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Explanation needed for what this is. See [[edX]] maybe?
'''19edX''' means division of a tenth interval into 19 equal parts.


==Intervals==
== Intervals ==
{| class="wikitable"
{| class="wikitable"
! rowspan="5" |Degrees
!Decade
! colspan="2" 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" |Aeolian-Dorian
| 6\5
! colspan="6" |Dorian
|75.790
! 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
|''76.316''
! 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
|76.454
|
|-
|-
! |Minimum
|17\14
! |Maximum
|76.692
!Minimum
|
!Maximum
|-
!Minimum
|11\9
!Maximum
|77.193
!Minimum
|Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
!Maximum
|-
!Minimum
|16\13
! |Maximum
|77.733
!Minimum
|
!Maximum
|-
! |Minimum
|21\17
!Maximum
|78.019
!Minimum
|
!Maximum
|-
!Minimum
|5\4
!Maximum
|''78.947''
!Minimum
|Subpental Dorian mode ends, Pental Dorian mode begins
! |Maximum
|-
|24\19
|79.778
|
|-
|19\15
|80.000
|
|-
|14\11
|80.383
|Pental Dorian mode ends, Superpental Dorian mode begins
|-
|23\18
|80.702
|
|-
|9\7
|81.203
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
|-
|31\24
|''81.579''
|
|-
|22\17
|81.734
|Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
|-
|35\27
|87.872
|
|-
|13\10
|82.105
|Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
|-
|17\13
|82.591
|
|-
|21\16
|82.896
|Subpental Mixolydian mode ends, Pental Mixolydian mode begins
|-
|25\19
|83.102
|
|-
|29\22
|83.253
|
|-
|33\25
|83.368
|
|-
|4\3
|''84.211''
|Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
|-
|19\14
|85.714
|
|-
|15\11
|86.124
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
|-
|26\19
|86.427
|
|-
|11\8
|''86.842''
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
|-
|18\13
|87.449
|
|-
|25\18
|87.719
|
|-
|7\5
|88.421
|Mixolydian-Ionian mode ends
|}Golden/Pyrite Tunings±13¢
{| 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
| |1
| colspan="2" |Gb
|Jb
| |75.7895
|Ab
| colspan="2" |77.193
|76.15-77.5185
| colspan="2" |78.947
|76.887-78.255
| colspan="2" |80.383
|79.435-80.804
| colspan="2" |81.203
|79.93-81.2985
| colspan="2" |82.105
| colspan="2" |82.895
| colspan="2" |84.2105
| colspan="2" |84.9365
| colspan="2" |87.114
| |88.421
|-
|-
| |2
| |2
| colspan="2" |F#
| colspan="2" |G#
| |151.579
|152.3-155.037
| colspan="2" |154.386
|153.774-156.5105
| colspan="2" |157.895
|158.87-161.607
| colspan="2" |160.766
|159.86-162.597
| colspan="2" |162.406
| colspan="2" |164.2105
| colspan="2" |165.7895
| colspan="2" |168.421
| colspan="2" |169.873
| colspan="2" |174.229
| |176.842
|-
|-
| |3
| |3
| colspan="2" |G
|J
| |227.368
|''A''
| colspan="2" |231.579
|228.45-232.555
| colspan="2" |236.842
|230.6605-234.766
| colspan="2" |241.148
|238.3055-242.411
| colspan="2" |243.609
|239.79-243.896
| colspan="2" |246.316
| colspan="2" |248.684
| colspan="2" |252.632
