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.
==Tuning spectrum==
==Intervals==
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="2" |Degrees
! rowspan="2" |Octatonic
! rowspan="2" |Octatonic
! colspan="20" |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
!5ed(21/16)
!Minimum
!8ed(14/9)
!Maximum
! |Minimum
! |Minimum
!3ed(13/11)
!Maximum
!4ed(5/4)
!Minimum
!10ed(7/4)
!Maximum
! |Golden
!<nowiki><… -3 0 8|/48</nowiki>
!7ed(40/27)
!<nowiki><-18 -4 13|\72</nowiki>
! |Median
!8ed(11/7)
!9ed(5/3)
!14ed(20/9)
! |Mean
! |5ed(4/3)
!7edf
!ed(15/7)
! |Maximum
|-
|-
| |1
| |1
| |F#/Gb
| |F#/Gb
|92.308
|92.308
|94.156
|96
|95.6145
| colspan="2" |101.5385
| |96
| colspan="2" |105.4945
|96.403
|110.769
|96.578
|96.883
| |97.098
|97.107
|97.207
|97.42
| |97.582
|97.8115
|98.262
|98.743
| |98.769
| |99.609
|100.279
|101.496
| |101.5385
|-
|-
| |2
| |2
| |G
| |G
|184.615
|184.615
|188.312
|192
|191.229
| colspan="2" |203.077
| |192
| colspan="2" |210.989
|192.8065
|221.5385
|193.157
|193.765
| |194.196
|194.213
|194.414
|194.8405
| |195.164
|195.623
|196.524
|197.486
| |197.5385
| |199.218
|200.559
|202.991
| |203.077
|-
|-
| |3
| |3
| |G#/Ab
| |G#/Ab
|276.923
|276.923
|282.469
|288
|286.843
| colspan="2" |304.615
| |288
| colspan="2" |316.4835
|289.21
|332.308
|289.735
|290.648
| |291.293
|291.322
|291.621
|292.261
| |292.747
|293.4345
|294.786
|286.229
| |296.308
| |298.827
|300.837
|304.487
| |304.615
|-
|-
| |4
| |4
| |A
| |A
|369.231
|369.231
|376.625
|384
|382.458
| colspan="2" |406.154
| |384
| colspan="2" |421.978
|385.613
|443.076
|386.314
|387.53
| |388.391
|388.429
|338.828
|389.681
| |390.329
|391.246
|393.048
|394.9725
| |395.076
| |398.436
|401.117
|405.982
| |406.154
|-
|-
| |5
| |5
| |B
| |B
|461.5385
|461.5385
|470.781
|480
|478.072
| colspan="2" |507.692
| |480
| colspan="2" |527.4725
|482.016
|553.846
|482.892
|484.413
| |485.489
|485.537
|486.035
|487.101
| |487.912
|489.0575
|491.31
|493.716
| |493.846
| |498.045
|501.396
|507.478
| |507.692
|-
|-
| |6
| |6
| |B#/Hb
| |B#/Hb
|553.846
|553.846
|564.937
|576
|573.687
| colspan="2" |609.231
| |576
| colspan="2" |632.967
|875.419
|664.615
|579.471
|581.2955
| |582.587
|582.644
|583.242
|584.5215
| |585.4945
|586.869
|589.5725
|592.459
| |592.615
| |597.654
|601.676
|608.974
| |609.231
|-
|-
| |7
| |7
| |H
| |H
|646.154
|646.154
|659.093
|672
|669.301
| colspan="2" |710.769
| |672
| colspan="2" |738.4615
|674.823
|775.385
|676.049
|678.178
| |679.685
|679.752
|680.448
|681.942
| |683.077
|684.6805
|687.835
|691.202
| |691.385
| |697.263
|701.955
|710.469
| |710.769
|-
|-
| |8
| |8
| |C
| |C
|738.4615
|738.4615
|753.2495
|768
|764.916
| colspan="2" |812.308
| |768
| colspan="2" |843.856
|771.226
|886.154
|772.627
|775.06
| |776.782
|776.859
|777.656
|779.362
| |780.659
|782.492
|786.097
|789.945
| |790.154
| |796.872
|802.234
|811.965
| |812.308
|-
|-
| |9
| |9
| |C#/Db
| |C#/Db
|830.769
|830.769
|847.406
|864
