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==Intervals==
This scale, a Long Common Practice minor mode, has the Grandfather 3L 5s MOS with a 4:1 ratio of large against small. It also gives the wide values for the period of the Greater [[Ragismic microtemperaments #Chlorine|Chlorine]] temperament.
== Intervals==
{| class="wikitable"
|+
!Nonet
!Period
!Notes
|-
|1/1
|''70.588''
|Soft Phrygian mode begins
|-
|25\24
|''73.529''
|
|-
|24\23
|73.657
|
|-
|23\22
|73.797
|
|-
|22\21
|73.950
|Soft Phrygian mode ends, Thirdtone Phrygian mode begins
|-
| 21\20
|74.118
|
|-
|20\19
|74.303
|
|-
|19\18
|74.510
|
|-
|37\35
|74.622
|
|-
|18\17
|74.740
|
|-
|17\16
|75.000
|
|-
|16\15
|75.294
|Thirdtone Phrygian mode ends
|-
|15\14
|75.630
|Semitone Phrygian mode begins
|-
|14\13
|76.018
|
|-
|27\25
|76.235
|
|-
|13\12
|''76.471''
|
|-
|12\11
|77.005
|
|-
|11\10
|77.647
|Semitone Phrygian mode ends, Intense Phrygian mode begins
|-
|21\19
| 78.019
|
|-
|10\9
|78.431
|Intense Phrygian mode ends, Intense Phrygian-Soft Aeolian mode begins
|-
|19\17
|78.893
|
|-
|9\8
|''79.412''
|Intense Phrygian-Soft Aeolian mode ends, Soft Aeolian mode begins
|-
|17\15
|80.000
|
|-
|8\7
|80.672
|Soft Aeolian mode ends, Flattone Aeolian mode begins
|-
|15\13
|81.448
|
|-
|22\19
|81.734
|Flattone Aeolian mode ends, Meantone Aeolian mode begins
|-
|29\25
|81.882
|
|-
|7\6
|''82.353''
|Meantone Aeolian mode ends, Superpyth Intense Aeolian mode begins
|-
|20\17
|83.045
|
|-
|13\11
|83.422
|Superpyth Intense Aeolian mode ends, Ultrapyth Intense Aeolian mode begins
|-
|19\16
|83.824
|
|-
|6\5
|84.706
|Ultrapyth Intense Aeolian mode ends
|}Golden/Pyrite Tunings±13¢


{| class="wikitable"
{| class="wikitable"
! rowspan="3" |Degrees
! colspan="2" rowspan="3" |Octatonic
! colspan="2" |Soft Phrygian
! colspan="4" |Phrygian
|-
|-
! | Degrees
! rowspan="2" |Min-Med
! | Octatonic
! rowspan="2" |Min-Max/Med-Max
! | Minimum
! colspan="2" |Thirdtone
! | Golden
! colspan="2" |Semitone
! | Median
! | Mean
! | ed(9/4)
! | Maximum
|-
|-
| | 1
!Min-Med/Min-Max
| | D
!Med-Max
| | 75.294
!Min-Med/Min-Max
| | 76.902
!Med-Max
| | 77.647
| | 80
| | 82.583
| | 84.706
|-
|-
| | 2
| |1
| | Eb
|A
| | 150.588
| |Ab
| | 153.804
|72.944-74.474
| | 155.294
|73.089-74.618
| | 160
|73.379-75.205
| | 165.166
|74.012-75.586
| | 169.412
|75.216-77.013
|75.75-77.635
|-
|-
| | 3
| |2
| | Eb^/D#v
|B\\
| | 225.882
| |G#v/Ab^
| | 230.7055
|145.889-148.948
| | 232.941
|146.178-149.236
| | 240
|146.758-150.409
| | 247.749
|148.023-151.173
| | 254.118
|150.432-154.025
|151.501-155.2705
|-
|-
| | 4
| |3
| | D#
|Apv/B\\^
| | 301.1765
| |G#
| | 307.607
|218.833-223.4215
| | 310.588
|219.266-223.855
| | 320
|220.137-225.614
| | 330.332
|222.035-226.759
| | 338.8235
|225.648-230.037
|227.251-232.906
|-
|-
| | 5
| |4
| | E
|Ap
| | 376.471
| |A
| | 384.509
|291.778-297.895
