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'''15edX''' is the scale which occurs as the dominant minor edX.
'''15edX''' is the scale which occurs as the dominant minor edX (equal division of a tenth interval). It also gives the period of the 15th-decade Alfincavallo branch of the Carrera temperament family.
==Intervals==
 
{| class="wikitable" style="text-align: center"
== Intervals ==
! rowspan="3" |Degrees
{| class="wikitable"
! colspan="2" rowspan="3" |.1225)
|+
! colspan="3" rowspan="2" |Intense Aeolian-Subpental Dorian
!Decade
! colspan="9" |Dorian
!Period
|-
!Notes
! colspan="3" |Subpental
! colspan="3" |Pental
! colspan="3" |Superpental
|-
|-
!Min-comma
|6\5
!Med
|96.000
! colspan="2" |Max+comma~Min-comma
|Intense Aeolian-Subpental Dorian mode begins
!Med
! colspan="2" |Max+comma~Min-comma
!Med
! colspan="2" |Max+comma~Min-comma
!Med
!Max+comma
|-
|-
| |1
|17\14
|G#/Jb
|''G#/Ab''
| |93.333-96
|97.143
|97.143
| colspan="2" |95.111-100.444
|
|98.4615
| colspan="2" |97.333-102.667
|101.333
| colspan="2" |99.1515-104.485
|102.222
|102.857-105.524
|-
|-
| |2
|11\9
|J
|97.778
|''A''
|Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
| |186.667-192
|194.286
| colspan="2" |190.222-200.889
|196.923
| colspan="2" |194.667-205.333
|202.667
| colspan="2" |198.303-208.97
|204.444
|205.714-211.048
|-
|-
| |3
|16\13
|J#/Ab
|98.462
|''A#/Bb''
|
| |280-288
|291.429
| colspan="2" |285.333-301.333
|295.385
| colspan="2" |292-308
|304
| colspan="2" |297.4545-313.4545
|306.667
|308.571-316.571
|-
|-
| |4
|21\17
|A
|98.824
|''B''
|
| |373.333-384
|388.571
| colspan="2" |380.444-401.778
|393.846
| colspan="2" |389.333-410.667
|405.333
| colspan="2" |396.606-417.939
|408.889
|411.429-422.095
|-
|-
| |5
|26\21
|B
|99.048
|''C''
|
| |466.667-480
|485.714
| colspan="2" |475.556-502.222
|492.308
| colspan="2" |486.667-513.333
|506.667
| colspan="2" |495.758-522.424
|511.111
|514.286-527.619
|-
| |6
|B#/Cb
|''C#/Qb''
| |560-576
|582.857
| colspan="2" |570.667-602.667
|590.769
| colspan="2" |584-616
|608
| colspan="2" |594.909-626.909
|613.333
|617.143-633.143
|-
|-
| |7
|5\4
|C
|100.000
|''Q''
|Subpental Dorian mode ends, Pental Dorian mode begins
| |653.333-672
|680
| colspan="2" |665.778-703.111
|689.231
| colspan="2" |681.333-718.667
|709.333
| colspan="2" |694.061-731.394
|715.556
|720-738.667
|-
|-
|8
|19\15
|C#/Qb
|101.333
|''Q#/Db''
|
|746.667-768
|757.143
| colspan="2" |760.889-803.556
|787.692
| colspan="2" |778.667-821.333
|810.667
| colspan="2" |793.212-835.879
|817.778
|822.857-844.1905
|-
|-
|9
|14\11
|Q
|101.818
|''D''
|Pental Dorian mode ends, Superpental Dorian mode begins
|840-864
|874.286
| colspan="2" |856-904
