User:Moremajorthanmajor/17edIX: Difference between revisions

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==Intervals==
==Intervals==
{| class="wikitable"
{| class="wikitable"
! rowspan="3" |Degrees
! rowspan="4" |Degrees
! colspan="2" rowspan="3" |Octatonic
! colspan="3" rowspan="3" |Octatonic
! colspan="3" |Soft Phrygian
! colspan="3" |Soft Phrygian
! colspan="6" |Phrygian
! colspan="6" |Phrygian
|-
|-
! rowspan="3" |Minimum-comma
! rowspan="3" |Median
! rowspan="3" |Maximum+comma
! colspan="3" |Thirdtone
! colspan="3" |Semitone
|-
! rowspan="2" |Minimum-comma
! rowspan="2" |Median
! rowspan="2" |Maximum+comma
! rowspan="2" |Minimum-comma
! rowspan="2" |Minimum-comma
! rowspan="2" |Median
! rowspan="2" |Median
! rowspan="2" |Maximum+comma
! rowspan="2" |Maximum+comma
! colspan="3" |Thirdtone
! colspan="3" |Semitone
|-
|-
!Minimum-comma
! colspan="2" |Natural
!Median
!Subset of 34edn
!Maximum+comma
!Minimum-comma
!Median
!Maximum+comma
|-
|-
| |1
| |1
|A
|A
| |Ab
| |Ab
|68.8235-''70.588''
|Ab
|68.235-''70.588''
|73.797
|73.797
| colspan="2" |72.185-75.714
| colspan="2" |71.597-76.3025
|74.51-74.622
|74.51-74.622
| colspan="2" |73.529-77.395
| colspan="2" |72.941-77.983
|76.235-''76.471''
|76.235-''76.471''
|77.647-79.412
|77.647-80
|-
|-
| |2
| |2
|B\\
|B\\
| |G#v/Ab^
| |G#v/Ab^
|137.647-''141.1765''
|G#^
|136.471-''141.1765''
|147.594
|147.594
| colspan="2" |144.37-151.429
| colspan="2" |143.193-152.605
|149.02-149.244
|149.02-149.244
| colspan="2" |147.059-154.79
| colspan="2" |145.882-155.966
|152.471-''152.941''
|152.471-''152.941''
|155.294-158.8235
|155.294-160
|-
|-
| |3
| |3
|Apv/B\\^
|Apv/B\\^
| |G#
| |G#
|206.471-''211.765''
|Bbv
|204.706-''211.765''
|221.39
|221.39
| colspan="2" |216.555-227.143
| colspan="2" |214.79-228.908
|223.529-213.8655
|223.529-213.8655
| colspan="2" |220.588-232.185
| colspan="2" |218.8235-233.95
|228.706-''229.1765''
|228.706-''229.1765''
|232.941-238.235
|232.941-240
|-
|-
| |4
| |4
|Ap
|Ap
| |A
| |A
|275.294-''282.353''
|Bb
|272.941-''282.353''
|295.187
|295.187
| colspan="2" |288.7395-302.857
| colspan="2" |286.386-305.21
|298.039-298.487
|298.039-298.487
| colspan="2" |294.118-209.58
| colspan="2" |291.765-311.933
|304.941-''305.647''
|304.941-''305.647''
|310.588-317.647
|310.588-320
|-
|-
| |5
| |5
| colspan="2" |B
| colspan="3" |B
|344.118-''352.941''
|341.1765-''352.941''
|368.984
|368.984
| colspan="2" |360.924-378.571
| colspan="2" |357.983-381.513
|372.549-373.109
|372.549-373.109
| colspan="2" |367.647-386.975
| colspan="2" |364.706-389.916
|381.1765-''382.118''
|381.1765-''382.118''
|387.235-397.058
|387.235-400
|-
|-
| |6
| |6
| colspan="2" |C
| colspan="2" |C
|412.941-''423.529''
|Cb
|409.412-''423.529''
|442.781
|442.781
| colspan="2" |433.109-454.286
| colspan="2" |429.58-457.815
|447.059-447.731
|447.059-447.731
| colspan="2" |431.1765-464.37
| colspan="2" |437.647-467.899
|457.412-''458.588''
|457.412-''458.588''
|464.882-476.471
|464.882-480
|-
|-
| |7
| |7
|Q
|Q
| |Qb
| |Qb
|481.765-''494.118''
|B#^
|477.647-''494.118''
|516.5775
|516.5775
| colspan="2" |505.294-530
| colspan="2" |501.1765-534.118
|521.569-522.353
|521.569-522.353
| colspan="2" |504.706-541.765
| colspan="2" |510.588-545.882
|533.647-''535.294''
|533.647-''535.294''
|542.529-555.882
|542.529-560
|-
|-
| |8
| |8
|D\\
|D\\
| |C#v/Qb^
| |C#v/Qb^
|550.588-''564.706''
|C^
|545.882-''564.706''
|590.374
|590.374
| colspan="2" |577.479-605.714
| colspan="2" |572.773-610.42
|596.078-596.975
|596.078-596.975
| colspan="2" |578.235-619.16
| colspan="2" |583.529-623.8655
|609.882-''611.235''
|609.882-''611.235''
|620.1765-635.294
|620.1765-640