| | 387.235
|292.355-298.473
| | 400
|293.5155-300.819
| | 412.915
|296.047-302.346
| | 423.529
|300.864-308.050
|303.002-301.541
|-
|-
| | 6
| |5
| | F
| colspan="2" |B
| | 451.765
|364.722-372.369
| | 461.411
|365.444-373.091
| | 464.822
|366.894-376.0235
| | 480
|370.059-377.932
| | 495.498
|376.08-385.063
| | 508.235
|378.752-388.176
|-
|-
| | 7
| |6
| | Gb
| colspan="2" |C
| | 527.059
|437.6665-446.843
| | 538.313
|438.533-447.709
| | 542.529
|440.273-451.228
| | 560
|444.070-453.519
| | 578.080'5
|451.296-462.075
| | 592.941
|454.5025-465.811
|-
|-
| | 8
| |7
| | Gb^/F#v
|Q
| | 602.353
| |Qb
| | 615.215
|510.611-521.317
| | 620.1765
|511.621-522.327
| | 640
|513.652-526.433
| | 660.663'5
|518.082-529.105
| | 677.647
|526.512-539.088
|530.253-543.447
|-
|-
| | 9
| |8
| | F#
|D\\
| | 677.647
| |C#v/Qb^
| | 692.117
|583.555-595.791
| | 697.8235
|584.71-596.9455
| | 720
|587.031-601.638
| | 743.246'5
|592.094-604.6915
| | 762.653
|601.728-616.101
|606.003-621.082
|-
|-
| | 10
| |9
| | G
|Qpv/D\\^
| | 752.941
| |C#
| | 769.018
|656.5-670.264
| | 777.471
|657.799-671.564
| | 800
|660.41-676.842
| | 825.829
|661.1055-680.278
| | 847.059
|676.944-693.1135
|681.754-698.717
|-
|-
| | 11
| |10
| | H
|Qp
| | 828.235
| |Q
| | 845.92
|729.444-744.738
| | 855.118
|730.888-746.182
| | 880
|733.789-752.047
| | 908.412
|740.117-755.864
| | 931.765
|752.16-770.126
|757.504-776.352
|-
|-
| | 12
| |11
| | A
| colspan="2" |D
| | 903.529
|802.3885-819.212
| | 922.822
|803.9765-820.8
| | 932.765
|807.468-827.252
| | 960
|814.129-831.451
| | 990.995
|827.376-847.139
| | 1016.471
|833.255-853.988
|-
|-
| | 13
| |12
| | Bb
| colspan="2" |E
| | 978.8235
|875.333-893.686
| | 999.724
|877.065-895.418
| | 1010.412
|880.5465-902.456
| | 1040
|888.141-907.037
| | 1073.578
|902.592-924.151
| | 1101.1765
|909.005-931.622
|-
|-
| | 14
| |13
| | Bb^/A#v
|F
| | 1055.118
| |Fb
| | 1076.626
|948.277-968.16
| | 1088.059
|950.154-970.0365
| | 1120
|953.925-977.661
| | 1156.161
|962.152-982.624
| | 1185.882
|977.808-1001.164
|984.755-1009.258
|-
|-
| | 15
|14
| | A#
|F\\
| | 1130.412
|E#v/Fb^
| | 1153.528
|1021.222-1042.6335
| | 1164.706
|1023.243-1044.655
| | 1200
|1027.304-1052.866
| | 1238.744
|1036.164-1058.21
| | 1270.588
|1053.024-1078.177
|1060.506-1086.893
|-
|-
| | 16
|15
| | B
|Fpv/G\\^
| | 1204.706
|E#
| | 1230.429
|1094.166-1117.107
| | 1242.353
|1096.332-1119.273
| | 1280
|1100.683-1128.0705
| | 1321.327
|1110.176-1133.7965
| | 1355.294
|1128.24-1155.189
|1136.256-1164.5285
|-
|-
| | 17
|16
| | C
|Fp
| | 1280
|F
| | 1307.331
|1167.111-1191.581
| | 1320
|1169.42-1193.891
| | 1360
|1174.062-1203.275
| | 1403.91
|1184.188-1209.382
| | 1440
|1203.456-1232.202
|1212.007-1242.164
|-
|17
| colspan="2" |G
|1240.055-1266.055
|1242.506-1268.509
|1247.441-1278.48
|1258.199-1284.969
|1278.672-1309.2145
