A 22 tone well tempered nonet (22WTN) is related to well temperaments of 18edo and 19edo, but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate division of the just perfect fifth into 11 equal parts (11EDF) with sequences of eleven equal steps of 54.54545 to 72.7273 cents each. This will create eleven 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
|
63.8141
|
66.667
|
63.1579
|
| 2
|
127.6282
|
133.333
|
126.3157
|
| 3
|
191.4423
|
200.000
|
189.4737
|
| 4
|
255.2564
|
266.667
|
252.6316
|
| 5
|
319.07045
|
333.333
|
315.7895
|
| 6
|
382.88455
|
400.000
|
378.9474
|
| 7
|
446.6986
|
466.667
|
442.1053
|
| 8
|
510.5127
|
533.333
|
505.2632
|
| 9
|
574.3268
|
600.000
|
568.42105
|
| 10
|
638.1409
|
666.667
|
631.57895
|
| 11
|
701.955
|
733.333
|
694.7368
|
| 12
|
773.1043
|
764.2106
|
800.000
|
757.8947
|
| 13
|
844.2536
|
826.466
|
866.667
|
821.0526
|
| 14
|
915.4029
|
888.7219
|
933.333
|
884.2105
|
| 15
|
986.5522
|
950.9775
|
1000.000
|
947.3684
|
| 16
|
1057.7014
|
1013.2331
|
1066.667
|
1010.5263
|
| 17
|
1128.8507
|
1075.48875
|
1133.333
|
1073.6843
|
| 18
|
1200
|
1137.7444
|
1200.000
|
1136.8421
|
| 19
|
1271.1493
|
1200
|
1250.9775
|
1200.000
|
| 20
|
1342.2986
|
1262.2556
|
1301.955
|
1267.97
|
| 21
|
1413.4479
|
1324.511
|
1352.9325
|
1333.94
|
| 22
|
1484.5971
|
1386.7669
|
1403.91
|
 |
Todo: clarify, unify precision |
