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'''18WTN''' is 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. | '''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. | ||
== | == Patent Intervals == | ||
{| class="wikitable" | {| class="wikitable" | ||
! | ! | ||
! | !Target a | ||
! | !Target b | ||
![ | !Alternating [[EDO|edo]] and *ed(9/8) a | ||
! | !Alternating edo and *ed(9/8) b | ||
|- | |- | ||
| |1 | | |1 | ||
! colspan=" | ! colspan="2" |77.995 | ||
|80 | |||
|75 | |||
|- | |- | ||
| |2 | | |2 | ||
! colspan=" | ! colspan="2" |155.99 | ||
|160 | |||
|150 | |||
|- | |- | ||
| |3 | | |3 | ||
! colspan=" | ! colspan="2" |233.985 | ||
|240 | |||
|225 | |||
|- | |- | ||
| |4 | | |4 | ||
! colspan=" | ! colspan="2" |311.98 | ||
|320 | |||
|300 | |||
|- | |- | ||
| |5 | | |5 | ||
! colspan=" | ! colspan="2" |389.975 | ||
|400 | |||
|375 | |||
|- | |- | ||
| |6 | | |6 | ||
! colspan=" | ! colspan="2" |467.97 | ||
|480 | |||
|450 | |||
|- | |- | ||
| |7 | | |7 | ||
! colspan=" | ! colspan="2" |545.965 | ||
|560 | |||
|525 | |||
|- | |- | ||
| |8 | | |8 | ||
! colspan=" | ! colspan="2" |623.96 | ||
|640 | |||
|600 | |||
|- | |- | ||
| |9 | | |9 | ||
! colspan=" | ! colspan="2" |701.955 | ||
|720 | |||
|675 | |||
|- | |- | ||
| |10 | | |10 | ||
|784.9625 | |784.9625 | ||
| | |773.104 | ||
| | |800 | ||
|750 | |||
|- | |- | ||
| |11 | | |11 | ||
|867.97 | |867.97 | ||
| | |844.253 | ||
| | |880 | ||
|825 | |||
|- | |- | ||
| |12 | | |12 | ||
|950.9775 | |950.9775 | ||
| | |915.403 | ||
| | |960 | ||
|900 | |||
|- | |- | ||
| |13 | | |13 | ||
|1033.985 | |1033.985 | ||
| | |986.552 | ||
| | |1040 | ||
|975 | |||
|- | |- | ||
| |14 | | |14 | ||
|1116.9925 | |1116.9925 | ||
| | |1057.701 | ||
| | |1120 | ||
|1050 | |||
|- | |- | ||
| |15 | | |15 | ||
|1200 | |1200 | ||
| | |1128.896 | ||
| | |1200 | ||
|1125 | |||
|- | |- | ||
| |16 | | |16 | ||
| | |1283.0075 | ||
| | |1200 | ||
| | |1267.97 | ||
| | |1200 | ||
|- | |- | ||
| |17 | | |17 | ||
| | |1366.015 | ||
| | |1262.2556 | ||
| | |1333.94 | ||
| | |1301.955 | ||
|- | |- | ||
| |18 | | |18 | ||
| | |1449.0225 | ||
| | |1324.511 | ||
| | ! colspan="2" |1403.91 | ||
|} | |} | ||
| Line 298: | Line 305: | ||
! colspan="4" |701.955 | ! colspan="4" |701.955 | ||
|} | |} | ||
[[Category:Well tempered nonet]] | |||