User:Moremajorthanmajor/30wtn: Difference between revisions

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A '''30 tone well tempered nonet''' (30WTN) is related to well temperaments of [[25edo]] and [[26edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF|division of the just perfect fifth]] into 15 equal parts (15EDF) with sequences of fifteen equal steps of 40 to 53.333 cents each. This will create fifteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.
A '''30 tone well tempered nonet''' (30WTN) is related to well temperaments of [[25edo]] and [[26edo]], but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate [[EDF|division of the just perfect fifth]] into 15 equal parts (15EDF) with sequences of fifteen equal steps of 40 to 53.333 cents each. This will create fifteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.


== Optimal Intervals ==
== 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
!1
! colspan="2" |46.797
! colspan="2" |46.797
|48
|46.154
|-
|-
!2
!2
! colspan="2" |93.594
! colspan="2" |93.594
|96
|92.308
|-
|-
!3
!3
! colspan="2" |140.391
! colspan="2" |140.391
|144
|138.4615
|-
|-
!4
!4
! colspan="2" |187.188
! colspan="2" |187.188
|192
|184.615
|-
|-
!5
!5
! colspan="2" |233.985
! colspan="2" |233.985
|240
|230.769
|-
|-
!6
!6
! colspan="2" |280.782
! colspan="2" |280.782
|288
|276.923
|-
|-
!7
!7
! colspan="2" |327.579
! colspan="2" |327.579
|336
|323.077
|-
|-
!8
!8
! colspan="2" |374.376
! colspan="2" |374.376
|384
|369.231
|-
|-
!9
!9
! colspan="2" |421.173
! colspan="2" |421.173
|432
|415.385
|-
|-
!10
!10
! colspan="2" |467.97
! colspan="2" |467.97
|480
|461.5385
|-
|-
!11
!11
! colspan="2" |514.767
! colspan="2" |514.767
|528
|507.692
|-
|-
!12
!12
! colspan="2" |561.564
! colspan="2" |561.564
|576
|553.846
|-
|-
!13
!13
! colspan="2" |608.361
! colspan="2" |608.361
|624
|600.00
|-
|-
!14
!14
! colspan="2" |655.158
! colspan="2" |655.158
|672
|646.154
|-
|-
!15
!15
! colspan="2" |701.955
! colspan="2" |701.955
|720
|692.308
|-
|-
|16
|16
|751.7595
|751.7595
|747.232
|747.232
|768
|738.4615
|-
|-
|17
|17
|801.564
|801.564
|792.509
|792.509
|816
|784.615
|-
|-
|18
|18
|851.3685
|851.3685
|837.7855
|837.7855
|864
|830.769
|-
|-
|19
|19
|901.173
|901.173
|883.062
|883.062
|912
|876.923
|-
|-
|20
|20
|950.9775
|950.9775
|928.339
|928.339
|960
|923.077
|-
|-
|21
|21
|1000.782
|1000.782
|973.616
|973.616
|1008
|969.231
|-
|-
|22
|22
|1050.6865
|1050.6865
|1018.938
|1018.938
|1056
|1015.385
|-
|-
|23
|23
|1100.391
|1100.391
|1064.1695
|1064.1695
|1104
|1061.5385
|-
|-
|24
|24
|1150.1955
|1150.1955
|1109.446
|1109.446
|1152
|1107.692
|-
|-
|25
|25
|1200
|1200
|1154.723
|1154.723
|1200
|1153.846
|-
|-
|26
|26
|1249.8045
|1249.8045
|1200
|1240.782
|1200
|1200
|-
|-
Line 100: Line 154:
|1299.609
|1299.609
|1245.277
|1245.277
|1281.564
|1250.9775
|-
|-
|28
|28
|1349.4135
|1349.4135
|1290.554
|1290.554
|1322.346
|1301.955
|-
|-
|29
|29
|1399.218
|1399.218
|1335.8305
|1335.8305
|1363.128
|1352.9325
|-
|-
|30
|30
|1449.0225
|1449.0225
|1381.107
|1381.107
! colspan="2" |1403.91
|}
|}