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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
|-
|-
! colspan="2" rowspan="3" |Intense Aeolian-Dorian
| 6\5
! colspan="6" |Dorian
|''84.706''
! colspan="2" rowspan="3" |Dorian-Mixolydian
|Intense Aeolian-Subpental Dorian mode begins
! colspan="8" |Mixolydian
! colspan="2" rowspan="3" |Mixolydian-Ionian
|-
|-
! colspan="2" rowspan="2" |Subpental
|29\24
! colspan="2" rowspan="2" |Pental
|''85.294''
! colspan="2" rowspan="2" |Superpental
|
! colspan="2" rowspan="2" |Subpental
! colspan="2" rowspan="2" |Pental
! colspan="4" |Superpental
|-
|-
! colspan="2" |Soft
|23\19
! colspan="2" |Intense
|85.449
|
|-
|-
! |Minimum
|17\14
! |Maximum
|85.714
!Minimum
|
!Maximum
|-
!Minimum
|11\9
!Maximum
|86.275
!Minimum
|Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
!Maximum
|-
!Minimum
|16\13
! |Maximum
|86.878
!Minimum
|
!Maximum
|-
! |Minimum
|21\17
!Maximum
|87.197
!Minimum
|
!Maximum
|-
!Minimum
|5\4
!Maximum
|''88.235''
!Minimum
|Subpental Dorian mode ends, Pental Dorian mode begins
! |Maximum
|-
|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¢
 
{| class="wikitable" style="text-align: center"
! rowspan="2" |Degrees
! colspan="4" rowspan="2" |Enneatonic
! rowspan="2" |Intense Aeolian-Subpental Dorian
! colspan="3" |Dorian
|-
!Subpental
!Pental
!Superpental
|-
|-
| |1
| |1
| colspan="2" |G
|J
| colspan="2" |Gb
|''A''
| |84.706
|Jb
| colspan="2" |86.2745
|''Ab''
| colspan="2" |88.235
|85.109-86.638
| colspan="2" |89.84
|85.932-87.462
| colspan="2" |90.756
|88.7805-90.6955
| colspan="2" |91.765
|89.334-90.863
| colspan="2" |92.647
| colspan="2" |94.118
| colspan="2" |94.929
| colspan="2" |97.363
| |98.8235
|-
|-
| |2
| |2
|J\\
|A\\
|''A\\''
|''B\\''
| colspan="2" |F#
| colspan="2" |G#
| |169.412
|170.218-173.277
| colspan="2" |172.549
|171.865-174.9235
| colspan="2" |176.471
|177.561-180.62
| colspan="2" |179.679
|178.667-181.726
| 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
| |3
| colspan="2" |Gp
|Jp
| colspan="2" |G
|''Ap''
| |254.118
|J
| colspan="2" |258.8235
|''A''
| colspan="2" |264.706
|255.327-259.915
| colspan="2" |269.519
|257.797-262.385
| colspan="2" |272.268
|266.341-270.93
| colspan="2" |275.294
|268.001-272.589
| colspan="2" |277.941
| colspan="2" |282.353
| colspan="2" |284.787
| colspan="2" |292.089
| |296.471
|-
|-
| |4
| |4
|J
|J
|''B''
|A
|A
|J
|''B''
|''A''
|340.4355-346.553
| |338.8235
|343.729-349.847
| colspan="2" |345.098
|355.122-361.2395
| colspan="2" |352.941
|357.335-363.452
| 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
| |5
|A
|B
|''B''
|''C''
|Ab
|Bb
|''Bb''
|''Cb''
| |423.529
|425.544-433.1915
| colspan="2" |431.3725
|429.662-437.309
| colspan="2" |441.1765
|442.902-451.5495
| colspan="2" |449.198
|446.668-454.315
