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User:Moremajorthanmajor/16edX: Difference between revisions

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Line 296: Line 296:
| colspan="2" |1655.172
| colspan="2" |1655.172
|1680
|1680
|}Golden tunings
|}Most harmonic tunings
{| class="wikitable"
{| class="wikitable"
|+
|-
! rowspan="4" |Degrees
! rowspan="2" |Degrees
! colspan="3" rowspan="4" |Enneatonic
! colspan="3" rowspan="2" |Enneatonic
! colspan="4" |Minor mode Middletown temperament
!Minor mode Middletown temperament
!Neutral mode Middletown temperament
!Neutral mode Middletown temperament
! colspan="5" |Major mode Middletown temperament
!Major mode Middletown temperament
|-
|-
! rowspan="3" |Aeolian-Dorian
!7/3±13¢
! colspan="3" |Dorian
!22/9±13¢
! rowspan="3" |Dorian-Mixolydian
!5/2±13¢
! colspan="4" |Mixolydian
! rowspan="3" |Mixolydian-Ionian
|-
|-
! rowspan="2" |Subpental
|1
! rowspan="2" |Pental
|1#/2b
! rowspan="2" |Superpental
| colspan="2" |F#/Gb
! rowspan="2" |Subpental
|90.867-92.492
! rowspan="2" |Pental
|95.9005-97.5255
! colspan="2" |Superpental
|98.332-99.957
|-
|-
!Soft
| |2
!Intense
|2
| colspan="2" |G
|181.734-184.984
|191.801-195.051
|196.664-199.914
|-
|3
|2#/3b
|G#/Jb
|''G#/Ab''
|272.601-277.476
|287.7015-292.5765
|294.996-299.871
|-
| |4
|3
|J
|''A''
|363.468-369.968
|383.602-390.102
|393.328-399.828
|-
|5
|3#/4b
|J#/Ab
|''A#/Bb''
|454.335-462.46
|479.5025-487.6275
|491.6605-499.7855
|-
| |6
|4
|A
|''B''
|545.202-554.952
|575.403-585.153
|589.993-599.743
|-
|7
|5
|B
|''H''
|636.0685-647.4435
|671.3035-382.6785
|688.325-699.7
|-
| |8
|5#/6b
|B#/Hb
|''H#/Cb''
|726.9355-739.9355
|767.204-780.204
|786.657-799.657
|-
|9
|6
|H
|''C''
|817.802-832.427
|863.1045-877.7295
|884.989-899.614
|-
| |10
|6#/7b
|H#/Cb
|''C#/Db''
|908.669-924.919
|959.005-975.255
|983.321-999.571
|-
|11
|7
|C
|''D''
|999.536-1017.411
|1054.9055-1072.7205
|1081.653-1099.528
|-
| |12
|7#/8b
|C#/Db
|''D#/Sb''
|1090.403-1109.903
|1150.806-1170.306
|1179.985-1199.485
|-
|13
|8
|D
|''S''
|1181.27-1202.395
|1246.7065-1267.8315
|1278.317-1299.442
|-
| |14
|8#/9b
|D#/Eb
|''S#/Eb''
|1272.137-1294.887
|1342.607-1365.357
|1376.6495-1399.3995
|-
|15
|9
| colspan="2" |E
|1363.004-1387.378
|1438.507-14661.882
|1474.982-1499.366
|-
|16
|1
| colspan="2" |F
|1453.871-1479.871
|1534.408-1560.408
|1573.314-1599.314
|}Golden tunings
 
Minor mode Middletown temperament
 
{| class="wikitable"
! rowspan="3" |Degrees
! colspan="3" rowspan="3" |Enneatonic
! colspan="3" |Aeolian-Dorian
! colspan="9" |Dorian
|-
! rowspan="2" |-13¢
! rowspan="2" |Mean
! rowspan="2" |-13¢ (s5D)
! colspan="3" |Subpental
! colspan="3" |Pental
! colspan="3" |Superpental
|-
!+13¢ (A-D)
!Mean
!+13¢
!-13¢
!-13¢ (S5)
!Mean
!Mean
!+13¢ (5)
!-13¢ (D-M)
|-
|-
|1
|1
|1#/2b
|1#/2b
| colspan="2" |F#/Gb
| colspan="2" |F#/Gb
|90.428
|91.241
|91.241
|91.303
|92.053
|92.116
|92.116
|92.928
|94.329
|94.917
|95.142
|95.142
|95.7295
|95.7295
|95.943
|96.369
|-
|2
|2
| colspan="2" |G
|180.856
|182.481
|182.606
|184.106
|184.231
|185.856
|188.2585
|189.834
|190.2835
|191.459
|191.9085
|192.728
|-
|3
|2#/3b
|G#/Jb
|''G#/Ab''
|271.2845
|273.722
|273.909
|276.159
|276.347
|278.784
|282.988
|284.751
|285.425
|287.1885
|287.863
|289.092
|-
|4
|3
|J
|''A''
|361.712
|364.962
|365.212
|368.213
|368.462
|371.712
|377.317
|379.668
|380.567
|382.918
|383.817
|385.456
|-
|5
|3#/4b
|J#/Ab
|''A#/Bb''
|452.141
|456.203
|456.5155
|460.266
|460.578
|464.6405
|471.646
|474.585.
