User:Moremajorthanmajor/15edX: Difference between revisions

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| 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="2" rowspan="4" |Enneatonic
! colspan="2" 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
| colspan="2" |F#/Gb
! rowspan="2" |Superpental
|96.925-98.658
! rowspan="2" |Subpental
|102.294-104.027
! rowspan="2" |Pental
|104.888-106.621
! colspan="2" |Superpental
|-
|-
!Soft
| |2
!Intense
| colspan="2" |G
|193.8495-197.316
|204.588-208.054
|209.77-213.242
|-
|3
|G#/Jb
|''G#/Ab''
|290.774-295.974
|306.8815-312.0815
|314.663-319.863
|-
| |4
|J
|''A''
|387.699-394.632
|409.1755-416.109
|419.559-426.484
|-
| |5
|A
|''B''
|484.624-493.29
|511.469-520.136
|524.438-533.105
|-
|6
|A#/Bb
|''B#/Hb''
|581.548-591.948
|613.763-624.163
|629.3255-392.7255
|-
| |7
|B
|''H''
|678.473-690.606
|716.057-728.19
|734.213-746.346
|-
|8
|B#/Hb
|''H#/Cb''
|775.398-789.2645
|818.351-832.218
|839.101-852.967
|-
|9
|H
|''C''
|872.3225-887.9225
|920.645-936.245
|943.988-959.588
|-
|10
|C
|''D''
|969.247-986.561
|1022.939-1040.272
|1048.876-1066.209
|-
| |11
|C#/Db
|''D#/Sb''
|1066.172-1085.239
|1125.2325-1144.299
|1153.763-1172.83
|-
|12
|D
|''S''
|1163.097-1183.897
|1227.526-1248.326
|1258.651-1279.451
|-
| |13
|D#/Eb
|''S#/Eb''
|1260.0215-1282.555
|1329.82-1352.3535
|1363.539-1386.072
|-
|14
| colspan="2" |E
|1356.946-1381.213
|1432.114-1456.381
|1468.426-1492.693
|-
|15
| 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="2" 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
| colspan="2" |F#/Gb
| colspan="2" |F#/Gb
|96.457
|97.323
|97.323
|97.39
|98.19
|98.257
|98.257
|99.123
|100.618
|101.245
|101.4845
|101.4845
|102.1115
|102.1115
|102.351
|102.788
|-
|2
| colspan="2" |G
|192.913
|194.647
|194.78
|196.38
|196.513
|198.247
|201.236
|202.49
|202.969
|204.223
|204.702
|205.576
|-
|3
|G#/Jb
|''G#/Ab''
|289.37
|291.97
|292.17
|294.57
|294.77
|297.37
|301.854
|303.734
|304.454
|306.334
|307.054
|308.365
|-
|4
|J
|''A''
|385.829
|389.294
|389.56
|392.76
|394.027
|396.493
|402.4715
|404.979
|405.938
|408.446
|409.405
|411.153
|-
|5
|A
|''B''
|482.284
|486.617
|486.95
|490.95
|491.283
|495.617
|503.089
|569.502
|507.423
|510.557
|511.756
|513.941
|-
|6
|A#/Bb
|''B#/Hb''
|578.74
|583.94
|584.334
|589.14
|589.54
|594.74
|603.707
|607.469
|608.907
|612.669
|614.107
|616.729
|-
|7
|B
|''H''
|675.197
|681.364
|681.73
|687.33
|687.7965
|693.863
|704.325
|708.7135
|710.392
|714.78
|716.4585
|719.5175
|-
|8
|B#/Hb
|''H#/Cb''
|771.654
|778.587
|779.12
|785.52
|786.053
|792.9865
|804.943
|809.958
|811.877
|816.892
|818.81
|822.306
|-
|9
|H
|''C''
|868.1105
|875.9105
|876.51
|883.7105
|884.31
|892.11
|905.561
|911.203
|913.361
|919.003
|921.161
|925.094
|-
|10
|C
|''D''
|964.567
|973.234
|973.9
|981.901
|982.5665
