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{{Infobox ET}}
{{Infobox ET}}
'''20edf''' is very close to the [[Carlos Gamma]] tuning.
{{ED intro}}


==Intervals==
== Theory ==
20edf corresponds to 34.1902edo. It is closely related to [[Carlos Gamma]] and the [[gammic]] temperament, which adds an independent dimension for the [[octave]] (although strictly speaking, the "canonical" optimized Carlos Gamma tuning is not exactly 20edf, with its fifth stretched by the microscopic amount of 0.016{{c}}). It very accurately represents the intervals [[5/4]], with 11 steps, and [[17/16]], with 3 steps.
 
20edf is closely approximated by every 5 steps of [[171edo]], while its full [[23-limit]] mapping is maybe better interpreted by every 3 steps of [[103edo]] 103h val.
 
=== Harmonics ===
{{Harmonics in equal|20|3|2|columns=11}}
{{Harmonics in equal|20|3|2|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 20edf (continued)}}
 
== Intervals ==
The first steps up to two just perfect fifths should give a feeling of the granularity of this system…
The first steps up to two just perfect fifths should give a feeling of the granularity of this system…
{| class="wikitable mw-collapsible"
{| class="wikitable mw-collapsible"
Line 8: Line 17:
|-
|-
!Degrees
!Degrees
!3/2.5/4.17/16 interpretation
![[103edo|103h]] val interpretation
!Cents
!Cents
|-
|-
|1
|1
|51/50
|
|35.1
|35.1
|-
|-
| |2
|2
| |70.2
|25/24
|[[28/27]], [[26/25]], [[25/24]], [[24/23]]
|70.2
|-
|-
| |3
|3
| |105.29
|17/16
|[[17/16]]
|105.29
|-
|-
| |4
|4
| |140.39
|625/576, 867/800
|[[13/12]], [[25/23]]
|140.39
|-
|-
| |5
|5
| |175.49
|320/289, 425/384
|[[21/19]]
|175.49
|-
|-
| |6
|6
| |210.59
|96/85
|[[26/23]]
|210.59
|-
|-
| |7
|7
| |245.68
|144/125
|[[23/20]], [[15/13]]
|245.68
|-
|-
| |8
|8
| |280.78
|20/17
|[[20/17]]
|280.78
|-
|-
| |9
|9
| |315.88
|6/5
|[[6/5]]
|315.88
|-
|-
| |10
|10
| |350.98
|153/125, 125/102
|[[11/9]], [[27/22]]
|350.98
|-
|-
| |11
|11
| |386.075
|5/4
|[[5/4]]
|386.075
|-
|-
| |12
|12
| |421.17
|51/40
|[[14/11]]
|421.17
|-
|-
| |13
|13
| |456.27
|125/96
|[[13/10]], [[30/23]]
|456.27
|-
|-
| |14
|14
| |491.37
|85/64
|
|491.37
|-
|-
| |15
|15
| |526.47
|576/425, 867/640
|[[23/17]], [[19/14]]
|526.47
|-
|-
| |16
|16
| |561.56
|400/289, 864/625
|[[18/13]]
|561.56
|-
|-
| |17
|17
| |596.66
|24/17
|[[38/27]], [[24/17]]
|596.66
|-
|-
| |18
|18
| |631.76
|36/25
|[[23/16]], [[36/25]]
|631.76
|-
|-
| |19
|19
| |666.86
|25/17
|[[22/15]], [[25/17]]
|666.86
|-
|-
| |20
|'''20'''
| |701.955
|'''3/2'''
|[[3/2]]
|'''701.955'''
|-
|-
|21
|21
|153/100
|[[32/21]], [[26/17]]
|737.05
|737.05
|-
|-
|22
|22
|25/16
|[[14/9]], [[25/16]], [[36/23]]
|772.15
|772.15
|-
|-
|23
|23
|51/32
|
|807.25
|807.25
|-
|-
|24
|24
|625/384
|[[34/21]], [[13/8]]
|842.35
|842.35
|-
|-
|25
|25
|425/256, 480/289
|
|877.44
|877.44
|-
|-
|26
|26
|144/85
|[[32/19]], [[22/13]]
|912.54
|912.54
|-
|-
|27
|27
|216/125
|[[19/11]]
|947.64
|947.64
|-
|-
|28
|28
|30/17
|[[44/25]], [[30/17]]
|982.74
|982.74
|-
|-
|29
|29
|9/5
|[[34/19]], [[9/5]]
|1017.835
|1017.835
|-
|-
|30
|30
|125/68
|[[11/6]]
|1052.93
|1052.93
|-
|-
|31
|31
|15/8
|[[28/15]], [[15/8]]
|1088.03
|1088.03
|-
|-
|32
|32
|153/80
|[[40/21]], [[21/11]], [[44/23]]
|1123.13
|1123.13
|-
|-
|33
|33
|125/64
|
|1158.23
|1158.23
|-
|-
|34
|34
|255/128
|
|1193.32
|1193.32
|-
|-
|35
|35
|864/425
|
|1228.42
|1228.42
|-
|-
|36
|36
|600/289
|[[27/13]]
|1263.52
|1263.52
|-
|-
|37
|37
|36/17
|[[40/19]], [[19/9]], [[36/17]]
|1298.62
|1298.62
|-
|-
|38
|38
|54/25
|[[28/13]], [[54/25]]
|1333.715
|1333.715
|-
|-
|39
|39
|75/34
|[[46/21]], [[11/5]]
|1368.81
|1368.81
|-
|-
|40
|'''40'''
|1403.91
|'''9/4'''
|[[56/25]], [[9/4]]
|'''1403.91'''
|}
|}


== Harmonics ==
== See also ==
{{Harmonics in equal|20|3|2|intervals=prime}}
* [[Alpha, beta, and gamma family of equal divisions]]
{{Harmonics in equal|20|3|2|start=12|collapsed=1|intervals=prime}}
 


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