User:Moremajorthanmajor/17edX: Difference between revisions

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==Intervals==
'''17edX''' means division of a tenth interval into 17 equal parts.
 
== Intervals ==
{| class="wikitable"
{| class="wikitable"
! rowspan="5" |Degrees
! Decade
! colspan="4" rowspan="5" |Enneatonic
!Period
! colspan="8" |Minor mode Middletown temperament
!Notes
! colspan="2" |Neutral mode Middletown temperament
|-
! colspan="10" |Major mode Middletown temperament
| 6\5
|''84.706''
|Intense Aeolian-Subpental Dorian mode begins
|-
|29\24
|''85.294''
|
|-
|23\19
|85.449
|
|-
|17\14
|85.714
|
|-
|11\9
|86.275
|Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
|-
|-
! colspan="2" rowspan="3" |Aeolian-Dorian
|16\13
! colspan="6" |Dorian
|86.878
! colspan="2" rowspan="3" |Dorian-Mixolydian
|
! colspan="8" |Mixolydian
! colspan="2" rowspan="3" |Mixolydian-Ionian
|-
|-
! colspan="2" rowspan="2" |Subpental
|21\17
! colspan="2" rowspan="2" |Pental
|87.197
! colspan="2" rowspan="2" |Superpental
|
! colspan="2" rowspan="2" |Subpental
! colspan="2" rowspan="2" |Pental
! colspan="4" |Superpental
|-
|-
! colspan="2" |Soft
|5\4
! colspan="2" |Intense
|''88.235''
|Subpental Dorian mode ends, Pental Dorian mode begins
|-
|-
! |Minimum
|24\19
! |Maximum
|89.164
!Minimum
|
!Maximum
!Minimum
!Maximum
!Minimum
!Maximum
!Minimum
! |Maximum
!Minimum
!Maximum
! |Minimum
!Maximum
!Minimum
!Maximum
!Minimum
!Maximum
!Minimum
! |Maximum
|-
|-
| |1
|19\15
| colspan="2" |G
|89.412
| colspan="2" |Gb
|
| |84.706
|-
| colspan="2" |86.2745
|14\11
| colspan="2" |88.235
|89.840
| colspan="2" |89.84
|Pental Dorian mode ends, Superpental Dorian mode begins
| colspan="2" |90.756
|-
| colspan="2" |91.765
|23\18
| colspan="2" |92.647
|90.196
| colspan="2" |94.118
|
| colspan="2" |94.929
|-
| colspan="2" |97.363
|9\7
| |98.8235
|90.756
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
|-
|-
| |2
|31\24
|J\\
|''91.176''
|''A\\''
|
| colspan="2" |F#
| |169.412
| colspan="2" |172.549
| colspan="2" |176.471
| colspan="2" |179.679
| colspan="2" |181.513
| colspan="2" |183.528
| colspan="2" |185.294
| colspan="2" |188.235
| colspan="2" |189.858
| colspan="2" |194.726
| |197.647
|-
|-
| |3
|22\17
| colspan="2" |Gp
|91.349
| colspan="2" |G
|Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
| |254.118
| colspan="2" |258.8235
| colspan="2" |264.706
| colspan="2" |269.519
| colspan="2" |272.268
| colspan="2" |275.294
| colspan="2" |277.941
| colspan="2" |282.353
| colspan="2" |284.787
| colspan="2" |292.089
| |296.471
|-
|-
| |4
|35\27
|J
|91.503
|A
|
|J
|''A''
| |338.8235
| colspan="2" |345.098
| colspan="2" |352.941
| colspan="2" |359.358
| colspan="2" |363.025
| colspan="2" |367.059
| colspan="2" |370.588
| colspan="2" |376.471
| colspan="2" |379.716
| colspan="2" |389.452
| |395.294
|-
|-
| |5
|13\10
|A
|91.765
|''B''
|Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
|Ab
|''Bb''
| |423.529
| colspan="2" |431.3725
| colspan="2" |441.1765
| colspan="2" |449.198
| colspan="2" |453.7815
| colspan="2" |458.8235
| colspan="2" |463.235
| colspan="2" |470.588
| colspan="2" |474.645
| colspan="2" |486.815
| |494.118
|-
|-
| |6
|17\13
|B\\
|92.308
|''H\\''
|
|J#
|''A#''
| |508.235
| colspan="2" |517.647
| colspan="2" |529.412
| colspan="2" |539.037
| colspan="2" |544.538
| colspan="2" |550.588
| colspan="2" |555.882