|886.154
| colspan="2" |876-924
|912
| colspan="2" |892.364-940.364
|920
|925.714-949.714
|-
|-
|10
|23\18
|D
|102.222
|''S''
|
|933.333-960
|971.429
| colspan="2" |951.111-1004.444
|984.615
| colspan="2" |973.333-1026.667
|1013.333
| colspan="2" |991.515-1044.8485
|1022.222
|1028.571-1055.238
|-
|-
|11
|9\7
|D#/Eb
|102.857
|''S#/Eb''
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
|1026.667-1056
|1068.571
| colspan="2" |1046.222-1104.889
|1083.077
| colspan="2" |1070.667-1129.333
|1114.667
| colspan="2" |1090.667-1149.333
|1124.444
|1131.429-1160.761
|-
|-
|12
|31\24
| colspan="2" |E
|103.333
|1120-1152
|
|1165.714
| colspan="2" |1141.333-1205.333
|1181.5385
| colspan="2" |1168-1232
|1216
| colspan="2" |1189.818-1253.818
|1226.667
|1234.286-1266.286
|-
|-
|13
|22\17
| colspan="2" |E#/Fb
|103.529
|1213.333-1248
|Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
|1262.857
| colspan="2" |1236.444-1305.778
|1280
| colspan="2" |1265.333-1334.667
|1317.333
| colspan="2" |1288.97-1358.303
|1328.889
|1337.143-1371.8095
|-
|-
|14
|35\27
| colspan="2" |F
|1306.667-1344
|1360
| colspan="2" |1331.556-1406.222
|1378.4615
| colspan="2" |1363.667-1437.333
|1418.667
| colspan="2" |1388.121-1462.788
|1431.111
|1440-1477.333
|-
|15
| colspan="2" |G
|1400-1440
|1457.143
| colspan="2" |1426.667-1506.667
|1476.923
| colspan="2" |1460-1540
|1520
| colspan="2" |1487.273-1567.273
|1533.333
|1542.857-1582.857
|}
 
{| class="wikitable" style="text-align: center"
! rowspan="2" |Degrees
! colspan="4" rowspan="2" |Enneatonic
! colspan="4" |Mohajira
! colspan="3" |Beatles
|-
!Min-comma
!''r¢''
!Med
! colspan="2" |Max+comma~Min-comma
!Med
!Max+comma
|-
| |1
| colspan="2" |F#/Gb
|G#/Jb
|''G#/Ab''
|100.1905-102.857
| colspan="2" |''103.333''
| colspan="2" |100.863-106.196
|103.704
|103.704
|104-106.667
|
|-
|-
| |2
|13\10
| colspan="2" |G
|104.000
|J
|Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
|''A''
|200.381-205.714
| colspan="2" |''206.667''
| colspan="2" |201.7255-212.392
|207.407
|208-213.333
|-
|-
| |3
|17\13
|G#/Jb
|104.615
|''G#/Ab''
|
|J#/Ab
|''A#/Bb''
|300.571-308.571
| colspan="2" |''310''
| colspan="2" |302.588-318.588
|311.111
|312-320
|-
|-
| |4
|21\16
|J
|105.000
|''A''
|Subpental Mixolydian mode ends, Pental Mixolydian mode begins
|A
|''B''
|400.702-411.429
| colspan="2" |''413.333''
| colspan="2" |403.451-424.784
|414.815
|416-426.667
|-
| |5
|A
|''B''
|B
|''C''
|500.952-514.286
| colspan="2" |''516.667''
| colspan="2" |504.314-530.98
|518.5185
|520-533.33
|-
| |6
|A#/Bb
|''B#/Hb''
|B#/Cb
|''C#/Qb''
|601.143-617.143
| colspan="2" |''620''
| colspan="2" |605.1765-637.1765
|622.222
|624-640
|-
|-
| |7
