User:Moremajorthanmajor/9edIX: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
No edit summary
Line 99: Line 99:
|1244.444
|1244.444
|1280
|1280
|}
Most harmonic tunings
{| class="wikitable"
|-
! rowspan="2" |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
|}Golden Tunings
Phrygian Mode (natural minor)
{| class="wikitable"
{| class="wikitable"
|-
|-
! rowspan="2"|Degrees
!Degrees
! colspan="3" |Phrygian Mode (natural minor)
!Min-Med-13c
!  colspan="2"|Phrygian-Aeolian Mode (intermediate minor)
!Min-Max-13c
! colspan="3" |Aeolian Mode (melodic/harmonic minor)
|-
!Min-Med
!Min-Max
!Med-Max
!Min-Med/Min-Max
!Med-Max
!Min-Med
!Min-Med
!Min-Max
!Min-Max
!Med-Max-13c
!Min-Med+13c
!Min-Max+13c
!Med-Max
!Med-Max
!Med-Max+13c
|-
|-
| |1
| |1
|139.774
|140.366
|141.218
|141.218
| |141.81
| |141.81
|142.075
|142.663
|143.254
|143.519
|143.519
| |148.392
|144.9635
|149.7015
|153.48
| |154.714
|157.066
|-
|-
| |2
| |2
|279.548
|280.731
|282.437
|282.437
| |283.62
| |283.62
|284.149
|285.3255
|286.509
|287.038
|287.038
| |296.7845
|289.927
|299.403
|306.961
| |308.429
|314.133
|-
|-
| |3
| |3
|419.3215
|421.097
|423.655
|423.655
| |424.43
| |424.43
|426.224
|427.988
|429.763
|430.557
|430.557
| |445.177
|434.891
|449.1045
|460.441
| |464.143
|471.199
|-
|-
| |4
| |4
|559.095
|561.462
|564.876
|564.876
| |566.24
| |566.24
|568.3
|570.650
|573.018
|574.076
|574.076
| |593.5695
|579.854
|598.806
|613.921
| |618.857
|628.266
|-
|-
| |5
| |5
|698.869
|701.828
|706.0915
|706.0915
| |709.05
| |709.05
|710.373
|713.314
|716.272
|717.5955
|717.5955
| |741.961
|724.818
|748.507
|767.4015
| |773.572
|785.332
|-
|-
| |6
| |6
|838.643
|842.193
|847.308
|847.308
| |850.86
| |850.86
|852.448
|855.976
|859.5265
|861.115
|861.115
| |890.354
|869.781
|898.209
|920.882
| |928.286
|942.399
|-
|-
| |7
| |7
|978.417
|982.559
|988.528
|988.528
| |992.67
| |992.67
|994.5225
|998.639
|1002.781
|1004.634
|1004.634
| |1038.746
|1014.745
|1047.91
|1074.362
| |1083
|1099.465
|-
|-
|8
|8
|1118.191
|1122.924
|1129.746
|1129.746
|1134.48
|1134.48
|1136.597
|1141.302
|1146.035
|1148.153
|1148.153
|1159.708
|}
Phrygian-Aeolian Mode (intermediate minor)
{| class="wikitable"
|-
!Degrees
!Min-Med/Min-Max-13c
!Med-Max-13c
!Min-Med/Min-Max
!Med-Max
!Min-Med/Min-Max+13c
!Med-Max+13c
!Min-Med-13c (Aeolian)
|-
| |1
|146.948
|148.257
|148.392
|149.7015
|149.836
|151.146
|152.036
|-
| |2
|293.896
|296.514
|296.7845
|299.403
|299.673
|302.292
|304.072
|-
| |3
|440.8435
|444.771
|445.177
|449.1045
|449.51
|453.438
|456.408
|-
| |4
|587.791
|593.028
|593.5695
|598.806
|599.347
|604.584
|608.143
|-
| |5
|734.739
|741.285
|741.961
|748.507
|749.184
|755.73
|760.179
|-
| |6
|881.687
|889.542
|890.354
|898.209
|899.02
|906.876
|912.215
|-
| |7
|1028.635
|1037.799
|1038.746
|1047.91
|1048.857
|1058.0215
|1064.251
|-
|8
|1175.583
|1186.056
|1187.138
|1187.138
|1197.612
|1197.612
|1198.694
|1209.1675
|1216.387
|}Aeolian Mode (melodic/harmonic minor)
{| class="wikitable"
|-
!Degrees
!Min-Med-13c
!Min-Med
!Min-Max
!Min-Med+13c
!Med-Max-13c
!Min-Max+13c
!Med-Max
!Med-Max+13c
|-
| |1
|153.27
|153.48
| |154.714
|154.925
|155.622
|156.159
|157.066
|158.511
|-
| |2
|306.54
|306.961
| |308.429
|309.8495
|311.244
|312.3175
|314.133
|317.022
|-
| |3
|459.81
|460.441
| |464.143
|464.774
|466.866
|468.476
|471.199
|475.533
|-
| |4
|613.0795
|613.921
| |618.857
|619.699
|622.488
|624.635
|628.266
|634.0435
|-
| |5
|766.349
|767.4015
| |773.572
|774.624
|778.11
|780.794
|785.332
|792.554
|-
| |6
|919.619
|920.882
| |928.286
|929.5845
|933.732
|936.953
|942.399
|951.065
|-
|7
|1072.889
|1074.362
|1083
|1084.473
|1089.354
|1093.111
|1099.465
|1109.576
|-
|8
|1226.159
|1227.842
|1227.842
|1237.715
|1237.715
|1239.398
|1244.976
|1249.27
|1256.531
|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]]
[[Category:ed9/4]]
[[Category:ed9/4]]

