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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 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.


== Theory ==
== Optimal 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¢''
!Minimum a
!“nonet” = 1351.429¢
!Maximum a
!“nonet” = 1460¢
!Minimum b
!''“fifth” 2 = 800¢''
!Maximum b
|-
|-
| |1
| |1
Line 42: Line 37:
|-
|-
| |10
| |10
|''768.622''
|781.955
|774.119
|787.669
|786.182
|770.526
|''790.844''
|775.424
|-
|-
| |11
| |11
|''835.288''
|861.955
|846.2825
|873.384
|870.409
|839.098
|''879.733''
|848.893
|-
|-
| |12
| |12
|''901.955''
|941.955
|918.446
|959.098
|954.637
|907.669
|''968.622''
|921.363
|-
|-
| |13
| |13
|''968.622''
|1021.955
|990.61
|1044.812
|1038.864
|976.241
|''1057.511''
|995.833
|-
|-
| |14
| |14
|''1035.288''
|1101.955
|1062.774
|1130.526
|1123.091
|1044.812
|''1146.399''
|1069.302
|-
|-
| |15
| |15
|''1101.955''
|1181.955
|1134.937
|1216.241
|1207.318
|1113.384
|''1235.288''
|1142.771
|-
|-
| |16
| |16
|''1168.622''
|1261.955
|1207.101
|1301.955
|1291.546
|1181.955
|''1324.177''
|1216.241
|-
|-
| |17
| |17
|''1235.288''
|1341.955
|1279.265
|1387.669
|1375.773
|1250.526
|''1413.066''
|1289.71
|-
|-
| |18
| |18
|''1301.955''
|1421.955
|1351.429
|1473.384
|1460
|1319.098
|''1501.955''
|1363.2245
|}
|}


== Common Tunings ==
== [[Valentine]] Tunings ==
{| class="wikitable"
{| class="wikitable"
!
!
Line 168: Line 163:
|-
|-
| |16
| |16
|1225.955
|1226.955
|1243.8905
|1243.8905
|1247.71
|1247.71
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