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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 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.


== Intervals ==
== Optimal Intervals ==
{| class="wikitable"
{| class="wikitable"
|+
|+
!
!
!''“fifth” 2 = 600¢''
!Minimum a
!“nonet” = 1351.429¢
!Maximum a
!“nonet” = 1460¢
!Minimum b
!''“fifth” 2 = 800¢''
!Maximum b
|-
|-
!1
!1
Line 41: Line 41:
|-
|-
|11
|11
|''761.955''
|770.526
|766.902
|775.424
|777.7595
|761.955
|''781.955''
|766.241
|-
|-
|12
|12
|''821.955''
|839.098
|831.85
|848.893
|853.564
|821.955
|''861.955''
|830.526
|-
|-
|13
|13
|''881.955''
|907.669
|896.797
|921.363
|929.3685
|881.955
|''941.955''
|894.812
|-
|-
|14
|14
|''941.955''
|976.241
|961.744
|995.833
|1005.173
|941.955
|''1021.955''
|959.098
|-
|-
|15
|15
|''1001.955''
|1044.812
|1026.692
|1069.302
|1080.9775
|1001.955
|''1101.955''
|1023.384
|-
|-
|16
|16
|''1061.955''
|1113.384
|1091.639
|1142.771
|1156.782
|1061.955
|''1181.955''
|1087.669
|-
|-
|17
|17
|''1121.955''
|1181.955
|1156.5865
|1216.241
|1232.5865
|1121.955
|''1261.955''
|1151.955
|-
|-
|18
|18
|''1181.955''
|1250.526
|1221.534
|1289.71
|1308.391
|1181.955
|''1341.955''
|1216.241
|-
|-
|19
|19
|''1241.955''
|1319.098
|1286.481
|1363.2245
|1384.1955
|1241.955
|''1421.955''
|1280.526
|-
|-
|20
|20
|''1301.955''
|1387.669
|1351.429
|1467.912
|1460
|1301.955
|''1501.955''
|''1501.955''
|}
== Common Tuning ==
{| class="wikitable"
|1
|70.1955
|-
|2
|140.391
|-
|3
|210.5865
|-
|4
|280.782
|-
|5
|350.9775
|-
|6
|421.173
|-
|7
|491.3685
|-
|8
|561.564
|-
|9
|631.7595
|-
|10
|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
|-
|11
|705.4805
|-
|12
|705.097
|-
|13
|704.7115
|-
|14
|704.311
|-
|15
|703.9185
|-
|16
|703.526
|-
|17
|703.1335
|-
|18
|702.741
|-
|19
|702.3475
|-
|20
|701.955
|}
|}
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