50wtn

A 50 tone well tempered nonet (50WTN) is related to well temperaments of 42edo and 43edo, but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate division of the just perfect fifth into 25 equal parts (25EDF) with sequences of twenty-five equal steps of 24 to 32 cents each. This will create twenty-five 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	28.0782		28.5714	27.907
2	56.1564		57.1429	55.81395
3	84.2346		85.7143	83.7209
4	112.3128		114.2857	111.6279
5	140.391		143.8571	139.5348
6	168.4692		171.4286	167.4419
7	196.5474		200.000	195.3489
8	224.6256		228.5714	223.2558
9	252.7038		257.1429	251.1628
10	280.782		285.7143	279.0698
11	308.8602		314.2857	306.9767
12	336.9384		342.8571	334.8837
13	365.0166		371.4286	362.7906
14	393.0948		400.000	390.6977
15	421.173		428.5714	418.60465
16	449.2512		457.1429	446.5116
17	477.3294		485.7143	474.4186
18	505.4076		514.2857	502.3255
19	533.4858		543.8571	530.23255
20	561.564		571.4286	558.1395
21	589.6422		600.000	586.0465
22	617.7204		628.5714	613.9535
23	645.7986		657.1429	641.8605
24	673.8768		685.7143	669.76745
25	701.955		714.2857	697.6745
26	731.2518	729.6242	742.8571	725.5814
27	760.5485	757.2933	771.4286	753.4884
28	789.8453	784.9625	800.000	781.39535
29	819.1421	812.6317	828.5714	809.3023
30	848.4388	840.3008	857.1429	837.2094
31	877.7356	867.97	885.7143	865.1163
32	907.03235	895.6392	914.2857	893.0233
33	936.3291	923.3083	942.8571	920.9302
34	965.6259	950.9775	971.4286	948.8372
35	994.92265	978.6467	1000.000	976.7442
36	1024.2194	1006.3158	1028.5714	1004.6511
37	1053.5162	1033.985	1057.1429	1032.5581
38	1082.8129	1061.6542	1085.7143	1060.4659
39	1112.1547	1089.3233	1114.2857	1088.3721
40	1141.4515	1116.9925	1142.8571	1116.2791
41	1170.7032	1144.6617	1171.4286	1144.18605
42	1200	1172.3308	1200	1172.093
43	1229.2968	1200	1225.48875	1200
44	1258.5935	1227.6692	1250.9775	1229.13
45	1287.8903	1255.3383	1276.45625	1258.26
46	1317.1871	1283.0075	1301.955	1287.39
47	1346.4838	1310.6767	1327.43375	1316.52
48	1375.7806	1338.3458	1352.9325	1345.65
49	1405.07735	1366.015	1378.42125	1374.78
50	1434.3741	1393.6842	1403.91