20ed11/5: Difference between revisions
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'''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 [[ | 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 9: | 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 | |5 | ||
|341.3 | |341.3 | ||
|[[17/14]], [[39/32]], [[11/9]] | |[[17/14]], [[39/32]], [[11/9]] | ||
|L#, Mb | |||
|- | |- | ||
|6 | |6 | ||
|409.5 | |409.5 | ||
|[[14/11]],[[81/64]], [[19/15]] | |[[14/11]],[[81/64]], [[19/15]] | ||
|M | |||
|- | |- | ||
|7 | |7 | ||
|477.8 | |477.8 | ||
|[[21/16]], [[33/25]] | |[[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 | |9 | ||
|614.3 | |614.3 | ||
|[[10/7]], [[121/85]] | |[[10/7]], [[121/85]] | ||
|N# | |||
|- | |- | ||
|10 | |10 | ||
|682.5 | |682.5 | ||
|[[3/2]], [[40/27]] | |[[3/2]], [[40/27]] | ||
|Ob | |||
|- | |- | ||
|11 | |11 | ||
|750.1 | |750.1 | ||
|[[17/11]], [[49/32]] | |[[17/11]], [[49/32]] | ||
|O | |||
|- | |- | ||
|12 | |12 | ||
|819.0 | |819.0 | ||
|[[8/5]], [[21/13]] | |[[8/5]], [[21/13]] | ||
|O#, Pb | |||
|- | |- | ||
|13 | |13 | ||
|887.3 | |887.3 | ||
|[[5/3]], [[38/23]] | |[[5/3]], [[38/23]] | ||
|P | |||
|- | |- | ||
|14 | |14 | ||
|955.5 | |955.5 | ||
|[[7/4]], [[26/15]] | |[[7/4]], [[26/15]] | ||
|P#, Qb | |||
|- | |- | ||
|15 | |15 | ||
|1023.8 | |1023.8 | ||
|[[9/5]], [[29/16]], [[20/11]] | |[[9/5]], [[29/16]], [[20/11]] | ||
|Q | |||
|- | |- | ||
|16 | |16 | ||
|1092.0 | |1092.0 | ||
|[[15/8]], [[32/17]] | |[[15/8]], [[32/17]] | ||
|Q#, Rb | |||
|- | |- | ||
|17 | |17 | ||
|1160.3 | |1160.3 | ||
|[[49/25]], [[35/18]] | |[[49/25]], [[35/18]] | ||
|R | |||
|- | |- | ||
|18 | |18 | ||
|1228.5 | |1228.5 | ||
|[[2/1]] | |[[2/1]] | ||
|R# | |||
|- | |- | ||
|19 | |19 | ||
|1296.8 | |1296.8 | ||
|[[15/7]] | |[[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]] | ||