User:Moremajorthanmajor/9edIX: Difference between revisions

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{| class="wikitable"
{| class="wikitable"
|-
! rowspan="3" |Degrees
! rowspan="3" |Degrees
! colspan="4" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
! colspan="5" |Soft Phrygian
! colspan="9" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
! colspan="11" |Phrygian
! colspan="3" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
|-
|-
! rowspan="2" |Absolute Minimum
!  rowspan="2"|Minimum
! rowspan="2" |Median
!  rowspan="2"|Maximum
!  colspan="3"|Intense Phrygian
! colspan="3" |Intense Phrygian-Soft Aeolian
! colspan="3" |Soft Aeolian
! rowspan="2" |Minimum
! rowspan="2" |Minimum
! rowspan="2" |Min-Med±13¢
! rowspan="2" |Median
! rowspan="2" |Median
! rowspan="2"|Maximum
! rowspan="2" |Min-Max/Med-Max±13¢
! rowspan="2" |Maximum
! colspan="5" |Thirdtone
! colspan="6" |Semitone
|-
|-
!Minimum
!Minimum
!Min-Med/Min-Max±13¢
!Median
!Median
!Med-Max±13¢
!Maximum
!Maximum
!Minimum
!Minimum
!Min-Med/Min-Max±13¢
!Median
!Median
!Maximum
!Med-Max±13¢
!Minimum
!15/7±13¢
!Median
!Maximum
!Maximum
|-
|-
| |1
|1
|133.333
|133.333
| |138.667
!137.784-140.673
|142.222
!139.394
| colspan="2" |146.667
!138.057-140.9455
|147.368
! colspan="2" |139.6825
| colspan="2" |148.148
!138.6045-142.053
|149.02
|140.741-140.952
| colspan="2" |150
!139.8-142.744
|151.111
| colspan="2" |142.222-142.857
| colspan="2" |152.381
!142.075-145.468
|155.556
!144-144.444
| |160
!143.084-146.444
|145.16-148.049
|146.667
|-
|-
| |2
|2
|266.667
|266.667
|277.333
!275.568-281.346
|284.444
!278.788
| colspan="2" |293.333
!276.113-281.891
|294.737
! colspan="2" |279.365
| colspan="2" |296.296
!277.209-284.107
|288.039
|281.4815-281.905
| colspan="2" |300
!279.6-285.549
|302.222
| colspan="2" |284.444-285.714
| colspan="2" |304.762
!284.149-290.9365
|311.111
!288-288.889
|320
!286.168-293.287
|290.321-296.098
|293.333
|-
|-
| |3
|3
|400
|400
|416
!413.352-422.018
|426.667
!418.182
| colspan="2" |440
!414.17-422.836
|442.105
! colspan="2" |419.048
| colspan="2" |444.444
!415.814-426.16
|447.059
|422.222-422.857
| colspan="2" |450
!419.4-428.323
|453.333
| colspan="2" |426.667-428.429
| colspan="2" |457.143
!426.224-436.405
|466.667
!432-433.333
|480
!429.252-439.933
|435.481-444.148
|440
|-
|-
| |4
|4
|533.333
|533.333
|554.667
!551.136-562.691
|568.889
!557.576
| colspan="2" |586.667
!552.226-563.782
|589.474
! colspan="2" |558.73
| colspan="2" |592.593
!554.418-568.213
|596.078
|562.963-563.8095
| colspan="2" |600
!559.2-571.0975
|604.444
| colspan="2" |568.889-571.429
| colspan="2" |609.524
!568.299-581.873
|622.222
!576-577.778
|640
!572.3365-586.577
|580.641-592.197
|586.667
|-
|-
| |5
|5
|666.667
|666.667
|693.333
!688.919-703.364
|711.111
!696.97
| colspan="2" |733.333
!690.283-704.727
|736.845
! colspan="2" |698.413
| colspan="2" |740.741
!693.023-710.267
|745.098
|703.704-704.762
| colspan="2" |750
!699-713.872
|755.556
| colspan="2" |711.111-714.286
| colspan="2" |761.905
!710.373-727.341
|777.778
!720-722.222
|800
!715.42-733.222
|725.802-740.246
|733.333
|-
|-
| |6
|6
|800
|800
|832
!826.70-844.037
|853.333
!836.364
| colspan="2" |880
!828.3395-845.673
