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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.
==Intervals==
==Intervals==
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
|+
! rowspan="2" |Octatonic
!Nonet
! colspan="4" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
!Period
! colspan="3" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
!Notes
! colspan="3" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
|-
|-
!Absolute Minimum
|1/1
!Minimum
|''92.308''
!Median
|Soft Phrygian mode begins
!Maximum
! |Minimum
!Median
!Maximum
!Minimum
!Median
!Maximum
|-
|-
| |1
|25\24
| |F#/Gb
|''96.154''
|92.308
|
|-
|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
|97.582
|98.4615
|
| colspan="2" |101.5385
|-
|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
|103.167
| colspan="2" |105.4945
|
|107.692
|-
|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
|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
| |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
| colspan="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
| colspan="2" |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
| colspan="2" |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
|}
{| class="wikitable"
|-
! rowspan="3" |Degrees
! colspan="4" rowspan="2" |Octatonic
! colspan="2" |Intense Phrygian
! colspan="2" |Intense Phrygian-Soft Aeolian
! colspan="2" |Soft Aeolian
|-
! rowspan="2" |Min-Med/Min-Max
! rowspan="2" |Med-Max
! rowspan="2" |Min-Med/Min-Max
! rowspan="2" |Med-Max
! rowspan="2" |Min-Med/Min-Max
! rowspan="2" |Med-Max
|-
! colspan="2" |Natural
! colspan="2" |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
| |2
| |G
| |G
|184.615
|A
|195.165
|G
|196.923
|A
| colspan="2" |203.077
|201.81-205.81
|206.335
|202.293-206.293
| colspan="2" |210.989
|204.037-208.037
|215.385
|204.641-208.641
|221.5385
|206.849-210.849
|207.624-211.624
|-
|-
| |3
| |3
| |G#/Ab
| |G#/Ab
|276.923
|A#/Bb
|292.747
|G#v/Ab^
|295.385
|A#v/Bb^
| colspan="2" |304.615
|302.715-308.715
|309.502
|303.44-309.44
| colspan="2" |316.4835
|306.056-312.056
|323.077
|306.961-312.961
|332.308
|310.274-316.274
|311.4365-317.4365
|-
|-
| |4
| |4
| |A
| |A
|369.231
|B
|390.33
|A
|393.846
|B
| colspan="2" |406.154
|403.62-411.62
|412.67
|404.586-412.586
| colspan="2" |421.978
|408.075-416.075
|430.769
|409.281-417.281
|443.076
|413.699-421.699
|415.249-423.249
|-
|-
| |5
| |5
| |B
| |B
|461.5385
|C
|487.912
|A#v/Bb^
|491.308
|B#v/Cb^
| colspan="2" |507.692
|504.525-514.525
|515.837
|505.733-515.733
| colspan="2" |527.4725
|510.093-520.093
|538.4615
|511.602-521.602
|553.846
|517.123-527.123
|519.061-529.061
|-
|-
| |6
| |6
| |B#/Hb
| |B#/Hb
|553.846
|C#/Qb
|585.4945
|B
|589.769
|C
| colspan="2" |609.231
|605.43-617.43