|-
|-
| |9
| |9
|Qpv/D\\^
|Qpv/D\\^
| |C#
| |C#
|619.412-''635.294''
|Q^
|614.118-''635.294''
|664.171
|664.171
| colspan="2" |946.664-681.429
| colspan="2" |644.37-686.723
|670.588-671.597
|670.588-671.597
| colspan="2" |651.765-696.555
| colspan="2" |656.471-701.849
|686.118-''688.765''
|686.118-''688.765''
|697.8235-714.706
|697.8235-720
|-
|-
| |10
| |10
|Qp
|Qp
| |Q
| |Q
|688.235-''705.882''
|Db
|682.353-''705.882''
|737.97
|737.97
| colspan="2" |721.849-757.143
| colspan="2" |715.966-763.025
|745.098-746.2185
|745.098-746.2185
| colspan="2" |745.294-773.95
| colspan="2" |729.412-779.832
|762.353-''764.706''
|762.353-''764.706''
|777.471-794.118
|777.471-800
|-
|-
| |11
| |11
| colspan="2" |D
| colspan="3" |D
|757.059-''776.471''
|750.588-''776.471''
|811.765
|811.765
| colspan="2" |794.034-832.857
| colspan="2" |787.563-839.328
|819.608-820.84
|819.608-820.84
| colspan="2" |808.8235-851.3445
| colspan="2" |802.353-857.815
|838.588-''841.412''
|838.588-''841.412''
|855.118-873.529
|855.118-880
|-
|-
| |12
| |12
| colspan="2" |E
| colspan="2" |E
|825.882-''847.059''
|Eb
|818.8235-''847.059''
|885.5616
|885.5616
| colspan="2" |866.2185-908.571
| colspan="2" |859.16-915.63
|894.118-895.462
|894.118-895.462
| colspan="2" |882.353-928.7395
| colspan="2" |875.294-935.798
|914.8235-''917.882''
|914.8235-''917.882''
|932.765-952.941
|932.765-960
|-
|-
| |13
| |13
|F
|F
| |Fb
| |Fb
|894.706-''917.647''
|D#^
|887.059-''917.647''
|959.358
|959.358
| colspan="2" |938.403-978.286
| colspan="2" |930.756-991.933
|968.6275-970.084
|968.6275-970.084
| colspan="2" |955.882-1006.1345
| colspan="2" |948.235-1013.7815
|991.059-''994.353''
|991.059-''994.353''
|1010.412-1032.353
|1010.412-1040
|-
|-
|14
|14
|F\\
|F\\
|E#v/Fb^
|E#v/Fb^
|963.529-''988.235''
|Fbv
|955.294-''988.235''
|1033.155
|1033.155
| colspan="2" |1010.588-1060
| colspan="2" |1002.353-1068.235
|1043.137-1044.706
|1043.137-1044.706
| colspan="2" |1029.412-1083.529
| colspan="2" |1021.1765-1091.765
|1067.294-''1080.8235''
|1067.294-''1080.8235''
|1088.059-1111.765
|1088.059-1120
|-
|-
|15
|15
|Fpv/G\\^
|Fpv/G\\^
|E#
|E#
|1031.353-''1058.8235''
|Fb
|1023.529-''1058.8235''
|1106.952
|1106.952
| colspan="2" |1082.773-1135.714
| colspan="2" |1073.95-1144.538
|1117.647-1119.328
|1117.647-1119.328
| colspan="2" |1102.941-1160.924
| colspan="2" |1094.118-1169.747
|1143.529-''1147.059''
|1143.529-''1147.059''
|1164.706-1191.1765
|1164.706-1200
|-
|-
|16
|16
|Fp
|Fp
|F
| colspan="2" |F
|1101.1765-''1129.412''
|1091.765-''1129.412''
|1180.749
|1180.749
| colspan="2" |1154.958-1211.429
| colspan="2" |1145.546-1220.84
|1192.156-1193.95
|1192.156-1193.95
| colspan="2" |1176.471-1238.319
| colspan="2" |1167.059-1247.731
|1219.765-''1223.529''
|1219.765-''1223.529''
|1242.353-1270.588
|1242.353-1280
|-
|-
|17
|17
| colspan="2" |G
| colspan="3" |G
|1170-''1200''
|1160-''1200''
|1254.5455
|1254.5455
| colspan="2" |1227.143-1287.143
| colspan="2" |1217.143-1297.143
|1266.667-1268.571
|1266.667-1268.571
| colspan="2" |1250-1315.714
| colspan="2" |1240-1325.714
|1296-''1300''
|1296-''1300''
|1320-1350
|1320-1360
|}
|}
{| class="wikitable"
{| class="wikitable"
|-
|-
! rowspan="2" |Degrees
! rowspan="3" |Degrees
! colspan="4" rowspan="2" |Octatonic
! colspan="6" rowspan="2" |Octatonic
! colspan="3" |Intense Phrygian
! colspan="3" |Intense Phrygian
! colspan="3" |Intense Phrygian-Soft Aeolian
! colspan="3" |Intense Phrygian-Soft Aeolian
! colspan="5" |Soft Aeolian
! colspan="4" |Soft Aeolian
|-
|-
!Minimum-comma
! rowspan="2" |Minimum-comma
!Median
! rowspan="2" |Median
!Maximum+comma
! rowspan="2" |Maximum+comma
!Minimum-comma