| colspan="2" |254.809
| colspan="2" |261.343
| |265.263
|-
|-
| |4
| |4
|J
|A
|''A''
|''B''
| |303.158
|304.6-310.074
| colspan="2" |308.772
|307.547-313.021
| colspan="2" |315.7895
|317.741-323.214
| colspan="2" |321.531
|319.72-325.164
| colspan="2" |324.812
| colspan="2" |328.421
| colspan="2" |331.579
| colspan="2" |336.842
| colspan="2" |339.746
| colspan="2" |348.457
| |353.684
|-
|-
| |5
| |5
|Ab
|Bb
|''Bb''
|''Cb''
| |378.947
|380.75-387.592
| colspan="2" |385.965
|384.434-391.276
| colspan="2" |394.737
|397.176-404.018
| colspan="2" |401.914
|399.6505-406.493
| colspan="2" |406.015
| colspan="2" |410.526
| colspan="2" |414.474
| colspan="2" |421.053
| colspan="2" |424.682
| colspan="2" |435.527
| |442.105
|-
|-
| |6
| |6
|J#
|A#
|''A#''
|''B#''
| |454.737
|456.9-465.111
| colspan="2" |463.158
|461.321-469.5315
| colspan="2" |473.684
|476.611-484.8215
| colspan="2" |482.297
|479.581-487.791
| colspan="2" |487.218
| colspan="2" |492.632
| colspan="2" |497.368
| colspan="2" |505.263
| colspan="2" |509.619
| colspan="2" |522.686
| |530.526
|-
|-
| |7
| |7
|A
|B
|''B''
|''C''
| |530.526
|533.05-542.926
| colspan="2" |540.351
|538.208-547.787
| colspan="2" |552.632
|556.046-565.625
| colspan="2" |592.679
|559.511-569.09
| colspan="2" |568.421
| colspan="2" |574.737
| colspan="2" |580.263
| colspan="2" |589.474
| colspan="2" |594.555
| colspan="2" |609.8
| |618.947
|-
|-
|8
|8
|B
|C
|''H''
|''Q''
|606.316
|609.2-620.148
| colspan="2" |617.544
|615.095-626.042
| colspan="2" |631.579
|635.481-648.429
| colspan="2" |643.062
|639.441-650.388
| colspan="2" |647.624
| colspan="2" |656.842
| colspan="2" |663.158
| colspan="2" |673.684
| colspan="2" |679.491
| colspan="2" |696.915
|707.368
|-
|-
|9
|9
|Hb
|Qb
|''Cb''
|''Db''
|682.105
|685.35-697.666
| colspan="2" |694.737
|691.981-704.297
| colspan="2" |710.526
|714.9165-727.232
| colspan="2" |723.445
|719.371-731.687
| colspan="2" |730.827
| colspan="2" |738.947
| colspan="2" |746.053
| colspan="2" |757.895
| colspan="2" |764.418
| colspan="2" |784.029
|795.7895
|-
|-
|10
|10
|B#
|C#
|''H#''
|''Q#''
|757.895
|761.5-775.185
| colspan="2" |771.93
|768.868-782.5525
| colspan="2" |789.474
|794.352-808.036
| colspan="2" |803.828
|799.301-812.985
| colspan="2" |812.03
| colspan="2" |821.053
| colspan="2" |828.947
| colspan="2" |842.105
| colspan="2" |849.365
| colspan="2" |871.143
|884.2105
|-
|-
|11
|11
|H
|Q
|''C''
|''D''
|833.654
|837.6505-852.703
| colspan="2" |849.123
|845.755-860.808
| colspan="2" |868.421
|873.787-888.8395
| colspan="2" |884.2105
|879.231-894.284
| colspan="2" |893.233
| colspan="2" |903.158
| colspan="2" |911.843
| colspan="2" |926.316
| colspan="2" |934.302
| colspan="2" |958.258
|972.632
|-
|-
|12
|12
|C
|D
|''D''
|''S''
|909.474
|913.8005-930.222
| colspan="2" |926.326
|922.642-939.063
| colspan="2" |947.378
|953.222-969.643
| colspan="2" |964.593
|959.161-975.582.
