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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="15" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
!Period
!Notes
|-
|-
!Absolute Minimum
|1/1
!5ed(21/16)
|''92.308''
! |Minimum
|Soft Phrygian mode begins
!4ed(5/4)
|-
!10ed(7/4)
|25\24
! |Golden
|''96.154''
!7ed(40/27)
|
!<nowiki><-1\4 -1\18 13\72|</nowiki>
|-
! |Median
|24\23
!9ed(5/3)
|96.321
!14ed(20/9)
|
! |Mean
|-
! |5ed(4/3)
|23\22
!7edf
|96.503
! |Maximum
|
|-
|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¢
{| 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
| |96
|95.578-97.578
|96.578
|95.957-98.345
|96.883
|96.785-98.844
| |97.098
|98.359-100.709
|97.207
|99.058-101.523
|97.42
| |97.582
|98.262
|98.743
| |98.769
| |99.609
|100.279
| |101.5385
|-
|-
| |2
| |2
| |G
| colspan="2" |A
|184.615
|190.778-194.778
|188.312
|191.155-195.155
| |192
|191.914-196.689
|193.157
|193.569-197.688
|193.765
|196.719-201.417
| |194.196
|198.1165-203.046
|194.414
|194.8405
| |195.164
|196.524
|197.486
| |197.5385
| |199.218
|200.559
| |203.077
|-
|-
| |3
| |3
| |G#/Ab
| |A#/Bb
|276.923
|A#v/Bb^
|282.469
|286.1665-292.1665
| |288
|286.733-292.733
|289.735
|287.871-295.034
|290.648
|290.354-296.531
| |291.293
|295.078-302.126
|291.621
|297.175-304.569
|292.261
| |292.747
|294.786
|286.229
| |296.308
| |298.827
|300.837
| |304.615
|-
|-
| |4
| |4
| |A
| colspan="2" |B
|369.231
|381.555-389.555
|376.625
|382.3105-390.3105
| |384
|383.828-393.378
|386.314
|387.138-395.375
|387.53
|393.4375-402.835
| |388.391
|396.233-406.092
|338.828
|389.681
| |390.329
|393.048
|394.9725
| |395.076
| |398.436
|401.117
| |406.154
|-
|-
| |5
| |5
| |B
| |C
|461.5385
|B#v/Cb^
|470.781
|476.944-486.944
| |480
|477.888-487.888
|482.892
|479.785-491.723
|484.413
|483.923-494.219
| |485.489
|491.797-503.544
|486.035
|495.291-507.615
|487.101
| |487.912
|491.31
|493.716
| |493.846
| |498.045
|501.396
| |507.692
|-
|-
| |6
| |6
| |B#/Hb
| |C#/Qb
|553.846
|C
|564.937
|572.333-584.333
| |576
|573.466-585.466
|579.471
|575.742-590.068
|581.2955
|580.707-593.063
| |582.587
|590.156-604.253
|583.242
|594.349-609.138
|584.5215
| |585.4945
|589.5725
|592.459
| |592.615
| |597.654
|601.676
| |609.231
|-
|-
| |7
| |7
| |H
| |Q
|646.154
|Db
|659.093
|667.722-681.722
| |672
|669.043-683.043
|676.049
|671.699-688.412
|678.178
|677.492-691.907
| |679.685
|688.516-704.962
|680.448
|693.408-710.661
|681.942
| |683.077
|687.835
|691.202
| |691.385
| |697.263
|701.955
| |710.769
|-
|-
| |8
| |8
| |C
| |D
|738.4615
|Q#
|753.2495
|763.111-781.111
| |768
|764.621-780.621
|772.627
|767.656-786.757
|775.06
|774.2765-790.75
| |776.782
|786.875-805.67
|777.656
|792.466-812.184
|779.362
| |780.659
|786.097
|789.945
| |790.154
| |796.872
|802.234
| |812.308
|-
|-
| |9
| |9
| |C#/Db
| |D#/Eb
|830.769
|Eb
|847.406
|858.5-876.5
| |864
|860.199-878.199
|869.206
|863.613-885.1015
|871.943
|871.061-889.594
| |873.880
|885.234-906.379
|874.862
|891.524-913.707
|876.782
| |878.242
|884.359
|888.688
| |888.923
| |896.481
|902.514
| |913.846
|-
|-
| |10
| |10
| |D
| |E
|923.077
|D#
|941.562
|953.8885-973.8885
| |960
|955.776-975.776
|965.784
|959.57-983.446
|968.826
|967.846-988.438
| |970.978
|983.594-1007.088
|972.07
|990.582-1015.23
|974.2025
| |975.824
|982.621
|987.431
| |987.692
| |996.09
|1002.793
| |1015.385
|-
|-
| |11
| |11
| |D#/Eb
| |E#/Fb
|1015.385
|Fb
|1035.718
|1049.277-1071.277
| |1056
|1051.354-1073.354
|1062.363
|1055.527-1081.791
|1065.7085
|1064.63-1087.282
| |1068.076
|1081.953-1107.797
|1069.277
|1089.641-1116.75
|1071.623
| |1073.407
|1080.882
|1086.174
| |1086.4615
| |1095.699
|1103.072
| |1116.923
|-
|-
| |12
| |12
| |E
| |F
|1107.692
|E#
|1129.874
|1144.666-1168.666
| |1152
|1146.932-1170.932
