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This scale, a Long Common Practice minor mode, has the Grandfather 3L 5s MOS with a 4:1 ratio of large against small.
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==
==Intervals==
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
|+
! colspan="2" rowspan="2" |Octatonic
!Nonet
! colspan="4" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
!Period
! colspan="3" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
!Notes
! colspan="3" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
|-
|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
|
|-
|-
!Absolute Minimum
|19\18
!Minimum
|74.510
!Median
|
!Maximum
! |Minimum
!Median
!Maximum
!Minimum
!Median
!Maximum
|-
|-
| |1
|37\35
|G
| |Gb
|70.588
|74.622
|74.622
|
|-
|18\17
|74.740
|
|-
|17\16
|75.000
|
|-
|16\15
|75.294
|75.294
| colspan="2" |77.647
|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
|78.893
| colspan="2" |80.672
|
|82.353
|-
|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
|84.706
|Ultrapyth Intense Aeolian mode ends
|}Golden/Pyrite Tunings±13¢
{| class="wikitable"
! rowspan="3" |Degrees
! colspan="2" rowspan="3" |Octatonic
! colspan="2" |Soft Phrygian
! colspan="4" |Phrygian
|-
! rowspan="2" |Min-Med
! rowspan="2" |Min-Max/Med-Max
! colspan="2" |Thirdtone
! colspan="2" |Semitone
|-
!Min-Med/Min-Max
!Med-Max
!Min-Med/Min-Max
!Med-Max
|-
| |1
|A
| |Ab
|72.944-74.474
|73.089-74.618
|73.379-75.205
|74.012-75.586
|75.216-77.013
|75.75-77.635
|-
|-
| |2
| |2
|A\\
|B\\
| |F#v/Gb^
| |G#v/Ab^
|141.1765
|145.889-148.948
|149.244
|146.178-149.236
|150.588
|146.758-150.409
| colspan="2" |155.294
|148.023-151.173
|157.7855
|150.432-154.025
| colspan="2" |161.3445
|151.501-155.2705
|164.706
|169.412
|-
|-
| |3
| |3
|Gpv/A\\^
|Apv/B\\^
| |F#
| |G#
|211.765
|218.833-223.4215
|213.8655
|219.266-223.855
|225.882
|220.137-225.614
| colspan="2" |232.941
|222.035-226.759
|236.678
|225.648-230.037
| colspan="2" |242.017
|227.251-232.906
|247.059
|254.118
|-
|-
| |4
| |4
|Gp
|Ap
| |G
| |A
|282.353
|291.778-297.895
|298.487
|292.355-298.473
|301.1765
|293.5155-300.819
| colspan="2" |310.588
|296.047-302.346
|315.571
|300.864-308.050
| colspan="2" |322.689
|303.002-301.541
|329.412
|338.8235
|-
|-
| |5
| |5
|A
| colspan="2" |B
| |A
|364.722-372.369
|352.941
|365.444-373.091
|373.109
|366.894-376.0235
|376.471
|370.059-377.932
| colspan="2" |387.235
|376.08-385.063
|394.464
|378.752-388.176
| colspan="2" |403.361
|411.765
|423.529
|-
|-
| |6
| |6
|B
| colspan="2" |C
| |B
|437.6665-446.843
|423.529
|438.533-447.709
|447.731
|440.273-451.228
|451.765
|444.070-453.519
| colspan="2" |464.822
|451.296-462.075
|473.356
|454.5025-465.811
| colspan="2" |484.034
|494.118
|508.235
|-
|-
| |7
| |7
|H
|Q
| |Hb