| colspan="2" |974.436
| colspan="2" |985.263
| colspan="2" |994.737
| colspan="2" |1010.526
| colspan="2" |1019.238
| colspan="2" |1045.372
|1061.053
|-
|-
|13
|13
|Db
| colspan="2" |Eb
|''Sb''
|989.951-1007.74
|985.263
|999.529-1017.318
| colspan="2" |1003.509
|1032.657-1050.447
| colspan="2" |1026.316
|1039.091-1056.881
| colspan="2" |1044.976
| colspan="2" |1055.639
| colspan="2" |1067.368
| colspan="2" |1077.612
| colspan="2" |1094.737
| colspan="2" |1104.172
| colspan="2" |1132.486
|1149.474
|-
|-
|14
|14
|C#
|D#
|''D#''
|''S#''
|1061.053
|1066.101-1085.2585
| colspan="2" |1080.702
|1076.416-1095.5735
| colspan="2" |1105.263
|1112.092-1131.25
| colspan="2" |1125.359
|1119.021-1138.179
| colspan="2" |1136.842
| colspan="2" |1149.474
| colspan="2" |1160.526
| colspan="2" |1178.947
| colspan="2" |1189.111
| colspan="2" |1220.601
|1237.895
|-
|-
|15
|15
|D
| colspan="2" |E
|''S''
|1142.251-1162.777
|1136.842
|1153.302-1173.829
| colspan="2" |1107.895
|1191.5275-1212.054
| colspan="2" |1184.2105
|1198.9515-1219.478
| colspan="2" |1205.742
| colspan="2" |1218.045
| colspan="2" |1231.579
| colspan="2" |1243.421
| colspan="2" |1263.158
| colspan="2" |1274.047
| colspan="2" |1306.715
|1326.316
|-
|-
|16
|16
| colspan="2" |Eb
| colspan="2" |Fb
|1212.632
|1218.401-1240.295
| colspan="2" |1235.088
|1230.159-1525.054
| colspan="2" |1363.156
|1270.963-1292.857
| colspan="2" |1286.124
|1279.882-1300.776
| colspan="2" |1299.248
| colspan="2" |1313.684
| colspan="2" |1326.316
| colspan="2" |1347.378
| colspan="2" |1359.984
| colspan="2" |1393.829
|1414.737
|-
|-
|17
|17
|D#
| colspan="2" |E#
|''S#''
|1294.551-1317.814
|1288.421
|1307.0769-1330.339
| colspan="2" |1312.181
|1350.298-1373.661
| colspan="2" |1042.105
|1358.612-1382.075
| colspan="2" |1366.507
| colspan="2" |1380.451
| colspan="2" |1395.7895
| colspan="2" |1408.2105
| colspan="2" |1431.579
| colspan="2" |1443.98
| colspan="2" |1480.944
|1503.158
|-
|-
|18
|18
| colspan="2" |E
| colspan="2" |F
|1364.2105
|1370.701-1395.332
| colspan="2" |1389.474
|1383.963-1408.594
| colspan="2" |1421.053
|1429.833-1454.465
| colspan="2" |1446.89
|1438.742-1463.373
| colspan="2" |1461.654
| colspan="2" |1477.895
| colspan="2" |1491.105
| colspan="2" |1515.7895
| colspan="2" |1526.8275
| colspan="2" |1568.058
|1591.579
|-
|-
|19
|19
| colspan="2" |F
| colspan="2" |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="4" |Enneatonic
| colspan="2" |1613.793
!Mohajira
| colspan="2" |1655.172
!Beatles
|1680
|}Most harmonic tunings
{| class="wikitable"
|-
|-
! rowspan="2" |Degrees
| |1
! colspan="2" 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" |Gb
| colspan="2" |Gb
|76.5195-77.888
|Jb
|80.758-82.127
|Ab
|82.806-84.174
|80.942-82.31
|81.149-82.517
|-
|-
|2
| |2
| colspan="2" |F#
| colspan="2" |F#
|153.039-155.776
| colspan="2" |G#
|161.517-164.2535
|161.884-164.621
|165.612-168.349
|162.297-165.034
|-
|-
| |3
| |3
| colspan="2" |G
| colspan="2" |G
|229.559-233.664
|J
|242.275-246.38
|''A''
|248.418-252.523
|242.826-246.931
|246.446-247.551
|-
|-
|4
| |4
|J
|J
|''A''
|''A''
|306.078-311.552
|A
|323.033-328.507
|''B''
|331.224-336.698
|323.7675-329.241
|324.594-330.068
|-
|-
| |5
| |5
|Ab
|Ab
|''Bb''
|''Bb''
|382.598-389.44
|Bb
|403.792-410.634
|''Cb''
|414.03-420.872
|404.709-411.5515
|405.716-412.585
|-
|-
| |6
| |6
|J#
|J#
|''A#''
|''A#''
|459.117-467.328
|A#
|484.55-492.76
|''B#''
|496.835-505.046
|485.651-493.862
|486.8915-495.102
|-
|-
|7
| |7
|A
|A
|''B''
|''B''
|535.637-545.216
|B
|565.308-574.887
|''C''
|579.342-589.221
|566.593-576.172
|568.04-577.619
|-
|-
| |8
|8
|B
|B
|''H''
|''H''
|612.156-623.1035
|C
|646.0665-657.014
|''Q''
|662.448-673.395
|647.535-658.482
|649.189-660.136
|-
|-
|9
|9
|Hb
|Hb
|''Cb''
|''Cb''
|688.676-700.9915
|Qb
|726.825-739.141
|''Db''
|745.254-757.57
|728.477-740.792
|730.337-742.653
|-
|-
|10
|10
|B#
|B#
|''H#''
|''H#''
|765.195-778.879
|C#
|807.583-821.267
|''Q#''
|828.06-841.744
|809.419-823.103
|811.486-825.17
|-
|-
|11
|11
|H
|H
|''C''
|''C''
|841.715-856.767.
