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 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.


== Optimal Intervals ==
== Patent Intervals ==
{| class="wikitable"
{| class="wikitable"
|+
|+
!
!
!Target a
!Target
!Target b
!Alternating [[edo]] and *ed(9/8)
|-
|-
!1
|1
! colspan="2" |70.1955
|70.1955
|70.588
|-
|-
!2
|2
! colspan="2" |140.391
|140.391
|141.1765
|-
|-
!3
|3
! colspan="2" |210.5865
|210.5865
|211.765
|-
|-
!4
|4
! colspan="2" |280.782
|280.782
|282.353
|-
|-
!5
|5
! colspan="2" |350.9775
|350.9775
|352.941
|-
|-
!6
|6
! colspan="2" |421.173
|421.173
|423.529
|-
|-
!7
|7
! colspan="2" |491.3685
|491.3685
|494.118
|-
|-
!8
|8
! colspan="2" |561.564
|561.564
|564.706
|-
|-
!9
|9
! colspan="2" |631.7595
|631.7595
|635.294
|-
|-
!10
|10
! colspan="2" |701.955
|701.955
|705.882
|-
|-
|11
|11
|773.104
|773.104
|764.2106
|776.471
|-
|-
|12
|12
|844.254
|844.254
|826.466
|847.059
|-
|-
|13
|13
|915.403
|915.403
|888.7219
|917.647
|-
|-
|14
|14
|986.552
|986.552
|950.9775
|988.235
|-
|-
|15
|15
|1057.701
|1057.701
|1013.2331
|1058.8235
|-
|-
|16
|16
|1128.896
|1128.896
|1075.48875
|1129.412
|-
|-
|17
|17
|1200
! colspan="2" |1200
|1137.7444
|-
|-
|18
|18
|1271.1493
|1271.149
|1200
|1267.97
|-
|-
|19
|19
|1342.2986
|1342.299
|1262.2556
|1333.94
|-
|-
|20
|20
|1413.4479
|1413.448
|1324.511
|1403.91
|}
|}
[[Category:Well tempered nonet]]

Latest revision as of 09:31, 1 September 2025

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 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 Alternating edo and *ed(9/8)
1 70.1955 70.588
2 140.391 141.1765
3 210.5865 211.765
4 280.782 282.353
5 350.9775 352.941
6 421.173 423.529
7 491.3685 494.118
8 561.564 564.706
9 631.7595 635.294
10 701.955 705.882
11 773.104 776.471
12 844.254 847.059
13 915.403 917.647
14 986.552 988.235
15 1057.701 1058.8235
16 1128.896 1129.412
17 1200
18 1271.149 1267.97
19 1342.299 1333.94
20 1413.448 1403.91
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