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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"
|+
!Nonet
!Period
!Notes
|-
|-
! rowspan="4" |Degrees
|1/1
! colspan="2" rowspan="3" |Octatonic
|''92.308''
! colspan="3" |Soft Phrygian  
|Soft Phrygian mode begins
! colspan="6" |Phrygian
|-
|-
! rowspan="3" |Minimum-comma
|25\24
! rowspan="3" |Median
|''96.154''
! rowspan="3" |Maximum+comma
|
! colspan="3" |Thirdtone
! colspan="3" |Semitone
|-
|-
! rowspan="2" |Minimum-comma
|24\23
! rowspan="2" |Median
|96.321
! colspan="2" rowspan="2" |Maximum+comma~Minimum-comma
|
! rowspan="2" |Median
! rowspan="2" |Maximum+comma
|-
|-
!Natural
|23\22
!Subset of 26edn
|96.503
|
|-
|-
| |1
|22\21
| |G#/Ab
|96.703
|G#v/Ab^
|Soft Phrygian mode ends, Thirdtone Phrygian mode begins
|89.231-''92.308''
|96.5035
| colspan="2" |93.626-99.78
|97.436-97.582
| colspan="2" |95.385-101.978
|99.692-''100''
|101.5385-104.615
|-
|-
| |2
|21\20
|  colspan="2"|A
|96.923
|178.4615-''184.615''
|
|193.007
| colspan="2" |187.253-199.56
|194.872-195.165
| colspan="2" |190.769-203.956
|199.385-''200''
|203.077-209.231
|-
|-
| |3
|20\19
| |A#/Bb
|97.166
|A#v/Bb^
|
|267.692-''276.923''
|289.5105
| colspan="2" |280.879-299.341
|292.308-292.747
| colspan="2" |286.154-305.934
|299.077-''300''
|304.615-313.846
|-
|-
| |4
|19\18
|  colspan="2"|B
|97.436
|356.923-''369.231''
|
|386.014
| colspan="2" |374.5055-399.121
|389.735-390.33
| colspan="2" |381.5385-407.912
|398.769-''400''
|406.154-418.4615
|-
|-
| |5
|37\35
| |C
|97.582
|B#v/Cb^
|
|446.154-''461.5385''
|482.5175
| colspan="2" |468.132-498.901
|487.1795-487.912
| colspan="2" |476.923-509.89
|498.4615-''500''
|507.692-523.077
|-
|-
| |6
|18\17
| |C#/Qb
|97.738
|C
|
|535.385-''553.846''
|579.021
| colspan="2" |561.758-598.681
|584.615-585.4945
| colspan="2" |572.308-611.868
|598.154-''600''
|609.231-627.692
|-
|-
| |7
|17\16
| |Q
|98.077
|Db
|
|624.615-''646.154''
|675.5245
| colspan="2" |655.385-698.4615
|682.051-683.077
| colspan="2" |667.692-713.846
|697.846-''700''
|710.769-732.308
|-
|-
| |8
|16\15
| |D
|98.462
|Q#
|Thirdtone Phrygian mode ends
|713.846-''738.4615''
|772.0228
| colspan="2" |749.011-798.242
|779.487-780.659
| colspan="2" |763.077-815.824
|797.5385-''800''
|812.308-836.932
|-
|-
| |9
|15\14
| |D#/Eb
|98.901
|Eb
|Semitone Phrygian mode begins
|802.077-''830.769''
|868.5315
| colspan="2" |842.637-898.022
|876.923-878.242
| colspan="2" |858.4615-917.802
|897.231-''900''
|913.846-941.5385
|-
|-
| |10
|14\13
| |E
|99.408
|D#
|
|892.308-''923.077''
|965.035
| colspan="2" |936.264-997.802
|974.359-975.824
| colspan="2" |953.846-1019.78
|996.923-''1000''
|1015.385-1046.154
|-
|-
| |11
|27\25
| |E#/Fb
|99.692
|Fb
|
|981.5385-''1015.385''
|1061.5385
| colspan="2" |1029.89-1097.582
|1071.795-1073.407
| colspan="2" |1049.231-1121.758
|1096.615-''1100''
|1116.923-1150.769
|-
|-
| |12
|13\12
| |F
|''100.000''
|E#
|
|1070.769-''1107.692''
|1158.042
