User:Moremajorthanmajor/13edIX: Difference between revisions

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Line 12: Line 12:
! rowspan="2" |Median
! rowspan="2" |Median
! rowspan="2" |Maximum
! rowspan="2" |Maximum
! colspan="3"|Intense Phrygian
! colspan="3" |Intense Phrygian
! colspan="3" |Intense Phrygian-Soft Aeolian
! colspan="3" |Intense Phrygian-Soft Aeolian
! colspan="3" |Soft Aeolian
! colspan="3" |Soft Aeolian
Line 322: Line 322:
!Degrees
!Degrees
!Octatonic
!Octatonic
!Min-Med-13c
!Min-Med±13¢
!Min-Max-13c
!Min-Max±13¢
!Min-Med
!Med-Max±13¢
!Min-Max
!Med-Max-13c
!Min-Med+13c
!Min-Max+13c
!Med-Max
!Med-Max+13c
|-
|-
| |1
| |1
| |F#/Gb
| |F#/Gb
|96.7665
|96.7665-98.7665
|97.176
|97.176-99.176
|97.7665
|98.359-100.359
|98.176
|98.359
|98.7665
|99.176
|99.359
|100.359
|-
|-
| |2
| |2
| |G
| |G
|193.533
|193.533-197.533
|194.352
|194.352-198.352
|195.533
|196.719-200.719
|196.352
|196.719
|197.533
|198.352
|198.719
|200.719
|-
|-
| |3
| |3
| |G#/Ab
| |G#/Ab
|291.2995
|290.2995-296.2995
|291.528
|291.528-297.528
|293.2995
|295.078-301.078
|294.528
|295.078
|296.2995
|297.528
|298.078
|301.078
|-
|-
| |4
| |4
| |A
| |A
|388.063
|387.063-395.063
|389.705
|388.705-396.705
|391.063
|393.4375-401.4375
|392.705
|393.4375
|394.063
|396.705
|397.4375
|401.4375
|-
|-
| |5
| |5
| |B
| |B
|484.833
|483.833-493.833
|486.881
|485.881-495.881
|488.833
|491.797-501.797
|490.881
|492.797
|492.833
|495.881
|496.797
|501.797
|-
|-
| |6
| |6
| |B#/Hb
| |B#/Hb
|581.299
|580.299-592.299
|583.057
|583.057-595.057
|586.299
|590.156-602.156
|589.057
|591.156
|591.299
|595.057
|596.156
|602.156
|-
|-
| |7
| |7
| |H
| |H
|678.366
|677.366-691.366
|681.233
|680.233-694.233
|684.366
|688.516-702.516
|687.233
|689.516
|690.366
|694.233
|695.516
|702.516
|-
|-
| |8
| |8
| |C
| |C
|775.132
|774.132-790.132
|778.409
|777.409-793.409
|782.132
|786.875-802.875
|785.409
|787.875
|789.132
|793.409
|794.875
|802.875
|-
|-
| |9
| |9
| |C#/Db
| |C#/Db
|871.899
|870.899-888.899
|874.585
|874.585-892.585
|879.899
|885.234-903.234
|883.585
|886.234
|888.899
|891.585
|894.234
|903.234
|-
|-
| |10
| |10
| |D
| |D
|967.665
|967.665-987.665
|971.761
|971.761-991.761
|977.665
|983.594-1003.594
|981.761
|984.594
|987.665
|991.761
|993.594
|1003.594
|-
|-
| |11
| |11
| |D#/Eb
| |D#/Eb
|1067.432
|1064.432-1086.432
|1068.9375
|1068.9375-1090.9375
|1075.432
|1081.953-1103.953
|1079.9375
|1082.953
|1086.432
|1091.9375
|1092.953
|1103.953
|-
|-
| |12
| |12
| |E
| |E
|1162.198
|1161.198-1185.198
|1166.114
|1166.114-1190.114
|1173.198
|1180.312-1204.312
|1178.114
|1181.312
|1185.198
|1190.114
|1192.312
|1204.312
|-
|-
| |13
| |13
| |F
| |F
|1257.965
|1257.965-1283.965
|1263.29
|1263.29-1289.29
|1270.965
|1278.672-1304.672
|1276.29
|1278.672
|1283.965
