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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.
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"
! rowspan="2" |Degrees
|+
! rowspan="2" |Octatonic
!Nonet
! colspan="20" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
!Period
!Notes
|-
|-
!Absolute Minimum
|1/1
!5ed(21/16)
|''92.308''
!8ed(14/9)
|Soft Phrygian mode begins
! |Minimum
|-
!3ed(13/11)
|25\24
!4ed(5/4)
|''96.154''
!10ed(7/4)
|
! |Golden
|-
!<nowiki><… -3 0 8|/48</nowiki>
|24\23
!7ed(40/27)
|96.321
!<nowiki><-18 -4 13|\72</nowiki>
|
! |Median
|-
!8ed(11/7)
|23\22
!9ed(5/3)
|96.503
!14ed(20/9)
|
! |Mean
|-
! |5ed(4/3)
|22\21
!7edf
|96.703
!ed(15/7)
|Soft Phrygian mode ends, Thirdtone Phrygian mode begins
! |Maximum
|-
|21\20
|96.923
|
|-
|20\19
|97.166
|
|-
|19\18
|97.436
|
|-
|37\35
|97.582
|
|-
|18\17
|97.738
|
|-
|17\16
|98.077
|
|-
|16\15
|98.462
|Thirdtone Phrygian mode ends
|-
|15\14
|98.901
|Semitone Phrygian mode begins
|-
|14\13
|99.408
|
|-
|27\25
|99.692
|
|-
|13\12
|''100.000''
|
|-
|12\11
|100.699
|
|-
|11\10
|101.538
|Semitone Phrygian mode ends, Intense Phrygian mode begins
|-
|21\19
|102.024
|
|-
|10\9
|102.564
|Intense Phrygian mode ends, Intense Phrygian-Soft Aeolian mode begins
|-
|19\17
|103.167
|
|-
|9\8
|''103.846''
|Intense Phrygian-Soft Aeolian mode ends, Soft Aeolian mode begins
|-
|17\15
|104.615
|
|-
|8\7
|105.495
|Soft Aeolian mode ends, Flattone Aeolian mode begins
|-
|15\13
|106.509
|
|-
|22\19
|106.883
|Flattone Aeolian mode ends, Meantone Aeolian mode begins
|-
|29\25
|107.077
|
|-
|7\6
|''107.692''
|Meantone Aeolian mode ends, Superpyth Intense Aeolian mode begins
|-
|20\17
|108.597
|
|-
|13\11
|109.091
|Superpyth Intense Aeolian mode ends, Ultrapyth Intense Aeolian mode begins
|-
|19\16
|109.615
|
|-
|6\5
|110.769
|Ultrapyth Intense Aeolian mode ends
|}Golden/Pyrite Tunings±13¢
{| class="wikitable"
|-
! rowspan="4" |Degrees
! colspan="2" rowspan="3" |Octatonic
! colspan="2" |Soft Phrygian
! colspan="4" |Phrygian
|-
! rowspan="3" |Min-Med
! rowspan="3" |Min-Max/Med-Max
! colspan="2" |Thirdtone
! colspan="2" |Semitone
|-
! rowspan="2" |Min-Med/Min-Max
! rowspan="2" |Med-Max
! rowspan="2" |Min-Med/Min-Max
! rowspan="2" |Med-Max
|-
!Natural
!Subset of 26edn
|-
|-
| |1
| |1
| |F#/Gb
| |G#/Ab
|92.308
|G#v/Ab^
|94.156
|95.389-97.389
|95.6145
|95.578-97.578
| |96
|95.957-98.345
|96.403
|96.785-98.844
|96.578
|98.359-100.709
|96.883
|99.058-101.523
| |97.098
|97.107
|97.207
|97.42
| |97.582
|97.8115
|98.262
|98.743
| |98.769
| |99.609
|100.279
|101.496
| |101.5385
|-
|-
| |2
| |2
| |G
| colspan="2" |A
|184.615
|190.778-194.778
|188.312
|191.155-195.155
|191.229
|191.914-196.689
| |192
|193.569-197.688
|192.8065
|196.719-201.417
|193.157
|198.1165-203.046
|193.765
| |194.196
