User:Moremajorthanmajor/8wtn: Difference between revisions

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Undo revision 71037 by Moremajorthanmajor (talk)
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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 ==
== Optimal Intervals ==
{| class="wikitable"
{| class="wikitable"
!
!
!''“fifth” 2 = 600¢''
!Minimum
!“nonet” = 1351.429¢
!Maximum
!step 2 = 10/9
!“nonet” = 1460¢
!''“fifth” 2 = 800¢''
|-
|-
!1
!1
! colspan="5" |175.48875
! colspan="2" |175.48875
|-
|-
!2
!2
! colspan="5" |350.9775
! colspan="2" |350.9775
|-
|-
!3
!3
! colspan="5" |526.46625
! colspan="2" |526.46625
|-
|-
!4
!4
! colspan="5" |701.955
! colspan="2" |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 ==
{| class="wikitable"
|1
|175.48875
|-
|2
|350.9775
|-
|3
|526.46625
|-
|4
|701.955
|-
|-
|5
|5
|861.955
|873.3836
|873.3836
|-
|-
|6
|6
|1021.955
|1044.8121
|1044.8121
|-
|-
|7
|7
|1181.955
|1216.2407
|1216.2407
|-
|-
|8
|8
|1341.955
|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 06:32, 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.

Optimal Intervals

Minimum Maximum
1 175.48875
2 350.9775
3 526.46625
4 701.955
5 861.955 873.3836
6 1021.955 1044.8121
7 1181.955 1216.2407
8 1341.955 1387.6693
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