Xenharmonic Wiki

34edf: Difference between revisions

VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,024 edits
Created page with "'''Division of the just perfect fifth into 34 equal parts''' (34EDF) is related to 58 edo, but with the 3/2 rather than the 2/1 being just. The octave is abo..."
Tags: Mobile edit Mobile web edit
 
→Theory: +subsets and supersets
 
(10 intermediate revisions by 4 users not shown)
Line 1: Line 1:
'''[[EDF|Division of the just perfect fifth]] into 34 equal parts''' (34EDF) is related to [[58edo|58 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 2.5474 cents compressed and the step size is about 20.6457 cents (corresponding to 58.1234 edo). The patent val has a generally flat tendency for harmonics up to 16, with the exception for 5. Unlike 58edo, it is only consistent up to the [[15-odd-limit|15-integer-limit]], with discrepancy for the 16th harmonic (four octaves).
{{Infobox ET}}
{{ED intro}}


Lookalikes: [[58edo]], [[92edt]]
== Theory ==
34edf corresponds to 58.1234…edo. It is related to [[58edo]], but with the [[3/2]] rather than the [[2/1]] being [[just]]. The octave is [[stretched and compressed tuning|compressed]] by about 2.5474 [[cents]].


[[Category:Edf]]
The [[patent val]] has a generally flat tendency for [[harmonic]]s up to [[16/1|16]] (four octaves), with the exception for [[5/1|5]]. Unlike 58edo, it is only consistent up to the [[integer limit|15-integer-limit]], with discrepancy for the 16th harmonic.
[[Category:Edonoi]]
 
=== Harmonics ===
{{Harmonics in equal|34|3|2|intervals=integer}}
{{Harmonics in equal|34|3|2|intervals=integer|columns=12|start=12|collapsed=1|title=Approximation of harmonics in 34edf (continued)}}
 
=== Subsets and supersets ===
Since 34 factors into primes as {{nowrap| 2 × 17 }}, 34edf contains [[2edf]] and [[17edf]] as subset edfs.
 
== Intervals ==
{| class="wikitable center-1 right-2"
|-
! #
! Cents
! Approximate ratios
|-
| 0
| 0.0
| 1/1
|-
| 1
| 20.6
| ''56/55'', 64/63, 81/80, 91/90, 105/104
|-
| 2
| 41.3
| 36/35, 40/39, 45/44, 49/48, 50/49, 55/54
|-
| 3
| 61.9
| 26/25, 27/26, 28/27, 33/32
|-
| 4
| 82.6
| 21/20, 22/21, ''25/24''
|-
| 5
| 103.2
| 16/15, 17/16, 18/17
|-
| 6
| 123.9
| 14/13, 15/14
|-
| 7·
| 144.5
| 12/11, 13/12
|-
| 8
| 165.2
| 11/10
|-
| 9
| 185.8
| 10/9
|-
| 10
| 206.5
| 9/8
|-
| 11
| 227.1
| 8/7
|-
| 12·
| 248.7
| 15/13
|-
| 13
| 268.4
| 7/6
|-
| 14
| 289.0
| 13/11, 20/17
|-
| 15
| 309.7
| 6/5
|-
| 16
| 330.3
| 17/14, 40/33
|-
| 17·
| 351.0
| 11/9, 16/13
|-
| 18
| 371.6
| 21/17, 26/21
|-
| 19
| 392.3
| 5/4
|-
| 20
| 412.9
| 14/11
|-
| 21
| 433.6
| 9/7
|-
| 22·
| 455.2
| 13/10, 17/13, 22/17
|-
| 23
| 474.9
| 21/16
|-
| 24
| 495.5
| 4/3
|-
| 25
| 516.1
| 27/20
|-
| 26
| 536.8
| 15/11
|-
| 27
| 557.4
| 11/8, 18/13
|-
| 28
| 578.1
| 7/5
|-
| 29
| 598.7
| 17/12, 24/17
|-
| 30
| 619.4
| 10/7
|-
| 31
| 640.0
| 13/9, 16/11
|-
| 32
| 660.7
| 22/15
|-
| 33
| 681.3
| 40/27
|-
| 34
| 702.0
| 3/2
|-
| 35
| 722.6
| 32/21
|-
| 36
| 743.2
| 17/11, 20/13, 26/17
|-
| 37
| 763.9
| 14/9
|-
| 38
| 784.5
| 11/7
|-
| 39
| 805.2
| 8/5
|-
| 40
| 825.8
| 21/13, 34/21
|-
| 41
| 846.5
| 13/8, 18/11
|-
| 42
| 867.1
| 28/17, 33/20
|-
| 43
| 887.8
| 5/3
|-
| 44
| 908.4
| 17/10, 22/13
|-
| 45
| 929.1
| 12/7
|-
| 46
| 949.7
| 26/15
|-
| 47
| 970.3
| 7/4
|-
| 48
| 991.0
| 16/9
|-
| 49
| 1011.7
| 9/5
|-
| 50
| 1032.3
| 20/11
|-
| 51
| 1052.9
| 11/6
|-
| 52
| 1073.6
| 13/7
|-
| 53
| 1094.2
| 15/8, 17/9
|-
| 54
| 1114.9
| 21/11
|-
| 55
| 1135.5
| 25/13, 27/14
|-
| 56
| 1156.2
| 35/18, 39/20, 49/25
|-
| 57
| 1176.8
| 55/28, 63/32
|-
| 58
| 1197.5
| 2/1
|-
| 59
| 1218.1
| 81/40, 91/45, 105/52
|-
| 60
| 1238.7
| 45/22, 49/24, 55/27
|-
| 61
| 1259.4
| 27/13, 33/16
|-
| 62
| 1280.0
| 21/10, 25/12
|-
| 63
| 1300.7
| 17/8
|-
| 64
| 1321.3
| 15/7
|-
| 65
| 1342.0
| 13/6
|-
| 66
| 1362.6
| 11/5
|-
| 67
| 1383.4
| 20/9
|-
| 68
| 1403.9
| 9/4
|}
 
== See also ==
* [[58edo]] – relative edo
* [[92edt]] – relative edt
* [[150ed6]] – relative ed6
* [[163ed7]] – relative ed7
Retrieved from "https://en.xen.wiki/w/34edf"