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'''[[EDF|Division of the just perfect fifth]] into 58 equal parts''' (58EDF) is related to [[99edo]], 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}}


== Intervals ==
== Theory ==
''todo: mapping for 11 and 13 should differ from 99edo''
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.  
{| class="wikitable"
 
|-
=== Harmonics ===
! Degrees
{{Harmonics in equal|58|3|2|intervals=integer|columns=11}}
! Cents Value
{{Harmonics in equal|58|3|2|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 58edf (continued)}}
! Five limit
 
! Seven limit
=== Subsets and supersets ===
! Eleven limit
Since 58 factors into primes as {{nowrap| 2 × 29 }}, 58edf contains [[2edf]] and [[29edf]] as subset edts.
! Thirteen limit
|-
| |1
| |12.1027
|2048/2025
|126/125
|99/98
|91/90
|-
| |2
| |24.2053
|81/80
|64/63
| colspan="2" |55/54
|-
| |3
| |36.308
|128/125
| colspan="3" |49/48
|-
| |4
| |48.4107
|250/243
|36/35
| colspan="2" |33/32
|-
| |5
| |60.5134
|648/625
| colspan="2" |28/27
|26/25
|-
| |6
| |72.616
| colspan="2" |25/24
| colspan="2" |22/21
|-
| |7
| |84.7187
|256/243
| colspan="3" |21/20
|-
| |8
| |96.8214
| colspan="2" |135/128
|81/77
|52/49
|-
| |9
| |108.92405
| colspan="4" |16/15
|-
| |10
| |121.0267
|2187/2048
| colspan="3" |15/14
|-
| |11
| |133.1294
| colspan="3" |27/25
|13/12
|-
| |12
| |145.2321
|625/576
| colspan="3" |49/45
|-
| |13
| |157.3347
|800/729
|35/32
| colspan="2" |11/10
|-
| |14
| |169.4374
|1125/1024
| colspan="3" |54/49
|-
| |15
| |181.54
|10/9
| colspan="3" |10/9
|-
| |16
| |193.6428
|4096/3645
| colspan="3" |28/25
|-
| |17
| |205.7454
| colspan="4" |9/8
|-
| |18
| |217.8481
|256/225
|245/216
|112/99
|91/80
|-
| |19
| |229.9508
|729/640
| colspan="3" |8/7
|-
| |20
| |242.05345
| colspan="2" |144/125
|63/55
|52/45
|-
| |21
| |254.1561
|125/108
| colspan="2" |81/70
|15/13
|-
| |22
| |266.2587
|729/625
| colspan="3" |7/6
|-
| |23
| |278.3615
| colspan="2" |75/64
| colspan="2" |33/28
|-
| |24
| |290.4641
|32/27
| colspan="2" |32/27
|13/11
|-
| |25
| |302.5668
|1215/1024
| colspan="3" |25/21
|-
| |26
| |314.6695
| colspan="4" |6/5
|-
| |27
| |326.7722
|3125/2592
| colspan="2" |98/81
|91/75
|-
| |28
| |338.8748
|243/200
|128/105
| colspan="2" |11/9
|-
| |29
| |350.9775
|625/512
| colspan="3" |49/40
|-
| |30
| |363.0802
| colspan="2" |100/81
|27/22
|16/13
|-
| |31
| |375.18285
|3888/3125
| colspan="3" |56/45
|-
| |32
| |387.2855
| colspan="4" |5/4
|-
| |33
| |399.3882
|512/405
| colspan="2" |63/50
|49/39
|-
| |34
| |411.4909
|81/64
| colspan="2" |80/63
|33/26
|-
| |35
| |423.5935
| colspan="2" |32/25
| colspan="2" |14/11
|-
| |36
| |435.6962
|625/486
| colspan="3" |9/7
|-
| |37
| |447.7989
|162/125
| colspan="2" |35/27
|13/10
|-
| |38
| |459.90155
|125/96
|64/49
| colspan="2" |55/42
|-
| |39
| |472.0042
|320/243
| colspan="3" |21/16
|-
| |40
| |484.1069
|675/512
| colspan="2" |250/189
|65/49
|-
| |41
| |469.2096
| colspan="4" |4/3
|-
| |42
| |508.3122
|8192/6075
|75/56
| colspan="2" |66/49
|-
| |43
| |520.4149
| colspan="4" |27/20
|-
| |44
| |532.5176
|512/375
| colspan="3" |49/36
|-
| |45
| |544.6203
|1000/729
|48/35
| colspan="2" |11/8
|-
| |46
| |556.7229
|864/625
| colspan="2" |112/81
|91/66
|-
| |47
| |568.8256
| colspan="3" |25/18
|18/13
|-
| |48
| |580.9283
|1024/729
| colspan="3" |7/5
|-
| |49
| |593.03095
| colspan="4" |45/32
|-
| |50
| |605.1336
| colspan="4" |64/45
|-
| |51
| |617.2362
|729/512
| colspan="3" |10/7
|-
| |52
| |629.339
| colspan="3" |36/25