|1289.29
|1291.672
|1304.672
|}
|}
Phrygian-Aeolian Mode (intermediate minor)
Phrygian-Aeolian Mode (intermediate minor)
{| class="wikitable"
{| class="wikitable"
|-
|-
!Degrees
! rowspan="2" |Degrees
!Octatonic
! rowspan="2" |Octatonic
!Min-Med/Min-Max-13c
! colspan="2" |Intense Phrygian
!Med-Max-13c
! colspan="2" |Intense Phrygian-Soft Aeolian
!Min-Med/Min-Max
! colspan="2" |Soft Aeolian
!Med-Max
|-
!Min-Med/Min-Max+13c
!Min-Med/Min-Max±13¢
!Med-Max+13c
!Med-Max±13¢
!Min-Med-13c (Aeolian)
!Min-Med/Min-Max±13¢
!Med-Max±13¢
!Min-Med/Min-Max±13¢
!Med-Max±13¢
|-
|-
| |1
| |1
| |F#/Gb
| |F#/Gb
|101.733
|100.905-102.905
|102.639
|101.1465-103.1465
|102.733
|102.019-104.019
|103.639
|102.32-104.32
|103.733
|103.425-105.425
|104.639
|103.812-105.812
|105.256
|-
|-
| |2
| |2
| |G
| |G
|203.466
|201.81-205.81
|205.279
|202.293-206.293
|205.466
|204.037-208.037
|207.279
|204.641-208.641
|207.466
|206.849-210.849
|205.279
|207.624-211.624
|210.511
|-
|-
| |3
| |3
| |G#/Ab
| |G#/Ab
|305.199
|302.715-308.715
|311.9185
|303.44-309.44
|308.199
|306.056-312.056
|310.9185
|306.961-312.961
|311.199
|310.274-316.274
|313.9185
|311.4365-317.4365
|315.767
|-
|-
| |4
| |4
| |A
| |A
|406.932
|403.62-411.62
|410.558
|404.586-412.586
|410.932
|408.075-416.075
|414.558
|409.281-417.281
|414.932
|413.699-421.699
|418.558
|415.249-423.249
|421.022
|-
|-
| |5
| |5
| |B
| |B
|508.6655
|504.525-514.525
|513.1975
|505.733-515.733
|513.6655
|510.093-520.093
|518.1975
|511.602-521.602
|518.6655
|517.123-527.123
|523.1975
|519.061-529.061
|526.278
|-
|-
| |6
| |6
| |B#/Hb
| |B#/Hb
|610.399
|605.43-617.43
|615.837
|606.879-618.879
|616.399
|612.112-624.112
|621.837
|613.922-625.922
|622.399
|620.548-632.548
|627.837
|622.873-634.873
|631.534
|-
|-
| |7
| |7
| |H
| |H
|712.132
|706.335-720.335
|718.4765
|708.026-722.026
|719.132
|714.131-728.131
|725.4765
|716.242-730.242
|726.132
|723.973-737.973
|732.4765
|726.685-740.685
|736.789
|-
|-
| |8
| |8
| |C
| |C
|813.865
|807.24-823.24
|821.116
|809.172-825.172
|821.865
|816.1495-832.1495
|829.116
|818.563-834.563
|829.865
|827.3975-843.3975
|837.116
|830.497-846.497
|842.045
|-
|-
| |9
| |9
| |C#/Db
| |C#/Db
|915.598
|908.145-926.145
|923.755
|910.319-928.319
|924.598
|918.168-936.168
|932.755
|920.883-938.883
|933.598
|930.822-948.822
|941.755
|934.309-952.309
|947.3
|-
|-
| |10
| |10
| |D
| |D
|1017.331
|1009.0505-1029.0505
|1026.395
|1011.465-1031.465
|1027.331
|1020.186-1040.186
|1036.395
|1023.2035-1043.2035
|1037.331
|1034.247-1054.2547
|1046.395
|1038.122-1058.122
|1052.556
|-
|-
| |11
| |11
| |D#/Eb
| |D#/Eb
|1119.064
|1109.9555-1131.9555
|1129.034
|1112.61-1134.612
|1130.064
|1122.2055-1143.2055
|1140.034
|1125.524-1147.524
|1141.064
|1137.672-1159.672
|1151.034
|1141.934-1163.934
|1157.8115