| |Qb
|494.118
|510.611-521.317
|522.353
|511.621-522.327
|527.059
|513.652-526.433
| colspan="2" |542.529
|518.082-529.105
|552.249
|526.512-539.088
| colspan="2" |564.706
|530.253-543.447
|576.471
|592.941
|-
|-
| |8
| |8
|C\\
|D\\
| |B#v/Hb^
| |C#v/Qb^
|564.706
|583.555-595.791
|596.975
|584.71-596.9455
|602.353
|587.031-601.638
| colspan="2" |620.1765
|592.094-604.6915
|651.142
|601.728-616.101
| colspan="2" |645.378
|606.003-621.082
|658.8235
|677.647
|-
|-
| |9
| |9
|Hpv/C\\^
|Qpv/D\\^
| |B#
| |C#
|635.294
|656.5-670.264
|671.597
|657.799-671.564
|677.647
|660.41-676.842
| colspan="2" |697.8235
|661.1055-680.278
|710.035
|676.944-693.1135
| colspan="2" |726.05
|681.754-698.717
|741.1765
|762.653
|-
|-
| |10
| |10
|Hp
|Qp
| |H
| |Q
|705.882
|729.444-744.738
|746.2185
|730.888-746.182
|752.941
|733.789-752.047
| colspan="2" |777.471
|740.117-755.864
|788.927
|752.16-770.126
| colspan="2" |806.723
|757.504-776.352
|823.529
|847.059
|-
|-
| |11
| |11
|C
| colspan="2" |D
| |C
|802.3885-819.212
|776.471
|803.9765-820.8
|820.84
|807.468-827.252
|828.235
|814.129-831.451
| colspan="2" |855.118
|827.376-847.139
|867.82
|833.255-853.988
| colspan="2" |887.395
|905.882
|931.765
|-
|-
| |12
| |12
|D
| colspan="2" |E
| |D
|875.333-893.686
|847.059
|877.065-895.418
|895.462
|880.5465-902.456
|903.529
|888.141-907.037
| colspan="2" |932.765
|902.592-924.151
|956.713
|909.005-931.622
| colspan="2" |968.067
|988.235
|1016.471
|-
|-
| |13
| |13
|F
| |Fb
|948.277-968.16
|950.154-970.0365
|953.925-977.661
|962.152-982.624
|977.808-1001.164
|984.755-1009.258
|-
|14
|F\\
|E#v/Fb^
|1021.222-1042.6335
|1023.243-1044.655
|1027.304-1052.866
|1036.164-1058.21
|1053.024-1078.177
|1060.506-1086.893
|-
|15
|Fpv/G\\^
|E#
|1094.166-1117.107
|1096.332-1119.273
|1100.683-1128.0705
|1110.176-1133.7965
|1128.24-1155.189
|1136.256-1164.5285
|-
|16
|Fp
|F
|1167.111-1191.581
|1169.42-1193.891
|1174.062-1203.275
|1184.188-1209.382
|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
|E
| |Eb
|Eb
|917.647
|F
|970.084
|Fb
|978.8235
|1003.115-1022.997
| colspan="2" |1010.412
|1005.516-1025.398
|1025.6055
|1014.186-1034.0668
| colspan="2" |1048.7395
|1017.185-1037.067
|1070.588
|1028.163-1048.045
|1101.1765
|1032.015-1051.8975
|-
|-
|14
|14
|F\\
|F\\
|D#v/Eb^
|D#v/Eb^
|988.235
|F\\
|1044.706
|E#v/Fb^
|1054.118
|1080.278-1101.689
| colspan="2" |1088.059
|1082.863-1104.275
|1104.598
|1092.2-1113.612
| colspan="2" |1129.412
|1095.43-1116.841
|1152.941
|1107.253-1128.664
|1185.882
|1111.401-1132.813
|-
|-
|15
|15
|Epv/F\\^
|Epv/F\\^
|D#
|D#
|1058.8235
|Fpv/G\\^
|1119.328
|E#
|1129.412
|1157.44-1180.381
| colspan="2" |1164.706
|1160.21-1183.151
|1183.391
|1170.214-1193.1555
| colspan="2" |1210.084
|1173.675-1196.616
|1233.294
|1186.3425-1209.283
|1270.588