|1158.941
|1151.484-1180.135
|1162.591
|1161.415-1186.126
| |1165.1735
|1180.312-1208.506
|1166.4835
|1188.699-1218.276
|1169.043
| |1170.989
|1179.145
|1184.9175
| |1185.231
| |1195.308
|1203.3514
| |1218.4615
|-
|-
| |13
| |13
| |F
| colspan="2" |G
|1200
|1240.055-1266.055
|1224.03
|1242.506-1268.509
| |1248
|1247.441-1278.48
|1255.52
|1258.199-1284.969
|1259.474
|1278.672-1309.2145
| |1262.271
|1287.757-1319.799
|1263.6905
|1266.463
| |1268.286
|1277.407
|1283.661
| |1284
| |1294.916
|1303.631
| |1320
|}
|}
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="2" |Octatonic
! colspan="14" |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
!14ed(16/7)
! colspan="2" |Soft Aeolian
! |Golden
|-
!<nowiki><17/48 1/6 -11/48|</nowiki>
! rowspan="2" |Min-Med/Min-Max
! |Mean
! rowspan="2" |Med-Max
!5ed(27/20)
! rowspan="2" |Min-Med/Min-Max
!7ed(32/21)
! rowspan="2" |Med-Max
!4ed(14/11)
! rowspan="2" |Min-Med/Min-Max
! |Median
! rowspan="2" |Med-Max
!3ed(6/5)
|-
! |Maximum
! colspan="2" |Natural
! colspan="2" |Subset of 26edn
|-
|-
| |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
|102.227
|101.1465-103.1465
| |102.733
|102.019-104.019
|103.462
|102.32-104.32
| |103.5165
|103.425-105.425
|103.91
|103.812-105.812
|104.174
|104.377
| |104.615
|105.213
| |105.4945
|-
|-
| |2
| |2
| |G
| |G
| |203.077
|A
|203.422
|G
|203.519
|A
| |203.91
|201.81-205.81
|204.453
|202.293-206.293
| |205.466
|204.037-208.037
|206.9245
|204.641-208.641
| |207.033
|206.849-210.849
|207.8205
|207.624-211.624
|208.348
|208.754
| |209.231
|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
|306.68
|303.44-309.44
| |308.199
|306.056-312.056
|310.387
|306.961-312.961
| |310.5465
|310.274-316.274
|311.731
|311.4365-317.4365
|312.5225
|313.131
| |313.846
|315.641
| |316.4835
|-
|-
| |4
| |4
| |A
| |A
| |406.154
|B
|406.843
|A
|407.0385
|B
| |407.82
|403.62-411.62
|408.907
|404.586-412.586
| |410.932
|408.075-416.075
|413.849
|409.281-417.281
| |414.066
|413.699-421.699
|415.641
|415.249-423.249
|416.697
|417.508
| |418.4615
|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
|511.134
|505.733-515.733
| |513.6655
|510.093-520.093
|517.311
|511.602-521.602
| |517.582
|517.123-527.123
|519.551
|519.061-529.061
|520.871
|521.885
| |523.077
|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
|613.36
|606.879-618.879
| |616.399
|612.112-624.112
|620.774
|613.922-625.922
| |621.099
|620.548-632.548
|623.4615
|622.873-634.873
|625.045
|626.262
| |627.692
|631.283
| |632.967
|-
|-
| |7
| |7
| |H
| |H
| |710.769
|Q
|711.976
|Cb
|712.317
|Db
| |713.685
|706.335-720.335
|715.587
|708.026-722.026
| |719.132
|714.131-728.131
|724.236
|716.242-730.242
| |724.615
|723.973-737.973
|727.372
|726.685-740.685
|729.219
|730.639
| |732.318
|736.496
| |738.4615
|-
|-
| |8
| |8
| |C
| |C
| |812.308
|D
|813.686
|H#
|814.077
|Q#
| |815.64
|807.24-823.24
|817.814
|809.172-825.172
| |821.865
|816.1495-832.1495
|827.698
|818.563-834.563
| |828.132
|827.3975-843.3975
|831.282
|830.497-846.497
|833.393
|835.016
| |836.923
|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
|920.041
|910.319-928.319
| |924.598
|918.168-936.168
|931.1605
|920.883-938.883
| |931.648
|930.822-948.822
|935.192
|934.309-952.309
|937.567
|939.393
| |941.5385
|946.924
| |949.4505
|-
|-
| |10
| |10
| |D
| |D
| |1015.385
|E
|1017.108
|C#
|1017.596
|D#
| |1019.55
|1009.0505-1029.0505
|1022.267
|1011.465-1031.465
| |1027.331
|1020.186-1040.186
|1034.623
|1023.2035-1043.2035
| |1035.165
|1034.247-1054.2547
|1039.103
|1038.122-1058.122
|1041.742
|1043.77
| |1046.154
|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
|1124.494
|1112.61-1134.612
| |1130.064
|1122.2055-1143.2055
|1138.085
|1125.524-1147.524
| |1138.681
|1137.672-1159.672
