User:Moremajorthanmajor/17edIX: Difference between revisions

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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="3" |Degrees
|+
! colspan="2" rowspan="3" |Octatonic
!Nonet
! colspan="4" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
!Period
! colspan="9" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
!Notes
! colspan="3" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
|-
|-
! rowspan="2" |Absolute Minimum
|1/1
! rowspan="2" |Minimum
|''70.588''
! rowspan="2" |Median
|Soft Phrygian mode begins
! rowspan="2" |Maximum
! colspan="3" |Intense Phrygian
! colspan="3" |Intense Phrygian-Soft Aeolian
! colspan="3" |Soft Aeolian
! rowspan="2" |Minimum
! rowspan="2" |Median
! rowspan="2" |Maximum
|-
|-
! |Minimum
|25\24
!Median
|''73.529''
!Maximum
|
!Minimum
!Median
!Maximum
!Minimum
!Median
!Maximum
|-
|-
| |1
|24\23
|G
|73.657
| |Gb
|
|70.588
|74.622
|75.294
| colspan="2" |77.647
|78.019
| colspan="2" |78.431
|78.893
| colspan="2" |79.412
|80
| colspan="2" |80.672
|82.353
|84.706
|-
|-
| |2
|23\22
|A\\
|73.797
| |F#v/Gb^
|
|141.1765
|149.244
|150.588
| colspan="2" |155.294
|156.037
| colspan="2" |156.863
|157.7855
| colspan="2" |158.8235
|160
| colspan="2" |161.3445
|164.706
|169.412
|-
|-
| |3
|22\21
|Gpv/A\\^
|73.950
| |F#
|Soft Phrygian mode ends, Thirdtone Phrygian mode begins
|211.765
|213.8655
|225.882
| colspan="2" |232.941
|234.056
| colspan="2" |235.294
|236.678
| colspan="2" |238.235
|240
| colspan="2" |242.017
|247.059
|254.118
|-
|-
| |4
| 21\20
|Gp
|74.118
| |G
|
|282.353
|298.487
|301.1765
| colspan="2" |310.588
|312.074
| colspan="2" |313.7255
|315.571
| colspan="2" |317.647
|320
| colspan="2" |322.689
|329.412
|338.8235
|-
|-
| |5
|20\19
| colspan="2" |A
|74.303
|352.941
|
|373.109
|376.471
| colspan="2" |387.235
|390.093
| colspan="2" |392.156
|394.464
| colspan="2" |397.058
|400
| colspan="2" |403.361
|411.765
|423.529
|-
|-
| |6
|19\18
| colspan="2" |B
|74.510
|423.529
|
|447.731
|451.765
| colspan="2" |464.822
|468.1115
| colspan="2" |470.588
|473.356
| colspan="2" |476.471
|480
| colspan="2" |484.034
|494.118
|508.235
|-
|-
| |7
|37\35
|H
|74.622
| |Hb
|
|494.118
|522.353
|527.059
| colspan="2" |542.529
|546.13
| colspan="2" |549.02
|552.249
| colspan="2" |555.882
|560
| colspan="2" |564.706
|576.471
|592.941
|-
|-
| |8
|18\17
|C\\
|74.740
| |B#v/Hb^
|
|564.706
|596.975
|602.353
| colspan="2" |620.1765
|624.149
| colspan="2" |627.451
|651.142
| colspan="2" |635.294
|640
| colspan="2" |645.378
|658.8235
|677.647
|-
|-
| |9
|17\16
|Hpv/C\\^
|75.000
| |B#
|
|635.294
|671.597
|677.647
| colspan="2" |697.8235
