User:Moremajorthanmajor/15edX: Difference between revisions

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'''15edX''' is the scale which occurs as the dominant minor edX (equal division of a tenth interval).
'''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 ==
== Intervals ==
{| class="wikitable" style="text-align: center"
{| class="wikitable"
! rowspan="3" |Degrees
|+
! colspan="2" rowspan="3" |Enneatonic
! colspan="4" |Decade
! colspan="3" rowspan="2" |Intense Aeolian-Subpental Dorian
!
! colspan="9" |Dorian
!Period
!Notes
|-
|-
! colspan="3" |Subpental
|6\5
! colspan="3" |Pental
|
! colspan="3" |Superpental
|
|
|
|96
|Intense Aeolian-Subpental Dorian mode begins
|-
|-
!Min-comma
|
!Med
|17\14
! colspan="2" |Max+comma~Min-comma
|
!Med
|
! colspan="2" |Max+comma~Min-comma
|
!Med
! colspan="2" |Max+comma~Min-comma
!Med
!Max+comma
|-
| |1
|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
|
|''A''
|
| |186.667-192
|
|194.286
|
| colspan="2" |190.222-200.889
|97.{{Overline|7}}
|196.923
|Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
| colspan="2" |194.667-205.333
|202.667
| colspan="2" |198.303-208.97
|204.444
|205.714-211.048
|-
|-
| |3
|
|J#/Ab
|16\13
|''A#/Bb''
|
| |280-288
|
|291.429
|
| colspan="2" |285.333-301.333
|98.4615
|295.385
|
| colspan="2" |292-308
|304
| colspan="2" |297.4545-313.4545
|306.667
|308.571-316.571
|-
|-
| |4
|
|A
|
|''B''
|21\17
| |373.333-384
|
|388.571
|
| colspan="2" |380.444-401.778
|98.8235
|393.846
|
| colspan="2" |389.333-410.667
|405.333
| colspan="2" |396.606-417.939
|408.889
|411.429-422.095
|-
|-
| |5
|
|B
|
|''C''
|
| |466.667-480
|26\21
|485.714
|
| colspan="2" |475.556-502.222
|99.0476
|492.308
|
| colspan="2" |486.667-513.333
|506.667
| colspan="2" |495.758-522.424
|511.111
|514.286-527.619
|-
|-
| |6
|5\4
|B#/Cb
|
|''C#/Qb''
|
| |560-576
|
|582.857
|
| colspan="2" |570.667-602.667
|100
|590.769
|Subpental Dorian mode ends, Pental Dorian mode begins
| colspan="2" |584-616
|608
| colspan="2" |594.909-626.909
|613.333
|617.143-633.143
|-
| |7
|C
|''Q''
| |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
|C#/Qb
|''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
|Q
|''D''
|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
|D
|''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
|D#/Eb
|''S#/Eb''
|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
| colspan="2" |E
|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
|
| colspan="2" |E#/Fb
|19\15
|1213.333-1248
|
|1262.857
|
| colspan="2" |1236.444-1305.778
|
|1280
|101.{{Overline|3}}
| colspan="2" |1265.333-1334.667
|
|1317.333
| colspan="2" |1288.97-1358.303
|1328.889
|1337.143-1371.8095
|-
|-
|14
|14\11
| colspan="2" |F
|
|1306.667-1344
|
|1360
|
| colspan="2" |1331.556-1406.222
|
|1378.4615
|101.{{Overline|81}}
| colspan="2" |1363.667-1437.333
|Pental Dorian mode ends, Superpental Dorian mode begins
|1418.667
| colspan="2" |1388.121-1462.788
|1431.111
|1440-1477.333
|-
|-
|15
|
| colspan="2" |G
|23\18
|1400-1440
|
|1457.143
|
| colspan="2" |1426.667-1506.667
|
|1476.923
|102.{{Overline|2}}
| 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
|9\7
!''r¢''
|
!Med
|
! colspan="2" |Max+comma~Min-comma
|
!Med
|
!Max+comma
|102.857
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
|-
|-
| |1
|
| colspan="2" |F#/Gb
|31\24
|G#/Jb
|
|''G#/Ab''
|
|100.1905-102.857
|
| colspan="2" |''103.333''
|103.{{Overline|3}}
| colspan="2" |100.863-106.196
|
|103.704
|104-106.667
|-
|-
| |2
|22\17
| colspan="2" |G
|
|J
|
|''A''
|
|200.381-205.714
|
| colspan="2" |''206.667''
|103.5294
| colspan="2" |201.7255-212.392
|Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
|207.407
|208-213.333
|-
|-
| |3
|
|G#/Jb
|35\27
|''G#/Ab''
|
|J#/Ab
|
|''A#/Bb''
|
|300.571-308.571
|103.{{Overline|703}}
| colspan="2" |''310''
|
| colspan="2" |302.588-318.588
|311.111
|312-320
|-
|-
| |4
|13\10
|J
|
|''A''
|
|A
|
|''B''
|
|400.702-411.429
|104
