11\10
|
|101.538
|
|Semitone Phrygian mode ends, Intense Phrygian mode begins
|
|
|203.077
|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
|21\19
|
|
|
|204.049
|102.024
|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
|10\9
|
|
|
|
|205.128
|102.564
|102.564
|205.128
|Intense Phrygian mode ends, Intense Phrygian-Soft Aeolian mode begins
|410.256
|512.8205
|
|-
|-
|
|19\17
|
|103.167
|
|
|49\44
|205.594
|102.797
|205.594
|411.189
|513.986
|
|
|-
|-
|
|9\8
|
|''103.846''
|
|Intense Phrygian-Soft Aeolian mode ends, Soft Aeolian mode begins
|39\35
|
|205.714
|102.857
|205.714
|411.429
|514.286
|
|-
|-
|
|17\15
|
|104.615
|
|
|68\61
|205.801
|102.9
|205.801
|411.6015
|514.502
|
|
|-
|-
|
|8\7
|
|105.495
|29\26
|Soft Aeolian mode ends, Flattone Aeolian mode begins
|
|
|205.917
|102.959
|205.917
|411.824
|514.799
|
|-
|-
|
|15\13
|
|106.509
|
|
|77\69
|206.02
|103.01
|206.02
|412.04
|515.05
|
|
|-
|-
|
|22\19
|
|106.883
|
|Flattone Aeolian mode ends, Meantone Aeolian mode begins
|48\43
|
|206.082
|103.041
|206.082
|412.165
|515.205
|
|-
|-
|
|29\25
|
|107.077
|
|
|67\60
|206.154
|103.077
|206.154
|412.308
|515.385
|
|
|-
|-
|
|7\6
|19\17
|''107.692''
|
|Meantone Aeolian mode ends, Superpyth Intense Aeolian mode begins
|
|
|206.335
|103.167
|206.335
|412.67
|515.837
|
|-
|-
|
|20\17
|
|108.597
|
|
|66\59
|206.519
|103.2595
|206.519
|413.038
|516.297
|
|
|-
|-
|
|13\11
|
|109.091
|
|Superpyth Intense Aeolian mode ends, Ultrapyth Intense Aeolian mode begins
|47\42
|
|206.593
|103.297
|206.593
|413.187
|516.4835
|
|-
|-
|
|19\16
|
|109.615
|
|
|75\67
|206.659
|103.3295
|206.659
|413.318
|516.6475
|
|
|-
|-
|
|6\5
|
|110.769
|28\25
|Ultrapyth Intense Aeolian mode ends
|
|}Golden/Pyrite Tunings±13¢
|
{| class="wikitable"
|206.769
|103.385
|206.769
|413.5385
|516.923
|
|-
|
|
|
|
|65\58
|206.897
|103.443
|206.897
|413.793
|517.241
|
|-
|
|
|
|37\33
|
|206.993
|103.4965
|206.993
|413.986
|517.4825
|
|-
|
|
|
|
|46\41
|207.1295
|103.565
|207.1295
|414.259
|517.824
|
|-
|-
|9\8
! rowspan="4" |Degrees
|
! colspan="2" rowspan="3" |Octatonic
|
! colspan="2" |Soft Phrygian
|
! colspan="4" |Phrygian
|
|207.692
|103.846
|207.692
|415.385
|519.231
|
|-
|-
|
! rowspan="3" |Min-Med
|
! rowspan="3" |Min-Max/Med-Max
|
! colspan="2" |Thirdtone
|
! colspan="2" |Semitone
|44\39
|208.284
|104.142
|208.284
|416.568
|520.71
|
|-
|-
|
! rowspan="2" |Min-Med/Min-Max
|
! rowspan="2" |Med-Max
|
! rowspan="2" |Min-Med/Min-Max
|35\31
! rowspan="2" |Med-Max
|
|208.437
|104.218
|208.437
|416.873