|194.213
|194.414
|194.8405
| |195.164
|195.623
|196.524
|197.486
| |197.5385
| |199.218
|200.559
|202.991
| |203.077
|-
|-
| |3
| |3
| |G#/Ab
| |A#/Bb
|276.923
|A#v/Bb^
|282.469
|286.1665-292.1665
|286.843
|286.733-292.733
| |288
|287.871-295.034
|289.21
|290.354-296.531
|289.735
|295.078-302.126
|290.648
|297.175-304.569
| |291.293
|291.322
|291.621
|292.261
| |292.747
|293.4345
|294.786
|286.229
| |296.308
| |298.827
|300.837
|304.487
| |304.615
|-
|-
| |4
| |4
| |A
| colspan="2" |B
|369.231
|381.555-389.555
|376.625
|382.3105-390.3105
|382.458
|383.828-393.378
| |384
|387.138-395.375
|385.613
|393.4375-402.835
|386.314
|396.233-406.092
|387.53
| |388.391
|388.429
|338.828
|389.681
| |390.329
|391.246
|393.048
|394.9725
| |395.076
| |398.436
|401.117
|405.982
| |406.154
|-
|-
| |5
| |5
| |B
| |C
|461.5385
|B#v/Cb^
|470.781
|476.944-486.944
|478.072
|477.888-487.888
| |480
|479.785-491.723
|482.016
|483.923-494.219
|482.892
|491.797-503.544
|484.413
|495.291-507.615
| |485.489
|485.537
|486.035
|487.101
| |487.912
|489.0575
|491.31
|493.716
| |493.846
| |498.045
|501.396
|507.478
| |507.692
|-
|-
| |6
| |6
| |B#/Hb
| |C#/Qb
|553.846
|C
|564.937
|572.333-584.333
|573.687
|573.466-585.466
| |576
|575.742-590.068
|875.419
|580.707-593.063
|579.471
|590.156-604.253
|581.2955
|594.349-609.138
| |582.587
|582.644
|583.242
|584.5215
| |585.4945
|586.869
|589.5725
|592.459
| |592.615
| |597.654
|601.676
|608.974
| |609.231
|-
|-
| |7
| |7
| |H
| |Q
|646.154
|Db
|659.093
|667.722-681.722
|669.301
|669.043-683.043
| |672
|671.699-688.412
|674.823
|677.492-691.907
|676.049
|688.516-704.962
|678.178
|693.408-710.661
| |679.685
|679.752
|680.448
|681.942
| |683.077
|684.6805
|687.835
|691.202
| |691.385
| |697.263
|701.955
|710.469
| |710.769
|-
|-
| |8
| |8
| |C
| |D
|738.4615
|Q#
|753.2495
|763.111-781.111
|764.916
|764.621-780.621
| |768
|767.656-786.757
|771.226
|774.2765-790.75
|772.627
|786.875-805.67
|775.06
|792.466-812.184
| |776.782
|776.859
|777.656
|779.362
| |780.659
|782.492
|786.097
|789.945
| |790.154
| |796.872
|802.234
|811.965
| |812.308
|-
|-
| |9
| |9
| |C#/Db
| |D#/Eb
|830.769
|Eb
|847.406
|858.5-876.5
|860.53
|860.199-878.199
| |864
|863.613-885.1015
|867.629
|871.061-889.594
|869.206
|885.234-906.379
|871.943
|891.524-913.707
| |873.880
|873.966
|874.862
|876.782
| |878.242
|880.3035
|884.359
|888.688
| |888.923
| |896.481
|902.514
|913.46
| |913.846
|-
|-
| |10
| |10
| |D
| |E
|923.077
|D#
|941.562
|953.8885-973.8885
|956.145
|955.776-975.776
| |960
|959.57-983.446
|964.032
|967.846-988.438
|965.784
|983.594-1007.088
|968.826
|990.582-1015.23
| |970.978
|971.073
|972.07
|974.2025
| |975.824
|978.115
|982.621
|987.431
| |987.692
| |996.09
|1002.793
|1014.956
| |1015.385
|-
|-
| |11
| |11
| |D#/Eb
| |E#/Fb
|1015.385