|702.167
| colspan="2" |705.882
|710.035
| colspan="2" |714.706
|720
| colspan="2" |726.05
|741.1765
|762.653
|-
|-
| |10
|16\15
|Hp
|75.294
| |H
|Thirdtone Phrygian mode ends
|705.882
|746.2185
|752.941
| colspan="2" |777.471
|780.186
| colspan="2" |784.314
|788.927
| colspan="2" |794.118
|800
| colspan="2" |806.723
|823.529
|847.059
|-
|-
| |11
|15\14
| colspan="2" |C
|75.630
|776.471
|Semitone Phrygian mode begins
|820.84
|828.235
| colspan="2" |855.118
|858.204
| colspan="2" |862.745
|867.82
| colspan="2" |873.529
|880
| colspan="2" |887.395
|905.882
|931.765
|-
|-
| |12
|14\13
| colspan="2" |D
|76.018
|847.059
|
|895.462
|903.529
| colspan="2" |932.765
|936.223
| colspan="2" |941.1765
|946.713
| colspan="2" |952.941
|960
| colspan="2" |968.067
|988.235
|1016.471
|-
|-
| |13
|27\25
|E
|76.235
| |Eb
|
|917.647
|970.084
|978.8235
| colspan="2" |1010.412
|1014.2415
| colspan="2" |1019.607
|1025.6055
| colspan="2" |1032.353
|1040
| colspan="2" |1048.7395
|1070.588
|1101.1765
|-
|-
|14
|13\12
|F\\
|''76.471''
|D#v/Eb^
|
|988.235
|1044.706
|1054.118
| colspan="2" |1088.059
|1092.26
| colspan="2" |1098.039
|1104.598
| colspan="2" |1111.765
|1120
| colspan="2" |1129.412
|1152.941
|1185.882
|-
|-
|15
|12\11
|Epv/F\\^
|77.005
|D#
|
|1058.8235
|1119.328
|1129.412
| colspan="2" |1164.706
|1170.028
| colspan="2" |1176.471
|1183.391
| colspan="2" |1191.1765
|1200
| colspan="2" |1210.084
|1233.294
|1270.588
|-
|-
|16
|11\10
|Ep
|77.647
|E
|Semitone Phrygian mode ends, Intense Phrygian mode begins
|1129.412
|1193.95
|1204.706
| colspan="2" |1242.353
|1248.297
| colspan="2" |1254.902
|1262.284
| colspan="2" |1270.588
|1280
| colspan="2" |1290.756
|1317.647
|1355.294
|-
|-
|17
|21\19
| colspan="2" |F
| 78.019
|1200
|
|1268.571
|1280
| colspan="2" |1320
|1326.316
| colspan="2" |1333.333
|1341.1765
| colspan="2" |1350
|1360
| colspan="2" |1371.429
|1400
|1440
|}Most harmonic tunings
{| class="wikitable"
|+
! rowspan="2" |Degrees
! colspan="2" rowspan="2" |Octatonic
!Phrygian Mode (natural minor)
!Phrygian-Aeolian Mode (intermediate minor)
!Aeolian Mode (melodic/harmonic minor)
|-
|-
!15/7±13¢
|10\9
!11/5±13¢
|78.431
!9/4±13¢
|Intense Phrygian mode ends, Intense Phrygian-Soft Aeolian mode begins
|-
|-
|1
|19\17
|G
|78.893
|Gb
|
|76.85-78.379
|79.53-81.059
|81.818-83.348
|-
|-
|2
|9\8
|A\\
|''79.412''
|F#v/Gb^
|Intense Phrygian-Soft Aeolian mode ends, Soft Aeolian mode begins
|153.7-156.758
|159.059-162.118
|163.6365-166.695
|-
|-
|3
|17\15
|Gpv/A\\^
|80.000
|F#
|
|230.549-235.137
|238.589-243.177
|245.455-250.043
|-
|-
|4
|8\7
|Gp
|80.672
|G
|Soft Aeolian mode ends, Flattone Aeolian mode begins
