A 34 tone well tempered nonet (34WTN) is related to well temperaments of 29edo and 30edo, but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate division of the just perfect fifth into 17 equal parts (17EDF) with sequences of seventeen equal steps of 35.2941 to 47.0588 cents each. This will create seventeen equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.
Patent Intervals
|
|
Target a
|
Alternating edo and *ed(9/8)
|
| 1
|
41.2915
|
41.3793
|
| 2
|
82.5829
|
82.7586
|
| 3
|
123.8744
|
124.1379
|
| 4
|
165.1659
|
165.5172
|
| 5
|
206.45735
|
206.89655
|
| 6
|
248.7488
|
248.2758
|
| 7·
|
289.0403
|
289.6552
|
| 8
|
330.3318
|
331.0345
|
| 9
|
371.6232
|
372.4137
|
| 10
|
412.9147
|
413.7931
|
| 11
|
455.2062
|
455.1724
|
| 12·
|
495.49765
|
496.5517
|
| 13
|
536.7891
|
537.931
|
| 14
|
578.0806
|
579.3103
|
| 15
|
619.3721
|
620.6897
|
| 16
|
660.6635
|
662.069
|
| 17·
|
701.955
|
703.4483
|
| 18
|
743.45875
|
744.8276
|
| 19
|
784.9625
|
786.2069
|
| 20
|
826.46625
|
827.5863
|
| 21
|
867.97
|
868.9655
|
| 22·
|
909.47375
|
910.3448
|
| 23
|
950.9775
|
951.7242
|
| 24
|
993.48125
|
993.10345
|
| 25
|
1033.985
|
1034.4828
|
| 26
|
1075.48875
|
1075.8621
|
| 27
|
1116.9925
|
1117.2414
|
| 28
|
1158.49625
|
1158.6207
|
| 29
|
1200
|
| 30
|
1241.50375
|
1240.782
|
| 31
|
1283.0075
|
1281.564
|
| 32
|
1324.51125
|
1322.346
|
| 33
|
1366.015
|
1363.128
|
| 34
|
1407.51875
|
1403.91
|
 |
Todo: clarify, unify precision |