| colspan="2" |564.706
| colspan="2" |569.574
| colspan="2" |584.1785
| |592.941
|-
|-
| |7
|21\16
|Ap
|92.647
|''Bp''
| Subpental Mixolydian mode ends, Pental Mixolydian mode begins
|A
|''B''
| |592.941
| colspan="2" |603.921
| colspan="2" |617.647
| colspan="2" |628.877
| colspan="2" |635.394
| colspan="2" |642.353
| colspan="2" |648.529
| colspan="2" |658.8235
| colspan="2" |664.503
| colspan="2" |681.542
| |691.765
|-
|-
|8
|25\19
|B
|92.879
|''H''
|
|B
|''H''
|677.647
| colspan="2" |690.169
| colspan="2" |705.882
| colspan="2" |718.717
| colspan="2" |726.05
| colspan="2" |734.118
| colspan="2" |741.1765
| colspan="2" |752.941
| colspan="2" |759.432
| colspan="2" |778.905
|790.588
|-
|-
|9
|29\22
|H
|93.048
|''C''
|
|Hb
|''Cb''
|762.653
| colspan="2" |776.471
| colspan="2" |794.118
| colspan="2" |808.556
| colspan="2" |816.806
| colspan="2" |825.882
| colspan="2" |833.8235
| colspan="2" |847.059
| colspan="2" |854.361
| colspan="2" |876.268
|889.412
|-
|-
|10
|33\25
|C\\
|93.176
|''D\\''
|
|B#
|''H#''
|847.059
| colspan="2" |862.745
| colspan="2" |882.353
| colspan="2" |898.396
| colspan="2" |907.563
| colspan="2" |917.647
| colspan="2" |926.471
| colspan="2" |941.1765
| colspan="2" |949.29
| colspan="2" |973.631
|988.235
|-
|-
|11
|4\3
|Hp
|''94.118''
|''Cp''
|Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
|H
|''C''
|931.765
| colspan="2" |949.02
| colspan="2" |970.588
| colspan="2" |988.235
| colspan="2" |998.319
| colspan="2" |1009.412
| colspan="2" |1019.118
| colspan="2" |1035.294
| colspan="2" |1044.219
| colspan="2" |1070.994
|1087.059
|-
|-
|12
|19\14
|C
|95.798
|''D''
|
|C
|''D''
|1016.471
| colspan="2" |1035.294
| colspan="2" |1058.8235
| colspan="2" |1078.075
| colspan="2" |1089.076
| colspan="2" |1101.1765
| colspan="2" |1111.765
| colspan="2" |1129.412
| colspan="2" |1139.148
| colspan="2" |1168.357
|1185.882
|-
|-
|13
|15\11
|D
|96.257
|''S''
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
|Db
|''Sb''
|1101.1765
| colspan="2" |1121.569
| colspan="2" |1147.059
| colspan="2" |1167.914
| colspan="2" |1179.832
| colspan="2" |1192.941
| colspan="2" |1204.412
| colspan="2" |1223.529
| colspan="2" |1234.077
| colspan="2" |1265.72
|1284.706
|-
|-
|14
|26\19
| colspan="2" |E
|96.594
|C#
|
|''D#''
|1185.882
| colspan="2" |1027.843
| colspan="2" |1235.294
| colspan="2" |1257.754
| colspan="2" |1270.588
| colspan="2" |1284.706
| colspan="2" |1297.059
| colspan="2" |1317.647
| colspan="2" |1329.006
| colspan="2" |1363.083
|1383.529
|-
|-
|15
|11\8
| colspan="2" |F\\
|''97.059''
|D
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
|''S''
|1270.588
| colspan="2" |1294.118
| colspan="2" |1323.529
| colspan="2" |1347.594
| colspan="2" |1361.3445
| colspan="2" |1376.471
| colspan="2" |1389.706
| colspan="2" |1411.765
| colspan="2" |1423.935
| colspan="2" |1460.446
|1482.352
|-
|-
|16
|18\13
| colspan="2" |Ep
|97.738
| colspan="2" |E
|
|1355.294
| colspan="2" |1380.392
| colspan="2" |1411.765
| colspan="2" |1437.433
| colspan="2" |1452.101
| colspan="2" |1468.235
| colspan="2" |1482.353
| colspan="2" |1505.882
| colspan="2" |1518.864
| colspan="2" |1557.809
|1581.1765
|-
|-
|17
|25\18
| colspan="2" |F
|98.032
| colspan="2" |F
|
|1440
| colspan="2" |1466.667
| colspan="2" |1500
| colspan="2" |1527.273
| colspan="2" |1542.857
| colspan="2" |1560
| colspan="2" |1575
| colspan="2" |1600
