User:Moremajorthanmajor/15edX: Difference between revisions

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==Intervals==
==Intervals==
{| class="wikitable" style="text-align: center"
{| class="wikitable" style="text-align: center"
! rowspan="5" |Degrees
! rowspan="3" |Degrees
! colspan="2" rowspan="5" |Enneatonic
! colspan="2" rowspan="3" |Enneatonic
! colspan="8" |Minor mode Middletown temperament
! colspan="4" rowspan="2" |Intense Aeolian-Subpental Dorian
! colspan="2" |Neutral mode Middletown temperament
! colspan="9" |Dorian
! colspan="10" |Major mode Middletown temperament
|-
|-
! colspan="2" rowspan="3" |Intense Aeolian-Dorian
! colspan="9" |Subpental
! colspan="6" |Dorian
! colspan="2" rowspan="3" |Dorian-Mixolydian
! colspan="8" |Mixolydian
! colspan="2" rowspan="3" |Mixolydian-Ionian
|-
|-
! colspan="2" rowspan="2" |Subpental
!Min
! colspan="2" rowspan="2" |Pental
!Golden±13¢
! colspan="2" rowspan="2" |Superpental
!7/3±13¢
! colspan="2" rowspan="2" |Subpental
!Max
! colspan="2" rowspan="2" |Pental
!Min
! colspan="4" |Superpental
!Golden±13¢
|-
!Max
! colspan="2" |Soft
!Min
! colspan="2" |Intense
!Golden±13¢
|-
!Max
! width="4%" | Min
!Min
! width="4%" | Max
!Golden±13¢
! width="4%" | Min
!Max
! width="4%" | Max
! width="4%" | Min
! width="4%" | Max
! width="4%" | Min
! width="4%" | Max
! width="4%" | Min
! width="4%" | Max
! width="4%" | Min
! width="4%" | Max
! width="4%" | Min
! width="4%" | Max
! width="4%" | Min
! width="4%" | Max
! width="4%" | Min
! width="4%" | Max
! width="4%" | Min
! width="4%" | Max
|-
|-
| |1
| |1
| colspan="2" |F#/Gb
|G#/Jb
|''G#/Ab''
| |96
| |96
|96.457-98.19
|96.925-98.658
| colspan="2" |97.778
| colspan="2" |97.778
|97.39-99.123
| colspan="2" |100
| colspan="2" |100
|100.618-102.351
| colspan="2" |101.818
| colspan="2" |101.818
| colspan="2" |102.857
|101.245-102.978
| colspan="2" |104
|102.857
| colspan="2" |105
| colspan="2" |106.667
| colspan="2" |107.586
| colspan="2" |110.345
| |112
|-
|-
| |2
| |2
| colspan="2" |G
|J
|''A''
| |192
| |192
|192.913-196.38
|193.8495-197.316
| colspan="2" |195.556
| colspan="2" |195.556
|194.78-198.247
| colspan="2" |200
| colspan="2" |200
|201.236-204.702
| colspan="2" |203.636
| colspan="2" |203.636
| colspan="2" |205.714
|202.49-205.956
| colspan="2" |208
|205.714
| colspan="2" |210
| colspan="2" |213.333
| colspan="2" |215.172
| colspan="2" |220.69
| |224
|-
|-
| |3
| |3
|G#/Jb
|J#/Ab
|''G#/Ab''
|''A#/Bb''
| |288
| |288
|289.37-294.57
|290.774-295.974
| colspan="2" |293.333
| colspan="2" |293.333
|292.17-297.37
| colspan="2" |300
| colspan="2" |300
|301.854-204.702
| colspan="2" |305.4545
| colspan="2" |305.4545
| colspan="2" |308.571
|303.734-308.934
| colspan="2" |312
|308.571
| colspan="2" |315
| colspan="2" |320
| colspan="2" |322.759
| colspan="2" |331.034
| |336
|-
|-
| |4
| |4
|J
|J
|''A''
|''B''
| |384
| |384
|385.829-392.76
|387.699-394.632
| colspan="2" |391.111
| colspan="2" |391.111
|389.56-396.493
| colspan="2" |400
| colspan="2" |400
|402.4715-307.054
| colspan="2" |407.273
| colspan="2" |407.273
| colspan="2" |411.429
|404.979-411.9215