! rowspan="2" |Minimum-comma
!Median
! rowspan="2" |Median
!Maximum+comma
! rowspan="2" |Maximum+comma
!Minimum-comma
! rowspan="2" |Minimum-comma
! colspan="2" |''r¢''
! rowspan="2" |''r¢''
!Median
! rowspan="2" |Median
!Maximum+comma
! rowspan="2" |Maximum+comma
|-
! colspan="4" |Natural
! colspan="2" |Subset of 34edn
|-
|-
|1
|1
Line 227: Line 246:
|A
|A
|Ab
|Ab
|75.8235-77.647
|Gb
|Ab
|75.294-77.647
|78.019
|78.019
| colspan="2" |76.667-80.196
| colspan="2" |76.078-80.784
|78.893
|78.893
| colspan="2" |77.647-81.1765
| colspan="2" |77.059-81.765
| colspan="2" |''79.412''
|''79.412''
|80
|80
|80.672-82.437
|80.672-83.025
|-
|-
|2
|2
Line 241: Line 262:
|B\\
|B\\
|G#v/Ab^
|G#v/Ab^
|151.647-155.294
|F#^
|G#^
|150.588-155.294
|156.037
|156.037
| colspan="2" |153.333-160.392
| colspan="2" |152.157-161.567
|157.7855
|157.7855
| colspan="2" |155.294-162.353
| colspan="2" |154.118-163.529
| colspan="2" |''158.8235''
|''158.8235''
|160
|160
|161.3445-164.874
|161.3445-166.05
|-
|-
|3
|3
Line 255: Line 278:
|Apv/B\\^
|Apv/B\\^
|G#
|G#
|227.471-232.941
|Abv
|Bbv
|225.882-232.941
|234.056
|234.056
| colspan="2" |230-240.588
| colspan="2" |228.235-242.353
|236.678
|236.678
| colspan="2" |232.941-243.529
| colspan="2" |231.1765-245.294
| colspan="2" |''238.235''
|''238.235''
|240
|240
|242.017-247.311
|242.017-249.076
|-
|-
|4
|4
Line 269: Line 294:
|Ap
|Ap
|A
|A
|303.294-310.588
|Ab
|Bb
|301.1765-310.588
|312.074
|312.074
| colspan="2" |306.667-320.784
| colspan="2" |304.314-323.137
|315.571
|315.571
| colspan="2" |310.588-324.706
| colspan="2" |308.235-327.059
| colspan="2" |''317.647''
|''317.647''
|320
|320
|322.689-329.748
|322.689-332.101
|-
|-
|5
|5
| colspan="2" |A
| colspan="2" |A
| colspan="2" |B
| colspan="2" |B
|379.118-387.235
|A
|B
|376.471-387.235
|390.093
|390.093
| colspan="2" |383.333-400.98
| colspan="2" |380.392-403.922
|394.464
|394.464
| colspan="2" |387.235-405.882
| colspan="2" |385.294-408.8235
| colspan="2" |''397.058''
|''397.058''
|400
|400
|403.361-412.185
|403.361-415.126
|-
|-
|6
|6
| colspan="2" |B
| colspan="2" |B
| colspan="2" |C
| colspan="2" |C
|454.941-464.822
|Bb
|Cb
|451.765-464.822
|468.1115
|468.1115
| colspan="2" |460-481.1765
| colspan="2" |456.471-484.706
|473.356
|473.356
| colspan="2" |464.882-487.059
| colspan="2" |462.353-490.588
| colspan="2" |''476.471''
|''476.471''
|480
|480
|484.034-494.622
|484.034-498.151
|-
|-
|7
|7
Line 307: Line 338:
|Q
|Q
|Qb
|Qb
|530.765-542.529
|A#^
|B#^
|527.059-542.529
|546.13
|546.13
| colspan="2" |536.667-561.3725
| colspan="2" |532.549-565.49
|552.249
|552.249
| colspan="2" |542.529-568.235
| colspan="2" |539.412-572.353
| colspan="2" |''555.882''
|''555.882''
|560
|560
|564.706-577.059
|564.706-581.1765
|-
|-
|8
|8
Line 321: Line 354:
|D\\
|D\\
|C#v/Qb^
|C#v/Qb^
|606.588-620.1765
|B^
|C^
|602.353-620.1765
|624.149
|624.149
| colspan="2" |613.333-641.569
| colspan="2" |608.6275-646.2745
|651.142
|651.142
| colspan="2" |620.1765-649.412
| colspan="2" |616.471-654.118
| colspan="2" |''635.294''
|''635.294''
|640
|640
|645.378-659.496
|645.378-664.202
|-
|-
|9
|9
Line 335: Line 370:
|Qpv/D\\^
|Qpv/D\\^
|C#
|C#
|683.412-697.8235
|H^
|Q^
|677.647-697.8235
|702.167
|702.167
| colspan="2" |690-721.765
| colspan="2" |684.706-727.059
|710.035
|710.035
| colspan="2" |697.8235-730.588
| colspan="2" |693.529-735.882
| colspan="2" |''714.706''
|''714.706''
|720
|720
|726.05-741.932
|726.05-747.227
|-
|-
|10
|10
Line 349: Line 386:
|Qp
|Qp
|Q
|Q
|759.235-777.471
|Cb
|Db
|752.353-777.471
|780.186
|780.186
| colspan="2" |766.667-801.961
| colspan="2" |760.784-807.843
|788.927
|788.927
| colspan="2" |777.471-811.765
