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This scale occurs in 12edo, where it is the equal division of the minor ninth.
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==
Phrygian Mode (aka Double) Neapolitan Temperament
{| class="wikitable"
{| class="wikitable"
!Degrees
|+
!Octatonic
!Nonet
!Minimum
!Period
!Mean
!Notes
!Median
|-
!Golden
|1/1
!Maximum
|''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
|-
|-
|1
|21\20
|F#/Gb
| rowspan="13" |see [[13edo]]
|96.923
|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
|100.699
|101.001
|
|101.5385
|-
|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
|-
|-
|2
! rowspan="2" |Min-Med/Min-Max
|G
! rowspan="2" |Med-Max
|193.846
! rowspan="2" |Min-Med/Min-Max
|201.399
! rowspan="2" |Med-Max
|202.002
|203.077
|-
|-
|3
!Natural
|A
!Subset of 26edn
|290.769
|302.098
|303.0035
|304.615
|-
|-
|4
| |1
|A#/Bb
| |G#/Ab
|387.692
|G#v/Ab^
|402.797
|95.389-97.389
|404.005
|95.578-97.578
|406.154
|95.957-98.345
|96.785-98.844
|98.359-100.709
|99.058-101.523
|-
|-
|5
| |2
|B
| colspan="2" |A
|484.615
|190.778-194.778
|503.4965
|191.155-195.155
|505.006
|191.914-196.689
|507.692
|193.569-197.688
|196.719-201.417
|198.1165-203.046
|-
|-
|6
| |3
|B#/Hb
| |A#/Bb
|581.5385
|A#v/Bb^
|604.196
|286.1665-292.1665
|606.007
|286.733-292.733
|609.231
|287.871-295.034
|290.354-296.531
|295.078-302.126
|297.175-304.569
|-
|-
|7
| |4
|H
| colspan="2" |B
|678.4615
|381.555-389.555
|704.895
|382.3105-390.3105
|707.008
|383.828-393.378
|710.769
|387.138-395.375
|393.4375-402.835
|396.233-406.092
|-
|-
|8
| |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
|C
|775.385
|572.333-584.333
|805.594
|573.466-585.466
|808.009
|575.742-590.068
|812.308
|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
|-
|-
|9
| |8
|C#/Db
| |D
|872.318
|Q#
|906.294
|763.111-781.111
|909.011
|764.621-780.621
|913.846
|767.656-786.757
|774.2765-790.75
|786.875-805.67
|792.466-812.184
|-
|-
|10
| |9
|D
| |D#/Eb
|969.231
|Eb
|1006.993
|858.5-876.5
|1010.012
|860.199-878.199
|1015.385
|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
| |11
|D#/Eb
| |E#/Fb
|1066.154
|Fb
|1107.692
|1049.277-1071.277
|1111.013
|1051.354-1073.354
|1116.923
|1055.527-1081.791
|1064.63-1087.282
|1081.953-1107.797
|1089.641-1116.75
|-
|-
|12
| |12
|E
| |F
|1163.077
|E#
|1208.392
|1144.666-1168.666
|1212.014
|1146.932-1170.932
|1218.4615
|1151.484-1180.135
|1161.415-1186.126
|1180.312-1208.506
|1188.699-1218.276
|-
|-
|13
| |13
|F
| colspan="2" |G
|1260
|1240.055-1266.055
|1309.091
|1242.506-1268.509
|1313.015
|1247.441-1278.48
|1320
|1258.199-1284.969
|1278.672-1309.2145
|1287.757-1319.799
|}
|}
Phrygian-Aeolian Mode Neapolitan Temperament
 
{| class="wikitable"
{| class="wikitable"
!Degrees
!Octatonic
!Minimum
!Golden
!Mean
!Median
!Maximum
|-
|-
|1
! rowspan="3" |Degrees
|F#/Gb
! colspan="4" rowspan="2" |Octatonic
|101.5385
! colspan="2" |Intense Phrygian
|102.733