| colspan="2" |1613.793
| colspan="2" |1655.172
|1680
|}Most harmonic tunings
{| class="wikitable"
|-
|-
|7\5
|98.824
|Mixolydian-Ionian mode ends
|}Golden/Pyrite Tunings±13¢
{| class="wikitable" style="text-align: center"
! rowspan="2" |Degrees
! rowspan="2" |Degrees
! colspan="4" rowspan="2" |Enneatonic
! colspan="4" rowspan="2" |Enneatonic
!Minor mode Middletown temperament
! rowspan="2" |Intense Aeolian-Subpental Dorian
!Neutral mode Middletown temperament
! colspan="3" |Dorian
!Major mode Middletown temperament
|-
|-
!7/3±13¢
!Subpental
!22/9±13¢
!Pental
!5/2±13¢
!Superpental
|-
|-
|1
| |1
| colspan="2" |G
|J
| colspan="2" |Gb
|''A''
|85.522-87.051
|Jb
|90.259-91.789
|''Ab''
|92.548-94.077
|85.109-86.638
|85.932-87.462
|88.7805-90.6955
|89.334-90.863
|-
|-
| |2
| |2
|J\\
|A\\
|''A\\''
|''B\\''
| colspan="2" |F#
| colspan="2" |G#
|171-044-174.1025
|170.218-173.277
|180.5185-183.577
|171.865-174.9235
|185.096-188.155
|177.561-180.62
|178.667-181.726
|-
|-
|3
| |3
| colspan="2" |Gp
|Jp
| colspan="2" |G
|''Ap''
|256.5655-261.154
|J
|270.778-275.366
|''A''
|277.644-282.232
|255.327-259.915
|257.797-262.385
|266.341-270.93
|268.001-272.589
|-
|-
| |4
| |4
|J
|J
|A
|J
|''A''
|342.087-348.205
|361.037-367.155
|370.1915-376.309
|-
|5
|A
|''B''
|''B''
|Ab
|''Bb''
|427.609-435.256
|451.2965-458.9435
|462.739-470.386
|-
| |6
|B\\
|''H\\''
|J#
|''A#''
|513.131-522.307
|541.556-550.732
|555.287-564.464
|-
|7
|Ap
|''Bp''
|A
|A
|''B''
|''B''
|598.653-609.359
|340.4355-346.553
|631.815-642.521
|343.729-349.847
|647.835-658.541
|355.122-361.2395
|357.335-363.452
|-
|-
| |8
| |5
|B
|B
|''H''
|B
|''H''
|684.1745-696.41.
|722.074-734.31
|740.383-752.618
|-
|9
|H
|''C''
|''C''
|Hb
|Bb
|''Cb''
|''Cb''
|769.696-783.461
|425.544-433.1915
|812.334-826.098
|429.662-437.309
|832.931-846.6955
|442.902-451.5495
|446.668-454.315
|-
|-
| |10
| |6
|C\\
|C\\
|''D\\''
|''Q\\''
|B#
|A#
|''H#''
|''B#''
|855.218-870.512
|510.653-519.83
|902.593-917.887
|515.594-524.7705
|925.479-940.773
|532.683-541.859
|536.002-545.178
|-
|-
|11
| |7
|Hp
|Bp
|''Cp''
|''Cp''
|H
|B
|''C''
|''C''
|940.74-957.5635
|595.762-606.468
|992.852.1009.676
|601.526-612.232
|1018.0265-1034.85
|621.463-632.169
|625.3355-636.041
|-
|-
| |12
|8
|C
|C
|''D''
|''Q''
|C
|C
|''Q''
|680.871-693.106
|687.459-699.694
|710.244-722.479
|714.996-726.904
|-
|9
|Q
|''D''
|''D''
|1026.262-1044.615
|Qb
|1083.1115-1101.464
|1110.574-1128.927
|-
|13
|D
|''S''
|Db
|Db
|''Sb''
|765.98-779.745
|1111.7847-1131.666
|773.391-787.156
|1173.371-1193.253
|799.024-812.789
|1203.122-1223.005
|804.003-817.768
|-
|-
| |14
|10
| colspan="2" |E
|D\\
|''Q\\''
|C#
|C#
|''D#''
|Q#
|1197.3055-1218.717
|851.089-866.383
|1353.889-1375.042
|859.323-874.6175
|1295.67-1317.082
|887.805-903.099
|-
|893.336-999.4935
|15
| colspan="2" |F\\
|D
|''S''
|1282.827-1305.768
|1444.149-1466.83
|1388.218-1411.159
|-
|16
| colspan="2" |Ep
| colspan="2" |E
|1368.249-1392.82
|1534.408-1558.619
|1480.766-1505.236
|-
|17
| colspan="2" |F
| 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="4" 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" |G
| colspan="2" |Gb
|85.109
|85.874
|85.932
|86.638
|86.697
|87.462
|88.7805
|89.334
|89.545
|90.098
|90.31
|90.6955
|-
|2
|J\\
|''A\\''
| colspan="2" |F#
|170.218
|171.747
|171.865
|173.277
|173.394
|174.9235
|177.561
|178.667
|179.09
|180.197
|180.62
|181.391
