User:Moremajorthanmajor/8wtn: Difference between revisions

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-WTN is the [[EDF|equal division of the just perfect fifth]] into four parts of 175.48875 [[cent|cents]] each alternated with a sequence of four equal steps of another interval between 150 and 200 cents in its patent tunings. Its best tunings are related to the [[Tetracot family|tetracot temperament]], which tempers out 20000/19683 in the 5-limit.
+'''8WTN''' is optimally the [[EDF|equal division of the just perfect fifth]] into four parts of 175.48875 [[cent]]s each alternated with a sequence of four equal steps of another interval between 150 and 200 cents in its patent tunings. Its best tunings are related to the [[Tetracot family|tetracot temperament]], which tempers out 20000/19683 in the 5-limit.
+== Patent Intervals<ref>a WT approach by J. Ruhf</ref> ==
-== Optimal Intervals ==
 {| class="wikitable"
-!
+|
-!Minimum
+! Optimal<ref>[[4 EDF]] + 3ED(4/3)</ref>
-!Maximum
+! Alternating EDO and *ed(9/8)<ref>[[7 EDO]] + 9/8</ref>
-![4\7 166.015¢]
 |-
-!1
+| 1
-! colspan="3" |175.48875
+| 175.48875
+| 171.429
 |-
-!2
+| 2
-! colspan="3" |350.9775
+| 350.9775
+| 342.857
 |-
-!3
+| 3
-! colspan="3" |526.46625
+| 526.46625
+| 514.286
 |-
-!4
+| 4
-! colspan="3" |701.955
+| 701.955
+| 685.714
 |-
-|5
+| 5
-|861.955
+| 867.97
-|873.3836
+| 857.143
-|867.97
 |-
-|6
+| 6
-|1021.955
+| 1032.985
-|1044.8121
+| 1028.571
-|1032.985
 |-
-|7
+| 7
-|1181.955
+| colspan="2" style="text-align:center" | 1200
-|1216.2407
-|1200
 |-
-|8
+| 8
-|1341.955
+| 1366.015
-! colspan="2" |1387.6693
+| 1403.91
 |}
+<references/>
+[[Category:Well tempered nonet]]
+{{todo|unify precision}}