User:Moremajorthanmajor/9edIX: Difference between revisions

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{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="3" |Degrees
! colspan="4" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
! colspan="4" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
! colspan="3" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
! colspan="9" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
! colspan="3" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
! colspan="3" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
|-
|-
!Absolute Minimum
! rowspan="2" |Absolute Minimum
! |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" |Median
!  rowspan="2"|Maximum
|-
!Minimum
!Median
!Median
! |Maximum
!Maximum
! |Minimum
!Minimum
!Median
!Median
! |Maximum
!Maximum
!Minimum
!Minimum
!Median
!Median
! |Maximum
!Maximum
|-
|-
| |1
| |1
Line 25: Line 35:
|142.222
|142.222
| colspan="2" |146.667
| colspan="2" |146.667
|147.368
| colspan="2" |148.148
|149.02
|149.02
| colspan="2" |150
|151.111
| colspan="2" |152.381
| colspan="2" |152.381
|155.556
|155.556
Line 35: Line 49:
|284.444
|284.444
| colspan="2" |293.333
| colspan="2" |293.333
|294.737
| colspan="2" |296.296
|288.039
|288.039
| colspan="2" |300
|302.222
| colspan="2" |304.762
| colspan="2" |304.762
|311.111
|311.111
Line 45: Line 63:
|426.667
|426.667
| colspan="2" |440
| colspan="2" |440
|442.105
| colspan="2" |444.444
|447.059
|447.059
| colspan="2" |450
|453.333
| colspan="2" |457.143
| colspan="2" |457.143
|466.667
|466.667
Line 55: Line 77:
|568.889
|568.889
| colspan="2" |586.667
| colspan="2" |586.667
|589.474
| colspan="2" |592.593
|596.078
|596.078
| colspan="2" |600
|604.444
| colspan="2" |609.524
| colspan="2" |609.524
|622.222
|622.222
Line 65: Line 91:
|711.111
|711.111
| colspan="2" |733.333
| colspan="2" |733.333
|736.845
| colspan="2" |740.741
|745.098
|745.098
| colspan="2" |750
|755.556
| colspan="2" |761.905
| colspan="2" |761.905
|777.778
|777.778
Line 75: Line 105:
|853.333
|853.333
| colspan="2" |880
| colspan="2" |880
|884.2015
| colspan="2" |888.889
|894.118
|894.118
| colspan="2" |900
|906.667
| colspan="2" |914.286
| colspan="2" |914.286
|933.333
|933.333
Line 85: Line 119:
|995.556
|995.556
| colspan="2" |1026.667
| colspan="2" |1026.667
|1031.158
| colspan="2" |1037.037
|1043.137
|1043.137
| colspan="2" |1050
|1057.778
| colspan="2" |1066.667
| colspan="2" |1066.667
|1088.889
|1088.889
Line 95: Line 133:
|1137.778
|1137.778
| colspan="2" |1177.333
| colspan="2" |1177.333
|1178.947
| colspan="2" |1185.1858
|1192.157
|1192.157
| colspan="2" |1200
|1208.889
| colspan="2" |1219.048
| colspan="2" |1219.048
|1244.444
|1244.444
Line 158: Line 200:
|-
|-
!Degrees
!Degrees
!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
|139.774
|139.774-142.663
|140.366
|140.366-143.254
|141.218
|142.075-144.9635
| |141.81
|142.075
|142.663
|143.254
|143.519
|144.9635
|-
|-
| |2
| |2
|279.548
|279.548-285.3255
|280.731
|280.731-286.509
|282.437
|284.149-289.927
| |283.62
|284.149
|285.3255
|286.509
|287.038
|289.927
|-
|-
| |3
| |3
|419.3215
|419.3215-427.988
|421.097
|421.097-429.763
|423.655
|426.224-434.891
| |424.43
|426.224
|427.988
|429.763
|430.557
|434.891
|-
|-
| |4
| |4
|559.095
|559.095-570.650
|561.462
|561.462-573.018
|564.876
|568.3-579.854
| |566.24
|568.3
|570.650
|573.018
|574.076
|579.854
|-
|-
| |5
| |5
|698.869
|698.869-713.314
|701.828
|701.828-716.272
|706.0915
|710.373-724.818
| |709.05
|710.373
|713.314
|716.272
|717.5955
|724.818
|-
|-
| |6
| |6
|838.643
|838.643-855.976
|842.193
|842.193-859.5265
|847.308
|852.448-869.781
| |850.86
|852.448
|855.976
|859.5265
|861.115
|869.781
|-
|-
| |7
| |7
|978.417
|978.417-998.639
