User:Moremajorthanmajor/13edIX: 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 minor ninth. It has the Grandfather 5L 3s 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 minor ninth. It has the Grandfather 5L 3s 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 19: Line 22:
| |F#/Gb
| |F#/Gb
|92.308
|92.308
|96
|97.582
|98.4615
| colspan="2" |101.5385
| colspan="2" |101.5385
|103.167
| colspan="2" |105.4945
| colspan="2" |105.4945
|107.692
|110.769
|110.769
|-
|-
Line 27: Line 33:
| |G
| |G
|184.615
|184.615
|192
|195.165
|196.923
| colspan="2" |203.077
| colspan="2" |203.077
|206.335
| colspan="2" |210.989
| colspan="2" |210.989
|215.385
|221.5385
|221.5385
|-
|-
Line 35: Line 44:
| |G#/Ab
| |G#/Ab
|276.923
|276.923
|288
|292.747
|295.385
| colspan="2" |304.615
| colspan="2" |304.615
|309.502
| colspan="2" |316.4835
| colspan="2" |316.4835
|323.077
|332.308
|332.308
|-
|-
Line 43: Line 55:
| |A
| |A
|369.231
|369.231
|384
|390.33
|393.846
| colspan="2" |406.154
| colspan="2" |406.154
|412.67
| colspan="2" |421.978
| colspan="2" |421.978
|430.769
|443.076
|443.076
|-
|-
Line 51: Line 66:
| |B
| |B
|461.5385
|461.5385
|480
|487.912
|491.308
| colspan="2" |507.692
| colspan="2" |507.692
|515.837
| colspan="2" |527.4725
| colspan="2" |527.4725
|538.4615
|553.846
|553.846
|-
|-
Line 59: Line 77:
| |B#/Hb
| |B#/Hb
|553.846
|553.846
|576
|585.4945
|589.769
| colspan="2" |609.231
| colspan="2" |609.231
|619.0045
| colspan="2" |632.967
| colspan="2" |632.967
|646.154
|664.615
|664.615
|-
|-
Line 67: Line 88:
| |H
| |H
|646.154
|646.154
|672
|683.077
|690.231
| colspan="2" |710.769
| colspan="2" |710.769
|722.172
| colspan="2" |738.4615
| colspan="2" |738.4615
|754.846
|775.385
|775.385
|-
|-
Line 75: Line 99:
| |C
| |C
|738.4615
|738.4615
|768
|780.66
|788.692
| colspan="2" |812.308
| colspan="2" |812.308
|825.339
| colspan="2" |843.856
| colspan="2" |843.856
|861.5385
|886.154
|886.154
|-
|-
Line 83: Line 110:
| |C#/Db
| |C#/Db
|830.769
|830.769
|864
|878.242
|896.154
| colspan="2" |913.846
| colspan="2" |913.846
|929.507
| colspan="2" |949.4505
| colspan="2" |949.4505
|969.231
|996.923
|996.923
|-
|-
Line 91: Line 121:
| |D
| |D
|923.077
|923.077
|960
|975.824
|984.615
| colspan="2" |1015.385
| colspan="2" |1015.385
|1031.674
| colspan="2" |1054.945
| colspan="2" |1054.945
|1076.923
|1107.692
|1107.692
|-
|-
Line 99: Line 132:
| |D#/Eb
| |D#/Eb
|1015.385
|1015.385
|1056
|1073.407
|1083.077
| colspan="2" |1116.923
| colspan="2" |1116.923
|1134.842
| colspan="2" |1160.44
| colspan="2" |1160.44
|1184.615
|1218.4615
|1218.4615
|-
|-
Line 107: Line 143:
| |E
| |E
|1107.692
|1107.692
|1152
|1170.99
|1181.5385
| colspan="2" |1218.4615
| colspan="2" |1218.4615
|1238.009
| colspan="2" |1265.9348
| colspan="2" |1265.9348
|1292.308
|1329.231
|1329.231
|-
|-
Line 115: Line 154:
| |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
|}
|}
Line 123: Line 165:
{| 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
|97.098
|97.7665
|98.176
|99.359
|102.733
|102.733
|103.639
|106.256
|107.11
|107.11
|108.738
|-
|-
| |2
| |2
| |G
| |G
|194.196
|195.533
|196.352
|198.719
|205.466
|205.466
|207.279
|212.511
|214.22
|214.22
|217.477
|-
|-
| |3
| |3
| |G#/Ab
| |G#/Ab
|291.293
|293.2995
|294.528
|298.078
|308.199
|308.199
|310.9185
|318.767
|321.33
|321.33
|326.215
|-
|-
| |4
| |4
| |A
| |A
|388.391
|391.063
|392.705