|Fb
|1035.718
|1049.277-1071.277
|1051.759
|1051.354-1073.354
| |1056
|1055.527-1081.791
|1060.436
|1064.63-1087.282
|1062.363
|1081.953-1107.797
|1065.7085
|1089.641-1116.75
| |1068.076
|1068.181
|1069.277
|1071.623
| |1073.407
|1075.9265
|1080.882
|1086.174
| |1086.4615
| |1095.699
|1103.072
|1116.451
| |1116.923
|-
|-
| |12
| |12
| |E
| |F
|1107.692
|E#
|1129.874
|1144.666-1168.666
|1147.374
|1146.932-1170.932
| |1152
|1151.484-1180.135
|1156.839
|1161.415-1186.126
|1158.941
|1180.312-1208.506
|1162.591
|1188.699-1218.276
| |1165.1735
|1165.2885
|1166.4835
|1169.043
| |1170.989
|1173.738
|1179.145
|1184.9175
| |1185.231
| |1195.308
|1203.3514
|1217.947
| |1218.4615
|-
|-
| |13
| |13
| |F
| colspan="2" |G
|1200
|1240.055-1266.055
|1224.03
|1242.506-1268.509
|1242.988
|1247.441-1278.48
| |1248
|1258.199-1284.969
|1253.242
|1278.672-1309.2145
|1255.52
|1287.757-1319.799
|1259.474
| |1262.271
|1262.396
|1263.6905
|1266.463
| |1268.571
|1271.55
|1277.407
|1283.661
| |1284
| |1294.916
|1303.631
|1319.443
| |1320
|}
|}
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="2" |Octatonic
! colspan="20" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
|-
|-
! |Minimum
! rowspan="3" |Degrees
!8ed(8/5)
! colspan="4" rowspan="2" |Octatonic
!10ed(9/5)
! colspan="2" |Intense Phrygian
! |2ed(9/8)
! colspan="2" |Intense Phrygian-Soft Aeolian
!9ed(17/10)
! colspan="2" |Soft Aeolian
!ed(28/13)
|-
!14ed(16/7)
! rowspan="2" |Min-Med/Min-Max
! |Golden
! rowspan="2" |Med-Max
!ed(13/6)
! rowspan="2" |Min-Med/Min-Max
!<nowiki><17 8 -11|/48</nowiki>
! rowspan="2" |Med-Max
! |Mean
! rowspan="2" |Min-Med/Min-Max
!9ed(12/7)
! rowspan="2" |Med-Max
!ed(24/11)
|-
!5ed(27/20)
! colspan="2" |Natural
!7ed(32/21)
! colspan="2" |Subset of 26edn
!4ed(14/11)
! |Median
!ed(11/5)
!3ed(6/5)
! |Maximum
|-
|-
| |1
| |1
| |F#/Gb
| |F#/Gb
| |101.5385
|G#/Ab
|101.711
|F#v/Gb^
|101.76
|G#v/Ab^
| |101.955
|100.905-102.905
|102.071
|101.1465-103.1465
|102.177
|102.019-104.019
|102.227
|102.32-104.32
| |102.733
|103.425-105.425
|102.967
|103.812-105.812
|103.462
| |103.5165
|103.681
|103.895
|103.91
|104.174
|104.377
| |104.615
|105
|105.213
| |105.4945
|-
|-
| |2
| |2
| |G
| |G
| |203.077
|A
|203.422
|G
|203.519
|A
| |203.91
|201.81-205.81
|204.143
|202.293-206.293
|204.354
|204.037-208.037
|204.453
|204.641-208.641
| |205.466
|206.849-210.849
|205.934
|207.624-211.624
|206.9245
| |207.033
|207.362
|207.79
|207.8205
|208.348
|208.754
| |209.231
|210.001
|210.4275
| |210.989
|-
|-
| |3
| |3
| |G#/Ab
| |G#/Ab
| |304.615
|A#/Bb
|305.132
|G#v/Ab^
|305.279
|A#v/Bb^
| |305.865
|302.715-308.715
|306.214
|303.44-309.44
|306.53
|306.056-312.056
|306.68
|306.961-312.961
| |308.199
|310.274-316.274
|308.901
|311.4365-317.4365
|310.387
| |310.5465
|311.043
|311.6855
|311.731
|312.5225