| colspan="2" |770.588-817.647
| colspan="2" |''794.118''
|''794.118''
|800
|800
|806.723-824.37
|806.723-830.252
|-
|-
|11
|11
| colspan="2" |C
| colspan="2" |C
| colspan="2" |D
| colspan="2" |D
|835.059-855.118
|C
|D
|828.235-855.118
|858.204
|858.204
| colspan="2" |843.333-882.157
| colspan="2" |836.862-888.6275
|867.82
|867.82
| colspan="2" |855.118-892.941
| colspan="2" |847.647-899.412
| colspan="2" |''873.529''
|''873.529''
|880
|880
|887.395-906.807
|887.395-913.277
|-
|-
|12
|12
| colspan="2" |D
| colspan="2" |D
| colspan="2" |E
| colspan="2" |E
|910.882-932.765
|Db
|Eb
|903.529-932.765
|936.223
|936.223
| colspan="2" |920-962.353
| colspan="2" |912.941-968.412
|946.713
|946.713
| colspan="2" |932.765-974.118
| colspan="2" |924.706-981.1765
| colspan="2" |''952.941''
|''952.941''
|960
|960
|968.067-989.244
|968.067-996.3025
|-
|-
|13
|13
Line 387: Line 430:
|F
|F
|Fb
|Fb
|986.706-1010.412
|C#^
|D#^
|978.8235-1010.412
|1014.2415
|1014.2415
| colspan="2" |996.667-1042.549
| colspan="2" |989.02-1050.196
|1025.6055
|1025.6055
| colspan="2" |1010.412-1055.294
| colspan="2" |1001.765-1062.941
| colspan="2" |''1032.353''
|''1032.353''
|1040
|1040
|1048.7395-1071.681
|1048.7395-1079.328
|-
|-
|14
|14
Line 401: Line 446:
|F\\
|F\\
|E#v/Fb^
|E#v/Fb^
|1062.529-1088.059
|Ebv
|Fbv
|1055.118-1088.059
|1092.26
|1092.26
| colspan="2" |1073.333-1122.745
| colspan="2" |1065.098-1130.98
|1104.598
|1104.598
| colspan="2" |1088.059-1136.429
| colspan="2" |1078.8235-1144.706
| colspan="2" |''1111.765''
|''1111.765''
|1120
|1120
|1129.412-1154.118
|1129.412-1162.353
|-
|-
|15
|15
Line 415: Line 462:
|Fpv/G\\^
|Fpv/G\\^
|E#
|E#
|1138.353-1164.706
|Eb
|Fb
|1129.412-1164.706
|1170.028
|1170.028
| colspan="2" |1150-1202.941
| colspan="2" |1141.1765-1210.765
|1183.391
|1183.391
| colspan="2" |1164.706-1217.647
| colspan="2" |1155.882-1226.471
| colspan="2" |''1191.1765''
|''1191.1765''
|1200
|1200
|1210.084-1236.555
|1210.084-1245.378
|-
|-
|16
|16
Line 429: Line 478:
|Fp
|Fp
|F
|F
|1214.1765-1242.353
|E
|F
|1204.706-1242.353
|1248.297
|1248.297
| colspan="2" |1226.667-1283.137
| colspan="2" |1217.255-1292.549
|1262.284
|1262.284
| colspan="2" |1242.353-1288.8235
| colspan="2" |1232.941-1308.235
| colspan="2" |''1270.588''
|''1270.588''
|1280
|1280
|1290.756-1318.992
|1290.756-1328.403
|-
|-
|17
|17
| colspan="2" |F
| colspan="2" |F
| colspan="2" |G
| colspan="2" |G
|1290-1320
|F
|G
|1280-1320
|1326.316
|1326.316
| colspan="2" |1303.333-1363.333
| colspan="2" |1293.333-1373.333
|1341.1765
|1341.1765
| colspan="2" |1320-1380
| colspan="2" |1310-1390
| colspan="2" |''1350''
|''1350''
|1360
|1360
|1371.429-1401.429
|1371.429-1411.429
|}
|}
{| class="wikitable"
{| class="wikitable"
! rowspan="3" |Degrees
! rowspan="4" |Degrees
! colspan="2" rowspan="3" |Octatonic
! colspan="3" rowspan="3" |Octatonic
! colspan="6" |Aeolian
! colspan="6" |Aeolian
! colspan="8" |Intense Aeolian
! colspan="7" |Intense Aeolian
|-
|-
! colspan="3" |Flattone
! colspan="3" |Flattone
! colspan="3" |Meantone
! colspan="3" |Meantone
! colspan="5" |Superpyth
! colspan="4" |Superpyth
! colspan="3" |Ultrapyth
! colspan="3" |Ultrapyth
|-
|-
!Minimum-comma
! rowspan="2" |Minimum-comma
!Median
! rowspan="2" |Median
!Maximum+comma
! rowspan="2" |Maximum+comma
!Minimum-comma
! rowspan="2" |Minimum-comma
!Median
! rowspan="2" |Median
!Maximum+comma
! rowspan="2" |Maximum+comma
!Minimum-comma
! rowspan="2" |Minimum-comma
! colspan="2" |''r¢''
! rowspan="2" |''r¢''
!Median
! rowspan="2" |Median
!Maximum+comma
! rowspan="2" |Maximum+comma
!Minimum-comma
! rowspan="2" |Minimum-comma
!Median
! rowspan="2" |Median