|307.398-313.516
|318.119-324.236
|327.272-333.391
|-
|-
|5
|15\13
| colspan="2" |A
|81.448
|384.248-391.895
|
|394.648-405.295
|409.091-416.738
|-
|-
|6
|22\19
| colspan="2" |B
|81.734
|461.0975-470.274
|Flattone Aeolian mode ends, Meantone Aeolian mode begins
|477.178-486.354
|490.909-500.086
|-
|-
|7
|29\25
|H
|81.882
|Hb
|
|537.947.548.653
|556.707-567.4135
|572.728-583.4335
|-
|-
|8
|7\6
|C\\
|''82.353''
|B#v/Hb^
|Meantone Aeolian mode ends, Superpyth Intense Aeolian mode begins
|614.797-627.032
|636.237-648.473
|654.546-666.781
|-
|-
|9
|20\17
|Hpv/C\\^
|83.045
|B#
|
|691.646-705.411
|715.767-729.532
|736.364-753.087
|-
|-
|10
|13\11
|Hp
|83.422
|H
|Superpyth Intense Aeolian mode ends, Ultrapyth Intense Aeolian mode begins
|768.496-783.79
|795.297-810.591
|818.182-833.4765
|-
|-
|11
|19\16
| colspan="2" |C
|83.824
|845.345-862.169
|
|874.826-891.65
|900.001-916.824
|-
|-
|12
|6\5
| colspan="2" |D
|84.706
|922.195-940.548
|Ultrapyth Intense Aeolian mode ends
|954.356-972.709
|}Golden/Pyrite Tunings±13¢
|981.819-100.172
|-
|13
|E
|Eb
|999.0445-1018.927
|1033.886-1053.768
|1063.637-1083.519
|-
|14
|F\\
|D#v/Eb^
|1075.894-1097.306
|1113.415-1134.827
|1145.455-1166.867
|-
|15
|Epv/F\\^
|D#
|1152.744-1175.685
|1189.945-1215.876
|1227.2735-1250.215
|-
|16
|Ep
|E
|1229.593-1254.064
|1272.474-1296.945
|1309.092-1333.562
|-
|17
| colspan="2" |F
|1306.443-1332.443
|1352.004-1378.004
|1390.91-1416.91
|}
Golden Tunings


Phrygian Mode (natural minor)
{| class="wikitable"
{| class="wikitable"
! rowspan="3" |Degrees
! colspan="2" rowspan="3" |Octatonic
! colspan="2" |Soft Phrygian
! colspan="4" |Phrygian
|-
|-
!Degrees
! rowspan="2" |Min-Med
! colspan="2" |Octatonic
! rowspan="2" |Min-Max/Med-Max
!Min-Med±13¢
! colspan="2" |Thirdtone
!Min-Max±13¢
! colspan="2" |Semitone
!Med-Max±13¢
|-
!Min-Med/Min-Max
!Med-Max
!Min-Med/Min-Max
!Med-Max
|-
|-
| |1
| |1
|G
|A
| |Gb
| |Ab
|73.998-75.527
|72.944-74.474
|74.311-75.841
|73.089-74.618
|75.216-76.745
|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^
|147.996-151.055
|145.889-148.948
|148.622-151.681
|146.178-149.236
|150.432-153.491
|146.758-150.409
|148.023-151.173
|150.432-154.025
|151.501-155.2705
|-
|-
| |3
| |3
|Gpv/A\\^
|Apv/B\\^
| |F#
| |G#
|221.994-226.582
|218.833-223.4215
|222.9335-227.522
|219.266-223.855
|225.648-230.236
|220.137-225.614
|222.035-226.759
|225.648-230.037
|227.251-232.906
|-
|-
| |4
| |4
|Gp
|Ap
| |G
| |A
|295.992-302.109
|291.778-297.895
|297.245-303.362
|292.355-298.473
|300.864-306.982
|293.5155-300.819
|296.047-302.346
|300.864-308.050
|303.002-301.541
|-
|-
| |5
| |5
| colspan="2" |A
| colspan="2" |B
|369.99-377.637
