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A '''32 tone well tempered nonet''' (32WTN) is related to well temperaments of [[27edo]] and [[28edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings alternate [[EDF|division of the just perfect fifth]] into 16 equal parts (16EDF) with sequences of sixteen equal steps of 37.5 to 50 cents each. This will create sixteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.
A '''32 tone well tempered nonet''' (32WTN) is related to well temperaments of [[27edo]] and [[28edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF|division of the just perfect fifth]] into 16 equal parts (16EDF) with sequences of sixteen equal steps of 37.5 to 50 cents each. This will create sixteen 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" |43.8722
! colspan="2" |43.8722
|44.4444
|42.8571
|-
|-
!2
|2
! colspan="4" |87.7444
! colspan="2" |87.7444
|88.8889
|85.7129
|-
|-
!3
|3
! colspan="4" |131.6166
! colspan="2" |131.6166
|133.3333
|128.5714
|-
|-
!4
|4
! colspan="4" |175.48875
! colspan="2" |175.48875
|177.7778
|171.4286
|-
|-
!5
|5
! colspan="4" |219.3609
! colspan="2" |219.3609
|222.2222
|214.2857
|-
|-
!6
|6
! colspan="4" |263.2331
! colspan="2" |263.2331
|266.6667
|257.1429
|-
|-
!7
|7
! colspan="4" |307.1053
! colspan="2" |307.1053
|311.1112
|300.00
|-
|-
!8
|8
! colspan="4" |350.9775
! colspan="2" |350.9775
|355.5556
|342.8571
|-
|-
!9
|9
! colspan="4" |394.8497
! colspan="2" |394.8497
|400.00
|385.7129
|-
|-
!10
|10
! colspan="4" |438.7219
! colspan="2" |438.7219
|444.4444
|428.5714
|-
|-
!11
|11
! colspan="4" |482.5941
! colspan="2" |482.5941
|488.8889
|471.4286
|-
|-
!12
|12
! colspan="4" |526.46625
! colspan="2" |526.46625
|533.3333
|514.2857
|-
|-
!13
|13
! colspan="4" |570.3384
! colspan="2" |570.3384
|577.7778
|557.1429
|-
|-
!14
|14
! colspan="4" |614.2106
! colspan="2" |614.2106
|622.2222
|600.00
|-
|-
!15
|15
! colspan="4" |658.0828
! colspan="2" |658.0828
|666.6667
|642.8571
|-
|-
!16
|16
! colspan="4" |701.9550
! colspan="2" |701.9550
|711.1111
|685.7129
|-
|-
|17
|17
|745.5914
|747.232
|748.70825
|743.459
|741.955
|755.5556
|744.8121
|728.5714
|-
|-
|18
|18
|789.2277
|792.509
|795.4615
|784.9625
|781.955
|800.00
|787.6692
|771.4286
|-
|-
|19
|19
|832.8641
|837.7855
|841.2147
|826.466
|821.955
|844.4444
|830.5264
|814.2857
|-
|-
|20
|20
|876.5005
|883.062
|888.9679
|867.97
|861.955
|888.8889
|873.3836
|857.1429
|-
|-
|21
|21
|920.1368
|928.339
|935.7212
|909.474
|901.955
|933.3333
|916.2407
|900.00
|-
|-
|22
|22
|963.7732
|973.616
|982.4745
|950.9775
|941.955
|977.7778
|959.0979
|942.8571
|-
|-
|23
|23
|1007.4095
|1018.938
|1029.2277
|993.481
|981.955
|1022.2222
|1001.955
|985.7129
|-
|-
|24
|24
|1051.0459
|1064.1695
|1075.9809
|1033.985
|1021.955
|1066.6667
|1044.8121
|1028.5714
|-
|-
|25
|25
|1094.6822
|1109.446
|1122.7342
|1075.489
|1061.955
|1111.1111
|1087.6692
|1071.4286
|-
|-
|26
|26
|1138.3186
|1154.723
|1169.4875
|1116.9925
|1101.955
|1155.5556
|1130.5264
|1114.2857
|-
|-
|27
|27
|1181.955
|1200
|1216.2407
|1158.496
|1141.955
|1200
|1173.3836
|1157.1429
|-
|-
|28
|28
|1225.5914
|1245.277
|1262.994
|1200
|1181.955
|1240.782
|1216.2407
|1200
|-
|-
|29
|29
|1269.2277
|1290.554
|1309.7472
|1241.504
|1221.955
|1281.564
|1259.0979
|1250.9775
|-
|-
|30
|30
|1312.8642
|1335.8305
|1356.5005
|1283.0075
|1261.955
|1322.346
|1301.955
|1301.955
|-
|-
|31
|31
|1356.5005
|1381.107
|1403.2537
|1324.511
|1301.955
|1363.128
|1344.8121
|1352.9325
|-
|-
|32
|32
|1400.1368
|1426.384
|1450.007
|1366.015
|1341.955
! colspan="2" |1403.91
|1387.6792
|}
|}
[[Category:Well tempered nonet]]
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