|860.53
| colspan="2" |913.846
| |864
| colspan="2" |949.4505
|867.629
|996.923
|869.206
|871.943
| |873.880
|873.966
|874.862
|876.782
| |878.242
|880.3035
|884.359
|888.688
| |888.923
| |896.481
|902.514
|913.46
| |913.846
|-
|-
| |10
| |10
| |D
| |D
|923.077
|923.077
|941.562
|960
|956.145
| colspan="2" |1015.385
| |960
| colspan="2" |1054.945
|964.032
|1107.692
|965.784
|968.826
| |970.978
|971.073
|972.07
|974.2025
| |975.824
|978.115
|982.621
|987.431
| |987.692
| |996.09
|1002.793
|1014.956
| |1015.385
|-
|-
| |11
| |11
| |D#/Eb
| |D#/Eb
|1015.385
|1015.385
|1035.718
|1056
|1051.759
| colspan="2" |1116.923
| |1056
| colspan="2" |1160.44
|1060.436
|1218.4615
|1062.363
|1065.7085
| |1068.076
|1068.181
|1069.277
|1071.623
| |1073.407
|1075.9265
|1080.882
|1086.174
| |1086.4615
| |1095.699
|1103.072
|1116.451
| |1116.923
|-
|-
| |12
| |12
| |E
| |E
|1107.692
|1107.692
|1129.874
|1152
|1147.374
| colspan="2" |1218.4615
| |1152
| colspan="2" |1265.9348
|1156.839
|1329.231
|1158.941
|1162.591
| |1165.1735
|1165.2885
|1166.4835
|1169.043
| |1170.989
|1173.738
|1179.145
|1184.9175
| |1185.231
| |1195.308
|1203.3514
|1217.947
| |1218.4615
|-
|-
| |13
| |13
| |F
| |F
|1200
|1200
|1224.03
|1248
|1242.988
| colspan="2" |1320
| |1248
| colspan="2" |1371.429
|1253.242
|1440
|1255.52
|1259.474
| |1262.271
|1262.396
|1263.6905
|1266.463
| |1268.571
|1271.55
|1277.407
|1283.661
| |1284
| |1294.916
|1303.631
|1319.443
| |1320
|}
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="2" |Octatonic
! colspan="20" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
|-
! |Minimum
!8ed(8/5)
!10ed(9/5)
! |2ed(9/8)
!9ed(17/10)
!ed(28/13)
!14ed(16/7)
! |Golden
!ed(13/6)
!<nowiki><17 8 -11|/48</nowiki>
! |Mean
!9ed(12/7)
!ed(24/11)
!5ed(27/20)
!7ed(32/21)
!4ed(14/11)
! |Median
!ed(11/5)
!3ed(6/5)
! |Maximum
|-
| |1
| |F#/Gb
| |101.5385
|101.711
|101.76
| |101.955
|102.071
|102.177
|102.227
| |102.733
|102.967
|103.462
| |103.5165
|103.681
|103.895
|103.91
|104.174
|104.377
| |104.615
|105
|105.213
| |105.4945
|-
| |2
| |G
| |203.077
|203.422
|203.519
| |203.91
|204.143
|204.354
|204.453
| |205.466
|205.934
|206.9245
| |207.033
|207.362
|207.79
|207.8205
|208.348
|208.754
| |209.231
|210.001
|210.4275
| |210.989
|-
| |3
| |G#/Ab
| |304.615
|305.132
|305.279
| |305.865
|306.214
|306.53
|306.68
| |308.199
|308.901
|310.387
| |310.5465
|311.043
|311.6855
|311.731
|312.5225
|313.131
| |313.846
|315.001
|315.641
| |316.4835
|-
| |4
| |A
| |406.154
|406.843
|407.0385
| |407.82
|408.285
|408.707
|408.907
| |410.932
|411.8685
|413.849
| |414.066
|414.724
|415.581
|415.641
|416.697
|417.508
| |418.4615
|420.001
|420.855
| |421.978
|-
| |5
| |B
| |507.692
|508.554
|508.798
| |509.775
|510.3565
|510.884
|511.134
| |513.6655
|514.836
|517.311
| |517.582
|518.405
|519.476
|519.551
|520.871
|521.885
| |523.077
|525.002
|526.069
| |527.4725
|-
| |6
| |B#/Hb
| |609.231
|610.265
|610.558
| |611.73
|612.428
|613.061
|613.36
