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'''[[EDF|Division of the just perfect fifth]] into 28 equal parts''' (28EDF) is related to [[48edo|48 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 25.0698 cents (corresponding to 47.8663 [[edo]]). It is related to the regular temperament which tempers out |187 -159 28> in the 5-limit; 6656/6655, 256000/255879, and 38671875/38614472 in the 13-limit (2.3.5.11.13 subgroup), which is supported by 335, [[383edo|383]], 718, [[1053edo|1053]], and 1101 EDOs.
{{Infobox ET}}
'''[[EDF|Division of the just perfect fifth]] into 28 equal parts''' (28EDF) is related to [[48edo|48 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 25.0698 cents (corresponding to 47.8663 [[edo]]).
 
It is related to the regular temperament which tempers out |187 -159 28> in the 5-limit; [[6656/6655]], [[256000/255879]], and [[38671875/38614472]] in the 13-limit (2.3.5.11.13 subgroup), which is supported by {{EDOs| 335, 383, 718, 1053, and 1101}} EDOs.
 
== Harmonics ==
{{Harmonics in equal|28|3|2|intervals=prime}}


== Intervals ==
== Intervals ==
{| class="wikitable"
{{Interval table}}
! rowspan="2" |
 
! rowspan="2" |''ed233\420-3.5¢ (51edo!)''
 
