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A '''34 tone well tempered nonet''' (34WTN) is related to well temperaments of [[29edo]] and [[30edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings alternate [[EDF|division of the just perfect fifth]] into 17 equal parts (17EDF) with sequences of seventeen equal steps of 35.2941 to 47.0588 cents each. This will create seventeen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.
A '''34 tone well tempered nonet''' (34WTN) is related to well temperaments of [[29edo]] and [[30edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF|division of the just perfect fifth]] into 17 equal parts (17EDF) with sequences of seventeen equal steps of 35.2941 to 47.0588 cents each. This will create seventeen 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
!Alternating [[edo]] and *ed(9/8)
!Minimum b
!Maximum b
|-
|-
!1
|1
! colspan="4" |41.2915
|41.2915
|41.3793
|-
|-
!2
|2
! colspan="4" |82.5829
|82.5829
|82.7586
|-
|-
!3
|3
! colspan="4" |123.8744
|123.8744
|124.1379
|-
|-
!4
|4
! colspan="4" |165.1659
|165.1659
|165.5172
|-
|-
!5
|5
! colspan="4" |206.45735
|206.45735
|206.89655
|-
|-
!6
|6
! colspan="4" |248.7488
|248.7488
|248.2758
|-
|-
!7·
|7·
! colspan="4" |289.0403
|289.0403
|289.6552
|-
|-
!8
|8
! colspan="4" |330.3318
|330.3318
|331.0345
|-
|-
!9
|9
! colspan="4" |371.6232
|371.6232
|372.4137
|-
|-
!10
|10
! colspan="4" |412.9147
|412.9147
|413.7931
|-
|-
!11
|11
! colspan="4" |455.2062
|455.2062
|455.1724
|-
|-
!12·
|12·
! colspan="4" |495.49765
|495.49765
|496.5517
|-
|-
!13
|13
! colspan="4" |536.7891
|536.7891
|537.931
|-
|-
!14
|14
! colspan="4" |578.0806
|578.0806
|579.3103
|-
|-
!15
|15
! colspan="4" |619.3721
|619.3721
|620.6897
|-
|-
!16
|16
! colspan="4" |660.6635
|660.6635
|662.069
|-
|-
!17·
|17·
! colspan="4" |701.955
|701.955
|703.4483
|-
|-
|18
|18
|741.955
|743.45875
|744.8121
|744.8276
|738.8781
|741.5154
|-
|-
|19
|19
|781.955
|784.9625
|787.6692
|786.2069
|775.80115
|781.0759
|-
|-
|20
|20
|821.955
|826.46625
|830.5264
|827.5863
|812.7242
|820.6363
|-
|-
|21
|21
|861.955
|867.97
|873.3836
|868.9655
|849.6473
|860.1968
|-
|-
|22·
|22·
|901.955
|909.47375
|916.2407
|910.3448
|886.5704
|899.7572
|-
|-
|23
|23
|941.955
|950.9775
|959.0979
|951.7242
|923.4935
|939.3177
|-
|-
|24
|24
|981.955
|993.48125
|1001.955
|993.10345
|960.4165
|978.8781
|-
|-
|25
|25
|1021.955
|1033.985
|1044.8121
|1034.4828
|997.3396
|1018.4385
|-
|-
|26
|26
|1061.955
|1075.48875
|1087.6692
|1075.8621
|1034.2627
|1057.999
|-
|-
|27
|27
|1101.955
|1116.9925
|1130.5264
|1117.2414
|1071.1858
|1097.5594
|-
|-
|28
|28
|1141.955
|1158.49625
|1173.3836
|1158.6207
|1108.10885
|1137.1198
|-
|-
|29
|29
|1181.955
! colspan="2" |1200
|1216.2407
|1145.0319
|1176.6803
|-
|-
|30
|30
|1221.955
|1241.50375
|1259.0979
|1240.782
|1181.955
|1216.2407
|-
|-
|31
|31
|1261.955
|1283.0075
|1301.955
|1281.564
|1218.8781
|1255.8012
|-
|-
|32
|32
|1301.955
|1324.51125
|1344.8121
|1322.346
|1255.80115
|1295.3616
|-
|-
|33
|33
|1341.955
|1366.015
|1387.6792
|1363.128
|1292.7242
|1334.922
|-
|-
|34
|34
|1381.955
|1407.51875
|1430.5264
|1403.91
|1329.6473
|1374.4825
|}
|}
[[Category:Well tempered nonet]]
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