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 optimally 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.
Patent Intervals
|
|
Target a
|
Target b
|
Alternating edo and *ed(9/8) a
|
Alternating edo and *ed(9/8) b
|
| 1
|
43.8722
|
44.4444
|
42.8571
|
| 2
|
87.7444
|
88.8889
|
85.7129
|
| 3
|
131.6166
|
133.3333
|
128.5714
|
| 4
|
175.48875
|
177.7778
|
171.4286
|
| 5
|
219.3609
|
222.2222
|
214.2857
|
| 6
|
263.2331
|
266.6667
|
257.1429
|
| 7
|
307.1053
|
311.1112
|
300.00
|
| 8
|
350.9775
|
355.5556
|
342.8571
|
| 9
|
394.8497
|
400.00
|
385.7129
|
| 10
|
438.7219
|
444.4444
|
428.5714
|
| 11
|
482.5941
|
488.8889
|
471.4286
|
| 12
|
526.46625
|
533.3333
|
514.2857
|
| 13
|
570.3384
|
577.7778
|
557.1429
|
| 14
|
614.2106
|
622.2222
|
600.00
|
| 15
|
658.0828
|
666.6667
|
642.8571
|
| 16
|
701.9550
|
711.1111
|
685.7129
|
| 17
|
747.232
|
743.459
|
755.5556
|
728.5714
|
| 18
|
792.509
|
784.9625
|
800.00
|
771.4286
|
| 19
|
837.7855
|
826.466
|
844.4444
|
814.2857
|
| 20
|
883.062
|
867.97
|
888.8889
|
857.1429
|
| 21
|
928.339
|
909.474
|
933.3333
|
900.00
|
| 22
|
973.616
|
950.9775
|
977.7778
|
942.8571
|
| 23
|
1018.938
|
993.481
|
1022.2222
|
985.7129
|
| 24
|
1064.1695
|
1033.985
|
1066.6667
|
1028.5714
|
| 25
|
1109.446
|
1075.489
|
1111.1111
|
1071.4286
|
| 26
|
1154.723
|
1116.9925
|
1155.5556
|
1114.2857
|
| 27
|
1200
|
1158.496
|
1200
|
1157.1429
|
| 28
|
1245.277
|
1200
|
1240.782
|
1200
|
| 29
|
1290.554
|
1241.504
|
1281.564
|
1250.9775
|
| 30
|
1335.8305
|
1283.0075
|
1322.346
|
1301.955
|
| 31
|
1381.107
|
1324.511
|
1363.128
|
1352.9325
|
| 32
|
1426.384
|
1366.015
|
1403.91
|
 |
Todo: clarify, unify precision |
