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 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]].
'''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]].


==Optimal Intervals==
==Patent Intervals==
{| class="wikitable"
{| class="wikitable"
!
!
!Target Minimum
!Optimal
!Target Minimum
!Alternating [[EDO|edo]] and *ed(9/8)
|-
|-
!1
|1
! colspan="2" |233.985
|233.985
|240
|-
|-
!2
|2
! colspan="2" |467.97
|467.97
|480
|-
|-
!3
|3
! colspan="2" |701.955
|701.955
|720
|-
|-
!4
|4
! colspan="2" |950.9775
|950.9775
|960
|-
|-
!5
!5
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|-
|-
|6
|6
|1400
|1449.0225
|1466.667
|1403.91
|}
|}
[[Category:Well tempered nonet]]