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A '''30 tone well tempered nonet''' (30WTN) is related to well temperaments of [[25edo]] and [[26edo]], but with a nonet rather than the 2/1 being constant. It alternates [[EDF|division of the just perfect fifth]] into 15 equal parts (15EDF) with sequences of fifteen equal steps of 40 to 53.333 cents each. This will create fifteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.
A '''30 tone well tempered nonet''' (30WTN) is related to well temperaments of [[25edo]] and [[26edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF|division of the just perfect fifth]] into 15 equal parts (15EDF) with sequences of fifteen equal steps of 40 to 53.333 cents each. This will create fifteen 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" |46.797
! colspan="2" |46.797
|48
|46.154
|-
|-
!2
!2
! colspan="4" |93.594
! colspan="2" |93.594
|96
|92.308
|-
|-
!3
!3
! colspan="4" |140.391
! colspan="2" |140.391
|144
|138.4615
|-
|-
!4
!4
! colspan="4" |187.188
! colspan="2" |187.188
|192
|184.615
|-
|-
!5
!5
! colspan="4" |233.985
! colspan="2" |233.985
|240
|230.769
|-
|-
!6
!6
! colspan="4" |280.782
! colspan="2" |280.782
|288
|276.923
|-
|-
!7
!7
! colspan="4" |327.579
! colspan="2" |327.579
|336
|323.077
|-
|-
!8
!8
! colspan="4" |374.376
! colspan="2" |374.376
|384
|369.231
|-
|-
!9
!9
! colspan="4" |421.173
! colspan="2" |421.173
|432
|415.385
|-
|-
!10
!10
! colspan="4" |467.97
! colspan="2" |467.97
|480
|461.5385
|-
|-
!11
!11
! colspan="4" |514.767
! colspan="2" |514.767
|528
|507.692
|-
|-
!12
!12
! colspan="4" |561.564
! colspan="2" |561.564
|576
|553.846
|-
|-
!13
!13
! colspan="4" |608.361
! colspan="2" |608.361
|624
|600.00
|-
|-
!14
!14
! colspan="4" |655.158
! colspan="2" |655.158
|672
|646.154
|-
|-
!15
!15
! colspan="4" |701.955
! colspan="2" |701.955
|720
|692.308
|-
|-
|16
|16
|749.955
|751.7595
|753.384
|747.232
|745.591
|768
|748.708
|738.4615
|-
|-
|17
|17
|797.955
|801.564
|804.812
|792.509
|789.228
|816
|795.4615
|784.615
|-
|-
|18
|18
|845.955
|851.3685
|856.241
|837.7855
|832.864
|864
|841.215
|830.769
|-
|-
|19
|19
|893.955
|901.173
|907.669
|883.062
|876.5005
|912
|888.968
|876.923
|-
|-
|20
|20
|941.955
|950.9775
|959.098
|928.339
|920.137
|960
|935.721
|923.077
|-
|-
|21
|21
|989.955
|1000.782
|1010.526
|973.616
|963.773
|1008
|982.4745
|969.231
|-
|-
|22
|22
|1037.955
|1050.6865
|1061.955
|1018.938
|1007.4095
|1056
|1029.228
|1015.385
|-
|-
|23
|23
|1085.955
|1100.391
|1113.384
|1064.1695
|1051.046
|1104
|1075.981
|1061.5385
|-
|-
|24
|24
|1133.995
|1150.1955
|1164.812
|1109.446
|1094.682
|1152
|1122.734
|1107.692
|-
|-
|25
|25
|1181.955
|1200
|1216.241
|1154.723
|1138.319
|1200
|1169.4875
|1153.846
|-
|-
|26
|26
|1229.995
|1249.8045
|1267.669
|1200
|1181.955
|1240.782
|1216.241
|1200
|-
|-
|27
|27
|1277.995
|1299.609
|1319.098
|1245.277
|1225.591
|1281.564
|1262.994
|1250.9775
|-
|-
|28
|28
|1325.995
|1349.4135
|1370.526
|1290.554
|1269.228
|1322.346
|1309.747
|1301.955
|-
|-
|29
|29
|1373.995
|1399.218
|1421.955
|1335.8305
|1312.864
|1363.128
|1356.5005
|1352.9325
|-
|-
|30
|30
|1421.955
|1449.0225
|1473.384
|1381.107
|1356.5005
! colspan="2" |1403.91
|1403.254
|}
|}
[[Category:Well tempered nonet]]
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