|884.2015
! colspan="2" |838.095
| colspan="2" |888.889
!831.627-852.32
|894.118
|844.444-845.714
| colspan="2" |900
!838.7995-856.646
|906.667
| colspan="2" |853.333-857.142
| colspan="2" |914.286
!853.448-872.81
|933.333
!864-866.667
|960
!858.505-879.866
|870.962-888.295
|880
|-
|-
| |7
|7
|933.333
|933.333
|970.667
!964.487-984.7095
|995.556
!975.7575
| colspan="2" |1026.667
!966.396-986.6148
|1031.158
! colspan="2" |977.778
| colspan="2" |1037.037
!970.232-994.373
|1043.137
|985.185-986.666-7
| colspan="2" |1050
!978.5995-999.421
|1057.778
| colspan="2" |995.556-1000
| colspan="2" |1066.667
!994.5225-1018.278
|1088.889
!1008-1011.111
|1120
!1001.589-1026.51
|1016.122-1036.344
|1026.667
|-
|-
|8
|8
|1066.667
|1066.667
|1109.333
!1102.271-1125.382-
|1137.778
!1115.1515
| colspan="2" |1177.333
!1104.453-1127.564
|1178.947
! colspan="2" |1116.46
| colspan="2" |1185.1858
!1108.836-1136.427
|1192.157
|1125.926-1127.619
| colspan="2" |1200
!1118.399-1142.195
|1208.889
| colspan="2" |1137.778-1142.857
| colspan="2" |1219.048
!1136.597-1163.746
|1244.444
!1152-1155.556
|1280
!1144.673-1173.155
|1161.2825-1184.395
|1177.333
|}
|}
Most harmonic tunings
{| class="wikitable"
{| class="wikitable"
|-
|-
! rowspan="2" |Degrees
! rowspan="2" |Degrees
!Phrygian Mode (natural minor)
! colspan="5" |Intense Phrygian
!Phrygian-Aeolian Mode (intermediate minor)
! colspan="5" |Intense Phrygian-Soft Aeolian
!Aeolian Mode (melodic/harmonic minor)
! colspan="6" |Soft Aeolian
|-
!15/7±13¢
!11/5±13¢
!9/4±13¢
|-
| |1
|145.16-148.049
|150.223-153.112
|154.546-157.434
|-
| |2
|290.321-296.098
|300.445-306.223
|309.091-314.869
|-
| |3
|435.481-444.148
|450.668459.335
|463.637-473.303
|-
| |4
|580.641-592.197
|600.891-612.446
|618.182-629.738
|-
| |5
|725.802-740.246
|751.1135-765.558
|772.728-787.172
|-
| |6
|870.962*888.295
|901.336-918.6695
|927.273-944.607
|-
| |7
|1016.122-1036.344
|1051.559-1071.781
|1081.819-1102.041
|-
|8
|1161.2825-1184.395
|1201.7815-1224.893
|1236.364-1259.476
|}Golden Tunings
 
Phrygian Mode (natural minor)
{| class="wikitable"
|-
!Degrees
!Min-Med±13¢
!Min-Max±13¢
!Med-Max±13¢
|-
| |1
|139.774-142.663
|140.366-143.254
|142.075-144.9635
|-
| |2
|279.548-285.3255
|280.731-286.509
|284.149-289.927
|-
| |3
|419.3215-427.988
|421.097-429.763
|426.224-434.891
|-
| |4
|559.095-570.650
|561.462-573.018
|568.3-579.854
|-
| |5
|698.869-713.314
|701.828-716.272
|710.373-724.818
|-
| |6
|838.643-855.976
|842.193-859.5265
|852.448-869.781
|-
| |7
|978.417-998.639
|982.559-1002.781
|994.5225-1014.745
|-
|8
|1118.191-1141.302
|1122.924-1146.035
|1136.597-1159.708
|}
Phrygian-Aeolian Mode (intermediate minor)
{| class="wikitable"
! rowspan="2" |Degrees
! colspan="2" |Intense Phrygian
! colspan="2" |Intense Phrygian-Soft Aeolian
! colspan="2" |Soft Aeolian
|-
|-
!Minimum
!Min-Med/Min-Max±13¢
!Min-Med/Min-Max±13¢
!Median
!Med-Max±13¢
!Med-Max±13¢
!Maximum
!Minimum
!Min-Med/Min-Max±13¢
!Min-Med/Min-Max±13¢
!Median
!Med-Max±13¢
!Med-Max±13¢
!Maximum
!Minimum
!Min-Med/Min-Max±13¢
!Min-Med/Min-Max±13¢
!Median
!Med-Max±13¢
!Med-Max±13¢
!11/5±13¢
!Maximum
|-
|-
| |1
|1
|146.667
|145.751-148.641
|145.751-148.641
|147.368
|146.101-148.99
|146.101-148.99
| colspan="2" |148.148
