User:Moremajorthanmajor/14edIX: Difference between revisions

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This scale occurs in 12edo, where it is the equal division of the major ninth.
This scale occurs in 12edo, where it is the equal division of the major ninth. It has the Macroshrutis MOS with a 2:1 ratio of large against small.


==Intervals==
==Intervals==
{| class="wikitable"
{| class="wikitable"
|+
! colspan="5" rowspan="2" |Period
! colspan="6" |Octatonic (6L 2s)
! rowspan="2" |Notes
|-
!L
!s
! colspan="4" |Pentachord
|-
|1\1edo
|
|
|
|
|171.429
|85.714
|171.429
|342.857
|514.286
|600
|Phrygian Mode (aka Double) Neapolitan Temperament from here …
|-
|
|
|
|
|15\14
|183.6735
|91.837
|183.6735
|367.347
|551.02
|642.857
|
|-
|
|
|
|14\13
|
|184.615
|92.308
|184.615
|369.231
|553.846
|646.154
|
|-
|
|
|
|
|27\25
|185.143
|92.571
|185.143
|370.286
|555.571
|648
|
|-
|
|
|13\12
|
|
|185.714
|92.857
|185.714
|371.429
|557.143
|650
|
|-
|
|
|
|
|38\35
|186.122
|93.061
|186.122
|372.245
|558.367
|651.429
|
|-
|
|
|
|25\23
|
|186.335
|93.168
|186.335
|372.671
|559.006
|652.174
|
|-
|
|
|
|
|37\34
|186.555
|93.278
|186.555
|373.109
|559.664
|652.941
|
|-
|
|12\11
|
|
|
|187.013
|93.5065
|187.013
|374.026
|561.039
|654.5455
|
|-
|
|
|
|
|46\43
|187.375
|93.688
|187.375
|374.751
|562.126
|655.813
|
|-
|
|
|
|35\32
|
|187.5
|93.75
|187.5
|375
|562.5
|656.25
|
|-
|
|
|
|
|58\53
|187.601
|93.8005
|187.601
|375.202
|562.803
|656.604
|
|-
|
|
|23\21
|
|
|187.755
|93.878
|187.755
|375.51
|563.265
|657.143
|
|-
|
|
|
|
|57\52
|187.912
|93.956
|187.912
|375.824
|563.736
|658.242
|
|-
|
|
|
|34\31
|
|188.018
|94.009
|188.018
|376.037
|564.055
|658.0645
|
|-
|
|
|
|
|45\41
|188.153
|94.077
|188.153
|376.307
|564.46
|658.537
|
|-
|11\10
|
|
|
|
|188.571
|94.286
|188.571
|377.143
|565.714
|660
|…to here
Phrygian-Aeolian Mode Neapolitan Temperament from here …
|-
|
|
|
|
|54\49
|188.921
|94.461
|188.921
|377.842
|566.764
|661.2245
|
|-
|
|
|
|43\39
|
|189.011
|94.5055
|189.011
|378.022
|567.033
|661.5385
|
|-
|
|
|
|
|75\68
|189.076
|94.538
|189.076
|378.151
|567.227
|661.765
|
|-
|
|
|32\29
|
|
|189.163
|94.581
|189.163
|378.325
|567.488
|662.069
|
|-
|
|
|
|
|85\77
|189.239
|94.62
|189.239
|378.478
|567.717
|662.338
|
|-
|
|
|
|53\48
|
|189.286
|94.643
|189.286
|378.571
|567.857
|662.5
|
|-
|
|
|
|
|74\67
|189.339
|94.6695
|189.339
|378.678
|568.017
|662.687
|
|-
|
|21\19
|
|
|
|189.474
|94.736
|189.474
|378.947
|568.421
|663.158
|
|-
|
|
|
|
|73\66
|189.61
|94.805
|189.61
|379.221
|568.831
|663.636
|
|-
|
|
|
|52\47
|
|189.666
|94.833
|189.666
|379.331
|568.997
|663.83
|
|-
|
|
|
|
|83\75
|189.714
|94.857
|189.714
|379.429
|569.143
|664
|
|-
|
|
|31\28
|
|
|189.796
|94.898
|189.796
|379.591
|569.388
|664.286
|
|-
|
|
|
|
|72\65
|189.89
|94.945
|189.89
|379.78
|569.67
|664.615
|
|-
|
|
|
|41\37
|
|189.961
|94.981
|189.961
|379.923
|569.884
|644.865
|
|-
|
|
|
|
|51\46
|190.062
|95.031
|190.062
|380.124
|570.186
|665.217
|
|-
|10\9
|
|
|
|
|190.476
|95.238
|190.476
|380.952
|571.429
