User:Moremajorthanmajor/14edIX: Difference between revisions

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|1400
|1400
|1440
|1440
|}Golden Tunings
|}Most harmonic tunings
{| class="wikitable"
{| class="wikitable"
|-
|-
! rowspan="2" |Degrees
! rowspan="2" |Degrees
! rowspan="2" |Octatonic
! rowspan="2" |Octatonic
! colspan="3" |Phrygian Mode (natural minor)
!Phrygian Mode (natural minor)
! colspan="2" |Phrygian-Aeolian Mode (intermediate minor)
!Phrygian-Aeolian Mode (intermediate minor)
! colspan="3" |Aeolian Mode (melodic/harmonic minor)
!Aeolian Mode (melodic/harmonic minor)
|-
!15/7±13¢
!11/5±13¢
!9/4±13¢
|-
| |1
| |F#/Gb
|93.317-95.1745
|96.572-98.429
|99.351-101.208
|-
| |2
| |G
|186.635-190.349
|193.1435-196.858
|198.701-202.416
|-
| |3
| |G#/Ab
|279.952-285.5235
|289.715-295.287
|298.052-303.624
|-
| |4
| |A
|373.269-380.698
|386.287-393.7155
|397.403-404.831
|-
| |5
| |A#/Bb
|466.587-475.872
|482.859-492.144
|496.754-506.039
|-
| |6
| |B
|559.904-571.047
|579.43-590.573
|596.104-607.247
|-
| |7
| |H
|653.224-666.221
|676.002-689.002
|695.455-708.455
|-
| |8
| |H#/Cb
|746.539-761.396
|772.574-787.431
|794.805-809.663
|-
| |9
| |C
|839.856-856.57
|869.146-885.86
|894.156-910.871
|-
| |10
| |C#/Db
|933.173-951.745
|965.717-984.289
|993.507-1012.079
|-
| |11
| |D
|1026.491-1046.919
|1062.289-1082.718
|1092.858-1113.286
|-
| |12
| |D#/Eb
|1119.808-1142.094
|1158.861-1181.1465
|1192.209-1214.494
|-
| |13
| |E
|1213.1255-1237.268
|1255.4325-1279.575
|1291.559-1315.702
|-
|14
|F
|1306.443-1332.443
|1352.004-1378.004
|1390.91-1416.91
|}Golden Tunings
 
