User:Moremajorthanmajor/13edIX: Difference between revisions

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This scale occurs in 12edo, where it is the equal division of the minor ninth.
This scale 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==
 
Phrygian Mode (aka Double) Neapolitan Temperament
{| class="wikitable"
{| class="wikitable"
!Degrees
|+
!Octatonic
! colspan="5" rowspan="2" |Period
!Minimum
! colspan="5" |Octatonic (5L 3s)
!Mean
! rowspan="2" |Notes
!Median
!Golden
!Maximum
|-
|-
|1
!L
|F#/Gb
!s
| rowspan="13" |see [[13edo]]
! colspan="3" |Tetrachord
|96.923
|-
|1\1edo
|
|
|
|
|184.615
|92.308
|184.615
|369.231
|461.5385
|Phrygian Mode (aka Double) Neapolitan Temperament from here …
|-
|
|
|
|
|15\14
|197.802
|98.901
|197.802
|395.604
|494.5055
|
|-
|
|
|
|14\13
|
|198.817
|99.408
|198.817
|397.633
|497.041
|
|-
|
|
|
|
|27\25
|199.385
|99.692
|199.385
|398.769
|498.4615
|
|-
|
|
|13\12
|
|
|200
|100
|200
|400
|500
|
|-
|
|
|
|
|38\35
|200.44
|100.22
|200.44
|400.879
|501.099
|
|-
|
|
|
|25\23
|
|200.669
|100.334
|200.669
|401.338
|501.672
|
|-
|
|
|
|
|37\34
|200.905
|100.4525
|200.905
|401.81
|502.262
|
|-
|
|12\11
|
|
|
|201.399
|100.699
|100.699
|101.001
|201.399
|402.797
|503.4965
|
|-
|
|
|
|
|47\43
|201.789
|100.8945
|201.789
|403.578
|504.472
|
|-
|
|
|
|35\32
|
|201.923
|100.9615
|201.923
|403.846
|504.808
|
|-
|
|
|
|
|58\53
|202.032
|101.016
|202.032
|404.064
|505.08
|
|-
|
|
|23\21
|
|
|202.198
|101.099
|202.198
|404.396
|505.4945
|
|-
|
|
|
|
|57\52
|202.367
|101.183
|202.367
|404.734
|505.917
|
|-
|
|
|
|34\31
|
|202.481
|101.241
|202.481
|404.963
|506.2035
|
|-
|
|
|
|
|45\41
|202.627
|101.313
|202.627
|405.253
|506.567
|
|-
|11\10
|
|
|
|
|203.077
|101.5385
|101.5385
|203.077
|406.154
|507.692
|…to here
Phrygian-Aeolian Mode Neapolitan Temperament from here …
|-
|
|
|
|
|54\49
|203.454
|101.757
|203.454
|406.907
|508.634
|
|-
|
|
|
|43\39
|
|203.55
|101.775
|203.55
|407.101
|508.876
|
|-
|
|
|
|
|75\68
|203.62
|101.81
|203.62
|407.24
|509.05
|
|-
|
|
|32\29
|
|
|203.7135
|101.857
|203.7135
|407.427
|509.284
|
|-
|
|
|
|
|85\77
|203.796
|101.898
|203.796
|407.592
|509.4905
|
|-
|
|
|
|53\48
|
|203.846
|101.923
|203.846
|407.692
|509.615
|
|-
|
|
|
|
|74\67
|203.904
|101.952
|203.904
|407.807
|509.759
|Square root of 9/8 is near here
|-
|
|21\19
|
|
|
|204.049
|102.024
|204.049
|408.097
|510.1215
|
|-
|
|
|
|
|73\66
|204.196
|102.098
|204.196
|408.392
|510.4895
|
|-
|
|
|
|52\47
|
