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'''13EDF''' is the [[EDF|equal division of the just perfect fifth]] into 13 parts of 53.9965 [[cent|cents]] each, corresponding to 22.2236 [[edo]]. It is nearly identical to every ninth step of [[200edo]].
{{Infobox ET}}
{{ED intro}}


It is the smallest representation of [[25/24]] you can get from an equal division of the fifth.
== Theory ==
13edf corresponds to 22.2236[[edo]]. It is nearly identical to every ninth step of [[200edo]], but not quite similar to [[22edo]]; the octave is compressed by 12.076{{c}}, a deviation that is small but significant enough to create a discrepancy for the [[7/1|7th]] and [[11/1|11th]] harmonics.


==Intervals==
== Harmonics ==
{| class="wikitable"
{{Harmonics in equal|13|3|2|intervals=prime|columns=8}}
{{Harmonics in equal|13|3|2|start=9|intervals=prime|columns=8}}
 
== Intervals ==
{| class="wikitable mw-collapsible"
|+ style="font-size: 105%;" | Intervals of 13edf
|-
|-
! | degree
! Degree
! | cents value
! Cents
! | corresponding <br>JI intervals
! Corresponding<br />JI intervals
! | comments
! Comments
|-
|-
! colspan="2" | 0
! colspan="2" | 0
| | '''exact [[1/1]]'''
| '''exact [[1/1]]'''
| |  
|  
|-
|-
| | 1
| 1
| | 53.9965
| 53.9965
| | 33/32
| 33/32
| | pseudo-[[25/24]]
| pseudo-[[25/24]]
|-
|-
| | 2
| 2
| | 107.9931
| 107.9931
| | [[17/16]], 117/110, [[16/15]]
| [[17/16]], 117/110, [[16/15]]
| |  
|  
|-
|-
| | 3
| 3
| | 161.9896
| 161.9896
| | [[11/10]]
| [[11/10]]
| |  
|  
|-
|-
| | 4
| 4
| | 215.9862
| 215.9862
| | [[17/15]]
| [[17/15]]
| |  
|  
|-
|-
| | 5
| 5
| | 269.9827
| 269.9827
| | [[7/6]]
| [[7/6]]
| |  
|  
|-
|-
| | 6
| 6
| | 323.9792
| 323.9792
| | [[77/64]]
| [[77/64]]
| | pseudo-[[6/5]]
| pseudo-[[6/5]]
|-
|-
| | 7
| 7
| | 377.9758
| 377.9758
| | 56/45
| 56/45
| | pseudo-[[5/4]]
| pseudo-[[5/4]]
|-
|-
| | 8
| 8
| | 431.9723
| 431.9723
| | [[9/7]]
| [[9/7]]
| |  
|  
|-
|-
| | 9
| 9
| | 485.9688
| 485.9688
| | 45/34
| 45/34
| | pseudo-[[4/3]]
| pseudo-[[4/3]]
|-
|-
| | 10
| 10
| | 539.9654
| 539.9654
| | [[15/11]]
| [[15/11]]
| |  
|  
|-
|-
| | 11
| 11
| | 593.9619
| 593.9619
| | 55/39, [[24/17]]
| 55/39, [[24/17]]
| |  
|  
|-
|-
| | 12
| 12
| | 647.9585
| 647.9585
| | [[16/11]]
| [[16/11]]
| |  
|  
|-
|-
| | 13
| 13
| | 701.9550
| 701.9550
| | '''exact [[3/2]]'''
| '''exact [[3/2]]'''
| | just perfect fifth
| just perfect fifth
|-
|-
| | 14
| 14
| | 755.9515
| 755.9515
| | 99/64
| 99/64
| |  
|  
|-
|-
| | 15
| 15
| | 809.9481
| 809.9481
| | 51/32, [[8/5]]
| 51/32, [[8/5]]
| |  
|  
|-
|-
| | 16
| 16
| | 863.9446
| 863.9446
| | 33/20
| 33/20
| |  
|  
|-
|-
| | 17
| 17
| | 917.9412
| 917.9412
| | [[17/10]]
| [[17/10]]
| |  
|  
|-
|-
| | 18
| 18
| | 971.9377
| 971.9377
| | [[7/4]]
| [[7/4]]
| |  
|  
|-
|-
| | 19
| 19
| | 1025.9342
| 1025.9342
| | [[29/16]]
| [[29/16]]
| | pseudo-[[9/5]]
| pseudo-[[9/5]]
|-
|-
| | 20
| 20
| | 1079.9308
| 1079.9308
| | [[28/15]]
| [[28/15]]
| | pseudo-[[15/8]]
| pseudo-[[15/8]]
|-
|-
| | 21
| 21
| | 1133.9273
| 1133.9273
| | 52/27, [[27/14]]
| 52/27, [[27/14]]
| |  
|  
|-
|-
| | 22
| 22
| | 1187.9238
| 1187.9238
| | 135/68
| 135/68
| | pseudo-[[octave]]
| pseudo-[[octave]]
|-
|-
| | 23
| 23
| | 1241.9204
| 1241.9204
| | [[45/44|45/22]]
| [[45/44|45/22]]
| |  
|  
|-
|-
| | 24
| 24
| | 1295.9169
| 1295.9169
| | [[19/18|19/9]], [[18/17|36/17]]
| [[19/18|19/9]], [[18/17|36/17]]
| |  
|  
|-
|-
| | 25
| 25
| | 1349.9135
| 1349.9135
| | [[12/11|24/11]]
| [[12/11|24/11]]
| |  
|  
|-
|-
| | 26
| 26
| | 1403.9100
| 1403.9100
| | '''exact [[9/4]]'''
| '''exact [[9/4]]'''
| | pythagorean major ninth
| pythagorean major ninth
|}
|}


[[Category:Edf]]
{{stub}}
[[Category:Edonoi]]
 
[[Category:22edo]]
Retrieved from "https://en.xen.wiki/w/13edf"