| colspan="2" |1123.363-1197.363
|1169.231-1170.989
| colspan="2" |1144.615-1223.736
|1196.308-''1200''
|1218.4615-1255.385
|-
|-
| |13
|12\11
|  colspan="2"|G
|100.699
|1160-''1200''
|
|1254.5455
| colspan="2" |1217.143-1297.143
|1266.667-1268.571
| colspan="2" |1240-1325.714
|1296-''1300''
|1320-1360
|}
 
{| class="wikitable"
|-
|-
! rowspan="3" |Degrees
|11\10
! colspan="4" rowspan="2" |Octatonic
|101.538
! colspan="3" |Intense Phrygian
|Semitone Phrygian mode ends, Intense Phrygian mode begins
! colspan="3" |Intense Phrygian-Soft Aeolian
! colspan="4" |Soft Aeolian
|-
|-
! rowspan="2" |Minimum-comma
|21\19
! rowspan="2" |Median
|102.024
! colspan="2" rowspan="2" |Maximum+comma~Minimum-comma
|
! rowspan="2" |Median
! colspan="2" rowspan="2" |Maximum+comma~Minimum-comma
! rowspan="2" |''r¢''
! rowspan="2" |Median
! rowspan="2" |Maximum+comma
|-
|-
! colspan="2" |Natural
|10\9
! colspan="2" |Subset of 26edn
|102.564
|Intense Phrygian mode ends, Intense Phrygian-Soft Aeolian mode begins
|-
|-
| |1
|19\17
| |F#/Gb
|G#/Ab
|F#v/Gb^
|G#v/Ab^
|98.4615-101.5385
|102.024
| colspan="2" |99.487-105.641
|103.167
|103.167
| colspan="2" |100.769-106.923
|
|-
|9\8
|''103.846''
|''103.846''
|Intense Phrygian-Soft Aeolian mode ends, Soft Aeolian mode begins
|-
|17\15
|104.615
|104.615
|105.4945-108.571
|
|-
|-
| |2
|8\7
| |G
|105.495
|A
|Soft Aeolian mode ends, Flattone Aeolian mode begins
|G
|A
|196.923-203.077
|204.0485
| colspan="2" |198.974-211.282
|206.335
| colspan="2" |201.5385-213.846
|''207.692''
|209.231
|210.989-217.143
|-
|-
| |3
|15\13
| |G#/Ab
|106.509
|A#/Bb
|
|G#v/Ab^
|A#v/Bb^
|295.385-304.615
|306.073
| colspan="2" |298.4615-316.923
|309.502
| colspan="2" |302.308-320.769
|''311.5385''
|313.846
|316.4835-325.714
|-
|-
| |4
|22\19
| |A
|106.883
|B
|Flattone Aeolian mode ends, Meantone Aeolian mode begins
|A
|B
|393.846-406.154
|408.097
| colspan="2" |397.949-422.564
|412.67
| colspan="2" |403.077-427.692
|''415.385''
|418.4615
|421.978-434.286
|-
|-
| |5
|29\25
| |B
|107.077
|C
|
|A#v/Bb^
|B#v/Cb^
|492.308-507.692
|510.1215
| colspan="2" |497.436-528.205
|515.837
| colspan="2" |503.846-534.615
|''519.231''
|523.077
|527.4725-542.857
|-
|-
| |6
|7\6
| |B#/Hb
|''107.692''
|C#/Qb
|Meantone Aeolian mode ends, Superpyth Intense Aeolian mode begins
|B
|C
|590.769-609.231
|612.146
| colspan="2" |596.923-633.846
|619.0045
| colspan="2" |604.615-641.5385
|''623.077''
|627.692
|632.967-651.429
|-
|-
| |7
|20\17
| |H
|108.597
|Q
|
|Cb
|Db
|689.231-710.769
|714.17
| colspan="2" |696.41-739.487
|722.172
| colspan="2" |705.385-748.465
|''726.923''
|732.308
|738.4615-760
|-
|-
| |8
|13\11
| |C
|109.091
|D
|Superpyth Intense Aeolian mode ends, Ultrapyth Intense Aeolian mode begins
|H#
|Q#
|787.692-812.308
|816.194
| colspan="2" |795.897-845.128
|825.339
| colspan="2" |806.154-855.385
|''830.769''
|836.923
|843.856-868.571
|-
|-
| |9
|19\16
| |C#/Db
|D#/Eb
|Db
|Eb
|886.154-913.846
