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A '''20 tone well tempered none'''t (20WTN) is related to well temperaments of [[17edo|17 edo]], but with a nonet rather than the 2/1 being constant. It  alternates [[EDF|division of the just perfect fifth]] into 10 equal parts (10EDF) with sequences of ten equal steps of 60 to 80 cents each. This will create ten equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.
A '''20 tone well tempered nonet''' (20WTN) is related to well temperaments of [[17edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF|division of the just perfect fifth]] into 10 equal parts (10EDF) with sequences of ten equal steps of 60 to 80 cents each. This will create ten equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.


== Intervals ==
== Patent Intervals ==
{| class="wikitable"
{| class="wikitable"
|+
|+
!
!
!''“fifth” 2 = 600¢''
!Target
!“nonet” = 1351.429¢
!Alternating [[edo]] and *ed(9/8)
!“nonet” = 1460¢
!''“fifth” 2 = 800¢''
|-
|-
!1
! colspan="4" |70.1955
|-
!2
! colspan="4" |140.391
|-
!3
! colspan="4" |210.5865
|-
!4
! colspan="4" |280.782
|-
!5
! colspan="4" |350.9775
|-
!6
! colspan="4" |421.173
|-
!7
! colspan="4" |491.3685
|-
!8
! colspan="4" |561.564
|-
!9
! colspan="4" |631.7595
|-
!10
! colspan="4" |701.955
|-
|11
|''761.955''
|766.902
|777.7595
|''781.955''
|-
|12
|''821.955''
|831.85
|853.564
|''861.955''
|-
|13
|''881.955''
|896.797
|929.3685
|''941.955''
|-
|14
|''941.955''
|961.744
|1005.173
|''1021.955''
|-
|15
|''1001.955''
|1026.692
|1080.9775
|''1101.955''
|-
|16
|''1061.955''
|1091.639
|1156.782
|''1181.955''
|-
|17
|''1121.955''
|1156.5865
|1232.5865
|''1261.955''
|-
|18
|''1181.955''
|1221.534
|1308.391
|''1341.955''
|-
|19
|''1241.955''
|1286.481
|1384.1955
|''1421.955''
|-
|20
|''1301.955''
|1351.429
|1460
|''1501.955''
|}
== Common Tuning ==
{| class="wikitable"
|1
|1
|70.1955
|70.1955
|70.588
|-
|-
|2
|2
|140.391
|140.391
|141.1765
|-
|-
|3
|3
|210.5865
|210.5865
|211.765
|-
|-
|4
|4
|280.782
|280.782
|282.353
|-
|-
|5
|5
|350.9775
|350.9775
|352.941
|-
|-
|6
|6
|421.173
|421.173
|423.529
|-
|-
|7
|7
|491.3685
|491.3685
|494.118
|-
|-
|8
|8
|561.564
|561.564
|564.706
|-
|-
|9
|9
|631.7595
|631.7595
|635.294
|-
|-
|10
|10
|701.955
|701.955
|-
|11
|772.543
|-
|12
|843.1315
|-
|13
|913.72
|-
|14
|984.308
|-
|15
|1054.896
|-
|16
|1125.484
|-
|17
|1196.073
|-
|18
|1266.661
|-
|19
|1337.245
|-
|20
|1407.837
|-
!
!Fifths
|-
|1
|702.3475
|-
|2
|702.741
|-
|3
|703.1335
|-
|4
|703.526
|-
|5
|703.9185
|-
|6
|704.311
|-
|7
|704.7115
|-
|8
|705.097
|-
|9
|705.4805
|-
|10
|705.882
|705.882
|-
|-
|11
|11
|705.4805
|773.104
|776.471
|-
|-
|12
|12
|705.097
|844.254
|847.059
|-
|-
|13
|13
|704.7115
|915.403
|917.647
|-
|-
|14
|14
|704.311
|986.552
|988.235
|-
|-
|15
|15
|703.9185
|1057.701
|1058.8235
|-
|-
|16
|16
|703.526
|1128.896
|1129.412
|-
|-
|17
|17
|703.1335
! colspan="2" |1200
|-
|-
|18
|18
|702.741
|1271.149
|1267.97
|-
|-
|19
|19
|702.3475
|1342.299
|1333.94
|-
|-
|20
|20
|701.955
|1413.448
|1403.91
|}
|}
[[Category:Well tempered nonet]]
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