|313.131
| |313.846
|315.001
|315.641
| |316.4835
|-
|-
| |4
| |4
| |A
| |A
| |406.154
|B
|406.843
|A
|407.0385
|B
| |407.82
|403.62-411.62
|408.285
|404.586-412.586
|408.707
|408.075-416.075
|408.907
|409.281-417.281
| |410.932
|413.699-421.699
|411.8685
|415.249-423.249
|413.849
| |414.066
|414.724
|415.581
|415.641
|416.697
|417.508
| |418.4615
|420.001
|420.855
| |421.978
|-
|-
| |5
| |5
| |B
| |B
| |507.692
|C
|508.554
|A#v/Bb^
|508.798
|B#v/Cb^
| |509.775
|504.525-514.525
|510.3565
|505.733-515.733
|510.884
|510.093-520.093
|511.134
|511.602-521.602
| |513.6655
|517.123-527.123
|514.836
|519.061-529.061
|517.311
| |517.582
|518.405
|519.476
|519.551
|520.871
|521.885
| |523.077
|525.002
|526.069
| |527.4725
|-
|-
| |6
| |6
| |B#/Hb
| |B#/Hb
| |609.231
|C#/Qb
|610.265
|B
|610.558
|C
| |611.73
|605.43-617.43
|612.428
|606.879-618.879
|613.061
|612.112-624.112
|613.36
|613.922-625.922
| |616.399
|620.548-632.548
|617.803
|622.873-634.873
|620.774
| |621.099
|622.086
|623.371
|623.4615
|625.045
|626.262
| |627.692
|630.002
|631.283
| |632.967
|-
|-
| |7
| |7
| |H
| |H
| |710.769
|Q
|711.976
|Cb
|712.317
|Db
| |713.685
|706.335-720.335
|714.499
|708.026-722.026
|715.2375
|714.131-728.131
|715.587
|716.242-730.242
| |719.132
|723.973-737.973
|720.769
|726.685-740.685
|724.236
| |724.615
|725.767
|727.266
|727.372
|729.219
|730.639
| |732.318
|735.002
|736.496
| |738.4615
|-
|-
| |8
| |8
| |C
| |C
| |812.308
|D
|813.686
|H#
|814.077
|Q#
| |815.64
|807.24-823.24
|816.57
|809.172-825.172
|817.414
|816.1495-832.1495
|817.814
|818.563-834.563
| |821.865
|827.3975-843.3975
|823.737
|830.497-846.497
|827.698
| |828.132
|829.448
|831.161
|831.282
|833.393
|835.016
| |836.923
|840.003
|841.71
| |843.856
|-
|-
| |9
| |9
| |C#/Db
| |C#/Db
| |913.846
|D#/Eb
|915.397
|Db
|915.837
|Eb
| |917.595
|908.145-926.145
|918.462
|910.319-928.319
|919.591
|918.168-936.168
|920.041
|920.883-938.883
| |924.598
|930.822-948.822
|926.704
|934.309-952.309
|931.1605
| |931.648
|933.129
|935.056
|935.192
|937.567
|939.393
| |941.5385
|945.003
|946.924
| |949.4505
|-
|-
| |10
| |10
| |D
| |D
| |1015.385
|E
|1017.108
|C#
|1017.596
|D#
| |1019.55
|1009.0505-1029.0505
|1020.712
|1011.465-1031.465
|1021.768
|1020.186-1040.186
|1022.267
|1023.2035-1043.2035
| |1027.331
|1034.247-1054.2547
|1029.671
|1038.122-1058.122
|1034.623
| |1035.165
|1036.81
|1038.952
|1039.103
|1041.742
|1043.77
| |1046.154
|1050.003
|1052.138
| |1054.945
|-
|-
| |11
| |11
| |D#/Eb
| |D#/Eb
| |1116.923
|E#/Fb
|1118.819
|Eb
|1119.356
|Fb
| |1121.505
|1109.9555-1131.9555
|1122.784
|1112.61-1134.612
|1123.945
|1122.2055-1143.2055
|1124.494
|1125.524-1147.524
| |1130.064
|1137.672-1159.672
|1132.638
|1141.934-1163.934
|1138.085
| |1138.681
|1140.491
|1142.847
|1143.013
|1145.916
|1148.147