| |616.399
|617.803
|620.774
| |621.099
|622.086
|623.371
|623.4615
|625.045
|626.262
| |627.692
|630.002
|631.283
| |632.967
|-
| |7
| |H
| |710.769
|711.976
|712.317
| |713.685
|714.499
|715.2375
|715.587
| |719.132
|720.769
|724.236
| |724.615
|725.767
|727.266
|727.372
|729.219
|730.639
| |732.318
|735.002
|736.496
| |738.4615
|-
| |8
| |C
| |812.308
|813.686
|814.077
| |815.64
|816.57
|817.414
|817.814
| |821.865
|823.737
|827.698
| |828.132
|829.448
|831.161
|831.282
|833.393
|835.016
| |836.923
|840.003
|841.71
| |843.856
|-
| |9
| |C#/Db
| |913.846
|915.397
|915.837
| |917.595
|918.462
|919.591
|920.041
| |924.598
|926.704
|931.1605
| |931.648
|933.129
|935.056
|935.192
|937.567
|939.393
| |941.5385
|945.003
|946.924
| |949.4505
|-
| |10
| |D
| |1015.385
|1017.108
|1017.596
| |1019.55
|1020.712
|1021.768
|1022.267
| |1027.331
|1029.671
|1034.623
| |1035.165
|1036.81
|1038.952
|1039.103
|1041.742
|1043.77
| |1046.154
|1050.003
|1052.138
| |1054.945
|-
| |11
| |D#/Eb
| |1116.923
|1118.819
|1119.356
| |1121.505
|1122.784
|1123.945
|1124.494
| |1130.064
|1132.638
|1138.085
| |1138.681
|1140.491
|1142.847
|1143.013
|1145.916
|1148.147
| |1150.769
|1155.004
|1157.351
| |1160.44
|-
| |12
| |E
| |1218.4615
|1220.529
|1221.1155
| |1223.46
|1224.856
|1226.1215
|1226.721
| |1232.797
|1235.6055
|1241.547
| |1242.198
|1244.172
|1246.742
|1246.923
|1250.09
|1252.524
| |1255.385
|1260.004
|1262.565
| |1265.9348
|-
| |13
| |F
| |1320
|1322.24
|1322.875
| |1325.415
|1326.927
|1328.298
|1238.947
| |1335.53
|1338.573
|1345.0095
| |1345.714
|1347.853
|1350.637
|1350.833
|1354.264
|1356.901
| |1360
|1365.004
|1367.779
| |1371.429
|}
|}
Golden Tunings
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="2" |Octatonic
! colspan="13" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
|-
|-
! |Minimum
!Degrees
!ed(20/9)
!Octatonic
! |Golden
!Phrygian Mode (natural minor)
!26ed5
!Phrygian-Aeolian Mode (intermediate minor)
! |Median
!Aeolian Mode (melodic/harmonic minor)
!9ed(5/3)
! |ed(9/4)
!52ed(180/7)
! |Mean
!4ed(9/7)
!26ed(36/7)
!ed(16/7)
! |Maximum
|-
|-
| |1
| |1
| |F#/Gb
| |F#/Gb
| |105.4945
|97.098
|106.339
|102.733
| |107.11
|107.11
|107.166
| |107.692
|98.262
| |107.993
|108.104
| |108.132
|108.771
|109.042
|110.09
| |110.769
|-
|-
| |2
| |2
| |G
| |G
| |210.989
|194.196
|212.6775
|205.466
| |214.22
|214.22
|214.332
| |214.385
|196.524
| |215.986
|216.208
| |216.264
|217.542
|218.083
|220.181
| |221.5385
|-
|-
| |3
| |3
| |G#/Ab
| |G#/Ab
| |304.615
|291.293
|319.016
|308.199
| |321.33
|321.33
|321.498
| |322.077
|294.786
| |323.979
|324.311
| |324.396
|326.313
|327.125
|330.271
| |332.308
|-
|-
| |4
| |4
| |A
| |A
| |421.978
|388.391
|425.355
|410.932
| |428.44
|428.44
|428.664
| |429.769
|393.048
| |431.972
|432.415
| |432.5275
|435.084
|436.167
|440.361
| |443.076
|-
|-
| |5
| |5
| |B
| |B
| |527.4725
|485.489
|531.694
|513.6655
| |535.55
|535.55
|535.83
| |583.4615
|491.31
| |539.965
