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{{Infobox ET}}
{{Infobox ET}}
'''56EDF''' is the [[EDF|equal division of the just perfect fifth]] into 56 parts of 12.5349 [[cent|cents]] each, corresponding to 95.7326 [[edo]]. It is related to the regular temperament which tempers out 2401/2400 and |91 -80 13 2> in the 7-limit, which is supported by [[383edo|383]], [[670edo|670]], [[1053edo|1053]], 1436, and 1723 EDOs.
'''56EDF''' is the [[EDF|equal division of the just perfect fifth]] into 56 parts of 12.5349 [[cent|cents]] each, corresponding to 95.7326 [[edo]].  


It is related to the [[regular temperament]] which tempers out [[2401/2400]] and |91 -80 13 2> in the [[7-limit]], which is supported by {{EDOs|383, 670, 1053, 1436, and 1723}} EDOs.
==Related regular temperaments==
===7-limit 383&670===
Commas: 2401/2400, |91 -80 13 2>
POTE generator: ~|-33 32 -4 -3> = 12.5357
Mapping: [<1 1 -1 1|, <0 56 318 173|]
EDOs: {{EDOs|383, 670, 1053, 1436, 1723}}
===11-limit 383&670===
Commas: 2401/2400, 14348907/14348180, 26214400/26198073
POTE generator: ~13504609503/13421772800 = 12.5359
Mapping: [<1 1 -1 1 3|, <0 56 318 173 44|]
EDOs: {{EDOs|383, 670, 1053, 1436, 1723}}
== Intervals==
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |
! colspan="2" |56ed3/2
! rowspan="2" |''ed233\420-5¢ (~101-102edo!)''
! rowspan="2" |ed31\54 (~98edo!)
! rowspan="2" |ed121/81 (~ed11\19)
! rowspan="2" |ed696¢
! rowspan="2" |ed32\55
! rowspan="2" |[[96edo]]=''r¢''
! rowspan="2" |ed3/2
! rowspan="2" |Golden 95-96edo
! colspan="2" |Pyrite
! rowspan="2" |[[95edo]]
! rowspan="2" |ed708¢
! rowspan="2" |ed122/81 (~ed13\22)
! rowspan="2" |ed34\57 (~94edo!)
! rowspan="2" |''ed37\60+5¢ (~90-91edo!)''
|-
!(~ed17\29)
!(~ed10\17)
|-
|-
|1
|1
|''11.7985-11.8878''
|12.3016
|12.4074
|12.4286
|12.4675
|''12.5''
|12.5349
|12.5349
|12.5499
|12.5649
|12.6046
|12.6316
|12.6429
|12.6619
|12.78195
|''13.2143-13.3039''
|-
|-
|2
|2
|''23.5969-23.7755''
|24.6032
|24.81485
|24.8571
|24.9351
|''25''
|25.0698
|25.0698
|25.0999
|25.1299
|25.2091
|25.2632
|25.2857
|25.3234
|25.5639
|''26.4286-26.6071''
|-
|-
|3
|3
|''35.3954-35.6633''
|36.9048
|37.2223
|37.2857
|37.4026
|''37.5''
|37.6047
|37.6047
|37.6498
|376.9479
|37.8139
|37.8947
|37.9286
|37.9856
|38.3459
|''39.6429-39.9107''
|-
|-
|4
|4
|''47.1939-47.551''
|49.20635
|49.6297
|49.7143
|49.8701
|''50''
|50.1396
|50.1396
|50.1997
|50.2597
|50.41825
|50.5263
|50.5714
|50.6475
|51.1278
|''52.8571-53.2143''
|-
|-
|5
|5
|''59.99235-59.4388''
|61.5079
|62.0371
|62.1429
|62.3377
|''62.5''
|62.67455
|62.67455
|62.7497
|62.82465
|63.0228
|63.1579
|63.2143
|63.3094
|63.9098
|''66.0714-66.5179''
|-
|-
|6
|6
|''70.7908-71.3625''
|73.8095
|74.4446
|74.5714
|74.8052
|''75''
|75.2095
|75.2095
|75.2996
|75.3896
|75.6274
|75.7895
|75.8571
|75.9712
|76.6917
|''79.2857-79.8214''
|-
|-
|7
|7
|''82.5893-83.2143''
|86.1111
|86.852
|87
|87.2727
|''87.5''
|87.7444
|87.7444
|87.8495
|879.545
|88.2319
|88.42105
|88.5
|88.6331
|89.4737
|''92.5-93.125''
|-
|-
|8
|8
|''94.3878-95.102''
|98.4127
|99.2594
|99.4286
|99.7403
|''100''
|100.2793
|100.2793
|100.3995
|100.5194
|100.8365
|101.0526
|101.1429
|101.295
|102.2556
|''105.7143-106.4286''
|-
|-
|9
|9
|''106.1862-106.9898''
|110.7143
|111.6668
|111.8571
|112.2078
|''112.5''
|112.8142
|112.8142
|112.9494
|113.0844
|113.44105
|113.6842
|113.7857
|113.9568
|115.0376
|''118.9286-119.7321''
|-
|-
|10
|10
|''117.9847-118.87755''
|123.0159
|124.0743
|124.2857
|124.6753
|''125''
|125.3491
