User:Moremajorthanmajor/32wtn: Difference between revisions

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Created page with "A '''32 tone well tempered nonet''' (32WTN) is related to well temperaments of 27edo and 28edo, but with a nonet rather than the 2/1 being constant. Its patent tunings..."
 
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!
!
!Minimum a
!Target a
!Maximum a
!Target b
!Minimum b
!Maximum b
|-
|-
!1
!1
! colspan="4" |43.8722
! colspan="2" |43.8722
|-
|-
!2
!2
! colspan="4" |87.7444
! colspan="2" |87.7444
|-
|-
!3
!3
! colspan="4" |131.6166
! colspan="2" |131.6166
|-
|-
!4
!4
! colspan="4" |175.48875
! colspan="2" |175.48875
|-
|-
!5
!5
! colspan="4" |219.3609
! colspan="2" |219.3609
|-
|-
!6
!6
! colspan="4" |263.2331
! colspan="2" |263.2331
|-
|-
!7
!7
! colspan="4" |307.1053
! colspan="2" |307.1053
|-
|-
!8
!8
! colspan="4" |350.9775
! colspan="2" |350.9775
|-
|-
!9
!9
! colspan="4" |394.8497
! colspan="2" |394.8497
|-
|-
!10
!10
! colspan="4" |438.7219
! colspan="2" |438.7219
|-
|-
!11
!11
! colspan="4" |482.5941
! colspan="2" |482.5941
|-
|-
!12
!12
! colspan="4" |526.46625
! colspan="2" |526.46625
|-
|-
!13
!13
! colspan="4" |570.3384
! colspan="2" |570.3384
|-
|-
!14
!14
! colspan="4" |614.2106
! colspan="2" |614.2106
|-
|-
!15
!15
! colspan="4" |658.0828
! colspan="2" |658.0828
|-
|-
!16
!16
! colspan="4" |701.9550
! colspan="2" |701.9550
|-
|-
|17
|17
|745.5914
|747.232
|748.70825
|743.459
|741.955
|744.8121
|-
|-
|18
|18
|789.2277
|792.509
|795.4615
|784.9625
|781.955
|787.6692
|-
|-
|19
|19
|832.8641
|837.7855
|841.2147
|826.466
|821.955
|830.5264
|-
|-
|20
|20
|876.5005
|883.062
|888.9679
|867.97
|861.955
|873.3836
|-
|-
|21
|21
|920.1368
|928.339
|935.7212
|909.474
|901.955
|916.2407
|-
|-
|22
|22
|963.7732
|973.616
|982.4745
|950.9775
|941.955
|959.0979
|-
|-
|23
|23
|1007.4095
|1018.938
|1029.2277
|993.481
|981.955
|1001.955
|-
|-
|24
|24
|1051.0459
|1064.1695
|1075.9809
|1033.985
|1021.955
|1044.8121
|-
|-
|25
|25
|1094.6822
|1109.446
|1122.7342
|1075.489
|1061.955
|1087.6692
|-
|-
|26
|26
|1138.3186
|1154.723
|1169.4875
|1116.9925
|1101.955
|1130.5264
|-
|-
|27
|27
|1181.955
|1200
|1216.2407
|1158.496
|1141.955
|1173.3836
|-
|-
|28
|28
|1225.5914
|1245.277
|1262.994
|1200
|1181.955
|1216.2407
|-
|-
|29
|29
|1269.2277
|1290.554
|1309.7472
|1241.504
|1221.955
|1259.0979
|-
|-
|30
|30
|1312.8642
|1335.8305
|1356.5005
|1283.0075
|1261.955
|1301.955
|-
|-
|31
|31
|1356.5005
|1381.107
|1403.2537
|1324.511
|1301.955
|1344.8121
|-
|-
|32
|32
|1400.1368
|1426.384
|1450.007
|1366.015
|1341.955
|1387.6792
|}
|}

Revision as of 17:50, 1 June 2021

A 32 tone well tempered nonet (32WTN) is related to well temperaments of 27edo and 28edo, but with a nonet rather than the 2/1 being constant. Its patent tunings alternate division of the just perfect fifth into 16 equal parts (16EDF) with sequences of sixteen equal steps of 37.5 to 50 cents each. This will create sixteen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.

Optimal Intervals

Target a Target b
1 43.8722
2 87.7444
3 131.6166
4 175.48875
5 219.3609
6 263.2331
7 307.1053
8 350.9775
9 394.8497
10 438.7219
11 482.5941
12 526.46625
13 570.3384
14 614.2106
15 658.0828
16 701.9550
17 747.232 743.459
18 792.509 784.9625
19 837.7855 826.466
20 883.062 867.97
21 928.339 909.474
22 973.616 950.9775
23 1018.938 993.481
24 1064.1695 1033.985
25 1109.446 1075.489
26 1154.723 1116.9925
27 1200 1158.496
28 1245.277 1200
29 1290.554 1241.504
30 1335.8305 1283.0075
31 1381.107 1324.511
32 1426.384 1366.015