|619.0045
|606.879-618.879
| colspan="2" |632.967
|612.112-624.112
|646.154
|613.922-625.922
|664.615
|620.548-632.548
|622.873-634.873
|-
|-
| |7
| |7
| |H
| |H
|646.154
|Q
|683.077
|Cb
|690.231
|Db
| colspan="2" |710.769
|706.335-720.335
|722.172
|708.026-722.026
| colspan="2" |738.4615
|714.131-728.131
|754.846
|716.242-730.242
|775.385
|723.973-737.973
|726.685-740.685
|-
|-
| |8
| |8
| |C
| |C
|738.4615
|D
|780.66
|H#
|788.692
|Q#
| colspan="2" |812.308
|807.24-823.24
|825.339
|809.172-825.172
| colspan="2" |843.856
|816.1495-832.1495
|861.5385
|818.563-834.563
|886.154
|827.3975-843.3975
|830.497-846.497
|-
|-
| |9
| |9
| |C#/Db
| |C#/Db
|830.769
|D#/Eb
|878.242
|Db
|896.154
|Eb
| colspan="2" |913.846
|908.145-926.145
|929.507
|910.319-928.319
| colspan="2" |949.4505
|918.168-936.168
|969.231
|920.883-938.883
|996.923
|930.822-948.822
|934.309-952.309
|-
|-
| |10
| |10
| |D
| |D
|923.077
|E
|975.824
|C#
|984.615
|D#
| colspan="2" |1015.385
|1009.0505-1029.0505
|1031.674
|1011.465-1031.465
| colspan="2" |1054.945
|1020.186-1040.186
|1076.923
|1023.2035-1043.2035
|1107.692
|1034.247-1054.2547
|1038.122-1058.122
|-
|-
| |11
| |11
| |D#/Eb
| |D#/Eb
|1015.385
|E#/Fb
|1073.407
|Eb
|1083.077
|Fb
| colspan="2" |1116.923
|1109.9555-1131.9555
|1134.842
|1112.61-1134.612
| colspan="2" |1160.44
|1122.2055-1143.2055
|1184.615
|1125.524-1147.524
|1218.4615
|1137.672-1159.672
|1141.934-1163.934
|-
|-
| |12
| |12
| |E
| |E
|1107.692
|F
|1170.99
|D#
|1181.5385
|E#
| colspan="2" |1218.4615
|1210.861-1234.861
|1238.009
|1213.758-1227.758
| colspan="2" |1265.9348
|1224.224-1248.224
|1292.308
|1225.844-1249.884
|1329.231
|1241.096-1265.096
|1245.746-1269.746
|-
|-
| |13
| |13
| |F
| |F
|1200
|G
|1268.571
|F
|1280
|G
| colspan="2" |1320
|1311.767-1337.767
|1341.1765
|1314.905-1340.905
| colspan="2" |1371.429
|1326.243-1352.243
|1400
|1343.1645-1396.1645
|1440
|1344.521-1370.521
|1349.558-1375.558
|}
|}
Golden Tunings
 
{| class="wikitable"
{| class="wikitable"
! rowspan="4" |Degrees
! colspan="2" rowspan="3" |Octatonic
! colspan="4" |Aeolian
! colspan="4" |Intense Aeolian
|-
|-
! rowspan="2" |Degrees
! colspan="2" |Flattone
! rowspan="2" |Octatonic
! colspan="2" |Meantone
! colspan="9" |Phrygian Mode (natural minor)
! colspan="2" |Superpyth
! colspan="7" |Phrygian-Aeolian Mode (intermediate minor)
! colspan="2" |Ultrapyth
! colspan="8" |Aeolian Mode (melodic/harmonic minor)
|-
|-
!Min-Med-13c
! rowspan="2" |Min-Med
!Min-Max-13c
! rowspan="2" |Med-Max~Min-Max
!Min-Med
! rowspan="2" |Min-Med/Min-Max
!Min-Max
! rowspan="2" |Med-Max
!Med-Max-13c
! rowspan="2" |Min-Med
!Min-Med+13c
! rowspan="2" |Min-Max/Med-Max
!Min-Max+13c
! rowspan="2" |Min-Med/Min-Max
!Med-Max
! rowspan="2" |Med-Max
!Med-Max+13c
|-
!Min-Med/Min-Max-13c