|991.233
|1006.179
|1012.448
|1014.8455
|1021.115
|1023.512
|1027.882
|-
|11
|C#/Db
|''D#/Sb''
|1061.024
|1070.557
|1071.39
|1080.091
|1080.823
|1090.356
|1106.797
|1113.693
|1116.33
|1123.226
|1125.863
|1130.67
|-
|12
|D
|''S''
|1157.481
|1167.881
|1168.68
|1178.281
|1179.08
|1189.48
|1207.4145
|1214.9375
|1217.8145
|1225.3375
|1228.2145
|1233.459
|-
|13
|D#/Eb
|''S#/Eb''
|1253.937
|1265.204
|1266.07
|1176.471
|1277.336
|1288.603
|1308.032
|1316.182
|1319.299
|1327.449
|1330.566
|1336.247
|-
|14
| colspan="2" |E
|1350.394
|1362.527
|1363.46
|1374.661
|1375.593
|1387.726
|1408.65
|1417.427
|1420.783
|1429.56
|1432.917
|1439.035
|-
|15
| 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="2" |Enneatonic
!+13¢ (S5D)
!Mean
!-13¢ (s5M)
|-
|1
| colspan="2" |F#/Gb
|102.978
|103.655
|103.655
|103.855
|-
|2
| colspan="2" |G
|205.956
|207.31
|207.709
|-
|3
|G#/Jb
|''G#/Ab''
|308.934
|310.965
|311.564
|-
|4
|J
|''A''
|411.9215
|414.6195
|415.419
|-
|5
|A
|''B''
|514.891
|518.274
|519.2735
|-
|6
|A#/Bb
|''B#/Hb''
|617.869
|621.929
|623.128
|-
|7
|B
|''H''
|720.847
|725.584
|726.983
|-
|8
|B#/Hb
|''H#/Cb''
|823.825
|829.239
|830.8375
|-
|9
|H
|''C''
|926.823
|932.893
|934.693
|-
|10
|C
|''D''
|1029.781
|1036.549
|1038.547
|-
|11
|C#/Db
|''D#/Sb''
|1132.759
|1140.204
|1142.402
|-
|12
|D
|''S''
|1235.7375
|1243.859
|1246.256
|-
|13
|D#/Eb
|''S#/Eb''
|1338.716
|1347.513
|1353.111
|-
|14
| colspan="2" |E
|1441.694
|1451.168
|1453.966
|-
|15
| colspan="2" |F
|1544.672
|1554.823
|1557.82
|}Major mode Middletown temperament
{| class="wikitable"
|+
|-
! rowspan="4" |Degrees
! colspan="2" 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
| colspan="2" |F#/Gb
|104.306
|104.5215
|104.721
|104.721
|105.173
|105.173
|105.788
|106.04
|106.664
|107.531
|107.531
|108.398
|108.4245
|109.291
|109.291
|109.6375
|110.158
|110.504
|110.504
|111.371
|-
|-
|2
|2
| colspan="2" |G
| colspan="2" |G
|194.647
|208.613
|196.513
|209.043
|202.969
|204.223
|207.31
|209.443
|209.443
|210.346
|210.346
|211.576
|212.08
|213.329
|215.032
|215.032
|216.795
|216.849
|218.582
|218.582
|219.275
|220.316
|221.008
|221.008
|222.742
|-
|-
|3
|3
|G#/Jb
|G#/Jb
|''G#/Ab''
|''G#/Ab''
|291.97
|312.919
|294.77
|313.565
|304.454
|306.334
|310.965
|314.164
|314.164
|315.519
|315.519
|317.364
|318.119
|319.993
|322.593
|322.593
|325.193
|325.273
|327.873
|327.873
|328.913
|330.473
|331.613
|331.613
|334.113
|-
|-
|4
|4
|J
|J
|''A''
|''A''
|389.294
|417.226
|394.027
|418.086
|405.938
|408.446
|414.6195
|418.885
|418.885
|420.639
|420.639
|423.152
|424.159
|426.657
|430.124
|430.124
|433.5905
|433.698
|437.1345
|437.1345
|438.55
|440.631
|442.017
|442.017
|445.4835
|-
|-
|5
|5
|A
|A
|''B''
|''B''
|486.617
|521.532
|491.283
|526.308
|507.423
|510.557
|518.274
|523.607
|523.607
|525.865
|525.865
|528.94
|530.199