|204.255
|102.128
|204.255
|408.511
|510.638
|
|-
|
|
|
|
|83\75
|204.308
|102.154
|204.308
|409.615
|510.769
|
|-
|
|
|31\28
|
|
|204.396
|102.198
|204.396
|408.792
|510.989
|
|-
|
|
|
|
|72\65
|204.497
|102.248
|204.497
|408.994
|511.242
|
|-
|
|
|
|41\37
|
|204.574
|102.287
|204.574
|409.148
|511.4345
|
|-
|
|
|
|
|51\46
|204.682
|102.341
|204.682
|409.3645
|511.706
|
|-
|10\9
|
|
|
|
|205.128
|102.564
|205.128
|410.256
|512.8205
|
|-
|
|
|
|
|49\44
|205.594
|102.797
|205.594
|411.189
|513.986
|
|-
|
|
|
|39\35
|
|205.714
|102.857
|205.714
|411.429
|514.286
|
|-
|
|
|
|
|68\61
|205.801
|102.9
|205.801
|411.6015
|514.502
|
|-
|
|
|29\26
|
|
|205.917
|102.959
|205.917
|411.824
|514.799
|
|-
|
|
|
|
|77\69
|206.02
|103.01
|206.02
|412.04
|515.05
|
|-
|
|
|
|48\43
|
|206.082
|103.041
|206.082
|412.165
|515.205
|
|-
|
|
|
|
|67\60
|206.154
|103.077
|206.154
|412.308
|515.385
|
|-
|
|19\17
|
|
|
|206.335
|103.167
|206.335
|412.67
|515.837
|
|-
|
|
|
|
|66\59
|206.519
|103.2595
|206.519
|413.038
|516.297
|
|-
|
|
|
|47\42
|
|206.593
|103.297
|206.593
|413.187
|516.4835
|
|-
|
|
|
|
|75\67
|206.659
|103.3295
|206.659
|413.318
|516.6475
|
|-
|-
|2
|
|G
|
|193.846
|28\25
|201.399
|
|202.002
|
|203.077
|206.769
|103.385
|206.769
|413.5385
|516.923
|
|-
|-
|3
|
|A
|
|290.769
|
|302.098
|
|303.0035
|65\58
|304.615
|206.897
|103.443
|206.897
|413.793
|517.241
|
|-
|-
|4
|
|A#/Bb
|
|387.692
|
|402.797
|37\33
|404.005
|
|406.154
|206.993
|103.4965
|206.993
|413.986
|517.4825
|
|-
|-
|5
|
|B
|
|484.615
|
|503.4965
|
|505.006
|46\41
|507.692
|207.1295
|103.565
|207.1295
|414.259
|517.824
|
|-
|-
|6
|9\8
|B#/Hb
|
|581.5385
|
|604.196
|
|606.007
|
|609.231
|207.692
|103.846
|207.692
|415.385
|519.231
|
|-
|-
|7
|
|H
|
|678.4615
|
|704.895
|
|707.008
|44\39
|710.769
|208.284
|104.142
|208.284
|416.568
|520.71
|
|-
|-
|8
|
|C
|
|775.385
|
|805.594
|35\31
|808.009
|
|812.308
|208.437
|104.218
|208.437
|416.873
|521.092
|
|-
|-
|9
|
|C#/Db
|
|872.318
|
|906.294
|
|909.011
|61\54
|913.846
|208.547
|104.2735
|208.547
|417.094
|521.3675
|
|-
|-
|10
|
|D
|
|969.231
|26\23
|1006.993
|
|1010.012
|
|1015.385
|208.696
|104.348
|208.696
|417.391
|521.739
|
|-
|-
|11
|
|D#/Eb
|
|1066.154
|
|1107.692
|
|1111.013
|69\61
|1116.923
|208.827
|104.414
|208.827
|417.6545
|522.068
|
|-
|-
|12
|
|E
|
|1163.077
|
|1208.392
|43\38
|1212.014
|
|1218.4615
|208.907
|104.453
|208.907
|417.814
|522.267
|
|-
|-
|13
|
|F
|
|1260
|
|1309.091
|
|1313.015
|60\53
|1320