! colspan="2" |Intense Phrygian-Soft Aeolian
|103.5165
! colspan="2" |Soft Aeolian
|104.615
|-
|105.4945
! 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
|A
|G
|G
|203.077
|205.466
|207.033
|209.231
|210.989
|-
|3
|A
|A
|304.615
|201.81-205.81
|308.199
|202.293-206.293
|310.5465
|204.037-208.037
|313.846
|204.641-208.641
|316.4835
|206.849-210.849
|207.624-211.624
|-
|-
|4
| |3
| |G#/Ab
|A#/Bb
|A#/Bb
|406.154
|G#v/Ab^
|410.932
|A#v/Bb^
|414.066
|302.715-308.715
|418.4615
|303.44-309.44
|421.978
|306.056-312.056
|306.961-312.961
|310.274-316.274
|311.4365-317.4365
|-
|-
|5
| |4
| |A
|B
|A
|B
|B
|507.692
|403.62-411.62
|513.6655
|404.586-412.586
|517.582
|408.075-416.075
|523.077
|409.281-417.281
|527.4725
|413.699-421.699
|415.249-423.249
|-
|-
|6
| |5
|B#/Hb
| |B
|609.231
|C
|616.399
|A#v/Bb^
|621.099
|B#v/Cb^
|627.692
|504.525-514.525
|632.967
|505.733-515.733
|510.093-520.093
|511.602-521.602
|517.123-527.123
|519.061-529.061
|-
|-
|7
| |6
|H
| |B#/Hb
|710.769
|C#/Qb
|719.132
|B
|724.615
|732.318
|738.4615
|-
|8
|C
|C
|812.308
|605.43-617.43
|821.865
|606.879-618.879
|828.132
|612.112-624.112
|836.923
|613.922-625.922
|843.856
|620.548-632.548
|622.873-634.873
|-
|-
|9
| |7
|C#/Db
| |H
|913.846
|Q
|924.598
|Cb
|931.648
|Db
|941.5385
|706.335-720.335
|949.4505
|708.026-722.026
|714.131-728.131
|716.242-730.242
|723.973-737.973
|726.685-740.685
|-
|-
|10
| |8
| |C
|D
|D
|1015.385
|H#
|1027.331
|Q#
|1035.165
|807.24-823.24
|1046.154
|809.172-825.172
|1054.945
|816.1495-832.1495
|818.563-834.563
|827.3975-843.3975
|830.497-846.497
|-
|-
|11
| |9
| |C#/Db
|D#/Eb
|D#/Eb
|1116.923
|Db
|1130.064
|Eb
|1138.681
|908.145-926.145
|1150.769
|910.319-928.319
|1160.44
|918.168-936.168
|920.883-938.883
|930.822-948.822
|934.309-952.309
|-
|-
|12
| |10
| |D
|E
|E
|1218.4615
|C#
|1232.797
|D#
|1242.198
|1009.0505-1029.0505
|1255.385
|1011.465-1031.465
|1265.9348
|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
|-
|-
|13
| |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
|F
|1320
|G
|1335.53
|1311.767-1337.767
|1345.714
|1314.905-1340.905
|1360
|1326.243-1352.243
|1371.429
|1343.1645-1396.1645
|1344.521-1370.521
|1349.558-1375.558
|}
|}
Aeolian Mode Neapolitan Temperament
 
{| class="wikitable"
{| 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
|-
! rowspan="2" |Min-Med
! rowspan="2" |Med-Max~Min-Max
! rowspan="2" |Min-Med/Min-Max
! rowspan="2" |Med-Max
! rowspan="2" |Min-Med
! rowspan="2" |Min-Max/Med-Max
! rowspan="2" |Min-Med/Min-Max
! rowspan="2" |Med-Max
|-
|-
! |Degrees
!Natural
! |Octatonic
!Subset of 26edn
! |Minimum
! |Golden
! |Median
! |ed(9/4)
! |Mean
! |Maximum
|-
|-
| |1
| |1
| |F#/Gb
| |F#/Gb
| |105.4945
|F#v/Gb^
| |107.11
|105.256-107.256
| |107.692
| colspan="2" |105.625-108.015
| |107.993
|106.156-108.156
| |108.132
|107.435-109.435
| |110.769
|107.738-109.738
|108.459-110.459
|108.802-110.802
|-
|-
| |2
| |2
| |G
| colspan="2" |G
| |210.989