|25\19
|B
|''H''
|C
|''Q''
|701.333-720
| colspan="2" |''723.333''
| colspan="2" |706.04-743.3725
|725.926
|728-746.667
|-
|8
|B#/Hb
|''H#/Cb''
|C#/Qb
|''Q#/Db''
|801.524-822.857
| colspan="2" |''826.667''
| colspan="2" |806.902-849.569
|829.63
|832-853.333
|-
|9
|H
|''C''
|Q
|''D''
|901.714-925.714
| colspan="2" |''930''
| colspan="2" |907.765-955.765
|933.333
|936-960
|-
|10
|C
|''D''
|D
|''S''
|1001.905-1048.571
| colspan="2" |''1033.333''
| colspan="2" |1008.6275-1061.961
|1037.037
|1040-1066.667
|-
|11
|C#/Db
|''D#/Sb''
|D#/Eb
|''S#/Eb''
|1102.095-1131.429
| colspan="2" |''1136.667''
| colspan="2" |1109.49-1168.157
|1140.741
|1144-1173.333
|-
|12
|D
|''S''
| colspan="2" |E
|1202.286-1234.286
| colspan="2" |''1240''
| colspan="2" |1210.353-1274.353
|1244.444
|1248-1280
|-
|13
|D#/Eb
|''S#/Eb''
| colspan="2" |E#/Fb
|1302.476-1337.143
| colspan="2" |''1343.333''
| colspan="2" |1311.216-1380.549
|1348.148
|1352-1386.667
|-
|14
| colspan="2" |E
| colspan="2" |F
|1402.667-1440
| colspan="2" |''1446.667''
| colspan="2" |1412.078-1486.745
|1451.852
|1456-1493.333
|-
|15
| colspan="2" |F
| colspan="2" |G
|1502.857-1542.857
| colspan="2" |''1550''
| colspan="2" |1512.941-1592.941
|1555.556
|1560-1600
|}
 
{| class="wikitable" style="text-align: center"
|-
! rowspan="4" |Degrees
! colspan="2" rowspan="4" |Enneatonic
! colspan="12" |Mixolydian
! colspan="3" rowspan="3" |Mixolydian-Ionian
|-
! colspan="3" rowspan="2" |Subpental
! colspan="3" rowspan="2" |Pental
! colspan="6" |Superpental
|-
! colspan="3" |Soft
! colspan="3" |Intense
|-
! width="4%" |Min-comma
!Med
! colspan="2" width="4%" |Max+comma~Min-comma
!Med
! colspan="2" width="4%" |Max+comma~Min-comma
!Med
! colspan="2" width="4%" |Max+comma~Min-comma
!Med
! colspan="2" width="4%" |Max+comma~Min-comma
!Med
!Max+comma
|-
| |1
| colspan="2" |F#/Gb
|101.333-104
|104.615
| colspan="2" |102.333-107.667
|105.263
|105.263
| colspan="2" |104-109.333
|
|107.5
| colspan="2" |104.9195-110.253
|108.9655
| colspan="2" |107.678-113.0115
|110.588
|112-114.667
|-
|-
| |2
|4\3
| colspan="2" |G
|106.667
|202.667-208
|Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
|209.231
| colspan="2" |204.667-215.333
|210.526
| colspan="2" |208-218.667
|215
| colspan="2" |209.809-220.506
|217.931
| colspan="2" |215.356-226.023
|221.1765
|224-229.333
|-
|-
| |3
|31\23
|G#/Jb
|107.826
|''G#/Ab''
|
|304-312
|313.846
| colspan="2" |307-323
|315.7895
| colspan="2" |312-328
|322.5
| colspan="2" |314.759-330.759
|326.897
| colspan="2" |323.0345-339.0345
|331.765
|336-344
|-
|-
| |4
|27\20
|J
|108.000
|''A''
|
|405.333-416
|418.4615
| colspan="2" |409.333-435.667
|421.053
| colspan="2" |416-437.333