|147.36-150.249
|147.36-150.249
|149.02
|147.796-150.685
|147.796-150.685
| colspan="2" |150
|149.391-152.28
|149.391-152.28
|151.111
|149.951-152.84
|149.951-152.84
|150.223-153.112
|152.381
|-
|-
| |2
|2
|293.333
|291.5035-297.282
|291.5035-297.282
|294.737
|292.201-297.979
|292.201-297.979
| colspan="2" |296.296
|294.721-300.498
|294.721-300.498
|288.039
|295.592-301.37
|295.592-301.37
| colspan="2" |300
|298.782-304.56
|298.782-304.56
|302.222
|299.902-305.68
|299.902-305.68
|300.445-306.223
|304.762
|-
|-
| |3
|3
|440
|437.255-445.922
|437.255-445.922
|442.105
|438.302-446.968
|438.302-446.968
| colspan="2" |444.444
|442.081-450.748
|442.081-450.748
|447.059
|443.388-452.055
|443.388-452.055
| colspan="2" |450
|448.174-456.84
|448.174-456.84
|453.333
|449.853-458.519
|449.853-458.519
|450.668459.335
|457.143
|-
|-
| |4
|4
|586.667
|583.007-594.5625
|583.007-594.5625
|589.474
|584.402-595.958
|584.402-595.958
| colspan="2" |592.593
|589.441-600.997
|589.441-600.997
|596.078
|591.164-602.74
|591.164-602.74
| colspan="2" |600
|597.565-609.12
|597.565-609.12
|604.444
|599.804-611.359
|599.804-611.359
|600.891-612.446
|609.524
|-
|-
| |5
|5
|733.333
|728.759-743.203
|728.759-743.203
|736.845
|730.502-744.947
|730.502-744.947
| colspan="2" |740.741
|736.802-751.246
|736.802-751.246
|745.098
|738.98-753.425
|738.98-753.425
| colspan="2" |750
|746.956-761.4005
|746.956-761.4005
|755.556
|749.755-764.199
|749.755-764.199
|751.1135-765.558
|761.905
|-
|-
| |6
|6
|880
|874.51-891.844
|874.51-891.844
|884.2015
|876.603-893.937
|876.603-893.937
| colspan="2" |888.889
|884.161-901.495
|884.161-901.495
|894.118
|886.776-904.11
|886.776-904.11
| colspan="2" |900
|896.347-913.681
|896.347-913.681
|906.667
|899.7055-917.039
|899.7055-917.039
|901.336-918.6695
|914.286
|-
|-
| |7
|7
|1026.667
|1020.262-1040.484
|1020.262-1040.484
|1031.158
|1022.704-1042.926
|1022.704-1042.926
| colspan="2" |1037.037
|1031.522-1051.7445
|1031.522-1051.7445
|1043.137
|1034.572-1054.795
|1034.572-1054.795
| colspan="2" |1050
|1045.7385-1065.961
|1045.7385-1065.961
|1057.778
|1049.6565-1069.879
|1049.6565-1069.879
|1051.559-1071.781
|1066.667
|-
|-
|8
|8
|1177.333
|1166.014-1189.125
|1166.014-1189.125
|1178.947
|1168.804-1191.9155
|1168.804-1191.9155
| colspan="2" |1185.1858
|1178.883-1201.994
|1178.883-1201.994
|1192.157
|1182.269-1205.48
|1182.269-1205.48
| colspan="2" |1200
|1195.13-1216.241
|1195.13-1216.241
|1208.889
|1199.607-1222.7185
|1199.607-1222.7185
|}Aeolian Mode (melodic/harmonic minor)
|1201.7815-1224.893
|1219.048
|}
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! colspan="5" |Aeolian
! colspan="6" |Intense Aeolian
|-
|-
!Degrees
!Minimum
!Min-Med±13¢
!Min-Med/Min-Max±13¢
!Min-Max±13¢
!Median
!Med-Max±13¢
!Med-Max±13¢
!Maximum
!Minimum
!9/4±13¢
!Min-Med/Min-Max±13¢
!Median
!Med-Max±13¢
!Maximum
|-
|-
| |1
|1
|152.381
|152.036-154.925
|152.036-154.925
|153.27-156.159
!153.846
!152.781-155.67
| colspan="2" |155.556
|154.546-157.434
|155.622-158.511
|155.622-158.511
!157.576
!156.663-159.552
|160
|-
|-
| |2
|2
|304.762
|304.072-309.8495
|304.072-309.8495
|306.54-312.3175
!307.692
!305.562-311.34
| colspan="2" |311.111
|309.091-314.869
|311.244-317.022
|311.244-317.022