|125.3491
|125.4993
|125.6493
|126.0456
|126.3158
|126.4286
|126.6187
|127.81955
|''132.1429-133.0357''
|-
|-
|11
|11
|''129.7832-130.7653''
|135.3175
|136.4817
|136.7143
|137.1429
|''137.5''
|137.884
|137.884
|138.0493
|138.2142
|138.6502
|138.9474
|139.0714
|139.2806
|140.6015
|''145.3571-146.3393''
|-
|-
|12
|12
|''141.5816-142.653''
|147.61905
|148.8891
|149.1429
|149.6104
|''150''
|150.4189
|150.4189
|150.5992
|150.77915
|151.2547
|151.57895
|151.7143
|151.9425
|153.3835
|''158.5714-159.6429''
|-
|-
|13
|13
|''153.3801-154.5408''
|159.9206
|161.2965
|161.5714
|162.0779
|''162.5''
|162.9538
|162.9538
|163.1491
|163.3441
|163.859
|164.2105
|164.3571
|164.6043
|166.1654
|''171.7857-172.9464''
|-
|-
|14
|14
|''165.1786-166.4285''
|172.2222
|173.704
|174
|174.54545
|''175''
|175.48875
|175.48875
|175.6991
|175.909
|176.4639
|176.8421
|177
|177.2662
|178.947
|''185-186.25''
|-
|-
|15
|15
|''176.977-178.3163''
|184.5238
|186.1114
|186.4286
|187.013
|''187.5''
|188.2366
|188.2366
|188.249
|188.4739
|189.0684
|189.4737
|189.6429
|189.9281
|191.7293
|''198.2143-199.5536''
|-
|-
|16
|16
|''188.7755-190.2041''
|196.8254
|198.5188
|198.8571
|199.4805
|''200''
|200.5586
|200.5586
|200.7989
|201.0389
|201.673
|202.1053
|202.2857
|202.5899
|204.5113
|''211.4286-212.8571''
|-
|-
|17
|17
|''200.574-202.0918''
|209.127
|210.92625
|211.2857
|211.94805
|''212.5''
|213.0935
|213.0935
|213.3489
|213.6038
|214.27755
|214.7368
|214.9286
|215.2518
|217.2932
|''224.6429-226.1607''
|-
|-
|18
|18
|''212.37245-213.9796''
|221.4286
|223.3337
|223.7143
|224.4156
|''225''
|225.6284
|225.6284
|225.8988
|226.1687
|226.8821
|227.3684
|227.5714
|227.9137
|230.0752
|''237.8571-239.4643''
|-
|-
|19
|19
|''224.1709-225.86735''
|233.7302
|235.7411
|236.1429
|236.8831
|''237.5''
|238.1633
|238.1633
|238.4487
|238.73365
|239.4867
|240
|240.2143
|240.7556
|242.8571
|''251.0714-252.7679''
|-
|-
|20
|20
|''235.9694-237.7551''
|246.03175
|248.1485
|248.5714
|249.35065
|''250''
|250.6982
|250.6982
|250.9987
|251.2986
|252.0912
|252.6316
|252.8571
|253.2374
|255.6391
|''264.2857-266.0714''
|-
|-
|21
|21
|''247.7674-249.6429''
|258.3333
|260.556
|261
|261.8182
|''262.5''
|263.2331
|263.2331
|263.5486
|263.8635
|264.6958
|265.2632
|265.5
|265.8993
|268.42105
|''277.5-279.375''
|-
|-
|22
|22
|''259.5663-261.5306''
|270.6349
|272.9634
|273.4286
|274.2857
|''275''
|275.768
|275.768
|276.0985
|276.4284
|277.3004
|277.8947
|278.1429
|278.5612
|281.203
|''290.7143-292.6786''
|-
|-
|23
|23
|''271.3648-273.4184''
|282.9365
|285.3708
|285.8571
|286.73525
|''287.5''
|288.30295
|288.30295
|288.6485
|288.9934
|289.9049
|290.5263
|290.7857
|291.223
|293.985
|''303.9286-305.9821''
|-
|-
|24
|24
|''283.1633-285.3061''
|295.2381
|297.782
|298.2857
|299.2208
|''300''
|300.8379
|300.8379
|301.1984
|301.5583
|302.5095
|303.1579
|303.4286
|303.8849
|306.7669
|''317.1429-319.2857''
|-
|-
|25
|25
|''294.9617-297.1939''
|307.5397
|310.1857
|310.7143
|311.6883
|''312.5''
|313.3728
|313.3728
|313.74835
|314.1232
|315.114
|315.7895
|316.0714
|316.5468
|319.5489
|''330.3571-332.5893''
|-
|-
|26
|26
|''306.7602-309.0816''
|319.8413
|322.5931
|323.1429
|324.1558
|''325''
|325.9077
|325.9077
|326.2983
|326.6682
|327.7186
|328.42105
|328.7143
|329.2087
|332.3308
|''343.5714-345.8929''
|-
|-
|27
|27
|''318.5588-320.9694''
|332.1429
|335.0005
|335.5714
|336.6234
|''337.5''
|338.4426
|338.4426
|338.8482
|339.2531
|340.3232
|341.0526
|341.3571
|341.8705
|345.1128
|''356.7857-359.1964''
|-
|-