Phrygian Mode (natural minor)
{| class="wikitable"
|-
|-
!Degrees
!Octatonic
!Min-Med-13c
!Min-Max-13c
!Min-Med
!Min-Med
!Min-Max
!Min-Max
!Med-Max
!Med-Max-13c
!Min-Med/Min-Max
!Min-Med+13c
!Med-Max
!Min-Max+13c
!Min-Med
!Min-Max-13c
!Min-Max
!Med-Max
|-
|-
| |1
| |1
| |F#/Gb
| |F#/Gb
|89.855
|90.235
|90.783
|90.783
|91.164
|91.164
|92.262
|91.334
|95.395
|91.712
|96.237
|92.092
|98.666
|98.531
|99.459
|100.971
|-
|-
| |2
| |2
| |G
| |G
|179.709
|180.47
|181.566
|181.566
|182.327
|182.327
|184.5245
|182.667
|190.79
|183.4235
|192.473
|184.184
|197.332
|197.061
|198.918
|201.943
|-
|-
| |3
| |3
| |G#/Ab
| |G#/Ab
|269.564
|270.705
|272.35
|272.35
|273.491
|273.491
|276.787
|274.001
|286.185
|275.135
|288.71
|276.276
|295.998
|295.592
|298.377
|302.913
|-
|-
| |4
| |4
| |A
| |A
|359.4185
|360.94
|363.133
|363.133
|364.654
|364.654
|396.049
|365.335
|381.58
|366.847
|384.947
|368.3685
|394.664
|394.123
|397.839
|403.885
|-
|-
| |5
| |5
| |A#/Bb
| |A#/Bb
|449.273
|451.175
|453.916
|453.916
|455.818
|455.818
|461.311
|456.6685
|476.975
|458.559
|481.183
|460.461
|493.3295
|492.653
|497.296
|504.856
|-
|-
| |6
| |6
| |B
| |B
|539.128
|541.41
|544.699
|544.699
|546.981
|546.981
|553.574
|548.002
|572.37
|550.271
|577.42
|552.553
|591.9955
|591.184
|597.755
|605.828
|-
|-
| |7
| |7
| |H
| |H
|628.982
|631.645
|635.482
|635.482
|638.145
|638.145
|645.836
|639.336
|667.765
|641.982
|673.658
|644.645
|690.661
|689.7145
|696.2145
|706.799
|-
|-
| |8
| |8
| |H#/Cb
| |H#/Cb
|718.837
|721.88
|726.2655
|726.2655
|729.3085
|729.3085
|738.098
|730.67
|763.16
|733.694
|769.893
|736.737
|789.327
|788.245
|795.674
|807.77
|-
|-
| |9
| |9
| |C
| |C
|808.692
|812.115
|817.049
|817.049
|820.472
|820.472
|830.3605
|822.003
|858.555
|825.406
|866.13
|828.829
|887.993
|886.776
|895.133
|908.7415
|-
|-
| |10
| |10
| |C#/Db
| |C#/Db
|898.546
|902.35
|907.832
|907.832
|911.636
|911.636
|922.623
|913.337
|953.95
|917.118
|962.367
|920.921
|986.659
|985.306
|994.592
|1009.713
|-
|-
| |11
| |11
| |D
| |D
|988.401
|992.585
|998.615
|998.615
|1002.799
|1002.799
|1014.885
|1007.671
|1049.345
|1008.829
|1058.603
|1013.013
|1085.325
|1083.837
|1094.051
|1110.684
|-
|-
| |12
| |12
| |D#/Eb
| |D#/Eb
|1078.255
|1082.82
|1089.398
|1089.398
|1093.963
|1093.963
|1107.147
|1096.004
|1144.74
|1100.541
|1154.84
|1105.106
|1183.991
|1182.368
|1193.5105
|1211.655
|-
|-
| |13
| |13
| |E
| |E
|1168.11
|1173.055
|1180.1815
|1180.1815
|1185.126
|1185.126
|1199.41
|1187.338
|1192.253
|1197.198
|1280.898
|-
|14
|F
|1257.965
|1263.29
|1270.965
|1276.29
|1278.672
|1283.965
|1289.29
|1379.429
|}
Phrygian-Aeolian Mode (intermediate minor)
{| class="wikitable"
|-
!Degrees
!Octatonic
!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
|F#/Gb
|94.4665
|95.308
|95.395
|96.237
|96.324
|97.165
|97.737
|-
|2
|G
|188.933
|190.616
|190.79
|192.473
|192.647
|194.3305
|195.475
|-
|3
|G#/Ab
|283.399
|285.924
|286.185
|288.71
|288.971
|291.496
|293.212
|-
|4
|A
|377.866
|381.228
|381.58
|384.947
|385.294
|388.661
|390.949
|-
|5
|A#/Bb
|472.332
|476.5405
|476.975
|481.183
|481.618
|485.826
|488.687
|-
|6
|B
|566.799
|571.849
|572.37
|577.42
|577.942
|582.9915
|586.424
|-
|7
|H
|661.265
|667.157
|667.765
|673.658
|674.265
|680.157
|684.161
|-
|8
|H#/Cb
|755.732
|762.465
|763.16
|769.893
|770.589
|777.322
|781.899
|-
|9
|C
|850.198
|857.773
|858.555
|866.13
|866.912
|874.487
|879.636
|-
|10
|C#/Db
|944.665
|953.081
|953.95
|962.367
|963.236
|971.652
|977.373
|-
|11
|D
|1039.131
|1048.298
|1049.345
|1058.603
|1059.56
|1068.818
|1075.111
|-
|12
|D#/Eb
|1113.5975
|1143.697
|1144.74
|1154.84
|1155.883
|1165.983
|1172.848
|-
|13
|E
|1228.064
|1239.005
|1240.435
|1240.435
|1251.077
|1251.077
|1252.207
|1263.148
|1270.585
|-
|14
|F
|1322.53
|1334.313
|1335.53
|1347.313
|1348.53
|1360.313
|1368.322
|}
Aeolian Mode (melodic/harmonic minor)
{| class="wikitable"
|-
!Degrees
!Octatonic
!Min-Max-13c
!Min-Med
!Min-Max
!Min-Med+13c
!Med-Max-13c
!Min-Max+13c
!Med-Max
!Med-Max+13c
|-
|1
|F#/Gb
|98.531
|98.666
|99.459
|99.5945
|100.043
|100.388
|100.971
|101.9
|-
|2
|G
|197.061
|197.332
|198.918
|199.189
|200.085
|200.776
|201.943
|203.8
|-
|3
|G#/Ab
|295.592
|295.998
|298.377
|298.783
|300.128
|301.163
|302.913
|305.6995
|-
|4
|A
|394.123
|394.664
|397.839
|398.378
|400.171
|401.551
|403.885
|407.599
|-
|5
|A#/Bb
|492.653
|493.3295
|497.296
|497.972
|500.2135
|501.939
|504.856
|509.499
|-
|6
|B
|591.184
|591.9955
|597.755
|597.567
|600.256
|602.327
|605.828
|611.399
|-
|7
|H
|689.7145
|690.661
|696.2145
|697.161
|700.299
|702.7145
|706.799
|713.299
|-
|8
|H#/Cb
|788.245
|789.327
|795.674
|796.756
|800.342
|803.102
|807.77
|815.199
|-
|9
|C
|886.776
|887.993
|895.133
|896.35
|900.384
|903.49
|908.7415
|917.099
|-
|10
|C#/Db
|985.306
|986.659
|994.592
|995.945
|1000.427
|1003.878
|1009.713
|1018.9985
|-
|11
|D
|1083.837
|1085.325
|1094.051
|1095.539
|1100.47
|1104.266
|1110.684
|1120.898
|-
|12
|D#/Eb
|1182.368
|1183.991
|1193.5105
|1195.134
|1200.512
|1204.653
|1211.655
|1222.798
|-
|13
|E
|1280.898
|1282.657
|1282.657
|1292.97
|1292.97
|1294.728
|1300.555
|1305.041
|1312.627
|1312.627
|1324.698
|-
|-
|14
|14
|F
|F
|1270.965
|1379.429
|1276.29
|1291.672
|1335.53
|1347.313
|1381.322
|1381.322
|1392.429
|1392.429
|1394.322
|1400.598
|1405.429
|1413.598
|1413.598
|1426.598
|}
|}
[[Category:14-tone]]
[[Category:14-tone]]