!315.1515
!313.326-319.104
|320
|-
|-
| |3
|3
|457.143
|456.408-464.774
|456.408-464.774
|459.81-468.476
!461.5385
!458.343-467.01
| colspan="2" |466.667
|463.637-473.303
|466.866-475.533
|466.866-475.533
!472.727
!469.989-478.656
|480
|-
|-
| |4
|4
|609.524
|608.143-619.699
|608.143-619.699
|613.0795-624.635
!615.385
!611.124-622.68
| colspan="2" |622.222
|618.182-629.738
|622.488-634.0435
|622.488-634.0435
!630.303
!626.652-638.2075
|640
|-
|-
| |5
|5
|761.905
|760.179-774.624
|760.179-774.624
|766.349-780.794
!769.231
!763.9055-778.35
| colspan="2" |777.778
|772.728-787.172
|778.11-792.554
|778.11-792.554
!787.879
!783.315-797.759
|800
|-
|-
| |6
|6
|914.286
|912.215-929.5845
|912.215-929.5845
|919.619-936.953
!923.077
!916.687-934.02
| colspan="2" |933.333
|927.273-944.607
|933.732-951.065
|933.732-951.065
!945.4545
!939.978-957.311
|960
|-
|-
|7
|7
|1066.667
|1064.251-1084.473
|1064.251-1084.473
|1072.889-1093.111
!1076.923
!1069.468-1089.69
| colspan="2" |1088.889
|1081.819-1102.041
|1089.354-1109.576
|1089.354-1109.576
!1103.03
!1096.641-1116.863
|1120
|-
|-
|8
|8
|1219.048
|1216.387-1239.398
|1216.387-1239.398
|1226.159-1249.27
!1230.769
!1222.249-1245.36
| colspan="2" |1244.444
|1236.364-1259.476
|1244.976-1268.087
|1244.976-1268.087
!1260.606
!1253.304-1276.415
|1280
|}By coincidence, using an equivalence wider than 1350 cents is identical to repeating a Phrygian mode Napoli scale one tone later.
|}By coincidence, using an equivalence wider than 1350 cents is identical to repeating a Phrygian mode Napoli scale one tone later.
[[Category:9-tone]]
[[Category:9-tone]]

Revision as of 20:01, 22 December 2018

This Long Common Practice minor mode is the neutral scale of the Fujiyama temperament family.

Intervals

Degrees Soft Phrygian Phrygian
Minimum Min-Med±13¢ Median Min-Max/Med-Max±13¢ Maximum Thirdtone Semitone
Minimum Min-Med/Min-Max±13¢ Median Med-Max±13¢ Maximum Minimum Min-Med/Min-Max±13¢ Median Med-Max±13¢ 15/7±13¢ Maximum
1 133.333 137.784-140.673 139.394 138.057-140.9455 139.6825 138.6045-142.053 140.741-140.952 139.8-142.744 142.222-142.857 142.075-145.468 144-144.444 143.084-146.444 145.16-148.049 146.667
2 266.667 275.568-281.346 278.788 276.113-281.891 279.365 277.209-284.107 281.4815-281.905 279.6-285.549 284.444-285.714 284.149-290.9365 288-288.889 286.168-293.287 290.321-296.098 293.333
3 400 413.352-422.018 418.182 414.17-422.836 419.048 415.814-426.16 422.222-422.857 419.4-428.323 426.667-428.429 426.224-436.405 432-433.333 429.252-439.933 435.481-444.148 440
4 533.333 551.136-562.691 557.576 552.226-563.782 558.73 554.418-568.213 562.963-563.8095 559.2-571.0975 568.889-571.429 568.299-581.873 576-577.778 572.3365-586.577 580.641-592.197 586.667
5 666.667 688.919-703.364 696.97 690.283-704.727 698.413 693.023-710.267 703.704-704.762 699-713.872 711.111-714.286 710.373-727.341 720-722.222 715.42-733.222 725.802-740.246 733.333
6 800 826.70-844.037 836.364 828.3395-845.673 838.095 831.627-852.32 844.444-845.714 838.7995-856.646 853.333-857.142 853.448-872.81 864-866.667 858.505-879.866 870.962-888.295 880
7 933.333 964.487-984.7095 975.7575 966.396-986.6148 977.778 970.232-994.373 985.185-986.666-7 978.5995-999.421 995.556-1000 994.5225-1018.278 1008-1011.111 1001.589-1026.51 1016.122-1036.344 1026.667