!Maximum+comma
! rowspan="2" |Maximum+comma
|-
! colspan="2" |Natural
!Subset of 34edn
|-
|-
|1
|1
|G
|G
|Gb
|Gb
|78.908-80.672
|Gb
|78.319-80.672
|81.448
|81.448
| colspan="2" |79.966-83.495
| colspan="2" |79.381-84.087
|81.882
|81.882
| colspan="2" |80.588-84.118
| colspan="2" |80-84.706
| colspan="2" |''82.353''
|''82.353''
|83.045
|83.045
| colspan="2" |81.658-85.187
| colspan="2" |81.0695-85.775
|83.8235
|83.8235
|84.706-86.471
|84.706-87.059
|-
|-
|2
|2
|A\\
|A\\
|F#v/Gb^
|F#v/Gb^
|157.815-161.3445
|F#^
|156.637-161.3445
|162.896
|162.896
| colspan="2" |159.932-166.991
| colspan="2" |158.761-169.173
|163.765
|163.765
| colspan="2" |161.1765-168.235
| colspan="2" |160-169.412
| colspan="2" |''164.706''
|''164.706''
|166.09
|166.09
| colspan="2" |163.3155-170.374
| colspan="2" |162.139-171.551
|167.647
|167.647
|169.412-172.941
|169.412-174.118
|-
|-
|3
|3
|Gpv/A\\^
|Gpv/A\\^
|F#
|F#
|236.723-242.017
|Abv
|234.958-242.017
|244.344
|244.344
| colspan="2" |239.898-250.486
| colspan="2" |238.142-252.26
|245.647
|245.647
| colspan="2" |241.765-252.353
| colspan="2" |240-254.118
| colspan="2" |''247.059''
|''247.059''
|249.135
|249.135
| colspan="2" |244.973-255.5615
| colspan="2" |243.209-257.326
|251.471
|251.471
|254.118-259.412
|254.118-261.1765
|-
|-
|4
|4
|Gp
|Gp
|G
|G
|315.63-322.689
|Ab
|313.277-322.689
|325.792
|325.792
| colspan="2" |319.864-333.981
| colspan="2" |317.523-336.347
|327.529
|327.529
| colspan="2" |322.353-336.471
| colspan="2" |320-338.8235
| colspan="2" |''329.412''
|''329.412''
|332.18
|332.18
| colspan="2" |326.631-340.749
| colspan="2" |324.278-343.102
|335.294
|335.294
|338.8235-345.882
|338.8235-348.235
|-
|-
|5
|5
| colspan="2" |A
| colspan="3" |A
|394.538-403.361
|391.597-403.361
|407.24
|407.24
| colspan="2" |399.829-417.477
| colspan="2" |396.904-420.433
|409.412
|409.412
| colspan="2" |402.941-420.588
| colspan="2" |400-423.529
| colspan="2" |''411.765''
|''411.765''
|415.225
|415.225
| colspan="2" |408.289-425.935
| colspan="2" |405.348-428.877
|419.118
|419.118
|423.529-432.353
|423.529-435.294
|-
|-
|6
|6
| colspan="2" |B
| colspan="2" |B
|473.445-484.034
|Bb
|469.916-484.034
|488.688
|488.688
| colspan="2" |479.796-500.972
| colspan="2" |476.285-504.52
|491.294
|491.294
| colspan="2" |483.529-504.706
| colspan="2" |480-508.235
| colspan="2" |''494.118''
|''494.118''
|498.27
|498.27
| colspan="2" |489.9465-511.123
| colspan="2" |486.417-514.652
|502.941
|502.941
|508.235-518.8235
|508.235-522.353
|-
|-
|7
|7
|H
|H
|Hb
|Hb
|552.353-564.706
|A#^
|548.235-564.706
|570.136
|570.136
| colspan="2" |559.762-584.4675
| colspan="2" |555.666-588.607
|573.1765
|573.1765
| colspan="2" |564.118-588.8235
| colspan="2" |560-592.941
| colspan="2" |''576.471''
|''576.471''
|581.315
|581.315
| colspan="2" |571.604-596.311
| colspan="2" |567.487-600.428
|586.768
|586.768
|592.941-605.294
|592.941-609.412
|-
|-
|8
|8
|C\\
|C\\
|B#v/Hb^
|B#v/Hb^
|631.2605-645.378
|B^
|626.555-645.378
|651.584
|651.584
| colspan="2" |639.728-667.963
| colspan="2" |635.046-672.6935
|655.059
|655.059
| colspan="2" |644.706-672.941
| colspan="2" |640-677.647
| colspan="2" |''658.8235''
|''658.8235''
|664.36
|664.36
| colspan="2" |653.262-671.497
| colspan="2" |648.556-686.203
|670.588
|670.588
|677.647-691.765
|677.647-696.471
|-
|-
|9
|9
|Hpv/C\\^
|Hpv/C\\^
|B#
|B#
|710.168-726.05
|H^
|704.874-726.05
|733.032
|733.032
| colspan="2" |719.6935-751.458
| colspan="2" |714.427-756.78
|736.941
|736.941
| colspan="2" |725.294-758.059
| colspan="2" |720-762.353
| colspan="2" |''741.1765''
|''741.1765''
|747.405
|747.405
| colspan="2" |734.92-656.6845
| colspan="2" |729.626-771.979
