A 36 tone well tempered nonet (36WTN) is related to well temperaments of 30edo and 31edo, but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate division of the just perfect fifth into 18 equal parts (18EDF) with sequences of eighteen equal steps of 33.3333 to 44.4444 cents each. This will create eighteen 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
|
38.9975
|
40
|
38.71
|
| 2
|
77.995
|
80
|
77.419
|
| 3
|
116.9925
|
120
|
116.129
|
| 4
|
155.99
|
160
|
154.839
|
| 5
|
194.9875
|
200
|
193.548
|
| 6
|
233.985
|
240
|
232.258
|
| 7
|
272.9825
|
280
|
270.968
|
| 8
|
311.98
|
320
|
309.677
|
| 9
|
350.9775
|
360
|
348.387
|
| 10
|
389.975
|
400
|
387.097
|
| 11
|
428.9725
|
440
|
425.8065
|
| 12
|
467.97
|
480
|
464.516
|
| 13
|
506.9675
|
520
|
503.226
|
| 14
|
545.965
|
560
|
541.9355
|
| 15
|
584.9625
|
600
|
580.645
|
| 16
|
623.96
|
640
|
619.355
|
| 17
|
662.9575
|
680
|
658.0645
|
| 18
|
701.955
|
720
|
696.764
|
| 19
|
743.45875
|
740.26615
|
760
|
735.484
|
| 20
|
784.9625
|
778.5773
|
800
|
774.1935
|
| 21
|
826.46625
|
816.8885
|
840
|
812.903
|
| 22
|
867.97
|
855.1996
|
880
|
851.613
|
| 23
|
909.47375
|
893.5108
|
920
|
890.323
|
| 24
|
950.9775
|
931.8119
|
960
|
929.032
|
| 25
|
993.48125
|
970.1331
|
1000
|
967.742
|
| 26
|
1033.985
|
1008.4492
|
1040
|
1006.452
|
| 27
|
1075.48875
|
1046.7554
|
1080
|
1045.161
|
| 28
|
1116.9925
|
1085.0665
|
1120
|
1083.871
|
| 29
|
1158.49625
|
1123.3777
|
1160
|
1122.581
|
| 30
|
1200
|
1161.68885
|
1200
|
1161.29
|
| 31
|
1241.50375
|
1200
|
1233.985
|
1200
|
| 32
|
1283.0075
|
1238.31115
|
1267.97
|
1240.782
|
| 33
|
1324.51125
|
1276.6223
|
1301.995
|
1281.564
|
| 34
|
1366.015
|
1314.9335
|
1335.94
|
1322.346
|
| 35
|
1407.51875
|
1353.2446
|
1369.925
|
1363.128
|
| 36
|
1449.0225
|
1391.5558
|
1403.91
|
 |
Todo: clarify, unify precision |