|521.092
|
|-
|-
|
!Natural
|
!Subset of 26edn
|
|
|61\54
|208.547
|104.2735
|208.547
|417.094
|521.3675
|
|-
|-
|
| |1
|
| |G#/Ab
|26\23
|G#v/Ab^
|
|95.389-97.389
|
|95.578-97.578
|208.696
|95.957-98.345
|104.348
|96.785-98.844
|208.696
|98.359-100.709
|417.391
|99.058-101.523
|521.739
|
|-
|-
|
| |2
|
| colspan="2" |A
|
|190.778-194.778
|
|191.155-195.155
|69\61
|191.914-196.689
|208.827
|193.569-197.688
|104.414
|196.719-201.417
|208.827
|198.1165-203.046
|417.6545
|522.068
|
|-
|-
|
| |3
|
| |A#/Bb
|
|A#v/Bb^
|43\38
|286.1665-292.1665
|
|286.733-292.733
|208.907
|287.871-295.034
|104.453
|290.354-296.531
|208.907
|295.078-302.126
|417.814
|297.175-304.569
|522.267
|
|-
|-
|
| |4
|
| colspan="2" |B
|
|381.555-389.555
|
|382.3105-390.3105
|60\53
|383.828-393.378
|208.9985
|387.138-395.375
|104.499
|393.4375-402.835
|208.9985
|396.233-406.092
|417.997
|522.496
|
|-
|-
|
| |5
|17\15
| |C
|
|B#v/Cb^
|
|476.944-486.944
|
|477.888-487.888
|209.231
|479.785-491.723
|104.615
|483.923-494.219
|209.231
|491.797-503.544
|418.4615
|495.291-507.615
|523.077
|
|-
|-
|
| |6
|
| |C#/Qb
|
|C
|
|572.333-584.333
|59\52
|573.466-585.466
|209.4675
|575.742-590.068
|104.734
|580.707-593.063
|209.4675
|590.156-604.253
|418.935
|594.349-609.138
|523.669
|
|-
|-
|
| |7
|
| |Q
|
|Db
|42\37
|667.722-681.722
|
|669.043-683.043
|209.563
|671.699-688.412
|104.782
|677.492-691.907
|209.563
|688.516-704.962
|419.127
|693.408-710.661
|523.9085
|
|-
|-
|
| |8
|
| |D
|
|Q#
|
|763.111-781.111
|67\59
|764.621-780.621
|209.648
|767.656-786.757
|104.824
|774.2765-790.75
|209.648
|786.875-805.67
|419.296
|792.466-812.184
|524.12
|
|-
|-
|
| |9
|
| |D#/Eb
|25\22
|Eb
|
|858.5-876.5
|
|860.199-878.199
|209.79
|863.613-885.1015
|104.895
|871.061-889.594
|209.79
|885.234-906.379
|419.58
|891.524-913.707
|524.4755
|
|-
|-
|
| |10
|
| |E
|
|D#
|
|953.8885-973.8885
|58\51
|955.776-975.776
|209.955
|959.57-983.446
|104.977
|967.846-988.438
|209.955
|983.594-1007.088
|419.91
|990.582-1015.23
|524.887
|
|-
|-
|
| |11
|
| |E#/Fb
|
|Fb
|33\29
|1049.277-1071.277
|
|1051.354-1073.354
|210.08
|1055.527-1081.791
|105.04
|1064.63-1087.282
|210.08
|1081.953-1107.797
|420.159
|1089.641-1116.75
|525.199
|
|-
|-
|
| |12
|
| |F
|
|E#
|
|1144.666-1168.666
|41\36
|1146.932-1170.932
|210.256
|1151.484-1180.135
|105.128
|1161.415-1186.126
|210.256
|1180.312-1208.506
|420.513
|1188.699-1218.276
|525.641
|
|-
|-
|8\7
| |13
|
| colspan="2" |G
|
|1240.055-1266.055
|
|1242.506-1268.509
|
|1247.441-1278.48
|210.989
|1258.199-1284.969
|105.4945