|Q
|888.341-903.394
|''D''
|910.866-925.9185
|890.361-905.413
|892.6345-907.687
|-
|-
| |12
|12
|C
|C
|''D''
|''D''
|918.234-934.655
|D
|969.1-985.52
|''S''
|993.672-1010.093
|971.302-987.7235
|973.783-990.204
|-
|-
|13
|13
|Db
|Db
|''Sb''
|''Sb''
|994.754-1012.543
| colspan="2" |Eb
|1049.858-1067.6475
|1052.244-1070.034
|1076.478-1094.267
|1054.932-1072.721
|-
|-
| |14
|14
|C#
|C#
|''D#''
|''D#''
|1071.273-1090.431
|D#
|1130.616-1149.774
|''S#''
|1159.284-1178.442
|1133.186-1152.344
|1136.08-1155.238
|-
|-
|15
|15
|D
|D
|''S''
|''S''
|1147.793-1168.319
| colspan="2" |E
|1211.375-1231.901
|1214.128-1234.654
|1242.09-1262.616
|1217.229-1237.755
|-
|-
|16
|16
| colspan="2" |Eb
| colspan="2" |Eb
|1224.312-1266.207
| colspan="2" |Fb
|1292.133-1314.028
|1295.07-1316.965
|1324.896-1346.7905
|1298.377-1320.272
|-
|-
|17
|17
|D#
|D#
|''S#''
|''S#''
|1300.832--1324.095
| colspan="2" |E#
|1372.891-1396.1545
|1376.012-1399.275
|1407.702-1430.965
|1379.526-1402.789
|-
|-
|18
|18
| colspan="2" |E
| colspan="2" |E
|1377.351-1401.983
| colspan="2" |F
|1453.65-1478.281
|1456.954-1481.585
|1490.507-1515.139
|1460.675-1485.306
|-
|-
|19
|19
| colspan="2" |F
| colspan="2" |F
|1453.871-1479.871
| colspan="2" |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="2" rowspan="4" |Enneatonic
! colspan="2" rowspan="3" |Enneatonic
! colspan="4" |Minor mode Middletown temperament
!Neutral mode Middletown temperament
! colspan="5" |Major mode Middletown temperament
|-
! rowspan="3" |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 489: Line 442:
| |1
| |1
| colspan="2" |Gb
| colspan="2" |Gb
| |76.15-77.5185
|76.887-78.255
|79.435-80.804
|79.93-81.2985
|81.149-82.517
|81.9905-83.359
|81.9905-83.359
|82.347-83.716
|82.347-83.716
Line 502: Line 450:
| |2
| |2
| colspan="2" |F#
| colspan="2" |F#
| |152.3-155.037
|153.774-156.5105
|158.87-161.607
|159.86-162.597
|162.297-165.034
|163.981-166.718
|163.981-166.718
|164.694-167.431
|164.694-167.431
Line 515: Line 458:
| |3
| |3
| colspan="2" |G
| colspan="2" |G
| |228.45-232.555
|230.6605-234.766
|238.3055-242.411
|239.79-243.896
|243.446-247.551
|245.971-250.077
|245.971-250.077
|247.0415-251.147
|247.0415-251.147
Line 529: Line 467:
|J
|J
|''A''
|''A''
| |304.6-310.074
|307.547-313.021
|317.741-323.214
|319.72-325.164
|324.594-330.068
|327.962-333.436
|327.962-333.436
|329.389-334.862
|329.389-334.862
Line 543: Line 476:
|Ab
|Ab
|''Bb''
|''Bb''
| |380.75-387.592
|384.434-391.276
|397.176-404.018
|399.6505-406.493
|405.743-412.585
|409.953-416.795
|409.953-416.795
|411.736-418.578
|411.736-418.578
Line 557: Line 485:
|J#
|J#
|''A#''
|''A#''
| |456.9-465.111
|461.321-469.5315
|476.611-484.8215
|479.581-487.791
|486.8915-495.102
|491.943-500.154
|491.943-500.154
|494.083-502.2935
|494.083-502.2935
Line 571: Line 494:
|A
|A
|''B''
|''B''
| |533.05-542.926
|538.208-547.787
|556.046-565.625
|559.511-569.09
