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'''[[EDF|Division of the just perfect fifth]] into 51 equal parts''' (51EDF) is related to [[87edo|87 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 2.5474 cents compressed and the step size is about 13.7638 cents (corresponding to 87.1851 edo). Unlike 87edo, it is only consistent up to the [[5-odd-limit|6-integer-limit]], with discrepancy for the 7th harmonic.
{{Infobox ET}}
'''[[EDF|Division of the just perfect fifth]] into 51 equal parts''' (51EDF) is related to [[87edo|87 edo]], but with the [[3/2]] rather than the [[2/1]] being [[just]]. The octave is [[Octave shrinking|compressed]] by about 2.5474 [[cents]] and the step size is about 13.7638 cents (corresponding to 87.1851 edo).  
 
Unlike 87edo, it is only [[consistent]] up to the 6-[[integer-limit]], with discrepancy for the 7th harmonic.


Lookalikes: [[87edo]], [[138edt]]
Lookalikes: [[87edo]], [[138edt]]
== Harmonics ==
{{Harmonics in equal|51|3|2|intervals=prime}}
{{Harmonics in equal|51|3|2|intervals=prime|start=12|collapsed=1}}


== Intervals ==
== Intervals ==
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! |Cents
! |Cents
|-
|-
| style="text-align:center;" |0
| colspan="2" style="text-align:center;" |0
| style="text-align:center;" |0
|-
|-
|1
|1
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|27.52765
|27.52765
|-
|-
| style="text-align:center;" |3
|3
| style="text-align:center;" |41.2915
|41.2915
|-
|-
|4
|4
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|68.8191
|68.8191
|-
|-
| style="text-align:center;" |6
|6
| style="text-align:center;" |82.5829
|82.5829
|-
|-
|7·
|7·
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|110.1106
|110.1106
|-
|-
| style="text-align:center;" |9
|9
| style="text-align:center;" |123.8744
|123.8744
|-
|-
|10
|10
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|151.0206
|151.0206
|-
|-
| style="text-align:center;" |12·
|12·
| style="text-align:center;" |165.1659
|165.1659
|-
|-
|13
|13
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|192.6935
|192.6935
|-
|-
| style="text-align:center;" |15
|15
| style="text-align:center;" |206.45735
|206.45735
|-
|-
|16
|16
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|233.985
|233.985
|-
|-
| style="text-align:center;" |18
|18
| style="text-align:center;" |248.7488
|248.7488
|-
|-
|19
|19
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|275.2765
|275.2765
|-
|-
| style="text-align:center;" |21
|21
| style="text-align:center;" |289.0403
|289.0403
|-
|-
|22·
|22·
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|316.5679
|316.5679
|-
|-
| style="text-align:center;" |24
|24
| style="text-align:center;" |330.3318
|330.3318
|-
|-
|25
|25
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|357.8594
|357.8594
|-
|-
| style="text-align:center;" |27
|27
| style="text-align:center;" |371.6232
|371.6232
|-
|-
|28
|28
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|399.1509
|399.1509
|-
|-
| style="text-align:center;" |30
|30
| style="text-align:center;" |412.9147
|412.9147
|-
|-
|31
|31
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|440.44253
|440.44253
|-
|-
| style="text-align:center;" |33
|33
| style="text-align:center;" |455.2062
|455.2062
|-
|-
|34
|34
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|481.7338
|481.7338
|-
|-
| style="text-align:center;" |36
|36
| style="text-align:center;" |495.49765
|495.49765
|-
|-
|37
|37
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|523.0253
|523.0253
|-
|-
| style="text-align:center;" |39
|39
| style="text-align:center;" |536.7891
|536.7891
|-
|-
|40
|40
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|564.3168
|564.3168
|-
|-
| style="text-align:center;" |42
|42
| style="text-align:center;" |578.0806
|578.0806
|-
|-
|43
|43
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|605.6082
|605.6082
|-
|-
| style="text-align:center;" |45
|45
| style="text-align:center;" |619.3721
|619.3721
|-
|-
|46
|46
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|646.8997
|646.8997
|-
|-
| style="text-align:center;" |48
|48
| style="text-align:center;" |660.6635
|660.6635
|-
|-
|49
|49
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|688.1912
|688.1912
|-
|-
| style="text-align:center;" |51
|51
| style="text-align:center;" |701.955
|701.955
|-
|-
|52
|52
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|729.48365
|729.48365
|-
|-
| style="text-align:center;" |54
|54
| style="text-align:center;" |743.2465
|743.2465
|-
|-
|55
|55
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|770.7741
|770.7741
|-
|-
| style="text-align:center;" |57
|57
| style="text-align:center;" |784.5379
|784.5379
|-
|-
|58
|58
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|812.0656
|812.0656
|-
|-
| style="text-align:center;" |60
|60
| style="text-align:center;" |825.8294
|825.8294
|-
|-
|61
|61
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|853.3571
|853.3571
|-
|-
| style="text-align:center;" |63
|63
| style="text-align:center;" |867.1209
|867.1209
|-
|-
|64
|64
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|894.6485
|894.6485
|-
|-
| style="text-align:center;" |66
|66
| style="text-align:center;" |908.41235
|908.41235
|-
|-
|67
|67
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|935.94
|935.94
|-
|-
| style="text-align:center;" |69
|69
| style="text-align:center;" |949.7038
|949.7038
|-
|-
|70
|70
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|977.2315
|977.2315
|-
|-
| style="text-align:center;" |72
|72
| style="text-align:center;" |990.9952
|990.9952
|-
|-
|73
|73
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|1018.5229
|1018.5229
|-
|-
| style="text-align:center;" |75
|75
| style="text-align:center;" |1032.32868
|1032.32868
|-
|-
|76
|76
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|1059.8144
|1059.8144
|-
|-
| style="text-align:center;" |78
|78
| style="text-align:center;" |1073.5782
|1073.5782
|-
|-
|79
|79
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|1101.1059
|1101.1059
|-
|-
| style="text-align:center;" |81
|81
| style="text-align:center;" |1114.8697
|1114.8697
|-
|-
|82
|82
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|1142.39735
|1142.39735
|-
|-
| style="text-align:center;" |84
|84
| style="text-align:center;" |1156.1612
|1156.1612
|-
|-
|85
|85
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|1183.6888
|1183.6888
|-
|-
| style="text-align:center;" |87
|87
| style="text-align:center;" |1197.45265
|1197.45265
|-
|-
|88
|88
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|1403.91
|1403.91
|}
|}
[[Category:Edf]]
 
[[Category:Edonoi]]
{{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.}}
 
{{todo|expand}}
Retrieved from "https://en.xen.wiki/w/51edf"