|533.321
|537.655
|537.655
|541.988
|542.122
|546.456
|546.456
|548.188
|550.789
|552.521
|552.521
|556.854
|-
|-
|6
|6
|A#/Bb
|A#/Bb
|''B#/Hb''
|''B#/Hb''
|583.94
|625.8385
|589.54
|627.129
|608.907
|612.669
|621.929
|628.328
|628.328
|631.0385
|631.0385
|634.728
|636.238
|639.987
|645.186
|645.186
|650.386
|650.547
|655.747
|655.747
|657.825
|660.947
|663.025
|663.025
|668.225
|-
|-
|7
|7
|B
|B
|''H''
|''H''
|681.364
|730.145
|687.7965
|731.651
|710.392
|714.78
|725.584
|733.0495
|733.0495
|736.212
|736.212
|740.516
|742.278
|746.65
|752.717
|752.717
|758.783
|758.971
|765.038
|765.038
|767.463
|771.105
|773.5235
|773.5235
|779.596
|-
|-
|8
|8
|B#/Hb
|B#/Hb
|''H#/Cb''
|''H#/Cb''
|778.587
|834.451
|786.053
|836.172
|811.877
|816.892
|829.239
|837.771
|837.771
|841.385
|841.385
|860.248
|846.304
|853.314
|899.98
|867.181
|914.605
|867.396
|874.329
|874.329
|877.1
|881.262
|884.033
|884.033
|890.967
|-
|-
|9
|9
|H
|H
|''C''
|''C''
|875.9105
|938.758
|884.31
|940.694
|913.361
|919.003
|932.893
|942.492
|942.492
|946.558
|946.558
|952.092
|954.358
|999.978
|967.7785
|967.7785
|1016.228
|975.82
|983.62
|983.62
|986.738
|991.42
|994.538
|994.538
|1002.338
|-
|-
|10
|10
|C
|C
|''D''
|''D''
|973.234
|1043.064
|982.5665
|1045.2155
|1014.8455
|1021.115
|1036.549
|1047.214
|1047.214
|1051.731
|1051.731
|1057.88
|1060.3975
|1066.643
|1075.3095
|1075.3095
|1083.976
|1084.245
|1092.911
|1092.911
|1096.3755
|1101.578
|1105.042
|1105.042
|1113.709
|-
|-
|11
|11
|C#/Db
|C#/Db
|''D#/Sb''
|''D#/Sb''
|1070.557
|1147.3705
|1080.823
|1149.737
|1116.33
|1123.226
|1140.204
|1151.935
|1151.935
|1156.904
|1156.904
|1163.668
|1166.437
|1173.307
|1182.84
|1182.84
|1192.374
|1192.669
|1202.202
|1202.202
|1206.013
|1211.736
|1215.546
|1215.546
|1225.08
|-
|-
|12
|12
|D
|D
|''S''
|''S''
|1167.881
|1251.677
|1179.08
|1254.259
|1217.8145
|1225.3375
|1243.859
|1256.656
|1256.656
|1262.077
|1262.077
|1269.456
|1272.477
|1279.971
|1290.371
|1290.371
|1300.771
|1301.0395
|1311.4935
|1311.4935
|1315.651
|1321.8935
|1326.051
|1326.051
|1336.451
|-
|-
|13
|13
|D#/Eb
|D#/Eb
|''S#/Eb''
|''S#/Eb''
|1265.204
|1355.983
|1277.336
|1358.78
|1319.299
|1327.449
|1347.513
|1361.378
|1361.378
|1367.25
|1367.25
|1275.244
|1378.517
|1386.636
|1397.902
|1397.902
|1409.169
|1409.518
|1420.785
|1420.785
|1438.993
|1425.288
|1436.555
|1436.555
|1447.8215
|-
|-
|14
|14
| colspan="2" |E
| colspan="2" |E
|1362.527
|1460.29
|1375.593
|1463.302
|1420.783
|1429.56
|1451.168
|1466.099
|1466.099
|1472.423
|1472.423
|1481.032
|1484.556
|1493.3
|1505.433
|1505.433
|1517.567
|1517.9425
|1530.076
|1530.076
|1541.778
|1534.926
|1547.059
|1547.059
|1559.192
|-
|-
|15
|15