|364.722-372.369
|371.556-379.203
|365.444-373.091
|376.08-383.727
|366.894-376.0235
|370.059-377.932
|376.08-385.063
|378.752-388.176
|-
|-
| |6
| |6
| colspan="2" |B
| colspan="2" |C
|443.9875-453.164
|437.6665-446.843
|445.867-455.0435
|438.533-447.709
|451.296-460.472
|440.273-451.228
|444.070-453.519
|451.296-462.075
|454.5025-465.811
|-
|-
| |7
| |7
|H
|Q
| |Hb
| |Qb
|517.985-528.691
|510.611-521.317
|520.178-530.884
|511.621-522.327
|526.512-537.218
|513.652-526.433
|518.082-529.105
|526.512-539.088
|530.253-543.447
|-
|-
| |8
| |8
|C\\
|D\\
| |B#v/Hb^
| |C#v/Qb^
|591.983-604.219
|583.555-595.791
|594.489-606.725
|584.71-596.9455
|601.728-612.963
|587.031-601.638
|592.094-604.6915
|601.728-616.101
|606.003-621.082
|-
|-
| |9
| |9
|Hpv/C\\^
|Qpv/D\\^
| |B#
| |C#
|665.981-679.746
|656.5-670.264
|668.8005-682.565
|657.799-671.564
|676.944-690.709
|660.41-676.842
|661.1055-680.278
|676.944-693.1135
|681.754-698.717
|-
|-
| |10
| |10
|Hp
|Qp
| |H
| |Q
|739.979-755.273
|729.444-744.738
|743.112-758.406
|730.888-746.182
|752.16-767.454
|733.789-752.047
|740.117-755.864
|752.16-770.126
|757.504-776.352
|-
|-
| |11
| |11
| colspan="2" |C
| colspan="2" |D
|813.977-830.801
|802.3885-819.212
|817.423-834.246
|803.9765-820.8
|827.376-844.166
|807.468-827.252
|814.129-831.451
|827.376-847.139
|833.255-853.988
|-
|-
| |12
| |12
| colspan="2" |D
| colspan="2" |E
|887.975-906.328
|875.333-893.686
|891.734-910.087
|877.065-895.418
|902.592-920.945
|880.5465-902.456
|888.141-907.037
|902.592-924.151
|909.005-931.622
|-
|-
| |13
| |13
|E
|F
| |Eb
| |Fb
|961.972-981.855
|948.277-968.16
|966.045-985.9275
|950.154-970.0365
|977.808-997.69
|953.925-977.661
|962.152-982.624
|977.808-1001.164
|984.755-1009.258
|-
|-
|14
|14
|F\\
|F\\
|D#v/Eb^
|E#v/Fb^
|1035.971-1057.383
|1021.222-1042.6335
|1040.356-1061.768
|1023.243-1044.655
|1053.024-1074.436
|1027.304-1052.866
|1036.164-1058.21
|1053.024-1078.177
|1060.506-1086.893
|-
|-
|15
|15
|Epv/F\\^
|Fpv/G\\^
|D#
|E#
|1109.969-1132.91
|1094.166-1117.107
|1114.6675-1137.609
|1096.332-1119.273
|1128.24-1151.181
|1100.683-1128.0705
|1110.176-1133.7965
|1128.24-1155.189
|1136.256-1164.5285
|-
|-
|16
|16
|Ep
|Fp
|E
|F
|1183.967-1208.437
|1167.111-1191.581
|1188.979-1213.449
|1169.42-1193.891
|1203.456-1227.926
|1174.062-1203.275
|1184.188-1209.382
|1203.456-1232.202
|1212.007-1242.164
|-
|-
|17
|17
| colspan="2" |F
| colspan="2" |G
|1257.965-1283.965
|1240.055-1266.055
|1263.29-1289.29
|1242.506-1268.509
|1278.672-1304.672
|1247.441-1278.48
|1258.199-1284.969
|1278.672-1309.2145
|1287.757-1319.799
|}
|}
Phrygian-Aeolian Mode (intermediate minor)
{| class="wikitable"