| colspan="2" |''413.333''
|Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
| colspan="2" |403.451-424.784
|414.815
|416-426.667
|-
|-
| |5
|17\13
|A
|
|''B''
|
|B
|
|''C''
|
|500.952-514.286
|104.615
| 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
|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
|21\16
|C
|
|''D''
|
|D
|
|''S''
|
|1001.905-1048.571
|105
| colspan="2" |''1033.333''
|Subpental Mixolydian mode ends, Pental Mixolydian mode begins
| colspan="2" |1008.6275-1061.961
|1037.037
|1040-1066.667
|-
|-
|11
|
|C#/Db
|25\19
|''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
| colspan="2" |G
|202.667-208
|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
|4\3
|G#/Jb
|
|''G#/Ab''
|
|304-312
|
|313.846
|
| colspan="2" |307-323
|106.{{Overline|6}}
|315.7895
|Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
| 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
|
|J
|
|''A''
|
|405.333-416
|
|418.4615
|31\23
| colspan="2" |409.333-435.667
|107.826
|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
|
|A
|
|''B''
|
|516.667-520
|27\20
|523.077
|
| colspan="2" |511.667-538.333
|108
|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
|
|A#/Bb
|
|''B#/Hb''
|23\17
|608-624
|
|627.692
|
| colspan="2" |614-646
|108.235
|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
|
|B
|19\14
|''H''
|
|709.333-728
|
|732.308
|
| colspan="2" |716.333-753.667
|108.571
|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
|15\11
|B#/Hb
|
|''H#/Cb''
|
|810.666-832
|
|836.923
|
| colspan="2" |818.667-861.333
|109.{{Overline|09}}
|842.103
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
| 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
|
|H
|26\19
|''C''
|
|912-936
|
|941.5385
|
| colspan="2" |921-969
|109.474
|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
|11\8
|C
|
|''D''
|
|1013.333-1040
|
|1046.154
|
| colspan="2" |1023.333-1076.667
|110
|1052.632
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
| 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
|
|C#/Db
|18\13
|''D#/Sb''
|
|1114.667-1144
|
|1150.769
|
| colspan="2" |1125.667-1184.333
|110.769
|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
|
|D
|
|''S''
|25\18
|1216-1248
|
|1255.385
|
| colspan="2" |1228-1292
|111.{{Overline|1}}
|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
|7\5
| colspan="2" |E
|
|1418.667-1456
|
|1464.615
|
| colspan="2" |1432.667-1506.333
|
|1473.684
|112.5
| colspan="2" |1456-1530.337
|Mixolydian-Ionian mode ends
|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 646: Line 253:
|G#/Jb
|G#/Jb
|''G#/Ab''
|''G#/Ab''
|96.667
|96.{{Overline|6}}
|100
|100
|106.667
|106.{{Overline|6}}
|110
|110
|-
|-
Line 654: Line 261:
|J
|J
|''A''
|''A''
|193.333
|193.{{Overline|3}}
|200
|200
|213.333
|213.{{Overline|3}}
|220
|220
|-
|-
Line 670: Line 277:
|A
|A
|''B''
|''B''
|386.667
|386.{{Overline|6}}
|400
|400
|426.667
|426.{{Overline|6}}
|440
|440
|-
|-
Line 678: Line 285:
|B
|B
|''C''
|''C''
|483.333
|483.{{Overline|3}}
|500
|500
|533.333
|533.{{Overline|3}}
|550
|550
|-
|-
Line 694: Line 301:
|C
|C
|''Q''
|''Q''
|676.667
|676.{{Overline|6}}
|700
|700
|746.667
|746.{{Overline|6}}
|770
|770
|-
|-
Line 702: Line 309:
|C#/Qb
|C#/Qb
|''Q#/Db''
|''Q#/Db''
|773.333
|773.{{Overline|3}}
|800
|800
|853.333
|853.{{Overline|3}}
|880
|880
|-
|-
Line 718: Line 325:
|D
|D
|''S''
|''S''
|966.667
|966.{{Overline|6}}
|1000
|1000
|1066.667
|1066.{{Overline|6}}
|1100
|1100
|-
|-
Line 726: Line 333:
|D#/Eb
|D#/Eb
|''S#/Eb''
|''S#/Eb''
|1063.333
|1063.{{Overline|3}}
|1100
|1100
|1173.333
|1173.{{Overline|3}}
|1210
|1210
|-
|-
Line 740: Line 347:
|13
|13
| colspan="2" |E#/Fb
| colspan="2" |E#/Fb
|1256.667
|1256.{{Overline|6}}
|1300
|1300
|1386.667
|1386.{{Overline|6}}
|1430
|1430
|-
|-
|14
|14
| colspan="2" |F
| colspan="2" |F
|1353.333
|1353.{{Overline|3}}
|1400
|1400
|1493.333
|1493.{{Overline|3}}
|1540
|1540
|-
|-
Line 760: Line 367:
|}
|}


