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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]], 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)}}


== 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
! 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 using 7\9edf
| 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]], [[11/8]]
|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]].
== Scales within 9edf ==
Livewire (this is the original/default tuning)
 
* 77.995
* 701.955
* 779.950
* 1403.905
* 1481.905
* 2105.865
* 2183.860
* 2807.820
* 2885.815
* 3509.775
* 3587.770
 
 
Corrugated (this is the original/default tuning)
 
* 155.990
* 701.955
* 857.945
* 1403.910
* 1559.900
* 2105.865
* 2261.855
* 2807.820
* 2963.810
* 3509.775
* 3665.765
* 4211.730
* 4367.720
* 4913.685
* 5069.675
* 5615.640
* 5771.630
* 6317.595
* 6473.585
* 7019.550
* 7175.540
* 7721.505
* 7877.495
* 8423.460
 
 
Snowcone (this is the original/default tuning)
 
* 233.985
* 701.955
* 935.940
* 1403.910
* 1637.895
* 2105.865
* 2339.850
* 2807.820
* 3041.805
* 3509.775
* 3743.760
* 4211.730
* 4445.715
* 4913.685
* 5147.670
* 5615.640
* 5849.625
* 6317.595
* 6551.580
* 7019.550
* 7253.535
* 7721.505
* 7955.490
* 8423.460
 
 
Swan (this is the original/default tuning)
 
* 311.980
* 701.955
* 1013.935
* 1403.910
* 1715.890
* 2105.865
* 2417.845
 
 
Cloudscape (this is the original/default tuning)
 
* 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
[[Category:Edf]]
[[Category:Listen]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/9edf"