| 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, the 15ed of the Golden tenth (7φ+6)\(5φ^2)edo is almost exactly every third degree of [[34edo]]. Additionally, those of the modal Golden tenths are almost exactly +1/28-syntonic comma 4ed(5/4) (Aeolian-Dorian), 9ed(5/3)/equal multiples of 18/17 (Subpental Dorian), 13ed(15/7) (Pental Dorian), 2ed(9/8) (Superpental Dorian), -1/12-syntonic comma 3ed(6/5) (Dorian-Mixolydian), 14ed(7/3)/equal multiples of 17/16/100π\3 cents (Subpental Mixolydian), 3ed(6/5) (Pental Mixolydian), -1/20-septimal comma 4ed(9/7)/-1/28-syntonic comma 14ed(12/5)/9ed(7/4) (Soft Superpental Mixolydian), 12ed(32/15) (Intense Superpental Mixolydian) and 8ed(5/3)/-1/9 schismic 9ed(16/9)/14ed(22/9) (Mixolydian-Ionian) respectively.
|}By a surprising coincidence, the 15ed of the Golden tenth (7φ+6)\(5φ^2)edo is almost exactly every third degree of [[34edo]]. Additionally, those of the modal Golden tenths are almost exactly +1/28-syntonic comma 4ed(5/4) (Aeolian-Dorian), 9ed(5/3)/equal multiples of 18/17 (Subpental Dorian), 13ed(15/7) (Pental Dorian), 2ed(9/8) (Superpental Dorian), -1/12-syntonic comma 3ed(6/5) (Dorian-Mixolydian), 14ed(7/3)/equal multiples of 17/16/100π\3 cents (Subpental Mixolydian), 3ed(6/5) (Pental Mixolydian), -1/20-septimal comma 4ed(9/7)/-1/28-syntonic comma 14ed(12/5)/9ed(7/4) (Soft Superpental Mixolydian), 12ed(32/15) (Intense Superpental Mixolydian) and 8ed(5/3)/-1/9 schismic 9ed(16/9)/14ed(22/9) (Mixolydian-Ionian) respectively.
[[Category:15-tone]]
[[Category:15-tone]]
[[Category:ed7/3]]
[[Category:ed7/3]]

Revision as of 17:41, 6 November 2018

15edX is the scale which occurs as the dominant minor 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 F#/Gb 96 97.778 100 101.818 102.857 104 105 106.667 107.586 110.345 112
2 G 192 195.556 200 203.636 205.714 208 210 213.333 215.172 220.69 224
3 G#/Jb G#/Ab 288 293.333 300 305.4545 308.571 312 315 320 322.759 331.034 336
4 J A 384 391.111 400 407.273 411.429 416 420 426.667 430.345 441.379 448
5 A B 480 488.889 500 509.091 514.286 520 525 533.333 537.931 551.724 560
6 A#/Bb B#/Hb 576 586.667 600 610.909 617.143 624 630 640 645.517 662.069 672
7 B H 672 684.444 700 712.727 720 728 735 746.667 753.103 772.414 784
8 B#/Hb H#/Cb 768 782.822 800 814.5455 822.857 832 845 853.333 860.69 882.759 896
9 H C 864 880 900 916.364 925.714 936 940 960 968.276 993.103 1008
10 C D 960 977.778 1000 1018.182 1028.571 1040 1050 1066.667 1075.862 1103.448 1120
11 C#/Db D#/Sb 1056 1075.556 1100 1120 1131.429 1144 1155 1173.333 1183.448 1213.379 1232
12 D S 1152 1173.333 1200 1221.818 1234.286 1248 1260 1280 1291.034 1324.138 1344
13 D#/Eb S#/Eb 1248 1271.111 1300 1323.636 1337.143 1352 1365 1386.667 1398.621 1424.483 1456
14 E 1344 1368.889 1400 1425.4545 1440 1456 1470 1493.333 1506.207 1544.827 1568
15 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 F#/Gb 96.925-98.658 102.294-104.027 104.888-106.621