| colspan="2" |416
|411.429
| colspan="2" |420
| colspan="2" |426.667
| colspan="2" |430.345
| colspan="2" |441.379
| |448
|-
|-
| |5
| |5
|A
|A
|''B''
|''C''
| |480
| |480
|482.284-490.95
|484.624-493.29
| colspan="2" |488.889
| colspan="2" |488.889
|486.95-495.617
| colspan="2" |500
| colspan="2" |500
|503.089-511.756
| colspan="2" |509.091
| colspan="2" |509.091
| colspan="2" |514.286
|509.502-514.891
| colspan="2" |520
|514.286
| colspan="2" |525
| colspan="2" |533.333
| colspan="2" |537.931
| colspan="2" |551.724
| |560
|-
|-
| |6
| |6
|A#/Bb
|A#/Bb
|''B#/Hb''
|''C#/Qb''
| |576
| |576
|578.74-589.14
|581.548-591.948
| colspan="2" |586.667
| colspan="2" |586.667
|584.334-594.74
| colspan="2" |600
| colspan="2" |600
|603.707-614.107
| colspan="2" |610.909
| colspan="2" |610.909
| colspan="2" |617.143
|607.469-617.869
| colspan="2" |624
|617.143
| colspan="2" |630
| colspan="2" |640
| colspan="2" |645.517
| colspan="2" |662.069
| |672
|-
|-
| |7
| |7
|B
|B
|''H''
|''Q''
| |672
| |672
|675.197-687.33
|678.473-690.606
| colspan="2" |684.444
| colspan="2" |684.444
|681.73-693.863
| colspan="2" |700
| colspan="2" |700
|704.325-716.4585
| colspan="2" |712.727
| colspan="2" |712.727
| colspan="2" |720
|708.7135-720.847
| colspan="2" |728
|720
| colspan="2" |735
| colspan="2" |746.667
| colspan="2" |753.103
| colspan="2" |772.414
| |784
|-
|-
|8
|8
|B#/Hb
|B#/Cb
|''H#/Cb''
|''Q#/Db''
|768
|768
|771.654-785.52
|775.398-789.2645
| colspan="2" |782.822
| colspan="2" |782.822
|779.12-792.9865
| colspan="2" |800
| colspan="2" |800
|804.943-818.81
| colspan="2" |814.5455
| colspan="2" |814.5455
| colspan="2" |822.857
|809.958-823.825
| colspan="2" |832
|822.857
| colspan="2" |840
| colspan="2" |853.333
| colspan="2" |860.69
| colspan="2" |882.759
|896
|-
|-
|9
|9
|H
|C
|''C''
|''D''
|864
|864
|868.1105-883.7105
|872.3225-887.9225
| colspan="2" |880
| colspan="2" |880
|876.51-892.11
| colspan="2" |900
| colspan="2" |900
|905.561-921.161
| colspan="2" |916.364
| colspan="2" |916.364
| colspan="2" |925.714
|911.203-926.823
| colspan="2" |936
|925.714
| colspan="2" |945
| colspan="2" |960
| colspan="2" |968.276
| colspan="2" |993.103
|1008
|-
|-
|10
|10
|C
|D
|''D''
|''S''
|960
|960
|964.567-981.901
|969.247-986.561
| colspan="2" |977.778
| colspan="2" |977.778
|973.9-991.233
| colspan="2" |1000
| colspan="2" |1000
|1006.179-1023.512
| colspan="2" |1018.182
| colspan="2" |1018.182
| colspan="2" |1028.571
|1012.448-1029.781
| colspan="2" |1040
|1028.571
| colspan="2" |1050
| colspan="2" |1066.667
| colspan="2" |1075.862
| colspan="2" |1103.448
|1120
|-
|-
|11
|11
|C#/Db
|D#/Eb
|''D#/Sb''
|''S#/Eb''
|1056
|1056
|1061.024-1080.091
|1066.172-1085.239
| colspan="2" |1075.556
| colspan="2" |1075.556
|1071.39-1090.356
| colspan="2" |1100
| colspan="2" |1100
|1106.797-1125.863
| colspan="2" |1120
| colspan="2" |1120
| colspan="2" |1131.429
|1113.693-1132.759
| colspan="2" |1144
|1131.429
| colspan="2" |1155
| colspan="2" |1173.333
| colspan="2" |1183.448
| colspan="2" |1213.379
|1232
|-
|-
|12
|12
|D
| colspan="2" |E
|''S''
|1152
|1152
|1157.481-1178.281
|1163.097-1183.897
