User:Moremajorthanmajor/14edIX: Difference between revisions

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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.
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==
==Intervals==
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="2" |Degrees
! rowspan="2" |Octatonic
! rowspan="2" |Octatonic
! colspan="3" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
! colspan="4" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
! colspan="2" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
! colspan="3" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
! colspan="2" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
! colspan="3" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
|-
|-
!Absolute Minimum
!Absolute Minimum
!Minimum
!Minimum
!Median
!Maximum
!Maximum
! |Minimum
! |Minimum
!Median
!Maximum
!Maximum
!Minimum
!Minimum
!Median
!Maximum
!Maximum
|-
|-
Line 20: Line 23:
|85.714
|85.714
|89.143
|89.143
|91.429
| colspan="2" |94.286
| colspan="2" |94.286
|95.798
| colspan="2" |97.959
| colspan="2" |97.959
|100
|102.857
|102.857
|-
|-
Line 28: Line 34:
|171.429
|171.429
|178.286
|178.286
|182.857
| colspan="2" |188.571
| colspan="2" |188.571
|191.597
| colspan="2" |195.918
| colspan="2" |195.918
|200
|205.714
|205.714
|-
|-
Line 36: Line 45:
|257.143
|257.143
|267.429
|267.429
|274.286
| colspan="2" |282.857
| colspan="2" |282.857
|287.395
| colspan="2" |293.878
| colspan="2" |293.878
|300
|308.571
|308.571
|-
|-
Line 44: Line 56:
|342.857
|342.857
|356.571
|356.571
|365.714
| colspan="2" |377.143
| colspan="2" |377.143
|383.193
| colspan="2" |391.836
| colspan="2" |391.836
|400
|411.429
|411.429
|-
|-
Line 52: Line 67:
|428.571
|428.571
|445.714
|445.714
|467.143
| colspan="2" |471.429
| colspan="2" |471.429
|478.992
| colspan="2" |489.796
| colspan="2" |489.796
|500
|514.286
|514.286
|-
|-
Line 60: Line 78:
|514.286
|514.286
|534.857
|534.857
|548.571
| colspan="2" |565.714
| colspan="2" |565.714
|574.79
| colspan="2" |587.755
| colspan="2" |587.755
|600
|617.143
|617.143
|-
|-
Line 68: Line 89:
|600
|600
|624
|624
|640
| colspan="2" |660
| colspan="2" |660
|670.588
| colspan="2" |685.714
| colspan="2" |685.714
|700
|720
|720
|-
|-
Line 76: Line 100:
|685.714
|685.714
|713.143
|713.143
|731.429
| colspan="2" |754.286
| colspan="2" |754.286
|766.387
| colspan="2" |783.6735
| colspan="2" |783.6735
|800
|822.857
|822.857
|-
|-
Line 84: Line 111:
|771.429
|771.429
|802.286
|802.286
|822.857
| colspan="2" |848.571
| colspan="2" |848.571
|862.185
| colspan="2" |881.633
| colspan="2" |881.633
|900
|925.714
|925.714
|-
|-
Line 92: Line 122:
|857.143
|857.143
|891.429
|891.429
|914.286
| colspan="2" |942.857
| colspan="2" |942.857
|957.983
| colspan="2" |979.592
| colspan="2" |979.592
|1000
|1028.571
|1028.571
|-
|-
Line 100: Line 133:
|942.857
|942.857
|980.571
|980.571
|1005.714
| colspan="2" |1037.143
| colspan="2" |1037.143
|1053.7815
| colspan="2" |1077.551
| colspan="2" |1077.551
|1100
|1131.429
|1131.429
|-
|-
Line 108: Line 144:
|1028.571
|1028.571
|1069.714
|1069.714
|1097.143
| colspan="2" |1131.429
| colspan="2" |1131.429
|1149.58
| colspan="2" |1175.51
| colspan="2" |1175.51
|1200
|1234.286
|1234.286
|-
|-
Line 116: Line 155:
|1114.286
|1114.286
|1158.857
|1158.857
|1188.571
| colspan="2" |1225.714
| colspan="2" |1225.714
|1245.378
| colspan="2" |1273.469
| colspan="2" |1273.469
|1300
|1337.143
|1337.143
|-
|-
Line 123: Line 165:
|F
|F
|1200
|1200
|1248
|1268.571
|1280
| colspan="2" |1320
| colspan="2" |1320
|1341.1765
| colspan="2" |1371.429
| colspan="2" |1371.429
|1400
|1440
|1440
|}Golden Tunings
|}Golden Tunings
{| class="wikitable"
{| class="wikitable"
|-
|-
!Degrees
! rowspan="2" |Degrees
!Octatonic
! rowspan="2" |Octatonic
!Phrygian Mode (natural minor)
! colspan="3" |Phrygian Mode (natural minor)
!Phrygian-Aeolian Mode (intermediate minor)
! colspan="2" |Phrygian-Aeolian Mode (intermediate minor)
!Aeolian Mode (melodic/harmonic minor)
! colspan="3" |Aeolian Mode (melodic/harmonic minor)
|-
!Min-Med
!Min-Max
!Med-Max
!Min-Med/Min-Max
!Med-Max
!Min-Med
!Min-Max
!Med-Max
|-
|-
| |1
| |1
| |F#/Gb
| |F#/Gb
|90.162
|90.783
|91.164
|92.262
|95.395
|95.395
|96.237
|98.666
|99.459
|99.459
|100.971
|-
|-
| |2
| |2
| |G
| |G
|180.3245
|181.566
|182.327
|184.5245
|190.79
|190.79
|192.473
|197.332
|198.918
|198.918
|201.943
|-
|-
| |3
| |3
| |G#/Ab
| |G#/Ab
|270.487
|272.35
|273.491
|276.787
|286.185
|286.185
|288.71
|295.998
|298.377
|298.377
|302.913
|-
|-
| |4
| |4
| |A
| |A
|360.649
|363.133
|364.654
|396.049
|381.58
|381.58
|384.947
|394.664
|397.839
|397.839
|403.885
|-
|-
| |5
| |5
| |A#/Bb
| |A#/Bb
|450.811
|453.916
|455.818
|461.311
|476.975
|476.975
|481.183
|493.3295
|497.296
|497.296
|504.856
|-
|-
| |6
| |6
| |B
| |B
|540.973
|544.699
|546.981
|553.574
|572.37
|572.37
|577.42
|591.9955
|597.755
|597.755
|605.828
|-
|-
| |7
| |7
| |H
| |H
|631.136
|635.482
|638.145
|645.836
|667.765
|667.765
|673.658
|690.661
|696.2145
|696.2145
|706.799
|-
|-
| |8
| |8
| |H#/Cb
| |H#/Cb
|721.298
|726.2655
|729.3085
|738.098
|763.16
|763.16
|769.893
|789.327
|795.674
|795.674
|807.77
|-
|-
| |9
| |9
| |C
| |C
|811.46
|817.049
|820.472
|830.3605
|858.555
|858.555
|866.13
|887.993
|895.133
|895.133
|908.7415
|-
|-
| |10
| |10
| |C#/Db
| |C#/Db
|901.622
|907.832
|911.636
|922.623
|953.95
|953.95
|962.367
|986.659
|994.592
|994.592
|1009.713
|-
|-
| |11
| |11
| |D
| |D
|991.785
|998.615
|1002.799
|1014.885
|1049.345
|1049.345
|1094..051
|1058.603
|1085.325
|1094.051
|1110.684
|-
|-
| |12
| |12
| |D#/Eb
| |D#/Eb
|1081.947
|1089.398
|1093.963
|1107.147
|1144.74
|1144.74
|1154.84
|1183.991
|1193.5105
|1193.5105
|1211.655
|-
|-
| |13
| |13
| |E
| |E
|1172.109
|1180.1815
|1185.126
|1199.41
|1240.435
|1240.435
|1251.077
|1282.657
|1292.97
|1292.97
|1312.627
|-
|-
|14
|14
|F
|F
|1262.271
|1270.965
|1276.29
|1291.672
|1335.53
|1335.53
|1347.313
|1381.322
|1392.429
|1392.429
|1413.598
|}
|}
[[Category:14-tone]]
[[Category:14-tone]]

