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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.
==Tuning spectrum==
==Intervals==
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="2" |Degrees
! rowspan="2" |Octatonic
! rowspan="2" |Octatonic
! colspan="10" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
! colspan="3" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
! colspan="2" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
! colspan="2" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
|-
|-
!Absolute Minimum
!Absolute Minimum
!3ed(7/6)
!Minimum
!Maximum
! |Minimum
! |Minimum
! |Golden
!Maximum
! |Median
!Minimum
! |Mean
!Maximum
!<nowiki><0 -11 0 11|/24</nowiki>
!5ed(21/16)
!ed(15/7)
! |Maximum
|-
|-
| |1
| |1
| |F#/Gb
| |F#/Gb
|85.714
|85.714
|88.957
|89.143
| |89.143
| colspan="2" |94.286
| |90.162
| colspan="2" |97.959
| |90.612
|110.769
| |91.714
|92.286
|94.156
|94.246
| |94.286
|-
|-
| |2
| |2
| |G
| |G
|171.429
|171.429
|177.914
|178.286
| |178.286
| colspan="2" |188.571
| |180.3245
| colspan="2" |195.918
| |181.2245
|221.5385
| |183.429
|184.5715
|188.312
|188.492
| |188.571
|-
|-
| |3
| |3
| |G#/Ab
| |G#/Ab
|257.143
|257.143
|266.871
|267.429
| |267.429
| colspan="2" |282.857
| |270.487
| colspan="2" |293.878
| |271.837
|332.308
| |275.143
|276.857
|282.469
|282.738
| |282.857
|-
|-
| |4
| |4
| |A
| |A
|342.857
|342.857
|355.828
|356.571
| |356.571
| colspan="2" |377.143
| |360.649
| colspan="2" |391.836
| |362.449
|443.076
| |366.857
|369.143
|376.625
|376.984
| |377.143
|-
|-
| |5
| |5
| |A#/Bb
| |A#/Bb
|428.571
|428.571
|444.785
|445.714
| |445.714
| colspan="2" |471.429
| |450.811
| colspan="2" |489.796
| |453.061
|553.846
| |458.571
|461.429
|470.781
|471.23
| |471.429
|-
|-
| |6
| |6
| |B
| |B
|514.286
|514.286
|533.742
|534.857
| |534.857
| colspan="2" |565.714
| |540.973
| colspan="2" |587.755
| |543.6735
|664.615
| |550.286
|553.714
|564.937
|565.4755
| |565.714
|-
|-
| |7
| |7
| |H
| |H
|600
|600
|622.698
|624
| |624
| colspan="2" |660
| |631.136
| colspan="2" |685.714
| |634.286
|775.385
| |642
|646
|659.093
|659.721
| |660
|-
|-
| |8
| |8
| |H#/Cb
| |H#/Cb
|685.714
|685.714
|711.656
|713.143
| |713.143
| colspan="2" |754.286
| |721.298
| colspan="2" |783.6735
| |724.898
|886.154
| |733.714
|738.286
|753.2495
|753.967
| |754.286
|-
|-
| |9
| |9
| |C
| |C
|771.429
|771.429
|800.612
|802.286
| |802.286
| colspan="2" |848.571
| |811.46
| colspan="2" |881.633
| |815.51
|996.923
| |825.429
|830.572
|847.406
|848.213
| |848.571
|-
|-
| |10
| |10
| |C#/Db
| |C#/Db
|857.143
|857.143
|889.57
|891.429
| |891.429
| colspan="2" |942.857
| |901.622
| colspan="2" |979.592
| |906.122
|1107.692
| |917.143
|922.857
|941.562
|942.459
| |942.857
|-
|-
| |11
| |11
| |D
| |D
|942.857
|942.857
|978.527
|980.571
| |980.571
| colspan="2" |1037.143
| |991.785
| colspan="2" |1077.551