|1278.672-1309.2145
|210.989
|1287.757-1319.799
|421.978
|}
|527.4725
 
|…to here
{| class="wikitable"
Aeolian Mode Neapolitan Temperament from here …
|-
|-
|
! rowspan="3" |Degrees
|
! colspan="4" rowspan="2" |Octatonic
|
! colspan="2" |Intense Phrygian
|
! colspan="2" |Intense Phrygian-Soft Aeolian
|39\34
! colspan="2" |Soft Aeolian
|211.765
|105.882
|211.765
|423.529
|529.412
|
|-
|-
|
! rowspan="2" |Min-Med/Min-Max
|
! rowspan="2" |Med-Max
|
! rowspan="2" |Min-Med/Min-Max
|31\27
! rowspan="2" |Med-Max
|
! rowspan="2" |Min-Med/Min-Max
|211.966
! rowspan="2" |Med-Max
|105.983
|211.966
|423.932
|529.9145
|
|-
|-
|
! colspan="2" |Natural
|
! colspan="2" |Subset of 26edn
|
|
|54\47
|212.111
|106.056
|212.111
|424.223
|530.278
|
|-
|-
|
| |1
|
| |F#/Gb
|23\20
|G#/Ab
|
|F#v/Gb^
|
|G#v/Ab^
|212.308
|100.905-102.905
|106.154
|101.1465-103.1465
|212.308
|102.019-104.019
|424.615
|102.32-104.32
|530.769
|103.425-105.425
|
|103.812-105.812
|-
|-
|
| |2
|
| |G
|
|A
|
|G
|61\53
|A
|212.482
|201.81-205.81
|106.241
|202.293-206.293
|212.482
|204.037-208.037
|424.964
|204.641-208.641
|531.205
|206.849-210.849
|
|207.624-211.624
|-
|-
|
| |3
|
| |G#/Ab
|
|A#/Bb
|38\33
|G#v/Ab^
|
|A#v/Bb^
|212.587
|302.715-308.715
|106.294
|303.44-309.44
|212.587
|306.056-312.056
|425.175
|306.961-312.961
|531.4685
|310.274-316.274
|
|311.4365-317.4365
|-
|-
|
| |4
|
| |A
|
|B
|
|A
|53\46
|B
|212.709
|403.62-411.62
|106.3595
|404.586-412.586
|212.709
|408.075-416.075
|425.418
|409.281-417.281
|531.773
|413.699-421.699
|
|415.249-423.249
|-
|-
|
| |5
|15\13
| |B
|
|C
|
|A#v/Bb^
|
|B#v/Cb^
|213.018
|504.525-514.525
|106.509
|505.733-515.733
|213.018
|510.093-520.093
|426.0355
|511.602-521.602
|532.544
|517.123-527.123
|
|519.061-529.061
|-
|-
|
| |6
|
| |B#/Hb
|
|C#/Qb
|
|B
|52\45
|C
|213.333
|605.43-617.43
|106.667
|606.879-618.879
|213.333
|612.112-624.112
|426.667
|613.922-625.922
|533.333
|620.548-632.548
|
|622.873-634.873
|-
|-
|
| |7
|
| |H
|
|Q
|37\32
|Cb
|
|Db
|213.4615
|706.335-720.335
|106.731
|708.026-722.026
|213.4615
|714.131-728.131
|426.923
|716.242-730.242
|533.654
|723.973-737.973
|
|726.685-740.685
|-
|-
|
| |8
|
| |C
|
|D
|
|H#
|59\51
|Q#
|213.575
|807.24-823.24
|106.787
|809.172-825.172
|213.575
|816.1495-832.1495
|427.149
|818.563-834.563
|533.937
|827.3975-843.3975
|
|830.497-846.497
|-
|-
|
| |9
|
| |C#/Db
|22\19
|D#/Eb
|
|Db
|
|Eb
|213.765
|908.145-926.145
|106.883
|910.319-928.319
|213.765
|918.168-936.168
|427.52
|920.883-938.883
|534.413
|930.822-948.822
|
|934.309-952.309
|-
|-
|