| colspan="2" |1173.333
| colspan="2" |1173.333
|1168.68-1189.48
| colspan="2" |1200
| colspan="2" |1200
|1207.4145-1228.2145
| colspan="2" |1221.818
| colspan="2" |1221.818
| colspan="2" |1234.286
|1214.9375-1235.7375
| colspan="2" |1248
|1234.286
| colspan="2" |1260
| colspan="2" |1280
| colspan="2" |1291.034
| colspan="2" |1324.138
|1344
|-
|-
|13
|13
|D#/Eb
| colspan="2" |E#/Fb
|''S#/Eb''
|1248
|1248
|1253.937-1276.471
|1260.0215-1282.555
| colspan="2" |1271.111
| colspan="2" |1271.111
|1266.07-1288.603
| colspan="2" |1300
| colspan="2" |1300
|1308.032-1330.566
| colspan="2" |1323.636
| colspan="2" |1323.636
| colspan="2" |1337.143
|1316.182-1338.716
| colspan="2" |1352
|1337.143
| colspan="2" |1365
| colspan="2" |1386.667
| colspan="2" |1398.621
| colspan="2" |1424.483
|1456
|-
|-
|14
|14
| colspan="2" |E
| colspan="2" |F
|1344
|1344
|1350.394-1374.661
|1356.946-1381.213
| colspan="2" |1368.889
| colspan="2" |1368.889
|1363.46-1387.726
| colspan="2" |1400
| colspan="2" |1400
|1408.65-1432.917
| colspan="2" |1425.4545
| colspan="2" |1425.4545
| colspan="2" |1440
|1417.427-1441.694
| colspan="2" |1456
|1440
| colspan="2" |1470
| colspan="2" |1493.333
| colspan="2" |1506.207
| colspan="2" |1544.827
|1568
|-
|-
|15
|15
| colspan="2" |F
| colspan="2" |G
|1440
|1440
|1446.851-1472.851
|1453.871-1479.871
| colspan="2" |1466.667
| colspan="2" |1466.667
|1460.85-1486.85
| colspan="2" |1500
| colspan="2" |1500
|1509.268-1535.268
| colspan="2" |1527.273
| colspan="2" |1527.273
| colspan="2" |1542.857
|1518.672-1544.672
| colspan="2" |1560
|1542.857
| colspan="2" |1575
| colspan="2" |1600
| colspan="2" |1613.793
| colspan="2" |1655.172
|1680
|}
|}


Most harmonic tunings
{| class="wikitable" style="text-align: center"
{| class="wikitable"
!Degrees
|-
! colspan="4" |Enneatonic
! rowspan="2" |Degrees
!Min
! colspan="2" rowspan="2" |Enneatonic
!Minor mode Middletown temperament
!Neutral mode Middletown temperament
!Major mode Middletown temperament
|-
!7/3±13¢
!22/9±13¢
!22/9±13¢
!5/2±13¢
!Golden±13¢
!Max
|-
|-
|1
| |1
| colspan="2" |F#/Gb
| colspan="2" |F#/Gb
|96.925-98.658
|G#/Jb
|''G#/Ab''
|102.857
|102.294-104.027
|102.294-104.027
|104.888-106.621
|102.788-104.5215
|104
|-
|-
| |2
| |2
| colspan="2" |G
| colspan="2" |G
|193.8495-197.316
|J
|''A''
|205.714
|204.588-208.054
|204.588-208.054
|209.77-213.242
|205.576-209.043
|208
|-
|-
|3
| |3
|G#/Jb
|G#/Jb
|''G#/Ab''
|''G#/Ab''
|290.774-295.974
|J#/Ab
|''A#/Bb''
|308.571
|306.8815-312.0815
|306.8815-312.0815
|314.663-319.863
|308.365-313.565
|312
|-
|-
| |4
| |4
|J
|J
|''A''
|''A''
|387.699-394.632
|J
|''B''
|411.429
|409.1755-416.109
|409.1755-416.109
|419.559-426.484
|411.153-418.086
|416
|-
|-
| |5
| |5
|A
|A
|''B''
|''B''
|484.624-493.29
|A
|''C''
|514.286
|511.469-520.136
|511.469-520.136
|524.438-533.105
|513.941-526.308
|520
|-
|-
|6
| |6
|A#/Bb
|A#/Bb
|''B#/Hb''
|''B#/Hb''
|581.548-591.948
|A#/Bb
|''C#/Qb''
|617.143
|613.763-624.163
|613.763-624.163
|629.3255-639.7255
|616.729-627.129
|624
|-
|-
| |7
| |7
|B
|B
|''H''
|''H''
|678.473-690.606
|B
|''Q''
|720
|716.057-728.19
|716.057-728.19
|734.213-746.346
