36wtn

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