8 1066.667 1102.271-1125.382- 1115.1515 1104.453-1127.564 1116.46 1108.836-1136.427 1125.926-1127.619 1118.399-1142.195 1137.778-1142.857 1136.597-1163.746 1152-1155.556 1144.673-1173.155 1161.2825-1184.395 1177.333
Degrees Intense Phrygian Intense Phrygian-Soft Aeolian Soft Aeolian
Minimum Min-Med/Min-Max±13¢ Median Med-Max±13¢ Maximum Minimum Min-Med/Min-Max±13¢ Median Med-Max±13¢ Maximum Minimum Min-Med/Min-Max±13¢ Median Med-Max±13¢ 11/5±13¢ Maximum
1 146.667 145.751-148.641 147.368 146.101-148.99 148.148 147.36-150.249 149.02 147.796-150.685 150 149.391-152.28 151.111 149.951-152.84 150.223-153.112 152.381
2 293.333 291.5035-297.282 294.737 292.201-297.979 296.296 294.721-300.498 288.039 295.592-301.37 300 298.782-304.56 302.222 299.902-305.68 300.445-306.223 304.762
3 440 437.255-445.922 442.105 438.302-446.968 444.444 442.081-450.748 447.059 443.388-452.055 450 448.174-456.84 453.333 449.853-458.519 450.668459.335 457.143
4 586.667 583.007-594.5625 589.474 584.402-595.958 592.593 589.441-600.997 596.078 591.164-602.74 600 597.565-609.12 604.444 599.804-611.359 600.891-612.446 609.524
5 733.333 728.759-743.203 736.845 730.502-744.947 740.741 736.802-751.246 745.098 738.98-753.425 750 746.956-761.4005 755.556 749.755-764.199 751.1135-765.558 761.905
6 880 874.51-891.844 884.2015 876.603-893.937 888.889 884.161-901.495 894.118 886.776-904.11 900 896.347-913.681 906.667 899.7055-917.039 901.336-918.6695 914.286
7 1026.667 1020.262-1040.484 1031.158 1022.704-1042.926 1037.037 1031.522-1051.7445 1043.137 1034.572-1054.795 1050 1045.7385-1065.961 1057.778 1049.6565-1069.879 1051.559-1071.781 1066.667
8 1177.333 1166.014-1189.125 1178.947 1168.804-1191.9155 1185.1858 1178.883-1201.994 1192.157 1182.269-1205.48 1200 1195.13-1216.241 1208.889 1199.607-1222.7185 1201.7815-1224.893 1219.048
Degrees Aeolian Intense Aeolian
Minimum Min-Med/Min-Max±13¢ Median Med-Max±13¢ Maximum Minimum 9/4±13¢ Min-Med/Min-Max±13¢ Median Med-Max±13¢ Maximum
1 152.381 152.036-154.925 153.846 152.781-155.67 155.556 154.546-157.434 155.622-158.511 157.576 156.663-159.552 160
2 304.762 304.072-309.8495 307.692 305.562-311.34 311.111 309.091-314.869 311.244-317.022 315.1515 313.326-319.104 320
3 457.143 456.408-464.774 461.5385 458.343-467.01 466.667 463.637-473.303 466.866-475.533 472.727 469.989-478.656 480
4 609.524 608.143-619.699 615.385 611.124-622.68 622.222 618.182-629.738 622.488-634.0435 630.303 626.652-638.2075 640
5 761.905 760.179-774.624 769.231 763.9055-778.35 777.778 772.728-787.172 778.11-792.554 787.879 783.315-797.759 800
6 914.286 912.215-929.5845 923.077 916.687-934.02 933.333 927.273-944.607 933.732-951.065 945.4545 939.978-957.311 960
7 1066.667 1064.251-1084.473 1076.923 1069.468-1089.69 1088.889 1081.819-1102.041 1089.354-1109.576 1103.03 1096.641-1116.863 1120
8 1219.048 1216.387-1239.398 1230.769 1222.249-1245.36 1244.444 1236.364-1259.476 1244.976-1268.087 1260.606 1253.304-1276.415 1280

By coincidence, using an equivalence wider than 1350 cents is identical to repeating a Phrygian mode Napoli scale one tone later.

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