| |10
|
| |D
|
|E
|
|C#
|51\44
|D#
|213.986
|1009.0505-1029.0505
|106.993
|1011.465-1031.465
|213.986
|1020.186-1040.186
|427.972
|1023.2035-1043.2035
|534.965
|1034.247-1054.2547
|
|1038.122-1058.122
|-
|-
|
| |11
|
| |D#/Eb
|
|E#/Fb
|29\25
|Eb
|
|Fb
|214.154
|1109.9555-1131.9555
|107.077
|1112.61-1134.612
|214.154
|1122.2055-1143.2055
|428.308
|1125.524-1147.524
|535.385
|1137.672-1159.672
|
|1141.934-1163.934
|-
|-
|
| |12
|
| |E
|
|F
|
|D#
|36\31
|E#
|214.392
|1210.861-1234.861
|107.196
|1213.758-1227.758
|214.392
|1224.224-1248.224
|428.784
|1225.844-1249.884
|535.98
|1241.096-1265.096
|
|1245.746-1269.746
|-
|-
|7\6
| |13
|
| |F
|
|G
|
|F
|
|G
|215.385
|1311.767-1337.767
|107.692
|1314.905-1340.905
|215.385
|1326.243-1352.243
|430.769
|1343.1645-1396.1645
|538.4615
|1344.521-1370.521
|
|1349.558-1375.558
|}
 
{| class="wikitable"
! rowspan="4" |Degrees
! colspan="2" rowspan="3" |Octatonic
! colspan="4" |Aeolian
! colspan="4" |Intense Aeolian
|-
|-
|
! colspan="2" |Flattone
|
! colspan="2" |Meantone
|
! colspan="2" |Superpyth
|
! colspan="2" |Ultrapyth
|34\29
|216.446
|108.223
|216.446
|432.891
|541.114
|
|-
|-
|
! rowspan="2" |Min-Med
|
! rowspan="2" |Med-Max~Min-Max
|
! rowspan="2" |Min-Med/Min-Max
|27\23
! rowspan="2" |Med-Max
|
! rowspan="2" |Min-Med
|216.722
! rowspan="2" |Min-Max/Med-Max
|108.361
! rowspan="2" |Min-Med/Min-Max
|216.722
! rowspan="2" |Med-Max
|433.445
|541.806
|
|-
|-
|
!Natural
|
!Subset of 26edn
|
|
|47\40
|216.923
|108.4615
|216.923
|433.846
|542.308
|
|-
|-
|
| |1
|
| |F#/Gb
|20\17
|F#v/Gb^
|
|105.256-107.256
|
| colspan="2" |105.625-108.015
|217.195
|106.156-108.156
|108.597
|107.435-109.435
|217.195
|107.738-109.738
|434.389
|108.459-110.459
|542.986
|108.802-110.802
|
|-
|-
|
| |2
|
| colspan="2" |G
|
|210.511-214.511
|
| colspan="2" |211.25-216.03
|53\45
|212.313-216.313
|217.436
|214.8705-218.8705
|108.718
|215.4765-219.4765
|217.436
|216.918-220.918
|434.872
|217.604-221.604
|543.59
|
|-
|-
|
| |3
|
| |G#/Ab
|
|G#v/Ab^
|33\28
|315.767-321.767
|
| colspan="2" |316.875-324.044
|217.582
|318.469-324.469
|108.791
|321.306-329.306
|217.582
|322.215-330.215
|435.165
|325.377-331.377
|543.956
|326.4065-332.4065
|
|-
|-
|
| |4
|
| colspan="2" |A
|
|421.022-429.022
|
| colspan="2" |422.501-432.059
|46\39
|424.626-432.626
|217.7515
|429.741-437.741
|108.876
|430.953-438.953
|217.7515
|433.836-437.836
|435.503
|435.209-443.209
|544.679
|
|-
|-
|
| |5
|13\11
| |B
|
|A#v/Bb^
|
|526.278-536.278
|
| colspan="2" |528.126-540.074
|218.182
|530.782-540.782