|208.9985
|}
|104.499
Phrygian-Aeolian Mode Neapolitan Temperament
|208.9985
{| class="wikitable"
|417.997
!Degrees
|522.496
!Octatonic
|
!Minimum
!Golden
!Mean
!Median
!Maximum
|-
|-
|1
|
|F#/Gb
|17\15
|101.5385
|
|102.733
|
|103.5165
|
|209.231
|104.615
|104.615
|209.231
|418.4615
|523.077
|
|-
|
|
|
|
|59\52
|209.4675
|104.734
|209.4675
|418.935
|523.669
|
|-
|
|
|
|42\37
|
|209.563
|104.782
|209.563
|419.127
|523.9085
|
|-
|
|
|
|
|67\59
|209.648
|104.824
|209.648
|419.296
|524.12
|
|-
|
|
|25\22
|
|
|209.79
|104.895
|209.79
|419.58
|524.4755
|
|-
|
|
|
|
|58\51
|209.955
|104.977
|209.955
|419.91
|524.887
|
|-
|
|
|
|33\29
|
|210.08
|105.04
|210.08
|420.159
|525.199
|
|-
|
|
|
|
|41\36
|210.256
|105.128
|210.256
|420.513
|525.641
|
|-
|8\7
|
|
|
|
|210.989
|105.4945
|105.4945
|210.989
|421.978
|527.4725
|…to here
Aeolian Mode Neapolitan Temperament from here …
|-
|
|
|
|
|39\34
|211.765
|105.882
|211.765
|423.529
|529.412
|
|-
|
|
|
|31\27
|
|211.966
|105.983
|211.966
|423.932
|529.9145
|
|-
|
|
|
|
|54\47
|212.111
|106.056
|212.111
|424.223
|530.278
|
|-
|-
|2
|
|G
|
|203.077
|23\20
|205.466
|
|207.033
|
|209.231
|212.308
|210.989
|106.154
|212.308
|424.615
|530.769
|
|-
|
|
|
|
|61\53
|212.482
|106.241
|212.482
|424.964
|531.205
|
|-
|
|
|
|38\33
|
|212.587
|106.294
|212.587
|425.175
|531.4685
|
|-
|
|
|
|
|53\46
|212.709
|106.3595
|212.709
|425.418
|531.773
|
|-
|-
|3
|
|A
|15\13
|304.615
|
|308.199
|
|310.5465
|
|313.846
|213.018
|316.4835
|106.509
|213.018
|426.0355
|532.544
|
|-
|-
|4
|
|A#/Bb
|
|406.154
|
|410.932
|
|414.066
|52\45
|418.4615
|213.333
|421.978
|106.667
|213.333
|426.667
|533.333
|
|-
|-
|5
|
|B
|
|507.692
|
|513.6655
|37\32
|517.582
|
|523.077
|213.4615
|527.4725
|106.731
|213.4615
|426.923
|533.654
|
|-
|-
|6
|
|B#/Hb
|
|609.231
|
|616.399
|
|621.099
|59\51
|627.692
|213.575
|632.967
|106.787
|213.575
|427.149
|533.937
|
|-
|-
|7
|
|H
|
|710.769
|22\19
|719.132
|
|724.615
|
|732.318
|213.765
|738.4615
|106.883
|213.765
|427.52
|534.413
|
|-
|-
|8
|
|C
|
|812.308
|
|821.865
|
|828.132
|51\44
|836.923
|213.986
|843.856
|106.993
|213.986
|427.972
|534.965
|
|-
|-
|9
|
|C#/Db
|
|913.846
|
|924.598
|29\25
|931.648
|
|941.5385
|214.154
|949.4505
|107.077
|214.154
|428.308
|535.385
|
|-
|-
|10
|
|D
|
|1015.385
|
|1027.331
|
|1035.165
|36\31
|1046.154
|214.392
|1054.945
|107.196
|214.392
|428.784
|535.98
|
|-
|-
|11
|7\6
|D#/Eb
|
|1116.923
|
|1130.064
|
|1138.681
|
|1150.769
|215.385
|1160.44
|107.692
|215.385
