# 40wtn

A 40 tone well tempered nonet (40WTN) is related to well temperaments of 34edo and 35edo, but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate division of the just perfect fifth into 20 equal parts (20EDF) with sequences of twenty equal steps of 30 to 40 cents each. This will create twenty 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 35.1 35.294 34.286
2 70.2 70.588 68.571
3 105.29 105.882 102.857
4 140.39 141.1765 137.143
5 175.49 176.471 171.429
6 210.59 211.765 205.714
7 245.68 247.059 240
8 280.78 282.353 274.286
9 315.88 317.647 308.571
10 350.98 352.941 342.857
11 386.075 388.235 377.143
12 421.17 423.529 411.429
13 456.27 458.8235 445.714
14 491.37 494.118 480
15 526.47 529.412 514.286
16 561.56 564.706 548.571
17 596.66 600.000 582.857
18 631.76 635.294 617.143
19 666.86 670.588 651.429
20 701.955 705.882 685.714
21 737.53 735.158 741.1765 720
22 773.104 768.361 776.471 754.286
23 808.679 801.564 811.765 788.571
24 844.2535 834.767 847.059 822.857
25 879.828 867.97 882.353 857.143
26 915.403. 901.173 917.647 891.429
27 950.9775 934.376 952.941 925.714
28 986.552 967.579 988.235 960
29 1022.127 1000.782 1023.529 994.286
30 1057.701 1033.985 1058.8235 1028.571
31 1093.276 1067.188 1094.118 1062.857
32 1128.851 1100.391 1129.412 1097.143
33 1164.425 1133.594 1164.706 1131.429
34 1200 1166.797 1200 1165.714
35 1235.575 1200 1233.985 1200
36 1271.149 1233.203 1267.97 1240.782
37 1306.724 1266.406 1301.995 1281.564
38 1342.2985 1299.609 1335.94 1322.346
39 1377.873 1332.812 1369.925 1363.128
40 1413.448 1366.015 1403.91