|1190.788-1213.728
|-
|-
|16
|16
|Ep
|Ep
|E
|E
|1129.412
|Fp
|1193.95
|F
|1204.706
|1234.603-1259.0735
| colspan="2" |1242.353
|1237.558-1262.028
|1262.284
|1248.229-1272.699
| colspan="2" |1290.756
|1251.9195-1276.39
|1317.647
|1265.4315-1289.902
|1355.294
|1270.173-1294.643
|-
|-
|17
|17
| colspan="2" |F
| colspan="2" |F
|1200
| colspan="2" |G
|1268.571
|1311.767-1337.767
|1280
|1314.905-1340.905
| colspan="2" |1320
|1326.243-1352.243
|1341.1765
|1330.1645-1356.1645
| colspan="2" |1371.429
|1344.521-1370.521
|1400
|1349.558-1375.558
|1440
|}
|}Golden Tunings
{| class="wikitable"
{| class="wikitable"
! rowspan="3" |Degrees
! colspan="2" rowspan="3" |Octatonic
! colspan="4" |Aeolian
! colspan="4" |Intense Aeolian
|-
|-
! rowspan="2" |Degrees
! colspan="2" |Flattone
! colspan="2" rowspan="2" |Octatonic
! colspan="2" |Meantone
! colspan="3" |Phrygian Mode (natural minor)
! colspan="2" |Superpyth
! colspan="2" |Phrygian-Aeolian Mode (intermediate minor)
! colspan="2" |Ultrapyth
! colspan="3" |Aeolian Mode (melodic/harmonic minor)
|-
|-
!Min-Med
!Min-Med
!Min-Max
!Med-Max~Min-Max
!Med-Max
!Min-Med/Min-Max
!Min-Med/Min-Max
!Med-Max
!Med-Max
!Min-Med
!Min-Med
!Min-Max
!Min-Max/Med-Max
!Min-Med/Min-Max
!Med-Max
!Med-Max
|-
|-
| |1
|1
|G
|G
| |Gb
|Gb
|74.763
|80.49-82.019
|75.076
| colspan="2" |80.772-82.6
|75.981
|81.178-82.707
|78.561
|82.156-83.686
|79.254
|82.388-83.9175
|81.254
|82.939-84.469
|81.908
|83.202-84.731
|83.153
|-
|-
| |2
|2
|A\\
|A\\
| |F#v/Gb^
|F#v/Gb^
|149.525
|160.979-164.038
|150.152
| colspan="2" |161.544-165.199
|151.961
|162.356-165.416
|157.121
|164.127-167.31715
|158.5075
|164.776-167.835
|162.509
|165.8785-168.937
|163.815
|166.403-169.462
|166.306
|-
|-
| |3
|3
|Gpv/A\\^
|Gpv/A\\^
| |F#
|F#
|224.288
|241.469-246.057
|225.228
| colspan="2" |242.316-247.799
|227.942
|243.535-248.1235
|235.982
|246.469-251.057
|237.761
|247.164-251.753
|243.763
|248.818-253.405
|245.723
|249.605-254.193
|249.458
|-
|-
| |4
|4
|Gp
|Gp
| |G
|G
|299.0505
|321.958-328.076
|300.3035
| colspan="2" |323.089-330.398
|303.923
|324.714-330.831
|314.242
|328.625-334.743
|317.015
|329.552-335.67
|325.017
|331.757-337.875
|327.63
|332.807-338.324
|332.611
|-
|-
| |5
|5
|A
| colspan="2" |A
| |A
|402.448-410.095
|373.813
| colspan="2" |403.861-412.998
|375.379
|405.892-413.539
|379.9035
|410.782-418.429
|392.803
|411.9405-419.588
|396.269
|414.696-422.343
|406.271
|416.008-423.655
|409.538
|415.764
|-
|-
| |6
|6
|B
| colspan="2" |B
| |B
|482.937-492.114
|448.576
| colspan="2" |484.633-495.597
|450.455
|487.071-496.247
|455.884
|492.938-502-115
|471.264
|494.329-503.505
|475.522
|497.635-506.812
|487.526
|499.21-508.386
|491.4455
|498.917
|-
|-
| |7
|7
|H
|H
| |Hb
|Hb
|523.338
|563.427-574.133
|525.531
| colspan="2" |565.405-578.197