|430.769
|538.4615
|
|-
|-
|12
|
|E
|
|1218.4615
|
|1232.797
|
|1242.198
|34\29
|1255.385
|216.446
|1265.9348
|108.223
|216.446
|432.891
|541.114
|
|-
|-
|13
|
|F
|
|1320
|
|1335.53
|27\23
|1345.714
|
|1360
|216.722
|1371.429
|108.361
|}
|216.722
Aeolian Mode Neapolitan Temperament
|433.445
{| class="wikitable"
|541.806
|
|-
|-
! |Degrees
|
! |Octatonic
|
! |Minimum
|
! |Golden
|
! |Median
|47\40
! |ed(9/4)
|216.923
! |Mean
|108.4615
! |Maximum
|216.923
|433.846
|542.308
|
|-
|-
| |1
|
| |F#/Gb
|
| |105.4945
|20\17
| |107.11
|
| |107.692
|
| |107.993
|217.195
| |108.132
|108.597
| |110.769
|217.195
|434.389
|542.986
|
|-
|-
| |2
|
| |G
|
| |210.989
|
| |214.22
|
| |214.385
|53\45
| |215.986
|217.436
| |216.264
|108.718
| |221.5385
|217.436
|434.872
|543.59
|
|-
|-
| |3
|
| |A
|
| |316.4835
|
| |321.33
|33\28
| |322.077
|
| |323.979
|217.582
| |324.396
|108.791
| |332.308
|217.582
|435.165
|543.956
|
|-
|-
| |4
|
| |A#/Bb
|
| |421.978
|
| |428.44
|
| |429.769
|46\39
| |431.972
|217.7515
| |432.5275
|108.876
| |443.076
|217.7515
|435.503
|544.679
|
|-
|-
| |5
|
| |B
|13\11
| |527.4725
|
| |535.55
|
| |583.4615
|
| |539.965
|218.182
| |540.659
|109.091
| |553.846
|218.182
|436.364
|545.4545
|
|-
|-
| |6
|
| |B#/Hb
|
| |632.967
|
| |642.6595
|
| |646.154
|45\38
| |647.9585
|218.6235
| |648.791
|109.312
| |664.615
|218.6235
|437.247
|546.5559
|
|-
|-
| |7
|
| |H
|
| |738.4615
|
| |749.769
|32\27
| |753.846
|
| |755.9515
|218.803
| |756.923
|109.402
| |775.385
|218.803
|437.606
|547.0085
|
|-
|-
| |8
|
| |C
|
| |843.856
|
| |856.879
|
| |861.5385
|51\43
| |863.945
|218.962
| |865.055
|109.461
| |886.154
|218.962
|406.6445
|547.406
|
|-
|-
| |9
|
| |C#/Db
|
| |949.4505
|19\16
| |963.989
|
| |969.231
|
| |971.938
|219.231
| |973.187
|109.615
| |996.923
|219.231
|438.4615
|548.077
|
|-
|-
| |10
|
| |D
|
| |1054.945
|
| |1071.099
|
| |1076.923
|44\37
| |1079.931
|219.543
| |1081.319
|109.771
| |1107.692
|219.543
|439.085
|548.8565
|
|-
|-
| |11
|
| |D#/Eb
|
| |1160.44
|
| |1178.209
|25\21
| |1184.615
|
| |1187.924
|219.78
| |1189.4505
|109.89
| |1218.4615
|219.78
|439.56
|549.4505
|
|-
|-
| |12
|
| |E
|
| |1265.9348
|
| |1285.319
|
| |1292.308
|31\26
| |1295.917
|220.118
| |1297.582
|110.059
| |1329.231
|220.118
|440.237
|550.296
|
|-
|-
| |13
|6\5
| |F
|
| |1371.429
|
| |1392.429
|
| |1400
|
| |1403.91
|221.5385
| |1405.714
|110.769
| |1440
|221.5385
|443.077
|553.846
|…to here
|}
|}
[[Category:13-tone]]
[[Category:13-tone]]