|-
|-
| |12
| |12
| |E
| |E
|1220.797
|1210.861-1234.861
|1231.674
|1213.758-1227.758
|1232.797
|1224.224-1248.224
|1243.674
|1225.844-1249.884
|1244.797
|1241.096-1265.096
|1255.674
|1245.746-1269.746
|1264.067
|-
|-
| |13
| |13
| |F
| |F
|1322.53
|1311.767-1337.767
|1334.313
|1314.905-1340.905
|1335.53
|1326.243-1352.243
|1347.313
|1343.1645-1396.1645
|1348.53
|1344.521-1370.521
|1360.313
|1349.558-1375.558
|1368.322
|}
|}
Aeolian Mode (melodic/harmonic minor)
Aeolian Mode (melodic/harmonic minor)
Line 636: Line 542:
!Degrees
!Degrees
!Octatonic
!Octatonic
!Min-Max-13c
!Min-Med±13¢
!Min-Med
!Min-Max±13¢
!Min-Max
!Min-Med+13c
!Med-Max-13c
!Med-Max-13c
!Min-Max+13c
!Med-Max
!Med-Max+13c
|-
|-
| |1
| |1
| |F#/Gb
| |F#/Gb
|106.11
|105.256-107.256
|106.256
|106.11-108.11
|107.11
|107.738-109.738
|107.256
|107.738
|108.11
|108.738
|109.738
|-
|-
| |2
| |2
| |G
| |G
|212.22
|210.511-214.511
|212.511
|212.22-216.22
|214.22
|215.477-219.477
|214.511
|215.477
|216.22
|217.477
|219.477
|-
|-
| |3
| |3
| |G#/Ab
| |G#/Ab
|318.33
|315.767-321.767
|318.767
|318.33-324.33
|321.33
|323.215-329.215
|321.767
|323.215
|324.33
|326.215
|329.215
|-
|-
| |4
| |4
| |A
| |A
|424.44
|421.022-429.022
|425.022
|424.44-432.44
|428.44
|430.953-438.953
|429.022
|430.953
|432.44
|434.953
|438.953
|-
|-
| |5
| |5
| |B
| |B
|530.55
|526.278-536.278
|531.278
|530.55-540.55
|535.55
|538.6915-548.6915
|536.278
|538.6915
|540.55
|543.6915
|548.6915
|-
|-
| |6
| |6
| |B#/Hb
| |B#/Hb
|636.6595
|631.534-643.534
|637.534
|636.6595-648.6595
|642.6595
|646.43-658.43
|643.534
|646.43
|648.6595
|652.43
|658.43
|-
|-
| |7
| |7
| |H
| |H
|742.769
|736.789-750.789
|743.789
|742.769-756.769
|749.769
|754.168-768.168
|750.789
|754.168
|756.769
|761.168
|768.168
|-
|-
| |8
| |8
| |C
| |C
|848.879
|842.045-858.045
|850.045
|848.879-864.879
|856.879
|861.906-877.906
|858.045
|861.906
|864.879
|869.906
|877.906
|-
|-
| |9
| |9
| |C#/Db
| |C#/Db
|954.989
|947.3-965.3
|956.3
|954.989-972.989
|963.989
|969.645-986.645
|965.3
|969.645
|972.989
|978.645
|986.645
|-
|-
| |10
| |10
| |D
| |D
|1061.099
|1052.556-1072.556
|1062.556
|1061.099-1081.099
|1071.099
|1077.383-1077.383
|1072.556
|1077.383
|1081.099
|1087.383
|1077.383
|-
|-
| |11
| |11
| |D#/Eb
| |D#/Eb
|1167.209
|1157.8115-1179.8115
|1168.8115
|1167.209-1189.209
|1178.209
|1185.121-1207.121
|1179.8115
|1185.121
|1189.209
|1196.121
|1207.121
|-
|-
| |12
| |12
| |E
| |E
|1273.319
|1264.067-1287.067
|1275.067
|1273.319-1297.319
|1285.319
|1292.86-1316.86
|1287.067
|1392.86
|1297.319
|1304.86
|1317.86
|-
|-
| |13
| |13
| |F
| |F
|1379.429
|1368.322-1394.322
|1381.322
|1379.429-1405.429
|1392.429
|1400.598-1426.598
|1394.322
|1400.598
|1405.429
|1413.598
|1426.598
|}
|}
[[Category:13-tone]]
[[Category:13-tone]]