|430
| colspan="2" |419.678-441.0115
|435.862
| colspan="2" |430.713-452.046
|442.353
|448-458.667
|-
|-
| |5
|23\17
|A
|108.235
|''B''
|
|516.667-520
|523.077
| colspan="2" |511.667-538.333
|526.316
| colspan="2" |520-546.667
|537.5
| colspan="2" |524.598-541.264
|544.828
| colspan="2" |538.391-565.0575
|552.941
|560-573.333
|-
|-
| |6
|19\14
|A#/Bb
|108.571
|''B#/Hb''
|
|608-624
|627.692
| colspan="2" |614-646
|631.579
| colspan="2" |624-656
|645
| colspan="2" |629.517-661.517
|653.793
| colspan="2" |646.069-678.069
|663.529
|672-688
|-
|-
| |7
|15\11
|B
|109.091
|''H''
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
|709.333-728
|732.308
| colspan="2" |716.333-753.667
|736.842
| colspan="2" |728-765.333
|752.5
| colspan="2" |734.437-771.77
|762.759
| colspan="2" |753.747-791.0805
|774.118
|784-802.667
|-
|-
|8
|26\19
|B#/Hb
|109.474
|''H#/Cb''
|
|810.666-832
|836.923
| colspan="2" |818.667-861.333
|842.103
| colspan="2" |832-874.667
|860
| colspan="2" |839.356-882.023
|871.724
| colspan="2" |861.425-904.092
|884.706
|896-917.333
|-
|-
|9
|11\8
|H
|110.000
|''C''
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
|912-936
|941.5385
| colspan="2" |921-969
|947.368
| colspan="2" |936-984
|967.5
| colspan="2" |944.276-992.276
|980.69
| colspan="2" |969.103-1007.103
|995.294
|1008-1032
|-
|-
|10
|18\13
|C
|110.769
|''D''
|
|1013.333-1040
|1046.154
| colspan="2" |1023.333-1076.667
|1052.632
| colspan="2" |1040-1093.333
|1075
| colspan="2" |1049.195-1102.529
|1089.655
| colspan="2" |1076.782-1130.115
|1105.882
|1120-1146.667
|-
|-
|11
|25\18
|C#/Db
|111.111
|''D#/Sb''
|
|1114.667-1144
|1150.769
| colspan="2" |1125.667-1184.333
|1157.895
| colspan="2" |1144-1202.667
|1182.5
| colspan="2" |1154.115-1212.782
|1198.621
| colspan="2" |1184.46-1243.126
|1216.471
|1232-1261.333
|-
|-
|12
|7\5
|D
|112.500
|''S''
|Mixolydian-Ionian mode ends
|1216-1248
|1255.385
| colspan="2" |1228-1292
|1263.158
| colspan="2" |1248-1312
|1290
| colspan="2" |1259.0345-1323.0345
|1307.586
| colspan="2" |1292.138-1356.138
|1327.059
|1344-1376
|-
|13
|D#/Eb
|''S#/Eb''
|1317.333-1352
|1360
| colspan="2" |1330.333-1399.667
|1368.421
| colspan="2" |1352-1421.333
|1397.5
| colspan="2" |1363.954-1433.287
|1416.552
| colspan="2" |1399.816-1469.149
|1437.647
|1456-1490.667
|-
|14
| colspan="2" |E
|1418.667-1456
|1464.615
| colspan="2" |1432.667-1506.333
|1473.684
| colspan="2" |1456-1530.337
|1505
| colspan="2" |1468.874-1534.54
|1525.517
| colspan="2" |1507.494-1582.161
|1548.235
|1568-1605.333
|-
|15
| colspan="2" |F
|1520-1560
|1569.231
| colspan="2" |1535-1615
|1578.947
| colspan="2" |1560-1640
|1612.5
| colspan="2" |1573.793-1653.793.