|28
|28
|''330.3571-332.857''1
|344.4444
|347.408
|348
|349.0909
|''350''
|350.9775
|350.9775
|351.39815
|351.818
|352.9277
|353.6842
|354
|354.5324
|357.8947
|''370-372.5''
|-
|-
|29
|29
|''342.1556-344.7449''
|356.749
|359.8154
|360.4286
|361.5584
|''362.5''
|363.5214
|363.5214
|363.9481
|364.38295
|365.5323
|366.3158
|366.6429
|367.1943
|370.6767
|''383.2143-385.8036''
|-
|-
|30
|30
|''353.9541-356.63265''
|369.0476
|372.2228
|372.8571
|374.026
|''375''
|376.0473
|376.0473
|376.498
|376.9479
|378.13685
|378.9474
|379.2857
|379.8561
|383.45865
|''396.4286-399.1071''
|-
|-
|31
|31
|''365.75255-368.5204''
|381.3492
|384.6302
|385.2857
|386.4935
|''387.5''
|388.5822
|388.5822
|389.04795
|389.5128
|390.7414
|391.57895
|391.9286
|392.518
|396.2406
|''409.6429-412.4107''
|-
|-
|32
|32
|''377.551-380.4082''
|393.6508
|397.03765
|397.7143
|398.961
|''400''
|401.1171
|401.1171
|401.5979
|402.0777
|403.346
|404.2105
|404.5714
|405.1799
|409.0226
|''422.8571-425.7143''
|-
|-
|33
|33
|''389.3495-392.2959''
|408.9524
|409.4451
|410.1429
|411.4286
|''412.5''
|413.65205
|413.65205
|414.1478
|414.6427
|415.9505
|416.8421
|417.2143
|417.8418
|421.8045
|''436.0714-439.0179''
|-
|-
|34
|34
|''401.148-404.1837''
|418.254
|421.8525
|421.5714
|423.8961
|''425''
|426.187
|426.187
|426.69775
|427.2076
|428.5551
|429.4736
|429.8571
|430.5036
|434.5865
|''449.2857-452.3214''
|-
|-
|35
|35
|''412.9464-416.0714''
|430.5556
|434.2599
|435
|436.3636
|''437.5''
|438.7219
|438.7219
|439.2477
|439.7725
|441.1597
|442.1053
|442.5
|443.1655
|447.3684
|''462.5-465.625''
|-
|-
|36
|36
|''424.7449-427.9592''
|442.8571
|446.66735
|447.4286
|448.8312
|''450''
|451.2568
|451.2568
|451.7976
|452.33745
|453.7642
|454.7368
|455.1429
|455.8274
|460.1504
|''475.7143-477.9286''
|-
|-
|37
|37
|''436.5434-439.8469''
|455.1875
|459.0748
|459.8571
|461.2987
|''462.5''
|463.7917
|463.7917
|464.34755
|464.9024
|466.3688
|467.3684
|467.7857
|468.4892
|472.9323
|''488.9286-492.2321''
|-
|-
|38
|38
|''448.3418-451.7347''
|467.460
|471.4822
|472.2857
|473.7662
|''475''
|476.3266
|476.3266
|476.8975
|477.4673
|478.9733
|480
|480.4286
|481.1511
|485.7143
|''502.1429-505.5357''
|-
|-
|39
|39
|''460.1403-463.62245''
|479.7619
|483.8896
|484.7143
|486.2338
|''487.5''
|488.8615
|488.8615
|489.4474
|490.0322
|491.5779
|492.6316
|493.0714
|493.913
|498.4962
|''515.3571-518.8393''
|-
|-
|40
|40
|''471.9388-475.5102''
|492.0635
|496.2971
|497.1429
|498.7013
|''500''
|501.3964
|501.3964
|501.97735
|502.5972
|504.1825
|505.2632
|505.7143
|506.4749
|511.2781
|''528.5714-532.1429''
|-
|-
|41
|41
|''483.7372-487.398''
|504.3651
|507.04485
|508.5714
|511.1688
|''512.5''
|513.9313
|513.9313
|514.5473
|515.1621
|516.787
|517.8947
|518.3571
|519.1367
|524.06015
|''541.7857-545.4464''
|-
|-
|42
|42
|''495.5357-499.2857''
|516.6667
|521.1119
|522
|523.6364
|''525''
|526.46625
|526.46625
|527.0972
|527.727
|529.3916
|530.5263
|531
|531.7986
|536.8421
|''555-558.75''
|-
|-
|43
|43
|''507.3342-511.1735''
|528.96825
|533.5193
|534.4286
|536.1039
|''537.5''
|539.0012
|539.0012
|539.64715
|540.29195
|541.99615
|543.1578
|543.6429
|544.4605
|549.6241
|''568.2143-572.0536''
|-
|-
|44
|44
|''519.13265-523.0612''
|541.2698
|545.9268
|546.8571
|548.5714
|''550''
|551.536
|551.536
|552.1971
|552.8569
|554.6007
|555.7895
|556.2857
|557.1223
|562.406
|''581.4286-585.3571''
|-
|-
|45
|45
|''530.9311-534.949''
|553.5714
|558.3341
|559.2857
|561.039
|''562.5''
|564.071
|564.071
|564.747
|565.4218
|567.2053
