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A '''22 tone well tempered nonet''' (22WTN) is related to well temperaments of [[18edo]] and [[19edo]], but with a nonet rather than the 2/1 being constant. It alternates [[EDF|division of the just perfect fifth]] into 11 equal parts (11EDF) with sequences of eleven equal steps of 54.54545 to 72.7273 cents each. This will create eleven equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.
A '''22 tone well tempered nonet''' (22WTN) is related to well temperaments of [[18edo]] and [[19edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF|division of the just perfect fifth]] into 11 equal parts (11EDF) with sequences of eleven equal steps of 54.54545 to 72.7273 cents each. This will create eleven equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.


==Optimal Intervals==
==Patent Intervals==
{| class="wikitable"
{| class="wikitable"
|+
|+
!
!
!Minimum a
!Target a
!Maximum a
!Target b
!Minimum b
!Alternating [[edo]] and *ed(9/8) a
!Maximum b
!Alternating edo and *ed(9/8) b
|-
|-
!1
|1
! colspan="4" |63.8141
! colspan="2" |63.8141
|66.667
|63.1579
|-
|-
!2
|2
! colspan="4" |127.6282
! colspan="2" |127.6282
|133.333
|126.3157
|-
|-
!3
|3
! colspan="4" |191.4423
! colspan="2" |191.4423
|200.000
|189.4737
|-
|-
!4
|4
! colspan="4" |255.2564
! colspan="2" |255.2564
|266.667
|252.6316
|-
|-
!5
|5
! colspan="4" |319.07045
! colspan="2" |319.07045
|333.333
|315.7895
|-
|-
!6
|6
! colspan="4" |382.88455
! colspan="2" |382.88455
|400.000
|378.9474
|-
|-
!7
|7
! colspan="4" |446.6986
! colspan="2" |446.6986
|466.667
|442.1053
|-
|-
!8
|8
! colspan="4" |510.5127
! colspan="2" |510.5127
|533.333
|505.2632
|-
|-
!9
|9
! colspan="4" |574.3268
! colspan="2" |574.3268
|600.000
|568.42105
|-
|-
!10
|10
! colspan="4" |638.1409
! colspan="2" |638.1409
|666.667
|631.57895
|-
|-
!11
|11
! colspan="4" |701.955
! colspan="2" |701.955
|733.333
|694.7368
|-
|-
|12
|12
|770.5264
|773.1043
|775.4244
|764.2106
|761.955
|800.000
|766.2407
|757.8947
|-
|-
|13
|13
|839.0979
|844.2536
|848.8938
|826.466
|821.955
|866.667
|830.5264
|821.0526
|-
|-
|14
|14
|907.6692
|915.4029
|921.3632
|888.7219
|881.955
|933.333
|894.8121
|884.2105
|-
|-
|15
|15
|976.2407
|986.5522
|995.83255
|950.9775
|941.955
|1000.000
|959.0979
|947.3684
|-
|-
|16
|16
|1044.8121
|1057.7014
|1069.3019
|1013.2331
|1001.955
|1066.667
|1023.3836
|1010.5263
|-
|-
|17
|17
|1113.3836
|1128.8507
|1142.7713
|1075.48875
|1061.955
|1133.333
|1087.6692
|1073.6843
|-
|-
|18
|18
|1181.955
|1200
|1216.2407
|1137.7444
|1121.955
|1200.000
|1151.955
|1136.8421
|-
|-
|19
|19
|1250.5264
|1271.1493
|1289.7101
|1200
|1181.955
|1250.9775
|1216.2407
|1200.000
|-
|-
|20
|20
|1319.0979
|1342.2986
|1363.1795
|1262.2556
|1241.955
|1301.955
|1280.5264
|1267.97
|-
|-
|21
|21
|1387.6692
|1413.4479
|1436.6489
|1324.511
|1301.955
|1352.9325
|1344.8121
|1333.94
|-
|-
|22
|22
|1456.2407
|1484.5971
|1510.1183
|1386.7669
|1361.955
! colspan="2" |1403.91
|1409.0907
|}
|}
[[Category:Well tempered nonet]]
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