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'''[[EDF|Division of the just perfect fifth]] into 58 equal parts''' (58EDF) is related to [[99edo|99 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 1.8354 cents compressed and the step size is about 12.1027 cents (corresponding to 99.1517 edo). It is consistent to the [[11-odd-limit|12-integer-limit]]. In comparison, 99edo is only consistent up to the [[9-odd-limit|10-integer-limit]].
{{Infobox ET}}
{{ED intro}}


Lookalikes: [[99edo]], [[157edt]]
== Theory ==
{| class="wikitable"
58edf corresponds to 99.1517…edo. It is related to [[99edo]], but with the [[3/2|perfect fifth]] rather than the [[2/1|octave]] being just. The octave is [[stretched and compressed tuning|compressed]] by about 1.84 cents. 58edf is [[consistent]] to the [[integer limit|12-integer-limit]]. In comparison, 99edo is only consistent up to the 10-integer-limit. 58edf has a flat tendency, with [[prime harmonic]]s 2, [[3/1|3]], [[5/1|5]], [[7/1|7]], and [[11/1|11]] all tuned flat of just.  
|-
 
! |Degrees
=== Harmonics ===
! |Cents Value
{{Harmonics in equal|58|3|2|intervals=integer|columns=11}}
|Five limit
{{Harmonics in equal|58|3|2|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 58edf (continued)}}
|Seven limit
 
|Eleven limit
=== Subsets and supersets ===
|Thirteen limit
Since 58 factors into primes as {{nowrap| 2 × 29 }}, 58edf contains [[2edf]] and [[29edf]] as subset edts.
|-
 