Revision as of 04:07, 5 November 2018

This scale, a Long Common Practice minor mode,occurs in 12edo, where it is the equal division of the major ninth. It has the Macroshrutis 6L 2s 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 Minimum Median Maximum Minimum Median Maximum
1 F#/Gb 85.714 89.143 91.429 94.286 95.798 97.959 100 102.857
2 G 171.429 178.286 182.857 188.571 191.597 195.918 200 205.714
3 G#/Ab 257.143 267.429 274.286 282.857 287.395 293.878 300 308.571
4 A 342.857 356.571 365.714 377.143 383.193 391.836 400 411.429
5 A#/Bb 428.571 445.714 467.143 471.429 478.992 489.796 500 514.286
6 B 514.286 534.857 548.571 565.714 574.79 587.755 600 617.143
7 H 600 624 640 660 670.588 685.714 700 720
8 H#/Cb 685.714 713.143 731.429 754.286 766.387 783.6735 800 822.857
9 C 771.429 802.286 822.857 848.571 862.185 881.633 900 925.714
10 C#/Db 857.143 891.429 914.286 942.857 957.983 979.592 1000 1028.571
11 D 942.857 980.571 1005.714 1037.143 1053.7815 1077.551 1100 1131.429
12 D#/Eb 1028.571 1069.714 1097.143 1131.429 1149.58 1175.51 1200 1234.286
13 E 1114.286 1158.857 1188.571 1225.714 1245.378 1273.469 1300 1337.143
14 F 1200 1268.571 1280 1320 1341.1765 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 93.317-95.1745 96.572-98.429 99.351-101.208
2 G 186.635-190.349 193.1435-196.858 198.701-202.416
3 G#/Ab 279.952-285.5235 289.715-295.287 298.052-303.624
4 A 373.269-380.698 386.287-393.7155 397.403-404.831
5 A#/Bb 466.587-475.872 482.859-492.144 496.754-506.039
6 B 559.904-571.047 579.43-590.573 596.104-607.247
7 H 653.224-666.221 676.002-689.002 695.455-708.455
8 H#/Cb 746.539-761.396 772.574-787.431 794.805-809.663
9 C 839.856-856.57 869.146-885.86 894.156-910.871
10 C#/Db 933.173-951.745 965.717-984.289 993.507-1012.079
11 D 1026.491-1046.919 1062.289-1082.718 1092.858-1113.286
12 D#/Eb 1119.808-1142.094 1158.861-1181.1465 1192.209-1214.494
13 E 1213.1255-1237.268 1255.4325-1279.575 1291.559-1315.702
14 F 1306.443-1332.443 1352.004-1378.004 1390.91-1416.91

Golden Tunings

Phrygian Mode (natural minor)

