User:Moremajorthanmajor/12wtn: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
VisualWikitext
Created page with "'''12WTN''' is the equal division of the just perfect fifth into six parts of 116.9925 cents each alternated with a sequence of six equal steps of another int..."
 
m Text replacement - "{{todo|clarify|unify precision|inline=1}}" to ""
 
(16 intermediate revisions by 3 users not shown)
Line 1: Line 1:
'''12WTN''' is the [[EDF|equal division of the just perfect fifth]] into six parts of 116.9925 [[cent|cents]] each alternated with a sequence of six equal steps of another interval between 100 and 133.333 cents. Its best tunings are related to the [[Gamelismic clan|miracle temperament]], which tempers out 225/224 and 1029/1024 in the 7-limit.
'''12WTN''' is optimally the [[EDF|equal division of the just perfect fifth]] into six parts of 116.9925 [[cent|cents]] each alternated with a sequence of six equal steps of another interval between 100 and 133.333 cents in its patent tunings. It is also the largest wtn with a patent tuning which alternates an [[EDO|edo]] and [[9/8]] and the wtn with a patent tuning related to an equal division of the smallest “wolf” nonet (1309.091 cents).


== Intervals ==
== Patent Intervals ==
{| class="wikitable"
{| class="wikitable"
|
|
!''“fifth” 2 = 600¢''
!Target a
!“nonet” = 1351.429¢
!Target b
!“nonet” = 1460¢
!Alternating edo and *ed(9/8) a
!''“fifth” 2 = 800¢''
!Alternating edo and *ed(9/8) b
|-
|-
|1
|1
| colspan="4" |116.9925
! colspan="2" |116.9925
|120
|109.0909
|-
|-
|2
|2
| colspan="4" |233.985
! colspan="2" |233.985
|240
|218.1818
|-
|-
|3
|3
| colspan="4" |350.9775
! colspan="2" |350.9775
|360
|327.2727
|-
|-
|4
|4
| colspan="4" |467.97
! colspan="2" |467.97
|480
|436.3636
|-
|-
|5
|5
| colspan="4" |584.9625
! colspan="2" |584.9625
|600
|545.45455
|-
|-
|6
|6
| colspan="4" |701.955
! colspan="2" |701.955
|720
|654.54545
|-
|-
|7
|7
|''801.955''
|826.46625
|810.201
|801.564
|828.296
|840
|''835.328''
|763.6364
|-
|-
|8
|8
|''901.955''
|950.9775
|918.446
|901.173
|954.637
|960
|''968.662''
|872.7273
|-
|-
|9
|9
|''1001.955''
|1075.48875
|1026.692
|1000.782
|1080.9775
|1080
|''1101.955''
|981.8182
|-
|-
|10
|10
|''1101.955''
|1200
|1134.937
|1101.391
|1207.318
|1200
|''1235.328''
|1090.9091
|-
|-
|11
|11
|''1201.955''
|1324.51125
|1243.183
|1200
|1333.695
|1301.955
|''1368.662''
|1200
|-
|-
|12
|12
|''1301.955''
|1449.0225
|1351.429
|1299.609
|1460
! colspan="2" |1403.91
|''1501.955''
|}
|}


== Common Tunings ==
[[Category:Well tempered nonet]]
{| class="wikitable"
|+
!
!fifth 2 = 6\11
!fifth 2 = 3\5
|-
|1
| colspan="2" |116.9925
|-
|2
| colspan="2" |233.985
|-
|3
| colspan="2" |350.9775
|-
|4
| colspan="2" |467.97
|-
|5
| colspan="2" |584.9625
|-
|6
| colspan="2" |701.955
|-
|7
|811.046
|821.955
|-
|8
|920.137
|941.955
|-
|9
|1029.228
|1061.955
|-
|10
|1138.319
|1181.955
|-
|11
|1247.4095
|1301.955
|-
|12
|1356.5005
|1421.955
|}

Latest revision as of 09:31, 1 September 2025

12WTN is optimally the equal division of the just perfect fifth into six parts of 116.9925 cents each alternated with a sequence of six equal steps of another interval between 100 and 133.333 cents in its patent tunings. It is also the largest wtn with a patent tuning which alternates an edo and 9/8 and the wtn with a patent tuning related to an equal division of the smallest “wolf” nonet (1309.091 cents).

Patent Intervals

Target a Target b Alternating edo and *ed(9/8) a Alternating edo and *ed(9/8) b
1 116.9925 120 109.0909
2 233.985 240 218.1818
3 350.9775 360 327.2727
4 467.97 480 436.3636
5 584.9625 600 545.45455
6 701.955 720 654.54545
7 826.46625 801.564 840 763.6364
8 950.9775 901.173 960 872.7273
9 1075.48875 1000.782 1080 981.8182
10 1200 1101.391 1200 1090.9091
11 1324.51125 1200 1301.955 1200
12 1449.0225 1299.609 1403.91
Retrieved from "https://en.xen.wiki/index.php?title=User:Moremajorthanmajor/12wtn&oldid=208950"