|568.42105
|568.9286
|569.7842
|575.188
|''594.6429-598.6607''
|-
|-
|46
|46
|''542.7296-546.8367''
|565.873
|570.7416
|571.7143
|573.5065
|''575''
|576.6059
|576.6059
|577.297
|577.9867
|579.8098
|581.0526
|581.5714
|582.4461
|587.9699
|''607.8571-611.9643''
|-
|-
|47
|47
|''554.5281-558.7245''
|578.1746
|583.149
|584.1429
|585.974
|''587.5''
|589.1408
|589.1408
|589.8469
|590.5517
|592.4144
|593.6842
|594.2143
|595.108
|600.7519
|''620.0714-625.2679''
|-
|-
|48
|48
|''566.3265-570.6122''
|590.4762
|595.5565
|596.5714
|598.4416
|''600''
|601.6757
|601.6757
|602.3968
|603.1166
|605.019
|606.3158
|606.8571
|607.7698
|613.5338
|''634.2857-638.5714''
|-
|-
|49
|49
|''578.125-582.5''
|602.7778
|607.9639
|609
|610.9091
|''612.5''
|614.2106
|614.2106
|614.9468
|615.6815
|617.6235
|618.9474
|619.5
|620.4317
|626.3158
|''647.5-651.875''
|-
|-
|50
|50
|''589.9235-594.3878''
|615.0794
|620.3713
|621.4286
|623.3766
|''625''
|626.7455
|626.7455
|627.4967
|628.2465
|630.2281
|631.57895
|632.1429
|633.0936
|639.0977
|''660.7143-665.1786''
|-
|-
|51
|51
|''601.7219-606.2755''
|627.38095
|632.77875
|633.8571
|635.8442
|''637.5''
|639.28045
|639.28045
|640.0466
|640.8114
|642.8326
|644.2015
|644.7857
|645.7554
|651.8797
|''673.9286-678.4821''
|-
|-
|52
|52
|''613.5204-618.1633''
|639.6825
|645.1862
|646.2857
|648.3117
|''650''
|651.8154
|651.8154
|652.5966
|653.3763
|655.4372
|656.8421
|657.4286
|658.4173
|664.66165
|''687.1429-691.7857''
|-
|-
|53
|53
|''625.3189-630.051''
|651.9841
|657.5936
|658.7143
|660.7792
|''662.5''
|664.3503
|664.3503
|665.1465
|665.9412
|668.0418
|669.4736
|670.0714
|671.0792
|677.4436
|''700.3571-705.0893''
|-
|-
|54
|54
|''637.11735-641.9388''
|664.2857
|670.001
|671.1429
|673.24765
|''675''
|676.8852
|676.8852
|677.6964
|678.5062
|680.6463
|682.1053
|682.7143
|983.7411
|690.2256
|''713.5714-718.3929''
|-
|-
|55
|55
|''648.9158-653.8265''
|676.5873
|682.40845
|683.5714
|685.7143
|''687.5''
|689.4201
|689.4201
|690.2464
|691.0711
|693.2509
|694.7368
|695.3571
|696.4029
|703.0075
|''726.7857-731.6964''
|-
|-
|56
|56
|''660.7143-665.714''3
|688.8889
|694.8158
|696
|698.1818
|''700''
|701.955
|701.955
|702.7963
|703.636
|705.85545
|707.3684
|708
|709.0648
|715.7895
|''740-745''
|-
|-
|57
|57
|''672.5128-677.602''
|701.1905
|707.2233
|708.4286
|710.64935
|''712.5''
|714.4899
|714.4899
|715.3462
|716.201
|718.46
|720
|720.6429
|721.7267
|728.5714
|''753.2143-756.3036''
|-
|-
|58
|58
|''684.3112-689.4898''
|713.4921
|719.6307
|720.8571
|723.1169
|''725''
|727.0248
|727.0248
|727.8962
|728.7659
|731.0646
|732.6316
|733.2857
|734.3885
|741.3534
|''766.4286-771.6071''
|-
|-
|59
|59
|''696.1097-701.37755''
|725.79365
|732.0382
|733.2857
|735.5844
|''737.5''
|739.5597
|739.5597
|740.4461
|741.3308
|743.6691
|745.2632
|745.9286
|747.0504
|754.1353
|''779.6429-784.9107''
|-
|-
|60
|60
|''707.9082-713.2653''
|738.0952
|744.4456
|745.7143
|748.05195
|''750''
|752.0946
|752.0946
|752.996
|753.89575
|756.2736
|757.8947
|758.5714
|759.7123
|766.9173
|''792.8571-798.2143''
|-
|-
|61
|61
|''719.7066-725.1531''
|750.3968
|756.853
|758.1429
|760.5195
|''762.5''
|764.62955
|764.62955
|765.546
|766.4607
|768.8783
|770.5263
|771.2143
|772.3742
|779.69925
|''805.0714-811.5179''
|-
|-
|62
|62
|''731.5051-737.0408''
|762.6984
|769.2604
|770.5714
|772.987
|''775''
|777.1645
|777.1645
|778.0959
|779.0256
|781.4828
|783.1579
|783.8571
|785.036
|792.4812
|''819.2857-824.8214''
|-
|-
|63
|63
|''743.3036-748.9286''
|775
|781.6679
|783