| |996.735
|1218.4615
| |1008.857
|1015.143
|1035.718
|1036.705
| |1037.143
|-
|-
| |12
| |12
| |D#/Eb
| |D#/Eb
|1028.571
|1028.571
|1067.484
|1069.714
| |1069.714
| colspan="2" |1131.429
| |1081.947
| colspan="2" |1175.51
| |1087.247
|1329.231
| |1100.571
|1107.429
|1129.874
|1130.951
| |1131.429
|-
|-
| |13
| |13
| |E
| |E
|1114.286
|1114.286
|1156.441
|1158.857
| |1158.857
| colspan="2" |1225.714
| |1172.109
| colspan="2" |1273.469
| |1177.959
|1440
| |1192.286
|1199.7145
|1224.03
|1225.197
| |1225.714
|-
|-
|14
|14
|F
|F
|1200
|1200
|1245.397
|1248
|1248
|1262.271
| colspan="2" |1320
|1268.571
| colspan="2" |1371.429
|1284
|
|1292
|}Golden Tunings
|1318.1865
|1319.443
|1320
|}
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="2" |Octatonic
! colspan="17" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
|-
|-
! |Minimum
!Degrees
!ed(28/13)
!Octatonic
! |Golden
!Phrygian Mode (natural minor)
!ed(13/6)
!Phrygian-Aeolian Mode (intermediate minor)
!8ed(14/9)
!Aeolian Mode (melodic/harmonic minor)
! |Mean
!3ed(13/11)
!ed(24/11)
!4ed(5/4)
!10ed(7/4)
!<nowiki><… -3 0 8|/48</nowiki>
! |Median
!7ed(40/27)
!<nowiki><-18 -4 13|\72</nowiki>
!ed(11/5)
!8ed(11/7)
! |Maximum
|-
|-
| |1
| |1
| |F#/Gb
| |F#/Gb
| |94.286
|90.162
|94.878
|95.395
| |95.395
|99.459
|95.612
|95.6145
| |96.122
|96.403
|96.474
|96.578
|96.883
|97.107
| |97.143
|97.207
|97.42
|97.5
|97.8115
| |97.959
|-
|-
| |2
| |2
| |G
| |G
| |188.571
|180.3245
|189.757
|190.79
| |190.79
|198.918
|191.225
|191.229
| |192.245
|192.8065
|192.948
|193.157
|193.765
|194.213
| |194.286
|194.414
|194.8405
|195.001
|195.623
| |195.918
|-
|-
| |3
| |3
| |G#/Ab
| |G#/Ab
| |282.857
|270.487
|284.635
|286.185
| |286.185
|298.377
|286.837
|286.843
| |288.367
|289.21
|289.422
|289.735
|290.648
|291.322
| |291.429
|291.621
|292.261
|292.501
|293.4345
| |293.878
|-
|-
| |4
| |4
| |A
| |A
| |377.143
|360.649
|379.512
|381.58
| |381.58
|397.839
|382.449
|382.458
| |384.488
|385.613
|385.896
|386.314
|387.53
|388.429
| |388.571
|338.828
|389.681
|390.001
|391.246
| |391.836
|-
|-
| |5
| |5
| |A#/Bb
| |A#/Bb
| |471.429
|450.811
|474.392
|476.975
| |476.975
|497.296
|478.062
|478.072
| |480.612
|482.016
|482.37
|482.892
|484.413
|485.537
| |485.714
|486.035
|487.101
|487.5015
|489.0575
| |489.796
|-
|-
| |6
| |6
| |B
| |B
| |565.714
|540.973
|569.271
|572.37
| |572.37
|597.755
|573.674
|573.687
| |576.735
|875.419
|578.8445
|579.471
|581.2955
|582.644
| |582.857
|583.242
|584.5215
|585.002
|586.869
| |587.755
|-
|-
| |7
| |7
| |H
| |H
| |660
|631.136
|664.149
|667.765
| |667.765
|696.2145
|669.286
|669.301
| |672.857
|674.823
|975.3185
|676.049
|678.178
|679.752
| |680
|680.448
|681.942
|682.002
|684.6805
| |685.714
|-
|-
| |8
| |8
| |H#/Cb
| |H#/Cb
| |754.286
|721.298
|759.028
|763.16
| |763.16
|795.674
|764.899
|764.916
| |768.98
|771.226
|771.793
|772.627
|775.06
