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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.
This scale, a reformed minor mode,occurs in [[12edo]], where it is the equal division of the major ninth. It has the Long Common Practice Macroshrutis 6L 2s MOS with a 2:1 ratio of large against small. It also gives the wide values for the period of the Greater [[Silicon]] temperament.
 
==Intervals==
==Tuning spectrum==
{| class="wikitable"
{| class="wikitable"
|+
|+
! colspan="5" rowspan="2" |Period
!Nonet
! colspan="6" |Octatonic (6L 2s)
!Period
! rowspan="2" |Notes
!Notes
|-
|-
!L
|1/1
!s
|''85.714''
! colspan="4" |Pentachord
|Soft Phrygian mode begins
|-
|-
|1\1edo
|23\22
|89.610
|
|
|-
|22\21
|89.796
|Soft Phrygian mode ends, Thirdtone Phrygian mode begins
|-
|21\20
|90.000
|
|
|-
|20\19
|90.226
|
|
|-
|19\18
|90.476
|
|
|171.429
|85.714
|171.429
|342.857
|514.286
|600
|Phrygian Mode (aka Double) Neapolitan Temperament from here …
|-
|-
|37\35
|90.612
|
|
|-
|18\17
|90.756
|
|
|-
|17\16
|91.071
|
|
|
|-
|16\15
|91.429
|Thirdtone Phrygian mode ends
|-
|15\14
|15\14
|183.6735
|91.837
|91.837
|183.6735
|Semitone Phrygian mode begins
|367.347
|551.02
|642.857
|
|-
|-
|
|
|
|14\13
|14\13
|
|184.615
|92.308
|92.308
|184.615
|369.231
|553.846
|646.154
|
|
|-
|-
|
|
|
|
|27\25
|27\25
|185.143
|92.571
|92.571
|185.143
|370.286
|555.571
|648
|
|
|-
|-
|
|
|13\12
|13\12
|
|''92.857''
|
|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
|12\11
|
|93.506
|
|
|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
|11\10
|
|
|
|
|188.571
|94.286
|94.286
|188.571
|Semitone Phrygian mode ends, Intense Phrygian mode begins
|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
|21\19
|
|94.737
|
|
|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
|10\9
|
|
|
|
|190.476
|95.238
|95.238
|190.476
|Intense Phrygian mode ends, Intense Phrygian-Soft Aeolian mode begins
|380.952
|571.429
|666.667
|
|-
|-
|
|19\17
|
|95.798
|
|
|49\44
|190.909
|95.4545
|190.909
|381.818
|572.727
|668.182
|
|
|-
|-
|
|9\8
|
|''96.429''
|
|Intense Phrygian-Soft Aeolian mode ends, Soft Aeolian mode begins
|39\35
|
|191.02
|95.51
|191.02
|382.041
|573.061
|668.571
|
|-
|-
|
|17\15
|
|97.143
|
|
|68\61
|191.101
|95.55
|191.101
|382.201
|573.302
|668.8525
|
|
|-
|-
|
|8\7
|
|97.959
|29\26
|Soft Aeolian mode ends, Flattone Aeolian mode begins
|
|
|191.209
|95.604
|191.209
|382.418
|573.626
|669.231
|
|-
|-
|
|15\13
|
|98.901
|
|
|77\69
|191.304
|95.652
|191.304
|382.609
|573.913
|669.567
|
|
|-
|-
|
|22\19
|
|99.248
|
|Flattone Aeolian mode ends, Meantone Aeolian mode begins
|48\43
|
|191.362
|95.681
|191.362
|382.724
|574.086
|669.767
|
|-
|-
|
|29\25
|
| 99.429
|
|
|67\60
|191.429