|719.5175-731.651
|728
|-
|-
|8
|8
|B#/Hb
|B#/Hb
|''H#/Cb''
|''H#/Cb''
|775.398-789.2645
|B#/Cb
|''Q#/Db''
|822.857
|818.351-832.218
|818.351-832.218
|839.101-852.967
|822.306-836.172
|832
|-
|-
|9
|9
|H
|H
|''C''
|''C''
|872.3225-887.9225
|C
|''D''
|925.714
|920.645-936.245
|920.645-936.245
|943.988-959.588
|925.094-940.694
|936
|-
|-
|10
|10
|C
|C
|''D''
|''D''
|969.247-986.561
|D
|''S''
|1028.571
|1022.939-1040.272
|1022.939-1040.272
|1048.876-1066.209
|1027.882-1045.2155
|1040
|-
|-
| |11
|11
|C#/Db
|C#/Db
|''D#/Sb''
|''D#/Sb''
|1066.172-1085.239
|D#/Eb
|''S#/Eb''
|1131.429
|1125.2325-1144.299
|1125.2325-1144.299
|1153.763-1172.83
|1130.67-1149.737
|1144
|-
|-
|12
|12
|D
|D
|''S''
|''S''
|1163.097-1183.897
| colspan="2" |E
|1234.286
|1227.526-1248.326
|1227.526-1248.326
|1258.651-1279.451
|1233.459-1254.259
|1248
|-
|-
| |13
|13
|D#/Eb
|D#/Eb
|''S#/Eb''
|''S#/Eb''
|1260.0215-1282.555
| colspan="2" |E#/Fb
|1337.143
|1329.82-1352.3535
|1329.82-1352.3535
|1363.539-1386.072
|1336.247-1358.78
|1352
|-
|-
|14
|14
| colspan="2" |E
| colspan="2" |E
|1356.946-1381.213
| colspan="2" |F
|1440
|1432.114-1456.381
|1432.114-1456.381
|1468.426-1492.693
|1439.035-1463.302
|1456
|-
|-
|15
|15
| colspan="2" |F
| colspan="2" |F
|1453.871-1479.871
| colspan="2" |G
|1542.857
|1534.408-1560.408
|1534.408-1560.408
|1573.314-1599.314
|1541.823-1567.823
|}Golden tunings±13¢
|1560
|}
 
{| class="wikitable" style="text-align: center"
{| class="wikitable" style="text-align: center"
|-
! rowspan="4" |Degrees
! rowspan="4" |Degrees
! colspan="2" rowspan="4" |Enneatonic
! colspan="2" rowspan="4" |Enneatonic
! colspan="4" |Minor mode Middletown temperament
! colspan="13" |Mixolydian
!Neutral mode Middletown temperament
! colspan="3" rowspan="3" |Mixolydian-Ionian
! colspan="6" |Major mode Middletown temperament
|-
|-
! rowspan="3" |Intense Aeolian-Dorian
! colspan="3" rowspan="2" |Subpental
! colspan="3" |Dorian
! colspan="4" rowspan="2" |Pental
! colspan="2" rowspan="3" |Dorian-Mixolydian
! colspan="6" |Superpental
! colspan="4" |Mixolydian
! rowspan="3" |Mixolydian-Ionian
|-
|-
! rowspan="2" |Subpental
! colspan="3" |Soft
! rowspan="2" |Pental
! colspan="3" |Intense
! rowspan="2" |Superpental
! rowspan="2" |Subpental
! rowspan="2" |Pental
! colspan="2" |Superpental
|-
|-
!Soft
! width="4%" | Min
!Intense
!Golden±13¢
! width="4%" | Max
! width="4%" | Min
!Golden±13¢
!5/2±13¢
! width="4%" | Max
! width="4%" | Min
!Golden±13¢
! width="4%" | Max
! width="4%" | Min
!Golden±13¢
! width="4%" | Max
! width="4%" | Min
!Golden±13¢
! width="4%" | Max
|-
|-
| |1
| |1
| colspan="2" |F#/Gb
| colspan="2" |F#/Gb
| |96.457-98.19
|104
|97.39-99.123
|100.618-102.351
|101.245-102.978
| colspan="2" |102.788-104.5215
|103.855-105.788
|103.855-105.788
| colspan="2" |105
|104.306-106.04
|104.306-106.04
|104.888-106.621
| colspan="2" |106.667
|106.664-108.398
|106.664-108.398
| colspan="2" |107.586
|108.4245-110.158
|108.4245-110.158
| colspan="2" |110.345
|109.6375-111.371
|109.6375-111.371
| |112
|-
|-
| |2
| |2
| colspan="2" |G
| colspan="2" |G
| |192.913-196.38
|208
|194.78-198.247