Revision as of 01:09, 27 September 2018

This scale 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

Period Octatonic (5L 3s) Notes
L s Tetrachord
1\1edo 184.615 92.308 184.615 369.231 461.5385 Phrygian Mode (aka Double) Neapolitan Temperament from here …
15\14 197.802 98.901 197.802 395.604 494.5055
14\13 198.817 99.408 198.817 397.633 497.041
27\25 199.385 99.692 199.385 398.769 498.4615
13\12 200 100 200 400 500
38\35 200.44 100.22 200.44 400.879 501.099
25\23 200.669 100.334 200.669 401.338 501.672
37\34 200.905 100.4525 200.905 401.81 502.262
12\11 201.399 100.699 201.399 402.797 503.4965
47\43 201.789 100.8945 201.789 403.578 504.472
35\32 201.923 100.9615 201.923 403.846 504.808
58\53 202.032 101.016 202.032 404.064 505.08
23\21 202.198 101.099 202.198 404.396 505.4945
57\52 202.367 101.183 202.367 404.734 505.917
34\31 202.481 101.241 202.481 404.963 506.2035
45\41 202.627 101.313 202.627 405.253 506.567
11\10 203.077 101.5385 203.077 406.154 507.692 …to here

Phrygian-Aeolian Mode Neapolitan Temperament from here …

54\49 203.454 101.757 203.454 406.907 508.634
43\39 203.55 101.775 203.55 407.101 508.876
75\68 203.62 101.81 203.62 407.24 509.05
32\29 203.7135 101.857 203.7135 407.427 509.284
85\77 203.796 101.898 203.796 407.592 509.4905
53\48 203.846 101.923 203.846 407.692 509.615
74\67 203.904 101.952 203.904 407.807 509.759 Square root of 9/8 is near here
21\19 204.049 102.024 204.049 408.097 510.1215
73\66 204.196 102.098 204.196 408.392 510.4895
52\47 204.255 102.128 204.255 408.511 510.638
83\75 204.308 102.154 204.308 409.615 510.769
31\28 204.396 102.198 204.396 408.792 510.989
72\65 204.497 102.248 204.497 408.994 511.242
41\37 204.574 102.287 204.574 409.148 511.4345
51\46 204.682 102.341 204.682 409.3645 511.706
10\9 205.128 102.564 205.128 410.256 512.8205
49\44 205.594 102.797 205.594 411.189 513.986
39\35 205.714 102.857 205.714 411.429 514.286
68\61 205.801 102.9 205.801 411.6015 514.502
29\26 205.917 102.959 205.917 411.824 514.799
77\69 206.02 103.01 206.02 412.04 515.05
48\43 206.082 103.041 206.082 412.165 515.205
67\60 206.154 103.077 206.154 412.308 515.385
19\17 206.335 103.167 206.335 412.67 515.837
66\59 206.519 103.2595 206.519 413.038 516.297
47\42 206.593 103.297 206.593 413.187 516.4835
75\67 206.659 103.3295 206.659 413.318 516.6475
28\25 206.769 103.385 206.769 413.5385 516.923
65\58 206.897 103.443 206.897 413.793 517.241
37\33 206.993 103.4965 206.993 413.986 517.4825
46\41 207.1295 103.565 207.1295 414.259 517.824
9\8 207.692 103.846 207.692 415.385 519.231
44\39 208.284 104.142 208.284 416.568 520.71
35\31 208.437 104.218 208.437 416.873 521.092
61\54 208.547 104.2735 208.547 417.094 521.3675
26\23 208.696 104.348 208.696 417.391 521.739
69\61 208.827 104.414 208.827 417.6545 522.068
43\38 208.907 104.453 208.907 417.814 522.267
60\53 208.9985 104.499 208.9985 417.997 522.496
17\15 209.231 104.615 209.231 418.4615 523.077
59\52 209.4675 104.734 209.4675 418.935 523.669
42\37 209.563 104.782 209.563 419.127 523.9085
67\59 209.648 104.824 209.648 419.296 524.12
25\22 209.79 104.895 209.79 419.58 524.4755
58\51 209.955 104.977 209.955 419.91 524.887
33\29 210.08 105.04 210.08 420.159 525.199
41\36 210.256 105.128 210.256 420.513 525.641
8\7 210.989 105.4945 210.989 421.978 527.4725 …to here

Aeolian Mode Neapolitan Temperament from here …

39\34 211.765 105.882 211.765 423.529 529.412
31\27 211.966 105.983 211.966 423.932 529.9145
54\47 212.111 106.056 212.111 424.223 530.278
23\20 212.308 106.154 212.308 424.615 530.769
61\53 212.482 106.241 212.482 424.964 531.205
38\33 212.587 106.294 212.587 425.175 531.4685
53\46 212.709 106.3595 212.709 425.418 531.773
15\13 213.018 106.509 213.018 426.0355 532.544
52\45 213.333 106.667 213.333 426.667 533.333
37\32 213.4615 106.731 213.4615 426.923 533.654
59\51 213.575 106.787 213.575 427.149 533.937
22\19 213.765 106.883 213.765 427.52 534.413
51\44 213.986 106.993 213.986 427.972 534.965
29\25 214.154 107.077 214.154 428.308 535.385
36\31 214.392 107.196 214.392 428.784 535.98
7\6 215.385 107.692 215.385 430.769 538.4615
34\29 216.446 108.223 216.446 432.891 541.114
27\23 216.722 108.361 216.722 433.445 541.806
47\40 216.923 108.4615 216.923 433.846 542.308
20\17 217.195 108.597 217.195 434.389 542.986
53\45 217.436 108.718 217.436 434.872 543.59
33\28 217.582 108.791 217.582 435.165 543.956
46\39 217.7515 108.876 217.7515 435.503 544.679
13\11 218.182 109.091 218.182 436.364 545.4545
45\38 218.6235 109.312 218.6235 437.247 546.5559
32\27 218.803 109.402 218.803 437.606 547.0085
51\43 218.962 109.461 218.962 406.6445 547.406
19\16 219.231 109.615 219.231 438.4615 548.077
44\37 219.543 109.771 219.543 439.085 548.8565
25\21 219.78 109.89 219.78 439.56 549.4505
31\26 220.118 110.059 220.118 440.237 550.296
6\5 221.5385 110.769 221.5385 443.077 553.846 …to here
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