|95.714
|191.429
|382.857
|574.286
|670
|
|
|-
|-
|
|7\6
|19\17
|''100.000''
|
|Meantone Aeolian mode ends, Superpyth Intense Aeolian mode begins
|
|
|191.597
|95.798
|191.597
|383.193
|574.79
|670.588
|
|-
|-
|
|20\17
|
|100.840
|
|
|66\59
|191.768
|95.884
|191.768
|383.535
|575.303
|671.187
|
|
|-
|-
|
|13\11
|
| 101.299
|
|Superpyth Intense Aeolian mode ends, Ultrapyth Intense Aeolian mode begins
|47\42
|
|191.837
|95.918
|191.837
|383.675
|575.51
|671.429
|
|-
|-
|
|19\16
|
|101.786
|
|
|75\67
|191.898
|95.949
|191.898
|383.795
|575.693
|671.642
|
|
|-
|-
|
|6\5
|
|102.857
|28\25
|Ultrapyth Intense Aeolian mode ends
|
|}Golden/Pyrite Tunings±13¢
|
{| class="wikitable"
|192
|96
|192
|384
|576
|672
|
|-
|-
|
! rowspan="3" |Degrees
|
! rowspan="3" |Octatonic
|
! colspan="2" |Soft Phrygian
|
! colspan="4" |Phrygian
|65\58
|192.118
|96.059
|192.118
|384.236
|576.355
|672.414
|
|-
|-
|
! rowspan="2" |Min-Med
|
! rowspan="2" |Min-Max/Med-Max
|
! colspan="2" |Thirdtone
|37\33
! colspan="2" |Semitone
|
|192.208
|96.104
|192.208
|384.416
|576.623
|672.727
|
|-
|-
|
!Min-Med/Min-Max
|
!Med-Max
|
!Min-Med/Min-Max
|
!Med-Max
|46\41
|192.334
|96.167
|192.334
|384.669
|577.0035
|673.171
|
|-
|-
|9\8
|1
|
|G#/Ab
|
|88.575-90.4325
|
|88.751-90.608
|
|89.103-91.32
|192.857
|89.871-91.7835
|96.429
|91.334-93.515
|192.857
|91.983-94.271
|385.714
|578.571
|675
|
|-
|-
|
|2
|
|A
|
|177.151-180.865
|
|177.501-181.216
|44\39
|178.206-182.64
|193.407
|179.743-183.567
|96.703
|182.667-187.031
|193.407
|183.965-188.543
|386.813
|580.22
|676.923
|
|-
|-
|
|3
|
|A#/Bb
|
|265.756-271.2975
|35\31
|266.252-271.823
|
|267.309-273.96
|193.548
|269.614-275.351
|96.774
|274.001-280.545
|193.548
|275.948-282.814
|387.097
|580.645
|677.419
|
|-
|-
|
|4
|
|B
|
|354.301-361.73
|
|355.003-362.431
|61\54
|356.412-365.28
|193.651
|359.4855-367.134
|96.825
|365.335-374.613
|193.651
|367.931-377.085
|387.302
|580.952
|677.778
|
|-
|-
|
|5
|
|B#/Cb
|26\23
|442.877-452.1625
|
|443.753-453.039
|
|445.515-456.6
|193.789
|449.357-458.918
|96.894
|456.6685-467.577
|193.789
|459.913-471.357
|387.578
|581.3665
|678.261
|
|-
|-
|
|6
|
|C
|
|531.452-542.595
|
|532.504-543.647
|69\61
|534.6175-547.92
|193.911
|539.228-550.701
|96.9555
|548.002-561.092
|193.911
|551.896-565.628
|387.822
|581.733
|678.6885
|
|-
|-
|
|7
|
|Q
|
|620.0275-633.0275
|43\38
|621.253-634.253
|
|623.7205-639.24
|193.985
|629.1-642.485
|96.9925
|639.335-654.335
|193.985
|643.879-659.8995
|387.97
|581.955
|678.947
|
|-
|-
|
|8
|
|Q#/Db
|
|708.603-723.46
|
|710.005-724.862
|60\53
|712.823-730.56
|194.07
|718.971-734
|97.035
|730.67-748.123
|194.07
|735.861-754.171
|388.14
|582.21
|679.245
|
|-
|-
|
|9
|17\15
|D
|
|797.178-813.8925
|
