User:Moremajorthanmajor/28wtn: Difference between revisions

Xenwolf (talk | contribs)
cat+todo, see comment
Line 1: Line 1:
A '''28 tone well tempered nonet''' (28WTN) is related to well temperaments of [[23edo]] and [[24edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF|division of the just perfect fifth]] into 14 equal parts (14EDF) with sequences of fourteen equal steps of 42.8571 to 57.1429 cents each. This will create fourteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.
A '''28 tone well tempered nonet''' (28WTN) is related to well temperaments of [[24edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF|division of the just perfect fifth]] into 14 equal parts (14EDF) with sequences of fourteen equal steps of 42.8571 to 57.1429 cents each. This will create fourteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth. It is also the largest wtn  related to well temperaments of a unique edo.


==Optimal Intervals==
==Patent Intervals==
{| class="wikitable"
{| class="wikitable"
|+
|+
!
|
!Target a
!Target
!Target b
!Alternating [[edo]] and *ed(9/8)
|-
|-
!1
|1
! colspan="2" |50.1396
|50.1396
|50
|-
|-
!2
|2
! colspan="2" |100.2793
|100.2793
|100
|-
|-
!3
|3
! colspan="2" |150.4189
|150.4189
|150
|-
|-
!4
|4
! colspan="2" |200.5586
|200.5586
|200
|-
|-
!5
|5
! colspan="2" |250.6982
|250.6982
|250
|-
|-
!6
|6
! colspan="2" |300.8379
|300.8379
|300
|-
|-
!7
|7
! colspan="2" |350.9775
|350.9775
|350
|-
|-
!8
|8
! colspan="2" |401.1171
|401.1171
|400
|-
|-
!9
|9
! colspan="2" |451.2568
|451.2568
|450
|-
|-
!10
|10
! colspan="2" |501.3964
|501.3964
|500
|-
|-
!11
|11
! colspan="2" |551.536
|551.536
|550
|-
|-
!12
|12
! colspan="2" |601.6757
|601.6757
|600
|-
|-
!13
|13
! colspan="2" |651.8154
|651.8154
|650
|-
|-
!14
|14
! colspan="2" |701.955
|701.955
|700
|-
|-
|15
|15
|757.2933
|751.7595
|751.7595
|750
|-
|-
|16
|16
|812.6317
|801.564
|801.564
|800
|-
|-
|17
|17
|867.97
|851.3685
|851.3685
|850
|-
|-
|18
|18
|923.3083
|901.173
|901.173
|900
|-
|-
|19
|19
|978.6467
|950.9775
|950.9775
|950
|-
|-
|20
|20
|1033.985
|1000.782
|1000.782
|1000
|-
|-
|21
|21
|1089.3233
|1050.6865
|1050.6865
|1050
|-
|-
|22
|22
|1144.6617
|1100.391
|1100.391
|1100
|-
|-
|23
|23
|1200
|1150.1955
|1150.1955
|1150
|-
|-
|24
|24
|1255.3383
|1200
|1200
|1200.000
|-
|-
|25
|25
|1310.6767
|1249.8045
|1249.8045
|1250.9775
|-
|-
|26
|26
|1366.015
|1299.609
|1299.609
|1301.955
|-
|-
|27
|27
|1421.3533
|1349.4135
|1349.4135
|1352.9325
|-
|-
|28
|28
|1476.6917
|1399.218
|1399.218
|1403.91
|}
|}