46wtn

A 46 tone well tempered nonet (46WTN) is related to well temperaments of 39edo and 40edo, but with a nonet rather than the 2/1 being constant. Its patent tunings optimally alternate division of the just perfect fifth into 23 equal parts (23EDF) with sequences of twenty-three equal steps of 26.087 to 34.7826 cents each. This will create twenty-three 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	30.5198		30.7692	30
2	61.0296		61.5385	60
3	91.5593		92.3077	90
4	122.0791		123.0769	120
5	152.5989		153.84615	150
6	183.1187		184.6154	180
7	213.6385		215.3846	210
8	244.1583		246.15385	240
9	274.678		276.9231	270
10	305.1978		307.6923	300
11	335.7176		338.4615	330
12	366.2374		369.2308	360
13	396.7572		400.0000	390
14	427.277		430.7692	420
15	457.7967		461.5385	450
16	488.3165		492.3077	480
17	518.8363		523.0769	510
18	549.3561		553.84615	540
19	579.8759		584.6154	570
20	610.39565		615.3846	600
21	640.9154		646.15385	630
22	671.4352		676.9231	660
23	701.955		707.6923	690
24	733.0828	731.2518	738.4615	720
25	764.2106	760.5485	769.2308	750
26	795.3384	789.8453	800.0000	780
27	826.46625	819.1421	830.7692	810
28	857.5941	848.4388	861.5385	840
29	888.7119	877.7356	892.3077	870
30	919.8397	907.03235	923.0769	900
31	950.9775	936.3291	953.84615	930
32	982.1053	965.6259	984.6154	960
33	1013.2331	994.92265	1015.3846	990
34	1044.3609	1024.2194	1046.15385	1020
35	1075.4887	1053.5162	1076.9231	1050
36	1106.6166	1082.8129	1107.6923	1080
37	1137.7444	1112.1547	1138.4615	1110
38	1168.8722	1141.4515	1169.2308	1140
39	1200	1170.7032	1200	1170
40	1231.1278	1200	1229.13	1200
41	1262.2556	1229.2968	1258.26	1233.985
42	1293.3934	1258.5935	1287.39	1267.97
43	1324.51125	1287.8903	1316.52	1301.995
44	1355.6391	1317.1871	1345.65	1335.94
45	1386.7669	1346.4838	1374.78	1369.925
46	1417.8847	1375.7806	1403.91