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{{Infobox ET}}
{{Infobox ET}}
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'''11EDF''' is the [[EDF|equal division of the just perfect fifth]] into 11 parts of 63.8141 [[cent|cents]] each, corresponding to 18.8046 [[edo]] (similar to every fifth step of [[94edo]]).
== 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.  


==Intervals==
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]].
{| class="wikitable"
 
11edf represents the upper bound of the [[phoenix]] tuning range. It benefits from all the desirable properties of phoenix tuning systems.
 
=== 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 ==
{| class="wikitable center-1 right-2"
|-
|-
! | degree
! #
! | cents 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
| | 319.0705
| 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]]
| |
|}
|}


[[Category:edf]]
== Music ==
[[Category:Todo:expand]]
; [[Francium]]
[[Category:Stub]]
* "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
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