! rowspan="2" |ed31\54 (~49edo!)
{{stub}}
! rowspan="2" |ed121/81 (~ed11\19)
! rowspan="2" |ed3/2
! colspan="2" |Pyrite
! rowspan="2" |ed122/81 (~ed13\22)
! rowspan="2" |ed34\57 (~47edo!)
! rowspan="2" |''ed37\60+3.5¢ (~91ed4!)''
|-
!(~ed17\29)
!(~ed10\17)
|-
|1
|''23.6505-23.7755''
|24.6032
|24.81485
|25.0698
|25.1299
|25.2091
|25.3234
|25.5639
|''26.4286-26.5536''
|-
|2
|''47.301-47.551''
|49.20635
|49.6297
|50.1396
|50.2597
|50.41825
|50.6475
|51.1278
|''52.8571-53.1071''
|-
|3
|''70.9515-71.3625''
|73.8095
|74.4446
|75.2095
|75.3896
|75.6274
|75.9712
|76.6917
|''79.2857-79.6607''
|-
|4
|''94.602-95.102''
|98.4127
|99.2594
|100.2793
|100.5194
|100.8365
|101.295
|102.2556
|''105.7143-106.2143''
|-
|5
|''118.25255-118.87755''
|123.0159
|124.0743
|125.3491
|125.6493
|10\26.0456
|126.6187
|127.81955
|''132.1429-132.7679''
|-
|6
|''141.903-142.653''
|147.61905
|148.8891
|150.4189
|150.77915
|151.2547
|151.9425
|153.3835
|''158.5714-159.3214''
|-
|7
|''165.5536-166.4285''
|172.2222
|173.704
|175.48875
|175.909
|176.4639
|177.2662
|178.947
|''185-185.875''
|-
|8
|''189.2041-190.2041''
|196.8254
|198.5188
|200.5586
|201.0389
|201.673
|202.5899
|204.5113
|''211.4286-212.4286''
|-
|9
|''212.8576-213.9796''
|221.4286
|223.3337
|225.6284
|226.1687
|226.8821
|227.9137
|230.0752
|''237.8571-238.9791''
|-
|10
|''236.5051-237.7551''
|246.03175
|248.1485
|250.6982
|251.2986
|252.0912
|253.2374
|255.6391
|''264.2857-265.5357''
|-
|11
|''260.1556-261.5306''
|270.6349
|272.9634
|275.768
|276.4284
|277.3004
|278.5612
|281.203
|''290.7143-292.0693''
|-
|12
|''283.8061-285.3061''
|295.2381
|297.782
|300.8379
|301.5583
|302.5095
|303.8849
|306.7669
|''317.1429-318.6429''
|-
|13
|''307.4566-309.0816''
|319.8413
|322.5931
|325.9077
|326.6682
|327.7186
|329.2087
|332.3308
|''343.5714-345.2664''
|-
|14
|''331.1071-332.857''1
|344.4444
|347.408
|350.9775
|351.818
|352.9277
|354.5324
|357.8947
|''370-371.75''
|-
|15
|''354.75765-356.63265''
|369.0476
|372.2228
|376.0473
|376.9479
|378.13685
|379.8561
|383.45865
|''396.4286-398.3036''
|-
|16
|''378.4082-380.4082''
|393.6508
|397.03765
|401.1171
|402.0777
|403.346
|405.1799
|409.0226
|''422.8571-424.8571''
|-
|17
|''402.0587-404.1837''
|418.254
|421.8525
|426.187
|427.2076
|428.5551
|430.5036
|434.5865
|''449.2857-451.4107''
|-
|18
|''425.7092-427.9592''
|442.8571
|446.66735
|451.2568
|452.33745
|453.7642
|455.8274
|460.1504
|''475.7143-477.9643''
|-
|19
|''449.3597-451.7347''
|467.460
|471.4822
|476.3266
|477.4673
|478.97333
|481.1511
|485.7143
|''502.1429-504.5179''
|-
|20
|''473.0102-475.5102''
|492.0635
|496.2971
|501.3964
|502.5972
|504.1825
|506.4749
|511.2781
|''528.5714-531.0714''
|-
|21
|''496.6507-499.2857''
|516.6667
|521.1119
|526.46625
|527.727
|529.3916
|531.7986
|536.8421
|''555-557.625''
|-
|22
|''520.3112-523.0612''
|541.2698
|545.9268
|551.536
|552.8569
|554.6007
|557.1223
|562.406
|''581.4286-584.1786''
|-
|23
|''543.6917-546.8367''
|565.873
|570.7416
|576.6059
|577.9867
|579.8098
|582.4461
|587.9699
|''607.8571-610.7321''
|-
|24
|''567.6122-570.6122''
|590.4762
|595.5565
|601.6757
|603.1166
|605.019
|607.7698
|613.5338
|''634.2857-637.2857''
|-
|25
|''591.2628-594.3878''
|615.0794
|620.3713
|626.7455
|628.2465
|630.2281
|633.0936
|639.0977
|''660.7143-663.8393''
|-
|26
|''614.9133-618.1633''
|639.6825
|645.1862
|651.8154
|653.3763
|655.4372
|658.4173
|664.66165
|''687.1429-690.3929''
|-
|27
|''638.5638-641.9388''
|664.2857
|670.001
|676.8852
|678.5062
|680.6463
|983.7411
|690.2256
|''713.5714-716.9264''
|-
|28
|''662.2143-665.714''3
|688.8889
|694.8158
|701.955
|703.636
|705.85545
|709.0648
|715.7895
|''740-743.5''
|-
|29
|''685.8648-689.4898''