|475.709
|478.6475
|479.771
|481.82
|-
|6
|4
|A
|''B''
|542.569
|547.444
|547.819
|552.319
|552.694
|557.569
|565.974
|569.502
|570.851
|574.377
|575.726
|578.184
|-
|7
|5
|B
|''H''
|632.997
|638.685
|639.122
|644.372
|644.809
|650.497
|660.305
|664.419
|665.992
|670.106
|671.68
|674.548
|-
|8
|5#/6b
|B#/Hb
|''H#/Cb''
|723.425
|729.925
|730.425
|736.425
|736.925
|743.425
|754.634
|759.336
|761.134
|765.836
|767.634
|770.912
|-
|9
|6
|H
|''C''
|813.854
|821.166
|821.728
|828.479
|829.04
|836.353
|848.963
|854.253
|856.276
|861.565
|863.588
|867.2755
|-
|10
|6#/7b
|H#/Cb
|''C#/Db''
|904.282
|912.407
|913.031
|920.532
|921.156
|920.281
|943.293
|949.17
|951.418
|957.295
|959.543
|963.6935
|-
|11
|7
|C
|''D''
|994.71
|1003.6475
|1004.334
|1012.585
|1013.272
|1022.209
|1037.622
|1044.087
|1046.559
|1053.024
|1055.497
|1060.0035
|-
|12
|7#/8b
|C#/Db
|''D#/Sb''
|1085.138
|1094.888
|1095.637
|1104.638
|1105.387
|1115.137
|1131.951
|1139.004
|1141.701
|1148.753
|1151.451
|1156.367
|-
|13
|8
|D
|''S''
|1175.566
|1186.129
|1186.94
|1106.691
|1197.502
|1208.065
|1226.38
|1233.921
|1236.843
|1244.483
|1247.405
|1252.731
|-
|14
|8#/9b
|D#/Eb
|''S#/Eb''
|1265.9945
|1277.3965
|1278.2435
|1288.7445
|1289.6185
|1300.9935
|1320.61
|1328.838
|1331.985
|1340.213
|1343.36
|1349.095
|-
|15
|9
| colspan="2" |E
|1356.423
|1368.61
|1369.547
|1380.798
|1381.734
|1393.922
|141.939
|1423.755
|1427.126
|1435.942
|1439.314
|1445.459
|-
|16
|1
| colspan="2" |F
|1446.851
|1459.851
|1460.85
|1472.851
|1473.85
|1486.85
|1509.268
|1518.672
|1522.268
|1531.672
|1535.268
|1541.823
|}
Neutral (Dorian-Mixolydian) mode Middletown temperament
{| class="wikitable"
|-
!Degrees
! colspan="3" |Enneatonic
!+13¢ (S5D)
!Mean
!-13¢ (s5M)
|-
|1
|1#/2b
| colspan="2" |F#/Gb
|96.542
|97.176
|97.176
|97.364
|-
|2
|2
| colspan="2" |G
|193.084
|194.353
|194.7275
|-
|3
|2#/3b
|G#/Jb
|''G#/Ab''
|289.626
|291.529
|292.091
|-
|4
|3
|J
|''A''
|386.168
|388.706
|389.455
|-
|5
|3#/4b
|J#/Ab
|''A#/Bb''
|482.71
|485.882
|486.819
|-
|6
|4
|A
|''B''
|579.252
|580.235
|584.183
|-
|7
|5
|B
|''H''
|675.794
|725.584
|681.546
|-
|8
|5#/6b
|B#/Hb
|''H#/Cb''
|771.336
|777.412
|779.41
|-
|9
|6
|H
|''C''
|868.878
|874.588
|876.274
|-
|10
|6#/7b
|H#/Cb
|''C#/Db''
|965.42
|971.7645
|973.638
|-
|11
|7
|C
|''D''
|1061.962
|1068.941
|1071.0015
|-
|12
|7#/8b
|C#/Db
|''D#/Sb''
|1158.503
|1166.117
|1168.365
|-
|13
|8
|D
|''S''
|1255.046
|1263.293
|1265.729
|-
|14
|8#/9b
|D#/Eb
|''S#/Eb''
|1351.588
|1360.47
|1363.093
|-
|15
|9
| colspan="2" |E
|1448.13
|1457.645
|1460.457
|-
|16
|1
| colspan="2" |F
|1544.672
|1554.823
|1557.82
|}
Major mode Middletown temperament
{| class="wikitable"
|+
|-
! rowspan="4" |Degrees
! colspan="3" rowspan="4" |Enneatonic
! colspan="13" |Mixolydian
! colspan="2" |Mixolydian-Ionian
|-
! colspan="3" |Subpental
! colspan="4" |Pental
! colspan="6" |Superpental
! rowspan="3" |Mean
! rowspan="3" |+13¢
|-
! rowspan="2" |-13¢ (5)
! rowspan="2" |+13¢ (D-M)
! rowspan="2" |Mean
! rowspan="2" |Mean