| |1150.769
|1155.004
|1157.351
| |1160.44
|-
|-
| |12
| |12
| |E
| |E
| |1218.4615
|F
|1220.529
|D#
|1221.1155
|E#
| |1223.46
|1210.861-1234.861
|1224.856
|1213.758-1227.758
|1226.1215
|1224.224-1248.224
|1226.721
|1225.844-1249.884
| |1232.797
|1241.096-1265.096
|1235.6055
|1245.746-1269.746
|1241.547
| |1242.198
|1244.172
|1246.742
|1246.923
|1250.09
|1252.524
| |1255.385
|1260.004
|1262.565
| |1265.9348
|-
|-
| |13
| |13
| |F
| |F
| |1320
|G
|1322.24
|F
|1322.875
|G
| |1325.415
|1311.767-1337.767
|1326.927
|1314.905-1340.905
|1328.298
|1326.243-1352.243
|1238.947
|1343.1645-1396.1645
| |1335.53
|1344.521-1370.521
|1338.573
|1349.558-1375.558
|1345.0095
| |1345.714
|1347.853
|1350.637
|1350.833
|1354.264
|1356.901
| |1360
|1365.004
|1367.779
| |1371.429
|}
|}
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="4" |Degrees
! rowspan="2" |Octatonic
! colspan="2" rowspan="3" |Octatonic
! colspan="13" |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
! rowspan="2" |Min-Med
!ed(20/9)
! rowspan="2" |Med-Max~Min-Max
! |Golden
! rowspan="2" |Min-Med/Min-Max
!26ed5
! rowspan="2" |Med-Max
! |Median
! rowspan="2" |Min-Med
!9ed(5/3)
! rowspan="2" |Min-Max/Med-Max
! |ed(9/4)
! rowspan="2" |Min-Med/Min-Max
!52ed(180/7)
! rowspan="2" |Med-Max
! |Mean
|-
!4ed(9/7)
!Natural
!26ed(36/7)
!Subset of 26edn
!ed(16/7)
! |Maximum
|-
|-
| |1
| |1
| |F#/Gb
| |F#/Gb
| |105.4945
|F#v/Gb^
|106.339
|105.256-107.256
| |107.11
| colspan="2" |105.625-108.015
|107.166
|106.156-108.156
| |107.692
|107.435-109.435
|98.262
|107.738-109.738
| |107.993
|108.459-110.459
|108.104
|108.802-110.802
| |108.132
|108.771
|109.042
|110.09
| |110.769
|-
|-
| |2
| |2
| |G
| colspan="2" |G
| |210.989
|210.511-214.511
|212.6775
| colspan="2" |211.25-216.03
| |214.22
|212.313-216.313
|214.332
|214.8705-218.8705
| |214.385
|215.4765-219.4765
|196.524
|216.918-220.918
| |215.986
|217.604-221.604
|216.208
| |216.264
|217.542
|218.083
|220.181
| |221.5385
|-
|-
| |3
| |3
| |G#/Ab
| |G#/Ab
| |304.615
|G#v/Ab^
|319.016
|315.767-321.767
| |321.33
| colspan="2" |316.875-324.044
|321.498
|318.469-324.469
| |322.077
|321.306-329.306
|294.786
|322.215-330.215
| |323.979
|325.377-331.377
|324.311
|326.4065-332.4065
| |324.396
|326.313
|327.125
|330.271
| |332.308
|-
|-
| |4
| |4
| |A
| colspan="2" |A
| |421.978
|421.022-429.022
|425.355
| colspan="2" |422.501-432.059
| |428.44
|424.626-432.626
|428.664
|429.741-437.741
| |429.769
|430.953-438.953
|393.048
|433.836-437.836
| |431.972
|435.209-443.209
|432.415
| |432.5275
|435.084
|436.167
|440.361
| |443.076
|-
|-
| |5
| |5
| |B
| |B
| |527.4725
|A#v/Bb^
|531.694
|526.278-536.278
| |535.55
| colspan="2" |528.126-540.074
|535.83
|530.782-540.782
| |583.4615
|547.176-547.176
|491.31
|538.6915-548.6915
| |539.965
|542.295-552.295
