User:Moremajorthanmajor/20wtn: Difference between revisions

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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.
-== Optimal Intervals ==
+== Patent Intervals ==
 {| class="wikitable"
 |+
 !
-!Minimum a
+!Target
-!Maximum a
+!Alternating [[edo]] and *ed(9/8)
-!Minimum b
-!Maximum b
 |-
-!1
+|1
-! colspan="4" |70.1955
+|70.1955
+|70.588
 |-
-!2
+|2
-! colspan="4" |140.391
+|140.391
+|141.1765
 |-
-!3
+|3
-! colspan="4" |210.5865
+|210.5865
+|211.765
 |-
-!4
+|4
-! colspan="4" |280.782
+|280.782
+|282.353
 |-
-!5
+|5
-! colspan="4" |350.9775
+|350.9775
+|352.941
 |-
-!6
+|6
-! colspan="4" |421.173
+|421.173
+|423.529
 |-
-!7
+|7
-! colspan="4" |491.3685
+|491.3685
+|494.118
 |-
-!8
+|8
-! colspan="4" |561.564
+|561.564
+|564.706
 |-
-!9
+|9
-! colspan="4" |631.7595
+|631.7595
+|635.294
 |-
-!10
+|10
-! colspan="4" |701.955
+|701.955
+|705.882
 |-
 |11
-|770.526
+|773.104
-|775.424
+|776.471
-|761.955
-|766.241
 |-
 |12
-|839.098
+|844.254
-|848.893
+|847.059
-|821.955
-|830.526
 |-
 |13
-|907.669
+|915.403
-|921.363
+|917.647
-|881.955
-|894.812
 |-
 |14
-|976.241
+|986.552
-|995.833
+|988.235
-|941.955
-|959.098
 |-
 |15
-|1044.812
+|1057.701
-|1069.302
+|1058.8235
-|1001.955
-|1023.384
 |-
 |16
-|1113.384
+|1128.896
-|1142.771
+|1129.412
-|1061.955
-|1087.669
 |-
 |17
-|1181.955
+! colspan="2" |1200
-|1216.241
-|1121.955
-|1151.955
 |-
 |18
-|1250.526
+|1271.149
-|1289.71
+|1267.97
-|1181.955
-|1216.241
 |-
 |19
-|1319.098
+|1342.299
-|1363.2245
+|1333.94
-|1241.955
-|1280.526
 |-
 |20
-|1387.669
+|1413.448
-|1467.912
+|1403.91
-|1301.955
-|1344.812
 |}
+[[Category:Well tempered nonet]]