|798.756-815.47
|
|801.926-821.88
|194.286
|808.842-826.032
|97.143
|822.003-841.78
|194.286
|827.844848.442
|388.571
|582.857
|680
|
|-
|-
|
|10
|
|D#/Eb
|
|885.754-904.325
|
|887.507-906.078
|59\52
|891.029-913.2
|194.5055
|898.714-917.835
|97.253
|913.337-935.153
|194.5055
|919.8265-942.7135
|389.011
|583.5165
|680.769
|
|-
|-
|
|11
|
|E
|
|974.329-994.7575
|42\37
|976.257-996.686
|
|980.132-1004.52
|194.595
|988.585-1009.619
|94.297
|1007.671-1028.6685
|194.595
|1011.809-1036.985
|389.189
|583.784
|681.081
|
|-
|-
|
|12
|
|E#/Fb
|
|1062.904-1085.19
|
|1065.008-1087.294
|67\59
|1069.235-1095.84
|194.673
|1078.4565-1101.023
|97.337
|1096.004-1121.1894
|194.673
|1103.792-1131.256
|389.346
|584.019
|681.356
|
|-
|-
|
|13
|
|F
|25\22
|1151.48-1175.6225
|
|1153.759-1177.901
|
|1158.338-1187.16
|194.805
|1168.328-1193.186
|97.403
|1187.338-1215.699
|194.805
|1195.7745-1225.528
|389.61
|584.416
|681.818
|
|-
|-
|
|14
|
|G
|
|1240.055-1266.055
|
|1242.506-1268.506
|58\51
|1247.441-1278.48
|194.958
|1258.199-1284.969
|97.479
|1278.672-1309.2145
|194.958
|1287.757-1319.799
|389.916
|}
|584.874
{| class="wikitable"
|682.353
|
|-
|-
|
! rowspan="2" |Degrees
|
! colspan="2" rowspan="2" |Octatonic
|
! colspan="2" |Intense Phrygian
|33\29
! colspan="2" |Intense Phrygian-Soft Aeolian
|
! colspan="2" |Soft Aeolian
|195.074
|97.537
|195.074
|390.148
|585.222
|682.759
|
|-
|-
|
!Min-Med/Min-Max
|
!Med-Max
|
!Min-Med/Min-Max
|
!Med-Max
|41\36
!Min-Med/Min-Max
|195.238
!Med-Max
|97.619
|195.238
|390.476
|585.714
|683.333
|
|-
|-
|8\7
|1
|
|F#/Gb
|
|G#/Ab
|
|93.6975-95.555
|
|93.922-95.779
|195.918
|94.732-96.589
|97.959
|95.012-96.869
|195.918
|96.037-97.894
|391.836
|96.397-98.254
|587.755
|685.714
|…to here
Aeolian Mode Neapolitan Temperament from here …
|-
|-
|
|2
|
|G
|
|A
|
|187.395-191.109
|39\34
|187.844-191.558
|196.639
|189.463-193.178
|98.314
|190.0235-193.738
|196.639
|192.074-195.789
|393.277
|192.794-196.508
|589.916
|688.235
|
|-
|-
|
|3
|
|G#/Ab
|
|A#/Bb
|31\27
|281.093-286.664
|
|281.765-287.337
|196.825
|284.195-289.766
|98.413
|285.035-290.607
|196.825
|288.112-293.683
|393.651
|289.191-294.7625
|590.476
|688.889
|
|-
|-
|
|4
|
|A
|
|B
|
|374.79-382.219
|54\47
|375.687-383.116
|196.9605
|378.9265-386.219
|98.48
|380.047-387.476
|196.9605
|384.149-391.577
|393.921
|385.588-393.017
|590.8815
|689.362
|
|-
|-
|
|5
|
|A#/Bb
|23\20
|B#/Cb
|
|468.488-477.773
|
|469.609-478.895
|197.143
|473.658-482.944
|98.571
|475.059-484.3445
|197.143
|480.186-489.472
|394.286
|481.985-491.271
|591.429
|690
|
|-
|-
|
|6
|
|B
|
|C
|
|562.185-573.328
|61\53
|563.531-574.674
|197.305
|568.39-579.533
|98.602
|570.0705-581.213
|197.305
|576.223-587.366
|394.609
|578.382-589.525