|918.219
| colspan="2" |895.385-948.769
|929.507
| colspan="2" |906.923-962.308
|''934.615''
|941.5385
|949.4505-977.143
|-
| |10
| |D
|E
|C#
|D#
|984.615-1015.385
|1020.243
| colspan="2" |994.872-1056.41
|1031.674
| colspan="2" |1007.692-1069.231
|''1038.4615''
|1046.154
|1054.945-1085.714
|-
| |11
| |D#/Eb
|E#/Fb
|Eb
|Fb
|1083.077-1116.923
|1123.267
| colspan="2" |1094.359-1162.051
|1134.842
| colspan="2" |1108.4615-1176.154
|''1142.308''
|1150.769
|1160.44-1194.286
|-
| |12
| |E
|F
|D#
|E#
|1181.5385-1218.4615
|1224.291
| colspan="2" |1193.846-1267.692
|1238.009
| colspan="2" |1209.231-1283.077
|''1246.154''
|1255.385
|1265.935-1302.857
|-
| |13
| |F
|G
|F
|G
|1280-1320
|1326.316
| colspan="2" |1293.333-1373.333
|1341.1765
| colspan="2" |1310-1390
|''1350''
|1360
|1371.429-1411.429
|}
 
{| class="wikitable"
! rowspan="4" |Degrees
! colspan="2" rowspan="3" |Octatonic
! colspan="6" |Aeolian
! colspan="8" |Intense Aeolian
|-
! colspan="3" |Flattone
! colspan="3" |Meantone
! colspan="5" |Superpyth
! colspan="3" |Ultrapyth
|-
!Minimum-comma
!Median
! colspan="2" |Maximum+comma~Minimum-comma
!Median
! colspan="2" |Maximum+comma~Minimum-comma
! colspan="2" |''r¢''
!Median
! colspan="2" |Maximum+comma~Minimum-comma
!Median
!Maximum+comma
|-
!Natural
!Subset of 26edn
!
!
!
!
!
!
!
!
!
!
!
!
!
!
|-
| |1
| |F#/Gb
|F#v/Gb^
|102.418-105.4945
|106.509
| colspan="2" |103.806-109.9595
|107.077
| colspan="2" |104.615-110.769
| colspan="2" |''107.692''
|108.597
| colspan="2" |106.014-112.168
|109.615
|109.615
|110.769-113.846
|
|-
| |2
|  colspan="2"|G
|204.835-210.989
|213.018
| colspan="2" |207.611-219.919
|214.154
| colspan="2" |209.231-221.5385
| colspan="2" |''215.385''
|217.1945
| colspan="2" |212.028-224.336
|219.231
|221.5385-227.692
|-
| |3
| |G#/Ab
|F#v/Gb^
|307.253-316.4835
|319.527
| colspan="2" |311.417-329.8785
|321.231
| colspan="2" |313.846-332.308
| colspan="2" |''323.077''
|325.792
| colspan="2" |318.042-336.5035
|328.846
|332.308-341.5385
|-
| |4
|  colspan="2"|A
|409.67-421.978
|426.036
| colspan="2" |415.223-439.838
|428.308
| colspan="2" |418.4615-443.077
| colspan="2" |''430.769''
|434.389
| colspan="2" |424.056-448.671
|438.4615
|443.077-455.385
|-
| |5
| |B
|A#v/Bb^
|512.088-527.4725
|532.544
| colspan="2" |519.028-549.798
|535.385
| colspan="2" |523.077-553.846
| colspan="2" |''538.4615''
|542.986
| colspan="2" |530.07-560.839
|548.077
|553.846-569.231
|-
| |6
| |B#/Hb
|B
|614.5055-632.967
|639.053
| colspan="2" |622.834-659.757
|642.4615
| colspan="2" |627.692-664.615
| colspan="2" |''646.154''
|651.584
| colspan="2" |636.084-673.007
|657.692
|664.615-683.077
|-
| |7
| |H
|Cb
|716.923-738.4615
|745.562
| colspan="2" |726.64-769.717
|749.5385
| colspan="2" |732.308-775.385
| colspan="2" |''754.846''
|760.181
| colspan="2" |742.098-785.175
|767.308
|775.385-796.923
|-
| |8
| |C
|H#
|819.341-843.856
|853.071
| colspan="2" |830.445-879.676
|856.615
| colspan="2" |836.923-886.154
