User:Moremajorthanmajor/6wtn: Difference between revisions
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'''6WTN''', 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, alternating these with three equal steps of another interval between 200 and 266.667 cents. This will create three equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth. 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]]. | '''6WTN''', if the attempt is made to use it as an actual scale, would optimally 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, alternating these with three equal steps of another interval between 200 and 266.667 cents in its patent tunings. This will create three equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth. 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]]. | ||
== | ==Patent Intervals== | ||
{| class="wikitable" | {| class="wikitable" | ||
! | ! | ||
! | !Optimal | ||
! | !Alternating [[EDO|edo]] and *ed(9/8) | ||
|- | |- | ||
|1 | |1 | ||
|233.985 | |233.985 | ||
|240 | |||
|- | |- | ||
|2 | |2 | ||
|467.97 | |467.97 | ||
|480 | |||
|- | |- | ||
|3 | |3 | ||
|701.955 | |701.955 | ||
|720 | |720 | ||
|- | |- | ||
|4 | |4 | ||
| | |950.9775 | ||
|960 | |||
|- | |- | ||
!5 | |||
| | ! colspan="2" |1200 | ||
|- | |- | ||
|6 | |6 | ||
| | |1449.0225 | ||
|1403.91 | |||
|} | |} | ||
[[Category:Well tempered nonet]] | |||