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. It alternates [[EDF|division of the just perfect fifth]] into 15 equal parts (15EDF) with sequences of ten 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"
|+
|+
!
!
!Minimum a
!Target a
!Maximum a
!Target b
!Minimum b
!Alternating [[edo]] and *ed(9/8) a
!Maximum b
!Alternating edo and *ed(9/8) b
|-
|-
!1
!1
! colspan="4" |46.797
! colspan="2" |46.797
|48
|46.154
|-
|-
!2
!2
! colspan="4" |93.594
! colspan="2" |93.594
|96
|92.308
|-
|-
!3
!3
! colspan="4" |140.391
! colspan="2" |140.391
|144
|138.4615
|-
|-
!4
!4
! colspan="4" |187.188
! colspan="2" |187.188
|192
|184.615
|-
|-
!5
!5
! colspan="4" |233.985
! colspan="2" |233.985
|240
|230.769
|-
|-
!6
!6
! colspan="4" |280.782
! colspan="2" |280.782
|288
|276.923
|-
|-
!7
!7
! colspan="4" |327.579
! colspan="2" |327.579
|336
|323.077
|-
|-
!8
!8
! colspan="4" |374.376
! colspan="2" |374.376
|384
|369.231
|-
|-
!9
!9
! colspan="4" |421.173
! colspan="2" |421.173
|432
|415.385
|-
|-
!10
!10
! colspan="4" |467.97
! colspan="2" |467.97
|480
|461.5385
|-
|-
!11
!11
! colspan="4" |514.767
! colspan="2" |514.767
|528
|507.692
|-
|-
!12
!12
! colspan="4" |561.564
! colspan="2" |561.564
|576
|553.846
|-
|-
!13
!13
! colspan="4" |608.361
! colspan="2" |608.361
|624
|600.00
|-
|-
!14
!14
! colspan="4" |655.158
! colspan="2" |655.158
|672
|646.154
|-
|-
!15
!15
! colspan="4" |701.955
! colspan="2" |701.955
|720
|692.308
|-
|-
|16
|16
|749.955
|751.7595
|753.384
|747.232
|745.591
|768
|748.698
|738.4615
|-
|-
|17
|17
|797.955
|801.564
|804.812
|792.509
|789.228
|816
|795.4615
|784.615
|-
|-
|18
|18
|845.955
|851.3685
|856.241
|837.7855
|832.864
|864
|841.215
|830.769
|-
|-
|19
|19
|893.955
|901.173
|907.669
|883.062
|876.5005
|912
|888.967
|876.923
|-
|-
|20
|20
|941.955
|950.9775
|959.098
|928.339
|920.137
|960
|935.721
|923.077
|-
|-
|21
|21
|989.955
|1000.782
|1010.526
|973.616
|963.773
|1008
|982.4745
|969.231
|-
|-
|22
|22
|1037.955
|1050.6865
|1061.955
|1018.938
|1007.4095
|1056
|1029.228
|1015.385
|-
|-
|23
|23
|1085.955
|1100.391
|1113.384
|1064.1695
|1051.046
|1104
|1075.981
|1061.5385
|-
|-
|24
|24
|1133.995
|1150.1955
|1164.812
|1109.446
|1094.682
|1152
|1122.734
|1107.692
|-
|-
|25
|25
|1181.955
|1200
|1216.241
|1154.723
|1138.319
|1200
|1169.4875
|1153.846
|-
|-
|26
|26
|1229.995
|1249.8045
|1267.669
|1200
|1181.955
|1240.782
|1216.241
|1200
|-
|-
|27
|27
|1277.995
|1299.609
|1319.098
|1245.277
|1225.591
|1281.564
|1262.993
|1250.9775
|-
|-
|28
|28
|1325.995
|1349.4135
|1370.526
|1290.554
|1269.228
|1322.346
|1309.747
|1301.955
|-
|-
|29
|29
|1373.995
|1399.218
|1421.955
|1335.8305
|1312.864
|1363.128
|1356.5005
|1352.9325
|-
|-
|30
|30
|1421.955
|1449.0225
|1473.384
|1381.107
|1356.5005
! colspan="2" |1403.91
|1403.254
|}
|}
[[Category:Well tempered nonet]]

Latest revision as of 09:31, 1 September 2025

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 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.

Patent Intervals

Target a Target b Alternating edo and *ed(9/8) a Alternating edo and *ed(9/8) b
1 46.797 48 46.154
2 93.594 96 92.308
3 140.391 144 138.4615
4 187.188 192 184.615
5 233.985 240 230.769
6 280.782 288 276.923
7 327.579 336 323.077
8 374.376 384 369.231
9 421.173 432 415.385
10 467.97 480 461.5385
11 514.767 528 507.692
12 561.564 576 553.846
13 608.361 624 600.00
14 655.158 672 646.154
15 701.955 720 692.308
16 751.7595 747.232 768 738.4615
17 801.564 792.509 816 784.615
18 851.3685 837.7855 864 830.769
19 901.173 883.062 912 876.923
20 950.9775 928.339 960 923.077
21 1000.782 973.616 1008 969.231
22 1050.6865 1018.938 1056 1015.385
23 1100.391 1064.1695 1104 1061.5385
24 1150.1955 1109.446 1152 1107.692
25 1200 1154.723 1200 1153.846
26 1249.8045 1200 1240.782 1200
27 1299.609 1245.277 1281.564 1250.9775
28 1349.4135 1290.554 1322.346 1301.955
29 1399.218 1335.8305 1363.128 1352.9325
30 1449.0225 1381.107 1403.91
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