|
|
| Line 1: |
Line 1: |
| 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.
| | #redirect [[13ed9/4]] |
| ==Intervals==
| |
| {| class="wikitable"
| |
| |+
| |
| ! colspan="4" |Nonet
| |
| !Period
| |
| !Notes
| |
| |-
| |
| |1/1
| |
| |
| |
| |
| |
| |
| |
| |''92.308''
| |
| | Soft Phrygian mode begins
| |
| |-
| |
| |
| |
| |23\22
| |
| |
| |
| |
| |
| | 96.5035
| |
| |
| |
| |-
| |
| |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
| |
| |
| |
| |
| |
| |
| |
| |98.4615
| |
| |Thirdtone Phrygian mode ends
| |
| |-
| |
| |15\14
| |
| |
| |
| |
| |
| |
| |
| |98.901
| |
| |Semitone Phrygian mode begins
| |
| |-
| |
| |14\13
| |
| |
| |
| |
| |
| |
| |
| |99.408
| |
| |
| |
| |-
| |
| |
| |
| |27\25
| |
| |
| |
| |
| |
| |99.692
| |
| |
| |
| |-
| |
| |13\12
| |
| |
| |
| |
| |
| |
| |
| |''100''
| |
| |
| |
| |-
| |
| |12\11
| |
| |
| |
| |
| |
| |
| |
| |100.699
| |
| |
| |
| |-
| |
| |11\10
| |
| |
| |
| |
| |
| |
| |
| |101.5385
| |
| |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
| |
| |
| |
| |
| |
| |
| |
| |105.4945
| |
| |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.{{Overline|09}}
| |
| |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
| |
| | |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
| |
| | |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
| |
| |}
| |
| | |
| {| 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
| |
| |-
| |
| !Natural
| |
| ! Subset of 26edn
| |
| |-
| |
| | |1
| |
| | |F#/Gb
| |
| |F#v/Gb^
| |
| |105.256-107.256
| |
| | colspan="2" |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
| |
| | colspan="2" |G
| |
| |210.511-214.511
| |
| | colspan="2" |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
| |
| | colspan="2" |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
| |
| | colspan="2" |A
| |
| |421.022-429.022
| |
| | colspan="2" |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
| |
| | colspan="2" |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
| |
| | colspan="2" |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
| |
| | colspan="2" |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
| |
| | colspan="2" |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
| |
| | colspan="2" |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
| |
| | colspan="2" |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
| |
| | colspan="2" |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
| |
| | colspan="2" |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
| |
| | colspan="2" |F
| |
| |1368.323-1394.323
| |
| | colspan="2" |1373.127-1404.193
| |
| |1380.033-1406.033
| |
| |1396.658-1422.658
| |
| |1400.598-1426.598
| |
| |1409.967-1435.967
| |
| | 1414.428-1440.428
| |
| |}
| |
| [[Category:13-tone scales]]
| |
| [[Category:ed9/4]]
| |
| [[Category:edIX]]
| |
| [[Category:todo:add_definition]]
| |
| [[Category:todo:unify_precision]]
| |