|666.667
|
|-
|
|
|
|
|49\44
|190.909
|95.4545
|190.909
|381.818
|572.727
|668.182
|
|-
|
|
|
|39\35
|
|191.02
|95.51
|191.02
|382.041
|573.061
|668.571
|
|-
|
|
|
|
|68\61
|191.101
|95.55
|191.101
|382.201
|573.302
|668.8525
|
|-
|
|
|29\26
|
|
|191.209
|95.604
|191.209
|382.418
|573.626
|669.231
|
|-
|
|
|
|
|77\69
|191.304
|95.652
|191.304
|382.609
|573.913
|669.567
|
|-
|
|
|
|48\43
|
|191.362
|95.681
|191.362
|382.724
|574.086
|669.767
|
|-
|
|
|
|
|67\60
|191.429
|95.714
|191.429
|382.857
|574.286
|670
|
|-
|
|19\17
|
|
|
|191.597
|95.798
|191.597
|383.193
|574.79
|670.588
|
|-
|
|
|
|
|66\59
|191.768
|95.884
|191.768
|383.535
|575.303
|671.187
|
|-
|
|
|
|47\42
|
|191.837
|95.918
|191.837
|383.675
|575.51
|671.429
|
|-
|
|
|
|
|75\67
|191.898
|95.949
|191.898
|383.795
|575.693
|671.642
|
|-
|
|
|28\25
|
|
|192
|96
|192
|384
|576
|672
|
|-
|
|
|
|
|65\58
|192.118
|96.059
|192.118
|384.236
|576.355
|672.414
|
|-
|
|
|
|37\33
|
|192.208
|96.104
|192.208
|384.416
|576.623
|672.727
|
|-
|
|
|
|
|46\41
|192.334
|96.167
|192.334
|384.669
|577.0035
|673.171
|
|-
|9\8
|
|
|
|
|192.857
|96.429
|192.857
|385.714
|578.571
|675
|
|-
|
|
|
|
|44\39
|193.407
|96.703
|193.407
|386.813
|580.22
|676.923
|
|-
|
|
|
|35\31
|
|193.548
|96.774
|193.548
|387.097
|580.645
|677.419
|
|-
|
|
|
|
|61\54
|193.651
|96.825
|193.651
|387.302
|580.952
|677.778
|
|-
|
|
|26\23
|
|
|193.789
|96.894
|193.789
|387.578
|581.3665
|678.261
|
|-
|
|
|
|
|69\61
|193.911
|96.9555
|193.911
|387.822
|581.733
|678.6885
|
|-
|
|
|
|43\38
|
|193.985
|96.9925
|193.985
|387.97
|581.955
|678.947
|
|-
|
|
|
|
|60\53
|194.07
|97.035
|194.07
|388.14
|582.21
|679.245
|
|-
|
|17\15
|
|
|
|194.286
|97.143
|194.286
|388.571
|582.857
|680
|
|-
|
|
|
|
|59\52
|194.5055
|97.253
|194.5055
|389.011
|583.5165
|680.769
|
|-
|
|
|
|42\37
|
|194.595
|94.297
|194.595
|389.189
|583.784
|681.081
|
|-
|
|
|
|
|67\59
|194.673
|97.337
|194.673
|389.346
|584.019
|681.356
|
|-
|
|
|25\22
|
|
|194.805
|97.403
|194.805
|389.61
|584.416
|681.818
|
|-
|
|
|
|
|58\51
|194.958
|97.479
|194.958
|389.916
|584.874
|682.353
|
|-
|
|
|
|33\29
|
|195.074
|97.537
|195.074
|390.148
|585.222
|682.759
|
|-
|
|
|
|
|41\36
|195.238
|97.619
|195.238
|390.476
|585.714
|683.333
|
|-
|8\7
|
|
|
|
|195.918
|97.959
|195.918
|391.836
|587.755
|685.714
|…to here
Aeolian Mode Neapolitan Temperament from here …
|-
|
|
|
|
|39\34
|196.639
|98.314
|196.639
|393.277
|589.916
|688.235
|
|-
|
|
|
|31\27
|
|196.825
|98.413
|196.825
|393.651
|590.476
|688.889
|
|-
|
|
|
|
|54\47
|196.9605
|98.48
|196.9605
|393.921
|590.8815
|689.362
|
|-
|
|
|23\20
|
|
|197.143
|98.571
|197.143
|394.286
|591.429
|690
|
|-
|
|
|
|
|61\53
|197.305
|98.602
|197.305
|394.609
|591.914
|690.566
|
|-
|
|
|
|38\33
|
|197.403
|98.701
|197.403
|394.805
|592.208
|690.909
|
|-
|
|
|
|
|53\46
|197.5155
|98.758
|197.5155
|395.031
|592.547
|691.304
|
|-
|
|15\13
|
|
|
|197.802
|98.901
|197.802
|395.604
|593.407
|692.308
|
|-
|
|
|
|
|52\45
|198.095
|99.048
|198.095
|396.1905
|594.286
|693.333
|
|-
|
|
|
|37\32
