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'''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]], and [[1053edo|1053]], 1436, and 1723 EDOs.
{{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 {{EDOs|383, 670, 1053, 1436, and 1723}} EDOs.


==Related regular temperaments==
==Related regular temperaments==
Line 7: Line 10:
POTE generator: ~|-33 32 -4 -3> = 12.5357
POTE generator: ~|-33 32 -4 -3> = 12.5357


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


EDOs: 383, 670, 1053, 1436, 1723
EDOs: {{EDOs|383, 670, 1053, 1436, 1723}}


===11-limit 383&670===
===11-limit 383&670===
Line 16: Line 19:
POTE generator: ~13504609503/13421772800 = 12.5359
POTE generator: ~13504609503/13421772800 = 12.5359


Map: [<1 1 -1 1 3|, <0 56 318 173 44|]
Mapping: [<1 1 -1 1 3|, <0 56 318 173 44|]
 
EDOs: {{EDOs|383, 670, 1053, 1436, 1723}}


EDOs: 383, 670, 1053, 1436, 1723
== Intervals==
{| class="wikitable"
! colspan="2" |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
|}


[[Category:Edf]]
{{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.}}
[[Category:Edonoi]]
Retrieved from "https://en.xen.wiki/w/56edf"