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'''[[EDF|Division of the just perfect fifth]] into 42 equal parts''' (42EDF) is related to [[72edo|72 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 16.7132 cents (corresponding to 71.7995 [[edo]], practically identical to every fifth step of [[359edo]]). Unlike 72edo, it is only consistent up to the [[7-odd-limit|7-integer-limit]], with discrepancy for the 8th harmonic (three octaves).
{{Infobox ET}}
{{ED intro}}


Lookalikes: [[72edo]], [[114edt]]
42EDF is related to [[72edo]], but with the [[3/2]] rather than the [[2/1]] being [[just]], which results in [[octave]]s being [[Octave stretch|stretched]] by about 3.3514{{c}}. This corresponds to 71.7995 [[edo]], practically identical to every fifth step of [[359edo]]. Unlike 72edo, it is only consistent up to the 7-[[integer-limit]], with discrepancy for the 8th harmonic (three octaves).
 
Lookalikes: [[72edo]], [[114edt]], [[186ed6]]
 
== Harmonics ==
{{Harmonics in equal|42|3|2|intervals=prime}}
{{Harmonics in equal|42|3|2|intervals=prime|start=12|collapsed=1}}
 
== Intervals ==
{| class="wikitable"
{| class="wikitable"
|-
|-
| |degrees
! Degrees
| |cents value
! Cents value
| |approximate ratios (11-limit)
! Approximate ratios (11-limit)
|-
| colspan="2" | 0
| 1/1
|-
| 1
| 16.7132
| 81/80
|-
| 2
| 33.4264
| 45/44
|-
| 3
| 50.1396
| 33/32
|-
| 4
| 66.8529
| 25/24
|-
| 5
| 83.5661
| 21/20
|-
| 6
| 100.2793
| 35/33
|-
| 7
| 116.9925
| 15/14
|-
| 8
| 133.7057
| 27/25
|-
| 9
| 150.4189
| 12/11
|-
| 10
| 167.1321
| 11/10
|-
| 11
| 183.8454
| 10/9
|-
|-
| |0
| 12
| |0
| 200.5586
| |1/1
| 9/8
|-
|-
| |1
| 13
| |16.7132
| 217.2717
| |81/80
| 25/22
|-
|-
| |2
| 14
| |33.4264
| 233.985
| |45/44
| 8/7
|-
|-
| |3
| 15
| |50.1396
| 250.6982
| |33/32
| 81/70
|-
|-
| |4
| 16
| |66.8529
| 267.4114
| |25/24
| 7/6
|-
|-
| |5
| 17
| |83.5661
| 284.1246
| |21/20
| 33/28
|-
|-
| |6
| 18
| |100.2793
| 300.8379
| |35/33
| 25/21
|-
|-
| |7
| 19
| |116.9925
| 317.5511
| |15/14
| 6/5
|-
|-
| |8
| 20
| |133.7057
| 334.2643
| |27/25
| 40/33
|-
|-
| |9
| 21
| |150.4189
| 350.9775
| |12/11
| 11/9
|-
|-
| |10
| 22
| |167.1321
| 367.6907
| |11/10
| 99/80
|-
|-
| |11
| 23
| |183.8454
| 384.4039
| |10/9
| 5/4
|-
|-
| |12
| 24
| |200.5586
| 401.1171
| |9/8
| 44/35
|-
|-
| |13
| 25
| |217.2717
| 417.8304
| |25/22
| 14/11
|-
|-
| |14
| 26
| |233.985
| 434.5436
| |8/7
| 9/7
|-
|-
| |15
| 27
| |250.6982
| 451.2568
| |81/70
| 35/27
|-
|-
| |16
| 28
| |267.4114
| 467.97
| |7/6
| 21/16
|-
|-
| |17
| 29
| |284.1246
| 484.6832
| |33/28
| 33/25
|-
|-
| |18
| 30
| |300.8379
| 501.3964
| |25/21
| 4/3
|-
|-
| |19
| 31
| |317.5511
| 518.1096
| |6/5
| 27/20
|-
|-
| |20
| 32
| |334.2643
| 534.8229
| |40/33
| 15/11
|-
|-
| |21
| 33
| |350.9775
| 551.536
| |11/9
| 11/8
|-
|-
| |22
| 34
| |367.6907
| 568.2493
| |99/80
| 25/18
|-
|-
| |23
| 35
| |384.4039
| 584.9625
| |5/4