2 G 193.8495-197.316 204.588-208.054 209.77-213.242
3 G#/Jb G#/Ab 290.774-295.974 306.8815-312.0815 314.663-319.863
4 J A 387.699-394.632 409.1755-416.109 419.559-426.484
5 A B 484.624-493.29 511.469-520.136 524.438-533.105
6 A#/Bb B#/Hb 581.548-591.948 613.763-624.163 629.3255-392.7255
7 B H 678.473-690.606 716.057-728.19 734.213-746.346
8 B#/Hb H#/Cb 775.398-789.2645 818.351-832.218 839.101-852.967
9 H C 872.3225-887.9225 920.645-936.245 943.988-959.588
10 C D 969.247-986.561 1022.939-1040.272 1048.876-1066.209
11 C#/Db D#/Sb 1066.172-1085.239 1125.2325-1144.299 1153.763-1172.83
12 D S 1163.097-1183.897 1227.526-1248.326 1258.651-1279.451
13 D#/Eb S#/Eb 1260.0215-1282.555 1329.82-1352.3535 1363.539-1386.072
14 E 1356.946-1381.213 1432.114-1456.381 1468.426-1492.693
15 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 F#/Gb 96.457 97.323 97.39 98.19 98.257 99.123 100.618 101.245 101.4845 102.1115 102.351 102.788
2 G 192.913 194.647 194.78 196.38 196.513 198.247 201.236 202.49 202.969 204.223 204.702 205.576
3 G#/Jb G#/Ab 289.37 291.97 292.17 294.57 294.77 297.37 301.854 303.734 304.454 306.334 307.054 308.365
4 J A 385.829 389.294 389.56 392.76 394.027 396.493 402.4715 404.979 405.938 408.446 409.405 411.153
5 A B 482.284 486.617 486.95 490.95 491.283 495.617 503.089 569.502 507.423 510.557 511.756 513.941
6 A#/Bb B#/Hb 578.74 583.94 584.334 589.14 589.54 594.74 603.707 607.469 608.907 612.669 614.107 616.729
7 B H 675.197 681.364 681.73 687.33 687.7965 693.863 704.325 708.7135 710.392 714.78 716.4585 719.5175
8 B#/Hb H#/Cb 771.654 778.587 779.12 785.52 786.053 792.9865 804.943 809.958 811.877 816.892 818.81 822.306
9 H C 868.1105 875.9105 876.51 883.7105 884.31 892.11 905.561 911.203 913.361 919.003 921.161 925.094
10 C D 964.567 973.234 973.9 981.901 982.5665 991.233 1006.179 1012.448 1014.8455 1021.115 1023.512 1027.882
11 C#/Db D#/Sb 1061.024 1070.557 1071.39 1080.091 1080.823 1090.356 1106.797 1113.693 1116.33 1123.226 1125.863 1130.67
12 D S 1157.481 1167.881 1168.68 1178.281 1179.08 1189.48 1207.4145 1214.9375 1217.8145 1225.3375 1228.2145 1233.459
13 D#/Eb S#/Eb 1253.937 1265.204 1266.07 1176.471 1277.336 1288.603 1308.032 1316.182 1319.299 1327.449 1330.566 1336.247
14 E 1350.394 1362.527 1363.46 1374.661 1375.593 1387.726 1408.65 1417.427 1420.783 1429.56 1432.917 1439.035
15 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 F#/Gb 102.978 103.655 103.855
2 G 205.956 207.31 207.709
3 G#/Jb G#/Ab 308.934 310.965 311.564
4 J A 411.9215 414.6195 415.419
5 A B 514.891 518.274 519.2735
6 A#/Bb B#/Hb 617.869 621.929 623.128
7 B H 720.847 725.584 726.983
8 B#/Hb H#/Cb 823.825 829.239 830.8375
9 H C 926.823 932.893 934.693
10 C D 1029.781 1036.549 1038.547
11 C#/Db D#/Sb 1132.759 1140.204 1142.402
12 D S 1235.7375 1243.859 1246.256
13 D#/Eb S#/Eb 1338.716 1347.513 1353.111
