Xenharmonic Wiki

User:Moremajorthanmajor/15edX: Difference between revisions

← Older editNewer edit →
VisualWikitext
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
→Intervals: horizontally shortened first table, mostly by abbreviating the words Minimum and Maximum - at the same time increases significance, aligned cell content horizontally
No edit summary
Line 157: Line 157:
| colspan="2" |822.857
| colspan="2" |822.857
| colspan="2" |832
| colspan="2" |832
| colspan="2" |845
| colspan="2" |840
| colspan="2" |853.333
| colspan="2" |853.333
| colspan="2" |860.69
| colspan="2" |860.69
Line 172: Line 172:
| colspan="2" |925.714
| colspan="2" |925.714
| colspan="2" |936
| colspan="2" |936
| colspan="2" |940
| colspan="2" |945
| colspan="2" |960
| colspan="2" |960
| colspan="2" |968.276
| colspan="2" |968.276
Line 380: Line 380:
|1534.408-1560.408
|1534.408-1560.408
|1573.314-1599.314
|1573.314-1599.314
|}Golden tunings
|}Golden tunings±13¢
 
{| class="wikitable" style="text-align: center"
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
| colspan="2" |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
| 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
|103.855
|-
|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
! rowspan="4" |Degrees
! colspan="2" rowspan="4" |Enneatonic
! colspan="2" rowspan="4" |Enneatonic
! colspan="13" |Mixolydian
! colspan="4" |Minor mode Middletown temperament
! colspan="2" |Mixolydian-Ionian
!Neutral mode Middletown temperament
! colspan="6" |Major mode Middletown temperament
|-
|-
! colspan="3" |Subpental
! rowspan="3" |Aeolian-Dorian
! colspan="4" |Pental
! colspan="3" |Dorian
! colspan="6" |Superpental
! colspan="2" rowspan="3" |Dorian-Mixolydian
! rowspan="3" |Mean
! colspan="4" |Mixolydian
! rowspan="3" |+13¢
! rowspan="3" |Mixolydian-Ionian
|-
|-
! rowspan="2" |-13¢ (5)
! rowspan="2" |Subpental
! rowspan="2" |+13¢ (D-M)
! rowspan="2" |Pental
! rowspan="2" |Mean
! rowspan="2" |Superpental
! rowspan="2" |Mean
! rowspan="2" |Subpental
! rowspan="2" |+13¢ (s5)
! rowspan="2" |Pental
! rowspan="2" |+13¢
! colspan="2" |Superpental
! rowspan="2" |-13¢ (Soft s5)
! rowspan="2" |Soft
! colspan="5" |Intense
|-
|-
!+13¢ (Soft s5)
!Soft
!-13¢
!Intense
!Mean
!-13¢ (M-I)
!+13¢
|-
|-
|1
| |1
| colspan="2" |F#/Gb
| colspan="2" |F#/Gb
|104.306
| |96.457-98.19
|104.5215
|97.39-99.123
|104.721
|100.618-102.351
|105.173
|101.245-102.978
|105.788
| colspan="2" |102.788-104.5215
|106.04
|103.855-105.788
|106.664
|104.306-106.04
|107.531
|106.664-108.398
|108.398
|108.4245-110.158
|108.4245
|109.6375-111.371
|109.291
|109.6375
|110.158
|110.504
|111.371
|-
|-
|2
| |2
| colspan="2" |G
| colspan="2" |G
|208.613
| |192.913-196.38
|209.043
|194.78-198.247
|209.443
|201.236-204.702
|210.346
|202.49-205.956
|211.576
| colspan="2" |205.576-209.043
|212.08
|207.709-211.576
|213.329
|208.613-212.08
|215.032
|213.329-216.795
|216.795
|216.849-220.316
|216.849
|219.275-222.742
|218.582
|219.275
|220.316
|221.008
|222.742
|-
|-
|3
| |3
|G#/Jb
|G#/Jb
|''G#/Ab''
|''G#/Ab''
|312.919
| |289.37-294.57
|313.565
|292.17-297.37
|314.164
|301.854-204.702
|315.519
|303.734-308.934
|317.364
| colspan="2" |308.365-313.565
|318.119
|311.564-317.364
|319.993
|312.919-318.119
|322.593
|319.993-325.193
|325.193
|325.273-330.473
|325.273
|328.913-334.113
|327.873
|328.913
|330.473
|331.613
|334.113
|-
|-
|4
| |4
|J
|J
|''A''
|''A''
|417.226
| |385.829-392.76
|418.086
|389.56-396.493
|418.885
|402.4715-307.054
|420.639
|404.979-411.9215
|423.152
| colspan="2" |411.153-418.086
|424.159
|415.419-423.152
|426.657
|417.226-424.159
|430.124
|426.657-433.5905
|433.5905
|433.698-440.631
|433.698
|438.55-445.4835
|437.1345
|438.55
|440.631
|442.017
|445.4835
|-
|-
|5
| |5
|A
|A
|''B''
|''B''
|521.532
| |482.284-490.95
|526.308
|486.95-495.617
|523.607
|503.089-511.756
|525.865
|509.502-514.891
|528.94
| colspan="2" |513.941-526.308
|530.199
|519.2735-528.94
|533.321
|521.532-530.199
|537.655
|533.321-541.988
|541.988
|542.122-550.789
|542.122
|548.188-556.854
|546.456
|548.188
|550.789
|552.521
