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'''[[EDF|Division of the just perfect fifth]] into 35 equal parts''' (35EDF) is related to [[60edo|60 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 20.0559 cents (corresponding to 59.8329 [[edo]], practically identical to every sixth step of [[359edo]]). The patent val has a generally sharp tendency for harmonics up to 18, with the exception for 13. Unlike 60edo, 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: [[60edo]], [[95edt]]
== Theory ==
35edf corresponds to 59.8329…[[edo]] and is practically identical to every sixth step of [[359edo]]. It is related to [[60edo]], but with the [[3/2|perfect fifth]] rather than the [[2/1|octave]] being [[just]]. The octave is [[Stretched and compressed tuning|stretched]] by about 3.35 [[cents]].
 
The [[patent val]] has a generally sharp tendency for [[prime harmonic]]s up to 17, with the exception for [[13/1|13]]. Unlike 60edo, which is [[consistent]] to the [[integer limit|10-integer-limit]], 35edf is only consistent up to the 7-integer-limit, with discrepancy for the 8th harmonic (three octaves).
 
=== Harmonics ===
{{Harmonics in equal|35|3|2|intervals=integer|columns=11}}
{{Harmonics in equal|35|3|2|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 35edf (continued)}}
 
=== Subsets and supersets ===
Since 35 factors into primes as {{nowrap| 5 × 7 }}, 35edf has subset edfs [[5edf]] and [[7edf]].


