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]].
-==Factoids about 6WTN==
+==Patent Intervals==
-The best tunings of 6WTN are related to the [[Gamelismic clan|gamelismic temperaments]], which temper out 1029/1024 in the 7-limit.
-==Optimal Intervals==
 {| class="wikitable"
 !
-!Minimum
+!Optimal
-!Maximum
+!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
-|941.955
+|950.9775
-|959.098
+|960
 |-
-|5
+!5
-|1181.955
+! colspan="2" |1200
-|1216.241
 |-
 |6
-|1421.955
+|1449.0225
-|1473.384
+|1403.91
 |}
+[[Category:Well tempered nonet]]