|785.45455
|''787.5''
|789.6994
|789.6994
|790.6458
|791.5905
|794.0874
|795.7895
|796.5
|797.6979
|805.2632
|''832.5-838.125''
|-
|-
|64
|64
|''755.102-760.8163''
|787.3016
|794.0753
|795.4286
|797.9221
|''800''
|802.2343
|802.2343
|803.1958
|804.1555
|806.6919
|808.42105
|809.1429
|810.3598
|818.0451
|''845.7143-851.4286''
|-
|-
|65
|65
|''766.9005-772.704''
|799.6032
|806.4827
|807.8571
|810.3896
|''812.5''
|814.7692
|814.7692
|815.7457
|816.7204
|819.2965
|821.0526
|821.7857
|823.0216
|830.8271
|''858.9286-864.7321''
|-
|-
|66
|66
|''778.699-784.5918''
|811.9048
|818.89015
|820.2857
|822.8571
|''825''
|827.3041
|827.3041
|828.2956
|829.2853
|831.9011
|833.6842
|834.4286
|835.6835
|843.609
|''872.1429-878.0357''
|-
|-
|67
|67
|''792.49745-796.4796''
|824.20635
|831.2976
|832.7143
|835.3247
|''837.5''
|839.839
|839.839
|840.8456
|841.85025
|844.5056
|846.3158
|846.0714
|848.3454
|856.391
|''885.3571-891.3393''
|-
|-
|68
|68
|''802.2959-808.36735''
|836.5079
|843.705
|845.1429
|847.7922
|''850''
|852.3739
|852.3739
|853.3955
|854.4152
|857.1102
|858.9474
|859.7143
|861.0073
|869.1729
|''898.5714-904.6429''
|-
|-
|69
|69
|''814.0944-820.2551''
|848.8095
|856.1124
|857.5714
|860.2597
|''862.5''
|864.9088
|864.9088
|865.9454
|866.9801
|869.71475
|871.57895
|872.3571
|873.6691
|881.9549
|''911.7857-917.9464''
|-
|-
|70
|70
|''825.8929-832.1429''
|861.1111
|868.51985
|870
|872.7273
|''875''
|877.44375
|877.44375
|878.4954
|879.545
|882.3193
|884.2105
|885
|886.331
|894.7368
|''925-931.25''
|-
|-
|71
|71
|''837.6913-844.9306''
|873.4127
|880.9273
|882.4286
|885.1948
|''887.5''
|889.9787
|889.9787
|891.0453
|892.11
|894.9239
|896.8421
|897.6429
|898.9929
|907.5188
|''938.2143-944.5536''
|-
|-
|72
|72
|''849.4898-855.9184''
|885.7143
|893.3347
|894.8571
|897.6623
|''900''
|902.5136
|902.5136
|903.5952
|904.6749
|907.5284
|909.4736
|910.2857
|911.6547
|920.30075
|''951.4286-957.8571''
|-
|-
|73
|73
|''861.2882-867.8061''
|898.0159
|905.7421
|907.2857
|910.1299
|''912.5''
|915.0485
|915.0485
|916.1452
|917.2398
|920.133
|922.1053
|922.9286
|924.3166
|933.0827
|''964.6429-971.1607''
|-
|-
|74
|74
|''873.0867-879.6939''
|910.3175
|918.1496
|919.7143
|922.5974
|''925''
|927.5834
|927.5834
|928.6951
|929.8048
|932.3767
|934.7368
|935.5714
|936.9785
|945.8647
|''977.8571-984.4643''
|-
|-
|75
|75
|''884.8852-891.5816''
|922.61905
|930.557
|932.1429
|935.0649
|''937.5''
|940.1183
|940.1183
|941.245
|942.3697
|945.3421
|947.3684
|948.2143
|949.6404
|958.6466
|''991.0714-997.7679''
|-
|-
|76
|76
|''896.6837-903.4694''
|934.9206
|942.9644
|944.5714
|947.5325
|''950''
|952.6532
|952.6532
|953.795
|954.9346
|957.9467
|960
|960.8571
|962.3022
|971.4286
|''1004.2857-1011.0714''
|-
|-
|77
|77
|''908.4821-915.3571''
|947.2222
|955.3718
|957
|960
|''962.5''
|965.1881
|965.1881
|966.3449
|967.4995
|970.55125
|972.6316
|973.5
|974.9641
|984.2105
|''1017.5-1024.375''
|-
|-
|78
|78
|''920.2806-927.2449''
|959.5238
|967.7793
|969.4286
|972.4675
|''975''
|977.723
|977.723
|978.8948
|980.0645
|983.1558
|985.2632
|986.1429
|987.626
|996.9925
|''1030.7143-1037.6786''
|-
|-
|79
|79
|''932.0791-939.13265''
|971.8254
|980.1867
|981.8571
|984.9351
|''987.5''
|990.25795
|990.25795
|911.4448
|992.6294
|995.7604
|997.8947
|998.7857
|1000.28785
|1009.7744
|''1043.9286-1050.9821''
|-
|-
|80
|80
|''943.87755-951.0204''
|984.127
|992.5941
|994.2857
|997.4126
|''1000''
|1002.7929
|1002.7929
|1003.9947
|1005.1943
|1008.3649
|1010.5263
|1011.4286
|1012.9497