|1143.013
|1141.934-1163.934
|1145.916
|1148.147
| |1150.769
|1157.351
| |1160.44
|-
|-
| |12
| |12
| |E
| |E
| |1218.4615
|F
|1220.529
|D#
|1221.1155
|E#
| |1223.46
|1210.861-1234.861
|1226.721
|1213.758-1227.758
| |1232.797
|1224.224-1248.224
|1241.547
|1225.844-1249.884
| |1242.198
|1241.096-1265.096
|1246.923
|1245.746-1269.746
|1250.09
|1252.524
| |1255.385
|1262.565
| |1265.9348
|-
|-
| |13
| |13
| |F
| |F
| |1320
|G
|1322.24
|F
|1322.875
|G
| |1325.415
|1311.767-1337.767
|1238.947
|1314.905-1340.905
| |1335.53
|1326.243-1352.243
|1345.0095
|1343.1645-1396.1645
| |1345.714
|1344.521-1370.521
|1350.833
|1349.558-1375.558
|1354.264
|1356.901
| |1360
|1367.779
| |1371.429
|}
|}
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="4" |Degrees
! rowspan="2" |Octatonic
! colspan="2" rowspan="3" |Octatonic
! colspan="11" |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
! |Median
! rowspan="2" |Med-Max
!9ed(5/3)
! rowspan="2" |Min-Med
! |ed(9/4)
! rowspan="2" |Min-Max/Med-Max
! |Mean
! rowspan="2" |Min-Med/Min-Max
!4ed(9/7)
! rowspan="2" |Med-Max
!26ed(36/7)
|-
!ed(16/7)
!Natural
! |Maximum
!Subset of 26edn
|-
|-
| |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
| |107.692
|106.156-108.156
|98.262
|107.435-109.435
| |107.993
|107.738-109.738
| |108.132
|108.459-110.459
|108.771
|108.802-110.802
|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
| |214.385
|214.8705-218.8705
|196.524
|215.4765-219.4765
| |215.986
|216.918-220.918
| |216.264
|217.604-221.604
|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
| |322.077
|318.469-324.469
|294.786
|321.306-329.306
| |323.979
|322.215-330.215
| |324.396
|325.377-331.377
|326.313
|326.4065-332.4065
|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
| |429.769
|429.741-437.741
|393.048
|430.953-438.953
| |431.972
|433.836-437.836
| |432.5275
|435.209-443.209
|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
| |583.4615
|530.782-540.782
|491.31
|547.176-547.176
| |539.965
|538.6915-548.6915
| |540.659
|542.295-552.295
|543.855
|544.011-554.011
|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
| |646.154
|636.9385-648.9385
|589.5725
|644.611-656.611
| |647.9585
|646.43-658.43
| |648.791
|650.754-666.754
|652.626
|652.813-664.813
|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
| |753.846
|743.095-757.095
|687.835
|752.047-766.047
| |755.9515
|754.168-768.168
| |756.923
|759.213-773.213
|761.397
|761.615-775.615
|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
| |861.5385
|849.251-865.521
|786.097
|859.482-875.482
| |863.945
|861.906-877.906
| |865.055
|867.672-883.672
|870.168
|870.417-886.417
|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
| |969.231
|958.408-976.408
|884.359
|966.917-984.917
| |971.938
|969.645-986.645
| |973.187
|976.131-994.131
|978.939
|979.219-997.219
|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
| |1076.923
|1061.564-1081.564
|982.621
|1074.352-1094.352
| |1079.931
|1077.383-1077.383
| |1081.319
|1084.59-1104.59
|1087.71
|1088.022-1108.022
|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
| |1184.615
|1167.7205-1189.7205
|1080.882
|1181.7875-1203.7875
| |1187.924
|1185.121-1207.121
| |1189.4505
|1193.049-1215.049
|1196.481
|1196.824-1218.824
|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
| |1292.308
|1273.877-1298.877
|1179.145
|1288.223-1312.223
| |1295.917
|1292.86-1316.86
| |1297.582
|1301.508-1325.508
|1305.252
|1304.626-1328-626
|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
| |1400
|1396.658-1422.658
|1277.407
|1400.598-1426.598
| |1403.91
|1409.967-1435.967
| |1405.714
|1414.428-1440.428
|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
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/13edIX"