|1287.757-1319.799
|}
|}
{| class="wikitable"
|-
! rowspan="2" |Degrees
! colspan="4" rowspan="2" |Octatonic
! colspan="2" |Intense Phrygian
! colspan="2" |Intense Phrygian-Soft Aeolian
! colspan="2" |Soft Aeolian
|-
!Min-Med/Min-Max
!Med-Max
!Min-Med/Min-Max
!Med-Max
!Min-Med/Min-Max
!Med-Max
|-
|1
|G
|Gb
|A
|Ab
|77.163-78.692
|77.347-78.877
|78.014-79.544
|78.245-79.774
|79.0895-80.618
|79.385-80.915
|-
|2
|A\\
|F#v/Gb^
|B\\
|G#v/Ab^
|155.325-157.384
|155.695-157.7535
|156.029-159.087
|156.49-159.549
|158.179-161.238
|158.772-161.83
|-
|3
|Gpv/A\\^
|F#
|Apv/B\\^
|G#
|231.488-236.076
|232.042-236.63
|234.043-238.631
|234.735-239.323
|237.268-241.857
|238.157-242.746
|-
|4
|Gp
|G
|Ap
|A
|308.651-314.768
|309.389-315.507
|312.057-318.175
|312.98-319.098
|316.358-322.4755
|317.543-323.661
|-
|5
| colspan="2" |A
| colspan="2" |B
|385.814-393.4605
|386.737-394.384
|390.071-397.7185
|391.225-398.872
|395.447-403.094
|396.929-404.576
|-
|6
| colspan="2" |B
| colspan="2" |C
|462.976-472.1525
|464.084-473.261
|468.086-477.262
|469.469-478.646
|474.537-483.713
|476.315-485.4913
|-
|7
|H
|Hb
|Q
|Qb
|540.139-550.845
|541.4315-549.423
|546.1-556.806
|547.715-558.421
|553.627-564.332
|555.7005-566.406
|-
|8
|C\\
|B#v/Hb^
|D\\
|C#v/Qb^
|617.3015-629.537
|618.779-631.014
|624.114-636.35
|625.96-638.195
|632.716-644.951
|635.086-647.322
|-
|9
|Hpv/C\\^
|B#
|Qpv/D\\^
|C#
|694.464-708.229
|696.126-709.891
|702.129-715.893
|704.205-717.969
|711.805-725.57
|714.805-728.237
|-
|10
|Hp
|H
|Qp
|Q
|771.629-786.921
|773.4735-788.768
|780.143-795.437
|782.45-797.744
|790.895-806.189
|793.858-809.152
|-
|11
| colspan="2" |C
| colspan="2" |D
|848.79-865.613
|865.821-867.644
|858.157-874.981
|860.695-877.518
|869.984-886.808
|873.243-890.067
|-
|12
| colspan="2" |D
| colspan="2" |E
|925.952-944.305
|928.168-946.521
|936.171-954.527
|938.94-957.293
|949.074-967.427
|952.692-970.982
|-
|13
|E
|Eb
|F
|Fb
|1003.115-1022.997
|1005.516-1025.398
|1014.186-1034.0668
|1017.185-1037.067
|1028.163-1048.045
|1032.015-1051.8975
|-
|14
|F\\
|D#v/Eb^
|F\\
|E#v/Fb^
|1080.278-1101.689
|1082.863-1104.275
|1092.2-1113.612
|1095.43-1116.841
|1107.253-1128.664
|1111.401-1132.813
|-
|15
|Epv/F\\^
|D#
|Fpv/G\\^
|E#
|1157.44-1180.381
|1160.21-1183.151
|1170.214-1193.1555
|1173.675-1196.616
|1186.3425-1209.283
|1190.788-1213.728
|-
|16
|Ep
|E
|Fp
|F
|1234.603-1259.0735
|1237.558-1262.028
|1248.229-1272.699
|1251.9195-1276.39
|1265.4315-1289.902
|1270.173-1294.643
|-
|17
| colspan="2" |F
| colspan="2" |G
|1311.767-1337.767
|1314.905-1340.905
|1326.243-1352.243
|1330.1645-1356.1645
|1344.521-1370.521
|1349.558-1375.558
|}
{| class="wikitable"
! rowspan="3" |Degrees
! colspan="2" rowspan="3" |Octatonic
! colspan="4" |Aeolian
! colspan="4" |Intense Aeolian
|-
! colspan="2" |Flattone
! colspan="2" |Meantone
! colspan="2" |Superpyth
! colspan="2" |Ultrapyth