|776.859
| |777.143
|777.656
|779.362
|780.002
|782.492
| |783.6735
|-
|-
| |9
| |9
| |C
| |C
| |848.571
|811.46
|853.906
|858.555
| |858.555
|895.133
|860.511
|860.53
| |865.102
|867.629
|868.267
|869.206
|871.943
|873.966
| |874.286
|874.862
|876.782
|877.503
|880.3035
| |881.633
|-
|-
| |10
| |10
| |C#/Db
| |C#/Db
| |942.857
|901.622
|948.7845
|953.95
| |953.95
|994.592
|956.123
|956.145
| |961.2245
|964.032
|964.741
|965.784
|968.826
|971.073
| |971.429
|972.07
|974.2025
|975.003
|978.115
| |979.592
|-
|-
| |11
| |11
| |D
| |D
| |1037.143
|991.785
|1043.663
|1049.345
| |1049.345
|1094..051
|1051.736
|1051.759
| |1057.347
|1060.436
|1061.215
|1062.363
|1065.7085
|1068.181
| |1068.579
|1069.277
|1071.623
|1072.503
|1075.9265
| |1077.551
|-
|-
| |12
| |12
| |D#/Eb
| |D#/Eb
| |1131.429
|1081.947
|1138.541
|1144.74
| |1144.74
|1193.5105
|1147.348
|1147.374
| |1153.469
|1156.839
|1157.689
|1158.941
|1162.591
|1165.2885
| |1165.714
|1166.4835
|1169.043
|1170.004
|1173.738
| |1175.51
|-
|-
| |13
| |13
| |E
| |E
| |1225.714
|1172.109
|1233.42
|1240.435
| |1240.435
|1292.97
|1242.96
|1242.988
| |1249.592
|1253.242
|1254.163
|1255.52
|1259.474
|1262.396
| |1262.857
|1263.6905
|1266.463
|1267.504
|1271.55
| |1273.469
|-
|-
|14
|14
|F
|F
|1320
|1262.271
|1328.298
|1335.53
|1335.53
|1338.573
|1338.603
|1345.714
|1349.645
|1350.637
|1352.089
|1356.356
|1359.503
|1360
|1360.897
|1363.884
|1365.004
|1369.361
|1371.429
|}
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="2" |Octatonic
! colspan="17" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
|-
! |Minimum
!9ed(5/3)
!ed(20/9)
! |Golden
!28ed5
!5ed(4/3)
! |Median
! |7edf
!56ed(180/7)
! |Mean
!28ed(36/7)
!8ed(8/5)
!10ed(9/5)
!2ed(9/8)
!9ed(17/10)
!ed(16/7)
! |Maximum
|-
| |1
| |F#/Gb
| |97.959
|98.262
|98.743
| |99.459
|99.511
|99.609
| |100
| |100.279
|100.382
| |100.408
|101.253
|101.711
|101.76
|101.955
|102.071
|102.227
| |102.857
|-
| |2
| |G
| |195.918
|196.524
|197.486
| |198.918
|199.022
|199.218
| |200
| |200.559
|200.764
| |200.816
|202.506
|203.422
|203.519
|203.91
|204.143
|204.453
| |205.714
|-
| |3
| |G#/Ab
| |293.878
|294.786
|286.229
| |298.377
|298.534
|298.827
| |300
| |300.837
|301.146
| |301.2245
|303.759
|305.132
|305.279
|305.865
|306.214
|306.68
| |308.571
|-
| |4
| |A
| |391.836
|393.048
|394.9725
| |397.839
|398.045
|398.436
| |400
| |401.117
|401.528
| |401.633
|405.012
|406.843
|407.0385
|407.82
|408.285
|408.907
| |411.429
|-
| |5
| |A#/Bb
| |489.796
|491.31
|493.716
| |497.296
|497.556
|498.045
| |500
| |501.396
|501.9105
| |502.041
|506.265
|508.554
|508.798
|509.775
|510.3565
|511.134
| |514.286
|-
| |6
| |B
| |587.755
|589.5725
|592.459
| |597.755
|597.067
|597.654
| |600
| |601.676
|602.293
| |602.449
|607.518
|610.265
|610.558
|611.73
|612.428
|613.36
| |617.143
|-
| |7
| |H
| |685.714
|687.835
|691.202
| |696.2145
|696.578
|697.263