|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
|
|-
|-
|
|7
|
|H
|
|Q
|
|655.883-668.883
|52\45
|657.4525-670.4525
|198.095
|663.121-676.121
|99.048
|665.082-678.082
|198.095
|672.2605-685.2605
|396.1905
|674.779-687.779
|594.286
|693.333
|
|-
|-
|
|8
|
|H#/Cb
|
|Q#/Db
|37\32
|749.58-764.4375
|
|751.374-766.231
|198.214
|757.853-772.71
|99.107
|760.094-774.951
|198.214
|768.298-783.155
|396.429
|771.176-786.033
|594.643
|693.75
|
|-
|-
|
|9
|
|C
|
|D
|
|843.278-859.992
|59\51
|845.296-862.01
|198.319
|852.585-869.299
|99.16
|855.105-871.82
|198.319
|864.335-881.049
|396.639
|867.573-884.2875
|594.958
|694.118
|
|-
|-
|
|10
|
|C#/Db
|22\19
|D#/Eb
|
|936.975-955.5546
|
|939.218-957.789
|198.496
|947.316-965.887
|99.248
|950.1175-968.689
|198.496
|960.372-978.9435
|396.9925
|963.97-982.542
|595.489
|694.737
|
|-
|-
|
|11
|
|D
|
|E
|
|1030.672-1051.101
|51\44
|1033.101-1053.568
|198.701
|1042.048-1062.477
|99.351
|1045.129-1065.558
|198.701
|1056.409-1076.838
|397.403
|1060.367-1080.796
|596.104
|695.4545
|
|-
|-
|
|12
|
|D#/Eb
|
|E#/Fb
|29\25
|1124.3705-1146.656
|
|1127.061-1149.347
|198.857
|1136.78-1159.065
|99.429
|1140.141-1162.427
|198.857
|1152.4465-1174.732
|397.714
|1156.764-1179.05
|596.571
|696
|
|-
|-
|
|13
|
|E
|
|F
|
|1218.068-1242.211
|36\31
|1220.983-1245.126
|199.078
|1231.511-1255.654
|99.539
|1235.153-1259.295
|199.078
|1248.484-1272.626
|398.157
|1253.161-1227.304
|597.235
|696.774
|
|-
|-
|7\6
|14
|
|F
|
|G
|
|1311.767-1337.767
|
|1314.905-1340.905
|200
|1326.243-1352.243
|100
|1330.1645-1356.1645
|200
|1344.521-1370.521
|400
|1349.558-1375.558
|600
|}
|700
{| class="wikitable"
|
! rowspan="3" |Degrees
! rowspan="3" |Octatonic
! colspan="4" |Aeolian
! colspan="4" |Intense Aeolian
|-
|-
|
! colspan="2" |Flattone
|
! colspan="2" |Meantone
|
! colspan="2" |Superpyth
|
! colspan="2" |Ultrapyth
|34\29
|200.985
|100.493
|200.985
|400.97
|602.956
|703.448
|
|-
|-
|
!Min-Med
|
!Med-Max~Min-Max
|
!Min-Med/Min-Max
|27\23
!Med-Max
|
!Min-Med
|201.242
!Min-Max/Med-Max
|101.621
!Min-Med/Min-Max
|201.242
!Med-Max
|402.4845
|603.727
|704.348
|
|-
|-
|
|1
|
|F#/Gb
|
|97.737-99.5945
|
| colspan="2" |98.0805-100.2995
|47\40
|98.574-100.431
|201.429
|99.761-101.618
|100.714
|100.043-101.9
|201.429
|100.712-102.569
|403.857
|101.031-102.888
|603.286
|705
|
|-
|-
|
|2
|
|G
|20\17
|195.475-199.189
|
| colspan="2" |196.161-200.599
|
|197.148-200.862
|201.681
|199.523-203.237
|100.84
|200.085-203.8
|201.681
|201.424-205.138
|403.361
|202.061.205.7755
|605.045
|705.882
|
|-
|-
|
|3
|
|G#/Ab
|
|293.212-298.783
|
| colspan="2" |294.2415-300.8985
|53\45
|295.721-301.293
|201.905
|299.284-304.885
|100.952
|300.128-305.6995
|201.905
|302.135-307.707
|403.8095