{| class="wikitable"
|-
! rowspan="2" |Degrees
! rowspan="2" |Degrees
! colspan="2" rowspan="2" |Octatonic
! colspan="4" rowspan="2" |Octatonic
! colspan="2" |Intense Phrygian
! colspan="2" |Intense Phrygian
! colspan="2" |Intense Phrygian-Soft Aeolian
! colspan="2" |Intense Phrygian-Soft Aeolian
! colspan="2" |Soft Aeolian
! colspan="2" |Soft Aeolian
|-
|-
!Min-Med/Min-Max±13¢
!Min-Med/Min-Max
!Med-Max±13¢
!Med-Max
!Min-Med/Min-Max±13¢
!Min-Med/Min-Max
!Med-Max±13¢
!Med-Max
!Min-Med/Min-Max±13¢
!Min-Med/Min-Max
!Med-Max±13¢
!Med-Max
|-
|-
| |1
|1
|G
|G
| |Gb
|Gb
|A
|Ab
|77.163-78.692
|77.163-78.692
|77.347-78.877
|77.347-78.877
Line 573: Line 344:
|79.385-80.915
|79.385-80.915
|-
|-
| |2
|2
|A\\
|A\\
| |F#v/Gb^
|F#v/Gb^
|B\\
|G#v/Ab^
|155.325-157.384
|155.325-157.384
|155.695-157.7535
|155.695-157.7535
Line 583: Line 356:
|158.772-161.83
|158.772-161.83
|-
|-
| |3
|3
|Gpv/A\\^
|Gpv/A\\^
| |F#
|F#
|Apv/B\\^
|G#
|231.488-236.076
|231.488-236.076
|232.042-236.63
|232.042-236.63
Line 593: Line 368:
|238.157-242.746
|238.157-242.746
|-
|-
| |4
|4
|Gp
|Gp
| |G
|G
|Ap
|A
|308.651-314.768
|308.651-314.768
|309.389-315.507
|309.389-315.507
Line 603: Line 380:
|317.543-323.661
|317.543-323.661
|-
|-
| |5
|5
| colspan="2" |A
| colspan="2" |A
| colspan="2" |B
|385.814-393.4605
|385.814-393.4605
|386.737-394.384
|386.737-394.384
Line 612: Line 390:
|396.929-404.576
|396.929-404.576
|-
|-
| |6
|6
| colspan="2" |B
| colspan="2" |B
| colspan="2" |C
|462.976-472.1525
|462.976-472.1525
|464.084-473.261
|464.084-473.261
Line 621: Line 400:
|476.315-485.4913
|476.315-485.4913
|-
|-
| |7
|7
|H
|H
| |Hb
|Hb
|Q
|Qb
|540.139-550.845
|540.139-550.845
|541.4315-549.423
|541.4315-549.423
Line 631: Line 412:
|555.7005-566.406
|555.7005-566.406
|-
|-
| |8
|8
|C\\
|C\\
| |B#v/Hb^
|B#v/Hb^
|D\\
|C#v/Qb^
|617.3015-629.537
|617.3015-629.537
|618.779-631.014
|618.779-631.014
Line 641: Line 424:
|635.086-647.322
|635.086-647.322
|-
|-
| |9
|9
|Hpv/C\\^
|Hpv/C\\^
| |B#
|B#
|Qpv/D\\^
|C#
|694.464-708.229
|694.464-708.229
|696.126-709.891
|696.126-709.891
Line 651: Line 436:
|714.805-728.237
|714.805-728.237
|-
|-
| |10
|10
|Hp
|Hp
| |H
|H
|Qp
|Q
|771.629-786.921
|771.629-786.921
|773.4735-788.768
|773.4735-788.768
Line 661: Line 448:
|793.858-809.152
|793.858-809.152
|-
|-
| |11
|11
| colspan="2" |C
| colspan="2" |C
| colspan="2" |D
|848.79-865.613
|848.79-865.613
|865.821-867.644
|865.821-867.644
Line 670: Line 458:
|873.243-890.067
|873.243-890.067
|-
|-
| |12
|12
| colspan="2" |D
| colspan="2" |D
| colspan="2" |E
|925.952-944.305
|925.952-944.305
|928.168-946.521
|928.168-946.521
Line 679: Line 468:
|952.692-970.982