|1022.5564
|''1057.1429-1064.2857''
|-
|-
|81
|81
|''955.676-962.9081''2
|996.4286
|1005.0015
|1006.7143
|1009.8701
|''1012.5''
|1015.3278
|1015.3278
|1016.5446
|1017.7593
|1020.9695
|1023.1579
|1024.0714
|1025.6116
|1035.3383
|''1070.3571-1077.5893''
|-
|-
|82
|82
|''967.4745-974.7959''
|1008.7302
|1017.409
|1019.1429
|1022.3377
|''1025''
|1027.8627
|1027.8627
|1029.0946
|1030.3242
|1033.57405
|1035.57895
|1036.7143
|1038.2735
|1048.1203
|''1083.5714-1090.8929''
|-
|-
|83
|83
|''979.273-986.6837''
|1021.03175
|1029.8164
|1031.5714
|1034.8052
|''1037.5''
|1040.3976
|1040.3976
|1041.6445
|1042.8891
|1046.1786
|1048.42105
|1049.3571
|1050.9353
|1060.9023
|''1096.7857-1104.1964''
|-
|-
|84
|84
|''991.0714-998.5714''
|1033.333
|1042.2238
|1044
|1047.2727
|''1050''
|1052.9325
|1052.9325
|1054.1944
|1055.454
|1058.7832
|1061.0526
|1062
|1063.5972
|1073.6842
|''1110-1117.5''
|-
|-
|85
|85
|''1002.8699-1010.4592''
|1045.6349
|1054.63125
|1056.4286
|1059.7403
|''1062.5''
|1065.4674
|1065.4674
|1066.7444
|1068.019
|1071.3877
|1073.6842
|1074.6429
|1076.2591
|1086.4662
|''1123.2143-1130.8036''
|-
|-
|86
|86
|''1014.6684-1022.3469''
|1057.9365
|1067.0386
|1068.8571
|1072.2078
|''1075''
|1078.0023
|1078.0023
|1079.2943
|1080.5839
|1083.9923
|1086.3158
|1087.2857
|1088.92095
|1099.2481
|''1136.4286-1144.1071''
|-
|-
|87
|87
|''1028.4668-1034.2437''
|1070.2381
|1079.4461
|1081.2857
|1084.6753
|''1087.5''
|1090.5372
|1090.5372
|1091.8442
|1093.1488
|1095.5967
|1098.9474
|1099.9286
|1101.5828
|1112.0301
|''1149.6429-1157.4107''
|-
|-
|88
|88
|''1038.2653-1046.12245''
|1082.5397
|1091.8535
|1093.7143
|1097.1429
|''1100''
|1103.0721
|1103.0721
|1104.3942
|1105.7138
|1109.2014
|1111.57895
|1112.5714
|1114.2447
|1124.812
|''1162.8571-1170.7143''
|-
|-
|89
|89
|''1050.0638-1058.0102''
|1094.8413
|1104.26095
|1106.1429
|1109.6104
|''1112.5''
|1115.6071
|1115.6071
|1164.9441
|1118.2787
|1121.806
|1124.2105
|1125.2143
|1126.9066
|1137.594
|''1175.0714-1184.0179''
|-
|-
|90
|90
|''1061.8622-1069.898''
|1107.1429
|1116.6684
|1118.5714
|1122.0779
|''1125''
|1128.142
|1128.142
|1129.49405
|1130.8436
|1137.41055
|1136.8421
|1137.8571
|1139.5684
|1150.3759
|''1189.2857-1197.3214''
|-
|-
|91
|91
|''1073.6607-1081.7857''
|1119.4444
|1129.0758
|1131
|1134.54545
|''1137.5''
|1140.6769
|1140.6769
|1142.044
|1143.40855
|1147.0151
|1149.4737
|1150.5
|1152.2303
|1163.1579
|''1202.5-1210.625''
|-
|-
|92
|92
|''1085.4592-1093.6735''
|1131.7646
|1141.4832
|1143.4286
|1147.013
|''1150''
|1153.2118
|1153.2118
|1154.5939
|1155.9735
|1159.6297
|1162.1052
|1163.1429
|1164.8922
|1175.93985
|''1215.7143-1223.9286''
|-
|-
|93
|93
|''1097.25765-1105.5612''
|1144.0476
|1153.8907
|1155.8571
|1159.4805
|''1162.5''
|1165.7467
|1165.7467
|1167.14385
|1168.5384
|1172.2242
|1174.7368
|1175.7857
|1177.55405
|1187.7218
|''1228.9286-1237.2321''
|-
|-
|94
|94
|''1109.0651-1117.449''
|1156.3492
|1166.2981
|1168.2857
|1171.94805
|''1175''
|1178.2816
|1178.2816
|1179.6938
|1181.1033
|1184.8288
|1187.3684
|1188.4286
|1190.2159
|1201.5038
|''1242.1429-1250.5357''
|-
|-
|95
|95
|''1120.8546-1129.3367''
|1168.6508
|1178.7055
|1180.7143
|1184.4156
|''1187.5''
|1190.8165
|1190.8165
|1192.2437
|1193.6683
|1197.4334
|1200
|1201.0714
|1202.8778
|1214.2857
|''1257.3571-1263.8393''
|-
|-
|96
|96
|''1132.6531-1141.2245''
|1180.9524
|1191.1129
|1193.1429
|1196.8831
|''1200''
|1203.3514
|1203.3514
|1204.7937
|1206.2332
|1210.0379
|1212.6316
|1213.7143
|1215.5397
|1227.0677
|''1268.5714-1277.1429''
