Xenharmonic Wiki

35edf: Difference between revisions

VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,024 edits
Created page with "'''Division of the just perfect fifth into 35 equal parts''' (35EDF) is related to 60 edo, but with the 3/2 rather than the 2/1 being just. The octave is abo..."
Tags: Mobile edit Mobile web edit
 
m →Intervals: cleanup
 
(8 intermediate revisions by 5 users not shown)
Line 1: Line 1:
'''[[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]].


[[Category:Edf]]
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).
[[Category:Edonoi]]
 
=== 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 ==
{| 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
|
|
|-
| 6
| 120.3
| 16/15
|
|-
| 7
| 140.4
|
|
|-
| 8
| 160.4
|
| 12/11, 11/10
|-
| 9
| 180.5
| 10/9
|
|-
| 10
| 200.6
| 9/8
|
|-
| 11
| 220.6
|
|
|-
| 12
| 240.7
| 15/13
| 8/7
|-
| 13
| 260.8
|
| 7/6
|-
| 14
| 280.8
|
|
|-
| 15
| 300.8
|
|
|-
| 16
| 320.9
| 6/5
|
|-
| 17
| 340.9
|
| 11/9
|-
| 18
| 361.0
| 16/13
|
|-
| 19
| 381.1
| 5/4
|
|-
| 20
| 401.1
|
|
|-
| 21
| 421.2
|
| 14/11
|-
| 22
| 441.2
|
| 9/7
|-
| 23
| 461.3
| 13/10
|
|-
| 24
| 481.3
|
|
|-
| 25
| 501.4
| 4/3
|
|-
| 26
| 521.5
|
|
|-
| 27
| 541.5
|
| 11/8, 15/11
|-
| 28
| 561.6
| 18/13
|
|-
| 29
| 581.6
|
| 7/5
|-
| 30
| 601.7
|
|
|-
| 31
| 621.7
|
| 10/7
|-
| 32
| 641.8
| 13/9
|
|-
| 33
| 661.8
|
| 16/11, 22/15
|-
| 34
| 681.9
|
|
|-
| 35
| 702.0
| 3/2
|
|-
| 36
| 722.0
|
|
|-
| 37
| 742.1
| 20/13
|
|-
| 38
| 762.1
|
| 14/9
|-
| 39
| 782.2
|
| 11/7
|-
| 40
| 802.2
|
|
|-
| 41
| 822.3
| 8/5
|
|-
| 42
| 842.3
| 13/8
|
|-
| 43
| 862.4
|
| 18/11
|-
| 44
| 882.5
| 5/3
|
|-
| 45
| 902.5
|
|
|-
| 46
| 922.6
|
|
|-
| 47
| 942.6
|
| 12/7
|-
| 48
| 962.7
| 26/15
| 7/4
|-
| 49
| 982.7
|
|
|-
| 50
| 1002.8
| 16/9
|
|-
| 51
| 1022.8
| 9/5
|
|-
| 52
| 1042.9
|
| 11/6, 20/11
|-
| 53
| 1063.0
|
|
|-
| 54
| 1083.0
| 15/8
|
|-
| 55
| 1103.1
|
|
|-
| 56
| 1123.1
|
|
|-
| 57
| 1143.2
|
|
|-
| 58
| 1163.2
|
|
|-
| 59
| 1183.3
|
|
|-
| 60
| 1203.4
|
|
|-
| 61
| 1223.4
| 81/40
|
|-
| 62
| 1243.5
|
|
|-
| 63
| 1263.5
| 56/27, 27/13
|
|-
| 64
| 1283.6
|
| 21/10
|-
| 65
| 1303.6
|
|
|-
| 66
| 1323.7
| 32/15
|
|-
| 67
| 1343.7
|
|
|-
| 68
| 1363.8
|
| 24/11, 11/5
|-
| 69
| 1383.9
| 20/9
|
|-
| 70
| 1403.9
| 9/4
|
|}
 
== See also ==
* [[60edo]] – relative edo
* [[95edt]] – relative edt
* [[139ed5]] – relative ed5
* [[155ed6]] – relative ed6
Retrieved from "https://en.xen.wiki/w/35edf"