|754.412
|754.412
|762.653-778.235
|762.653-783.529
|-
|-
|10
|10
|Hp
|Hp
|H
|H
|789.076-806.723
|Cb
|783.193-806.723
|814.48
|814.48
| colspan="2" |799.659-834.954
| colspan="2" |793.808-840.867
|818.8235
|818.8235
| colspan="2" |805.882-841.1765
| colspan="2" |800-847.059
| colspan="2" |''823.529''
|''823.529''
|830.45
|830.45
| colspan="2" |816.5775-851.872
| colspan="2" |810.695-857.754
|838.235
|838.235
|847.059-864.706
|847.059-870.588
|-
|-
|11
|11
| colspan="2" |C
| colspan="3" |C
|867.983-887.395
|861.513-887.395
|895.928
|895.928
| colspan="2" |879.625-918.449
| colspan="2" |873.189-924.954
|900.706
|900.706
| colspan="2" |886.471-925.294
| colspan="2" |880-931.765
| colspan="2" |''905.882''
|''905.882''
|913.495
|913.495
| colspan="2" |898.235-937.059
| colspan="2" |891.765-943.529
|922.059
|922.059
|931.765-951.1765
|931.765-957.647
|-
|-
|12
|12
| colspan="2" |D
| colspan="2" |D
|946.891-968.067
|Db
|939.831-968.067
|977.376
|977.376
| colspan="2" |959.591-1001.944
| colspan="2" |952.57-1009.04
|982.588
|982.588
| colspan="2" |967.059-1009.412
| colspan="2" |960-1016.471
| colspan="2" |''988.235''
|''988.235''
|996.54
|996.54
| colspan="2" |979.893-1022.246
| colspan="2" |972.834-1029.305
|1005.882
|1005.882
|1016.471-1037.647
|1016.471-1044.706
|-
|-
|13
|13
|E
|E
|Eb
|Eb
|1025.798-1048.7395
|C#^
|1018.151-1048.7395
|1058.8235
|1058.8235
| colspan="2" |1039.557-1085.44
| colspan="2" |1031.9505-1093.127
|1064.471
|1064.471
| colspan="2" |1047.647-1093.529
| colspan="2" |1040-1101.1765
| colspan="2" |''1070.588''
|''1070.588''
|1079.585
|1079.585
| colspan="2" |1061.551-1107.433
| colspan="2" |1053.904-1115.08
|1089.706
|1089.706
|1101.1765-1124.118
|1101.1765-1131.765
|-
|-
|14
|14
|F\\
|F\\
|D#v/Eb^
|D#v/Eb^
|1104.706-1129.412
|Ebv
|1096.471-1129.412
|1140.2715
|1140.2715
| colspan="2" |1119.523-1168.935
| colspan="2" |1111.331-1177.214
|1146.353
|1146.353
| colspan="2" |1128.235-1177.647
| colspan="2" |1120-1185.882
| colspan="2" |''1152.941''
|''1152.941''
|1162.63
|1162.63
| colspan="2" |1143.209-1192.62
| colspan="2" |1134.973-1200.856
|1173.529
|1173.529
|1185.882-1210.588
|1185.882-1218.8235
|-
|-
|15
|15
|Epv/F\\^
|Epv/F\\^
|D#
|D#
|1183.613-1210.084
|Eb
|1174.79-1210.084
|1221.7195
|1221.7195
| colspan="2" |1199.489-1252.43
| colspan="2" |1190.712-1261.3
|1228.235
|1228.235
| colspan="2" |1208.8235-1261.765
| colspan="2" |1200-1270.588
| colspan="2" |''1233.294''
|''1233.294''
|1245.675
|1245.675
| colspan="2" |1224.866-1277.8075
| colspan="2" |1216.043-1286.631
|1257.353
|1257.353
|1270.588-1297.059
|1270.588-1305.882
|-
|-
|16
|16
|Ep
|Ep
|E
| colspan="2" |E
|1262.521-1290.756
|1253.109-1290.756
|1303.167
|1303.167
| colspan="2" |1279.455-1335.925
| colspan="2" |1270.093-1345.39
|1310.118
|1310.118
| colspan="2" |1289.412-1345.882
| colspan="2" |1280-1355.294
| colspan="2" |''1317.647''
|''1317.647''
|1328.72
|1328.72
| colspan="2" |1306.652-1362.995
| colspan="2" |1297.112-1372.406
|1341.1765
|1341.1765
|1355.294-1383.529
|1355.294-1392.941
|-
|-
|17
|17
| colspan="2" |F
| colspan="3" |F
|1341.429-1371.429
|1331.429-1371.429
|1384.615
|1384.615
| colspan="2" |1359.474-1419.474
| colspan="2" |1349.474-1429.474
|1392
|1392
| colspan="2" |1370-1430
| colspan="2" |1360-1440
| colspan="2" |''1400''
|''1400''
|1411.765
|1411.765
| colspan="2" |1388.182-1448.182
| colspan="2" |1378.182-1458.182
|1425
|1425
|1440-1470
|1440-1480
|}
|}
Golden/Pyrite Tunings±13¢
Golden/Pyrite Tunings±13¢

Revision as of 20:06, 10 June 2019

This scale, a Long Common Practice minor mode, has the Grandfather 3L 5s MOS with a 4:1 ratio of large against small.

