3edf: Difference between revisions
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rewrite temperament interpretation; + harmonics |
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{{Infobox ET}} | |||
{{ED intro}} | |||
==Factoids about | == Theory == | ||
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]]. | |||
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. | |||
=== 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 == | == Intervals == | ||
{| class="wikitable" | {| class="wikitable center-all" | ||
! # | |||
! Cents | |||
!Approximate JI Ratios | |||
! | |||
! | |||
! | |||
|- | |- | ||
|1 | | 1 | ||
| 233.99 | |||
|233. | | [[8/7]] | ||
| | |||
|- | |- | ||
|2 | | 2 | ||
| 467.97 | |||
|467.97 | | [[21/16]], [[17/13]] | ||
| | |||
|- | |- | ||
|3 | | 3 | ||
| 701.96 | |||
|701. | | exact [[3/2]] | ||
| | |||
|} | |} | ||
[ | |||
[[Category: | == Music == | ||
* [https://www.youtube.com/watch?v=0ecvufTJowE Sequences & Chaos] by Bazil Müzik | |||
[[Category:Listen]] | |||