|-
!Min-Med
!Med-Max~Min-Max
!Min-Med/Min-Max
!Med-Max
!Min-Med
!Min-Max/Med-Max
!Min-Med/Min-Max
!Med-Max
|-
|1
|G
|Gb
|80.49-82.019
| colspan="2" |80.772-82.6
|81.178-82.707
|82.156-83.686
|82.388-83.9175
|82.939-84.469
|83.202-84.731
|-
|2
|A\\
|F#v/Gb^
|160.979-164.038
| colspan="2" |161.544-165.199
|162.356-165.416
|164.127-167.31715
|164.776-167.835
|165.8785-168.937
|166.403-169.462
|-
|3
|Gpv/A\\^
|F#
|241.469-246.057
| colspan="2" |242.316-247.799
|243.535-248.1235
|246.469-251.057
|247.164-251.753
|248.818-253.405
|249.605-254.193
|-
|4
|Gp
|G
|321.958-328.076
| colspan="2" |323.089-330.398
|324.714-330.831
|328.625-334.743
|329.552-335.67
|331.757-337.875
|332.807-338.324
|-
|5
| colspan="2" |A
|402.448-410.095
| colspan="2" |403.861-412.998
|405.892-413.539
|410.782-418.429
|411.9405-419.588
|414.696-422.343
|416.008-423.655
|-
|6
| colspan="2" |B
|482.937-492.114
| colspan="2" |484.633-495.597
|487.071-496.247
|492.938-502-115
|494.329-503.505
|497.635-506.812
|499.21-508.386
|-
|7
|H
|Hb
|563.427-574.133
| colspan="2" |565.405-578.197
|568.249-578.955
|575.0945-585.8
|576.717-587.423
|580.575-591.2805
|582.416-593.117
|-
|8
|C\\
|B#v/Hb^
|643.917-656.152
| colspan="2" |647.177-660.797
|649.4275-661.663
|657.251-669.486
|659.105-671.34
|663.514-675.749
|665.613-677.8485
|-
|9
|Hpv/C\\^
|B#
|724.406-738.171
| colspan="2" |726.9495-743.396
|730.606-744.371
|739.407-753.172
|741.493-755.258
|746.453-760.218
|748.815-762.58
|-
|10
|Hp
|H
|804.896-820.19
| colspan="2" |807.722-825.996
|811.784-827.0785
|821.5635-836.858
|823.881-839.175
|829.392-844.686
|832.0165-847.311
|-
|11
| colspan="2" |C
|885.385-902.209
| colspan="2" |888.494-908.595
|892.963-909.7886
|903.72-920.543
|906.269-923.093
|912.331-929.155
|915.218-932.041
|-
|12
| colspan="2" |D
|965.875-984.228
| colspan="2" |969.266-991.195
|974.141-992.494
|985.876-1004.229
|988.657-1007.01
|995.271-1013.624
|998.419-1016.773
|-
|13
|E
|Eb
|1046.364-1066.247
| colspan="2" |1050.004-1073.794
|1055.32-1075.202
|1068.033-1087.915
|1071.045-1090.928
|1078.21-1098.092
|1081.6215-1101.504-
|-
|14
|F\\
|D#v/Eb^
|1126.854-1148.266
| colspan="2" |1130.81-1156.394
|1136.498-1157.91
|1150.189-1171.601
|1153.4335-1174.845
|1161.149-1182.561
|1164.823-1186.235
|-
|15
|Epv/F\\^
|D#
|1207.344-1230.285
| colspan="2" |1211.583-1238.9935
|1217.6765-1240.617
|1232.345-1255.2865
|1235.822-1258.762
|1244.088-1267.03
|1248.025-1270.966
|-
|16
|Ep
|E
|1287.833-1312.304
| colspan="2" |1292.3545-1321.593
|1298.855-1323.3255
|1314.502-1338.972
|1318.21-1342.68
|1327.028-1351.498
|1331.226-1355.697
|-
|17
| colspan="2" |F
|1368.322-1394.322
| colspan="2" |1373.127-1404.193
|1380.033-1406.033
|1396.658-1422.658
|1400.598-1426.598
|1409.967-1435.967
|1414.428-1440.428
|}
[[Category:edIX]]
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