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8WTN is optimally 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 | | 175.48875 | ||
| 171.429 | |||
|- | |- | ||
|2 | | 2 | ||
|350.9775 | | 350.9775 | ||
| 342.857 | |||
|- | |- | ||
|3 | | 3 | ||
|526.46625 | | 526.46625 | ||
| 514.286 | |||
|- | |- | ||
|4 | | 4 | ||
|701.955 | | 701.955 | ||
| 685.714 | |||
|- | |- | ||
|5 | | 5 | ||
|867.97 | | 867.97 | ||
| 857.143 | |||
|- | |- | ||
|6 | | 6 | ||
|1032.985 | | 1032.985 | ||
| 1028.571 | |||
|- | |- | ||
|7 | | 7 | ||
|1200 | | colspan="2" style="text-align:center" | 1200 | ||
|- | |- | ||
|8 | | 8 | ||
|1366.015 | | 1366.015 | ||
| 1403.91 | |||
|} | |} | ||
<references/> | |||
[[Category:Well tempered nonet]] | |||
{{todo|unify precision}} | |||