|303.092-308.663
|605.714
|706.667
|
|-
|-
|
|4
|
|A
|
|390.949-398.378
|33\28
| colspan="2" |392.322-401.198
|
|394.295-401.724
|202.041
|399.045-406.474
|101.02
|400.171-407.599
|202.041
|402.848-410.276
|404.082
|404.122-411.551
|606.122
|707.143
|
|-
|-
|
|5
|
|A#/Bb
|
|488.687-497.972
|
| colspan="2" |490.4025-501.497
|46\39
|492.869-502.155
|202.198
|498.806-508.092
|101.099
|500.2135-509.499
|202.198
|503.56-512.845
|404.396
|505.153-514.439
|606.593
|707.692
|
|-
|-
|
|6
|13\11
|B
|
|586.424-597.567
|
| colspan="2" |588.483-601.797
|
|591.443-602.586
|202.597
|598.568-609.711
|101.299
|600.256-611.399
|202.597
|604.2715-615.414
|405.195
|606.1835-617.326
|607.792
|709.091
|
|-
|-
|
|7
|
|H
|
|684.161-697.161
|
| colspan="2" |686.5635-702.096
|45\38
|690.017-703.017
|203.0075
|698.329-711.329
|101.504
|700.299-713.299
|203.0075
|704.983-717.983
|406.015
|707.214-720.214
|609.023
|710.526
|
|-
|-
|
|8
|
|H#/Cb
|
|781.899-796.756
|32\27
| colspan="2" |784.644-802.3955
|
|788.5905-803.448
|203.175
|798.09-812.947
|101.587
|800.342-815.199
|203.175
|805.695-820.5525
|406.349
|808.245-823.102
|609.524
|711.111
|
|-
|-
|
|9
|
|C
|
|879.636-896.35
|
| colspan="2" |882.724-902.695
|51\43
|887.164-903.879
|203.322
|897.8582-914.566.
|101.661
|900.384-917.099
|203.322
|906.407-923.1215
|406.6445
|909.275-925.9895
|609.967
|711.629
|
|-
|-
|
|10
|
|C#/Db
|19\16
|977.373-995.945
|
| colspan="2" |980.805-1002.995
|
|985.738-1004.3095
|203.571
|997.613-1016.184
|101.786
|1000.427-1018.9985
|203.571
|1007.119-1025.691
|407.143
|1010.306-1028.877
|610.714
|712.5
|
|-
|-
|
|11
|
|D
|
|1075.111-1095.539
|
| colspan="2" |1078.885-1003.294
|44\37
|1084.312-1104.7405
|203.861
|1097.374-1117.803
|101.9305
|1100.47-1120.898
|203.861
|1107.831-1128.26
|407.722
|1111.134-1131.765
|611.583
|713.5135
|
|-
|-
|
|12
|
|D#/Eb
|
|1172.848-1195.134
|25\21
| colspan="2" |1176.966-1203.594
|
|1182.886-1205.171
|204.082
|1197.135-1219.421
|102.041
|1200.512-1222.798
|204.082
|1208.543-1230.829
|408.163
|1212.367-1234.653
|612.245
|714.286
|
|-
|-
|
|13
|
|E
|
|1270.585-1294.728
|
| colspan="2" |1275.046-1303.893
|31\26
|1281.4956-1305.603
|204.396
|1296.867-1321.04
|102.198
|1300.555-1324.698
|204.396
|1309.255-1333.398
|408.791
|1313.3975-1337.54
|613.187
|715.384
|
|-
|-
|6\5
|14
|
|F
|
|1368.323-1394.324
|
| colspan="2" |1373.127-1404.193
|
|1380.033-1406.033
|205.714
|1396.658-1422.658
|102.857
|1400.598-1426.598
|205.714
|1409.967-1435.967
|411.429
|1414.428-1440.428
|617.143
|720
|…to here
|}
|}
[[Category:14-tone]]
[[Category:ed9/4]]
[[Category:edIX]]
[[Category:todo:add_definition]]
[[Category:todo:unify_precision]]
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/14edIX"