|568.04-577.619
|573.934-583.513
|573.934-583.513
|576.43-586.001
|576.43-586.001
Line 585: Line 503:
|B
|B
|''H''
|''H''
|609.2-620.148
|615.095-626.042
|635.481-648.429
|639.441-650.388
|649.189-660.136
|655.924-666.872
|655.924-666.872
|658.777-669.725
|658.777-669.725
Line 599: Line 512:
|Hb
|Hb
|''Cb''
|''Cb''
|685.35-697.666
|691.981-704.297
|714.9165-727.232
|719.371-731.687
|730.337-742.653
|737.915-750.231
|737.915-750.231
|741.1245-752.44
|741.1245-752.44
|757.878-770.194
|757.878-770.194
|770.384-782.7
|770.384-782.7
|779.004-791.31+
|779.004-791.319
|-
|-
|10
|10
|B#
|B#
|''H#''
|''H#''
|761.5-775.185
|768.868-782.5525
|794.352-808.036
|799.301-812.985
|811.486-825.17
|819.9055-833.59
|819.9055-833.59
|834.451-837.156
|834.451-837.156
Line 627: Line 530:
|H
|H
|''C''
|''C''
|837.6505-852.703
|845.755-860.808
|873.787-888.8395
|879.231-894.284
|892.6345-907.687
|901.896-916.949
|901.896-916.949
|905.819-917.156
|905.819-917.156
Line 641: Line 539:
|C
|C
|''D''
|''D''
|913.8005-930.222
|922.642-939.063
|953.222-969.643
|959.161-975.582.
|973.783-990.304
|983.887-1000.308
|983.887-1000.308
|988.166-1000.8715
|988.166-1000.8715
Line 655: Line 548:
|Db
|Db
|''Sb''
|''Sb''
|989.951-1007.74
|999.529-1017.318
|1032.657-1050.447
|1039.091-1056.881
|1054.932-1072.721
|1065.877-1083.667
|1065.877-1083.667
|1070.513-1084.587
|1070.513-1084.587
Line 669: Line 557:
|C#
|C#
|''D#''
|''D#''
|1066.101-1085.2585
|1076.416-1095.5735
|1112.092-1131.25
|1119.021-1138.179
|1136.08-1152.238
|1147.868-1167.026
|1147.868-1167.026
|1152.86-1168.303
|1152.86-1168.303
Line 683: Line 566:
|D
|D
|''S''
|''S''
|1142.251-1162.777
|1153.302-1173.829
|1191.5275-1212.054
|1198.9515-1219.478
|1217.229-1237.755
|1229.858-1250.3845
|1229.858-1250.3845
|1235.2075-1252.018
|1235.2075-1252.018
Line 696: Line 574:
|16
|16
| colspan="2" |Eb
| colspan="2" |Eb
|1218.401-1240.295
|1230.159-1525.054
|1270.963-1292.857
|1279.882-1300.776
|1298.377-1320.272
|1311.849-1333.743
|1311.849-1333.743
|1317.555-1339.734
|1317.555-1339.734
Line 710: Line 583:
|D#
|D#
|''S#''
|''S#''
|1294.551-1317.814
|1307.0769-1330.339
|1350.298-1373.661
|1358.612-1382.075
|1379.526-1402.789
|1393.839-1417.1025
|1393.839-1417.1025
|1399.912-1423.165
|1399.912-1423.165
Line 723: Line 591:
|18
|18
| colspan="2" |E
| colspan="2" |E
|1370.701-1395.332
|1383.963-1408.594
|1429.833-1454.465
|1438.742-1463.373
|1460.675-1485.306
|1475.83-1500.461
|1475.83-1500.461
|1399.902-1499.446
|1399.902-1499.446
Line 736: Line 599:
|19
|19
| colspan="2" |F
| colspan="2" |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 747: Line 605:
|1644.563-1670.563
|1644.563-1670.563
|}
|}
== See also ==
* [[19ed5/2]] - equal division of the classic major tenth
* [[19ed7/3]] - equal division of the septimal minor tenth
[[Category:EdX]]
[[Category:EdX]]
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/19edX"