|201.236-204.702
|202.49-205.956
| colspan="2" |205.576-209.043
|207.709-211.576
|207.709-211.576
| colspan="2" |210
|208.613-212.08
|208.613-212.08
|209.77-213.242
| colspan="2" |213.333
|213.329-216.795
|213.329-216.795
| colspan="2" |215.172
|216.849-220.316
|216.849-220.316
| colspan="2" |220.69
|219.275-222.742
|219.275-222.742
| |224
|-
|-
| |3
| |3
|G#/Jb
|G#/Jb
|''G#/Ab''
|''G#/Ab''
| |289.37-294.57
|312
|292.17-297.37
|301.854-204.702
|303.734-308.934
| colspan="2" |308.365-313.565
|311.564-317.364
|311.564-317.364
| colspan="2" |315
|312.919-318.119
|312.919-318.119
|314.663-319.863
| colspan="2" |320
|319.993-325.193
|319.993-325.193
| colspan="2" |322.759
|325.273-330.473
|325.273-330.473
| colspan="2" |331.034
|328.913-334.113
|328.913-334.113
| |336
|-
|-
| |4
| |4
|J
|J
|''A''
|''A''
| |385.829-392.76
|416
|389.56-396.493
|402.4715-307.054
|404.979-411.9215
| colspan="2" |411.153-418.086
|415.419-423.152
|415.419-423.152
| colspan="2" |420
|417.226-424.159
|417.226-424.159
|419.559-426.484
| colspan="2" |426.667
|426.657-433.5905
|426.657-433.5905
| colspan="2" |430.345
|433.698-440.631
|433.698-440.631
| colspan="2" |441.379
|438.55-445.4835
|438.55-445.4835
| |448
|-
|-
| |5
| |5
|A
|A
|''B''
|''B''
| |482.284-490.95
|520
|486.95-495.617
|503.089-511.756
|509.502-514.891
| colspan="2" |513.941-526.308
|519.2735-528.94
|519.2735-528.94
| colspan="2" |525
|521.532-530.199
|521.532-530.199
|524.438-533.105
| colspan="2" |533.333
|533.321-541.988
|533.321-541.988
| colspan="2" |537.931
|542.122-550.789
|542.122-550.789
| colspan="2" |551.724
|548.188-556.854
|548.188-556.854
| |560
|-
|-
| |6
| |6
|A#/Bb
|A#/Bb
|''B#/Hb''
|''B#/Hb''
| |578.74-589.14
|624
|584.334-594.74
|603.707-614.107
|607.469-617.869
| colspan="2" |616.729-627.129
|623.128-634.728
|623.128-634.728
| colspan="2" |630
|625.8385-636.238
|625.8385-636.238
|629.3255-639.7255
| colspan="2" |640
|639.987-650.386
|639.987-650.386
| colspan="2" |645.517
|650.547-660.947
|650.547-660.947
| colspan="2" |662.069
|657.825-668.225
|657.825-668.225
| |672
|-
|-
| |7
| |7
|B
|B
|''H''
|''H''
| |675.197-687.33
|728
|681.73-693.863
|704.325-716.4585
|708.7135-720.847
| colspan="2" |719.5175-731.651
|726.983-740.516
|726.983-740.516
| colspan="2" |735
|730.145-742.278
|730.145-742.278
|734.213-746.346
| colspan="2" |746.667
|746.65-758.783
|746.65-758.783
| colspan="2" |753.103
|758.971-771.105
|758.971-771.105
| colspan="2" |772.414
|767.463-779.596
|767.463-779.596
| |784
|-
|-
|8
|8
|B#/Hb
|B#/Hb
|''H#/Cb''
|''H#/Cb''
|771.654-785.52
|832
|779.12-792.9865
|804.943-818.81
|809.958-823.825
| colspan="2" |822.306-836.172
|830.8375-844.704
|830.8375-844.704
| colspan="2" |840
|834.451-848.318
|834.451-848.318
|839.101-852.967
| colspan="2" |853.333
|853.314-867.181
|853.314-867.181
| colspan="2" |860.69
|867.396-881.262
|867.396-881.262
| colspan="2" |882.759
|877.1-890.967
|877.1-890.967
|896
|-
|-
|9
|9
|H
|H
|''C''
|''C''
|868.1105-883.7105
|936
|876.51-892.11
|905.561-921.161
|911.203-926.823
| colspan="2" |925.094-940.694
|934.693-952.092
|934.693-952.092
| colspan="2" |945