|556.854
|-
|-
|6
| |6
|A#/Bb
|A#/Bb
|''B#/Hb''
|''B#/Hb''
|625.8385
| |578.74-589.14
|627.129
|584.334-594.74
|628.328
|603.707-614.107
|631.0385
|607.469-617.869
|634.728
| colspan="2" |616.729-627.129
|636.238
|623.128-634.728
|639.987
|625.8385-636.238
|645.186
|639.987-650.386
|650.386
|650.547-660.947
|650.547
|657.825-668.225
|655.747
|657.825
|660.947
|663.025
|668.225
|-
|-
|7
| |7
|B
|B
|''H''
|''H''
|730.145
| |675.197-687.33
|731.651
|681.73-693.863
|733.0495
|704.325-716.4585
|736.212
|708.7135-720.847
|740.516
| colspan="2" |719.5175-731.651
|742.278
|726.983-740.516
|746.65
|730.145-742.278
|752.717
|746.65-758.783
|758.783
|758.971-771.105
|758.971
|767.463-779.596
|765.038
|767.463
|771.105
|773.5235
|779.596
|-
|-
|8
|8
|B#/Hb
|B#/Hb
|''H#/Cb''
|''H#/Cb''
|834.451
|771.654-785.52
|836.172
|779.12-792.9865
|837.771
|804.943-818.81
|841.385
|809.958-823.825
|846.304
| colspan="2" |822.306-836.172
|853.314
|830.8375-844.704
|899.98
|834.451-848.318
|867.181
|853.314-867.181
|914.605
|867.396-881.262
|867.396
|877.1-890.967
|874.329
|877.1
|881.262
|884.033
|890.967
|-
|-
|9
|9
|H
|H
|''C''
|''C''
|938.758
|868.1105-883.7105
|940.694
|876.51-892.11
|942.492
|905.561-921.161
|946.558
|911.203-926.823
|952.092
| colspan="2" |925.094-940.694
|954.358
|934.693-952.092
|999.978
|938.758-954.358
|967.7785
|959.9785-975.5785
|1016.228
|975.82-991.42
|975.82
|986.738-1002.338
|983.62
|986.738
|991.42
|994.538
|1002.338
|-
|-
|10
|10
|C
|C
|''D''
|''D''
|1043.064
|964.567-981.901
|1045.2155
|973.9-991.233
|1047.214
|1006.179-1023.512
|1051.731
|1012.448-1029.781
|1057.88
| colspan="2" |1027.882-1045.2155
|1060.3975
|1038.547-1057.88
|1066.643
|1043.064-1060.3975
|1075.3095
|1066.643-1083.976
|1083.976
|1084.245-1101.578
|1084.245
|1096.3755-1113.709
|1092.911
|1096.3755
|1101.578
|1105.042
|1113.709
|-
|-
|11
|11
|C#/Db
|C#/Db
|''D#/Sb''
|''D#/Sb''
|1147.3705
|1061.024-1080.091
|1149.737
|1071.39-1090.356
|1151.935
|1106.797-1125.863
|1156.904
|1113.693-1132.759
|1163.668
| colspan="2" |1130.67-1149.737
|1166.437
|1142.402-1163.668
|1173.307
|1147.3705-1166.437
|1182.84
|1173.307-1192.374
|1192.374
|1192.669-1211.736
|1192.669
|1206.013-1225.08
|1202.202
|1206.013
|1211.736
|1215.546
|1225.08
|-
|-
|12
|12
|D
|D
|''S''
|''S''
|1251.677
|1157.481-1178.281
|1254.259
|1168.68-1189.48
|1256.656
|1207.4145-1228.2145
|1262.077
|1214.9375-1235.7375
|1269.456
| colspan="2" |1233.459-1254.259
|1272.477
|1246.256-1269.456
|1279.971
|1251.677-1272.477
|1290.371
|1279.971-1300.771
|1300.771
|1301.0395-1321.8935
|1301.0395
|1315.651-1336.451
|1311.4935
|1315.651
|1321.8935
|1326.051
|1336.451
|-
|-
|13
|13
|D#/Eb
|D#/Eb
|''S#/Eb''
|''S#/Eb''
|1355.983
|1253.937-1276.471
|1358.78
|1266.07-1288.603
|1361.378
|1308.032-1330.566
|1367.25
|1316.182-1338.716
|1275.244
| colspan="2" |1336.247-1358.78
|1378.517
|1353.111-1275.244
|1386.636
|1355.983-1378.517
|1397.902
|1386.636-1409.169
|1409.169
|1409.518-1425.288
|1409.518
|1438.993-1447.8215
|1420.785
|1438.993
|1425.288
|1436.555
|1447.8215
|-
|-
|14
|14
| colspan="2" |E
| colspan="2" |E
|1460.29
|1350.394-1374.661
|1463.302
|1363.46-1387.726
|1466.099
|1408.65-1432.917
|1472.423
|1417.427-1441.694
|1481.032
| colspan="2" |1439.035-1463.302
|1484.556
|1453.966-1481.032
|1493.3
|1460.29-1484.556
|1505.433
|1493.3-1517.567
|1517.567
|1517.9425-1534.926
|1517.9425
|1541.778-1559.192
|1530.076
|1541.778
|1534.926
|1547.059
|1559.192
|-
|-
|15
|15
| colspan="2" |F
| colspan="2" |F
|1564.596
|1446.851-1472.851
|1567.96
|1460.85-1486.85
|1570.82
|1509.268-1535.268
|1577.596
|1518.672-1544.672
|1583.82
| colspan="2" |1541.823-1567.823
|1590.596
|1557.82-1583.82
|1599.964
|1564.596-1590.596
|1612.964
|1599.964-1625.964
|1625.964
|1626.366-1652.366
|1626.366
|1644.563-1670.563
|1639.366
|}
|1644.563
 
|1652.366
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.
|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.
[[Category:15-tone]]
[[Category:15-tone]]
[[Category:ed7/3]]
[[Category:ed7/3]]
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/15edX"