|540.519
| |540.659
|543.855
|545.2085
|550.452
| |553.846
|-
|-
| |6
| |6
| |B#/Hb
| |B#/Hb
| |609.231
|582.587
|638.0325
|616.399
| |642.6595
|642.6595
|642.9945
| |646.154
|589.5725
| |647.9585
|948.943
| |648.791
|652.626
|654.25
|660.542
| |664.615
|-
|-
| |7
| |7
| |H
| |H
| |710.769
|679.685
|744.371
|719.132
| |749.769
|749.769
|750.161
| |753.846
|687.835
| |755.9515
|756.727
| |756.923
|761.397
|863.292
|770.632
| |775.385
|-
|-
| |8
| |8
| |C
| |C
| |812.308
|776.782
|850.71
|821.865
| |856.879
|856.879
|857.327
| |861.5385
|786.097
| |863.945
|864.83
| |865.055
|870.168
|872.334
|880.7225
| |886.154
|-
|-
| |9
| |9
| |C#/Db
| |C#/Db
| |913.846
|873.880
|957.049
|924.598
| |963.989
|963.989
|964.493
| |969.231
|884.359
| |971.938
|972.934
| |973.187
|978.939
|981.375
|990.813
| |996.923
|-
|-
| |10
| |10
| |D
| |D
| |1015.385
|970.978
|1063.3875
|1027.331
| |1071.099
|1071.099
|1071.659
| |1076.923
|982.621
| |1079.931
|1081.038
| |1081.319
|1087.71
|1090.416
|1100.903
| |1107.692
|-
|-
| |11
| |11
| |D#/Eb
| |D#/Eb
| |1116.923
|1068.076
|1169.726
|1130.064
| |1178.209
|1178.209
|1178.825
| |1184.615
|1080.882
| |1187.924
|1189.142
| |1189.4505
|1196.481
|1199.459
|1210.9935
| |1218.4615
|-
|-
| |12
| |12
| |E
| |E
| |1218.4615
|1165.1735
|1276.065
|1232.797
| |1285.319
|1285.319
|1285.991
| |1292.308
|1179.145
| |1295.917
|1297.246
| |1297.582
|1305.252
|1308.5
|1321.084
| |1329.231
|-
|-
| |13
| |13
| |F
| |F
| |1371.429
|1262.271
|1382.403
|1335.53
| |1392.429
|1392.429
|1393.157
| |1400
|1277.407
| |1403.91
|1405.3495
| |1405.714
|1414.023
|1417.524
|1431.174
| |1440
|}
|}
[[Category:13-tone]]
[[Category:13-tone]]

Revision as of 22:02, 21 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 Maximum Minimum Maximum Minimum Maximum
1 F#/Gb 92.308 96 101.5385 105.4945 110.769
2 G 184.615 192 203.077 210.989 221.5385
3 G#/Ab 276.923 288 304.615 316.4835 332.308
4 A 369.231 384 406.154 421.978 443.076
5 B 461.5385 480 507.692 527.4725 553.846
6 B#/Hb 553.846 576 609.231 632.967 664.615
7 H 646.154 672 710.769 738.4615 775.385
8 C 738.4615 768 812.308 843.856 886.154
9 C#/Db 830.769 864 913.846 949.4505 996.923
10 D 923.077 960 1015.385 1054.945 1107.692
11 D#/Eb 1015.385 1056 1116.923 1160.44 1218.4615
12 E 1107.692 1152 1218.4615 1265.9348 1329.231
13 F 1200 1248 1320 1371.429 1440

Golden Tunings

Degrees Octatonic Phrygian Mode (natural minor) Phrygian-Aeolian Mode (intermediate minor) Aeolian Mode (melodic/harmonic minor)
1 F#/Gb 97.098 102.733 107.11
2 G 194.196 205.466 214.22
3 G#/Ab 291.293 308.199 321.33
4 A 388.391 410.932 428.44
5 B 485.489 513.6655 535.55
6 B#/Hb 582.587 616.399 642.6595
7 H 679.685 719.132 749.769
8 C 776.782 821.865 856.879
9 C#/Db 873.880 924.598 963.989
10 D 970.978 1027.331 1071.099
11 D#/Eb 1068.076 1130.064 1178.209
12 E 1165.1735 1232.797 1285.319
13 F 1262.271 1335.53 1392.429
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