|938.758-954.358
|938.758-954.358
|943.988-959.588
| colspan="2" |960
|959.9785-975.5785
|959.9785-975.5785
| colspan="2" |968.276
|975.82-991.42
|975.82-991.42
| colspan="2" |993.103
|986.738-1002.338
|986.738-1002.338
|1008
|-
|-
|10
|10
|C
|C
|''D''
|''D''
|964.567-981.901
|1040
|973.9-991.233
|1006.179-1023.512
|1012.448-1029.781
| colspan="2" |1027.882-1045.2155
|1038.547-1057.88
|1038.547-1057.88
| colspan="2" |1050
|1043.064-1060.3975
|1043.064-1060.3975
|1048.876-1066.209
| colspan="2" |1066.667
|1066.643-1083.976
|1066.643-1083.976
| colspan="2" |1075.862
|1084.245-1101.578
|1084.245-1101.578
| colspan="2" |1103.448
|1096.3755-1113.709
|1096.3755-1113.709
|1120
|-
|-
|11
|11
|C#/Db
|C#/Db
|''D#/Sb''
|''D#/Sb''
|1061.024-1080.091
|1144
|1071.39-1090.356
|1106.797-1125.863
|1113.693-1132.759
| colspan="2" |1130.67-1149.737
|1142.402-1163.668
|1142.402-1163.668
| colspan="2" |1155
|1147.3705-1166.437
|1147.3705-1166.437
|1153.763-1172.83
| colspan="2" |1173.333
|1173.307-1192.374
|1173.307-1192.374
| colspan="2" |1183.448
|1192.669-1211.736
|1192.669-1211.736
| colspan="2" |1213.379
|1206.013-1225.08
|1206.013-1225.08
|1232
|-
|-
|12
|12
|D
|D
|''S''
|''S''
|1157.481-1178.281
|1248
|1168.68-1189.48
|1207.4145-1228.2145
|1214.9375-1235.7375
| colspan="2" |1233.459-1254.259
|1246.256-1269.456
|1246.256-1269.456
| colspan="2" |1260
|1251.677-1272.477
|1251.677-1272.477
|1258.651-1279.451
| colspan="2" |1280
|1279.971-1300.771
|1279.971-1300.771
| colspan="2" |1291.034
|1301.0395-1321.8935
|1301.0395-1321.8935
| colspan="2" |1324.138
|1315.651-1336.451
|1315.651-1336.451
|1344
|-
|-
|13
|13
|D#/Eb
|D#/Eb
|''S#/Eb''
|''S#/Eb''
|1253.937-1276.471
|1352
|1266.07-1288.603
|1308.032-1330.566
|1316.182-1338.716
| colspan="2" |1336.247-1358.78
|1353.111-1275.244
|1353.111-1275.244
| colspan="2" |1365
|1355.983-1378.517
|1355.983-1378.517
|1363.539-1386.072
| colspan="2" |1386.667
|1386.636-1409.169
|1386.636-1409.169
| colspan="2" |1398.621
|1409.518-1425.288
|1409.518-1425.288
| colspan="2" |1424.483
|1438.993-1447.8215
|1438.993-1447.8215
|1456
|-
|-
|14
|14
| colspan="2" |E
| colspan="2" |E
|1350.394-1374.661
|1456
|1363.46-1387.726
|1408.65-1432.917
|1417.427-1441.694
| colspan="2" |1439.035-1463.302
|1453.966-1481.032
|1453.966-1481.032
| colspan="2" |1470
|1460.29-1484.556
|1460.29-1484.556
|1468.426-1492.693
| colspan="2" |1493.333
|1493.3-1517.567
|1493.3-1517.567
| colspan="2" |1506.207
|1517.9425-1534.926
|1517.9425-1534.926
| colspan="2" |1544.827
|1541.778-1559.192
|1541.778-1559.192
|1568
|-
|-
|15
|15
| colspan="2" |F
| colspan="2" |F
|1446.851-1472.851
|1560
|1460.85-1486.85
|1509.268-1535.268
|1518.672-1544.672
| colspan="2" |1541.823-1567.823
|1557.82-1583.82
|1557.82-1583.82
| colspan="2" |1575
|1564.596-1590.596
|1564.596-1590.596
|1573.314-1599.314
| colspan="2" |1600
|1599.964-1625.964
|1599.964-1625.964
| colspan="2" |1613.793
|1626.366-1652.366
|1626.366-1652.366
| colspan="2" |1655.172
|1644.563-1670.563
|1644.563-1670.563
|1680
|}
|}


Revision as of 20:38, 22 December 2018

15edX is the scale which occurs as the dominant minor edX.