|-
|3
| colspan="2" |Gp
| colspan="2" |G
|255.327
|257.621
|257.797
|259.915
|260.091
|262.385
|266.341
|268.001
|268.636
|270.295
|270.93
|272.086
|-
|4
|J
|A
|J
|''A''
|340.4355
|343.494
|343.729
|346.553
|346.788
|349.847
|355.122
|357.335
|358.181
|360.393
|361.2395
|362.782
|-
|5
|A
|''B''
|Ab
|''Bb''
|425.544
|429.368
|429.662
|433.1915
|433.485
|437.309
|442.902
|446.668
|447.726
|450.492
|451.5495
|453.477
|-
|6
|B\\
|''H\\''
|J#
|''A#''
|510.653
|515.2415
|515.594
|519.83
|520.182
|524.7705
|532.683
|536.002
|537.271
|540.59
|541.859
|544.173
|-
|7
|Ap
|''Bp''
|A
|''B''
|595.762
|601.115
|601.526
|606.468
|606.879
|612.232
|621.463
|625.3355
|626.516
|630.688
|632.169
|634.868
|-
|8
|B
|''H''
|B
|''H''
|680.871
|686.989
|687.459
|693.106
|693.576
|699.694
|710.244
|714.996
|716.3615
|720.787
|722.479
|725.563
|-
|9
|H
|''C''
|Hb
|''Cb''
|765.98
|772.862
|773.391
|779.745
|780.273
|787.156
|799.024
|804.003
|805.907
|810.885
|812.789
|816.259
|-
|10
|C\\
|''D\\''
|B#
|''H#''
|851.089
|858.736
|859.323
|866.383
|866.97
|874.6175
|887.805
|893.336
|895.452
|900.983
|903.099
|906.955
|-
|-
|11
|11
|Hp
|Qp
|''Cp''
|''Dp''
|H
|Q
|''C''
|''D''
|936.198
|936.198-953.021
|944.609
|945.256-962.079
|945.256
|976.585-993.409
|953.021
|982.67-1090.357
|953.667
|962.079
|976.585
|982.67
|984.997
|991.082
|993.409
|997.65
|-
|-
|12
|12
|C
| colspan="2" |D
|''D''
|D
|C
|''S''
|''D''
|1021.3065-1039.66
|1021.3065
|1031.188-1049.541
|1030.483
|1065.366-1083.719
|1031.188
|1072.004-1181.22
|1039.66
|1040.3645
|1049.541
|1065.366
|1072.004
|1074.542
|1081.18
|1083.719
|1088.346
|-
|-
|13
|13
|D
|E
|''S''
|''S''
|Db
| colspan="2" |Eb
|''Sb''
|1106.415-1186.94
|1106.415
|1117.12-1137.003
|1116.3565
|1154.146-1174.029.
|1117.12
|1161.337-1272.083
|1186.94
|1127.0615
|1137.003
|1154.146
|1161.337
|1164.087
|1171.2785
|1174.029.
|1179.041
|-
|-
|14
|14
| colspan="2" |E
| colspan="2" |F
|C#
|D#
|''D#''
|''S#''
|1191.524
|1191.524-1212.936
|1202.23
|1203.052-1224.464
|1203.052
|1242.927-1264.3385
|1212.936
|1250.671-1362.946
|1213.759
|1224.464
|1242.927
|1250.671
|1253.633
|1261.377
|1264.3385
|1269.737
|-
|-
|15
|15
| colspan="2" |F\\
| colspan="2" |G\\
|D
| colspan="2" |E
|''S''
|1276.633-1299.5745
|1276.633
|1288.985-1311.926
|1288.104
|1331.707-1354.648
|1288.985
|1340.005-1453.809
|1299.5745
|1300.456
|1311.926
|1331.707
|1340.005
|1343.178
|1351.475
|1354.648
|1360.432
|-
|-
|16
|16
| colspan="2" |Ep
| colspan="2" |Fp
| colspan="2" |E
| colspan="2" |F
|1361.741
|1361.741-1386.213
|1373.977
|1374.917-1399.388
|1374.917
|1420.488-1424.958
|1386.213
|1426.338-1453.809
|1387.153
|1399.388
|1420.488
|1426.338
|1432.723
|1441.5735
|1424.958
|1451.128
|-
|-
|17
|17
| colspan="2" |F
| colspan="4" |G
| colspan="2" |F
|1446.851-1472.851
|1446.851
|1460.85-1486.85
|1459.851
|1509.268-1535.268
|1460.85
|1518.672-1544.672
|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" style="text-align: center"
{| class="wikitable"
|-
!Degrees
!Degrees
! colspan="4" |Enneatonic
! colspan="8" |Enneatonic
!+13¢ (S5D)
!Mohajira
!Mean
!Beatles
!-13¢ (s5M)
|-
|-
|1
| |1
| colspan="2" |G
| colspan="2" |G
| colspan="2" |Gb
| colspan="2" |Gb
|90.863
|J
|91.46
|''A''
|92.019
|Jb
|''Ab''
|90.464-91.994
|90.6955-92.225
|-
|-
|2
| |2
|J\\
|J\\
|''A\\''
|''A\\''
| colspan="2" |F#
| colspan="2" |F#
|181.726
|A\\
|182.92
|''B\\''
|184.038