|540.519
|544.011-554.011
| |540.659
|543.855
|545.2085
|550.452
| |553.846
|-
|-
| |6
| |6
| |B#/Hb
| |B#/Hb
| |609.231
|B
|638.0325
|631.534-643.534
| |642.6595
| colspan="2" |633.751-648.089
|642.9945
|636.9385-648.9385
| |646.154
|644.611-656.611
|589.5725
|646.43-658.43
| |647.9585
|650.754-666.754
|948.943
|652.813-664.813
| |648.791
|652.626
|654.25
|660.542
| |664.615
|-
|-
| |7
| |7
| |H
| |H
| |710.769
|Cb
|744.371
|736.789-750.789
| |749.769
| colspan="2" |739.376-756.104
|750.161
|743.095-757.095
| |753.846
|752.047-766.047
|687.835
|754.168-768.168
| |755.9515
|759.213-773.213
|756.727
|761.615-775.615
| |756.923
|761.397
|863.292
|770.632
| |775.385
|-
|-
| |8
| |8
| |C
| |C
| |812.308
|H#
|850.71
|842.045-858.045
| |856.879
| colspan="2" |845.001-864.1185
|857.327
|849.251-865.521
| |861.5385
|859.482-875.482
|786.097
|861.906-877.906
| |863.945
|867.672-883.672
|864.83
|870.417-886.417
| |865.055
|870.168
|872.334
|880.7225
| |886.154
|-
|-
| |9
| |9
| |C#/Db
| |C#/Db
| |913.846
|Db
|957.049
|947.3-965.3
| |963.989
| colspan="2" |950.626-972.133
|964.493
|958.408-976.408
| |969.231
|966.917-984.917
|884.359
|969.645-986.645
| |971.938
|976.131-994.131
|972.934
|979.219-997.219
| |973.187
|978.939
|981.375
|990.813
| |996.923
|-
|-
| |10
| |10
| |D
| |D
| |1015.385
|C#
|1063.3875
|1052.556-1072.556
| |1071.099
| colspan="2" |1056.2515-1080.148
|1071.659
|1061.564-1081.564
| |1076.923
|1074.352-1094.352
|982.621
|1077.383-1077.383
| |1079.931
|1084.59-1104.59
|1081.038
|1088.022-1108.022
| |1081.319
|1087.71
|1090.416
|1100.903
| |1107.692
|-
|-
| |11
| |11
| |D#/Eb
| |D#/Eb
| |1116.923
|Eb
|1169.726
|1157.8115-1179.8115
| |1178.209
| colspan="2" |1161.877-1188.163
|1178.825
|1167.7205-1189.7205
| |1184.615
|1181.7875-1203.7875
|1080.882
|1185.121-1207.121
| |1187.924
|1193.049-1215.049
|1189.142
|1196.824-1218.824
| |1189.4505
|1196.481
|1199.459
|1210.9935
| |1218.4615
|-
|-
| |12
| |12
| |E
| |E
| |1218.4615
|D#
|1276.065
|1264.067-1287.067
| |1285.319
| colspan="2" |1267.502-1296.178
|1285.991
|1273.877-1298.877
| |1292.308
|1288.223-1312.223
|1179.145
|1292.86-1316.86
| |1295.917
|1301.508-1325.508
|1297.246
|1304.626-1328-626
| |1297.582
|1305.252
|1308.5
|1321.084
| |1329.231
|-
|-
| |13
| |13
| |F
| colspan="2" |F
| |1371.429
|1368.323-1394.323
|1382.403
| colspan="2" |1373.127-1404.193
| |1392.429
|1380.033-1406.033
|1393.157
|1396.658-1422.658
| |1400
|1400.598-1426.598
|1277.407
|1409.967-1435.967
| |1403.91
|1414.428-1440.428
|1405.3495
| |1405.714
|1414.023
|1417.524
|1431.174
| |1440
|}
|}
[[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

Latest revision as of 18:49, 1 August 2025

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 Triskaidekic, tridecatonic, trideci and aluminium temperaments.

