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|cents]] each alternated with a sequence of four equal steps of another interval between 150 and 200 cents. Its best tunings are related to the [[Tetracot family|tetracot temperament]], which tempers out 20000/19683 in the 5-limit. | 8WTN 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. Its best tunings are related to the [[Tetracot family|tetracot temperament]], which tempers out 20000/19683 in the 5-limit. | ||
== | == Intervals == | ||
{| class="wikitable" | {| class="wikitable" | ||
! | ! | ||
! | !''“fifth” 2 = 600¢'' | ||
! | !“nonet” = 1351.429¢ | ||
!step 2 = 10/9 | |||
!“nonet” = 1460¢ | |||
!''“fifth” 2 = 800¢'' | |||
|- | |- | ||
!1 | !1 | ||
! colspan=" | ! colspan="5" |175.48875 | ||
|- | |- | ||
!2 | !2 | ||
! colspan=" | ! colspan="5" |350.9775 | ||
|- | |- | ||
!3 | !3 | ||
! colspan=" | ! colspan="5" |526.46625 | ||
|- | |- | ||
!4 | !4 | ||
! colspan=" | ! colspan="5" |701.955 | ||
|- | |- | ||
|5 | |5 | ||
| | |''851.955'' | ||
| | |864.3234 | ||
|884.3587 | |||
|891.46625 | |||
|''901.955'' | |||
|- | |- | ||
|6 | |6 | ||
| | |''1001.955'' | ||
| | |1026.692 | ||
|1066.7624 | |||
|1080.9775 | |||
|''1101.955'' | |||
|- | |- | ||
|7 | |7 | ||
| | |''1151.955'' | ||
|1216. | |1189.0602 | ||
|1249.1661 | |||
|1270.48875 | |||
|''1301.955'' | |||
|- | |||
|8 | |||
|''1301.955'' | |||
|1351.429 | |||
|1431.56985 | |||
|1460 | |||
|''1501.955'' | |||
|} | |||
== Common Tuning == | |||
{| class="wikitable" | |||
|1 | |||
|175.48875 | |||
|- | |||
|2 | |||
|350.9775 | |||
|- | |||
|3 | |||
|526.46625 | |||
|- | |||
|4 | |||
|701.955 | |||
|- | |||
|5 | |||
|873.3836 | |||
|- | |||
|6 | |||
|1044.8121 | |||
|- | |||
|7 | |||
|1216.2407 | |||
|- | |- | ||
|8 | |8 | ||
|1387.6693 | |1387.6693 | ||
|- | |||
! | |||
!Fifths | |||
|- | |||
|1 | |||
|697.8948 | |||
|- | |||
|2 | |||
|693.8346 | |||
|- | |||
|3 | |||
|689.7745 | |||
|- | |||
|4 | |||
|685.7143 | |||
|- | |||
|5 | |||
|689.7745 | |||
|- | |||
|6 | |||
|693.8346 | |||
|- | |||
|7 | |||
|697.8948 | |||
|- | |||
|8 | |||
|701.955 | |||
|} | |} | ||
Revision as of 06:28, 30 May 2021
8WTN is 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. Its best tunings are related to the tetracot temperament, which tempers out 20000/19683 in the 5-limit.
Intervals
| “fifth” 2 = 600¢ | “nonet” = 1351.429¢ | step 2 = 10/9 | “nonet” = 1460¢ | “fifth” 2 = 800¢ | |
|---|---|---|---|---|---|
| 1 | 175.48875 | ||||
| 2 | 350.9775 | ||||
| 3 | 526.46625 | ||||
| 4 | 701.955 | ||||
| 5 | 851.955 | 864.3234 | 884.3587 | 891.46625 | 901.955 |
| 6 | 1001.955 | 1026.692 | 1066.7624 | 1080.9775 | 1101.955 |
| 7 | 1151.955 | 1189.0602 | 1249.1661 | 1270.48875 | 1301.955 |
| 8 | 1301.955 | 1351.429 | 1431.56985 | 1460 | 1501.955 |
Common Tuning
| 1 | 175.48875 |
| 2 | 350.9775 |
| 3 | 526.46625 |
| 4 | 701.955 |
| 5 | 873.3836 |
| 6 | 1044.8121 |
| 7 | 1216.2407 |
| 8 | 1387.6693 |
| Fifths | |
|---|---|
| 1 | 697.8948 |
| 2 | 693.8346 |
| 3 | 689.7745 |
| 4 | 685.7143 |
| 5 | 689.7745 |
| 6 | 693.8346 |
| 7 | 697.8948 |
| 8 | 701.955 |