|531.865
|568.249-578.955
|549.924
|575.0945-585.8
|554.776
|576.717-587.423
|568.78
|580.575-591.2805
|573.353
|582.416-593.117
|582.07
|-
|-
| |8
|8
|C\\
|C\\
| |B#v/Hb^
|B#v/Hb^
|598.101
|643.917-656.152
|600.607
| colspan="2" |647.177-660.797
|607.846
|649.4275-661.663
|628.485
|657.251-669.486
|634.03
|659.105-671.34
|650.034
|663.514-675.749
|655.261
|665.613-677.8485
|665.2225
|-
|-
| |9
|9
|Hpv/C\\^
|Hpv/C\\^
| |B#
|B#
|672.864
|724.406-738.171
|675.683
| colspan="2" |726.9495-743.396
|683.826
|730.606-744.371
|707.0455
|739.407-753.172
|713.284
|741.493-755.258
|731.2885
|746.453-760.218
|737.168
|748.815-762.58
|748.375
|-
|-
| |10
|10
|Hp
|Hp
| |H
|H
|747.626
|804.896-820.19
|750.759
| colspan="2" |807.722-825.996
|759.807
|811.784-827.0785
|785.606
|821.5635-836.858
|792.537
|823.881-839.175
|812.543
|829.392-844.686
|819.076
|832.0165-847.311
|831.528
|-
|-
| |11
|11
|C
| colspan="2" |C
| |C
|885.385-902.209
|822.389
| colspan="2" |888.494-908.595
|825.835
|892.963-909.7886
|835.788
|903.72-920.543
|864.168
|906.269-923.093
|871.791
|912.331-929.155
|893.797
|915.218-932.041
|900.983
|914.681
|-
|-
| |12
|12
|D
| colspan="2" |D
| |D
|965.875-984.228
|897.1515
| colspan="2" |969.266-991.195
|900.9105
|974.141-992.494
|911.768
|985.876-1004.229
|942.727
|988.657-1007.01
|951.045
|995.271-1013.624
|975.051
|998.419-1016.773
|982.891
|997.833
|-
|-
| |13
|13
|E
|E
| |Eb
|Eb
|971.914
|1046.364-1066.247
|975.986
| colspan="2" |1050.004-1073.794
|987.749
|1055.32-1075.202
|1021.288
|1068.033-1087.915
|1030.2985
|1071.045-1090.928
|1056.306
|1078.21-1098.092
|1064.799
|1081.6215-1101.504-
|1080.986
|-
|-
|14
|14
|F\\
|F\\
|D#v/Eb^
|D#v/Eb^
|1046.877
|1126.854-1148.266
|1051.062
| colspan="2" |1130.81-1156.394
|1063.728
|1136.498-1157.91
|1099.849
|1150.189-1171.601
|1109.552
|1153.4335-1174.845
|1137.56
|1161.149-1182.561
|1146.706
|1164.823-1186.235
|1164.139
|-
|-
|15
|15
|Epv/F\\^
|Epv/F\\^
|D#
|D#
|1121.439
|1207.344-1230.285
|1126.138
| colspan="2" |1211.583-1238.9935
|1139.71
|1217.6765-1240.617
|1178.409
|1232.345-1255.2865
|1188.806
|1235.822-1258.762
|1218.814
|1244.088-1267.03
|1228.614
|1248.025-1270.966
|1247.292
|-
|-
|16
|16
|Ep
|Ep
|E
|E
|1196.202
|1287.833-1312.304
|1201.214
| colspan="2" |1292.3545-1321.593
|1215.69
|1298.855-1323.3255
|1256.97
|1314.502-1338.972
|1268.06
|1318.21-1342.68
|1300.0685
|1327.028-1351.498
|1310.521
|1331.226-1355.697
|1330.445
|-
|-
|17
|17
| colspan="2" |F
| colspan="2" |F
|1270.965
|1368.322-1394.322
|1276.29
| colspan="2" |1373.127-1404.193
|1291.672
|1380.033-1406.033
|1335.53
|1396.658-1422.658
|1347.313
|1400.598-1426.598
|1381.322
|1409.967-1435.967
|1392.429
|1414.428-1440.428
|1413.598
|}
|}
[[Category:edIX]]
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