!Natural
!Med-Max-13c
!Subset of 26edn
!Min-Med/Min-Max
!Med-Max
!Min-Med/Min-Max+13c
!Med-Max+13c
!Min-Med-13c (Aeolian)
!Min-Max-13c
!Min-Med
!Min-Max
!Min-Med+13c
!Med-Max-13c
!Min-Max+13c
!Med-Max
!Med-Max+13c
|-
|-
| |1
| |1
| |F#/Gb
| |F#/Gb
|96.7665
|F#v/Gb^
|97.176
|105.256-107.256
|97.7665
| colspan="2" |105.625-108.015
|98.176
|106.156-108.156
|98.359
|107.435-109.435
|98.7665
|107.738-109.738
|99.176
|108.459-110.459
|99.359
|108.802-110.802
|100.359
|101.733
|102.639
|102.733
|103.639
|103.733
|104.639
|105.256
|106.11
|106.256
|107.11
|107.256
|107.738
|108.11
|108.738
|109.738
|-
|-
| |2
| |2
| |G
| colspan="2" |G
|193.533
|210.511-214.511
|194.352
| colspan="2" |211.25-216.03
|195.533
|212.313-216.313
|196.352
|214.8705-218.8705
|196.719
|215.4765-219.4765
|197.533
|216.918-220.918
|198.352
|217.604-221.604
|198.719
|200.719
|203.466
|205.279
|205.466
|207.279
|207.466
|205.279
|210.511
|212.22
|212.511
|214.22
|214.511
|215.477
|216.22
|217.477
|219.477
|-
|-
| |3
| |3
| |G#/Ab
| |G#/Ab
|291.2995
|G#v/Ab^
|291.528
|315.767-321.767
|293.2995
| colspan="2" |316.875-324.044
|294.528
|318.469-324.469
|295.078
|321.306-329.306
|296.2995
|322.215-330.215
|297.528
|325.377-331.377
|298.078
|326.4065-332.4065
|301.078
|305.199
|311.9185
|308.199
|310.9185
|311.199
|313.9185
|315.767
|318.33
|318.767
|321.33
|321.767
|323.215
|324.33
|326.215
|329.215
|-
|-
| |4
| |4
| |A
| colspan="2" |A
|388.063
|421.022-429.022
|389.705
| colspan="2" |422.501-432.059
|391.063
|424.626-432.626
|392.705
|429.741-437.741
|393.4375
|430.953-438.953
|394.063
|433.836-437.836
|396.705
|435.209-443.209
|397.4375
|401.4375
|406.932
|410.558
|410.932
|414.558
|414.932
|418.558
|421.022
|424.44
|425.022
|428.44
|429.022
|430.953
|432.44
|434.953
|438.953
|-
|-
| |5
| |5
| |B
| |B
|484.833
|A#v/Bb^
|486.881
|526.278-536.278
|488.833
| colspan="2" |528.126-540.074
|490.881
|530.782-540.782
|492.797
|547.176-547.176
|492.833
|538.6915-548.6915
|495.881
|542.295-552.295
|496.797
|544.011-554.011
|501.797
|508.6655
|513.1975
|513.6655
|518.1975
|518.6655
|523.1975
|526.278
|530.55
|531.278
|535.55
|536.278
|538.6915
|540.55
|543.6915
|548.6915
|-
|-
| |6
| |6
| |B#/Hb
| |B#/Hb
|581.299
|B
|583.057
|631.534-643.534
|586.299
| colspan="2" |633.751-648.089
|589.057
|636.9385-648.9385
|591.156
|644.611-656.611
|591.299
|646.43-658.43
|595.057
|650.754-666.754
|596.156
|652.813-664.813
|602.156
|610.399
|615.837
|616.399
|621.837
|622.399
|627.837
|631.534
|636.6595
|637.534
|642.6595
|643.534
|646.43
|648.6595
|652.43
|658.43
|-
|-
| |7
| |7
| |H
| |H
|678.366
|Cb
|681.233
|736.789-750.789
|684.366
| colspan="2" |739.376-756.104
|687.233
|743.095-757.095
|689.516
|752.047-766.047
|690.366
|754.168-768.168
|694.233