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"
! rowspan="2" |Degrees
! colspan="2" rowspan="2" |Enneatonic
! 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.
 
== See also ==
== See also ==
* [[15ed5/2]] - equal division of the classic major tenth
* [[15ed5/2]] - equal division of the classic major tenth

Revision as of 03:02, 16 May 2023

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

Decade Period Notes
6\5 96 Intense Aeolian-Subpental Dorian mode begins
17\14 97.143
11\9 97.7 Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
16\13 98.4615
21\17 98.8235
26\21 99.0476
5\4 100 Subpental Dorian mode ends, Pental Dorian mode begins
19\15 101.3
14\11 101.81 Pental Dorian mode ends, Superpental Dorian mode begins
23\18 102.2
9\7 102.857 Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
31\24 103.3
22\17 103.5294 Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
35\27 103.703
13\10 104 Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
17\13 104.615
21\16 105 Subpental Mixolydian mode ends, Pental Mixolydian mode begins
25\19 105.263
4\3 106.6 Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
31\23 107.826
27\20 108
23\17 108.235
19\14 108.571
15\11 109.09 Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
26\19 109.474
11\8 110 Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
18\13 110.769
25\18 111.1
7\5 112.5 Mixolydian-Ionian mode ends

Relative cents

Degrees Enneatonic Intense Aeolian-Subpental Dorian Dorian Subpental-Soft Superpental Mixolydian Intense Superpental Mixolydian ~ Mixolydian-Ionian
1 G#/Jb G#/Ab 96.6 100 106.6 110
2 J A 193.3 200 213.3 220
3 J#/Ab A#/Bb 290 300 320 330
4 A B 386.6 400 426.6 440
5 B C 483.3 500 533.3 550
6 B#/Cb C#/Qb 580 600 640 660
7 C Q 676.6 700 746.6 770
8 C#/Qb Q#/Db 773.3 800 853.3 880
9 Q D 870 900 960 990
10 D S 966.6 1000 1066.6 1100
11 D#/Eb S#/Eb 1063.3 1100 1173.3 1210
12 E 1160 1200 1280 1320
13 E#/Fb 1256.6 1300 1386.6 1430
14 F 1353.3 1400 1493.3 1540
15 G 1450 1500 1600 1650

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), 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.

See also

  • 15ed5/2 - equal division of the classic major tenth
  • 15ed7/3 - equal division of the septimal minor tenth
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