Intervals

Degrees Octatonic Soft Phrygian Phrygian
Minimum-comma Median Maximum+comma Thirdtone Semitone
Minimum-comma Median Maximum+comma Minimum-comma Median Maximum+comma
Natural Subset of 34edn
1 A Ab Ab 68.235-70.588 73.797 71.597-76.3025 74.51-74.622 72.941-77.983 76.235-76.471 77.647-80
2 B\\ G#v/Ab^ G#^ 136.471-141.1765 147.594 143.193-152.605 149.02-149.244 145.882-155.966 152.471-152.941 155.294-160
3 Apv/B\\^ G# Bbv 204.706-211.765 221.39 214.79-228.908 223.529-213.8655 218.8235-233.95 228.706-229.1765 232.941-240
4 Ap A Bb 272.941-282.353 295.187 286.386-305.21 298.039-298.487 291.765-311.933 304.941-305.647 310.588-320
5 B 341.1765-352.941 368.984 357.983-381.513 372.549-373.109 364.706-389.916 381.1765-382.118 387.235-400
6 C Cb 409.412-423.529 442.781 429.58-457.815 447.059-447.731 437.647-467.899 457.412-458.588 464.882-480
7 Q Qb B#^ 477.647-494.118 516.5775 501.1765-534.118 521.569-522.353 510.588-545.882 533.647-535.294 542.529-560
8 D\\ C#v/Qb^ C^ 545.882-564.706 590.374 572.773-610.42 596.078-596.975 583.529-623.8655 609.882-611.235 620.1765-640
9 Qpv/D\\^ C# Q^ 614.118-635.294 664.171 644.37-686.723 670.588-671.597 656.471-701.849 686.118-688.765 697.8235-720
10 Qp Q Db 682.353-705.882 737.97 715.966-763.025 745.098-746.2185 729.412-779.832 762.353-764.706 777.471-800
11 D 750.588-776.471 811.765 787.563-839.328 819.608-820.84 802.353-857.815 838.588-841.412 855.118-880
12 E Eb 818.8235-847.059 885.5616 859.16-915.63 894.118-895.462 875.294-935.798 914.8235-917.882 932.765-960
13 F Fb D#^ 887.059-917.647 959.358 930.756-991.933 968.6275-970.084 948.235-1013.7815 991.059-994.353 1010.412-1040
14 F\\ E#v/Fb^ Fbv 955.294-988.235 1033.155 1002.353-1068.235 1043.137-1044.706 1021.1765-1091.765 1067.294-1080.8235 1088.059-1120
15 Fpv/G\\^ E# Fb 1023.529-1058.8235 1106.952 1073.95-1144.538 1117.647-1119.328 1094.118-1169.747 1143.529-1147.059 1164.706-1200
16 Fp F 1091.765-1129.412 1180.749 1145.546-1220.84 1192.156-1193.95 1167.059-1247.731 1219.765-1223.529 1242.353-1280
17 G 1160-1200 1254.5455 1217.143-1297.143 1266.667-1268.571 1240-1325.714 1296-1300 1320-1360
Degrees Octatonic Intense Phrygian Intense Phrygian-Soft Aeolian Soft Aeolian
Minimum-comma Median Maximum+comma Minimum-comma Median Maximum+comma Minimum-comma r¢ Median Maximum+comma
Natural Subset of 34edn
1 G Gb A Ab Gb Ab 75.294-77.647 78.019 76.078-80.784 78.893 77.059-81.765 79.412 80 80.672-83.025
2 A\\ F#v/Gb^ B\\ G#v/Ab^ F#^ G#^ 150.588-155.294 156.037 152.157-161.567 157.7855 154.118-163.529 158.8235 160 161.3445-166.05
3 Gpv/A\\^ F# Apv/B\\^ G# Abv Bbv 225.882-232.941 234.056 228.235-242.353 236.678 231.1765-245.294 238.235 240 242.017-249.076
4 Gp G Ap A Ab Bb 301.1765-310.588 312.074 304.314-323.137 315.571 308.235-327.059 317.647 320 322.689-332.101
5 A B A B 376.471-387.235 390.093 380.392-403.922 394.464 385.294-408.8235 397.058 400 403.361-415.126
6 B C Bb Cb 451.765-464.822 468.1115 456.471-484.706 473.356 462.353-490.588 476.471 480 484.034-498.151
7 H Hb Q Qb A#^ B#^ 527.059-542.529 546.13 532.549-565.49 552.249 539.412-572.353 555.882 560 564.706-581.1765
8 C\\ B#v/Hb^ D\\ C#v/Qb^ B^ C^ 602.353-620.1765 624.149 608.6275-646.2745 651.142 616.471-654.118 635.294 640 645.378-664.202
9 Hpv/C\\^ B# Qpv/D\\^ C# H^ Q^ 677.647-697.8235 702.167 684.706-727.059 710.035 693.529-735.882 714.706 720 726.05-747.227
10 Hp H Qp Q Cb Db 752.353-777.471 780.186 760.784-807.843 788.927 770.588-817.647 794.118 800 806.723-830.252