| |1
== See also ==
| |12.1027
* [[99edo]] – relative edo
|2048/2025
* [[157edt]] – relative edt
|126/125
* [[256ed6]] – relative ed6
|99/98
|91/90
|-
| |2
| |24.2053
|81/80
|64/63
|55/54
|55/54
|-
| |3
| |36.308
|128/125
|49/48
|49/48
|49/48
|-
| |4
| |48.4107
|250/243
|36/35
|33/32
|33/32
|-
| |5
| |60.5134
|648/625
|28/27
|28/27
|26/25
|-
| |6
| |72.616
|25/24
|25/24
|22/21
|22/21
|-
| |7
| |84.7187
|256/243
|21/20
|21/20
|21/20
|-
| |8
| |96.8214
|135/128
|135/128
|81/77
|52/49
|-
| |9
| |108.92405
|16/15
|16/15
|16/15
|16/15
|-
| |10
| |121.0267
|2187/2048
|15/14
|15/14
|15/14
|-
| |11
| |133.1294
|27/25
|27/25
|27/25
|13/12
|-
| |12
| |145.2321
|625/576
|49/45
|49/45
|49/45
|-
| |13
| |157.3347
|800/729
|35/32
|11/10
|11/10
|-
| |14
| |169.4374
|1125/1024
|54/49
|54/49
|54/49
|-
| |15
| |181.54
|10/9
|10/9
|10/9
|10/9
|-
| |16
| |193.6428
|4096/3645
|28/25
|28/25
|28/25
|-
| |17
| |205.7454
|9/8
|9/8
|9/8
|9/8
|-
| |18
| |217.8481
|256/225
|245/216
|112/99
|91/80
|-
| |19
| |229.9508
|729/640
|8/7
|8/7
|8/7
|-
| |20
| |242.05345
|144/125
|144/125
|63/55
|52/45
|-
| |21
| |254.1561
|125/108
|81/70
|81/70
|15/13
|-
| |22
| |266.2587
|729/625
|7/6
|7/6
|7/6
|-
| |23
| |278.3615
|75/64
|75/64
|33/28
|33/28
|-
| |24
| |290.4641
|32/27
|32/27
|32/27
|13/11
|-
| |25
| |302.5668
|1215/1024
|25/21
|25/21
|25/21
|-
| |26
| |314.6695
|6/5
|6/5
|6/5
|6/5
|-
| |27
| |326.7722
|3125/2592
|98/81
|98/81
|91/75
|-
| |28
| |338.8748
|243/200
|128/105
|11/9
|11/9
|-
| |29
| |350.9775
|625/512
|49/40
|49/40
|49/40
|-
| |30
| |363.0802
|100/81
|100/81
|27/22
|16/13
|-
| |31
| |375.18285
|3888/3125
|56/45
|56/45
|56/45
|-
| |32
| |387.2855
|5/4
|5/4
|5/4
|5/4
|-
| |33
| |399.3882
|512/405
|63/50
|63/50
|49/39
|-
| |34
| |411.4909
|81/64
|80/63
|80/63
|33/26
|-
| |35
| |423.5935
|32/25
|32/25
|14/11
|14/11
|-
| |36
| |435.6962
|625/486
|9/7
|9/7
|9/7
|-
| |37
| |447.7989
|162/125
|35/27
|35/27
|13/10
|-
| |38
| |459.90155
|125/96
|64/49
|55/42
|55/42
|-
| |39
| |472.0042
|320/243
|21/16
|21/16
|21/16
|-
| |40
| |484.1069
|675/512
|250/189
|250/189
|65/49
|-
| |41
| |469.2096
|4/3
|4/3
|4/3
|4/3
|-
| |42
| |508.3122
|8192/6075
|75/56
|66/49
|66/49
|-
| |43
| |520.4149
|27/20
|27/20
|27/20
|27/20
|-
| |44
| |532.5176
|512/375
|49/36
|49/36
|49/36
|-
| |45
| |544.6203
|1000/729
|48/35
|11/8
|11/8
|-
| |46
| |556.7229
|864/625
|112/81
|112/81
|91/66
|-
| |47
| |568.8256
|25/18
|25/18
|25/18
|18/13
|-
| |48
| |580.9283
|1024/729
|7/5
|7/5
|7/5
|-
| |49
| |593.03095
|45/32
|45/32
|45/32
|45/32
|-
| |50
| |605.1336
|64/45
|64/45
|64/45
|64/45
|-
| |51
| |617.2362
|729/512
|10/7
|10/7
|10/7
|-
| |52
| |629.339
|36/25
|36/25
|36/25
|13/9
|-
| |53
| |641.4416
|625/432
|81/56
|81/56
|75/52
|-
| |54
| |653.5443
|729/500
|35/24
|16/11
|16/11
|-
| |55
| |665.647
|375/256
|72/49
|72/49
|72/49
|-
| |56
| |677.7497
|40/27
|40/27
|40/27
|40/27
|-
| |57
| |689.8523
|6075/4096
|112/75
|49/33
|49/33
|-
| |58
| |701.955
|3/2
|3/2
|3/2
|3/2
|-
| |59
| |714.0577
|1024/675
|189/125
|189/125
|91/60
|-
| |60
| |726.16035
|243/160
|32/21
|32/21
|32/21
|-
| |61
| |738.263
|192/125
|49/32
|49/32
|49/32
|-
| |62
| |750.3657
|125/81
|54/35
|54/35
|20/13
|-
| |63
| |762.4684
|972/625
|14/9
|14/9
|14/9
|-
| |64
| |774.571
|25/16
|25/16
|11/7
|11/7
|-
| |65
| |786.6737
|128/81
|63/40
|63/40
|52/33
|-
| |66
| |798.7764
|405/256
|100/63
|100/63
|78/49
|-
| |67
| |810.87905
|8/5
|8/5
|8/5
|8/5
|-
| |68
| |822.9817
|3125/1944
|45/28
|45/28
|45/28
|-
| |69
| |835.0844
|81/50
|81/50
|44/27
|13/8
|-
| |70
| |847.1871
|625/384
|49/30
|49/30
|49/30
|-
| |71
| |859.2897
|400/243
|105/64
|18/11
|18/11
|-
| |72
| |871.3924
|3375/2048
|81/49
|81/49
|81/49
|-
| |73
| |883.4951
|5/3
|5/3
|5/3
|5/3
|-
| |74
| |895.5978
|2048/1215
|42/25
|42/25
|42/25
|-
| |75
| |907.7004
|27/16
|27/16
|27/16
|22/13
|-
| |76
| |919.8031
|128/75
|128/75
|56/33
|56/33
|-
| |77
| |931.9058
|1250/729
|12/7
|12/7
|12/7
|-
| |78
| |944.00845
|216/125
|140/81
|140/81
|26/15
|-
| |79
| |956.1111
|125/72
|125/72
|110/63
|45/26
|-
| |80
| |968.2138
|1280/729
|7/4
|7/4
|7/4
|-
| |81
| |980.3165
|225/128
|225/128
|99/56
|99/56
|-
|82
|992.4191
|16/9
|16/9
|16/9
|16/9
|-
|83
|1004.5218
|3645/2048
|25/14
|25/14
|25/14
|-
|84
|1016.6245
|9/5
|9/5
|9/5
|9/5
|-
|85
|1028.7272
|2048/1125
|49/27
|49/27
|49/27
|-
|86
|1040.8298
|729/400
|64/35
|11/6
|11/6
|-
|87
|1052.9325
|1152/625
|90/49
|90/49
|90/49
|-
|88
|1065.0352
|50/27
|50/27
|50/27
|13/7
|-
|89
|1077.13785
|4096/2187
|28/15
|28/15
|28/15
|-
|90
|1089.2405
|15/8
|15/8
|15/8
|15/8
|-
|91
|1101.3432
|256/135
|189/100
|154/81
|49/26
|-
|92
|1113.4459
|243/128
|40/21
|40/21
|40/21
|-
|93
|1125.5485
|48/25
|48/25
|21/11
|21/11
|-
|94
|1137.6512
|625/324
|27/14
|27/14
|25/13
|-
|95
|1149.7539
|243/125
|35/18
|35/18
|35/18
|-
|96
|1161.8566
|125/64
|49/25
|49/25
|49/25
|-
|97
|1173.9592
|160/81
|63/32
|63/32
|63/32
|-
|98
|1186.0619
|2025/1024
|125/63
|125/63
|125/63
|-
|99
|1198.1646
|2/1
|2/1
|2/1
|2/1
|}
[[Category:Edf]]
[[Category:Edonoi]]
Retrieved from "https://en.xen.wiki/w/58edf"