Intervals

Nonet Period Notes
1/1 92.308 Soft Phrygian mode begins
25\24 96.154
24\23 96.321
23\22 96.503
22\21 96.703 Soft Phrygian mode ends, Thirdtone Phrygian mode begins
21\20 96.923
20\19 97.166
19\18 97.436
37\35 97.582
18\17 97.738
17\16 98.077
16\15 98.462 Thirdtone Phrygian mode ends
15\14 98.901 Semitone Phrygian mode begins
14\13 99.408
27\25 99.692
13\12 100.000
12\11 100.699
11\10 101.538 Semitone Phrygian mode ends, Intense Phrygian mode begins
21\19 102.024
10\9 102.564 Intense Phrygian mode ends, Intense Phrygian-Soft Aeolian mode begins
19\17 103.167
9\8 103.846 Intense Phrygian-Soft Aeolian mode ends, Soft Aeolian mode begins
17\15 104.615
8\7 105.495 Soft Aeolian mode ends, Flattone Aeolian mode begins
15\13 106.509
22\19 106.883 Flattone Aeolian mode ends, Meantone Aeolian mode begins
29\25 107.077
7\6 107.692 Meantone Aeolian mode ends, Superpyth Intense Aeolian mode begins
20\17 108.597
13\11 109.091 Superpyth Intense Aeolian mode ends, Ultrapyth Intense Aeolian mode begins
19\16 109.615
6\5 110.769 Ultrapyth Intense Aeolian mode ends

Golden/Pyrite Tunings±13¢

Degrees Octatonic Soft Phrygian Phrygian
Min-Med Min-Max/Med-Max Thirdtone Semitone
Min-Med/Min-Max Med-Max Min-Med/Min-Max Med-Max
Natural Subset of 26edn
1 G#/Ab G#v/Ab^ 95.389-97.389 95.578-97.578 95.957-98.345 96.785-98.844 98.359-100.709 99.058-101.523
2 A 190.778-194.778 191.155-195.155 191.914-196.689 193.569-197.688 196.719-201.417 198.1165-203.046
3 A#/Bb A#v/Bb^ 286.1665-292.1665 286.733-292.733 287.871-295.034 290.354-296.531 295.078-302.126 297.175-304.569
4 B 381.555-389.555 382.3105-390.3105 383.828-393.378 387.138-395.375 393.4375-402.835 396.233-406.092
5 C B#v/Cb^ 476.944-486.944 477.888-487.888 479.785-491.723 483.923-494.219 491.797-503.544 495.291-507.615
6 C#/Qb C 572.333-584.333 573.466-585.466 575.742-590.068 580.707-593.063 590.156-604.253 594.349-609.138
7 Q Db 667.722-681.722 669.043-683.043 671.699-688.412 677.492-691.907 688.516-704.962 693.408-710.661
8 D Q# 763.111-781.111 764.621-780.621 767.656-786.757 774.2765-790.75 786.875-805.67 792.466-812.184
9 D#/Eb Eb 858.5-876.5 860.199-878.199 863.613-885.1015 871.061-889.594 885.234-906.379 891.524-913.707
10 E D# 953.8885-973.8885 955.776-975.776 959.57-983.446 967.846-988.438 983.594-1007.088 990.582-1015.23
11 E#/Fb Fb 1049.277-1071.277 1051.354-1073.354 1055.527-1081.791 1064.63-1087.282 1081.953-1107.797 1089.641-1116.75
12 F E# 1144.666-1168.666 1146.932-1170.932 1151.484-1180.135 1161.415-1186.126 1180.312-1208.506 1188.699-1218.276
13 G 1240.055-1266.055 1242.506-1268.509 1247.441-1278.48 1258.199-1284.969 1278.672-1309.2145 1287.757-1319.799
Degrees Octatonic Intense Phrygian Intense Phrygian-Soft Aeolian Soft Aeolian
Min-Med/Min-Max Med-Max Min-Med/Min-Max Med-Max Min-Med/Min-Max Med-Max
Natural Subset of 26edn
1 F#/Gb G#/Ab F#v/Gb^ G#v/Ab^ 100.905-102.905 101.1465-103.1465 102.019-104.019 102.32-104.32 103.425-105.425 103.812-105.812
2 G A G A 201.81-205.81 202.293-206.293 204.037-208.037 204.641-208.641 206.849-210.849 207.624-211.624
3 G#/Ab A#/Bb G#v/Ab^ A#v/Bb^ 302.715-308.715 303.44-309.44 306.056-312.056 306.961-312.961 310.274-316.274 311.4365-317.4365