== Intervals ==
== Intervals ==
{| class="wikitable"
{| class="wikitable center-1 right-2 mw-collapsible"
|+ Intervals in 35edf
|-
! #
! Cents
! Approximate ratios<br>in the 2.3.5.13 subgroup
! Additional ratios<br>of 7 and 11 (assuming flat values for primes)
|-
| 0
| 0.0
|
|
|-
| 1
| 20.1
| 81/80
|
|-
| 2
| 40.1
|
|
|-
| 3
| 60.2
| 28/27, 27/26
|
|-
| 4
| 80.2
|
| 21/20
|-
| 5
| 100.3
|
|
|-
|-
| |degrees of 60edo
| 6
| |cents value
| 120.3
| |approximate ratios in the 2.3.5.13 subgroup
| 16/15
| |additional ratios of 7 and 11 (assuming flat values for primes)
|  
|-
|-
| |0
| 7
| |0
| 140.4
| |
|  
| |
|  
|-
|-
| |1
| 8
| |20.0559
| 160.4
| |
|  
| |
| 12/11, 11/10
|-
|-
| |2
| 9
| |40.1117
| 180.5
| |
| 10/9
| |
|  
|-
|-
| |3
| 10
| |60.1676
| 200.6
| |
| 9/8
| |
|  
|-
|-
| |4
| 11
| |80.2234
| 220.6
| |
|  
| |
|  
|-
|-
| |5
| 12
| |100.2793
| 240.7
| |
| 15/13
| |
| 8/7
|-
|-
| |6
| 13
| |120.3351
| 260.8
| |16/15
|  
| |
| 7/6
|-
|-
| |7
| 14
| |140.391
| 280.8
| |
|  
| |
|  
|-
|-
| |8
| 15
| |160.4469
| 300.8
| |
|  
| |12/11, 11/10
|  
|-
|-
| |9
| 16
| |180.5027
| 320.9
| |10/9
| 6/5
| |
|  
|-
|-
| |10
| 17
| |200.5586
| 340.9
| |9/8
|  
| |
| 11/9
|-
|-
| |11
| 18
| |220.6144
| 361.0
| |
| 16/13
| |
|  
|-
|-
| |12
| 19
| |240.6703
| 381.1
| |15/13
| 5/4
| |8/7
|  
|-
|-
| |13
| 20
| |260.7621
| 401.1
| |
|  
| |7/6
|  
|-
|-
| |14
| 21
| |280.782
| 421.2
| |
|  
| |
| 14/11
|-
|-
| |15
| 22
| |300.8379
| 441.2
| |
|  
| |
| 9/7
|-
|-
| |16
| 23
| |320.8937
| 461.3
| |6/5
| 13/10
| |
|  
|-
|-
| |17
| 24
| |340.9496
| 481.3
| |
|  
| |11/9
|  
|-
|-
| |18
| 25
| |361.0054
| 501.4
| |16/13
| 4/3
| |
|  
|-
|-
| |19
| 26
| |381.0613
| 521.5
| |5/4
|  
| |
|  
|-
|-
| |20
| 27
| |401.1171
| 541.5
| |
|  
| |
| 11/8, 15/11
|-
|-
| |21
| 28
| |421.173
| 561.6
| |
| 18/13
| |14/11
|  
|-
|-
| |22
| 29
| |441.2289
| 581.6
| |
|  
| |9/7
| 7/5
|-
|-
| |23
| 30
| |461.2847
| 601.7
| |13/10
|  
| |
|  
|-
|-
| |24
| 31
| |481.3406
| 621.7
| |
|  
| |
| 10/7
|-
|-
| |25
| 32
| |501.3964
| 641.8
| |4/3
| 13/9
| |
|  
|-
|-
| |26
| 33
| |521.4523
| 661.8
| |
|  
| |
| 16/11, 22/15
|-
|-
| |27
| 34
| |541.5081
| 681.9
| |
|  
| |11/8, 15/11
|  
|-
|-
| |28
| 35
| |561.564
| 702.0
| |18/13
| 3/2
| |
|  
|-
|-
| |29
| 36
| |581.6199
| 722.0
| |
|  
| |7/5
|  
|-
|-
| |30
| 37
| |601.6757
| 742.1
| |
| 20/13
| |
|  
|-
|-
| |31
| 38
| |621.7315
| 762.1
| |
|  
| |10/7
| 14/9
|-
|-
| |32
| 39
| |641.7874
| 782.2
| |13/9
|  
| |
| 11/7
|-
|-
| |33
| 40
| |661.8433
| 802.2
| |
|  
| |16/11, 22/15
|  
|-
|-
| |34
| 41
| |681.8891
| 822.3
| |
| 8/5
| |
|  
|-
|-
| |35
| 42
| |701.955
| 842.3
| |3/2
| 13/8
| |
|  
|-
|-
| |36
| 43
| |722.0109
| 862.4
| |
|  
| |
| 18/11
|-
|-
| |37
| 44
| |742.0667
| 882.5
| |20/13
| 5/3
| |
|  
|-
|-
| |38
| 45
| |762.1226
| 902.5
| |
|  
| |14/9
|  
|-
|-
| |39
| 46
| |782.1784
| 922.6
| |
|  
| |11/7
|  
|-
|-
| |40
| 47
| |802.2343
| 942.6
| |
|  
| |
| 12/7
|-
|-
| |41
| 48
| |822.2901
| 962.7
| |8/5
| 26/15
| |
| 7/4
|-
|-
| |42
| 49
| |842.346
| 982.7
| |13/8
|  
| |
|  
|-
|-
| |43
| 50
| |862.4019
| 1002.8
| |
| 16/9
| |18/11
|  
|-
|-
| |44
| 51
| |882.4577
| 1022.8
| |5/3
| 9/5
| |
|  
|-
|-
| |45
| 52
| |902.5136
| 1042.9
| |
|  
| |
| 11/6, 20/11
|-
|-
| |46
| 53
| |922.5694
| 1063.0
| |
|  
| |
|  
|-
|-
| |47
| 54
| |942.6253
| 1083.0
| |
| 15/8
| |12/7
|  
|-
|-
| |48
| 55
| |962..6811
| 1103.1
| |26/15
|  
| |7/4
|  
|-
|-
| |49
| 56
| |982.737
| 1123.1
| |
|  
| |
|  
|-
|-
| |50
| 57
| |1002.7929
| 1143.2
| |16/9
|  
| |
|  
|-
|-
| |51
| 58
| |1022.8487
| 1163.2
| |9/5
|  
| |
|  
|-
|-
| |52
| 59
| |1042.9046
| 1183.3
| |
|  
| |11/6, 20/11
|  
|-
|-
| |53
| 60
| |1062.9604
| 1203.4
| |
|  
| |
|  
|-
|-
| |54
| 61
| |1083.0163
| 1223.4
| |15/8
| 81/40
| |
|  
|-
|-
| |55
| 62
| |1103.0721
| 1243.5
| |
|  
| |
|  
|-
|-
| |56
| 63
| |1123.128
| 1263.5
| |
| 56/27, 27/13
| |
|  
|-
|-
| |57
| 64
| |1143.1839
| 1283.6
| |
|  
| |
| 21/10
|-
|-
| |58
| 65
| |1163.2397
| 1303.6
| |
|  
| |
|  
|-
|-
| |59
| 66
| |1183.2956
| 1323.7
| |
| 32/15
| |
|  
|-
|-
| |60
| 67
| |1203.3514
| 1343.7
| |
|
| |
|  
|-
| 68
| 1363.8
|
| 24/11, 11/5
|-
| 69
| 1383.9
| 20/9
|
|-
| 70
| 1403.9
| 9/4
|  
|}
|}
[[Category:Edf]]
 
[[Category:Edonoi]]
== See also ==
* [[60edo]] – relative edo
* [[95edt]] – relative edt
* [[139ed5]] – relative ed5
* [[155ed6]] – relative ed6
Retrieved from "https://en.xen.wiki/w/35edf"