|982.559
|982.559-1002.781
|988.528
|994.5225-1014.745
| |992.67
|994.5225
|998.639
|1002.781
|1004.634
|1014.745
|-
|-
|8
|8
|1118.191
|1118.191-1141.302
|1122.924
|1122.924-1146.035
|1129.746
|1136.597-1159.708
|1134.48
|1136.597
|1141.302
|1146.035
|1148.153
|1159.708
|}
|}
Phrygian-Aeolian Mode (intermediate minor)
Phrygian-Aeolian Mode (intermediate minor)
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! colspan="2" |Intense Phrygian
! colspan="2" |Intense Phrygian-Soft Aeolian
! colspan="2" |Soft Aeolian
|-
|-
!Degrees
!Min-Med/Min-Max±13¢
!Min-Med/Min-Max-13c
!Med-Max±13¢
!Med-Max-13c
!Min-Med/Min-Max±13¢
!Min-Med/Min-Max
!Med-Max±13¢
!Med-Max
!Min-Med/Min-Max±13¢
!Min-Med/Min-Max+13c
!Med-Max±13¢
!Med-Max+13c
!Min-Med-13c (Aeolian)
|-
|-
| |1
| |1
|146.948
|145.751-148.641
|148.257
|146.101-148.99
|148.392
|147.36-150.249
|149.7015
|147.796-150.685
|149.836
|149.391-152.28
|151.146
|149.951-152.84
|152.036
|-
|-
| |2
| |2
|293.896
|291.5035-297.282
|296.514
|292.201-297.979
|296.7845
|294.721-300.498
|299.403
|295.592-301.37
|299.673
|298.782-304.56
|302.292
|299.902-305.68
|304.072
|-
|-
| |3
| |3
|440.8435
|437.255-445.922
|444.771
|438.302-446.968
|445.177
|442.081-450.748
|449.1045
|443.388-452.055
|449.51
|448.174-456.84
|453.438
|449.853-458.519
|456.408
|-
|-
| |4
| |4
|587.791
|583.007-594.5625
|593.028
|584.402-595.958
|593.5695
|589.441-600.997
|598.806
|591.164-602.74
|599.347
|597.565-609.12
|604.584
|599.804-611.359
|608.143
|-
|-
| |5
| |5
|734.739
|728.759-743.203
|741.285
|730.502-744.947
|741.961
|736.802-751.246
|748.507
|738.98-753.425
|749.184
|746.956-761.4005
|755.73
|749.755-764.199
|760.179
|-
|-
| |6
| |6
|881.687
|874.51-891.844
|889.542
|876.603-893.937
|890.354
|884.161-901.495
|898.209
|886.776-904.11
|899.02
|896.347-913.681
|906.876
|899.7055-917.039
|912.215
|-
|-
| |7
| |7
|1028.635
|1020.262-1040.484
|1037.799
|1022.704-1042.926
|1038.746
|1031.522-1051.7445
|1047.91
|1034.572-1054.795
|1048.857
|1045.7385-1065.961
|1058.0215
|1049.6565-1069.879
|1064.251
|-
|-
|8
|8
|1175.583
|1166.014-1189.125
|1186.056
|1168.804-1191.9155
|1187.138
|1178.883-1201.994
|1197.612
|1182.269-1205.48
|1198.694
|1195.13-1216.241
|1209.1675
|1199.607-1222.7185
|1216.387
|}Aeolian Mode (melodic/harmonic minor)
|}Aeolian Mode (melodic/harmonic minor)
{| class="wikitable"
{| class="wikitable"
|-
|-
!Degrees
!Degrees
!Min-Med-13c
!Min-Med±13¢
!Min-Med
!Min-Max±13¢
!Min-Max
!Med-Max±13¢
!Min-Med+13c
!Med-Max-13c
!Min-Max+13c
!Med-Max
!Med-Max+13c
|-
|-
| |1
| |1
|153.27
|152.036-154.925
|153.48
|153.27-156.159
| |154.714
|155.622-158.511
|154.925
|155.622
|156.159
|157.066
|158.511
|-
|-
| |2
| |2
|306.54
|304.072-309.8495
|306.961
|306.54-312.3175
| |308.429
|311.244-317.022
|309.8495
|311.244
|312.3175
|314.133
|317.022
|-
|-
| |3
| |3
|459.81
|456.408-464.774
|460.441
|459.81-468.476
| |464.143
|466.866-475.533
|464.774
|466.866
|468.476
|471.199
|475.533
|-
|-
| |4
| |4
|613.0795
|608.143-619.699
|613.921
|613.0795-624.635
| |618.857
|622.488-634.0435
|619.699
|622.488
|624.635
|628.266
|634.0435
|-
|-
| |5
| |5
|766.349
|760.179-774.624
|767.4015
|766.349-780.794
| |773.572
|778.11-792.554
|774.624
|778.11
|780.794
|785.332
|792.554
|-
|-
| |6
| |6
|919.619
|912.215-929.5845
|920.882
|919.619-936.953
| |928.286
|933.732-951.065
|929.5845
|933.732
|936.953
|942.399
|951.065
|-
|-
|7
|7
|1072.889
|1064.251-1084.473
|1074.362
|1072.889-1093.111
|1083
|1089.354-1109.576
|1084.473
|1089.354
|1093.111
|1099.465
|1109.576
|-
|-
|8
|8
|1226.159
|1216.387-1239.398
|1227.842
|1226.159-1249.27
|1237.715
|1244.976-1268.087
|1239.398
|1244.976
|1249.27
|1256.531
|1268.087
|}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 20:37, 23 November 2018

