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20ed11/5: Difference between revisions

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WIP
{{Infobox ET}}
{{Infobox ET}}
'''20ed11/5''' is the [[ed11/5|equal division of the neutral ninth]] into 20 parts of 68.3 cents each.
'''20ed11/5''' is the [[ed11/5|equal division of the neutral ninth]] into 20 parts of 68.3 cents each.
== Temperaments ==
== Temperaments ==
20ed11/5 tempers out 2093663/2088025 and 54925/54043 in the no-twos-or-threes 17-limit which means it supports [[salmon]] temperament, which can be viewed as the no-twos-or-threes-analog of [[meantone]]. However, its [[13/11]] approximation is quite flat (closer to a subminor third) which affects the quality of the 11:13:17 chord, one of the most consonant no-twos-or-threes chords.
20ed11/5 tempers out 2093663/2088025 and 54925/54043 in the no-twos-or-threes 17-limit which means it supports [[catfish]] temperament, which can be viewed as the no-twos-or-threes-analog of [[meantone]]. However, its [[13/11]] approximation is quite flat (closer to a subminor third) which affects the quality of the 11:13:17 chord, one of the most consonant no-twos-or-threes chords.
== Intervals ==
== Intervals ==
{|class="wikitable"
{|class="wikitable"
Line 11: Line 9:
!Cents
!Cents
!Approximate ratios
!Approximate ratios
![[Catfish]] nonatonic notation (J = 1/1)
|-
|-
|0
|0
|0.0
|0.0
|[[1/1]]
|[[1/1]]
|J
|-
|-
|1
|1
|68.3
|68.3
|[[28/27]], [[27/26]], [[26/25]], [[25/24]]
|[[28/27]], [[27/26]], [[26/25]], [[25/24]]
|J#, Kb
|-
|-
|2
|2
|136.5
|136.5
|[[14/13]], [[27/25]], [[13/12]]
|[[14/13]], [[27/25]], [[13/12]]
|K
|-
|-
|3
|3
|204.8
|204.8
[[9/8]]
|[[9/8]]
|K#, Lb
|-
|-
|4
|4
|273.0
|273.0
|[[7/6]], [[75/64]]
|[[7/6]], [[75/64]]
|L
|-
|5
|341.3
|[[17/14]], [[39/32]], [[11/9]]
|L#, Mb
|-
|6
|409.5
|[[14/11]],[[81/64]], [[19/15]]
|M
|-
|7
|477.8
|[[21/16]], [[33/25]]
|M#, Nb
|-
|-
|8
|8
|546.0
|546.0
|[[11/8]], [[15/11]], [[48/35]]
|[[11/8]], [[15/11]], [[48/35]]
|N
|-
|9
|614.3
|[[10/7]], [[121/85]]
|N#
|-
|10
|682.5
|[[3/2]], [[40/27]]
|Ob
|-
|11
|750.1
|[[17/11]], [[49/32]]
|O
|-
|-
|12
|12
|819.0
|819.0
|[[8/5]], [[21/13]]
|[[8/5]], [[21/13]]
|O#, Pb
|-
|13
|887.3
|[[5/3]], [[38/23]]
|P
|-
|14
|955.5
|[[7/4]], [[26/15]]
|P#, Qb
|-
|15
|1023.8
|[[9/5]], [[29/16]], [[20/11]]
|Q
|-
|-
|16
|16
|1092.0
|1092.0
|[[15/8]], [[32/17]]
|[[15/8]], [[32/17]]
|Q#, Rb
|-
|17
|1160.3
|[[49/25]], [[35/18]]
|R
|-
|18
|1228.5
|[[2/1]]
|R#
|-
|19
|1296.8
|[[15/7]]
|Jb
|-
|-
|20
|20
|1365.0
|1365.0
|[[11/5]]
|[[11/5]]
|J
|}
|}
== Harmonics ==
{{Harmonics in equal
| steps = 20
| num = 11
| denom = 5
}}
{{Harmonics in equal
| steps = 20
| num = 11
| denom = 5
| start = 12
| collapsed = 1
}}


[[Category:Nonoctave]]
[[Category:Nonoctave]]
[[Category:Equal-step tunings]]
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