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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]], and can be used as a temperament of the [[Half-prime subgroup|3/2.5/4.7/8.11/8 subgroup]]. Carlos Alpha 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
! Approximate ratios
! [[1L 3s (fifth-equivalent)|Neptunian]] notation<br>using 7\9edf
|-
| 0
| 0.0
| [[1/1]]
| C
|-
| 1
| 78.0
| [[21/20]], [[22/21]], [[25/24]]
| C#
|-
| 2
| 156.0
| [[11/10]], [[12/11]]
| Db
|-
| 3
| 234.0
| [[8/7]]
| D
|-
|-
!#
| 4
!Cents
| 312.0
!Approximate ratios
| [[6/5]]
![[1L 3s (fifth-equivalent)|Neptunian]] notation
| D#, Eb
|-
|-
|0
| 5
|0.0
| 390.0
|[[1/1]]
| [[5/4]]
|C
| E
|-
|-
|1
| 6
|78.0
| 468.0
|[[25/24]], [[21/20]]
| [[21/16]]
|C#
| E#, Fb
|-
|-
|2
| 7
|156.0
| 546.0
|[[12/11]], [[11/10]]
| [[11/8]], [[15/11]]
|Db
| F
|-
|-
| 8
| 624.0
| [[10/7]], [[36/25]]
| F#, Cb
|-
| 9
| 701.9
| [[3/2]]
| C
|}
== Scales ==
{| 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
|3
|234.0
|234.0
|[[8/7]]
|[[8/7]]
|D
|''[[Budjarn Lambeth]] (2023)''
|-
|-
|4
|Pylon
|312.0
|6 3
|[[6/5]]
|9
|D#, Eb
|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)''
|-
|-
|5
|Swan
|390.0
|4 5 4 5 4 5 4
|[[5/4]]
|31
|E
|2417.8
|[[4/1]]
|''Budjarn Lambeth (2023)''
|-
|-
|6
|Livewire
|468.0
|1 8 1 8 1 8 1 8 1 8 1
|[[21/16]]
|46
|E#, Fb
|3587.8
|[[8/1]]
|''Budjarn Lambeth (2023)''
|-
|-
|7
|Purgatory
|546.0
|8 1 8 1 8 1 8 1 8 1 8 1 8
|[[15/11], [[1/8]]
|62
|F
|4835.7
|[[16/1]]
|''Budjarn Lambeth (2023)''
|-
|-
|8
|Cloudscape
|624.0
|5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5
|[[10/7]], [[36/25]]
|72
|F#, Cb
|5615.6
|[[128/5]]
|''Budjarn Lambeth (2023)''
|-
|-
|9
|Corrugated
|702.0
|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
|[[3/2]]
|135
|C
|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.


[[Category:Edf]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/9edf"