User:Moremajorthanmajor/20wtn: Difference between revisions
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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]] 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. | ||
== | == Patent Intervals == | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ | |+ | ||
| Line 7: | Line 7: | ||
!Target a | !Target a | ||
!Target b | !Target b | ||
!Alternating edo and *ed(9/8) a | |||
!Alternating edo and *ed(9/8) b | |||
|- | |- | ||
|1 | |||
! colspan="2" |70.1955 | ! colspan="2" |70.1955 | ||
|70.588 | |||
|66.667 | |||
|- | |- | ||
|2 | |||
! colspan="2" |140.391 | ! colspan="2" |140.391 | ||
|141.1765 | |||
|133.333 | |||
|- | |- | ||
|3 | |||
! colspan="2" |210.5865 | ! colspan="2" |210.5865 | ||
|211.765 | |||
|200.000 | |||
|- | |- | ||
|4 | |||
! colspan="2" |280.782 | ! colspan="2" |280.782 | ||
|282.353 | |||
|266.667 | |||
|- | |- | ||
|5 | |||
! colspan="2" |350.9775 | ! colspan="2" |350.9775 | ||
|352.941 | |||
|333.333 | |||
|- | |- | ||
|6 | |||
! colspan="2" |421.173 | ! colspan="2" |421.173 | ||
|423.529 | |||
|400.000 | |||
|- | |- | ||
|7 | |||
! colspan="2" |491.3685 | ! colspan="2" |491.3685 | ||
|494.118 | |||
|466.667 | |||
|- | |- | ||
|8 | |||
! colspan="2" |561.564 | ! colspan="2" |561.564 | ||
|564.706 | |||
|533.333 | |||
|- | |- | ||
|9 | |||
! colspan="2" |631.7595 | ! colspan="2" |631.7595 | ||
|635.294 | |||
|600.000 | |||
|- | |- | ||
|10 | |||
! colspan="2" |701.955 | ! colspan="2" |701.955 | ||
|705.882 | |||
|666.667 | |||
|- | |- | ||
|11 | |11 | ||
|773.104 | |773.104 | ||
|764.211 | |764.211 | ||
|776.471 | |||
|733.333 | |||
|- | |- | ||
|12 | |12 | ||
|844.254 | |844.254 | ||
|826.466 | |826.466 | ||
|847.059 | |||
|800.000 | |||
|- | |- | ||
|13 | |13 | ||
|915.403 | |915.403 | ||
|888.722 | |888.722 | ||
|917.647 | |||
|866.667 | |||
|- | |- | ||
|14 | |14 | ||
|986.552 | |986.552 | ||
|950.9775 | |950.9775 | ||
|988.235 | |||
|933.333 | |||
|- | |- | ||
|15 | |15 | ||
|1057.701 | |1057.701 | ||
|1013.233 | |1013.233 | ||
|1058.8235 | |||
|1000.000 | |||
|- | |- | ||
|16 | |16 | ||
|1128.896 | |1128.896 | ||
|1075.489 | |1075.489 | ||
|1129.412 | |||
|1066.667 | |||
|- | |- | ||
|17 | |17 | ||
|1200 | |1200 | ||
|1137.744 | |1137.744 | ||
|1200 | |||
|1133.333 | |||
|- | |- | ||
|18 | |18 | ||
|1271.149 | |1271.149 | ||
|1200 | |||
|1267.97 | |||
|1200 | |1200 | ||
|- | |- | ||
| Line 73: | Line 111: | ||
|1342.299 | |1342.299 | ||
|1262.256 | |1262.256 | ||
|1333.94 | |||
|1301.955 | |||
|- | |- | ||
|20 | |20 | ||
|1413.448 | |1413.448 | ||
|1324.511 | |1324.511 | ||
! colspan="2" |1403.91 | |||
|} | |} | ||