4 A B A B 403.62-411.62 404.586-412.586 408.075-416.075 409.281-417.281 413.699-421.699 415.249-423.249
5 B C A#v/Bb^ B#v/Cb^ 504.525-514.525 505.733-515.733 510.093-520.093 511.602-521.602 517.123-527.123 519.061-529.061
6 B#/Hb C#/Qb B C 605.43-617.43 606.879-618.879 612.112-624.112 613.922-625.922 620.548-632.548 622.873-634.873
7 H Q Cb Db 706.335-720.335 708.026-722.026 714.131-728.131 716.242-730.242 723.973-737.973 726.685-740.685
8 C D H# Q# 807.24-823.24 809.172-825.172 816.1495-832.1495 818.563-834.563 827.3975-843.3975 830.497-846.497
9 C#/Db D#/Eb Db Eb 908.145-926.145 910.319-928.319 918.168-936.168 920.883-938.883 930.822-948.822 934.309-952.309
10 D E C# D# 1009.0505-1029.0505 1011.465-1031.465 1020.186-1040.186 1023.2035-1043.2035 1034.247-1054.2547 1038.122-1058.122
11 D#/Eb E#/Fb Eb Fb 1109.9555-1131.9555 1112.61-1134.612 1122.2055-1143.2055 1125.524-1147.524 1137.672-1159.672 1141.934-1163.934
12 E F D# E# 1210.861-1234.861 1213.758-1227.758 1224.224-1248.224 1225.844-1249.884 1241.096-1265.096 1245.746-1269.746
13 F G F G 1311.767-1337.767 1314.905-1340.905 1326.243-1352.243 1343.1645-1396.1645 1344.521-1370.521 1349.558-1375.558
Degrees Octatonic Aeolian Intense Aeolian
Flattone Meantone Superpyth Ultrapyth
Min-Med Med-Max~Min-Max Min-Med/Min-Max Med-Max Min-Med Min-Max/Med-Max Min-Med/Min-Max Med-Max
Natural Subset of 26edn
1 F#/Gb F#v/Gb^ 105.256-107.256 105.625-108.015 106.156-108.156 107.435-109.435 107.738-109.738 108.459-110.459 108.802-110.802
2 G 210.511-214.511 211.25-216.03 212.313-216.313 214.8705-218.8705 215.4765-219.4765 216.918-220.918 217.604-221.604
3 G#/Ab G#v/Ab^ 315.767-321.767 316.875-324.044 318.469-324.469 321.306-329.306 322.215-330.215 325.377-331.377 326.4065-332.4065
4 A 421.022-429.022 422.501-432.059 424.626-432.626 429.741-437.741 430.953-438.953 433.836-437.836 435.209-443.209
5 B A#v/Bb^ 526.278-536.278 528.126-540.074 530.782-540.782 547.176-547.176 538.6915-548.6915 542.295-552.295 544.011-554.011
6 B#/Hb B 631.534-643.534 633.751-648.089 636.9385-648.9385 644.611-656.611 646.43-658.43 650.754-666.754 652.813-664.813
7 H Cb 736.789-750.789 739.376-756.104 743.095-757.095 752.047-766.047 754.168-768.168 759.213-773.213 761.615-775.615
8 C H# 842.045-858.045 845.001-864.1185 849.251-865.521 859.482-875.482 861.906-877.906 867.672-883.672 870.417-886.417
9 C#/Db Db 947.3-965.3 950.626-972.133 958.408-976.408 966.917-984.917 969.645-986.645 976.131-994.131 979.219-997.219
10 D C# 1052.556-1072.556 1056.2515-1080.148 1061.564-1081.564 1074.352-1094.352 1077.383-1077.383 1084.59-1104.59 1088.022-1108.022
11 D#/Eb Eb 1157.8115-1179.8115 1161.877-1188.163 1167.7205-1189.7205 1181.7875-1203.7875 1185.121-1207.121 1193.049-1215.049 1196.824-1218.824
12 E D# 1264.067-1287.067 1267.502-1296.178 1273.877-1298.877 1288.223-1312.223 1292.86-1316.86 1301.508-1325.508 1304.626-1328-626
13 F 1368.323-1394.323 1373.127-1404.193 1380.033-1406.033 1396.658-1422.658 1400.598-1426.598 1409.967-1435.967 1414.428-1440.428

See also

13ed33/16 - equal division of the harmonic subminor ninth

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

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