| |700
| |701.955
|702.675
| |702.857
|708.771
|711.976
|712.317
|713.685
|714.499
|715.587
| |720
|-
| |8
| |H#/Cb
| |783.6735
|786.097
|789.945
| |795.674
|796.099
|796.872
| |800
| |802.234
|803.057
| |803.265
|810.024
|813.686
|814.077
|815.64
|816.57
|817.814
| |822.857
|-
| |9
| |C
| |881.633
|884.359
|888.688
| |895.133
|895.301
|896.481
| |900
| |902.514
|903.439
| |903.6735
|911.277
|915.397
|915.837
|917.595
|918.462
|920.041
| |925.714
|-
| |10
| |C#/Db
| |979.592
|982.621
|987.431
| |994.592
|995.112
|996.09
| |1000
| |1002.793
|1003.821
| |1004.4082
|1012.53
|1017.108
|1017.596
|1019.55
|1020.712
|1022.267
| |1028.571
|-
| |11
| |D
| |1077.551
|1080.882
|1086.174
| |1094..051
|1094.623
|1095.699
| |1100
| |1103.072
|1104.203
| |1104.49
|1113.783
|1118.819
|1119.356
|1121.505
|1122.784
|1124.494
| |1131.429
|-
| |12
| |D#/Eb
| |1175.51
|1179.145
|1184.9175
| |1193.5105
|1194.134
|1195.308
| |1200
| |1203.3514
|1204.585
| |1204.898
|1215.036
|1220.529
|1221.1155
|1223.46
|1224.856
|1226.721
| |1234.286
|-
| |13
| |E
| |1273.469
|1277.407
|1283.661
| |1292.97
|1293.646
|1294.916
| |1300
| |1303.631
|1304.967
| |1305.306
|1316.289
|1322.24
|1322.875
|1325.415
|1326.927
|1238.947
| |1337.143
|-
|14
|F
|1371.429
|1375.669
|1382.403
|1392.429
|1392.429
|1393.157
|1394.526
|1400
|1403.91
|1405.3495
|1405.714
|1417.524
|1423.951
|1424.635
|1427.37
|1428.998
|1431.174
|1440
|}
|}
[[Category:14-tone]]
[[Category:14-tone]]

Revision as of 22:12, 21 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 Maximum Minimum Maximum Minimum Maximum
1 F#/Gb 85.714 89.143 94.286 97.959 110.769
2 G 171.429 178.286 188.571 195.918 221.5385
3 G#/Ab 257.143 267.429 282.857 293.878 332.308
4 A 342.857 356.571 377.143 391.836 443.076
5 A#/Bb 428.571 445.714 471.429 489.796 553.846
6 B 514.286 534.857 565.714 587.755 664.615
7 H 600 624 660 685.714 775.385
8 H#/Cb 685.714 713.143 754.286 783.6735 886.154
9 C 771.429 802.286 848.571 881.633 996.923
10 C#/Db 857.143 891.429 942.857 979.592 1107.692
11 D 942.857 980.571 1037.143 1077.551 1218.4615
12 D#/Eb 1028.571 1069.714 1131.429 1175.51 1329.231
13 E 1114.286 1158.857 1225.714 1273.469 1440
14 F 1200 1248 1320 1371.429

Golden Tunings

Degrees Octatonic Phrygian Mode (natural minor) Phrygian-Aeolian Mode (intermediate minor) Aeolian Mode (melodic/harmonic minor)
1 F#/Gb 90.162 95.395 99.459
2 G 180.3245 190.79 198.918
3 G#/Ab 270.487 286.185 298.377
4 A 360.649 381.58 397.839
5 A#/Bb 450.811 476.975 497.296
6 B 540.973 572.37 597.755
7 H 631.136 667.765 696.2145
8 H#/Cb 721.298 763.16 795.674
9 C 811.46 858.555 895.133
10 C#/Db 901.622 953.95 994.592
11 D 991.785 1049.345 1094..051
12 D#/Eb 1081.947 1144.74 1193.5105
13 E 1172.109 1240.435 1292.97
14 F 1262.271 1335.53 1392.429
Retrieved from "https://en.xen.wiki/index.php?title=User:Moremajorthanmajor/14edIX&oldid=37450"