| colspan="2" |G#
|180.929-183.988
|181.391-184.45
|-
|-
|3
| |3
| colspan="2" |Gp
| colspan="2" |Gp
| colspan="2" |G
| colspan="2" |G
|272.589
|Jp
|274.381
|''Ap''
|276.0565
|J
|''A''
|271.393-275.9815
|272.086-276.675
|-
|-
|4
| |4
|J
|J
|A
|A
|J
|J
|''A''
|''A''
|363.452
|J
|365.841
|''B''
|368.075
|A
|''B''
|361.858-367.975
|362.782-368.91
|-
|-
|5
| |5
|A
|A
|''B''
|''B''
|Ab
|Ab
|''Bb''
|''Bb''
|454.315
|B
|457.301
|''C''
|460.094
|Bb
|''Cb''
|452.322-459.969
|453.477-461.124
|-
|-
|6
| |6
|B\\
|B\\
|''H\\''
|''H\\''
|J#
|J#
|''A#''
|''A#''
|545.178
|C\\
|548.761
|''Q\\''
|552.113
|A#
|''B#''
|542.787-551.963
|544.173-553.349
|-
|-
|7
| |7
|Ap
|Ap
|''Bp''
|''Bp''
|A
|A
|''B''
|''B''
|636.041
|Bp
|640.221
|''Cp''
|664.132
|B
|''C''
|633.251-643.957
|634.868-645.574
|-
|-
|8
|8
Line 868: Line 386:
|B
|B
|''H''
|''H''
|726.904
|C
|731.6815
|''Q''
|736.151
|C
|''Q''
|723.7155-735.951
|725.564-737.799
|-
|-
|9
|9
Line 877: Line 398:
|Hb
|Hb
|''Cb''
|''Cb''
|817.767
|Q
|823.142
|''D''
|828.17
|Qb
|Db
|814.18-827.945
|816.259-830.024
|-
|-
|10
|10
Line 886: Line 410:
|B#
|B#
|''H#''
|''H#''
|908.6305
|D\\
|914.602
|''Q\\''
|920.1885
|C#
|Q#
|904.644-919.9385
|906.955-922.289
|-
|-
|11
|11
Line 895: Line 422:
|H
|H
|''C''
|''C''
|999.4935
|Qp
|1006.062
|''Dp''
|1012.207
|Q
|''D''
|995.109-1011.932
|997.65-1014.474
|-
|-
|12
|12
Line 904: Line 434:
|C
|C
|''D''
|''D''
|1090.357
| colspan="2" |D
|1097.522
|D
|1104.226
|''S''
|1085.573-1103.926
|1088.346-1106.699
|-
|-
|13
|13
Line 913: Line 445:
|Db
|Db
|''Sb''
|''Sb''
|1181.22
|E
|1188.982
|''S''
|1196.245
| colspan="2" |Eb
|1176.038-1195.92
|1179.041-1198.9235
|-
|-
|14
|14
Line 921: Line 455:
|C#
|C#
|''D#''
|''D#''
|1272.083
| colspan="2" |F
|1280.443
|D#
|1288.234
|''S#''
|1266.502-1287.914
|1269.737-1291.1485
|-
|-
|15
|15
Line 929: Line 465:
|D
|D
|''S''
|''S''
|1362.946
| colspan="2" |G\\
|1371.903
| colspan="2" |E
|1380.283
|1356.967-1379.908
|1360.432-1383.373
|-
|-
|16
|16
| colspan="2" |Ep
| colspan="2" |Ep
| colspan="2" |E
| colspan="2" |E
|1453.809
| colspan="2" |Fp
|1463.363
| colspan="2" |F
|1472.3015
|1447.431-1471.902
|1451.128-1475.598
|-
|-
|17
|17
| colspan="2" |F
| colspan="4" |F
| colspan="2" |F
| colspan="4" |G
|1544.672
|1537.8955-1563.8955
|1554.823
|1541.823-1577.823
|1557.82
|}
|}Major mode Middletown temperament
{| class="wikitable" style="text-align: center"
{| class="wikitable"
! rowspan="3" |Degrees
|+
! colspan="4" rowspan="3" |Enneatonic
! colspan="4" |Mixolydian
! rowspan="3" |Mixolydian-Ionian
|-
|-
! rowspan="4" |Degrees
! rowspan="2" |Subpental
! colspan="4" rowspan="4" |Enneatonic
! rowspan="2" |Pental
! colspan="13" |Mixolydian
! colspan="2" |Superpental
! colspan="2" |Mixolydian-Ionian
|-
|-
! colspan="3" |Subpental
!Soft
! colspan="4" |Pental
!Intense
! colspan="6" |Superpental
! rowspan="3" |Mean
! rowspan="3" |+13¢
|-
|-
! rowspan="2" |-13¢ (5)
| |1
! 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" |G
| colspan="2" |G
| colspan="2" |Gb
| colspan="2" |Gb
|92.035
|92.019-93.548
|92.225
|92.035-93.5645
|92.401
|94.1155-95.645
|92.8
|95.669-97.198
|93.548
|96.739-98.268
|93.5645
|94.1155
|94.88
|95.645
|95.669
|96.433
|96.739
|97.198
|97.504
|98.268
|-
|-
|2
| |2
|J\\
|J\\
|''A\\''
|''A\\''
| colspan="2" |F#
| colspan="2" |F#
|184.07
|184.038-187.139
|184.45
|184.07-187.129
|184.802
|188.231-191.29
|185.6
