User:Moremajorthanmajor/8wtn: Difference between revisions
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8WTN is the [[EDF|equal division of the just perfect fifth]] into four parts of 175.48875 [[cent | '''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> == | |||
{| class="wikitable" | {| class="wikitable" | ||
| | |||
! | ! Optimal<ref>[[4 EDF]] + 3ED(4/3)</ref> | ||
! | ! Alternating EDO and *ed(9/8)<ref>[[7 EDO]] + 9/8</ref> | ||
|- | |- | ||
|1 | | 1 | ||
| 175.48875 | |||
| 171.429 | |||
|- | |- | ||
|2 | | 2 | ||
| 350.9775 | |||
| 342.857 | |||
|- | |- | ||
|3 | | 3 | ||
| 526.46625 | |||
| 514.286 | |||
|- | |- | ||
|4 | | 4 | ||
| 701.955 | |||
| 685.714 | |||
|- | |- | ||
|5 | | 5 | ||
| | | 867.97 | ||
| | | 857.143 | ||
|- | |- | ||
|6 | | 6 | ||
| | | 1032.985 | ||
| | | 1028.571 | ||
|- | |- | ||
|7 | | 7 | ||
| | | colspan="2" style="text-align:center" | 1200 | ||
| | |||
|- | |- | ||
|8 | | 8 | ||
| | | 1366.015 | ||
| | | 1403.91 | ||
|} | |} | ||
<references/> | |||
[[Category:Well tempered nonet]] | |||
{{todo|unify precision}} | |||
|} | |||