|210.511-214.511
| |214.22
| colspan="2" |211.25-216.03
| |214.385
|212.313-216.313
| |215.986
|214.8705-218.8705
| |216.264
|215.4765-219.4765
| |221.5385
|216.918-220.918
|217.604-221.604
|-
|-
| |3
| |3
| |A
| |G#/Ab
| |316.4835
|G#v/Ab^
| |321.33
|315.767-321.767
| |322.077
| colspan="2" |316.875-324.044
| |323.979
|318.469-324.469
| |324.396
|321.306-329.306
| |332.308
|322.215-330.215
|325.377-331.377
|326.4065-332.4065
|-
|-
| |4
| |4
| |A#/Bb
| colspan="2" |A
| |421.978
|421.022-429.022
| |428.44
| colspan="2" |422.501-432.059
| |429.769
|424.626-432.626
| |431.972
|429.741-437.741
| |432.5275
|430.953-438.953
| |443.076
|433.836-437.836
|435.209-443.209
|-
|-
| |5
| |5
| |B
| |B
| |527.4725
|A#v/Bb^
| |535.55
|526.278-536.278
| |583.4615
| colspan="2" |528.126-540.074
| |539.965
|530.782-540.782
| |540.659
|547.176-547.176
| |553.846
|538.6915-548.6915
|542.295-552.295
|544.011-554.011
|-
|-
| |6
| |6
| |B#/Hb
| |B#/Hb
| |632.967
|B
| |642.6595
|631.534-643.534
| |646.154
| colspan="2" |633.751-648.089
| |647.9585
|636.9385-648.9385
| |648.791
|644.611-656.611
| |664.615
|646.43-658.43
|650.754-666.754
|652.813-664.813
|-
|-
| |7
| |7
| |H
| |H
| |738.4615
|Cb
| |749.769
|736.789-750.789
| |753.846
| colspan="2" |739.376-756.104
| |755.9515
|743.095-757.095
| |756.923
|752.047-766.047
| |775.385
|754.168-768.168
|759.213-773.213
|761.615-775.615
|-
|-
| |8
| |8
| |C
| |C
| |843.856
|H#
| |856.879
|842.045-858.045
| |861.5385
| colspan="2" |845.001-864.1185
| |863.945
|849.251-865.521
| |865.055
|859.482-875.482
| |886.154
|861.906-877.906
|867.672-883.672
|870.417-886.417
|-
|-
| |9
| |9
| |C#/Db
| |C#/Db
| |949.4505
|Db
| |963.989
|947.3-965.3
| |969.231
| colspan="2" |950.626-972.133
| |971.938
|958.408-976.408
| |973.187
|966.917-984.917
| |996.923
|969.645-986.645
|976.131-994.131
|979.219-997.219
|-
|-
| |10
| |10
| |D
| |D
| |1054.945
|C#
| |1071.099
|1052.556-1072.556
| |1076.923
| colspan="2" |1056.2515-1080.148
| |1079.931
|1061.564-1081.564
| |1081.319
|1074.352-1094.352
| |1107.692
|1077.383-1077.383
|1084.59-1104.59
|1088.022-1108.022
|-
|-
| |11
| |11
| |D#/Eb
| |D#/Eb
| |1160.44
|Eb
| |1178.209
|1157.8115-1179.8115
| |1184.615
| colspan="2" |1161.877-1188.163
| |1187.924
|1167.7205-1189.7205
| |1189.4505
|1181.7875-1203.7875
| |1218.4615
|1185.121-1207.121
|1193.049-1215.049
|1196.824-1218.824
|-
|-
| |12
| |12
| |E
| |E
| |1265.9348
|D#
| |1285.319
|1264.067-1287.067
| |1292.308
| colspan="2" |1267.502-1296.178
| |1295.917
|1273.877-1298.877
| |1297.582
|1288.223-1312.223
| |1329.231
|1292.86-1316.86
|1301.508-1325.508
|1304.626-1328-626
|-
|-
| |13
| |13
| |F
| colspan="2" |F
| |1371.429
|1368.323-1394.323
| |1392.429
| colspan="2" |1373.127-1404.193
| |1400
|1380.033-1406.033
| |1403.91
|1396.658-1422.658
| |1405.714
|1400.598-1426.598
| |1440
|1409.967-1435.967
|1414.428-1440.428
|}
|}
[[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"