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{{Infobox ET}}
{{Infobox ET}}
{{ED intro}} It corresponds to 18.8046[[edo]], is is similar to [[19edo]], and nearly identical to [[Carlos Beta]].
{{ED intro}}


While the fifth is just, the fourth is very sharp and significantly less accurate than in 19edo, being about four cents flat of that of [[7edo]].
== Theory ==
11edf corresponds to 18.8046…[[edo]]. It is similar to [[19edo]], and nearly identical to [[Carlos Beta]]. Unlike 19edo, which is [[consistent]] to the [[integer limit|10-integer-limit]], 11edf is only consistent to the 7-integer-limit.  


11edf represents the upper bound of the [[phoenix]] tuning range. 11edf benefits from all the desirable properties of phoenix tuning systems.
While the fifth is just, the fourth is very sharp and significantly less accurate than in 19edo. At 510.51{{c}}, it is 12.47{{c}} sharper than just and 3.7{{c}} flat of that of [[7edo]].


== Harmonics ==
11edf represents the upper bound of the [[phoenix]] tuning range. It benefits from all the desirable properties of phoenix tuning systems.
{{Harmonics in equal|11|3|2|prec=2|columns=15}}
 
=== Harmonics ===
{{Harmonics in equal|11|3|2|intervals=integer|columns=11}}
{{Harmonics in equal|11|3|2|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 11edf (continued)}}
 
=== Subsets and supersets ===
11edf is the fifth [[prime equal division|prime edf]], past [[7edf]] and before [[13edf]]. It does not contain any nontrivial subset edfs.


== Intervals ==
== Intervals ==
{| class="wikitable"
{| class="wikitable center-1 right-2"
|-
|-
! Degree
! #
! Cent value
! Cents
! Corresponding<br />JI intervals
! Approximate ratios
! Comments
|-
|-
| colspan="2" | 0
| 0
| '''exact [[1/1]]'''
| 0.0
|
| [[1/1]]
|-
|-
| 1
| 1
| 63.8141
| 63.8
| ([[28/27]]), ([[27/26]])
| [[21/20]], [[25/24]], [[27/26]], [[28/27]]
|
|-
|-
| 2
| 2
| 127.6282
| 127.6
| [[14/13]]
| [[13/12]], [[14/13]], [[15/14]], [[16/15]]
|
|-
|-
| 3
| 3
| 191.4423
| 191.4
|
| [[9/8]], [[10/9]]
|  
|-
|-
| 4
| 4
| 255.2564
| 255.3
|
| [[7/6]], ''[[8/7]]''
|  
|-
|-
| 5
| 5
| 319.07045
| 319.1
| 6/5
| [[6/5]]
|
|-
|-
| 6
| 6
| 382.8845
| 382.9
| 5/4
| [[5/4]]
|
|-
|-
| 7
| 7
| 446.6986
| 446.7
|
| [[9/7]]
|  
|-
|-
| 8
| 8
| 510.5127
| 510.5
|
| [[4/3]]
|  
|-
|-
| 9
| 9
| 574.3268
| 574.3
| 39/28
| [[7/5]]
|
|-
|-
| 10
| 10
| 638.1409
| 638.1
| ([[13/9]])
| [[13/9]]
|
|-
|-
| 11
| 11
| 701.955
| 702.0
| '''exact [[3/2]]'''
| [[3/2]]
| just perfect fifth
|-
|-
| 12
| 12
| 765.7691
| 765.8
| 14/9, 81/52
| [[14/9]]
|
|-
|-
| 13
| 13
| 828.5732
| 828.6
| 21/13
| [[8/5]], [[13/8]], [[21/13]]
|
|-
|-
| 14
| 14
| 893.3973
| 893.4
|
| [[5/3]]
|  
|-
|-
| 15
| 15
| 956.2114
| 956.2
|
| [[7/4]]
|  
|-
|-
| 16
| 16
| 1020.0255
| 1020.0
| 9/5
| [[9/5]]
|
|-
|-
| 17
| 17
| 1084.8395
| 1084.8
| 15/8
| [[15/8]]
|
|-
|-
| 18
| 18
| 1148.6536
| 1148.7
|
| [[27/14]], [[35/18]]
|  
|-
|-
| 19
| 19
| 1211.4677
| 1211.5
|
| [[2/1]]
|  
|-
|-
| 20
| 20
| 1276.2816
| 1276.3
| 117/56
| [[21/10]], [[25/12]], [[27/13]]
|
|-
|-
| 21
| 21
| 1340.0959
| 1340.1
| 13/6
| [[13/6]]
|
|-
|-
| 22
| 22
| 1403.91
| 1403.9
| '''exact''' 9/4
| [[9/4]]
|
|}
|}


{{todo|expand}}
== Music ==
; [[Francium]]
* "McGarfyGarf" from ''Microtonal Six-Dimensional Cats'' (2025) – [https://open.spotify.com/track/2iaicUkq6EcjcGM8RioFZj Spotify] | [https://francium223.bandcamp.com/track/mcgarfygarf Bandcamp] | [https://www.youtube.com/watch?v=sI8X6PNOiXE YouTube]
 
== See also ==
* [[19edo]] – relative edo
* [[30edt]] – relative edt
* [[49ed6]] – relative ed6
* [[53ed7]] – relative ed7
* [[68ed12]] – relative ed12
* [[93ed30]] – relative ed30
* [[Alpha, beta, and gamma family of equal divisions]]
Retrieved from "https://en.xen.wiki/w/11edf"