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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 15.391524edo. It is nearly identical to [[Carlos Alpha]].  
{{ED intro}}
{{todo|improve synopsis|text=Make it longer, describe more about the tuning.}}
 
== 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)}}


== Approximation of harmonics ==
{{Harmonics in equal
| steps = 9
| num = 3
| denom = 2
| columns = 18
}}
== Intervals ==
== Intervals ==
{|class="wikitable"
{|class="wikitable center-1 right-2"
|-
|-
!#
! #
!Cents
! Cents
!Approximate ratios
! Approximate ratios
![[1L 3s (fifth-equivalent)|Neptunian]] notation using 7\9edf
! [[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]], [[11/8]]
| [[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
|}
|}


== Scales within 9edf ==
== Scales ==
Livewire (this is the original/default tuning)
{{Idiosyncratic terms}}


* 77.995
{| class="wikitable sortable"
* 701.955
|+
* 779.950
! rowspan="2" | Name
* 1403.905
! rowspan="2" | Step pattern within 1 period
* 1481.905
! colspan="3" | Interval of repetition
* 2105.865
! rowspan="2" | First described by
* 2183.860
|-
* 2807.820
! (In 9edf steps)
* 2885.815
! (In cents)
* 3509.775
! (Nearby JI)
* 3587.770
|-
 
| Molten [[slendro]]
 
| 3
Corrugated (this is the original/default tuning)
| 3
 
| 234.0
* 155.990
| [[8/7]]
* 701.955
| ''[[Budjarn Lambeth]] (2023)''
* 857.945
|-
* 1403.910
| Pylon
* 1559.900
| 6 3
* 2105.865
| 9
* 2261.855
| 702.0
* 2807.820
| [[3/2]]
* 2963.810
| ''Budjarn Lambeth (2023)''
* 3509.775
|-
* 3665.765
| Quest
* 4211.730
| 7 2
* 4367.720
| 9
* 4913.685
| 702.0
* 5069.675
| [[3/2]]
* 5615.640
| ''Budjarn Lambeth (2023)''
* 5771.630
|-
* 6317.595
| Snowcone
* 6473.585
| 3 6
* 7019.550
| 9
* 7175.540
| 702.0
* 7721.505
| [[3/2]]
* 7877.495
| ''Budjarn Lambeth (2023)''
* 8423.460
|-
 
| Molten [[pelog]]
 
| 2 2 5 2 5
Snowcone (this is the original/default tuning)
| 16
 
| 1247.9
* 233.985
| [[33/16]]
* 701.955
| ''Budjarn Lambeth (2023)''
* 935.940
|-
* 1403.910
| Swan
* 1637.895
| 4 5 4 5 4 5 4
* 2105.865
| 31
* 2339.850
| 2417.8
* 2807.820
| [[4/1]]
* 3041.805
| ''Budjarn Lambeth (2023)''
* 3509.775
|-
* 3743.760
| Livewire
* 4211.730
| 1 8 1 8 1 8 1 8 1 8 1
* 4445.715
| 46
* 4913.685
| 3587.8
* 5147.670
| [[8/1]]
* 5615.640
| ''Budjarn Lambeth (2023)''
* 5849.625
|-
* 6317.595
| Purgatory
* 6551.580
| 8 1 8 1 8 1 8 1 8 1 8 1 8
* 7019.550
| 62
* 7253.535
| 4835.7
* 7721.505
| [[16/1]]
* 7955.490
| ''Budjarn Lambeth (2023)''
* 8423.460
|-
 
| Cloudscape
 
| 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5
Swan (this is the original/default tuning)
| 72
 
| 5615.6
* 311.980
| [[128/5]]
* 701.955
| ''Budjarn Lambeth (2023)''
* 1013.935
|-
* 1403.910
| Corrugated
* 1715.890
| 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
* 2105.865
| 135
* 2417.845
| 10529.3
 
| [[437/1]]
 
| ''Budjarn Lambeth (2023)''
Cloudscape (this is the original/default tuning)
|}
 
None of these scales are approximated from another tuning unless specified otherwise. For exact [[cents]] values see [[User:BudjarnLambeth/Longer versions of scales#9edf]].
* 389.975
* 701.955
* 1091.930
* 1403.910
* 1793.885
* 2105.865
* 2495.840
* 2807.820
* 3197.795
* 3509.775
* 3899.750
* 4211.730
* 4601.705
* 4913.685
* 5303.660
* 5615.640
* 6005.615
 
 
Pylon (this is the original/default tuning)
 
* 467.970
* 701.955
* 1169.925
* 1403.910
* 1871.880
* 2105.865
* 2573.835
* 2807.820
* 3275.790
* 3509.775
* 3977.745
* 4211.730
* 4679.700
* 4913.685
* 5381.655
* 5615.640
* 6083.610
* 6317.595
* 6785.565
* 7019.550
* 7487.520
* 7721.505
* 8189.475
* 8423.460
 
 
Quest (this is the original/default tuning)
 
* 545.965
* 701.955
* 1247.920
* 1403.910
* 1949.875
* 2105.865
* 2651.830
* 2807.820
* 3353.785
* 3509.775
* 4055.740
* 4211.730
* 4757.695
* 4913.685
* 5459.650
* 5615.640
* 6161.605
* 6317.595
* 6863.560
* 7019.550
* 7565.515
* 7721.505
* 8267.470
* 8423.460
 
 
Purgatory (this is the original/default tuning)
 
* 623.960
* 701.955
* 1325.915
* 1403.910
* 2027.870
* 2105.865
* 2729.825
* 2807.820
* 3431.780
* 3509.775
* 4133.735
* 4211.730
* 4835.690
 
 
Molten [[Pelog]] (this is the original/default tuning)
 
* 155.990
* 311.980
* 701.955
* 857.945
* 1247.920
 
 
Molten [[Slendro]] (exact tuning from [[3edf]])
 
* 233.985
* 467.970
* 701.955
* 935.940
* 1169.925


== Music ==
== Music ==
See [[Carlos Alpha #Music]]. Many are tuned to exactly 9edf.


* ’HUH?’ by Mandrake (2022): https://m.youtube.com/watch?v=J5gntG5LrOk
== See also ==
* [[Alpha, beta, and gamma family of equal divisions]]


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