! rowspan="2" |+13¢ (s5)
! rowspan="2" |+13¢
! rowspan="2" |-13¢ (Soft s5)
! rowspan="2" |Soft
! colspan="5" |Intense
|-
!+13¢ (Soft s5)
!-13¢
!Mean
!-13¢ (M-I)
!+13¢
|-
|1
|1#/2b
| colspan="2" |F#/Gb
|97.787
|97.989
|98.176
|98.176
|98.6
|98.6
|98.989
|99.412
|99.998
|100.81
|100.81
|101.623
|101.648
|102.46
|102.46
|102.785
|103.273
|103.598
|103.598
|104.41
|-
|-
|2
|2
|2
|2
| colspan="2" |G
| colspan="2" |G
|182.481
|195.5745
|184.231
|195.978
|190.2835
|191.459
|194.353
|196.3525
|196.3525
|197.1995
|197.1995
|197.9775
|198.8245
|199.9955
|201.6205
|201.6205
|203.2455
|203.296
|204.921
|204.921
|205.57
|206.546
|207.195
|207.195
|208.82
|-
|-
|3
|3
Line 353: Line 933:
|G#/Jb
|G#/Jb
|''G#/Ab''
|''G#/Ab''
|273.722
|293.362
|276.347
|293.967
|285.425
|287.1885
|291.529
|294.529
|294.529
|295.799
|295.799
|296.966
|298.237
|299.993
|302.431
|302.431
|304.868
|304.944
|307.381
|307.381
|308.356
|309.819
|310.793
|310.793
|313.231
|-
|-
|4
|4
Line 368: Line 953:
|J
|J
|''A''
|''A''
|364.962
|391.149
|368.462
|391.956
|380.567
|382.918
|388.706
|392.705
|392.705
|394.399
|394.399
|395.955
|397.649
|399.991
|403.241
|403.241
|406.491
|406.592
|409.842
|409.842
|411.141
|413.092
|414.391
|414.391
|417.641
|-
|-
|5
|5
Line 383: Line 973:
|J#/Ab
|J#/Ab
|''A#/Bb''
|''A#/Bb''
|456.203
|488.936
|460.578
|489.945
|475.709
|478.6475
|485.882
|490.881
|490.881
|492.999
|492.999
|494.944
|497.061
|499.989
|504.051
|504.051
|508.114
|508.24
|512.302
|512.302
|513.926
|516.365
|517.9885
|517.9885
|522.051
|-
|-
|6
|6
Line 398: Line 993:
|A
|A
|''B''
|''B''
|547.444
|586.724
|552.694
|587.934
|570.851
|574.377
|680.235
|589.058
|589.058
|591.599
|591.599
|604.862
|593.933
|596.474
|599.987
|599.987
|609.737
|609.888
|614.763
|614.763
|616.711
|619.638
|621.586
|621.586
|626.461
|-
|-
|7
|7
Line 413: Line 1,013:
|B
|B
|''H''
|''H''
|638.685
|684.511
|644.809
|685.923
|665.992
|670.106
|725.584
|687.234
|687.234
|690.198
|690.198
|692.921
|695.886
|699.984
|705.672
|705.672
|711.359
|711.5355
|717.223
|717.223
|719.496
|722.9105
|725.184
|725.184
|730.871
|-
|-
|8
|8
Line 428: Line 1,033:
|B#/Hb
|B#/Hb
|''H#/Cb''
|''H#/Cb''
|729.925
|782.298
|736.925
|783.912
|761.134
|765.836
|777.412
|785.41
|785.41
|788.798
|788.798
|806.482
|791.91
|795.298
|799.982
|799.982
|812.982
|813.1835
|819.6835
|819.6835
|822.282
|826.1835
|828.781
|828.781
|835.282
|-
|-
|9
|9
Line 443: Line 1,053:
|H
|H
|''C''
|''C''
|821.166
|880.085
|829.04
|881.9005
|856.276
|861.565
|874.588
|883.5865
|883.5865
|887.398
|887.398
|890.899
|894.71
|899.98
|907.292
|907.292
|914.605
|914.831
|922.144
|922.144
|925.067
|929.456
|932.379
|932.379
|939.692
|-
|-
|10
|10
Line 458: Line 1,073:
|H#/Cb
|H#/Cb
|''C#/Db''
|''C#/Db''
|912.407
|977.872
|921.156
|979.8895
|951.418
|957.295
|971.7645
|981.763
|981.763
|985.998
|985.998
|989.888
|994.123
|999.978
|1008.103
|1008.103
|1016.228
|1016.479
|1024.604
|1024.604
|1027.852
|1032.729
|1035.977
|1035.977
|1044.102
|-
|-
|11
|11
Line 473: Line 1,093:
|C
|C
|''D''
|''D''
|1003.6475
|1075.66
|1013.272
|1087.8785
|1046.559
|1053.024
|1068.941
|1079.939
|1079.939
|1084.597
|1084.597
|1088.8765
|1093.535
|1099.975
|1108.913
|1108.913
|1117.85
|1118.127
|1127.065
|1127.065
|1130.637
|1136.002
|1139.575
|1139.575
|1148.512
|-
|-
|12
|12
Line 488: Line 1,113:
|C#/Db
|C#/Db
|''D#/Sb''
|''D#/Sb''
|1094.888
|1173.447
|1105.387
|1175.867
|1141.701
|1148.753
|1166.117
|1178.115
|1178.115
|1183.197
|1183.197
|1189.865
|1192.947
|1199.973
|1209.723
|1209.723
|1219.473
|1219.775
|1229.525
|1229.525
|1233.422
|1239.275
|1243.172
|1243.172
|1252.922
|-
|-
|13
|13
Line 503: Line 1,133:
|D
|D
|''S''
|''S''
|1186.129
|1271.234
|1197.502
|1273.856
|1236.843
|1244.483
|1263.293
|1276.292
|1276.292
|1281.797
|1281.797
|1286.854
|1292.359
|1299.971
|1310.533
|1310.533
|1321.096
|1321.423
|1331.986
|1331.986
|1336.208
|1342.548
|1346.77
|1346.77
|1357.333
|-
|-
|14
|14
Line 518: Line 1,153:
|D#/Eb
|D#/Eb
|''S#/Eb''
|''S#/Eb''
|1277.3965
|1369.022
|1289.6185
|1371.845
|1331.985
|1340.213
|1360.47
|1374.468
|1374.468
|1380.397
|1380.397
|1385.843
|1391.772
|1399.968
|1411.344
|1411.344
|1422.719
|1423.071
|1434.446
|1434.446
|1438.993
|1445.821
|1450.368
|1450.368
|1461.743
|-
|-
|15
|15
|9
|9
| colspan="2" |E
| colspan="2" |E
|1368.61
|1455.809
|1381.734
|1469.834
|1427.126
|1435.942
|1457.645
|1472.644
|1472.644
|1478.996
|1478.996
|1484.832
|1491.184
|1499.9665
|1512.154
|1512.154
|1524.3415
|1524.719
|1536.9065
|1536.9065
|1541.778
|1549.094
|1553.9655
|1553.9655
|1566.153
|-
|-
|16
|16
|1
|1
| colspan="2" |F
| colspan="2" |F
|1459.851
|1564.596
|1473.85
|1567.96
|1522.268
|1531.672
|1554.823
|1570.82
|1570.82
|1577.596
|1577.596
|1583.82
|1590.596
|1599.964
|1612.964
|1612.964
|1625.964
|1626.366
|1639.366
|1639.366
|1644.563
|1652.366
|1657.563
|1657.563
|1670.563
|}By a surprising coincidence, neutral 16edX turns out to be a false Pelogic temperament with a very pure 5:4 (mistuned by no more than 3.596 cents), and tuning 5:3 pure creates a tenth almost exactly equal to 38/29edo or almost exactly the Golden Subpental Mixolydian step or every ninth step of [[110edo]], and tuning 4:3 pure creates an almost exact 43/74edo fifth. Also, the Golden Soft Superpental Mixolydian step is almost exactly (25/24)^(10/7) and tuning 12:7 pure creates almost exactly the Golden Mixolydian-Ionian step.
|}By a surprising coincidence, neutral 16edX turns out to be a false Pelogic temperament with a very pure 5:4 (mistuned by no more than 3.596 cents), and tuning 5:3 pure creates a tenth almost exactly equal to 38/29edo or almost exactly the Golden Subpental Mixolydian step or every ninth step of [[110edo]], and tuning 4:3 pure creates an almost exact 43/74edo fifth. Also, the Golden Soft Superpental Mixolydian step is almost exactly (25/24)^(10/7) and tuning 12:7 pure creates almost exactly the Golden Mixolydian-Ionian step.
[[Category:16-tone]]
[[Category:16-tone]]
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