|
|198.214
|99.107
|198.214
|396.429
|594.643
|693.75
|
|-
|
|
|
|
|59\51
|198.319
|99.16
|198.319
|396.639
|594.958
|694.118
|
|-
|
|
|22\19
|
|
|198.496
|99.248
|198.496
|396.9925
|595.489
|694.737
|
|-
|
|
|
|
|51\44
|198.701
|99.351
|198.701
|397.403
|596.104
|695.4545
|
|-
|
|
|
|29\25
|
|198.857
|99.429
|198.857
|397.714
|596.571
|696
|
|-
|
|
|
|
|36\31
|199.078
|99.539
|199.078
|398.157
|597.235
|696.774
|
|-
|7\6
|
|
|
|
|200
|100
|200
|400
|600
|700
|
|-
|
|
|
|
|34\29
|200.985
|100.493
|200.985
|400.97
|602.956
|703.448
|
|-
|-
! | Degrees
|
! | Octatonic
|
! | Minimum
|
! | Golden
|27\23
! | Median
|
! | Mean
|201.242
! | ed(9/4)
|101.621
! | Maximum
|201.242
|402.4845
|603.727
|704.348
|
|-
|-
| | 1
|
| | A#/Bb
|
| | 91.429
|
| | 93.381
|
| | 94.286
|47\40
| | 97.143
|201.429
| | 100.279
|100.714
| | 102.857
|201.429
|403.857
|603.286
|705
|
|-
|-
| | 2
|
| | B
|
| | 182.857
|20\17
| | 186.762
|
| | 188.571
|
| | 194.286
|201.681
| | 200.559
|100.84
| | 205.714
|201.681
|403.361
|605.045
|705.882
|
|-
|-
| | 3
|
| | B#/Cb
|
| | 274.286
|
| | 280.142
|
| | 282.857
|53\45
| | 291.429
|201.905
| | 300.838
|100.952
| | 308.571
|201.905
|403.8095
|605.714
|706.667
|
|-
|-
| | 4
|
| | C
|
| | 365.714
|
| | 373.523
|33\28
| | 377.143
|
| | 388.571
|202.041
| | 401.117
|101.02
| | 411.429
|202.041
|404.082
|606.122
|707.143
|
|-
|-
| | 5
|
| | D
|
| | 457.143
|
| | 466.904
|
| | 471.429
|46\39
| | 485.714
|202.198
| | 501.396
|101.099
| | 514.286
|202.198
|404.396
|606.593
|707.692
|
|-
|-
| | 6
|
| | D#/Eb
|13\11
| | 548.571
|
| | 560.285
|
| | 565.714
|
| | 582.857
|202.597
| | 601.676
|101.299
| | 617.143
|202.597
|405.195
|607.792
|709.091
|
|-
|-
| | 7
|
| | E
|
| | 640
|
| | 653.666
|
| | 660
|45\38
| | 680
|203.0075
| | 701.955
|101.504
| | 720
|203.0075
|406.015
|609.023
|710.526
|
|-
|-
| | 8
|
| | E#/Fb
|
| | 731.429
|
| | 747.047
|32\27
| | 754.286
|
| | 777.143
|203.175
| | 802.234
|101.587
| | 822.857
|203.175
|406.349
|609.524
|711.111
|
|-
|-
| | 9
|
| | F
|
| | 822.857
|
| | 840.427
|
| | 848.571
|51\43
| | 874.286
|203.322
| | 902.514
|101.661
| | 925.714
|203.322
|406.6445
|609.967
|711.629
|
|-
|-
| | 10
|
| | F#/Gb
|
| | 914.286
|19\16
| | 933.808
|
| | 942.857
|
| | 971.429
|203.571
| | 1002.793
|101.786
| | 1028.571
|203.571
|407.143
|610.714
|712.5
|
|-
|-
| | 11
|
| | G
|
| | 1005.714
|
| | 1027.188
|
| | 1037.143
|44\37
| | 1068.579
|203.861
| | 1103.072
|101.9305
| | 1131.429
|203.861
|407.722
|611.583
|713.5135
|
|-
|-
| | 12
|
| | H
|
| | 1097.143
|
| | 1120.57
|25\21
| | 1131.429
|
| | 1165.714
|204.082
| | 1203.351
|102.041
| | 1234.286
|204.082
|408.163
|612.245
|714.286
|
|-
|-
| | 13
|
| | H#/Ab
|
| | 1188.571
|
| | 1213.9505
|
| | 1225.714
|31\26
| | 1262.857
|204.396
| | 1303.631
|102.198
| | 1337.143
|204.396
|408.791
|613.187
|715.384
|
|-
|-
| | 14
|6\5
| | A
|
| | 1280
|
| | 1307.331
|
| | 1320
|
| | 1360
|205.714
| | 1403.91
|102.857
| | 1440
|205.714
|411.429
|617.143
|720
|…to here
|}
|}
[[Category:14-tone]]
[[Category:14-tone]]