|13/9
|-
| |53
| |641.4416
|625/432
| colspan="2" |81/56
|75/52
|-
| |54
| |653.5443
|729/500
|35/24
| colspan="2" |16/11
|-
| |55
| |665.647
|375/256
| colspan="3" |72/49
|-
| |56
| |677.7497
| colspan="4" |40/27
|-
| |57
| |689.8523
|6075/4096
|112/75
| colspan="2" |49/33
|-
| |58
| |701.955
| colspan="4" |3/2
|-
| |59
| |714.0577
|1024/675
| colspan="2" |189/125
|91/60
|-
| |60
| |726.16035
|243/160
| colspan="3" |32/21
|-
| |61
| |738.263
|192/125
| colspan="3" |49/32
|-
| |62
| |750.3657
|125/81
| colspan="2" |54/35
|20/13
|-
| |63
| |762.4684
|972/625
| colspan="3" |14/9
|-
| |64
| |774.571
| colspan="2" |25/16
| colspan="2" |11/7
|-
| |65
| |786.6737
|128/81
| colspan="2" |63/40
|52/33
|-
| |66
| |798.7764
|405/256
| colspan="2" |100/63
|78/49
|-
| |67
| |810.87905
| colspan="4" |8/5
|-
| |68
| |822.9817
|3125/1944
| colspan="3" |45/28
|-
| |69
| |835.0844
| colspan="2" |81/50
|44/27
|13/8
|-
| |70
| |847.1871
|625/384
| colspan="3" |49/30
|-
| |71
| |859.2897
|400/243
|105/64
| colspan="2" |18/11
|-
| |72
| |871.3924
|3375/2048
| colspan="3" |81/49
|-
| |73
| |883.4951
| colspan="4" |5/3
|-
| |74
| |895.5978
|2048/1215
| colspan="3" |42/25
|-
| |75
| |907.7004
| colspan="3" |27/16
|22/13
|-
| |76
| |919.8031
| colspan="2" |128/75
|56/33
|56/33
|-
| |77
| |931.9058
|1250/729
| colspan="3" |12/7
|-
| |78
| |944.00845
|216/125
| colspan="2" |140/81
|26/15
|-
| |79
| |956.1111
| colspan="2" |125/72
|110/63
|45/26
|-
| |80
| |968.2138
|1280/729
| colspan="3" |7/4
|-
| |81
| |980.3165
|225/128
|225/128
| colspan="2" |99/56
|-
|82
|992.4191
| colspan="4" |16/9
|-
|83
|1004.5218
|3645/2048
| colspan="3" |25/14
|-
|84
|1016.6245
| colspan="4" |9/5
|-
|85
|1028.7272
|2048/1125
| colspan="3" |49/27
|-
|86
|1040.8298
|729/400
|64/35
| colspan="2" |11/6
|-
|87
|1052.9325
|1152/625
| colspan="3" |90/49
|-
|88
|1065.0352
| colspan="4" |50/27
|-
|89
|1077.13785
|4096/2187
| colspan="3" |28/15
|-
|90
|1089.2405
| colspan="4" |15/8
|-
|91
|1101.3432
|256/135
|189/100
|154/81
|49/26
|-
|92
|1113.4459
|243/128
| colspan="3" |40/21
|-
|93
|1125.5485
| colspan="4" |48/25
|-
|94
|1137.6512
|625/324
| colspan="2" |27/14
|25/13
|-
|95
|1149.7539
|243/125
| colspan="2" |35/18
|35/18
|-
|96
|1161.8566
|125/64
| colspan="2" |49/25
|49/25
|-
|97
|1173.9592
|160/81
| colspan="3" |63/32
|-
|98
|1186.0619
|2025/1024
| colspan="3" |125/63
|-
|99
|1198.1646
| colspan="4" |2/1
|-
|100
|1210.2672
|4096/2025
|252/125
|99/49
|91/45
|-
|101
|1222.3699
|81/40
|128/63
| colspan="2" |55/27
|-
|102
|1234.4726
|256/125
| colspan="3" |49/24
|-
|103
|1246.5753
|500/243
|72/35
| colspan="2" |33/16
|-
|104
|1258.6779
|1296/625
| colspan="2" |56/27
|52/25
|-
|105
|1270.7806
| colspan="2" |25/12
| colspan="2" |44/21
|-
|106
|1282.8833
|512/243
| colspan="3" |21/10
|-
|107
|1294.98595
| colspan="2" |135/64
|162/77
|104/49
|-
|108
|1307.0886
| colspan="4" |32/15
|-
|109
|1319.1913
|2187/1024
| colspan="3" |15/7
|-
|110
|1331.294
| colspan="3" |54/25
|13/6
|-
|111
|1343.3966
|625/288
| colspan="3" |98/45
|-
|112
|1355.4993
|1600/729
|35/16
| colspan="2" |11/5
|-
|113
|1367.602
|1125/512
| colspan="3" |108/49
|-
|114
|1379.7047
| colspan="4" |20/9
|-
|115
|1391.8073
|8192/3645
| colspan="3" |56/25
|-
|116
|1403.91
| colspan="4" |9/4
|}


== See also ==
== See also ==
* [[99edo]]
* [[99edo]] – relative edo
* [[157edt]]
* [[157edt]] – relative edt
 
* [[256ed6]] – relative ed6
[[Category:Edf]]
[[Category:Edonoi]]
[[Category:99edo]]
Retrieved from "https://en.xen.wiki/w/58edf"