|397.4375
|410.932
|410.932
|414.558
|425.022
|428.44
|428.44
|434.953
|-
|-
| |5
| |5
| |B
| |B
|485.489
|488.833
|490.881
|469.797
|513.6655
|513.6655
|518.1975
|531.278
|535.55
|535.55
|543.6915
|-
|-
| |6
| |6
| |B#/Hb
| |B#/Hb
|582.587
|586.299
|589.057
|596.156
|616.399
|616.399
|621.837
|637.534
|642.6595
|642.6595
|652.43
|-
|-
| |7
| |7
| |H
| |H
|679.685
|684.366
|687.233
|695.516
|719.132
|719.132
|725.4765
|743.789
|749.769
|749.769
|761.168
|-
|-
| |8
| |8
| |C
| |C
|776.782
|782.132
|785.409
|794.875
|821.865
|821.865
|829.116
|850.045
|856.879
|856.879
|869.906
|-
|-
| |9
| |9
| |C#/Db
| |C#/Db
|873.880
|879.899
|883.585
|894.234
|924.598
|924.598
|932.755
|956.3
|963.989
|963.989
|978.645
|-
|-
| |10
| |10
| |D
| |D
|970.978
|977.665
|981.761
|993.594
|1027.331
|1027.331
|1036.395
|1062.556
|1071.099
|1071.099
|1087.383
|-
|-
| |11
| |11
| |D#/Eb
| |D#/Eb
|1068.076
|1075.432
|1079.9375
|1092.953
|1130.064
|1130.064
|1140.034
|1168.8115
|1178.209
|1178.209
|1196.121
|-
|-
| |12
| |12
| |E
| |E
|1165.1735
|1173.198
|1178.114
|1192.312
|1232.797
|1232.797
|1243.674
|1275.067
|1285.319
|1285.319
|1304.86
|-
|-
| |13
| |13
| |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:13-tone]]
[[Category:13-tone]]

Revision as of 18:07, 26 October 2018

This scale, a Long Common Practice minor mode, occurs in 12edo; where it is the equal division of the minor ninth. It has the Grandfather 5L 3s 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 92.308 97.582 98.4615 101.5385 103.167 105.4945 107.692 110.769
2 G 184.615 195.165 196.923 203.077 206.335 210.989 215.385 221.5385
3 G#/Ab 276.923 292.747 295.385 304.615 309.502 316.4835 323.077 332.308
4 A 369.231 390.33 393.846 406.154 412.67 421.978 430.769 443.076
5 B 461.5385 487.912 491.308 507.692 515.837 527.4725 538.4615 553.846
6 B#/Hb 553.846 585.4945 589.769 609.231 619.0045 632.967 646.154 664.615
7 H 646.154 683.077 690.231 710.769 722.172 738.4615 754.846 775.385
8 C 738.4615 780.66 788.692 812.308 825.339 843.856 861.5385 886.154
9 C#/Db 830.769 878.242 896.154 913.846 929.507 949.4505 969.231 996.923
10 D 923.077 975.824 984.615 1015.385 1031.674 1054.945 1076.923 1107.692
11 D#/Eb 1015.385 1073.407 1083.077 1116.923 1134.842 1160.44 1184.615 1218.4615
12 E 1107.692 1170.99 1181.5385 1218.4615 1238.009 1265.9348 1292.308 1329.231
13 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 97.7665 98.176 99.359 102.733 103.639 106.256 107.11 108.738
2 G 195.533 196.352 198.719 205.466 207.279 212.511 214.22 217.477
3 G#/Ab 293.2995 294.528 298.078 308.199 310.9185 318.767 321.33 326.215
4 A 391.063 392.705 397.4375 410.932 414.558 425.022 428.44 434.953
5 B 488.833 490.881 469.797 513.6655 518.1975 531.278 535.55 543.6915
6 B#/Hb 586.299 589.057 596.156 616.399 621.837 637.534 642.6595 652.43
7 H 684.366 687.233 695.516 719.132 725.4765 743.789 749.769 761.168
8 C 782.132 785.409 794.875 821.865 829.116 850.045 856.879 869.906
9 C#/Db 879.899 883.585 894.234 924.598 932.755 956.3 963.989 978.645
10 D 977.665 981.761 993.594 1027.331 1036.395 1062.556 1071.099 1087.383
11 D#/Eb 1075.432 1079.9375 1092.953 1130.064 1140.034 1168.8115 1178.209 1196.121
12 E 1173.198 1178.114 1192.312 1232.797 1243.674 1275.067 1285.319 1304.86
13 F 1270.965 1276.29 1291.672 1335.53 1347.313 1381.322 1392.429 1413.598
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