Degrees Octatonic Min-Med-13c Min-Max-13c Min-Med Min-Max Med-Max-13c Min-Med+13c Min-Max+13c Min-Max-13c
1 F#/Gb 89.855 90.235 90.783 91.164 91.334 91.712 92.092 98.531
2 G 179.709 180.47 181.566 182.327 182.667 183.4235 184.184 197.061
3 G#/Ab 269.564 270.705 272.35 273.491 274.001 275.135 276.276 295.592
4 A 359.4185 360.94 363.133 364.654 365.335 366.847 368.3685 394.123
5 A#/Bb 449.273 451.175 453.916 455.818 456.6685 458.559 460.461 492.653
6 B 539.128 541.41 544.699 546.981 548.002 550.271 552.553 591.184
7 H 628.982 631.645 635.482 638.145 639.336 641.982 644.645 689.7145
8 H#/Cb 718.837 721.88 726.2655 729.3085 730.67 733.694 736.737 788.245
9 C 808.692 812.115 817.049 820.472 822.003 825.406 828.829 886.776
10 C#/Db 898.546 902.35 907.832 911.636 913.337 917.118 920.921 985.306
11 D 988.401 992.585 998.615 1002.799 1007.671 1008.829 1013.013 1083.837
12 D#/Eb 1078.255 1082.82 1089.398 1093.963 1096.004 1100.541 1105.106 1182.368
13 E 1168.11 1173.055 1180.1815 1185.126 1187.338 1192.253 1197.198 1280.898
14 F 1257.965 1263.29 1270.965 1276.29 1278.672 1283.965 1289.29 1379.429

Phrygian-Aeolian Mode (intermediate minor)

Degrees Octatonic 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 F#/Gb 94.4665 95.308 95.395 96.237 96.324 97.165 97.737
2 G 188.933 190.616 190.79 192.473 192.647 194.3305 195.475
3 G#/Ab 283.399 285.924 286.185 288.71 288.971 291.496 293.212
4 A 377.866 381.228 381.58 384.947 385.294 388.661 390.949
5 A#/Bb 472.332 476.5405 476.975 481.183 481.618 485.826 488.687
6 B 566.799 571.849 572.37 577.42 577.942 582.9915 586.424
7 H 661.265 667.157 667.765 673.658 674.265 680.157 684.161
8 H#/Cb 755.732 762.465 763.16 769.893 770.589 777.322 781.899
9 C 850.198 857.773 858.555 866.13 866.912 874.487 879.636
10 C#/Db 944.665 953.081 953.95 962.367 963.236 971.652 977.373
11 D 1039.131 1048.298 1049.345 1058.603 1059.56 1068.818 1075.111
12 D#/Eb 1113.5975 1143.697 1144.74 1154.84 1155.883 1165.983 1172.848
13 E 1228.064 1239.005 1240.435 1251.077 1252.207 1263.148 1270.585
14 F 1322.53 1334.313 1335.53 1347.313 1348.53 1360.313 1368.322

Aeolian Mode (melodic/harmonic minor)

Degrees Octatonic Min-Max-13c Min-Med Min-Max Min-Med+13c Med-Max-13c Min-Max+13c Med-Max Med-Max+13c
1 F#/Gb 98.531 98.666 99.459 99.5945 100.043 100.388 100.971 101.9
2 G 197.061 197.332 198.918 199.189 200.085 200.776 201.943 203.8
3 G#/Ab 295.592 295.998 298.377 298.783 300.128 301.163 302.913 305.6995
4 A 394.123 394.664 397.839 398.378 400.171 401.551 403.885 407.599
5 A#/Bb 492.653 493.3295 497.296 497.972 500.2135 501.939 504.856 509.499
6 B 591.184 591.9955 597.755 597.567 600.256 602.327 605.828 611.399
7 H 689.7145 690.661 696.2145 697.161 700.299 702.7145 706.799 713.299
8 H#/Cb 788.245 789.327 795.674 796.756 800.342 803.102 807.77 815.199
9 C 886.776 887.993 895.133 896.35 900.384 903.49 908.7415 917.099
10 C#/Db 985.306 986.659 994.592 995.945 1000.427 1003.878 1009.713 1018.9985
11 D 1083.837 1085.325 1094.051 1095.539 1100.47 1104.266 1110.684 1120.898
12 D#/Eb 1182.368 1183.991 1193.5105 1195.134 1200.512 1204.653 1211.655 1222.798
13 E 1280.898 1282.657 1292.97 1294.728 1300.555 1305.041 1312.627 1324.698
14 F 1379.429 1381.322 1392.429 1394.322 1400.598 1405.429 1413.598 1426.598
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