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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}}
{{ED intro}}


{| class="wikitable"
== Theory ==
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"
|-
|-
! | degree
! #
! | cents value
! Cents
! | corresponding <br>JI intervals
! Approximate ratios
! | comments
|-
|-
| | 0
| 0
| | 0.0000
| 0.0
| | '''exact [[1/1]]'''
| [[1/1]]
| |
|-
|-
| | 1
| 1
| | 63.5628
| 63.6
| |
| [[21/20]], [[25/24]], [[27/26]], [[28/27]]
| |
|-
|-
| | 2
| 2
| | 127.1255
| 127.1
| |
| [[13/12]], [[14/13]], [[15/14]], [[16/15]]
| |
|-
|-
| | 3
| 3
| | 190.6883
| 190.7
| |
| [[9/8]], [[10/9]]
| |
|-
|-
| | 4
| 4
| | 254.2510
| 254.3
| |
| [[7/6]], [[8/7]]
| |
|-
|-
| | 5
| 5
| | 317.8138
| 317.8
| |
| [[6/5]]
| |
|-
|-
| | 6
| 6
| | 381.3765
| 381.4
| |
| [[5/4]]
| |
|-
|-
| | 7
| 7
| | 444.9393
| 444.9
| |
| [[9/7]]
| |
|-
|-
| | 8
| 8
| | 508.5020
| 508.5
| |
| [[4/3]]
| |
|-
|-
| | 9
| 9
| | 572.0648
| 572.1
| |
| [[7/5]], [[18/13]]
| |
|-
|-
| | 10
| 10
| | 635.6275
| 635.6
| |
| [[10/7]], [[13/9]]
| |
|-
|-
| | 11
| 11
| | 699.1903
| 699.2
| |
| [[3/2]]
| |
|-
|-
| | 12
| 12
| | 762.7530
| 762.8
| |
| [[14/9]]
| |
|-
|-
| | 13
| 13
| | 826.3158
| 826.3
| |
| [[8/5]], [[13/8]]
| |
|-
|-
| | 14
| 14
| | 889.8785
| 889.9
| |
| [[5/3]]
| |
|-
|-
| | 15
| 15
| | 953.4413
| 953.4
| |
| [[7/4]], [[12/7]]
| |
|-
|-
| | 16
| 16
| | 1017.0040
| 1017.0
| |
| [[9/5]]
| |
|-
|-
| | 17
| 17
| | 1080.5668
| 1080.6
| |
| [[15/8]]
| |
|-
|-
| | 18
| 18
| | 1144.1296
| 1144.1
| |
| [[27/14]], [[35/18]]
| |
|-
|-
| | 19
| 19
| | 1207.6923
| 1207.7
| |
| [[2/1]]
| |
|-
|-
| | 20
| 20
| | 1271.2551
| 1271.3
| |
| [[21/10]], [[25/12]]
| |
|-
|-
| | 21
| 21
| | 1334.8178
| 1334.8
| |
| [[13/6]]
| |
|-
|-
| | 22
| 22
| | 1398.3806
| 1398.4
| |
| [[9/4]]
| |
|-
|-
| | 23
| 23
| | 1461.9433
| 1461.9
| |
| [[7/3]]
| |
|-
|-
| | 24
| 24
| | 1525.5061
| 1525.5
| |
| [[12/5]]
| |
|-
|-
| | 25
| 25
| | 1589.0688
| 1589.1
| |
| [[5/2]]
| |
|-
|-
| | 26
| 26
| | 1652.6316
| 1652.6
| |
| [[13/5]]
| |
|-
|-
| | 27
| 27
| | 1716.1943
| 1716.2
| |
| [[8/3]]
| |
|-
|-
| | 28
| 28
| | 1779.7571
| 1779.8
| |
| [[14/5]]
| |
|-
|-
| | 29
| 29
| | 1843.3198
| 1843.3
| |
| [[20/7]], [[26/9]]
| |
|-
|-
| | 30
| 30
| | 1906.8826
| 1906.9
| |
| [[3/1]]
| |
|-
|-
| | 31
| 31
| | 1970.4453
| 1970.4
| |
| [[25/8]], [[28/9]]
| |
|-
|-
| | 32
| 32
| | 2034.0081
| 2034.0
| |
| [[13/4]]
| |
|-
|-
| | 33
| 33
| | 2097.5708
| 2097.6
| |
| [[10/3]]
| |
|-
|-
| | 34
| 34
| | 2161.1336
| 2161.1
| |
| [[7/2]]
| |
|-
|-
| | 35
| 35
| | 2224.6964
| 2224.7
| |
| [[18/5]]
| |
|-
|-
| | 36
| 36
| | 2288.2591
| 2288.3
| |
| [[15/4]]
| |
|-
|-
| | 37
| 37
| | 2351.8219
| 2351.8
| |
| [[35/9]]
| |
|-
|-
| | 38
| 38
| | 2415.3846
| 2415.4
| |
| [[4/1]]
| |
|-
|-
| | 39
| 39
| | 2478.9474
| 2478.9
| |
| [[21/5]], [[25/6]]
| |
|-
|-
| | 40
| 40
| | 2542.5101
| 2542.5
| |
| [[13/3]]
| |
|-
|-
| | 41
| 41
| | 2606.0729
| 2606.1
| |
| [[9/2]]
| |
|-
|-
| | 42
| 42
| | 2669.6356
| 2669.6
| |
| [[14/3]]
| |
|-
|-
| | 43
| 43
| |
| 2733.2
| |
| [[24/5]]
| |
|-
|-
| | 44
| 44
| |
| 2796.8
| |
| [[5/1]]
| |
|-
|-
| | 45
| 45
| |
| 2860.3
| |
| [[21/4]], [[26/5]]
| |
|-
|-
| | 46
| 46
| |
| 2923.9
| |
| [[16/3]]
| |
|-
|-
| | 47
| 47
| |
| 2987.4
| |
| [[28/5]]
| |
|-
|-
| | 48
| 48
| |
| 3051.0
| |
| [[35/6]]
| |
|-
|-
| | 49
| 49
| |
| 3114.6
| |
| [[6/1]]
| |
|-
|-
| | 50
| 50
| |
| 3178.1
| |
| [[50/8]], [[56/9]]
| |
|-
|-
| | 51
| 51
| |
| 3241.7
| |
| [[13/2]]
| |
|-
|-
| | 52
| 52
| |
| 3305.3
| |
| [[27/4]]
| |
|-
|-
| | 53
| 53
| | 3368.8259
| 3368.8
| | '''exact [[7/1]]'''
| [[7/1]]
| | [[7/4|harmonic seventh]] plus two octaves
|}
|}


[[Category:Ed7]]
== See also ==
[[Category:Edonoi]]
* [[11edf]] – relative edf
* [[19edo]] – relative edo
* [[30edt]] – relative edt
* [[49ed6]] – relative ed6
* [[68ed12]] – relative ed12
* [[93ed30]] – relative ed30
Retrieved from "https://en.xen.wiki/w/53ed7"