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'''18WTN''' is the non-octave well temperament where [[EDF|equal division of the just perfect fifth]] into nine parts of 77.995 cents each (9ED3/2) alternates with sequences of nine equal steps of 66.667 to 88.889 cents each. This will create nine equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.
'''18WTN''' is optimally the non-octave well temperament with patent tunings where [[EDF|equal division of the just perfect fifth]] into nine parts of 77.995 cents each (9ED3/2) alternates with sequences of nine equal steps of 66.667 to 88.889 cents each. This will create nine equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth. It also has the peculiar property of being a patent wtn related to equal divisions of nonets of two different integer cent sizes.


== Theory ==
== Patent Intervals ==
The best tunings of 18WTN are very closely related to [[Carlos Alpha]] and [[Starling temperaments #Valentine temperament|valentine temperament]]. For a list of 11-limit [[dyadic chord]]s of Carlos Alpha, see [[Chords of valentine]].
 
They have a very good representation of the 7:8:10:11:12 chord from the harmonic series.
 
== Intervals ==
{| class="wikitable"
{| class="wikitable"
!
!
!''“fifth” 2 = 600¢''
!Target a
!“nonet” = 1351.429¢
!Target b
!“nonet” = 1460¢
!Alternating [[EDO|edo]] and *ed(9/8) a
!''“fifth” 2 = 800¢''
!Alternating edo and *ed(9/8) b
|-
|-
| |1
| |1
! colspan="4" |77.995
! colspan="2" |77.995
|80
|75
|-
|-
| |2
| |2
! colspan="4" |155.99
! colspan="2" |155.99
|160
|150
|-
|-
| |3
| |3
! colspan="4" |233.985
! colspan="2" |233.985
|240
|225
|-
|-
| |4
| |4
! colspan="4" |311.98
! colspan="2" |311.98
|320
|300
|-
|-
| |5
| |5
! colspan="4" |389.975
! colspan="2" |389.975
|400
|375
|-
|-
| |6
| |6
! colspan="4" |467.97
! colspan="2" |467.97
|480
|450
|-
|-
| |7
| |7
! colspan="4" |545.965
! colspan="2" |545.965
|560
|525
|-
|-
| |8
| |8
! colspan="4" |623.96
! colspan="2" |623.96
|640
|600
|-
|-
| |9
| |9
! colspan="4" |701.955
! colspan="2" |701.955
|720
|675
|-
|-
| |10
| |10
|''768.622''
|784.9625
|774.119
|773.104
|786.182
|800
|''790.844''
|750
|-
|-
| |11
| |11
|''835.288''
|867.97
|846.2825
|844.253
|870.409
|880
|''879.733''
|825
|-
|-
| |12
| |12
|''901.955''
|950.9775
|918.446
|915.403
|954.637
|960
|''968.622''
|900
|-
|-
| |13
| |13
|''968.622''
|1033.985
|990.61
|986.552
|1038.864
|1040
|''1057.511''
|975
|-
|-
| |14
| |14
|''1035.288''
|1116.9925
|1062.774
|1057.701
|1123.091
|1120
|''1146.399''
|1050
|-
|-
| |15
| |15
|''1101.955''
|1200
|1134.937
|1128.896
|1207.318
|1200
|''1235.288''
|1125
|-
|-
| |16
| |16
|''1168.622''
|1283.0075
|1207.101
|1200
|1291.546
|1267.97
|''1324.177''
|1200
|-
|-
| |17
| |17
|''1235.288''
|1366.015
|1279.265
|1262.2556
|1375.773
|1333.94
|''1413.066''
|1301.955
|-
|-
| |18
| |18
|''1301.955''
|1449.0225
|1351.429
|1324.511
|1460
! colspan="2" |1403.91
|''1501.955''
|}
|}


== Common Tunings ==
== [[Valentine]] Tunings ==
{| class="wikitable"
{| class="wikitable"
!
!
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|-
|-
| |16
| |16
|1225.955
|1226.955
|1243.8905
|1243.8905
|1247.71
|1247.71
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! colspan="4" |701.955
! colspan="4" |701.955
|}
|}
[[Category:Well tempered nonet]]
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