|952.692-970.982
|-
|-
| |13
|13
|E
|E
| |Eb
|Eb
|F
|Fb
|1003.115-1022.997
|1003.115-1022.997
|1005.516-1025.398
|1005.516-1025.398
Line 692: Line 483:
|F\\
|F\\
|D#v/Eb^
|D#v/Eb^
|F\\
|E#v/Fb^
|1080.278-1101.689
|1080.278-1101.689
|1082.863-1104.275
|1082.863-1104.275
Line 702: Line 495:
|Epv/F\\^
|Epv/F\\^
|D#
|D#
|Fpv/G\\^
|E#
|1157.44-1180.381
|1157.44-1180.381
|1160.21-1183.151
|1160.21-1183.151
Line 712: Line 507:
|Ep
|Ep
|E
|E
|Fp
|F
|1234.603-1259.0735
|1234.603-1259.0735
|1237.558-1262.028
|1237.558-1262.028
Line 721: Line 518:
|17
|17
| colspan="2" |F
| colspan="2" |F
| colspan="2" |G
|1311.767-1337.767
|1311.767-1337.767
|1314.905-1340.905
|1314.905-1340.905
Line 728: Line 526:
|1349.558-1375.558
|1349.558-1375.558
|}
|}
Aeolian Mode (melodic/harmonic minor)
{| class="wikitable"
{| class="wikitable"
! rowspan="3" |Degrees
! colspan="2" rowspan="3" |Octatonic
! colspan="4" |Aeolian
! colspan="4" |Intense Aeolian
|-
|-
!Degrees
! colspan="2" |Flattone
! colspan="2" |Octatonic
! colspan="2" |Meantone
!Min-Med±13¢
! colspan="2" |Superpyth
!Min-Max±13¢
! colspan="2" |Ultrapyth
!Med-Max±13¢
|-
!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
|1
Line 741: Line 550:
|Gb
|Gb
|80.49-82.019
|80.49-82.019
|81.143-82.672
| colspan="2" |80.772-82.6
|81.178-82.707
|82.156-83.686
|82.388-83.9175
|82.388-83.9175
|82.939-84.469
|83.202-84.731
|-
|-
|2
|2
Line 748: Line 561:
|F#v/Gb^
|F#v/Gb^
|160.979-164.038
|160.979-164.038
|162.286-165.345
| colspan="2" |161.544-165.199
|162.356-165.416
|164.127-167.31715
|164.776-167.835
|164.776-167.835
|165.8785-168.937
|166.403-169.462
|-
|-
|3
|3
Line 755: Line 572:
|F#
|F#
|241.469-246.057
|241.469-246.057
|243.429-248.017
| colspan="2" |242.316-247.799
|243.535-248.1235
|246.469-251.057
|247.164-251.753
|247.164-251.753
|248.818-253.405
|249.605-254.193
|-
|-
|4
|4
Line 762: Line 583:
|G
|G
|321.958-328.076
|321.958-328.076
|324.5715-330.689
| colspan="2" |323.089-330.398
|324.714-330.831
|328.625-334.743
|329.552-335.67
|329.552-335.67
|331.757-337.875
|332.807-338.324
|-
|-
|5
|5
| colspan="2" |A
| colspan="2" |A
|402.448-410.095
|402.448-410.095
|405.714-413.3615
| colspan="2" |403.861-412.998
|405.892-413.539
|410.782-418.429
|411.9405-419.588
|411.9405-419.588
|414.696-422.343
|416.008-423.655
|-
|-
|6
|6
| colspan="2" |B
| colspan="2" |B
|482.937-492.114
|482.937-492.114
|486.857-496.034
| colspan="2" |484.633-495.597
|487.071-496.247
|492.938-502-115
|494.329-503.505
|494.329-503.505
|497.635-506.812
|499.21-508.386
|-
|-
|7
|7
Line 781: Line 614:
|Hb
|Hb
|563.427-574.133
|563.427-574.133
|568-578.716
| colspan="2" |565.405-578.197
