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'''3EDF''', if the attempt is made to use it as an actual scale, would divide the [[just perfect fifth]] into three equal parts, each of size 233.985 cents, which is to say (3/2)^(1/3) as a frequency ratio. It corresponds to 5.1285 [[edo]]. If we want to consider it to be a temperament, it tempers out [[16/15]], [[21/20]], [[28/27]], [[81/80]], and [[256/243]] as well as [[5edo]].
{{Infobox ET}}
{{ED intro}}


==Factoids about 3EDF==
== Theory ==
3EDF is related to the [[Gamelismic clan|gamelismic temperaments]], which temper out 1029/1024 in the 7-limit.
3edf, if the attempt is made to use it as an actual scale, would divide the [[just perfect fifth]] into three equal parts, each of size 233.985 cents, which is to say (3/2)<sup>1/3</sup> as a frequency ratio. It corresponds to 5.1285 [[edo]].


[[Category:Edf]]
It can also be treated as a heavily compressed version of [[5edo]], with the octave compressed by about 30 cents. Its [[patent val]] matches that of 5edo up to the [[7-limit]], and thus tempers out the same commas.
[[Category:Edonoi]]
 
=== Harmonics ===
{{Harmonics in equal|3|3|2}}
 
== Factoids about 3edf ==
3edf is essentially equivalent to the [[slendric]] temperament, which tempers out 1029/1024 in the 2.3.7 subgroup, without octave repetition, and its step size is the 1/3-comma tuning of the slendric generator (approximated by, for instance, [[41edo|8\41]] and [[200edo|39\200]]). It also works well as a tuning for [[Extraclassical tonality|arto and tendo chords.]]
 
== Intervals ==
{| class="wikitable center-all"
! #
! Cents
!Approximate JI Ratios
|-
| 1
| 233.99
| [[8/7]]
|-
| 2
| 467.97
| [[21/16]], [[17/13]]
|-
| 3
| 701.96
| exact [[3/2]]
|}
 
== Music ==
* [https://www.youtube.com/watch?v=0ecvufTJowE Sequences & Chaos] by Bazil Müzik
 
[[Category:Listen]]
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