| 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
| |6
|B\\
|C\\
|''H\\''
|''Q\\''
|J#
|A#
|''A#''
|''B#''
| |508.235
|510.653-519.83
| colspan="2" |517.647
|515.594-524.7705
| colspan="2" |529.412
|532.683-541.859
| colspan="2" |539.037
|536.002-545.178
| 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
| |7
|Ap
|Bp
|''Bp''
|''Cp''
|A
|B
|''B''
|''C''
| |592.941
|595.762-606.468
| colspan="2" |603.921
|601.526-612.232
| colspan="2" |617.647
|621.463-632.169
| colspan="2" |628.877
|625.3355-636.041
| 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
|8
|B
|C
|''H''
|''Q''
|B
|C
|''H''
|''Q''
|677.647
|680.871-693.106
| colspan="2" |690.169
|687.459-699.694
| colspan="2" |705.882
|710.244-722.479
| colspan="2" |718.717
|714.996-726.904
| 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
|9
|H
|Q
|''C''
|''D''
|Hb
|Qb
|''Cb''
|Db
|762.653
|765.98-779.745
| colspan="2" |776.471
|773.391-787.156
| colspan="2" |794.118
|799.024-812.789
| colspan="2" |808.556
|804.003-817.768
| 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
|10
|C\\
|D\\
|''D\\''
|''Q\\''
|B#
|C#
|''H#''
|Q#
|847.059
|851.089-866.383
| colspan="2" |862.745
|859.323-874.6175
| colspan="2" |882.353
|887.805-903.099
| colspan="2" |898.396
|893.336-999.4935
| 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
|11
|Hp
|Qp
|''Cp''
|''Dp''
|H
|Q
|''C''
|''D''
|931.765
|936.198-953.021
| colspan="2" |949.02
|945.256-962.079
| colspan="2" |970.588
|976.585-993.409
| colspan="2" |988.235
|982.67-1090.357
| 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
|12
|C
| colspan="2" |D
|''D''
|D
|C
|''S''
|''D''
|1021.3065-1039.66
|1016.471
|1031.188-1049.541
| colspan="2" |1035.294
|1065.366-1083.719
| colspan="2" |1058.8235
|1072.004-1181.22
| 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
|13
|D
|E
|''S''
|''S''
|Db
| colspan="2" |Eb
|''Sb''
|1106.415-1186.94
|1101.1765
|1117.12-1137.003
| colspan="2" |1121.569
|1154.146-1174.029.
| colspan="2" |1147.059
|1161.337-1272.083
| 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
|14
| colspan="2" |E
| colspan="2" |F
|C#
|D#
|''D#''
|''S#''
|1185.882
|1191.524-1212.936
| colspan="2" |1027.843
|1203.052-1224.464
| colspan="2" |1235.294
|1242.927-1264.3385
| colspan="2" |1257.754
|1250.671-1362.946
| 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
|15
| colspan="2" |F\\
| colspan="2" |G\\
|D
| colspan="2" |E
|''S''
|1276.633-1299.5745
|1270.588
|1288.985-1311.926
| colspan="2" |1294.118
|1331.707-1354.648
| colspan="2" |1323.529
|1340.005-1453.809
| 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
|16
| colspan="2" |Ep
| colspan="2" |Fp
| colspan="2" |E
| colspan="2" |F
|1355.294
|1361.741-1386.213
| colspan="2" |1380.392
|1374.917-1399.388
| colspan="2" |1411.765
|1420.488-1424.958