|759.213-773.213
|695.516
|761.615-775.615
|702.516
|712.132
|718.4765
|719.132
|725.4765
|726.132
|732.4765
|736.789
|742.769
|743.789
|749.769
|750.789
|754.168
|756.769
|761.168
|768.168
|-
|-
| |8
| |8
| |C
| |C
|775.132
|H#
|778.409
|842.045-858.045
|782.132
| colspan="2" |845.001-864.1185
|785.409
|849.251-865.521
|787.875
|859.482-875.482
|789.132
|861.906-877.906
|793.409
|867.672-883.672
|794.875
|870.417-886.417
|802.875
|813.865
|821.116
|821.865
|829.116
|829.865
|837.116
|842.045
|848.879
|850.045
|856.879
|858.045
|861.906
|864.879
|869.906
|877.906
|-
|-
| |9
| |9
| |C#/Db
| |C#/Db
|871.899
|Db
|874.585
|947.3-965.3
|879.899
| colspan="2" |950.626-972.133
|883.585
|958.408-976.408
|886.234
|966.917-984.917
|888.899
|969.645-986.645
|891.585
|976.131-994.131
|894.234
|979.219-997.219
|903.234
|915.598
|923.755
|924.598
|932.755
|933.598
|941.755
|947.3
|954.989
|956.3
|963.989
|965.3
|969.645
|972.989
|978.645
|986.645
|-
|-
| |10
| |10
| |D
| |D
|967.665
|C#
|971.761
|1052.556-1072.556
|977.665
| colspan="2" |1056.2515-1080.148
|981.761
|1061.564-1081.564
|984.594
|1074.352-1094.352
|987.665
|1077.383-1077.383
|991.761
|1084.59-1104.59
|993.594
|1088.022-1108.022
|1003.594
|1017.331
|1026.395
|1027.331
|1036.395
|1037.331
|1046.395
|1052.556
|1061.099
|1062.556
|1071.099
|1072.556
|1077.383
|1081.099
|1087.383
|1077.383
|-
|-
| |11
| |11
| |D#/Eb
| |D#/Eb
|1067.432
|Eb
|1068.9375
|1157.8115-1179.8115
|1075.432
| colspan="2" |1161.877-1188.163
|1079.9375
|1167.7205-1189.7205
|1082.953
|1181.7875-1203.7875
|1086.432
|1185.121-1207.121
|1091.9375
|1193.049-1215.049
|1092.953
|1196.824-1218.824
|1103.953
|1119.064
|1129.034
|1130.064
|1140.034
|1141.064
|1151.034
|1157.8115
|1167.209
|1168.8115
|1178.209
|1179.8115
|1185.121
|1189.209
|1196.121
|1207.121
|-
|-
| |12
| |12
| |E
| |E
|1162.198
|D#
|1166.114
|1264.067-1287.067
|1173.198
| colspan="2" |1267.502-1296.178
|1178.114
|1273.877-1298.877
|1181.312
|1288.223-1312.223
|1185.198
|1292.86-1316.86
|1190.114
|1301.508-1325.508
|1192.312
|1304.626-1328-626
|1204.312
|1220.797
|1231.674
|1232.797
|1243.674
|1244.797
|1255.674
|1264.067
|1273.319
|1275.067
|1285.319
|1287.067
|1392.86
|1297.319
|1304.86
|1317.86
|-
|-
| |13
| |13
| |F
| colspan="2" |F
|1257.965
|1368.323-1394.323
|1263.29
| colspan="2" |1373.127-1404.193
|1270.965
|1380.033-1406.033
|1276.29
|1396.658-1422.658
|1278.672
|1400.598-1426.598
|1283.965
|1409.967-1435.967
|1289.29
|1414.428-1440.428
|1291.672
|1304.672
|1322.53
|1334.313
|1335.53
|1347.313
|1348.53
|1360.313
|1368.322
|1379.429
|1381.322
|1392.429
|1394.322
|1400.598
|1405.429
|1413.598
|1426.598
|}
|}
[[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
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