|1634.483
| colspan="2" |1615.172-1695.172
|1658.8235
|1680-1720
|}
|}
Relative cents
Relative cents
{| class="wikitable" style="text-align: center"
{| class="wikitable" style="text-align: center"
!Degrees
!Degrees
Line 639: Line 130:
!Intense Aeolian-Subpental Dorian
!Intense Aeolian-Subpental Dorian
!Dorian
!Dorian
!Dorian-Mixolydian
!Subpental-Soft Superpental Mixolydian
!Subpental-Soft Superpental Mixolydian
!Intense Superpental Mixolydian ~ Mixolydian-Ionian
!Intense Superpental Mixolydian ~ Mixolydian-Ionian
Line 645: Line 137:
|G#/Jb
|G#/Jb
|''G#/Ab''
|''G#/Ab''
|96.667
|96.{{Overline|6}}
|100
|100
|106.667
|103.{{Overline|3}}
|106.{{Overline|6}}
|110
|110
|-
|-
Line 653: Line 146:
|J
|J
|''A''
|''A''
|193.333
|193.{{Overline|3}}
|200
|200
|213.333
|206.{{Overline|6}}
|213.{{Overline|3}}
|220
|220
|-
|-
Line 663: Line 157:
|290
|290
|300
|300
|310
|320
|320
|330
|330
Line 669: Line 164:
|A
|A
|''B''
|''B''
|386.667
|386.{{Overline|6}}
|400
|400
|426.667
|413.{{Overline|3}}
|426.{{Overline|6}}
|440
|440
|-
|-
Line 677: Line 173:
|B
|B
|''C''
|''C''
|483.333
|483.{{Overline|3}}
|500
|500
|533.333
|516.{{Overline|6}}
|533.{{Overline|3}}
|550
|550
|-
|-
Line 687: Line 184:
|580
|580
|600
|600
|620
|640
|640
|660
|660
Line 693: Line 191:
|C
|C
|''Q''
|''Q''
|676.667
|676.{{Overline|6}}
|700
|700
|746.667
|723.{{Overline|3}}
|746.{{Overline|6}}
|770
|770
|-
|-
Line 701: Line 200:
|C#/Qb
|C#/Qb
|''Q#/Db''
|''Q#/Db''
|773.333
|773.{{Overline|3}}
|800
|800
|853.333
|826.{{Overline|6}}
|853.{{Overline|3}}
|880
|880
|-
|-
Line 711: Line 211:
|870
|870
|900
|900
|930
|960
|960
|990
|990
Line 717: Line 218:
|D
|D
|''S''
|''S''
|966.667
|966.{{Overline|6}}
|1000
|1000
|1066.667
|1033.{{Overline|3}}
|1066.{{Overline|6}}
|1100
|1100
|-
|-
Line 725: Line 227:
|D#/Eb
|D#/Eb
|''S#/Eb''
|''S#/Eb''
|1063.333
|1063.{{Overline|3}}
|1100
|1100
|1173.333
|1136.{{Overline|6}}
|1173.{{Overline|3}}
|1210
|1210
|-
|-
Line 734: Line 237:
|1160
|1160
|1200
|1200
|1240
|1280
|1280
|1320
|1320
Line 739: Line 243:
|13
|13
| colspan="2" |E#/Fb
| colspan="2" |E#/Fb
|1256.667
|1256.{{Overline|6}}
|1300
|1300
|1386.667
|1343.{{Overline|3}}
|1386.{{Overline|6}}
|1430
|1430
|-
|-
|14
|14
| colspan="2" |F
| colspan="2" |F
|1353.333
|1353.{{Overline|3}}
|1400
|1400
|1493.333
|1446.{{Overline|6}}
|1493.{{Overline|3}}
|1540
|1540
|-
|-
Line 755: Line 261:
|1450
|1450
|1500
|1500
|1550
|1600
|1600
|1650
|1650
|}
|}


Golden/Pyrite Tunings±13¢
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-Subpental Dorian), [[9ed5/3|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), 4ed(9/7)/+1/36-syntonic comma 14ed(12/5) (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.