|-
|-
|97
|97
|''1144.4515-1153.11225''
|1193.254
|1203.5204
|1205.5714
|1209.35065
|''1212.5''
|1215.8863
|1215.8863
|1217.3436
|1218.7981
|1222.6425
|1225.2632
|1226.3571
|1228.2015
|1239.985
|''1281.7857-1290.4464''
|-
|-
|98
|98
|''1156.25-1165''
|1205.5556
|1215.9278
|1218
|1221.8182
|''1225''
|1228.42125
|1228.42125
|1229.8935
|1231.6306
|1235.247
|1237.8947
|1239
|1240.8634
|1252.6316
|''1295-1303.75''
|-
|-
|99
|99
|''1168.0485-1176.8878''
|1217.8571
|1228.3352
|1230.4286
|1234.2857
|''1237.5''
|1240.9561
|1240.9561
|1242.44345
|1243.328
|1247.8516
|1250.5263
|1251.6429
|1253.5253
|1265.4135
|''1308.2143-1317.0536''
|-
|-
|100
|100
|''1179.8469-1188.7755''
|1230.1587
|1240.74265
|1242.8571
|1246.75325
|''1250''
|1253.4911
|1253.4911
|1254.9934
|1256.4929
|1260.4561
|1263.1579
|1264.2857
|1266.18715
|1278.1955
|''1321.4286-1330.3571''
|-
|-
|101
|101
|''1191.6454-1200.6633''
|1242.4603
|1253.1501
|1255.2857
|1259.2208
|''1262.5''
|1266.026
|1266.026
|1267.5433
|1269.0578
|1273.0607
|1275.7895
|1276.9286
|1278.849
|1290.9774
|''1334.6429-1343.6607''
|-
|-
|102
|102
|''1203.4439-1212.551''
|1254.7619
|1265.5575
|1267.7143
|1271.6883
|''1275''
|1278.5609
|1278.5609
|1280.09325
|1281.6228
|1286.653
|1288.42105
|1289.5714
|1291.5109
|1303.7594
|''1347.8571-1356.9643''
|-
|-
|103
|103
|''1215.24235-1224.3878''
|1267.0635
|1277.9649
|1280.1429
|1284.1558
|''1287.5''
|1291.0958
|1291.0958
|1292.6432
|12974.1877
|1298.26985
|1301.0526
|1302.2143
|1304.1728
|1316.54135
|''1361.0714-1370.2679''
|-
|-
|104
|104
|''1227.0408-1236.3265''
|1279.3651
|1290.37235
|1292.5714
|1296.6234
|''1300''
|1303.6307
|1303.6307
|1305.1931
|1306.7526
|1310.8744
|1313.6842
|1314.8571
|1316.8346
|1329.3233
|''1374.2857-1383.5714''
|-
|-
|105
|105
|''1238.8393-1248.2143''
|1291.6667
|1302.7798
|1305
|1309.0909
|''1312.5''
|1316.1656
|1316.1656
|1317.74305
|1319.3176
|1323.479
|1326.3158
|1327.5
|1329.4965
|1342.1053
|''1387.5-1396.875''
|-
|-
|106
|106
|''1250.6378-1260.102''
|1303.96825
|1315.1872
|1317.4286
|1321.5584
|''1325''
|1328.7005
|1328.7005
|1330.293
|1331.8825
|1336.0835
|1338.9474
|1340.1429
|1342.1584
|1354.8872
|''1400.7143-1410.1786''
|-
|-
|107
|107
|''1262.4362-1271.9898''
|1316.2698
|1327.5946
|1329.8571
|1334.026
|''1337.5''
|1341.23545
|1341.23545
|1342.8429
|1344.4474
|1348.6881
|1351.57895
|1352.7857
|1354.82025
|1367.6692
|''1413.9286-1423.4821''
|-
|-
|108
|108
|''1274.2347-1283.87755''
|1328.5714
|1340.0021
|1342.2857
|1346.4395
|''1350''
|1353.7704
|1353.7704
|1355.39586
|1357.01235
|1361.2927
|1364.2105
|1365.4286
|1367.4821
|1380.4511
|''1427.1429-1436.7857''
|-
|-
|109
|109
|''1286.0331-1295.7653''
|1340.873
|1352.4095
|1355.7143
|1358.961
|''1362.5''
|1366.3053
|1366.3053
|1367.9428
|1369.5773
|1373.8972
|1376.8421
|1378.0714
|1380.144
|1393.233
|''1440.3571-1450.0893''
|-
|-
|110
|110
|''1297.8316-1307.6531''
|1353.1746
|1364.8169
|1367.1429
|1371.4286
|''1375''
|1378.8418
|1378.8418
|1380.4927
|1382.1422
|1386.5018
|1389.4737
|1390.7143
|1392.8059
|1406.015
|''1453.5714-1463.3929''
|-
|-
|111
|111
|''1309.6301-1319.5408''
|1365.4762
|1377.2243
|1379.5714
|1383.8961
|''1387.5''
|1391.3751
|1391.3751
|1393.0427
|1394.7071
|1399.1063
|1402.1053
|1403.3571
|1405.4677
|1418.797
|''1470.7857-1476.6964''
|-
|-
|112
|112
|''1321.4286-1331.4286''
|1377.7778
|1389.6318
|1392
|1396.3636
|''1400''
|1403.91
|1403.91
|1405.5926
|1407.2721
|1411.7109
|1414.7368
|1416
|1418.1296
|1431.57895
|''1480-1490''
|}
|}


