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A '''24 tone well tempered nonet''' (24WTN) is related to well temperaments of [[20edo]] and [[21edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings alternate [[EDF|division of the just perfect fifth]] into 12 equal parts (12EDF) with sequences of twelve equal steps of 50 to 66.6667 cents each. This will create twelve equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.
A '''24 tone well tempered nonet''' (24WTN) is related to well temperaments of [[20edo]] and [[21edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF|division of the just perfect fifth]] into 12 equal parts (12EDF) with sequences of twelve equal steps of 50 to 66.6667 cents each. This will create twelve 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" |58.49625
! colspan="2" |58.49625
|60
|57.1429
|-
|-
!2
!2
! colspan="4" |116.9925
! colspan="2" |116.9925
|120
|114.2857
|-
|-
!3
!3
! colspan="4" |175.48875
! colspan="2" |175.48875
|180
|171.4286
|-
|-
!4
!4
! colspan="4" |233.985
! colspan="2" |233.985
|240
|228.5714
|-
|-
!5
!5
! colspan="4" |292.48125
! colspan="2" |292.48125
|300
|285.7143
|-
|-
!6
!6
! colspan="4" |350.9775
! colspan="2" |350.9775
|360
|342.8571
|-
|-
!7
!7
! colspan="4" |409.47375
! colspan="2" |409.47375
|420
|400.00
|-
|-
!8
!8
! colspan="4" |467.97
! colspan="2" |467.97
|480
|457.1429
|-
|-
!9
!9
! colspan="4" |526.46625
! colspan="2" |526.46625
|540
|514.2857
|-
|-
!10
!10
! colspan="4" |584.9625
! colspan="2" |584.9625
|600
|571.4286
|-
|-
!11
!11
! colspan="4" |643.45875
! colspan="2" |643.45875
|660
|628.5714
|-
|-
!12
!12
! colspan="4" |701.955
! colspan="2" |701.955
|720
|685.7143
|-
|-
|13
|13
|761.955
|764.2106
|766.2407
|757.2933
|755.2883
|780
|759.0979
|742.8571
|-
|-
|14
|14
|821.955
|826.466
|830.5264
|812.6317
|808.6117
|840
|816.2407
|800.00
|-
|-
|15
|15
|881.955
|888.7219
|894.8121
|867.97
|861.955
|900
|873.3836
|857.1429
|-
|-
|16
|16
|941.955
|950.9775
|959.0979
|923.3083
|915.2883
|960
|930.5264
|914.285
|-
|-
|17
|17
|1001.955
|1013.2331
|1023.3836
|978.6467
|968.6117
|1020
|987.6693
|971.4286
|-
|-
|18
|18
|1061.955
|1075.48875
|1087.6693
|1033.985
|1021.955
|1080
|1044.8121
|1028.5714
|-
|-
|19
|19
|1121.955
|1137.7444
|1151.955
|1089.3233
|1075.2883
|1140
|1101.955
|1085.7143
|-
|-
|20
|20
|1181.955
|1200
|1216.2407
|1144.6617
|1128.6117
|1200.000
|1159.0979
|1142.8571
|-
|-
|21
|21
|1241.955
|1262.2556
|1280.5264
|1200
|1181.955
|1250.9775
|1216.2407
|1200.000
|-
|-
|22
|22
|1324.511
|1255.3383
|1301.955
|1301.955
|1344.8121
|1267.97
|1235.2883
|1273.3836
|-
|-
|23
|23
|1361.955
|1386.7669
|1409.0907
|1310.6767
|1288.6117
|1352.9325
|1330.5264
|1333.94
|-
|-
|24
|24
|1441.955
|1449.0225
|1473.3836
|1366.015
|1341.955
! colspan="2" |1403.91
|1387.6693
|}
|}
[[Category:Well tempered nonet]]
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