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 | |||
|} | |} | ||
Revision as of 16:31, 2 June 2021
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 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
| Target a | Target b | Alternating edo and *ed(9/8) a | Alternating edo and *ed(9/8) b | |
|---|---|---|---|---|
| 1 | 70.1955 | 70.588 | 66.667 | |
| 2 | 140.391 | 141.1765 | 133.333 | |
| 3 | 210.5865 | 211.765 | 200.000 | |
| 4 | 280.782 | 282.353 | 266.667 | |
| 5 | 350.9775 | 352.941 | 333.333 | |
| 6 | 421.173 | 423.529 | 400.000 | |
| 7 | 491.3685 | 494.118 | 466.667 | |
| 8 | 561.564 | 564.706 | 533.333 | |
| 9 | 631.7595 | 635.294 | 600.000 | |
| 10 | 701.955 | 705.882 | 666.667 | |
| 11 | 773.104 | 764.211 | 776.471 | 733.333 |
| 12 | 844.254 | 826.466 | 847.059 | 800.000 |
| 13 | 915.403 | 888.722 | 917.647 | 866.667 |
| 14 | 986.552 | 950.9775 | 988.235 | 933.333 |
| 15 | 1057.701 | 1013.233 | 1058.8235 | 1000.000 |
| 16 | 1128.896 | 1075.489 | 1129.412 | 1066.667 |
| 17 | 1200 | 1137.744 | 1200 | 1133.333 |
| 18 | 1271.149 | 1200 | 1267.97 | 1200 |
| 19 | 1342.299 | 1262.256 | 1333.94 | 1301.955 |
| 20 | 1413.448 | 1324.511 | 1403.91 | |
|
Todo: clarify, unify precision |