==Related regular temperaments==
{{todo|inline=1|complete table|text=Add a third column that comments on the intervals, either what [[JI]] they approximate, what they are named, or how they can be used musically.}}
===7-limit 383&670===
Commas: 2401/2400, |91 -80 13 2>
 
POTE generator: ~|-33 32 -4 -3> = 12.5357
 
Mapping: [<1 1 -1 1|, <0 56 318 173|]
 
EDOs: 383, 670, 1053, 1436, 1723
 
===11-limit 383&670===
Commas: 2401/2400, 14348907/14348180, 26214400/26198073
 
POTE generator: ~13504609503/13421772800 = 12.5359
 
Mapping: [<1 1 -1 1 3|, <0 56 318 173 44|]
 
EDOs: 383, 670, 1053, 1436, 1723
 
[[Category:Edf]]
[[Category:Edonoi]]

Latest revision as of 19:23, 1 August 2025

← 55edf 56edf 57edf →
Prime factorization 23 × 7
Step size 12.5349 ¢ 
Octave 96\56edf (1203.35 ¢) (→ 12\7edf)
Twelfth 152\56edf (1905.31 ¢) (→ 19\7edf)
Consistency limit 3
Distinct consistency limit 3

56EDF is the equal division of the just perfect fifth into 56 parts of 12.5349 cents each, corresponding to 95.7326 edo.

It is related to the regular temperament which tempers out 2401/2400 and |91 -80 13 2> in the 7-limit, which is supported by 383, 670, 1053, 1436, and 1723 EDOs.

Related regular temperaments

7-limit 383&670

Commas: 2401/2400, |91 -80 13 2>

POTE generator: ~|-33 32 -4 -3> = 12.5357

Mapping: [<1 1 -1 1|, <0 56 318 173|]

EDOs: 383, 670, 1053, 1436, 1723

11-limit 383&670

Commas: 2401/2400, 14348907/14348180, 26214400/26198073

POTE generator: ~13504609503/13421772800 = 12.5359

Mapping: [<1 1 -1 1 3|, <0 56 318 173 44|]

EDOs: 383, 670, 1053, 1436, 1723

Intervals

56ed3/2
1 12.5349
2 25.0698
3 37.6047
4 50.1396
5 62.67455
6 75.2095
7 87.7444
8 100.2793
9 112.8142
10 125.3491
11 137.884
12 150.4189
13 162.9538
14 175.48875
15 188.2366
16 200.5586
17 213.0935
18 225.6284
19 238.1633
20 250.6982
21 263.2331
22 275.768
23 288.30295
24 300.8379
25 313.3728
26 325.9077
27 338.4426
28 350.9775
29 363.5214
30 376.0473
31 388.5822
32 401.1171
33 413.65205
34 426.187
35 438.7219
36 451.2568
37 463.7917
38 476.3266
39 488.8615
40 501.3964
41 513.9313
42 526.46625
43 539.0012
44 551.536
45 564.071
46 576.6059
47 589.1408
48 601.6757
49 614.2106
50 626.7455
51 639.28045
52 651.8154
53 664.3503
54 676.8852
55 689.4201
56 701.955
57 714.4899
58 727.0248
59 739.5597
60 752.0946
61 764.62955
62 777.1645
63 789.6994
64 802.2343
65 814.7692
66 827.3041
67 839.839
68 852.3739
69 864.9088
70 877.44375
71 889.9787
72 902.5136
73 915.0485
74 927.5834
75 940.1183
76 952.6532
77 965.1881
78 977.723
79 990.25795
80 1002.7929
81 1015.3278
82 1027.8627
83 1040.3976
84 1052.9325
85 1065.4674
86 1078.0023
87 1090.5372
88 1103.0721
89 1115.6071
90 1128.142
91 1140.6769
92 1153.2118
93 1165.7467
94 1178.2816
95 1190.8165
96 1203.3514
97 1215.8863
98 1228.42125
99 1240.9561
100 1253.4911
101 1266.026
102 1278.5609
103 1291.0958
104 1303.6307
105 1316.1656
106 1328.7005
107 1341.23545
108 1353.7704
109 1366.3053
110 1378.8418
111 1391.3751
112 1403.91
Todo: complete table

Add a third column that comments on the intervals, either what JI they approximate, what they are named, or how they can be used musically.

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