| colspan="2" |''861.5385''
|868.778
| colspan="2" |848.112-897.343
|876.923
|886.154-910.769
|-
| |9
| |C#/Db
|Db
|921.758-949.4505
|958.58
| colspan="2" |934.251-989.636
|963.692
| colspan="2" |941.5385-996.923
| colspan="2" |''969.231''
|977.376
| colspan="2" |954.126-1009.5105
|986.5385
|996.923-1024.615
|-
|-
| |10
|6\5
| |D
|110.769
|C#
|Ultrapyth Intense Aeolian mode ends
|1024.176-1054.945
|}Golden/Pyrite Tunings±13¢
|1065.089
| colspan="2" |1038.057-1099.595
|1070.769
| colspan="2" |1046.154-1107.692
| colspan="2" |''1076.923''
|1085.973
| colspan="2" |1060.14-1121.678
|1096.154
|1107.692-1138.4615
|-
| |11
| |D#/Eb
|Eb
|1126.593-1160.44
|1171.598
| colspan="2" |1141.862-1209.555
|1177.846
| colspan="2" |1150.769-1218.4685
| colspan="2" |''1184.615''
|1194.57
| colspan="2" |1166.154-1233.846
|1205.769
|1218.4615-1252.308
|-
| |12
| |E
|D#
|1229.011-1265.934
|1278.1065
| colspan="2" |1245.668-1319.514
|1284.923
| colspan="2" |1255.385-1329.231
| colspan="2" |''1292.308''
|1303.167
| colspan="2" |1272.168-1346.014
|1315.385
|1329.231-1366.154
|-
| |13
|  colspan="2"|F
|1331.429-1371.429
|1384.615
| colspan="2" |1349.474-1429.474
|1392
| colspan="2" |1360-1440
| colspan="2" |''1400''
|1411.765
| colspan="2" |1378.182-1458.182
|1425
|1440-1480
|}
Golden/Pyrite Tunings±13¢
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 617: Line 166:
|-
|-
| |2
| |2
| colspan="2"|A
| colspan="2" |A
|190.778-194.778
|190.778-194.778
|191.155-195.155
|191.155-195.155
Line 636: Line 185:
|-
|-
| |4
| |4
| colspan="2"|B
| colspan="2" |B
|381.555-389.555
|381.555-389.555
|382.3105-390.3105
|382.3105-390.3105
Line 725: Line 274:
|-
|-
| |13
| |13
| colspan="2"|G
| colspan="2" |G
|1240.055-1266.055
|1240.055-1266.055
|1242.506-1268.509
|1242.506-1268.509
Line 920: Line 469:
! colspan="2" |Ultrapyth
! colspan="2" |Ultrapyth
|-
|-
!Min-Med
! rowspan="2" |Min-Med
!Med-Max~Min-Max
! rowspan="2" |Med-Max~Min-Max
!Min-Med/Min-Max
! rowspan="2" |Min-Med/Min-Max
!Med-Max
! rowspan="2" |Med-Max
!Min-Med
! rowspan="2" |Min-Med
!Min-Max/Med-Max
! rowspan="2" |Min-Max/Med-Max
!Min-Med/Min-Max
! rowspan="2" |Min-Med/Min-Max
!Med-Max
! rowspan="2" |Med-Max
|-
|-
!Natural
!Natural
!Subset of 26edn
!Subset of 26edn
!
!
!
!
!
!
!
!
|-
|-
| |1
| |1
Line 952: Line 493:
|-
|-
| |2
| |2
| colspan="2"|G
| colspan="2" |G
|210.511-214.511
|210.511-214.511
| colspan="2" |211.25-216.03
| colspan="2" |211.25-216.03
Line 973: Line 514:
|-
|-
| |4
| |4
| colspan="2"|A
| colspan="2" |A
|421.022-429.022
|421.022-429.022
| colspan="2" |422.501-432.059
| colspan="2" |422.501-432.059
Line 1,071: Line 612:
|-
|-
| |13
| |13
| colspan="2"|F
| colspan="2" |F
|1368.323-1394.323
|1368.323-1394.323
| colspan="2" |1373.127-1404.193
| colspan="2" |1373.127-1404.193
Line 1,080: Line 621:
|1414.428-1440.428
|1414.428-1440.428
|}
|}
[[Category:13-tone scales]]
 
[[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"