Revision as of 00:25, 25 September 2018

This scale occurs in 12edo, where it is the equal division of the major ninth. It has the Macroshrutis MOS with a 2:1 ratio of large against small.

Intervals

Period Octatonic (6L 2s) Notes
L s Pentachord
1\1edo 171.429 85.714 171.429 342.857 514.286 600 Phrygian Mode (aka Double) Neapolitan Temperament from here …
15\14 183.6735 91.837 183.6735 367.347 551.02 642.857
14\13 184.615 92.308 184.615 369.231 553.846 646.154
27\25 185.143 92.571 185.143 370.286 555.571 648
13\12 185.714 92.857 185.714 371.429 557.143 650
38\35 186.122 93.061 186.122 372.245 558.367 651.429
25\23 186.335 93.168 186.335 372.671 559.006 652.174
37\34 186.555 93.278 186.555 373.109 559.664 652.941
12\11 187.013 93.5065 187.013 374.026 561.039 654.5455
46\43 187.375 93.688 187.375 374.751 562.126 655.813
35\32 187.5 93.75 187.5 375 562.5 656.25
58\53 187.601 93.8005 187.601 375.202 562.803 656.604
23\21 187.755 93.878 187.755 375.51 563.265 657.143
57\52 187.912 93.956 187.912 375.824 563.736 658.242
34\31 188.018 94.009 188.018 376.037 564.055 658.0645
45\41 188.153 94.077 188.153 376.307 564.46 658.537
11\10 188.571 94.286 188.571 377.143 565.714 660 …to here