Revision as of 17:42, 24 November 2018

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.

Intervals

Degrees Octatonic Phrygian Mode (aka Double) Neapolitan Temperament (natural minor) Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor) Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
Absolute Minimum Minimum Median Maximum Intense Phrygian Intense Phrygian-Soft Aeolian Soft Aeolian Minimum Median Maximum
Minimum Median Maximum Minimum Median Maximum Minimum Median Maximum
1 F#/Gb 92.308 97.582 98.4615 101.5385 102.024 102.564 103.167 103.846 104.615 105.4945 107.692 110.769
2 G 184.615 195.165 196.923 203.077 204.0485 205.128 206.335 207.692 209.231 210.989 215.385 221.5385
3 G#/Ab 276.923 292.747 295.385 304.615 306.073 307.692 309.502 311.5385 313.846 316.4835 323.077 332.308
4 A 369.231 390.33 393.846 406.154 408.097 410.256 412.67 415.385 418.4615 421.978 430.769 443.076
5 B 461.5385 487.912 491.308 507.692 510.1215 512.8205 515.837 519.231 523.077 527.4725 538.4615 553.846
6 B#/Hb 553.846 585.4945 589.769 609.231 612.146 615.384 619.0045 623.077 627.692 632.967 646.154 664.615
7 H 646.154 683.077 690.231 710.769 714.17 717.945 722.172 736.923 732.308 738.4615 754.846 775.385
8 C 738.4615 780.66 788.692 812.308 816.194 820.513 825.339 830.769 836.923 843.856 861.5385 886.154
9 C#/Db 830.769 878.242 896.154 913.846 918.219 923.077 929.507 934.615 941.5385 949.4505 969.231 996.923
10 D 923.077 975.824 984.615 1015.385 1020.243 1025.641 1031.674 1038.4165 1046.154 1054.945 1076.923 1107.692
11 D#/Eb 1015.385 1073.407 1083.077 1116.923 1123.267 1128.205 1134.842 1142.308 1150.769 1160.44 1184.615 1218.4615
12 E 1107.692 1170.99 1181.5385 1218.4615 1224.291 1230.769 1238.009 1246.154 1255.385 1265.9348 1292.308 1329.231
13 F 1200 1268.571 1280 1320 1326.316 1333.333 1341.1765 1350 1360 1371.429 1400 1440

