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]]

Revision as of 02:47, 6 November 2018

This is the scale which occurs as the dominant major edX.

Intervals

Degrees Enneatonic Minor mode Middletown temperament Neutral mode Middletown temperament Major mode Middletown temperament
Aeolian-Dorian Dorian Dorian-Mixolydian Mixolydian Mixolydian-Ionian
Subpental Pental Superpental Subpental Pental Superpental
Soft Intense
Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum
1 1#/2b F#/Gb 90 91.667 93.75 95.4545 96.429 97.5 98.4375 100 100.862 103.448 105
2 2 G 180 183.333 187.5 190.909 192.857 195 196.875 200 201.724 206.897 210
3 2#/3b G#/Jb G#/Ab 270 275 281.25 286.364 289.286 292.5 295.3125 300 302.586 310.345 315
4 3 J A 360 366.667 375 381.818 385.714 390 393.75 400 403.448 413.793 420
5 3#/4b J#/Ab A#/Bb 450 458.333 468.75 477.273 482.143 487.5 492.1875 500 504.31 517.241 525
6 4 A B 540 550 562.5 572.727 578.571 585 590.625 600 605.172 620.69 630
7 5 B H 630 641.667 656.25 668.182 675 682.5 689.0625 700 706.0345 724.138 735
8 5#/6b B#/Hb H#/Cb 720 733.333 750 763.636 771.429 780 787.5 800 806.897 827.586 840
9 6 H C 810 825 843.75 859.091 867.857 877.5 885.9375 900 907.759 931.0345 945
10 6#/7b H#/Cb C#/Db 900 916.667 937.5 954.5455 964.286 975 984.375 1000 1008.621 1034.483 1050
11 7 C D 990 1018.333 1031.25 1050 1060.714 1072.5 1082.8125 1100 1109.483 1137.931 1155
12 7#/8b C#/Db D#/Sb 1080 1100 1125 1145.4545 1157.143 1170 1181.25 1200 1210.345 1241.379 1260
13 8 D S 1170 1191.667 1218.75 1240.909 1253.571 1267.5 1279.6875 1300 1311.207 1344.828 1365
14 8#/9b D#/Eb S#/Eb 1260 1283.333 1312.5 1336.364 1350 1365 1378.125 1400 1412.069 1448.276 1470
15 9 E 1350 1375 1406.25 1431.818 1446.429 1462.5 1476.5625 1500 1512.931 1551.724 1575
16 1 F 1440 1466.667 1500 1527.273 1542.857 1560 1575 1600 1613.793 1655.172 1680

Most harmonic tunings

Degrees Enneatonic Minor mode Middletown temperament Neutral mode Middletown temperament Major mode Middletown temperament
7/3±13¢ 22/9±13¢ 5/2±13¢
1 1#/2b F#/Gb 90.867-92.492 95.9005-97.5255 98.332-99.957
2 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 E 1363.004-1387.378 1438.507-14661.882 1474.982-1499.366
16 1 F 1453.871-1479.871 1534.408-1560.408 1573.314-1599.314

Golden tunings

Minor mode Middletown temperament

Degrees Enneatonic Aeolian-Dorian Dorian
-13¢ Mean -13¢ (s5D) Subpental Pental Superpental
+13¢ (A-D) Mean +13¢ -13¢ -13¢ (S5) Mean Mean +13¢ (5) -13¢ (D-M)
1 1#/2b F#/Gb 90.428 91.241 91.303 92.053 92.116 92.928 94.329 94.917 95.142 95.7295 95.943 96.369
2 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 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 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

Degrees Enneatonic +13¢ (S5D) Mean -13¢ (s5M)
1 1#/2b F#/Gb 96.542 97.176 97.364
2 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 E 1448.13 1457.645 1460.457
16 1 F 1544.672 1554.823 1557.82

Major mode Middletown temperament

Degrees Enneatonic Mixolydian Mixolydian-Ionian
Subpental Pental Superpental Mean +13¢
-13¢ (5) +13¢ (D-M) Mean Mean +13¢ (s5) +13¢ -13¢ (Soft s5) Soft Intense
+13¢ (Soft s5) -13¢ Mean -13¢ (M-I) +13¢
1 1#/2b F#/Gb 97.787 97.989 98.176 98.6 98.989 99.412 99.998 100.81 101.623 101.648 102.46 102.785 103.273 103.598 104.41
2 2 G 195.5745 195.978 196.3525 197.1995 197.9775 198.8245 199.9955 201.6205 203.2455 203.296 204.921 205.57 206.546 207.195 208.82
3 2#/3b G#/Jb G#/Ab 293.362 293.967 294.529 295.799 296.966 298.237 299.993 302.431 304.868 304.944 307.381 308.356 309.819 310.793 313.231
4 3 J A 391.149 391.956 392.705 394.399 395.955 397.649 399.991 403.241 406.491 406.592 409.842 411.141 413.092 414.391 417.641
5 3#/4b J#/Ab A#/Bb 488.936 489.945 490.881 492.999 494.944 497.061 499.989 504.051 508.114 508.24 512.302 513.926 516.365 517.9885 522.051
6 4 A B 586.724 587.934 589.058 591.599 593.933 596.474 599.987 599.987 609.737 609.888 614.763 616.711 619.638 621.586 626.461
7 5 B H 684.511 685.923 687.234 690.198 692.921 695.886 699.984 705.672 711.359 711.5355 717.223 719.496 722.9105 725.184 730.871
8 5#/6b B#/Hb H#/Cb 782.298 783.912 785.41 788.798 791.91 795.298 799.982 799.982 812.982 813.1835 819.6835 822.282 826.1835 828.781 835.282
9 6 H C 880.085 881.9005 883.5865 887.398 890.899 894.71 899.98 907.292 914.605 914.831 922.144 925.067 929.456 932.379 939.692
10 6#/7b H#/Cb C#/Db 977.872 979.8895 981.763 985.998 989.888 994.123 999.978 1008.103 1016.228 1016.479 1024.604 1027.852 1032.729 1035.977 1044.102
11 7 C D 1075.66 1087.8785 1079.939 1084.597 1088.8765 1093.535 1099.975 1108.913 1117.85 1118.127 1127.065 1130.637 1136.002 1139.575 1148.512
12 7#/8b C#/Db D#/Sb 1173.447 1175.867 1178.115 1183.197 1189.865 1192.947 1199.973 1209.723 1219.473 1219.775 1229.525 1233.422 1239.275 1243.172 1252.922
13 8 D S 1271.234 1273.856 1276.292 1281.797 1286.854 1292.359 1299.971 1310.533 1321.096 1321.423 1331.986 1336.208 1342.548 1346.77 1357.333
14 8#/9b D#/Eb S#/Eb 1369.022 1371.845 1374.468 1380.397 1385.843 1391.772 1399.968 1411.344 1422.719 1423.071 1434.446 1438.993 1445.821 1450.368 1461.743
15 9 E 1455.809 1469.834 1472.644 1478.996 1484.832 1491.184 1499.9665 1512.154 1524.3415 1524.719 1536.9065 1541.778 1549.094 1553.9655 1566.153
16 1 F 1564.596 1567.96 1570.82 1577.596 1583.82 1590.596 1599.964 1612.964 1625.964 1626.366 1639.366 1644.563 1652.366 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.

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