Phrygian-Aeolian Mode Neapolitan Temperament from here …

54\49 188.921 94.461 188.921 377.842 566.764 661.2245
43\39 189.011 94.5055 189.011 378.022 567.033 661.5385
75\68 189.076 94.538 189.076 378.151 567.227 661.765
32\29 189.163 94.581 189.163 378.325 567.488 662.069
85\77 189.239 94.62 189.239 378.478 567.717 662.338
53\48 189.286 94.643 189.286 378.571 567.857 662.5
74\67 189.339 94.6695 189.339 378.678 568.017 662.687
21\19 189.474 94.736 189.474 378.947 568.421 663.158
73\66 189.61 94.805 189.61 379.221 568.831 663.636
52\47 189.666 94.833 189.666 379.331 568.997 663.83
83\75 189.714 94.857 189.714 379.429 569.143 664
31\28 189.796 94.898 189.796 379.591 569.388 664.286
72\65 189.89 94.945 189.89 379.78 569.67 664.615
41\37 189.961 94.981 189.961 379.923 569.884 644.865
51\46 190.062 95.031 190.062 380.124 570.186 665.217
10\9 190.476 95.238 190.476 380.952 571.429 666.667
49\44 190.909 95.4545 190.909 381.818 572.727 668.182
39\35 191.02 95.51 191.02 382.041 573.061 668.571
68\61 191.101 95.55 191.101 382.201 573.302 668.8525
29\26 191.209 95.604 191.209 382.418 573.626 669.231
77\69 191.304 95.652 191.304 382.609 573.913 669.567
48\43 191.362 95.681 191.362 382.724 574.086 669.767
67\60 191.429 95.714 191.429 382.857 574.286 670
19\17 191.597 95.798 191.597 383.193 574.79 670.588
66\59 191.768 95.884 191.768 383.535 575.303 671.187
47\42 191.837 95.918 191.837 383.675 575.51 671.429
75\67 191.898 95.949 191.898 383.795 575.693 671.642
28\25 192 96 192 384 576 672
65\58 192.118 96.059 192.118 384.236 576.355 672.414
37\33 192.208 96.104 192.208 384.416 576.623 672.727
46\41 192.334 96.167 192.334 384.669 577.0035 673.171
9\8 192.857 96.429 192.857 385.714 578.571 675
44\39 193.407 96.703 193.407 386.813 580.22 676.923
35\31 193.548 96.774 193.548 387.097 580.645 677.419
61\54 193.651 96.825 193.651 387.302 580.952 677.778
26\23 193.789 96.894 193.789 387.578 581.3665 678.261
69\61 193.911 96.9555 193.911 387.822 581.733 678.6885
43\38 193.985 96.9925 193.985 387.97 581.955 678.947
60\53 194.07 97.035 194.07 388.14 582.21 679.245
17\15 194.286 97.143 194.286 388.571 582.857 680
59\52 194.5055 97.253 194.5055 389.011 583.5165 680.769
42\37 194.595 94.297 194.595 389.189 583.784 681.081
67\59 194.673 97.337 194.673 389.346 584.019 681.356
25\22 194.805 97.403 194.805 389.61 584.416 681.818
58\51 194.958 97.479 194.958 389.916 584.874 682.353
33\29 195.074 97.537 195.074 390.148 585.222 682.759
41\36 195.238 97.619 195.238 390.476 585.714 683.333
8\7 195.918 97.959 195.918 391.836 587.755 685.714 …to here

Aeolian Mode Neapolitan Temperament from here …

39\34 196.639 98.314 196.639 393.277 589.916 688.235
31\27 196.825 98.413 196.825 393.651 590.476 688.889
54\47 196.9605 98.48 196.9605 393.921 590.8815 689.362
23\20 197.143 98.571 197.143 394.286 591.429 690
61\53 197.305 98.602 197.305 394.609 591.914 690.566
38\33 197.403 98.701 197.403 394.805 592.208 690.909
53\46 197.5155 98.758 197.5155 395.031 592.547 691.304
15\13 197.802 98.901 197.802 395.604 593.407 692.308
52\45 198.095 99.048 198.095 396.1905 594.286 693.333
37\32 198.214 99.107 198.214 396.429 594.643 693.75
59\51 198.319 99.16 198.319 396.639 594.958 694.118
22\19 198.496 99.248 198.496 396.9925 595.489 694.737
51\44 198.701 99.351 198.701 397.403 596.104 695.4545
29\25 198.857 99.429 198.857 397.714 596.571 696
36\31 199.078 99.539 199.078 398.157 597.235 696.774
7\6 200 100 200 400 600 700
34\29 200.985 100.493 200.985 400.97 602.956 703.448
27\23 201.242 101.621 201.242 402.4845 603.727 704.348
47\40 201.429 100.714 201.429 403.857 603.286 705
20\17 201.681 100.84 201.681 403.361 605.045 705.882
53\45 201.905 100.952 201.905 403.8095 605.714 706.667
33\28 202.041 101.02 202.041 404.082 606.122 707.143
46\39 202.198 101.099 202.198 404.396 606.593 707.692
13\11 202.597 101.299 202.597 405.195 607.792 709.091
45\38 203.0075 101.504 203.0075 406.015 609.023 710.526
32\27 203.175 101.587 203.175 406.349 609.524 711.111
51\43 203.322 101.661 203.322 406.6445 609.967 711.629
19\16 203.571 101.786 203.571 407.143 610.714 712.5
44\37 203.861 101.9305 203.861 407.722 611.583 713.5135
25\21 204.082 102.041 204.082 408.163 612.245 714.286
31\26 204.396 102.198 204.396 408.791 613.187 715.384
6\5 205.714 102.857 205.714 411.429 617.143 720 …to here
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