Most harmonic tunings

Degrees Octatonic Phrygian Mode (natural minor) Phrygian-Aeolian Mode (intermediate minor) Aeolian Mode (melodic/harmonic minor)
15/7±13¢ 11/5±13¢ 9/4±13¢
1 F#/Gb 100.496-102.496 104-106 106.993-108.993
2 G 200.991-204.912 208.001-212.001 213.986-217.986
3 G#/Ab 301.487-307.487 312.001-318.001 320.979-326.979
4 A 401.982-409.982 416.001-424.001 427.972-435.972
5 B 502.478-512.478 520.002-530.002 534.965-544.965
6 B#/Hb 602.974-614.974 624.002-636.002 641.9585-653.9585
7 H 703.469-717.469 728.002-742.0022 748.9515-762.9515
8 C 803.965-819.965 832.003-848.002 855.945-871.945
9 C#/Db 904.46-922.46 936.003-924.003 962.938-980.938
10 D 1004.956-1024.956 1040.003-1060.003 1069.931-1089.931
11 D#/Eb 1105.452-1127.452 1144.004-1166.004 1177-924-1199.924
12 E 1205.947-1299.947 1248.004-1272.004 1283.917-1307.917
13 F 1306.443-1332.443 1352.004-1378.004 1390.91-1416.91

Golden Tunings

Phrygian Mode (natural minor)

Degrees Octatonic Min-Med±13¢ Min-Max±13¢ Med-Max±13¢
1 F#/Gb 96.7665-98.7665 97.176-99.176 98.359-100.359
2 G 193.533-197.533 194.352-198.352 196.719-200.719
3 G#/Ab 290.2995-296.2995 291.528-297.528 295.078-301.078
4 A 387.063-395.063 388.705-396.705 393.4375-401.4375
5 B 483.833-493.833 485.881-495.881 491.797-501.797
6 B#/Hb 580.299-592.299 583.057-595.057 590.156-602.156
7 H 677.366-691.366 680.233-694.233 688.516-702.516
8 C 774.132-790.132 777.409-793.409 786.875-802.875
9 C#/Db 870.899-888.899 874.585-892.585 885.234-903.234
10 D 967.665-987.665 971.761-991.761 983.594-1003.594
11 D#/Eb 1064.432-1086.432 1068.9375-1090.9375 1081.953-1103.953
12 E 1161.198-1185.198 1166.114-1190.114 1180.312-1204.312
13 F 1257.965-1283.965 1263.29-1289.29 1278.672-1304.672

Phrygian-Aeolian Mode (intermediate minor)

Degrees Octatonic Intense Phrygian Intense Phrygian-Soft Aeolian Soft Aeolian
Min-Med/Min-Max±13¢ Med-Max±13¢ Min-Med/Min-Max±13¢ Med-Max±13¢ Min-Med/Min-Max±13¢ Med-Max±13¢
1 F#/Gb 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 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 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 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 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 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 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 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 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 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 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 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 1311.767-1337.767 1314.905-1340.905 1326.243-1352.243 1343.1645-1396.1645 1344.521-1370.521 1349.558-1375.558

Aeolian Mode (melodic/harmonic minor)

Degrees Octatonic Min-Med±13¢ Min-Max±13¢ Med-Max-13c
1 F#/Gb 105.256-107.256 106.11-108.11 107.738-109.738
2 G 210.511-214.511 212.22-216.22 215.477-219.477
3 G#/Ab 315.767-321.767 318.33-324.33 323.215-329.215
4 A 421.022-429.022 424.44-432.44 430.953-438.953
5 B 526.278-536.278 530.55-540.55 538.6915-548.6915
6 B#/Hb 631.534-643.534 636.6595-648.6595 646.43-658.43
7 H 736.789-750.789 742.769-756.769 754.168-768.168
8 C 842.045-858.045 848.879-864.879 861.906-877.906
9 C#/Db 947.3-965.3 954.989-972.989 969.645-986.645
10 D 1052.556-1072.556 1061.099-1081.099 1077.383-1077.383
11 D#/Eb 1157.8115-1179.8115 1167.209-1189.209 1185.121-1207.121
12 E 1264.067-1287.067 1273.319-1297.319 1292.86-1316.86
13 F 1368.322-1394.322 1379.429-1405.429 1400.598-1426.598
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