|713.4921
|719.6307
|727.0248
|728.7659
|731.0646
|734.3885
|741.3534
|''766.4286-770.0536''
|-
|30
|''709.5153-713.2653''
|738.0952
|744.4456
|752.0946
|753.89575
|756.2736
|759.7123
|766.9173
|''792.8571-796.6071''
|-
|31
|''733.1658-737.0408''
|762.6984
|769.2604
|777.1645
|779.0256
|781.4828
|785.036
|792.4812
|''819.2857-823.1607''
|-
|32
|''756.8163-760.8163''
|787.3016
|794.0753
|802.2343
|804.1555
|806.6919
|810.3598
|818.0451
|''845.7143-849.7143''
|-
|33
|''780.4668-784.5918''
|811.9048
|818.89015
|827.3041
|829.2853
|831.9011
|835.6835
|843.609
|''872.1429-876.2679''
|-
|34
|''804.11735-808.36735''
|836.5079
|843.705
|852.3739
|854.4152
|857.1102
|961.0073
|869.1729
|''898.5714-902.8214''
|-
|35
|''827.7679-832.1429''
|861.1111
|868.51985
|877.44375
|879.545
|882.3193
|886.331
|894.7368
|''925-929.375''
|-
|36
|''851.4184-855.9184''
|885.7143
|893.3347
|902.5136
|904.6749
|907.5284
|911.6547
|920.30075
|''951.4286-955.9286''
|-
|37
|''875.0689-879.6939''
|910.3175
|918.1496
|927.5834
|929.8048
|932.3767
|936.9785
|945.8647
|''977.8571-982.4821''
|-
|38
|''898.7194-903.4694''
|934.9206
|942.9644
|952.6532
|954.9346
|957.9467
|962.3022
|971.4286
|''1004.2857-1009.0357''
|-
|39
|''922.3699-927.2449''
|959.5238
|967.7793
|977.723
|980.0645
|983.1558
|987.626
|996.9925
|''1030.7143-1035.5893''
|-
|40
|''946.0204-951.0204''
|984.127
|992.5941
|1002.7929
|1005.1943
|1008.3649
|1012.9497
|1022.5564
|''1057.1429-1062.1429''
|-
|41
|''696.6709-974.7959''
|1008.7302
|1017.409
|1027.8627
|1030.3242
|1033.57405
|1038.2735
|1048.1203
|''1083.5714-1088.6964''
|-
|42
|''993.3214-998.5714''
|1033.333
|1042.2238
|1052.9325
|1055.454
|1058.7832
|1063.5972
|1073.6842
|''1110-1115.25''
|-
|43
|''1013.9719-1022.3469''
|1057.9365
|1067.0386
|1078.0023
|1080.5839
|1083.9923
|1088.92095
|1099.2481
|''1136.4286-1141.8036''
|-
|44
|''1040.62245-1046.12245''
|1082.5397
|1091.8535
|1103.0721
|1105.7138
|1109.2014
|1114.2447
|1124.812
|''1162.8571-1167.3571''
|-
|45
|''1064.273-1069.898''
|1107.1429
|1116.6684
|1128.142
|1130.8436
|1137.41055
|1139.5684
|1150.3759
|''1189.2857-1194.9107''
|-
|46
|''1088.9235-1093.6735''
|1131.7646
|1141.4832
|1153.2118
|1155.9735
|1159.6297
|1164.8922
|1175.93985
|''1215.7143-1221.4643''
|-
|47
|''1111.574-1117.449''
|1156.3492
|1166.2981
|1178.2816
|1181.1033
|1184.8288
|1190.2159
|1201.5038
|''1242.1429-1248.0179''
|-
|48
|''1135.2245-1141.2245''
|1180.9524
|1191.1129
|1203.3514
|1206.2332
|1210.0379
|1215.5397
|1227.0677
|''1268.5714-1274.5714''
|-
|49
|''1158.875-1165''
|1205.5556
|1215.9278
|1228.42125
|1231.6306
|1235.247
|1240.8634
|1252.6316
|''1295-1301.125''
|-
|50
|''1182.5255-1188.7755''
|1230.1587
|1240.74265
|1253.4911
|1256.4929
|1260.4561
|1266.18715
|1278.1955
|''1321.4286-1327.6786''
|-
|51
|''1206.176-1212.551''
|1254.7619
|1265.5575
|1278.5609
|1281.6228
|128.6653
|1291.5109
|1303.7594
|''1347.8571-1354.2321''
|-
|52
|''1229.8265-1236.3265''
|1279.3651
|1290.37235
|1303.6307
|1306.7526
|1310.8744
|1316.8346
|1329.3233
|''1374.2857-1380.7857''
|-
|53
|''1253.477-1260.102''
|1303.96825
|1315.1872
|1328.7005
|1331.8825
|1336.0835
|1342.1584
|1354.8872
|''1400.7143-1407.3393''
|-
|54
|''1277.12755-1283.87755''
|1328.5714
|1340.0021
|1353.7704
|1357.01235
|1361.2927
|1367.4821
|1380.4511
|''1427.1429-1433.8929''
|-
|55
|''1300.7781-1307.6531''
|1353.1746
|1364.8169
|1378.8418
|1382.1422
|1386.5018
|1392.8059
|1406.015
|''1453.5714-1460.4464''
|-
|56
|''1324.4286-1331.4286''
|1377.7778
|1389.6318
|1403.91
|1407.2721
|1411.7109
|1418.1296
|1431.57895
|''1480-1487''
|}
[[Category:Edf]]
[[Category:Edonoi]]
Retrieved from "https://en.xen.wiki/w/28edf"