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

Intervals

Degrees 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
1 133.333 138.667 142.222 146.667 147.368 148.148 149.02 150 151.111 152.381 155.556 160
2 266.667 277.333 284.444 293.333 294.737 296.296 288.039 300 302.222 304.762 311.111 320
3 400 416 426.667 440 442.105 444.444 447.059 450 453.333 457.143 466.667 480
4 533.333 554.667 568.889 586.667 589.474 592.593 596.078 600 604.444 609.524 622.222 640
5 666.667 693.333 711.111 733.333 736.845 740.741 745.098 750 755.556 761.905 777.778 800
6 800 832 853.333 880 884.2015 888.889 894.118 900 906.667 914.286 933.333 960
7 933.333 970.667 995.556 1026.667 1031.158 1037.037 1043.137 1050 1057.778 1066.667 1088.889 1120
8 1066.667 1109.333 1137.778 1177.333 1178.947 1185.1858 1192.157 1200 1208.889 1219.048 1244.444 1280

Most harmonic tunings

Degrees Phrygian Mode (natural minor) Phrygian-Aeolian Mode (intermediate minor) Aeolian Mode (melodic/harmonic minor)
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)

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)

Degrees 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¢
1 145.751-148.641 146.101-148.99 147.36-150.249 147.796-150.685 149.391-152.28 149.951-152.84
2 291.5035-297.282 292.201-297.979 294.721-300.498 295.592-301.37 298.782-304.56 299.902-305.68
3 437.255-445.922 438.302-446.968 442.081-450.748 443.388-452.055 448.174-456.84 449.853-458.519
4 583.007-594.5625 584.402-595.958 589.441-600.997 591.164-602.74 597.565-609.12 599.804-611.359
5 728.759-743.203 730.502-744.947 736.802-751.246 738.98-753.425 746.956-761.4005 749.755-764.199
6 874.51-891.844 876.603-893.937 884.161-901.495 886.776-904.11 896.347-913.681 899.7055-917.039
7 1020.262-1040.484 1022.704-1042.926 1031.522-1051.7445 1034.572-1054.795 1045.7385-1065.961 1049.6565-1069.879
8 1166.014-1189.125 1168.804-1191.9155 1178.883-1201.994 1182.269-1205.48 1195.13-1216.241 1199.607-1222.7185

Aeolian Mode (melodic/harmonic minor)

Degrees Min-Med±13¢ Min-Max±13¢ Med-Max±13¢
1 152.036-154.925 153.27-156.159 155.622-158.511
2 304.072-309.8495 306.54-312.3175 311.244-317.022
3 456.408-464.774 459.81-468.476 466.866-475.533
4 608.143-619.699 613.0795-624.635 622.488-634.0435
5 760.179-774.624 766.349-780.794 778.11-792.554
6 912.215-929.5845 919.619-936.953 933.732-951.065
7 1064.251-1084.473 1072.889-1093.111 1089.354-1109.576
8 1216.387-1239.398 1226.159-1249.27 1244.976-1268.087

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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