Intervals

Degrees Enneatonic Intense Aeolian-Subpental Dorian Dorian
Subpental
Min Golden±13¢ 7/3±13¢ Max Min Golden±13¢ Max Min Golden±13¢ Max Min Golden±13¢ Max
1 G#/Jb G#/Ab 96 96.457-98.19 96.925-98.658 97.778 97.39-99.123 100 100.618-102.351 101.818 101.245-102.978 102.857
2 J A 192 192.913-196.38 193.8495-197.316 195.556 194.78-198.247 200 201.236-204.702 203.636 202.49-205.956 205.714
3 J#/Ab A#/Bb 288 289.37-294.57 290.774-295.974 293.333 292.17-297.37 300 301.854-204.702 305.4545 303.734-308.934 308.571
4 J B 384 385.829-392.76 387.699-394.632 391.111 389.56-396.493 400 402.4715-307.054 407.273 404.979-411.9215 411.429
5 A C 480 482.284-490.95 484.624-493.29 488.889 486.95-495.617 500 503.089-511.756 509.091 509.502-514.891 514.286
6 A#/Bb C#/Qb 576 578.74-589.14 581.548-591.948 586.667 584.334-594.74 600 603.707-614.107 610.909 607.469-617.869 617.143
7 B Q 672 675.197-687.33 678.473-690.606 684.444 681.73-693.863 700 704.325-716.4585 712.727 708.7135-720.847 720
8 B#/Cb Q#/Db 768 771.654-785.52 775.398-789.2645 782.822 779.12-792.9865 800 804.943-818.81 814.5455 809.958-823.825 822.857
9 C D 864 868.1105-883.7105 872.3225-887.9225 880 876.51-892.11 900 905.561-921.161 916.364 911.203-926.823 925.714
10 D S 960 964.567-981.901 969.247-986.561 977.778 973.9-991.233 1000 1006.179-1023.512 1018.182 1012.448-1029.781 1028.571
11 D#/Eb S#/Eb 1056 1061.024-1080.091 1066.172-1085.239 1075.556 1071.39-1090.356 1100 1106.797-1125.863 1120 1113.693-1132.759 1131.429
12 E 1152 1157.481-1178.281 1163.097-1183.897 1173.333 1168.68-1189.48 1200 1207.4145-1228.2145 1221.818 1214.9375-1235.7375 1234.286
13 E#/Fb 1248 1253.937-1276.471 1260.0215-1282.555 1271.111 1266.07-1288.603 1300 1308.032-1330.566 1323.636 1316.182-1338.716 1337.143
14 F 1344 1350.394-1374.661 1356.946-1381.213 1368.889 1363.46-1387.726 1400 1408.65-1432.917 1425.4545 1417.427-1441.694 1440
15 G 1440 1446.851-1472.851 1453.871-1479.871 1466.667 1460.85-1486.85 1500 1509.268-1535.268 1527.273 1518.672-1544.672 1542.857
Degrees Enneatonic Min 22/9±13¢ Golden±13¢ Max
1 F#/Gb G#/Jb G#/Ab 102.857 102.294-104.027 102.788-104.5215 104
2 G J A 205.714 204.588-208.054 205.576-209.043 208
3 G#/Jb G#/Ab J#/Ab A#/Bb 308.571 306.8815-312.0815 308.365-313.565 312
4 J A J B 411.429 409.1755-416.109 411.153-418.086 416
5 A B A C 514.286 511.469-520.136 513.941-526.308 520
6 A#/Bb B#/Hb A#/Bb C#/Qb 617.143 613.763-624.163 616.729-627.129 624
7 B H B Q 720 716.057-728.19 719.5175-731.651 728
8 B#/Hb H#/Cb B#/Cb Q#/Db 822.857 818.351-832.218 822.306-836.172 832
9 H C C D 925.714 920.645-936.245 925.094-940.694 936
10 C D D S 1028.571 1022.939-1040.272 1027.882-1045.2155 1040
11 C#/Db D#/Sb D#/Eb S#/Eb 1131.429 1125.2325-1144.299 1130.67-1149.737 1144
12 D S E 1234.286 1227.526-1248.326 1233.459-1254.259 1248
13 D#/Eb S#/Eb E#/Fb 1337.143 1329.82-1352.3535 1336.247-1358.78 1352