11 C D C D 828.235-855.118 858.204 836.862-888.6275 867.82 847.647-899.412 873.529 880 887.395-913.277
12 D E Db Eb 903.529-932.765 936.223 912.941-968.412 946.713 924.706-981.1765 952.941 960 968.067-996.3025
13 E Eb F Fb C#^ D#^ 978.8235-1010.412 1014.2415 989.02-1050.196 1025.6055 1001.765-1062.941 1032.353 1040 1048.7395-1079.328
14 F\\ D#v/Eb^ F\\ E#v/Fb^ Ebv Fbv 1055.118-1088.059 1092.26 1065.098-1130.98 1104.598 1078.8235-1144.706 1111.765 1120 1129.412-1162.353
15 Epv/F\\^ D# Fpv/G\\^ E# Eb Fb 1129.412-1164.706 1170.028 1141.1765-1210.765 1183.391 1155.882-1226.471 1191.1765 1200 1210.084-1245.378
16 Ep E Fp F E F 1204.706-1242.353 1248.297 1217.255-1292.549 1262.284 1232.941-1308.235 1270.588 1280 1290.756-1328.403
17 F G F G 1280-1320 1326.316 1293.333-1373.333 1341.1765 1310-1390 1350 1360 1371.429-1411.429
Degrees Octatonic Aeolian Intense Aeolian
Flattone Meantone Superpyth Ultrapyth
Minimum-comma Median Maximum+comma Minimum-comma Median Maximum+comma Minimum-comma r¢ Median Maximum+comma Minimum-comma Median Maximum+comma
Natural Subset of 34edn
1 G Gb Gb 78.319-80.672 81.448 79.381-84.087 81.882 80-84.706 82.353 83.045 81.0695-85.775 83.8235 84.706-87.059
2 A\\ F#v/Gb^ F#^ 156.637-161.3445 162.896 158.761-169.173 163.765 160-169.412 164.706 166.09 162.139-171.551 167.647 169.412-174.118
3 Gpv/A\\^ F# Abv 234.958-242.017 244.344 238.142-252.26 245.647 240-254.118 247.059 249.135 243.209-257.326 251.471 254.118-261.1765
4 Gp G Ab 313.277-322.689 325.792 317.523-336.347 327.529 320-338.8235 329.412 332.18 324.278-343.102 335.294 338.8235-348.235
5 A 391.597-403.361 407.24 396.904-420.433 409.412 400-423.529 411.765 415.225 405.348-428.877 419.118 423.529-435.294
6 B Bb 469.916-484.034 488.688 476.285-504.52 491.294 480-508.235 494.118 498.27 486.417-514.652 502.941 508.235-522.353
7 H Hb A#^ 548.235-564.706 570.136 555.666-588.607 573.1765 560-592.941 576.471 581.315 567.487-600.428 586.768 592.941-609.412
8 C\\ B#v/Hb^ B^ 626.555-645.378 651.584 635.046-672.6935 655.059 640-677.647 658.8235 664.36 648.556-686.203 670.588 677.647-696.471
9 Hpv/C\\^ B# H^ 704.874-726.05 733.032 714.427-756.78 736.941 720-762.353 741.1765 747.405 729.626-771.979 754.412 762.653-783.529
10 Hp H Cb 783.193-806.723 814.48 793.808-840.867 818.8235 800-847.059 823.529 830.45 810.695-857.754 838.235 847.059-870.588
11 C 861.513-887.395 895.928 873.189-924.954 900.706 880-931.765 905.882 913.495 891.765-943.529 922.059 931.765-957.647
12 D Db 939.831-968.067 977.376 952.57-1009.04 982.588 960-1016.471 988.235 996.54 972.834-1029.305 1005.882 1016.471-1044.706
13 E Eb C#^ 1018.151-1048.7395 1058.8235 1031.9505-1093.127 1064.471 1040-1101.1765 1070.588 1079.585 1053.904-1115.08 1089.706 1101.1765-1131.765
14 F\\ D#v/Eb^ Ebv 1096.471-1129.412 1140.2715 1111.331-1177.214 1146.353 1120-1185.882 1152.941 1162.63 1134.973-1200.856 1173.529 1185.882-1218.8235
15 Epv/F\\^ D# Eb 1174.79-1210.084 1221.7195 1190.712-1261.3 1228.235 1200-1270.588 1233.294 1245.675 1216.043-1286.631 1257.353 1270.588-1305.882
16 Ep E 1253.109-1290.756 1303.167 1270.093-1345.39 1310.118 1280-1355.294 1317.647 1328.72 1297.112-1372.406 1341.1765 1355.294-1392.941
17 F 1331.429-1371.429 1384.615 1349.474-1429.474 1392 1360-1440 1400 1411.765 1378.182-1458.182 1425 1440-1480

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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