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'''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
|-
!2
! colspan="4" |233.985
|-
!3
! colspan="4" |350.9775
|-
!4
! colspan="4" |467.97
|-
!5
! colspan="4" |584.9625
|-
!6
! colspan="4" |701.955
|-
|7
|''801.955''
|810.201
|828.296
|''835.328''
|-
|8
|''901.955''
|918.446
|954.637
|''968.662''
|-
|9
|''1001.955''
|1026.692
|1080.9775
|''1101.955''
|-
|10
|''1101.955''
|1134.937
|1207.318
|''1235.328''
|-
|11
|''1201.955''
|1243.183
|1333.695
|''1368.662''
|-
|12
|''1301.955''
|1351.429
|1460
|''1501.955''
|}
 
== Common Tunings ==
{| class="wikitable"
|+
!
!fifth 2 = 6\11
!fifth 2 = 3\5
|-
!1
! colspan="2" |116.9925
! colspan="2" |116.9925
|120
|109.0909
|-
|-
!2
|2
! colspan="2" |233.985
! colspan="2" |233.985
|240
|218.1818
|-
|-
!3
|3
! colspan="2" |350.9775
! colspan="2" |350.9775
|360
|327.2727
|-
|-
!4
|4
! colspan="2" |467.97
! colspan="2" |467.97
|480
|436.3636
|-
|-
!5
|5
! colspan="2" |584.9625
! colspan="2" |584.9625
|600
|545.45455
|-
|-
!6
|6
! colspan="2" |701.955
! colspan="2" |701.955
|720
|654.54545
|-
|-
|7
|7
|811.046
|826.46625
|821.955
|801.564
|840
|763.6364
|-
|-
|8
|8
|920.137
|950.9775
|941.955
|901.173
|960
|872.7273
|-
|-
|9
|9
|1029.228
|1075.48875
|1061.955
|1000.782
|1080
|981.8182
|-
|-
|10
|10
|1138.319
|1200
|1181.955
|1101.391
|1200
|1090.9091
|-
|-
|11
|11
|1247.4095
|1324.51125
|1200
|1301.955
|1301.955
|1200
|-
|-
|12
|12
|1356.5005
|1449.0225
|1421.955
|1299.609
|-
! colspan="2" |1403.91
!
! colspan="2" |Fifths
|-
|1
|694.053
|704.9625
|-
|2
|686.152
|707.97
|-
|3
|678.25
|710.9775
|-
|4
|670.349
|713.985
|-
|5
|662.4705
|716.9925
|-
|6
|654.5455
|720
|-
|7
|662.4705
|716.9925
|-
|8
|670.349
|713.985
|-
|9
|678.25
|710.9775
|-
|10
|686.152
|707.97
|-
|11
|694.053
|704.9625
|-
!12
! colspan="2" |701.955
|}
|}
[[Category:Well tempered nonet]]
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