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A '''28 tone well tempered nonet''' (28WTN) is related to well temperaments of [[23edo]] and [[24edo]], but with a nonet rather than the 2/1 being constant. It alternates [[EDF|division of the just perfect fifth]] into 14 equal parts (14EDF) with sequences of fourteen equal steps of 42.8571 to 57.1429 cents each. This will create fourteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.
A '''28 tone well tempered nonet''' (28WTN) is related to well temperaments of [[24edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF|division of the just perfect fifth]] into 14 equal parts (14EDF) with sequences of fourteen equal steps of 42.8571 to 57.1429 cents each. This will create fourteen 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
!Maximum a
!Alternating [[edo]] and *ed(9/8)
!Minimum b
!Maximum b
|-
|-
!1
|1
! colspan="4" |50.1396
|50.1396
|50
|-
|-
!2
|2
! colspan="4" |100.2793
|100.2793
|100
|-
|-
!3
|3
! colspan="4" |150.4189
|150.4189
|150
|-
|-
!4
|4
! colspan="4" |200.5586
|200.5586
|200
|-
|-
!5
|5
! colspan="4" |250.6982
|250.6982
|250
|-
|-
!6
|6
! colspan="4" |300.8379
|300.8379
|300
|-
|-
!7
|7
! colspan="4" |350.9775
|350.9775
|350
|-
|-
!8
|8
! colspan="4" |401.1171
|401.1171
|400
|-
|-
!9
|9
! colspan="4" |451.2568
|451.2568
|450
|-
|-
!10
|10
! colspan="4" |501.3964
|501.3964
|500
|-
|-
!11
|11
! colspan="4" |551.536
|551.536
|550
|-
|-
!12
|12
! colspan="4" |601.6757
|601.6757
|600
|-
|-
!13
|13
! colspan="4" |651.8154
|651.8154
|650
|-
|-
!14
|14
! colspan="4" |701.955
|701.955
|700
|-
|-
|15
|15
|755.2883
|751.7595
|759.0979
|750
|749.955
|753.3836
|-
|-
|16
|16
|808.6117
|801.564
|816.2407
|800
|797.955
|804.8121
|-
|-
|17
|17
|861.955
|851.3685
|873.3836
|850
|845.955
|856.2407
|-
|-
|18
|18
|915.2883
|901.173
|930.5264
|900
|893.955
|907.6693
|-
|-
|19
|19
|968.6117
|950.9775
|987.6693
|950
|941.955
|959.0979
|-
|-
|20
|20
|1021.955
|1000.782
|1044.8121
|1000
|989.955
|1010.5264
|-
|-
|21
|21
|1075.2883
|1050.6865
|1101.955
|1050
|1037.955
|1061.955
|-
|-
|22
|22
|1128.6117
|1100.391
|1159.0979
|1100
|1085.955
|1113.3836
|-
|-
|23
|23
|1181.955
|1150.1955
|1216.2407
|1150
|1133.995
|1164.8121
|-
|-
|24
|24
|1235.2883
|1200
|1273.3836
|1200.000
|1181.955
|1216.2407
|-
|-
|25
|25
|1288.6117
|1249.8045
|1330.5264
|1250.9775
|1229.995
|1267.6693
|-
|-
|26
|26
|1341.955
|1299.609
|1387.6693
|1301.955
|1277.995
|1319.0979
|-
|-
|27
|27
|1395.2883
|1349.4135
|1444.8121
|1352.9325
|1325.995
|1370.5264
|-
|-
|28
|28
|1448.6117
|1399.218
|1501.955
|1403.91
|1373.995
|1421.955
|}
|}
[[Category:Well tempered nonet]]
{{todo|clarify|unify precision|comment="Target a" and "Target b" are not self-explanatory, how are the values calculated?|inline=1}}
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