|191.337-194.396
|187.139
|193.478-196.537
|198.8245
|188.231
|189.7605
|191.29
|191.337
|192.867
|193.478
|194.396
|195.007
|196.537
|-
|-
|3
| |3
| colspan="2" |Gp
| colspan="2" |Gp
| colspan="2" |G
| colspan="2" |G
|276.105
|276.0565-280.645
|276.675
|276.105-280.693
|277.204
|282.347-286.935
|278.399
|287.006-291.594
|280.645
|290.217-294.805
|280.693
|282.347
|284.641
|286.935
|287.006
|289.3
|290.217
|291.594
|292.511
|294.805
|-
|-
|4
| |4
|J
|J
|A
|A
|J
|J
|''A''
|''A''
|368.14
|368.075-374.193
|368.9
|368.14-374.258
|369.605
|376.462-382.58
|371.199
|382.675-388.792
|374.193
|386.956-393.074
|374.258
|376.462
|379.521
|382.58
|382.675
|385.733
|386.956
|388.792
|390.015
|393.074
|-
|-
|5
| |5
|A
|A
|''B''
|''B''
|Ab
|Ab
|''Bb''
|''Bb''
|460.175
|460.094-467.741
|461.1245
|460.175-467.822
|462.006
|470.578-478.225
|463.999
|478.343-485.99
|467.741
|483.695-491.342
|467.822
|470.578
|474.401
|478.225
|478.343
|482.167
|483.695
|485.99
|487.519
|491.342
|-
|-
|6
| |6
|B\\
|B\\
|''H\\''
|''H\\''
|J#
|J#
|''A#''
|''A#''
|552.21
|552.113-561.29
|553.349
|552.21-561.387
|554.407
|564.693-573.87
|556.799
|574.012-583.188
|561.29
|580.434-589.6105
|561.387
|564.693
|569.2815
|573.87
|574.012
|578.6
|580.434
|583.188
|585.022
|589.6105
|-
|-
|7
| |7
|Ap
|Ap
|''Bp''
|''Bp''
|A
|A
|''B''
|''B''
|644.2455
|644.132-654.838
|645.574
|644.2455-654.951
|646.808
|658.809-669.515
|649.598
|669.6805-680.386
|654.838
|677.173-687.879
|654.951
|658.809
|664.162
|669.515
|669.6805
|675.033
|677.173
|680.386
|682.526
|687.879
|-
|-
|8
|8
Line 1,124: Line 574:
|B
|B
|''H''
|''H''
|736.281
|736.151-748.386
|737.8
|736.281-748.516
|739.21
|752.924-765.16
|742.398
|765.349-777.584
|748.386
|773.912-783.147
|748.516
|752.924
|759.042
|765.16
|765.349
|771.467
|773.912
|777.584
|780.03
|783.147
|-
|-
|9
|9
Line 1,145: Line 585:
|Hb
|Hb
|''Cb''
|''Cb''
|828.316
|828.17-841.934
|830.024
|828.316-842.08
|831.611
|847.04-860.805
|835.198
|861.018-874.7852
|841.934
|870.416-884.416
|842.08
|847.04
|853.922
|860.805
|861.018
|867.9
|870.416
|874.7852
|877.5335
|884.416
|-
|-
|10
|10
Line 1,166: Line 596:
|B#
|B#
|''H#''
|''H#''
|920.351
|920.1885-935.483
|922.249
|920.351-935.645
|924.012
|941.155-956.45
|927.998
|956.6865-971.9805
|935.483
|967.39-982.684
|935.645
|941.155
|948.8025
|956.45
|956.6865
|964.3335
|967.39
|971.9805
|975.037
|982.684
|-
|-
|11
|11
Line 1,187: Line 607:
|H
|H
|''C''
|''C''
|1012.386
|1012.207-1029.031
|1014.474
|1012.386-1029.209
|1016.413
|1035.271-1052.0945
|1020.7975
|1052.355-1069.179
|1029.031
|1064.129-1080.953
|1029.209
|1035.271
|1043.683
|1052.0945
|1052.355
|1060.767
|1064.129
|1069.179
|1072.541
|1080.953
|-
|-
|12
|12
Line 1,208: Line 618:
|C
|C
|''D''
|''D''
|1104.421
|1104.226-1122.579
|1106.699
|1104.421-1122.774
|1108.814
|1129.3865-1147.7395
|1113.567
|1148.024-1166.377
|1122.579
|1160.868-1179.221
|1122.774
|1129.3865
|1138.563
|1147.7395
|1148.024
|1157.2
|1160.868
|1166.377
|1170.045
|1179.221
|-
|-
|13
|13
Line 1,229: Line 629:
|Db
|Db
|''Sb''
|''Sb''
|1196.456
|1196.245-1216.127
|1198.924
|1196.456-1216.338
|1201.216
|1223.502-1243.384
|1206.397
|1243.692-1263.575
|1216.127
|1257.607-1277.4895
|1216.338
|1223.502
|1233.443
|1243.384
|1243.692
|1253.6335
|1257.607
|1263.575
|1267.548
|1277.4895
|-
|-
|14
|14
Line 1,249: Line 639:
|C#
|C#
|''D#''
|''D#''
|1288.491