{| class="wikitable" style="text-align: center"
== See also ==
! rowspan="2" |Degrees
* [[15ed5/2]] - equal division of the classic major tenth
! colspan="2" rowspan="2" |Enneatonic
* [[15ed7/3]] - equal division of the septimal minor tenth
! rowspan="2" |Intense Aeolian-Subpental Dorian
! colspan="3" |Dorian
|-
!Subpental
!Pental
!Superpental
|-
| |1
|G#/Jb
|''G#/Ab''
|96.457-98.19
|97.39-99.123
|100.618-102.351
|101.245-102.978
|-
| |2
|J
|''A''
|192.913-196.38
|194.78-198.247
|201.236-204.702
|202.49-205.956
|-
| |3
|J#/Ab
|''A#/Bb''
|289.37-294.57
|292.17-297.37
|301.854-204.702
|303.734-308.934
|-
| |4
|A
|''B''
|385.829-392.76
|389.56-396.493
|402.4715-307.054
|404.979-411.9215
|-
| |5
|B
|''C''
|482.284-490.95
|486.95-495.617
|503.089-511.756
|509.502-514.891
|-
| |6
|B#/Cb
|''C#/Qb''
|578.74-589.14
|584.334-594.74
|603.707-614.107
|607.469-617.869
|-
| |7
|C
|''Q''
|675.197-687.33
|681.73-693.863
|704.325-716.4585
|708.7135-720.847
|-
|8
|C#/Qb
|''Q#/Db''
|771.654-785.52
|779.12-792.9865
|804.943-818.81
|809.958-823.825
|-
|9
|Q
|''D''
|868.1105-883.7105
|876.51-892.11
|905.561-921.161
|911.203-926.823
|-
|10
|D
|''S''
|964.567-981.901
|973.9-991.233
|1006.179-1023.512
|1012.448-1029.781
|-
|11
|D#/Eb
|''S#/Eb''
|1061.024-1080.091
|1071.39-1090.356
|1106.797-1125.863
|1113.693-1132.759
|-
|12
| colspan="2" |E
|1157.481-1178.281
|1168.68-1189.48
|1207.4145-1228.2145
|1214.9375-1235.7375
|-
|13
| colspan="2" |E#/Fb
|1253.937-1276.471
|1266.07-1288.603
|1308.032-1330.566
|1316.182-1338.716
|-
|14
| colspan="2" |F
|1350.394-1374.661
|1363.46-1387.726
|1408.65-1432.917
|1417.427-1441.694
|-
|15
| colspan="2" |G
|1446.851-1472.851
|1460.85-1486.85
|1509.268-1535.268
|1518.672-1544.672
|}
 
{| class="wikitable" style="text-align: center"
!Degrees
! colspan="4" |Enneatonic
!Mohajira
!Beatles
|-
| |1
| colspan="2" |F#/Gb
|G#/Jb
|''G#/Ab''
|102.526-104.26
|102.788-104.5215
|-
| |2
| colspan="2" |G
|J
|''A''
|205.053-208.519
|205.576-209.431
|-
| |3
|G#/Jb
|''G#/Ab''
|J#/Ab
|''A#/Bb''
|307.579-312.779.
