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'''[[Ed7|Division of the 7th harmonic]] into 53 equal parts''' (53ed7) is related to [[19edo]] and [[30edt]], but with the 7/1 rather than the 2/1 being just. The octave is about 7.6923 cents stretched and the step size is about 63.5628 cents. The patent val has a generally sharp tendency for harmonics up to 16, with exception for 11th harmonic.
{{Infobox ET}}
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[[Category:Ed7]]
== Theory ==
[[Category:Edonoi]]
53ed7 is related to [[19edo]], [[30edt]], and [[Carlos Beta]], but with the 7/1 rather than the [[2/1]] being just. The octave is about 7.6923 cents stretched. Like 19edo, 53ed7 is [[consistent]] to the [[integer limit|10-integer-limit]], but the [[patent val]] has a generally sharp tendency for [[harmonic]]s up to 16, with exception for [[11/1|11th harmonic]].
 
=== Harmonics ===
{{Harmonics in equal|53|7|1|intervals=integer|columns=11}}
{{Harmonics in equal|53|7|1|intervals=integer|columns=11|start=12|collapsed=1|title=Approximation of harmonics in 53ed7 (continued)}}
 
=== Subsets and supersets ===
53ed7 is the 16th [[prime equal division|prime ed7]]. It does not contain any nontrivial subset ed7's.
 
== Intervals ==
{| class="wikitable center-1 right-2 mw-collapsible"
|-
! #
! Cents
! Approximate ratios
|-
| 0
| 0.0
| [[1/1]]
|-
| 1
| 63.6
| [[21/20]], [[25/24]], [[27/26]], [[28/27]]
|-
| 2
| 127.1
| [[13/12]], [[14/13]], [[15/14]], [[16/15]]
|-
| 3
| 190.7
| [[9/8]], [[10/9]]
|-
| 4
| 254.3
| [[7/6]], [[8/7]]
|-
| 5
| 317.8
| [[6/5]]
|-
| 6
| 381.4
| [[5/4]]
|-
| 7
| 444.9
| [[9/7]]
|-
| 8
| 508.5
| [[4/3]]
|-
| 9
| 572.1
| [[7/5]], [[18/13]]
|-
| 10
| 635.6
| [[10/7]], [[13/9]]
|-
| 11
| 699.2
| [[3/2]]
|-
| 12
| 762.8
| [[14/9]]
|-
| 13
| 826.3
| [[8/5]], [[13/8]]
|-
| 14
| 889.9
| [[5/3]]
|-
| 15
| 953.4
| [[7/4]], [[12/7]]
|-
| 16
| 1017.0
| [[9/5]]
|-
| 17
| 1080.6
| [[15/8]]
|-
| 18
| 1144.1
| [[27/14]], [[35/18]]
|-
| 19
| 1207.7
| [[2/1]]
|-
| 20
| 1271.3
| [[21/10]], [[25/12]]
|-
| 21
| 1334.8
| [[13/6]]
|-
| 22
| 1398.4
| [[9/4]]
|-
| 23
| 1461.9
| [[7/3]]
|-
| 24
| 1525.5
| [[12/5]]
|-
| 25
| 1589.1
| [[5/2]]
|-
| 26
| 1652.6
| [[13/5]]
|-
| 27
| 1716.2
| [[8/3]]
|-
| 28
| 1779.8
| [[14/5]]
|-
| 29
| 1843.3
| [[20/7]], [[26/9]]
|-
| 30
| 1906.9
| [[3/1]]
|-
| 31
| 1970.4
| [[25/8]], [[28/9]]
|-
| 32
| 2034.0
| [[13/4]]
|-
| 33
| 2097.6
| [[10/3]]
|-
| 34
| 2161.1
| [[7/2]]
|-
| 35
| 2224.7
| [[18/5]]
|-
| 36
| 2288.3
| [[15/4]]
|-
| 37
| 2351.8
| [[35/9]]
|-
| 38
| 2415.4
| [[4/1]]
|-
| 39
| 2478.9
| [[21/5]], [[25/6]]
|-
| 40
| 2542.5
| [[13/3]]
|-
| 41
| 2606.1
| [[9/2]]
|-
| 42
| 2669.6
| [[14/3]]
|-
| 43
| 2733.2
| [[24/5]]
|-
| 44
| 2796.8
| [[5/1]]
|-
| 45
| 2860.3
| [[21/4]], [[26/5]]
|-
| 46
| 2923.9
| [[16/3]]
|-
| 47
| 2987.4
| [[28/5]]
|-
| 48
| 3051.0
| [[35/6]]
|-
| 49
| 3114.6
| [[6/1]]
|-
| 50
| 3178.1
| [[50/8]], [[56/9]]
|-
| 51
| 3241.7
| [[13/2]]
|-
| 52
| 3305.3
| [[27/4]]
|-
| 53
| 3368.8
| [[7/1]]
|}
 
== See also ==
* [[11edf]] – relative edf
* [[19edo]] – relative edo
* [[30edt]] – relative edt
* [[49ed6]] – relative ed6
* [[68ed12]] – relative ed12
* [[93ed30]] – relative ed30
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