|1288.234-1309.676
|1291.1485
|1288.491-1309.903
|1293.617
|1317.618-1339.026
|1299.197
|1339.361-1360.773
|1309.676
|1354.346-1375.758
|1309.903
|1317.618
|1328.3235
|1339.026
|1339.361
|1350.067
|1354.346
|1360.773
|1365.052
|1375.758
|-
|-
|15
|15
Line 1,269: Line 649:
|D
|D
|''S''
|''S''
|1380.526
|1380.283-1403.224
|1383.373
|1380.526-1403.467
|1386.018
|1411.733-1434.674
|1391.997
|1435.03-1457.97
|1403.224
|1451.085-1474.026
|1403.467
|1411.733
|1423.204
|1434.674
|1435.03
|1446.5
|1451.085
|1457.97
|1462.556
|1474.026
|-
|-
|16
|16
| colspan="2" |Ep
| colspan="2" |Ep
| colspan="2" |E
| colspan="2" |E
|1472.561
|1472.3015-1496.772
|1475.598
|1472.561-1497.032
|1478.419
|1505.849-1530.319
|1484.796
|1530.698-1555.168
|1496.772
|1547.824-1572.295
|1497.032
|1505.849
|1518.083
|1530.319
|1530.698
|1542.934
|1547.824
|1555.169
|1560.0595
|1572.295
|-
|-
|17
|17
| colspan="2" |F
| colspan="4" |F
| colspan="2" |F
|1557.82-1583.82
|1564.596
|1564.596-1590.596
|1567.96
|1599.964-1625.964
|1570.82
|1626.366-1652.366
|1577.596
|1644.563-1670.563
|1583.82
|1590.596
|1599.964
|1612.964
|1625.964
|1626.366
|1639.366
|1644.563
|1652.366
|1657.563
|1670.563
|}
|}
[[Category:EdX]]
 
== See also ==
* [[17ed5/2]] - equal division of the classic major tenth
* [[17ed7/3]] - equal division of the septimal minor tenth

Latest revision as of 13:40, 6 March 2026

17edX means division of a tenth interval into 17 equal parts.

Intervals

Decade Period Notes
6\5 84.706 Intense Aeolian-Subpental Dorian mode begins
29\24 85.294
23\19 85.449
17\14 85.714
11\9 86.275 Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
16\13 86.878
21\17 87.197
5\4 88.235 Subpental Dorian mode ends, Pental Dorian mode begins
24\19 89.164
19\15 89.412
14\11 89.840 Pental Dorian mode ends, Superpental Dorian mode begins
23\18 90.196
9\7 90.756 Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
31\24 91.176
22\17 91.349 Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
35\27 91.503
13\10 91.765 Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
17\13 92.308
21\16 92.647 Subpental Mixolydian mode ends, Pental Mixolydian mode begins
25\19 92.879
29\22 93.048
33\25 93.176
4\3 94.118 Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
19\14 95.798
15\11 96.257 Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
26\19 96.594
11\8 97.059 Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
18\13 97.738
25\18 98.032
7\5 98.824 Mixolydian-Ionian mode ends

Golden/Pyrite Tunings±13¢

Degrees Enneatonic Intense Aeolian-Subpental Dorian Dorian
Subpental Pental Superpental
1 J A Jb Ab 85.109-86.638 85.932-87.462 88.7805-90.6955 89.334-90.863
2 A\\ B\\ G# 170.218-173.277 171.865-174.9235 177.561-180.62 178.667-181.726
3 Jp Ap J A 255.327-259.915 257.797-262.385 266.341-270.93 268.001-272.589
4 J B A B 340.4355-346.553 343.729-349.847 355.122-361.2395 357.335-363.452
5 B C Bb Cb 425.544-433.1915 429.662-437.309 442.902-451.5495 446.668-454.315
6 C\\ Q\\ A# B# 510.653-519.83 515.594-524.7705 532.683-541.859 536.002-545.178
7 Bp Cp B C 595.762-606.468 601.526-612.232 621.463-632.169 625.3355-636.041
8 C Q C Q 680.871-693.106 687.459-699.694 710.244-722.479 714.996-726.904
9 Q D Qb Db 765.98-779.745 773.391-787.156 799.024-812.789 804.003-817.768
10 D\\ Q\\ C# Q# 851.089-866.383 859.323-874.6175 887.805-903.099 893.336-999.4935