|568.249-578.955
|575.0945-585.8
|576.717-587.423
|576.717-587.423
|580.575-591.2805
|582.416-593.117
|-
|-
|8
|8
Line 788: Line 625:
|B#v/Hb^
|B#v/Hb^
|643.917-656.152
|643.917-656.152
|649.143-661.378
| colspan="2" |647.177-660.797
|649.4275-661.663
|657.251-669.486
|659.105-671.34
|659.105-671.34
|663.514-675.749
|665.613-677.8485
|-
|-
|9
|9
Line 795: Line 636:
|B#
|B#
|724.406-738.171
|724.406-738.171
|730.286-744.051
| colspan="2" |726.9495-743.396
|730.606-744.371
|739.407-753.172
|741.493-755.258
|741.493-755.258
|746.453-760.218
|748.815-762.58
|-
|-
|10
|10
Line 802: Line 647:
|H
|H
|804.896-820.19
|804.896-820.19
|811.429-826.723
| colspan="2" |807.722-825.996
|811.784-827.0785
|821.5635-836.858
|823.881-839.175
|823.881-839.175
|829.392-844.686
|832.0165-847.311
|-
|-
|11
|11
|C
| colspan="2" |C
|C
|885.385-902.209
|885.385-902.209
|892.572-909.395
| colspan="2" |888.494-908.595
|892.963-909.7886
|903.72-920.543
|906.269-923.093
|906.269-923.093
|912.331-929.155
|915.218-932.041
|-
|-
|12
|12
|D
| colspan="2" |D
|D
|965.875-984.228
|965.875-984.228
|973.715-992.0675
| colspan="2" |969.266-991.195
|974.141-992.494
|985.876-1004.229
|988.657-1007.01
|988.657-1007.01
|995.271-1013.624
|998.419-1016.773
|-
|-
|13
|13
Line 823: Line 678:
|Eb
|Eb
|1046.364-1066.247
|1046.364-1066.247
|1054.857-1074.74
| colspan="2" |1050.004-1073.794
|1055.32-1075.202
|1068.033-1087.915
|1071.045-1090.928
|1071.045-1090.928
|1078.21-1098.092
|1081.6215-1101.504-
|-
|-
|14
|14
Line 830: Line 689:
|D#v/Eb^
|D#v/Eb^
|1126.854-1148.266
|1126.854-1148.266
|1136-1157.412
| colspan="2" |1130.81-1156.394
|1136.498-1157.91
|1150.189-1171.601
|1153.4335-1174.845
|1153.4335-1174.845
|1161.149-1182.561
|1164.823-1186.235
|-
|-
|15
|15
Line 837: Line 700:
|D#
|D#
|1207.344-1230.285
|1207.344-1230.285
|1217.143-1240.084
| colspan="2" |1211.583-1238.9935
|1217.6765-1240.617
|1232.345-1255.2865
|1235.822-1258.762
|1235.822-1258.762
|1244.088-1267.03
|1248.025-1270.966
|-
|-
|16
|16
Line 844: Line 711:
|E
|E
|1287.833-1312.304
|1287.833-1312.304
|1298.286-1332.757
| colspan="2" |1292.3545-1321.593
|1298.855-1323.3255
|1314.502-1338.972
|1318.21-1342.68
|1318.21-1342.68
|1327.028-1351.498
|1331.226-1355.697
|-
|-
|17
|17
| colspan="2" |F
| colspan="2" |F
|1368.322-1394.322
|1368.322-1394.322
|1379.429-1405.429
| colspan="2" |1373.127-1404.193
|1380.033-1406.033
|1396.658-1422.658
|1400.598-1426.598
|1400.598-1426.598
|1409.967-1435.967
|1414.428-1440.428
|}
|}


[[Category:edIX]]
[[Category:edIX]]

Latest revision as of 03:27, 27 November 2024

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 Chlorine temperament.

