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{{Infobox ET}}
{{Infobox ET}}
9edf is the equal division of the just perfect fifth into 9 parts of 78 cents each, corresponding to 22.2236 edo. It is nearly identical to [[Carlos Alpha]].
{{ED intro}}
 
== Theory ==
9edf corresponds to 15.385602edo. It is closely related to [[Carlos Alpha]] (though the Carlos Alpha generator is 0.03{{C}} narrower at 77.965{{C}}), and can be used as a temperament of the 3/2.5/4.8/7.11/8 subgroup. [[Valentine]] can be seen as 9edf with an independent dimension for 2.  
 
=== Harmonics ===
{{Harmonics in equal|9|3|2|columns=11}}
{{Harmonics in equal|9|3|2|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 9edf (continued)}}


== Intervals ==
== Intervals ==
{|class="wikitable"
{|class="wikitable center-1 right-2"
|-
|-
!#
! #
!Cents
! Cents
!Approximate ratios
! Approximate ratios
![[1L 3s (fifth-equivalent)|Neptunian]] notation
! [[1L 3s (fifth-equivalent)|Neptunian]] notation<br>using 7\9edf
|-
|-
|0
| 0
|0.0
| 0.0
|[[1/1]]
| [[1/1]]
|C
| C
|-
|-
|1
| 1
|78.0
| 78.0
|[[25/24]], [[21/20]]
| [[21/20]], [[22/21]], [[25/24]]
|C#
| C#
|-
|-
|2
| 2
|156.0
| 156.0
|[[12/11]], [[11/10]]
| [[11/10]], [[12/11]]
|Db
| Db
|-
|-
|3
| 3
|234.0
| 234.0
|[[8/7]]
| [[8/7]]
|D
| D
|-
|-
|4
| 4
|312.0
| 312.0
|[[6/5]]
| [[6/5]]
|D#, Eb
| D#, Eb
|-
|-
|5
| 5
|390.0
| 390.0
|[[5/4]]
| [[5/4]]
|E
| E
|-
|-
|6
| 6
|468.0
| 468.0
|[[21/16]]
| [[21/16]]
|E#, Fb
| E#, Fb
|-
|-
|7
| 7
|546.0
| 546.0
|[[15/11], [[1/8]]
| [[11/8]], [[15/11]]
|F
| F
|-
|-
|8
| 8
|624.0
| 624.0
|[[10/7]], [[36/25]]
| [[10/7]], [[36/25]]
|F#, Cb
| F#, Cb
|-
|-
|9
| 9
|702.0
| 702.0
|[[3/2]]
| [[3/2]]
|C
| C
|}
|}


[[Category:Edf]]
== Scales ==
{{Idiosyncratic terms}}
 
{| class="wikitable sortable"
|+
! rowspan="2" | Name
! rowspan="2" | Step pattern within 1 period
! colspan="3" | Interval of repetition
! rowspan="2" | First described by
|-
! (In 9edf steps)
! (In cents)
! (Nearby JI)
|-
| Molten [[slendro]]
| 3
| 3
| 234.0
| [[8/7]]
| ''[[Budjarn Lambeth]] (2023)''
|-
| Pylon
| 6 3
| 9
| 702.0
| [[3/2]]
| ''Budjarn Lambeth (2023)''
|-
| Quest
| 7 2
| 9
| 702.0
| [[3/2]]
| ''Budjarn Lambeth (2023)''
|-
| Snowcone
| 3 6
| 9
| 702.0
| [[3/2]]
| ''Budjarn Lambeth (2023)''
|-
| Molten [[pelog]]
| 2 2 5 2 5
| 16
| 1247.9
| [[33/16]]
| ''Budjarn Lambeth (2023)''
|-
| Swan
| 4 5 4 5 4 5 4
| 31
| 2417.8
| [[4/1]]
| ''Budjarn Lambeth (2023)''
|-
| Livewire
| 1 8 1 8 1 8 1 8 1 8 1
| 46
| 3587.8
| [[8/1]]
| ''Budjarn Lambeth (2023)''
|-
| Purgatory
| 8 1 8 1 8 1 8 1 8 1 8 1 8
| 62
| 4835.7
| [[16/1]]
| ''Budjarn Lambeth (2023)''
|-
| Cloudscape
| 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5
| 72
| 5615.6
| [[128/5]]
| ''Budjarn Lambeth (2023)''
|-
| Corrugated
| 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2 7 2
| 135
| 10529.3
| [[437/1]]
| ''Budjarn Lambeth (2023)''
|}
None of these scales are approximated from another tuning unless specified otherwise. For exact [[cents]] values see [[User:BudjarnLambeth/Longer versions of scales#9edf]].
 
== Music ==
See [[Carlos Alpha #Music]]. Many are tuned to exactly 9edf.
 
=== 21st century ===
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/U-XewMZiBC0 ''9ed(3/2) + 10ed(3/2) + 11ed(3/2) locked at 6:8:11 improv''] (2026, polymicrotonal, playing in 3 tuning systems simultaneously)
 
== See also ==
* [[Alpha, beta, and gamma family of equal divisions]]
 
[[Category:Listen]]
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