|109.091
|547.176-547.176
|218.182
|538.6915-548.6915
|436.364
|542.295-552.295
|545.4545
|544.011-554.011
|
|-
|-
|
| |6
|
| |B#/Hb
|
|B
|
|631.534-643.534
|45\38
| colspan="2" |633.751-648.089
|218.6235
|636.9385-648.9385
|109.312
|644.611-656.611
|218.6235
|646.43-658.43
|437.247
|650.754-666.754
|546.5559
|652.813-664.813
|
|-
|-
|
| |7
|
| |H
|
|Cb
|32\27
|736.789-750.789
|
| colspan="2" |739.376-756.104
|218.803
|743.095-757.095
|109.402
|752.047-766.047
|218.803
|754.168-768.168
|437.606
|759.213-773.213
|547.0085
|761.615-775.615
|
|-
|-
|
| |8
|
| |C
|
|H#
|
|842.045-858.045
|51\43
| colspan="2" |845.001-864.1185
|218.962
|849.251-865.521
|109.461
|859.482-875.482
|218.962
|861.906-877.906
|406.6445
|867.672-883.672
|547.406
|870.417-886.417
|
|-
|-
|
| |9
|
| |C#/Db
|19\16
|Db
|
|947.3-965.3
|
| colspan="2" |950.626-972.133
|219.231
|958.408-976.408
|109.615
|966.917-984.917
|219.231
|969.645-986.645
|438.4615
|976.131-994.131
|548.077
|979.219-997.219
|
|-
|-
|
| |10
|
| |D
|
|C#
|
|1052.556-1072.556
|44\37
| colspan="2" |1056.2515-1080.148
|219.543
|1061.564-1081.564
|109.771
|1074.352-1094.352
|219.543
|1077.383-1077.383
|439.085
|1084.59-1104.59
|548.8565
|1088.022-1108.022
|
|-
|-
|
| |11
|
| |D#/Eb
|
|Eb
|25\21
|1157.8115-1179.8115
|
| colspan="2" |1161.877-1188.163
|219.78
|1167.7205-1189.7205
|109.89
|1181.7875-1203.7875
|219.78
|1185.121-1207.121
|439.56
|1193.049-1215.049
|549.4505
|1196.824-1218.824
|
|-
|-
|
| |12
|
| |E
|
|D#
|
|1264.067-1287.067
|31\26
| colspan="2" |1267.502-1296.178
|220.118
|1273.877-1298.877
|110.059
|1288.223-1312.223
|220.118
|1292.86-1316.86
|440.237
|1301.508-1325.508
|550.296
|1304.626-1328-626
|
|-
|-
|6\5
| |13
|
| colspan="2" |F
|
|1368.323-1394.323
|
| colspan="2" |1373.127-1404.193
|
|1380.033-1406.033
|221.5385
|1396.658-1422.658
|110.769
|1400.598-1426.598
|221.5385
|1409.967-1435.967
|443.077
|1414.428-1440.428
|553.846
|…to here
|}
|}
[[Category:13-tone]]
 
[[Category:ed9/4]]
== See also ==
[[Category:edIX]]
[[13ed33/16]] - equal division of the harmonic subminor ninth
[[Category:todo:add_definition]]
 
[[Category:todo:unify_precision]]
[[13ed44/21]] - equal division of the Neogothic minor ninth
 
[[13ed21/10]] - equal division of the septimal chromatic minor ninth
 
[[13ed15/7]] - equal division of the septimal diatonic minor ninth
 
[[13ed11/5]] - equal division of the undecimal neutral ninth
 
[[13ed9/4]] - equal division of the classic major ninth
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/13edIX"