A 24 tone well tempered nonet (24WTN) is related to well temperaments of 20edo and 21edo, but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate division of the just perfect fifth into 12 equal parts (12EDF) with sequences of twelve equal steps of 50 to 66.6667 cents each. This will create twelve 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
|
58.49625
|
60
|
57.1429
|
| 2
|
116.9925
|
120
|
114.2857
|
| 3
|
175.48875
|
180
|
171.4286
|
| 4
|
233.985
|
240
|
228.5714
|
| 5
|
292.48125
|
300
|
285.7143
|
| 6
|
350.9775
|
360
|
342.8571
|
| 7
|
409.47375
|
420
|
400.00
|
| 8
|
467.97
|
480
|
457.1429
|
| 9
|
526.46625
|
540
|
514.2857
|
| 10
|
584.9625
|
600
|
571.4286
|
| 11
|
643.45875
|
660
|
628.5714
|
| 12
|
701.955
|
720
|
685.7143
|
| 13
|
764.2106
|
757.2933
|
780
|
742.8571
|
| 14
|
826.466
|
812.6317
|
840
|
800.00
|
| 15
|
888.7219
|
867.97
|
900
|
857.1429
|
| 16
|
950.9775
|
923.3083
|
960
|
914.285
|
| 17
|
1013.2331
|
978.6467
|
1020
|
971.4286
|
| 18
|
1075.48875
|
1033.985
|
1080
|
1028.5714
|
| 19
|
1137.7444
|
1089.3233
|
1140
|
1085.7143
|
| 20
|
1200
|
1144.6617
|
1200.000
|
1142.8571
|
| 21
|
1262.2556
|
1200
|
1250.9775
|
1200.000
|
| 22
|
1324.511
|
1255.3383
|
1301.955
|
1267.97
|
| 23
|
1386.7669
|
1310.6767
|
1352.9325
|
1333.94
|
| 24
|
1449.0225
|
1366.015
|
1403.91
|
 |
Todo: clarify, unify precision |
