User:Moremajorthanmajor/18wtn: Difference between revisions

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'''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.
'''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.


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


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[[Category:Well tempered nonet]]
[[Category:Well tempered nonet]]
{{todo|clarify|unify precision|inline=1}}