User:Moremajorthanmajor/20wtn: Difference between revisions

m Text replacement - "{{todo|clarify|unify precision|inline=1}}" to ""
 
(4 intermediate revisions by 2 users not shown)
Line 1: Line 1:
A '''20 tone well tempered nonet''' (20WTN) is related to well temperaments of [[17edo]] and [[18edo]], 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.
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.


== Patent Intervals ==
== Patent Intervals ==
Line 5: Line 5:
|+
|+
!
!
!Target a
!Target
!Target b
!Alternating [[edo]] and *ed(9/8)
!Alternating edo and *ed(9/8) a
!Alternating edo and *ed(9/8) b
|-
|-
|1
|1
! colspan="2" |70.1955
|70.1955
|70.588
|70.588
|66.667
|-
|-
|2
|2
! colspan="2" |140.391
|140.391
|141.1765
|141.1765
|133.333
|-
|-
|3
|3
! colspan="2" |210.5865
|210.5865
|211.765
|211.765
|200.000
|-
|-
|4
|4
! colspan="2" |280.782
|280.782
|282.353
|282.353
|266.667
|-
|-
|5
|5
! colspan="2" |350.9775
|350.9775
|352.941
|352.941
|333.333
|-
|-
|6
|6
! colspan="2" |421.173
|421.173
|423.529
|423.529
|400.000
|-
|-
|7
|7
! colspan="2" |491.3685
|491.3685
|494.118
|494.118
|466.667
|-
|-
|8
|8
! colspan="2" |561.564
|561.564
|564.706
|564.706
|533.333
|-
|-
|9
|9
! colspan="2" |631.7595
|631.7595
|635.294
|635.294
|600.000
|-
|-
|10
|10
! colspan="2" |701.955
|701.955
|705.882
|705.882
|666.667
|-
|-
|11
|11
|773.104
|773.104
|764.211
|776.471
|776.471
|733.333
|-
|-
|12
|12
|844.254
|844.254
|826.466
|847.059
|847.059
|800.000
|-
|-
|13
|13
|915.403
|915.403
|888.722
|917.647
|917.647
|866.667
|-
|-
|14
|14
|986.552
|986.552
|950.9775
|988.235
|988.235
|933.333
|-
|-
|15
|15
|1057.701
|1057.701
|1013.233
|1058.8235
|1058.8235
|1000.000
|-
|-
|16
|16
|1128.896
|1128.896
|1075.489
|1129.412
|1129.412
|1066.667
|-
|-
|17
|17
|1200
! colspan="2" |1200
|1137.744
|1200
|1133.333
|-
|-
|18
|18
|1271.149
|1271.149
|1200
|1267.97
|1267.97
|1200
|-
|-
|19
|19
|1342.299
|1342.299
|1262.256
|1333.94
|1333.94
|1301.955
|-
|-
|20
|20
|1413.448
|1413.448
|1324.511
|1403.91
! colspan="2" |1403.91
|}
|}


[[Category:Well tempered nonet]]
[[Category:Well tempered nonet]]
{{todo|clarify|unify precision|inline=1}}