| colspan="2" |1437.433
|1426.338-1453.809
| 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
|17
| colspan="4" |F
| colspan="4" |G
|1440
|1446.851-1472.851
| colspan="2" |1466.667
|1460.85-1486.85
| colspan="2" |1500
|1509.268-1535.268
| colspan="2" |1527.273
|1518.672-1544.672
| colspan="2" |1542.857
|}
| colspan="2" |1560
{| class="wikitable" style="text-align: center"
| colspan="2" |1575
!Degrees
| colspan="2" |1600
! colspan="8" |Enneatonic
| colspan="2" |1613.793
!Mohajira
| colspan="2" |1655.172
!Beatles
|1680
|}Most harmonic tunings
{| class="wikitable"
|-
|-
! rowspan="2" |Degrees
| |1
! colspan="4" rowspan="2" |Enneatonic
!Minor mode Middletown temperament
!Neutral mode Middletown temperament
!Major mode Middletown temperament
|-
!7/3±13¢
!22/9±13¢
!5/2±13¢
|-
|1
| colspan="2" |G
| colspan="2" |G
| colspan="2" |Gb
| colspan="2" |Gb
|85.522-87.051
|J
|90.259-91.789
|''A''
|92.548-94.077
|Jb
|''Ab''
|90.464-91.994
|90.6955-92.225
|-
|-
| |2
| |2
Line 344: Line 317:
|''A\\''
|''A\\''
| colspan="2" |F#
| colspan="2" |F#
|171-044-174.1025
|A\\
|180.5185-183.577
|''B\\''
|185.096-188.155
| 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
|256.5655-261.154
|Jp
|270.778-275.366
|''Ap''
|277.644-282.232
|J
|''A''
|271.393-275.9815
|272.086-276.675
|-
|-
| |4
| |4
Line 360: Line 338:
|J
|J
|''A''
|''A''
|342.087-348.205
|J
|361.037-367.155
|''B''
|370.1915-376.309
|A
|''B''
|361.858-367.975
|362.782-368.91
|-
|-
|5
| |5
|A
|A
|''B''
|''B''
|Ab
|Ab
|''Bb''
|''Bb''
|427.609-435.256
|B
|451.2965-458.9435
|''C''
|462.739-470.386
|Bb
|''Cb''
|452.322-459.969
|453.477-461.124
|-
|-
| |6
| |6
Line 378: Line 362:
|J#
|J#
|''A#''
|''A#''
|513.131-522.307
|C\\
|541.556-550.732
|''Q\\''
|555.287-564.464
|A#
|''B#''
|542.787-551.963
|544.173-553.349
|-
|-
|7
| |7
|Ap
|Ap
|''Bp''
|''Bp''
|A
|A
|''B''
|''B''
|598.653-609.359
|Bp
|631.815-642.521
|''Cp''
|647.835-658.541
|B
|''C''
|633.251-643.957
|634.868-645.574
|-
|-
| |8
|8
|B
|B
|''H''
|''H''
|B
|B
|''H''
|''H''
|684.1745-696.41.
|C
|722.074-734.31
|''Q''
|740.383-752.618
|C
|''Q''
|723.7155-735.951
|725.564-737.799
|-
|-
|9
|9
Line 405: Line 398:
|Hb
|Hb
|''Cb''
|''Cb''
|769.696-783.461
|Q
|812.334-826.098
|''D''
|832.931-846.6955
|Qb
|Db
|814.18-827.945
|816.259-830.024
|-
|-
| |10
|10
|C\\
|C\\
|''D\\''
|''D\\''
|B#
|B#
|''H#''
|''H#''
|855.218-870.512
|D\\
|902.593-917.887
|''Q\\''
|925.479-940.773
|C#
|Q#
|904.644-919.9385
|906.955-922.289
|-
|-
|11
|11
Line 423: Line 422:
|H
|H
|''C''
|''C''
|940.74-957.5635
|Qp
|992.852.1009.676
|''Dp''
|1018.0265-1034.85
|Q
|''D''
|995.109-1011.932
|997.65-1014.474
|-
|-
| |12
|12
|C
|C
|''D''
|''D''
|C
|C
|''D''
|''D''
|1026.262-1044.615
| colspan="2" |D
|1083.1115-1101.464
|D
|1110.574-1128.927
|''S''
|1085.573-1103.926
|1088.346-1106.699
|-
|-
|13