Intervals

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¢

Degrees Octatonic Soft Phrygian Phrygian
Min-Med Min-Max/Med-Max Thirdtone 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 B\\ G#v/Ab^ 145.889-148.948 146.178-149.236 146.758-150.409 148.023-151.173 150.432-154.025 151.501-155.2705
3 Apv/B\\^ G# 218.833-223.4215 219.266-223.855 220.137-225.614 222.035-226.759 225.648-230.037 227.251-232.906
4 Ap A 291.778-297.895 292.355-298.473 293.5155-300.819 296.047-302.346 300.864-308.050 303.002-301.541
5 B 364.722-372.369 365.444-373.091 366.894-376.0235 370.059-377.932 376.08-385.063 378.752-388.176
6 C 437.6665-446.843 438.533-447.709 440.273-451.228 444.070-453.519 451.296-462.075 454.5025-465.811
7 Q Qb 510.611-521.317 511.621-522.327 513.652-526.433 518.082-529.105 526.512-539.088 530.253-543.447
8 D\\ C#v/Qb^ 583.555-595.791 584.71-596.9455 587.031-601.638 592.094-604.6915 601.728-616.101 606.003-621.082
9 Qpv/D\\^ C# 656.5-670.264 657.799-671.564 660.41-676.842 661.1055-680.278 676.944-693.1135 681.754-698.717
10 Qp Q 729.444-744.738 730.888-746.182 733.789-752.047 740.117-755.864 752.16-770.126 757.504-776.352
11 D 802.3885-819.212 803.9765-820.8 807.468-827.252 814.129-831.451 827.376-847.139 833.255-853.988
12 E 875.333-893.686 877.065-895.418 880.5465-902.456 888.141-907.037 902.592-924.151 909.005-931.622
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 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
Degrees Octatonic Intense Phrygian Intense Phrygian-Soft Aeolian 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 A 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 B 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 C 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 D 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 F 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
Degrees Octatonic Aeolian Intense Aeolian
Flattone Meantone Superpyth 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 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^ 160.979-164.038 161.544-165.199 162.356-165.416 164.127-167.31715 164.776-167.835 165.8785-168.937 166.403-169.462
3 Gpv/A\\^ F# 241.469-246.057 242.316-247.799 243.535-248.1235 246.469-251.057 247.164-251.753 248.818-253.405 249.605-254.193
4 Gp G 321.958-328.076 323.089-330.398 324.714-330.831 328.625-334.743 329.552-335.67 331.757-337.875 332.807-338.324
5 A 402.448-410.095 403.861-412.998 405.892-413.539 410.782-418.429 411.9405-419.588 414.696-422.343 416.008-423.655
6 B 482.937-492.114 484.633-495.597 487.071-496.247 492.938-502-115 494.329-503.505 497.635-506.812 499.21-508.386
7 H Hb 563.427-574.133 565.405-578.197 568.249-578.955 575.0945-585.8 576.717-587.423 580.575-591.2805 582.416-593.117
8 C\\ B#v/Hb^ 643.917-656.152 647.177-660.797 649.4275-661.663 657.251-669.486 659.105-671.34 663.514-675.749 665.613-677.8485
9 Hpv/C\\^ B# 724.406-738.171 726.9495-743.396 730.606-744.371 739.407-753.172 741.493-755.258 746.453-760.218 748.815-762.58
10 Hp H 804.896-820.19 807.722-825.996 811.784-827.0785 821.5635-836.858 823.881-839.175 829.392-844.686 832.0165-847.311
11 C 885.385-902.209 888.494-908.595 892.963-909.7886 903.72-920.543 906.269-923.093 912.331-929.155 915.218-932.041
12 D 965.875-984.228 969.266-991.195 974.141-992.494 985.876-1004.229 988.657-1007.01 995.271-1013.624 998.419-1016.773
13 E Eb 1046.364-1066.247 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 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 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 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 F 1368.322-1394.322 1373.127-1404.193 1380.033-1406.033 1396.658-1422.658 1400.598-1426.598 1409.967-1435.967 1414.428-1440.428
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