Revision as of 19:31, 26 October 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

Golden Tunings

Degrees Octatonic Phrygian Mode (natural minor) Phrygian-Aeolian Mode (intermediate minor) Aeolian Mode (melodic/harmonic minor)
Min-Med Min-Max Med-Max Min-Med/Min-Max Med-Max Min-Med Min-Max Med-Max
1 F#/Gb 90.783 91.164 92.262 95.395 96.237 98.666 99.459 100.971
2 G 181.566 182.327 184.5245 190.79 192.473 197.332 198.918 201.943
3 G#/Ab 272.35 273.491 276.787 286.185 288.71 295.998 298.377 302.913
4 A 363.133 364.654 396.049 381.58 384.947 394.664 397.839 403.885
5 A#/Bb 453.916 455.818 461.311 476.975 481.183 493.3295 497.296 504.856
6 B 544.699 546.981 553.574 572.37 577.42 591.9955 597.755 605.828
7 H 635.482 638.145 645.836 667.765 673.658 690.661 696.2145 706.799
8 H#/Cb 726.2655 729.3085 738.098 763.16 769.893 789.327 795.674 807.77
9 C 817.049 820.472 830.3605 858.555 866.13 887.993 895.133 908.7415
10 C#/Db 907.832 911.636 922.623 953.95 962.367 986.659 994.592 1009.713
11 D 998.615 1002.799 1014.885 1049.345 1058.603 1085.325 1094.051 1110.684
12 D#/Eb 1089.398 1093.963 1107.147 1144.74 1154.84 1183.991 1193.5105 1211.655
13 E 1180.1815 1185.126 1199.41 1240.435 1251.077 1282.657 1292.97 1312.627
14 F 1270.965 1276.29 1291.672 1335.53 1347.313 1381.322 1392.429 1413.598
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