| 7/5
|-
|-
| |24
| 36
| |401.1171
| 601.6757
| |44/35
| 99/70
|-
|-
| |25
| 37
| |417.8304
| 618.3889
| |14/11
| 10/7
|-
|-
| |26
| 38
| |434.5436
| 635.1021
| |9/7
| 36/25
|-
|-
| |27
| 39
| |451.2568
| 651.8154
| |35/27
| 16/11
|-
|-
| |28
| 40
| |467.97
| 668.5286
| |21/16
| 22/15
|-
|-
| |29
| 41
| |484.6832
| 685.2418
| |33/25
| 40/27
|-
|-
| |30
| 42
| |501.3964
| 701.955
| |4/3
| 3/2
|-
|-
| |31
| 43
| |518.1096
| 718.6682
| |27/20
| 50/33
|-
|-
| |32
| 44
| |534.8229
| 735.3814
| |15/11
| 32/21
|-
|-
| |33
| 45
| |551.536
| 752.0946
| |11/8
| 54/35
|-
|-
| |34
| 46
| |568.2493
| 768.8079
| |25/18
| 14/9
|-
|-
| |35
| 47
| |584.9625
| 785.5211
| |7/5
| 11/7
|-
|-
| |36
| 48
| |601.6757
| 802.2343
| |99/70
| 35/22
|-
|-
| |37
| 49
| |618.3889
| 818.9475
| |10/7
| 8/5
|-
|-
| |38
| 50
| |635.1021
| 835.6607
| |36/25
| 81/50
|-
|-
| |39
| 51
| |651.8154
| 852.3739
| |16/11
| 18/11
|-
|-
| |40
| 52
| |668.5286
| 869.0871
| |22/15
| 33/20
|-
|-
| |41
| 53
| |685.2418
| 885.8004
| |40/27
| 5/3
|-
|-
| |42
| 54
| |701.955
| 902.5136
| |3/2
| 27/16
|-
|-
| |43
| 55
| |718.6682
| 919.2268
| |50/33
| 56/33
|-
|-
| |44
| 56
| |735.3814
| 935.94
| |32/21
| 12/7
|-
|-
| |45
| 57
| |752.0946
| 952.6532
| |54/35
| 121/70
|-
|-
| |46
| 58
| |768.8079
| 969.3664
| |14/9
| 7/4
|-
|-
| |47
| 59
| |785.5211
| 986.0796
| |11/7
| 44/25
|-
|-
| |48
| 60
| |802.2343
| 1002.7929
| |35/22
| 16/9
|-
|-
| |49
| 61
| |818.9475
| 1019.506
| |8/5
| 9/5
|-
|-
| |50
| 62
| |835.6607
| 1036.2193
| |81/50
| 20/11
|-
|-
| |51
| 63
| |852.3739
| 1052.9235
| |18/11
| 11/6
|-
|-
| |52
| 64
| |869.0871
| 1069.6457
| |33/20
| 50/27
|-
|-
| |53
| 65
| |885.8004
| 1086.3589
| |5/3
| 15/8
|-
|-
| |54
| 66
| |902.5136
| 1103.0721
| |27/16
| 66/35
|-
|-
| |55
| 67
| |919.2268
| 1119.7854
| |56/33
| 21/11
|-
|-
| |56
| 68
| |935.94
| 1136.4986
| |12/7
| 27/14
|-
|-
| |57
| 69
| |952.6532
| 1153.2118
| |121/70
| 35/18
|-
|-
| |58
| 70
| |969.3664
| 1169.925
| |7/4
| 49/25
|-
|-
| |59
| 71
| |986.0796
| 1186.6382
| |44/25
| 99/50
|-
|-
| |60
| 72
| |1002.7929
| 1203.3514
| |16/9
| 2/1
|-
|-
| |61
| 73
| |1019.506
| 1220.0646
| |9/5
| 81/40
|-
|-
| |62
| 74
| |1036.2193
| 1236.7779
| |20/11
| 45/22
|-
|-
| |63
| 75
| |1052.9235
| 1253.4911
| |11/6
| 33/16
|-
|-
| |64
| 76
| |1069.6457
| 1270.2043
| |50/27
| 56/27
|-
|-
| |65
| 77
| |1086.3589
| 1286.9175
| |15/8
| 21/10
|-
|-
| |66
| 78
| |1103.0721
| 1303.6307
| |66/35
| 70/33
|-
|-
| |67
| 79
| |1119.7854
| 1320.3439
| |21/11
| 15/7
|-
|-
| |68
| 80
| |1136.4986
| 1337.05715
| |27/14
| 54/25
|-
|-
| |69
| 81
| |1153.2118
| 1353.7704
| |35/18
| 24/11
|-
|-
| |70
| 82
| |1169.925
| 1370.4836
| |49/25
| 11/5
|-
|-
| |71
| 83
| |1186.6382
| 1387.1968
| |99/50
| 20/9
|-
|-
| |72
| 84
| |1203.3514
| 1403.91
| |2/1
| 9/4
|}
|}
[[Category:Edf]]
 
[[Category:Edonoi]]
{{todo|expand}}
Retrieved from "https://en.xen.wiki/w/42edf"