|13
Line 441: Line 445:
|Db
|Db
|''Sb''
|''Sb''
|1111.7847-1131.666
|E
|1173.371-1193.253
|''S''
|1203.122-1223.005
| colspan="2" |Eb
|1176.038-1195.92
|1179.041-1198.9235
|-
|-
| |14
|14
| colspan="2" |E
| colspan="2" |E
|C#
|C#
|''D#''
|''D#''
|1197.3055-1218.717
| colspan="2" |F
|1353.889-1375.042
|D#
|1295.67-1317.082
|''S#''
|1266.502-1287.914
|1269.737-1291.1485
|-
|-
|15
|15
Line 457: Line 465:
|D
|D
|''S''
|''S''
|1282.827-1305.768
| colspan="2" |G\\
|1444.149-1466.83
| colspan="2" |E
|1388.218-1411.159
|1356.967-1379.908
|1360.432-1383.373
|-
|-
|16
|16
| colspan="2" |Ep
| colspan="2" |Ep
| colspan="2" |E
| colspan="2" |E
|1368.249-1392.82
| colspan="2" |Fp
|1534.408-1558.619
| colspan="2" |F
|1480.766-1505.236
|1447.431-1471.902
|1451.128-1475.598
|-
|-
|17
|17
| colspan="4" |F
| colspan="4" |F
|1453.871-1479.871
| colspan="4" |G
|1534.408-1560.408
|1537.8955-1563.8955
|1573.314-1599.314
|1541.823-1577.823
|}Golden tunings±13¢
|}
{| class="wikitable"
{| class="wikitable" style="text-align: center"
! rowspan="4" |Degrees
! rowspan="3" |Degrees
! colspan="4" rowspan="4" |Enneatonic
! colspan="4" rowspan="3" |Enneatonic
! colspan="4" |Minor mode Middletown temperament
!Neutral mode Middletown temperament
! colspan="5" |Major mode Middletown temperament
|-
! rowspan="3" |Intense Aeolian-Dorian
! colspan="3" |Dorian
! rowspan="3" |Dorian-Mixolydian
! colspan="4" |Mixolydian
! colspan="4" |Mixolydian
! rowspan="3" |Mixolydian-Ionian
! rowspan="3" |Mixolydian-Ionian
|-
|-
! rowspan="2" |Subpental
! rowspan="2" |Pental
! rowspan="2" |Superpental
! rowspan="2" |Subpental
! rowspan="2" |Subpental
! rowspan="2" |Pental
! rowspan="2" |Pental
Line 500: Line 500:
| colspan="2" |G
| colspan="2" |G
| colspan="2" |Gb
| colspan="2" |Gb
| |85.109-86.638
|85.932-87.462
|88.7805-90.6955
|89.334-90.863
|90.6955-92.225
|92.019-93.548
|92.019-93.548
|92.035-93.5645
|92.035-93.5645
Line 515: Line 510:
|''A\\''
|''A\\''
| colspan="2" |F#
| colspan="2" |F#
| |170.218-173.277
|171.865-174.9235
|177.561-180.62
|178.667-181.726
|181.391-184.45
|184.038-187.139
|184.038-187.139
|184.07-187.129
|184.07-187.129
Line 529: Line 519:
| colspan="2" |Gp
| colspan="2" |Gp
| colspan="2" |G
| colspan="2" |G
| |255.327-259.915
|257.797-262.385
|266.341-270.93
|268.001-272.589
|272.086-276.675
|276.0565-280.645
|276.0565-280.645
|276.105-280.693
|276.105-280.693
Line 545: Line 530:
|J
|J
|''A''
|''A''
| |340.4355-346.553
|343.729-349.847
|355.122-361.2395
|357.335-363.452
|362.782-368.9
|368.075-374.193
|368.075-374.193
|368.14-374.258
|368.14-374.258
Line 561: Line 541:
|Ab
|Ab
|''Bb''
|''Bb''
| |425.544-433.1915
|429.662-437.309
|442.902-451.5495
|446.668-454.315
|453.477-461.1245
|460.094-467.741
|460.094-467.741
|460.175-467.822
|460.175-467.822
Line 577: Line 552:
|J#
|J#
|''A#''
|''A#''
| |510.653-519.83
|515.594-524.7705
|532.683-541.859
|536.002-545.178
|544.173-553.349
|552.113-561.29
|552.113-561.29
|552.21-561.387
|552.21-561.387
Line 593: Line 563:
|A
|A
|''B''
|''B''
| |595.762-606.468
|601.526-612.232
|621.463-632.169
|625.3355-636.041
|634.869-645.574
|644.132-654.838
|644.132-654.838
|644.2455-654.951
|644.2455-654.951
Line 609: Line 574:
|B
|B
|''H''
|''H''
|680.871-693.106
|687.459-699.694
|710.244-722.479
|714.996-726.904
|725.564-737.8
|736.151-748.386
|736.151-748.386
|736.281-748.516
|736.281-748.516
Line 625: Line 585:
|Hb
|Hb
|''Cb''
|''Cb''
|765.98-779.745
|773.391-787.156
|799.024-812.789
|804.003-817.768
|816.259-830.014
|828.17-841.934
|828.17-841.934
|828.316-842.08
|828.316-842.08
Line 641: Line 596:
|B#
|B#
|''H#''
|''H#''
|851.089-866.383
|859.323-874.6175
|887.805-903.099
|893.336-999.4935
|906.955-922.249
|920.1885-935.483
|920.1885-935.483
|920.351-935.645
|920.351-935.645
Line 657: Line 607:
|H
|H
|''C''
|''C''
|936.198-953.021
|945.256-962.079
|976.585-993.409
|982.67-1090.357
|997.65-1014.474
|1012.207-1029.031
|1012.207-1029.031
|1012.386-1029.209
|1012.386-1029.209
Line 673: Line 618:
|C
|C
|''D''
|''D''
|1021.3065-1039.66
|1031.188-1049.541
|1065.366-1083.719
|1072.004-1181.22
|1088.346-1106.699
|1104.226-1122.579
|1104.226-1122.579
|1104.421-1122.774
|1104.421-1122.774
Line 689: Line 629:
|Db
|Db
|''Sb''
|''Sb''
|1106.415-1186.94
|1117.12-1137.003
|1154.146-1174.029.
|1161.337-1272.083
|1179.041-1198.924
|1196.245-1216.127
|1196.245-1216.127
|1196.456-1216.338
|1196.456-1216.338
Line 704: Line 639:
|C#
|C#
|''D#''
|''D#''
|1191.524-1212.936
|1203.052-1224.464
|1242.927-1264.3385
|1250.671-1362.946
|1269.737-1291.1485
|1288.234-1309.676
|1288.234-1309.676
|1288.491-1309.903
|1288.491-1309.903
Line 719: Line 649:
|D
|D
|''S''
|''S''
|1276.633-1299.5745
|1288.985-1311.926
|1331.707-1354.648
|1340.005-1453.809
|1360.432-1383.373
|1380.283-1403.224
|1380.283-1403.224
|1380.526-1403.467
|1380.526-1403.467
Line 733: Line 658:
| colspan="2" |Ep
| colspan="2" |Ep
| colspan="2" |E
| colspan="2" |E
|1361.741-1386.213
|1374.917-1399.388
|1420.488-1424.958
|1426.338-1453.809
|1451.128-1475.598
|1472.3015-1496.772
|1472.3015-1496.772
|1472.561-1497.032
|1472.561-1497.032
Line 746: Line 666:
|17
|17
| colspan="4" |F
| colspan="4" |F
|1446.851-1472.851
|1460.85-1486.85
|1509.268-1535.268
|1518.672-1544.672
|1541.823-1567.823
|1557.82-1583.82
|1557.82-1583.82
|1564.596-1590.596
|1564.596-1590.596
Line 757: Line 672:
|1644.563-1670.563
|1644.563-1670.563
|}
|}
[[Category:EdX]]
 
== See also ==
* [[17ed5/2]] - equal division of the classic major tenth
* [[17ed7/3]] - equal division of the septimal minor tenth
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/17edX"