User:Moremajorthanmajor/8wtn: Difference between revisions
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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>WT Approach by J. Ruhf</ref> == | |||
{| class="wikitable" | {| class="wikitable" | ||
| | | | ||
!Optimal | ! Optimal<ref>4EDF + 3ED(4/3)</ref> | ||
!Alternating | ! Alternating EDO and *ed(9/8)<ref>7EDO + 1ED(9/8)</ref> | ||
|- | |- | ||
|1 | | 1 | ||
|175.48875 | | 175.48875 | ||
|171.429 | | 171.429 | ||
|- | |- | ||
|2 | | 2 | ||
|350.9775 | | 350.9775 | ||
|342.857 | | 342.857 | ||
|- | |- | ||
|3 | | 3 | ||
|526.46625 | | 526.46625 | ||
|514.286 | | 514.286 | ||
|- | |- | ||
|4 | | 4 | ||
|701.955 | | 701.955 | ||
|685.714 | | 685.714 | ||
|- | |- | ||
|5 | | 5 | ||
|867.97 | | 867.97 | ||
|857.143 | | 857.143 | ||
|- | |- | ||
|6 | | 6 | ||
|1032.985 | | 1032.985 | ||
|1028.571 | | 1028.571 | ||
|- | |- | ||
| 7 | |||
| colspan="2" style="text-align:center" | 1200 | |||
|- | |- | ||
|8 | | 8 | ||
|1366.015 | | 1366.015 | ||
|1403.91 | | 1403.91 | ||
|} | |} | ||
<references/> | |||
[[Category:Well tempered nonet]] | [[Category:Well tempered nonet]] | ||
{{todo | {{todo|unify precision}} | ||
Revision as of 10:10, 13 June 2021
8WTN is optimally the equal division of the just perfect fifth into four parts of 175.48875 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 temperament, which tempers out 20000/19683 in the 5-limit.
Patent Intervals[1]
| Optimal[2] | Alternating EDO and *ed(9/8)[3] | |
|---|---|---|
| 1 | 175.48875 | 171.429 |
| 2 | 350.9775 | 342.857 |
| 3 | 526.46625 | 514.286 |
| 4 | 701.955 | 685.714 |
| 5 | 867.97 | 857.143 |
| 6 | 1032.985 | 1028.571 |
| 7 | 1200 | |
| 8 | 1366.015 | 1403.91 |