42wtn

A 42 tone well tempered nonet (42WTN) is related to well temperaments of 36edo, but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate division of the just perfect fifth into 21 equal parts (21EDF) with sequences of twenty-one equal steps of 28.5714 to 38.0952 cents each. This will create twenty-one equally-spaced intervals between an interval between 600 and 800 cents and the just perfect fifth.

Patent Intervals

	Target	Alternating edo and *ed(9/8)
1	33.4264	33.3333
2	66.8529	66.6667
3	100.2793	100
4	133.7057	133.3333
5	167.1321	166.6667
6	200.5586	200
7	233.985	233.3333
8	267.4114	266.6667
9	300.8379	300
10	334.2643	333.3333
11	367.6907	366.6667
12	401.1171	400
13	434.5436	433.3333
14	467.97	466.6667
15	501.3964	500.00
16	534.8229	533.3333
17	568.2493	566.6667
18	601.6757	600
19	635.1021	633.3333
20	668.5286	666.6667
21	701.955	700
22	735.158	733.3333
23	768.361	766.6667
24	801.564	800
25	834.767	833.3333
26	867.97	866.6667
27	901.173	900
28	934.376	933.3333
29	967.579	966.6667
30	1000.782	1000
31	1033.985	1033.3333
32	1067.188	1066.6667
33	1100.391	1100
34	1133.594	1133.3333
35	1166.797	1166.6667
36	1200	1200
37	1233.203	1233.985
38	1266.406	1267.97
39	1299.609	1301.995
40	1332.812	1335.94
41	1366.015	1369.925
42	1399.218	1403.91