14 E 1441.694 1451.168 1453.966
15 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 F#/Gb 104.306 104.5215 104.721 105.173 105.788 106.04 106.664 107.531 108.398 108.4245 109.291 109.6375 110.158 110.504 111.371
2 G 208.613 209.043 209.443 210.346 211.576 212.08 213.329 215.032 216.795 216.849 218.582 219.275 220.316 221.008 222.742
3 G#/Jb G#/Ab 312.919 313.565 314.164 315.519 317.364 318.119 319.993 322.593 325.193 325.273 327.873 328.913 330.473 331.613 334.113
4 J A 417.226 418.086 418.885 420.639 423.152 424.159 426.657 430.124 433.5905 433.698 437.1345 438.55 440.631 442.017 445.4835
5 A B 521.532 526.308 523.607 525.865 528.94 530.199 533.321 537.655 541.988 542.122 546.456 548.188 550.789 552.521 556.854
6 A#/Bb B#/Hb 625.8385 627.129 628.328 631.0385 634.728 636.238 639.987 645.186 650.386 650.547 655.747 657.825 660.947 663.025 668.225
7 B H 730.145 731.651 733.0495 736.212 740.516 742.278 746.65 752.717 758.783 758.971 765.038 767.463 771.105 773.5235 779.596
8 B#/Hb H#/Cb 834.451 836.172 837.771 841.385 846.304 853.314 899.98 867.181 914.605 867.396 874.329 877.1 881.262 884.033 890.967
9 H C 938.758 940.694 942.492 946.558 952.092 954.358 999.978 967.7785 1016.228 975.82 983.62 986.738 991.42 994.538 1002.338
10 C D 1043.064 1045.2155 1047.214 1051.731 1057.88 1060.3975 1066.643 1075.3095 1083.976 1084.245 1092.911 1096.3755 1101.578 1105.042 1113.709
11 C#/Db D#/Sb 1147.3705 1149.737 1151.935 1156.904 1163.668 1166.437 1173.307 1182.84 1192.374 1192.669 1202.202 1206.013 1211.736 1215.546 1225.08
12 D S 1251.677 1254.259 1256.656 1262.077 1269.456 1272.477 1279.971 1290.371 1300.771 1301.0395 1311.4935 1315.651 1321.8935 1326.051 1336.451
13 D#/Eb S#/Eb 1355.983 1358.78 1361.378 1367.25 1275.244 1378.517 1386.636 1397.902 1409.169 1409.518 1420.785 1438.993 1425.288 1436.555 1447.8215
14 E 1460.29 1463.302 1466.099 1472.423 1481.032 1484.556 1493.3 1505.433 1517.567 1517.9425 1530.076 1541.778 1534.926 1547.059 1559.192
15 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, the 15ed of the Golden tenth (7φ+6)\(5φ^2)edo is almost exactly every third degree of 34edo. Additionally, those of the modal Golden tenths are almost exactly +1/28-syntonic comma 4ed(5/4) (Aeolian-Dorian), 9ed(5/3)/equal multiples of 18/17 (Subpental Dorian), 13ed(15/7) (Pental Dorian), 2ed(9/8) (Superpental Dorian), -1/12-syntonic comma 3ed(6/5) (Dorian-Mixolydian), 14ed(7/3)/equal multiples of 17/16/100π\3 cents (Subpental Mixolydian), 3ed(6/5) (Pental Mixolydian), -1/20-septimal comma 4ed(9/7)/-1/28-syntonic comma 14ed(12/5)/9ed(7/4) (Soft Superpental Mixolydian), 12ed(32/15) (Intense Superpental Mixolydian) and 8ed(5/3)/-1/9 schismic 9ed(16/9)/14ed(22/9) (Mixolydian-Ionian) respectively.

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