14 E F 1440 1432.114-1456.381 1439.035-1463.302 1456
15 F G 1542.857 1534.408-1560.408 1541.823-1567.823 1560
Degrees Enneatonic Mixolydian Mixolydian-Ionian
Subpental Pental Superpental
Soft Intense
Min Golden±13¢ Max Min Golden±13¢ 5/2±13¢ Max Min Golden±13¢ Max Min Golden±13¢ Max Min Golden±13¢ Max
1 F#/Gb 104 103.855-105.788 105 104.306-106.04 104.888-106.621 106.667 106.664-108.398 107.586 108.4245-110.158 110.345 109.6375-111.371 112
2 G 208 207.709-211.576 210 208.613-212.08 209.77-213.242 213.333 213.329-216.795 215.172 216.849-220.316 220.69 219.275-222.742 224
3 G#/Jb G#/Ab 312 311.564-317.364 315 312.919-318.119 314.663-319.863 320 319.993-325.193 322.759 325.273-330.473 331.034 328.913-334.113 336
4 J A 416 415.419-423.152 420 417.226-424.159 419.559-426.484 426.667 426.657-433.5905 430.345 433.698-440.631 441.379 438.55-445.4835 448
5 A B 520 519.2735-528.94 525 521.532-530.199 524.438-533.105 533.333 533.321-541.988 537.931 542.122-550.789 551.724 548.188-556.854 560
6 A#/Bb B#/Hb 624 623.128-634.728 630 625.8385-636.238 629.3255-639.7255 640 639.987-650.386 645.517 650.547-660.947 662.069 657.825-668.225 672
7 B H 728 726.983-740.516 735 730.145-742.278 734.213-746.346 746.667 746.65-758.783 753.103 758.971-771.105 772.414 767.463-779.596 784
8 B#/Hb H#/Cb 832 830.8375-844.704 840 834.451-848.318 839.101-852.967 853.333 853.314-867.181 860.69 867.396-881.262 882.759 877.1-890.967 896
9 H C 936 934.693-952.092 945 938.758-954.358 943.988-959.588 960 959.9785-975.5785 968.276 975.82-991.42 993.103 986.738-1002.338 1008
10 C D 1040 1038.547-1057.88 1050 1043.064-1060.3975 1048.876-1066.209 1066.667 1066.643-1083.976 1075.862 1084.245-1101.578 1103.448 1096.3755-1113.709 1120
11 C#/Db D#/Sb 1144 1142.402-1163.668 1155 1147.3705-1166.437 1153.763-1172.83 1173.333 1173.307-1192.374 1183.448 1192.669-1211.736 1213.379 1206.013-1225.08 1232
12 D S 1248 1246.256-1269.456 1260 1251.677-1272.477 1258.651-1279.451 1280 1279.971-1300.771 1291.034 1301.0395-1321.8935 1324.138 1315.651-1336.451 1344
13 D#/Eb S#/Eb 1352 1353.111-1275.244 1365 1355.983-1378.517 1363.539-1386.072 1386.667 1386.636-1409.169 1398.621 1409.518-1425.288 1424.483 1438.993-1447.8215 1456
14 E 1456 1453.966-1481.032 1470 1460.29-1484.556 1468.426-1492.693 1493.333 1493.3-1517.567 1506.207 1517.9425-1534.926 1544.827 1541.778-1559.192 1568
15 F 1560 1557.82-1583.82 1575 1564.596-1590.596 1573.314-1599.314 1600 1599.964-1625.964 1613.793 1626.366-1652.366 1655.172 1644.563-1670.563 1680

By a surprising coincidence, the 15ed of the Pyrite tenth (7φ+6)\(5φ^2)edo is almost exactly every third degree of 34edo. Additionally, those of the modal Golden and Pyrite tenths are almost exactly +1/28-syntonic comma 4ed(5/4) (Intense 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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