Revision as of 05:30, 5 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 Minimum Median Maximum Minimum Median Maximum
1 133.333 138.667 142.222 146.667 149.02 152.381 155.556 160
2 266.667 277.333 284.444 293.333 288.039 304.762 311.111 320
3 400 416 426.667 440 447.059 457.143 466.667 480
4 533.333 554.667 568.889 586.667 596.078 609.524 622.222 640
5 666.667 693.333 711.111 733.333 745.098 761.905 777.778 800
6 800 832 853.333 880 894.118 914.286 933.333 960
7 933.333 970.667 995.556 1026.667 1043.137 1066.667 1088.889 1120
8 1066.667 1109.333 1137.778 1177.333 1192.157 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-13c Min-Max-13c Min-Med Min-Max Med-Max-13c Min-Med+13c Min-Max+13c Med-Max Med-Max+13c
1 139.774 140.366 141.218 141.81 142.075 142.663 143.254 143.519 144.9635
2 279.548 280.731 282.437 283.62 284.149 285.3255 286.509 287.038 289.927
3 419.3215 421.097 423.655 424.43 426.224 427.988 429.763 430.557 434.891
4 559.095 561.462 564.876 566.24 568.3 570.650 573.018 574.076 579.854
5 698.869 701.828 706.0915 709.05 710.373 713.314 716.272 717.5955 724.818
6 838.643 842.193 847.308 850.86 852.448 855.976 859.5265 861.115 869.781
7 978.417 982.559 988.528 992.67 994.5225 998.639 1002.781 1004.634 1014.745
8 1118.191 1122.924 1129.746 1134.48 1136.597 1141.302 1146.035 1148.153 1159.708

Phrygian-Aeolian Mode (intermediate minor)

Degrees Min-Med/Min-Max-13c Med-Max-13c Min-Med/Min-Max Med-Max Min-Med/Min-Max+13c Med-Max+13c Min-Med-13c (Aeolian)
1 146.948 148.257 148.392 149.7015 149.836 151.146 152.036
2 293.896 296.514 296.7845 299.403 299.673 302.292 304.072
3 440.8435 444.771 445.177 449.1045 449.51 453.438 456.408
4 587.791 593.028 593.5695 598.806 599.347 604.584 608.143
5 734.739 741.285 741.961 748.507 749.184 755.73 760.179
6 881.687 889.542 890.354 898.209 899.02 906.876 912.215
7 1028.635 1037.799 1038.746 1047.91 1048.857 1058.0215 1064.251
8 1175.583 1186.056 1187.138 1197.612 1198.694 1209.1675 1216.387

Aeolian Mode (melodic/harmonic minor)

Degrees Min-Med-13c Min-Med Min-Max Min-Med+13c Med-Max-13c Min-Max+13c Med-Max Med-Max+13c
1 153.27 153.48 154.714 154.925 155.622 156.159 157.066 158.511
2 306.54 306.961 308.429 309.8495 311.244 312.3175 314.133 317.022
3 459.81 460.441 464.143 464.774 466.866 468.476 471.199 475.533
4 613.0795 613.921 618.857 619.699 622.488 624.635 628.266 634.0435
5 766.349 767.4015 773.572 774.624 778.11 780.794 785.332 792.554
6 919.619 920.882 928.286 929.5845 933.732 936.953 942.399 951.065
7 1072.889 1074.362 1083 1084.473 1089.354 1093.111 1099.465 1109.576
8 1226.159 1227.842 1237.715 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.

Retrieved from "https://en.xen.wiki/index.php?title=User:Moremajorthanmajor/9edIX&oldid=38362"