11 Qp Dp Q D 936.198-953.021 945.256-962.079 976.585-993.409 982.67-1090.357
12 D D S 1021.3065-1039.66 1031.188-1049.541 1065.366-1083.719 1072.004-1181.22
13 E S Eb 1106.415-1186.94 1117.12-1137.003 1154.146-1174.029. 1161.337-1272.083
14 F D# S# 1191.524-1212.936 1203.052-1224.464 1242.927-1264.3385 1250.671-1362.946
15 G\\ E 1276.633-1299.5745 1288.985-1311.926 1331.707-1354.648 1340.005-1453.809
16 Fp F 1361.741-1386.213 1374.917-1399.388 1420.488-1424.958 1426.338-1453.809
17 G 1446.851-1472.851 1460.85-1486.85 1509.268-1535.268 1518.672-1544.672
Degrees Enneatonic Mohajira Beatles
1 G Gb J A Jb Ab 90.464-91.994 90.6955-92.225
2 J\\ A\\ F# A\\ B\\ G# 180.929-183.988 181.391-184.45
3 Gp G Jp Ap J A 271.393-275.9815 272.086-276.675
4 J A J A J B A B 361.858-367.975 362.782-368.91
5 A B Ab Bb B C Bb Cb 452.322-459.969 453.477-461.124
6 B\\ H\\ J# A# C\\ Q\\ A# B# 542.787-551.963 544.173-553.349
7 Ap Bp A B Bp Cp B C 633.251-643.957 634.868-645.574
8 B H B H C Q C Q 723.7155-735.951 725.564-737.799
9 H C Hb Cb Q D Qb Db 814.18-827.945 816.259-830.024
10 C\\ D\\ B# H# D\\ Q\\ C# Q# 904.644-919.9385 906.955-922.289
11 Hp Cp H C Qp Dp Q D 995.109-1011.932 997.65-1014.474
12 C D C D D D S 1085.573-1103.926 1088.346-1106.699
13 D S Db Sb E S Eb 1176.038-1195.92 1179.041-1198.9235
14 E C# D# F D# S# 1266.502-1287.914 1269.737-1291.1485
15 F\\ D S G\\ E 1356.967-1379.908 1360.432-1383.373
16 Ep E Fp F 1447.431-1471.902 1451.128-1475.598
17 F G 1537.8955-1563.8955 1541.823-1577.823
Degrees Enneatonic Mixolydian Mixolydian-Ionian
Subpental Pental Superpental
Soft Intense
1 G Gb 92.019-93.548 92.035-93.5645 94.1155-95.645 95.669-97.198 96.739-98.268
2 J\\ A\\ F# 184.038-187.139 184.07-187.129 188.231-191.29 191.337-194.396 193.478-196.537
3 Gp G 276.0565-280.645 276.105-280.693 282.347-286.935 287.006-291.594 290.217-294.805
4 J A J A 368.075-374.193 368.14-374.258 376.462-382.58 382.675-388.792 386.956-393.074
5 A B Ab Bb 460.094-467.741 460.175-467.822 470.578-478.225 478.343-485.99 483.695-491.342
6 B\\ H\\ J# A# 552.113-561.29 552.21-561.387 564.693-573.87 574.012-583.188 580.434-589.6105
7 Ap Bp A B 644.132-654.838 644.2455-654.951 658.809-669.515 669.6805-680.386 677.173-687.879
8 B H B H 736.151-748.386 736.281-748.516 752.924-765.16 765.349-777.584 773.912-783.147
9 H C Hb Cb 828.17-841.934 828.316-842.08 847.04-860.805 861.018-874.7852 870.416-884.416
10 C\\ D\\ B# H# 920.1885-935.483 920.351-935.645 941.155-956.45 956.6865-971.9805 967.39-982.684
11 Hp Cp H C 1012.207-1029.031 1012.386-1029.209 1035.271-1052.0945 1052.355-1069.179 1064.129-1080.953
12 C D C D 1104.226-1122.579 1104.421-1122.774 1129.3865-1147.7395 1148.024-1166.377 1160.868-1179.221
13 D S Db Sb 1196.245-1216.127 1196.456-1216.338 1223.502-1243.384 1243.692-1263.575 1257.607-1277.4895
14 E C# D# 1288.234-1309.676 1288.491-1309.903 1317.618-1339.026 1339.361-1360.773 1354.346-1375.758
15 F\\ D S 1380.283-1403.224 1380.526-1403.467 1411.733-1434.674 1435.03-1457.97 1451.085-1474.026
16 Ep E 1472.3015-1496.772 1472.561-1497.032 1505.849-1530.319 1530.698-1555.168 1547.824-1572.295
17 F 1557.82-1583.82 1564.596-1590.596 1599.964-1625.964 1626.366-1652.366 1644.563-1670.563

See also

  • 17ed5/2 - equal division of the classic major tenth
  • 17ed7/3 - equal division of the septimal minor tenth
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