|308.365-313.565
|-
| |4
|J
|''A''
|A
|''B''
|410.1055-417.099
|411.153-418.086
|-
| |5
|A
|''B''
|B
|''C''
|512.632-521.2985
|513.941-522.607
|-
| |6
|A#/Bb
|''B#/Hb''
|B#/Cb
|''C#/Qb''
|615.158-625.558
|616.729-627.129
|-
| |7
|B
|''H''
|C
|''Q''
|717.685-729.818
|719.5175-731.651
|-
|8
|B#/Hb
|''H#/Cb''
|C#/Qb
|''Q#/Db''
|820.211-834.078
|822.306-836.172
|-
|9
|H
|''C''
|Q
|''D''
|922.737-938.337
|925.094-940.694
|-
|10
|C
|''D''
|D
|''S''
|1025.264-1042.597
|1027.882-1045.215
|-
|11
|C#/Db
|''D#/Sb''
|D#/Eb
|''S#/Eb''
|1127.79-1146.857
|1130.67-1149.737
|-
|12
|D
|''S''
| colspan="2" |E
|1230.316-1251.116
|1233.459-1254.259
|-
|13
|D#/Eb
|''S#/Eb''
| colspan="2" |E#/Fb
|1332.843-1355.376
|1336.247-1358.78
|-
|14
| colspan="2" |E
| colspan="2" |F
|1435.369-1459.666
|1439.035-1463.302
|-
|15
| colspan="2" |F
| colspan="2" |G
|1537.8955-1563.8955
|1541.823-1577.823
|}
 
{| class="wikitable" style="text-align: center"
! rowspan="3" |Degrees
! colspan="2" rowspan="3" |Enneatonic
! colspan="4" |Mixolydian
! rowspan="3" |Mixolydian-Ionian
|-
! rowspan="2" |Subpental
! rowspan="2" |Pental
! colspan="2" |Superpental
|-
!Soft
!Intense
|-
| |1
| colspan="2" |F#/Gb
|103.855-105.788
|104.306-106.04
|106.664-108.398
|108.4245-110.158
|109.6375-111.371
|-
| |2
| colspan="2" |G
|207.709-211.576
|208.613-212.08
|213.329-216.795
|216.849-220.316
|219.275-222.742
|-
| |3
|G#/Jb
|''G#/Ab''
|311.564-317.364
|312.919-318.119
|319.993-325.193
|325.273-330.473
|328.913-334.113
|-
| |4
|J
|''A''
|415.419-423.152
|417.226-424.159
|426.657-433.5905
|433.698-440.631
|438.55-445.4835
|-
| |5
|A
|''B''
|519.2735-528.94
|521.532-530.199
|533.321-541.988
|542.122-550.789
|548.188-556.854
|-
| |6
|A#/Bb
|''B#/Hb''
|623.128-634.728
|625.8385-636.238
|639.987-650.386
|650.547-660.947
|657.825-668.225
|-
| |7
|B
|''H''
|726.983-740.516
|730.145-742.278
|746.65-758.783
|758.971-771.105
|767.463-779.596
|-
|8
|B#/Hb
|''H#/Cb''
|830.8375-844.704
|834.451-848.318
|853.314-867.181
|867.396-881.262
|877.1-890.967
|-
|9
|H
|''C''
|934.693-952.092
|938.758-954.358
|959.9785-975.5785
|975.82-991.42
|986.738-1002.338
|-
|10
|C
|''D''
|1038.547-1057.88
|1043.064-1060.3975
|1066.643-1083.976
|1084.245-1101.578
|1096.3755-1113.709
|-
|11
|C#/Db
|''D#/Sb''
|1142.402-1163.668
|1147.3705-1166.437
|1173.307-1192.374
|1192.669-1211.736
|1206.013-1225.08
|-
|12
|D
|''S''
|1246.256-1269.456
|1251.677-1272.477
|1279.971-1300.771
|1301.0395-1321.8935
|1315.651-1336.451
|-
|13
|D#/Eb
|''S#/Eb''
|1353.111-1275.244
|1355.983-1378.517
|1386.636-1409.169
|1409.518-1425.288
|1438.993-1447.8215
|-
|14
| colspan="2" |E
|1453.966-1481.032
|1460.29-1484.556
|1493.3-1517.567
|1517.9425-1534.926
|1541.778-1559.192
|-
|15
| colspan="2" |F
|1557.82-1583.82
|1564.596-1590.596
|1599.964-1625.964
|1626.366-1652.366
|1644.563-1670.563
|}


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-Subpental Dorian), [[9ed5/3|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 scales]]
[[Category:15-tone]]
[[Category:EdX]]
[[Category:ed7/3]]
[[Category:edX]]
[[Category:todo:add_definition]]
[[Category:todo:unify_precision]]
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/15edX"